[Boost-commit] svn:boost r49972 - in sandbox/tools/auto_index/example/math/doc/sf_and_dist: . html html/index html/math_toolkit html/math_toolkit/backgrounders html/math_toolkit/dist html/math_toolkit/dist/dist_ref html/math_toolkit/dist/dist_ref/dists html/math_toolkit/dist/stat_tut html/math_toolkit/dist/stat_tut/weg html/math_toolkit/dist/stat_tut/weg/binom_eg html/math_toolkit/dist/stat_tut/weg/cs_eg html/math_toolkit/dist/stat_tut/weg/find_eg html/math_toolkit/dist/stat_tut/weg/nccs_eg html/math_toolkit/dist/stat_tut/weg/neg_binom_eg html/math_toolkit/dist/stat_tut/weg/normal_example html/math_toolkit/dist/stat_tut/weg/st_eg html/math_toolkit/main_overview html/math_toolkit/perf html/math_toolkit/policy html/math_toolkit/policy/pol_ref html/math_toolkit/policy/pol_tutorial html/math_toolkit/special html/math_toolkit/special/bessel html/math_toolkit/special/ellint html/math_toolkit/special/expint html/math_toolkit/special/extern_c html/math_toolkit/special/factorials html/math_toolkit/special/inv_hyper html/math_toolkit/special/next_float html/math_toolkit/special/powers html/math_toolkit/special/rounding html/math_toolkit/special/sf_beta html/math_toolkit/special/sf_erf html/math_toolkit/special/sf_gamma html/math_toolkit/special/sf_poly html/math_toolkit/special/sinc html/math_toolkit/special/zetas html/math_toolkit/status html/math_toolkit/toolkit html/math_toolkit/toolkit/internals1 html/math_toolkit/toolkit/internals2 html/math_toolkit/using_udt

Subject: [Boost-commit] svn:boost r49972 - in sandbox/tools/auto_index/example/math/doc/sf_and_dist: . html html/index html/math_toolkit html/math_toolkit/backgrounders html/math_toolkit/dist html/math_toolkit/dist/dist_ref html/math_toolkit/dist/dist_ref/dists html/math_toolkit/dist/stat_tut html/math_toolkit/dist/stat_tut/weg html/math_toolkit/dist/stat_tut/weg/binom_eg html/math_toolkit/dist/stat_tut/weg/cs_eg html/math_toolkit/dist/stat_tut/weg/find_eg html/math_toolkit/dist/stat_tut/weg/nccs_eg html/math_toolkit/dist/stat_tut/weg/neg_binom_eg html/math_toolkit/dist/stat_tut/weg/normal_example html/math_toolkit/dist/stat_tut/weg/st_eg html/math_toolkit/main_overview html/math_toolkit/perf html/math_toolkit/policy html/math_toolkit/policy/pol_ref html/math_toolkit/policy/pol_tutorial html/math_toolkit/special html/math_toolkit/special/bessel html/math_toolkit/special/ellint html/math_toolkit/special/expint html/math_toolkit/special/extern_c html/math_toolkit/special/factorials html/math_toolkit/special/inv_hyper html/math_toolkit/special/next_float html/math_toolkit/special/powers html/math_toolkit/special/rounding html/math_toolkit/special/sf_beta html/math_toolkit/special/sf_erf html/math_toolkit/special/sf_gamma html/math_toolkit/special/sf_poly html/math_toolkit/special/sinc html/math_toolkit/special/zetas html/math_toolkit/status html/math_toolkit/toolkit html/math_toolkit/toolkit/internals1 html/math_toolkit/toolkit/internals2 html/math_toolkit/using_udt
From: john_at_[hidden]
Date: 2008-11-28 05:25:50

Author: johnmaddock
Date: 2008-11-28 05:25:28 EST (Fri, 28 Nov 2008)
New Revision: 49972
URL: http://svn.boost.org/trac/boost/changeset/49972

Log:
Added generated docs.
Added:
   sandbox/tools/auto_index/example/math/doc/sf_and_dist/html/index/
   sandbox/tools/auto_index/example/math/doc/sf_and_dist/html/index.html   (contents, props changed)
   sandbox/tools/auto_index/example/math/doc/sf_and_dist/html/index/s10.html   (contents, props changed)
   sandbox/tools/auto_index/example/math/doc/sf_and_dist/html/index/s11.html   (contents, props changed)
   sandbox/tools/auto_index/example/math/doc/sf_and_dist/html/index/s12.html   (contents, props changed)
   sandbox/tools/auto_index/example/math/doc/sf_and_dist/html/index/s13.html   (contents, props changed)
   sandbox/tools/auto_index/example/math/doc/sf_and_dist/html/index/s14.html   (contents, props changed)
   sandbox/tools/auto_index/example/math/doc/sf_and_dist/html/math_toolkit/
   sandbox/tools/auto_index/example/math/doc/sf_and_dist/html/math_toolkit/backgrounders/
   sandbox/tools/auto_index/example/math/doc/sf_and_dist/html/math_toolkit/backgrounders.html   (contents, props changed)
   sandbox/tools/auto_index/example/math/doc/sf_and_dist/html/math_toolkit/backgrounders/implementation.html   (contents, props changed)
   sandbox/tools/auto_index/example/math/doc/sf_and_dist/html/math_toolkit/backgrounders/lanczos.html   (contents, props changed)
   sandbox/tools/auto_index/example/math/doc/sf_and_dist/html/math_toolkit/backgrounders/refs.html   (contents, props changed)
   sandbox/tools/auto_index/example/math/doc/sf_and_dist/html/math_toolkit/backgrounders/relative_error.html   (contents, props changed)
   sandbox/tools/auto_index/example/math/doc/sf_and_dist/html/math_toolkit/backgrounders/remez.html   (contents, props changed)
   sandbox/tools/auto_index/example/math/doc/sf_and_dist/html/math_toolkit/dist/
   sandbox/tools/auto_index/example/math/doc/sf_and_dist/html/math_toolkit/dist.html   (contents, props changed)
   sandbox/tools/auto_index/example/math/doc/sf_and_dist/html/math_toolkit/dist/dist_ref/
   sandbox/tools/auto_index/example/math/doc/sf_and_dist/html/math_toolkit/dist/dist_ref.html   (contents, props changed)
   sandbox/tools/auto_index/example/math/doc/sf_and_dist/html/math_toolkit/dist/dist_ref/dist_algorithms.html   (contents, props changed)
   sandbox/tools/auto_index/example/math/doc/sf_and_dist/html/math_toolkit/dist/dist_ref/dists/
   sandbox/tools/auto_index/example/math/doc/sf_and_dist/html/math_toolkit/dist/dist_ref/dists.html   (contents, props changed)
   sandbox/tools/auto_index/example/math/doc/sf_and_dist/html/math_toolkit/dist/dist_ref/dists/bernoulli_dist.html   (contents, props changed)
   sandbox/tools/auto_index/example/math/doc/sf_and_dist/html/math_toolkit/dist/dist_ref/dists/beta_dist.html   (contents, props changed)
   sandbox/tools/auto_index/example/math/doc/sf_and_dist/html/math_toolkit/dist/dist_ref/dists/binomial_dist.html   (contents, props changed)
   sandbox/tools/auto_index/example/math/doc/sf_and_dist/html/math_toolkit/dist/dist_ref/dists/cauchy_dist.html   (contents, props changed)
   sandbox/tools/auto_index/example/math/doc/sf_and_dist/html/math_toolkit/dist/dist_ref/dists/chi_squared_dist.html   (contents, props changed)
   sandbox/tools/auto_index/example/math/doc/sf_and_dist/html/math_toolkit/dist/dist_ref/dists/exp_dist.html   (contents, props changed)
   sandbox/tools/auto_index/example/math/doc/sf_and_dist/html/math_toolkit/dist/dist_ref/dists/extreme_dist.html   (contents, props changed)
   sandbox/tools/auto_index/example/math/doc/sf_and_dist/html/math_toolkit/dist/dist_ref/dists/f_dist.html   (contents, props changed)
   sandbox/tools/auto_index/example/math/doc/sf_and_dist/html/math_toolkit/dist/dist_ref/dists/gamma_dist.html   (contents, props changed)
   sandbox/tools/auto_index/example/math/doc/sf_and_dist/html/math_toolkit/dist/dist_ref/dists/logistic_dist.html   (contents, props changed)
   sandbox/tools/auto_index/example/math/doc/sf_and_dist/html/math_toolkit/dist/dist_ref/dists/lognormal_dist.html   (contents, props changed)
   sandbox/tools/auto_index/example/math/doc/sf_and_dist/html/math_toolkit/dist/dist_ref/dists/nc_beta_dist.html   (contents, props changed)
   sandbox/tools/auto_index/example/math/doc/sf_and_dist/html/math_toolkit/dist/dist_ref/dists/nc_chi_squared_dist.html   (contents, props changed)
   sandbox/tools/auto_index/example/math/doc/sf_and_dist/html/math_toolkit/dist/dist_ref/dists/nc_f_dist.html   (contents, props changed)
   sandbox/tools/auto_index/example/math/doc/sf_and_dist/html/math_toolkit/dist/dist_ref/dists/nc_t_dist.html   (contents, props changed)
   sandbox/tools/auto_index/example/math/doc/sf_and_dist/html/math_toolkit/dist/dist_ref/dists/negative_binomial_dist.html   (contents, props changed)
   sandbox/tools/auto_index/example/math/doc/sf_and_dist/html/math_toolkit/dist/dist_ref/dists/normal_dist.html   (contents, props changed)
   sandbox/tools/auto_index/example/math/doc/sf_and_dist/html/math_toolkit/dist/dist_ref/dists/pareto.html   (contents, props changed)
   sandbox/tools/auto_index/example/math/doc/sf_and_dist/html/math_toolkit/dist/dist_ref/dists/poisson_dist.html   (contents, props changed)
   sandbox/tools/auto_index/example/math/doc/sf_and_dist/html/math_toolkit/dist/dist_ref/dists/rayleigh.html   (contents, props changed)
   sandbox/tools/auto_index/example/math/doc/sf_and_dist/html/math_toolkit/dist/dist_ref/dists/students_t_dist.html   (contents, props changed)
   sandbox/tools/auto_index/example/math/doc/sf_and_dist/html/math_toolkit/dist/dist_ref/dists/triangular_dist.html   (contents, props changed)
   sandbox/tools/auto_index/example/math/doc/sf_and_dist/html/math_toolkit/dist/dist_ref/dists/uniform_dist.html   (contents, props changed)
   sandbox/tools/auto_index/example/math/doc/sf_and_dist/html/math_toolkit/dist/dist_ref/dists/weibull.html   (contents, props changed)
   sandbox/tools/auto_index/example/math/doc/sf_and_dist/html/math_toolkit/dist/dist_ref/nmp.html   (contents, props changed)
   sandbox/tools/auto_index/example/math/doc/sf_and_dist/html/math_toolkit/dist/future.html   (contents, props changed)
   sandbox/tools/auto_index/example/math/doc/sf_and_dist/html/math_toolkit/dist/stat_tut/
   sandbox/tools/auto_index/example/math/doc/sf_and_dist/html/math_toolkit/dist/stat_tut.html   (contents, props changed)
   sandbox/tools/auto_index/example/math/doc/sf_and_dist/html/math_toolkit/dist/stat_tut/dist_params.html   (contents, props changed)
   sandbox/tools/auto_index/example/math/doc/sf_and_dist/html/math_toolkit/dist/stat_tut/overview.html   (contents, props changed)
   sandbox/tools/auto_index/example/math/doc/sf_and_dist/html/math_toolkit/dist/stat_tut/variates.html   (contents, props changed)
   sandbox/tools/auto_index/example/math/doc/sf_and_dist/html/math_toolkit/dist/stat_tut/weg/
   sandbox/tools/auto_index/example/math/doc/sf_and_dist/html/math_toolkit/dist/stat_tut/weg.html   (contents, props changed)
   sandbox/tools/auto_index/example/math/doc/sf_and_dist/html/math_toolkit/dist/stat_tut/weg/binom_eg/
   sandbox/tools/auto_index/example/math/doc/sf_and_dist/html/math_toolkit/dist/stat_tut/weg/binom_eg.html   (contents, props changed)
   sandbox/tools/auto_index/example/math/doc/sf_and_dist/html/math_toolkit/dist/stat_tut/weg/binom_eg/binom_conf.html   (contents, props changed)
   sandbox/tools/auto_index/example/math/doc/sf_and_dist/html/math_toolkit/dist/stat_tut/weg/binom_eg/binom_size_eg.html   (contents, props changed)
   sandbox/tools/auto_index/example/math/doc/sf_and_dist/html/math_toolkit/dist/stat_tut/weg/binom_eg/binomial_coinflip_example.html   (contents, props changed)
   sandbox/tools/auto_index/example/math/doc/sf_and_dist/html/math_toolkit/dist/stat_tut/weg/binom_eg/binomial_quiz_example.html   (contents, props changed)
   sandbox/tools/auto_index/example/math/doc/sf_and_dist/html/math_toolkit/dist/stat_tut/weg/cs_eg/
   sandbox/tools/auto_index/example/math/doc/sf_and_dist/html/math_toolkit/dist/stat_tut/weg/cs_eg.html   (contents, props changed)
   sandbox/tools/auto_index/example/math/doc/sf_and_dist/html/math_toolkit/dist/stat_tut/weg/cs_eg/chi_sq_intervals.html   (contents, props changed)
   sandbox/tools/auto_index/example/math/doc/sf_and_dist/html/math_toolkit/dist/stat_tut/weg/cs_eg/chi_sq_size.html   (contents, props changed)
   sandbox/tools/auto_index/example/math/doc/sf_and_dist/html/math_toolkit/dist/stat_tut/weg/cs_eg/chi_sq_test.html   (contents, props changed)
   sandbox/tools/auto_index/example/math/doc/sf_and_dist/html/math_toolkit/dist/stat_tut/weg/dist_construct_eg.html   (contents, props changed)
   sandbox/tools/auto_index/example/math/doc/sf_and_dist/html/math_toolkit/dist/stat_tut/weg/error_eg.html   (contents, props changed)
   sandbox/tools/auto_index/example/math/doc/sf_and_dist/html/math_toolkit/dist/stat_tut/weg/f_eg.html   (contents, props changed)
   sandbox/tools/auto_index/example/math/doc/sf_and_dist/html/math_toolkit/dist/stat_tut/weg/find_eg/
   sandbox/tools/auto_index/example/math/doc/sf_and_dist/html/math_toolkit/dist/stat_tut/weg/find_eg.html   (contents, props changed)
   sandbox/tools/auto_index/example/math/doc/sf_and_dist/html/math_toolkit/dist/stat_tut/weg/find_eg/find_location_eg.html   (contents, props changed)
   sandbox/tools/auto_index/example/math/doc/sf_and_dist/html/math_toolkit/dist/stat_tut/weg/find_eg/find_mean_and_sd_eg.html   (contents, props changed)
   sandbox/tools/auto_index/example/math/doc/sf_and_dist/html/math_toolkit/dist/stat_tut/weg/find_eg/find_scale_eg.html   (contents, props changed)
   sandbox/tools/auto_index/example/math/doc/sf_and_dist/html/math_toolkit/dist/stat_tut/weg/nag_library.html   (contents, props changed)
   sandbox/tools/auto_index/example/math/doc/sf_and_dist/html/math_toolkit/dist/stat_tut/weg/nccs_eg/
   sandbox/tools/auto_index/example/math/doc/sf_and_dist/html/math_toolkit/dist/stat_tut/weg/nccs_eg.html   (contents, props changed)
   sandbox/tools/auto_index/example/math/doc/sf_and_dist/html/math_toolkit/dist/stat_tut/weg/nccs_eg/nccs_power_eg.html   (contents, props changed)
   sandbox/tools/auto_index/example/math/doc/sf_and_dist/html/math_toolkit/dist/stat_tut/weg/neg_binom_eg/
   sandbox/tools/auto_index/example/math/doc/sf_and_dist/html/math_toolkit/dist/stat_tut/weg/neg_binom_eg.html   (contents, props changed)
   sandbox/tools/auto_index/example/math/doc/sf_and_dist/html/math_toolkit/dist/stat_tut/weg/neg_binom_eg/neg_binom_conf.html   (contents, props changed)
   sandbox/tools/auto_index/example/math/doc/sf_and_dist/html/math_toolkit/dist/stat_tut/weg/neg_binom_eg/neg_binom_size_eg.html   (contents, props changed)
   sandbox/tools/auto_index/example/math/doc/sf_and_dist/html/math_toolkit/dist/stat_tut/weg/neg_binom_eg/negative_binomial_example1.html   (contents, props changed)
   sandbox/tools/auto_index/example/math/doc/sf_and_dist/html/math_toolkit/dist/stat_tut/weg/neg_binom_eg/negative_binomial_example2.html   (contents, props changed)
   sandbox/tools/auto_index/example/math/doc/sf_and_dist/html/math_toolkit/dist/stat_tut/weg/normal_example/
   sandbox/tools/auto_index/example/math/doc/sf_and_dist/html/math_toolkit/dist/stat_tut/weg/normal_example.html   (contents, props changed)
   sandbox/tools/auto_index/example/math/doc/sf_and_dist/html/math_toolkit/dist/stat_tut/weg/normal_example/normal_misc.html   (contents, props changed)
   sandbox/tools/auto_index/example/math/doc/sf_and_dist/html/math_toolkit/dist/stat_tut/weg/st_eg/
   sandbox/tools/auto_index/example/math/doc/sf_and_dist/html/math_toolkit/dist/stat_tut/weg/st_eg.html   (contents, props changed)
   sandbox/tools/auto_index/example/math/doc/sf_and_dist/html/math_toolkit/dist/stat_tut/weg/st_eg/paired_st.html   (contents, props changed)
   sandbox/tools/auto_index/example/math/doc/sf_and_dist/html/math_toolkit/dist/stat_tut/weg/st_eg/tut_mean_intervals.html   (contents, props changed)
   sandbox/tools/auto_index/example/math/doc/sf_and_dist/html/math_toolkit/dist/stat_tut/weg/st_eg/tut_mean_size.html   (contents, props changed)
   sandbox/tools/auto_index/example/math/doc/sf_and_dist/html/math_toolkit/dist/stat_tut/weg/st_eg/tut_mean_test.html   (contents, props changed)
   sandbox/tools/auto_index/example/math/doc/sf_and_dist/html/math_toolkit/dist/stat_tut/weg/st_eg/two_sample_students_t.html   (contents, props changed)
   sandbox/tools/auto_index/example/math/doc/sf_and_dist/html/math_toolkit/main_overview/
   sandbox/tools/auto_index/example/math/doc/sf_and_dist/html/math_toolkit/main_overview.html   (contents, props changed)
   sandbox/tools/auto_index/example/math/doc/sf_and_dist/html/math_toolkit/main_overview/building.html   (contents, props changed)
   sandbox/tools/auto_index/example/math/doc/sf_and_dist/html/math_toolkit/main_overview/compilers_overview.html   (contents, props changed)
   sandbox/tools/auto_index/example/math/doc/sf_and_dist/html/math_toolkit/main_overview/contact.html   (contents, props changed)
   sandbox/tools/auto_index/example/math/doc/sf_and_dist/html/math_toolkit/main_overview/directories.html   (contents, props changed)
   sandbox/tools/auto_index/example/math/doc/sf_and_dist/html/math_toolkit/main_overview/error_handling.html   (contents, props changed)
   sandbox/tools/auto_index/example/math/doc/sf_and_dist/html/math_toolkit/main_overview/history1.html   (contents, props changed)
   sandbox/tools/auto_index/example/math/doc/sf_and_dist/html/math_toolkit/main_overview/intro.html   (contents, props changed)
   sandbox/tools/auto_index/example/math/doc/sf_and_dist/html/math_toolkit/main_overview/namespaces.html   (contents, props changed)
   sandbox/tools/auto_index/example/math/doc/sf_and_dist/html/math_toolkit/main_overview/navigation.html   (contents, props changed)
   sandbox/tools/auto_index/example/math/doc/sf_and_dist/html/math_toolkit/main_overview/perf_over.html   (contents, props changed)
   sandbox/tools/auto_index/example/math/doc/sf_and_dist/html/math_toolkit/main_overview/pol_overview.html   (contents, props changed)
   sandbox/tools/auto_index/example/math/doc/sf_and_dist/html/math_toolkit/main_overview/result_type.html   (contents, props changed)
   sandbox/tools/auto_index/example/math/doc/sf_and_dist/html/math_toolkit/main_overview/threads.html   (contents, props changed)
   sandbox/tools/auto_index/example/math/doc/sf_and_dist/html/math_toolkit/main_overview/tr1.html   (contents, props changed)
   sandbox/tools/auto_index/example/math/doc/sf_and_dist/html/math_toolkit/perf/
   sandbox/tools/auto_index/example/math/doc/sf_and_dist/html/math_toolkit/perf.html   (contents, props changed)
   sandbox/tools/auto_index/example/math/doc/sf_and_dist/html/math_toolkit/perf/comp_compilers.html   (contents, props changed)
   sandbox/tools/auto_index/example/math/doc/sf_and_dist/html/math_toolkit/perf/comparisons.html   (contents, props changed)
   sandbox/tools/auto_index/example/math/doc/sf_and_dist/html/math_toolkit/perf/getting_best.html   (contents, props changed)
   sandbox/tools/auto_index/example/math/doc/sf_and_dist/html/math_toolkit/perf/interp.html   (contents, props changed)
   sandbox/tools/auto_index/example/math/doc/sf_and_dist/html/math_toolkit/perf/perf_over.html   (contents, props changed)
   sandbox/tools/auto_index/example/math/doc/sf_and_dist/html/math_toolkit/perf/perf_test_app.html   (contents, props changed)
   sandbox/tools/auto_index/example/math/doc/sf_and_dist/html/math_toolkit/perf/tuning.html   (contents, props changed)
   sandbox/tools/auto_index/example/math/doc/sf_and_dist/html/math_toolkit/policy/
   sandbox/tools/auto_index/example/math/doc/sf_and_dist/html/math_toolkit/policy.html   (contents, props changed)
   sandbox/tools/auto_index/example/math/doc/sf_and_dist/html/math_toolkit/policy/pol_overview.html   (contents, props changed)
   sandbox/tools/auto_index/example/math/doc/sf_and_dist/html/math_toolkit/policy/pol_ref/
   sandbox/tools/auto_index/example/math/doc/sf_and_dist/html/math_toolkit/policy/pol_ref.html   (contents, props changed)
   sandbox/tools/auto_index/example/math/doc/sf_and_dist/html/math_toolkit/policy/pol_ref/assert_undefined.html   (contents, props changed)
   sandbox/tools/auto_index/example/math/doc/sf_and_dist/html/math_toolkit/policy/pol_ref/discrete_quant_ref.html   (contents, props changed)
   sandbox/tools/auto_index/example/math/doc/sf_and_dist/html/math_toolkit/policy/pol_ref/error_handling_policies.html   (contents, props changed)
   sandbox/tools/auto_index/example/math/doc/sf_and_dist/html/math_toolkit/policy/pol_ref/internal_promotion.html   (contents, props changed)
   sandbox/tools/auto_index/example/math/doc/sf_and_dist/html/math_toolkit/policy/pol_ref/iteration_pol.html   (contents, props changed)
   sandbox/tools/auto_index/example/math/doc/sf_and_dist/html/math_toolkit/policy/pol_ref/namespace_pol.html   (contents, props changed)
   sandbox/tools/auto_index/example/math/doc/sf_and_dist/html/math_toolkit/policy/pol_ref/pol_ref_ref.html   (contents, props changed)
   sandbox/tools/auto_index/example/math/doc/sf_and_dist/html/math_toolkit/policy/pol_ref/policy_defaults.html   (contents, props changed)
   sandbox/tools/auto_index/example/math/doc/sf_and_dist/html/math_toolkit/policy/pol_ref/precision_pol.html   (contents, props changed)
   sandbox/tools/auto_index/example/math/doc/sf_and_dist/html/math_toolkit/policy/pol_tutorial/
   sandbox/tools/auto_index/example/math/doc/sf_and_dist/html/math_toolkit/policy/pol_tutorial.html   (contents, props changed)
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   sandbox/tools/auto_index/example/math/doc/sf_and_dist/html/math_toolkit/policy/pol_tutorial/changing_policy_defaults.html   (contents, props changed)
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+++ sandbox/tools/auto_index/example/math/doc/sf_and_dist/html/index.html	2008-11-28 05:25:28 EST (Fri, 28 Nov 2008)
@@ -0,0 +1,471 @@
+<html>
+<head>
+<meta http-equiv="Content-Type" content="text/html; charset=ISO-8859-1">
+<title>Math Toolkit</title>
+<link rel="stylesheet" href="boostbook.css" type="text/css">
+<meta name="generator" content="DocBook XSL Stylesheets Vsnapshot_8125">
+<link rel="home" href="index.html" title="Math Toolkit">
+<link rel="next" href="math_toolkit/main_overview.html" title="Overview">
+</head>
+<body bgcolor="white" text="black" link="#0000FF" vlink="#840084" alink="#0000FF">
+<table cellpadding="2" width="100%"><tr>
+<td valign="top"><img alt="Boost C++ Libraries" width="277" height="86" src="../../boost.png"></td>
+<td align="center">Home</td>
+<td align="center">Libraries</td>
+<td align="center">People</td>
+<td align="center">FAQ</td>
+<td align="center">More</td>
+</tr></table>
+<hr>
+<div class="spirit-nav"><a accesskey="n" href="math_toolkit/main_overview.html"><img src="../../doc/html/images/next.png" alt="Next"></a></div>
+<div class="article" lang="en">
+<div class="titlepage">
+<div>
+<div><h2 class="title">
+<a name="math_toolkit"></a>Math Toolkit</h2></div>
+<div><div class="authorgroup">
+<div class="author"><h3 class="author">
+<span class="firstname">John</span> <span class="surname">Maddock</span>
+</h3></div>
+<div class="author"><h3 class="author">
+<span class="firstname">Paul A.</span> <span class="surname">Bristow</span>
+</h3></div>
+<div class="author"><h3 class="author">
+<span class="firstname">Hubert</span> <span class="surname">Holin</span>
+</h3></div>
+<div class="author"><h3 class="author">
+<span class="firstname">Xiaogang</span> <span class="surname">Zhang</span>
+</h3></div>
+<div class="author"><h3 class="author">
+<span class="firstname">Bruno</span> <span class="surname">Lalande</span>
+</h3></div>
+<div class="author"><h3 class="author">
+<span class="firstname">Gautam</span> <span class="surname">Sewani</span>
+</h3></div>
+</div></div>
+<div><p class="copyright">Copyright © 2006 , 2007, 2008 John Maddock, Paul A. Bristow, Hubert
+      Holin, Xiaogang Zhang, Bruno Lalande and Gautam Sewani</p></div>
+<div><div class="legalnotice">
+<a name="id485634"></a><p>
+        Distributed under the Boost Software License, Version 1.0. (See accompanying
+        file LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_0.txt)
+      </p>
+</div></div>
+</div>
+<hr>
+</div>
+<div class="toc">
+<p><b>Table of Contents</b></p>
+<dl>
+<dt><span class="section"> Overview</span></dt>
+<dd><dl>
+<dt><span class="section"> About the Math Toolkit</span></dt>
+<dt><span class="section"> Navigation</span></dt>
+<dt><span class="section"><a href="math_toolkit/main_overview/directories.html"> Directory and
+      File Structure</a></span></dt>
+<dt><span class="section"> Namespaces</span></dt>
+<dt><span class="section"><a href="math_toolkit/main_overview/result_type.html"> Calculation
+      of the Type of the Result</a></span></dt>
+<dt><span class="section"> Error Handling</span></dt>
+<dt><span class="section"> Compilers</span></dt>
+<dt><span class="section"><a href="math_toolkit/main_overview/pol_overview.html"> Configuration
+      and Policies</a></span></dt>
+<dt><span class="section"> Thread Safety</span></dt>
+<dt><span class="section"> Performance</span></dt>
+<dt><span class="section"><a href="math_toolkit/main_overview/building.html"> If and How to Build
+      the Library and its Examples and Tests</a></span></dt>
+<dt><span class="section"><a href="math_toolkit/main_overview/history1.html"> History and What's
+      New</a></span></dt>
+<dt><span class="section"> C99 and TR1 C Functions</span></dt>
+<dt><span class="section"><a href="math_toolkit/main_overview/contact.html"> Contact Info and
+      Support</a></span></dt>
+</dl></dd>
+<dt><span class="section"> Statistical Distributions and Functions</span></dt>
+<dd><dl>
+<dt><span class="section"><a href="math_toolkit/dist/stat_tut.html"> Statistical Distributions
+      Tutorial</a></span></dt>
+<dd><dl>
+<dt><span class="section"> Overview</span></dt>
+<dt><span class="section"> Worked Examples</span></dt>
+<dd><dl>
+<dt><span class="section"><a href="math_toolkit/dist/stat_tut/weg/dist_construct_eg.html">
+          Distribution Construction Example</a></span></dt>
+<dt><span class="section"><a href="math_toolkit/dist/stat_tut/weg/st_eg.html"> Student's
+          t Distribution Examples</a></span></dt>
+<dt><span class="section"><a href="math_toolkit/dist/stat_tut/weg/cs_eg.html"> Chi Squared
+          Distribution Examples</a></span></dt>
+<dt><span class="section"><a href="math_toolkit/dist/stat_tut/weg/f_eg.html"> F Distribution
+          Examples</a></span></dt>
+<dt><span class="section"><a href="math_toolkit/dist/stat_tut/weg/binom_eg.html"> Binomial
+          Distribution Examples</a></span></dt>
+<dt><span class="section"><a href="math_toolkit/dist/stat_tut/weg/neg_binom_eg.html"> Negative
+          Binomial Distribution Examples</a></span></dt>
+<dt><span class="section"><a href="math_toolkit/dist/stat_tut/weg/normal_example.html"> Normal
+          Distribution Examples</a></span></dt>
+<dt><span class="section"><a href="math_toolkit/dist/stat_tut/weg/nccs_eg.html"> Non Central
+          Chi Squared Example</a></span></dt>
+<dt><span class="section"><a href="math_toolkit/dist/stat_tut/weg/error_eg.html"> Error Handling
+          Example</a></span></dt>
+<dt><span class="section"><a href="math_toolkit/dist/stat_tut/weg/find_eg.html"> Find Location
+          and Scale Examples</a></span></dt>
+<dt><span class="section"><a href="math_toolkit/dist/stat_tut/weg/nag_library.html"> Comparison
+          with C, R, FORTRAN-style Free Functions</a></span></dt>
+</dl></dd>
+<dt><span class="section"><a href="math_toolkit/dist/stat_tut/variates.html"> Random Variates
+        and Distribution Parameters</a></span></dt>
+<dt><span class="section"><a href="math_toolkit/dist/stat_tut/dist_params.html"> Discrete Probability
+        Distributions</a></span></dt>
+</dl></dd>
+<dt><span class="section"><a href="math_toolkit/dist/dist_ref.html"> Statistical Distributions
+      Reference</a></span></dt>
+<dd><dl>
+<dt><span class="section"> Non-Member Properties</span></dt>
+<dt><span class="section"> Distributions</span></dt>
+<dd><dl>
+<dt><span class="section"><a href="math_toolkit/dist/dist_ref/dists/bernoulli_dist.html">
+          Bernoulli Distribution</a></span></dt>
+<dt><span class="section"><a href="math_toolkit/dist/dist_ref/dists/beta_dist.html"> Beta
+          Distribution</a></span></dt>
+<dt><span class="section"><a href="math_toolkit/dist/dist_ref/dists/binomial_dist.html">
+          Binomial Distribution</a></span></dt>
+<dt><span class="section"><a href="math_toolkit/dist/dist_ref/dists/cauchy_dist.html"> Cauchy-Lorentz
+          Distribution</a></span></dt>
+<dt><span class="section"><a href="math_toolkit/dist/dist_ref/dists/chi_squared_dist.html">
+          Chi Squared Distribution</a></span></dt>
+<dt><span class="section"><a href="math_toolkit/dist/dist_ref/dists/exp_dist.html"> Exponential
+          Distribution</a></span></dt>
+<dt><span class="section"><a href="math_toolkit/dist/dist_ref/dists/extreme_dist.html"> Extreme
+          Value Distribution</a></span></dt>
+<dt><span class="section"> F Distribution</span></dt>
+<dt><span class="section"><a href="math_toolkit/dist/dist_ref/dists/gamma_dist.html"> Gamma
+          (and Erlang) Distribution</a></span></dt>
+<dt><span class="section"><a href="math_toolkit/dist/dist_ref/dists/logistic_dist.html">
+          Logistic Distribution</a></span></dt>
+<dt><span class="section"><a href="math_toolkit/dist/dist_ref/dists/lognormal_dist.html">
+          Log Normal Distribution</a></span></dt>
+<dt><span class="section"><a href="math_toolkit/dist/dist_ref/dists/negative_binomial_dist.html">
+          Negative Binomial Distribution</a></span></dt>
+<dt><span class="section"><a href="math_toolkit/dist/dist_ref/dists/nc_beta_dist.html"> Noncentral
+          Beta Distribution</a></span></dt>
+<dt><span class="section"><a href="math_toolkit/dist/dist_ref/dists/nc_chi_squared_dist.html">
+          Noncentral Chi-Squared Distribution</a></span></dt>
+<dt><span class="section"><a href="math_toolkit/dist/dist_ref/dists/nc_f_dist.html"> Noncentral
+          F Distribution</a></span></dt>
+<dt><span class="section"><a href="math_toolkit/dist/dist_ref/dists/nc_t_dist.html"> Noncentral
+          T Distribution</a></span></dt>
+<dt><span class="section"><a href="math_toolkit/dist/dist_ref/dists/normal_dist.html"> Normal
+          (Gaussian) Distribution</a></span></dt>
+<dt><span class="section"><a href="math_toolkit/dist/dist_ref/dists/pareto.html"> Pareto
+          Distribution</a></span></dt>
+<dt><span class="section"><a href="math_toolkit/dist/dist_ref/dists/poisson_dist.html"> Poisson
+          Distribution</a></span></dt>
+<dt><span class="section"><a href="math_toolkit/dist/dist_ref/dists/rayleigh.html"> Rayleigh
+          Distribution</a></span></dt>
+<dt><span class="section"><a href="math_toolkit/dist/dist_ref/dists/students_t_dist.html">
+          Students t Distribution</a></span></dt>
+<dt><span class="section"><a href="math_toolkit/dist/dist_ref/dists/triangular_dist.html">
+          Triangular Distribution</a></span></dt>
+<dt><span class="section"><a href="math_toolkit/dist/dist_ref/dists/weibull.html"> Weibull
+          Distribution</a></span></dt>
+<dt><span class="section"><a href="math_toolkit/dist/dist_ref/dists/uniform_dist.html"> Uniform
+          Distribution</a></span></dt>
+</dl></dd>
+<dt><span class="section"><a href="math_toolkit/dist/dist_ref/dist_algorithms.html"> Distribution
+        Algorithms</a></span></dt>
+</dl></dd>
+<dt><span class="section"> Extras/Future Directions</span></dt>
+</dl></dd>
+<dt><span class="section"> Special Functions</span></dt>
+<dd><dl>
+<dt><span class="section"> Gamma Functions</span></dt>
+<dd><dl>
+<dt><span class="section"> Gamma</span></dt>
+<dt><span class="section"> Log Gamma</span></dt>
+<dt><span class="section"> Digamma</span></dt>
+<dt><span class="section"><a href="math_toolkit/special/sf_gamma/gamma_ratios.html"> Ratios
+        of Gamma Functions</a></span></dt>
+<dt><span class="section"><a href="math_toolkit/special/sf_gamma/igamma.html"> Incomplete Gamma
+        Functions</a></span></dt>
+<dt><span class="section"><a href="math_toolkit/special/sf_gamma/igamma_inv.html"> Incomplete
+        Gamma Function Inverses</a></span></dt>
+<dt><span class="section"><a href="math_toolkit/special/sf_gamma/gamma_derivatives.html"> Derivative
+        of the Incomplete Gamma Function</a></span></dt>
+</dl></dd>
+<dt><span class="section"><a href="math_toolkit/special/factorials.html"> Factorials and Binomial
+      Coefficients</a></span></dt>
+<dd><dl>
+<dt><span class="section"> Factorial</span></dt>
+<dt><span class="section"><a href="math_toolkit/special/factorials/sf_double_factorial.html">
+        Double Factorial</a></span></dt>
+<dt><span class="section"><a href="math_toolkit/special/factorials/sf_rising_factorial.html">
+        Rising Factorial</a></span></dt>
+<dt><span class="section"><a href="math_toolkit/special/factorials/sf_falling_factorial.html">
+        Falling Factorial</a></span></dt>
+<dt><span class="section"><a href="math_toolkit/special/factorials/sf_binomial.html"> Binomial
+        Coefficients</a></span></dt>
+</dl></dd>
+<dt><span class="section"> Beta Functions</span></dt>
+<dd><dl>
+<dt><span class="section"> Beta</span></dt>
+<dt><span class="section"><a href="math_toolkit/special/sf_beta/ibeta_function.html"> Incomplete
+        Beta Functions</a></span></dt>
+<dt><span class="section"><a href="math_toolkit/special/sf_beta/ibeta_inv_function.html"> The
+        Incomplete Beta Function Inverses</a></span></dt>
+<dt><span class="section"><a href="math_toolkit/special/sf_beta/beta_derivative.html"> Derivative
+        of the Incomplete Beta Function</a></span></dt>
+</dl></dd>
+<dt><span class="section"> Error Functions</span></dt>
+<dd><dl>
+<dt><span class="section"><a href="math_toolkit/special/sf_erf/error_function.html"> Error
+        Functions</a></span></dt>
+<dt><span class="section"><a href="math_toolkit/special/sf_erf/error_inv.html"> Error Function
+        Inverses</a></span></dt>
+</dl></dd>
+<dt><span class="section"> Polynomials</span></dt>
+<dd><dl>
+<dt><span class="section"><a href="math_toolkit/special/sf_poly/legendre.html"> Legendre (and
+        Associated) Polynomials</a></span></dt>
+<dt><span class="section"><a href="math_toolkit/special/sf_poly/laguerre.html"> Laguerre (and
+        Associated) Polynomials</a></span></dt>
+<dt><span class="section"> Hermite Polynomials</span></dt>
+<dt><span class="section"> Spherical Harmonics</span></dt>
+</dl></dd>
+<dt><span class="section"> Bessel Functions</span></dt>
+<dd><dl>
+<dt><span class="section"><a href="math_toolkit/special/bessel/bessel_over.html"> Bessel Function
+        Overview</a></span></dt>
+<dt><span class="section"><a href="math_toolkit/special/bessel/bessel.html"> Bessel Functions
+        of the First and Second Kinds</a></span></dt>
+<dt><span class="section"><a href="math_toolkit/special/bessel/mbessel.html"> Modified Bessel
+        Functions of the First and Second Kinds</a></span></dt>
+<dt><span class="section"><a href="math_toolkit/special/bessel/sph_bessel.html"> Spherical
+        Bessel Functions of the First and Second Kinds</a></span></dt>
+</dl></dd>
+<dt><span class="section"> Elliptic Integrals</span></dt>
+<dd><dl>
+<dt><span class="section"><a href="math_toolkit/special/ellint/ellint_intro.html"> Elliptic
+        Integral Overview</a></span></dt>
+<dt><span class="section"><a href="math_toolkit/special/ellint/ellint_carlson.html"> Elliptic
+        Integrals - Carlson Form</a></span></dt>
+<dt><span class="section"><a href="math_toolkit/special/ellint/ellint_1.html"> Elliptic Integrals
+        of the First Kind - Legendre Form</a></span></dt>
+<dt><span class="section"><a href="math_toolkit/special/ellint/ellint_2.html"> Elliptic Integrals
+        of the Second Kind - Legendre Form</a></span></dt>
+<dt><span class="section"><a href="math_toolkit/special/ellint/ellint_3.html"> Elliptic Integrals
+        of the Third Kind - Legendre Form</a></span></dt>
+</dl></dd>
+<dt><span class="section"> Zeta Functions</span></dt>
+<dd><dl><dt><span class="section"> Riemann Zeta Function</span></dt></dl></dd>
+<dt><span class="section"> Exponential Integrals</span></dt>
+<dd><dl>
+<dt><span class="section"><a href="math_toolkit/special/expint/expint_n.html"> Exponential
+        Integral En</a></span></dt>
+<dt><span class="section"><a href="math_toolkit/special/expint/expint_i.html"> Exponential
+        Integral Ei</a></span></dt>
+</dl></dd>
+<dt><span class="section"><a href="math_toolkit/special/powers.html"> Logs, Powers, Roots and
+      Exponentials</a></span></dt>
+<dd><dl>
+<dt><span class="section"> log1p</span></dt>
+<dt><span class="section"> expm1</span></dt>
+<dt><span class="section"> cbrt</span></dt>
+<dt><span class="section"> sqrt1pm1</span></dt>
+<dt><span class="section"> powm1</span></dt>
+<dt><span class="section"> hypot</span></dt>
+<dt><span class="section"><a href="math_toolkit/special/powers/ct_pow.html"> Compile Time Power
+        of a Runtime Base</a></span></dt>
+</dl></dd>
+<dt><span class="section"><a href="math_toolkit/special/sinc.html"> Sinus Cardinal and Hyperbolic
+      Sinus Cardinal Functions</a></span></dt>
+<dd><dl>
+<dt><span class="section"><a href="math_toolkit/special/sinc/sinc_overview.html"> Sinus Cardinal
+        and Hyperbolic Sinus Cardinal Functions Overview</a></span></dt>
+<dt><span class="section">sinc_pi</span></dt>
+<dt><span class="section">sinhc_pi</span></dt>
+</dl></dd>
+<dt><span class="section"> Inverse Hyperbolic Functions</span></dt>
+<dd><dl>
+<dt><span class="section"><a href="math_toolkit/special/inv_hyper/inv_hyper_over.html"> Inverse
+        Hyperbolic Functions Overview</a></span></dt>
+<dt><span class="section"> acosh</span></dt>
+<dt><span class="section"> asinh</span></dt>
+<dt><span class="section"> atanh</span></dt>
+</dl></dd>
+<dt><span class="section"><a href="math_toolkit/special/rounding.html"> Rounding Truncation and
+      Integer Conversion</a></span></dt>
+<dd><dl>
+<dt><span class="section"> Rounding Functions</span></dt>
+<dt><span class="section"> Truncation Functions</span></dt>
+<dt><span class="section"><a href="math_toolkit/special/rounding/modf.html"> Integer and Fractional
+        Part Splitting (modf)</a></span></dt>
+</dl></dd>
+<dt><span class="section"><a href="math_toolkit/special/fpclass.html"> Floating-Point Classification:
+      Infinities and NaN's</a></span></dt>
+<dt><span class="section"><a href="math_toolkit/special/next_float.html"> Floating-Point Representation
+      Distance (ULP), and Finding Adjacent Floating-Point Values</a></span></dt>
+<dd><dl>
+<dt><span class="section"><a href="math_toolkit/special/next_float/nextafter.html"> Finding
+        the Next Representable Value in a Specific Direction (nextafter)</a></span></dt>
+<dt><span class="section"><a href="math_toolkit/special/next_float/float_next.html"> Finding
+        the Next Greater Representable Value (float_next)</a></span></dt>
+<dt><span class="section"><a href="math_toolkit/special/next_float/float_prior.html"> Finding
+        the Next Smaller Representable Value (float_prior)</a></span></dt>
+<dt><span class="section"><a href="math_toolkit/special/next_float/float_distance.html"> Calculating
+        the Representation Distance Between Two Floating Point Values (ULP) float_distance</a></span></dt>
+<dt><span class="section"><a href="math_toolkit/special/next_float/float_advance.html"> Advancing
+        a Floating Point Value by a Specific Representation Distance (ULP) float_advance</a></span></dt>
+</dl></dd>
+<dt><span class="section"><a href="math_toolkit/special/extern_c.html"> TR1 and C99 external
+      "C" Functions</a></span></dt>
+<dd><dl>
+<dt><span class="section"><a href="math_toolkit/special/extern_c/tr1.html"> C99 and TR1 C Functions
+        Overview</a></span></dt>
+<dt><span class="section"> C99 C Functions</span></dt>
+<dt><span class="section"><a href="math_toolkit/special/extern_c/tr1_ref.html"> TR1 C Functions
+        Quick Reference</a></span></dt>
+</dl></dd>
+</dl></dd>
+<dt><span class="section"> Internal Details and Tools (Experimental)</span></dt>
+<dd><dl>
+<dt><span class="section"> Overview</span></dt>
+<dt><span class="section"> Reused Utilities</span></dt>
+<dd><dl>
+<dt><span class="section"><a href="math_toolkit/toolkit/internals1/constants.html"> Numeric
+        Constants</a></span></dt>
+<dt><span class="section"><a href="math_toolkit/toolkit/internals1/series_evaluation.html">
+        Series Evaluation</a></span></dt>
+<dt><span class="section"><a href="math_toolkit/toolkit/internals1/cf.html"> Continued Fraction
+        Evaluation</a></span></dt>
+<dt><span class="section"><a href="math_toolkit/toolkit/internals1/rational.html"> Polynomial
+        and Rational Function Evaluation</a></span></dt>
+<dt><span class="section"><a href="math_toolkit/toolkit/internals1/roots.html"> Root Finding
+        With Derivatives</a></span></dt>
+<dt><span class="section"><a href="math_toolkit/toolkit/internals1/roots2.html"> Root Finding
+        Without Derivatives</a></span></dt>
+<dt><span class="section"><a href="math_toolkit/toolkit/internals1/minima.html"> Locating Function
+        Minima</a></span></dt>
+</dl></dd>
+<dt><span class="section"> Testing and Development</span></dt>
+<dd><dl>
+<dt><span class="section"> Polynomials</span></dt>
+<dt><span class="section"><a href="math_toolkit/toolkit/internals2/minimax.html"> Minimax Approximations
+        and the Remez Algorithm</a></span></dt>
+<dt><span class="section"><a href="math_toolkit/toolkit/internals2/error_test.html"> Relative
+        Error and Testing</a></span></dt>
+<dt><span class="section"><a href="math_toolkit/toolkit/internals2/test_data.html"> Graphing,
+        Profiling, and Generating Test Data for Special Functions</a></span></dt>
+</dl></dd>
+</dl></dd>
+<dt><span class="section"><a href="math_toolkit/using_udt.html"> Use with User-Defined Floating-Point
+    Types</a></span></dt>
+<dd><dl>
+<dt><span class="section"><a href="math_toolkit/using_udt/use_ntl.html"> Using With NTL - a High-Precision
+      Floating-Point Library</a></span></dt>
+<dt><span class="section"><a href="math_toolkit/using_udt/use_mpfr.html"> Using With MPFR / GMP
+      - a High-Precision Floating-Point Library</a></span></dt>
+<dt><span class="section"><a href="math_toolkit/using_udt/concepts.html"> Conceptual Requirements
+      for Real Number Types</a></span></dt>
+<dt><span class="section"><a href="math_toolkit/using_udt/dist_concept.html"> Conceptual Requirements
+      for Distribution Types</a></span></dt>
+<dt><span class="section"><a href="math_toolkit/using_udt/archetypes.html"> Conceptual Archetypes
+      and Testing</a></span></dt>
+</dl></dd>
+<dt><span class="section"> Policies</span></dt>
+<dd><dl>
+<dt><span class="section"> Policy Overview</span></dt>
+<dt><span class="section"> Policy Tutorial</span></dt>
+<dd><dl>
+<dt><span class="section"><a href="math_toolkit/policy/pol_tutorial/what_is_a_policy.html">
+        So Just What is a Policy Anyway?</a></span></dt>
+<dt><span class="section"><a href="math_toolkit/policy/pol_tutorial/policy_tut_defaults.html">
+        Policies Have Sensible Defaults</a></span></dt>
+<dt><span class="section"><a href="math_toolkit/policy/pol_tutorial/policy_usage.html"> So
+        How are Policies Used Anyway?</a></span></dt>
+<dt><span class="section"><a href="math_toolkit/policy/pol_tutorial/changing_policy_defaults.html">
+        Changing the Policy Defaults</a></span></dt>
+<dt><span class="section"><a href="math_toolkit/policy/pol_tutorial/ad_hoc_dist_policies.html">
+        Setting Policies for Distributions on an Ad Hoc Basis</a></span></dt>
+<dt><span class="section"><a href="math_toolkit/policy/pol_tutorial/ad_hoc_sf_policies.html">
+        Changing the Policy on an Ad Hoc Basis for the Special Functions</a></span></dt>
+<dt><span class="section"><a href="math_toolkit/policy/pol_tutorial/namespace_policies.html">
+        Setting Policies at Namespace or Translation Unit Scope</a></span></dt>
+<dt><span class="section"><a href="math_toolkit/policy/pol_tutorial/user_def_err_pol.html">
+        Calling User Defined Error Handlers</a></span></dt>
+<dt><span class="section"><a href="math_toolkit/policy/pol_tutorial/understand_dis_quant.html">
+        Understanding Quantiles of Discrete Distributions</a></span></dt>
+</dl></dd>
+<dt><span class="section"> Policy Reference</span></dt>
+<dd><dl>
+<dt><span class="section"><a href="math_toolkit/policy/pol_ref/error_handling_policies.html">
+        Error Handling Policies</a></span></dt>
+<dt><span class="section"><a href="math_toolkit/policy/pol_ref/internal_promotion.html"> Internal
+        Promotion Policies</a></span></dt>
+<dt><span class="section"><a href="math_toolkit/policy/pol_ref/assert_undefined.html"> Mathematically
+        Undefined Function Policies</a></span></dt>
+<dt><span class="section"><a href="math_toolkit/policy/pol_ref/discrete_quant_ref.html"> Discrete
+        Quantile Policies</a></span></dt>
+<dt><span class="section"><a href="math_toolkit/policy/pol_ref/precision_pol.html"> Precision
+        Policies</a></span></dt>
+<dt><span class="section"><a href="math_toolkit/policy/pol_ref/iteration_pol.html"> Iteration
+        Limits Policies</a></span></dt>
+<dt><span class="section"><a href="math_toolkit/policy/pol_ref/policy_defaults.html"> Using
+        macros to Change the Policy Defaults</a></span></dt>
+<dt><span class="section"><a href="math_toolkit/policy/pol_ref/namespace_pol.html"> Setting
+        Polices at Namespace Scope</a></span></dt>
+<dt><span class="section"><a href="math_toolkit/policy/pol_ref/pol_ref_ref.html"> Policy Class
+        Reference</a></span></dt>
+</dl></dd>
+</dl></dd>
+<dt><span class="section"> Performance</span></dt>
+<dd><dl>
+<dt><span class="section"> Performance Overview</span></dt>
+<dt><span class="section"> Interpreting these Results</span></dt>
+<dt><span class="section"><a href="math_toolkit/perf/getting_best.html"> Getting the Best Performance
+      from this Library</a></span></dt>
+<dt><span class="section"> Comparing Compilers</span></dt>
+<dt><span class="section"> Performance Tuning Macros</span></dt>
+<dt><span class="section"><a href="math_toolkit/perf/comparisons.html"> Comparisons to Other
+      Open Source Libraries</a></span></dt>
+<dt><span class="section"><a href="math_toolkit/perf/perf_test_app.html"> The Performance Test
+      Application</a></span></dt>
+</dl></dd>
+<dt><span class="section"> Backgrounders</span></dt>
+<dd><dl>
+<dt><span class="section"><a href="math_toolkit/backgrounders/implementation.html"> Additional
+      Implementation Notes</a></span></dt>
+<dt><span class="section"><a href="math_toolkit/backgrounders/relative_error.html"> Relative
+      Error</a></span></dt>
+<dt><span class="section"> The Lanczos Approximation</span></dt>
+<dt><span class="section"> The Remez Method</span></dt>
+<dt><span class="section"> References</span></dt>
+</dl></dd>
+<dt><span class="section"> Library Status</span></dt>
+<dd><dl>
+<dt><span class="section"> History and What's New</span></dt>
+<dt><span class="section"> Compilers</span></dt>
+<dt><span class="section"> Known Issues, and Todo List</span></dt>
+<dt><span class="section"> Credits and Acknowledgements</span></dt>
+</dl></dd>
+<dt><span class="section">Class Index</span></dt>
+<dt><span class="section">Typedef Index</span></dt>
+<dt><span class="section">Function Index</span></dt>
+<dt><span class="section">Macro Index</span></dt>
+<dt><span class="section">Index</span></dt>
+</dl>
+</div>
+<p>
+    ISBN 0-9504833-2-X 978-0-9504833-2-0, Classification 519.2-dc22
+  </p>
+<p>
+    This manual is also available in <a href="http://svn.boost.org/svn/boost/sandbox/pdf/math/release/math.pdf" target="_top">printer
+    friendly PDF format</a>.
+  </p>
+</div>
+<table xmlns:rev="http://www.cs.rpi.edu/~gregod/boost/tools/doc/revision" width="100%"><tr>
+<td align="left"><p><small>Last revised: November 28, 2008 at 08:58:32 GMT</small></p></td>
+<td align="right"><div class="copyright-footer"></div></td>
+</tr></table>
+<hr>
+<div class="spirit-nav"><a accesskey="n" href="math_toolkit/main_overview.html"><img src="../../doc/html/images/next.png" alt="Next"></a></div>
+</body>
+</html>

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==============================================================================
--- (empty file)
+++ sandbox/tools/auto_index/example/math/doc/sf_and_dist/html/index/s10.html	2008-11-28 05:25:28 EST (Fri, 28 Nov 2008)
@@ -0,0 +1,342 @@
+<html>
+<head>
+<meta http-equiv="Content-Type" content="text/html; charset=ISO-8859-1">
+<title>Class Index</title>
+<link rel="stylesheet" href="../boostbook.css" type="text/css">
+<meta name="generator" content="DocBook XSL Stylesheets Vsnapshot_8125">
+<link rel="home" href="../index.html" title="Math Toolkit">
+<link rel="up" href="../index.html" title="Math Toolkit">
+<link rel="prev" href="../math_toolkit/status/credits.html" title="Credits and Acknowledgements">
+<link rel="next" href="s11.html" title="Typedef Index">
+</head>
+<body bgcolor="white" text="black" link="#0000FF" vlink="#840084" alink="#0000FF">
+<table cellpadding="2" width="100%"><tr>
+<td valign="top"><img alt="Boost C++ Libraries" width="277" height="86" src="../../../boost.png"></td>
+<td align="center">Home</td>
+<td align="center">Libraries</td>
+<td align="center">People</td>
+<td align="center">FAQ</td>
+<td align="center">More</td>
+</tr></table>
+<hr>
+<div class="spirit-nav">
+<a accesskey="p" href="../math_toolkit/status/credits.html"><img src="../../../doc/html/images/prev.png" alt="Prev"></a><a accesskey="u" href="../index.html"><img src="../../../doc/html/images/up.png" alt="Up"></a><a accesskey="h" href="../index.html"><img src="../../../doc/html/images/home.png" alt="Home"></a><a accesskey="n" href="s11.html"><img src="../../../doc/html/images/next.png" alt="Next"></a>
+</div>
+<div class="section" lang="en">
+<div class="titlepage"><div><div><h2 class="title" style="clear: both">
+<a name="id923194"></a>Class Index</h2></div></div></div>
+<p><a class="link" href="s10.html#idx_id_0">B</a> <a class="link" href="s10.html#idx_id_1">C</a> <a class="link" href="s10.html#idx_id_2">D</a> <a class="link" href="s10.html#idx_id_3">E</a> <a class="link" href="s10.html#idx_id_4">F</a> <a class="link" href="s10.html#idx_id_5">G</a> <a class="link" href="s10.html#idx_id_6">L</a> <a class="link" href="s10.html#idx_id_7">M</a> <a class="link" href="s10.html#idx_id_8">N</a> <a class="link" href="s10.html#idx_id_9">P</a> <a class="link" href="s10.html#idx_id_10">R</a> <a class="link" href="s10.html#idx_id_11">S</a> <a class="link" href="s10.html#idx_id_12">T</a> <a class="link" href="s10.html#idx_id_13">U</a> <a class="link" href="s10.html#idx_id_14">W</a> </p>
+<div class="variablelist"><dl>
+<dt>
+<a name="idx_id_0"></a><span class="term">B</span>
+</dt>
+<dd><div class="variablelist"><dl>
+<dt><span class="term">bernoulli_distribution</span></dt>
+<dd><table class="simplelist" border="0" summary="Simple list"><tr><td><p><a class="link" href="../math_toolkit/dist/dist_ref/dists/bernoulli_dist.html" title="Bernoulli Distribution">Bernoulli Distribution</a></p></td></tr></table></dd>
+<dt><span class="term">beta_distribution</span></dt>
+<dd><table class="simplelist" border="0" summary="Simple list">
+<tr><td><p><a class="link" href="../math_toolkit/dist/dist_ref/dists/beta_dist.html" title="Beta Distribution">Beta Distribution</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/dist/stat_tut/weg/dist_construct_eg.html" title="Distribution Construction Example">Distribution Construction Example</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/dist/stat_tut/overview.html" title="Overview">Overview</a></p></td></tr>
+</table></dd>
+<dt><span class="term">binomial_distribution</span></dt>
+<dd><table class="simplelist" border="0" summary="Simple list">
+<tr><td><p><a class="link" href="../math_toolkit/dist/dist_ref/dists/bernoulli_dist.html" title="Bernoulli Distribution">Bernoulli Distribution</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/dist/dist_ref/dists/binomial_dist.html" title="Binomial Distribution">Binomial Distribution</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/dist/stat_tut/weg/binom_eg/binomial_quiz_example.html" title="Binomial Quiz Example">Binomial Quiz Example</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/dist/stat_tut/weg/binom_eg/binom_conf.html" title="Calculating Confidence Limits on the Frequency of Occurrence for a Binomial Distribution">Calculating Confidence Limits on the Frequency of Occurrence for a Binomial Distribution</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/dist/stat_tut/weg/dist_construct_eg.html" title="Distribution Construction Example">Distribution Construction Example</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/dist/stat_tut/overview.html" title="Overview">Overview</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/dist/stat_tut/variates.html" title="Random Variates and Distribution Parameters">Random Variates and Distribution Parameters</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/policy/pol_tutorial/ad_hoc_dist_policies.html" title="Setting Policies for Distributions on an Ad Hoc Basis">Setting Policies for Distributions on an Ad Hoc Basis</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/policy/pol_tutorial/understand_dis_quant.html" title="Understanding Quantiles of Discrete Distributions">Understanding Quantiles of Discrete Distributions</a></p></td></tr>
+</table></dd>
+</dl></div></dd>
+<dt>
+<a name="idx_id_1"></a><span class="term">C</span>
+</dt>
+<dd><div class="variablelist"><dl>
+<dt><span class="term">cauchy_distribution</span></dt>
+<dd><table class="simplelist" border="0" summary="Simple list">
+<tr><td><p><a class="link" href="../math_toolkit/dist/dist_ref/dists/cauchy_dist.html" title="Cauchy-Lorentz Distribution">Cauchy-Lorentz Distribution</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/dist/stat_tut/weg/find_eg/find_location_eg.html" title="Find Location (Mean) Example">Find Location (Mean) Example</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/dist/stat_tut/weg/find_eg/find_mean_and_sd_eg.html" title="Find mean and standard deviation example">Find mean and standard deviation example</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/policy/pol_ref/assert_undefined.html" title="Mathematically Undefined Function Policies">Mathematically Undefined Function Policies</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/policy/pol_ref/namespace_pol.html" title="Setting Polices at Namespace Scope">Setting Polices at Namespace Scope</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/policy/pol_tutorial/namespace_policies.html" title="Setting Policies at Namespace or Translation Unit Scope">Setting Policies at Namespace or Translation Unit Scope</a></p></td></tr>
+</table></dd>
+<dt><span class="term">cbrt_functor</span></dt>
+<dd><table class="simplelist" border="0" summary="Simple list"><tr><td><p><a class="link" href="../math_toolkit/toolkit/internals1/roots.html" title="Root Finding With Derivatives">Root Finding With Derivatives</a></p></td></tr></table></dd>
+<dt><span class="term">chi_squared_distribution</span></dt>
+<dd><table class="simplelist" border="0" summary="Simple list">
+<tr><td><p><a class="link" href="../math_toolkit/dist/dist_ref/dists/chi_squared_dist.html" title="Chi Squared Distribution">Chi Squared Distribution</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/dist/stat_tut/weg/cs_eg/chi_sq_size.html" title="Estimating the Required Sample Sizes for a Chi-Square Test for the Standard Deviation">Estimating the Required Sample Sizes for a Chi-Square Test for the Standard Deviation</a></p></td></tr>
+</table></dd>
+<dt><span class="term">complemented3_type</span></dt>
+<dd><table class="simplelist" border="0" summary="Simple list"><tr><td><p><a class="link" href="../math_toolkit/dist/dist_ref/dists/nc_chi_squared_dist.html" title="Noncentral Chi-Squared Distribution">Noncentral Chi-Squared Distribution</a></p></td></tr></table></dd>
+</dl></div></dd>
+<dt>
+<a name="idx_id_2"></a><span class="term">D</span>
+</dt>
+<dd><div class="variablelist"><dl>
+<dt><span class="term">default_policy</span></dt>
+<dd><table class="simplelist" border="0" summary="Simple list"><tr><td><p><a class="link" href="../math_toolkit/policy/pol_ref/pol_ref_ref.html" title="Policy Class Reference">Policy Class Reference</a></p></td></tr></table></dd>
+<dt><span class="term">DistributionConcept</span></dt>
+<dd><table class="simplelist" border="0" summary="Simple list"><tr><td><p><a class="link" href="../math_toolkit/using_udt/archetypes.html" title="Conceptual Archetypes and Testing">Conceptual Archetypes and Testing</a></p></td></tr></table></dd>
+<dt><span class="term">distribution_archetype</span></dt>
+<dd><table class="simplelist" border="0" summary="Simple list"><tr><td><p><a class="link" href="../math_toolkit/using_udt/archetypes.html" title="Conceptual Archetypes and Testing">Conceptual Archetypes and Testing</a></p></td></tr></table></dd>
+</dl></div></dd>
+<dt>
+<a name="idx_id_3"></a><span class="term">E</span>
+</dt>
+<dd><div class="variablelist"><dl>
+<dt><span class="term">eps_tolerance</span></dt>
+<dd><table class="simplelist" border="0" summary="Simple list"><tr><td><p><a class="link" href="../math_toolkit/toolkit/internals1/roots2.html" title="Root Finding Without Derivatives">Root Finding Without Derivatives</a></p></td></tr></table></dd>
+<dt><span class="term">equal_ceil</span></dt>
+<dd><table class="simplelist" border="0" summary="Simple list"><tr><td><p><a class="link" href="../math_toolkit/toolkit/internals1/roots2.html" title="Root Finding Without Derivatives">Root Finding Without Derivatives</a></p></td></tr></table></dd>
+<dt><span class="term">equal_floor</span></dt>
+<dd><table class="simplelist" border="0" summary="Simple list"><tr><td><p><a class="link" href="../math_toolkit/toolkit/internals1/roots2.html" title="Root Finding Without Derivatives">Root Finding Without Derivatives</a></p></td></tr></table></dd>
+<dt><span class="term">equal_nearest_integer</span></dt>
+<dd><table class="simplelist" border="0" summary="Simple list"><tr><td><p><a class="link" href="../math_toolkit/toolkit/internals1/roots2.html" title="Root Finding Without Derivatives">Root Finding Without Derivatives</a></p></td></tr></table></dd>
+<dt><span class="term">evaluation_error</span></dt>
+<dd><table class="simplelist" border="0" summary="Simple list">
+<tr><td><p><a class="link" href="../math_toolkit/policy/pol_tutorial/user_def_err_pol.html" title="Calling User Defined Error Handlers">Calling User Defined Error Handlers</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/policy/pol_tutorial/ad_hoc_sf_policies.html" title="Changing the Policy on an Ad Hoc Basis for the Special Functions">Changing the Policy on an Ad Hoc Basis for the Special Functions</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/main_overview/pol_overview.html" title="Configuration and Policies">Configuration and Policies</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/main_overview/error_handling.html" title="Error Handling">Error Handling</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/policy/pol_ref/error_handling_policies.html" title="Error Handling Policies">Error Handling Policies</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/main_overview/history1.html" title="History and What's New">History and What's New</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/policy/pol_ref/iteration_pol.html" title="Iteration Limits Policies">Iteration Limits Policies</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/policy/pol_tutorial/policy_tut_defaults.html" title="Policies Have Sensible Defaults">Policies Have Sensible Defaults</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/policy/pol_ref/pol_ref_ref.html" title="Policy Class Reference">Policy Class Reference</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/policy/pol_overview.html" title="Policy Overview">Policy Overview</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/main_overview/error_handling.html" title="Error Handling">Possible Actions for Internal Evaluation Errors</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/policy/pol_tutorial/namespace_policies.html" title="Setting Policies at Namespace or Translation Unit Scope">Setting Policies at Namespace or Translation Unit Scope</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/policy/pol_ref/policy_defaults.html" title="Using macros to Change the Policy Defaults">Using macros to Change the Policy Defaults</a></p></td></tr>
+</table></dd>
+<dt><span class="term">exponential_distribution</span></dt>
+<dd><table class="simplelist" border="0" summary="Simple list"><tr><td><p><a class="link" href="../math_toolkit/dist/dist_ref/dists/exp_dist.html" title="Exponential Distribution">Exponential Distribution</a></p></td></tr></table></dd>
+<dt><span class="term">extreme_value_distribution</span></dt>
+<dd><table class="simplelist" border="0" summary="Simple list"><tr><td><p><a class="link" href="../math_toolkit/dist/dist_ref/dists/extreme_dist.html" title="Extreme Value Distribution">Extreme Value Distribution</a></p></td></tr></table></dd>
+</dl></div></dd>
+<dt>
+<a name="idx_id_4"></a><span class="term">F</span>
+</dt>
+<dd><div class="variablelist"><dl>
+<dt><span class="term">fisher_f_distribution</span></dt>
+<dd><table class="simplelist" border="0" summary="Simple list">
+<tr><td><p><a class="link" href="../math_toolkit/dist/dist_ref/dists/f_dist.html" title="F Distribution">F Distribution</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/policy/pol_tutorial/ad_hoc_dist_policies.html" title="Setting Policies for Distributions on an Ad Hoc Basis">Setting Policies for Distributions on an Ad Hoc Basis</a></p></td></tr>
+</table></dd>
+<dt><span class="term">fraction_traits</span></dt>
+<dd><table class="simplelist" border="0" summary="Simple list"><tr><td><p><a class="link" href="../math_toolkit/toolkit/internals1/cf.html" title="Continued Fraction Evaluation">Continued Fraction Evaluation</a></p></td></tr></table></dd>
+</dl></div></dd>
+<dt>
+<a name="idx_id_5"></a><span class="term">G</span>
+</dt>
+<dd><div class="variablelist"><dl>
+<dt><span class="term">gamma_distribution</span></dt>
+<dd><table class="simplelist" border="0" summary="Simple list">
+<tr><td><p><a class="link" href="../math_toolkit/dist/stat_tut/weg/dist_construct_eg.html" title="Distribution Construction Example">Distribution Construction Example</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/dist/dist_ref/dists/gamma_dist.html" title="Gamma (and Erlang) Distribution">Gamma (and Erlang) Distribution</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/policy/pol_ref/namespace_pol.html" title="Setting Polices at Namespace Scope">Setting Polices at Namespace Scope</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/policy/pol_tutorial/namespace_policies.html" title="Setting Policies at Namespace or Translation Unit Scope">Setting Policies at Namespace or Translation Unit Scope</a></p></td></tr>
+</table></dd>
+</dl></div></dd>
+<dt>
+<a name="idx_id_6"></a><span class="term">L</span>
+</dt>
+<dd><div class="variablelist"><dl>
+<dt><span class="term">lanczos</span></dt>
+<dd><table class="simplelist" border="0" summary="Simple list">
+<tr><td><p><a class="link" href="../math_toolkit/using_udt/concepts.html" title="Conceptual Requirements for Real Number Types">Conceptual Requirements for Real Number Types</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/special/sf_gamma/tgamma.html" title="Gamma">Gamma</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/special/sf_gamma/lgamma.html" title="Log Gamma">Log Gamma</a></p></td></tr>
+</table></dd>
+<dt><span class="term">log1p_series</span></dt>
+<dd><table class="simplelist" border="0" summary="Simple list"><tr><td><p><a class="link" href="../math_toolkit/toolkit/internals1/series_evaluation.html" title="Series Evaluation">Series Evaluation</a></p></td></tr></table></dd>
+<dt><span class="term">lognormal_distribution</span></dt>
+<dd><table class="simplelist" border="0" summary="Simple list"><tr><td><p><a class="link" href="../math_toolkit/dist/dist_ref/dists/lognormal_dist.html" title="Log Normal Distribution">Log Normal Distribution</a></p></td></tr></table></dd>
+</dl></div></dd>
+<dt>
+<a name="idx_id_7"></a><span class="term">M</span>
+</dt>
+<dd><div class="variablelist"><dl>
+<dt><span class="term">max_factorial</span></dt>
+<dd><table class="simplelist" border="0" summary="Simple list"><tr><td><p><a class="link" href="../math_toolkit/special/factorials/sf_factorial.html" title="Factorial">Factorial</a></p></td></tr></table></dd>
+</dl></div></dd>
+<dt>
+<a name="idx_id_8"></a><span class="term">N</span>
+</dt>
+<dd><div class="variablelist"><dl>
+<dt><span class="term">negative_binomial_distribution</span></dt>
+<dd><table class="simplelist" border="0" summary="Simple list">
+<tr><td><p><a class="link" href="../math_toolkit/dist/stat_tut/weg/neg_binom_eg/neg_binom_conf.html" title="Calculating Confidence Limits on the Frequency of Occurrence for the Negative Binomial Distribution">Calculating Confidence Limits on the Frequency of Occurrence for the Negative Binomial Distribution</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/policy/pol_ref/discrete_quant_ref.html" title="Discrete Quantile Policies">Discrete Quantile Policies</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/dist/stat_tut/weg/dist_construct_eg.html" title="Distribution Construction Example">Distribution Construction Example</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/dist/dist_ref/dists/negative_binomial_dist.html" title="Negative Binomial Distribution">Negative Binomial Distribution</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/dist/stat_tut/weg/neg_binom_eg/negative_binomial_example1.html" title="Negative Binomial Sales Quota Example.">Negative Binomial Sales Quota Example.</a></p></td></tr>
+</table></dd>
+<dt><span class="term">non_central_beta_distribution</span></dt>
+<dd><table class="simplelist" border="0" summary="Simple list"><tr><td><p><a class="link" href="../math_toolkit/dist/dist_ref/dists/nc_beta_dist.html" title="Noncentral Beta Distribution">Noncentral Beta Distribution</a></p></td></tr></table></dd>
+<dt><span class="term">non_central_chi_squared_distribution</span></dt>
+<dd><table class="simplelist" border="0" summary="Simple list"><tr><td><p><a class="link" href="../math_toolkit/dist/dist_ref/dists/nc_chi_squared_dist.html" title="Noncentral Chi-Squared Distribution">Noncentral Chi-Squared Distribution</a></p></td></tr></table></dd>
+<dt><span class="term">non_central_f_distribution</span></dt>
+<dd><table class="simplelist" border="0" summary="Simple list"><tr><td><p><a class="link" href="../math_toolkit/dist/dist_ref/dists/nc_f_dist.html" title="Noncentral F Distribution">Noncentral F Distribution</a></p></td></tr></table></dd>
+<dt><span class="term">non_central_t_distribution</span></dt>
+<dd><table class="simplelist" border="0" summary="Simple list"><tr><td><p><a class="link" href="../math_toolkit/dist/dist_ref/dists/nc_t_dist.html" title="Noncentral T Distribution">Noncentral T Distribution</a></p></td></tr></table></dd>
+<dt><span class="term">normalise</span></dt>
+<dd><table class="simplelist" border="0" summary="Simple list"><tr><td><p><a class="link" href="../math_toolkit/policy/pol_ref/pol_ref_ref.html" title="Policy Class Reference">Policy Class Reference</a></p></td></tr></table></dd>
+<dt><span class="term">normal_distribution</span></dt>
+<dd><table class="simplelist" border="0" summary="Simple list">
+<tr><td><p><a class="link" href="../math_toolkit/dist/stat_tut/weg/dist_construct_eg.html" title="Distribution Construction Example">Distribution Construction Example</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/policy/pol_ref/error_handling_policies.html" title="Error Handling Policies">Error Handling Policies</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/dist/stat_tut/weg/find_eg/find_location_eg.html" title="Find Location (Mean) Example">Find Location (Mean) Example</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/dist/stat_tut/weg/find_eg/find_mean_and_sd_eg.html" title="Find mean and standard deviation example">Find mean and standard deviation example</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/dist/stat_tut/weg/find_eg/find_scale_eg.html" title="Find Scale (Standard Deviation) Example">Find Scale (Standard Deviation) Example</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/policy/pol_ref/internal_promotion.html" title="Internal Promotion Policies">Internal Promotion Policies</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/dist/dist_ref/dists/normal_dist.html" title="Normal (Gaussian) Distribution">Normal (Gaussian) Distribution</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/policy/pol_ref/precision_pol.html" title="Precision Policies">Precision Policies</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/policy/pol_tutorial/namespace_policies.html" title="Setting Policies at Namespace or Translation Unit Scope">Setting Policies at Namespace or Translation Unit Scope</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/dist/stat_tut/weg/normal_example/normal_misc.html" title="Some Miscellaneous Examples of the Normal (Gaussian) Distribution">Some Miscellaneous Examples of the Normal (Gaussian) Distribution</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/policy/pol_ref/policy_defaults.html" title="Using macros to Change the Policy Defaults">Using macros to Change the Policy Defaults</a></p></td></tr>
+</table></dd>
+</dl></div></dd>
+<dt>
+<a name="idx_id_9"></a><span class="term">P</span>
+</dt>
+<dd><div class="variablelist"><dl>
+<dt><span class="term">parameter_info</span></dt>
+<dd><table class="simplelist" border="0" summary="Simple list"><tr><td><p><a class="link" href="../math_toolkit/toolkit/internals2/test_data.html" title="Graphing, Profiling, and Generating Test Data for Special Functions">Graphing, Profiling, and Generating Test Data for Special Functions</a></p></td></tr></table></dd>
+<dt><span class="term">pareto_distribution</span></dt>
+<dd><table class="simplelist" border="0" summary="Simple list"><tr><td><p><a class="link" href="../math_toolkit/dist/dist_ref/dists/pareto.html" title="Pareto Distribution">Pareto Distribution</a></p></td></tr></table></dd>
+<dt><span class="term">poisson_distribution</span></dt>
+<dd><table class="simplelist" border="0" summary="Simple list"><tr><td><p><a class="link" href="../math_toolkit/dist/dist_ref/dists/poisson_dist.html" title="Poisson Distribution">Poisson Distribution</a></p></td></tr></table></dd>
+<dt><span class="term">promote_args</span></dt>
+<dd><table class="simplelist" border="0" summary="Simple list">
+<tr><td><p><a class="link" href="../math_toolkit/policy/pol_tutorial/user_def_err_pol.html" title="Calling User Defined Error Handlers">Calling User Defined Error Handlers</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/policy/pol_tutorial/namespace_policies.html" title="Setting Policies at Namespace or Translation Unit Scope">Setting Policies at Namespace or Translation Unit Scope</a></p></td></tr>
+</table></dd>
+</dl></div></dd>
+<dt>
+<a name="idx_id_10"></a><span class="term">R</span>
+</dt>
+<dd><div class="variablelist"><dl>
+<dt><span class="term">rayleigh_distribution</span></dt>
+<dd><table class="simplelist" border="0" summary="Simple list"><tr><td><p><a class="link" href="../math_toolkit/dist/dist_ref/dists/rayleigh.html" title="Rayleigh Distribution">Rayleigh Distribution</a></p></td></tr></table></dd>
+<dt><span class="term">real_concept</span></dt>
+<dd><table class="simplelist" border="0" summary="Simple list">
+<tr><td><p><a class="link" href="../math_toolkit/using_udt/archetypes.html" title="Conceptual Archetypes and Testing">Conceptual Archetypes and Testing</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/main_overview/directories.html" title="Directory and File Structure">Directory and File Structure</a></p></td></tr>
+</table></dd>
+<dt><span class="term">rounding_error</span></dt>
+<dd><table class="simplelist" border="0" summary="Simple list">
+<tr><td><p><a class="link" href="../math_toolkit/main_overview/error_handling.html" title="Error Handling">Error Handling</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/policy/pol_ref/error_handling_policies.html" title="Error Handling Policies">Error Handling Policies</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/special/rounding/modf.html" title="Integer and Fractional Part Splitting (modf)">Integer and Fractional Part Splitting (modf)</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/policy/pol_tutorial/policy_tut_defaults.html" title="Policies Have Sensible Defaults">Policies Have Sensible Defaults</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/policy/pol_ref/pol_ref_ref.html" title="Policy Class Reference">Policy Class Reference</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/main_overview/error_handling.html" title="Error Handling">Possible Actions for Rounding Errors</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/special/rounding/round.html" title="Rounding Functions">Rounding Functions</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/special/rounding/trunc.html" title="Truncation Functions">Truncation Functions</a></p></td></tr>
+</table></dd>
+<dt><span class="term">RR</span></dt>
+<dd><table class="simplelist" border="0" summary="Simple list">
+<tr><td><p><a class="link" href="../math_toolkit/backgrounders/implementation.html" title="Additional Implementation Notes">Additional Implementation Notes</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/special/sf_beta/beta_function.html" title="Beta">Beta</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/main_overview/result_type.html" title="Calculation of the Type of the Result">Calculation of the Type of the Result</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/special/powers/cbrt.html" title="cbrt">cbrt</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/using_udt/archetypes.html" title="Conceptual Archetypes and Testing">Conceptual Archetypes and Testing</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/using_udt/concepts.html" title="Conceptual Requirements for Real Number Types">Conceptual Requirements for Real Number Types</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/main_overview/directories.html" title="Directory and File Structure">Directory and File Structure</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/dist/stat_tut/weg/dist_construct_eg.html" title="Distribution Construction Example">Distribution Construction Example</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/special/ellint/ellint_carlson.html" title="Elliptic Integrals - Carlson Form">Elliptic Integrals - Carlson Form</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/special/ellint/ellint_1.html" title="Elliptic Integrals of the First Kind - Legendre Form">Elliptic Integrals of the First Kind - Legendre Form</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/special/ellint/ellint_2.html" title="Elliptic Integrals of the Second Kind - Legendre Form">Elliptic Integrals of the Second Kind - Legendre Form</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/special/ellint/ellint_3.html" title="Elliptic Integrals of the Third Kind - Legendre Form">Elliptic Integrals of the Third Kind - Legendre Form</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/special/sf_erf/error_function.html" title="Error Functions">Error Functions</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/special/powers/expm1.html" title="expm1">expm1</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/special/expint/expint_i.html" title="Exponential Integral Ei">Exponential Integral Ei</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/special/expint/expint_n.html" title="Exponential Integral En">Exponential Integral En</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/special/next_float.html" title="Floating-Point Representation Distance (ULP), and Finding Adjacent Floating-Point Values">Floating-Point Representation Distance (ULP), and Finding Adjacent Floating-Point Values</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/toolkit/internals2/test_data.html" title="Graphing, Profiling, and Generating Test Data for Special Functions">Graphing, Profiling, and Generating Test Data for Special Functions</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/special/sf_poly/hermite.html" title="Hermite Polynomials">Hermite Polynomials</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/special/sf_beta/ibeta_function.html" title="Incomplete Beta Functions">Incomplete Beta Functions</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/special/sf_gamma/igamma.html" title="Incomplete Gamma Functions">Incomplete Gamma Functions</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/special/sf_poly/laguerre.html" title="Laguerre (and Associated) Polynomials">Laguerre (and Associated) Polynomials</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/special/sf_poly/legendre.html" title="Legendre (and Associated) Polynomials">Legendre (and Associated) Polynomials</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/special/powers/log1p.html" title="log1p">log1p</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/toolkit/internals2/minimax.html" title="Minimax Approximations and the Remez Algorithm">Minimax Approximations and the Remez Algorithm</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/special/powers/powm1.html" title="powm1">powm1</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/special/sf_gamma/gamma_ratios.html" title="Ratios of Gamma Functions">Ratios of Gamma Functions</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/dist/dist_ref/dists/rayleigh.html" title="Rayleigh Distribution">Rayleigh Distribution</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/special/zetas/zeta.html" title="Riemann Zeta Function">Riemann Zeta Function</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/toolkit/internals1/roots.html" title="Root Finding With Derivatives">Root Finding With Derivatives</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/special/sf_poly/sph_harm.html" title="Spherical Harmonics">Spherical Harmonics</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/special/powers/sqrt1pm1.html" title="sqrt1pm1">sqrt1pm1</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/using_udt/use_ntl.html" title="Using With NTL - a High-Precision Floating-Point Library">Using With NTL - a High-Precision Floating-Point Library</a></p></td></tr>
+</table></dd>
+</dl></div></dd>
+<dt>
+<a name="idx_id_11"></a><span class="term">S</span>
+</dt>
+<dd><div class="variablelist"><dl>
+<dt><span class="term">std_real_concept</span></dt>
+<dd><table class="simplelist" border="0" summary="Simple list"><tr><td><p><a class="link" href="../math_toolkit/using_udt/archetypes.html" title="Conceptual Archetypes and Testing">Conceptual Archetypes and Testing</a></p></td></tr></table></dd>
+<dt><span class="term">students_t_distribution</span></dt>
+<dd><table class="simplelist" border="0" summary="Simple list">
+<tr><td><p><a class="link" href="../math_toolkit/policy/pol_tutorial/changing_policy_defaults.html" title="Changing the Policy Defaults">Changing the Policy Defaults</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/dist/stat_tut/weg/error_eg.html" title="Error Handling Example">Error Handling Example</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/dist/stat_tut/weg/st_eg/tut_mean_size.html" title="Estimating how large a sample size would have to become in order to give a significant Students-t test result with a single sample test">Estimating how large a sample size would have to become in order to give a significant Students-t test result with a single sample test</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/main_overview/namespaces.html" title="Namespaces">Namespaces</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/dist/stat_tut/overview.html" title="Overview">Overview</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/dist/dist_ref/dists/students_t_dist.html" title="Students t Distribution">Students t Distribution</a></p></td></tr>
+</table></dd>
+</dl></div></dd>
+<dt>
+<a name="idx_id_12"></a><span class="term">T</span>
+</dt>
+<dd><div class="variablelist"><dl>
+<dt><span class="term">test_data</span></dt>
+<dd><table class="simplelist" border="0" summary="Simple list"><tr><td><p><a class="link" href="../math_toolkit/toolkit/internals2/test_data.html" title="Graphing, Profiling, and Generating Test Data for Special Functions">Graphing, Profiling, and Generating Test Data for Special Functions</a></p></td></tr></table></dd>
+<dt><span class="term">test_result</span></dt>
+<dd><table class="simplelist" border="0" summary="Simple list"><tr><td><p><a class="link" href="../math_toolkit/toolkit/internals2/error_test.html" title="Relative Error and Testing">Relative Error and Testing</a></p></td></tr></table></dd>
+<dt><span class="term">triangular_distribution</span></dt>
+<dd><table class="simplelist" border="0" summary="Simple list">
+<tr><td><p><a class="link" href="../math_toolkit/backgrounders/implementation.html" title="Additional Implementation Notes">Additional Implementation Notes</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/dist/dist_ref/dists/triangular_dist.html" title="Triangular Distribution">Triangular Distribution</a></p></td></tr>
+</table></dd>
+</dl></div></dd>
+<dt>
+<a name="idx_id_13"></a><span class="term">U</span>
+</dt>
+<dd><div class="variablelist"><dl>
+<dt><span class="term">uniform_distribution</span></dt>
+<dd><table class="simplelist" border="0" summary="Simple list"><tr><td><p><a class="link" href="../math_toolkit/dist/dist_ref/dists/uniform_dist.html" title="Uniform Distribution">Uniform Distribution</a></p></td></tr></table></dd>
+<dt><span class="term">upper_incomplete_gamma_fract</span></dt>
+<dd><table class="simplelist" border="0" summary="Simple list"><tr><td><p><a class="link" href="../math_toolkit/toolkit/internals2/test_data.html" title="Graphing, Profiling, and Generating Test Data for Special Functions">Graphing, Profiling, and Generating Test Data for Special Functions</a></p></td></tr></table></dd>
+</dl></div></dd>
+<dt>
+<a name="idx_id_14"></a><span class="term">W</span>
+</dt>
+<dd><div class="variablelist"><dl>
+<dt><span class="term">weibull_distribution</span></dt>
+<dd><table class="simplelist" border="0" summary="Simple list"><tr><td><p><a class="link" href="../math_toolkit/dist/dist_ref/dists/weibull.html" title="Weibull Distribution">Weibull Distribution</a></p></td></tr></table></dd>
+</dl></div></dd>
+</dl></div>
+</div>
+<table xmlns:rev="http://www.cs.rpi.edu/~gregod/boost/tools/doc/revision" width="100%"><tr>
+<td align="left"></td>
+<td align="right"><div class="copyright-footer">Copyright © 2006 , 2007, 2008 John Maddock, Paul A. Bristow, Hubert
+      Holin, Xiaogang Zhang, Bruno Lalande and Gautam Sewani<p>
+        Distributed under the Boost Software License, Version 1.0. (See accompanying
+        file LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_0.txt)
+      </p>
+</div></td>
+</tr></table>
+<hr>
+<div class="spirit-nav">
+<a accesskey="p" href="../math_toolkit/status/credits.html"><img src="../../../doc/html/images/prev.png" alt="Prev"></a><a accesskey="u" href="../index.html"><img src="../../../doc/html/images/up.png" alt="Up"></a><a accesskey="h" href="../index.html"><img src="../../../doc/html/images/home.png" alt="Home"></a><a accesskey="n" href="s11.html"><img src="../../../doc/html/images/next.png" alt="Next"></a>
+</div>
+</body>
+</html>

Added: sandbox/tools/auto_index/example/math/doc/sf_and_dist/html/index/s11.html
==============================================================================
--- (empty file)
+++ sandbox/tools/auto_index/example/math/doc/sf_and_dist/html/index/s11.html	2008-11-28 05:25:28 EST (Fri, 28 Nov 2008)
@@ -0,0 +1,498 @@
+<html>
+<head>
+<meta http-equiv="Content-Type" content="text/html; charset=ISO-8859-1">
+<title>Typedef Index</title>
+<link rel="stylesheet" href="../boostbook.css" type="text/css">
+<meta name="generator" content="DocBook XSL Stylesheets Vsnapshot_8125">
+<link rel="home" href="../index.html" title="Math Toolkit">
+<link rel="up" href="../index.html" title="Math Toolkit">
+<link rel="prev" href="s10.html" title="Class Index">
+<link rel="next" href="s12.html" title="Function Index">
+</head>
+<body bgcolor="white" text="black" link="#0000FF" vlink="#840084" alink="#0000FF">
+<table cellpadding="2" width="100%"><tr>
+<td valign="top"><img alt="Boost C++ Libraries" width="277" height="86" src="../../../boost.png"></td>
+<td align="center">Home</td>
+<td align="center">Libraries</td>
+<td align="center">People</td>
+<td align="center">FAQ</td>
+<td align="center">More</td>
+</tr></table>
+<hr>
+<div class="spirit-nav">
+<a accesskey="p" href="s10.html"><img src="../../../doc/html/images/prev.png" alt="Prev"></a><a accesskey="u" href="../index.html"><img src="../../../doc/html/images/up.png" alt="Up"></a><a accesskey="h" href="../index.html"><img src="../../../doc/html/images/home.png" alt="Home"></a><a accesskey="n" href="s12.html"><img src="../../../doc/html/images/next.png" alt="Next"></a>
+</div>
+<div class="section" lang="en">
+<div class="titlepage"><div><div><h2 class="title" style="clear: both">
+<a name="id925394"></a>Typedef Index</h2></div></div></div>
+<p><a class="link" href="s11.html#idx_id_15">A</a> <a class="link" href="s11.html#idx_id_16">B</a> <a class="link" href="s11.html#idx_id_17">C</a> <a class="link" href="s11.html#idx_id_18">D</a> <a class="link" href="s11.html#idx_id_19">E</a> <a class="link" href="s11.html#idx_id_20">F</a> <a class="link" href="s11.html#idx_id_21">G</a> <a class="link" href="s11.html#idx_id_22">I</a> <a class="link" href="s11.html#idx_id_23">L</a> <a class="link" href="s11.html#idx_id_24">N</a> <a class="link" href="s11.html#idx_id_25">O</a> <a class="link" href="s11.html#idx_id_26">P</a> <a class="link" href="s11.html#idx_id_27">R</a> <a class="link" href="s11.html#idx_id_28">S</a> <a class="link" href="s11.html#idx_id_29">T</a> <a class="link" href="s11.html#idx_id_30">U</a> <a class="link" href="s11.html#idx_id_31">V</a> <a class="link" href="s11.html#idx_id_32">W</a> </p>
+<div class="variablelist"><dl>
+<dt>
+<a name="idx_id_15"></a><span class="term">A</span>
+</dt>
+<dd><div class="variablelist"><dl>
+<dt><span class="term">assert_undefined_type</span></dt>
+<dd><table class="simplelist" border="0" summary="Simple list"><tr><td><p><a class="link" href="../math_toolkit/policy/pol_ref/pol_ref_ref.html" title="Policy Class Reference">Policy Class Reference</a></p></td></tr></table></dd>
+</dl></div></dd>
+<dt>
+<a name="idx_id_16"></a><span class="term">B</span>
+</dt>
+<dd><div class="variablelist"><dl>
+<dt><span class="term">bernoulli</span></dt>
+<dd><table class="simplelist" border="0" summary="Simple list"><tr><td><p><a class="link" href="../math_toolkit/dist/dist_ref/dists/bernoulli_dist.html" title="Bernoulli Distribution">Bernoulli Distribution</a></p></td></tr></table></dd>
+<dt><span class="term">beta</span></dt>
+<dd><table class="simplelist" border="0" summary="Simple list">
+<tr><td><p><a class="link" href="../math_toolkit/main_overview/intro.html" title="About the Math Toolkit">About the Math Toolkit</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/backgrounders/implementation.html" title="Additional Implementation Notes">Additional Implementation Notes</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/special/sf_beta/beta_function.html" title="Beta">beta</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/dist/dist_ref/dists/beta_dist.html" title="Beta Distribution">Beta Distribution</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/special/factorials/sf_binomial.html" title="Binomial Coefficients">Binomial Coefficients</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/dist/dist_ref/dists/binomial_dist.html" title="Binomial Distribution">Binomial Distribution</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/main_overview/tr1.html" title="C99 and TR1 C Functions">C99 and TR1 C Functions</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/special/extern_c/tr1.html" title="C99 and TR1 C Functions Overview">C99 and TR1 C Functions Overview</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/dist/dist_ref/dists/chi_squared_dist.html" title="Chi Squared Distribution">Chi Squared Distribution</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/using_udt/concepts.html" title="Conceptual Requirements for Real Number Types">Conceptual Requirements for Real Number Types</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/status/credits.html" title="Credits and Acknowledgements">Credits and Acknowledgements</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/special/sf_beta/beta_derivative.html" title="Derivative of the Incomplete Beta Function">Derivative of the Incomplete Beta Function</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/main_overview/directories.html" title="Directory and File Structure">Directory and File Structure</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/dist/stat_tut/weg/dist_construct_eg.html" title="Distribution Construction Example">Distribution Construction Example</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/special/sf_beta/ibeta_function.html" title="Incomplete Beta Functions">Errors In the Function beta(a, b, x)</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/dist/stat_tut/weg/st_eg/tut_mean_size.html" title="Estimating how large a sample size would have to become in order to give a significant Students-t test result with a single sample test">Estimating how large a sample size would have to become in order to give a significant Students-t test result with a single sample test</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/dist/stat_tut/weg/cs_eg/chi_sq_size.html" title="Estimating the Required Sample Sizes for a Chi-Square Test for the Standard Deviation">Estimating the Required Sample Sizes for a Chi-Square Test for the Standard Deviation</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/dist/dist_ref/dists/f_dist.html" title="F Distribution">F Distribution</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/special/sf_beta/beta_function.html" title="Beta">gamma</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/toolkit/internals2/test_data.html" title="Graphing, Profiling, and Generating Test Data for Special Functions">Graphing, Profiling, and Generating Test Data for Special Functions</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/main_overview/history1.html" title="History and What's New">History and What's New</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/special/sf_beta/ibeta_function.html" title="Incomplete Beta Functions">Incomplete Beta Functions</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/special/sf_beta/beta_function.html" title="Beta">Lanczos approximation</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/dist/dist_ref/dists/negative_binomial_dist.html" title="Negative Binomial Distribution">Negative Binomial Distribution</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/dist/dist_ref/dists/nc_beta_dist.html" title="Noncentral Beta Distribution">Noncentral Beta Distribution</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/dist/dist_ref/dists/nc_f_dist.html" title="Noncentral F Distribution">Noncentral F Distribution</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/dist/dist_ref/dists/nc_t_dist.html" title="Noncentral T Distribution">Noncentral T Distribution</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/dist/stat_tut/overview.html" title="Overview">Overview</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/special/sf_gamma/gamma_ratios.html" title="Ratios of Gamma Functions">Ratios of Gamma Functions</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/special/sf_beta/beta_function.html" title="Beta">RR</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/dist/dist_ref/dists/students_t_dist.html" title="Students t Distribution">Students t Distribution</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/dist/stat_tut/weg/nccs_eg/nccs_power_eg.html" title="Tables of the power function of the &#967;2 test.">Tables of the power function of the &#967; 2 test.</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/special/sf_beta/ibeta_inv_function.html" title="The Incomplete Beta Function Inverses">The Incomplete Beta Function Inverses</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/backgrounders/lanczos.html" title="The Lanczos Approximation">The Lanczos Approximation</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/special/extern_c/tr1_ref.html" title="TR1 C Functions Quick Reference">TR1 C Functions Quick Reference</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/dist/dist_ref/dists/triangular_dist.html" title="Triangular Distribution">Triangular Distribution</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/dist/dist_ref/dists/weibull.html" title="Weibull Distribution">Weibull Distribution</a></p></td></tr>
+</table></dd>
+<dt><span class="term">binomial</span></dt>
+<dd><table class="simplelist" border="0" summary="Simple list">
+<tr><td><p><a class="link" href="../math_toolkit/main_overview/intro.html" title="About the Math Toolkit">About the Math Toolkit</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/backgrounders/implementation.html" title="Additional Implementation Notes">Additional Implementation Notes</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/dist/dist_ref/dists/bernoulli_dist.html" title="Bernoulli Distribution">Bernoulli Distribution</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/dist/dist_ref/dists/beta_dist.html" title="Beta Distribution">Beta Distribution</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/special/factorials/sf_binomial.html" title="Binomial Coefficients">Binomial Coefficients</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/dist/stat_tut/weg/binom_eg/binomial_coinflip_example.html" title="Binomial Coin-Flipping Example">Binomial Coin-Flipping Example</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/dist/dist_ref/dists/binomial_dist.html" title="Binomial Distribution">Binomial Distribution</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/dist/stat_tut/weg/binom_eg/binomial_quiz_example.html" title="Binomial Quiz Example">Binomial Quiz Example</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/dist/stat_tut/weg/binom_eg/binom_conf.html" title="Calculating Confidence Limits on the Frequency of Occurrence for a Binomial Distribution">Calculating Confidence Limits on the Frequency of Occurrence for a Binomial Distribution</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/dist/stat_tut/weg/neg_binom_eg/neg_binom_conf.html" title="Calculating Confidence Limits on the Frequency of Occurrence for the Negative Binomial Distribution">Calculating Confidence Limits on the Frequency of Occurrence for the Negative Binomial Distribution</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/dist/stat_tut/weg/nag_library.html" title="Comparison with C, R, FORTRAN-style Free Functions">Comparison with C, R, FORTRAN-style Free Functions</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/main_overview/pol_overview.html" title="Configuration and Policies">Configuration and Policies</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/dist/stat_tut/dist_params.html" title="Discrete Probability Distributions">Discrete Probability Distributions</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/dist/stat_tut/weg/dist_construct_eg.html" title="Distribution Construction Example">Distribution Construction Example</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/dist/stat_tut/weg/binom_eg/binom_size_eg.html" title="Estimating Sample Sizes for a Binomial Distribution.">Estimating Sample Sizes for a Binomial Distribution.</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/dist/stat_tut/weg/neg_binom_eg/neg_binom_size_eg.html" title="Estimating Sample Sizes for the Negative Binomial.">Estimating Sample Sizes for the Negative Binomial.</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/special/sf_beta/ibeta_function.html" title="Incomplete Beta Functions">Incomplete Beta Functions</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/dist/dist_ref/dists/binomial_dist.html" title="Binomial Distribution">Meaning of the non-member accessors</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/dist/dist_ref/dists/negative_binomial_dist.html" title="Negative Binomial Distribution">Negative Binomial Distribution</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/dist/stat_tut/weg/neg_binom_eg/negative_binomial_example1.html" title="Negative Binomial Sales Quota Example.">Negative Binomial Sales Quota Example.</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/dist/stat_tut/overview.html" title="Overview">Overview</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/policy/pol_overview.html" title="Policy Overview">Policy Overview</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/dist/stat_tut/variates.html" title="Random Variates and Distribution Parameters">Random Variates and Distribution Parameters</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/policy/pol_tutorial/namespace_policies.html" title="Setting Policies at Namespace or Translation Unit Scope">Setting Policies at Namespace or Translation Unit Scope</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/policy/pol_tutorial/ad_hoc_dist_policies.html" title="Setting Policies for Distributions on an Ad Hoc Basis">Setting Policies for Distributions on an Ad Hoc Basis</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/special/sf_beta/ibeta_inv_function.html" title="The Incomplete Beta Function Inverses">The Incomplete Beta Function Inverses</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/policy/pol_tutorial/understand_dis_quant.html" title="Understanding Quantiles of Discrete Distributions">Understanding Quantiles of Discrete Distributions</a></p></td></tr>
+</table></dd>
+</dl></div></dd>
+<dt>
+<a name="idx_id_17"></a><span class="term">C</span>
+</dt>
+<dd><div class="variablelist"><dl>
+<dt><span class="term">cauchy</span></dt>
+<dd><table class="simplelist" border="0" summary="Simple list">
+<tr><td><p><a class="link" href="../math_toolkit/backgrounders/implementation.html" title="Additional Implementation Notes">Additional Implementation Notes</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/dist/dist_ref/dists/cauchy_dist.html" title="Cauchy-Lorentz Distribution">Cauchy-Lorentz Distribution</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/dist/stat_tut/weg/find_eg/find_location_eg.html" title="Find Location (Mean) Example">Find Location (Mean) Example</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/dist/stat_tut/weg/find_eg/find_mean_and_sd_eg.html" title="Find mean and standard deviation example">Find mean and standard deviation example</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/policy/pol_ref/assert_undefined.html" title="Mathematically Undefined Function Policies">Mathematically Undefined Function Policies</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/policy/pol_ref/namespace_pol.html" title="Setting Polices at Namespace Scope">Setting Polices at Namespace Scope</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/policy/pol_tutorial/namespace_policies.html" title="Setting Policies at Namespace or Translation Unit Scope">Setting Policies at Namespace or Translation Unit Scope</a></p></td></tr>
+</table></dd>
+<dt><span class="term">chi_squared</span></dt>
+<dd><table class="simplelist" border="0" summary="Simple list">
+<tr><td><p><a class="link" href="../math_toolkit/dist/dist_ref/dists/chi_squared_dist.html" title="Chi Squared Distribution">Chi Squared Distribution</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/dist/stat_tut/weg/cs_eg/chi_sq_test.html" title="Chi-Square Test for the Standard Deviation">Chi-Square Test for the Standard Deviation</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/dist/stat_tut/weg/cs_eg/chi_sq_intervals.html" title="Confidence Intervals on the Standard Deviation">Confidence Intervals on the Standard Deviation</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/dist/stat_tut/weg/cs_eg/chi_sq_size.html" title="Estimating the Required Sample Sizes for a Chi-Square Test for the Standard Deviation">Estimating the Required Sample Sizes for a Chi-Square Test for the Standard Deviation</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/dist/stat_tut/weg/nccs_eg/nccs_power_eg.html" title="Tables of the power function of the &#967;2 test.">Tables of the power function of the &#967; 2 test.</a></p></td></tr>
+</table></dd>
+</dl></div></dd>
+<dt>
+<a name="idx_id_18"></a><span class="term">D</span>
+</dt>
+<dd><div class="variablelist"><dl>
+<dt><span class="term">denorm_error_type</span></dt>
+<dd><table class="simplelist" border="0" summary="Simple list"><tr><td><p><a class="link" href="../math_toolkit/policy/pol_ref/pol_ref_ref.html" title="Policy Class Reference">Policy Class Reference</a></p></td></tr></table></dd>
+<dt><span class="term">discrete_quantile_type</span></dt>
+<dd><table class="simplelist" border="0" summary="Simple list"><tr><td><p><a class="link" href="../math_toolkit/policy/pol_ref/pol_ref_ref.html" title="Policy Class Reference">Policy Class Reference</a></p></td></tr></table></dd>
+<dt><span class="term">domain_error_type</span></dt>
+<dd><table class="simplelist" border="0" summary="Simple list"><tr><td><p><a class="link" href="../math_toolkit/policy/pol_ref/pol_ref_ref.html" title="Policy Class Reference">Policy Class Reference</a></p></td></tr></table></dd>
+<dt><span class="term">double_t</span></dt>
+<dd><table class="simplelist" border="0" summary="Simple list">
+<tr><td><p><a class="link" href="../math_toolkit/main_overview/tr1.html" title="C99 and TR1 C Functions">C99 and TR1 C Functions</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/special/extern_c/tr1.html" title="C99 and TR1 C Functions Overview">C99 and TR1 C Functions Overview</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/special/extern_c/c99.html" title="C99 C Functions">C99 C Functions</a></p></td></tr>
+</table></dd>
+</dl></div></dd>
+<dt>
+<a name="idx_id_19"></a><span class="term">E</span>
+</dt>
+<dd><div class="variablelist"><dl>
+<dt><span class="term">evaluation_error_type</span></dt>
+<dd><table class="simplelist" border="0" summary="Simple list"><tr><td><p><a class="link" href="../math_toolkit/policy/pol_ref/pol_ref_ref.html" title="Policy Class Reference">Policy Class Reference</a></p></td></tr></table></dd>
+<dt><span class="term">exponential</span></dt>
+<dd><table class="simplelist" border="0" summary="Simple list">
+<tr><td><p><a class="link" href="../math_toolkit/backgrounders/implementation.html" title="Additional Implementation Notes">Additional Implementation Notes</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/main_overview/tr1.html" title="C99 and TR1 C Functions">C99 and TR1 C Functions</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/special/extern_c/tr1.html" title="C99 and TR1 C Functions Overview">C99 and TR1 C Functions Overview</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/dist/dist_ref/dists/exp_dist.html" title="Exponential Distribution">Exponential Distribution</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/special/expint/expint_i.html" title="Exponential Integral Ei">Exponential Integral Ei</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/special/expint/expint_n.html" title="Exponential Integral En">Exponential Integral En</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/special/inv_hyper/inv_hyper_over.html" title="Inverse Hyperbolic Functions Overview">Inverse Hyperbolic Functions Overview</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/special/bessel/mbessel.html" title="Modified Bessel Functions of the First and Second Kinds">Modified Bessel Functions of the First and Second Kinds</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/special/extern_c/tr1_ref.html" title="TR1 C Functions Quick Reference">TR1 C Functions Quick Reference</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/dist/dist_ref/dists/weibull.html" title="Weibull Distribution">Weibull Distribution</a></p></td></tr>
+</table></dd>
+<dt><span class="term">extreme_value</span></dt>
+<dd><table class="simplelist" border="0" summary="Simple list"><tr><td><p><a class="link" href="../math_toolkit/dist/dist_ref/dists/extreme_dist.html" title="Extreme Value Distribution">Extreme Value Distribution</a></p></td></tr></table></dd>
+</dl></div></dd>
+<dt>
+<a name="idx_id_20"></a><span class="term">F</span>
+</dt>
+<dd><div class="variablelist"><dl>
+<dt><span class="term">fisher_f</span></dt>
+<dd><table class="simplelist" border="0" summary="Simple list">
+<tr><td><p><a class="link" href="../math_toolkit/dist/dist_ref/dists/f_dist.html" title="F Distribution">F Distribution</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/dist/stat_tut/weg/f_eg.html" title="F Distribution Examples">F Distribution Examples</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/policy/pol_tutorial/ad_hoc_dist_policies.html" title="Setting Policies for Distributions on an Ad Hoc Basis">Setting Policies for Distributions on an Ad Hoc Basis</a></p></td></tr>
+</table></dd>
+<dt><span class="term">float_t</span></dt>
+<dd><table class="simplelist" border="0" summary="Simple list">
+<tr><td><p><a class="link" href="../math_toolkit/main_overview/tr1.html" title="C99 and TR1 C Functions">C99 and TR1 C Functions</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/special/extern_c/tr1.html" title="C99 and TR1 C Functions Overview">C99 and TR1 C Functions Overview</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/special/extern_c/c99.html" title="C99 C Functions">C99 C Functions</a></p></td></tr>
+</table></dd>
+</dl></div></dd>
+<dt>
+<a name="idx_id_21"></a><span class="term">G</span>
+</dt>
+<dd><div class="variablelist"><dl>
+<dt><span class="term">gamma</span></dt>
+<dd><table class="simplelist" border="0" summary="Simple list">
+<tr><td><p><a class="link" href="../math_toolkit/main_overview/intro.html" title="About the Math Toolkit">About the Math Toolkit</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/backgrounders/implementation.html" title="Additional Implementation Notes">Additional Implementation Notes</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/special/bessel/bessel.html" title="Bessel Functions of the First and Second Kinds">Bessel Functions of the First and Second Kinds</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/special/sf_beta/beta_function.html" title="Beta">Beta</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/special/extern_c/c99.html" title="C99 C Functions">C99 C Functions</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/policy/pol_tutorial/ad_hoc_sf_policies.html" title="Changing the Policy on an Ad Hoc Basis for the Special Functions">Changing the Policy on an Ad Hoc Basis for the Special Functions</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/dist/dist_ref/dists/chi_squared_dist.html" title="Chi Squared Distribution">Chi Squared Distribution</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/using_udt/concepts.html" title="Conceptual Requirements for Real Number Types">Conceptual Requirements for Real Number Types</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/status/credits.html" title="Credits and Acknowledgements">Credits and Acknowledgements</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/special/sf_gamma/gamma_derivatives.html" title="Derivative of the Incomplete Gamma Function">Derivative of the Incomplete Gamma Function</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/special/sf_gamma/digamma.html" title="Digamma">Digamma</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/main_overview/directories.html" title="Directory and File Structure">Directory and File Structure</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/dist/stat_tut/weg/dist_construct_eg.html" title="Distribution Construction Example">Distribution Construction Example</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/special/factorials/sf_double_factorial.html" title="Double Factorial">Double Factorial</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/special/sf_erf/error_function.html" title="Error Functions">Error Functions</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/policy/pol_ref/error_handling_policies.html" title="Error Handling Policies">Error Handling Policies</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/special/sf_gamma/tgamma.html" title="Gamma">expm1</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/special/sf_gamma/tgamma.html" title="Gamma">factorial</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/special/factorials/sf_falling_factorial.html" title="Falling Factorial">Falling Factorial</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/special/sf_gamma/tgamma.html" title="Gamma">gamma</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/dist/dist_ref/dists/gamma_dist.html" title="Gamma (and Erlang) Distribution">Gamma (and Erlang) Distribution</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/toolkit/internals2/test_data.html" title="Graphing, Profiling, and Generating Test Data for Special Functions">Graphing, Profiling, and Generating Test Data for Special Functions</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/main_overview/history1.html" title="History and What's New">History and What's New</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/special/sf_beta/ibeta_function.html" title="Incomplete Beta Functions">Incomplete Beta Functions</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/special/sf_gamma/igamma_inv.html" title="Incomplete Gamma Function Inverses">Incomplete Gamma Function Inverses</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/special/sf_gamma/igamma.html" title="Incomplete Gamma Functions">Incomplete Gamma Functions</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/policy/pol_ref/internal_promotion.html" title="Internal Promotion Policies">Internal Promotion Policies</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/special/sf_gamma/tgamma.html" title="Gamma">lanczos</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/special/sf_gamma/tgamma.html" title="Gamma">Lanczos approximation</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/special/sf_gamma/tgamma.html" title="Gamma">lgamma</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/special/sf_gamma/lgamma.html" title="Log Gamma">Log Gamma</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/special/bessel/mbessel.html" title="Modified Bessel Functions of the First and Second Kinds">Modified Bessel Functions of the First and Second Kinds</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/dist/dist_ref/dists/nc_chi_squared_dist.html" title="Noncentral Chi-Squared Distribution">Noncentral Chi-Squared Distribution</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/dist/stat_tut/overview.html" title="Overview">Overview</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/dist/dist_ref/dists/poisson_dist.html" title="Poisson Distribution">Poisson Distribution</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/policy/pol_ref/precision_pol.html" title="Precision Policies">Precision Policies</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/special/sf_gamma/gamma_ratios.html" title="Ratios of Gamma Functions">Ratios of Gamma Functions</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/backgrounders/refs.html" title="References">References</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/special/factorials/sf_rising_factorial.html" title="Rising Factorial">Rising Factorial</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/policy/pol_ref/namespace_pol.html" title="Setting Polices at Namespace Scope">Setting Polices at Namespace Scope</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/policy/pol_tutorial/namespace_policies.html" title="Setting Policies at Namespace or Translation Unit Scope">Setting Policies at Namespace or Translation Unit Scope</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/special/sf_gamma/tgamma.html" title="Gamma">tgamma</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/special/sf_gamma/tgamma.html" title="Gamma">tgamma1pm1</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/special/sf_beta/ibeta_inv_function.html" title="The Incomplete Beta Function Inverses">The Incomplete Beta Function Inverses</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/backgrounders/lanczos.html" title="The Lanczos Approximation">The Lanczos Approximation</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/using_udt/use_mpfr.html" title="Using With MPFR / GMP - a High-Precision Floating-Point Library">Using With MPFR / GMP - a High-Precision Floating-Point Library</a></p></td></tr>
+</table></dd>
+</dl></div></dd>
+<dt>
+<a name="idx_id_22"></a><span class="term">I</span>
+</dt>
+<dd><div class="variablelist"><dl>
+<dt><span class="term">indeterminate_result_error_type</span></dt>
+<dd><table class="simplelist" border="0" summary="Simple list"><tr><td><p><a class="link" href="../math_toolkit/policy/pol_ref/pol_ref_ref.html" title="Policy Class Reference">Policy Class Reference</a></p></td></tr></table></dd>
+</dl></div></dd>
+<dt>
+<a name="idx_id_23"></a><span class="term">L</span>
+</dt>
+<dd><div class="variablelist"><dl>
+<dt><span class="term">lognormal</span></dt>
+<dd><table class="simplelist" border="0" summary="Simple list">
+<tr><td><p><a class="link" href="../math_toolkit/backgrounders/implementation.html" title="Additional Implementation Notes">Additional Implementation Notes</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/dist/dist_ref/dist_algorithms.html" title="Distribution Algorithms">Distribution Algorithms</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/dist/dist_ref/dists/gamma_dist.html" title="Gamma (and Erlang) Distribution">Gamma (and Erlang) Distribution</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/dist/dist_ref/dists/lognormal_dist.html" title="Log Normal Distribution">Log Normal Distribution</a></p></td></tr>
+</table></dd>
+</dl></div></dd>
+<dt>
+<a name="idx_id_24"></a><span class="term">N</span>
+</dt>
+<dd><div class="variablelist"><dl>
+<dt><span class="term">negative_binomial</span></dt>
+<dd><table class="simplelist" border="0" summary="Simple list">
+<tr><td><p><a class="link" href="../math_toolkit/dist/stat_tut/weg/neg_binom_eg/neg_binom_conf.html" title="Calculating Confidence Limits on the Frequency of Occurrence for the Negative Binomial Distribution">Calculating Confidence Limits on the Frequency of Occurrence for the Negative Binomial Distribution</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/policy/pol_ref/discrete_quant_ref.html" title="Discrete Quantile Policies">Discrete Quantile Policies</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/dist/stat_tut/weg/dist_construct_eg.html" title="Distribution Construction Example">Distribution Construction Example</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/dist/stat_tut/weg/neg_binom_eg/neg_binom_size_eg.html" title="Estimating Sample Sizes for the Negative Binomial.">Estimating Sample Sizes for the Negative Binomial.</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/dist/dist_ref/dists/negative_binomial_dist.html" title="Negative Binomial Distribution">Meaning of the non-member accessors.</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/dist/dist_ref/dists/negative_binomial_dist.html" title="Negative Binomial Distribution">Negative Binomial Distribution</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/dist/stat_tut/weg/neg_binom_eg/negative_binomial_example1.html" title="Negative Binomial Sales Quota Example.">Negative Binomial Sales Quota Example.</a></p></td></tr>
+</table></dd>
+<dt><span class="term">non_central_beta</span></dt>
+<dd><table class="simplelist" border="0" summary="Simple list"><tr><td><p><a class="link" href="../math_toolkit/dist/dist_ref/dists/nc_beta_dist.html" title="Noncentral Beta Distribution">Noncentral Beta Distribution</a></p></td></tr></table></dd>
+<dt><span class="term">non_central_chi_squared</span></dt>
+<dd><table class="simplelist" border="0" summary="Simple list">
+<tr><td><p><a class="link" href="../math_toolkit/dist/dist_ref/dists/nc_chi_squared_dist.html" title="Noncentral Chi-Squared Distribution">Noncentral Chi-Squared Distribution</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/dist/stat_tut/weg/nccs_eg/nccs_power_eg.html" title="Tables of the power function of the &#967;2 test.">Tables of the power function of the &#967; 2 test.</a></p></td></tr>
+</table></dd>
+<dt><span class="term">non_central_f</span></dt>
+<dd><table class="simplelist" border="0" summary="Simple list"><tr><td><p><a class="link" href="../math_toolkit/dist/dist_ref/dists/nc_f_dist.html" title="Noncentral F Distribution">Noncentral F Distribution</a></p></td></tr></table></dd>
+<dt><span class="term">non_central_t</span></dt>
+<dd><table class="simplelist" border="0" summary="Simple list"><tr><td><p><a class="link" href="../math_toolkit/dist/dist_ref/dists/nc_t_dist.html" title="Noncentral T Distribution">Noncentral T Distribution</a></p></td></tr></table></dd>
+<dt><span class="term">normal</span></dt>
+<dd><table class="simplelist" border="0" summary="Simple list">
+<tr><td><p><a class="link" href="../math_toolkit/perf/comparisons.html" title="Comparisons to Other Open Source Libraries">A Comparison to the R Statistical Library on Linux</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/perf/comparisons.html" title="Comparisons to Other Open Source Libraries">A Comparison to the R Statistical Library on Windows XP</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/main_overview/intro.html" title="About the Math Toolkit">About the Math Toolkit</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/backgrounders/implementation.html" title="Additional Implementation Notes">Additional Implementation Notes</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/dist/dist_ref/dists/binomial_dist.html" title="Binomial Distribution">Binomial Distribution</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/dist/stat_tut/weg/st_eg/tut_mean_intervals.html" title="Calculating confidence intervals on the mean with the Students-t distribution">Calculating confidence intervals on the mean with the Students-t distribution</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/dist/dist_ref/dist_algorithms.html" title="Distribution Algorithms">Distribution Algorithms</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/dist/stat_tut/weg/dist_construct_eg.html" title="Distribution Construction Example">Distribution Construction Example</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/policy/pol_ref/error_handling_policies.html" title="Error Handling Policies">Error Handling Policies</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/dist/dist_ref/dists/f_dist.html" title="F Distribution">F Distribution</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/dist/stat_tut/weg/find_eg/find_location_eg.html" title="Find Location (Mean) Example">Find Location (Mean) Example</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/dist/stat_tut/weg/find_eg/find_mean_and_sd_eg.html" title="Find mean and standard deviation example">Find mean and standard deviation example</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/dist/stat_tut/weg/find_eg/find_scale_eg.html" title="Find Scale (Standard Deviation) Example">Find Scale (Standard Deviation) Example</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/special/fpclass.html" title="Floating-Point Classification: Infinities and NaN's">Floating-Point Classification: Infinities and NaN's</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/special/sf_gamma/igamma_inv.html" title="Incomplete Gamma Function Inverses">Incomplete Gamma Function Inverses</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/policy/pol_ref/internal_promotion.html" title="Internal Promotion Policies">Internal Promotion Policies</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/status/issues.html" title="Known Issues, and Todo List">Known Issues, and Todo List</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/dist/dist_ref/dists/negative_binomial_dist.html" title="Negative Binomial Distribution">Negative Binomial Distribution</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/dist/dist_ref/nmp.html" title="Non-Member Properties">Non-Member Properties</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/dist/dist_ref/dists/nc_chi_squared_dist.html" title="Noncentral Chi-Squared Distribution">Noncentral Chi-Squared Distribution</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/dist/dist_ref/dists/nc_t_dist.html" title="Noncentral T Distribution">Noncentral T Distribution</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/dist/dist_ref/dists/normal_dist.html" title="Normal (Gaussian) Distribution">Normal (Gaussian) Distribution</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/dist/stat_tut/overview.html" title="Overview">Overview</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/policy/pol_ref/precision_pol.html" title="Precision Policies">Precision Policies</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/dist/dist_ref/dists/rayleigh.html" title="Rayleigh Distribution">Rayleigh Distribution</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/policy/pol_tutorial/namespace_policies.html" title="Setting Policies at Namespace or Translation Unit Scope">Setting Policies at Namespace or Translation Unit Scope</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/dist/stat_tut/weg/normal_example/normal_misc.html" title="Some Miscellaneous Examples of the Normal (Gaussian) Distribution">Some Miscellaneous Examples of the Normal (Gaussian) Distribution</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/dist/dist_ref/dists/students_t_dist.html" title="Students t Distribution">Students t Distribution</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/special/sf_beta/ibeta_inv_function.html" title="The Incomplete Beta Function Inverses">The Incomplete Beta Function Inverses</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/dist/dist_ref/dists/triangular_dist.html" title="Triangular Distribution">Triangular Distribution</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/policy/pol_ref/policy_defaults.html" title="Using macros to Change the Policy Defaults">Using macros to Change the Policy Defaults</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/dist/dist_ref/dists/weibull.html" title="Weibull Distribution">Weibull Distribution</a></p></td></tr>
+</table></dd>
+</dl></div></dd>
+<dt>
+<a name="idx_id_25"></a><span class="term">O</span>
+</dt>
+<dd><div class="variablelist"><dl>
+<dt><span class="term">overflow_error_type</span></dt>
+<dd><table class="simplelist" border="0" summary="Simple list"><tr><td><p><a class="link" href="../math_toolkit/policy/pol_ref/pol_ref_ref.html" title="Policy Class Reference">Policy Class Reference</a></p></td></tr></table></dd>
+</dl></div></dd>
+<dt>
+<a name="idx_id_26"></a><span class="term">P</span>
+</dt>
+<dd><div class="variablelist"><dl>
+<dt><span class="term">pareto</span></dt>
+<dd><table class="simplelist" border="0" summary="Simple list"><tr><td><p><a class="link" href="../math_toolkit/dist/dist_ref/dists/pareto.html" title="Pareto Distribution">Pareto Distribution</a></p></td></tr></table></dd>
+<dt><span class="term">poisson</span></dt>
+<dd><table class="simplelist" border="0" summary="Simple list">
+<tr><td><p><a class="link" href="../math_toolkit/dist/dist_ref/dists/negative_binomial_dist.html" title="Negative Binomial Distribution">Negative Binomial Distribution</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/dist/dist_ref/dists/poisson_dist.html" title="Poisson Distribution">Poisson Distribution</a></p></td></tr>
+</table></dd>
+<dt><span class="term">pole_error_type</span></dt>
+<dd><table class="simplelist" border="0" summary="Simple list"><tr><td><p><a class="link" href="../math_toolkit/policy/pol_ref/pol_ref_ref.html" title="Policy Class Reference">Policy Class Reference</a></p></td></tr></table></dd>
+<dt><span class="term">policy_type</span></dt>
+<dd><table class="simplelist" border="0" summary="Simple list">
+<tr><td><p><a class="link" href="../math_toolkit/dist/dist_ref/dists/bernoulli_dist.html" title="Bernoulli Distribution">Bernoulli Distribution</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/dist/dist_ref/dists/beta_dist.html" title="Beta Distribution">Beta Distribution</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/dist/dist_ref/dists/binomial_dist.html" title="Binomial Distribution">Binomial Distribution</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/dist/dist_ref/dists/cauchy_dist.html" title="Cauchy-Lorentz Distribution">Cauchy-Lorentz Distribution</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/dist/dist_ref/dists/chi_squared_dist.html" title="Chi Squared Distribution">Chi Squared Distribution</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/using_udt/dist_concept.html" title="Conceptual Requirements for Distribution Types">Conceptual Requirements for Distribution Types</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/dist/dist_ref/dists/exp_dist.html" title="Exponential Distribution">Exponential Distribution</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/dist/dist_ref/dists/gamma_dist.html" title="Gamma (and Erlang) Distribution">Gamma (and Erlang) Distribution</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/dist/dist_ref/dists/lognormal_dist.html" title="Log Normal Distribution">Log Normal Distribution</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/dist/dist_ref/dists/logistic_dist.html" title="Logistic Distribution">Logistic Distribution</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/dist/dist_ref/dists/negative_binomial_dist.html" title="Negative Binomial Distribution">Negative Binomial Distribution</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/dist/dist_ref/dists/nc_beta_dist.html" title="Noncentral Beta Distribution">Noncentral Beta Distribution</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/dist/dist_ref/dists/nc_chi_squared_dist.html" title="Noncentral Chi-Squared Distribution">Noncentral Chi-Squared Distribution</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/dist/dist_ref/dists/nc_f_dist.html" title="Noncentral F Distribution">Noncentral F Distribution</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/dist/dist_ref/dists/nc_t_dist.html" title="Noncentral T Distribution">Noncentral T Distribution</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/dist/dist_ref/dists/normal_dist.html" title="Normal (Gaussian) Distribution">Normal (Gaussian) Distribution</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/dist/dist_ref/dists/poisson_dist.html" title="Poisson Distribution">Poisson Distribution</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/dist/dist_ref/dists/rayleigh.html" title="Rayleigh Distribution">Rayleigh Distribution</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/dist/dist_ref/dists/students_t_dist.html" title="Students t Distribution">Students t Distribution</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/dist/dist_ref/dists/triangular_dist.html" title="Triangular Distribution">Triangular Distribution</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/dist/dist_ref/dists/weibull.html" title="Weibull Distribution">Weibull Distribution</a></p></td></tr>
+</table></dd>
+<dt><span class="term">precision_type</span></dt>
+<dd><table class="simplelist" border="0" summary="Simple list"><tr><td><p><a class="link" href="../math_toolkit/policy/pol_ref/pol_ref_ref.html" title="Policy Class Reference">Policy Class Reference</a></p></td></tr></table></dd>
+<dt><span class="term">promote_double_type</span></dt>
+<dd><table class="simplelist" border="0" summary="Simple list"><tr><td><p><a class="link" href="../math_toolkit/policy/pol_ref/pol_ref_ref.html" title="Policy Class Reference">Policy Class Reference</a></p></td></tr></table></dd>
+<dt><span class="term">promote_float_type</span></dt>
+<dd><table class="simplelist" border="0" summary="Simple list"><tr><td><p><a class="link" href="../math_toolkit/policy/pol_ref/pol_ref_ref.html" title="Policy Class Reference">Policy Class Reference</a></p></td></tr></table></dd>
+</dl></div></dd>
+<dt>
+<a name="idx_id_27"></a><span class="term">R</span>
+</dt>
+<dd><div class="variablelist"><dl>
+<dt><span class="term">rayleigh</span></dt>
+<dd><table class="simplelist" border="0" summary="Simple list"><tr><td><p><a class="link" href="../math_toolkit/dist/dist_ref/dists/rayleigh.html" title="Rayleigh Distribution">Rayleigh Distribution</a></p></td></tr></table></dd>
+<dt><span class="term">rounding_error_type</span></dt>
+<dd><table class="simplelist" border="0" summary="Simple list"><tr><td><p><a class="link" href="../math_toolkit/policy/pol_ref/pol_ref_ref.html" title="Policy Class Reference">Policy Class Reference</a></p></td></tr></table></dd>
+</dl></div></dd>
+<dt>
+<a name="idx_id_28"></a><span class="term">S</span>
+</dt>
+<dd><div class="variablelist"><dl>
+<dt><span class="term">students_t</span></dt>
+<dd><table class="simplelist" border="0" summary="Simple list">
+<tr><td><p><a class="link" href="../math_toolkit/dist/stat_tut/weg/st_eg/tut_mean_intervals.html" title="Calculating confidence intervals on the mean with the Students-t distribution">Calculating confidence intervals on the mean with the Students-t distribution</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/policy/pol_tutorial/changing_policy_defaults.html" title="Changing the Policy Defaults">Changing the Policy Defaults</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/dist/stat_tut/weg/st_eg/two_sample_students_t.html" title="Comparing the means of two samples with the Students-t test">Comparing the means of two samples with the Students-t test</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/dist/stat_tut/weg/error_eg.html" title="Error Handling Example">Error Handling Example</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/dist/stat_tut/weg/st_eg/tut_mean_size.html" title="Estimating how large a sample size would have to become in order to give a significant Students-t test result with a single sample test">Estimating how large a sample size would have to become in order to give a significant Students-t test result with a single sample test</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/main_overview/namespaces.html" title="Namespaces">Namespaces</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/dist/stat_tut/overview.html" title="Overview">Overview</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/dist/dist_ref/dists/students_t_dist.html" title="Students t Distribution">Students t Distribution</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/dist/stat_tut/weg/st_eg/tut_mean_test.html" title='Testing a sample mean for difference from a "true" mean'>Testing a sample mean for difference from a "true" mean</a></p></td></tr>
+</table></dd>
+</dl></div></dd>
+<dt>
+<a name="idx_id_29"></a><span class="term">T</span>
+</dt>
+<dd><div class="variablelist"><dl>
+<dt><span class="term">triangular</span></dt>
+<dd><table class="simplelist" border="0" summary="Simple list">
+<tr><td><p><a class="link" href="../math_toolkit/backgrounders/implementation.html" title="Additional Implementation Notes">Additional Implementation Notes</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/dist/dist_ref/dists/beta_dist.html" title="Beta Distribution">Beta Distribution</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/dist/dist_ref/dist_algorithms.html" title="Distribution Algorithms">Distribution Algorithms</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/dist/stat_tut/overview.html" title="Overview">Overview</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/dist/dist_ref/dists/triangular_dist.html" title="Triangular Distribution">Triangular Distribution</a></p></td></tr>
+</table></dd>
+</dl></div></dd>
+<dt>
+<a name="idx_id_30"></a><span class="term">U</span>
+</dt>
+<dd><div class="variablelist"><dl>
+<dt><span class="term">underflow_error_type</span></dt>
+<dd><table class="simplelist" border="0" summary="Simple list"><tr><td><p><a class="link" href="../math_toolkit/policy/pol_ref/pol_ref_ref.html" title="Policy Class Reference">Policy Class Reference</a></p></td></tr></table></dd>
+<dt><span class="term">uniform</span></dt>
+<dd><table class="simplelist" border="0" summary="Simple list">
+<tr><td><p><a class="link" href="../math_toolkit/backgrounders/implementation.html" title="Additional Implementation Notes">Additional Implementation Notes</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/dist/dist_ref/dists/beta_dist.html" title="Beta Distribution">Beta Distribution</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/toolkit/internals2/test_data.html" title="Graphing, Profiling, and Generating Test Data for Special Functions">Graphing, Profiling, and Generating Test Data for Special Functions</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/dist/stat_tut/overview.html" title="Overview">Overview</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/dist/dist_ref/dists/triangular_dist.html" title="Triangular Distribution">Triangular Distribution</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/dist/dist_ref/dists/uniform_dist.html" title="Uniform Distribution">Uniform Distribution</a></p></td></tr>
+</table></dd>
+</dl></div></dd>
+<dt>
+<a name="idx_id_31"></a><span class="term">V</span>
+</dt>
+<dd><div class="variablelist"><dl>
+<dt><span class="term">value_type</span></dt>
+<dd><table class="simplelist" border="0" summary="Simple list">
+<tr><td><p><a class="link" href="../math_toolkit/dist/dist_ref/dists/bernoulli_dist.html" title="Bernoulli Distribution">Bernoulli Distribution</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/dist/dist_ref/dists/beta_dist.html" title="Beta Distribution">Beta Distribution</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/dist/dist_ref/dists/binomial_dist.html" title="Binomial Distribution">Binomial Distribution</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/dist/dist_ref/dists/cauchy_dist.html" title="Cauchy-Lorentz Distribution">Cauchy-Lorentz Distribution</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/dist/dist_ref/dists/chi_squared_dist.html" title="Chi Squared Distribution">Chi Squared Distribution</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/using_udt/archetypes.html" title="Conceptual Archetypes and Testing">Conceptual Archetypes and Testing</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/using_udt/dist_concept.html" title="Conceptual Requirements for Distribution Types">Conceptual Requirements for Distribution Types</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/dist/dist_ref/dist_algorithms.html" title="Distribution Algorithms">Distribution Algorithms</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/dist/dist_ref/dists/exp_dist.html" title="Exponential Distribution">Exponential Distribution</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/dist/future.html" title="Extras/Future Directions">Extras/Future Directions</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/dist/dist_ref/dists/extreme_dist.html" title="Extreme Value Distribution">Extreme Value Distribution</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/dist/dist_ref/dists/f_dist.html" title="F Distribution">F Distribution</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/dist/dist_ref/dists/gamma_dist.html" title="Gamma (and Erlang) Distribution">Gamma (and Erlang) Distribution</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/toolkit/internals2/test_data.html" title="Graphing, Profiling, and Generating Test Data for Special Functions">Graphing, Profiling, and Generating Test Data for Special Functions</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/dist/dist_ref/dists/lognormal_dist.html" title="Log Normal Distribution">Log Normal Distribution</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/dist/dist_ref/dists/logistic_dist.html" title="Logistic Distribution">Logistic Distribution</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/dist/dist_ref/dists/negative_binomial_dist.html" title="Negative Binomial Distribution">Negative Binomial Distribution</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/dist/dist_ref/dists/nc_beta_dist.html" title="Noncentral Beta Distribution">Noncentral Beta Distribution</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/dist/dist_ref/dists/nc_chi_squared_dist.html" title="Noncentral Chi-Squared Distribution">Noncentral Chi-Squared Distribution</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/dist/dist_ref/dists/nc_f_dist.html" title="Noncentral F Distribution">Noncentral F Distribution</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/dist/dist_ref/dists/nc_t_dist.html" title="Noncentral T Distribution">Noncentral T Distribution</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/dist/dist_ref/dists/normal_dist.html" title="Normal (Gaussian) Distribution">Normal (Gaussian) Distribution</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/dist/dist_ref/dists/pareto.html" title="Pareto Distribution">Pareto Distribution</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/dist/dist_ref/dists/poisson_dist.html" title="Poisson Distribution">Poisson Distribution</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/toolkit/internals2/polynomials.html" title="Polynomials">Polynomials</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/dist/dist_ref/dists/rayleigh.html" title="Rayleigh Distribution">Rayleigh Distribution</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/toolkit/internals2/error_test.html" title="Relative Error and Testing">Relative Error and Testing</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/dist/dist_ref/dists/students_t_dist.html" title="Students t Distribution">Students t Distribution</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/dist/dist_ref/dists/triangular_dist.html" title="Triangular Distribution">Triangular Distribution</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/dist/dist_ref/dists/uniform_dist.html" title="Uniform Distribution">Uniform Distribution</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/dist/dist_ref/dists/weibull.html" title="Weibull Distribution">Weibull Distribution</a></p></td></tr>
+</table></dd>
+</dl></div></dd>
+<dt>
+<a name="idx_id_32"></a><span class="term">W</span>
+</dt>
+<dd><div class="variablelist"><dl>
+<dt><span class="term">weibull</span></dt>
+<dd><table class="simplelist" border="0" summary="Simple list">
+<tr><td><p><a class="link" href="../math_toolkit/dist/stat_tut/overview.html" title="Overview">Overview</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/dist/dist_ref/dists/weibull.html" title="Weibull Distribution">Weibull Distribution</a></p></td></tr>
+</table></dd>
+</dl></div></dd>
+</dl></div>
+</div>
+<table xmlns:rev="http://www.cs.rpi.edu/~gregod/boost/tools/doc/revision" width="100%"><tr>
+<td align="left"></td>
+<td align="right"><div class="copyright-footer">Copyright © 2006 , 2007, 2008 John Maddock, Paul A. Bristow, Hubert
+      Holin, Xiaogang Zhang, Bruno Lalande and Gautam Sewani<p>
+        Distributed under the Boost Software License, Version 1.0. (See accompanying
+        file LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_0.txt)
+      </p>
+</div></td>
+</tr></table>
+<hr>
+<div class="spirit-nav">
+<a accesskey="p" href="s10.html"><img src="../../../doc/html/images/prev.png" alt="Prev"></a><a accesskey="u" href="../index.html"><img src="../../../doc/html/images/up.png" alt="Up"></a><a accesskey="h" href="../index.html"><img src="../../../doc/html/images/home.png" alt="Home"></a><a accesskey="n" href="s12.html"><img src="../../../doc/html/images/next.png" alt="Next"></a>
+</div>
+</body>
+</html>

Added: sandbox/tools/auto_index/example/math/doc/sf_and_dist/html/index/s12.html
==============================================================================
--- (empty file)
+++ sandbox/tools/auto_index/example/math/doc/sf_and_dist/html/index/s12.html	2008-11-28 05:25:28 EST (Fri, 28 Nov 2008)
@@ -0,0 +1,1331 @@
+<html>
+<head>
+<meta http-equiv="Content-Type" content="text/html; charset=ISO-8859-1">
+<title>Function Index</title>
+<link rel="stylesheet" href="../boostbook.css" type="text/css">
+<meta name="generator" content="DocBook XSL Stylesheets Vsnapshot_8125">
+<link rel="home" href="../index.html" title="Math Toolkit">
+<link rel="up" href="../index.html" title="Math Toolkit">
+<link rel="prev" href="s11.html" title="Typedef Index">
+<link rel="next" href="s13.html" title="Macro Index">
+</head>
+<body bgcolor="white" text="black" link="#0000FF" vlink="#840084" alink="#0000FF">
+<table cellpadding="2" width="100%"><tr>
+<td valign="top"><img alt="Boost C++ Libraries" width="277" height="86" src="../../../boost.png"></td>
+<td align="center">Home</td>
+<td align="center">Libraries</td>
+<td align="center">People</td>
+<td align="center">FAQ</td>
+<td align="center">More</td>
+</tr></table>
+<hr>
+<div class="spirit-nav">
+<a accesskey="p" href="s11.html"><img src="../../../doc/html/images/prev.png" alt="Prev"></a><a accesskey="u" href="../index.html"><img src="../../../doc/html/images/up.png" alt="Up"></a><a accesskey="h" href="../index.html"><img src="../../../doc/html/images/home.png" alt="Home"></a><a accesskey="n" href="s13.html"><img src="../../../doc/html/images/next.png" alt="Next"></a>
+</div>
+<div class="section" lang="en">
+<div class="titlepage"><div><div><h2 class="title" style="clear: both">
+<a name="id929043"></a>Function Index</h2></div></div></div>
+<p><a class="link" href="s12.html#idx_id_33">A</a> <a class="link" href="s12.html#idx_id_34">B</a> <a class="link" href="s12.html#idx_id_35">C</a> <a class="link" href="s12.html#idx_id_36">D</a> <a class="link" href="s12.html#idx_id_37">E</a> <a class="link" href="s12.html#idx_id_38">F</a> <a class="link" href="s12.html#idx_id_39">G</a> <a class="link" href="s12.html#idx_id_40">H</a> <a class="link" href="s12.html#idx_id_41">I</a> <a class="link" href="s12.html#idx_id_42">K</a> <a class="link" href="s12.html#idx_id_43">L</a> <a class="link" href="s12.html#idx_id_44">M</a> <a class="link" href="s12.html#idx_id_45">N</a> <a class="link" href="s12.html#idx_id_46">P</a> <a class="link" href="s12.html#idx_id_47">Q</a> <a class="link" href="s12.html#idx_id_48">R</a> <a class="link" href="s12.html#idx_id_49">S</a> <a class="link" href="s12.html#idx_id_50">T</a> <a class="link" href="s12.html#idx_id_51">V</a> <a class="link" href="s12.html#idx_id_52">Z</a> </p>
+<div class="variablelist"><dl>
+<dt>
+<a name="idx_id_33"></a><span class="term">A</span>
+</dt>
+<dd><div class="variablelist"><dl>
+<dt><span class="term">acosh</span></dt>
+<dd><table class="simplelist" border="0" summary="Simple list">
+<tr><td><p><a class="link" href="../math_toolkit/special/inv_hyper/acosh.html" title="acosh">acosh</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/main_overview/tr1.html" title="C99 and TR1 C Functions">C99 and TR1 C Functions</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/special/extern_c/tr1.html" title="C99 and TR1 C Functions Overview">C99 and TR1 C Functions Overview</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/special/extern_c/c99.html" title="C99 C Functions">C99 C Functions</a></p></td></tr>
+</table></dd>
+<dt><span class="term">asinh</span></dt>
+<dd><table class="simplelist" border="0" summary="Simple list">
+<tr><td><p><a class="link" href="../math_toolkit/special/inv_hyper/asinh.html" title="asinh">asinh</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/main_overview/tr1.html" title="C99 and TR1 C Functions">C99 and TR1 C Functions</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/special/extern_c/tr1.html" title="C99 and TR1 C Functions Overview">C99 and TR1 C Functions Overview</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/special/extern_c/c99.html" title="C99 C Functions">C99 C Functions</a></p></td></tr>
+</table></dd>
+<dt><span class="term">atanh</span></dt>
+<dd><table class="simplelist" border="0" summary="Simple list">
+<tr><td><p><a class="link" href="../math_toolkit/special/inv_hyper/atanh.html" title="atanh">atanh</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/main_overview/tr1.html" title="C99 and TR1 C Functions">C99 and TR1 C Functions</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/special/extern_c/tr1.html" title="C99 and TR1 C Functions Overview">C99 and TR1 C Functions Overview</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/special/extern_c/c99.html" title="C99 C Functions">C99 C Functions</a></p></td></tr>
+</table></dd>
+</dl></div></dd>
+<dt>
+<a name="idx_id_34"></a><span class="term">B</span>
+</dt>
+<dd><div class="variablelist"><dl>
+<dt><span class="term">betac</span></dt>
+<dd><table class="simplelist" border="0" summary="Simple list">
+<tr><td><p><a class="link" href="../math_toolkit/special/sf_beta/ibeta_function.html" title="Incomplete Beta Functions">Errors In the Function betac(a,b,x)</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/special/sf_beta/ibeta_function.html" title="Incomplete Beta Functions">Incomplete Beta Functions</a></p></td></tr>
+</table></dd>
+<dt><span class="term">binomial_coefficient</span></dt>
+<dd><table class="simplelist" border="0" summary="Simple list"><tr><td><p><a class="link" href="../math_toolkit/special/factorials/sf_binomial.html" title="Binomial Coefficients">Binomial Coefficients</a></p></td></tr></table></dd>
+</dl></div></dd>
+<dt>
+<a name="idx_id_35"></a><span class="term">C</span>
+</dt>
+<dd><div class="variablelist"><dl>
+<dt><span class="term">cbrt</span></dt>
+<dd><table class="simplelist" border="0" summary="Simple list">
+<tr><td><p><a class="link" href="../math_toolkit/main_overview/tr1.html" title="C99 and TR1 C Functions">C99 and TR1 C Functions</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/special/extern_c/tr1.html" title="C99 and TR1 C Functions Overview">C99 and TR1 C Functions Overview</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/special/extern_c/c99.html" title="C99 C Functions">C99 C Functions</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/special/powers/cbrt.html" title="cbrt">cbrt</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/main_overview/directories.html" title="Directory and File Structure">Directory and File Structure</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/toolkit/internals1/roots.html" title="Root Finding With Derivatives">Root Finding With Derivatives</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/special/powers/cbrt.html" title="cbrt">RR</a></p></td></tr>
+</table></dd>
+<dt><span class="term">cdf</span></dt>
+<dd><table class="simplelist" border="0" summary="Simple list">
+<tr><td><p><a class="link" href="../math_toolkit/backgrounders/implementation.html" title="Additional Implementation Notes">Additional Implementation Notes</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/dist/dist_ref/dists/bernoulli_dist.html" title="Bernoulli Distribution">Bernoulli Distribution</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/dist/dist_ref/dists/beta_dist.html" title="Beta Distribution">Beta Distribution</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/dist/stat_tut/weg/binom_eg/binomial_coinflip_example.html" title="Binomial Coin-Flipping Example">Binomial Coin-Flipping Example</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/dist/dist_ref/dists/binomial_dist.html" title="Binomial Distribution">Binomial Distribution</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/dist/stat_tut/weg/binom_eg/binomial_quiz_example.html" title="Binomial Quiz Example">Binomial Quiz Example</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/dist/dist_ref/dists/cauchy_dist.html" title="Cauchy-Lorentz Distribution">Cauchy-Lorentz Distribution</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/policy/pol_tutorial/changing_policy_defaults.html" title="Changing the Policy Defaults">Changing the Policy Defaults</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/dist/dist_ref/dists/chi_squared_dist.html" title="Chi Squared Distribution">Chi Squared Distribution</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/dist/stat_tut/weg/st_eg/two_sample_students_t.html" title="Comparing the means of two samples with the Students-t test">Comparing the means of two samples with the Students-t test</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/dist/stat_tut/weg/nag_library.html" title="Comparison with C, R, FORTRAN-style Free Functions">Comparison with C, R, FORTRAN-style Free Functions</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/using_udt/dist_concept.html" title="Conceptual Requirements for Distribution Types">Conceptual Requirements for Distribution Types</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/policy/pol_ref/discrete_quant_ref.html" title="Discrete Quantile Policies">Discrete Quantile Policies</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/dist/stat_tut/weg/error_eg.html" title="Error Handling Example">Error Handling Example</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/dist/dist_ref/dists/exp_dist.html" title="Exponential Distribution">Exponential Distribution</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/dist/future.html" title="Extras/Future Directions">Extras/Future Directions</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/dist/dist_ref/dists/extreme_dist.html" title="Extreme Value Distribution">Extreme Value Distribution</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/dist/dist_ref/dists/f_dist.html" title="F Distribution">F Distribution</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/dist/stat_tut/weg/find_eg/find_location_eg.html" title="Find Location (Mean) Example">Find Location (Mean) Example</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/dist/stat_tut/weg/find_eg/find_mean_and_sd_eg.html" title="Find mean and standard deviation example">Find mean and standard deviation example</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/dist/stat_tut/weg/find_eg/find_scale_eg.html" title="Find Scale (Standard Deviation) Example">Find Scale (Standard Deviation) Example</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/dist/dist_ref/dists/gamma_dist.html" title="Gamma (and Erlang) Distribution">Gamma (and Erlang) Distribution</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/dist/dist_ref/dists/lognormal_dist.html" title="Log Normal Distribution">Log Normal Distribution</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/dist/dist_ref/dists/logistic_dist.html" title="Logistic Distribution">Logistic Distribution</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/dist/dist_ref/dists/binomial_dist.html" title="Binomial Distribution">Meaning of the non-member accessors</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/dist/dist_ref/dists/negative_binomial_dist.html" title="Negative Binomial Distribution">Meaning of the non-member accessors.</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/dist/dist_ref/dists/negative_binomial_dist.html" title="Negative Binomial Distribution">Negative Binomial Distribution</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/dist/stat_tut/weg/neg_binom_eg/negative_binomial_example1.html" title="Negative Binomial Sales Quota Example.">Negative Binomial Sales Quota Example.</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/dist/stat_tut/weg/neg_binom_eg/negative_binomial_example2.html" title="Negative Binomial Table Printing Example.">Negative Binomial Table Printing Example.</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/dist/dist_ref/nmp.html" title="Non-Member Properties">Non-Member Properties</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/dist/dist_ref/dists/nc_chi_squared_dist.html" title="Noncentral Chi-Squared Distribution">Noncentral Chi-Squared Distribution</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/dist/dist_ref/dists/nc_f_dist.html" title="Noncentral F Distribution">Noncentral F Distribution</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/dist/dist_ref/dists/normal_dist.html" title="Normal (Gaussian) Distribution">Normal (Gaussian) Distribution</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/dist/stat_tut/overview.html" title="Overview">Overview</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/dist/dist_ref/dists/pareto.html" title="Pareto Distribution">Pareto Distribution</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/dist/dist_ref/dists/poisson_dist.html" title="Poisson Distribution">Poisson Distribution</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/dist/dist_ref/dists/rayleigh.html" title="Rayleigh Distribution">Rayleigh Distribution</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/dist/stat_tut/weg/normal_example/normal_misc.html" title="Some Miscellaneous Examples of the Normal (Gaussian) Distribution">Some Miscellaneous Examples of the Normal (Gaussian) Distribution</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/dist/dist_ref/dists/students_t_dist.html" title="Students t Distribution">Students t Distribution</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/dist/stat_tut/weg/nccs_eg/nccs_power_eg.html" title="Tables of the power function of the &#967;2 test.">Tables of the power function of the &#967; 2 test.</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/dist/stat_tut/weg/st_eg/tut_mean_test.html" title='Testing a sample mean for difference from a "true" mean'>Testing a sample mean for difference from a "true" mean</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/dist/dist_ref/dists/triangular_dist.html" title="Triangular Distribution">Triangular Distribution</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/policy/pol_tutorial/understand_dis_quant.html" title="Understanding Quantiles of Discrete Distributions">Understanding Quantiles of Discrete Distributions</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/dist/dist_ref/dists/uniform_dist.html" title="Uniform Distribution">Uniform Distribution</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/dist/dist_ref/dists/weibull.html" title="Weibull Distribution">Weibull Distribution</a></p></td></tr>
+</table></dd>
+<dt><span class="term">checked_narrowing_cast</span></dt>
+<dd><table class="simplelist" border="0" summary="Simple list"><tr><td><p><a class="link" href="../math_toolkit/main_overview/error_handling.html" title="Error Handling">Error Handling</a></p></td></tr></table></dd>
+<dt><span class="term">check_triangular</span></dt>
+<dd><table class="simplelist" border="0" summary="Simple list"><tr><td><p><a class="link" href="../math_toolkit/backgrounders/implementation.html" title="Additional Implementation Notes">Additional Implementation Notes</a></p></td></tr></table></dd>
+<dt><span class="term">chf</span></dt>
+<dd><table class="simplelist" border="0" summary="Simple list">
+<tr><td><p><a class="link" href="../math_toolkit/using_udt/archetypes.html" title="Conceptual Archetypes and Testing">Conceptual Archetypes and Testing</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/using_udt/dist_concept.html" title="Conceptual Requirements for Distribution Types">Conceptual Requirements for Distribution Types</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/dist/dist_ref/nmp.html" title="Non-Member Properties">Non-Member Properties</a></p></td></tr>
+</table></dd>
+<dt><span class="term">coefficient_of_variation</span></dt>
+<dd><table class="simplelist" border="0" summary="Simple list"><tr><td><p><a class="link" href="../math_toolkit/using_udt/archetypes.html" title="Conceptual Archetypes and Testing">Conceptual Archetypes and Testing</a></p></td></tr></table></dd>
+<dt><span class="term">comp_ellint_2</span></dt>
+<dd><table class="simplelist" border="0" summary="Simple list">
+<tr><td><p><a class="link" href="../math_toolkit/main_overview/tr1.html" title="C99 and TR1 C Functions">C99 and TR1 C Functions</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/special/extern_c/tr1.html" title="C99 and TR1 C Functions Overview">C99 and TR1 C Functions Overview</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/special/extern_c/tr1_ref.html" title="TR1 C Functions Quick Reference">TR1 C Functions Quick Reference</a></p></td></tr>
+</table></dd>
+<dt><span class="term">comp_ellint_3</span></dt>
+<dd><table class="simplelist" border="0" summary="Simple list">
+<tr><td><p><a class="link" href="../math_toolkit/main_overview/tr1.html" title="C99 and TR1 C Functions">C99 and TR1 C Functions</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/special/extern_c/tr1.html" title="C99 and TR1 C Functions Overview">C99 and TR1 C Functions Overview</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/special/extern_c/tr1_ref.html" title="TR1 C Functions Quick Reference">TR1 C Functions Quick Reference</a></p></td></tr>
+</table></dd>
+<dt><span class="term">continued_fraction_a</span></dt>
+<dd><table class="simplelist" border="0" summary="Simple list">
+<tr><td><p><a class="link" href="../math_toolkit/toolkit/internals1/cf.html" title="Continued Fraction Evaluation">Continued Fraction Evaluation</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/toolkit/internals2/test_data.html" title="Graphing, Profiling, and Generating Test Data for Special Functions">Graphing, Profiling, and Generating Test Data for Special Functions</a></p></td></tr>
+</table></dd>
+<dt><span class="term">continued_fraction_b</span></dt>
+<dd><table class="simplelist" border="0" summary="Simple list"><tr><td><p><a class="link" href="../math_toolkit/toolkit/internals1/cf.html" title="Continued Fraction Evaluation">Continued Fraction Evaluation</a></p></td></tr></table></dd>
+<dt><span class="term">cyl_bessel_i</span></dt>
+<dd><table class="simplelist" border="0" summary="Simple list">
+<tr><td><p><a class="link" href="../math_toolkit/special/bessel/bessel_over.html" title="Bessel Function Overview">Bessel Function Overview</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/main_overview/tr1.html" title="C99 and TR1 C Functions">C99 and TR1 C Functions</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/special/extern_c/tr1.html" title="C99 and TR1 C Functions Overview">C99 and TR1 C Functions Overview</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/special/bessel/mbessel.html" title="Modified Bessel Functions of the First and Second Kinds">Errors Rates in cyl_bessel_i</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/special/bessel/mbessel.html" title="Modified Bessel Functions of the First and Second Kinds">Modified Bessel Functions of the First and Second Kinds</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/dist/dist_ref/dists/nc_chi_squared_dist.html" title="Noncentral Chi-Squared Distribution">Noncentral Chi-Squared Distribution</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/special/extern_c/tr1_ref.html" title="TR1 C Functions Quick Reference">TR1 C Functions Quick Reference</a></p></td></tr>
+</table></dd>
+<dt><span class="term">cyl_bessel_j</span></dt>
+<dd><table class="simplelist" border="0" summary="Simple list">
+<tr><td><p><a class="link" href="../math_toolkit/special/bessel/bessel_over.html" title="Bessel Function Overview">Bessel Function Overview</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/special/bessel/bessel.html" title="Bessel Functions of the First and Second Kinds">Bessel Functions of the First and Second Kinds</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/main_overview/tr1.html" title="C99 and TR1 C Functions">C99 and TR1 C Functions</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/special/extern_c/tr1.html" title="C99 and TR1 C Functions Overview">C99 and TR1 C Functions Overview</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/main_overview/result_type.html" title="Calculation of the Type of the Result">Calculation of the Type of the Result</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/special/bessel/bessel.html" title="Bessel Functions of the First and Second Kinds">Errors Rates in cyl_bessel_j</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/special/bessel/mbessel.html" title="Modified Bessel Functions of the First and Second Kinds">Modified Bessel Functions of the First and Second Kinds</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/special/bessel/sph_bessel.html" title="Spherical Bessel Functions of the First and Second Kinds">Spherical Bessel Functions of the First and Second Kinds</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/special/extern_c/tr1_ref.html" title="TR1 C Functions Quick Reference">TR1 C Functions Quick Reference</a></p></td></tr>
+</table></dd>
+<dt><span class="term">cyl_bessel_k</span></dt>
+<dd><table class="simplelist" border="0" summary="Simple list">
+<tr><td><p><a class="link" href="../math_toolkit/special/bessel/bessel_over.html" title="Bessel Function Overview">Bessel Function Overview</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/main_overview/tr1.html" title="C99 and TR1 C Functions">C99 and TR1 C Functions</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/special/extern_c/tr1.html" title="C99 and TR1 C Functions Overview">C99 and TR1 C Functions Overview</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/special/bessel/mbessel.html" title="Modified Bessel Functions of the First and Second Kinds">Errors Rates in cyl_bessel_k</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/special/bessel/mbessel.html" title="Modified Bessel Functions of the First and Second Kinds">Modified Bessel Functions of the First and Second Kinds</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/special/extern_c/tr1_ref.html" title="TR1 C Functions Quick Reference">TR1 C Functions Quick Reference</a></p></td></tr>
+</table></dd>
+<dt><span class="term">cyl_neumann</span></dt>
+<dd><table class="simplelist" border="0" summary="Simple list">
+<tr><td><p><a class="link" href="../math_toolkit/special/bessel/bessel_over.html" title="Bessel Function Overview">Bessel Function Overview</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/special/bessel/bessel.html" title="Bessel Functions of the First and Second Kinds">Bessel Functions of the First and Second Kinds</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/main_overview/tr1.html" title="C99 and TR1 C Functions">C99 and TR1 C Functions</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/special/extern_c/tr1.html" title="C99 and TR1 C Functions Overview">C99 and TR1 C Functions Overview</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/special/bessel/bessel.html" title="Bessel Functions of the First and Second Kinds">Errors Rates in cyl_neumann</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/special/bessel/mbessel.html" title="Modified Bessel Functions of the First and Second Kinds">Modified Bessel Functions of the First and Second Kinds</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/special/bessel/sph_bessel.html" title="Spherical Bessel Functions of the First and Second Kinds">Spherical Bessel Functions of the First and Second Kinds</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/special/extern_c/tr1_ref.html" title="TR1 C Functions Quick Reference">TR1 C Functions Quick Reference</a></p></td></tr>
+</table></dd>
+</dl></div></dd>
+<dt>
+<a name="idx_id_36"></a><span class="term">D</span>
+</dt>
+<dd><div class="variablelist"><dl>
+<dt><span class="term">digamma</span></dt>
+<dd><table class="simplelist" border="0" summary="Simple list">
+<tr><td><p><a class="link" href="../math_toolkit/main_overview/intro.html" title="About the Math Toolkit">About the Math Toolkit</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/special/sf_gamma/digamma.html" title="Digamma">digamma</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/special/sf_gamma/digamma.html" title="Digamma">gamma</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/main_overview/history1.html" title="History and What's New">History and What's New</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/special/sf_gamma/digamma.html" title="Digamma">Lanczos approximation</a></p></td></tr>
+</table></dd>
+<dt><span class="term">double_factorial</span></dt>
+<dd><table class="simplelist" border="0" summary="Simple list"><tr><td><p><a class="link" href="../math_toolkit/special/factorials/sf_double_factorial.html" title="Double Factorial">Double Factorial</a></p></td></tr></table></dd>
+</dl></div></dd>
+<dt>
+<a name="idx_id_37"></a><span class="term">E</span>
+</dt>
+<dd><div class="variablelist"><dl>
+<dt><span class="term">ellint_1</span></dt>
+<dd><table class="simplelist" border="0" summary="Simple list">
+<tr><td><p><a class="link" href="../math_toolkit/main_overview/tr1.html" title="C99 and TR1 C Functions">C99 and TR1 C Functions</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/special/extern_c/tr1.html" title="C99 and TR1 C Functions Overview">C99 and TR1 C Functions Overview</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/special/ellint/ellint_1.html" title="Elliptic Integrals of the First Kind - Legendre Form">Elliptic Integrals of the First Kind - Legendre Form</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/special/extern_c/tr1_ref.html" title="TR1 C Functions Quick Reference">TR1 C Functions Quick Reference</a></p></td></tr>
+</table></dd>
+<dt><span class="term">ellint_2</span></dt>
+<dd><table class="simplelist" border="0" summary="Simple list">
+<tr><td><p><a class="link" href="../math_toolkit/main_overview/tr1.html" title="C99 and TR1 C Functions">C99 and TR1 C Functions</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/special/extern_c/tr1.html" title="C99 and TR1 C Functions Overview">C99 and TR1 C Functions Overview</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/special/ellint/ellint_2.html" title="Elliptic Integrals of the Second Kind - Legendre Form">Elliptic Integrals of the Second Kind - Legendre Form</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/special/extern_c/tr1_ref.html" title="TR1 C Functions Quick Reference">TR1 C Functions Quick Reference</a></p></td></tr>
+</table></dd>
+<dt><span class="term">ellint_3</span></dt>
+<dd><table class="simplelist" border="0" summary="Simple list">
+<tr><td><p><a class="link" href="../math_toolkit/main_overview/tr1.html" title="C99 and TR1 C Functions">C99 and TR1 C Functions</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/special/extern_c/tr1.html" title="C99 and TR1 C Functions Overview">C99 and TR1 C Functions Overview</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/special/ellint/ellint_3.html" title="Elliptic Integrals of the Third Kind - Legendre Form">Elliptic Integrals of the Third Kind - Legendre Form</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/status/issues.html" title="Known Issues, and Todo List">Known Issues, and Todo List</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/special/extern_c/tr1_ref.html" title="TR1 C Functions Quick Reference">TR1 C Functions Quick Reference</a></p></td></tr>
+</table></dd>
+<dt><span class="term">ellint_rc</span></dt>
+<dd><table class="simplelist" border="0" summary="Simple list"><tr><td><p><a class="link" href="../math_toolkit/special/ellint/ellint_carlson.html" title="Elliptic Integrals - Carlson Form">Elliptic Integrals - Carlson Form</a></p></td></tr></table></dd>
+<dt><span class="term">ellint_rd</span></dt>
+<dd><table class="simplelist" border="0" summary="Simple list"><tr><td><p><a class="link" href="../math_toolkit/special/ellint/ellint_carlson.html" title="Elliptic Integrals - Carlson Form">Elliptic Integrals - Carlson Form</a></p></td></tr></table></dd>
+<dt><span class="term">ellint_rf</span></dt>
+<dd><table class="simplelist" border="0" summary="Simple list"><tr><td><p><a class="link" href="../math_toolkit/special/ellint/ellint_carlson.html" title="Elliptic Integrals - Carlson Form">Elliptic Integrals - Carlson Form</a></p></td></tr></table></dd>
+<dt><span class="term">ellint_rj</span></dt>
+<dd><table class="simplelist" border="0" summary="Simple list"><tr><td><p><a class="link" href="../math_toolkit/special/ellint/ellint_carlson.html" title="Elliptic Integrals - Carlson Form">Elliptic Integrals - Carlson Form</a></p></td></tr></table></dd>
+<dt><span class="term">erf</span></dt>
+<dd><table class="simplelist" border="0" summary="Simple list">
+<tr><td><p><a class="link" href="../math_toolkit/main_overview/intro.html" title="About the Math Toolkit">About the Math Toolkit</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/main_overview/tr1.html" title="C99 and TR1 C Functions">C99 and TR1 C Functions</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/special/extern_c/tr1.html" title="C99 and TR1 C Functions Overview">C99 and TR1 C Functions Overview</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/special/extern_c/c99.html" title="C99 C Functions">C99 C Functions</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/policy/pol_tutorial/user_def_err_pol.html" title="Calling User Defined Error Handlers">Calling User Defined Error Handlers</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/using_udt/concepts.html" title="Conceptual Requirements for Real Number Types">Conceptual Requirements for Real Number Types</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/status/credits.html" title="Credits and Acknowledgements">Credits and Acknowledgements</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/main_overview/directories.html" title="Directory and File Structure">Directory and File Structure</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/special/sf_erf/error_inv.html" title="Error Function Inverses">Error Function Inverses</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/special/sf_erf/error_function.html" title="Error Functions">Error Functions</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/special/sf_erf/error_function.html" title="Error Functions">Errors In the Function erf(z)</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/main_overview/history1.html" title="History and What's New">History and What's New</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/perf/getting_best.html" title="Getting the Best Performance from this Library">Performance Comparison of Release and Debug Settings</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/perf/comp_compilers.html" title="Comparing Compilers">Performance Comparison of Various Windows Compilers</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/perf/tuning.html" title="Performance Tuning Macros">Performance Comparison with and Without Internal Promotion to long double</a></p></td></tr>
+</table></dd>
+<dt><span class="term">erfc</span></dt>
+<dd><table class="simplelist" border="0" summary="Simple list">
+<tr><td><p><a class="link" href="../math_toolkit/main_overview/tr1.html" title="C99 and TR1 C Functions">C99 and TR1 C Functions</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/special/extern_c/tr1.html" title="C99 and TR1 C Functions Overview">C99 and TR1 C Functions Overview</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/special/extern_c/c99.html" title="C99 C Functions">C99 C Functions</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/special/sf_erf/error_inv.html" title="Error Function Inverses">Error Function Inverses</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/special/sf_erf/error_function.html" title="Error Functions">Error Functions</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/special/sf_erf/error_function.html" title="Error Functions">Errors In the Function erfc(z)</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/main_overview/history1.html" title="History and What's New">History and What's New</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/special/sf_gamma/igamma.html" title="Incomplete Gamma Functions">Incomplete Gamma Functions</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/dist/dist_ref/dists/normal_dist.html" title="Normal (Gaussian) Distribution">Normal (Gaussian) Distribution</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/backgrounders/remez.html" title="The Remez Method">The Remez Method</a></p></td></tr>
+</table></dd>
+<dt><span class="term">erfc_inv</span></dt>
+<dd><table class="simplelist" border="0" summary="Simple list">
+<tr><td><p><a class="link" href="../math_toolkit/special/sf_erf/error_inv.html" title="Error Function Inverses">Error Function Inverses</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/dist/dist_ref/dists/normal_dist.html" title="Normal (Gaussian) Distribution">Normal (Gaussian) Distribution</a></p></td></tr>
+</table></dd>
+<dt><span class="term">erf_inv</span></dt>
+<dd><table class="simplelist" border="0" summary="Simple list">
+<tr><td><p><a class="link" href="../math_toolkit/policy/pol_tutorial/user_def_err_pol.html" title="Calling User Defined Error Handlers">Calling User Defined Error Handlers</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/special/sf_erf/error_inv.html" title="Error Function Inverses">Error Function Inverses</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/perf/getting_best.html" title="Getting the Best Performance from this Library">Performance Comparison of Release and Debug Settings</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/perf/comp_compilers.html" title="Comparing Compilers">Performance Comparison of Various Windows Compilers</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/perf/tuning.html" title="Performance Tuning Macros">Performance Comparison with and Without Internal Promotion to long double</a></p></td></tr>
+</table></dd>
+<dt><span class="term">evaluate_even_polynomial</span></dt>
+<dd><table class="simplelist" border="0" summary="Simple list"><tr><td><p><a class="link" href="../math_toolkit/toolkit/internals1/rational.html" title="Polynomial and Rational Function Evaluation">Polynomial and Rational Function Evaluation</a></p></td></tr></table></dd>
+<dt><span class="term">evaluate_odd_polynomial</span></dt>
+<dd><table class="simplelist" border="0" summary="Simple list"><tr><td><p><a class="link" href="../math_toolkit/toolkit/internals1/rational.html" title="Polynomial and Rational Function Evaluation">Polynomial and Rational Function Evaluation</a></p></td></tr></table></dd>
+<dt><span class="term">evaluate_polynomial</span></dt>
+<dd><table class="simplelist" border="0" summary="Simple list"><tr><td><p><a class="link" href="../math_toolkit/toolkit/internals1/rational.html" title="Polynomial and Rational Function Evaluation">Polynomial and Rational Function Evaluation</a></p></td></tr></table></dd>
+<dt><span class="term">evaluate_rational</span></dt>
+<dd><table class="simplelist" border="0" summary="Simple list">
+<tr><td><p><a class="link" href="../math_toolkit/perf/tuning.html" title="Performance Tuning Macros">Performance Tuning Macros</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/toolkit/internals1/rational.html" title="Polynomial and Rational Function Evaluation">Polynomial and Rational Function Evaluation</a></p></td></tr>
+</table></dd>
+<dt><span class="term">expint</span></dt>
+<dd><table class="simplelist" border="0" summary="Simple list">
+<tr><td><p><a class="link" href="../math_toolkit/main_overview/tr1.html" title="C99 and TR1 C Functions">C99 and TR1 C Functions</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/special/extern_c/tr1.html" title="C99 and TR1 C Functions Overview">C99 and TR1 C Functions Overview</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/special/expint/expint_n.html" title="Exponential Integral En">Errors In the Function expint(n, z)</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/special/expint/expint_i.html" title="Exponential Integral Ei">Errors In the Function expint(z)</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/special/expint/expint_i.html" title="Exponential Integral Ei">Exponential Integral Ei</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/special/expint/expint_n.html" title="Exponential Integral En">Exponential Integral En</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/special/extern_c/tr1_ref.html" title="TR1 C Functions Quick Reference">TR1 C Functions Quick Reference</a></p></td></tr>
+</table></dd>
+<dt><span class="term">expm1</span></dt>
+<dd><table class="simplelist" border="0" summary="Simple list">
+<tr><td><p><a class="link" href="../math_toolkit/main_overview/tr1.html" title="C99 and TR1 C Functions">C99 and TR1 C Functions</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/special/extern_c/tr1.html" title="C99 and TR1 C Functions Overview">C99 and TR1 C Functions Overview</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/special/extern_c/c99.html" title="C99 C Functions">C99 C Functions</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/special/powers/expm1.html" title="expm1">expm1</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/dist/dist_ref/dists/exp_dist.html" title="Exponential Distribution">Exponential Distribution</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/dist/dist_ref/dists/extreme_dist.html" title="Extreme Value Distribution">Extreme Value Distribution</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/special/sf_gamma/tgamma.html" title="Gamma">Gamma</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/dist/dist_ref/dists/pareto.html" title="Pareto Distribution">Pareto Distribution</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/special/powers/powm1.html" title="powm1">powm1</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/dist/dist_ref/dists/rayleigh.html" title="Rayleigh Distribution">Rayleigh Distribution</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/special/powers/expm1.html" title="expm1">RR</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/special/powers/sqrt1pm1.html" title="sqrt1pm1">sqrt1pm1</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/dist/dist_ref/dists/weibull.html" title="Weibull Distribution">Weibull Distribution</a></p></td></tr>
+</table></dd>
+</dl></div></dd>
+<dt>
+<a name="idx_id_38"></a><span class="term">F</span>
+</dt>
+<dd><div class="variablelist"><dl>
+<dt><span class="term">factorial</span></dt>
+<dd><table class="simplelist" border="0" summary="Simple list">
+<tr><td><p><a class="link" href="../math_toolkit/main_overview/intro.html" title="About the Math Toolkit">About the Math Toolkit</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/status/credits.html" title="Credits and Acknowledgements">Credits and Acknowledgements</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/special/factorials/sf_double_factorial.html" title="Double Factorial">Double Factorial</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/special/factorials/sf_factorial.html" title="Factorial">factorial</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/special/factorials/sf_falling_factorial.html" title="Falling Factorial">Falling Factorial</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/special/sf_gamma/tgamma.html" title="Gamma">Gamma</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/main_overview/history1.html" title="History and What's New">History and What's New</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/special/inv_hyper/inv_hyper_over.html" title="Inverse Hyperbolic Functions Overview">Inverse Hyperbolic Functions Overview</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/special/factorials/sf_factorial.html" title="Factorial">max_factorial</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/special/sf_gamma/gamma_ratios.html" title="Ratios of Gamma Functions">Ratios of Gamma Functions</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/special/factorials/sf_rising_factorial.html" title="Rising Factorial">Rising Factorial</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/special/factorials/sf_factorial.html" title="Factorial">tgamma</a></p></td></tr>
+</table></dd>
+<dt><span class="term">falling_factorial</span></dt>
+<dd><table class="simplelist" border="0" summary="Simple list"><tr><td><p><a class="link" href="../math_toolkit/special/factorials/sf_falling_factorial.html" title="Falling Factorial">Falling Factorial</a></p></td></tr></table></dd>
+<dt><span class="term">find_degrees_of_freedom</span></dt>
+<dd><table class="simplelist" border="0" summary="Simple list">
+<tr><td><p><a class="link" href="../math_toolkit/dist/dist_ref/dists/chi_squared_dist.html" title="Chi Squared Distribution">Chi Squared Distribution</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/dist/stat_tut/weg/st_eg/tut_mean_size.html" title="Estimating how large a sample size would have to become in order to give a significant Students-t test result with a single sample test">Estimating how large a sample size would have to become in order to give a significant Students-t test result with a single sample test</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/dist/stat_tut/weg/cs_eg/chi_sq_size.html" title="Estimating the Required Sample Sizes for a Chi-Square Test for the Standard Deviation">Estimating the Required Sample Sizes for a Chi-Square Test for the Standard Deviation</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/dist/dist_ref/dists/nc_chi_squared_dist.html" title="Noncentral Chi-Squared Distribution">Noncentral Chi-Squared Distribution</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/dist/stat_tut/overview.html" title="Overview">Overview</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/dist/dist_ref/dists/students_t_dist.html" title="Students t Distribution">Students t Distribution</a></p></td></tr>
+</table></dd>
+<dt><span class="term">find_location</span></dt>
+<dd><table class="simplelist" border="0" summary="Simple list">
+<tr><td><p><a class="link" href="../math_toolkit/dist/dist_ref/dist_algorithms.html" title="Distribution Algorithms">Distribution Algorithms</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/dist/stat_tut/weg/find_eg/find_location_eg.html" title="Find Location (Mean) Example">Find Location (Mean) Example</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/dist/stat_tut/weg/find_eg/find_mean_and_sd_eg.html" title="Find mean and standard deviation example">Find mean and standard deviation example</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/dist/dist_ref/dists/normal_dist.html" title="Normal (Gaussian) Distribution">Normal (Gaussian) Distribution</a></p></td></tr>
+</table></dd>
+<dt><span class="term">find_lower_bound_on_p</span></dt>
+<dd><table class="simplelist" border="0" summary="Simple list">
+<tr><td><p><a class="link" href="../math_toolkit/dist/dist_ref/dists/binomial_dist.html" title="Binomial Distribution">Binomial Distribution</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/dist/stat_tut/weg/binom_eg/binom_conf.html" title="Calculating Confidence Limits on the Frequency of Occurrence for a Binomial Distribution">Calculating Confidence Limits on the Frequency of Occurrence for a Binomial Distribution</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/dist/stat_tut/weg/neg_binom_eg/neg_binom_conf.html" title="Calculating Confidence Limits on the Frequency of Occurrence for the Negative Binomial Distribution">Calculating Confidence Limits on the Frequency of Occurrence for the Negative Binomial Distribution</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/dist/dist_ref/dists/negative_binomial_dist.html" title="Negative Binomial Distribution">Negative Binomial Distribution</a></p></td></tr>
+</table></dd>
+<dt><span class="term">find_non_centrality</span></dt>
+<dd><table class="simplelist" border="0" summary="Simple list"><tr><td><p><a class="link" href="../math_toolkit/dist/dist_ref/dists/nc_chi_squared_dist.html" title="Noncentral Chi-Squared Distribution">Noncentral Chi-Squared Distribution</a></p></td></tr></table></dd>
+<dt><span class="term">find_scale</span></dt>
+<dd><table class="simplelist" border="0" summary="Simple list">
+<tr><td><p><a class="link" href="../math_toolkit/dist/dist_ref/dist_algorithms.html" title="Distribution Algorithms">Distribution Algorithms</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/dist/stat_tut/weg/find_eg/find_location_eg.html" title="Find Location (Mean) Example">Find Location (Mean) Example</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/dist/stat_tut/weg/find_eg/find_mean_and_sd_eg.html" title="Find mean and standard deviation example">Find mean and standard deviation example</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/dist/stat_tut/weg/find_eg/find_scale_eg.html" title="Find Scale (Standard Deviation) Example">Find Scale (Standard Deviation) Example</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/dist/dist_ref/dists/normal_dist.html" title="Normal (Gaussian) Distribution">Normal (Gaussian) Distribution</a></p></td></tr>
+</table></dd>
+<dt><span class="term">find_upper_bound_on_p</span></dt>
+<dd><table class="simplelist" border="0" summary="Simple list">
+<tr><td><p><a class="link" href="../math_toolkit/dist/dist_ref/dists/binomial_dist.html" title="Binomial Distribution">Binomial Distribution</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/dist/stat_tut/weg/binom_eg/binom_conf.html" title="Calculating Confidence Limits on the Frequency of Occurrence for a Binomial Distribution">Calculating Confidence Limits on the Frequency of Occurrence for a Binomial Distribution</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/dist/stat_tut/weg/neg_binom_eg/neg_binom_conf.html" title="Calculating Confidence Limits on the Frequency of Occurrence for the Negative Binomial Distribution">Calculating Confidence Limits on the Frequency of Occurrence for the Negative Binomial Distribution</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/dist/dist_ref/dists/negative_binomial_dist.html" title="Negative Binomial Distribution">Negative Binomial Distribution</a></p></td></tr>
+</table></dd>
+<dt><span class="term">float_advance</span></dt>
+<dd><table class="simplelist" border="0" summary="Simple list"><tr><td><p><a class="link" href="../math_toolkit/special/next_float/float_advance.html" title="Advancing a Floating Point Value by a Specific Representation Distance (ULP) float_advance">Advancing a Floating Point Value by a Specific Representation Distance (ULP) float_advance</a></p></td></tr></table></dd>
+<dt><span class="term">float_distance</span></dt>
+<dd><table class="simplelist" border="0" summary="Simple list">
+<tr><td><p><a class="link" href="../math_toolkit/special/next_float/float_advance.html" title="Advancing a Floating Point Value by a Specific Representation Distance (ULP) float_advance">Advancing a Floating Point Value by a Specific Representation Distance (ULP) float_advance</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/special/next_float/float_distance.html" title="Calculating the Representation Distance Between Two Floating Point Values (ULP) float_distance">Calculating the Representation Distance Between Two Floating Point Values (ULP) float_distance</a></p></td></tr>
+</table></dd>
+<dt><span class="term">float_next</span></dt>
+<dd><table class="simplelist" border="0" summary="Simple list">
+<tr><td><p><a class="link" href="../math_toolkit/special/next_float/float_distance.html" title="Calculating the Representation Distance Between Two Floating Point Values (ULP) float_distance">Calculating the Representation Distance Between Two Floating Point Values (ULP) float_distance</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/special/next_float/float_next.html" title="Finding the Next Greater Representable Value (float_next)">Finding the Next Greater Representable Value (float_next)</a></p></td></tr>
+</table></dd>
+<dt><span class="term">float_prior</span></dt>
+<dd><table class="simplelist" border="0" summary="Simple list">
+<tr><td><p><a class="link" href="../math_toolkit/special/next_float/float_distance.html" title="Calculating the Representation Distance Between Two Floating Point Values (ULP) float_distance">Calculating the Representation Distance Between Two Floating Point Values (ULP) float_distance</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/special/next_float/float_prior.html" title="Finding the Next Smaller Representable Value (float_prior)">Finding the Next Smaller Representable Value (float_prior)</a></p></td></tr>
+</table></dd>
+</dl></div></dd>
+<dt>
+<a name="idx_id_39"></a><span class="term">G</span>
+</dt>
+<dd><div class="variablelist"><dl>
+<dt><span class="term">gamma_p</span></dt>
+<dd><table class="simplelist" border="0" summary="Simple list">
+<tr><td><p><a class="link" href="../math_toolkit/dist/dist_ref/dists/chi_squared_dist.html" title="Chi Squared Distribution">Chi Squared Distribution</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/perf/comparisons.html" title="Comparisons to Other Open Source Libraries">Comparisons to Other Open Source Libraries</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/special/sf_gamma/gamma_derivatives.html" title="Derivative of the Incomplete Gamma Function">Derivative of the Incomplete Gamma Function</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/special/sf_gamma/igamma.html" title="Incomplete Gamma Functions">Errors In the Function gamma_p(a,z)</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/dist/dist_ref/dists/gamma_dist.html" title="Gamma (and Erlang) Distribution">Gamma (and Erlang) Distribution</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/special/sf_gamma/igamma_inv.html" title="Incomplete Gamma Function Inverses">Incomplete Gamma Function Inverses</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/special/sf_gamma/igamma.html" title="Incomplete Gamma Functions">Incomplete Gamma Functions</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/perf/getting_best.html" title="Getting the Best Performance from this Library">Performance Comparison of Release and Debug Settings</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/perf/comp_compilers.html" title="Comparing Compilers">Performance Comparison of Various Windows Compilers</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/perf/tuning.html" title="Performance Tuning Macros">Performance Comparison with and Without Internal Promotion to long double</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/dist/dist_ref/dists/poisson_dist.html" title="Poisson Distribution">Poisson Distribution</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/backgrounders/lanczos.html" title="The Lanczos Approximation">The Lanczos Approximation</a></p></td></tr>
+</table></dd>
+<dt><span class="term">gamma_p_derivative</span></dt>
+<dd><table class="simplelist" border="0" summary="Simple list">
+<tr><td><p><a class="link" href="../math_toolkit/dist/dist_ref/dists/chi_squared_dist.html" title="Chi Squared Distribution">Chi Squared Distribution</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/special/sf_gamma/gamma_derivatives.html" title="Derivative of the Incomplete Gamma Function">Derivative of the Incomplete Gamma Function</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/dist/dist_ref/dists/gamma_dist.html" title="Gamma (and Erlang) Distribution">Gamma (and Erlang) Distribution</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/dist/dist_ref/dists/nc_chi_squared_dist.html" title="Noncentral Chi-Squared Distribution">Noncentral Chi-Squared Distribution</a></p></td></tr>
+</table></dd>
+<dt><span class="term">gamma_p_inv</span></dt>
+<dd><table class="simplelist" border="0" summary="Simple list">
+<tr><td><p><a class="link" href="../math_toolkit/dist/dist_ref/dists/chi_squared_dist.html" title="Chi Squared Distribution">Chi Squared Distribution</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/perf/comparisons.html" title="Comparisons to Other Open Source Libraries">Comparisons to Other Open Source Libraries</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/dist/dist_ref/dists/gamma_dist.html" title="Gamma (and Erlang) Distribution">Gamma (and Erlang) Distribution</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/special/sf_gamma/igamma_inv.html" title="Incomplete Gamma Function Inverses">Incomplete Gamma Function Inverses</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/perf/getting_best.html" title="Getting the Best Performance from this Library">Performance Comparison of Release and Debug Settings</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/perf/comp_compilers.html" title="Comparing Compilers">Performance Comparison of Various Windows Compilers</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/perf/tuning.html" title="Performance Tuning Macros">Performance Comparison with and Without Internal Promotion to long double</a></p></td></tr>
+</table></dd>
+<dt><span class="term">gamma_p_inva</span></dt>
+<dd><table class="simplelist" border="0" summary="Simple list">
+<tr><td><p><a class="link" href="../math_toolkit/special/sf_gamma/igamma_inv.html" title="Incomplete Gamma Function Inverses">Incomplete Gamma Function Inverses</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/perf/getting_best.html" title="Getting the Best Performance from this Library">Performance Comparison of Release and Debug Settings</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/perf/comp_compilers.html" title="Comparing Compilers">Performance Comparison of Various Windows Compilers</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/perf/tuning.html" title="Performance Tuning Macros">Performance Comparison with and Without Internal Promotion to long double</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/dist/dist_ref/dists/poisson_dist.html" title="Poisson Distribution">Poisson Distribution</a></p></td></tr>
+</table></dd>
+<dt><span class="term">gamma_q</span></dt>
+<dd><table class="simplelist" border="0" summary="Simple list">
+<tr><td><p><a class="link" href="../math_toolkit/dist/dist_ref/dists/chi_squared_dist.html" title="Chi Squared Distribution">Chi Squared Distribution</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/perf/comparisons.html" title="Comparisons to Other Open Source Libraries">Comparisons to Other Open Source Libraries</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/special/sf_gamma/gamma_derivatives.html" title="Derivative of the Incomplete Gamma Function">Derivative of the Incomplete Gamma Function</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/special/sf_gamma/igamma.html" title="Incomplete Gamma Functions">Errors In the Function gamma_q(a,z)</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/dist/dist_ref/dists/gamma_dist.html" title="Gamma (and Erlang) Distribution">Gamma (and Erlang) Distribution</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/special/sf_gamma/igamma_inv.html" title="Incomplete Gamma Function Inverses">Incomplete Gamma Function Inverses</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/special/sf_gamma/igamma.html" title="Incomplete Gamma Functions">Incomplete Gamma Functions</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/perf/getting_best.html" title="Getting the Best Performance from this Library">Performance Comparison of Release and Debug Settings</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/perf/comp_compilers.html" title="Comparing Compilers">Performance Comparison of Various Windows Compilers</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/perf/tuning.html" title="Performance Tuning Macros">Performance Comparison with and Without Internal Promotion to long double</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/dist/dist_ref/dists/poisson_dist.html" title="Poisson Distribution">Poisson Distribution</a></p></td></tr>
+</table></dd>
+<dt><span class="term">gamma_q_inv</span></dt>
+<dd><table class="simplelist" border="0" summary="Simple list">
+<tr><td><p><a class="link" href="../math_toolkit/dist/dist_ref/dists/chi_squared_dist.html" title="Chi Squared Distribution">Chi Squared Distribution</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/perf/comparisons.html" title="Comparisons to Other Open Source Libraries">Comparisons to Other Open Source Libraries</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/dist/dist_ref/dists/gamma_dist.html" title="Gamma (and Erlang) Distribution">Gamma (and Erlang) Distribution</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/special/sf_gamma/igamma_inv.html" title="Incomplete Gamma Function Inverses">Incomplete Gamma Function Inverses</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/perf/getting_best.html" title="Getting the Best Performance from this Library">Performance Comparison of Release and Debug Settings</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/perf/comp_compilers.html" title="Comparing Compilers">Performance Comparison of Various Windows Compilers</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/perf/tuning.html" title="Performance Tuning Macros">Performance Comparison with and Without Internal Promotion to long double</a></p></td></tr>
+</table></dd>
+<dt><span class="term">gamma_q_inva</span></dt>
+<dd><table class="simplelist" border="0" summary="Simple list">
+<tr><td><p><a class="link" href="../math_toolkit/special/sf_gamma/igamma_inv.html" title="Incomplete Gamma Function Inverses">Incomplete Gamma Function Inverses</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/perf/getting_best.html" title="Getting the Best Performance from this Library">Performance Comparison of Release and Debug Settings</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/perf/comp_compilers.html" title="Comparing Compilers">Performance Comparison of Various Windows Compilers</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/perf/tuning.html" title="Performance Tuning Macros">Performance Comparison with and Without Internal Promotion to long double</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/dist/dist_ref/dists/poisson_dist.html" title="Poisson Distribution">Poisson Distribution</a></p></td></tr>
+</table></dd>
+<dt><span class="term">get_user_parameter_info</span></dt>
+<dd><table class="simplelist" border="0" summary="Simple list"><tr><td><p><a class="link" href="../math_toolkit/toolkit/internals2/test_data.html" title="Graphing, Profiling, and Generating Test Data for Special Functions">Graphing, Profiling, and Generating Test Data for Special Functions</a></p></td></tr></table></dd>
+</dl></div></dd>
+<dt>
+<a name="idx_id_40"></a><span class="term">H</span>
+</dt>
+<dd><div class="variablelist"><dl>
+<dt><span class="term">halley_iterate</span></dt>
+<dd><table class="simplelist" border="0" summary="Simple list"><tr><td><p><a class="link" href="../math_toolkit/toolkit/internals1/roots.html" title="Root Finding With Derivatives">Root Finding With Derivatives</a></p></td></tr></table></dd>
+<dt><span class="term">hazard</span></dt>
+<dd><table class="simplelist" border="0" summary="Simple list">
+<tr><td><p><a class="link" href="../math_toolkit/backgrounders/implementation.html" title="Additional Implementation Notes">Additional Implementation Notes</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/using_udt/archetypes.html" title="Conceptual Archetypes and Testing">Conceptual Archetypes and Testing</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/using_udt/dist_concept.html" title="Conceptual Requirements for Distribution Types">Conceptual Requirements for Distribution Types</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/dist/dist_ref/nmp.html" title="Non-Member Properties">Non-Member Properties</a></p></td></tr>
+</table></dd>
+<dt><span class="term">hermite</span></dt>
+<dd><table class="simplelist" border="0" summary="Simple list">
+<tr><td><p><a class="link" href="../math_toolkit/main_overview/tr1.html" title="C99 and TR1 C Functions">C99 and TR1 C Functions</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/special/extern_c/tr1.html" title="C99 and TR1 C Functions Overview">C99 and TR1 C Functions Overview</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/special/sf_poly/hermite.html" title="Hermite Polynomials">Hermite Polynomials</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/special/extern_c/tr1_ref.html" title="TR1 C Functions Quick Reference">TR1 C Functions Quick Reference</a></p></td></tr>
+</table></dd>
+<dt><span class="term">hermite_next</span></dt>
+<dd><table class="simplelist" border="0" summary="Simple list"><tr><td><p><a class="link" href="../math_toolkit/special/sf_poly/hermite.html" title="Hermite Polynomials">Hermite Polynomials</a></p></td></tr></table></dd>
+<dt><span class="term">hypot</span></dt>
+<dd><table class="simplelist" border="0" summary="Simple list">
+<tr><td><p><a class="link" href="../math_toolkit/main_overview/tr1.html" title="C99 and TR1 C Functions">C99 and TR1 C Functions</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/special/extern_c/tr1.html" title="C99 and TR1 C Functions Overview">C99 and TR1 C Functions Overview</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/special/extern_c/c99.html" title="C99 C Functions">C99 C Functions</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/special/powers/hypot.html" title="hypot">hypot</a></p></td></tr>
+</table></dd>
+</dl></div></dd>
+<dt>
+<a name="idx_id_41"></a><span class="term">I</span>
+</dt>
+<dd><div class="variablelist"><dl>
+<dt><span class="term">ibeta</span></dt>
+<dd><table class="simplelist" border="0" summary="Simple list">
+<tr><td><p><a class="link" href="../math_toolkit/dist/dist_ref/dists/beta_dist.html" title="Beta Distribution">Beta Distribution</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/dist/dist_ref/dists/binomial_dist.html" title="Binomial Distribution">Binomial Distribution</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/perf/comparisons.html" title="Comparisons to Other Open Source Libraries">Comparisons to Other Open Source Libraries</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/special/sf_beta/beta_derivative.html" title="Derivative of the Incomplete Beta Function">Derivative of the Incomplete Beta Function</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/special/sf_beta/ibeta_function.html" title="Incomplete Beta Functions">Errors In the Function ibeta(a,b,x)</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/dist/dist_ref/dists/f_dist.html" title="F Distribution">F Distribution</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/special/sf_beta/ibeta_function.html" title="Incomplete Beta Functions">Incomplete Beta Functions</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/dist/dist_ref/dists/negative_binomial_dist.html" title="Negative Binomial Distribution">Negative Binomial Distribution</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/perf/getting_best.html" title="Getting the Best Performance from this Library">Performance Comparison of Release and Debug Settings</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/perf/comp_compilers.html" title="Comparing Compilers">Performance Comparison of Various Windows Compilers</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/perf/tuning.html" title="Performance Tuning Macros">Performance Comparison with and Without Internal Promotion to long double</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/dist/dist_ref/dists/students_t_dist.html" title="Students t Distribution">Students t Distribution</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/special/sf_beta/ibeta_inv_function.html" title="The Incomplete Beta Function Inverses">The Incomplete Beta Function Inverses</a></p></td></tr>
+</table></dd>
+<dt><span class="term">ibetac</span></dt>
+<dd><table class="simplelist" border="0" summary="Simple list">
+<tr><td><p><a class="link" href="../math_toolkit/dist/dist_ref/dists/beta_dist.html" title="Beta Distribution">Beta Distribution</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/dist/dist_ref/dists/binomial_dist.html" title="Binomial Distribution">Binomial Distribution</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/perf/comparisons.html" title="Comparisons to Other Open Source Libraries">Comparisons to Other Open Source Libraries</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/special/sf_beta/ibeta_function.html" title="Incomplete Beta Functions">Errors In the Function ibetac(a,b,x)</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/dist/dist_ref/dists/f_dist.html" title="F Distribution">F Distribution</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/special/sf_beta/ibeta_function.html" title="Incomplete Beta Functions">Incomplete Beta Functions</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/dist/dist_ref/dists/negative_binomial_dist.html" title="Negative Binomial Distribution">Negative Binomial Distribution</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/perf/getting_best.html" title="Getting the Best Performance from this Library">Performance Comparison of Release and Debug Settings</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/perf/comp_compilers.html" title="Comparing Compilers">Performance Comparison of Various Windows Compilers</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/perf/tuning.html" title="Performance Tuning Macros">Performance Comparison with and Without Internal Promotion to long double</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/dist/dist_ref/dists/students_t_dist.html" title="Students t Distribution">Students t Distribution</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/special/sf_beta/ibeta_inv_function.html" title="The Incomplete Beta Function Inverses">The Incomplete Beta Function Inverses</a></p></td></tr>
+</table></dd>
+<dt><span class="term">ibetac_inv</span></dt>
+<dd><table class="simplelist" border="0" summary="Simple list">
+<tr><td><p><a class="link" href="../math_toolkit/dist/dist_ref/dists/beta_dist.html" title="Beta Distribution">Beta Distribution</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/dist/dist_ref/dists/binomial_dist.html" title="Binomial Distribution">Binomial Distribution</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/perf/comparisons.html" title="Comparisons to Other Open Source Libraries">Comparisons to Other Open Source Libraries</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/dist/dist_ref/dists/f_dist.html" title="F Distribution">F Distribution</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/dist/dist_ref/dists/negative_binomial_dist.html" title="Negative Binomial Distribution">Negative Binomial Distribution</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/perf/getting_best.html" title="Getting the Best Performance from this Library">Performance Comparison of Release and Debug Settings</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/perf/comp_compilers.html" title="Comparing Compilers">Performance Comparison of Various Windows Compilers</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/perf/tuning.html" title="Performance Tuning Macros">Performance Comparison with and Without Internal Promotion to long double</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/special/sf_beta/ibeta_inv_function.html" title="The Incomplete Beta Function Inverses">The Incomplete Beta Function Inverses</a></p></td></tr>
+</table></dd>
+<dt><span class="term">ibetac_inva</span></dt>
+<dd><table class="simplelist" border="0" summary="Simple list">
+<tr><td><p><a class="link" href="../math_toolkit/dist/dist_ref/dists/negative_binomial_dist.html" title="Negative Binomial Distribution">Negative Binomial Distribution</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/perf/getting_best.html" title="Getting the Best Performance from this Library">Performance Comparison of Release and Debug Settings</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/perf/comp_compilers.html" title="Comparing Compilers">Performance Comparison of Various Windows Compilers</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/perf/tuning.html" title="Performance Tuning Macros">Performance Comparison with and Without Internal Promotion to long double</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/special/sf_beta/ibeta_inv_function.html" title="The Incomplete Beta Function Inverses">The Incomplete Beta Function Inverses</a></p></td></tr>
+</table></dd>
+<dt><span class="term">ibetac_invb</span></dt>
+<dd><table class="simplelist" border="0" summary="Simple list">
+<tr><td><p><a class="link" href="../math_toolkit/dist/dist_ref/dists/binomial_dist.html" title="Binomial Distribution">Binomial Distribution</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/dist/dist_ref/dists/negative_binomial_dist.html" title="Negative Binomial Distribution">Negative Binomial Distribution</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/perf/getting_best.html" title="Getting the Best Performance from this Library">Performance Comparison of Release and Debug Settings</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/perf/comp_compilers.html" title="Comparing Compilers">Performance Comparison of Various Windows Compilers</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/perf/tuning.html" title="Performance Tuning Macros">Performance Comparison with and Without Internal Promotion to long double</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/special/sf_beta/ibeta_inv_function.html" title="The Incomplete Beta Function Inverses">The Incomplete Beta Function Inverses</a></p></td></tr>
+</table></dd>
+<dt><span class="term">ibeta_derivative</span></dt>
+<dd><table class="simplelist" border="0" summary="Simple list">
+<tr><td><p><a class="link" href="../math_toolkit/dist/dist_ref/dists/beta_dist.html" title="Beta Distribution">Beta Distribution</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/dist/dist_ref/dists/binomial_dist.html" title="Binomial Distribution">Binomial Distribution</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/special/sf_beta/beta_derivative.html" title="Derivative of the Incomplete Beta Function">Derivative of the Incomplete Beta Function</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/dist/dist_ref/dists/f_dist.html" title="F Distribution">F Distribution</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/dist/dist_ref/dists/negative_binomial_dist.html" title="Negative Binomial Distribution">Negative Binomial Distribution</a></p></td></tr>
+</table></dd>
+<dt><span class="term">ibeta_inv</span></dt>
+<dd><table class="simplelist" border="0" summary="Simple list">
+<tr><td><p><a class="link" href="../math_toolkit/dist/dist_ref/dists/beta_dist.html" title="Beta Distribution">Beta Distribution</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/dist/dist_ref/dists/binomial_dist.html" title="Binomial Distribution">Binomial Distribution</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/perf/comparisons.html" title="Comparisons to Other Open Source Libraries">Comparisons to Other Open Source Libraries</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/dist/dist_ref/dists/f_dist.html" title="F Distribution">F Distribution</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/dist/dist_ref/dists/negative_binomial_dist.html" title="Negative Binomial Distribution">Negative Binomial Distribution</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/perf/getting_best.html" title="Getting the Best Performance from this Library">Performance Comparison of Release and Debug Settings</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/perf/comp_compilers.html" title="Comparing Compilers">Performance Comparison of Various Windows Compilers</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/perf/tuning.html" title="Performance Tuning Macros">Performance Comparison with and Without Internal Promotion to long double</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/dist/dist_ref/dists/students_t_dist.html" title="Students t Distribution">Students t Distribution</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/special/sf_beta/ibeta_inv_function.html" title="The Incomplete Beta Function Inverses">The Incomplete Beta Function Inverses</a></p></td></tr>
+</table></dd>
+<dt><span class="term">ibeta_inva</span></dt>
+<dd><table class="simplelist" border="0" summary="Simple list">
+<tr><td><p><a class="link" href="../math_toolkit/dist/dist_ref/dists/beta_dist.html" title="Beta Distribution">Beta Distribution</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/dist/dist_ref/dists/negative_binomial_dist.html" title="Negative Binomial Distribution">Negative Binomial Distribution</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/perf/getting_best.html" title="Getting the Best Performance from this Library">Performance Comparison of Release and Debug Settings</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/perf/comp_compilers.html" title="Comparing Compilers">Performance Comparison of Various Windows Compilers</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/perf/tuning.html" title="Performance Tuning Macros">Performance Comparison with and Without Internal Promotion to long double</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/special/sf_beta/ibeta_inv_function.html" title="The Incomplete Beta Function Inverses">The Incomplete Beta Function Inverses</a></p></td></tr>
+</table></dd>
+<dt><span class="term">ibeta_invb</span></dt>
+<dd><table class="simplelist" border="0" summary="Simple list">
+<tr><td><p><a class="link" href="../math_toolkit/dist/dist_ref/dists/beta_dist.html" title="Beta Distribution">Beta Distribution</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/dist/dist_ref/dists/negative_binomial_dist.html" title="Negative Binomial Distribution">Negative Binomial Distribution</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/perf/getting_best.html" title="Getting the Best Performance from this Library">Performance Comparison of Release and Debug Settings</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/perf/comp_compilers.html" title="Comparing Compilers">Performance Comparison of Various Windows Compilers</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/perf/tuning.html" title="Performance Tuning Macros">Performance Comparison with and Without Internal Promotion to long double</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/special/sf_beta/ibeta_inv_function.html" title="The Incomplete Beta Function Inverses">The Incomplete Beta Function Inverses</a></p></td></tr>
+</table></dd>
+<dt><span class="term">iround</span></dt>
+<dd><table class="simplelist" border="0" summary="Simple list">
+<tr><td><p><a class="link" href="../math_toolkit/using_udt/concepts.html" title="Conceptual Requirements for Real Number Types">Conceptual Requirements for Real Number Types</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/special/rounding/round.html" title="Rounding Functions">Rounding Functions</a></p></td></tr>
+</table></dd>
+<dt><span class="term">itrunc</span></dt>
+<dd><table class="simplelist" border="0" summary="Simple list">
+<tr><td><p><a class="link" href="../math_toolkit/using_udt/concepts.html" title="Conceptual Requirements for Real Number Types">Conceptual Requirements for Real Number Types</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/special/rounding/trunc.html" title="Truncation Functions">Truncation Functions</a></p></td></tr>
+</table></dd>
+</dl></div></dd>
+<dt>
+<a name="idx_id_42"></a><span class="term">K</span>
+</dt>
+<dd><div class="variablelist"><dl>
+<dt><span class="term">kahan_sum_series</span></dt>
+<dd><table class="simplelist" border="0" summary="Simple list"><tr><td><p><a class="link" href="../math_toolkit/toolkit/internals1/series_evaluation.html" title="Series Evaluation">Series Evaluation</a></p></td></tr></table></dd>
+<dt><span class="term">kurtosis</span></dt>
+<dd><table class="simplelist" border="0" summary="Simple list">
+<tr><td><p><a class="link" href="../math_toolkit/backgrounders/implementation.html" title="Additional Implementation Notes">Additional Implementation Notes</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/dist/dist_ref/dists/bernoulli_dist.html" title="Bernoulli Distribution">Bernoulli Distribution</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/dist/dist_ref/dists/beta_dist.html" title="Beta Distribution">Beta Distribution</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/dist/dist_ref/dists/binomial_dist.html" title="Binomial Distribution">Binomial Distribution</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/dist/dist_ref/dists/cauchy_dist.html" title="Cauchy-Lorentz Distribution">Cauchy-Lorentz Distribution</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/dist/dist_ref/dists/chi_squared_dist.html" title="Chi Squared Distribution">Chi Squared Distribution</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/using_udt/dist_concept.html" title="Conceptual Requirements for Distribution Types">Conceptual Requirements for Distribution Types</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/dist/dist_ref/dists/exp_dist.html" title="Exponential Distribution">Exponential Distribution</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/dist/dist_ref/dists/extreme_dist.html" title="Extreme Value Distribution">Extreme Value Distribution</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/dist/dist_ref/dists/f_dist.html" title="F Distribution">F Distribution</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/dist/dist_ref/dists/gamma_dist.html" title="Gamma (and Erlang) Distribution">Gamma (and Erlang) Distribution</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/dist/dist_ref/dists/lognormal_dist.html" title="Log Normal Distribution">Log Normal Distribution</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/dist/dist_ref/dists/logistic_dist.html" title="Logistic Distribution">Logistic Distribution</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/dist/dist_ref/dists/negative_binomial_dist.html" title="Negative Binomial Distribution">Negative Binomial Distribution</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/dist/dist_ref/nmp.html" title="Non-Member Properties">Non-Member Properties</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/dist/dist_ref/dists/nc_beta_dist.html" title="Noncentral Beta Distribution">Noncentral Beta Distribution</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/dist/dist_ref/dists/nc_chi_squared_dist.html" title="Noncentral Chi-Squared Distribution">Noncentral Chi-Squared Distribution</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/dist/dist_ref/dists/nc_f_dist.html" title="Noncentral F Distribution">Noncentral F Distribution</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/dist/dist_ref/dists/nc_t_dist.html" title="Noncentral T Distribution">Noncentral T Distribution</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/dist/dist_ref/dists/normal_dist.html" title="Normal (Gaussian) Distribution">Normal (Gaussian) Distribution</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/dist/dist_ref/dists/pareto.html" title="Pareto Distribution">Pareto Distribution</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/dist/dist_ref/dists/poisson_dist.html" title="Poisson Distribution">Poisson Distribution</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/dist/dist_ref/dists/rayleigh.html" title="Rayleigh Distribution">Rayleigh Distribution</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/dist/dist_ref/dists/students_t_dist.html" title="Students t Distribution">Students t Distribution</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/dist/dist_ref/dists/triangular_dist.html" title="Triangular Distribution">Triangular Distribution</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/dist/dist_ref/dists/uniform_dist.html" title="Uniform Distribution">Uniform Distribution</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/dist/dist_ref/dists/weibull.html" title="Weibull Distribution">Weibull Distribution</a></p></td></tr>
+</table></dd>
+<dt><span class="term">kurtosis_excess</span></dt>
+<dd><table class="simplelist" border="0" summary="Simple list">
+<tr><td><p><a class="link" href="../math_toolkit/dist/dist_ref/dists/bernoulli_dist.html" title="Bernoulli Distribution">Bernoulli Distribution</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/dist/dist_ref/dists/beta_dist.html" title="Beta Distribution">Beta Distribution</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/dist/dist_ref/dists/binomial_dist.html" title="Binomial Distribution">Binomial Distribution</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/dist/dist_ref/dists/cauchy_dist.html" title="Cauchy-Lorentz Distribution">Cauchy-Lorentz Distribution</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/dist/dist_ref/dists/chi_squared_dist.html" title="Chi Squared Distribution">Chi Squared Distribution</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/using_udt/dist_concept.html" title="Conceptual Requirements for Distribution Types">Conceptual Requirements for Distribution Types</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/dist/dist_ref/dists/exp_dist.html" title="Exponential Distribution">Exponential Distribution</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/dist/dist_ref/dists/extreme_dist.html" title="Extreme Value Distribution">Extreme Value Distribution</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/dist/dist_ref/dists/f_dist.html" title="F Distribution">F Distribution</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/dist/dist_ref/dists/gamma_dist.html" title="Gamma (and Erlang) Distribution">Gamma (and Erlang) Distribution</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/dist/dist_ref/dists/lognormal_dist.html" title="Log Normal Distribution">Log Normal Distribution</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/dist/dist_ref/dists/logistic_dist.html" title="Logistic Distribution">Logistic Distribution</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/dist/dist_ref/dists/negative_binomial_dist.html" title="Negative Binomial Distribution">Negative Binomial Distribution</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/dist/dist_ref/nmp.html" title="Non-Member Properties">Non-Member Properties</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/dist/dist_ref/dists/nc_beta_dist.html" title="Noncentral Beta Distribution">Noncentral Beta Distribution</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/dist/dist_ref/dists/nc_chi_squared_dist.html" title="Noncentral Chi-Squared Distribution">Noncentral Chi-Squared Distribution</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/dist/dist_ref/dists/nc_f_dist.html" title="Noncentral F Distribution">Noncentral F Distribution</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/dist/dist_ref/dists/nc_t_dist.html" title="Noncentral T Distribution">Noncentral T Distribution</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/dist/dist_ref/dists/normal_dist.html" title="Normal (Gaussian) Distribution">Normal (Gaussian) Distribution</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/dist/dist_ref/dists/pareto.html" title="Pareto Distribution">Pareto Distribution</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/dist/dist_ref/dists/poisson_dist.html" title="Poisson Distribution">Poisson Distribution</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/dist/dist_ref/dists/rayleigh.html" title="Rayleigh Distribution">Rayleigh Distribution</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/dist/dist_ref/dists/students_t_dist.html" title="Students t Distribution">Students t Distribution</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/dist/dist_ref/dists/triangular_dist.html" title="Triangular Distribution">Triangular Distribution</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/dist/dist_ref/dists/uniform_dist.html" title="Uniform Distribution">Uniform Distribution</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/dist/dist_ref/dists/weibull.html" title="Weibull Distribution">Weibull Distribution</a></p></td></tr>
+</table></dd>
+</dl></div></dd>
+<dt>
+<a name="idx_id_43"></a><span class="term">L</span>
+</dt>
+<dd><div class="variablelist"><dl>
+<dt><span class="term">laguerre</span></dt>
+<dd><table class="simplelist" border="0" summary="Simple list">
+<tr><td><p><a class="link" href="../math_toolkit/main_overview/tr1.html" title="C99 and TR1 C Functions">C99 and TR1 C Functions</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/special/extern_c/tr1.html" title="C99 and TR1 C Functions Overview">C99 and TR1 C Functions Overview</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/special/sf_poly/laguerre.html" title="Laguerre (and Associated) Polynomials">Laguerre (and Associated) Polynomials</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/special/extern_c/tr1_ref.html" title="TR1 C Functions Quick Reference">TR1 C Functions Quick Reference</a></p></td></tr>
+</table></dd>
+<dt><span class="term">laguerre_next</span></dt>
+<dd><table class="simplelist" border="0" summary="Simple list"><tr><td><p><a class="link" href="../math_toolkit/special/sf_poly/laguerre.html" title="Laguerre (and Associated) Polynomials">Laguerre (and Associated) Polynomials</a></p></td></tr></table></dd>
+<dt><span class="term">ldexp</span></dt>
+<dd><table class="simplelist" border="0" summary="Simple list">
+<tr><td><p><a class="link" href="../math_toolkit/using_udt/concepts.html" title="Conceptual Requirements for Real Number Types">Conceptual Requirements for Real Number Types</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/toolkit/internals1/roots.html" title="Root Finding With Derivatives">Root Finding With Derivatives</a></p></td></tr>
+</table></dd>
+<dt><span class="term">legendre_next</span></dt>
+<dd><table class="simplelist" border="0" summary="Simple list"><tr><td><p><a class="link" href="../math_toolkit/special/sf_poly/legendre.html" title="Legendre (and Associated) Polynomials">Legendre (and Associated) Polynomials</a></p></td></tr></table></dd>
+<dt><span class="term">legendre_p</span></dt>
+<dd><table class="simplelist" border="0" summary="Simple list">
+<tr><td><p><a class="link" href="../math_toolkit/special/sf_poly/legendre.html" title="Legendre (and Associated) Polynomials">Legendre (and Associated) Polynomials</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/special/extern_c/tr1_ref.html" title="TR1 C Functions Quick Reference">TR1 C Functions Quick Reference</a></p></td></tr>
+</table></dd>
+<dt><span class="term">legendre_q</span></dt>
+<dd><table class="simplelist" border="0" summary="Simple list"><tr><td><p><a class="link" href="../math_toolkit/special/sf_poly/legendre.html" title="Legendre (and Associated) Polynomials">Legendre (and Associated) Polynomials</a></p></td></tr></table></dd>
+<dt><span class="term">lgamma</span></dt>
+<dd><table class="simplelist" border="0" summary="Simple list">
+<tr><td><p><a class="link" href="../math_toolkit/main_overview/tr1.html" title="C99 and TR1 C Functions">C99 and TR1 C Functions</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/special/extern_c/tr1.html" title="C99 and TR1 C Functions Overview">C99 and TR1 C Functions Overview</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/special/extern_c/c99.html" title="C99 C Functions">C99 C Functions</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/perf/comparisons.html" title="Comparisons to Other Open Source Libraries">Comparisons to Other Open Source Libraries</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/main_overview/directories.html" title="Directory and File Structure">Directory and File Structure</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/special/sf_gamma/tgamma.html" title="Gamma">Gamma</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/toolkit/internals2/test_data.html" title="Graphing, Profiling, and Generating Test Data for Special Functions">Graphing, Profiling, and Generating Test Data for Special Functions</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/main_overview/history1.html" title="History and What's New">History and What's New</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/special/sf_gamma/lgamma.html" title="Log Gamma">Log Gamma</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/dist/dist_ref/dists/negative_binomial_dist.html" title="Negative Binomial Distribution">Negative Binomial Distribution</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/toolkit/internals2/error_test.html" title="Relative Error and Testing">Relative Error and Testing</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/policy/pol_ref/namespace_pol.html" title="Setting Polices at Namespace Scope">Setting Polices at Namespace Scope</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/backgrounders/lanczos.html" title="The Lanczos Approximation">The Lanczos Approximation</a></p></td></tr>
+</table></dd>
+<dt><span class="term">llround</span></dt>
+<dd><table class="simplelist" border="0" summary="Simple list">
+<tr><td><p><a class="link" href="../math_toolkit/main_overview/tr1.html" title="C99 and TR1 C Functions">C99 and TR1 C Functions</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/special/extern_c/tr1.html" title="C99 and TR1 C Functions Overview">C99 and TR1 C Functions Overview</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/special/extern_c/c99.html" title="C99 C Functions">C99 C Functions</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/using_udt/concepts.html" title="Conceptual Requirements for Real Number Types">Conceptual Requirements for Real Number Types</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/special/rounding/round.html" title="Rounding Functions">Rounding Functions</a></p></td></tr>
+</table></dd>
+<dt><span class="term">lltrunc</span></dt>
+<dd><table class="simplelist" border="0" summary="Simple list">
+<tr><td><p><a class="link" href="../math_toolkit/using_udt/concepts.html" title="Conceptual Requirements for Real Number Types">Conceptual Requirements for Real Number Types</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/special/rounding/trunc.html" title="Truncation Functions">Truncation Functions</a></p></td></tr>
+</table></dd>
+<dt><span class="term">log1p</span></dt>
+<dd><table class="simplelist" border="0" summary="Simple list">
+<tr><td><p><a class="link" href="../math_toolkit/special/powers/log1p.html" title="log1p">BOOST_HAS_LOG1P</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/main_overview/tr1.html" title="C99 and TR1 C Functions">C99 and TR1 C Functions</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/special/extern_c/tr1.html" title="C99 and TR1 C Functions Overview">C99 and TR1 C Functions Overview</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/special/extern_c/c99.html" title="C99 C Functions">C99 C Functions</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/dist/dist_ref/dists/exp_dist.html" title="Exponential Distribution">Exponential Distribution</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/dist/dist_ref/dists/extreme_dist.html" title="Extreme Value Distribution">Extreme Value Distribution</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/status/issues.html" title="Known Issues, and Todo List">Known Issues, and Todo List</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/special/sf_gamma/lgamma.html" title="Log Gamma">Log Gamma</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/special/powers/log1p.html" title="log1p">log1p</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/dist/dist_ref/dists/rayleigh.html" title="Rayleigh Distribution">Rayleigh Distribution</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/special/powers/log1p.html" title="log1p">RR</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/toolkit/internals1/series_evaluation.html" title="Series Evaluation">Series Evaluation</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/special/powers/sqrt1pm1.html" title="sqrt1pm1">sqrt1pm1</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/dist/dist_ref/dists/weibull.html" title="Weibull Distribution">Weibull Distribution</a></p></td></tr>
+</table></dd>
+<dt><span class="term">lround</span></dt>
+<dd><table class="simplelist" border="0" summary="Simple list">
+<tr><td><p><a class="link" href="../math_toolkit/main_overview/tr1.html" title="C99 and TR1 C Functions">C99 and TR1 C Functions</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/special/extern_c/tr1.html" title="C99 and TR1 C Functions Overview">C99 and TR1 C Functions Overview</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/special/extern_c/c99.html" title="C99 C Functions">C99 C Functions</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/using_udt/concepts.html" title="Conceptual Requirements for Real Number Types">Conceptual Requirements for Real Number Types</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/special/rounding/round.html" title="Rounding Functions">Rounding Functions</a></p></td></tr>
+</table></dd>
+<dt><span class="term">ltrunc</span></dt>
+<dd><table class="simplelist" border="0" summary="Simple list">
+<tr><td><p><a class="link" href="../math_toolkit/using_udt/concepts.html" title="Conceptual Requirements for Real Number Types">Conceptual Requirements for Real Number Types</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/special/rounding/trunc.html" title="Truncation Functions">Truncation Functions</a></p></td></tr>
+</table></dd>
+</dl></div></dd>
+<dt>
+<a name="idx_id_44"></a><span class="term">M</span>
+</dt>
+<dd><div class="variablelist"><dl>
+<dt><span class="term">make_policy</span></dt>
+<dd><table class="simplelist" border="0" summary="Simple list">
+<tr><td><p><a class="link" href="../math_toolkit/policy/pol_tutorial/ad_hoc_sf_policies.html" title="Changing the Policy on an Ad Hoc Basis for the Special Functions">Changing the Policy on an Ad Hoc Basis for the Special Functions</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/policy/pol_ref/error_handling_policies.html" title="Error Handling Policies">Error Handling Policies</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/policy/pol_ref/internal_promotion.html" title="Internal Promotion Policies">Internal Promotion Policies</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/policy/pol_ref/pol_ref_ref.html" title="Policy Class Reference">Policy Class Reference</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/policy/pol_ref/precision_pol.html" title="Precision Policies">Precision Policies</a></p></td></tr>
+</table></dd>
+<dt><span class="term">mean</span></dt>
+<dd><table class="simplelist" border="0" summary="Simple list">
+<tr><td><p><a class="link" href="../math_toolkit/backgrounders/implementation.html" title="Additional Implementation Notes">Additional Implementation Notes</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/dist/dist_ref/dists/bernoulli_dist.html" title="Bernoulli Distribution">Bernoulli Distribution</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/dist/dist_ref/dists/beta_dist.html" title="Beta Distribution">Beta Distribution</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/dist/stat_tut/weg/binom_eg/binomial_coinflip_example.html" title="Binomial Coin-Flipping Example">Binomial Coin-Flipping Example</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/dist/dist_ref/dists/binomial_dist.html" title="Binomial Distribution">Binomial Distribution</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/dist/stat_tut/weg/binom_eg/binomial_quiz_example.html" title="Binomial Quiz Example">Binomial Quiz Example</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/dist/stat_tut/weg/st_eg/tut_mean_intervals.html" title="Calculating confidence intervals on the mean with the Students-t distribution">Calculating confidence intervals on the mean with the Students-t distribution</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/dist/dist_ref/dists/cauchy_dist.html" title="Cauchy-Lorentz Distribution">Cauchy-Lorentz Distribution</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/policy/pol_tutorial/changing_policy_defaults.html" title="Changing the Policy Defaults">Changing the Policy Defaults</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/dist/dist_ref/dists/chi_squared_dist.html" title="Chi Squared Distribution">Chi Squared Distribution</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/dist/stat_tut/weg/st_eg/two_sample_students_t.html" title="Comparing the means of two samples with the Students-t test">Comparing the means of two samples with the Students-t test</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/dist/stat_tut/weg/st_eg/paired_st.html" title="Comparing two paired samples with the Student's t distribution">Comparing two paired samples with the Student's t distribution</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/using_udt/dist_concept.html" title="Conceptual Requirements for Distribution Types">Conceptual Requirements for Distribution Types</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/dist/dist_ref/dist_algorithms.html" title="Distribution Algorithms">Distribution Algorithms</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/dist/stat_tut/weg/dist_construct_eg.html" title="Distribution Construction Example">Distribution Construction Example</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/dist/stat_tut/weg/st_eg/tut_mean_size.html" title="Estimating how large a sample size would have to become in order to give a significant Students-t test result with a single sample test">Estimating how large a sample size would have to become in order to give a significant Students-t test result with a single sample test</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/dist/dist_ref/dists/exp_dist.html" title="Exponential Distribution">Exponential Distribution</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/dist/future.html" title="Extras/Future Directions">Extras/Future Directions</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/dist/dist_ref/dists/extreme_dist.html" title="Extreme Value Distribution">Extreme Value Distribution</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/dist/dist_ref/dists/f_dist.html" title="F Distribution">F Distribution</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/dist/stat_tut/weg/find_eg/find_location_eg.html" title="Find Location (Mean) Example">Find Location (Mean) Example</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/dist/stat_tut/weg/find_eg/find_mean_and_sd_eg.html" title="Find mean and standard deviation example">Find mean and standard deviation example</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/dist/stat_tut/weg/find_eg/find_scale_eg.html" title="Find Scale (Standard Deviation) Example">Find Scale (Standard Deviation) Example</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/special/fpclass.html" title="Floating-Point Classification: Infinities and NaN's">Floating-Point Classification: Infinities and NaN's</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/dist/dist_ref/dists/gamma_dist.html" title="Gamma (and Erlang) Distribution">Gamma (and Erlang) Distribution</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/special/sf_beta/ibeta_function.html" title="Incomplete Beta Functions">Incomplete Beta Functions</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/special/sf_gamma/igamma.html" title="Incomplete Gamma Functions">Incomplete Gamma Functions</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/dist/dist_ref/dists/lognormal_dist.html" title="Log Normal Distribution">Log Normal Distribution</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/dist/dist_ref/dists/logistic_dist.html" title="Logistic Distribution">Logistic Distribution</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/policy/pol_ref/assert_undefined.html" title="Mathematically Undefined Function Policies">Mathematically Undefined Function Policies</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/dist/dist_ref/dists/negative_binomial_dist.html" title="Negative Binomial Distribution">Negative Binomial Distribution</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/dist/dist_ref/nmp.html" title="Non-Member Properties">Non-Member Properties</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/dist/dist_ref/dists/nc_beta_dist.html" title="Noncentral Beta Distribution">Noncentral Beta Distribution</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/dist/dist_ref/dists/nc_chi_squared_dist.html" title="Noncentral Chi-Squared Distribution">Noncentral Chi-Squared Distribution</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/dist/dist_ref/dists/nc_f_dist.html" title="Noncentral F Distribution">Noncentral F Distribution</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/dist/dist_ref/dists/nc_t_dist.html" title="Noncentral T Distribution">Noncentral T Distribution</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/dist/dist_ref/dists/normal_dist.html" title="Normal (Gaussian) Distribution">Normal (Gaussian) Distribution</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/dist/stat_tut/overview.html" title="Overview">Overview</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/dist/dist_ref/dists/pareto.html" title="Pareto Distribution">Pareto Distribution</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/dist/dist_ref/dists/poisson_dist.html" title="Poisson Distribution">Poisson Distribution</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/dist/dist_ref/dists/rayleigh.html" title="Rayleigh Distribution">Rayleigh Distribution</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/toolkit/internals2/error_test.html" title="Relative Error and Testing">Relative Error and Testing</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/policy/pol_ref/namespace_pol.html" title="Setting Polices at Namespace Scope">Setting Polices at Namespace Scope</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/policy/pol_tutorial/what_is_a_policy.html" title="So Just What is a Policy Anyway?">So Just What is a Policy Anyway?</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/dist/stat_tut/weg/normal_example/normal_misc.html" title="Some Miscellaneous Examples of the Normal (Gaussian) Distribution">Some Miscellaneous Examples of the Normal (Gaussian) Distribution</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/dist/dist_ref/dists/students_t_dist.html" title="Students t Distribution">Students t Distribution</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/dist/stat_tut/weg/st_eg/tut_mean_test.html" title='Testing a sample mean for difference from a "true" mean'>Testing a sample mean for difference from a "true" mean</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/backgrounders/remez.html" title="The Remez Method">The Remez Method</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/dist/dist_ref/dists/triangular_dist.html" title="Triangular Distribution">Triangular Distribution</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/dist/dist_ref/dists/uniform_dist.html" title="Uniform Distribution">Uniform Distribution</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/dist/dist_ref/dists/weibull.html" title="Weibull Distribution">Weibull Distribution</a></p></td></tr>
+</table></dd>
+<dt><span class="term">median</span></dt>
+<dd><table class="simplelist" border="0" summary="Simple list">
+<tr><td><p><a class="link" href="../math_toolkit/backgrounders/implementation.html" title="Additional Implementation Notes">Additional Implementation Notes</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/dist/dist_ref/dists/bernoulli_dist.html" title="Bernoulli Distribution">Bernoulli Distribution</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/dist/dist_ref/dists/beta_dist.html" title="Beta Distribution">Beta Distribution</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/dist/dist_ref/dists/binomial_dist.html" title="Binomial Distribution">Binomial Distribution</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/dist/dist_ref/dists/cauchy_dist.html" title="Cauchy-Lorentz Distribution">Cauchy-Lorentz Distribution</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/dist/dist_ref/dists/chi_squared_dist.html" title="Chi Squared Distribution">Chi Squared Distribution</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/dist/stat_tut/weg/cs_eg/chi_sq_intervals.html" title="Confidence Intervals on the Standard Deviation">Confidence Intervals on the Standard Deviation</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/dist/dist_ref/dists/exp_dist.html" title="Exponential Distribution">Exponential Distribution</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/dist/dist_ref/dists/extreme_dist.html" title="Extreme Value Distribution">Extreme Value Distribution</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/dist/dist_ref/dists/f_dist.html" title="F Distribution">F Distribution</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/dist/dist_ref/dists/gamma_dist.html" title="Gamma (and Erlang) Distribution">Gamma (and Erlang) Distribution</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/dist/dist_ref/dists/lognormal_dist.html" title="Log Normal Distribution">Log Normal Distribution</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/dist/dist_ref/dists/logistic_dist.html" title="Logistic Distribution">Logistic Distribution</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/dist/dist_ref/dists/negative_binomial_dist.html" title="Negative Binomial Distribution">Negative Binomial Distribution</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/dist/dist_ref/nmp.html" title="Non-Member Properties">Non-Member Properties</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/dist/dist_ref/dists/nc_beta_dist.html" title="Noncentral Beta Distribution">Noncentral Beta Distribution</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/dist/dist_ref/dists/nc_chi_squared_dist.html" title="Noncentral Chi-Squared Distribution">Noncentral Chi-Squared Distribution</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/dist/dist_ref/dists/nc_f_dist.html" title="Noncentral F Distribution">Noncentral F Distribution</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/dist/dist_ref/dists/nc_t_dist.html" title="Noncentral T Distribution">Noncentral T Distribution</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/dist/dist_ref/dists/normal_dist.html" title="Normal (Gaussian) Distribution">Normal (Gaussian) Distribution</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/dist/dist_ref/dists/pareto.html" title="Pareto Distribution">Pareto Distribution</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/dist/dist_ref/dists/poisson_dist.html" title="Poisson Distribution">Poisson Distribution</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/dist/dist_ref/dists/rayleigh.html" title="Rayleigh Distribution">Rayleigh Distribution</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/dist/dist_ref/dists/students_t_dist.html" title="Students t Distribution">Students t Distribution</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/dist/dist_ref/dists/triangular_dist.html" title="Triangular Distribution">Triangular Distribution</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/dist/dist_ref/dists/uniform_dist.html" title="Uniform Distribution">Uniform Distribution</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/dist/dist_ref/dists/weibull.html" title="Weibull Distribution">Weibull Distribution</a></p></td></tr>
+</table></dd>
+<dt><span class="term">mode</span></dt>
+<dd><table class="simplelist" border="0" summary="Simple list">
+<tr><td><p><a class="link" href="../math_toolkit/backgrounders/implementation.html" title="Additional Implementation Notes">Additional Implementation Notes</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/dist/dist_ref/dists/bernoulli_dist.html" title="Bernoulli Distribution">Bernoulli Distribution</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/dist/dist_ref/dists/beta_dist.html" title="Beta Distribution">Beta Distribution</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/dist/stat_tut/weg/binom_eg/binomial_coinflip_example.html" title="Binomial Coin-Flipping Example">Binomial Coin-Flipping Example</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/dist/dist_ref/dists/binomial_dist.html" title="Binomial Distribution">Binomial Distribution</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/dist/stat_tut/weg/binom_eg/binomial_quiz_example.html" title="Binomial Quiz Example">Binomial Quiz Example</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/main_overview/tr1.html" title="C99 and TR1 C Functions">C99 and TR1 C Functions</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/special/extern_c/tr1.html" title="C99 and TR1 C Functions Overview">C99 and TR1 C Functions Overview</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/dist/dist_ref/dists/cauchy_dist.html" title="Cauchy-Lorentz Distribution">Cauchy-Lorentz Distribution</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/dist/dist_ref/dists/chi_squared_dist.html" title="Chi Squared Distribution">Chi Squared Distribution</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/perf/comparisons.html" title="Comparisons to Other Open Source Libraries">Comparisons to Other Open Source Libraries</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/using_udt/dist_concept.html" title="Conceptual Requirements for Distribution Types">Conceptual Requirements for Distribution Types</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/dist/dist_ref/dists/exp_dist.html" title="Exponential Distribution">Exponential Distribution</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/dist/dist_ref/dists/extreme_dist.html" title="Extreme Value Distribution">Extreme Value Distribution</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/dist/dist_ref/dists/f_dist.html" title="F Distribution">F Distribution</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/dist/dist_ref/dists/gamma_dist.html" title="Gamma (and Erlang) Distribution">Gamma (and Erlang) Distribution</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/perf/getting_best.html" title="Getting the Best Performance from this Library">Getting the Best Performance from this Library</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/dist/dist_ref/dists/lognormal_dist.html" title="Log Normal Distribution">Log Normal Distribution</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/dist/dist_ref/dists/logistic_dist.html" title="Logistic Distribution">Logistic Distribution</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/dist/dist_ref/dists/negative_binomial_dist.html" title="Negative Binomial Distribution">Negative Binomial Distribution</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/dist/dist_ref/nmp.html" title="Non-Member Properties">Non-Member Properties</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/dist/dist_ref/dists/nc_beta_dist.html" title="Noncentral Beta Distribution">Noncentral Beta Distribution</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/dist/dist_ref/dists/nc_chi_squared_dist.html" title="Noncentral Chi-Squared Distribution">Noncentral Chi-Squared Distribution</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/dist/dist_ref/dists/nc_f_dist.html" title="Noncentral F Distribution">Noncentral F Distribution</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/dist/dist_ref/dists/nc_t_dist.html" title="Noncentral T Distribution">Noncentral T Distribution</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/dist/dist_ref/dists/normal_dist.html" title="Normal (Gaussian) Distribution">Normal (Gaussian) Distribution</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/dist/dist_ref/dists/pareto.html" title="Pareto Distribution">Pareto Distribution</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/dist/dist_ref/dists/poisson_dist.html" title="Poisson Distribution">Poisson Distribution</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/dist/dist_ref/dists/rayleigh.html" title="Rayleigh Distribution">Rayleigh Distribution</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/dist/dist_ref/dists/students_t_dist.html" title="Students t Distribution">Students t Distribution</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/dist/dist_ref/dists/triangular_dist.html" title="Triangular Distribution">Triangular Distribution</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/dist/dist_ref/dists/uniform_dist.html" title="Uniform Distribution">Uniform Distribution</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/dist/dist_ref/dists/weibull.html" title="Weibull Distribution">Weibull Distribution</a></p></td></tr>
+</table></dd>
+</dl></div></dd>
+<dt>
+<a name="idx_id_45"></a><span class="term">N</span>
+</dt>
+<dd><div class="variablelist"><dl>
+<dt><span class="term">newton_raphson_iterate</span></dt>
+<dd><table class="simplelist" border="0" summary="Simple list"><tr><td><p><a class="link" href="../math_toolkit/toolkit/internals1/roots.html" title="Root Finding With Derivatives">Root Finding With Derivatives</a></p></td></tr></table></dd>
+<dt><span class="term">nextafter</span></dt>
+<dd><table class="simplelist" border="0" summary="Simple list">
+<tr><td><p><a class="link" href="../math_toolkit/main_overview/tr1.html" title="C99 and TR1 C Functions">C99 and TR1 C Functions</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/special/extern_c/tr1.html" title="C99 and TR1 C Functions Overview">C99 and TR1 C Functions Overview</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/special/extern_c/c99.html" title="C99 C Functions">C99 C Functions</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/special/next_float/float_next.html" title="Finding the Next Greater Representable Value (float_next)">Finding the Next Greater Representable Value (float_next)</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/special/next_float/nextafter.html" title="Finding the Next Representable Value in a Specific Direction (nextafter)">Finding the Next Representable Value in a Specific Direction (nextafter)</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/special/next_float/float_prior.html" title="Finding the Next Smaller Representable Value (float_prior)">Finding the Next Smaller Representable Value (float_prior)</a></p></td></tr>
+</table></dd>
+<dt><span class="term">norm</span></dt>
+<dd><table class="simplelist" border="0" summary="Simple list">
+<tr><td><p><a class="link" href="../math_toolkit/dist/dist_ref/nmp.html" title="Non-Member Properties">Non-Member Properties</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/policy/pol_tutorial/namespace_policies.html" title="Setting Policies at Namespace or Translation Unit Scope">Setting Policies at Namespace or Translation Unit Scope</a></p></td></tr>
+</table></dd>
+</dl></div></dd>
+<dt>
+<a name="idx_id_46"></a><span class="term">P</span>
+</dt>
+<dd><div class="variablelist"><dl>
+<dt><span class="term">pdf</span></dt>
+<dd><table class="simplelist" border="0" summary="Simple list">
+<tr><td><p><a class="link" href="../math_toolkit/backgrounders/implementation.html" title="Additional Implementation Notes">Additional Implementation Notes</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/dist/dist_ref/dists/bernoulli_dist.html" title="Bernoulli Distribution">Bernoulli Distribution</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/dist/dist_ref/dists/beta_dist.html" title="Beta Distribution">Beta Distribution</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/dist/stat_tut/weg/binom_eg/binomial_coinflip_example.html" title="Binomial Coin-Flipping Example">Binomial Coin-Flipping Example</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/dist/dist_ref/dists/binomial_dist.html" title="Binomial Distribution">Binomial Distribution</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/dist/stat_tut/weg/binom_eg/binomial_quiz_example.html" title="Binomial Quiz Example">Binomial Quiz Example</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/dist/dist_ref/dists/cauchy_dist.html" title="Cauchy-Lorentz Distribution">Cauchy-Lorentz Distribution</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/dist/dist_ref/dists/chi_squared_dist.html" title="Chi Squared Distribution">Chi Squared Distribution</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/dist/stat_tut/weg/nag_library.html" title="Comparison with C, R, FORTRAN-style Free Functions">Comparison with C, R, FORTRAN-style Free Functions</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/using_udt/archetypes.html" title="Conceptual Archetypes and Testing">Conceptual Archetypes and Testing</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/using_udt/dist_concept.html" title="Conceptual Requirements for Distribution Types">Conceptual Requirements for Distribution Types</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/status/credits.html" title="Credits and Acknowledgements">Credits and Acknowledgements</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/main_overview/directories.html" title="Directory and File Structure">Directory and File Structure</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/dist/dist_ref/dists/exp_dist.html" title="Exponential Distribution">Exponential Distribution</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/dist/dist_ref/dists/extreme_dist.html" title="Extreme Value Distribution">Extreme Value Distribution</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/dist/dist_ref/dists/f_dist.html" title="F Distribution">F Distribution</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/dist/dist_ref/dists/gamma_dist.html" title="Gamma (and Erlang) Distribution">Gamma (and Erlang) Distribution</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/dist/dist_ref/dists/lognormal_dist.html" title="Log Normal Distribution">Log Normal Distribution</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/dist/dist_ref/dists/logistic_dist.html" title="Logistic Distribution">Logistic Distribution</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/dist/dist_ref/dists/binomial_dist.html" title="Binomial Distribution">Meaning of the non-member accessors</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/dist/dist_ref/dists/negative_binomial_dist.html" title="Negative Binomial Distribution">Meaning of the non-member accessors.</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/dist/dist_ref/dists/negative_binomial_dist.html" title="Negative Binomial Distribution">Negative Binomial Distribution</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/dist/stat_tut/weg/neg_binom_eg/negative_binomial_example1.html" title="Negative Binomial Sales Quota Example.">Negative Binomial Sales Quota Example.</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/dist/stat_tut/weg/neg_binom_eg/negative_binomial_example2.html" title="Negative Binomial Table Printing Example.">Negative Binomial Table Printing Example.</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/dist/dist_ref/nmp.html" title="Non-Member Properties">Non-Member Properties</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/dist/dist_ref/dists/nc_f_dist.html" title="Noncentral F Distribution">Noncentral F Distribution</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/dist/dist_ref/dists/normal_dist.html" title="Normal (Gaussian) Distribution">Normal (Gaussian) Distribution</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/dist/stat_tut/overview.html" title="Overview">Overview</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/dist/dist_ref/dists/pareto.html" title="Pareto Distribution">Pareto Distribution</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/dist/dist_ref/dists/poisson_dist.html" title="Poisson Distribution">Poisson Distribution</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/dist/stat_tut/variates.html" title="Random Variates and Distribution Parameters">Random Variates and Distribution Parameters</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/dist/dist_ref/dists/rayleigh.html" title="Rayleigh Distribution">Rayleigh Distribution</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/backgrounders/refs.html" title="References">References</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/dist/stat_tut/weg/normal_example/normal_misc.html" title="Some Miscellaneous Examples of the Normal (Gaussian) Distribution">Some Miscellaneous Examples of the Normal (Gaussian) Distribution</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/dist/dist_ref/dists/students_t_dist.html" title="Students t Distribution">Students t Distribution</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/dist/dist_ref/dists/triangular_dist.html" title="Triangular Distribution">Triangular Distribution</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/dist/dist_ref/dists/uniform_dist.html" title="Uniform Distribution">Uniform Distribution</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/dist/dist_ref/dists/weibull.html" title="Weibull Distribution">Weibull Distribution</a></p></td></tr>
+</table></dd>
+<dt><span class="term">powm1</span></dt>
+<dd><table class="simplelist" border="0" summary="Simple list">
+<tr><td><p><a class="link" href="../math_toolkit/special/powers/powm1.html" title="powm1">expm1</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/special/sf_gamma/igamma.html" title="Incomplete Gamma Functions">Incomplete Gamma Functions</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/special/powers/powm1.html" title="powm1">powm1</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/special/powers/powm1.html" title="powm1">RR</a></p></td></tr>
+</table></dd>
+</dl></div></dd>
+<dt>
+<a name="idx_id_47"></a><span class="term">Q</span>
+</dt>
+<dd><div class="variablelist"><dl>
+<dt><span class="term">quantile</span></dt>
+<dd><table class="simplelist" border="0" summary="Simple list">
+<tr><td><p><a class="link" href="../math_toolkit/backgrounders/implementation.html" title="Additional Implementation Notes">Additional Implementation Notes</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/dist/dist_ref/dists/bernoulli_dist.html" title="Bernoulli Distribution">Bernoulli Distribution</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/dist/dist_ref/dists/beta_dist.html" title="Beta Distribution">Beta Distribution</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/dist/dist_ref/dists/binomial_dist.html" title="Binomial Distribution">Binomial Distribution</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/dist/stat_tut/weg/binom_eg/binomial_quiz_example.html" title="Binomial Quiz Example">Binomial Quiz Example</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/dist/stat_tut/weg/st_eg/tut_mean_intervals.html" title="Calculating confidence intervals on the mean with the Students-t distribution">Calculating confidence intervals on the mean with the Students-t distribution</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/dist/dist_ref/dists/cauchy_dist.html" title="Cauchy-Lorentz Distribution">Cauchy-Lorentz Distribution</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/dist/dist_ref/dists/chi_squared_dist.html" title="Chi Squared Distribution">Chi Squared Distribution</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/dist/stat_tut/weg/cs_eg/chi_sq_test.html" title="Chi-Square Test for the Standard Deviation">Chi-Square Test for the Standard Deviation</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/using_udt/dist_concept.html" title="Conceptual Requirements for Distribution Types">Conceptual Requirements for Distribution Types</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/dist/stat_tut/weg/cs_eg/chi_sq_intervals.html" title="Confidence Intervals on the Standard Deviation">Confidence Intervals on the Standard Deviation</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/dist/stat_tut/dist_params.html" title="Discrete Probability Distributions">Discrete Probability Distributions</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/policy/pol_ref/discrete_quant_ref.html" title="Discrete Quantile Policies">Discrete Quantile Policies</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/policy/pol_ref/error_handling_policies.html" title="Error Handling Policies">Error Handling Policies</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/dist/dist_ref/dists/exp_dist.html" title="Exponential Distribution">Exponential Distribution</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/dist/dist_ref/dists/extreme_dist.html" title="Extreme Value Distribution">Extreme Value Distribution</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/dist/dist_ref/dists/f_dist.html" title="F Distribution">F Distribution</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/dist/stat_tut/weg/f_eg.html" title="F Distribution Examples">F Distribution Examples</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/dist/stat_tut/weg/find_eg/find_mean_and_sd_eg.html" title="Find mean and standard deviation example">Find mean and standard deviation example</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/dist/dist_ref/dists/gamma_dist.html" title="Gamma (and Erlang) Distribution">Gamma (and Erlang) Distribution</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/policy/pol_ref/internal_promotion.html" title="Internal Promotion Policies">Internal Promotion Policies</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/dist/dist_ref/dists/lognormal_dist.html" title="Log Normal Distribution">Log Normal Distribution</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/dist/dist_ref/dists/logistic_dist.html" title="Logistic Distribution">Logistic Distribution</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/dist/dist_ref/dists/binomial_dist.html" title="Binomial Distribution">Meaning of the non-member accessors</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/dist/dist_ref/dists/negative_binomial_dist.html" title="Negative Binomial Distribution">Meaning of the non-member accessors.</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/dist/dist_ref/dists/negative_binomial_dist.html" title="Negative Binomial Distribution">Negative Binomial Distribution</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/dist/stat_tut/weg/neg_binom_eg/negative_binomial_example1.html" title="Negative Binomial Sales Quota Example.">Negative Binomial Sales Quota Example.</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/dist/dist_ref/nmp.html" title="Non-Member Properties">Non-Member Properties</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/dist/dist_ref/dists/nc_beta_dist.html" title="Noncentral Beta Distribution">Noncentral Beta Distribution</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/dist/dist_ref/dists/nc_chi_squared_dist.html" title="Noncentral Chi-Squared Distribution">Noncentral Chi-Squared Distribution</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/dist/dist_ref/dists/nc_f_dist.html" title="Noncentral F Distribution">Noncentral F Distribution</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/dist/dist_ref/dists/nc_t_dist.html" title="Noncentral T Distribution">Noncentral T Distribution</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/dist/dist_ref/dists/normal_dist.html" title="Normal (Gaussian) Distribution">Normal (Gaussian) Distribution</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/dist/stat_tut/overview.html" title="Overview">Overview</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/dist/dist_ref/dists/pareto.html" title="Pareto Distribution">Pareto Distribution</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/dist/dist_ref/dists/poisson_dist.html" title="Poisson Distribution">Poisson Distribution</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/policy/pol_tutorial/policy_tut_defaults.html" title="Policies Have Sensible Defaults">Policies Have Sensible Defaults</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/policy/pol_ref/precision_pol.html" title="Precision Policies">Precision Policies</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/dist/dist_ref/dists/rayleigh.html" title="Rayleigh Distribution">Rayleigh Distribution</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/policy/pol_tutorial/namespace_policies.html" title="Setting Policies at Namespace or Translation Unit Scope">Setting Policies at Namespace or Translation Unit Scope</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/policy/pol_tutorial/ad_hoc_dist_policies.html" title="Setting Policies for Distributions on an Ad Hoc Basis">Setting Policies for Distributions on an Ad Hoc Basis</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/policy/pol_tutorial/what_is_a_policy.html" title="So Just What is a Policy Anyway?">So Just What is a Policy Anyway?</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/dist/stat_tut/weg/normal_example/normal_misc.html" title="Some Miscellaneous Examples of the Normal (Gaussian) Distribution">Some Miscellaneous Examples of the Normal (Gaussian) Distribution</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/dist/dist_ref/dists/students_t_dist.html" title="Students t Distribution">Students t Distribution</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/dist/stat_tut/weg/nccs_eg/nccs_power_eg.html" title="Tables of the power function of the &#967;2 test.">Tables of the power function of the &#967; 2 test.</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/dist/dist_ref/dists/triangular_dist.html" title="Triangular Distribution">Triangular Distribution</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/policy/pol_tutorial/understand_dis_quant.html" title="Understanding Quantiles of Discrete Distributions">Understanding Quantiles of Discrete Distributions</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/dist/dist_ref/dists/uniform_dist.html" title="Uniform Distribution">Uniform Distribution</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/dist/dist_ref/dists/weibull.html" title="Weibull Distribution">Weibull Distribution</a></p></td></tr>
+</table></dd>
+</dl></div></dd>
+<dt>
+<a name="idx_id_48"></a><span class="term">R</span>
+</dt>
+<dd><div class="variablelist"><dl>
+<dt><span class="term">raise_denorm_error</span></dt>
+<dd><table class="simplelist" border="0" summary="Simple list"><tr><td><p><a class="link" href="../math_toolkit/main_overview/error_handling.html" title="Error Handling">Error Handling</a></p></td></tr></table></dd>
+<dt><span class="term">raise_domain_error</span></dt>
+<dd><table class="simplelist" border="0" summary="Simple list"><tr><td><p><a class="link" href="../math_toolkit/main_overview/error_handling.html" title="Error Handling">Error Handling</a></p></td></tr></table></dd>
+<dt><span class="term">raise_evaluation_error</span></dt>
+<dd><table class="simplelist" border="0" summary="Simple list"><tr><td><p><a class="link" href="../math_toolkit/main_overview/error_handling.html" title="Error Handling">Error Handling</a></p></td></tr></table></dd>
+<dt><span class="term">raise_overflow_error</span></dt>
+<dd><table class="simplelist" border="0" summary="Simple list"><tr><td><p><a class="link" href="../math_toolkit/main_overview/error_handling.html" title="Error Handling">Error Handling</a></p></td></tr></table></dd>
+<dt><span class="term">raise_pole_error</span></dt>
+<dd><table class="simplelist" border="0" summary="Simple list"><tr><td><p><a class="link" href="../math_toolkit/main_overview/error_handling.html" title="Error Handling">Error Handling</a></p></td></tr></table></dd>
+<dt><span class="term">raise_rounding_error</span></dt>
+<dd><table class="simplelist" border="0" summary="Simple list"><tr><td><p><a class="link" href="../math_toolkit/main_overview/error_handling.html" title="Error Handling">Error Handling</a></p></td></tr></table></dd>
+<dt><span class="term">raise_underflow_error</span></dt>
+<dd><table class="simplelist" border="0" summary="Simple list"><tr><td><p><a class="link" href="../math_toolkit/main_overview/error_handling.html" title="Error Handling">Error Handling</a></p></td></tr></table></dd>
+<dt><span class="term">real_cast</span></dt>
+<dd><table class="simplelist" border="0" summary="Simple list"><tr><td><p><a class="link" href="../math_toolkit/toolkit/internals2/test_data.html" title="Graphing, Profiling, and Generating Test Data for Special Functions">Graphing, Profiling, and Generating Test Data for Special Functions</a></p></td></tr></table></dd>
+<dt><span class="term">relative_error</span></dt>
+<dd><table class="simplelist" border="0" summary="Simple list">
+<tr><td><p><a class="link" href="../math_toolkit/toolkit/internals2/test_data.html" title="Graphing, Profiling, and Generating Test Data for Special Functions">Graphing, Profiling, and Generating Test Data for Special Functions</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/toolkit/internals2/error_test.html" title="Relative Error and Testing">Relative Error and Testing</a></p></td></tr>
+</table></dd>
+<dt><span class="term">rescale</span></dt>
+<dd><table class="simplelist" border="0" summary="Simple list">
+<tr><td><p><a class="link" href="../math_toolkit/toolkit/internals2/minimax.html" title="Minimax Approximations and the Remez Algorithm">Minimax Approximations and the Remez Algorithm</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/backgrounders/remez.html" title="The Remez Method">The Remez Method</a></p></td></tr>
+</table></dd>
+<dt><span class="term">rising_factorial</span></dt>
+<dd><table class="simplelist" border="0" summary="Simple list"><tr><td><p><a class="link" href="../math_toolkit/special/factorials/sf_rising_factorial.html" title="Rising Factorial">Rising Factorial</a></p></td></tr></table></dd>
+<dt><span class="term">rotate</span></dt>
+<dd><table class="simplelist" border="0" summary="Simple list">
+<tr><td><p><a class="link" href="../math_toolkit/toolkit/internals2/minimax.html" title="Minimax Approximations and the Remez Algorithm">Minimax Approximations and the Remez Algorithm</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/backgrounders/remez.html" title="The Remez Method">The Remez Method</a></p></td></tr>
+</table></dd>
+<dt><span class="term">round</span></dt>
+<dd><table class="simplelist" border="0" summary="Simple list">
+<tr><td><p><a class="link" href="../math_toolkit/backgrounders/implementation.html" title="Additional Implementation Notes">Additional Implementation Notes</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/main_overview/tr1.html" title="C99 and TR1 C Functions">C99 and TR1 C Functions</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/special/extern_c/tr1.html" title="C99 and TR1 C Functions Overview">C99 and TR1 C Functions Overview</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/special/extern_c/c99.html" title="C99 C Functions">C99 C Functions</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/using_udt/concepts.html" title="Conceptual Requirements for Real Number Types">Conceptual Requirements for Real Number Types</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/policy/pol_ref/discrete_quant_ref.html" title="Discrete Quantile Policies">Discrete Quantile Policies</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/special/sf_erf/error_inv.html" title="Error Function Inverses">Error Function Inverses</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/special/sf_erf/error_function.html" title="Error Functions">Error Functions</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/main_overview/error_handling.html" title="Error Handling">Error Handling</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/policy/pol_ref/error_handling_policies.html" title="Error Handling Policies">Error Handling Policies</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/dist/stat_tut/weg/find_eg/find_scale_eg.html" title="Find Scale (Standard Deviation) Example">Find Scale (Standard Deviation) Example</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/special/sf_gamma/igamma_inv.html" title="Incomplete Gamma Function Inverses">Incomplete Gamma Function Inverses</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/toolkit/internals1/roots2.html" title="Root Finding Without Derivatives">Root Finding Without Derivatives</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/special/rounding/round.html" title="Rounding Functions">Rounding Functions</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/special/sf_beta/ibeta_inv_function.html" title="The Incomplete Beta Function Inverses">The Incomplete Beta Function Inverses</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/backgrounders/remez.html" title="The Remez Method">The Remez Method</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/special/rounding/trunc.html" title="Truncation Functions">Truncation Functions</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/policy/pol_tutorial/understand_dis_quant.html" title="Understanding Quantiles of Discrete Distributions">Understanding Quantiles of Discrete Distributions</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/policy/pol_ref/policy_defaults.html" title="Using macros to Change the Policy Defaults">Using macros to Change the Policy Defaults</a></p></td></tr>
+</table></dd>
+</dl></div></dd>
+<dt>
+<a name="idx_id_49"></a><span class="term">S</span>
+</dt>
+<dd><div class="variablelist"><dl>
+<dt><span class="term">schroeder_iterate</span></dt>
+<dd><table class="simplelist" border="0" summary="Simple list"><tr><td><p><a class="link" href="../math_toolkit/toolkit/internals1/roots.html" title="Root Finding With Derivatives">Root Finding With Derivatives</a></p></td></tr></table></dd>
+<dt><span class="term">SetOutputPrecision</span></dt>
+<dd><table class="simplelist" border="0" summary="Simple list"><tr><td><p><a class="link" href="../math_toolkit/toolkit/internals2/test_data.html" title="Graphing, Profiling, and Generating Test Data for Special Functions">Graphing, Profiling, and Generating Test Data for Special Functions</a></p></td></tr></table></dd>
+<dt><span class="term">SetPrecision</span></dt>
+<dd><table class="simplelist" border="0" summary="Simple list"><tr><td><p><a class="link" href="../math_toolkit/toolkit/internals2/test_data.html" title="Graphing, Profiling, and Generating Test Data for Special Functions">Graphing, Profiling, and Generating Test Data for Special Functions</a></p></td></tr></table></dd>
+<dt><span class="term">sinc_pi</span></dt>
+<dd><table class="simplelist" border="0" summary="Simple list">
+<tr><td><p><a class="link" href="../math_toolkit/special/sinc/sinc_pi.html" title="sinc_pi">sinc_pi</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/special/sinc/sinc_overview.html" title="Sinus Cardinal and Hyperbolic Sinus Cardinal Functions Overview">Sinus Cardinal and Hyperbolic Sinus Cardinal Functions Overview</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/special/bessel/sph_bessel.html" title="Spherical Bessel Functions of the First and Second Kinds">Spherical Bessel Functions of the First and Second Kinds</a></p></td></tr>
+</table></dd>
+<dt><span class="term">sinhc_pi</span></dt>
+<dd><table class="simplelist" border="0" summary="Simple list">
+<tr><td><p><a class="link" href="../math_toolkit/special/sinc/sinhc_pi.html" title="sinhc_pi">sinhc_pi</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/special/sinc/sinc_overview.html" title="Sinus Cardinal and Hyperbolic Sinus Cardinal Functions Overview">Sinus Cardinal and Hyperbolic Sinus Cardinal Functions Overview</a></p></td></tr>
+</table></dd>
+<dt><span class="term">skewness</span></dt>
+<dd><table class="simplelist" border="0" summary="Simple list">
+<tr><td><p><a class="link" href="../math_toolkit/dist/dist_ref/dists/bernoulli_dist.html" title="Bernoulli Distribution">Bernoulli Distribution</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/dist/dist_ref/dists/beta_dist.html" title="Beta Distribution">Beta Distribution</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/dist/stat_tut/weg/binom_eg/binomial_coinflip_example.html" title="Binomial Coin-Flipping Example">Binomial Coin-Flipping Example</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/dist/dist_ref/dists/binomial_dist.html" title="Binomial Distribution">Binomial Distribution</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/dist/stat_tut/weg/binom_eg/binomial_quiz_example.html" title="Binomial Quiz Example">Binomial Quiz Example</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/dist/dist_ref/dists/cauchy_dist.html" title="Cauchy-Lorentz Distribution">Cauchy-Lorentz Distribution</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/dist/dist_ref/dists/chi_squared_dist.html" title="Chi Squared Distribution">Chi Squared Distribution</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/using_udt/dist_concept.html" title="Conceptual Requirements for Distribution Types">Conceptual Requirements for Distribution Types</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/dist/dist_ref/dists/exp_dist.html" title="Exponential Distribution">Exponential Distribution</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/dist/dist_ref/dists/extreme_dist.html" title="Extreme Value Distribution">Extreme Value Distribution</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/dist/dist_ref/dists/f_dist.html" title="F Distribution">F Distribution</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/dist/dist_ref/dists/gamma_dist.html" title="Gamma (and Erlang) Distribution">Gamma (and Erlang) Distribution</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/dist/dist_ref/dists/lognormal_dist.html" title="Log Normal Distribution">Log Normal Distribution</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/dist/dist_ref/dists/logistic_dist.html" title="Logistic Distribution">Logistic Distribution</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/dist/dist_ref/dists/negative_binomial_dist.html" title="Negative Binomial Distribution">Negative Binomial Distribution</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/dist/dist_ref/nmp.html" title="Non-Member Properties">Non-Member Properties</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/dist/dist_ref/dists/nc_beta_dist.html" title="Noncentral Beta Distribution">Noncentral Beta Distribution</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/dist/dist_ref/dists/nc_chi_squared_dist.html" title="Noncentral Chi-Squared Distribution">Noncentral Chi-Squared Distribution</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/dist/dist_ref/dists/nc_f_dist.html" title="Noncentral F Distribution">Noncentral F Distribution</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/dist/dist_ref/dists/nc_t_dist.html" title="Noncentral T Distribution">Noncentral T Distribution</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/dist/dist_ref/dists/normal_dist.html" title="Normal (Gaussian) Distribution">Normal (Gaussian) Distribution</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/dist/dist_ref/dists/pareto.html" title="Pareto Distribution">Pareto Distribution</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/dist/dist_ref/dists/poisson_dist.html" title="Poisson Distribution">Poisson Distribution</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/dist/dist_ref/dists/rayleigh.html" title="Rayleigh Distribution">Rayleigh Distribution</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/dist/dist_ref/dists/students_t_dist.html" title="Students t Distribution">Students t Distribution</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/dist/dist_ref/dists/triangular_dist.html" title="Triangular Distribution">Triangular Distribution</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/dist/dist_ref/dists/uniform_dist.html" title="Uniform Distribution">Uniform Distribution</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/dist/dist_ref/dists/weibull.html" title="Weibull Distribution">Weibull Distribution</a></p></td></tr>
+</table></dd>
+<dt><span class="term">spherical_harmonic_i</span></dt>
+<dd><table class="simplelist" border="0" summary="Simple list"><tr><td><p><a class="link" href="../math_toolkit/special/sf_poly/sph_harm.html" title="Spherical Harmonics">Spherical Harmonics</a></p></td></tr></table></dd>
+<dt><span class="term">spherical_harmonic_r</span></dt>
+<dd><table class="simplelist" border="0" summary="Simple list"><tr><td><p><a class="link" href="../math_toolkit/special/sf_poly/sph_harm.html" title="Spherical Harmonics">Spherical Harmonics</a></p></td></tr></table></dd>
+<dt><span class="term">sph_bessel</span></dt>
+<dd><table class="simplelist" border="0" summary="Simple list">
+<tr><td><p><a class="link" href="../math_toolkit/special/bessel/bessel_over.html" title="Bessel Function Overview">Bessel Function Overview</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/main_overview/tr1.html" title="C99 and TR1 C Functions">C99 and TR1 C Functions</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/special/extern_c/tr1.html" title="C99 and TR1 C Functions Overview">C99 and TR1 C Functions Overview</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/main_overview/result_type.html" title="Calculation of the Type of the Result">Calculation of the Type of the Result</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/special/bessel/sph_bessel.html" title="Spherical Bessel Functions of the First and Second Kinds">Spherical Bessel Functions of the First and Second Kinds</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/special/extern_c/tr1_ref.html" title="TR1 C Functions Quick Reference">TR1 C Functions Quick Reference</a></p></td></tr>
+</table></dd>
+<dt><span class="term">sph_neumann</span></dt>
+<dd><table class="simplelist" border="0" summary="Simple list">
+<tr><td><p><a class="link" href="../math_toolkit/special/bessel/bessel_over.html" title="Bessel Function Overview">Bessel Function Overview</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/main_overview/tr1.html" title="C99 and TR1 C Functions">C99 and TR1 C Functions</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/special/extern_c/tr1.html" title="C99 and TR1 C Functions Overview">C99 and TR1 C Functions Overview</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/special/bessel/sph_bessel.html" title="Spherical Bessel Functions of the First and Second Kinds">Spherical Bessel Functions of the First and Second Kinds</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/special/extern_c/tr1_ref.html" title="TR1 C Functions Quick Reference">TR1 C Functions Quick Reference</a></p></td></tr>
+</table></dd>
+<dt><span class="term">standard_deviation</span></dt>
+<dd><table class="simplelist" border="0" summary="Simple list">
+<tr><td><p><a class="link" href="../math_toolkit/dist/stat_tut/weg/binom_eg/binomial_coinflip_example.html" title="Binomial Coin-Flipping Example">Binomial Coin-Flipping Example</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/dist/stat_tut/weg/binom_eg/binomial_quiz_example.html" title="Binomial Quiz Example">Binomial Quiz Example</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/using_udt/dist_concept.html" title="Conceptual Requirements for Distribution Types">Conceptual Requirements for Distribution Types</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/dist/stat_tut/weg/find_eg/find_location_eg.html" title="Find Location (Mean) Example">Find Location (Mean) Example</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/dist/stat_tut/weg/find_eg/find_mean_and_sd_eg.html" title="Find mean and standard deviation example">Find mean and standard deviation example</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/dist/stat_tut/weg/find_eg/find_scale_eg.html" title="Find Scale (Standard Deviation) Example">Find Scale (Standard Deviation) Example</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/dist/dist_ref/nmp.html" title="Non-Member Properties">Non-Member Properties</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/dist/dist_ref/dists/normal_dist.html" title="Normal (Gaussian) Distribution">Normal (Gaussian) Distribution</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/dist/stat_tut/weg/normal_example/normal_misc.html" title="Some Miscellaneous Examples of the Normal (Gaussian) Distribution">Some Miscellaneous Examples of the Normal (Gaussian) Distribution</a></p></td></tr>
+</table></dd>
+<dt><span class="term">sum_series</span></dt>
+<dd><table class="simplelist" border="0" summary="Simple list"><tr><td><p><a class="link" href="../math_toolkit/toolkit/internals1/series_evaluation.html" title="Series Evaluation">Series Evaluation</a></p></td></tr></table></dd>
+</dl></div></dd>
+<dt>
+<a name="idx_id_50"></a><span class="term">T</span>
+</dt>
+<dd><div class="variablelist"><dl>
+<dt><span class="term">tgamma</span></dt>
+<dd><table class="simplelist" border="0" summary="Simple list">
+<tr><td><p><a class="link" href="../math_toolkit/main_overview/tr1.html" title="C99 and TR1 C Functions">C99 and TR1 C Functions</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/special/extern_c/tr1.html" title="C99 and TR1 C Functions Overview">C99 and TR1 C Functions Overview</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/special/extern_c/c99.html" title="C99 C Functions">C99 C Functions</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/policy/pol_tutorial/user_def_err_pol.html" title="Calling User Defined Error Handlers">Calling User Defined Error Handlers</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/policy/pol_tutorial/ad_hoc_sf_policies.html" title="Changing the Policy on an Ad Hoc Basis for the Special Functions">Changing the Policy on an Ad Hoc Basis for the Special Functions</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/perf/comparisons.html" title="Comparisons to Other Open Source Libraries">Comparisons to Other Open Source Libraries</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/main_overview/directories.html" title="Directory and File Structure">Directory and File Structure</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/main_overview/error_handling.html" title="Error Handling">Error Handling</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/policy/pol_ref/error_handling_policies.html" title="Error Handling Policies">Error Handling Policies</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/special/sf_gamma/igamma.html" title="Incomplete Gamma Functions">Errors In the Function tgamma(a,z)</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/special/factorials/sf_factorial.html" title="Factorial">Factorial</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/special/sf_gamma/tgamma.html" title="Gamma">Gamma</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/special/sf_gamma/igamma.html" title="Incomplete Gamma Functions">Incomplete Gamma Functions</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/policy/pol_ref/internal_promotion.html" title="Internal Promotion Policies">Internal Promotion Policies</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/status/issues.html" title="Known Issues, and Todo List">Known Issues, and Todo List</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/special/sf_gamma/lgamma.html" title="Log Gamma">Log Gamma</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/policy/pol_ref/precision_pol.html" title="Precision Policies">Precision Policies</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/toolkit/internals2/error_test.html" title="Relative Error and Testing">Relative Error and Testing</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/policy/pol_ref/namespace_pol.html" title="Setting Polices at Namespace Scope">Setting Polices at Namespace Scope</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/policy/pol_tutorial/namespace_policies.html" title="Setting Policies at Namespace or Translation Unit Scope">Setting Policies at Namespace or Translation Unit Scope</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/using_udt/use_mpfr.html" title="Using With MPFR / GMP - a High-Precision Floating-Point Library">Using With MPFR / GMP - a High-Precision Floating-Point Library</a></p></td></tr>
+</table></dd>
+<dt><span class="term">tgamma1pm1</span></dt>
+<dd><table class="simplelist" border="0" summary="Simple list">
+<tr><td><p><a class="link" href="../math_toolkit/special/sf_gamma/tgamma.html" title="Gamma">Gamma</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/special/sf_gamma/igamma.html" title="Incomplete Gamma Functions">Incomplete Gamma Functions</a></p></td></tr>
+</table></dd>
+<dt><span class="term">tgamma_delta_ratio</span></dt>
+<dd><table class="simplelist" border="0" summary="Simple list">
+<tr><td><p><a class="link" href="../math_toolkit/special/sf_gamma/gamma_ratios.html" title="Ratios of Gamma Functions">Errors In the Function tgamma_delta_ratio(a, delta)</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/special/factorials/sf_falling_factorial.html" title="Falling Factorial">Falling Factorial</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/special/sf_gamma/gamma_ratios.html" title="Ratios of Gamma Functions">Ratios of Gamma Functions</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/special/factorials/sf_rising_factorial.html" title="Rising Factorial">Rising Factorial</a></p></td></tr>
+</table></dd>
+<dt><span class="term">tgamma_lower</span></dt>
+<dd><table class="simplelist" border="0" summary="Simple list">
+<tr><td><p><a class="link" href="../math_toolkit/special/sf_gamma/igamma.html" title="Incomplete Gamma Functions">Errors In the Function tgamma_lower(a,z)</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/special/sf_gamma/igamma.html" title="Incomplete Gamma Functions">Incomplete Gamma Functions</a></p></td></tr>
+</table></dd>
+<dt><span class="term">tgamma_ratio</span></dt>
+<dd><table class="simplelist" border="0" summary="Simple list">
+<tr><td><p><a class="link" href="../math_toolkit/special/sf_gamma/gamma_ratios.html" title="Ratios of Gamma Functions">Errors In the Function tgamma_ratio(a, b)</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/special/sf_gamma/gamma_ratios.html" title="Ratios of Gamma Functions">Ratios of Gamma Functions</a></p></td></tr>
+</table></dd>
+<dt><span class="term">trunc</span></dt>
+<dd><table class="simplelist" border="0" summary="Simple list">
+<tr><td><p><a class="link" href="../math_toolkit/main_overview/tr1.html" title="C99 and TR1 C Functions">C99 and TR1 C Functions</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/special/extern_c/tr1.html" title="C99 and TR1 C Functions Overview">C99 and TR1 C Functions Overview</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/special/extern_c/c99.html" title="C99 C Functions">C99 C Functions</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/using_udt/concepts.html" title="Conceptual Requirements for Real Number Types">Conceptual Requirements for Real Number Types</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/main_overview/error_handling.html" title="Error Handling">Error Handling</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/policy/pol_ref/error_handling_policies.html" title="Error Handling Policies">Error Handling Policies</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/special/rounding/trunc.html" title="Truncation Functions">Truncation Functions</a></p></td></tr>
+</table></dd>
+</dl></div></dd>
+<dt>
+<a name="idx_id_51"></a><span class="term">V</span>
+</dt>
+<dd><div class="variablelist"><dl>
+<dt><span class="term">variance</span></dt>
+<dd><table class="simplelist" border="0" summary="Simple list">
+<tr><td><p><a class="link" href="../math_toolkit/dist/dist_ref/dists/bernoulli_dist.html" title="Bernoulli Distribution">Bernoulli Distribution</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/dist/dist_ref/dists/beta_dist.html" title="Beta Distribution">Beta Distribution</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/dist/dist_ref/dists/binomial_dist.html" title="Binomial Distribution">Binomial Distribution</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/dist/dist_ref/dists/cauchy_dist.html" title="Cauchy-Lorentz Distribution">Cauchy-Lorentz Distribution</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/dist/dist_ref/dists/chi_squared_dist.html" title="Chi Squared Distribution">Chi Squared Distribution</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/dist/stat_tut/weg/st_eg/two_sample_students_t.html" title="Comparing the means of two samples with the Students-t test">Comparing the means of two samples with the Students-t test</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/using_udt/dist_concept.html" title="Conceptual Requirements for Distribution Types">Conceptual Requirements for Distribution Types</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/dist/stat_tut/weg/cs_eg/chi_sq_size.html" title="Estimating the Required Sample Sizes for a Chi-Square Test for the Standard Deviation">Estimating the Required Sample Sizes for a Chi-Square Test for the Standard Deviation</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/dist/dist_ref/dists/exp_dist.html" title="Exponential Distribution">Exponential Distribution</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/dist/dist_ref/dists/extreme_dist.html" title="Extreme Value Distribution">Extreme Value Distribution</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/dist/dist_ref/dists/f_dist.html" title="F Distribution">F Distribution</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/dist/dist_ref/dists/gamma_dist.html" title="Gamma (and Erlang) Distribution">Gamma (and Erlang) Distribution</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/dist/dist_ref/dists/lognormal_dist.html" title="Log Normal Distribution">Log Normal Distribution</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/dist/dist_ref/dists/logistic_dist.html" title="Logistic Distribution">Logistic Distribution</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/dist/dist_ref/dists/negative_binomial_dist.html" title="Negative Binomial Distribution">Negative Binomial Distribution</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/dist/dist_ref/nmp.html" title="Non-Member Properties">Non-Member Properties</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/dist/dist_ref/dists/nc_beta_dist.html" title="Noncentral Beta Distribution">Noncentral Beta Distribution</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/dist/dist_ref/dists/nc_chi_squared_dist.html" title="Noncentral Chi-Squared Distribution">Noncentral Chi-Squared Distribution</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/dist/dist_ref/dists/nc_f_dist.html" title="Noncentral F Distribution">Noncentral F Distribution</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/dist/dist_ref/dists/nc_t_dist.html" title="Noncentral T Distribution">Noncentral T Distribution</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/dist/dist_ref/dists/normal_dist.html" title="Normal (Gaussian) Distribution">Normal (Gaussian) Distribution</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/dist/dist_ref/dists/pareto.html" title="Pareto Distribution">Pareto Distribution</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/dist/dist_ref/dists/poisson_dist.html" title="Poisson Distribution">Poisson Distribution</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/dist/dist_ref/dists/rayleigh.html" title="Rayleigh Distribution">Rayleigh Distribution</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/toolkit/internals2/error_test.html" title="Relative Error and Testing">Relative Error and Testing</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/dist/dist_ref/dists/students_t_dist.html" title="Students t Distribution">Students t Distribution</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/dist/dist_ref/dists/triangular_dist.html" title="Triangular Distribution">Triangular Distribution</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/dist/dist_ref/dists/uniform_dist.html" title="Uniform Distribution">Uniform Distribution</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/dist/dist_ref/dists/weibull.html" title="Weibull Distribution">Weibull Distribution</a></p></td></tr>
+</table></dd>
+</dl></div></dd>
+<dt>
+<a name="idx_id_52"></a><span class="term">Z</span>
+</dt>
+<dd><div class="variablelist"><dl>
+<dt><span class="term">zeta</span></dt>
+<dd><table class="simplelist" border="0" summary="Simple list">
+<tr><td><p><a class="link" href="../math_toolkit/main_overview/tr1.html" title="C99 and TR1 C Functions">C99 and TR1 C Functions</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/special/extern_c/tr1.html" title="C99 and TR1 C Functions Overview">C99 and TR1 C Functions Overview</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/special/zetas/zeta.html" title="Riemann Zeta Function">Errors In the Function zeta(z)</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/special/expint/expint_i.html" title="Exponential Integral Ei">Exponential Integral Ei</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/dist/dist_ref/dists/extreme_dist.html" title="Extreme Value Distribution">Extreme Value Distribution</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/special/zetas/zeta.html" title="Riemann Zeta Function">Riemann Zeta Function</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/special/extern_c/tr1_ref.html" title="TR1 C Functions Quick Reference">TR1 C Functions Quick Reference</a></p></td></tr>
+</table></dd>
+</dl></div></dd>
+</dl></div>
+</div>
+<table xmlns:rev="http://www.cs.rpi.edu/~gregod/boost/tools/doc/revision" width="100%"><tr>
+<td align="left"></td>
+<td align="right"><div class="copyright-footer">Copyright © 2006 , 2007, 2008 John Maddock, Paul A. Bristow, Hubert
+      Holin, Xiaogang Zhang, Bruno Lalande and Gautam Sewani<p>
+        Distributed under the Boost Software License, Version 1.0. (See accompanying
+        file LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_0.txt)
+      </p>
+</div></td>
+</tr></table>
+<hr>
+<div class="spirit-nav">
+<a accesskey="p" href="s11.html"><img src="../../../doc/html/images/prev.png" alt="Prev"></a><a accesskey="u" href="../index.html"><img src="../../../doc/html/images/up.png" alt="Up"></a><a accesskey="h" href="../index.html"><img src="../../../doc/html/images/home.png" alt="Home"></a><a accesskey="n" href="s13.html"><img src="../../../doc/html/images/next.png" alt="Next"></a>
+</div>
+</body>
+</html>

Added: sandbox/tools/auto_index/example/math/doc/sf_and_dist/html/index/s13.html
==============================================================================
--- (empty file)
+++ sandbox/tools/auto_index/example/math/doc/sf_and_dist/html/index/s13.html	2008-11-28 05:25:28 EST (Fri, 28 Nov 2008)
@@ -0,0 +1,148 @@
+<html>
+<head>
+<meta http-equiv="Content-Type" content="text/html; charset=ISO-8859-1">
+<title>Macro Index</title>
+<link rel="stylesheet" href="../boostbook.css" type="text/css">
+<meta name="generator" content="DocBook XSL Stylesheets Vsnapshot_8125">
+<link rel="home" href="../index.html" title="Math Toolkit">
+<link rel="up" href="../index.html" title="Math Toolkit">
+<link rel="prev" href="s12.html" title="Function Index">
+<link rel="next" href="s14.html" title="Index">
+</head>
+<body bgcolor="white" text="black" link="#0000FF" vlink="#840084" alink="#0000FF">
+<table cellpadding="2" width="100%"><tr>
+<td valign="top"><img alt="Boost C++ Libraries" width="277" height="86" src="../../../boost.png"></td>
+<td align="center">Home</td>
+<td align="center">Libraries</td>
+<td align="center">People</td>
+<td align="center">FAQ</td>
+<td align="center">More</td>
+</tr></table>
+<hr>
+<div class="spirit-nav">
+<a accesskey="p" href="s12.html"><img src="../../../doc/html/images/prev.png" alt="Prev"></a><a accesskey="u" href="../index.html"><img src="../../../doc/html/images/up.png" alt="Up"></a><a accesskey="h" href="../index.html"><img src="../../../doc/html/images/home.png" alt="Home"></a><a accesskey="n" href="s14.html"><img src="../../../doc/html/images/next.png" alt="Next"></a>
+</div>
+<div class="section" lang="en">
+<div class="titlepage"><div><div><h2 class="title" style="clear: both">
+<a name="id939584"></a>Macro Index</h2></div></div></div>
+<p><a class="link" href="s13.html#idx_id_53">B</a> <a class="link" href="s13.html#idx_id_54">F</a> </p>
+<div class="variablelist"><dl>
+<dt>
+<a name="idx_id_53"></a><span class="term">B</span>
+</dt>
+<dd><div class="variablelist"><dl>
+<dt><span class="term">BOOST_DEFINE_MATH_CONSTANT</span></dt>
+<dd><table class="simplelist" border="0" summary="Simple list"><tr><td><p><a class="link" href="../math_toolkit/backgrounders/implementation.html" title="Additional Implementation Notes">Additional Implementation Notes</a></p></td></tr></table></dd>
+<dt><span class="term">BOOST_HAS_LOG1P</span></dt>
+<dd><table class="simplelist" border="0" summary="Simple list"><tr><td><p><a class="link" href="../math_toolkit/special/powers/log1p.html" title="log1p">log1p</a></p></td></tr></table></dd>
+<dt><span class="term">BOOST_MATH_ASSERT_UNDEFINED_POLICY</span></dt>
+<dd><table class="simplelist" border="0" summary="Simple list">
+<tr><td><p><a class="link" href="../math_toolkit/policy/pol_tutorial/changing_policy_defaults.html" title="Changing the Policy Defaults">Changing the Policy Defaults</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/policy/pol_ref/policy_defaults.html" title="Using macros to Change the Policy Defaults">Using macros to Change the Policy Defaults</a></p></td></tr>
+</table></dd>
+<dt><span class="term">BOOST_MATH_DECLARE_DISTRIBUTIONS</span></dt>
+<dd><table class="simplelist" border="0" summary="Simple list">
+<tr><td><p><a class="link" href="../math_toolkit/policy/pol_ref/namespace_pol.html" title="Setting Polices at Namespace Scope">Setting Polices at Namespace Scope</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/policy/pol_tutorial/namespace_policies.html" title="Setting Policies at Namespace or Translation Unit Scope">Setting Policies at Namespace or Translation Unit Scope</a></p></td></tr>
+</table></dd>
+<dt><span class="term">BOOST_MATH_DECLARE_SPECIAL_FUNCTIONS</span></dt>
+<dd><table class="simplelist" border="0" summary="Simple list">
+<tr><td><p><a class="link" href="../math_toolkit/policy/pol_tutorial/user_def_err_pol.html" title="Calling User Defined Error Handlers">Calling User Defined Error Handlers</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/policy/pol_ref/namespace_pol.html" title="Setting Polices at Namespace Scope">Setting Polices at Namespace Scope</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/policy/pol_tutorial/namespace_policies.html" title="Setting Policies at Namespace or Translation Unit Scope">Setting Policies at Namespace or Translation Unit Scope</a></p></td></tr>
+</table></dd>
+<dt><span class="term">BOOST_MATH_DENORM_ERROR_POLICY</span></dt>
+<dd><table class="simplelist" border="0" summary="Simple list"><tr><td><p><a class="link" href="../math_toolkit/policy/pol_ref/policy_defaults.html" title="Using macros to Change the Policy Defaults">Using macros to Change the Policy Defaults</a></p></td></tr></table></dd>
+<dt><span class="term">BOOST_MATH_DIGITS10_POLICY</span></dt>
+<dd><table class="simplelist" border="0" summary="Simple list"><tr><td><p><a class="link" href="../math_toolkit/policy/pol_ref/policy_defaults.html" title="Using macros to Change the Policy Defaults">Using macros to Change the Policy Defaults</a></p></td></tr></table></dd>
+<dt><span class="term">BOOST_MATH_DISCRETE_QUANTILE_POLICY</span></dt>
+<dd><table class="simplelist" border="0" summary="Simple list">
+<tr><td><p><a class="link" href="../math_toolkit/dist/stat_tut/weg/binom_eg/binomial_quiz_example.html" title="Binomial Quiz Example">Binomial Quiz Example</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/dist/stat_tut/weg/neg_binom_eg/negative_binomial_example1.html" title="Negative Binomial Sales Quota Example.">Negative Binomial Sales Quota Example.</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/policy/pol_ref/policy_defaults.html" title="Using macros to Change the Policy Defaults">Using macros to Change the Policy Defaults</a></p></td></tr>
+</table></dd>
+<dt><span class="term">BOOST_MATH_DOMAIN_ERROR_POLICY</span></dt>
+<dd><table class="simplelist" border="0" summary="Simple list">
+<tr><td><p><a class="link" href="../math_toolkit/backgrounders/implementation.html" title="Additional Implementation Notes">Additional Implementation Notes</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/policy/pol_tutorial/changing_policy_defaults.html" title="Changing the Policy Defaults">Changing the Policy Defaults</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/dist/stat_tut/weg/error_eg.html" title="Error Handling Example">Error Handling Example</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/policy/pol_ref/policy_defaults.html" title="Using macros to Change the Policy Defaults">Using macros to Change the Policy Defaults</a></p></td></tr>
+</table></dd>
+<dt><span class="term">BOOST_MATH_EVALUATION_ERROR_POLICY</span></dt>
+<dd><table class="simplelist" border="0" summary="Simple list"><tr><td><p><a class="link" href="../math_toolkit/policy/pol_ref/policy_defaults.html" title="Using macros to Change the Policy Defaults">Using macros to Change the Policy Defaults</a></p></td></tr></table></dd>
+<dt><span class="term">BOOST_MATH_INDETERMINATE_RESULT_ERROR_POLICY</span></dt>
+<dd><table class="simplelist" border="0" summary="Simple list"><tr><td><p><a class="link" href="../math_toolkit/policy/pol_ref/policy_defaults.html" title="Using macros to Change the Policy Defaults">Using macros to Change the Policy Defaults</a></p></td></tr></table></dd>
+<dt><span class="term">BOOST_MATH_INT_TABLE_TYPE</span></dt>
+<dd><table class="simplelist" border="0" summary="Simple list"><tr><td><p><a class="link" href="../math_toolkit/perf/tuning.html" title="Performance Tuning Macros">Performance Tuning Macros</a></p></td></tr></table></dd>
+<dt><span class="term">BOOST_MATH_MAX_POLY_ORDER</span></dt>
+<dd><table class="simplelist" border="0" summary="Simple list"><tr><td><p><a class="link" href="../math_toolkit/perf/tuning.html" title="Performance Tuning Macros">Performance Tuning Macros</a></p></td></tr></table></dd>
+<dt><span class="term">BOOST_MATH_MAX_ROOT_ITERATION_POLICY</span></dt>
+<dd><table class="simplelist" border="0" summary="Simple list">
+<tr><td><p><a class="link" href="../math_toolkit/policy/pol_ref/iteration_pol.html" title="Iteration Limits Policies">Iteration Limits Policies</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/policy/pol_ref/policy_defaults.html" title="Using macros to Change the Policy Defaults">Using macros to Change the Policy Defaults</a></p></td></tr>
+</table></dd>
+<dt><span class="term">BOOST_MATH_MAX_SERIES_ITERATION_POLICY</span></dt>
+<dd><table class="simplelist" border="0" summary="Simple list">
+<tr><td><p><a class="link" href="../math_toolkit/policy/pol_ref/iteration_pol.html" title="Iteration Limits Policies">Iteration Limits Policies</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/policy/pol_ref/policy_defaults.html" title="Using macros to Change the Policy Defaults">Using macros to Change the Policy Defaults</a></p></td></tr>
+</table></dd>
+<dt><span class="term">BOOST_MATH_NO_LONG_DOUBLE_MATH_FUNCTIONS</span></dt>
+<dd><table class="simplelist" border="0" summary="Simple list"><tr><td><p><a class="link" href="../math_toolkit/main_overview/compilers_overview.html" title="Compilers">Supported/Tested Compilers</a></p></td></tr></table></dd>
+<dt><span class="term">BOOST_MATH_OVERFLOW_ERROR_POLICY</span></dt>
+<dd><table class="simplelist" border="0" summary="Simple list">
+<tr><td><p><a class="link" href="../math_toolkit/policy/pol_tutorial/changing_policy_defaults.html" title="Changing the Policy Defaults">Changing the Policy Defaults</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/special/powers/ct_pow.html" title="Compile Time Power of a Runtime Base">Compile Time Power of a Runtime Base</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/dist/stat_tut/weg/error_eg.html" title="Error Handling Example">Error Handling Example</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/dist/stat_tut/weg/neg_binom_eg/negative_binomial_example1.html" title="Negative Binomial Sales Quota Example.">Negative Binomial Sales Quota Example.</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/policy/pol_ref/policy_defaults.html" title="Using macros to Change the Policy Defaults">Using macros to Change the Policy Defaults</a></p></td></tr>
+</table></dd>
+<dt><span class="term">BOOST_MATH_POLE_ERROR_POLICY</span></dt>
+<dd><table class="simplelist" border="0" summary="Simple list"><tr><td><p><a class="link" href="../math_toolkit/policy/pol_ref/policy_defaults.html" title="Using macros to Change the Policy Defaults">Using macros to Change the Policy Defaults</a></p></td></tr></table></dd>
+<dt><span class="term">BOOST_MATH_POLY_METHOD</span></dt>
+<dd><table class="simplelist" border="0" summary="Simple list"><tr><td><p><a class="link" href="../math_toolkit/perf/tuning.html" title="Performance Tuning Macros">Performance Tuning Macros</a></p></td></tr></table></dd>
+<dt><span class="term">BOOST_MATH_PROMOTE_DOUBLE_POLICY</span></dt>
+<dd><table class="simplelist" border="0" summary="Simple list">
+<tr><td><p><a class="link" href="../math_toolkit/perf/tuning.html" title="Performance Tuning Macros">Performance Tuning Macros</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/policy/pol_ref/policy_defaults.html" title="Using macros to Change the Policy Defaults">Using macros to Change the Policy Defaults</a></p></td></tr>
+</table></dd>
+<dt><span class="term">BOOST_MATH_PROMOTE_FLOAT_POLICY</span></dt>
+<dd><table class="simplelist" border="0" summary="Simple list"><tr><td><p><a class="link" href="../math_toolkit/policy/pol_ref/policy_defaults.html" title="Using macros to Change the Policy Defaults">Using macros to Change the Policy Defaults</a></p></td></tr></table></dd>
+<dt><span class="term">BOOST_MATH_RATIONAL_METHOD</span></dt>
+<dd><table class="simplelist" border="0" summary="Simple list"><tr><td><p><a class="link" href="../math_toolkit/perf/tuning.html" title="Performance Tuning Macros">Performance Tuning Macros</a></p></td></tr></table></dd>
+<dt><span class="term">BOOST_MATH_ROUNDING_ERROR_POLICY</span></dt>
+<dd><table class="simplelist" border="0" summary="Simple list"><tr><td><p><a class="link" href="../math_toolkit/policy/pol_ref/policy_defaults.html" title="Using macros to Change the Policy Defaults">Using macros to Change the Policy Defaults</a></p></td></tr></table></dd>
+<dt><span class="term">BOOST_MATH_UNDERFLOW_ERROR_POLICY</span></dt>
+<dd><table class="simplelist" border="0" summary="Simple list"><tr><td><p><a class="link" href="../math_toolkit/policy/pol_ref/policy_defaults.html" title="Using macros to Change the Policy Defaults">Using macros to Change the Policy Defaults</a></p></td></tr></table></dd>
+</dl></div></dd>
+<dt>
+<a name="idx_id_54"></a><span class="term">F</span>
+</dt>
+<dd><div class="variablelist"><dl>
+<dt><span class="term">FP_INFINITE</span></dt>
+<dd><table class="simplelist" border="0" summary="Simple list"><tr><td><p><a class="link" href="../math_toolkit/special/fpclass.html" title="Floating-Point Classification: Infinities and NaN's">Floating-Point Classification: Infinities and NaN's</a></p></td></tr></table></dd>
+<dt><span class="term">FP_NAN</span></dt>
+<dd><table class="simplelist" border="0" summary="Simple list"><tr><td><p><a class="link" href="../math_toolkit/special/fpclass.html" title="Floating-Point Classification: Infinities and NaN's">Floating-Point Classification: Infinities and NaN's</a></p></td></tr></table></dd>
+<dt><span class="term">FP_NORMAL</span></dt>
+<dd><table class="simplelist" border="0" summary="Simple list"><tr><td><p><a class="link" href="../math_toolkit/special/fpclass.html" title="Floating-Point Classification: Infinities and NaN's">Floating-Point Classification: Infinities and NaN's</a></p></td></tr></table></dd>
+<dt><span class="term">FP_SUBNORMAL</span></dt>
+<dd><table class="simplelist" border="0" summary="Simple list"><tr><td><p><a class="link" href="../math_toolkit/special/fpclass.html" title="Floating-Point Classification: Infinities and NaN's">Floating-Point Classification: Infinities and NaN's</a></p></td></tr></table></dd>
+<dt><span class="term">FP_ZERO</span></dt>
+<dd><table class="simplelist" border="0" summary="Simple list"><tr><td><p><a class="link" href="../math_toolkit/special/fpclass.html" title="Floating-Point Classification: Infinities and NaN's">Floating-Point Classification: Infinities and NaN's</a></p></td></tr></table></dd>
+</dl></div></dd>
+</dl></div>
+</div>
+<table xmlns:rev="http://www.cs.rpi.edu/~gregod/boost/tools/doc/revision" width="100%"><tr>
+<td align="left"></td>
+<td align="right"><div class="copyright-footer">Copyright © 2006 , 2007, 2008 John Maddock, Paul A. Bristow, Hubert
+      Holin, Xiaogang Zhang, Bruno Lalande and Gautam Sewani<p>
+        Distributed under the Boost Software License, Version 1.0. (See accompanying
+        file LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_0.txt)
+      </p>
+</div></td>
+</tr></table>
+<hr>
+<div class="spirit-nav">
+<a accesskey="p" href="s12.html"><img src="../../../doc/html/images/prev.png" alt="Prev"></a><a accesskey="u" href="../index.html"><img src="../../../doc/html/images/up.png" alt="Up"></a><a accesskey="h" href="../index.html"><img src="../../../doc/html/images/home.png" alt="Home"></a><a accesskey="n" href="s14.html"><img src="../../../doc/html/images/next.png" alt="Next"></a>
+</div>
+</body>
+</html>

Added: sandbox/tools/auto_index/example/math/doc/sf_and_dist/html/index/s14.html
==============================================================================
--- (empty file)
+++ sandbox/tools/auto_index/example/math/doc/sf_and_dist/html/index/s14.html	2008-11-28 05:25:28 EST (Fri, 28 Nov 2008)
@@ -0,0 +1,3663 @@
+<html>
+<head>
+<meta http-equiv="Content-Type" content="text/html; charset=ISO-8859-1">
+<title>Index</title>
+<link rel="stylesheet" href="../boostbook.css" type="text/css">
+<meta name="generator" content="DocBook XSL Stylesheets Vsnapshot_8125">
+<link rel="home" href="../index.html" title="Math Toolkit">
+<link rel="up" href="../index.html" title="Math Toolkit">
+<link rel="prev" href="s13.html" title="Macro Index">
+</head>
+<body bgcolor="white" text="black" link="#0000FF" vlink="#840084" alink="#0000FF">
+<table cellpadding="2" width="100%"><tr>
+<td valign="top"><img alt="Boost C++ Libraries" width="277" height="86" src="../../../boost.png"></td>
+<td align="center">Home</td>
+<td align="center">Libraries</td>
+<td align="center">People</td>
+<td align="center">FAQ</td>
+<td align="center">More</td>
+</tr></table>
+<hr>
+<div class="spirit-nav">
+<a accesskey="p" href="s13.html"><img src="../../../doc/html/images/prev.png" alt="Prev"></a><a accesskey="u" href="../index.html"><img src="../../../doc/html/images/up.png" alt="Up"></a><a accesskey="h" href="../index.html"><img src="../../../doc/html/images/home.png" alt="Home"></a>
+</div>
+<div class="section" lang="en">
+<div class="titlepage"><div><div><h2 class="title" style="clear: both">
+<a name="id940369"></a>Index</h2></div></div></div>
+<p><a class="link" href="s14.html#idx_id_55">A</a> <a class="link" href="s14.html#idx_id_56">B</a> <a class="link" href="s14.html#idx_id_57">C</a> <a class="link" href="s14.html#idx_id_58">D</a> <a class="link" href="s14.html#idx_id_59">E</a> <a class="link" href="s14.html#idx_id_60">F</a> <a class="link" href="s14.html#idx_id_61">G</a> <a class="link" href="s14.html#idx_id_62">H</a> <a class="link" href="s14.html#idx_id_63">I</a> <a class="link" href="s14.html#idx_id_64">K</a> <a class="link" href="s14.html#idx_id_65">L</a> <a class="link" href="s14.html#idx_id_66">M</a> <a class="link" href="s14.html#idx_id_67">N</a> <a class="link" href="s14.html#idx_id_68">O</a> <a class="link" href="s14.html#idx_id_69">P</a> <a class="link" href="s14.html#idx_id_70">Q</a> <a class="link" href="s14.html#idx_id_71">R</a> <a class="link" href="s14.html#idx_id_72">S</a> <a class="link" href="s14.html#idx_id_73">T</a> <a class="link" href="s14.html#idx_id_74">U</a> <a class="link" href="s14.html#idx_id_75">V</a> <a class="l
ink" href="s14.html#idx_id_76">W</a> <a class="link" href="s14.html#idx_id_77">Z</a> </p>
+<div class="variablelist"><dl>
+<dt>
+<a name="idx_id_55"></a><span class="term">A</span>
+</dt>
+<dd><div class="variablelist"><dl>
+<dt><span class="term">About the Math Toolkit</span></dt>
+<dd><table class="simplelist" border="0" summary="Simple list">
+<tr><td><p><a class="link" href="../math_toolkit/main_overview/intro.html" title="About the Math Toolkit">beta</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/main_overview/intro.html" title="About the Math Toolkit">binomial</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/main_overview/intro.html" title="About the Math Toolkit">digamma</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/main_overview/intro.html" title="About the Math Toolkit">erf</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/main_overview/intro.html" title="About the Math Toolkit">factorial</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/main_overview/intro.html" title="About the Math Toolkit">gamma</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/main_overview/intro.html" title="About the Math Toolkit">normal</a></p></td></tr>
+</table></dd>
+<dt><span class="term">acosh</span></dt>
+<dd><table class="simplelist" border="0" summary="Simple list">
+<tr><td><p><a class="link" href="../math_toolkit/special/inv_hyper/acosh.html" title="acosh">acosh</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/main_overview/tr1.html" title="C99 and TR1 C Functions">C99 and TR1 C Functions</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/special/extern_c/tr1.html" title="C99 and TR1 C Functions Overview">C99 and TR1 C Functions Overview</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/special/extern_c/c99.html" title="C99 C Functions">C99 C Functions</a></p></td></tr>
+</table></dd>
+<dt><span class="term">Advancing a Floating Point Value by a Specific Representation Distance (ULP) float_advance</span></dt>
+<dd><table class="simplelist" border="0" summary="Simple list">
+<tr><td><p><a class="link" href="../math_toolkit/special/next_float/float_advance.html" title="Advancing a Floating Point Value by a Specific Representation Distance (ULP) float_advance">float_advance</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/special/next_float/float_advance.html" title="Advancing a Floating Point Value by a Specific Representation Distance (ULP) float_advance">float_distance</a></p></td></tr>
+</table></dd>
+<dt><span class="term">asinh</span></dt>
+<dd><table class="simplelist" border="0" summary="Simple list">
+<tr><td><p><a class="link" href="../math_toolkit/special/inv_hyper/asinh.html" title="asinh">asinh</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/main_overview/tr1.html" title="C99 and TR1 C Functions">C99 and TR1 C Functions</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/special/extern_c/tr1.html" title="C99 and TR1 C Functions Overview">C99 and TR1 C Functions Overview</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/special/extern_c/c99.html" title="C99 C Functions">C99 C Functions</a></p></td></tr>
+</table></dd>
+<dt><span class="term">assert_undefined_type</span></dt>
+<dd><table class="simplelist" border="0" summary="Simple list"><tr><td><p><a class="link" href="../math_toolkit/policy/pol_ref/pol_ref_ref.html" title="Policy Class Reference">Policy Class Reference</a></p></td></tr></table></dd>
+<dt><span class="term">atanh</span></dt>
+<dd><table class="simplelist" border="0" summary="Simple list">
+<tr><td><p><a class="link" href="../math_toolkit/special/inv_hyper/atanh.html" title="atanh">atanh</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/main_overview/tr1.html" title="C99 and TR1 C Functions">C99 and TR1 C Functions</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/special/extern_c/tr1.html" title="C99 and TR1 C Functions Overview">C99 and TR1 C Functions Overview</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/special/extern_c/c99.html" title="C99 C Functions">C99 C Functions</a></p></td></tr>
+</table></dd>
+</dl></div></dd>
+<dt>
+<a name="idx_id_56"></a><span class="term">B</span>
+</dt>
+<dd><div class="variablelist"><dl>
+<dt><span class="term">bernoulli</span></dt>
+<dd><table class="simplelist" border="0" summary="Simple list"><tr><td><p><a class="link" href="../math_toolkit/dist/dist_ref/dists/bernoulli_dist.html" title="Bernoulli Distribution">Bernoulli Distribution</a></p></td></tr></table></dd>
+<dt><span class="term">Bernoulli Distribution</span></dt>
+<dd><table class="simplelist" border="0" summary="Simple list">
+<tr><td><p><a class="link" href="../math_toolkit/dist/dist_ref/dists/bernoulli_dist.html" title="Bernoulli Distribution">bernoulli</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/dist/dist_ref/dists/bernoulli_dist.html" title="Bernoulli Distribution">bernoulli_distribution</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/dist/dist_ref/dists/bernoulli_dist.html" title="Bernoulli Distribution">binomial</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/dist/dist_ref/dists/bernoulli_dist.html" title="Bernoulli Distribution">binomial_distribution</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/dist/dist_ref/dists/bernoulli_dist.html" title="Bernoulli Distribution">cdf</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/dist/dist_ref/dists/bernoulli_dist.html" title="Bernoulli Distribution">kurtosis</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/dist/dist_ref/dists/bernoulli_dist.html" title="Bernoulli Distribution">kurtosis_excess</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/dist/dist_ref/dists/bernoulli_dist.html" title="Bernoulli Distribution">mean</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/dist/dist_ref/dists/bernoulli_dist.html" title="Bernoulli Distribution">median</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/dist/dist_ref/dists/bernoulli_dist.html" title="Bernoulli Distribution">mode</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/dist/dist_ref/dists/bernoulli_dist.html" title="Bernoulli Distribution">pdf</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/dist/dist_ref/dists/bernoulli_dist.html" title="Bernoulli Distribution">policy_type</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/dist/dist_ref/dists/bernoulli_dist.html" title="Bernoulli Distribution">quantile</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/dist/dist_ref/dists/bernoulli_dist.html" title="Bernoulli Distribution">skewness</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/dist/dist_ref/dists/bernoulli_dist.html" title="Bernoulli Distribution">value_type</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/dist/dist_ref/dists/bernoulli_dist.html" title="Bernoulli Distribution">variance</a></p></td></tr>
+</table></dd>
+<dt><span class="term">bernoulli_distribution</span></dt>
+<dd><table class="simplelist" border="0" summary="Simple list"><tr><td><p><a class="link" href="../math_toolkit/dist/dist_ref/dists/bernoulli_dist.html" title="Bernoulli Distribution">Bernoulli Distribution</a></p></td></tr></table></dd>
+<dt><span class="term">Bessel Function Overview</span></dt>
+<dd><table class="simplelist" border="0" summary="Simple list">
+<tr><td><p><a class="link" href="../math_toolkit/special/bessel/bessel_over.html" title="Bessel Function Overview">cyl_bessel_i</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/special/bessel/bessel_over.html" title="Bessel Function Overview">cyl_bessel_j</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/special/bessel/bessel_over.html" title="Bessel Function Overview">cyl_bessel_k</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/special/bessel/bessel_over.html" title="Bessel Function Overview">cyl_neumann</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/special/bessel/bessel_over.html" title="Bessel Function Overview">sph_bessel</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/special/bessel/bessel_over.html" title="Bessel Function Overview">sph_neumann</a></p></td></tr>
+</table></dd>
+<dt><span class="term">Bessel Functions of the First and Second Kinds</span></dt>
+<dd><table class="simplelist" border="0" summary="Simple list">
+<tr><td><p><a class="link" href="../math_toolkit/special/bessel/bessel.html" title="Bessel Functions of the First and Second Kinds">cyl_bessel_j</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/special/bessel/bessel.html" title="Bessel Functions of the First and Second Kinds">cyl_neumann</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/special/bessel/bessel.html" title="Bessel Functions of the First and Second Kinds">gamma</a></p></td></tr>
+</table></dd>
+<dt><span class="term">beta</span></dt>
+<dd><table class="simplelist" border="0" summary="Simple list">
+<tr><td><p><a class="link" href="../math_toolkit/main_overview/intro.html" title="About the Math Toolkit">About the Math Toolkit</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/backgrounders/implementation.html" title="Additional Implementation Notes">Additional Implementation Notes</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/special/sf_beta/beta_function.html" title="Beta">beta</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/dist/dist_ref/dists/beta_dist.html" title="Beta Distribution">Beta Distribution</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/special/factorials/sf_binomial.html" title="Binomial Coefficients">Binomial Coefficients</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/dist/dist_ref/dists/binomial_dist.html" title="Binomial Distribution">Binomial Distribution</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/main_overview/tr1.html" title="C99 and TR1 C Functions">C99 and TR1 C Functions</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/special/extern_c/tr1.html" title="C99 and TR1 C Functions Overview">C99 and TR1 C Functions Overview</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/dist/dist_ref/dists/chi_squared_dist.html" title="Chi Squared Distribution">Chi Squared Distribution</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/using_udt/concepts.html" title="Conceptual Requirements for Real Number Types">Conceptual Requirements for Real Number Types</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/status/credits.html" title="Credits and Acknowledgements">Credits and Acknowledgements</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/special/sf_beta/beta_derivative.html" title="Derivative of the Incomplete Beta Function">Derivative of the Incomplete Beta Function</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/main_overview/directories.html" title="Directory and File Structure">Directory and File Structure</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/dist/stat_tut/weg/dist_construct_eg.html" title="Distribution Construction Example">Distribution Construction Example</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/special/sf_beta/ibeta_function.html" title="Incomplete Beta Functions">Errors In the Function beta(a, b, x)</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/dist/stat_tut/weg/st_eg/tut_mean_size.html" title="Estimating how large a sample size would have to become in order to give a significant Students-t test result with a single sample test">Estimating how large a sample size would have to become in order to give a significant Students-t test result with a single sample test</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/dist/stat_tut/weg/cs_eg/chi_sq_size.html" title="Estimating the Required Sample Sizes for a Chi-Square Test for the Standard Deviation">Estimating the Required Sample Sizes for a Chi-Square Test for the Standard Deviation</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/dist/dist_ref/dists/f_dist.html" title="F Distribution">F Distribution</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/special/sf_beta/beta_function.html" title="Beta">gamma</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/toolkit/internals2/test_data.html" title="Graphing, Profiling, and Generating Test Data for Special Functions">Graphing, Profiling, and Generating Test Data for Special Functions</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/main_overview/history1.html" title="History and What's New">History and What's New</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/special/sf_beta/ibeta_function.html" title="Incomplete Beta Functions">Incomplete Beta Functions</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/special/sf_beta/beta_function.html" title="Beta">Lanczos approximation</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/dist/dist_ref/dists/negative_binomial_dist.html" title="Negative Binomial Distribution">Negative Binomial Distribution</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/dist/dist_ref/dists/nc_beta_dist.html" title="Noncentral Beta Distribution">Noncentral Beta Distribution</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/dist/dist_ref/dists/nc_f_dist.html" title="Noncentral F Distribution">Noncentral F Distribution</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/dist/dist_ref/dists/nc_t_dist.html" title="Noncentral T Distribution">Noncentral T Distribution</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/dist/stat_tut/overview.html" title="Overview">Overview</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/special/sf_gamma/gamma_ratios.html" title="Ratios of Gamma Functions">Ratios of Gamma Functions</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/special/sf_beta/beta_function.html" title="Beta">RR</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/dist/dist_ref/dists/students_t_dist.html" title="Students t Distribution">Students t Distribution</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/dist/stat_tut/weg/nccs_eg/nccs_power_eg.html" title="Tables of the power function of the &#967;2 test.">Tables of the power function of the &#967; 2 test.</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/special/sf_beta/ibeta_inv_function.html" title="The Incomplete Beta Function Inverses">The Incomplete Beta Function Inverses</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/backgrounders/lanczos.html" title="The Lanczos Approximation">The Lanczos Approximation</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/special/extern_c/tr1_ref.html" title="TR1 C Functions Quick Reference">TR1 C Functions Quick Reference</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/dist/dist_ref/dists/triangular_dist.html" title="Triangular Distribution">Triangular Distribution</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/dist/dist_ref/dists/weibull.html" title="Weibull Distribution">Weibull Distribution</a></p></td></tr>
+</table></dd>
+<dt><span class="term">Beta Distribution</span></dt>
+<dd><table class="simplelist" border="0" summary="Simple list">
+<tr><td><p><a class="link" href="../math_toolkit/dist/dist_ref/dists/beta_dist.html" title="Beta Distribution">beta</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/dist/dist_ref/dists/beta_dist.html" title="Beta Distribution">beta_distribution</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/dist/dist_ref/dists/beta_dist.html" title="Beta Distribution">binomial</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/dist/dist_ref/dists/beta_dist.html" title="Beta Distribution">cdf</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/dist/dist_ref/dists/beta_dist.html" title="Beta Distribution">ibeta</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/dist/dist_ref/dists/beta_dist.html" title="Beta Distribution">ibetac</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/dist/dist_ref/dists/beta_dist.html" title="Beta Distribution">ibetac_inv</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/dist/dist_ref/dists/beta_dist.html" title="Beta Distribution">ibeta_derivative</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/dist/dist_ref/dists/beta_dist.html" title="Beta Distribution">ibeta_inv</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/dist/dist_ref/dists/beta_dist.html" title="Beta Distribution">ibeta_inva</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/dist/dist_ref/dists/beta_dist.html" title="Beta Distribution">ibeta_invb</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/dist/dist_ref/dists/beta_dist.html" title="Beta Distribution">kurtosis</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/dist/dist_ref/dists/beta_dist.html" title="Beta Distribution">kurtosis_excess</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/dist/dist_ref/dists/beta_dist.html" title="Beta Distribution">mean</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/dist/dist_ref/dists/beta_dist.html" title="Beta Distribution">median</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/dist/dist_ref/dists/beta_dist.html" title="Beta Distribution">mode</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/dist/dist_ref/dists/beta_dist.html" title="Beta Distribution">pdf</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/dist/dist_ref/dists/beta_dist.html" title="Beta Distribution">policy_type</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/dist/dist_ref/dists/beta_dist.html" title="Beta Distribution">quantile</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/dist/dist_ref/dists/beta_dist.html" title="Beta Distribution">skewness</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/dist/dist_ref/dists/beta_dist.html" title="Beta Distribution">triangular</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/dist/dist_ref/dists/beta_dist.html" title="Beta Distribution">uniform</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/dist/dist_ref/dists/beta_dist.html" title="Beta Distribution">value_type</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/dist/dist_ref/dists/beta_dist.html" title="Beta Distribution">variance</a></p></td></tr>
+</table></dd>
+<dt><span class="term">betac</span></dt>
+<dd><table class="simplelist" border="0" summary="Simple list">
+<tr><td><p><a class="link" href="../math_toolkit/special/sf_beta/ibeta_function.html" title="Incomplete Beta Functions">Errors In the Function betac(a,b,x)</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/special/sf_beta/ibeta_function.html" title="Incomplete Beta Functions">Incomplete Beta Functions</a></p></td></tr>
+</table></dd>
+<dt><span class="term">beta_distribution</span></dt>
+<dd><table class="simplelist" border="0" summary="Simple list">
+<tr><td><p><a class="link" href="../math_toolkit/dist/dist_ref/dists/beta_dist.html" title="Beta Distribution">Beta Distribution</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/dist/stat_tut/weg/dist_construct_eg.html" title="Distribution Construction Example">Distribution Construction Example</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/dist/stat_tut/overview.html" title="Overview">Overview</a></p></td></tr>
+</table></dd>
+<dt><span class="term">binomial</span></dt>
+<dd><table class="simplelist" border="0" summary="Simple list">
+<tr><td><p><a class="link" href="../math_toolkit/main_overview/intro.html" title="About the Math Toolkit">About the Math Toolkit</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/backgrounders/implementation.html" title="Additional Implementation Notes">Additional Implementation Notes</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/dist/dist_ref/dists/bernoulli_dist.html" title="Bernoulli Distribution">Bernoulli Distribution</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/dist/dist_ref/dists/beta_dist.html" title="Beta Distribution">Beta Distribution</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/special/factorials/sf_binomial.html" title="Binomial Coefficients">Binomial Coefficients</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/dist/stat_tut/weg/binom_eg/binomial_coinflip_example.html" title="Binomial Coin-Flipping Example">Binomial Coin-Flipping Example</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/dist/dist_ref/dists/binomial_dist.html" title="Binomial Distribution">Binomial Distribution</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/dist/stat_tut/weg/binom_eg/binomial_quiz_example.html" title="Binomial Quiz Example">Binomial Quiz Example</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/dist/stat_tut/weg/binom_eg/binom_conf.html" title="Calculating Confidence Limits on the Frequency of Occurrence for a Binomial Distribution">Calculating Confidence Limits on the Frequency of Occurrence for a Binomial Distribution</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/dist/stat_tut/weg/neg_binom_eg/neg_binom_conf.html" title="Calculating Confidence Limits on the Frequency of Occurrence for the Negative Binomial Distribution">Calculating Confidence Limits on the Frequency of Occurrence for the Negative Binomial Distribution</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/dist/stat_tut/weg/nag_library.html" title="Comparison with C, R, FORTRAN-style Free Functions">Comparison with C, R, FORTRAN-style Free Functions</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/main_overview/pol_overview.html" title="Configuration and Policies">Configuration and Policies</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/dist/stat_tut/dist_params.html" title="Discrete Probability Distributions">Discrete Probability Distributions</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/dist/stat_tut/weg/dist_construct_eg.html" title="Distribution Construction Example">Distribution Construction Example</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/dist/stat_tut/weg/binom_eg/binom_size_eg.html" title="Estimating Sample Sizes for a Binomial Distribution.">Estimating Sample Sizes for a Binomial Distribution.</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/dist/stat_tut/weg/neg_binom_eg/neg_binom_size_eg.html" title="Estimating Sample Sizes for the Negative Binomial.">Estimating Sample Sizes for the Negative Binomial.</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/special/sf_beta/ibeta_function.html" title="Incomplete Beta Functions">Incomplete Beta Functions</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/dist/dist_ref/dists/binomial_dist.html" title="Binomial Distribution">Meaning of the non-member accessors</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/dist/dist_ref/dists/negative_binomial_dist.html" title="Negative Binomial Distribution">Negative Binomial Distribution</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/dist/stat_tut/weg/neg_binom_eg/negative_binomial_example1.html" title="Negative Binomial Sales Quota Example.">Negative Binomial Sales Quota Example.</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/dist/stat_tut/overview.html" title="Overview">Overview</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/policy/pol_overview.html" title="Policy Overview">Policy Overview</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/dist/stat_tut/variates.html" title="Random Variates and Distribution Parameters">Random Variates and Distribution Parameters</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/policy/pol_tutorial/namespace_policies.html" title="Setting Policies at Namespace or Translation Unit Scope">Setting Policies at Namespace or Translation Unit Scope</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/policy/pol_tutorial/ad_hoc_dist_policies.html" title="Setting Policies for Distributions on an Ad Hoc Basis">Setting Policies for Distributions on an Ad Hoc Basis</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/special/sf_beta/ibeta_inv_function.html" title="The Incomplete Beta Function Inverses">The Incomplete Beta Function Inverses</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/policy/pol_tutorial/understand_dis_quant.html" title="Understanding Quantiles of Discrete Distributions">Understanding Quantiles of Discrete Distributions</a></p></td></tr>
+</table></dd>
+<dt><span class="term">Binomial Coefficients</span></dt>
+<dd><table class="simplelist" border="0" summary="Simple list">
+<tr><td><p><a class="link" href="../math_toolkit/special/factorials/sf_binomial.html" title="Binomial Coefficients">beta</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/special/factorials/sf_binomial.html" title="Binomial Coefficients">binomial</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/special/factorials/sf_binomial.html" title="Binomial Coefficients">binomial_coefficient</a></p></td></tr>
+</table></dd>
+<dt><span class="term">Binomial Distribution</span></dt>
+<dd><table class="simplelist" border="0" summary="Simple list">
+<tr><td><p><a class="link" href="../math_toolkit/dist/dist_ref/dists/binomial_dist.html" title="Binomial Distribution">beta</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/dist/dist_ref/dists/binomial_dist.html" title="Binomial Distribution">binomial</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/dist/dist_ref/dists/binomial_dist.html" title="Binomial Distribution">binomial_distribution</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/dist/dist_ref/dists/binomial_dist.html" title="Binomial Distribution">cdf</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/dist/dist_ref/dists/binomial_dist.html" title="Binomial Distribution">find_lower_bound_on_p</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/dist/dist_ref/dists/binomial_dist.html" title="Binomial Distribution">find_upper_bound_on_p</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/dist/dist_ref/dists/binomial_dist.html" title="Binomial Distribution">ibeta</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/dist/dist_ref/dists/binomial_dist.html" title="Binomial Distribution">ibetac</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/dist/dist_ref/dists/binomial_dist.html" title="Binomial Distribution">ibetac_inv</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/dist/dist_ref/dists/binomial_dist.html" title="Binomial Distribution">ibetac_invb</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/dist/dist_ref/dists/binomial_dist.html" title="Binomial Distribution">ibeta_derivative</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/dist/dist_ref/dists/binomial_dist.html" title="Binomial Distribution">ibeta_inv</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/dist/dist_ref/dists/binomial_dist.html" title="Binomial Distribution">kurtosis</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/dist/dist_ref/dists/binomial_dist.html" title="Binomial Distribution">kurtosis_excess</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/dist/dist_ref/dists/binomial_dist.html" title="Binomial Distribution">mean</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/dist/dist_ref/dists/binomial_dist.html" title="Binomial Distribution">median</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/dist/dist_ref/dists/binomial_dist.html" title="Binomial Distribution">mode</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/dist/dist_ref/dists/binomial_dist.html" title="Binomial Distribution">normal</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/dist/dist_ref/dists/binomial_dist.html" title="Binomial Distribution">pdf</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/dist/dist_ref/dists/binomial_dist.html" title="Binomial Distribution">policy_type</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/dist/dist_ref/dists/binomial_dist.html" title="Binomial Distribution">quantile</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/dist/dist_ref/dists/binomial_dist.html" title="Binomial Distribution">skewness</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/dist/dist_ref/dists/binomial_dist.html" title="Binomial Distribution">value_type</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/dist/dist_ref/dists/binomial_dist.html" title="Binomial Distribution">variance</a></p></td></tr>
+</table></dd>
+<dt><span class="term">binomial_coefficient</span></dt>
+<dd><table class="simplelist" border="0" summary="Simple list"><tr><td><p><a class="link" href="../math_toolkit/special/factorials/sf_binomial.html" title="Binomial Coefficients">Binomial Coefficients</a></p></td></tr></table></dd>
+<dt><span class="term">binomial_distribution</span></dt>
+<dd><table class="simplelist" border="0" summary="Simple list">
+<tr><td><p><a class="link" href="../math_toolkit/dist/dist_ref/dists/bernoulli_dist.html" title="Bernoulli Distribution">Bernoulli Distribution</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/dist/dist_ref/dists/binomial_dist.html" title="Binomial Distribution">Binomial Distribution</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/dist/stat_tut/weg/binom_eg/binomial_quiz_example.html" title="Binomial Quiz Example">Binomial Quiz Example</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/dist/stat_tut/weg/binom_eg/binom_conf.html" title="Calculating Confidence Limits on the Frequency of Occurrence for a Binomial Distribution">Calculating Confidence Limits on the Frequency of Occurrence for a Binomial Distribution</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/dist/stat_tut/weg/dist_construct_eg.html" title="Distribution Construction Example">Distribution Construction Example</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/dist/stat_tut/overview.html" title="Overview">Overview</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/dist/stat_tut/variates.html" title="Random Variates and Distribution Parameters">Random Variates and Distribution Parameters</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/policy/pol_tutorial/ad_hoc_dist_policies.html" title="Setting Policies for Distributions on an Ad Hoc Basis">Setting Policies for Distributions on an Ad Hoc Basis</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/policy/pol_tutorial/understand_dis_quant.html" title="Understanding Quantiles of Discrete Distributions">Understanding Quantiles of Discrete Distributions</a></p></td></tr>
+</table></dd>
+<dt><span class="term">BOOST_DEFINE_MATH_CONSTANT</span></dt>
+<dd><table class="simplelist" border="0" summary="Simple list"><tr><td><p><a class="link" href="../math_toolkit/backgrounders/implementation.html" title="Additional Implementation Notes">Additional Implementation Notes</a></p></td></tr></table></dd>
+<dt><span class="term">BOOST_HAS_LOG1P</span></dt>
+<dd><table class="simplelist" border="0" summary="Simple list"><tr><td><p><a class="link" href="../math_toolkit/special/powers/log1p.html" title="log1p">log1p</a></p></td></tr></table></dd>
+<dt><span class="term">BOOST_MATH_ASSERT_UNDEFINED_POLICY</span></dt>
+<dd><table class="simplelist" border="0" summary="Simple list">
+<tr><td><p><a class="link" href="../math_toolkit/policy/pol_tutorial/changing_policy_defaults.html" title="Changing the Policy Defaults">Changing the Policy Defaults</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/policy/pol_ref/policy_defaults.html" title="Using macros to Change the Policy Defaults">Using macros to Change the Policy Defaults</a></p></td></tr>
+</table></dd>
+<dt><span class="term">BOOST_MATH_DECLARE_DISTRIBUTIONS</span></dt>
+<dd><table class="simplelist" border="0" summary="Simple list">
+<tr><td><p><a class="link" href="../math_toolkit/policy/pol_ref/namespace_pol.html" title="Setting Polices at Namespace Scope">Setting Polices at Namespace Scope</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/policy/pol_tutorial/namespace_policies.html" title="Setting Policies at Namespace or Translation Unit Scope">Setting Policies at Namespace or Translation Unit Scope</a></p></td></tr>
+</table></dd>
+<dt><span class="term">BOOST_MATH_DECLARE_SPECIAL_FUNCTIONS</span></dt>
+<dd><table class="simplelist" border="0" summary="Simple list">
+<tr><td><p><a class="link" href="../math_toolkit/policy/pol_tutorial/user_def_err_pol.html" title="Calling User Defined Error Handlers">Calling User Defined Error Handlers</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/policy/pol_ref/namespace_pol.html" title="Setting Polices at Namespace Scope">Setting Polices at Namespace Scope</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/policy/pol_tutorial/namespace_policies.html" title="Setting Policies at Namespace or Translation Unit Scope">Setting Policies at Namespace or Translation Unit Scope</a></p></td></tr>
+</table></dd>
+<dt><span class="term">BOOST_MATH_DENORM_ERROR_POLICY</span></dt>
+<dd><table class="simplelist" border="0" summary="Simple list"><tr><td><p><a class="link" href="../math_toolkit/policy/pol_ref/policy_defaults.html" title="Using macros to Change the Policy Defaults">Using macros to Change the Policy Defaults</a></p></td></tr></table></dd>
+<dt><span class="term">BOOST_MATH_DIGITS10_POLICY</span></dt>
+<dd><table class="simplelist" border="0" summary="Simple list"><tr><td><p><a class="link" href="../math_toolkit/policy/pol_ref/policy_defaults.html" title="Using macros to Change the Policy Defaults">Using macros to Change the Policy Defaults</a></p></td></tr></table></dd>
+<dt><span class="term">BOOST_MATH_DISCRETE_QUANTILE_POLICY</span></dt>
+<dd><table class="simplelist" border="0" summary="Simple list">
+<tr><td><p><a class="link" href="../math_toolkit/dist/stat_tut/weg/binom_eg/binomial_quiz_example.html" title="Binomial Quiz Example">Binomial Quiz Example</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/dist/stat_tut/weg/neg_binom_eg/negative_binomial_example1.html" title="Negative Binomial Sales Quota Example.">Negative Binomial Sales Quota Example.</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/policy/pol_ref/policy_defaults.html" title="Using macros to Change the Policy Defaults">Using macros to Change the Policy Defaults</a></p></td></tr>
+</table></dd>
+<dt><span class="term">BOOST_MATH_DOMAIN_ERROR_POLICY</span></dt>
+<dd><table class="simplelist" border="0" summary="Simple list">
+<tr><td><p><a class="link" href="../math_toolkit/backgrounders/implementation.html" title="Additional Implementation Notes">Additional Implementation Notes</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/policy/pol_tutorial/changing_policy_defaults.html" title="Changing the Policy Defaults">Changing the Policy Defaults</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/dist/stat_tut/weg/error_eg.html" title="Error Handling Example">Error Handling Example</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/policy/pol_ref/policy_defaults.html" title="Using macros to Change the Policy Defaults">Using macros to Change the Policy Defaults</a></p></td></tr>
+</table></dd>
+<dt><span class="term">BOOST_MATH_EVALUATION_ERROR_POLICY</span></dt>
+<dd><table class="simplelist" border="0" summary="Simple list"><tr><td><p><a class="link" href="../math_toolkit/policy/pol_ref/policy_defaults.html" title="Using macros to Change the Policy Defaults">Using macros to Change the Policy Defaults</a></p></td></tr></table></dd>
+<dt><span class="term">BOOST_MATH_INDETERMINATE_RESULT_ERROR_POLICY</span></dt>
+<dd><table class="simplelist" border="0" summary="Simple list"><tr><td><p><a class="link" href="../math_toolkit/policy/pol_ref/policy_defaults.html" title="Using macros to Change the Policy Defaults">Using macros to Change the Policy Defaults</a></p></td></tr></table></dd>
+<dt><span class="term">BOOST_MATH_INT_TABLE_TYPE</span></dt>
+<dd><table class="simplelist" border="0" summary="Simple list"><tr><td><p><a class="link" href="../math_toolkit/perf/tuning.html" title="Performance Tuning Macros">Performance Tuning Macros</a></p></td></tr></table></dd>
+<dt><span class="term">BOOST_MATH_MAX_POLY_ORDER</span></dt>
+<dd><table class="simplelist" border="0" summary="Simple list"><tr><td><p><a class="link" href="../math_toolkit/perf/tuning.html" title="Performance Tuning Macros">Performance Tuning Macros</a></p></td></tr></table></dd>
+<dt><span class="term">BOOST_MATH_MAX_ROOT_ITERATION_POLICY</span></dt>
+<dd><table class="simplelist" border="0" summary="Simple list">
+<tr><td><p><a class="link" href="../math_toolkit/policy/pol_ref/iteration_pol.html" title="Iteration Limits Policies">Iteration Limits Policies</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/policy/pol_ref/policy_defaults.html" title="Using macros to Change the Policy Defaults">Using macros to Change the Policy Defaults</a></p></td></tr>
+</table></dd>
+<dt><span class="term">BOOST_MATH_MAX_SERIES_ITERATION_POLICY</span></dt>
+<dd><table class="simplelist" border="0" summary="Simple list">
+<tr><td><p><a class="link" href="../math_toolkit/policy/pol_ref/iteration_pol.html" title="Iteration Limits Policies">Iteration Limits Policies</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/policy/pol_ref/policy_defaults.html" title="Using macros to Change the Policy Defaults">Using macros to Change the Policy Defaults</a></p></td></tr>
+</table></dd>
+<dt><span class="term">BOOST_MATH_NO_LONG_DOUBLE_MATH_FUNCTIONS</span></dt>
+<dd><table class="simplelist" border="0" summary="Simple list"><tr><td><p><a class="link" href="../math_toolkit/main_overview/compilers_overview.html" title="Compilers">Supported/Tested Compilers</a></p></td></tr></table></dd>
+<dt><span class="term">BOOST_MATH_OVERFLOW_ERROR_POLICY</span></dt>
+<dd><table class="simplelist" border="0" summary="Simple list">
+<tr><td><p><a class="link" href="../math_toolkit/policy/pol_tutorial/changing_policy_defaults.html" title="Changing the Policy Defaults">Changing the Policy Defaults</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/special/powers/ct_pow.html" title="Compile Time Power of a Runtime Base">Compile Time Power of a Runtime Base</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/dist/stat_tut/weg/error_eg.html" title="Error Handling Example">Error Handling Example</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/dist/stat_tut/weg/neg_binom_eg/negative_binomial_example1.html" title="Negative Binomial Sales Quota Example.">Negative Binomial Sales Quota Example.</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/policy/pol_ref/policy_defaults.html" title="Using macros to Change the Policy Defaults">Using macros to Change the Policy Defaults</a></p></td></tr>
+</table></dd>
+<dt><span class="term">BOOST_MATH_POLE_ERROR_POLICY</span></dt>
+<dd><table class="simplelist" border="0" summary="Simple list"><tr><td><p><a class="link" href="../math_toolkit/policy/pol_ref/policy_defaults.html" title="Using macros to Change the Policy Defaults">Using macros to Change the Policy Defaults</a></p></td></tr></table></dd>
+<dt><span class="term">BOOST_MATH_POLY_METHOD</span></dt>
+<dd><table class="simplelist" border="0" summary="Simple list"><tr><td><p><a class="link" href="../math_toolkit/perf/tuning.html" title="Performance Tuning Macros">Performance Tuning Macros</a></p></td></tr></table></dd>
+<dt><span class="term">BOOST_MATH_PROMOTE_DOUBLE_POLICY</span></dt>
+<dd><table class="simplelist" border="0" summary="Simple list">
+<tr><td><p><a class="link" href="../math_toolkit/perf/tuning.html" title="Performance Tuning Macros">Performance Tuning Macros</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/policy/pol_ref/policy_defaults.html" title="Using macros to Change the Policy Defaults">Using macros to Change the Policy Defaults</a></p></td></tr>
+</table></dd>
+<dt><span class="term">BOOST_MATH_PROMOTE_FLOAT_POLICY</span></dt>
+<dd><table class="simplelist" border="0" summary="Simple list"><tr><td><p><a class="link" href="../math_toolkit/policy/pol_ref/policy_defaults.html" title="Using macros to Change the Policy Defaults">Using macros to Change the Policy Defaults</a></p></td></tr></table></dd>
+<dt><span class="term">BOOST_MATH_RATIONAL_METHOD</span></dt>
+<dd><table class="simplelist" border="0" summary="Simple list"><tr><td><p><a class="link" href="../math_toolkit/perf/tuning.html" title="Performance Tuning Macros">Performance Tuning Macros</a></p></td></tr></table></dd>
+<dt><span class="term">BOOST_MATH_ROUNDING_ERROR_POLICY</span></dt>
+<dd><table class="simplelist" border="0" summary="Simple list"><tr><td><p><a class="link" href="../math_toolkit/policy/pol_ref/policy_defaults.html" title="Using macros to Change the Policy Defaults">Using macros to Change the Policy Defaults</a></p></td></tr></table></dd>
+<dt><span class="term">BOOST_MATH_UNDERFLOW_ERROR_POLICY</span></dt>
+<dd><table class="simplelist" border="0" summary="Simple list"><tr><td><p><a class="link" href="../math_toolkit/policy/pol_ref/policy_defaults.html" title="Using macros to Change the Policy Defaults">Using macros to Change the Policy Defaults</a></p></td></tr></table></dd>
+</dl></div></dd>
+<dt>
+<a name="idx_id_57"></a><span class="term">C</span>
+</dt>
+<dd><div class="variablelist"><dl>
+<dt><span class="term">C99 and TR1 C Functions</span></dt>
+<dd><table class="simplelist" border="0" summary="Simple list">
+<tr><td><p><a class="link" href="../math_toolkit/main_overview/tr1.html" title="C99 and TR1 C Functions">acosh</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/main_overview/tr1.html" title="C99 and TR1 C Functions">asinh</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/main_overview/tr1.html" title="C99 and TR1 C Functions">atanh</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/main_overview/tr1.html" title="C99 and TR1 C Functions">beta</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/main_overview/tr1.html" title="C99 and TR1 C Functions">cbrt</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/main_overview/tr1.html" title="C99 and TR1 C Functions">comp_ellint_2</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/main_overview/tr1.html" title="C99 and TR1 C Functions">comp_ellint_3</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/main_overview/tr1.html" title="C99 and TR1 C Functions">cyl_bessel_i</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/main_overview/tr1.html" title="C99 and TR1 C Functions">cyl_bessel_j</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/main_overview/tr1.html" title="C99 and TR1 C Functions">cyl_bessel_k</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/main_overview/tr1.html" title="C99 and TR1 C Functions">cyl_neumann</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/main_overview/tr1.html" title="C99 and TR1 C Functions">double_t</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/main_overview/tr1.html" title="C99 and TR1 C Functions">ellint_1</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/main_overview/tr1.html" title="C99 and TR1 C Functions">ellint_2</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/main_overview/tr1.html" title="C99 and TR1 C Functions">ellint_3</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/main_overview/tr1.html" title="C99 and TR1 C Functions">erf</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/main_overview/tr1.html" title="C99 and TR1 C Functions">erfc</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/main_overview/tr1.html" title="C99 and TR1 C Functions">expint</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/main_overview/tr1.html" title="C99 and TR1 C Functions">expm1</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/main_overview/tr1.html" title="C99 and TR1 C Functions">exponential</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/main_overview/tr1.html" title="C99 and TR1 C Functions">float_t</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/main_overview/tr1.html" title="C99 and TR1 C Functions">hermite</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/main_overview/tr1.html" title="C99 and TR1 C Functions">hypot</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/main_overview/tr1.html" title="C99 and TR1 C Functions">laguerre</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/main_overview/tr1.html" title="C99 and TR1 C Functions">lgamma</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/main_overview/tr1.html" title="C99 and TR1 C Functions">llround</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/main_overview/tr1.html" title="C99 and TR1 C Functions">log1p</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/main_overview/tr1.html" title="C99 and TR1 C Functions">lround</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/main_overview/tr1.html" title="C99 and TR1 C Functions">mode</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/main_overview/tr1.html" title="C99 and TR1 C Functions">nextafter</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/main_overview/tr1.html" title="C99 and TR1 C Functions">round</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/main_overview/tr1.html" title="C99 and TR1 C Functions">sph_bessel</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/main_overview/tr1.html" title="C99 and TR1 C Functions">sph_neumann</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/main_overview/tr1.html" title="C99 and TR1 C Functions">tgamma</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/main_overview/tr1.html" title="C99 and TR1 C Functions">trunc</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/main_overview/tr1.html" title="C99 and TR1 C Functions">zeta</a></p></td></tr>
+</table></dd>
+<dt><span class="term">C99 and TR1 C Functions Overview</span></dt>
+<dd><table class="simplelist" border="0" summary="Simple list">
+<tr><td><p><a class="link" href="../math_toolkit/special/extern_c/tr1.html" title="C99 and TR1 C Functions Overview">acosh</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/special/extern_c/tr1.html" title="C99 and TR1 C Functions Overview">asinh</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/special/extern_c/tr1.html" title="C99 and TR1 C Functions Overview">atanh</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/special/extern_c/tr1.html" title="C99 and TR1 C Functions Overview">beta</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/special/extern_c/tr1.html" title="C99 and TR1 C Functions Overview">cbrt</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/special/extern_c/tr1.html" title="C99 and TR1 C Functions Overview">comp_ellint_2</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/special/extern_c/tr1.html" title="C99 and TR1 C Functions Overview">comp_ellint_3</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/special/extern_c/tr1.html" title="C99 and TR1 C Functions Overview">cyl_bessel_i</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/special/extern_c/tr1.html" title="C99 and TR1 C Functions Overview">cyl_bessel_j</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/special/extern_c/tr1.html" title="C99 and TR1 C Functions Overview">cyl_bessel_k</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/special/extern_c/tr1.html" title="C99 and TR1 C Functions Overview">cyl_neumann</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/special/extern_c/tr1.html" title="C99 and TR1 C Functions Overview">double_t</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/special/extern_c/tr1.html" title="C99 and TR1 C Functions Overview">ellint_1</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/special/extern_c/tr1.html" title="C99 and TR1 C Functions Overview">ellint_2</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/special/extern_c/tr1.html" title="C99 and TR1 C Functions Overview">ellint_3</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/special/extern_c/tr1.html" title="C99 and TR1 C Functions Overview">erf</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/special/extern_c/tr1.html" title="C99 and TR1 C Functions Overview">erfc</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/special/extern_c/tr1.html" title="C99 and TR1 C Functions Overview">expint</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/special/extern_c/tr1.html" title="C99 and TR1 C Functions Overview">expm1</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/special/extern_c/tr1.html" title="C99 and TR1 C Functions Overview">exponential</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/special/extern_c/tr1.html" title="C99 and TR1 C Functions Overview">float_t</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/special/extern_c/tr1.html" title="C99 and TR1 C Functions Overview">hermite</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/special/extern_c/tr1.html" title="C99 and TR1 C Functions Overview">hypot</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/special/extern_c/tr1.html" title="C99 and TR1 C Functions Overview">laguerre</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/special/extern_c/tr1.html" title="C99 and TR1 C Functions Overview">lgamma</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/special/extern_c/tr1.html" title="C99 and TR1 C Functions Overview">llround</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/special/extern_c/tr1.html" title="C99 and TR1 C Functions Overview">log1p</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/special/extern_c/tr1.html" title="C99 and TR1 C Functions Overview">lround</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/special/extern_c/tr1.html" title="C99 and TR1 C Functions Overview">mode</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/special/extern_c/tr1.html" title="C99 and TR1 C Functions Overview">nextafter</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/special/extern_c/tr1.html" title="C99 and TR1 C Functions Overview">round</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/special/extern_c/tr1.html" title="C99 and TR1 C Functions Overview">sph_bessel</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/special/extern_c/tr1.html" title="C99 and TR1 C Functions Overview">sph_neumann</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/special/extern_c/tr1.html" title="C99 and TR1 C Functions Overview">tgamma</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/special/extern_c/tr1.html" title="C99 and TR1 C Functions Overview">trunc</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/special/extern_c/tr1.html" title="C99 and TR1 C Functions Overview">zeta</a></p></td></tr>
+</table></dd>
+<dt><span class="term">C99 C Functions</span></dt>
+<dd><table class="simplelist" border="0" summary="Simple list">
+<tr><td><p><a class="link" href="../math_toolkit/special/extern_c/c99.html" title="C99 C Functions">acosh</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/special/extern_c/c99.html" title="C99 C Functions">asinh</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/special/extern_c/c99.html" title="C99 C Functions">atanh</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/special/extern_c/c99.html" title="C99 C Functions">cbrt</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/special/extern_c/c99.html" title="C99 C Functions">double_t</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/special/extern_c/c99.html" title="C99 C Functions">erf</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/special/extern_c/c99.html" title="C99 C Functions">erfc</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/special/extern_c/c99.html" title="C99 C Functions">expm1</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/special/extern_c/c99.html" title="C99 C Functions">float_t</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/special/extern_c/c99.html" title="C99 C Functions">gamma</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/special/extern_c/c99.html" title="C99 C Functions">hypot</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/special/extern_c/c99.html" title="C99 C Functions">lgamma</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/special/extern_c/c99.html" title="C99 C Functions">llround</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/special/extern_c/c99.html" title="C99 C Functions">log1p</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/special/extern_c/c99.html" title="C99 C Functions">lround</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/special/extern_c/c99.html" title="C99 C Functions">nextafter</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/special/extern_c/c99.html" title="C99 C Functions">round</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/special/extern_c/c99.html" title="C99 C Functions">tgamma</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/special/extern_c/c99.html" title="C99 C Functions">trunc</a></p></td></tr>
+</table></dd>
+<dt><span class="term">Calculation of the Type of the Result</span></dt>
+<dd><table class="simplelist" border="0" summary="Simple list">
+<tr><td><p><a class="link" href="../math_toolkit/main_overview/result_type.html" title="Calculation of the Type of the Result">cyl_bessel_j</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/main_overview/result_type.html" title="Calculation of the Type of the Result">RR</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/main_overview/result_type.html" title="Calculation of the Type of the Result">sph_bessel</a></p></td></tr>
+</table></dd>
+<dt><span class="term">Calling User Defined Error Handlers</span></dt>
+<dd><table class="simplelist" border="0" summary="Simple list">
+<tr><td><p><a class="link" href="../math_toolkit/policy/pol_tutorial/user_def_err_pol.html" title="Calling User Defined Error Handlers">BOOST_MATH_DECLARE_SPECIAL_FUNCTIONS</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/policy/pol_tutorial/user_def_err_pol.html" title="Calling User Defined Error Handlers">erf</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/policy/pol_tutorial/user_def_err_pol.html" title="Calling User Defined Error Handlers">erf_inv</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/policy/pol_tutorial/user_def_err_pol.html" title="Calling User Defined Error Handlers">evaluation_error</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/policy/pol_tutorial/user_def_err_pol.html" title="Calling User Defined Error Handlers">promote_args</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/policy/pol_tutorial/user_def_err_pol.html" title="Calling User Defined Error Handlers">tgamma</a></p></td></tr>
+</table></dd>
+<dt><span class="term">cauchy</span></dt>
+<dd><table class="simplelist" border="0" summary="Simple list">
+<tr><td><p><a class="link" href="../math_toolkit/backgrounders/implementation.html" title="Additional Implementation Notes">Additional Implementation Notes</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/dist/dist_ref/dists/cauchy_dist.html" title="Cauchy-Lorentz Distribution">Cauchy-Lorentz Distribution</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/dist/stat_tut/weg/find_eg/find_location_eg.html" title="Find Location (Mean) Example">Find Location (Mean) Example</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/dist/stat_tut/weg/find_eg/find_mean_and_sd_eg.html" title="Find mean and standard deviation example">Find mean and standard deviation example</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/policy/pol_ref/assert_undefined.html" title="Mathematically Undefined Function Policies">Mathematically Undefined Function Policies</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/policy/pol_ref/namespace_pol.html" title="Setting Polices at Namespace Scope">Setting Polices at Namespace Scope</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/policy/pol_tutorial/namespace_policies.html" title="Setting Policies at Namespace or Translation Unit Scope">Setting Policies at Namespace or Translation Unit Scope</a></p></td></tr>
+</table></dd>
+<dt><span class="term">Cauchy-Lorentz Distribution</span></dt>
+<dd><table class="simplelist" border="0" summary="Simple list">
+<tr><td><p><a class="link" href="../math_toolkit/dist/dist_ref/dists/cauchy_dist.html" title="Cauchy-Lorentz Distribution">cauchy</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/dist/dist_ref/dists/cauchy_dist.html" title="Cauchy-Lorentz Distribution">cauchy_distribution</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/dist/dist_ref/dists/cauchy_dist.html" title="Cauchy-Lorentz Distribution">cdf</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/dist/dist_ref/dists/cauchy_dist.html" title="Cauchy-Lorentz Distribution">kurtosis</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/dist/dist_ref/dists/cauchy_dist.html" title="Cauchy-Lorentz Distribution">kurtosis_excess</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/dist/dist_ref/dists/cauchy_dist.html" title="Cauchy-Lorentz Distribution">mean</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/dist/dist_ref/dists/cauchy_dist.html" title="Cauchy-Lorentz Distribution">median</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/dist/dist_ref/dists/cauchy_dist.html" title="Cauchy-Lorentz Distribution">mode</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/dist/dist_ref/dists/cauchy_dist.html" title="Cauchy-Lorentz Distribution">pdf</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/dist/dist_ref/dists/cauchy_dist.html" title="Cauchy-Lorentz Distribution">policy_type</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/dist/dist_ref/dists/cauchy_dist.html" title="Cauchy-Lorentz Distribution">quantile</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/dist/dist_ref/dists/cauchy_dist.html" title="Cauchy-Lorentz Distribution">skewness</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/dist/dist_ref/dists/cauchy_dist.html" title="Cauchy-Lorentz Distribution">value_type</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/dist/dist_ref/dists/cauchy_dist.html" title="Cauchy-Lorentz Distribution">variance</a></p></td></tr>
+</table></dd>
+<dt><span class="term">cauchy_distribution</span></dt>
+<dd><table class="simplelist" border="0" summary="Simple list">
+<tr><td><p><a class="link" href="../math_toolkit/dist/dist_ref/dists/cauchy_dist.html" title="Cauchy-Lorentz Distribution">Cauchy-Lorentz Distribution</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/dist/stat_tut/weg/find_eg/find_location_eg.html" title="Find Location (Mean) Example">Find Location (Mean) Example</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/dist/stat_tut/weg/find_eg/find_mean_and_sd_eg.html" title="Find mean and standard deviation example">Find mean and standard deviation example</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/policy/pol_ref/assert_undefined.html" title="Mathematically Undefined Function Policies">Mathematically Undefined Function Policies</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/policy/pol_ref/namespace_pol.html" title="Setting Polices at Namespace Scope">Setting Polices at Namespace Scope</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/policy/pol_tutorial/namespace_policies.html" title="Setting Policies at Namespace or Translation Unit Scope">Setting Policies at Namespace or Translation Unit Scope</a></p></td></tr>
+</table></dd>
+<dt><span class="term">cbrt</span></dt>
+<dd><table class="simplelist" border="0" summary="Simple list">
+<tr><td><p><a class="link" href="../math_toolkit/main_overview/tr1.html" title="C99 and TR1 C Functions">C99 and TR1 C Functions</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/special/extern_c/tr1.html" title="C99 and TR1 C Functions Overview">C99 and TR1 C Functions Overview</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/special/extern_c/c99.html" title="C99 C Functions">C99 C Functions</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/special/powers/cbrt.html" title="cbrt">cbrt</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/main_overview/directories.html" title="Directory and File Structure">Directory and File Structure</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/toolkit/internals1/roots.html" title="Root Finding With Derivatives">Root Finding With Derivatives</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/special/powers/cbrt.html" title="cbrt">RR</a></p></td></tr>
+</table></dd>
+<dt><span class="term">cbrt_functor</span></dt>
+<dd><table class="simplelist" border="0" summary="Simple list"><tr><td><p><a class="link" href="../math_toolkit/toolkit/internals1/roots.html" title="Root Finding With Derivatives">Root Finding With Derivatives</a></p></td></tr></table></dd>
+<dt><span class="term">cdf</span></dt>
+<dd><table class="simplelist" border="0" summary="Simple list">
+<tr><td><p><a class="link" href="../math_toolkit/backgrounders/implementation.html" title="Additional Implementation Notes">Additional Implementation Notes</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/dist/dist_ref/dists/bernoulli_dist.html" title="Bernoulli Distribution">Bernoulli Distribution</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/dist/dist_ref/dists/beta_dist.html" title="Beta Distribution">Beta Distribution</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/dist/stat_tut/weg/binom_eg/binomial_coinflip_example.html" title="Binomial Coin-Flipping Example">Binomial Coin-Flipping Example</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/dist/dist_ref/dists/binomial_dist.html" title="Binomial Distribution">Binomial Distribution</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/dist/stat_tut/weg/binom_eg/binomial_quiz_example.html" title="Binomial Quiz Example">Binomial Quiz Example</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/dist/dist_ref/dists/cauchy_dist.html" title="Cauchy-Lorentz Distribution">Cauchy-Lorentz Distribution</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/policy/pol_tutorial/changing_policy_defaults.html" title="Changing the Policy Defaults">Changing the Policy Defaults</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/dist/dist_ref/dists/chi_squared_dist.html" title="Chi Squared Distribution">Chi Squared Distribution</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/dist/stat_tut/weg/st_eg/two_sample_students_t.html" title="Comparing the means of two samples with the Students-t test">Comparing the means of two samples with the Students-t test</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/dist/stat_tut/weg/nag_library.html" title="Comparison with C, R, FORTRAN-style Free Functions">Comparison with C, R, FORTRAN-style Free Functions</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/using_udt/dist_concept.html" title="Conceptual Requirements for Distribution Types">Conceptual Requirements for Distribution Types</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/policy/pol_ref/discrete_quant_ref.html" title="Discrete Quantile Policies">Discrete Quantile Policies</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/dist/stat_tut/weg/error_eg.html" title="Error Handling Example">Error Handling Example</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/dist/dist_ref/dists/exp_dist.html" title="Exponential Distribution">Exponential Distribution</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/dist/future.html" title="Extras/Future Directions">Extras/Future Directions</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/dist/dist_ref/dists/extreme_dist.html" title="Extreme Value Distribution">Extreme Value Distribution</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/dist/dist_ref/dists/f_dist.html" title="F Distribution">F Distribution</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/dist/stat_tut/weg/find_eg/find_location_eg.html" title="Find Location (Mean) Example">Find Location (Mean) Example</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/dist/stat_tut/weg/find_eg/find_mean_and_sd_eg.html" title="Find mean and standard deviation example">Find mean and standard deviation example</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/dist/stat_tut/weg/find_eg/find_scale_eg.html" title="Find Scale (Standard Deviation) Example">Find Scale (Standard Deviation) Example</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/dist/dist_ref/dists/gamma_dist.html" title="Gamma (and Erlang) Distribution">Gamma (and Erlang) Distribution</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/dist/dist_ref/dists/lognormal_dist.html" title="Log Normal Distribution">Log Normal Distribution</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/dist/dist_ref/dists/logistic_dist.html" title="Logistic Distribution">Logistic Distribution</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/dist/dist_ref/dists/binomial_dist.html" title="Binomial Distribution">Meaning of the non-member accessors</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/dist/dist_ref/dists/negative_binomial_dist.html" title="Negative Binomial Distribution">Meaning of the non-member accessors.</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/dist/dist_ref/dists/negative_binomial_dist.html" title="Negative Binomial Distribution">Negative Binomial Distribution</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/dist/stat_tut/weg/neg_binom_eg/negative_binomial_example1.html" title="Negative Binomial Sales Quota Example.">Negative Binomial Sales Quota Example.</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/dist/stat_tut/weg/neg_binom_eg/negative_binomial_example2.html" title="Negative Binomial Table Printing Example.">Negative Binomial Table Printing Example.</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/dist/dist_ref/nmp.html" title="Non-Member Properties">Non-Member Properties</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/dist/dist_ref/dists/nc_chi_squared_dist.html" title="Noncentral Chi-Squared Distribution">Noncentral Chi-Squared Distribution</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/dist/dist_ref/dists/nc_f_dist.html" title="Noncentral F Distribution">Noncentral F Distribution</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/dist/dist_ref/dists/normal_dist.html" title="Normal (Gaussian) Distribution">Normal (Gaussian) Distribution</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/dist/stat_tut/overview.html" title="Overview">Overview</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/dist/dist_ref/dists/pareto.html" title="Pareto Distribution">Pareto Distribution</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/dist/dist_ref/dists/poisson_dist.html" title="Poisson Distribution">Poisson Distribution</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/dist/dist_ref/dists/rayleigh.html" title="Rayleigh Distribution">Rayleigh Distribution</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/dist/stat_tut/weg/normal_example/normal_misc.html" title="Some Miscellaneous Examples of the Normal (Gaussian) Distribution">Some Miscellaneous Examples of the Normal (Gaussian) Distribution</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/dist/dist_ref/dists/students_t_dist.html" title="Students t Distribution">Students t Distribution</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/dist/stat_tut/weg/nccs_eg/nccs_power_eg.html" title="Tables of the power function of the &#967;2 test.">Tables of the power function of the &#967; 2 test.</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/dist/stat_tut/weg/st_eg/tut_mean_test.html" title='Testing a sample mean for difference from a "true" mean'>Testing a sample mean for difference from a "true" mean</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/dist/dist_ref/dists/triangular_dist.html" title="Triangular Distribution">Triangular Distribution</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/policy/pol_tutorial/understand_dis_quant.html" title="Understanding Quantiles of Discrete Distributions">Understanding Quantiles of Discrete Distributions</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/dist/dist_ref/dists/uniform_dist.html" title="Uniform Distribution">Uniform Distribution</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/dist/dist_ref/dists/weibull.html" title="Weibull Distribution">Weibull Distribution</a></p></td></tr>
+</table></dd>
+<dt><span class="term">Changing the Policy Defaults</span></dt>
+<dd><table class="simplelist" border="0" summary="Simple list">
+<tr><td><p><a class="link" href="../math_toolkit/policy/pol_tutorial/changing_policy_defaults.html" title="Changing the Policy Defaults">BOOST_MATH_ASSERT_UNDEFINED_POLICY</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/policy/pol_tutorial/changing_policy_defaults.html" title="Changing the Policy Defaults">BOOST_MATH_DOMAIN_ERROR_POLICY</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/policy/pol_tutorial/changing_policy_defaults.html" title="Changing the Policy Defaults">BOOST_MATH_OVERFLOW_ERROR_POLICY</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/policy/pol_tutorial/changing_policy_defaults.html" title="Changing the Policy Defaults">cdf</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/policy/pol_tutorial/changing_policy_defaults.html" title="Changing the Policy Defaults">mean</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/policy/pol_tutorial/changing_policy_defaults.html" title="Changing the Policy Defaults">students_t</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/policy/pol_tutorial/changing_policy_defaults.html" title="Changing the Policy Defaults">students_t_distribution</a></p></td></tr>
+</table></dd>
+<dt><span class="term">Changing the Policy on an Ad Hoc Basis for the Special Functions</span></dt>
+<dd><table class="simplelist" border="0" summary="Simple list">
+<tr><td><p><a class="link" href="../math_toolkit/policy/pol_tutorial/ad_hoc_sf_policies.html" title="Changing the Policy on an Ad Hoc Basis for the Special Functions">evaluation_error</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/policy/pol_tutorial/ad_hoc_sf_policies.html" title="Changing the Policy on an Ad Hoc Basis for the Special Functions">gamma</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/policy/pol_tutorial/ad_hoc_sf_policies.html" title="Changing the Policy on an Ad Hoc Basis for the Special Functions">make_policy</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/policy/pol_tutorial/ad_hoc_sf_policies.html" title="Changing the Policy on an Ad Hoc Basis for the Special Functions">tgamma</a></p></td></tr>
+</table></dd>
+<dt><span class="term">checked_narrowing_cast</span></dt>
+<dd><table class="simplelist" border="0" summary="Simple list"><tr><td><p><a class="link" href="../math_toolkit/main_overview/error_handling.html" title="Error Handling">Error Handling</a></p></td></tr></table></dd>
+<dt><span class="term">check_triangular</span></dt>
+<dd><table class="simplelist" border="0" summary="Simple list"><tr><td><p><a class="link" href="../math_toolkit/backgrounders/implementation.html" title="Additional Implementation Notes">Additional Implementation Notes</a></p></td></tr></table></dd>
+<dt><span class="term">chf</span></dt>
+<dd><table class="simplelist" border="0" summary="Simple list">
+<tr><td><p><a class="link" href="../math_toolkit/using_udt/archetypes.html" title="Conceptual Archetypes and Testing">Conceptual Archetypes and Testing</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/using_udt/dist_concept.html" title="Conceptual Requirements for Distribution Types">Conceptual Requirements for Distribution Types</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/dist/dist_ref/nmp.html" title="Non-Member Properties">Non-Member Properties</a></p></td></tr>
+</table></dd>
+<dt><span class="term">Chi Squared Distribution</span></dt>
+<dd><table class="simplelist" border="0" summary="Simple list">
+<tr><td><p><a class="link" href="../math_toolkit/dist/dist_ref/dists/chi_squared_dist.html" title="Chi Squared Distribution">beta</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/dist/dist_ref/dists/chi_squared_dist.html" title="Chi Squared Distribution">cdf</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/dist/dist_ref/dists/chi_squared_dist.html" title="Chi Squared Distribution">chi_squared</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/dist/dist_ref/dists/chi_squared_dist.html" title="Chi Squared Distribution">chi_squared_distribution</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/dist/dist_ref/dists/chi_squared_dist.html" title="Chi Squared Distribution">find_degrees_of_freedom</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/dist/dist_ref/dists/chi_squared_dist.html" title="Chi Squared Distribution">gamma</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/dist/dist_ref/dists/chi_squared_dist.html" title="Chi Squared Distribution">gamma_p</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/dist/dist_ref/dists/chi_squared_dist.html" title="Chi Squared Distribution">gamma_p_derivative</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/dist/dist_ref/dists/chi_squared_dist.html" title="Chi Squared Distribution">gamma_p_inv</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/dist/dist_ref/dists/chi_squared_dist.html" title="Chi Squared Distribution">gamma_q</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/dist/dist_ref/dists/chi_squared_dist.html" title="Chi Squared Distribution">gamma_q_inv</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/dist/dist_ref/dists/chi_squared_dist.html" title="Chi Squared Distribution">kurtosis</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/dist/dist_ref/dists/chi_squared_dist.html" title="Chi Squared Distribution">kurtosis_excess</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/dist/dist_ref/dists/chi_squared_dist.html" title="Chi Squared Distribution">mean</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/dist/dist_ref/dists/chi_squared_dist.html" title="Chi Squared Distribution">median</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/dist/dist_ref/dists/chi_squared_dist.html" title="Chi Squared Distribution">mode</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/dist/dist_ref/dists/chi_squared_dist.html" title="Chi Squared Distribution">pdf</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/dist/dist_ref/dists/chi_squared_dist.html" title="Chi Squared Distribution">policy_type</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/dist/dist_ref/dists/chi_squared_dist.html" title="Chi Squared Distribution">quantile</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/dist/dist_ref/dists/chi_squared_dist.html" title="Chi Squared Distribution">skewness</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/dist/dist_ref/dists/chi_squared_dist.html" title="Chi Squared Distribution">value_type</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/dist/dist_ref/dists/chi_squared_dist.html" title="Chi Squared Distribution">variance</a></p></td></tr>
+</table></dd>
+<dt><span class="term">chi_squared</span></dt>
+<dd><table class="simplelist" border="0" summary="Simple list">
+<tr><td><p><a class="link" href="../math_toolkit/dist/dist_ref/dists/chi_squared_dist.html" title="Chi Squared Distribution">Chi Squared Distribution</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/dist/stat_tut/weg/cs_eg/chi_sq_test.html" title="Chi-Square Test for the Standard Deviation">Chi-Square Test for the Standard Deviation</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/dist/stat_tut/weg/cs_eg/chi_sq_intervals.html" title="Confidence Intervals on the Standard Deviation">Confidence Intervals on the Standard Deviation</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/dist/stat_tut/weg/cs_eg/chi_sq_size.html" title="Estimating the Required Sample Sizes for a Chi-Square Test for the Standard Deviation">Estimating the Required Sample Sizes for a Chi-Square Test for the Standard Deviation</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/dist/stat_tut/weg/nccs_eg/nccs_power_eg.html" title="Tables of the power function of the &#967;2 test.">Tables of the power function of the &#967; 2 test.</a></p></td></tr>
+</table></dd>
+<dt><span class="term">chi_squared_distribution</span></dt>
+<dd><table class="simplelist" border="0" summary="Simple list">
+<tr><td><p><a class="link" href="../math_toolkit/dist/dist_ref/dists/chi_squared_dist.html" title="Chi Squared Distribution">Chi Squared Distribution</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/dist/stat_tut/weg/cs_eg/chi_sq_size.html" title="Estimating the Required Sample Sizes for a Chi-Square Test for the Standard Deviation">Estimating the Required Sample Sizes for a Chi-Square Test for the Standard Deviation</a></p></td></tr>
+</table></dd>
+<dt><span class="term">coefficient_of_variation</span></dt>
+<dd><table class="simplelist" border="0" summary="Simple list"><tr><td><p><a class="link" href="../math_toolkit/using_udt/archetypes.html" title="Conceptual Archetypes and Testing">Conceptual Archetypes and Testing</a></p></td></tr></table></dd>
+<dt><span class="term">Comparison to the R Statistical Library on Linux</span></dt>
+<dd><table class="simplelist" border="0" summary="Simple list"><tr><td><p><a class="link" href="../math_toolkit/perf/comparisons.html" title="Comparisons to Other Open Source Libraries">normal</a></p></td></tr></table></dd>
+<dt><span class="term">Comparison to the R Statistical Library on Windows XP</span></dt>
+<dd><table class="simplelist" border="0" summary="Simple list"><tr><td><p><a class="link" href="../math_toolkit/perf/comparisons.html" title="Comparisons to Other Open Source Libraries">normal</a></p></td></tr></table></dd>
+<dt><span class="term">Comparisons to Other Open Source Libraries</span></dt>
+<dd><table class="simplelist" border="0" summary="Simple list">
+<tr><td><p><a class="link" href="../math_toolkit/perf/comparisons.html" title="Comparisons to Other Open Source Libraries">gamma_p</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/perf/comparisons.html" title="Comparisons to Other Open Source Libraries">gamma_p_inv</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/perf/comparisons.html" title="Comparisons to Other Open Source Libraries">gamma_q</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/perf/comparisons.html" title="Comparisons to Other Open Source Libraries">gamma_q_inv</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/perf/comparisons.html" title="Comparisons to Other Open Source Libraries">ibeta</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/perf/comparisons.html" title="Comparisons to Other Open Source Libraries">ibetac</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/perf/comparisons.html" title="Comparisons to Other Open Source Libraries">ibetac_inv</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/perf/comparisons.html" title="Comparisons to Other Open Source Libraries">ibeta_inv</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/perf/comparisons.html" title="Comparisons to Other Open Source Libraries">lgamma</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/perf/comparisons.html" title="Comparisons to Other Open Source Libraries">mode</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/perf/comparisons.html" title="Comparisons to Other Open Source Libraries">tgamma</a></p></td></tr>
+</table></dd>
+<dt><span class="term">Compile Time Power of a Runtime Base</span></dt>
+<dd><table class="simplelist" border="0" summary="Simple list"><tr><td><p><a class="link" href="../math_toolkit/special/powers/ct_pow.html" title="Compile Time Power of a Runtime Base">BOOST_MATH_OVERFLOW_ERROR_POLICY</a></p></td></tr></table></dd>
+<dt><span class="term">complemented3_type</span></dt>
+<dd><table class="simplelist" border="0" summary="Simple list"><tr><td><p><a class="link" href="../math_toolkit/dist/dist_ref/dists/nc_chi_squared_dist.html" title="Noncentral Chi-Squared Distribution">Noncentral Chi-Squared Distribution</a></p></td></tr></table></dd>
+<dt><span class="term">comp_ellint_2</span></dt>
+<dd><table class="simplelist" border="0" summary="Simple list">
+<tr><td><p><a class="link" href="../math_toolkit/main_overview/tr1.html" title="C99 and TR1 C Functions">C99 and TR1 C Functions</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/special/extern_c/tr1.html" title="C99 and TR1 C Functions Overview">C99 and TR1 C Functions Overview</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/special/extern_c/tr1_ref.html" title="TR1 C Functions Quick Reference">TR1 C Functions Quick Reference</a></p></td></tr>
+</table></dd>
+<dt><span class="term">comp_ellint_3</span></dt>
+<dd><table class="simplelist" border="0" summary="Simple list">
+<tr><td><p><a class="link" href="../math_toolkit/main_overview/tr1.html" title="C99 and TR1 C Functions">C99 and TR1 C Functions</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/special/extern_c/tr1.html" title="C99 and TR1 C Functions Overview">C99 and TR1 C Functions Overview</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/special/extern_c/tr1_ref.html" title="TR1 C Functions Quick Reference">TR1 C Functions Quick Reference</a></p></td></tr>
+</table></dd>
+<dt><span class="term">Conceptual Archetypes and Testing</span></dt>
+<dd><table class="simplelist" border="0" summary="Simple list">
+<tr><td><p><a class="link" href="../math_toolkit/using_udt/archetypes.html" title="Conceptual Archetypes and Testing">chf</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/using_udt/archetypes.html" title="Conceptual Archetypes and Testing">coefficient_of_variation</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/using_udt/archetypes.html" title="Conceptual Archetypes and Testing">DistributionConcept</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/using_udt/archetypes.html" title="Conceptual Archetypes and Testing">distribution_archetype</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/using_udt/archetypes.html" title="Conceptual Archetypes and Testing">hazard</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/using_udt/archetypes.html" title="Conceptual Archetypes and Testing">pdf</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/using_udt/archetypes.html" title="Conceptual Archetypes and Testing">real_concept</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/using_udt/archetypes.html" title="Conceptual Archetypes and Testing">RR</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/using_udt/archetypes.html" title="Conceptual Archetypes and Testing">std_real_concept</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/using_udt/archetypes.html" title="Conceptual Archetypes and Testing">value_type</a></p></td></tr>
+</table></dd>
+<dt><span class="term">Conceptual Requirements for Distribution Types</span></dt>
+<dd><table class="simplelist" border="0" summary="Simple list">
+<tr><td><p><a class="link" href="../math_toolkit/using_udt/dist_concept.html" title="Conceptual Requirements for Distribution Types">cdf</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/using_udt/dist_concept.html" title="Conceptual Requirements for Distribution Types">chf</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/using_udt/dist_concept.html" title="Conceptual Requirements for Distribution Types">hazard</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/using_udt/dist_concept.html" title="Conceptual Requirements for Distribution Types">kurtosis</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/using_udt/dist_concept.html" title="Conceptual Requirements for Distribution Types">kurtosis_excess</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/using_udt/dist_concept.html" title="Conceptual Requirements for Distribution Types">mean</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/using_udt/dist_concept.html" title="Conceptual Requirements for Distribution Types">mode</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/using_udt/dist_concept.html" title="Conceptual Requirements for Distribution Types">pdf</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/using_udt/dist_concept.html" title="Conceptual Requirements for Distribution Types">policy_type</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/using_udt/dist_concept.html" title="Conceptual Requirements for Distribution Types">quantile</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/using_udt/dist_concept.html" title="Conceptual Requirements for Distribution Types">skewness</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/using_udt/dist_concept.html" title="Conceptual Requirements for Distribution Types">standard_deviation</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/using_udt/dist_concept.html" title="Conceptual Requirements for Distribution Types">value_type</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/using_udt/dist_concept.html" title="Conceptual Requirements for Distribution Types">variance</a></p></td></tr>
+</table></dd>
+<dt><span class="term">Conceptual Requirements for Real Number Types</span></dt>
+<dd><table class="simplelist" border="0" summary="Simple list">
+<tr><td><p><a class="link" href="../math_toolkit/using_udt/concepts.html" title="Conceptual Requirements for Real Number Types">beta</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/using_udt/concepts.html" title="Conceptual Requirements for Real Number Types">erf</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/using_udt/concepts.html" title="Conceptual Requirements for Real Number Types">gamma</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/using_udt/concepts.html" title="Conceptual Requirements for Real Number Types">iround</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/using_udt/concepts.html" title="Conceptual Requirements for Real Number Types">itrunc</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/using_udt/concepts.html" title="Conceptual Requirements for Real Number Types">lanczos</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/using_udt/concepts.html" title="Conceptual Requirements for Real Number Types">Lanczos approximation</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/using_udt/concepts.html" title="Conceptual Requirements for Real Number Types">ldexp</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/using_udt/concepts.html" title="Conceptual Requirements for Real Number Types">llround</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/using_udt/concepts.html" title="Conceptual Requirements for Real Number Types">lltrunc</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/using_udt/concepts.html" title="Conceptual Requirements for Real Number Types">lround</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/using_udt/concepts.html" title="Conceptual Requirements for Real Number Types">ltrunc</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/using_udt/concepts.html" title="Conceptual Requirements for Real Number Types">round</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/using_udt/concepts.html" title="Conceptual Requirements for Real Number Types">RR</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/using_udt/concepts.html" title="Conceptual Requirements for Real Number Types">trunc</a></p></td></tr>
+</table></dd>
+<dt><span class="term">confidence intervals on the mean with the Students-t distribution</span></dt>
+<dd><table class="simplelist" border="0" summary="Simple list">
+<tr><td><p><a class="link" href="../math_toolkit/dist/stat_tut/weg/st_eg/tut_mean_intervals.html" title="Calculating confidence intervals on the mean with the Students-t distribution">mean</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/dist/stat_tut/weg/st_eg/tut_mean_intervals.html" title="Calculating confidence intervals on the mean with the Students-t distribution">normal</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/dist/stat_tut/weg/st_eg/tut_mean_intervals.html" title="Calculating confidence intervals on the mean with the Students-t distribution">quantile</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/dist/stat_tut/weg/st_eg/tut_mean_intervals.html" title="Calculating confidence intervals on the mean with the Students-t distribution">students_t</a></p></td></tr>
+</table></dd>
+<dt><span class="term">Confidence Limits on the Frequency of Occurrence for a Binomial Distribution</span></dt>
+<dd><table class="simplelist" border="0" summary="Simple list">
+<tr><td><p><a class="link" href="../math_toolkit/dist/stat_tut/weg/binom_eg/binom_conf.html" title="Calculating Confidence Limits on the Frequency of Occurrence for a Binomial Distribution">binomial</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/dist/stat_tut/weg/binom_eg/binom_conf.html" title="Calculating Confidence Limits on the Frequency of Occurrence for a Binomial Distribution">binomial_distribution</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/dist/stat_tut/weg/binom_eg/binom_conf.html" title="Calculating Confidence Limits on the Frequency of Occurrence for a Binomial Distribution">find_lower_bound_on_p</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/dist/stat_tut/weg/binom_eg/binom_conf.html" title="Calculating Confidence Limits on the Frequency of Occurrence for a Binomial Distribution">find_upper_bound_on_p</a></p></td></tr>
+</table></dd>
+<dt><span class="term">Confidence Limits on the Frequency of Occurrence for the Negative Binomial Distribution</span></dt>
+<dd><table class="simplelist" border="0" summary="Simple list">
+<tr><td><p><a class="link" href="../math_toolkit/dist/stat_tut/weg/neg_binom_eg/neg_binom_conf.html" title="Calculating Confidence Limits on the Frequency of Occurrence for the Negative Binomial Distribution">binomial</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/dist/stat_tut/weg/neg_binom_eg/neg_binom_conf.html" title="Calculating Confidence Limits on the Frequency of Occurrence for the Negative Binomial Distribution">find_lower_bound_on_p</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/dist/stat_tut/weg/neg_binom_eg/neg_binom_conf.html" title="Calculating Confidence Limits on the Frequency of Occurrence for the Negative Binomial Distribution">find_upper_bound_on_p</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/dist/stat_tut/weg/neg_binom_eg/neg_binom_conf.html" title="Calculating Confidence Limits on the Frequency of Occurrence for the Negative Binomial Distribution">negative_binomial</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/dist/stat_tut/weg/neg_binom_eg/neg_binom_conf.html" title="Calculating Confidence Limits on the Frequency of Occurrence for the Negative Binomial Distribution">negative_binomial_distribution</a></p></td></tr>
+</table></dd>
+<dt><span class="term">Configuration and Policies</span></dt>
+<dd><table class="simplelist" border="0" summary="Simple list">
+<tr><td><p><a class="link" href="../math_toolkit/main_overview/pol_overview.html" title="Configuration and Policies">binomial</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/main_overview/pol_overview.html" title="Configuration and Policies">evaluation_error</a></p></td></tr>
+</table></dd>
+<dt><span class="term">Continued Fraction Evaluation</span></dt>
+<dd><table class="simplelist" border="0" summary="Simple list">
+<tr><td><p><a class="link" href="../math_toolkit/toolkit/internals1/cf.html" title="Continued Fraction Evaluation">continued_fraction_a</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/toolkit/internals1/cf.html" title="Continued Fraction Evaluation">continued_fraction_b</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/toolkit/internals1/cf.html" title="Continued Fraction Evaluation">fraction_traits</a></p></td></tr>
+</table></dd>
+<dt><span class="term">continued_fraction_a</span></dt>
+<dd><table class="simplelist" border="0" summary="Simple list">
+<tr><td><p><a class="link" href="../math_toolkit/toolkit/internals1/cf.html" title="Continued Fraction Evaluation">Continued Fraction Evaluation</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/toolkit/internals2/test_data.html" title="Graphing, Profiling, and Generating Test Data for Special Functions">Graphing, Profiling, and Generating Test Data for Special Functions</a></p></td></tr>
+</table></dd>
+<dt><span class="term">continued_fraction_b</span></dt>
+<dd><table class="simplelist" border="0" summary="Simple list"><tr><td><p><a class="link" href="../math_toolkit/toolkit/internals1/cf.html" title="Continued Fraction Evaluation">Continued Fraction Evaluation</a></p></td></tr></table></dd>
+<dt><span class="term">Credits and Acknowledgements</span></dt>
+<dd><table class="simplelist" border="0" summary="Simple list">
+<tr><td><p><a class="link" href="../math_toolkit/status/credits.html" title="Credits and Acknowledgements">beta</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/status/credits.html" title="Credits and Acknowledgements">erf</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/status/credits.html" title="Credits and Acknowledgements">factorial</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/status/credits.html" title="Credits and Acknowledgements">gamma</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/status/credits.html" title="Credits and Acknowledgements">pdf</a></p></td></tr>
+</table></dd>
+<dt><span class="term">cyl_bessel_i</span></dt>
+<dd><table class="simplelist" border="0" summary="Simple list">
+<tr><td><p><a class="link" href="../math_toolkit/special/bessel/bessel_over.html" title="Bessel Function Overview">Bessel Function Overview</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/main_overview/tr1.html" title="C99 and TR1 C Functions">C99 and TR1 C Functions</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/special/extern_c/tr1.html" title="C99 and TR1 C Functions Overview">C99 and TR1 C Functions Overview</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/special/bessel/mbessel.html" title="Modified Bessel Functions of the First and Second Kinds">Errors Rates in cyl_bessel_i</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/special/bessel/mbessel.html" title="Modified Bessel Functions of the First and Second Kinds">Modified Bessel Functions of the First and Second Kinds</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/dist/dist_ref/dists/nc_chi_squared_dist.html" title="Noncentral Chi-Squared Distribution">Noncentral Chi-Squared Distribution</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/special/extern_c/tr1_ref.html" title="TR1 C Functions Quick Reference">TR1 C Functions Quick Reference</a></p></td></tr>
+</table></dd>
+<dt><span class="term">cyl_bessel_j</span></dt>
+<dd><table class="simplelist" border="0" summary="Simple list">
+<tr><td><p><a class="link" href="../math_toolkit/special/bessel/bessel_over.html" title="Bessel Function Overview">Bessel Function Overview</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/special/bessel/bessel.html" title="Bessel Functions of the First and Second Kinds">Bessel Functions of the First and Second Kinds</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/main_overview/tr1.html" title="C99 and TR1 C Functions">C99 and TR1 C Functions</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/special/extern_c/tr1.html" title="C99 and TR1 C Functions Overview">C99 and TR1 C Functions Overview</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/main_overview/result_type.html" title="Calculation of the Type of the Result">Calculation of the Type of the Result</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/special/bessel/bessel.html" title="Bessel Functions of the First and Second Kinds">Errors Rates in cyl_bessel_j</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/special/bessel/mbessel.html" title="Modified Bessel Functions of the First and Second Kinds">Modified Bessel Functions of the First and Second Kinds</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/special/bessel/sph_bessel.html" title="Spherical Bessel Functions of the First and Second Kinds">Spherical Bessel Functions of the First and Second Kinds</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/special/extern_c/tr1_ref.html" title="TR1 C Functions Quick Reference">TR1 C Functions Quick Reference</a></p></td></tr>
+</table></dd>
+<dt><span class="term">cyl_bessel_k</span></dt>
+<dd><table class="simplelist" border="0" summary="Simple list">
+<tr><td><p><a class="link" href="../math_toolkit/special/bessel/bessel_over.html" title="Bessel Function Overview">Bessel Function Overview</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/main_overview/tr1.html" title="C99 and TR1 C Functions">C99 and TR1 C Functions</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/special/extern_c/tr1.html" title="C99 and TR1 C Functions Overview">C99 and TR1 C Functions Overview</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/special/bessel/mbessel.html" title="Modified Bessel Functions of the First and Second Kinds">Errors Rates in cyl_bessel_k</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/special/bessel/mbessel.html" title="Modified Bessel Functions of the First and Second Kinds">Modified Bessel Functions of the First and Second Kinds</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/special/extern_c/tr1_ref.html" title="TR1 C Functions Quick Reference">TR1 C Functions Quick Reference</a></p></td></tr>
+</table></dd>
+<dt><span class="term">cyl_neumann</span></dt>
+<dd><table class="simplelist" border="0" summary="Simple list">
+<tr><td><p><a class="link" href="../math_toolkit/special/bessel/bessel_over.html" title="Bessel Function Overview">Bessel Function Overview</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/special/bessel/bessel.html" title="Bessel Functions of the First and Second Kinds">Bessel Functions of the First and Second Kinds</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/main_overview/tr1.html" title="C99 and TR1 C Functions">C99 and TR1 C Functions</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/special/extern_c/tr1.html" title="C99 and TR1 C Functions Overview">C99 and TR1 C Functions Overview</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/special/bessel/bessel.html" title="Bessel Functions of the First and Second Kinds">Errors Rates in cyl_neumann</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/special/bessel/mbessel.html" title="Modified Bessel Functions of the First and Second Kinds">Modified Bessel Functions of the First and Second Kinds</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/special/bessel/sph_bessel.html" title="Spherical Bessel Functions of the First and Second Kinds">Spherical Bessel Functions of the First and Second Kinds</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/special/extern_c/tr1_ref.html" title="TR1 C Functions Quick Reference">TR1 C Functions Quick Reference</a></p></td></tr>
+</table></dd>
+</dl></div></dd>
+<dt>
+<a name="idx_id_58"></a><span class="term">D</span>
+</dt>
+<dd><div class="variablelist"><dl>
+<dt><span class="term">default_policy</span></dt>
+<dd><table class="simplelist" border="0" summary="Simple list"><tr><td><p><a class="link" href="../math_toolkit/policy/pol_ref/pol_ref_ref.html" title="Policy Class Reference">Policy Class Reference</a></p></td></tr></table></dd>
+<dt><span class="term">denorm_error_type</span></dt>
+<dd><table class="simplelist" border="0" summary="Simple list"><tr><td><p><a class="link" href="../math_toolkit/policy/pol_ref/pol_ref_ref.html" title="Policy Class Reference">Policy Class Reference</a></p></td></tr></table></dd>
+<dt><span class="term">Derivative of the Incomplete Beta Function</span></dt>
+<dd><table class="simplelist" border="0" summary="Simple list">
+<tr><td><p><a class="link" href="../math_toolkit/special/sf_beta/beta_derivative.html" title="Derivative of the Incomplete Beta Function">beta</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/special/sf_beta/beta_derivative.html" title="Derivative of the Incomplete Beta Function">ibeta</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/special/sf_beta/beta_derivative.html" title="Derivative of the Incomplete Beta Function">ibeta_derivative</a></p></td></tr>
+</table></dd>
+<dt><span class="term">Derivative of the Incomplete Gamma Function</span></dt>
+<dd><table class="simplelist" border="0" summary="Simple list">
+<tr><td><p><a class="link" href="../math_toolkit/special/sf_gamma/gamma_derivatives.html" title="Derivative of the Incomplete Gamma Function">gamma</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/special/sf_gamma/gamma_derivatives.html" title="Derivative of the Incomplete Gamma Function">gamma_p</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/special/sf_gamma/gamma_derivatives.html" title="Derivative of the Incomplete Gamma Function">gamma_p_derivative</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/special/sf_gamma/gamma_derivatives.html" title="Derivative of the Incomplete Gamma Function">gamma_q</a></p></td></tr>
+</table></dd>
+<dt><span class="term">digamma</span></dt>
+<dd><table class="simplelist" border="0" summary="Simple list">
+<tr><td><p><a class="link" href="../math_toolkit/main_overview/intro.html" title="About the Math Toolkit">About the Math Toolkit</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/special/sf_gamma/digamma.html" title="Digamma">digamma</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/special/sf_gamma/digamma.html" title="Digamma">gamma</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/main_overview/history1.html" title="History and What's New">History and What's New</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/special/sf_gamma/digamma.html" title="Digamma">Lanczos approximation</a></p></td></tr>
+</table></dd>
+<dt><span class="term">Directory and File Structure</span></dt>
+<dd><table class="simplelist" border="0" summary="Simple list">
+<tr><td><p><a class="link" href="../math_toolkit/main_overview/directories.html" title="Directory and File Structure">beta</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/main_overview/directories.html" title="Directory and File Structure">cbrt</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/main_overview/directories.html" title="Directory and File Structure">erf</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/main_overview/directories.html" title="Directory and File Structure">gamma</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/main_overview/directories.html" title="Directory and File Structure">lgamma</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/main_overview/directories.html" title="Directory and File Structure">pdf</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/main_overview/directories.html" title="Directory and File Structure">real_concept</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/main_overview/directories.html" title="Directory and File Structure">RR</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/main_overview/directories.html" title="Directory and File Structure">tgamma</a></p></td></tr>
+</table></dd>
+<dt><span class="term">Discrete Probability Distributions</span></dt>
+<dd><table class="simplelist" border="0" summary="Simple list">
+<tr><td><p><a class="link" href="../math_toolkit/dist/stat_tut/dist_params.html" title="Discrete Probability Distributions">binomial</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/dist/stat_tut/dist_params.html" title="Discrete Probability Distributions">quantile</a></p></td></tr>
+</table></dd>
+<dt><span class="term">Discrete Quantile Policies</span></dt>
+<dd><table class="simplelist" border="0" summary="Simple list">
+<tr><td><p><a class="link" href="../math_toolkit/policy/pol_ref/discrete_quant_ref.html" title="Discrete Quantile Policies">cdf</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/policy/pol_ref/discrete_quant_ref.html" title="Discrete Quantile Policies">negative_binomial</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/policy/pol_ref/discrete_quant_ref.html" title="Discrete Quantile Policies">negative_binomial_distribution</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/policy/pol_ref/discrete_quant_ref.html" title="Discrete Quantile Policies">quantile</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/policy/pol_ref/discrete_quant_ref.html" title="Discrete Quantile Policies">round</a></p></td></tr>
+</table></dd>
+<dt><span class="term">discrete_quantile_type</span></dt>
+<dd><table class="simplelist" border="0" summary="Simple list"><tr><td><p><a class="link" href="../math_toolkit/policy/pol_ref/pol_ref_ref.html" title="Policy Class Reference">Policy Class Reference</a></p></td></tr></table></dd>
+<dt><span class="term">Distribution Algorithms</span></dt>
+<dd><table class="simplelist" border="0" summary="Simple list">
+<tr><td><p><a class="link" href="../math_toolkit/dist/dist_ref/dist_algorithms.html" title="Distribution Algorithms">find_location</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/dist/dist_ref/dist_algorithms.html" title="Distribution Algorithms">find_scale</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/dist/dist_ref/dist_algorithms.html" title="Distribution Algorithms">lognormal</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/dist/dist_ref/dist_algorithms.html" title="Distribution Algorithms">mean</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/dist/dist_ref/dist_algorithms.html" title="Distribution Algorithms">normal</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/dist/dist_ref/dist_algorithms.html" title="Distribution Algorithms">triangular</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/dist/dist_ref/dist_algorithms.html" title="Distribution Algorithms">value_type</a></p></td></tr>
+</table></dd>
+<dt><span class="term">DistributionConcept</span></dt>
+<dd><table class="simplelist" border="0" summary="Simple list"><tr><td><p><a class="link" href="../math_toolkit/using_udt/archetypes.html" title="Conceptual Archetypes and Testing">Conceptual Archetypes and Testing</a></p></td></tr></table></dd>
+<dt><span class="term">distribution_archetype</span></dt>
+<dd><table class="simplelist" border="0" summary="Simple list"><tr><td><p><a class="link" href="../math_toolkit/using_udt/archetypes.html" title="Conceptual Archetypes and Testing">Conceptual Archetypes and Testing</a></p></td></tr></table></dd>
+<dt><span class="term">domain_error_type</span></dt>
+<dd><table class="simplelist" border="0" summary="Simple list"><tr><td><p><a class="link" href="../math_toolkit/policy/pol_ref/pol_ref_ref.html" title="Policy Class Reference">Policy Class Reference</a></p></td></tr></table></dd>
+<dt><span class="term">Double Factorial</span></dt>
+<dd><table class="simplelist" border="0" summary="Simple list">
+<tr><td><p><a class="link" href="../math_toolkit/special/factorials/sf_double_factorial.html" title="Double Factorial">double_factorial</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/special/factorials/sf_double_factorial.html" title="Double Factorial">factorial</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/special/factorials/sf_double_factorial.html" title="Double Factorial">gamma</a></p></td></tr>
+</table></dd>
+<dt><span class="term">double_factorial</span></dt>
+<dd><table class="simplelist" border="0" summary="Simple list"><tr><td><p><a class="link" href="../math_toolkit/special/factorials/sf_double_factorial.html" title="Double Factorial">Double Factorial</a></p></td></tr></table></dd>
+<dt><span class="term">double_t</span></dt>
+<dd><table class="simplelist" border="0" summary="Simple list">
+<tr><td><p><a class="link" href="../math_toolkit/main_overview/tr1.html" title="C99 and TR1 C Functions">C99 and TR1 C Functions</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/special/extern_c/tr1.html" title="C99 and TR1 C Functions Overview">C99 and TR1 C Functions Overview</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/special/extern_c/c99.html" title="C99 C Functions">C99 C Functions</a></p></td></tr>
+</table></dd>
+</dl></div></dd>
+<dt>
+<a name="idx_id_59"></a><span class="term">E</span>
+</dt>
+<dd><div class="variablelist"><dl>
+<dt><span class="term">ellint_1</span></dt>
+<dd><table class="simplelist" border="0" summary="Simple list">
+<tr><td><p><a class="link" href="../math_toolkit/main_overview/tr1.html" title="C99 and TR1 C Functions">C99 and TR1 C Functions</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/special/extern_c/tr1.html" title="C99 and TR1 C Functions Overview">C99 and TR1 C Functions Overview</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/special/ellint/ellint_1.html" title="Elliptic Integrals of the First Kind - Legendre Form">Elliptic Integrals of the First Kind - Legendre Form</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/special/extern_c/tr1_ref.html" title="TR1 C Functions Quick Reference">TR1 C Functions Quick Reference</a></p></td></tr>
+</table></dd>
+<dt><span class="term">ellint_2</span></dt>
+<dd><table class="simplelist" border="0" summary="Simple list">
+<tr><td><p><a class="link" href="../math_toolkit/main_overview/tr1.html" title="C99 and TR1 C Functions">C99 and TR1 C Functions</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/special/extern_c/tr1.html" title="C99 and TR1 C Functions Overview">C99 and TR1 C Functions Overview</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/special/ellint/ellint_2.html" title="Elliptic Integrals of the Second Kind - Legendre Form">Elliptic Integrals of the Second Kind - Legendre Form</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/special/extern_c/tr1_ref.html" title="TR1 C Functions Quick Reference">TR1 C Functions Quick Reference</a></p></td></tr>
+</table></dd>
+<dt><span class="term">ellint_3</span></dt>
+<dd><table class="simplelist" border="0" summary="Simple list">
+<tr><td><p><a class="link" href="../math_toolkit/main_overview/tr1.html" title="C99 and TR1 C Functions">C99 and TR1 C Functions</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/special/extern_c/tr1.html" title="C99 and TR1 C Functions Overview">C99 and TR1 C Functions Overview</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/special/ellint/ellint_3.html" title="Elliptic Integrals of the Third Kind - Legendre Form">Elliptic Integrals of the Third Kind - Legendre Form</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/status/issues.html" title="Known Issues, and Todo List">Known Issues, and Todo List</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/special/extern_c/tr1_ref.html" title="TR1 C Functions Quick Reference">TR1 C Functions Quick Reference</a></p></td></tr>
+</table></dd>
+<dt><span class="term">ellint_rc</span></dt>
+<dd><table class="simplelist" border="0" summary="Simple list"><tr><td><p><a class="link" href="../math_toolkit/special/ellint/ellint_carlson.html" title="Elliptic Integrals - Carlson Form">Elliptic Integrals - Carlson Form</a></p></td></tr></table></dd>
+<dt><span class="term">ellint_rd</span></dt>
+<dd><table class="simplelist" border="0" summary="Simple list"><tr><td><p><a class="link" href="../math_toolkit/special/ellint/ellint_carlson.html" title="Elliptic Integrals - Carlson Form">Elliptic Integrals - Carlson Form</a></p></td></tr></table></dd>
+<dt><span class="term">ellint_rf</span></dt>
+<dd><table class="simplelist" border="0" summary="Simple list"><tr><td><p><a class="link" href="../math_toolkit/special/ellint/ellint_carlson.html" title="Elliptic Integrals - Carlson Form">Elliptic Integrals - Carlson Form</a></p></td></tr></table></dd>
+<dt><span class="term">ellint_rj</span></dt>
+<dd><table class="simplelist" border="0" summary="Simple list"><tr><td><p><a class="link" href="../math_toolkit/special/ellint/ellint_carlson.html" title="Elliptic Integrals - Carlson Form">Elliptic Integrals - Carlson Form</a></p></td></tr></table></dd>
+<dt><span class="term">Elliptic Integrals - Carlson Form</span></dt>
+<dd><table class="simplelist" border="0" summary="Simple list">
+<tr><td><p><a class="link" href="../math_toolkit/special/ellint/ellint_carlson.html" title="Elliptic Integrals - Carlson Form">ellint_rc</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/special/ellint/ellint_carlson.html" title="Elliptic Integrals - Carlson Form">ellint_rd</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/special/ellint/ellint_carlson.html" title="Elliptic Integrals - Carlson Form">ellint_rf</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/special/ellint/ellint_carlson.html" title="Elliptic Integrals - Carlson Form">ellint_rj</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/special/ellint/ellint_carlson.html" title="Elliptic Integrals - Carlson Form">RR</a></p></td></tr>
+</table></dd>
+<dt><span class="term">Elliptic Integrals of the First Kind - Legendre Form</span></dt>
+<dd><table class="simplelist" border="0" summary="Simple list">
+<tr><td><p><a class="link" href="../math_toolkit/special/ellint/ellint_1.html" title="Elliptic Integrals of the First Kind - Legendre Form">ellint_1</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/special/ellint/ellint_1.html" title="Elliptic Integrals of the First Kind - Legendre Form">RR</a></p></td></tr>
+</table></dd>
+<dt><span class="term">Elliptic Integrals of the Second Kind - Legendre Form</span></dt>
+<dd><table class="simplelist" border="0" summary="Simple list">
+<tr><td><p><a class="link" href="../math_toolkit/special/ellint/ellint_2.html" title="Elliptic Integrals of the Second Kind - Legendre Form">ellint_2</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/special/ellint/ellint_2.html" title="Elliptic Integrals of the Second Kind - Legendre Form">RR</a></p></td></tr>
+</table></dd>
+<dt><span class="term">Elliptic Integrals of the Third Kind - Legendre Form</span></dt>
+<dd><table class="simplelist" border="0" summary="Simple list">
+<tr><td><p><a class="link" href="../math_toolkit/special/ellint/ellint_3.html" title="Elliptic Integrals of the Third Kind - Legendre Form">ellint_3</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/special/ellint/ellint_3.html" title="Elliptic Integrals of the Third Kind - Legendre Form">RR</a></p></td></tr>
+</table></dd>
+<dt><span class="term">eps_tolerance</span></dt>
+<dd><table class="simplelist" border="0" summary="Simple list"><tr><td><p><a class="link" href="../math_toolkit/toolkit/internals1/roots2.html" title="Root Finding Without Derivatives">Root Finding Without Derivatives</a></p></td></tr></table></dd>
+<dt><span class="term">equal_ceil</span></dt>
+<dd><table class="simplelist" border="0" summary="Simple list"><tr><td><p><a class="link" href="../math_toolkit/toolkit/internals1/roots2.html" title="Root Finding Without Derivatives">Root Finding Without Derivatives</a></p></td></tr></table></dd>
+<dt><span class="term">equal_floor</span></dt>
+<dd><table class="simplelist" border="0" summary="Simple list"><tr><td><p><a class="link" href="../math_toolkit/toolkit/internals1/roots2.html" title="Root Finding Without Derivatives">Root Finding Without Derivatives</a></p></td></tr></table></dd>
+<dt><span class="term">equal_nearest_integer</span></dt>
+<dd><table class="simplelist" border="0" summary="Simple list"><tr><td><p><a class="link" href="../math_toolkit/toolkit/internals1/roots2.html" title="Root Finding Without Derivatives">Root Finding Without Derivatives</a></p></td></tr></table></dd>
+<dt><span class="term">erf</span></dt>
+<dd><table class="simplelist" border="0" summary="Simple list">
+<tr><td><p><a class="link" href="../math_toolkit/main_overview/intro.html" title="About the Math Toolkit">About the Math Toolkit</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/main_overview/tr1.html" title="C99 and TR1 C Functions">C99 and TR1 C Functions</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/special/extern_c/tr1.html" title="C99 and TR1 C Functions Overview">C99 and TR1 C Functions Overview</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/special/extern_c/c99.html" title="C99 C Functions">C99 C Functions</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/policy/pol_tutorial/user_def_err_pol.html" title="Calling User Defined Error Handlers">Calling User Defined Error Handlers</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/using_udt/concepts.html" title="Conceptual Requirements for Real Number Types">Conceptual Requirements for Real Number Types</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/status/credits.html" title="Credits and Acknowledgements">Credits and Acknowledgements</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/main_overview/directories.html" title="Directory and File Structure">Directory and File Structure</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/special/sf_erf/error_inv.html" title="Error Function Inverses">Error Function Inverses</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/special/sf_erf/error_function.html" title="Error Functions">Error Functions</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/special/sf_erf/error_function.html" title="Error Functions">Errors In the Function erf(z)</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/main_overview/history1.html" title="History and What's New">History and What's New</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/perf/getting_best.html" title="Getting the Best Performance from this Library">Performance Comparison of Release and Debug Settings</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/perf/comp_compilers.html" title="Comparing Compilers">Performance Comparison of Various Windows Compilers</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/perf/tuning.html" title="Performance Tuning Macros">Performance Comparison with and Without Internal Promotion to long double</a></p></td></tr>
+</table></dd>
+<dt><span class="term">erfc</span></dt>
+<dd><table class="simplelist" border="0" summary="Simple list">
+<tr><td><p><a class="link" href="../math_toolkit/main_overview/tr1.html" title="C99 and TR1 C Functions">C99 and TR1 C Functions</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/special/extern_c/tr1.html" title="C99 and TR1 C Functions Overview">C99 and TR1 C Functions Overview</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/special/extern_c/c99.html" title="C99 C Functions">C99 C Functions</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/special/sf_erf/error_inv.html" title="Error Function Inverses">Error Function Inverses</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/special/sf_erf/error_function.html" title="Error Functions">Error Functions</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/special/sf_erf/error_function.html" title="Error Functions">Errors In the Function erfc(z)</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/main_overview/history1.html" title="History and What's New">History and What's New</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/special/sf_gamma/igamma.html" title="Incomplete Gamma Functions">Incomplete Gamma Functions</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/dist/dist_ref/dists/normal_dist.html" title="Normal (Gaussian) Distribution">Normal (Gaussian) Distribution</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/backgrounders/remez.html" title="The Remez Method">The Remez Method</a></p></td></tr>
+</table></dd>
+<dt><span class="term">erfc_inv</span></dt>
+<dd><table class="simplelist" border="0" summary="Simple list">
+<tr><td><p><a class="link" href="../math_toolkit/special/sf_erf/error_inv.html" title="Error Function Inverses">Error Function Inverses</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/dist/dist_ref/dists/normal_dist.html" title="Normal (Gaussian) Distribution">Normal (Gaussian) Distribution</a></p></td></tr>
+</table></dd>
+<dt><span class="term">erf_inv</span></dt>
+<dd><table class="simplelist" border="0" summary="Simple list">
+<tr><td><p><a class="link" href="../math_toolkit/policy/pol_tutorial/user_def_err_pol.html" title="Calling User Defined Error Handlers">Calling User Defined Error Handlers</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/special/sf_erf/error_inv.html" title="Error Function Inverses">Error Function Inverses</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/perf/getting_best.html" title="Getting the Best Performance from this Library">Performance Comparison of Release and Debug Settings</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/perf/comp_compilers.html" title="Comparing Compilers">Performance Comparison of Various Windows Compilers</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/perf/tuning.html" title="Performance Tuning Macros">Performance Comparison with and Without Internal Promotion to long double</a></p></td></tr>
+</table></dd>
+<dt><span class="term">Error Function Inverses</span></dt>
+<dd><table class="simplelist" border="0" summary="Simple list">
+<tr><td><p><a class="link" href="../math_toolkit/special/sf_erf/error_inv.html" title="Error Function Inverses">erf</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/special/sf_erf/error_inv.html" title="Error Function Inverses">erfc</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/special/sf_erf/error_inv.html" title="Error Function Inverses">erfc_inv</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/special/sf_erf/error_inv.html" title="Error Function Inverses">erf_inv</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/special/sf_erf/error_inv.html" title="Error Function Inverses">round</a></p></td></tr>
+</table></dd>
+<dt><span class="term">Error Functions</span></dt>
+<dd><table class="simplelist" border="0" summary="Simple list">
+<tr><td><p><a class="link" href="../math_toolkit/special/sf_erf/error_function.html" title="Error Functions">erf</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/special/sf_erf/error_function.html" title="Error Functions">erfc</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/special/sf_erf/error_function.html" title="Error Functions">gamma</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/special/sf_erf/error_function.html" title="Error Functions">round</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/special/sf_erf/error_function.html" title="Error Functions">RR</a></p></td></tr>
+</table></dd>
+<dt><span class="term">Error Handling</span></dt>
+<dd><table class="simplelist" border="0" summary="Simple list">
+<tr><td><p><a class="link" href="../math_toolkit/main_overview/error_handling.html" title="Error Handling">checked_narrowing_cast</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/main_overview/error_handling.html" title="Error Handling">evaluation_error</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/main_overview/error_handling.html" title="Error Handling">raise_denorm_error</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/main_overview/error_handling.html" title="Error Handling">raise_domain_error</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/main_overview/error_handling.html" title="Error Handling">raise_evaluation_error</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/main_overview/error_handling.html" title="Error Handling">raise_overflow_error</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/main_overview/error_handling.html" title="Error Handling">raise_pole_error</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/main_overview/error_handling.html" title="Error Handling">raise_rounding_error</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/main_overview/error_handling.html" title="Error Handling">raise_underflow_error</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/main_overview/error_handling.html" title="Error Handling">round</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/main_overview/error_handling.html" title="Error Handling">rounding_error</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/main_overview/error_handling.html" title="Error Handling">tgamma</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/main_overview/error_handling.html" title="Error Handling">trunc</a></p></td></tr>
+</table></dd>
+<dt><span class="term">Error Handling Policies</span></dt>
+<dd><table class="simplelist" border="0" summary="Simple list">
+<tr><td><p><a class="link" href="../math_toolkit/policy/pol_ref/error_handling_policies.html" title="Error Handling Policies">evaluation_error</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/policy/pol_ref/error_handling_policies.html" title="Error Handling Policies">gamma</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/policy/pol_ref/error_handling_policies.html" title="Error Handling Policies">make_policy</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/policy/pol_ref/error_handling_policies.html" title="Error Handling Policies">normal</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/policy/pol_ref/error_handling_policies.html" title="Error Handling Policies">normal_distribution</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/policy/pol_ref/error_handling_policies.html" title="Error Handling Policies">quantile</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/policy/pol_ref/error_handling_policies.html" title="Error Handling Policies">round</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/policy/pol_ref/error_handling_policies.html" title="Error Handling Policies">rounding_error</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/policy/pol_ref/error_handling_policies.html" title="Error Handling Policies">tgamma</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/policy/pol_ref/error_handling_policies.html" title="Error Handling Policies">trunc</a></p></td></tr>
+</table></dd>
+<dt><span class="term">Errors In the Function beta(a, b, x)</span></dt>
+<dd><table class="simplelist" border="0" summary="Simple list"><tr><td><p><a class="link" href="../math_toolkit/special/sf_beta/ibeta_function.html" title="Incomplete Beta Functions">beta</a></p></td></tr></table></dd>
+<dt><span class="term">Errors In the Function betac(a,b,x)</span></dt>
+<dd><table class="simplelist" border="0" summary="Simple list"><tr><td><p><a class="link" href="../math_toolkit/special/sf_beta/ibeta_function.html" title="Incomplete Beta Functions">betac</a></p></td></tr></table></dd>
+<dt><span class="term">Errors In the Function erf(z)</span></dt>
+<dd><table class="simplelist" border="0" summary="Simple list"><tr><td><p><a class="link" href="../math_toolkit/special/sf_erf/error_function.html" title="Error Functions">erf</a></p></td></tr></table></dd>
+<dt><span class="term">Errors In the Function erfc(z)</span></dt>
+<dd><table class="simplelist" border="0" summary="Simple list"><tr><td><p><a class="link" href="../math_toolkit/special/sf_erf/error_function.html" title="Error Functions">erfc</a></p></td></tr></table></dd>
+<dt><span class="term">Errors In the Function expint(n, z)</span></dt>
+<dd><table class="simplelist" border="0" summary="Simple list"><tr><td><p><a class="link" href="../math_toolkit/special/expint/expint_n.html" title="Exponential Integral En">expint</a></p></td></tr></table></dd>
+<dt><span class="term">Errors In the Function expint(z)</span></dt>
+<dd><table class="simplelist" border="0" summary="Simple list"><tr><td><p><a class="link" href="../math_toolkit/special/expint/expint_i.html" title="Exponential Integral Ei">expint</a></p></td></tr></table></dd>
+<dt><span class="term">Errors In the Function gamma_p(a,z)</span></dt>
+<dd><table class="simplelist" border="0" summary="Simple list"><tr><td><p><a class="link" href="../math_toolkit/special/sf_gamma/igamma.html" title="Incomplete Gamma Functions">gamma_p</a></p></td></tr></table></dd>
+<dt><span class="term">Errors In the Function gamma_q(a,z)</span></dt>
+<dd><table class="simplelist" border="0" summary="Simple list"><tr><td><p><a class="link" href="../math_toolkit/special/sf_gamma/igamma.html" title="Incomplete Gamma Functions">gamma_q</a></p></td></tr></table></dd>
+<dt><span class="term">Errors In the Function ibeta(a,b,x)</span></dt>
+<dd><table class="simplelist" border="0" summary="Simple list"><tr><td><p><a class="link" href="../math_toolkit/special/sf_beta/ibeta_function.html" title="Incomplete Beta Functions">ibeta</a></p></td></tr></table></dd>
+<dt><span class="term">Errors In the Function ibetac(a,b,x)</span></dt>
+<dd><table class="simplelist" border="0" summary="Simple list"><tr><td><p><a class="link" href="../math_toolkit/special/sf_beta/ibeta_function.html" title="Incomplete Beta Functions">ibetac</a></p></td></tr></table></dd>
+<dt><span class="term">Errors In the Function tgamma(a,z)</span></dt>
+<dd><table class="simplelist" border="0" summary="Simple list"><tr><td><p><a class="link" href="../math_toolkit/special/sf_gamma/igamma.html" title="Incomplete Gamma Functions">tgamma</a></p></td></tr></table></dd>
+<dt><span class="term">Errors In the Function tgamma_delta_ratio(a, delta)</span></dt>
+<dd><table class="simplelist" border="0" summary="Simple list"><tr><td><p><a class="link" href="../math_toolkit/special/sf_gamma/gamma_ratios.html" title="Ratios of Gamma Functions">tgamma_delta_ratio</a></p></td></tr></table></dd>
+<dt><span class="term">Errors In the Function tgamma_lower(a,z)</span></dt>
+<dd><table class="simplelist" border="0" summary="Simple list"><tr><td><p><a class="link" href="../math_toolkit/special/sf_gamma/igamma.html" title="Incomplete Gamma Functions">tgamma_lower</a></p></td></tr></table></dd>
+<dt><span class="term">Errors In the Function tgamma_ratio(a, b)</span></dt>
+<dd><table class="simplelist" border="0" summary="Simple list"><tr><td><p><a class="link" href="../math_toolkit/special/sf_gamma/gamma_ratios.html" title="Ratios of Gamma Functions">tgamma_ratio</a></p></td></tr></table></dd>
+<dt><span class="term">Errors In the Function zeta(z)</span></dt>
+<dd><table class="simplelist" border="0" summary="Simple list"><tr><td><p><a class="link" href="../math_toolkit/special/zetas/zeta.html" title="Riemann Zeta Function">zeta</a></p></td></tr></table></dd>
+<dt><span class="term">Errors Rates in cyl_bessel_i</span></dt>
+<dd><table class="simplelist" border="0" summary="Simple list"><tr><td><p><a class="link" href="../math_toolkit/special/bessel/mbessel.html" title="Modified Bessel Functions of the First and Second Kinds">cyl_bessel_i</a></p></td></tr></table></dd>
+<dt><span class="term">Errors Rates in cyl_bessel_j</span></dt>
+<dd><table class="simplelist" border="0" summary="Simple list"><tr><td><p><a class="link" href="../math_toolkit/special/bessel/bessel.html" title="Bessel Functions of the First and Second Kinds">cyl_bessel_j</a></p></td></tr></table></dd>
+<dt><span class="term">Errors Rates in cyl_bessel_k</span></dt>
+<dd><table class="simplelist" border="0" summary="Simple list"><tr><td><p><a class="link" href="../math_toolkit/special/bessel/mbessel.html" title="Modified Bessel Functions of the First and Second Kinds">cyl_bessel_k</a></p></td></tr></table></dd>
+<dt><span class="term">Errors Rates in cyl_neumann</span></dt>
+<dd><table class="simplelist" border="0" summary="Simple list"><tr><td><p><a class="link" href="../math_toolkit/special/bessel/bessel.html" title="Bessel Functions of the First and Second Kinds">cyl_neumann</a></p></td></tr></table></dd>
+<dt><span class="term">evaluate_even_polynomial</span></dt>
+<dd><table class="simplelist" border="0" summary="Simple list"><tr><td><p><a class="link" href="../math_toolkit/toolkit/internals1/rational.html" title="Polynomial and Rational Function Evaluation">Polynomial and Rational Function Evaluation</a></p></td></tr></table></dd>
+<dt><span class="term">evaluate_odd_polynomial</span></dt>
+<dd><table class="simplelist" border="0" summary="Simple list"><tr><td><p><a class="link" href="../math_toolkit/toolkit/internals1/rational.html" title="Polynomial and Rational Function Evaluation">Polynomial and Rational Function Evaluation</a></p></td></tr></table></dd>
+<dt><span class="term">evaluate_polynomial</span></dt>
+<dd><table class="simplelist" border="0" summary="Simple list"><tr><td><p><a class="link" href="../math_toolkit/toolkit/internals1/rational.html" title="Polynomial and Rational Function Evaluation">Polynomial and Rational Function Evaluation</a></p></td></tr></table></dd>
+<dt><span class="term">evaluate_rational</span></dt>
+<dd><table class="simplelist" border="0" summary="Simple list">
+<tr><td><p><a class="link" href="../math_toolkit/perf/tuning.html" title="Performance Tuning Macros">Performance Tuning Macros</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/toolkit/internals1/rational.html" title="Polynomial and Rational Function Evaluation">Polynomial and Rational Function Evaluation</a></p></td></tr>
+</table></dd>
+<dt><span class="term">evaluation_error</span></dt>
+<dd><table class="simplelist" border="0" summary="Simple list">
+<tr><td><p><a class="link" href="../math_toolkit/policy/pol_tutorial/user_def_err_pol.html" title="Calling User Defined Error Handlers">Calling User Defined Error Handlers</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/policy/pol_tutorial/ad_hoc_sf_policies.html" title="Changing the Policy on an Ad Hoc Basis for the Special Functions">Changing the Policy on an Ad Hoc Basis for the Special Functions</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/main_overview/pol_overview.html" title="Configuration and Policies">Configuration and Policies</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/main_overview/error_handling.html" title="Error Handling">Error Handling</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/policy/pol_ref/error_handling_policies.html" title="Error Handling Policies">Error Handling Policies</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/main_overview/history1.html" title="History and What's New">History and What's New</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/policy/pol_ref/iteration_pol.html" title="Iteration Limits Policies">Iteration Limits Policies</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/policy/pol_tutorial/policy_tut_defaults.html" title="Policies Have Sensible Defaults">Policies Have Sensible Defaults</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/policy/pol_ref/pol_ref_ref.html" title="Policy Class Reference">Policy Class Reference</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/policy/pol_overview.html" title="Policy Overview">Policy Overview</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/main_overview/error_handling.html" title="Error Handling">Possible Actions for Internal Evaluation Errors</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/policy/pol_tutorial/namespace_policies.html" title="Setting Policies at Namespace or Translation Unit Scope">Setting Policies at Namespace or Translation Unit Scope</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/policy/pol_ref/policy_defaults.html" title="Using macros to Change the Policy Defaults">Using macros to Change the Policy Defaults</a></p></td></tr>
+</table></dd>
+<dt><span class="term">evaluation_error_type</span></dt>
+<dd><table class="simplelist" border="0" summary="Simple list"><tr><td><p><a class="link" href="../math_toolkit/policy/pol_ref/pol_ref_ref.html" title="Policy Class Reference">Policy Class Reference</a></p></td></tr></table></dd>
+<dt><span class="term">Examples</span></dt>
+<dd><table class="simplelist" border="0" summary="Simple list">
+<tr><td><p><a class="link" href="../math_toolkit/dist/stat_tut/weg/dist_construct_eg.html" title="Distribution Construction Example">beta</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/dist/stat_tut/weg/dist_construct_eg.html" title="Distribution Construction Example">beta_distribution</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/dist/stat_tut/weg/dist_construct_eg.html" title="Distribution Construction Example">binomial</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/dist/stat_tut/weg/dist_construct_eg.html" title="Distribution Construction Example">binomial_distribution</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/dist/stat_tut/weg/binom_eg/binomial_quiz_example.html" title="Binomial Quiz Example">BOOST_MATH_DISCRETE_QUANTILE_POLICY</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/dist/stat_tut/weg/error_eg.html" title="Error Handling Example">BOOST_MATH_DOMAIN_ERROR_POLICY</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/dist/stat_tut/weg/neg_binom_eg/negative_binomial_example1.html" title="Negative Binomial Sales Quota Example.">BOOST_MATH_OVERFLOW_ERROR_POLICY</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/dist/stat_tut/weg/find_eg/find_location_eg.html" title="Find Location (Mean) Example">cauchy</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/dist/stat_tut/weg/find_eg/find_location_eg.html" title="Find Location (Mean) Example">cauchy_distribution</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/dist/stat_tut/weg/st_eg/tut_mean_test.html" title='Testing a sample mean for difference from a "true" mean'>cdf</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/dist/stat_tut/weg/cs_eg/chi_sq_intervals.html" title="Confidence Intervals on the Standard Deviation">chi_squared</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/dist/stat_tut/weg/cs_eg/chi_sq_size.html" title="Estimating the Required Sample Sizes for a Chi-Square Test for the Standard Deviation">chi_squared_distribution</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/dist/stat_tut/weg/st_eg/tut_mean_size.html" title="Estimating how large a sample size would have to become in order to give a significant Students-t test result with a single sample test">find_degrees_of_freedom</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/dist/stat_tut/weg/find_eg/find_location_eg.html" title="Find Location (Mean) Example">find_location</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/dist/stat_tut/weg/find_eg/find_location_eg.html" title="Find Location (Mean) Example">find_scale</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/dist/stat_tut/weg/f_eg.html" title="F Distribution Examples">fisher_f</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/dist/stat_tut/weg/dist_construct_eg.html" title="Distribution Construction Example">gamma</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/dist/stat_tut/weg/dist_construct_eg.html" title="Distribution Construction Example">gamma_distribution</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/dist/stat_tut/weg/dist_construct_eg.html" title="Distribution Construction Example">mean</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/dist/stat_tut/weg/cs_eg/chi_sq_intervals.html" title="Confidence Intervals on the Standard Deviation">median</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/dist/stat_tut/weg/binom_eg/binomial_coinflip_example.html" title="Binomial Coin-Flipping Example">mode</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/dist/stat_tut/weg/dist_construct_eg.html" title="Distribution Construction Example">negative_binomial</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/dist/stat_tut/weg/dist_construct_eg.html" title="Distribution Construction Example">negative_binomial_distribution</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/dist/stat_tut/weg/nccs_eg/nccs_power_eg.html" title="Tables of the power function of the &#967;2 test.">non_central_chi_squared</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/dist/stat_tut/weg/dist_construct_eg.html" title="Distribution Construction Example">normal</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/dist/stat_tut/weg/dist_construct_eg.html" title="Distribution Construction Example">normal_distribution</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/dist/stat_tut/weg/binom_eg/binomial_coinflip_example.html" title="Binomial Coin-Flipping Example">pdf</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/dist/stat_tut/weg/cs_eg/chi_sq_intervals.html" title="Confidence Intervals on the Standard Deviation">quantile</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/dist/stat_tut/weg/find_eg/find_scale_eg.html" title="Find Scale (Standard Deviation) Example">round</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/dist/stat_tut/weg/dist_construct_eg.html" title="Distribution Construction Example">RR</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/dist/stat_tut/weg/binom_eg/binomial_coinflip_example.html" title="Binomial Coin-Flipping Example">skewness</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/dist/stat_tut/weg/binom_eg/binomial_coinflip_example.html" title="Binomial Coin-Flipping Example">standard_deviation</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/dist/stat_tut/weg/st_eg/tut_mean_test.html" title='Testing a sample mean for difference from a "true" mean'>students_t</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/dist/stat_tut/weg/st_eg/tut_mean_size.html" title="Estimating how large a sample size would have to become in order to give a significant Students-t test result with a single sample test">students_t_distribution</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/dist/stat_tut/weg/st_eg/two_sample_students_t.html" title="Comparing the means of two samples with the Students-t test">variance</a></p></td></tr>
+</table></dd>
+<dt><span class="term">expint</span></dt>
+<dd><table class="simplelist" border="0" summary="Simple list">
+<tr><td><p><a class="link" href="../math_toolkit/main_overview/tr1.html" title="C99 and TR1 C Functions">C99 and TR1 C Functions</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/special/extern_c/tr1.html" title="C99 and TR1 C Functions Overview">C99 and TR1 C Functions Overview</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/special/expint/expint_n.html" title="Exponential Integral En">Errors In the Function expint(n, z)</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/special/expint/expint_i.html" title="Exponential Integral Ei">Errors In the Function expint(z)</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/special/expint/expint_i.html" title="Exponential Integral Ei">Exponential Integral Ei</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/special/expint/expint_n.html" title="Exponential Integral En">Exponential Integral En</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/special/extern_c/tr1_ref.html" title="TR1 C Functions Quick Reference">TR1 C Functions Quick Reference</a></p></td></tr>
+</table></dd>
+<dt><span class="term">expm1</span></dt>
+<dd><table class="simplelist" border="0" summary="Simple list">
+<tr><td><p><a class="link" href="../math_toolkit/main_overview/tr1.html" title="C99 and TR1 C Functions">C99 and TR1 C Functions</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/special/extern_c/tr1.html" title="C99 and TR1 C Functions Overview">C99 and TR1 C Functions Overview</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/special/extern_c/c99.html" title="C99 C Functions">C99 C Functions</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/special/powers/expm1.html" title="expm1">expm1</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/dist/dist_ref/dists/exp_dist.html" title="Exponential Distribution">Exponential Distribution</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/dist/dist_ref/dists/extreme_dist.html" title="Extreme Value Distribution">Extreme Value Distribution</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/special/sf_gamma/tgamma.html" title="Gamma">Gamma</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/dist/dist_ref/dists/pareto.html" title="Pareto Distribution">Pareto Distribution</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/special/powers/powm1.html" title="powm1">powm1</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/dist/dist_ref/dists/rayleigh.html" title="Rayleigh Distribution">Rayleigh Distribution</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/special/powers/expm1.html" title="expm1">RR</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/special/powers/sqrt1pm1.html" title="sqrt1pm1">sqrt1pm1</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/dist/dist_ref/dists/weibull.html" title="Weibull Distribution">Weibull Distribution</a></p></td></tr>
+</table></dd>
+<dt><span class="term">exponential</span></dt>
+<dd><table class="simplelist" border="0" summary="Simple list">
+<tr><td><p><a class="link" href="../math_toolkit/backgrounders/implementation.html" title="Additional Implementation Notes">Additional Implementation Notes</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/main_overview/tr1.html" title="C99 and TR1 C Functions">C99 and TR1 C Functions</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/special/extern_c/tr1.html" title="C99 and TR1 C Functions Overview">C99 and TR1 C Functions Overview</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/dist/dist_ref/dists/exp_dist.html" title="Exponential Distribution">Exponential Distribution</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/special/expint/expint_i.html" title="Exponential Integral Ei">Exponential Integral Ei</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/special/expint/expint_n.html" title="Exponential Integral En">Exponential Integral En</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/special/inv_hyper/inv_hyper_over.html" title="Inverse Hyperbolic Functions Overview">Inverse Hyperbolic Functions Overview</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/special/bessel/mbessel.html" title="Modified Bessel Functions of the First and Second Kinds">Modified Bessel Functions of the First and Second Kinds</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/special/extern_c/tr1_ref.html" title="TR1 C Functions Quick Reference">TR1 C Functions Quick Reference</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/dist/dist_ref/dists/weibull.html" title="Weibull Distribution">Weibull Distribution</a></p></td></tr>
+</table></dd>
+<dt><span class="term">Exponential Distribution</span></dt>
+<dd><table class="simplelist" border="0" summary="Simple list">
+<tr><td><p><a class="link" href="../math_toolkit/dist/dist_ref/dists/exp_dist.html" title="Exponential Distribution">cdf</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/dist/dist_ref/dists/exp_dist.html" title="Exponential Distribution">expm1</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/dist/dist_ref/dists/exp_dist.html" title="Exponential Distribution">exponential</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/dist/dist_ref/dists/exp_dist.html" title="Exponential Distribution">exponential_distribution</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/dist/dist_ref/dists/exp_dist.html" title="Exponential Distribution">kurtosis</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/dist/dist_ref/dists/exp_dist.html" title="Exponential Distribution">kurtosis_excess</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/dist/dist_ref/dists/exp_dist.html" title="Exponential Distribution">log1p</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/dist/dist_ref/dists/exp_dist.html" title="Exponential Distribution">mean</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/dist/dist_ref/dists/exp_dist.html" title="Exponential Distribution">median</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/dist/dist_ref/dists/exp_dist.html" title="Exponential Distribution">mode</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/dist/dist_ref/dists/exp_dist.html" title="Exponential Distribution">pdf</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/dist/dist_ref/dists/exp_dist.html" title="Exponential Distribution">policy_type</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/dist/dist_ref/dists/exp_dist.html" title="Exponential Distribution">quantile</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/dist/dist_ref/dists/exp_dist.html" title="Exponential Distribution">skewness</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/dist/dist_ref/dists/exp_dist.html" title="Exponential Distribution">value_type</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/dist/dist_ref/dists/exp_dist.html" title="Exponential Distribution">variance</a></p></td></tr>
+</table></dd>
+<dt><span class="term">Exponential Integral Ei</span></dt>
+<dd><table class="simplelist" border="0" summary="Simple list">
+<tr><td><p><a class="link" href="../math_toolkit/special/expint/expint_i.html" title="Exponential Integral Ei">expint</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/special/expint/expint_i.html" title="Exponential Integral Ei">exponential</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/special/expint/expint_i.html" title="Exponential Integral Ei">RR</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/special/expint/expint_i.html" title="Exponential Integral Ei">zeta</a></p></td></tr>
+</table></dd>
+<dt><span class="term">Exponential Integral En</span></dt>
+<dd><table class="simplelist" border="0" summary="Simple list">
+<tr><td><p><a class="link" href="../math_toolkit/special/expint/expint_n.html" title="Exponential Integral En">expint</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/special/expint/expint_n.html" title="Exponential Integral En">exponential</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/special/expint/expint_n.html" title="Exponential Integral En">RR</a></p></td></tr>
+</table></dd>
+<dt><span class="term">exponential_distribution</span></dt>
+<dd><table class="simplelist" border="0" summary="Simple list"><tr><td><p><a class="link" href="../math_toolkit/dist/dist_ref/dists/exp_dist.html" title="Exponential Distribution">Exponential Distribution</a></p></td></tr></table></dd>
+<dt><span class="term">Extras/Future Directions</span></dt>
+<dd><table class="simplelist" border="0" summary="Simple list">
+<tr><td><p><a class="link" href="../math_toolkit/dist/future.html" title="Extras/Future Directions">cdf</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/dist/future.html" title="Extras/Future Directions">mean</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/dist/future.html" title="Extras/Future Directions">value_type</a></p></td></tr>
+</table></dd>
+<dt><span class="term">Extreme Value Distribution</span></dt>
+<dd><table class="simplelist" border="0" summary="Simple list">
+<tr><td><p><a class="link" href="../math_toolkit/dist/dist_ref/dists/extreme_dist.html" title="Extreme Value Distribution">cdf</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/dist/dist_ref/dists/extreme_dist.html" title="Extreme Value Distribution">expm1</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/dist/dist_ref/dists/extreme_dist.html" title="Extreme Value Distribution">extreme_value</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/dist/dist_ref/dists/extreme_dist.html" title="Extreme Value Distribution">extreme_value_distribution</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/dist/dist_ref/dists/extreme_dist.html" title="Extreme Value Distribution">kurtosis</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/dist/dist_ref/dists/extreme_dist.html" title="Extreme Value Distribution">kurtosis_excess</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/dist/dist_ref/dists/extreme_dist.html" title="Extreme Value Distribution">log1p</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/dist/dist_ref/dists/extreme_dist.html" title="Extreme Value Distribution">mean</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/dist/dist_ref/dists/extreme_dist.html" title="Extreme Value Distribution">median</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/dist/dist_ref/dists/extreme_dist.html" title="Extreme Value Distribution">mode</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/dist/dist_ref/dists/extreme_dist.html" title="Extreme Value Distribution">pdf</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/dist/dist_ref/dists/extreme_dist.html" title="Extreme Value Distribution">quantile</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/dist/dist_ref/dists/extreme_dist.html" title="Extreme Value Distribution">skewness</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/dist/dist_ref/dists/extreme_dist.html" title="Extreme Value Distribution">value_type</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/dist/dist_ref/dists/extreme_dist.html" title="Extreme Value Distribution">variance</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/dist/dist_ref/dists/extreme_dist.html" title="Extreme Value Distribution">zeta</a></p></td></tr>
+</table></dd>
+<dt><span class="term">extreme_value</span></dt>
+<dd><table class="simplelist" border="0" summary="Simple list"><tr><td><p><a class="link" href="../math_toolkit/dist/dist_ref/dists/extreme_dist.html" title="Extreme Value Distribution">Extreme Value Distribution</a></p></td></tr></table></dd>
+<dt><span class="term">extreme_value_distribution</span></dt>
+<dd><table class="simplelist" border="0" summary="Simple list"><tr><td><p><a class="link" href="../math_toolkit/dist/dist_ref/dists/extreme_dist.html" title="Extreme Value Distribution">Extreme Value Distribution</a></p></td></tr></table></dd>
+</dl></div></dd>
+<dt>
+<a name="idx_id_60"></a><span class="term">F</span>
+</dt>
+<dd><div class="variablelist"><dl>
+<dt><span class="term">F Distribution</span></dt>
+<dd><table class="simplelist" border="0" summary="Simple list">
+<tr><td><p><a class="link" href="../math_toolkit/dist/dist_ref/dists/f_dist.html" title="F Distribution">beta</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/dist/dist_ref/dists/f_dist.html" title="F Distribution">cdf</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/dist/dist_ref/dists/f_dist.html" title="F Distribution">fisher_f</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/dist/dist_ref/dists/f_dist.html" title="F Distribution">fisher_f_distribution</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/dist/dist_ref/dists/f_dist.html" title="F Distribution">ibeta</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/dist/dist_ref/dists/f_dist.html" title="F Distribution">ibetac</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/dist/dist_ref/dists/f_dist.html" title="F Distribution">ibetac_inv</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/dist/dist_ref/dists/f_dist.html" title="F Distribution">ibeta_derivative</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/dist/dist_ref/dists/f_dist.html" title="F Distribution">ibeta_inv</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/dist/dist_ref/dists/f_dist.html" title="F Distribution">kurtosis</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/dist/dist_ref/dists/f_dist.html" title="F Distribution">kurtosis_excess</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/dist/dist_ref/dists/f_dist.html" title="F Distribution">mean</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/dist/dist_ref/dists/f_dist.html" title="F Distribution">median</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/dist/dist_ref/dists/f_dist.html" title="F Distribution">mode</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/dist/dist_ref/dists/f_dist.html" title="F Distribution">normal</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/dist/dist_ref/dists/f_dist.html" title="F Distribution">pdf</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/dist/dist_ref/dists/f_dist.html" title="F Distribution">quantile</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/dist/dist_ref/dists/f_dist.html" title="F Distribution">skewness</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/dist/dist_ref/dists/f_dist.html" title="F Distribution">value_type</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/dist/dist_ref/dists/f_dist.html" title="F Distribution">variance</a></p></td></tr>
+</table></dd>
+<dt><span class="term">factorial</span></dt>
+<dd><table class="simplelist" border="0" summary="Simple list">
+<tr><td><p><a class="link" href="../math_toolkit/main_overview/intro.html" title="About the Math Toolkit">About the Math Toolkit</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/status/credits.html" title="Credits and Acknowledgements">Credits and Acknowledgements</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/special/factorials/sf_double_factorial.html" title="Double Factorial">Double Factorial</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/special/factorials/sf_factorial.html" title="Factorial">factorial</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/special/factorials/sf_falling_factorial.html" title="Falling Factorial">Falling Factorial</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/special/sf_gamma/tgamma.html" title="Gamma">Gamma</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/main_overview/history1.html" title="History and What's New">History and What's New</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/special/inv_hyper/inv_hyper_over.html" title="Inverse Hyperbolic Functions Overview">Inverse Hyperbolic Functions Overview</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/special/factorials/sf_factorial.html" title="Factorial">max_factorial</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/special/sf_gamma/gamma_ratios.html" title="Ratios of Gamma Functions">Ratios of Gamma Functions</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/special/factorials/sf_rising_factorial.html" title="Rising Factorial">Rising Factorial</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/special/factorials/sf_factorial.html" title="Factorial">tgamma</a></p></td></tr>
+</table></dd>
+<dt><span class="term">Falling Factorial</span></dt>
+<dd><table class="simplelist" border="0" summary="Simple list">
+<tr><td><p><a class="link" href="../math_toolkit/special/factorials/sf_falling_factorial.html" title="Falling Factorial">factorial</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/special/factorials/sf_falling_factorial.html" title="Falling Factorial">falling_factorial</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/special/factorials/sf_falling_factorial.html" title="Falling Factorial">gamma</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/special/factorials/sf_falling_factorial.html" title="Falling Factorial">tgamma_delta_ratio</a></p></td></tr>
+</table></dd>
+<dt><span class="term">falling_factorial</span></dt>
+<dd><table class="simplelist" border="0" summary="Simple list"><tr><td><p><a class="link" href="../math_toolkit/special/factorials/sf_falling_factorial.html" title="Falling Factorial">Falling Factorial</a></p></td></tr></table></dd>
+<dt><span class="term">Finding the Next Greater Representable Value (float_next)</span></dt>
+<dd><table class="simplelist" border="0" summary="Simple list">
+<tr><td><p><a class="link" href="../math_toolkit/special/next_float/float_next.html" title="Finding the Next Greater Representable Value (float_next)">float_next</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/special/next_float/float_next.html" title="Finding the Next Greater Representable Value (float_next)">nextafter</a></p></td></tr>
+</table></dd>
+<dt><span class="term">Finding the Next Representable Value in a Specific Direction (nextafter)</span></dt>
+<dd><table class="simplelist" border="0" summary="Simple list"><tr><td><p><a class="link" href="../math_toolkit/special/next_float/nextafter.html" title="Finding the Next Representable Value in a Specific Direction (nextafter)">nextafter</a></p></td></tr></table></dd>
+<dt><span class="term">Finding the Next Smaller Representable Value (float_prior)</span></dt>
+<dd><table class="simplelist" border="0" summary="Simple list">
+<tr><td><p><a class="link" href="../math_toolkit/special/next_float/float_prior.html" title="Finding the Next Smaller Representable Value (float_prior)">float_prior</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/special/next_float/float_prior.html" title="Finding the Next Smaller Representable Value (float_prior)">nextafter</a></p></td></tr>
+</table></dd>
+<dt><span class="term">find_degrees_of_freedom</span></dt>
+<dd><table class="simplelist" border="0" summary="Simple list">
+<tr><td><p><a class="link" href="../math_toolkit/dist/dist_ref/dists/chi_squared_dist.html" title="Chi Squared Distribution">Chi Squared Distribution</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/dist/stat_tut/weg/st_eg/tut_mean_size.html" title="Estimating how large a sample size would have to become in order to give a significant Students-t test result with a single sample test">Estimating how large a sample size would have to become in order to give a significant Students-t test result with a single sample test</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/dist/stat_tut/weg/cs_eg/chi_sq_size.html" title="Estimating the Required Sample Sizes for a Chi-Square Test for the Standard Deviation">Estimating the Required Sample Sizes for a Chi-Square Test for the Standard Deviation</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/dist/dist_ref/dists/nc_chi_squared_dist.html" title="Noncentral Chi-Squared Distribution">Noncentral Chi-Squared Distribution</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/dist/stat_tut/overview.html" title="Overview">Overview</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/dist/dist_ref/dists/students_t_dist.html" title="Students t Distribution">Students t Distribution</a></p></td></tr>
+</table></dd>
+<dt><span class="term">find_location</span></dt>
+<dd><table class="simplelist" border="0" summary="Simple list">
+<tr><td><p><a class="link" href="../math_toolkit/dist/dist_ref/dist_algorithms.html" title="Distribution Algorithms">Distribution Algorithms</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/dist/stat_tut/weg/find_eg/find_location_eg.html" title="Find Location (Mean) Example">Find Location (Mean) Example</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/dist/stat_tut/weg/find_eg/find_mean_and_sd_eg.html" title="Find mean and standard deviation example">Find mean and standard deviation example</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/dist/dist_ref/dists/normal_dist.html" title="Normal (Gaussian) Distribution">Normal (Gaussian) Distribution</a></p></td></tr>
+</table></dd>
+<dt><span class="term">find_lower_bound_on_p</span></dt>
+<dd><table class="simplelist" border="0" summary="Simple list">
+<tr><td><p><a class="link" href="../math_toolkit/dist/dist_ref/dists/binomial_dist.html" title="Binomial Distribution">Binomial Distribution</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/dist/stat_tut/weg/binom_eg/binom_conf.html" title="Calculating Confidence Limits on the Frequency of Occurrence for a Binomial Distribution">Calculating Confidence Limits on the Frequency of Occurrence for a Binomial Distribution</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/dist/stat_tut/weg/neg_binom_eg/neg_binom_conf.html" title="Calculating Confidence Limits on the Frequency of Occurrence for the Negative Binomial Distribution">Calculating Confidence Limits on the Frequency of Occurrence for the Negative Binomial Distribution</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/dist/dist_ref/dists/negative_binomial_dist.html" title="Negative Binomial Distribution">Negative Binomial Distribution</a></p></td></tr>
+</table></dd>
+<dt><span class="term">find_non_centrality</span></dt>
+<dd><table class="simplelist" border="0" summary="Simple list"><tr><td><p><a class="link" href="../math_toolkit/dist/dist_ref/dists/nc_chi_squared_dist.html" title="Noncentral Chi-Squared Distribution">Noncentral Chi-Squared Distribution</a></p></td></tr></table></dd>
+<dt><span class="term">find_scale</span></dt>
+<dd><table class="simplelist" border="0" summary="Simple list">
+<tr><td><p><a class="link" href="../math_toolkit/dist/dist_ref/dist_algorithms.html" title="Distribution Algorithms">Distribution Algorithms</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/dist/stat_tut/weg/find_eg/find_location_eg.html" title="Find Location (Mean) Example">Find Location (Mean) Example</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/dist/stat_tut/weg/find_eg/find_mean_and_sd_eg.html" title="Find mean and standard deviation example">Find mean and standard deviation example</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/dist/stat_tut/weg/find_eg/find_scale_eg.html" title="Find Scale (Standard Deviation) Example">Find Scale (Standard Deviation) Example</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/dist/dist_ref/dists/normal_dist.html" title="Normal (Gaussian) Distribution">Normal (Gaussian) Distribution</a></p></td></tr>
+</table></dd>
+<dt><span class="term">find_upper_bound_on_p</span></dt>
+<dd><table class="simplelist" border="0" summary="Simple list">
+<tr><td><p><a class="link" href="../math_toolkit/dist/dist_ref/dists/binomial_dist.html" title="Binomial Distribution">Binomial Distribution</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/dist/stat_tut/weg/binom_eg/binom_conf.html" title="Calculating Confidence Limits on the Frequency of Occurrence for a Binomial Distribution">Calculating Confidence Limits on the Frequency of Occurrence for a Binomial Distribution</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/dist/stat_tut/weg/neg_binom_eg/neg_binom_conf.html" title="Calculating Confidence Limits on the Frequency of Occurrence for the Negative Binomial Distribution">Calculating Confidence Limits on the Frequency of Occurrence for the Negative Binomial Distribution</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/dist/dist_ref/dists/negative_binomial_dist.html" title="Negative Binomial Distribution">Negative Binomial Distribution</a></p></td></tr>
+</table></dd>
+<dt><span class="term">fisher_f</span></dt>
+<dd><table class="simplelist" border="0" summary="Simple list">
+<tr><td><p><a class="link" href="../math_toolkit/dist/dist_ref/dists/f_dist.html" title="F Distribution">F Distribution</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/dist/stat_tut/weg/f_eg.html" title="F Distribution Examples">F Distribution Examples</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/policy/pol_tutorial/ad_hoc_dist_policies.html" title="Setting Policies for Distributions on an Ad Hoc Basis">Setting Policies for Distributions on an Ad Hoc Basis</a></p></td></tr>
+</table></dd>
+<dt><span class="term">fisher_f_distribution</span></dt>
+<dd><table class="simplelist" border="0" summary="Simple list">
+<tr><td><p><a class="link" href="../math_toolkit/dist/dist_ref/dists/f_dist.html" title="F Distribution">F Distribution</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/policy/pol_tutorial/ad_hoc_dist_policies.html" title="Setting Policies for Distributions on an Ad Hoc Basis">Setting Policies for Distributions on an Ad Hoc Basis</a></p></td></tr>
+</table></dd>
+<dt><span class="term">Floating-Point Classification: Infinities and NaN's</span></dt>
+<dd><table class="simplelist" border="0" summary="Simple list">
+<tr><td><p><a class="link" href="../math_toolkit/special/fpclass.html" title="Floating-Point Classification: Infinities and NaN's">FP_INFINITE</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/special/fpclass.html" title="Floating-Point Classification: Infinities and NaN's">FP_NAN</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/special/fpclass.html" title="Floating-Point Classification: Infinities and NaN's">FP_NORMAL</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/special/fpclass.html" title="Floating-Point Classification: Infinities and NaN's">FP_SUBNORMAL</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/special/fpclass.html" title="Floating-Point Classification: Infinities and NaN's">FP_ZERO</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/special/fpclass.html" title="Floating-Point Classification: Infinities and NaN's">mean</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/special/fpclass.html" title="Floating-Point Classification: Infinities and NaN's">normal</a></p></td></tr>
+</table></dd>
+<dt><span class="term">Floating-Point Representation Distance (ULP), and Finding Adjacent Floating-Point Values</span></dt>
+<dd><table class="simplelist" border="0" summary="Simple list"><tr><td><p><a class="link" href="../math_toolkit/special/next_float.html" title="Floating-Point Representation Distance (ULP), and Finding Adjacent Floating-Point Values">RR</a></p></td></tr></table></dd>
+<dt><span class="term">float_advance</span></dt>
+<dd><table class="simplelist" border="0" summary="Simple list"><tr><td><p><a class="link" href="../math_toolkit/special/next_float/float_advance.html" title="Advancing a Floating Point Value by a Specific Representation Distance (ULP) float_advance">Advancing a Floating Point Value by a Specific Representation Distance (ULP) float_advance</a></p></td></tr></table></dd>
+<dt><span class="term">float_distance</span></dt>
+<dd><table class="simplelist" border="0" summary="Simple list">
+<tr><td><p><a class="link" href="../math_toolkit/special/next_float/float_advance.html" title="Advancing a Floating Point Value by a Specific Representation Distance (ULP) float_advance">Advancing a Floating Point Value by a Specific Representation Distance (ULP) float_advance</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/special/next_float/float_distance.html" title="Calculating the Representation Distance Between Two Floating Point Values (ULP) float_distance">Calculating the Representation Distance Between Two Floating Point Values (ULP) float_distance</a></p></td></tr>
+</table></dd>
+<dt><span class="term">float_next</span></dt>
+<dd><table class="simplelist" border="0" summary="Simple list">
+<tr><td><p><a class="link" href="../math_toolkit/special/next_float/float_distance.html" title="Calculating the Representation Distance Between Two Floating Point Values (ULP) float_distance">Calculating the Representation Distance Between Two Floating Point Values (ULP) float_distance</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/special/next_float/float_next.html" title="Finding the Next Greater Representable Value (float_next)">Finding the Next Greater Representable Value (float_next)</a></p></td></tr>
+</table></dd>
+<dt><span class="term">float_prior</span></dt>
+<dd><table class="simplelist" border="0" summary="Simple list">
+<tr><td><p><a class="link" href="../math_toolkit/special/next_float/float_distance.html" title="Calculating the Representation Distance Between Two Floating Point Values (ULP) float_distance">Calculating the Representation Distance Between Two Floating Point Values (ULP) float_distance</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/special/next_float/float_prior.html" title="Finding the Next Smaller Representable Value (float_prior)">Finding the Next Smaller Representable Value (float_prior)</a></p></td></tr>
+</table></dd>
+<dt><span class="term">float_t</span></dt>
+<dd><table class="simplelist" border="0" summary="Simple list">
+<tr><td><p><a class="link" href="../math_toolkit/main_overview/tr1.html" title="C99 and TR1 C Functions">C99 and TR1 C Functions</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/special/extern_c/tr1.html" title="C99 and TR1 C Functions Overview">C99 and TR1 C Functions Overview</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/special/extern_c/c99.html" title="C99 C Functions">C99 C Functions</a></p></td></tr>
+</table></dd>
+<dt><span class="term">FP_INFINITE</span></dt>
+<dd><table class="simplelist" border="0" summary="Simple list"><tr><td><p><a class="link" href="../math_toolkit/special/fpclass.html" title="Floating-Point Classification: Infinities and NaN's">Floating-Point Classification: Infinities and NaN's</a></p></td></tr></table></dd>
+<dt><span class="term">FP_NAN</span></dt>
+<dd><table class="simplelist" border="0" summary="Simple list"><tr><td><p><a class="link" href="../math_toolkit/special/fpclass.html" title="Floating-Point Classification: Infinities and NaN's">Floating-Point Classification: Infinities and NaN's</a></p></td></tr></table></dd>
+<dt><span class="term">FP_NORMAL</span></dt>
+<dd><table class="simplelist" border="0" summary="Simple list"><tr><td><p><a class="link" href="../math_toolkit/special/fpclass.html" title="Floating-Point Classification: Infinities and NaN's">Floating-Point Classification: Infinities and NaN's</a></p></td></tr></table></dd>
+<dt><span class="term">FP_SUBNORMAL</span></dt>
+<dd><table class="simplelist" border="0" summary="Simple list"><tr><td><p><a class="link" href="../math_toolkit/special/fpclass.html" title="Floating-Point Classification: Infinities and NaN's">Floating-Point Classification: Infinities and NaN's</a></p></td></tr></table></dd>
+<dt><span class="term">FP_ZERO</span></dt>
+<dd><table class="simplelist" border="0" summary="Simple list"><tr><td><p><a class="link" href="../math_toolkit/special/fpclass.html" title="Floating-Point Classification: Infinities and NaN's">Floating-Point Classification: Infinities and NaN's</a></p></td></tr></table></dd>
+<dt><span class="term">fraction_traits</span></dt>
+<dd><table class="simplelist" border="0" summary="Simple list"><tr><td><p><a class="link" href="../math_toolkit/toolkit/internals1/cf.html" title="Continued Fraction Evaluation">Continued Fraction Evaluation</a></p></td></tr></table></dd>
+</dl></div></dd>
+<dt>
+<a name="idx_id_61"></a><span class="term">G</span>
+</dt>
+<dd><div class="variablelist"><dl>
+<dt><span class="term">gamma</span></dt>
+<dd><table class="simplelist" border="0" summary="Simple list">
+<tr><td><p><a class="link" href="../math_toolkit/main_overview/intro.html" title="About the Math Toolkit">About the Math Toolkit</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/backgrounders/implementation.html" title="Additional Implementation Notes">Additional Implementation Notes</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/special/bessel/bessel.html" title="Bessel Functions of the First and Second Kinds">Bessel Functions of the First and Second Kinds</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/special/sf_beta/beta_function.html" title="Beta">Beta</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/special/extern_c/c99.html" title="C99 C Functions">C99 C Functions</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/policy/pol_tutorial/ad_hoc_sf_policies.html" title="Changing the Policy on an Ad Hoc Basis for the Special Functions">Changing the Policy on an Ad Hoc Basis for the Special Functions</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/dist/dist_ref/dists/chi_squared_dist.html" title="Chi Squared Distribution">Chi Squared Distribution</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/using_udt/concepts.html" title="Conceptual Requirements for Real Number Types">Conceptual Requirements for Real Number Types</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/status/credits.html" title="Credits and Acknowledgements">Credits and Acknowledgements</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/special/sf_gamma/gamma_derivatives.html" title="Derivative of the Incomplete Gamma Function">Derivative of the Incomplete Gamma Function</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/special/sf_gamma/digamma.html" title="Digamma">Digamma</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/main_overview/directories.html" title="Directory and File Structure">Directory and File Structure</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/dist/stat_tut/weg/dist_construct_eg.html" title="Distribution Construction Example">Distribution Construction Example</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/special/factorials/sf_double_factorial.html" title="Double Factorial">Double Factorial</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/special/sf_erf/error_function.html" title="Error Functions">Error Functions</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/policy/pol_ref/error_handling_policies.html" title="Error Handling Policies">Error Handling Policies</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/special/sf_gamma/tgamma.html" title="Gamma">expm1</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/special/sf_gamma/tgamma.html" title="Gamma">factorial</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/special/factorials/sf_falling_factorial.html" title="Falling Factorial">Falling Factorial</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/special/sf_gamma/tgamma.html" title="Gamma">gamma</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/dist/dist_ref/dists/gamma_dist.html" title="Gamma (and Erlang) Distribution">Gamma (and Erlang) Distribution</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/toolkit/internals2/test_data.html" title="Graphing, Profiling, and Generating Test Data for Special Functions">Graphing, Profiling, and Generating Test Data for Special Functions</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/main_overview/history1.html" title="History and What's New">History and What's New</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/special/sf_beta/ibeta_function.html" title="Incomplete Beta Functions">Incomplete Beta Functions</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/special/sf_gamma/igamma_inv.html" title="Incomplete Gamma Function Inverses">Incomplete Gamma Function Inverses</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/special/sf_gamma/igamma.html" title="Incomplete Gamma Functions">Incomplete Gamma Functions</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/policy/pol_ref/internal_promotion.html" title="Internal Promotion Policies">Internal Promotion Policies</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/special/sf_gamma/tgamma.html" title="Gamma">lanczos</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/special/sf_gamma/tgamma.html" title="Gamma">Lanczos approximation</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/special/sf_gamma/tgamma.html" title="Gamma">lgamma</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/special/sf_gamma/lgamma.html" title="Log Gamma">Log Gamma</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/special/bessel/mbessel.html" title="Modified Bessel Functions of the First and Second Kinds">Modified Bessel Functions of the First and Second Kinds</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/dist/dist_ref/dists/nc_chi_squared_dist.html" title="Noncentral Chi-Squared Distribution">Noncentral Chi-Squared Distribution</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/dist/stat_tut/overview.html" title="Overview">Overview</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/dist/dist_ref/dists/poisson_dist.html" title="Poisson Distribution">Poisson Distribution</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/policy/pol_ref/precision_pol.html" title="Precision Policies">Precision Policies</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/special/sf_gamma/gamma_ratios.html" title="Ratios of Gamma Functions">Ratios of Gamma Functions</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/backgrounders/refs.html" title="References">References</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/special/factorials/sf_rising_factorial.html" title="Rising Factorial">Rising Factorial</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/policy/pol_ref/namespace_pol.html" title="Setting Polices at Namespace Scope">Setting Polices at Namespace Scope</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/policy/pol_tutorial/namespace_policies.html" title="Setting Policies at Namespace or Translation Unit Scope">Setting Policies at Namespace or Translation Unit Scope</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/special/sf_gamma/tgamma.html" title="Gamma">tgamma</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/special/sf_gamma/tgamma.html" title="Gamma">tgamma1pm1</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/special/sf_beta/ibeta_inv_function.html" title="The Incomplete Beta Function Inverses">The Incomplete Beta Function Inverses</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/backgrounders/lanczos.html" title="The Lanczos Approximation">The Lanczos Approximation</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/using_udt/use_mpfr.html" title="Using With MPFR / GMP - a High-Precision Floating-Point Library">Using With MPFR / GMP - a High-Precision Floating-Point Library</a></p></td></tr>
+</table></dd>
+<dt><span class="term">Gamma (and Erlang) Distribution</span></dt>
+<dd><table class="simplelist" border="0" summary="Simple list">
+<tr><td><p><a class="link" href="../math_toolkit/dist/dist_ref/dists/gamma_dist.html" title="Gamma (and Erlang) Distribution">cdf</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/dist/dist_ref/dists/gamma_dist.html" title="Gamma (and Erlang) Distribution">gamma</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/dist/dist_ref/dists/gamma_dist.html" title="Gamma (and Erlang) Distribution">gamma_distribution</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/dist/dist_ref/dists/gamma_dist.html" title="Gamma (and Erlang) Distribution">gamma_p</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/dist/dist_ref/dists/gamma_dist.html" title="Gamma (and Erlang) Distribution">gamma_p_derivative</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/dist/dist_ref/dists/gamma_dist.html" title="Gamma (and Erlang) Distribution">gamma_p_inv</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/dist/dist_ref/dists/gamma_dist.html" title="Gamma (and Erlang) Distribution">gamma_q</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/dist/dist_ref/dists/gamma_dist.html" title="Gamma (and Erlang) Distribution">gamma_q_inv</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/dist/dist_ref/dists/gamma_dist.html" title="Gamma (and Erlang) Distribution">kurtosis</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/dist/dist_ref/dists/gamma_dist.html" title="Gamma (and Erlang) Distribution">kurtosis_excess</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/dist/dist_ref/dists/gamma_dist.html" title="Gamma (and Erlang) Distribution">lognormal</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/dist/dist_ref/dists/gamma_dist.html" title="Gamma (and Erlang) Distribution">mean</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/dist/dist_ref/dists/gamma_dist.html" title="Gamma (and Erlang) Distribution">median</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/dist/dist_ref/dists/gamma_dist.html" title="Gamma (and Erlang) Distribution">mode</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/dist/dist_ref/dists/gamma_dist.html" title="Gamma (and Erlang) Distribution">pdf</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/dist/dist_ref/dists/gamma_dist.html" title="Gamma (and Erlang) Distribution">policy_type</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/dist/dist_ref/dists/gamma_dist.html" title="Gamma (and Erlang) Distribution">quantile</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/dist/dist_ref/dists/gamma_dist.html" title="Gamma (and Erlang) Distribution">skewness</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/dist/dist_ref/dists/gamma_dist.html" title="Gamma (and Erlang) Distribution">value_type</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/dist/dist_ref/dists/gamma_dist.html" title="Gamma (and Erlang) Distribution">variance</a></p></td></tr>
+</table></dd>
+<dt><span class="term">gamma_distribution</span></dt>
+<dd><table class="simplelist" border="0" summary="Simple list">
+<tr><td><p><a class="link" href="../math_toolkit/dist/stat_tut/weg/dist_construct_eg.html" title="Distribution Construction Example">Distribution Construction Example</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/dist/dist_ref/dists/gamma_dist.html" title="Gamma (and Erlang) Distribution">Gamma (and Erlang) Distribution</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/policy/pol_ref/namespace_pol.html" title="Setting Polices at Namespace Scope">Setting Polices at Namespace Scope</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/policy/pol_tutorial/namespace_policies.html" title="Setting Policies at Namespace or Translation Unit Scope">Setting Policies at Namespace or Translation Unit Scope</a></p></td></tr>
+</table></dd>
+<dt><span class="term">gamma_p</span></dt>
+<dd><table class="simplelist" border="0" summary="Simple list">
+<tr><td><p><a class="link" href="../math_toolkit/dist/dist_ref/dists/chi_squared_dist.html" title="Chi Squared Distribution">Chi Squared Distribution</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/perf/comparisons.html" title="Comparisons to Other Open Source Libraries">Comparisons to Other Open Source Libraries</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/special/sf_gamma/gamma_derivatives.html" title="Derivative of the Incomplete Gamma Function">Derivative of the Incomplete Gamma Function</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/special/sf_gamma/igamma.html" title="Incomplete Gamma Functions">Errors In the Function gamma_p(a,z)</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/dist/dist_ref/dists/gamma_dist.html" title="Gamma (and Erlang) Distribution">Gamma (and Erlang) Distribution</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/special/sf_gamma/igamma_inv.html" title="Incomplete Gamma Function Inverses">Incomplete Gamma Function Inverses</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/special/sf_gamma/igamma.html" title="Incomplete Gamma Functions">Incomplete Gamma Functions</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/perf/getting_best.html" title="Getting the Best Performance from this Library">Performance Comparison of Release and Debug Settings</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/perf/comp_compilers.html" title="Comparing Compilers">Performance Comparison of Various Windows Compilers</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/perf/tuning.html" title="Performance Tuning Macros">Performance Comparison with and Without Internal Promotion to long double</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/dist/dist_ref/dists/poisson_dist.html" title="Poisson Distribution">Poisson Distribution</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/backgrounders/lanczos.html" title="The Lanczos Approximation">The Lanczos Approximation</a></p></td></tr>
+</table></dd>
+<dt><span class="term">gamma_p_derivative</span></dt>
+<dd><table class="simplelist" border="0" summary="Simple list">
+<tr><td><p><a class="link" href="../math_toolkit/dist/dist_ref/dists/chi_squared_dist.html" title="Chi Squared Distribution">Chi Squared Distribution</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/special/sf_gamma/gamma_derivatives.html" title="Derivative of the Incomplete Gamma Function">Derivative of the Incomplete Gamma Function</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/dist/dist_ref/dists/gamma_dist.html" title="Gamma (and Erlang) Distribution">Gamma (and Erlang) Distribution</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/dist/dist_ref/dists/nc_chi_squared_dist.html" title="Noncentral Chi-Squared Distribution">Noncentral Chi-Squared Distribution</a></p></td></tr>
+</table></dd>
+<dt><span class="term">gamma_p_inv</span></dt>
+<dd><table class="simplelist" border="0" summary="Simple list">
+<tr><td><p><a class="link" href="../math_toolkit/dist/dist_ref/dists/chi_squared_dist.html" title="Chi Squared Distribution">Chi Squared Distribution</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/perf/comparisons.html" title="Comparisons to Other Open Source Libraries">Comparisons to Other Open Source Libraries</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/dist/dist_ref/dists/gamma_dist.html" title="Gamma (and Erlang) Distribution">Gamma (and Erlang) Distribution</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/special/sf_gamma/igamma_inv.html" title="Incomplete Gamma Function Inverses">Incomplete Gamma Function Inverses</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/perf/getting_best.html" title="Getting the Best Performance from this Library">Performance Comparison of Release and Debug Settings</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/perf/comp_compilers.html" title="Comparing Compilers">Performance Comparison of Various Windows Compilers</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/perf/tuning.html" title="Performance Tuning Macros">Performance Comparison with and Without Internal Promotion to long double</a></p></td></tr>
+</table></dd>
+<dt><span class="term">gamma_p_inva</span></dt>
+<dd><table class="simplelist" border="0" summary="Simple list">
+<tr><td><p><a class="link" href="../math_toolkit/special/sf_gamma/igamma_inv.html" title="Incomplete Gamma Function Inverses">Incomplete Gamma Function Inverses</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/perf/getting_best.html" title="Getting the Best Performance from this Library">Performance Comparison of Release and Debug Settings</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/perf/comp_compilers.html" title="Comparing Compilers">Performance Comparison of Various Windows Compilers</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/perf/tuning.html" title="Performance Tuning Macros">Performance Comparison with and Without Internal Promotion to long double</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/dist/dist_ref/dists/poisson_dist.html" title="Poisson Distribution">Poisson Distribution</a></p></td></tr>
+</table></dd>
+<dt><span class="term">gamma_q</span></dt>
+<dd><table class="simplelist" border="0" summary="Simple list">
+<tr><td><p><a class="link" href="../math_toolkit/dist/dist_ref/dists/chi_squared_dist.html" title="Chi Squared Distribution">Chi Squared Distribution</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/perf/comparisons.html" title="Comparisons to Other Open Source Libraries">Comparisons to Other Open Source Libraries</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/special/sf_gamma/gamma_derivatives.html" title="Derivative of the Incomplete Gamma Function">Derivative of the Incomplete Gamma Function</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/special/sf_gamma/igamma.html" title="Incomplete Gamma Functions">Errors In the Function gamma_q(a,z)</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/dist/dist_ref/dists/gamma_dist.html" title="Gamma (and Erlang) Distribution">Gamma (and Erlang) Distribution</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/special/sf_gamma/igamma_inv.html" title="Incomplete Gamma Function Inverses">Incomplete Gamma Function Inverses</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/special/sf_gamma/igamma.html" title="Incomplete Gamma Functions">Incomplete Gamma Functions</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/perf/getting_best.html" title="Getting the Best Performance from this Library">Performance Comparison of Release and Debug Settings</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/perf/comp_compilers.html" title="Comparing Compilers">Performance Comparison of Various Windows Compilers</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/perf/tuning.html" title="Performance Tuning Macros">Performance Comparison with and Without Internal Promotion to long double</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/dist/dist_ref/dists/poisson_dist.html" title="Poisson Distribution">Poisson Distribution</a></p></td></tr>
+</table></dd>
+<dt><span class="term">gamma_q_inv</span></dt>
+<dd><table class="simplelist" border="0" summary="Simple list">
+<tr><td><p><a class="link" href="../math_toolkit/dist/dist_ref/dists/chi_squared_dist.html" title="Chi Squared Distribution">Chi Squared Distribution</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/perf/comparisons.html" title="Comparisons to Other Open Source Libraries">Comparisons to Other Open Source Libraries</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/dist/dist_ref/dists/gamma_dist.html" title="Gamma (and Erlang) Distribution">Gamma (and Erlang) Distribution</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/special/sf_gamma/igamma_inv.html" title="Incomplete Gamma Function Inverses">Incomplete Gamma Function Inverses</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/perf/getting_best.html" title="Getting the Best Performance from this Library">Performance Comparison of Release and Debug Settings</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/perf/comp_compilers.html" title="Comparing Compilers">Performance Comparison of Various Windows Compilers</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/perf/tuning.html" title="Performance Tuning Macros">Performance Comparison with and Without Internal Promotion to long double</a></p></td></tr>
+</table></dd>
+<dt><span class="term">gamma_q_inva</span></dt>
+<dd><table class="simplelist" border="0" summary="Simple list">
+<tr><td><p><a class="link" href="../math_toolkit/special/sf_gamma/igamma_inv.html" title="Incomplete Gamma Function Inverses">Incomplete Gamma Function Inverses</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/perf/getting_best.html" title="Getting the Best Performance from this Library">Performance Comparison of Release and Debug Settings</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/perf/comp_compilers.html" title="Comparing Compilers">Performance Comparison of Various Windows Compilers</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/perf/tuning.html" title="Performance Tuning Macros">Performance Comparison with and Without Internal Promotion to long double</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/dist/dist_ref/dists/poisson_dist.html" title="Poisson Distribution">Poisson Distribution</a></p></td></tr>
+</table></dd>
+<dt><span class="term">Getting the Best Performance from this Library</span></dt>
+<dd><table class="simplelist" border="0" summary="Simple list"><tr><td><p><a class="link" href="../math_toolkit/perf/getting_best.html" title="Getting the Best Performance from this Library">mode</a></p></td></tr></table></dd>
+<dt><span class="term">get_user_parameter_info</span></dt>
+<dd><table class="simplelist" border="0" summary="Simple list"><tr><td><p><a class="link" href="../math_toolkit/toolkit/internals2/test_data.html" title="Graphing, Profiling, and Generating Test Data for Special Functions">Graphing, Profiling, and Generating Test Data for Special Functions</a></p></td></tr></table></dd>
+<dt><span class="term">Graphing, Profiling, and Generating Test Data for Special Functions</span></dt>
+<dd><table class="simplelist" border="0" summary="Simple list">
+<tr><td><p><a class="link" href="../math_toolkit/toolkit/internals2/test_data.html" title="Graphing, Profiling, and Generating Test Data for Special Functions">beta</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/toolkit/internals2/test_data.html" title="Graphing, Profiling, and Generating Test Data for Special Functions">continued_fraction_a</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/toolkit/internals2/test_data.html" title="Graphing, Profiling, and Generating Test Data for Special Functions">gamma</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/toolkit/internals2/test_data.html" title="Graphing, Profiling, and Generating Test Data for Special Functions">get_user_parameter_info</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/toolkit/internals2/test_data.html" title="Graphing, Profiling, and Generating Test Data for Special Functions">lgamma</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/toolkit/internals2/test_data.html" title="Graphing, Profiling, and Generating Test Data for Special Functions">parameter_info</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/toolkit/internals2/test_data.html" title="Graphing, Profiling, and Generating Test Data for Special Functions">real_cast</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/toolkit/internals2/test_data.html" title="Graphing, Profiling, and Generating Test Data for Special Functions">relative_error</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/toolkit/internals2/test_data.html" title="Graphing, Profiling, and Generating Test Data for Special Functions">RR</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/toolkit/internals2/test_data.html" title="Graphing, Profiling, and Generating Test Data for Special Functions">SetOutputPrecision</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/toolkit/internals2/test_data.html" title="Graphing, Profiling, and Generating Test Data for Special Functions">SetPrecision</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/toolkit/internals2/test_data.html" title="Graphing, Profiling, and Generating Test Data for Special Functions">test_data</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/toolkit/internals2/test_data.html" title="Graphing, Profiling, and Generating Test Data for Special Functions">uniform</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/toolkit/internals2/test_data.html" title="Graphing, Profiling, and Generating Test Data for Special Functions">upper_incomplete_gamma_fract</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/toolkit/internals2/test_data.html" title="Graphing, Profiling, and Generating Test Data for Special Functions">value_type</a></p></td></tr>
+</table></dd>
+</dl></div></dd>
+<dt>
+<a name="idx_id_62"></a><span class="term">H</span>
+</dt>
+<dd><div class="variablelist"><dl>
+<dt><span class="term">halley_iterate</span></dt>
+<dd><table class="simplelist" border="0" summary="Simple list"><tr><td><p><a class="link" href="../math_toolkit/toolkit/internals1/roots.html" title="Root Finding With Derivatives">Root Finding With Derivatives</a></p></td></tr></table></dd>
+<dt><span class="term">hazard</span></dt>
+<dd><table class="simplelist" border="0" summary="Simple list">
+<tr><td><p><a class="link" href="../math_toolkit/backgrounders/implementation.html" title="Additional Implementation Notes">Additional Implementation Notes</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/using_udt/archetypes.html" title="Conceptual Archetypes and Testing">Conceptual Archetypes and Testing</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/using_udt/dist_concept.html" title="Conceptual Requirements for Distribution Types">Conceptual Requirements for Distribution Types</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/dist/dist_ref/nmp.html" title="Non-Member Properties">Non-Member Properties</a></p></td></tr>
+</table></dd>
+<dt><span class="term">hermite</span></dt>
+<dd><table class="simplelist" border="0" summary="Simple list">
+<tr><td><p><a class="link" href="../math_toolkit/main_overview/tr1.html" title="C99 and TR1 C Functions">C99 and TR1 C Functions</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/special/extern_c/tr1.html" title="C99 and TR1 C Functions Overview">C99 and TR1 C Functions Overview</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/special/sf_poly/hermite.html" title="Hermite Polynomials">Hermite Polynomials</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/special/extern_c/tr1_ref.html" title="TR1 C Functions Quick Reference">TR1 C Functions Quick Reference</a></p></td></tr>
+</table></dd>
+<dt><span class="term">Hermite Polynomials</span></dt>
+<dd><table class="simplelist" border="0" summary="Simple list">
+<tr><td><p><a class="link" href="../math_toolkit/special/sf_poly/hermite.html" title="Hermite Polynomials">hermite</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/special/sf_poly/hermite.html" title="Hermite Polynomials">hermite_next</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/special/sf_poly/hermite.html" title="Hermite Polynomials">RR</a></p></td></tr>
+</table></dd>
+<dt><span class="term">hermite_next</span></dt>
+<dd><table class="simplelist" border="0" summary="Simple list"><tr><td><p><a class="link" href="../math_toolkit/special/sf_poly/hermite.html" title="Hermite Polynomials">Hermite Polynomials</a></p></td></tr></table></dd>
+<dt><span class="term">History and What's New</span></dt>
+<dd><table class="simplelist" border="0" summary="Simple list">
+<tr><td><p><a class="link" href="../math_toolkit/main_overview/history1.html" title="History and What's New">beta</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/main_overview/history1.html" title="History and What's New">digamma</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/main_overview/history1.html" title="History and What's New">erf</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/main_overview/history1.html" title="History and What's New">erfc</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/main_overview/history1.html" title="History and What's New">evaluation_error</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/main_overview/history1.html" title="History and What's New">factorial</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/main_overview/history1.html" title="History and What's New">gamma</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/main_overview/history1.html" title="History and What's New">lgamma</a></p></td></tr>
+</table></dd>
+<dt><span class="term">hypot</span></dt>
+<dd><table class="simplelist" border="0" summary="Simple list">
+<tr><td><p><a class="link" href="../math_toolkit/main_overview/tr1.html" title="C99 and TR1 C Functions">C99 and TR1 C Functions</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/special/extern_c/tr1.html" title="C99 and TR1 C Functions Overview">C99 and TR1 C Functions Overview</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/special/extern_c/c99.html" title="C99 C Functions">C99 C Functions</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/special/powers/hypot.html" title="hypot">hypot</a></p></td></tr>
+</table></dd>
+</dl></div></dd>
+<dt>
+<a name="idx_id_63"></a><span class="term">I</span>
+</dt>
+<dd><div class="variablelist"><dl>
+<dt><span class="term">ibeta</span></dt>
+<dd><table class="simplelist" border="0" summary="Simple list">
+<tr><td><p><a class="link" href="../math_toolkit/dist/dist_ref/dists/beta_dist.html" title="Beta Distribution">Beta Distribution</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/dist/dist_ref/dists/binomial_dist.html" title="Binomial Distribution">Binomial Distribution</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/perf/comparisons.html" title="Comparisons to Other Open Source Libraries">Comparisons to Other Open Source Libraries</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/special/sf_beta/beta_derivative.html" title="Derivative of the Incomplete Beta Function">Derivative of the Incomplete Beta Function</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/special/sf_beta/ibeta_function.html" title="Incomplete Beta Functions">Errors In the Function ibeta(a,b,x)</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/dist/dist_ref/dists/f_dist.html" title="F Distribution">F Distribution</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/special/sf_beta/ibeta_function.html" title="Incomplete Beta Functions">Incomplete Beta Functions</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/dist/dist_ref/dists/negative_binomial_dist.html" title="Negative Binomial Distribution">Negative Binomial Distribution</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/perf/getting_best.html" title="Getting the Best Performance from this Library">Performance Comparison of Release and Debug Settings</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/perf/comp_compilers.html" title="Comparing Compilers">Performance Comparison of Various Windows Compilers</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/perf/tuning.html" title="Performance Tuning Macros">Performance Comparison with and Without Internal Promotion to long double</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/dist/dist_ref/dists/students_t_dist.html" title="Students t Distribution">Students t Distribution</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/special/sf_beta/ibeta_inv_function.html" title="The Incomplete Beta Function Inverses">The Incomplete Beta Function Inverses</a></p></td></tr>
+</table></dd>
+<dt><span class="term">ibetac</span></dt>
+<dd><table class="simplelist" border="0" summary="Simple list">
+<tr><td><p><a class="link" href="../math_toolkit/dist/dist_ref/dists/beta_dist.html" title="Beta Distribution">Beta Distribution</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/dist/dist_ref/dists/binomial_dist.html" title="Binomial Distribution">Binomial Distribution</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/perf/comparisons.html" title="Comparisons to Other Open Source Libraries">Comparisons to Other Open Source Libraries</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/special/sf_beta/ibeta_function.html" title="Incomplete Beta Functions">Errors In the Function ibetac(a,b,x)</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/dist/dist_ref/dists/f_dist.html" title="F Distribution">F Distribution</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/special/sf_beta/ibeta_function.html" title="Incomplete Beta Functions">Incomplete Beta Functions</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/dist/dist_ref/dists/negative_binomial_dist.html" title="Negative Binomial Distribution">Negative Binomial Distribution</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/perf/getting_best.html" title="Getting the Best Performance from this Library">Performance Comparison of Release and Debug Settings</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/perf/comp_compilers.html" title="Comparing Compilers">Performance Comparison of Various Windows Compilers</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/perf/tuning.html" title="Performance Tuning Macros">Performance Comparison with and Without Internal Promotion to long double</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/dist/dist_ref/dists/students_t_dist.html" title="Students t Distribution">Students t Distribution</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/special/sf_beta/ibeta_inv_function.html" title="The Incomplete Beta Function Inverses">The Incomplete Beta Function Inverses</a></p></td></tr>
+</table></dd>
+<dt><span class="term">ibetac_inv</span></dt>
+<dd><table class="simplelist" border="0" summary="Simple list">
+<tr><td><p><a class="link" href="../math_toolkit/dist/dist_ref/dists/beta_dist.html" title="Beta Distribution">Beta Distribution</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/dist/dist_ref/dists/binomial_dist.html" title="Binomial Distribution">Binomial Distribution</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/perf/comparisons.html" title="Comparisons to Other Open Source Libraries">Comparisons to Other Open Source Libraries</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/dist/dist_ref/dists/f_dist.html" title="F Distribution">F Distribution</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/dist/dist_ref/dists/negative_binomial_dist.html" title="Negative Binomial Distribution">Negative Binomial Distribution</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/perf/getting_best.html" title="Getting the Best Performance from this Library">Performance Comparison of Release and Debug Settings</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/perf/comp_compilers.html" title="Comparing Compilers">Performance Comparison of Various Windows Compilers</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/perf/tuning.html" title="Performance Tuning Macros">Performance Comparison with and Without Internal Promotion to long double</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/special/sf_beta/ibeta_inv_function.html" title="The Incomplete Beta Function Inverses">The Incomplete Beta Function Inverses</a></p></td></tr>
+</table></dd>
+<dt><span class="term">ibetac_inva</span></dt>
+<dd><table class="simplelist" border="0" summary="Simple list">
+<tr><td><p><a class="link" href="../math_toolkit/dist/dist_ref/dists/negative_binomial_dist.html" title="Negative Binomial Distribution">Negative Binomial Distribution</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/perf/getting_best.html" title="Getting the Best Performance from this Library">Performance Comparison of Release and Debug Settings</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/perf/comp_compilers.html" title="Comparing Compilers">Performance Comparison of Various Windows Compilers</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/perf/tuning.html" title="Performance Tuning Macros">Performance Comparison with and Without Internal Promotion to long double</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/special/sf_beta/ibeta_inv_function.html" title="The Incomplete Beta Function Inverses">The Incomplete Beta Function Inverses</a></p></td></tr>
+</table></dd>
+<dt><span class="term">ibetac_invb</span></dt>
+<dd><table class="simplelist" border="0" summary="Simple list">
+<tr><td><p><a class="link" href="../math_toolkit/dist/dist_ref/dists/binomial_dist.html" title="Binomial Distribution">Binomial Distribution</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/dist/dist_ref/dists/negative_binomial_dist.html" title="Negative Binomial Distribution">Negative Binomial Distribution</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/perf/getting_best.html" title="Getting the Best Performance from this Library">Performance Comparison of Release and Debug Settings</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/perf/comp_compilers.html" title="Comparing Compilers">Performance Comparison of Various Windows Compilers</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/perf/tuning.html" title="Performance Tuning Macros">Performance Comparison with and Without Internal Promotion to long double</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/special/sf_beta/ibeta_inv_function.html" title="The Incomplete Beta Function Inverses">The Incomplete Beta Function Inverses</a></p></td></tr>
+</table></dd>
+<dt><span class="term">ibeta_derivative</span></dt>
+<dd><table class="simplelist" border="0" summary="Simple list">
+<tr><td><p><a class="link" href="../math_toolkit/dist/dist_ref/dists/beta_dist.html" title="Beta Distribution">Beta Distribution</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/dist/dist_ref/dists/binomial_dist.html" title="Binomial Distribution">Binomial Distribution</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/special/sf_beta/beta_derivative.html" title="Derivative of the Incomplete Beta Function">Derivative of the Incomplete Beta Function</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/dist/dist_ref/dists/f_dist.html" title="F Distribution">F Distribution</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/dist/dist_ref/dists/negative_binomial_dist.html" title="Negative Binomial Distribution">Negative Binomial Distribution</a></p></td></tr>
+</table></dd>
+<dt><span class="term">ibeta_inv</span></dt>
+<dd><table class="simplelist" border="0" summary="Simple list">
+<tr><td><p><a class="link" href="../math_toolkit/dist/dist_ref/dists/beta_dist.html" title="Beta Distribution">Beta Distribution</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/dist/dist_ref/dists/binomial_dist.html" title="Binomial Distribution">Binomial Distribution</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/perf/comparisons.html" title="Comparisons to Other Open Source Libraries">Comparisons to Other Open Source Libraries</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/dist/dist_ref/dists/f_dist.html" title="F Distribution">F Distribution</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/dist/dist_ref/dists/negative_binomial_dist.html" title="Negative Binomial Distribution">Negative Binomial Distribution</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/perf/getting_best.html" title="Getting the Best Performance from this Library">Performance Comparison of Release and Debug Settings</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/perf/comp_compilers.html" title="Comparing Compilers">Performance Comparison of Various Windows Compilers</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/perf/tuning.html" title="Performance Tuning Macros">Performance Comparison with and Without Internal Promotion to long double</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/dist/dist_ref/dists/students_t_dist.html" title="Students t Distribution">Students t Distribution</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/special/sf_beta/ibeta_inv_function.html" title="The Incomplete Beta Function Inverses">The Incomplete Beta Function Inverses</a></p></td></tr>
+</table></dd>
+<dt><span class="term">ibeta_inva</span></dt>
+<dd><table class="simplelist" border="0" summary="Simple list">
+<tr><td><p><a class="link" href="../math_toolkit/dist/dist_ref/dists/beta_dist.html" title="Beta Distribution">Beta Distribution</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/dist/dist_ref/dists/negative_binomial_dist.html" title="Negative Binomial Distribution">Negative Binomial Distribution</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/perf/getting_best.html" title="Getting the Best Performance from this Library">Performance Comparison of Release and Debug Settings</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/perf/comp_compilers.html" title="Comparing Compilers">Performance Comparison of Various Windows Compilers</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/perf/tuning.html" title="Performance Tuning Macros">Performance Comparison with and Without Internal Promotion to long double</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/special/sf_beta/ibeta_inv_function.html" title="The Incomplete Beta Function Inverses">The Incomplete Beta Function Inverses</a></p></td></tr>
+</table></dd>
+<dt><span class="term">ibeta_invb</span></dt>
+<dd><table class="simplelist" border="0" summary="Simple list">
+<tr><td><p><a class="link" href="../math_toolkit/dist/dist_ref/dists/beta_dist.html" title="Beta Distribution">Beta Distribution</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/dist/dist_ref/dists/negative_binomial_dist.html" title="Negative Binomial Distribution">Negative Binomial Distribution</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/perf/getting_best.html" title="Getting the Best Performance from this Library">Performance Comparison of Release and Debug Settings</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/perf/comp_compilers.html" title="Comparing Compilers">Performance Comparison of Various Windows Compilers</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/perf/tuning.html" title="Performance Tuning Macros">Performance Comparison with and Without Internal Promotion to long double</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/special/sf_beta/ibeta_inv_function.html" title="The Incomplete Beta Function Inverses">The Incomplete Beta Function Inverses</a></p></td></tr>
+</table></dd>
+<dt><span class="term">Implementation Notes</span></dt>
+<dd><table class="simplelist" border="0" summary="Simple list">
+<tr><td><p><a class="link" href="../math_toolkit/backgrounders/implementation.html" title="Additional Implementation Notes">beta</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/backgrounders/implementation.html" title="Additional Implementation Notes">binomial</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/backgrounders/implementation.html" title="Additional Implementation Notes">BOOST_DEFINE_MATH_CONSTANT</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/backgrounders/implementation.html" title="Additional Implementation Notes">BOOST_MATH_DOMAIN_ERROR_POLICY</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/backgrounders/implementation.html" title="Additional Implementation Notes">cauchy</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/backgrounders/implementation.html" title="Additional Implementation Notes">cdf</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/backgrounders/implementation.html" title="Additional Implementation Notes">check_triangular</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/backgrounders/implementation.html" title="Additional Implementation Notes">exponential</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/backgrounders/implementation.html" title="Additional Implementation Notes">gamma</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/backgrounders/implementation.html" title="Additional Implementation Notes">hazard</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/backgrounders/implementation.html" title="Additional Implementation Notes">kurtosis</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/backgrounders/implementation.html" title="Additional Implementation Notes">lognormal</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/backgrounders/implementation.html" title="Additional Implementation Notes">mean</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/backgrounders/implementation.html" title="Additional Implementation Notes">median</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/backgrounders/implementation.html" title="Additional Implementation Notes">mode</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/backgrounders/implementation.html" title="Additional Implementation Notes">normal</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/backgrounders/implementation.html" title="Additional Implementation Notes">pdf</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/backgrounders/implementation.html" title="Additional Implementation Notes">quantile</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/backgrounders/implementation.html" title="Additional Implementation Notes">round</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/backgrounders/implementation.html" title="Additional Implementation Notes">RR</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/backgrounders/implementation.html" title="Additional Implementation Notes">triangular</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/backgrounders/implementation.html" title="Additional Implementation Notes">triangular_distribution</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/backgrounders/implementation.html" title="Additional Implementation Notes">uniform</a></p></td></tr>
+</table></dd>
+<dt><span class="term">Incomplete Beta Function Inverses</span></dt>
+<dd><table class="simplelist" border="0" summary="Simple list">
+<tr><td><p><a class="link" href="../math_toolkit/special/sf_beta/ibeta_inv_function.html" title="The Incomplete Beta Function Inverses">beta</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/special/sf_beta/ibeta_inv_function.html" title="The Incomplete Beta Function Inverses">binomial</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/special/sf_beta/ibeta_inv_function.html" title="The Incomplete Beta Function Inverses">gamma</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/special/sf_beta/ibeta_inv_function.html" title="The Incomplete Beta Function Inverses">ibeta</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/special/sf_beta/ibeta_inv_function.html" title="The Incomplete Beta Function Inverses">ibetac</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/special/sf_beta/ibeta_inv_function.html" title="The Incomplete Beta Function Inverses">ibetac_inv</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/special/sf_beta/ibeta_inv_function.html" title="The Incomplete Beta Function Inverses">ibetac_inva</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/special/sf_beta/ibeta_inv_function.html" title="The Incomplete Beta Function Inverses">ibetac_invb</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/special/sf_beta/ibeta_inv_function.html" title="The Incomplete Beta Function Inverses">ibeta_inv</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/special/sf_beta/ibeta_inv_function.html" title="The Incomplete Beta Function Inverses">ibeta_inva</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/special/sf_beta/ibeta_inv_function.html" title="The Incomplete Beta Function Inverses">ibeta_invb</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/special/sf_beta/ibeta_inv_function.html" title="The Incomplete Beta Function Inverses">normal</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/special/sf_beta/ibeta_inv_function.html" title="The Incomplete Beta Function Inverses">round</a></p></td></tr>
+</table></dd>
+<dt><span class="term">Incomplete Beta Functions</span></dt>
+<dd><table class="simplelist" border="0" summary="Simple list">
+<tr><td><p><a class="link" href="../math_toolkit/special/sf_beta/ibeta_function.html" title="Incomplete Beta Functions">beta</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/special/sf_beta/ibeta_function.html" title="Incomplete Beta Functions">betac</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/special/sf_beta/ibeta_function.html" title="Incomplete Beta Functions">binomial</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/special/sf_beta/ibeta_function.html" title="Incomplete Beta Functions">gamma</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/special/sf_beta/ibeta_function.html" title="Incomplete Beta Functions">ibeta</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/special/sf_beta/ibeta_function.html" title="Incomplete Beta Functions">ibetac</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/special/sf_beta/ibeta_function.html" title="Incomplete Beta Functions">mean</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/special/sf_beta/ibeta_function.html" title="Incomplete Beta Functions">RR</a></p></td></tr>
+</table></dd>
+<dt><span class="term">Incomplete Gamma Function Inverses</span></dt>
+<dd><table class="simplelist" border="0" summary="Simple list">
+<tr><td><p><a class="link" href="../math_toolkit/special/sf_gamma/igamma_inv.html" title="Incomplete Gamma Function Inverses">gamma</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/special/sf_gamma/igamma_inv.html" title="Incomplete Gamma Function Inverses">gamma_p</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/special/sf_gamma/igamma_inv.html" title="Incomplete Gamma Function Inverses">gamma_p_inv</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/special/sf_gamma/igamma_inv.html" title="Incomplete Gamma Function Inverses">gamma_p_inva</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/special/sf_gamma/igamma_inv.html" title="Incomplete Gamma Function Inverses">gamma_q</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/special/sf_gamma/igamma_inv.html" title="Incomplete Gamma Function Inverses">gamma_q_inv</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/special/sf_gamma/igamma_inv.html" title="Incomplete Gamma Function Inverses">gamma_q_inva</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/special/sf_gamma/igamma_inv.html" title="Incomplete Gamma Function Inverses">normal</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/special/sf_gamma/igamma_inv.html" title="Incomplete Gamma Function Inverses">round</a></p></td></tr>
+</table></dd>
+<dt><span class="term">Incomplete Gamma Functions</span></dt>
+<dd><table class="simplelist" border="0" summary="Simple list">
+<tr><td><p><a class="link" href="../math_toolkit/special/sf_gamma/igamma.html" title="Incomplete Gamma Functions">erfc</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/special/sf_gamma/igamma.html" title="Incomplete Gamma Functions">gamma</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/special/sf_gamma/igamma.html" title="Incomplete Gamma Functions">gamma_p</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/special/sf_gamma/igamma.html" title="Incomplete Gamma Functions">gamma_q</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/special/sf_gamma/igamma.html" title="Incomplete Gamma Functions">Lanczos approximation</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/special/sf_gamma/igamma.html" title="Incomplete Gamma Functions">mean</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/special/sf_gamma/igamma.html" title="Incomplete Gamma Functions">powm1</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/special/sf_gamma/igamma.html" title="Incomplete Gamma Functions">RR</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/special/sf_gamma/igamma.html" title="Incomplete Gamma Functions">tgamma</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/special/sf_gamma/igamma.html" title="Incomplete Gamma Functions">tgamma1pm1</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/special/sf_gamma/igamma.html" title="Incomplete Gamma Functions">tgamma_lower</a></p></td></tr>
+</table></dd>
+<dt><span class="term">indeterminate_result_error_type</span></dt>
+<dd><table class="simplelist" border="0" summary="Simple list"><tr><td><p><a class="link" href="../math_toolkit/policy/pol_ref/pol_ref_ref.html" title="Policy Class Reference">Policy Class Reference</a></p></td></tr></table></dd>
+<dt><span class="term">Integer and Fractional Part Splitting (modf)</span></dt>
+<dd><table class="simplelist" border="0" summary="Simple list"><tr><td><p><a class="link" href="../math_toolkit/special/rounding/modf.html" title="Integer and Fractional Part Splitting (modf)">rounding_error</a></p></td></tr></table></dd>
+<dt><span class="term">Internal Promotion Policies</span></dt>
+<dd><table class="simplelist" border="0" summary="Simple list">
+<tr><td><p><a class="link" href="../math_toolkit/policy/pol_ref/internal_promotion.html" title="Internal Promotion Policies">gamma</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/policy/pol_ref/internal_promotion.html" title="Internal Promotion Policies">make_policy</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/policy/pol_ref/internal_promotion.html" title="Internal Promotion Policies">normal</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/policy/pol_ref/internal_promotion.html" title="Internal Promotion Policies">normal_distribution</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/policy/pol_ref/internal_promotion.html" title="Internal Promotion Policies">quantile</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/policy/pol_ref/internal_promotion.html" title="Internal Promotion Policies">tgamma</a></p></td></tr>
+</table></dd>
+<dt><span class="term">Inverse Hyperbolic Functions Overview</span></dt>
+<dd><table class="simplelist" border="0" summary="Simple list">
+<tr><td><p><a class="link" href="../math_toolkit/special/inv_hyper/inv_hyper_over.html" title="Inverse Hyperbolic Functions Overview">exponential</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/special/inv_hyper/inv_hyper_over.html" title="Inverse Hyperbolic Functions Overview">factorial</a></p></td></tr>
+</table></dd>
+<dt><span class="term">iround</span></dt>
+<dd><table class="simplelist" border="0" summary="Simple list">
+<tr><td><p><a class="link" href="../math_toolkit/using_udt/concepts.html" title="Conceptual Requirements for Real Number Types">Conceptual Requirements for Real Number Types</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/special/rounding/round.html" title="Rounding Functions">Rounding Functions</a></p></td></tr>
+</table></dd>
+<dt><span class="term">Iteration Limits Policies</span></dt>
+<dd><table class="simplelist" border="0" summary="Simple list">
+<tr><td><p><a class="link" href="../math_toolkit/policy/pol_ref/iteration_pol.html" title="Iteration Limits Policies">BOOST_MATH_MAX_ROOT_ITERATION_POLICY</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/policy/pol_ref/iteration_pol.html" title="Iteration Limits Policies">BOOST_MATH_MAX_SERIES_ITERATION_POLICY</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/policy/pol_ref/iteration_pol.html" title="Iteration Limits Policies">evaluation_error</a></p></td></tr>
+</table></dd>
+<dt><span class="term">itrunc</span></dt>
+<dd><table class="simplelist" border="0" summary="Simple list">
+<tr><td><p><a class="link" href="../math_toolkit/using_udt/concepts.html" title="Conceptual Requirements for Real Number Types">Conceptual Requirements for Real Number Types</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/special/rounding/trunc.html" title="Truncation Functions">Truncation Functions</a></p></td></tr>
+</table></dd>
+</dl></div></dd>
+<dt>
+<a name="idx_id_64"></a><span class="term">K</span>
+</dt>
+<dd><div class="variablelist"><dl>
+<dt><span class="term">kahan_sum_series</span></dt>
+<dd><table class="simplelist" border="0" summary="Simple list"><tr><td><p><a class="link" href="../math_toolkit/toolkit/internals1/series_evaluation.html" title="Series Evaluation">Series Evaluation</a></p></td></tr></table></dd>
+<dt><span class="term">Known Issues, and Todo List</span></dt>
+<dd><table class="simplelist" border="0" summary="Simple list">
+<tr><td><p><a class="link" href="../math_toolkit/status/issues.html" title="Known Issues, and Todo List">ellint_3</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/status/issues.html" title="Known Issues, and Todo List">Lanczos approximation</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/status/issues.html" title="Known Issues, and Todo List">log1p</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/status/issues.html" title="Known Issues, and Todo List">normal</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/status/issues.html" title="Known Issues, and Todo List">tgamma</a></p></td></tr>
+</table></dd>
+<dt><span class="term">kurtosis</span></dt>
+<dd><table class="simplelist" border="0" summary="Simple list">
+<tr><td><p><a class="link" href="../math_toolkit/backgrounders/implementation.html" title="Additional Implementation Notes">Additional Implementation Notes</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/dist/dist_ref/dists/bernoulli_dist.html" title="Bernoulli Distribution">Bernoulli Distribution</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/dist/dist_ref/dists/beta_dist.html" title="Beta Distribution">Beta Distribution</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/dist/dist_ref/dists/binomial_dist.html" title="Binomial Distribution">Binomial Distribution</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/dist/dist_ref/dists/cauchy_dist.html" title="Cauchy-Lorentz Distribution">Cauchy-Lorentz Distribution</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/dist/dist_ref/dists/chi_squared_dist.html" title="Chi Squared Distribution">Chi Squared Distribution</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/using_udt/dist_concept.html" title="Conceptual Requirements for Distribution Types">Conceptual Requirements for Distribution Types</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/dist/dist_ref/dists/exp_dist.html" title="Exponential Distribution">Exponential Distribution</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/dist/dist_ref/dists/extreme_dist.html" title="Extreme Value Distribution">Extreme Value Distribution</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/dist/dist_ref/dists/f_dist.html" title="F Distribution">F Distribution</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/dist/dist_ref/dists/gamma_dist.html" title="Gamma (and Erlang) Distribution">Gamma (and Erlang) Distribution</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/dist/dist_ref/dists/lognormal_dist.html" title="Log Normal Distribution">Log Normal Distribution</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/dist/dist_ref/dists/logistic_dist.html" title="Logistic Distribution">Logistic Distribution</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/dist/dist_ref/dists/negative_binomial_dist.html" title="Negative Binomial Distribution">Negative Binomial Distribution</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/dist/dist_ref/nmp.html" title="Non-Member Properties">Non-Member Properties</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/dist/dist_ref/dists/nc_beta_dist.html" title="Noncentral Beta Distribution">Noncentral Beta Distribution</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/dist/dist_ref/dists/nc_chi_squared_dist.html" title="Noncentral Chi-Squared Distribution">Noncentral Chi-Squared Distribution</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/dist/dist_ref/dists/nc_f_dist.html" title="Noncentral F Distribution">Noncentral F Distribution</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/dist/dist_ref/dists/nc_t_dist.html" title="Noncentral T Distribution">Noncentral T Distribution</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/dist/dist_ref/dists/normal_dist.html" title="Normal (Gaussian) Distribution">Normal (Gaussian) Distribution</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/dist/dist_ref/dists/pareto.html" title="Pareto Distribution">Pareto Distribution</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/dist/dist_ref/dists/poisson_dist.html" title="Poisson Distribution">Poisson Distribution</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/dist/dist_ref/dists/rayleigh.html" title="Rayleigh Distribution">Rayleigh Distribution</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/dist/dist_ref/dists/students_t_dist.html" title="Students t Distribution">Students t Distribution</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/dist/dist_ref/dists/triangular_dist.html" title="Triangular Distribution">Triangular Distribution</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/dist/dist_ref/dists/uniform_dist.html" title="Uniform Distribution">Uniform Distribution</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/dist/dist_ref/dists/weibull.html" title="Weibull Distribution">Weibull Distribution</a></p></td></tr>
+</table></dd>
+<dt><span class="term">kurtosis_excess</span></dt>
+<dd><table class="simplelist" border="0" summary="Simple list">
+<tr><td><p><a class="link" href="../math_toolkit/dist/dist_ref/dists/bernoulli_dist.html" title="Bernoulli Distribution">Bernoulli Distribution</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/dist/dist_ref/dists/beta_dist.html" title="Beta Distribution">Beta Distribution</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/dist/dist_ref/dists/binomial_dist.html" title="Binomial Distribution">Binomial Distribution</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/dist/dist_ref/dists/cauchy_dist.html" title="Cauchy-Lorentz Distribution">Cauchy-Lorentz Distribution</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/dist/dist_ref/dists/chi_squared_dist.html" title="Chi Squared Distribution">Chi Squared Distribution</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/using_udt/dist_concept.html" title="Conceptual Requirements for Distribution Types">Conceptual Requirements for Distribution Types</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/dist/dist_ref/dists/exp_dist.html" title="Exponential Distribution">Exponential Distribution</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/dist/dist_ref/dists/extreme_dist.html" title="Extreme Value Distribution">Extreme Value Distribution</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/dist/dist_ref/dists/f_dist.html" title="F Distribution">F Distribution</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/dist/dist_ref/dists/gamma_dist.html" title="Gamma (and Erlang) Distribution">Gamma (and Erlang) Distribution</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/dist/dist_ref/dists/lognormal_dist.html" title="Log Normal Distribution">Log Normal Distribution</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/dist/dist_ref/dists/logistic_dist.html" title="Logistic Distribution">Logistic Distribution</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/dist/dist_ref/dists/negative_binomial_dist.html" title="Negative Binomial Distribution">Negative Binomial Distribution</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/dist/dist_ref/nmp.html" title="Non-Member Properties">Non-Member Properties</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/dist/dist_ref/dists/nc_beta_dist.html" title="Noncentral Beta Distribution">Noncentral Beta Distribution</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/dist/dist_ref/dists/nc_chi_squared_dist.html" title="Noncentral Chi-Squared Distribution">Noncentral Chi-Squared Distribution</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/dist/dist_ref/dists/nc_f_dist.html" title="Noncentral F Distribution">Noncentral F Distribution</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/dist/dist_ref/dists/nc_t_dist.html" title="Noncentral T Distribution">Noncentral T Distribution</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/dist/dist_ref/dists/normal_dist.html" title="Normal (Gaussian) Distribution">Normal (Gaussian) Distribution</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/dist/dist_ref/dists/pareto.html" title="Pareto Distribution">Pareto Distribution</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/dist/dist_ref/dists/poisson_dist.html" title="Poisson Distribution">Poisson Distribution</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/dist/dist_ref/dists/rayleigh.html" title="Rayleigh Distribution">Rayleigh Distribution</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/dist/dist_ref/dists/students_t_dist.html" title="Students t Distribution">Students t Distribution</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/dist/dist_ref/dists/triangular_dist.html" title="Triangular Distribution">Triangular Distribution</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/dist/dist_ref/dists/uniform_dist.html" title="Uniform Distribution">Uniform Distribution</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/dist/dist_ref/dists/weibull.html" title="Weibull Distribution">Weibull Distribution</a></p></td></tr>
+</table></dd>
+</dl></div></dd>
+<dt>
+<a name="idx_id_65"></a><span class="term">L</span>
+</dt>
+<dd><div class="variablelist"><dl>
+<dt><span class="term">laguerre</span></dt>
+<dd><table class="simplelist" border="0" summary="Simple list">
+<tr><td><p><a class="link" href="../math_toolkit/main_overview/tr1.html" title="C99 and TR1 C Functions">C99 and TR1 C Functions</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/special/extern_c/tr1.html" title="C99 and TR1 C Functions Overview">C99 and TR1 C Functions Overview</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/special/sf_poly/laguerre.html" title="Laguerre (and Associated) Polynomials">Laguerre (and Associated) Polynomials</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/special/extern_c/tr1_ref.html" title="TR1 C Functions Quick Reference">TR1 C Functions Quick Reference</a></p></td></tr>
+</table></dd>
+<dt><span class="term">Laguerre (and Associated) Polynomials</span></dt>
+<dd><table class="simplelist" border="0" summary="Simple list">
+<tr><td><p><a class="link" href="../math_toolkit/special/sf_poly/laguerre.html" title="Laguerre (and Associated) Polynomials">laguerre</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/special/sf_poly/laguerre.html" title="Laguerre (and Associated) Polynomials">laguerre_next</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/special/sf_poly/laguerre.html" title="Laguerre (and Associated) Polynomials">RR</a></p></td></tr>
+</table></dd>
+<dt><span class="term">laguerre_next</span></dt>
+<dd><table class="simplelist" border="0" summary="Simple list"><tr><td><p><a class="link" href="../math_toolkit/special/sf_poly/laguerre.html" title="Laguerre (and Associated) Polynomials">Laguerre (and Associated) Polynomials</a></p></td></tr></table></dd>
+<dt><span class="term">lanczos</span></dt>
+<dd><table class="simplelist" border="0" summary="Simple list">
+<tr><td><p><a class="link" href="../math_toolkit/using_udt/concepts.html" title="Conceptual Requirements for Real Number Types">Conceptual Requirements for Real Number Types</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/special/sf_gamma/tgamma.html" title="Gamma">Gamma</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/special/sf_gamma/lgamma.html" title="Log Gamma">Log Gamma</a></p></td></tr>
+</table></dd>
+<dt><span class="term">Lanczos approximation</span></dt>
+<dd><table class="simplelist" border="0" summary="Simple list">
+<tr><td><p><a class="link" href="../math_toolkit/special/sf_beta/beta_function.html" title="Beta">Beta</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/using_udt/concepts.html" title="Conceptual Requirements for Real Number Types">Conceptual Requirements for Real Number Types</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/special/sf_gamma/digamma.html" title="Digamma">Digamma</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/special/sf_gamma/tgamma.html" title="Gamma">Gamma</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/backgrounders/lanczos.html" title="The Lanczos Approximation">gamma_p</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/special/sf_gamma/igamma.html" title="Incomplete Gamma Functions">Incomplete Gamma Functions</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/status/issues.html" title="Known Issues, and Todo List">Known Issues, and Todo List</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/backgrounders/lanczos.html" title="The Lanczos Approximation">Lanczos approximation</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/backgrounders/lanczos.html" title="The Lanczos Approximation">lgamma</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/special/sf_gamma/lgamma.html" title="Log Gamma">Log Gamma</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/dist/dist_ref/dists/negative_binomial_dist.html" title="Negative Binomial Distribution">Negative Binomial Distribution</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/perf/tuning.html" title="Performance Tuning Macros">Performance Tuning Macros</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/backgrounders/refs.html" title="References">References</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/backgrounders/lanczos.html" title="The Lanczos Approximation">The Lanczos Approximation</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/using_udt/use_mpfr.html" title="Using With MPFR / GMP - a High-Precision Floating-Point Library">Using With MPFR / GMP - a High-Precision Floating-Point Library</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/using_udt/use_ntl.html" title="Using With NTL - a High-Precision Floating-Point Library">Using With NTL - a High-Precision Floating-Point Library</a></p></td></tr>
+</table></dd>
+<dt><span class="term">ldexp</span></dt>
+<dd><table class="simplelist" border="0" summary="Simple list">
+<tr><td><p><a class="link" href="../math_toolkit/using_udt/concepts.html" title="Conceptual Requirements for Real Number Types">Conceptual Requirements for Real Number Types</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/toolkit/internals1/roots.html" title="Root Finding With Derivatives">Root Finding With Derivatives</a></p></td></tr>
+</table></dd>
+<dt><span class="term">Legendre (and Associated) Polynomials</span></dt>
+<dd><table class="simplelist" border="0" summary="Simple list">
+<tr><td><p><a class="link" href="../math_toolkit/special/sf_poly/legendre.html" title="Legendre (and Associated) Polynomials">legendre_next</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/special/sf_poly/legendre.html" title="Legendre (and Associated) Polynomials">legendre_p</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/special/sf_poly/legendre.html" title="Legendre (and Associated) Polynomials">legendre_q</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/special/sf_poly/legendre.html" title="Legendre (and Associated) Polynomials">RR</a></p></td></tr>
+</table></dd>
+<dt><span class="term">legendre_next</span></dt>
+<dd><table class="simplelist" border="0" summary="Simple list"><tr><td><p><a class="link" href="../math_toolkit/special/sf_poly/legendre.html" title="Legendre (and Associated) Polynomials">Legendre (and Associated) Polynomials</a></p></td></tr></table></dd>
+<dt><span class="term">legendre_p</span></dt>
+<dd><table class="simplelist" border="0" summary="Simple list">
+<tr><td><p><a class="link" href="../math_toolkit/special/sf_poly/legendre.html" title="Legendre (and Associated) Polynomials">Legendre (and Associated) Polynomials</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/special/extern_c/tr1_ref.html" title="TR1 C Functions Quick Reference">TR1 C Functions Quick Reference</a></p></td></tr>
+</table></dd>
+<dt><span class="term">legendre_q</span></dt>
+<dd><table class="simplelist" border="0" summary="Simple list"><tr><td><p><a class="link" href="../math_toolkit/special/sf_poly/legendre.html" title="Legendre (and Associated) Polynomials">Legendre (and Associated) Polynomials</a></p></td></tr></table></dd>
+<dt><span class="term">lgamma</span></dt>
+<dd><table class="simplelist" border="0" summary="Simple list">
+<tr><td><p><a class="link" href="../math_toolkit/main_overview/tr1.html" title="C99 and TR1 C Functions">C99 and TR1 C Functions</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/special/extern_c/tr1.html" title="C99 and TR1 C Functions Overview">C99 and TR1 C Functions Overview</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/special/extern_c/c99.html" title="C99 C Functions">C99 C Functions</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/perf/comparisons.html" title="Comparisons to Other Open Source Libraries">Comparisons to Other Open Source Libraries</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/main_overview/directories.html" title="Directory and File Structure">Directory and File Structure</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/special/sf_gamma/tgamma.html" title="Gamma">Gamma</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/toolkit/internals2/test_data.html" title="Graphing, Profiling, and Generating Test Data for Special Functions">Graphing, Profiling, and Generating Test Data for Special Functions</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/main_overview/history1.html" title="History and What's New">History and What's New</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/special/sf_gamma/lgamma.html" title="Log Gamma">Log Gamma</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/dist/dist_ref/dists/negative_binomial_dist.html" title="Negative Binomial Distribution">Negative Binomial Distribution</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/toolkit/internals2/error_test.html" title="Relative Error and Testing">Relative Error and Testing</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/policy/pol_ref/namespace_pol.html" title="Setting Polices at Namespace Scope">Setting Polices at Namespace Scope</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/backgrounders/lanczos.html" title="The Lanczos Approximation">The Lanczos Approximation</a></p></td></tr>
+</table></dd>
+<dt><span class="term">llround</span></dt>
+<dd><table class="simplelist" border="0" summary="Simple list">
+<tr><td><p><a class="link" href="../math_toolkit/main_overview/tr1.html" title="C99 and TR1 C Functions">C99 and TR1 C Functions</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/special/extern_c/tr1.html" title="C99 and TR1 C Functions Overview">C99 and TR1 C Functions Overview</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/special/extern_c/c99.html" title="C99 C Functions">C99 C Functions</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/using_udt/concepts.html" title="Conceptual Requirements for Real Number Types">Conceptual Requirements for Real Number Types</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/special/rounding/round.html" title="Rounding Functions">Rounding Functions</a></p></td></tr>
+</table></dd>
+<dt><span class="term">lltrunc</span></dt>
+<dd><table class="simplelist" border="0" summary="Simple list">
+<tr><td><p><a class="link" href="../math_toolkit/using_udt/concepts.html" title="Conceptual Requirements for Real Number Types">Conceptual Requirements for Real Number Types</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/special/rounding/trunc.html" title="Truncation Functions">Truncation Functions</a></p></td></tr>
+</table></dd>
+<dt><span class="term">Log Gamma</span></dt>
+<dd><table class="simplelist" border="0" summary="Simple list">
+<tr><td><p><a class="link" href="../math_toolkit/special/sf_gamma/lgamma.html" title="Log Gamma">gamma</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/special/sf_gamma/lgamma.html" title="Log Gamma">lanczos</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/special/sf_gamma/lgamma.html" title="Log Gamma">Lanczos approximation</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/special/sf_gamma/lgamma.html" title="Log Gamma">lgamma</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/special/sf_gamma/lgamma.html" title="Log Gamma">log1p</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/special/sf_gamma/lgamma.html" title="Log Gamma">tgamma</a></p></td></tr>
+</table></dd>
+<dt><span class="term">Log Normal Distribution</span></dt>
+<dd><table class="simplelist" border="0" summary="Simple list">
+<tr><td><p><a class="link" href="../math_toolkit/dist/dist_ref/dists/lognormal_dist.html" title="Log Normal Distribution">cdf</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/dist/dist_ref/dists/lognormal_dist.html" title="Log Normal Distribution">kurtosis</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/dist/dist_ref/dists/lognormal_dist.html" title="Log Normal Distribution">kurtosis_excess</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/dist/dist_ref/dists/lognormal_dist.html" title="Log Normal Distribution">lognormal</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/dist/dist_ref/dists/lognormal_dist.html" title="Log Normal Distribution">lognormal_distribution</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/dist/dist_ref/dists/lognormal_dist.html" title="Log Normal Distribution">mean</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/dist/dist_ref/dists/lognormal_dist.html" title="Log Normal Distribution">median</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/dist/dist_ref/dists/lognormal_dist.html" title="Log Normal Distribution">mode</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/dist/dist_ref/dists/lognormal_dist.html" title="Log Normal Distribution">pdf</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/dist/dist_ref/dists/lognormal_dist.html" title="Log Normal Distribution">policy_type</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/dist/dist_ref/dists/lognormal_dist.html" title="Log Normal Distribution">quantile</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/dist/dist_ref/dists/lognormal_dist.html" title="Log Normal Distribution">skewness</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/dist/dist_ref/dists/lognormal_dist.html" title="Log Normal Distribution">value_type</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/dist/dist_ref/dists/lognormal_dist.html" title="Log Normal Distribution">variance</a></p></td></tr>
+</table></dd>
+<dt><span class="term">log1p</span></dt>
+<dd><table class="simplelist" border="0" summary="Simple list">
+<tr><td><p><a class="link" href="../math_toolkit/special/powers/log1p.html" title="log1p">BOOST_HAS_LOG1P</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/main_overview/tr1.html" title="C99 and TR1 C Functions">C99 and TR1 C Functions</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/special/extern_c/tr1.html" title="C99 and TR1 C Functions Overview">C99 and TR1 C Functions Overview</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/special/extern_c/c99.html" title="C99 C Functions">C99 C Functions</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/dist/dist_ref/dists/exp_dist.html" title="Exponential Distribution">Exponential Distribution</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/dist/dist_ref/dists/extreme_dist.html" title="Extreme Value Distribution">Extreme Value Distribution</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/status/issues.html" title="Known Issues, and Todo List">Known Issues, and Todo List</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/special/sf_gamma/lgamma.html" title="Log Gamma">Log Gamma</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/special/powers/log1p.html" title="log1p">log1p</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/dist/dist_ref/dists/rayleigh.html" title="Rayleigh Distribution">Rayleigh Distribution</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/special/powers/log1p.html" title="log1p">RR</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/toolkit/internals1/series_evaluation.html" title="Series Evaluation">Series Evaluation</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/special/powers/sqrt1pm1.html" title="sqrt1pm1">sqrt1pm1</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/dist/dist_ref/dists/weibull.html" title="Weibull Distribution">Weibull Distribution</a></p></td></tr>
+</table></dd>
+<dt><span class="term">log1p_series</span></dt>
+<dd><table class="simplelist" border="0" summary="Simple list"><tr><td><p><a class="link" href="../math_toolkit/toolkit/internals1/series_evaluation.html" title="Series Evaluation">Series Evaluation</a></p></td></tr></table></dd>
+<dt><span class="term">Logistic Distribution</span></dt>
+<dd><table class="simplelist" border="0" summary="Simple list">
+<tr><td><p><a class="link" href="../math_toolkit/dist/dist_ref/dists/logistic_dist.html" title="Logistic Distribution">cdf</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/dist/dist_ref/dists/logistic_dist.html" title="Logistic Distribution">kurtosis</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/dist/dist_ref/dists/logistic_dist.html" title="Logistic Distribution">kurtosis_excess</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/dist/dist_ref/dists/logistic_dist.html" title="Logistic Distribution">mean</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/dist/dist_ref/dists/logistic_dist.html" title="Logistic Distribution">median</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/dist/dist_ref/dists/logistic_dist.html" title="Logistic Distribution">mode</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/dist/dist_ref/dists/logistic_dist.html" title="Logistic Distribution">pdf</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/dist/dist_ref/dists/logistic_dist.html" title="Logistic Distribution">policy_type</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/dist/dist_ref/dists/logistic_dist.html" title="Logistic Distribution">quantile</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/dist/dist_ref/dists/logistic_dist.html" title="Logistic Distribution">skewness</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/dist/dist_ref/dists/logistic_dist.html" title="Logistic Distribution">value_type</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/dist/dist_ref/dists/logistic_dist.html" title="Logistic Distribution">variance</a></p></td></tr>
+</table></dd>
+<dt><span class="term">lognormal</span></dt>
+<dd><table class="simplelist" border="0" summary="Simple list">
+<tr><td><p><a class="link" href="../math_toolkit/backgrounders/implementation.html" title="Additional Implementation Notes">Additional Implementation Notes</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/dist/dist_ref/dist_algorithms.html" title="Distribution Algorithms">Distribution Algorithms</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/dist/dist_ref/dists/gamma_dist.html" title="Gamma (and Erlang) Distribution">Gamma (and Erlang) Distribution</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/dist/dist_ref/dists/lognormal_dist.html" title="Log Normal Distribution">Log Normal Distribution</a></p></td></tr>
+</table></dd>
+<dt><span class="term">lognormal_distribution</span></dt>
+<dd><table class="simplelist" border="0" summary="Simple list"><tr><td><p><a class="link" href="../math_toolkit/dist/dist_ref/dists/lognormal_dist.html" title="Log Normal Distribution">Log Normal Distribution</a></p></td></tr></table></dd>
+<dt><span class="term">lround</span></dt>
+<dd><table class="simplelist" border="0" summary="Simple list">
+<tr><td><p><a class="link" href="../math_toolkit/main_overview/tr1.html" title="C99 and TR1 C Functions">C99 and TR1 C Functions</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/special/extern_c/tr1.html" title="C99 and TR1 C Functions Overview">C99 and TR1 C Functions Overview</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/special/extern_c/c99.html" title="C99 C Functions">C99 C Functions</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/using_udt/concepts.html" title="Conceptual Requirements for Real Number Types">Conceptual Requirements for Real Number Types</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/special/rounding/round.html" title="Rounding Functions">Rounding Functions</a></p></td></tr>
+</table></dd>
+<dt><span class="term">ltrunc</span></dt>
+<dd><table class="simplelist" border="0" summary="Simple list">
+<tr><td><p><a class="link" href="../math_toolkit/using_udt/concepts.html" title="Conceptual Requirements for Real Number Types">Conceptual Requirements for Real Number Types</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/special/rounding/trunc.html" title="Truncation Functions">Truncation Functions</a></p></td></tr>
+</table></dd>
+</dl></div></dd>
+<dt>
+<a name="idx_id_66"></a><span class="term">M</span>
+</dt>
+<dd><div class="variablelist"><dl>
+<dt><span class="term">make_policy</span></dt>
+<dd><table class="simplelist" border="0" summary="Simple list">
+<tr><td><p><a class="link" href="../math_toolkit/policy/pol_tutorial/ad_hoc_sf_policies.html" title="Changing the Policy on an Ad Hoc Basis for the Special Functions">Changing the Policy on an Ad Hoc Basis for the Special Functions</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/policy/pol_ref/error_handling_policies.html" title="Error Handling Policies">Error Handling Policies</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/policy/pol_ref/internal_promotion.html" title="Internal Promotion Policies">Internal Promotion Policies</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/policy/pol_ref/pol_ref_ref.html" title="Policy Class Reference">Policy Class Reference</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/policy/pol_ref/precision_pol.html" title="Precision Policies">Precision Policies</a></p></td></tr>
+</table></dd>
+<dt><span class="term">Mathematically Undefined Function Policies</span></dt>
+<dd><table class="simplelist" border="0" summary="Simple list">
+<tr><td><p><a class="link" href="../math_toolkit/policy/pol_ref/assert_undefined.html" title="Mathematically Undefined Function Policies">cauchy</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/policy/pol_ref/assert_undefined.html" title="Mathematically Undefined Function Policies">cauchy_distribution</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/policy/pol_ref/assert_undefined.html" title="Mathematically Undefined Function Policies">mean</a></p></td></tr>
+</table></dd>
+<dt><span class="term">max_factorial</span></dt>
+<dd><table class="simplelist" border="0" summary="Simple list"><tr><td><p><a class="link" href="../math_toolkit/special/factorials/sf_factorial.html" title="Factorial">Factorial</a></p></td></tr></table></dd>
+<dt><span class="term">mean</span></dt>
+<dd><table class="simplelist" border="0" summary="Simple list">
+<tr><td><p><a class="link" href="../math_toolkit/backgrounders/implementation.html" title="Additional Implementation Notes">Additional Implementation Notes</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/dist/dist_ref/dists/bernoulli_dist.html" title="Bernoulli Distribution">Bernoulli Distribution</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/dist/dist_ref/dists/beta_dist.html" title="Beta Distribution">Beta Distribution</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/dist/stat_tut/weg/binom_eg/binomial_coinflip_example.html" title="Binomial Coin-Flipping Example">Binomial Coin-Flipping Example</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/dist/dist_ref/dists/binomial_dist.html" title="Binomial Distribution">Binomial Distribution</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/dist/stat_tut/weg/binom_eg/binomial_quiz_example.html" title="Binomial Quiz Example">Binomial Quiz Example</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/dist/stat_tut/weg/st_eg/tut_mean_intervals.html" title="Calculating confidence intervals on the mean with the Students-t distribution">Calculating confidence intervals on the mean with the Students-t distribution</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/dist/dist_ref/dists/cauchy_dist.html" title="Cauchy-Lorentz Distribution">Cauchy-Lorentz Distribution</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/policy/pol_tutorial/changing_policy_defaults.html" title="Changing the Policy Defaults">Changing the Policy Defaults</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/dist/dist_ref/dists/chi_squared_dist.html" title="Chi Squared Distribution">Chi Squared Distribution</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/dist/stat_tut/weg/st_eg/two_sample_students_t.html" title="Comparing the means of two samples with the Students-t test">Comparing the means of two samples with the Students-t test</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/dist/stat_tut/weg/st_eg/paired_st.html" title="Comparing two paired samples with the Student's t distribution">Comparing two paired samples with the Student's t distribution</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/using_udt/dist_concept.html" title="Conceptual Requirements for Distribution Types">Conceptual Requirements for Distribution Types</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/dist/dist_ref/dist_algorithms.html" title="Distribution Algorithms">Distribution Algorithms</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/dist/stat_tut/weg/dist_construct_eg.html" title="Distribution Construction Example">Distribution Construction Example</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/dist/stat_tut/weg/st_eg/tut_mean_size.html" title="Estimating how large a sample size would have to become in order to give a significant Students-t test result with a single sample test">Estimating how large a sample size would have to become in order to give a significant Students-t test result with a single sample test</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/dist/dist_ref/dists/exp_dist.html" title="Exponential Distribution">Exponential Distribution</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/dist/future.html" title="Extras/Future Directions">Extras/Future Directions</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/dist/dist_ref/dists/extreme_dist.html" title="Extreme Value Distribution">Extreme Value Distribution</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/dist/dist_ref/dists/f_dist.html" title="F Distribution">F Distribution</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/dist/stat_tut/weg/find_eg/find_location_eg.html" title="Find Location (Mean) Example">Find Location (Mean) Example</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/dist/stat_tut/weg/find_eg/find_mean_and_sd_eg.html" title="Find mean and standard deviation example">Find mean and standard deviation example</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/dist/stat_tut/weg/find_eg/find_scale_eg.html" title="Find Scale (Standard Deviation) Example">Find Scale (Standard Deviation) Example</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/special/fpclass.html" title="Floating-Point Classification: Infinities and NaN's">Floating-Point Classification: Infinities and NaN's</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/dist/dist_ref/dists/gamma_dist.html" title="Gamma (and Erlang) Distribution">Gamma (and Erlang) Distribution</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/special/sf_beta/ibeta_function.html" title="Incomplete Beta Functions">Incomplete Beta Functions</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/special/sf_gamma/igamma.html" title="Incomplete Gamma Functions">Incomplete Gamma Functions</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/dist/dist_ref/dists/lognormal_dist.html" title="Log Normal Distribution">Log Normal Distribution</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/dist/dist_ref/dists/logistic_dist.html" title="Logistic Distribution">Logistic Distribution</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/policy/pol_ref/assert_undefined.html" title="Mathematically Undefined Function Policies">Mathematically Undefined Function Policies</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/dist/dist_ref/dists/negative_binomial_dist.html" title="Negative Binomial Distribution">Negative Binomial Distribution</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/dist/dist_ref/nmp.html" title="Non-Member Properties">Non-Member Properties</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/dist/dist_ref/dists/nc_beta_dist.html" title="Noncentral Beta Distribution">Noncentral Beta Distribution</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/dist/dist_ref/dists/nc_chi_squared_dist.html" title="Noncentral Chi-Squared Distribution">Noncentral Chi-Squared Distribution</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/dist/dist_ref/dists/nc_f_dist.html" title="Noncentral F Distribution">Noncentral F Distribution</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/dist/dist_ref/dists/nc_t_dist.html" title="Noncentral T Distribution">Noncentral T Distribution</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/dist/dist_ref/dists/normal_dist.html" title="Normal (Gaussian) Distribution">Normal (Gaussian) Distribution</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/dist/stat_tut/overview.html" title="Overview">Overview</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/dist/dist_ref/dists/pareto.html" title="Pareto Distribution">Pareto Distribution</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/dist/dist_ref/dists/poisson_dist.html" title="Poisson Distribution">Poisson Distribution</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/dist/dist_ref/dists/rayleigh.html" title="Rayleigh Distribution">Rayleigh Distribution</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/toolkit/internals2/error_test.html" title="Relative Error and Testing">Relative Error and Testing</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/policy/pol_ref/namespace_pol.html" title="Setting Polices at Namespace Scope">Setting Polices at Namespace Scope</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/policy/pol_tutorial/what_is_a_policy.html" title="So Just What is a Policy Anyway?">So Just What is a Policy Anyway?</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/dist/stat_tut/weg/normal_example/normal_misc.html" title="Some Miscellaneous Examples of the Normal (Gaussian) Distribution">Some Miscellaneous Examples of the Normal (Gaussian) Distribution</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/dist/dist_ref/dists/students_t_dist.html" title="Students t Distribution">Students t Distribution</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/dist/stat_tut/weg/st_eg/tut_mean_test.html" title='Testing a sample mean for difference from a "true" mean'>Testing a sample mean for difference from a "true" mean</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/backgrounders/remez.html" title="The Remez Method">The Remez Method</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/dist/dist_ref/dists/triangular_dist.html" title="Triangular Distribution">Triangular Distribution</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/dist/dist_ref/dists/uniform_dist.html" title="Uniform Distribution">Uniform Distribution</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/dist/dist_ref/dists/weibull.html" title="Weibull Distribution">Weibull Distribution</a></p></td></tr>
+</table></dd>
+<dt><span class="term">Meaning of the non-member accessors</span></dt>
+<dd><table class="simplelist" border="0" summary="Simple list">
+<tr><td><p><a class="link" href="../math_toolkit/dist/dist_ref/dists/binomial_dist.html" title="Binomial Distribution">binomial</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/dist/dist_ref/dists/binomial_dist.html" title="Binomial Distribution">cdf</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/dist/dist_ref/dists/binomial_dist.html" title="Binomial Distribution">pdf</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/dist/dist_ref/dists/binomial_dist.html" title="Binomial Distribution">quantile</a></p></td></tr>
+</table></dd>
+<dt><span class="term">Meaning of the non-member accessors.</span></dt>
+<dd><table class="simplelist" border="0" summary="Simple list">
+<tr><td><p><a class="link" href="../math_toolkit/dist/dist_ref/dists/negative_binomial_dist.html" title="Negative Binomial Distribution">cdf</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/dist/dist_ref/dists/negative_binomial_dist.html" title="Negative Binomial Distribution">negative_binomial</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/dist/dist_ref/dists/negative_binomial_dist.html" title="Negative Binomial Distribution">pdf</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/dist/dist_ref/dists/negative_binomial_dist.html" title="Negative Binomial Distribution">quantile</a></p></td></tr>
+</table></dd>
+<dt><span class="term">median</span></dt>
+<dd><table class="simplelist" border="0" summary="Simple list">
+<tr><td><p><a class="link" href="../math_toolkit/backgrounders/implementation.html" title="Additional Implementation Notes">Additional Implementation Notes</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/dist/dist_ref/dists/bernoulli_dist.html" title="Bernoulli Distribution">Bernoulli Distribution</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/dist/dist_ref/dists/beta_dist.html" title="Beta Distribution">Beta Distribution</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/dist/dist_ref/dists/binomial_dist.html" title="Binomial Distribution">Binomial Distribution</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/dist/dist_ref/dists/cauchy_dist.html" title="Cauchy-Lorentz Distribution">Cauchy-Lorentz Distribution</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/dist/dist_ref/dists/chi_squared_dist.html" title="Chi Squared Distribution">Chi Squared Distribution</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/dist/stat_tut/weg/cs_eg/chi_sq_intervals.html" title="Confidence Intervals on the Standard Deviation">Confidence Intervals on the Standard Deviation</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/dist/dist_ref/dists/exp_dist.html" title="Exponential Distribution">Exponential Distribution</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/dist/dist_ref/dists/extreme_dist.html" title="Extreme Value Distribution">Extreme Value Distribution</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/dist/dist_ref/dists/f_dist.html" title="F Distribution">F Distribution</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/dist/dist_ref/dists/gamma_dist.html" title="Gamma (and Erlang) Distribution">Gamma (and Erlang) Distribution</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/dist/dist_ref/dists/lognormal_dist.html" title="Log Normal Distribution">Log Normal Distribution</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/dist/dist_ref/dists/logistic_dist.html" title="Logistic Distribution">Logistic Distribution</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/dist/dist_ref/dists/negative_binomial_dist.html" title="Negative Binomial Distribution">Negative Binomial Distribution</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/dist/dist_ref/nmp.html" title="Non-Member Properties">Non-Member Properties</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/dist/dist_ref/dists/nc_beta_dist.html" title="Noncentral Beta Distribution">Noncentral Beta Distribution</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/dist/dist_ref/dists/nc_chi_squared_dist.html" title="Noncentral Chi-Squared Distribution">Noncentral Chi-Squared Distribution</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/dist/dist_ref/dists/nc_f_dist.html" title="Noncentral F Distribution">Noncentral F Distribution</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/dist/dist_ref/dists/nc_t_dist.html" title="Noncentral T Distribution">Noncentral T Distribution</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/dist/dist_ref/dists/normal_dist.html" title="Normal (Gaussian) Distribution">Normal (Gaussian) Distribution</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/dist/dist_ref/dists/pareto.html" title="Pareto Distribution">Pareto Distribution</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/dist/dist_ref/dists/poisson_dist.html" title="Poisson Distribution">Poisson Distribution</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/dist/dist_ref/dists/rayleigh.html" title="Rayleigh Distribution">Rayleigh Distribution</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/dist/dist_ref/dists/students_t_dist.html" title="Students t Distribution">Students t Distribution</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/dist/dist_ref/dists/triangular_dist.html" title="Triangular Distribution">Triangular Distribution</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/dist/dist_ref/dists/uniform_dist.html" title="Uniform Distribution">Uniform Distribution</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/dist/dist_ref/dists/weibull.html" title="Weibull Distribution">Weibull Distribution</a></p></td></tr>
+</table></dd>
+<dt><span class="term">Minimax Approximations and the Remez Algorithm</span></dt>
+<dd><table class="simplelist" border="0" summary="Simple list">
+<tr><td><p><a class="link" href="../math_toolkit/toolkit/internals2/minimax.html" title="Minimax Approximations and the Remez Algorithm">rescale</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/toolkit/internals2/minimax.html" title="Minimax Approximations and the Remez Algorithm">rotate</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/toolkit/internals2/minimax.html" title="Minimax Approximations and the Remez Algorithm">RR</a></p></td></tr>
+</table></dd>
+<dt><span class="term">mode</span></dt>
+<dd><table class="simplelist" border="0" summary="Simple list">
+<tr><td><p><a class="link" href="../math_toolkit/backgrounders/implementation.html" title="Additional Implementation Notes">Additional Implementation Notes</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/dist/dist_ref/dists/bernoulli_dist.html" title="Bernoulli Distribution">Bernoulli Distribution</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/dist/dist_ref/dists/beta_dist.html" title="Beta Distribution">Beta Distribution</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/dist/stat_tut/weg/binom_eg/binomial_coinflip_example.html" title="Binomial Coin-Flipping Example">Binomial Coin-Flipping Example</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/dist/dist_ref/dists/binomial_dist.html" title="Binomial Distribution">Binomial Distribution</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/dist/stat_tut/weg/binom_eg/binomial_quiz_example.html" title="Binomial Quiz Example">Binomial Quiz Example</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/main_overview/tr1.html" title="C99 and TR1 C Functions">C99 and TR1 C Functions</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/special/extern_c/tr1.html" title="C99 and TR1 C Functions Overview">C99 and TR1 C Functions Overview</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/dist/dist_ref/dists/cauchy_dist.html" title="Cauchy-Lorentz Distribution">Cauchy-Lorentz Distribution</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/dist/dist_ref/dists/chi_squared_dist.html" title="Chi Squared Distribution">Chi Squared Distribution</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/perf/comparisons.html" title="Comparisons to Other Open Source Libraries">Comparisons to Other Open Source Libraries</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/using_udt/dist_concept.html" title="Conceptual Requirements for Distribution Types">Conceptual Requirements for Distribution Types</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/dist/dist_ref/dists/exp_dist.html" title="Exponential Distribution">Exponential Distribution</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/dist/dist_ref/dists/extreme_dist.html" title="Extreme Value Distribution">Extreme Value Distribution</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/dist/dist_ref/dists/f_dist.html" title="F Distribution">F Distribution</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/dist/dist_ref/dists/gamma_dist.html" title="Gamma (and Erlang) Distribution">Gamma (and Erlang) Distribution</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/perf/getting_best.html" title="Getting the Best Performance from this Library">Getting the Best Performance from this Library</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/dist/dist_ref/dists/lognormal_dist.html" title="Log Normal Distribution">Log Normal Distribution</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/dist/dist_ref/dists/logistic_dist.html" title="Logistic Distribution">Logistic Distribution</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/dist/dist_ref/dists/negative_binomial_dist.html" title="Negative Binomial Distribution">Negative Binomial Distribution</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/dist/dist_ref/nmp.html" title="Non-Member Properties">Non-Member Properties</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/dist/dist_ref/dists/nc_beta_dist.html" title="Noncentral Beta Distribution">Noncentral Beta Distribution</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/dist/dist_ref/dists/nc_chi_squared_dist.html" title="Noncentral Chi-Squared Distribution">Noncentral Chi-Squared Distribution</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/dist/dist_ref/dists/nc_f_dist.html" title="Noncentral F Distribution">Noncentral F Distribution</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/dist/dist_ref/dists/nc_t_dist.html" title="Noncentral T Distribution">Noncentral T Distribution</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/dist/dist_ref/dists/normal_dist.html" title="Normal (Gaussian) Distribution">Normal (Gaussian) Distribution</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/dist/dist_ref/dists/pareto.html" title="Pareto Distribution">Pareto Distribution</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/dist/dist_ref/dists/poisson_dist.html" title="Poisson Distribution">Poisson Distribution</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/dist/dist_ref/dists/rayleigh.html" title="Rayleigh Distribution">Rayleigh Distribution</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/dist/dist_ref/dists/students_t_dist.html" title="Students t Distribution">Students t Distribution</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/dist/dist_ref/dists/triangular_dist.html" title="Triangular Distribution">Triangular Distribution</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/dist/dist_ref/dists/uniform_dist.html" title="Uniform Distribution">Uniform Distribution</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/dist/dist_ref/dists/weibull.html" title="Weibull Distribution">Weibull Distribution</a></p></td></tr>
+</table></dd>
+<dt><span class="term">Modified Bessel Functions of the First and Second Kinds</span></dt>
+<dd><table class="simplelist" border="0" summary="Simple list">
+<tr><td><p><a class="link" href="../math_toolkit/special/bessel/mbessel.html" title="Modified Bessel Functions of the First and Second Kinds">cyl_bessel_i</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/special/bessel/mbessel.html" title="Modified Bessel Functions of the First and Second Kinds">cyl_bessel_j</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/special/bessel/mbessel.html" title="Modified Bessel Functions of the First and Second Kinds">cyl_bessel_k</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/special/bessel/mbessel.html" title="Modified Bessel Functions of the First and Second Kinds">cyl_neumann</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/special/bessel/mbessel.html" title="Modified Bessel Functions of the First and Second Kinds">exponential</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/special/bessel/mbessel.html" title="Modified Bessel Functions of the First and Second Kinds">gamma</a></p></td></tr>
+</table></dd>
+</dl></div></dd>
+<dt>
+<a name="idx_id_67"></a><span class="term">N</span>
+</dt>
+<dd><div class="variablelist"><dl>
+<dt><span class="term">Namespaces</span></dt>
+<dd><table class="simplelist" border="0" summary="Simple list">
+<tr><td><p><a class="link" href="../math_toolkit/main_overview/namespaces.html" title="Namespaces">students_t</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/main_overview/namespaces.html" title="Namespaces">students_t_distribution</a></p></td></tr>
+</table></dd>
+<dt><span class="term">Negative Binomial Distribution</span></dt>
+<dd><table class="simplelist" border="0" summary="Simple list">
+<tr><td><p><a class="link" href="../math_toolkit/dist/dist_ref/dists/negative_binomial_dist.html" title="Negative Binomial Distribution">beta</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/dist/dist_ref/dists/negative_binomial_dist.html" title="Negative Binomial Distribution">binomial</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/dist/dist_ref/dists/negative_binomial_dist.html" title="Negative Binomial Distribution">cdf</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/dist/dist_ref/dists/negative_binomial_dist.html" title="Negative Binomial Distribution">find_lower_bound_on_p</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/dist/dist_ref/dists/negative_binomial_dist.html" title="Negative Binomial Distribution">find_upper_bound_on_p</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/dist/dist_ref/dists/negative_binomial_dist.html" title="Negative Binomial Distribution">ibeta</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/dist/dist_ref/dists/negative_binomial_dist.html" title="Negative Binomial Distribution">ibetac</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/dist/dist_ref/dists/negative_binomial_dist.html" title="Negative Binomial Distribution">ibetac_inv</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/dist/dist_ref/dists/negative_binomial_dist.html" title="Negative Binomial Distribution">ibetac_inva</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/dist/dist_ref/dists/negative_binomial_dist.html" title="Negative Binomial Distribution">ibetac_invb</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/dist/dist_ref/dists/negative_binomial_dist.html" title="Negative Binomial Distribution">ibeta_derivative</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/dist/dist_ref/dists/negative_binomial_dist.html" title="Negative Binomial Distribution">ibeta_inv</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/dist/dist_ref/dists/negative_binomial_dist.html" title="Negative Binomial Distribution">ibeta_inva</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/dist/dist_ref/dists/negative_binomial_dist.html" title="Negative Binomial Distribution">ibeta_invb</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/dist/dist_ref/dists/negative_binomial_dist.html" title="Negative Binomial Distribution">kurtosis</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/dist/dist_ref/dists/negative_binomial_dist.html" title="Negative Binomial Distribution">kurtosis_excess</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/dist/dist_ref/dists/negative_binomial_dist.html" title="Negative Binomial Distribution">Lanczos approximation</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/dist/dist_ref/dists/negative_binomial_dist.html" title="Negative Binomial Distribution">lgamma</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/dist/dist_ref/dists/negative_binomial_dist.html" title="Negative Binomial Distribution">mean</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/dist/dist_ref/dists/negative_binomial_dist.html" title="Negative Binomial Distribution">median</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/dist/dist_ref/dists/negative_binomial_dist.html" title="Negative Binomial Distribution">mode</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/dist/dist_ref/dists/negative_binomial_dist.html" title="Negative Binomial Distribution">negative_binomial</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/dist/dist_ref/dists/negative_binomial_dist.html" title="Negative Binomial Distribution">negative_binomial_distribution</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/dist/dist_ref/dists/negative_binomial_dist.html" title="Negative Binomial Distribution">normal</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/dist/dist_ref/dists/negative_binomial_dist.html" title="Negative Binomial Distribution">pdf</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/dist/dist_ref/dists/negative_binomial_dist.html" title="Negative Binomial Distribution">poisson</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/dist/dist_ref/dists/negative_binomial_dist.html" title="Negative Binomial Distribution">policy_type</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/dist/dist_ref/dists/negative_binomial_dist.html" title="Negative Binomial Distribution">quantile</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/dist/dist_ref/dists/negative_binomial_dist.html" title="Negative Binomial Distribution">skewness</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/dist/dist_ref/dists/negative_binomial_dist.html" title="Negative Binomial Distribution">value_type</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/dist/dist_ref/dists/negative_binomial_dist.html" title="Negative Binomial Distribution">variance</a></p></td></tr>
+</table></dd>
+<dt><span class="term">negative_binomial</span></dt>
+<dd><table class="simplelist" border="0" summary="Simple list">
+<tr><td><p><a class="link" href="../math_toolkit/dist/stat_tut/weg/neg_binom_eg/neg_binom_conf.html" title="Calculating Confidence Limits on the Frequency of Occurrence for the Negative Binomial Distribution">Calculating Confidence Limits on the Frequency of Occurrence for the Negative Binomial Distribution</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/policy/pol_ref/discrete_quant_ref.html" title="Discrete Quantile Policies">Discrete Quantile Policies</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/dist/stat_tut/weg/dist_construct_eg.html" title="Distribution Construction Example">Distribution Construction Example</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/dist/stat_tut/weg/neg_binom_eg/neg_binom_size_eg.html" title="Estimating Sample Sizes for the Negative Binomial.">Estimating Sample Sizes for the Negative Binomial.</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/dist/dist_ref/dists/negative_binomial_dist.html" title="Negative Binomial Distribution">Meaning of the non-member accessors.</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/dist/dist_ref/dists/negative_binomial_dist.html" title="Negative Binomial Distribution">Negative Binomial Distribution</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/dist/stat_tut/weg/neg_binom_eg/negative_binomial_example1.html" title="Negative Binomial Sales Quota Example.">Negative Binomial Sales Quota Example.</a></p></td></tr>
+</table></dd>
+<dt><span class="term">negative_binomial_distribution</span></dt>
+<dd><table class="simplelist" border="0" summary="Simple list">
+<tr><td><p><a class="link" href="../math_toolkit/dist/stat_tut/weg/neg_binom_eg/neg_binom_conf.html" title="Calculating Confidence Limits on the Frequency of Occurrence for the Negative Binomial Distribution">Calculating Confidence Limits on the Frequency of Occurrence for the Negative Binomial Distribution</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/policy/pol_ref/discrete_quant_ref.html" title="Discrete Quantile Policies">Discrete Quantile Policies</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/dist/stat_tut/weg/dist_construct_eg.html" title="Distribution Construction Example">Distribution Construction Example</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/dist/dist_ref/dists/negative_binomial_dist.html" title="Negative Binomial Distribution">Negative Binomial Distribution</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/dist/stat_tut/weg/neg_binom_eg/negative_binomial_example1.html" title="Negative Binomial Sales Quota Example.">Negative Binomial Sales Quota Example.</a></p></td></tr>
+</table></dd>
+<dt><span class="term">newton_raphson_iterate</span></dt>
+<dd><table class="simplelist" border="0" summary="Simple list"><tr><td><p><a class="link" href="../math_toolkit/toolkit/internals1/roots.html" title="Root Finding With Derivatives">Root Finding With Derivatives</a></p></td></tr></table></dd>
+<dt><span class="term">nextafter</span></dt>
+<dd><table class="simplelist" border="0" summary="Simple list">
+<tr><td><p><a class="link" href="../math_toolkit/main_overview/tr1.html" title="C99 and TR1 C Functions">C99 and TR1 C Functions</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/special/extern_c/tr1.html" title="C99 and TR1 C Functions Overview">C99 and TR1 C Functions Overview</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/special/extern_c/c99.html" title="C99 C Functions">C99 C Functions</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/special/next_float/float_next.html" title="Finding the Next Greater Representable Value (float_next)">Finding the Next Greater Representable Value (float_next)</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/special/next_float/nextafter.html" title="Finding the Next Representable Value in a Specific Direction (nextafter)">Finding the Next Representable Value in a Specific Direction (nextafter)</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/special/next_float/float_prior.html" title="Finding the Next Smaller Representable Value (float_prior)">Finding the Next Smaller Representable Value (float_prior)</a></p></td></tr>
+</table></dd>
+<dt><span class="term">Non-Member Properties</span></dt>
+<dd><table class="simplelist" border="0" summary="Simple list">
+<tr><td><p><a class="link" href="../math_toolkit/dist/dist_ref/nmp.html" title="Non-Member Properties">cdf</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/dist/dist_ref/nmp.html" title="Non-Member Properties">chf</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/dist/dist_ref/nmp.html" title="Non-Member Properties">hazard</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/dist/dist_ref/nmp.html" title="Non-Member Properties">kurtosis</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/dist/dist_ref/nmp.html" title="Non-Member Properties">kurtosis_excess</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/dist/dist_ref/nmp.html" title="Non-Member Properties">mean</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/dist/dist_ref/nmp.html" title="Non-Member Properties">median</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/dist/dist_ref/nmp.html" title="Non-Member Properties">mode</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/dist/dist_ref/nmp.html" title="Non-Member Properties">norm</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/dist/dist_ref/nmp.html" title="Non-Member Properties">normal</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/dist/dist_ref/nmp.html" title="Non-Member Properties">pdf</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/dist/dist_ref/nmp.html" title="Non-Member Properties">quantile</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/dist/dist_ref/nmp.html" title="Non-Member Properties">skewness</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/dist/dist_ref/nmp.html" title="Non-Member Properties">standard_deviation</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/dist/dist_ref/nmp.html" title="Non-Member Properties">variance</a></p></td></tr>
+</table></dd>
+<dt><span class="term">Noncentral Beta Distribution</span></dt>
+<dd><table class="simplelist" border="0" summary="Simple list">
+<tr><td><p><a class="link" href="../math_toolkit/dist/dist_ref/dists/nc_beta_dist.html" title="Noncentral Beta Distribution">beta</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/dist/dist_ref/dists/nc_beta_dist.html" title="Noncentral Beta Distribution">kurtosis</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/dist/dist_ref/dists/nc_beta_dist.html" title="Noncentral Beta Distribution">kurtosis_excess</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/dist/dist_ref/dists/nc_beta_dist.html" title="Noncentral Beta Distribution">mean</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/dist/dist_ref/dists/nc_beta_dist.html" title="Noncentral Beta Distribution">median</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/dist/dist_ref/dists/nc_beta_dist.html" title="Noncentral Beta Distribution">mode</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/dist/dist_ref/dists/nc_beta_dist.html" title="Noncentral Beta Distribution">non_central_beta</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/dist/dist_ref/dists/nc_beta_dist.html" title="Noncentral Beta Distribution">non_central_beta_distribution</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/dist/dist_ref/dists/nc_beta_dist.html" title="Noncentral Beta Distribution">policy_type</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/dist/dist_ref/dists/nc_beta_dist.html" title="Noncentral Beta Distribution">quantile</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/dist/dist_ref/dists/nc_beta_dist.html" title="Noncentral Beta Distribution">skewness</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/dist/dist_ref/dists/nc_beta_dist.html" title="Noncentral Beta Distribution">value_type</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/dist/dist_ref/dists/nc_beta_dist.html" title="Noncentral Beta Distribution">variance</a></p></td></tr>
+</table></dd>
+<dt><span class="term">Noncentral Chi-Squared Distribution</span></dt>
+<dd><table class="simplelist" border="0" summary="Simple list">
+<tr><td><p><a class="link" href="../math_toolkit/dist/dist_ref/dists/nc_chi_squared_dist.html" title="Noncentral Chi-Squared Distribution">cdf</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/dist/dist_ref/dists/nc_chi_squared_dist.html" title="Noncentral Chi-Squared Distribution">complemented3_type</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/dist/dist_ref/dists/nc_chi_squared_dist.html" title="Noncentral Chi-Squared Distribution">cyl_bessel_i</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/dist/dist_ref/dists/nc_chi_squared_dist.html" title="Noncentral Chi-Squared Distribution">find_degrees_of_freedom</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/dist/dist_ref/dists/nc_chi_squared_dist.html" title="Noncentral Chi-Squared Distribution">find_non_centrality</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/dist/dist_ref/dists/nc_chi_squared_dist.html" title="Noncentral Chi-Squared Distribution">gamma</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/dist/dist_ref/dists/nc_chi_squared_dist.html" title="Noncentral Chi-Squared Distribution">gamma_p_derivative</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/dist/dist_ref/dists/nc_chi_squared_dist.html" title="Noncentral Chi-Squared Distribution">kurtosis</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/dist/dist_ref/dists/nc_chi_squared_dist.html" title="Noncentral Chi-Squared Distribution">kurtosis_excess</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/dist/dist_ref/dists/nc_chi_squared_dist.html" title="Noncentral Chi-Squared Distribution">mean</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/dist/dist_ref/dists/nc_chi_squared_dist.html" title="Noncentral Chi-Squared Distribution">median</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/dist/dist_ref/dists/nc_chi_squared_dist.html" title="Noncentral Chi-Squared Distribution">mode</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/dist/dist_ref/dists/nc_chi_squared_dist.html" title="Noncentral Chi-Squared Distribution">non_central_chi_squared</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/dist/dist_ref/dists/nc_chi_squared_dist.html" title="Noncentral Chi-Squared Distribution">non_central_chi_squared_distribution</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/dist/dist_ref/dists/nc_chi_squared_dist.html" title="Noncentral Chi-Squared Distribution">normal</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/dist/dist_ref/dists/nc_chi_squared_dist.html" title="Noncentral Chi-Squared Distribution">policy_type</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/dist/dist_ref/dists/nc_chi_squared_dist.html" title="Noncentral Chi-Squared Distribution">quantile</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/dist/dist_ref/dists/nc_chi_squared_dist.html" title="Noncentral Chi-Squared Distribution">skewness</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/dist/dist_ref/dists/nc_chi_squared_dist.html" title="Noncentral Chi-Squared Distribution">value_type</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/dist/dist_ref/dists/nc_chi_squared_dist.html" title="Noncentral Chi-Squared Distribution">variance</a></p></td></tr>
+</table></dd>
+<dt><span class="term">Noncentral F Distribution</span></dt>
+<dd><table class="simplelist" border="0" summary="Simple list">
+<tr><td><p><a class="link" href="../math_toolkit/dist/dist_ref/dists/nc_f_dist.html" title="Noncentral F Distribution">beta</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/dist/dist_ref/dists/nc_f_dist.html" title="Noncentral F Distribution">cdf</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/dist/dist_ref/dists/nc_f_dist.html" title="Noncentral F Distribution">kurtosis</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/dist/dist_ref/dists/nc_f_dist.html" title="Noncentral F Distribution">kurtosis_excess</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/dist/dist_ref/dists/nc_f_dist.html" title="Noncentral F Distribution">mean</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/dist/dist_ref/dists/nc_f_dist.html" title="Noncentral F Distribution">median</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/dist/dist_ref/dists/nc_f_dist.html" title="Noncentral F Distribution">mode</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/dist/dist_ref/dists/nc_f_dist.html" title="Noncentral F Distribution">non_central_f</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/dist/dist_ref/dists/nc_f_dist.html" title="Noncentral F Distribution">non_central_f_distribution</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/dist/dist_ref/dists/nc_f_dist.html" title="Noncentral F Distribution">pdf</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/dist/dist_ref/dists/nc_f_dist.html" title="Noncentral F Distribution">policy_type</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/dist/dist_ref/dists/nc_f_dist.html" title="Noncentral F Distribution">quantile</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/dist/dist_ref/dists/nc_f_dist.html" title="Noncentral F Distribution">skewness</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/dist/dist_ref/dists/nc_f_dist.html" title="Noncentral F Distribution">value_type</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/dist/dist_ref/dists/nc_f_dist.html" title="Noncentral F Distribution">variance</a></p></td></tr>
+</table></dd>
+<dt><span class="term">Noncentral T Distribution</span></dt>
+<dd><table class="simplelist" border="0" summary="Simple list">
+<tr><td><p><a class="link" href="../math_toolkit/dist/dist_ref/dists/nc_t_dist.html" title="Noncentral T Distribution">beta</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/dist/dist_ref/dists/nc_t_dist.html" title="Noncentral T Distribution">kurtosis</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/dist/dist_ref/dists/nc_t_dist.html" title="Noncentral T Distribution">kurtosis_excess</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/dist/dist_ref/dists/nc_t_dist.html" title="Noncentral T Distribution">mean</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/dist/dist_ref/dists/nc_t_dist.html" title="Noncentral T Distribution">median</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/dist/dist_ref/dists/nc_t_dist.html" title="Noncentral T Distribution">mode</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/dist/dist_ref/dists/nc_t_dist.html" title="Noncentral T Distribution">non_central_t</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/dist/dist_ref/dists/nc_t_dist.html" title="Noncentral T Distribution">non_central_t_distribution</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/dist/dist_ref/dists/nc_t_dist.html" title="Noncentral T Distribution">normal</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/dist/dist_ref/dists/nc_t_dist.html" title="Noncentral T Distribution">policy_type</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/dist/dist_ref/dists/nc_t_dist.html" title="Noncentral T Distribution">quantile</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/dist/dist_ref/dists/nc_t_dist.html" title="Noncentral T Distribution">skewness</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/dist/dist_ref/dists/nc_t_dist.html" title="Noncentral T Distribution">value_type</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/dist/dist_ref/dists/nc_t_dist.html" title="Noncentral T Distribution">variance</a></p></td></tr>
+</table></dd>
+<dt><span class="term">non_central_beta</span></dt>
+<dd><table class="simplelist" border="0" summary="Simple list"><tr><td><p><a class="link" href="../math_toolkit/dist/dist_ref/dists/nc_beta_dist.html" title="Noncentral Beta Distribution">Noncentral Beta Distribution</a></p></td></tr></table></dd>
+<dt><span class="term">non_central_beta_distribution</span></dt>
+<dd><table class="simplelist" border="0" summary="Simple list"><tr><td><p><a class="link" href="../math_toolkit/dist/dist_ref/dists/nc_beta_dist.html" title="Noncentral Beta Distribution">Noncentral Beta Distribution</a></p></td></tr></table></dd>
+<dt><span class="term">non_central_chi_squared</span></dt>
+<dd><table class="simplelist" border="0" summary="Simple list">
+<tr><td><p><a class="link" href="../math_toolkit/dist/dist_ref/dists/nc_chi_squared_dist.html" title="Noncentral Chi-Squared Distribution">Noncentral Chi-Squared Distribution</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/dist/stat_tut/weg/nccs_eg/nccs_power_eg.html" title="Tables of the power function of the &#967;2 test.">Tables of the power function of the &#967; 2 test.</a></p></td></tr>
+</table></dd>
+<dt><span class="term">non_central_chi_squared_distribution</span></dt>
+<dd><table class="simplelist" border="0" summary="Simple list"><tr><td><p><a class="link" href="../math_toolkit/dist/dist_ref/dists/nc_chi_squared_dist.html" title="Noncentral Chi-Squared Distribution">Noncentral Chi-Squared Distribution</a></p></td></tr></table></dd>
+<dt><span class="term">non_central_f</span></dt>
+<dd><table class="simplelist" border="0" summary="Simple list"><tr><td><p><a class="link" href="../math_toolkit/dist/dist_ref/dists/nc_f_dist.html" title="Noncentral F Distribution">Noncentral F Distribution</a></p></td></tr></table></dd>
+<dt><span class="term">non_central_f_distribution</span></dt>
+<dd><table class="simplelist" border="0" summary="Simple list"><tr><td><p><a class="link" href="../math_toolkit/dist/dist_ref/dists/nc_f_dist.html" title="Noncentral F Distribution">Noncentral F Distribution</a></p></td></tr></table></dd>
+<dt><span class="term">non_central_t</span></dt>
+<dd><table class="simplelist" border="0" summary="Simple list"><tr><td><p><a class="link" href="../math_toolkit/dist/dist_ref/dists/nc_t_dist.html" title="Noncentral T Distribution">Noncentral T Distribution</a></p></td></tr></table></dd>
+<dt><span class="term">non_central_t_distribution</span></dt>
+<dd><table class="simplelist" border="0" summary="Simple list"><tr><td><p><a class="link" href="../math_toolkit/dist/dist_ref/dists/nc_t_dist.html" title="Noncentral T Distribution">Noncentral T Distribution</a></p></td></tr></table></dd>
+<dt><span class="term">norm</span></dt>
+<dd><table class="simplelist" border="0" summary="Simple list">
+<tr><td><p><a class="link" href="../math_toolkit/dist/dist_ref/nmp.html" title="Non-Member Properties">Non-Member Properties</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/policy/pol_tutorial/namespace_policies.html" title="Setting Policies at Namespace or Translation Unit Scope">Setting Policies at Namespace or Translation Unit Scope</a></p></td></tr>
+</table></dd>
+<dt><span class="term">normal</span></dt>
+<dd><table class="simplelist" border="0" summary="Simple list">
+<tr><td><p><a class="link" href="../math_toolkit/perf/comparisons.html" title="Comparisons to Other Open Source Libraries">A Comparison to the R Statistical Library on Linux</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/perf/comparisons.html" title="Comparisons to Other Open Source Libraries">A Comparison to the R Statistical Library on Windows XP</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/main_overview/intro.html" title="About the Math Toolkit">About the Math Toolkit</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/backgrounders/implementation.html" title="Additional Implementation Notes">Additional Implementation Notes</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/dist/dist_ref/dists/binomial_dist.html" title="Binomial Distribution">Binomial Distribution</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/dist/stat_tut/weg/st_eg/tut_mean_intervals.html" title="Calculating confidence intervals on the mean with the Students-t distribution">Calculating confidence intervals on the mean with the Students-t distribution</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/dist/dist_ref/dist_algorithms.html" title="Distribution Algorithms">Distribution Algorithms</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/dist/stat_tut/weg/dist_construct_eg.html" title="Distribution Construction Example">Distribution Construction Example</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/policy/pol_ref/error_handling_policies.html" title="Error Handling Policies">Error Handling Policies</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/dist/dist_ref/dists/f_dist.html" title="F Distribution">F Distribution</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/dist/stat_tut/weg/find_eg/find_location_eg.html" title="Find Location (Mean) Example">Find Location (Mean) Example</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/dist/stat_tut/weg/find_eg/find_mean_and_sd_eg.html" title="Find mean and standard deviation example">Find mean and standard deviation example</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/dist/stat_tut/weg/find_eg/find_scale_eg.html" title="Find Scale (Standard Deviation) Example">Find Scale (Standard Deviation) Example</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/special/fpclass.html" title="Floating-Point Classification: Infinities and NaN's">Floating-Point Classification: Infinities and NaN's</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/special/sf_gamma/igamma_inv.html" title="Incomplete Gamma Function Inverses">Incomplete Gamma Function Inverses</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/policy/pol_ref/internal_promotion.html" title="Internal Promotion Policies">Internal Promotion Policies</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/status/issues.html" title="Known Issues, and Todo List">Known Issues, and Todo List</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/dist/dist_ref/dists/negative_binomial_dist.html" title="Negative Binomial Distribution">Negative Binomial Distribution</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/dist/dist_ref/nmp.html" title="Non-Member Properties">Non-Member Properties</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/dist/dist_ref/dists/nc_chi_squared_dist.html" title="Noncentral Chi-Squared Distribution">Noncentral Chi-Squared Distribution</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/dist/dist_ref/dists/nc_t_dist.html" title="Noncentral T Distribution">Noncentral T Distribution</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/dist/dist_ref/dists/normal_dist.html" title="Normal (Gaussian) Distribution">Normal (Gaussian) Distribution</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/dist/stat_tut/overview.html" title="Overview">Overview</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/policy/pol_ref/precision_pol.html" title="Precision Policies">Precision Policies</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/dist/dist_ref/dists/rayleigh.html" title="Rayleigh Distribution">Rayleigh Distribution</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/policy/pol_tutorial/namespace_policies.html" title="Setting Policies at Namespace or Translation Unit Scope">Setting Policies at Namespace or Translation Unit Scope</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/dist/stat_tut/weg/normal_example/normal_misc.html" title="Some Miscellaneous Examples of the Normal (Gaussian) Distribution">Some Miscellaneous Examples of the Normal (Gaussian) Distribution</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/dist/dist_ref/dists/students_t_dist.html" title="Students t Distribution">Students t Distribution</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/special/sf_beta/ibeta_inv_function.html" title="The Incomplete Beta Function Inverses">The Incomplete Beta Function Inverses</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/dist/dist_ref/dists/triangular_dist.html" title="Triangular Distribution">Triangular Distribution</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/policy/pol_ref/policy_defaults.html" title="Using macros to Change the Policy Defaults">Using macros to Change the Policy Defaults</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/dist/dist_ref/dists/weibull.html" title="Weibull Distribution">Weibull Distribution</a></p></td></tr>
+</table></dd>
+<dt><span class="term">Normal (Gaussian) Distribution</span></dt>
+<dd><table class="simplelist" border="0" summary="Simple list">
+<tr><td><p><a class="link" href="../math_toolkit/dist/dist_ref/dists/normal_dist.html" title="Normal (Gaussian) Distribution">cdf</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/dist/dist_ref/dists/normal_dist.html" title="Normal (Gaussian) Distribution">erfc</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/dist/dist_ref/dists/normal_dist.html" title="Normal (Gaussian) Distribution">erfc_inv</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/dist/dist_ref/dists/normal_dist.html" title="Normal (Gaussian) Distribution">find_location</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/dist/dist_ref/dists/normal_dist.html" title="Normal (Gaussian) Distribution">find_scale</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/dist/dist_ref/dists/normal_dist.html" title="Normal (Gaussian) Distribution">kurtosis</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/dist/dist_ref/dists/normal_dist.html" title="Normal (Gaussian) Distribution">kurtosis_excess</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/dist/dist_ref/dists/normal_dist.html" title="Normal (Gaussian) Distribution">mean</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/dist/dist_ref/dists/normal_dist.html" title="Normal (Gaussian) Distribution">median</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/dist/dist_ref/dists/normal_dist.html" title="Normal (Gaussian) Distribution">mode</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/dist/dist_ref/dists/normal_dist.html" title="Normal (Gaussian) Distribution">normal</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/dist/dist_ref/dists/normal_dist.html" title="Normal (Gaussian) Distribution">normal_distribution</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/dist/dist_ref/dists/normal_dist.html" title="Normal (Gaussian) Distribution">pdf</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/dist/dist_ref/dists/normal_dist.html" title="Normal (Gaussian) Distribution">policy_type</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/dist/dist_ref/dists/normal_dist.html" title="Normal (Gaussian) Distribution">quantile</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/dist/dist_ref/dists/normal_dist.html" title="Normal (Gaussian) Distribution">skewness</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/dist/dist_ref/dists/normal_dist.html" title="Normal (Gaussian) Distribution">standard_deviation</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/dist/dist_ref/dists/normal_dist.html" title="Normal (Gaussian) Distribution">value_type</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/dist/dist_ref/dists/normal_dist.html" title="Normal (Gaussian) Distribution">variance</a></p></td></tr>
+</table></dd>
+<dt><span class="term">normalise</span></dt>
+<dd><table class="simplelist" border="0" summary="Simple list"><tr><td><p><a class="link" href="../math_toolkit/policy/pol_ref/pol_ref_ref.html" title="Policy Class Reference">Policy Class Reference</a></p></td></tr></table></dd>
+<dt><span class="term">normal_distribution</span></dt>
+<dd><table class="simplelist" border="0" summary="Simple list">
+<tr><td><p><a class="link" href="../math_toolkit/dist/stat_tut/weg/dist_construct_eg.html" title="Distribution Construction Example">Distribution Construction Example</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/policy/pol_ref/error_handling_policies.html" title="Error Handling Policies">Error Handling Policies</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/dist/stat_tut/weg/find_eg/find_location_eg.html" title="Find Location (Mean) Example">Find Location (Mean) Example</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/dist/stat_tut/weg/find_eg/find_mean_and_sd_eg.html" title="Find mean and standard deviation example">Find mean and standard deviation example</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/dist/stat_tut/weg/find_eg/find_scale_eg.html" title="Find Scale (Standard Deviation) Example">Find Scale (Standard Deviation) Example</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/policy/pol_ref/internal_promotion.html" title="Internal Promotion Policies">Internal Promotion Policies</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/dist/dist_ref/dists/normal_dist.html" title="Normal (Gaussian) Distribution">Normal (Gaussian) Distribution</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/policy/pol_ref/precision_pol.html" title="Precision Policies">Precision Policies</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/policy/pol_tutorial/namespace_policies.html" title="Setting Policies at Namespace or Translation Unit Scope">Setting Policies at Namespace or Translation Unit Scope</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/dist/stat_tut/weg/normal_example/normal_misc.html" title="Some Miscellaneous Examples of the Normal (Gaussian) Distribution">Some Miscellaneous Examples of the Normal (Gaussian) Distribution</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/policy/pol_ref/policy_defaults.html" title="Using macros to Change the Policy Defaults">Using macros to Change the Policy Defaults</a></p></td></tr>
+</table></dd>
+</dl></div></dd>
+<dt>
+<a name="idx_id_68"></a><span class="term">O</span>
+</dt>
+<dd><div class="variablelist"><dl>
+<dt><span class="term">overflow_error_type</span></dt>
+<dd><table class="simplelist" border="0" summary="Simple list"><tr><td><p><a class="link" href="../math_toolkit/policy/pol_ref/pol_ref_ref.html" title="Policy Class Reference">Policy Class Reference</a></p></td></tr></table></dd>
+<dt><span class="term">Overview</span></dt>
+<dd><table class="simplelist" border="0" summary="Simple list">
+<tr><td><p><a class="link" href="../math_toolkit/dist/stat_tut/overview.html" title="Overview">beta</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/dist/stat_tut/overview.html" title="Overview">beta_distribution</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/dist/stat_tut/overview.html" title="Overview">binomial</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/dist/stat_tut/overview.html" title="Overview">binomial_distribution</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/dist/stat_tut/overview.html" title="Overview">cdf</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/dist/stat_tut/overview.html" title="Overview">find_degrees_of_freedom</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/dist/stat_tut/overview.html" title="Overview">gamma</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/dist/stat_tut/overview.html" title="Overview">mean</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/dist/stat_tut/overview.html" title="Overview">normal</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/dist/stat_tut/overview.html" title="Overview">pdf</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/dist/stat_tut/overview.html" title="Overview">quantile</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/dist/stat_tut/overview.html" title="Overview">students_t</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/dist/stat_tut/overview.html" title="Overview">students_t_distribution</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/dist/stat_tut/overview.html" title="Overview">triangular</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/dist/stat_tut/overview.html" title="Overview">uniform</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/dist/stat_tut/overview.html" title="Overview">weibull</a></p></td></tr>
+</table></dd>
+</dl></div></dd>
+<dt>
+<a name="idx_id_69"></a><span class="term">P</span>
+</dt>
+<dd><div class="variablelist"><dl>
+<dt><span class="term">parameter_info</span></dt>
+<dd><table class="simplelist" border="0" summary="Simple list"><tr><td><p><a class="link" href="../math_toolkit/toolkit/internals2/test_data.html" title="Graphing, Profiling, and Generating Test Data for Special Functions">Graphing, Profiling, and Generating Test Data for Special Functions</a></p></td></tr></table></dd>
+<dt><span class="term">pareto</span></dt>
+<dd><table class="simplelist" border="0" summary="Simple list"><tr><td><p><a class="link" href="../math_toolkit/dist/dist_ref/dists/pareto.html" title="Pareto Distribution">Pareto Distribution</a></p></td></tr></table></dd>
+<dt><span class="term">Pareto Distribution</span></dt>
+<dd><table class="simplelist" border="0" summary="Simple list">
+<tr><td><p><a class="link" href="../math_toolkit/dist/dist_ref/dists/pareto.html" title="Pareto Distribution">cdf</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/dist/dist_ref/dists/pareto.html" title="Pareto Distribution">expm1</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/dist/dist_ref/dists/pareto.html" title="Pareto Distribution">kurtosis</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/dist/dist_ref/dists/pareto.html" title="Pareto Distribution">kurtosis_excess</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/dist/dist_ref/dists/pareto.html" title="Pareto Distribution">mean</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/dist/dist_ref/dists/pareto.html" title="Pareto Distribution">median</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/dist/dist_ref/dists/pareto.html" title="Pareto Distribution">mode</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/dist/dist_ref/dists/pareto.html" title="Pareto Distribution">pareto</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/dist/dist_ref/dists/pareto.html" title="Pareto Distribution">pareto_distribution</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/dist/dist_ref/dists/pareto.html" title="Pareto Distribution">pdf</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/dist/dist_ref/dists/pareto.html" title="Pareto Distribution">quantile</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/dist/dist_ref/dists/pareto.html" title="Pareto Distribution">skewness</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/dist/dist_ref/dists/pareto.html" title="Pareto Distribution">value_type</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/dist/dist_ref/dists/pareto.html" title="Pareto Distribution">variance</a></p></td></tr>
+</table></dd>
+<dt><span class="term">pareto_distribution</span></dt>
+<dd><table class="simplelist" border="0" summary="Simple list"><tr><td><p><a class="link" href="../math_toolkit/dist/dist_ref/dists/pareto.html" title="Pareto Distribution">Pareto Distribution</a></p></td></tr></table></dd>
+<dt><span class="term">pdf</span></dt>
+<dd><table class="simplelist" border="0" summary="Simple list">
+<tr><td><p><a class="link" href="../math_toolkit/backgrounders/implementation.html" title="Additional Implementation Notes">Additional Implementation Notes</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/dist/dist_ref/dists/bernoulli_dist.html" title="Bernoulli Distribution">Bernoulli Distribution</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/dist/dist_ref/dists/beta_dist.html" title="Beta Distribution">Beta Distribution</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/dist/stat_tut/weg/binom_eg/binomial_coinflip_example.html" title="Binomial Coin-Flipping Example">Binomial Coin-Flipping Example</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/dist/dist_ref/dists/binomial_dist.html" title="Binomial Distribution">Binomial Distribution</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/dist/stat_tut/weg/binom_eg/binomial_quiz_example.html" title="Binomial Quiz Example">Binomial Quiz Example</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/dist/dist_ref/dists/cauchy_dist.html" title="Cauchy-Lorentz Distribution">Cauchy-Lorentz Distribution</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/dist/dist_ref/dists/chi_squared_dist.html" title="Chi Squared Distribution">Chi Squared Distribution</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/dist/stat_tut/weg/nag_library.html" title="Comparison with C, R, FORTRAN-style Free Functions">Comparison with C, R, FORTRAN-style Free Functions</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/using_udt/archetypes.html" title="Conceptual Archetypes and Testing">Conceptual Archetypes and Testing</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/using_udt/dist_concept.html" title="Conceptual Requirements for Distribution Types">Conceptual Requirements for Distribution Types</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/status/credits.html" title="Credits and Acknowledgements">Credits and Acknowledgements</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/main_overview/directories.html" title="Directory and File Structure">Directory and File Structure</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/dist/dist_ref/dists/exp_dist.html" title="Exponential Distribution">Exponential Distribution</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/dist/dist_ref/dists/extreme_dist.html" title="Extreme Value Distribution">Extreme Value Distribution</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/dist/dist_ref/dists/f_dist.html" title="F Distribution">F Distribution</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/dist/dist_ref/dists/gamma_dist.html" title="Gamma (and Erlang) Distribution">Gamma (and Erlang) Distribution</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/dist/dist_ref/dists/lognormal_dist.html" title="Log Normal Distribution">Log Normal Distribution</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/dist/dist_ref/dists/logistic_dist.html" title="Logistic Distribution">Logistic Distribution</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/dist/dist_ref/dists/binomial_dist.html" title="Binomial Distribution">Meaning of the non-member accessors</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/dist/dist_ref/dists/negative_binomial_dist.html" title="Negative Binomial Distribution">Meaning of the non-member accessors.</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/dist/dist_ref/dists/negative_binomial_dist.html" title="Negative Binomial Distribution">Negative Binomial Distribution</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/dist/stat_tut/weg/neg_binom_eg/negative_binomial_example1.html" title="Negative Binomial Sales Quota Example.">Negative Binomial Sales Quota Example.</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/dist/stat_tut/weg/neg_binom_eg/negative_binomial_example2.html" title="Negative Binomial Table Printing Example.">Negative Binomial Table Printing Example.</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/dist/dist_ref/nmp.html" title="Non-Member Properties">Non-Member Properties</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/dist/dist_ref/dists/nc_f_dist.html" title="Noncentral F Distribution">Noncentral F Distribution</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/dist/dist_ref/dists/normal_dist.html" title="Normal (Gaussian) Distribution">Normal (Gaussian) Distribution</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/dist/stat_tut/overview.html" title="Overview">Overview</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/dist/dist_ref/dists/pareto.html" title="Pareto Distribution">Pareto Distribution</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/dist/dist_ref/dists/poisson_dist.html" title="Poisson Distribution">Poisson Distribution</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/dist/stat_tut/variates.html" title="Random Variates and Distribution Parameters">Random Variates and Distribution Parameters</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/dist/dist_ref/dists/rayleigh.html" title="Rayleigh Distribution">Rayleigh Distribution</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/backgrounders/refs.html" title="References">References</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/dist/stat_tut/weg/normal_example/normal_misc.html" title="Some Miscellaneous Examples of the Normal (Gaussian) Distribution">Some Miscellaneous Examples of the Normal (Gaussian) Distribution</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/dist/dist_ref/dists/students_t_dist.html" title="Students t Distribution">Students t Distribution</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/dist/dist_ref/dists/triangular_dist.html" title="Triangular Distribution">Triangular Distribution</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/dist/dist_ref/dists/uniform_dist.html" title="Uniform Distribution">Uniform Distribution</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/dist/dist_ref/dists/weibull.html" title="Weibull Distribution">Weibull Distribution</a></p></td></tr>
+</table></dd>
+<dt><span class="term">Performance Comparison of Release and Debug Settings</span></dt>
+<dd><table class="simplelist" border="0" summary="Simple list">
+<tr><td><p><a class="link" href="../math_toolkit/perf/getting_best.html" title="Getting the Best Performance from this Library">erf</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/perf/getting_best.html" title="Getting the Best Performance from this Library">erf_inv</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/perf/getting_best.html" title="Getting the Best Performance from this Library">gamma_p</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/perf/getting_best.html" title="Getting the Best Performance from this Library">gamma_p_inv</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/perf/getting_best.html" title="Getting the Best Performance from this Library">gamma_p_inva</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/perf/getting_best.html" title="Getting the Best Performance from this Library">gamma_q</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/perf/getting_best.html" title="Getting the Best Performance from this Library">gamma_q_inv</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/perf/getting_best.html" title="Getting the Best Performance from this Library">gamma_q_inva</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/perf/getting_best.html" title="Getting the Best Performance from this Library">ibeta</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/perf/getting_best.html" title="Getting the Best Performance from this Library">ibetac</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/perf/getting_best.html" title="Getting the Best Performance from this Library">ibetac_inv</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/perf/getting_best.html" title="Getting the Best Performance from this Library">ibetac_inva</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/perf/getting_best.html" title="Getting the Best Performance from this Library">ibetac_invb</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/perf/getting_best.html" title="Getting the Best Performance from this Library">ibeta_inv</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/perf/getting_best.html" title="Getting the Best Performance from this Library">ibeta_inva</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/perf/getting_best.html" title="Getting the Best Performance from this Library">ibeta_invb</a></p></td></tr>
+</table></dd>
+<dt><span class="term">Performance Comparison of Various Windows Compilers</span></dt>
+<dd><table class="simplelist" border="0" summary="Simple list">
+<tr><td><p><a class="link" href="../math_toolkit/perf/comp_compilers.html" title="Comparing Compilers">erf</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/perf/comp_compilers.html" title="Comparing Compilers">erf_inv</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/perf/comp_compilers.html" title="Comparing Compilers">gamma_p</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/perf/comp_compilers.html" title="Comparing Compilers">gamma_p_inv</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/perf/comp_compilers.html" title="Comparing Compilers">gamma_p_inva</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/perf/comp_compilers.html" title="Comparing Compilers">gamma_q</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/perf/comp_compilers.html" title="Comparing Compilers">gamma_q_inv</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/perf/comp_compilers.html" title="Comparing Compilers">gamma_q_inva</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/perf/comp_compilers.html" title="Comparing Compilers">ibeta</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/perf/comp_compilers.html" title="Comparing Compilers">ibetac</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/perf/comp_compilers.html" title="Comparing Compilers">ibetac_inv</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/perf/comp_compilers.html" title="Comparing Compilers">ibetac_inva</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/perf/comp_compilers.html" title="Comparing Compilers">ibetac_invb</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/perf/comp_compilers.html" title="Comparing Compilers">ibeta_inv</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/perf/comp_compilers.html" title="Comparing Compilers">ibeta_inva</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/perf/comp_compilers.html" title="Comparing Compilers">ibeta_invb</a></p></td></tr>
+</table></dd>
+<dt><span class="term">Performance Comparison with and Without Internal Promotion to long double</span></dt>
+<dd><table class="simplelist" border="0" summary="Simple list">
+<tr><td><p><a class="link" href="../math_toolkit/perf/tuning.html" title="Performance Tuning Macros">erf</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/perf/tuning.html" title="Performance Tuning Macros">erf_inv</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/perf/tuning.html" title="Performance Tuning Macros">gamma_p</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/perf/tuning.html" title="Performance Tuning Macros">gamma_p_inv</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/perf/tuning.html" title="Performance Tuning Macros">gamma_p_inva</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/perf/tuning.html" title="Performance Tuning Macros">gamma_q</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/perf/tuning.html" title="Performance Tuning Macros">gamma_q_inv</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/perf/tuning.html" title="Performance Tuning Macros">gamma_q_inva</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/perf/tuning.html" title="Performance Tuning Macros">ibeta</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/perf/tuning.html" title="Performance Tuning Macros">ibetac</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/perf/tuning.html" title="Performance Tuning Macros">ibetac_inv</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/perf/tuning.html" title="Performance Tuning Macros">ibetac_inva</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/perf/tuning.html" title="Performance Tuning Macros">ibetac_invb</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/perf/tuning.html" title="Performance Tuning Macros">ibeta_inv</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/perf/tuning.html" title="Performance Tuning Macros">ibeta_inva</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/perf/tuning.html" title="Performance Tuning Macros">ibeta_invb</a></p></td></tr>
+</table></dd>
+<dt><span class="term">Performance Tuning Macros</span></dt>
+<dd><table class="simplelist" border="0" summary="Simple list">
+<tr><td><p><a class="link" href="../math_toolkit/perf/tuning.html" title="Performance Tuning Macros">BOOST_MATH_INT_TABLE_TYPE</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/perf/tuning.html" title="Performance Tuning Macros">BOOST_MATH_MAX_POLY_ORDER</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/perf/tuning.html" title="Performance Tuning Macros">BOOST_MATH_POLY_METHOD</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/perf/tuning.html" title="Performance Tuning Macros">BOOST_MATH_PROMOTE_DOUBLE_POLICY</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/perf/tuning.html" title="Performance Tuning Macros">BOOST_MATH_RATIONAL_METHOD</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/perf/tuning.html" title="Performance Tuning Macros">evaluate_rational</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/perf/tuning.html" title="Performance Tuning Macros">Lanczos approximation</a></p></td></tr>
+</table></dd>
+<dt><span class="term">poisson</span></dt>
+<dd><table class="simplelist" border="0" summary="Simple list">
+<tr><td><p><a class="link" href="../math_toolkit/dist/dist_ref/dists/negative_binomial_dist.html" title="Negative Binomial Distribution">Negative Binomial Distribution</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/dist/dist_ref/dists/poisson_dist.html" title="Poisson Distribution">Poisson Distribution</a></p></td></tr>
+</table></dd>
+<dt><span class="term">Poisson Distribution</span></dt>
+<dd><table class="simplelist" border="0" summary="Simple list">
+<tr><td><p><a class="link" href="../math_toolkit/dist/dist_ref/dists/poisson_dist.html" title="Poisson Distribution">cdf</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/dist/dist_ref/dists/poisson_dist.html" title="Poisson Distribution">gamma</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/dist/dist_ref/dists/poisson_dist.html" title="Poisson Distribution">gamma_p</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/dist/dist_ref/dists/poisson_dist.html" title="Poisson Distribution">gamma_p_inva</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/dist/dist_ref/dists/poisson_dist.html" title="Poisson Distribution">gamma_q</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/dist/dist_ref/dists/poisson_dist.html" title="Poisson Distribution">gamma_q_inva</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/dist/dist_ref/dists/poisson_dist.html" title="Poisson Distribution">kurtosis</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/dist/dist_ref/dists/poisson_dist.html" title="Poisson Distribution">kurtosis_excess</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/dist/dist_ref/dists/poisson_dist.html" title="Poisson Distribution">mean</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/dist/dist_ref/dists/poisson_dist.html" title="Poisson Distribution">median</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/dist/dist_ref/dists/poisson_dist.html" title="Poisson Distribution">mode</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/dist/dist_ref/dists/poisson_dist.html" title="Poisson Distribution">pdf</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/dist/dist_ref/dists/poisson_dist.html" title="Poisson Distribution">poisson</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/dist/dist_ref/dists/poisson_dist.html" title="Poisson Distribution">poisson_distribution</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/dist/dist_ref/dists/poisson_dist.html" title="Poisson Distribution">policy_type</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/dist/dist_ref/dists/poisson_dist.html" title="Poisson Distribution">quantile</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/dist/dist_ref/dists/poisson_dist.html" title="Poisson Distribution">skewness</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/dist/dist_ref/dists/poisson_dist.html" title="Poisson Distribution">value_type</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/dist/dist_ref/dists/poisson_dist.html" title="Poisson Distribution">variance</a></p></td></tr>
+</table></dd>
+<dt><span class="term">poisson_distribution</span></dt>
+<dd><table class="simplelist" border="0" summary="Simple list"><tr><td><p><a class="link" href="../math_toolkit/dist/dist_ref/dists/poisson_dist.html" title="Poisson Distribution">Poisson Distribution</a></p></td></tr></table></dd>
+<dt><span class="term">pole_error_type</span></dt>
+<dd><table class="simplelist" border="0" summary="Simple list"><tr><td><p><a class="link" href="../math_toolkit/policy/pol_ref/pol_ref_ref.html" title="Policy Class Reference">Policy Class Reference</a></p></td></tr></table></dd>
+<dt><span class="term">Policies Have Sensible Defaults</span></dt>
+<dd><table class="simplelist" border="0" summary="Simple list">
+<tr><td><p><a class="link" href="../math_toolkit/policy/pol_tutorial/policy_tut_defaults.html" title="Policies Have Sensible Defaults">evaluation_error</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/policy/pol_tutorial/policy_tut_defaults.html" title="Policies Have Sensible Defaults">quantile</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/policy/pol_tutorial/policy_tut_defaults.html" title="Policies Have Sensible Defaults">rounding_error</a></p></td></tr>
+</table></dd>
+<dt><span class="term">Policy Class Reference</span></dt>
+<dd><table class="simplelist" border="0" summary="Simple list">
+<tr><td><p><a class="link" href="../math_toolkit/policy/pol_ref/pol_ref_ref.html" title="Policy Class Reference">assert_undefined_type</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/policy/pol_ref/pol_ref_ref.html" title="Policy Class Reference">default_policy</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/policy/pol_ref/pol_ref_ref.html" title="Policy Class Reference">denorm_error_type</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/policy/pol_ref/pol_ref_ref.html" title="Policy Class Reference">discrete_quantile_type</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/policy/pol_ref/pol_ref_ref.html" title="Policy Class Reference">domain_error_type</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/policy/pol_ref/pol_ref_ref.html" title="Policy Class Reference">evaluation_error</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/policy/pol_ref/pol_ref_ref.html" title="Policy Class Reference">evaluation_error_type</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/policy/pol_ref/pol_ref_ref.html" title="Policy Class Reference">indeterminate_result_error_type</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/policy/pol_ref/pol_ref_ref.html" title="Policy Class Reference">make_policy</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/policy/pol_ref/pol_ref_ref.html" title="Policy Class Reference">normalise</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/policy/pol_ref/pol_ref_ref.html" title="Policy Class Reference">overflow_error_type</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/policy/pol_ref/pol_ref_ref.html" title="Policy Class Reference">pole_error_type</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/policy/pol_ref/pol_ref_ref.html" title="Policy Class Reference">precision_type</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/policy/pol_ref/pol_ref_ref.html" title="Policy Class Reference">promote_double_type</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/policy/pol_ref/pol_ref_ref.html" title="Policy Class Reference">promote_float_type</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/policy/pol_ref/pol_ref_ref.html" title="Policy Class Reference">rounding_error</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/policy/pol_ref/pol_ref_ref.html" title="Policy Class Reference">rounding_error_type</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/policy/pol_ref/pol_ref_ref.html" title="Policy Class Reference">underflow_error_type</a></p></td></tr>
+</table></dd>
+<dt><span class="term">Policy Overview</span></dt>
+<dd><table class="simplelist" border="0" summary="Simple list">
+<tr><td><p><a class="link" href="../math_toolkit/policy/pol_overview.html" title="Policy Overview">binomial</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/policy/pol_overview.html" title="Policy Overview">evaluation_error</a></p></td></tr>
+</table></dd>
+<dt><span class="term">policy_type</span></dt>
+<dd><table class="simplelist" border="0" summary="Simple list">
+<tr><td><p><a class="link" href="../math_toolkit/dist/dist_ref/dists/bernoulli_dist.html" title="Bernoulli Distribution">Bernoulli Distribution</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/dist/dist_ref/dists/beta_dist.html" title="Beta Distribution">Beta Distribution</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/dist/dist_ref/dists/binomial_dist.html" title="Binomial Distribution">Binomial Distribution</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/dist/dist_ref/dists/cauchy_dist.html" title="Cauchy-Lorentz Distribution">Cauchy-Lorentz Distribution</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/dist/dist_ref/dists/chi_squared_dist.html" title="Chi Squared Distribution">Chi Squared Distribution</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/using_udt/dist_concept.html" title="Conceptual Requirements for Distribution Types">Conceptual Requirements for Distribution Types</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/dist/dist_ref/dists/exp_dist.html" title="Exponential Distribution">Exponential Distribution</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/dist/dist_ref/dists/gamma_dist.html" title="Gamma (and Erlang) Distribution">Gamma (and Erlang) Distribution</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/dist/dist_ref/dists/lognormal_dist.html" title="Log Normal Distribution">Log Normal Distribution</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/dist/dist_ref/dists/logistic_dist.html" title="Logistic Distribution">Logistic Distribution</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/dist/dist_ref/dists/negative_binomial_dist.html" title="Negative Binomial Distribution">Negative Binomial Distribution</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/dist/dist_ref/dists/nc_beta_dist.html" title="Noncentral Beta Distribution">Noncentral Beta Distribution</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/dist/dist_ref/dists/nc_chi_squared_dist.html" title="Noncentral Chi-Squared Distribution">Noncentral Chi-Squared Distribution</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/dist/dist_ref/dists/nc_f_dist.html" title="Noncentral F Distribution">Noncentral F Distribution</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/dist/dist_ref/dists/nc_t_dist.html" title="Noncentral T Distribution">Noncentral T Distribution</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/dist/dist_ref/dists/normal_dist.html" title="Normal (Gaussian) Distribution">Normal (Gaussian) Distribution</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/dist/dist_ref/dists/poisson_dist.html" title="Poisson Distribution">Poisson Distribution</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/dist/dist_ref/dists/rayleigh.html" title="Rayleigh Distribution">Rayleigh Distribution</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/dist/dist_ref/dists/students_t_dist.html" title="Students t Distribution">Students t Distribution</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/dist/dist_ref/dists/triangular_dist.html" title="Triangular Distribution">Triangular Distribution</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/dist/dist_ref/dists/weibull.html" title="Weibull Distribution">Weibull Distribution</a></p></td></tr>
+</table></dd>
+<dt><span class="term">Polynomial and Rational Function Evaluation</span></dt>
+<dd><table class="simplelist" border="0" summary="Simple list">
+<tr><td><p><a class="link" href="../math_toolkit/toolkit/internals1/rational.html" title="Polynomial and Rational Function Evaluation">evaluate_even_polynomial</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/toolkit/internals1/rational.html" title="Polynomial and Rational Function Evaluation">evaluate_odd_polynomial</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/toolkit/internals1/rational.html" title="Polynomial and Rational Function Evaluation">evaluate_polynomial</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/toolkit/internals1/rational.html" title="Polynomial and Rational Function Evaluation">evaluate_rational</a></p></td></tr>
+</table></dd>
+<dt><span class="term">Polynomials</span></dt>
+<dd><table class="simplelist" border="0" summary="Simple list"><tr><td><p><a class="link" href="../math_toolkit/toolkit/internals2/polynomials.html" title="Polynomials">value_type</a></p></td></tr></table></dd>
+<dt><span class="term">Possible Actions for Internal Evaluation Errors</span></dt>
+<dd><table class="simplelist" border="0" summary="Simple list"><tr><td><p><a class="link" href="../math_toolkit/main_overview/error_handling.html" title="Error Handling">evaluation_error</a></p></td></tr></table></dd>
+<dt><span class="term">Possible Actions for Rounding Errors</span></dt>
+<dd><table class="simplelist" border="0" summary="Simple list"><tr><td><p><a class="link" href="../math_toolkit/main_overview/error_handling.html" title="Error Handling">rounding_error</a></p></td></tr></table></dd>
+<dt><span class="term">powm1</span></dt>
+<dd><table class="simplelist" border="0" summary="Simple list">
+<tr><td><p><a class="link" href="../math_toolkit/special/powers/powm1.html" title="powm1">expm1</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/special/sf_gamma/igamma.html" title="Incomplete Gamma Functions">Incomplete Gamma Functions</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/special/powers/powm1.html" title="powm1">powm1</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/special/powers/powm1.html" title="powm1">RR</a></p></td></tr>
+</table></dd>
+<dt><span class="term">Precision Policies</span></dt>
+<dd><table class="simplelist" border="0" summary="Simple list">
+<tr><td><p><a class="link" href="../math_toolkit/policy/pol_ref/precision_pol.html" title="Precision Policies">gamma</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/policy/pol_ref/precision_pol.html" title="Precision Policies">make_policy</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/policy/pol_ref/precision_pol.html" title="Precision Policies">normal</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/policy/pol_ref/precision_pol.html" title="Precision Policies">normal_distribution</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/policy/pol_ref/precision_pol.html" title="Precision Policies">quantile</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/policy/pol_ref/precision_pol.html" title="Precision Policies">tgamma</a></p></td></tr>
+</table></dd>
+<dt><span class="term">precision_type</span></dt>
+<dd><table class="simplelist" border="0" summary="Simple list"><tr><td><p><a class="link" href="../math_toolkit/policy/pol_ref/pol_ref_ref.html" title="Policy Class Reference">Policy Class Reference</a></p></td></tr></table></dd>
+<dt><span class="term">promote_args</span></dt>
+<dd><table class="simplelist" border="0" summary="Simple list">
+<tr><td><p><a class="link" href="../math_toolkit/policy/pol_tutorial/user_def_err_pol.html" title="Calling User Defined Error Handlers">Calling User Defined Error Handlers</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/policy/pol_tutorial/namespace_policies.html" title="Setting Policies at Namespace or Translation Unit Scope">Setting Policies at Namespace or Translation Unit Scope</a></p></td></tr>
+</table></dd>
+<dt><span class="term">promote_double_type</span></dt>
+<dd><table class="simplelist" border="0" summary="Simple list"><tr><td><p><a class="link" href="../math_toolkit/policy/pol_ref/pol_ref_ref.html" title="Policy Class Reference">Policy Class Reference</a></p></td></tr></table></dd>
+<dt><span class="term">promote_float_type</span></dt>
+<dd><table class="simplelist" border="0" summary="Simple list"><tr><td><p><a class="link" href="../math_toolkit/policy/pol_ref/pol_ref_ref.html" title="Policy Class Reference">Policy Class Reference</a></p></td></tr></table></dd>
+</dl></div></dd>
+<dt>
+<a name="idx_id_70"></a><span class="term">Q</span>
+</dt>
+<dd><div class="variablelist"><dl>
+<dt><span class="term">quantile</span></dt>
+<dd><table class="simplelist" border="0" summary="Simple list">
+<tr><td><p><a class="link" href="../math_toolkit/backgrounders/implementation.html" title="Additional Implementation Notes">Additional Implementation Notes</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/dist/dist_ref/dists/bernoulli_dist.html" title="Bernoulli Distribution">Bernoulli Distribution</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/dist/dist_ref/dists/beta_dist.html" title="Beta Distribution">Beta Distribution</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/dist/dist_ref/dists/binomial_dist.html" title="Binomial Distribution">Binomial Distribution</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/dist/stat_tut/weg/binom_eg/binomial_quiz_example.html" title="Binomial Quiz Example">Binomial Quiz Example</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/dist/stat_tut/weg/st_eg/tut_mean_intervals.html" title="Calculating confidence intervals on the mean with the Students-t distribution">Calculating confidence intervals on the mean with the Students-t distribution</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/dist/dist_ref/dists/cauchy_dist.html" title="Cauchy-Lorentz Distribution">Cauchy-Lorentz Distribution</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/dist/dist_ref/dists/chi_squared_dist.html" title="Chi Squared Distribution">Chi Squared Distribution</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/dist/stat_tut/weg/cs_eg/chi_sq_test.html" title="Chi-Square Test for the Standard Deviation">Chi-Square Test for the Standard Deviation</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/using_udt/dist_concept.html" title="Conceptual Requirements for Distribution Types">Conceptual Requirements for Distribution Types</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/dist/stat_tut/weg/cs_eg/chi_sq_intervals.html" title="Confidence Intervals on the Standard Deviation">Confidence Intervals on the Standard Deviation</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/dist/stat_tut/dist_params.html" title="Discrete Probability Distributions">Discrete Probability Distributions</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/policy/pol_ref/discrete_quant_ref.html" title="Discrete Quantile Policies">Discrete Quantile Policies</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/policy/pol_ref/error_handling_policies.html" title="Error Handling Policies">Error Handling Policies</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/dist/dist_ref/dists/exp_dist.html" title="Exponential Distribution">Exponential Distribution</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/dist/dist_ref/dists/extreme_dist.html" title="Extreme Value Distribution">Extreme Value Distribution</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/dist/dist_ref/dists/f_dist.html" title="F Distribution">F Distribution</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/dist/stat_tut/weg/f_eg.html" title="F Distribution Examples">F Distribution Examples</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/dist/stat_tut/weg/find_eg/find_mean_and_sd_eg.html" title="Find mean and standard deviation example">Find mean and standard deviation example</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/dist/dist_ref/dists/gamma_dist.html" title="Gamma (and Erlang) Distribution">Gamma (and Erlang) Distribution</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/policy/pol_ref/internal_promotion.html" title="Internal Promotion Policies">Internal Promotion Policies</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/dist/dist_ref/dists/lognormal_dist.html" title="Log Normal Distribution">Log Normal Distribution</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/dist/dist_ref/dists/logistic_dist.html" title="Logistic Distribution">Logistic Distribution</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/dist/dist_ref/dists/binomial_dist.html" title="Binomial Distribution">Meaning of the non-member accessors</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/dist/dist_ref/dists/negative_binomial_dist.html" title="Negative Binomial Distribution">Meaning of the non-member accessors.</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/dist/dist_ref/dists/negative_binomial_dist.html" title="Negative Binomial Distribution">Negative Binomial Distribution</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/dist/stat_tut/weg/neg_binom_eg/negative_binomial_example1.html" title="Negative Binomial Sales Quota Example.">Negative Binomial Sales Quota Example.</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/dist/dist_ref/nmp.html" title="Non-Member Properties">Non-Member Properties</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/dist/dist_ref/dists/nc_beta_dist.html" title="Noncentral Beta Distribution">Noncentral Beta Distribution</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/dist/dist_ref/dists/nc_chi_squared_dist.html" title="Noncentral Chi-Squared Distribution">Noncentral Chi-Squared Distribution</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/dist/dist_ref/dists/nc_f_dist.html" title="Noncentral F Distribution">Noncentral F Distribution</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/dist/dist_ref/dists/nc_t_dist.html" title="Noncentral T Distribution">Noncentral T Distribution</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/dist/dist_ref/dists/normal_dist.html" title="Normal (Gaussian) Distribution">Normal (Gaussian) Distribution</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/dist/stat_tut/overview.html" title="Overview">Overview</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/dist/dist_ref/dists/pareto.html" title="Pareto Distribution">Pareto Distribution</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/dist/dist_ref/dists/poisson_dist.html" title="Poisson Distribution">Poisson Distribution</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/policy/pol_tutorial/policy_tut_defaults.html" title="Policies Have Sensible Defaults">Policies Have Sensible Defaults</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/policy/pol_ref/precision_pol.html" title="Precision Policies">Precision Policies</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/dist/dist_ref/dists/rayleigh.html" title="Rayleigh Distribution">Rayleigh Distribution</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/policy/pol_tutorial/namespace_policies.html" title="Setting Policies at Namespace or Translation Unit Scope">Setting Policies at Namespace or Translation Unit Scope</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/policy/pol_tutorial/ad_hoc_dist_policies.html" title="Setting Policies for Distributions on an Ad Hoc Basis">Setting Policies for Distributions on an Ad Hoc Basis</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/policy/pol_tutorial/what_is_a_policy.html" title="So Just What is a Policy Anyway?">So Just What is a Policy Anyway?</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/dist/stat_tut/weg/normal_example/normal_misc.html" title="Some Miscellaneous Examples of the Normal (Gaussian) Distribution">Some Miscellaneous Examples of the Normal (Gaussian) Distribution</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/dist/dist_ref/dists/students_t_dist.html" title="Students t Distribution">Students t Distribution</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/dist/stat_tut/weg/nccs_eg/nccs_power_eg.html" title="Tables of the power function of the &#967;2 test.">Tables of the power function of the &#967; 2 test.</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/dist/dist_ref/dists/triangular_dist.html" title="Triangular Distribution">Triangular Distribution</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/policy/pol_tutorial/understand_dis_quant.html" title="Understanding Quantiles of Discrete Distributions">Understanding Quantiles of Discrete Distributions</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/dist/dist_ref/dists/uniform_dist.html" title="Uniform Distribution">Uniform Distribution</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/dist/dist_ref/dists/weibull.html" title="Weibull Distribution">Weibull Distribution</a></p></td></tr>
+</table></dd>
+</dl></div></dd>
+<dt>
+<a name="idx_id_71"></a><span class="term">R</span>
+</dt>
+<dd><div class="variablelist"><dl>
+<dt><span class="term">raise_denorm_error</span></dt>
+<dd><table class="simplelist" border="0" summary="Simple list"><tr><td><p><a class="link" href="../math_toolkit/main_overview/error_handling.html" title="Error Handling">Error Handling</a></p></td></tr></table></dd>
+<dt><span class="term">raise_domain_error</span></dt>
+<dd><table class="simplelist" border="0" summary="Simple list"><tr><td><p><a class="link" href="../math_toolkit/main_overview/error_handling.html" title="Error Handling">Error Handling</a></p></td></tr></table></dd>
+<dt><span class="term">raise_evaluation_error</span></dt>
+<dd><table class="simplelist" border="0" summary="Simple list"><tr><td><p><a class="link" href="../math_toolkit/main_overview/error_handling.html" title="Error Handling">Error Handling</a></p></td></tr></table></dd>
+<dt><span class="term">raise_overflow_error</span></dt>
+<dd><table class="simplelist" border="0" summary="Simple list"><tr><td><p><a class="link" href="../math_toolkit/main_overview/error_handling.html" title="Error Handling">Error Handling</a></p></td></tr></table></dd>
+<dt><span class="term">raise_pole_error</span></dt>
+<dd><table class="simplelist" border="0" summary="Simple list"><tr><td><p><a class="link" href="../math_toolkit/main_overview/error_handling.html" title="Error Handling">Error Handling</a></p></td></tr></table></dd>
+<dt><span class="term">raise_rounding_error</span></dt>
+<dd><table class="simplelist" border="0" summary="Simple list"><tr><td><p><a class="link" href="../math_toolkit/main_overview/error_handling.html" title="Error Handling">Error Handling</a></p></td></tr></table></dd>
+<dt><span class="term">raise_underflow_error</span></dt>
+<dd><table class="simplelist" border="0" summary="Simple list"><tr><td><p><a class="link" href="../math_toolkit/main_overview/error_handling.html" title="Error Handling">Error Handling</a></p></td></tr></table></dd>
+<dt><span class="term">Random Variates and Distribution Parameters</span></dt>
+<dd><table class="simplelist" border="0" summary="Simple list">
+<tr><td><p><a class="link" href="../math_toolkit/dist/stat_tut/variates.html" title="Random Variates and Distribution Parameters">binomial</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/dist/stat_tut/variates.html" title="Random Variates and Distribution Parameters">binomial_distribution</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/dist/stat_tut/variates.html" title="Random Variates and Distribution Parameters">pdf</a></p></td></tr>
+</table></dd>
+<dt><span class="term">Ratios of Gamma Functions</span></dt>
+<dd><table class="simplelist" border="0" summary="Simple list">
+<tr><td><p><a class="link" href="../math_toolkit/special/sf_gamma/gamma_ratios.html" title="Ratios of Gamma Functions">beta</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/special/sf_gamma/gamma_ratios.html" title="Ratios of Gamma Functions">factorial</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/special/sf_gamma/gamma_ratios.html" title="Ratios of Gamma Functions">gamma</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/special/sf_gamma/gamma_ratios.html" title="Ratios of Gamma Functions">RR</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/special/sf_gamma/gamma_ratios.html" title="Ratios of Gamma Functions">tgamma_delta_ratio</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/special/sf_gamma/gamma_ratios.html" title="Ratios of Gamma Functions">tgamma_ratio</a></p></td></tr>
+</table></dd>
+<dt><span class="term">rayleigh</span></dt>
+<dd><table class="simplelist" border="0" summary="Simple list"><tr><td><p><a class="link" href="../math_toolkit/dist/dist_ref/dists/rayleigh.html" title="Rayleigh Distribution">Rayleigh Distribution</a></p></td></tr></table></dd>
+<dt><span class="term">Rayleigh Distribution</span></dt>
+<dd><table class="simplelist" border="0" summary="Simple list">
+<tr><td><p><a class="link" href="../math_toolkit/dist/dist_ref/dists/rayleigh.html" title="Rayleigh Distribution">cdf</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/dist/dist_ref/dists/rayleigh.html" title="Rayleigh Distribution">expm1</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/dist/dist_ref/dists/rayleigh.html" title="Rayleigh Distribution">kurtosis</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/dist/dist_ref/dists/rayleigh.html" title="Rayleigh Distribution">kurtosis_excess</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/dist/dist_ref/dists/rayleigh.html" title="Rayleigh Distribution">log1p</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/dist/dist_ref/dists/rayleigh.html" title="Rayleigh Distribution">mean</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/dist/dist_ref/dists/rayleigh.html" title="Rayleigh Distribution">median</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/dist/dist_ref/dists/rayleigh.html" title="Rayleigh Distribution">mode</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/dist/dist_ref/dists/rayleigh.html" title="Rayleigh Distribution">normal</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/dist/dist_ref/dists/rayleigh.html" title="Rayleigh Distribution">pdf</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/dist/dist_ref/dists/rayleigh.html" title="Rayleigh Distribution">policy_type</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/dist/dist_ref/dists/rayleigh.html" title="Rayleigh Distribution">quantile</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/dist/dist_ref/dists/rayleigh.html" title="Rayleigh Distribution">rayleigh</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/dist/dist_ref/dists/rayleigh.html" title="Rayleigh Distribution">rayleigh_distribution</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/dist/dist_ref/dists/rayleigh.html" title="Rayleigh Distribution">RR</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/dist/dist_ref/dists/rayleigh.html" title="Rayleigh Distribution">skewness</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/dist/dist_ref/dists/rayleigh.html" title="Rayleigh Distribution">value_type</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/dist/dist_ref/dists/rayleigh.html" title="Rayleigh Distribution">variance</a></p></td></tr>
+</table></dd>
+<dt><span class="term">rayleigh_distribution</span></dt>
+<dd><table class="simplelist" border="0" summary="Simple list"><tr><td><p><a class="link" href="../math_toolkit/dist/dist_ref/dists/rayleigh.html" title="Rayleigh Distribution">Rayleigh Distribution</a></p></td></tr></table></dd>
+<dt><span class="term">real_cast</span></dt>
+<dd><table class="simplelist" border="0" summary="Simple list"><tr><td><p><a class="link" href="../math_toolkit/toolkit/internals2/test_data.html" title="Graphing, Profiling, and Generating Test Data for Special Functions">Graphing, Profiling, and Generating Test Data for Special Functions</a></p></td></tr></table></dd>
+<dt><span class="term">real_concept</span></dt>
+<dd><table class="simplelist" border="0" summary="Simple list">
+<tr><td><p><a class="link" href="../math_toolkit/using_udt/archetypes.html" title="Conceptual Archetypes and Testing">Conceptual Archetypes and Testing</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/main_overview/directories.html" title="Directory and File Structure">Directory and File Structure</a></p></td></tr>
+</table></dd>
+<dt><span class="term">References</span></dt>
+<dd><table class="simplelist" border="0" summary="Simple list">
+<tr><td><p><a class="link" href="../math_toolkit/backgrounders/refs.html" title="References">gamma</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/backgrounders/refs.html" title="References">Lanczos approximation</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/backgrounders/refs.html" title="References">pdf</a></p></td></tr>
+</table></dd>
+<dt><span class="term">Relative Error and Testing</span></dt>
+<dd><table class="simplelist" border="0" summary="Simple list">
+<tr><td><p><a class="link" href="../math_toolkit/toolkit/internals2/error_test.html" title="Relative Error and Testing">lgamma</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/toolkit/internals2/error_test.html" title="Relative Error and Testing">mean</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/toolkit/internals2/error_test.html" title="Relative Error and Testing">relative_error</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/toolkit/internals2/error_test.html" title="Relative Error and Testing">test_result</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/toolkit/internals2/error_test.html" title="Relative Error and Testing">tgamma</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/toolkit/internals2/error_test.html" title="Relative Error and Testing">value_type</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/toolkit/internals2/error_test.html" title="Relative Error and Testing">variance</a></p></td></tr>
+</table></dd>
+<dt><span class="term">relative_error</span></dt>
+<dd><table class="simplelist" border="0" summary="Simple list">
+<tr><td><p><a class="link" href="../math_toolkit/toolkit/internals2/test_data.html" title="Graphing, Profiling, and Generating Test Data for Special Functions">Graphing, Profiling, and Generating Test Data for Special Functions</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/toolkit/internals2/error_test.html" title="Relative Error and Testing">Relative Error and Testing</a></p></td></tr>
+</table></dd>
+<dt><span class="term">Remez Method</span></dt>
+<dd><table class="simplelist" border="0" summary="Simple list">
+<tr><td><p><a class="link" href="../math_toolkit/backgrounders/remez.html" title="The Remez Method">erfc</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/backgrounders/remez.html" title="The Remez Method">mean</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/backgrounders/remez.html" title="The Remez Method">rescale</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/backgrounders/remez.html" title="The Remez Method">rotate</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/backgrounders/remez.html" title="The Remez Method">round</a></p></td></tr>
+</table></dd>
+<dt><span class="term">Representation Distance Between Two Floating Point Values (ULP) float_distance</span></dt>
+<dd><table class="simplelist" border="0" summary="Simple list">
+<tr><td><p><a class="link" href="../math_toolkit/special/next_float/float_distance.html" title="Calculating the Representation Distance Between Two Floating Point Values (ULP) float_distance">float_distance</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/special/next_float/float_distance.html" title="Calculating the Representation Distance Between Two Floating Point Values (ULP) float_distance">float_next</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/special/next_float/float_distance.html" title="Calculating the Representation Distance Between Two Floating Point Values (ULP) float_distance">float_prior</a></p></td></tr>
+</table></dd>
+<dt><span class="term">rescale</span></dt>
+<dd><table class="simplelist" border="0" summary="Simple list">
+<tr><td><p><a class="link" href="../math_toolkit/toolkit/internals2/minimax.html" title="Minimax Approximations and the Remez Algorithm">Minimax Approximations and the Remez Algorithm</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/backgrounders/remez.html" title="The Remez Method">The Remez Method</a></p></td></tr>
+</table></dd>
+<dt><span class="term">Riemann Zeta Function</span></dt>
+<dd><table class="simplelist" border="0" summary="Simple list">
+<tr><td><p><a class="link" href="../math_toolkit/special/zetas/zeta.html" title="Riemann Zeta Function">RR</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/special/zetas/zeta.html" title="Riemann Zeta Function">zeta</a></p></td></tr>
+</table></dd>
+<dt><span class="term">Rising Factorial</span></dt>
+<dd><table class="simplelist" border="0" summary="Simple list">
+<tr><td><p><a class="link" href="../math_toolkit/special/factorials/sf_rising_factorial.html" title="Rising Factorial">factorial</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/special/factorials/sf_rising_factorial.html" title="Rising Factorial">gamma</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/special/factorials/sf_rising_factorial.html" title="Rising Factorial">rising_factorial</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/special/factorials/sf_rising_factorial.html" title="Rising Factorial">tgamma_delta_ratio</a></p></td></tr>
+</table></dd>
+<dt><span class="term">rising_factorial</span></dt>
+<dd><table class="simplelist" border="0" summary="Simple list"><tr><td><p><a class="link" href="../math_toolkit/special/factorials/sf_rising_factorial.html" title="Rising Factorial">Rising Factorial</a></p></td></tr></table></dd>
+<dt><span class="term">Root Finding With Derivatives</span></dt>
+<dd><table class="simplelist" border="0" summary="Simple list">
+<tr><td><p><a class="link" href="../math_toolkit/toolkit/internals1/roots.html" title="Root Finding With Derivatives">cbrt</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/toolkit/internals1/roots.html" title="Root Finding With Derivatives">cbrt_functor</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/toolkit/internals1/roots.html" title="Root Finding With Derivatives">halley_iterate</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/toolkit/internals1/roots.html" title="Root Finding With Derivatives">ldexp</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/toolkit/internals1/roots.html" title="Root Finding With Derivatives">newton_raphson_iterate</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/toolkit/internals1/roots.html" title="Root Finding With Derivatives">RR</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/toolkit/internals1/roots.html" title="Root Finding With Derivatives">schroeder_iterate</a></p></td></tr>
+</table></dd>
+<dt><span class="term">Root Finding Without Derivatives</span></dt>
+<dd><table class="simplelist" border="0" summary="Simple list">
+<tr><td><p><a class="link" href="../math_toolkit/toolkit/internals1/roots2.html" title="Root Finding Without Derivatives">eps_tolerance</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/toolkit/internals1/roots2.html" title="Root Finding Without Derivatives">equal_ceil</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/toolkit/internals1/roots2.html" title="Root Finding Without Derivatives">equal_floor</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/toolkit/internals1/roots2.html" title="Root Finding Without Derivatives">equal_nearest_integer</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/toolkit/internals1/roots2.html" title="Root Finding Without Derivatives">round</a></p></td></tr>
+</table></dd>
+<dt><span class="term">rotate</span></dt>
+<dd><table class="simplelist" border="0" summary="Simple list">
+<tr><td><p><a class="link" href="../math_toolkit/toolkit/internals2/minimax.html" title="Minimax Approximations and the Remez Algorithm">Minimax Approximations and the Remez Algorithm</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/backgrounders/remez.html" title="The Remez Method">The Remez Method</a></p></td></tr>
+</table></dd>
+<dt><span class="term">round</span></dt>
+<dd><table class="simplelist" border="0" summary="Simple list">
+<tr><td><p><a class="link" href="../math_toolkit/backgrounders/implementation.html" title="Additional Implementation Notes">Additional Implementation Notes</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/main_overview/tr1.html" title="C99 and TR1 C Functions">C99 and TR1 C Functions</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/special/extern_c/tr1.html" title="C99 and TR1 C Functions Overview">C99 and TR1 C Functions Overview</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/special/extern_c/c99.html" title="C99 C Functions">C99 C Functions</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/using_udt/concepts.html" title="Conceptual Requirements for Real Number Types">Conceptual Requirements for Real Number Types</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/policy/pol_ref/discrete_quant_ref.html" title="Discrete Quantile Policies">Discrete Quantile Policies</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/special/sf_erf/error_inv.html" title="Error Function Inverses">Error Function Inverses</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/special/sf_erf/error_function.html" title="Error Functions">Error Functions</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/main_overview/error_handling.html" title="Error Handling">Error Handling</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/policy/pol_ref/error_handling_policies.html" title="Error Handling Policies">Error Handling Policies</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/dist/stat_tut/weg/find_eg/find_scale_eg.html" title="Find Scale (Standard Deviation) Example">Find Scale (Standard Deviation) Example</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/special/sf_gamma/igamma_inv.html" title="Incomplete Gamma Function Inverses">Incomplete Gamma Function Inverses</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/toolkit/internals1/roots2.html" title="Root Finding Without Derivatives">Root Finding Without Derivatives</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/special/rounding/round.html" title="Rounding Functions">Rounding Functions</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/special/sf_beta/ibeta_inv_function.html" title="The Incomplete Beta Function Inverses">The Incomplete Beta Function Inverses</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/backgrounders/remez.html" title="The Remez Method">The Remez Method</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/special/rounding/trunc.html" title="Truncation Functions">Truncation Functions</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/policy/pol_tutorial/understand_dis_quant.html" title="Understanding Quantiles of Discrete Distributions">Understanding Quantiles of Discrete Distributions</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/policy/pol_ref/policy_defaults.html" title="Using macros to Change the Policy Defaults">Using macros to Change the Policy Defaults</a></p></td></tr>
+</table></dd>
+<dt><span class="term">Rounding Functions</span></dt>
+<dd><table class="simplelist" border="0" summary="Simple list">
+<tr><td><p><a class="link" href="../math_toolkit/special/rounding/round.html" title="Rounding Functions">iround</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/special/rounding/round.html" title="Rounding Functions">llround</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/special/rounding/round.html" title="Rounding Functions">lround</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/special/rounding/round.html" title="Rounding Functions">round</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/special/rounding/round.html" title="Rounding Functions">rounding_error</a></p></td></tr>
+</table></dd>
+<dt><span class="term">rounding_error</span></dt>
+<dd><table class="simplelist" border="0" summary="Simple list">
+<tr><td><p><a class="link" href="../math_toolkit/main_overview/error_handling.html" title="Error Handling">Error Handling</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/policy/pol_ref/error_handling_policies.html" title="Error Handling Policies">Error Handling Policies</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/special/rounding/modf.html" title="Integer and Fractional Part Splitting (modf)">Integer and Fractional Part Splitting (modf)</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/policy/pol_tutorial/policy_tut_defaults.html" title="Policies Have Sensible Defaults">Policies Have Sensible Defaults</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/policy/pol_ref/pol_ref_ref.html" title="Policy Class Reference">Policy Class Reference</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/main_overview/error_handling.html" title="Error Handling">Possible Actions for Rounding Errors</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/special/rounding/round.html" title="Rounding Functions">Rounding Functions</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/special/rounding/trunc.html" title="Truncation Functions">Truncation Functions</a></p></td></tr>
+</table></dd>
+<dt><span class="term">rounding_error_type</span></dt>
+<dd><table class="simplelist" border="0" summary="Simple list"><tr><td><p><a class="link" href="../math_toolkit/policy/pol_ref/pol_ref_ref.html" title="Policy Class Reference">Policy Class Reference</a></p></td></tr></table></dd>
+<dt><span class="term">RR</span></dt>
+<dd><table class="simplelist" border="0" summary="Simple list">
+<tr><td><p><a class="link" href="../math_toolkit/backgrounders/implementation.html" title="Additional Implementation Notes">Additional Implementation Notes</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/special/sf_beta/beta_function.html" title="Beta">Beta</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/main_overview/result_type.html" title="Calculation of the Type of the Result">Calculation of the Type of the Result</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/special/powers/cbrt.html" title="cbrt">cbrt</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/using_udt/archetypes.html" title="Conceptual Archetypes and Testing">Conceptual Archetypes and Testing</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/using_udt/concepts.html" title="Conceptual Requirements for Real Number Types">Conceptual Requirements for Real Number Types</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/main_overview/directories.html" title="Directory and File Structure">Directory and File Structure</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/dist/stat_tut/weg/dist_construct_eg.html" title="Distribution Construction Example">Distribution Construction Example</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/special/ellint/ellint_carlson.html" title="Elliptic Integrals - Carlson Form">Elliptic Integrals - Carlson Form</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/special/ellint/ellint_1.html" title="Elliptic Integrals of the First Kind - Legendre Form">Elliptic Integrals of the First Kind - Legendre Form</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/special/ellint/ellint_2.html" title="Elliptic Integrals of the Second Kind - Legendre Form">Elliptic Integrals of the Second Kind - Legendre Form</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/special/ellint/ellint_3.html" title="Elliptic Integrals of the Third Kind - Legendre Form">Elliptic Integrals of the Third Kind - Legendre Form</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/special/sf_erf/error_function.html" title="Error Functions">Error Functions</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/special/powers/expm1.html" title="expm1">expm1</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/special/expint/expint_i.html" title="Exponential Integral Ei">Exponential Integral Ei</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/special/expint/expint_n.html" title="Exponential Integral En">Exponential Integral En</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/special/next_float.html" title="Floating-Point Representation Distance (ULP), and Finding Adjacent Floating-Point Values">Floating-Point Representation Distance (ULP), and Finding Adjacent Floating-Point Values</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/toolkit/internals2/test_data.html" title="Graphing, Profiling, and Generating Test Data for Special Functions">Graphing, Profiling, and Generating Test Data for Special Functions</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/special/sf_poly/hermite.html" title="Hermite Polynomials">Hermite Polynomials</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/special/sf_beta/ibeta_function.html" title="Incomplete Beta Functions">Incomplete Beta Functions</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/special/sf_gamma/igamma.html" title="Incomplete Gamma Functions">Incomplete Gamma Functions</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/special/sf_poly/laguerre.html" title="Laguerre (and Associated) Polynomials">Laguerre (and Associated) Polynomials</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/special/sf_poly/legendre.html" title="Legendre (and Associated) Polynomials">Legendre (and Associated) Polynomials</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/special/powers/log1p.html" title="log1p">log1p</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/toolkit/internals2/minimax.html" title="Minimax Approximations and the Remez Algorithm">Minimax Approximations and the Remez Algorithm</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/special/powers/powm1.html" title="powm1">powm1</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/special/sf_gamma/gamma_ratios.html" title="Ratios of Gamma Functions">Ratios of Gamma Functions</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/dist/dist_ref/dists/rayleigh.html" title="Rayleigh Distribution">Rayleigh Distribution</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/special/zetas/zeta.html" title="Riemann Zeta Function">Riemann Zeta Function</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/toolkit/internals1/roots.html" title="Root Finding With Derivatives">Root Finding With Derivatives</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/special/sf_poly/sph_harm.html" title="Spherical Harmonics">Spherical Harmonics</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/special/powers/sqrt1pm1.html" title="sqrt1pm1">sqrt1pm1</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/using_udt/use_ntl.html" title="Using With NTL - a High-Precision Floating-Point Library">Using With NTL - a High-Precision Floating-Point Library</a></p></td></tr>
+</table></dd>
+</dl></div></dd>
+<dt>
+<a name="idx_id_72"></a><span class="term">S</span>
+</dt>
+<dd><div class="variablelist"><dl>
+<dt><span class="term">schroeder_iterate</span></dt>
+<dd><table class="simplelist" border="0" summary="Simple list"><tr><td><p><a class="link" href="../math_toolkit/toolkit/internals1/roots.html" title="Root Finding With Derivatives">Root Finding With Derivatives</a></p></td></tr></table></dd>
+<dt><span class="term">Series Evaluation</span></dt>
+<dd><table class="simplelist" border="0" summary="Simple list">
+<tr><td><p><a class="link" href="../math_toolkit/toolkit/internals1/series_evaluation.html" title="Series Evaluation">kahan_sum_series</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/toolkit/internals1/series_evaluation.html" title="Series Evaluation">log1p</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/toolkit/internals1/series_evaluation.html" title="Series Evaluation">log1p_series</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/toolkit/internals1/series_evaluation.html" title="Series Evaluation">sum_series</a></p></td></tr>
+</table></dd>
+<dt><span class="term">SetOutputPrecision</span></dt>
+<dd><table class="simplelist" border="0" summary="Simple list"><tr><td><p><a class="link" href="../math_toolkit/toolkit/internals2/test_data.html" title="Graphing, Profiling, and Generating Test Data for Special Functions">Graphing, Profiling, and Generating Test Data for Special Functions</a></p></td></tr></table></dd>
+<dt><span class="term">SetPrecision</span></dt>
+<dd><table class="simplelist" border="0" summary="Simple list"><tr><td><p><a class="link" href="../math_toolkit/toolkit/internals2/test_data.html" title="Graphing, Profiling, and Generating Test Data for Special Functions">Graphing, Profiling, and Generating Test Data for Special Functions</a></p></td></tr></table></dd>
+<dt><span class="term">Setting Polices at Namespace Scope</span></dt>
+<dd><table class="simplelist" border="0" summary="Simple list">
+<tr><td><p><a class="link" href="../math_toolkit/policy/pol_ref/namespace_pol.html" title="Setting Polices at Namespace Scope">BOOST_MATH_DECLARE_DISTRIBUTIONS</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/policy/pol_ref/namespace_pol.html" title="Setting Polices at Namespace Scope">BOOST_MATH_DECLARE_SPECIAL_FUNCTIONS</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/policy/pol_ref/namespace_pol.html" title="Setting Polices at Namespace Scope">cauchy</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/policy/pol_ref/namespace_pol.html" title="Setting Polices at Namespace Scope">cauchy_distribution</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/policy/pol_ref/namespace_pol.html" title="Setting Polices at Namespace Scope">gamma</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/policy/pol_ref/namespace_pol.html" title="Setting Polices at Namespace Scope">gamma_distribution</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/policy/pol_ref/namespace_pol.html" title="Setting Polices at Namespace Scope">lgamma</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/policy/pol_ref/namespace_pol.html" title="Setting Polices at Namespace Scope">mean</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/policy/pol_ref/namespace_pol.html" title="Setting Polices at Namespace Scope">tgamma</a></p></td></tr>
+</table></dd>
+<dt><span class="term">Setting Policies at Namespace or Translation Unit Scope</span></dt>
+<dd><table class="simplelist" border="0" summary="Simple list">
+<tr><td><p><a class="link" href="../math_toolkit/policy/pol_tutorial/namespace_policies.html" title="Setting Policies at Namespace or Translation Unit Scope">binomial</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/policy/pol_tutorial/namespace_policies.html" title="Setting Policies at Namespace or Translation Unit Scope">BOOST_MATH_DECLARE_DISTRIBUTIONS</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/policy/pol_tutorial/namespace_policies.html" title="Setting Policies at Namespace or Translation Unit Scope">BOOST_MATH_DECLARE_SPECIAL_FUNCTIONS</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/policy/pol_tutorial/namespace_policies.html" title="Setting Policies at Namespace or Translation Unit Scope">cauchy</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/policy/pol_tutorial/namespace_policies.html" title="Setting Policies at Namespace or Translation Unit Scope">cauchy_distribution</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/policy/pol_tutorial/namespace_policies.html" title="Setting Policies at Namespace or Translation Unit Scope">evaluation_error</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/policy/pol_tutorial/namespace_policies.html" title="Setting Policies at Namespace or Translation Unit Scope">gamma</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/policy/pol_tutorial/namespace_policies.html" title="Setting Policies at Namespace or Translation Unit Scope">gamma_distribution</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/policy/pol_tutorial/namespace_policies.html" title="Setting Policies at Namespace or Translation Unit Scope">norm</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/policy/pol_tutorial/namespace_policies.html" title="Setting Policies at Namespace or Translation Unit Scope">normal</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/policy/pol_tutorial/namespace_policies.html" title="Setting Policies at Namespace or Translation Unit Scope">normal_distribution</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/policy/pol_tutorial/namespace_policies.html" title="Setting Policies at Namespace or Translation Unit Scope">promote_args</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/policy/pol_tutorial/namespace_policies.html" title="Setting Policies at Namespace or Translation Unit Scope">quantile</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/policy/pol_tutorial/namespace_policies.html" title="Setting Policies at Namespace or Translation Unit Scope">tgamma</a></p></td></tr>
+</table></dd>
+<dt><span class="term">Setting Policies for Distributions on an Ad Hoc Basis</span></dt>
+<dd><table class="simplelist" border="0" summary="Simple list">
+<tr><td><p><a class="link" href="../math_toolkit/policy/pol_tutorial/ad_hoc_dist_policies.html" title="Setting Policies for Distributions on an Ad Hoc Basis">binomial</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/policy/pol_tutorial/ad_hoc_dist_policies.html" title="Setting Policies for Distributions on an Ad Hoc Basis">binomial_distribution</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/policy/pol_tutorial/ad_hoc_dist_policies.html" title="Setting Policies for Distributions on an Ad Hoc Basis">fisher_f</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/policy/pol_tutorial/ad_hoc_dist_policies.html" title="Setting Policies for Distributions on an Ad Hoc Basis">fisher_f_distribution</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/policy/pol_tutorial/ad_hoc_dist_policies.html" title="Setting Policies for Distributions on an Ad Hoc Basis">quantile</a></p></td></tr>
+</table></dd>
+<dt><span class="term">sinc_pi</span></dt>
+<dd><table class="simplelist" border="0" summary="Simple list">
+<tr><td><p><a class="link" href="../math_toolkit/special/sinc/sinc_pi.html" title="sinc_pi">sinc_pi</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/special/sinc/sinc_overview.html" title="Sinus Cardinal and Hyperbolic Sinus Cardinal Functions Overview">Sinus Cardinal and Hyperbolic Sinus Cardinal Functions Overview</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/special/bessel/sph_bessel.html" title="Spherical Bessel Functions of the First and Second Kinds">Spherical Bessel Functions of the First and Second Kinds</a></p></td></tr>
+</table></dd>
+<dt><span class="term">sinhc_pi</span></dt>
+<dd><table class="simplelist" border="0" summary="Simple list">
+<tr><td><p><a class="link" href="../math_toolkit/special/sinc/sinhc_pi.html" title="sinhc_pi">sinhc_pi</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/special/sinc/sinc_overview.html" title="Sinus Cardinal and Hyperbolic Sinus Cardinal Functions Overview">Sinus Cardinal and Hyperbolic Sinus Cardinal Functions Overview</a></p></td></tr>
+</table></dd>
+<dt><span class="term">Sinus Cardinal and Hyperbolic Sinus Cardinal Functions Overview</span></dt>
+<dd><table class="simplelist" border="0" summary="Simple list">
+<tr><td><p><a class="link" href="../math_toolkit/special/sinc/sinc_overview.html" title="Sinus Cardinal and Hyperbolic Sinus Cardinal Functions Overview">sinc_pi</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/special/sinc/sinc_overview.html" title="Sinus Cardinal and Hyperbolic Sinus Cardinal Functions Overview">sinhc_pi</a></p></td></tr>
+</table></dd>
+<dt><span class="term">skewness</span></dt>
+<dd><table class="simplelist" border="0" summary="Simple list">
+<tr><td><p><a class="link" href="../math_toolkit/dist/dist_ref/dists/bernoulli_dist.html" title="Bernoulli Distribution">Bernoulli Distribution</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/dist/dist_ref/dists/beta_dist.html" title="Beta Distribution">Beta Distribution</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/dist/stat_tut/weg/binom_eg/binomial_coinflip_example.html" title="Binomial Coin-Flipping Example">Binomial Coin-Flipping Example</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/dist/dist_ref/dists/binomial_dist.html" title="Binomial Distribution">Binomial Distribution</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/dist/stat_tut/weg/binom_eg/binomial_quiz_example.html" title="Binomial Quiz Example">Binomial Quiz Example</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/dist/dist_ref/dists/cauchy_dist.html" title="Cauchy-Lorentz Distribution">Cauchy-Lorentz Distribution</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/dist/dist_ref/dists/chi_squared_dist.html" title="Chi Squared Distribution">Chi Squared Distribution</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/using_udt/dist_concept.html" title="Conceptual Requirements for Distribution Types">Conceptual Requirements for Distribution Types</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/dist/dist_ref/dists/exp_dist.html" title="Exponential Distribution">Exponential Distribution</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/dist/dist_ref/dists/extreme_dist.html" title="Extreme Value Distribution">Extreme Value Distribution</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/dist/dist_ref/dists/f_dist.html" title="F Distribution">F Distribution</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/dist/dist_ref/dists/gamma_dist.html" title="Gamma (and Erlang) Distribution">Gamma (and Erlang) Distribution</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/dist/dist_ref/dists/lognormal_dist.html" title="Log Normal Distribution">Log Normal Distribution</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/dist/dist_ref/dists/logistic_dist.html" title="Logistic Distribution">Logistic Distribution</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/dist/dist_ref/dists/negative_binomial_dist.html" title="Negative Binomial Distribution">Negative Binomial Distribution</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/dist/dist_ref/nmp.html" title="Non-Member Properties">Non-Member Properties</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/dist/dist_ref/dists/nc_beta_dist.html" title="Noncentral Beta Distribution">Noncentral Beta Distribution</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/dist/dist_ref/dists/nc_chi_squared_dist.html" title="Noncentral Chi-Squared Distribution">Noncentral Chi-Squared Distribution</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/dist/dist_ref/dists/nc_f_dist.html" title="Noncentral F Distribution">Noncentral F Distribution</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/dist/dist_ref/dists/nc_t_dist.html" title="Noncentral T Distribution">Noncentral T Distribution</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/dist/dist_ref/dists/normal_dist.html" title="Normal (Gaussian) Distribution">Normal (Gaussian) Distribution</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/dist/dist_ref/dists/pareto.html" title="Pareto Distribution">Pareto Distribution</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/dist/dist_ref/dists/poisson_dist.html" title="Poisson Distribution">Poisson Distribution</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/dist/dist_ref/dists/rayleigh.html" title="Rayleigh Distribution">Rayleigh Distribution</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/dist/dist_ref/dists/students_t_dist.html" title="Students t Distribution">Students t Distribution</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/dist/dist_ref/dists/triangular_dist.html" title="Triangular Distribution">Triangular Distribution</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/dist/dist_ref/dists/uniform_dist.html" title="Uniform Distribution">Uniform Distribution</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/dist/dist_ref/dists/weibull.html" title="Weibull Distribution">Weibull Distribution</a></p></td></tr>
+</table></dd>
+<dt><span class="term">So Just What is a Policy Anyway?</span></dt>
+<dd><table class="simplelist" border="0" summary="Simple list">
+<tr><td><p><a class="link" href="../math_toolkit/policy/pol_tutorial/what_is_a_policy.html" title="So Just What is a Policy Anyway?">mean</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/policy/pol_tutorial/what_is_a_policy.html" title="So Just What is a Policy Anyway?">quantile</a></p></td></tr>
+</table></dd>
+<dt><span class="term">Spherical Bessel Functions of the First and Second Kinds</span></dt>
+<dd><table class="simplelist" border="0" summary="Simple list">
+<tr><td><p><a class="link" href="../math_toolkit/special/bessel/sph_bessel.html" title="Spherical Bessel Functions of the First and Second Kinds">cyl_bessel_j</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/special/bessel/sph_bessel.html" title="Spherical Bessel Functions of the First and Second Kinds">cyl_neumann</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/special/bessel/sph_bessel.html" title="Spherical Bessel Functions of the First and Second Kinds">sinc_pi</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/special/bessel/sph_bessel.html" title="Spherical Bessel Functions of the First and Second Kinds">sph_bessel</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/special/bessel/sph_bessel.html" title="Spherical Bessel Functions of the First and Second Kinds">sph_neumann</a></p></td></tr>
+</table></dd>
+<dt><span class="term">Spherical Harmonics</span></dt>
+<dd><table class="simplelist" border="0" summary="Simple list">
+<tr><td><p><a class="link" href="../math_toolkit/special/sf_poly/sph_harm.html" title="Spherical Harmonics">RR</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/special/sf_poly/sph_harm.html" title="Spherical Harmonics">spherical_harmonic_i</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/special/sf_poly/sph_harm.html" title="Spherical Harmonics">spherical_harmonic_r</a></p></td></tr>
+</table></dd>
+<dt><span class="term">spherical_harmonic_i</span></dt>
+<dd><table class="simplelist" border="0" summary="Simple list"><tr><td><p><a class="link" href="../math_toolkit/special/sf_poly/sph_harm.html" title="Spherical Harmonics">Spherical Harmonics</a></p></td></tr></table></dd>
+<dt><span class="term">spherical_harmonic_r</span></dt>
+<dd><table class="simplelist" border="0" summary="Simple list"><tr><td><p><a class="link" href="../math_toolkit/special/sf_poly/sph_harm.html" title="Spherical Harmonics">Spherical Harmonics</a></p></td></tr></table></dd>
+<dt><span class="term">sph_bessel</span></dt>
+<dd><table class="simplelist" border="0" summary="Simple list">
+<tr><td><p><a class="link" href="../math_toolkit/special/bessel/bessel_over.html" title="Bessel Function Overview">Bessel Function Overview</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/main_overview/tr1.html" title="C99 and TR1 C Functions">C99 and TR1 C Functions</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/special/extern_c/tr1.html" title="C99 and TR1 C Functions Overview">C99 and TR1 C Functions Overview</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/main_overview/result_type.html" title="Calculation of the Type of the Result">Calculation of the Type of the Result</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/special/bessel/sph_bessel.html" title="Spherical Bessel Functions of the First and Second Kinds">Spherical Bessel Functions of the First and Second Kinds</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/special/extern_c/tr1_ref.html" title="TR1 C Functions Quick Reference">TR1 C Functions Quick Reference</a></p></td></tr>
+</table></dd>
+<dt><span class="term">sph_neumann</span></dt>
+<dd><table class="simplelist" border="0" summary="Simple list">
+<tr><td><p><a class="link" href="../math_toolkit/special/bessel/bessel_over.html" title="Bessel Function Overview">Bessel Function Overview</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/main_overview/tr1.html" title="C99 and TR1 C Functions">C99 and TR1 C Functions</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/special/extern_c/tr1.html" title="C99 and TR1 C Functions Overview">C99 and TR1 C Functions Overview</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/special/bessel/sph_bessel.html" title="Spherical Bessel Functions of the First and Second Kinds">Spherical Bessel Functions of the First and Second Kinds</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/special/extern_c/tr1_ref.html" title="TR1 C Functions Quick Reference">TR1 C Functions Quick Reference</a></p></td></tr>
+</table></dd>
+<dt><span class="term">sqrt1pm1</span></dt>
+<dd><table class="simplelist" border="0" summary="Simple list">
+<tr><td><p><a class="link" href="../math_toolkit/special/powers/sqrt1pm1.html" title="sqrt1pm1">expm1</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/special/powers/sqrt1pm1.html" title="sqrt1pm1">log1p</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/special/powers/sqrt1pm1.html" title="sqrt1pm1">RR</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/special/powers/sqrt1pm1.html" title="sqrt1pm1">sqrt1pm1</a></p></td></tr>
+</table></dd>
+<dt><span class="term">standard_deviation</span></dt>
+<dd><table class="simplelist" border="0" summary="Simple list">
+<tr><td><p><a class="link" href="../math_toolkit/dist/stat_tut/weg/binom_eg/binomial_coinflip_example.html" title="Binomial Coin-Flipping Example">Binomial Coin-Flipping Example</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/dist/stat_tut/weg/binom_eg/binomial_quiz_example.html" title="Binomial Quiz Example">Binomial Quiz Example</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/using_udt/dist_concept.html" title="Conceptual Requirements for Distribution Types">Conceptual Requirements for Distribution Types</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/dist/stat_tut/weg/find_eg/find_location_eg.html" title="Find Location (Mean) Example">Find Location (Mean) Example</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/dist/stat_tut/weg/find_eg/find_mean_and_sd_eg.html" title="Find mean and standard deviation example">Find mean and standard deviation example</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/dist/stat_tut/weg/find_eg/find_scale_eg.html" title="Find Scale (Standard Deviation) Example">Find Scale (Standard Deviation) Example</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/dist/dist_ref/nmp.html" title="Non-Member Properties">Non-Member Properties</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/dist/dist_ref/dists/normal_dist.html" title="Normal (Gaussian) Distribution">Normal (Gaussian) Distribution</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/dist/stat_tut/weg/normal_example/normal_misc.html" title="Some Miscellaneous Examples of the Normal (Gaussian) Distribution">Some Miscellaneous Examples of the Normal (Gaussian) Distribution</a></p></td></tr>
+</table></dd>
+<dt><span class="term">std_real_concept</span></dt>
+<dd><table class="simplelist" border="0" summary="Simple list"><tr><td><p><a class="link" href="../math_toolkit/using_udt/archetypes.html" title="Conceptual Archetypes and Testing">Conceptual Archetypes and Testing</a></p></td></tr></table></dd>
+<dt><span class="term">Students t Distribution</span></dt>
+<dd><table class="simplelist" border="0" summary="Simple list">
+<tr><td><p><a class="link" href="../math_toolkit/dist/dist_ref/dists/students_t_dist.html" title="Students t Distribution">beta</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/dist/dist_ref/dists/students_t_dist.html" title="Students t Distribution">cdf</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/dist/dist_ref/dists/students_t_dist.html" title="Students t Distribution">find_degrees_of_freedom</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/dist/dist_ref/dists/students_t_dist.html" title="Students t Distribution">ibeta</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/dist/dist_ref/dists/students_t_dist.html" title="Students t Distribution">ibetac</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/dist/dist_ref/dists/students_t_dist.html" title="Students t Distribution">ibeta_inv</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/dist/dist_ref/dists/students_t_dist.html" title="Students t Distribution">kurtosis</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/dist/dist_ref/dists/students_t_dist.html" title="Students t Distribution">kurtosis_excess</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/dist/dist_ref/dists/students_t_dist.html" title="Students t Distribution">mean</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/dist/dist_ref/dists/students_t_dist.html" title="Students t Distribution">median</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/dist/dist_ref/dists/students_t_dist.html" title="Students t Distribution">mode</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/dist/dist_ref/dists/students_t_dist.html" title="Students t Distribution">normal</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/dist/dist_ref/dists/students_t_dist.html" title="Students t Distribution">pdf</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/dist/dist_ref/dists/students_t_dist.html" title="Students t Distribution">policy_type</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/dist/dist_ref/dists/students_t_dist.html" title="Students t Distribution">quantile</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/dist/dist_ref/dists/students_t_dist.html" title="Students t Distribution">skewness</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/dist/dist_ref/dists/students_t_dist.html" title="Students t Distribution">students_t</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/dist/dist_ref/dists/students_t_dist.html" title="Students t Distribution">students_t_distribution</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/dist/dist_ref/dists/students_t_dist.html" title="Students t Distribution">value_type</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/dist/dist_ref/dists/students_t_dist.html" title="Students t Distribution">variance</a></p></td></tr>
+</table></dd>
+<dt><span class="term">students_t</span></dt>
+<dd><table class="simplelist" border="0" summary="Simple list">
+<tr><td><p><a class="link" href="../math_toolkit/dist/stat_tut/weg/st_eg/tut_mean_intervals.html" title="Calculating confidence intervals on the mean with the Students-t distribution">Calculating confidence intervals on the mean with the Students-t distribution</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/policy/pol_tutorial/changing_policy_defaults.html" title="Changing the Policy Defaults">Changing the Policy Defaults</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/dist/stat_tut/weg/st_eg/two_sample_students_t.html" title="Comparing the means of two samples with the Students-t test">Comparing the means of two samples with the Students-t test</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/dist/stat_tut/weg/error_eg.html" title="Error Handling Example">Error Handling Example</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/dist/stat_tut/weg/st_eg/tut_mean_size.html" title="Estimating how large a sample size would have to become in order to give a significant Students-t test result with a single sample test">Estimating how large a sample size would have to become in order to give a significant Students-t test result with a single sample test</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/main_overview/namespaces.html" title="Namespaces">Namespaces</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/dist/stat_tut/overview.html" title="Overview">Overview</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/dist/dist_ref/dists/students_t_dist.html" title="Students t Distribution">Students t Distribution</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/dist/stat_tut/weg/st_eg/tut_mean_test.html" title='Testing a sample mean for difference from a "true" mean'>Testing a sample mean for difference from a "true" mean</a></p></td></tr>
+</table></dd>
+<dt><span class="term">students_t_distribution</span></dt>
+<dd><table class="simplelist" border="0" summary="Simple list">
+<tr><td><p><a class="link" href="../math_toolkit/policy/pol_tutorial/changing_policy_defaults.html" title="Changing the Policy Defaults">Changing the Policy Defaults</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/dist/stat_tut/weg/error_eg.html" title="Error Handling Example">Error Handling Example</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/dist/stat_tut/weg/st_eg/tut_mean_size.html" title="Estimating how large a sample size would have to become in order to give a significant Students-t test result with a single sample test">Estimating how large a sample size would have to become in order to give a significant Students-t test result with a single sample test</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/main_overview/namespaces.html" title="Namespaces">Namespaces</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/dist/stat_tut/overview.html" title="Overview">Overview</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/dist/dist_ref/dists/students_t_dist.html" title="Students t Distribution">Students t Distribution</a></p></td></tr>
+</table></dd>
+<dt><span class="term">sum_series</span></dt>
+<dd><table class="simplelist" border="0" summary="Simple list"><tr><td><p><a class="link" href="../math_toolkit/toolkit/internals1/series_evaluation.html" title="Series Evaluation">Series Evaluation</a></p></td></tr></table></dd>
+<dt><span class="term">Supported/Tested Compilers</span></dt>
+<dd><table class="simplelist" border="0" summary="Simple list"><tr><td><p><a class="link" href="../math_toolkit/main_overview/compilers_overview.html" title="Compilers">BOOST_MATH_NO_LONG_DOUBLE_MATH_FUNCTIONS</a></p></td></tr></table></dd>
+</dl></div></dd>
+<dt>
+<a name="idx_id_73"></a><span class="term">T</span>
+</dt>
+<dd><div class="variablelist"><dl>
+<dt><span class="term">test_data</span></dt>
+<dd><table class="simplelist" border="0" summary="Simple list"><tr><td><p><a class="link" href="../math_toolkit/toolkit/internals2/test_data.html" title="Graphing, Profiling, and Generating Test Data for Special Functions">Graphing, Profiling, and Generating Test Data for Special Functions</a></p></td></tr></table></dd>
+<dt><span class="term">test_result</span></dt>
+<dd><table class="simplelist" border="0" summary="Simple list"><tr><td><p><a class="link" href="../math_toolkit/toolkit/internals2/error_test.html" title="Relative Error and Testing">Relative Error and Testing</a></p></td></tr></table></dd>
+<dt><span class="term">tgamma</span></dt>
+<dd><table class="simplelist" border="0" summary="Simple list">
+<tr><td><p><a class="link" href="../math_toolkit/main_overview/tr1.html" title="C99 and TR1 C Functions">C99 and TR1 C Functions</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/special/extern_c/tr1.html" title="C99 and TR1 C Functions Overview">C99 and TR1 C Functions Overview</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/special/extern_c/c99.html" title="C99 C Functions">C99 C Functions</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/policy/pol_tutorial/user_def_err_pol.html" title="Calling User Defined Error Handlers">Calling User Defined Error Handlers</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/policy/pol_tutorial/ad_hoc_sf_policies.html" title="Changing the Policy on an Ad Hoc Basis for the Special Functions">Changing the Policy on an Ad Hoc Basis for the Special Functions</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/perf/comparisons.html" title="Comparisons to Other Open Source Libraries">Comparisons to Other Open Source Libraries</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/main_overview/directories.html" title="Directory and File Structure">Directory and File Structure</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/main_overview/error_handling.html" title="Error Handling">Error Handling</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/policy/pol_ref/error_handling_policies.html" title="Error Handling Policies">Error Handling Policies</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/special/sf_gamma/igamma.html" title="Incomplete Gamma Functions">Errors In the Function tgamma(a,z)</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/special/factorials/sf_factorial.html" title="Factorial">Factorial</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/special/sf_gamma/tgamma.html" title="Gamma">Gamma</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/special/sf_gamma/igamma.html" title="Incomplete Gamma Functions">Incomplete Gamma Functions</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/policy/pol_ref/internal_promotion.html" title="Internal Promotion Policies">Internal Promotion Policies</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/status/issues.html" title="Known Issues, and Todo List">Known Issues, and Todo List</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/special/sf_gamma/lgamma.html" title="Log Gamma">Log Gamma</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/policy/pol_ref/precision_pol.html" title="Precision Policies">Precision Policies</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/toolkit/internals2/error_test.html" title="Relative Error and Testing">Relative Error and Testing</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/policy/pol_ref/namespace_pol.html" title="Setting Polices at Namespace Scope">Setting Polices at Namespace Scope</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/policy/pol_tutorial/namespace_policies.html" title="Setting Policies at Namespace or Translation Unit Scope">Setting Policies at Namespace or Translation Unit Scope</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/using_udt/use_mpfr.html" title="Using With MPFR / GMP - a High-Precision Floating-Point Library">Using With MPFR / GMP - a High-Precision Floating-Point Library</a></p></td></tr>
+</table></dd>
+<dt><span class="term">tgamma1pm1</span></dt>
+<dd><table class="simplelist" border="0" summary="Simple list">
+<tr><td><p><a class="link" href="../math_toolkit/special/sf_gamma/tgamma.html" title="Gamma">Gamma</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/special/sf_gamma/igamma.html" title="Incomplete Gamma Functions">Incomplete Gamma Functions</a></p></td></tr>
+</table></dd>
+<dt><span class="term">tgamma_delta_ratio</span></dt>
+<dd><table class="simplelist" border="0" summary="Simple list">
+<tr><td><p><a class="link" href="../math_toolkit/special/sf_gamma/gamma_ratios.html" title="Ratios of Gamma Functions">Errors In the Function tgamma_delta_ratio(a, delta)</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/special/factorials/sf_falling_factorial.html" title="Falling Factorial">Falling Factorial</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/special/sf_gamma/gamma_ratios.html" title="Ratios of Gamma Functions">Ratios of Gamma Functions</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/special/factorials/sf_rising_factorial.html" title="Rising Factorial">Rising Factorial</a></p></td></tr>
+</table></dd>
+<dt><span class="term">tgamma_lower</span></dt>
+<dd><table class="simplelist" border="0" summary="Simple list">
+<tr><td><p><a class="link" href="../math_toolkit/special/sf_gamma/igamma.html" title="Incomplete Gamma Functions">Errors In the Function tgamma_lower(a,z)</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/special/sf_gamma/igamma.html" title="Incomplete Gamma Functions">Incomplete Gamma Functions</a></p></td></tr>
+</table></dd>
+<dt><span class="term">tgamma_ratio</span></dt>
+<dd><table class="simplelist" border="0" summary="Simple list">
+<tr><td><p><a class="link" href="../math_toolkit/special/sf_gamma/gamma_ratios.html" title="Ratios of Gamma Functions">Errors In the Function tgamma_ratio(a, b)</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/special/sf_gamma/gamma_ratios.html" title="Ratios of Gamma Functions">Ratios of Gamma Functions</a></p></td></tr>
+</table></dd>
+<dt><span class="term">TR1 C Functions Quick Reference</span></dt>
+<dd><table class="simplelist" border="0" summary="Simple list">
+<tr><td><p><a class="link" href="../math_toolkit/special/extern_c/tr1_ref.html" title="TR1 C Functions Quick Reference">beta</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/special/extern_c/tr1_ref.html" title="TR1 C Functions Quick Reference">comp_ellint_2</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/special/extern_c/tr1_ref.html" title="TR1 C Functions Quick Reference">comp_ellint_3</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/special/extern_c/tr1_ref.html" title="TR1 C Functions Quick Reference">cyl_bessel_i</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/special/extern_c/tr1_ref.html" title="TR1 C Functions Quick Reference">cyl_bessel_j</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/special/extern_c/tr1_ref.html" title="TR1 C Functions Quick Reference">cyl_bessel_k</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/special/extern_c/tr1_ref.html" title="TR1 C Functions Quick Reference">cyl_neumann</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/special/extern_c/tr1_ref.html" title="TR1 C Functions Quick Reference">ellint_1</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/special/extern_c/tr1_ref.html" title="TR1 C Functions Quick Reference">ellint_2</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/special/extern_c/tr1_ref.html" title="TR1 C Functions Quick Reference">ellint_3</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/special/extern_c/tr1_ref.html" title="TR1 C Functions Quick Reference">expint</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/special/extern_c/tr1_ref.html" title="TR1 C Functions Quick Reference">exponential</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/special/extern_c/tr1_ref.html" title="TR1 C Functions Quick Reference">hermite</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/special/extern_c/tr1_ref.html" title="TR1 C Functions Quick Reference">laguerre</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/special/extern_c/tr1_ref.html" title="TR1 C Functions Quick Reference">legendre_p</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/special/extern_c/tr1_ref.html" title="TR1 C Functions Quick Reference">sph_bessel</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/special/extern_c/tr1_ref.html" title="TR1 C Functions Quick Reference">sph_neumann</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/special/extern_c/tr1_ref.html" title="TR1 C Functions Quick Reference">zeta</a></p></td></tr>
+</table></dd>
+<dt><span class="term">triangular</span></dt>
+<dd><table class="simplelist" border="0" summary="Simple list">
+<tr><td><p><a class="link" href="../math_toolkit/backgrounders/implementation.html" title="Additional Implementation Notes">Additional Implementation Notes</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/dist/dist_ref/dists/beta_dist.html" title="Beta Distribution">Beta Distribution</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/dist/dist_ref/dist_algorithms.html" title="Distribution Algorithms">Distribution Algorithms</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/dist/stat_tut/overview.html" title="Overview">Overview</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/dist/dist_ref/dists/triangular_dist.html" title="Triangular Distribution">Triangular Distribution</a></p></td></tr>
+</table></dd>
+<dt><span class="term">Triangular Distribution</span></dt>
+<dd><table class="simplelist" border="0" summary="Simple list">
+<tr><td><p><a class="link" href="../math_toolkit/dist/dist_ref/dists/triangular_dist.html" title="Triangular Distribution">beta</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/dist/dist_ref/dists/triangular_dist.html" title="Triangular Distribution">cdf</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/dist/dist_ref/dists/triangular_dist.html" title="Triangular Distribution">kurtosis</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/dist/dist_ref/dists/triangular_dist.html" title="Triangular Distribution">kurtosis_excess</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/dist/dist_ref/dists/triangular_dist.html" title="Triangular Distribution">mean</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/dist/dist_ref/dists/triangular_dist.html" title="Triangular Distribution">median</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/dist/dist_ref/dists/triangular_dist.html" title="Triangular Distribution">mode</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/dist/dist_ref/dists/triangular_dist.html" title="Triangular Distribution">normal</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/dist/dist_ref/dists/triangular_dist.html" title="Triangular Distribution">pdf</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/dist/dist_ref/dists/triangular_dist.html" title="Triangular Distribution">policy_type</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/dist/dist_ref/dists/triangular_dist.html" title="Triangular Distribution">quantile</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/dist/dist_ref/dists/triangular_dist.html" title="Triangular Distribution">skewness</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/dist/dist_ref/dists/triangular_dist.html" title="Triangular Distribution">triangular</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/dist/dist_ref/dists/triangular_dist.html" title="Triangular Distribution">triangular_distribution</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/dist/dist_ref/dists/triangular_dist.html" title="Triangular Distribution">uniform</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/dist/dist_ref/dists/triangular_dist.html" title="Triangular Distribution">value_type</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/dist/dist_ref/dists/triangular_dist.html" title="Triangular Distribution">variance</a></p></td></tr>
+</table></dd>
+<dt><span class="term">triangular_distribution</span></dt>
+<dd><table class="simplelist" border="0" summary="Simple list">
+<tr><td><p><a class="link" href="../math_toolkit/backgrounders/implementation.html" title="Additional Implementation Notes">Additional Implementation Notes</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/dist/dist_ref/dists/triangular_dist.html" title="Triangular Distribution">Triangular Distribution</a></p></td></tr>
+</table></dd>
+<dt><span class="term">trunc</span></dt>
+<dd><table class="simplelist" border="0" summary="Simple list">
+<tr><td><p><a class="link" href="../math_toolkit/main_overview/tr1.html" title="C99 and TR1 C Functions">C99 and TR1 C Functions</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/special/extern_c/tr1.html" title="C99 and TR1 C Functions Overview">C99 and TR1 C Functions Overview</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/special/extern_c/c99.html" title="C99 C Functions">C99 C Functions</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/using_udt/concepts.html" title="Conceptual Requirements for Real Number Types">Conceptual Requirements for Real Number Types</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/main_overview/error_handling.html" title="Error Handling">Error Handling</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/policy/pol_ref/error_handling_policies.html" title="Error Handling Policies">Error Handling Policies</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/special/rounding/trunc.html" title="Truncation Functions">Truncation Functions</a></p></td></tr>
+</table></dd>
+<dt><span class="term">Truncation Functions</span></dt>
+<dd><table class="simplelist" border="0" summary="Simple list">
+<tr><td><p><a class="link" href="../math_toolkit/special/rounding/trunc.html" title="Truncation Functions">itrunc</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/special/rounding/trunc.html" title="Truncation Functions">lltrunc</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/special/rounding/trunc.html" title="Truncation Functions">ltrunc</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/special/rounding/trunc.html" title="Truncation Functions">round</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/special/rounding/trunc.html" title="Truncation Functions">rounding_error</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/special/rounding/trunc.html" title="Truncation Functions">trunc</a></p></td></tr>
+</table></dd>
+</dl></div></dd>
+<dt>
+<a name="idx_id_74"></a><span class="term">U</span>
+</dt>
+<dd><div class="variablelist"><dl>
+<dt><span class="term">underflow_error_type</span></dt>
+<dd><table class="simplelist" border="0" summary="Simple list"><tr><td><p><a class="link" href="../math_toolkit/policy/pol_ref/pol_ref_ref.html" title="Policy Class Reference">Policy Class Reference</a></p></td></tr></table></dd>
+<dt><span class="term">Understanding Quantiles of Discrete Distributions</span></dt>
+<dd><table class="simplelist" border="0" summary="Simple list">
+<tr><td><p><a class="link" href="../math_toolkit/policy/pol_tutorial/understand_dis_quant.html" title="Understanding Quantiles of Discrete Distributions">binomial</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/policy/pol_tutorial/understand_dis_quant.html" title="Understanding Quantiles of Discrete Distributions">binomial_distribution</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/policy/pol_tutorial/understand_dis_quant.html" title="Understanding Quantiles of Discrete Distributions">cdf</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/policy/pol_tutorial/understand_dis_quant.html" title="Understanding Quantiles of Discrete Distributions">quantile</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/policy/pol_tutorial/understand_dis_quant.html" title="Understanding Quantiles of Discrete Distributions">round</a></p></td></tr>
+</table></dd>
+<dt><span class="term">uniform</span></dt>
+<dd><table class="simplelist" border="0" summary="Simple list">
+<tr><td><p><a class="link" href="../math_toolkit/backgrounders/implementation.html" title="Additional Implementation Notes">Additional Implementation Notes</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/dist/dist_ref/dists/beta_dist.html" title="Beta Distribution">Beta Distribution</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/toolkit/internals2/test_data.html" title="Graphing, Profiling, and Generating Test Data for Special Functions">Graphing, Profiling, and Generating Test Data for Special Functions</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/dist/stat_tut/overview.html" title="Overview">Overview</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/dist/dist_ref/dists/triangular_dist.html" title="Triangular Distribution">Triangular Distribution</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/dist/dist_ref/dists/uniform_dist.html" title="Uniform Distribution">Uniform Distribution</a></p></td></tr>
+</table></dd>
+<dt><span class="term">Uniform Distribution</span></dt>
+<dd><table class="simplelist" border="0" summary="Simple list">
+<tr><td><p><a class="link" href="../math_toolkit/dist/dist_ref/dists/uniform_dist.html" title="Uniform Distribution">cdf</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/dist/dist_ref/dists/uniform_dist.html" title="Uniform Distribution">kurtosis</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/dist/dist_ref/dists/uniform_dist.html" title="Uniform Distribution">kurtosis_excess</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/dist/dist_ref/dists/uniform_dist.html" title="Uniform Distribution">mean</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/dist/dist_ref/dists/uniform_dist.html" title="Uniform Distribution">median</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/dist/dist_ref/dists/uniform_dist.html" title="Uniform Distribution">mode</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/dist/dist_ref/dists/uniform_dist.html" title="Uniform Distribution">pdf</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/dist/dist_ref/dists/uniform_dist.html" title="Uniform Distribution">quantile</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/dist/dist_ref/dists/uniform_dist.html" title="Uniform Distribution">skewness</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/dist/dist_ref/dists/uniform_dist.html" title="Uniform Distribution">uniform</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/dist/dist_ref/dists/uniform_dist.html" title="Uniform Distribution">uniform_distribution</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/dist/dist_ref/dists/uniform_dist.html" title="Uniform Distribution">value_type</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/dist/dist_ref/dists/uniform_dist.html" title="Uniform Distribution">variance</a></p></td></tr>
+</table></dd>
+<dt><span class="term">uniform_distribution</span></dt>
+<dd><table class="simplelist" border="0" summary="Simple list"><tr><td><p><a class="link" href="../math_toolkit/dist/dist_ref/dists/uniform_dist.html" title="Uniform Distribution">Uniform Distribution</a></p></td></tr></table></dd>
+<dt><span class="term">upper_incomplete_gamma_fract</span></dt>
+<dd><table class="simplelist" border="0" summary="Simple list"><tr><td><p><a class="link" href="../math_toolkit/toolkit/internals2/test_data.html" title="Graphing, Profiling, and Generating Test Data for Special Functions">Graphing, Profiling, and Generating Test Data for Special Functions</a></p></td></tr></table></dd>
+<dt><span class="term">Using macros to Change the Policy Defaults</span></dt>
+<dd><table class="simplelist" border="0" summary="Simple list">
+<tr><td><p><a class="link" href="../math_toolkit/policy/pol_ref/policy_defaults.html" title="Using macros to Change the Policy Defaults">BOOST_MATH_ASSERT_UNDEFINED_POLICY</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/policy/pol_ref/policy_defaults.html" title="Using macros to Change the Policy Defaults">BOOST_MATH_DENORM_ERROR_POLICY</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/policy/pol_ref/policy_defaults.html" title="Using macros to Change the Policy Defaults">BOOST_MATH_DIGITS10_POLICY</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/policy/pol_ref/policy_defaults.html" title="Using macros to Change the Policy Defaults">BOOST_MATH_DISCRETE_QUANTILE_POLICY</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/policy/pol_ref/policy_defaults.html" title="Using macros to Change the Policy Defaults">BOOST_MATH_DOMAIN_ERROR_POLICY</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/policy/pol_ref/policy_defaults.html" title="Using macros to Change the Policy Defaults">BOOST_MATH_EVALUATION_ERROR_POLICY</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/policy/pol_ref/policy_defaults.html" title="Using macros to Change the Policy Defaults">BOOST_MATH_INDETERMINATE_RESULT_ERROR_POLICY</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/policy/pol_ref/policy_defaults.html" title="Using macros to Change the Policy Defaults">BOOST_MATH_MAX_ROOT_ITERATION_POLICY</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/policy/pol_ref/policy_defaults.html" title="Using macros to Change the Policy Defaults">BOOST_MATH_MAX_SERIES_ITERATION_POLICY</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/policy/pol_ref/policy_defaults.html" title="Using macros to Change the Policy Defaults">BOOST_MATH_OVERFLOW_ERROR_POLICY</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/policy/pol_ref/policy_defaults.html" title="Using macros to Change the Policy Defaults">BOOST_MATH_POLE_ERROR_POLICY</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/policy/pol_ref/policy_defaults.html" title="Using macros to Change the Policy Defaults">BOOST_MATH_PROMOTE_DOUBLE_POLICY</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/policy/pol_ref/policy_defaults.html" title="Using macros to Change the Policy Defaults">BOOST_MATH_PROMOTE_FLOAT_POLICY</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/policy/pol_ref/policy_defaults.html" title="Using macros to Change the Policy Defaults">BOOST_MATH_ROUNDING_ERROR_POLICY</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/policy/pol_ref/policy_defaults.html" title="Using macros to Change the Policy Defaults">BOOST_MATH_UNDERFLOW_ERROR_POLICY</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/policy/pol_ref/policy_defaults.html" title="Using macros to Change the Policy Defaults">evaluation_error</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/policy/pol_ref/policy_defaults.html" title="Using macros to Change the Policy Defaults">normal</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/policy/pol_ref/policy_defaults.html" title="Using macros to Change the Policy Defaults">normal_distribution</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/policy/pol_ref/policy_defaults.html" title="Using macros to Change the Policy Defaults">round</a></p></td></tr>
+</table></dd>
+<dt><span class="term">Using With MPFR / GMP - a High-Precision Floating-Point Library</span></dt>
+<dd><table class="simplelist" border="0" summary="Simple list">
+<tr><td><p><a class="link" href="../math_toolkit/using_udt/use_mpfr.html" title="Using With MPFR / GMP - a High-Precision Floating-Point Library">gamma</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/using_udt/use_mpfr.html" title="Using With MPFR / GMP - a High-Precision Floating-Point Library">Lanczos approximation</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/using_udt/use_mpfr.html" title="Using With MPFR / GMP - a High-Precision Floating-Point Library">tgamma</a></p></td></tr>
+</table></dd>
+<dt><span class="term">Using With NTL - a High-Precision Floating-Point Library</span></dt>
+<dd><table class="simplelist" border="0" summary="Simple list">
+<tr><td><p><a class="link" href="../math_toolkit/using_udt/use_ntl.html" title="Using With NTL - a High-Precision Floating-Point Library">Lanczos approximation</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/using_udt/use_ntl.html" title="Using With NTL - a High-Precision Floating-Point Library">RR</a></p></td></tr>
+</table></dd>
+</dl></div></dd>
+<dt>
+<a name="idx_id_75"></a><span class="term">V</span>
+</dt>
+<dd><div class="variablelist"><dl>
+<dt><span class="term">value_type</span></dt>
+<dd><table class="simplelist" border="0" summary="Simple list">
+<tr><td><p><a class="link" href="../math_toolkit/dist/dist_ref/dists/bernoulli_dist.html" title="Bernoulli Distribution">Bernoulli Distribution</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/dist/dist_ref/dists/beta_dist.html" title="Beta Distribution">Beta Distribution</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/dist/dist_ref/dists/binomial_dist.html" title="Binomial Distribution">Binomial Distribution</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/dist/dist_ref/dists/cauchy_dist.html" title="Cauchy-Lorentz Distribution">Cauchy-Lorentz Distribution</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/dist/dist_ref/dists/chi_squared_dist.html" title="Chi Squared Distribution">Chi Squared Distribution</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/using_udt/archetypes.html" title="Conceptual Archetypes and Testing">Conceptual Archetypes and Testing</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/using_udt/dist_concept.html" title="Conceptual Requirements for Distribution Types">Conceptual Requirements for Distribution Types</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/dist/dist_ref/dist_algorithms.html" title="Distribution Algorithms">Distribution Algorithms</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/dist/dist_ref/dists/exp_dist.html" title="Exponential Distribution">Exponential Distribution</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/dist/future.html" title="Extras/Future Directions">Extras/Future Directions</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/dist/dist_ref/dists/extreme_dist.html" title="Extreme Value Distribution">Extreme Value Distribution</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/dist/dist_ref/dists/f_dist.html" title="F Distribution">F Distribution</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/dist/dist_ref/dists/gamma_dist.html" title="Gamma (and Erlang) Distribution">Gamma (and Erlang) Distribution</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/toolkit/internals2/test_data.html" title="Graphing, Profiling, and Generating Test Data for Special Functions">Graphing, Profiling, and Generating Test Data for Special Functions</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/dist/dist_ref/dists/lognormal_dist.html" title="Log Normal Distribution">Log Normal Distribution</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/dist/dist_ref/dists/logistic_dist.html" title="Logistic Distribution">Logistic Distribution</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/dist/dist_ref/dists/negative_binomial_dist.html" title="Negative Binomial Distribution">Negative Binomial Distribution</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/dist/dist_ref/dists/nc_beta_dist.html" title="Noncentral Beta Distribution">Noncentral Beta Distribution</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/dist/dist_ref/dists/nc_chi_squared_dist.html" title="Noncentral Chi-Squared Distribution">Noncentral Chi-Squared Distribution</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/dist/dist_ref/dists/nc_f_dist.html" title="Noncentral F Distribution">Noncentral F Distribution</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/dist/dist_ref/dists/nc_t_dist.html" title="Noncentral T Distribution">Noncentral T Distribution</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/dist/dist_ref/dists/normal_dist.html" title="Normal (Gaussian) Distribution">Normal (Gaussian) Distribution</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/dist/dist_ref/dists/pareto.html" title="Pareto Distribution">Pareto Distribution</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/dist/dist_ref/dists/poisson_dist.html" title="Poisson Distribution">Poisson Distribution</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/toolkit/internals2/polynomials.html" title="Polynomials">Polynomials</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/dist/dist_ref/dists/rayleigh.html" title="Rayleigh Distribution">Rayleigh Distribution</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/toolkit/internals2/error_test.html" title="Relative Error and Testing">Relative Error and Testing</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/dist/dist_ref/dists/students_t_dist.html" title="Students t Distribution">Students t Distribution</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/dist/dist_ref/dists/triangular_dist.html" title="Triangular Distribution">Triangular Distribution</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/dist/dist_ref/dists/uniform_dist.html" title="Uniform Distribution">Uniform Distribution</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/dist/dist_ref/dists/weibull.html" title="Weibull Distribution">Weibull Distribution</a></p></td></tr>
+</table></dd>
+<dt><span class="term">variance</span></dt>
+<dd><table class="simplelist" border="0" summary="Simple list">
+<tr><td><p><a class="link" href="../math_toolkit/dist/dist_ref/dists/bernoulli_dist.html" title="Bernoulli Distribution">Bernoulli Distribution</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/dist/dist_ref/dists/beta_dist.html" title="Beta Distribution">Beta Distribution</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/dist/dist_ref/dists/binomial_dist.html" title="Binomial Distribution">Binomial Distribution</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/dist/dist_ref/dists/cauchy_dist.html" title="Cauchy-Lorentz Distribution">Cauchy-Lorentz Distribution</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/dist/dist_ref/dists/chi_squared_dist.html" title="Chi Squared Distribution">Chi Squared Distribution</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/dist/stat_tut/weg/st_eg/two_sample_students_t.html" title="Comparing the means of two samples with the Students-t test">Comparing the means of two samples with the Students-t test</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/using_udt/dist_concept.html" title="Conceptual Requirements for Distribution Types">Conceptual Requirements for Distribution Types</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/dist/stat_tut/weg/cs_eg/chi_sq_size.html" title="Estimating the Required Sample Sizes for a Chi-Square Test for the Standard Deviation">Estimating the Required Sample Sizes for a Chi-Square Test for the Standard Deviation</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/dist/dist_ref/dists/exp_dist.html" title="Exponential Distribution">Exponential Distribution</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/dist/dist_ref/dists/extreme_dist.html" title="Extreme Value Distribution">Extreme Value Distribution</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/dist/dist_ref/dists/f_dist.html" title="F Distribution">F Distribution</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/dist/dist_ref/dists/gamma_dist.html" title="Gamma (and Erlang) Distribution">Gamma (and Erlang) Distribution</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/dist/dist_ref/dists/lognormal_dist.html" title="Log Normal Distribution">Log Normal Distribution</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/dist/dist_ref/dists/logistic_dist.html" title="Logistic Distribution">Logistic Distribution</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/dist/dist_ref/dists/negative_binomial_dist.html" title="Negative Binomial Distribution">Negative Binomial Distribution</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/dist/dist_ref/nmp.html" title="Non-Member Properties">Non-Member Properties</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/dist/dist_ref/dists/nc_beta_dist.html" title="Noncentral Beta Distribution">Noncentral Beta Distribution</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/dist/dist_ref/dists/nc_chi_squared_dist.html" title="Noncentral Chi-Squared Distribution">Noncentral Chi-Squared Distribution</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/dist/dist_ref/dists/nc_f_dist.html" title="Noncentral F Distribution">Noncentral F Distribution</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/dist/dist_ref/dists/nc_t_dist.html" title="Noncentral T Distribution">Noncentral T Distribution</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/dist/dist_ref/dists/normal_dist.html" title="Normal (Gaussian) Distribution">Normal (Gaussian) Distribution</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/dist/dist_ref/dists/pareto.html" title="Pareto Distribution">Pareto Distribution</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/dist/dist_ref/dists/poisson_dist.html" title="Poisson Distribution">Poisson Distribution</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/dist/dist_ref/dists/rayleigh.html" title="Rayleigh Distribution">Rayleigh Distribution</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/toolkit/internals2/error_test.html" title="Relative Error and Testing">Relative Error and Testing</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/dist/dist_ref/dists/students_t_dist.html" title="Students t Distribution">Students t Distribution</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/dist/dist_ref/dists/triangular_dist.html" title="Triangular Distribution">Triangular Distribution</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/dist/dist_ref/dists/uniform_dist.html" title="Uniform Distribution">Uniform Distribution</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/dist/dist_ref/dists/weibull.html" title="Weibull Distribution">Weibull Distribution</a></p></td></tr>
+</table></dd>
+</dl></div></dd>
+<dt>
+<a name="idx_id_76"></a><span class="term">W</span>
+</dt>
+<dd><div class="variablelist"><dl>
+<dt><span class="term">weibull</span></dt>
+<dd><table class="simplelist" border="0" summary="Simple list">
+<tr><td><p><a class="link" href="../math_toolkit/dist/stat_tut/overview.html" title="Overview">Overview</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/dist/dist_ref/dists/weibull.html" title="Weibull Distribution">Weibull Distribution</a></p></td></tr>
+</table></dd>
+<dt><span class="term">Weibull Distribution</span></dt>
+<dd><table class="simplelist" border="0" summary="Simple list">
+<tr><td><p><a class="link" href="../math_toolkit/dist/dist_ref/dists/weibull.html" title="Weibull Distribution">beta</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/dist/dist_ref/dists/weibull.html" title="Weibull Distribution">cdf</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/dist/dist_ref/dists/weibull.html" title="Weibull Distribution">expm1</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/dist/dist_ref/dists/weibull.html" title="Weibull Distribution">exponential</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/dist/dist_ref/dists/weibull.html" title="Weibull Distribution">kurtosis</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/dist/dist_ref/dists/weibull.html" title="Weibull Distribution">kurtosis_excess</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/dist/dist_ref/dists/weibull.html" title="Weibull Distribution">log1p</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/dist/dist_ref/dists/weibull.html" title="Weibull Distribution">mean</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/dist/dist_ref/dists/weibull.html" title="Weibull Distribution">median</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/dist/dist_ref/dists/weibull.html" title="Weibull Distribution">mode</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/dist/dist_ref/dists/weibull.html" title="Weibull Distribution">normal</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/dist/dist_ref/dists/weibull.html" title="Weibull Distribution">pdf</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/dist/dist_ref/dists/weibull.html" title="Weibull Distribution">policy_type</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/dist/dist_ref/dists/weibull.html" title="Weibull Distribution">quantile</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/dist/dist_ref/dists/weibull.html" title="Weibull Distribution">skewness</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/dist/dist_ref/dists/weibull.html" title="Weibull Distribution">value_type</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/dist/dist_ref/dists/weibull.html" title="Weibull Distribution">variance</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/dist/dist_ref/dists/weibull.html" title="Weibull Distribution">weibull</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/dist/dist_ref/dists/weibull.html" title="Weibull Distribution">weibull_distribution</a></p></td></tr>
+</table></dd>
+<dt><span class="term">weibull_distribution</span></dt>
+<dd><table class="simplelist" border="0" summary="Simple list"><tr><td><p><a class="link" href="../math_toolkit/dist/dist_ref/dists/weibull.html" title="Weibull Distribution">Weibull Distribution</a></p></td></tr></table></dd>
+</dl></div></dd>
+<dt>
+<a name="idx_id_77"></a><span class="term">Z</span>
+</dt>
+<dd><div class="variablelist"><dl>
+<dt><span class="term">zeta</span></dt>
+<dd><table class="simplelist" border="0" summary="Simple list">
+<tr><td><p><a class="link" href="../math_toolkit/main_overview/tr1.html" title="C99 and TR1 C Functions">C99 and TR1 C Functions</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/special/extern_c/tr1.html" title="C99 and TR1 C Functions Overview">C99 and TR1 C Functions Overview</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/special/zetas/zeta.html" title="Riemann Zeta Function">Errors In the Function zeta(z)</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/special/expint/expint_i.html" title="Exponential Integral Ei">Exponential Integral Ei</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/dist/dist_ref/dists/extreme_dist.html" title="Extreme Value Distribution">Extreme Value Distribution</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/special/zetas/zeta.html" title="Riemann Zeta Function">Riemann Zeta Function</a></p></td></tr>
+<tr><td><p><a class="link" href="../math_toolkit/special/extern_c/tr1_ref.html" title="TR1 C Functions Quick Reference">TR1 C Functions Quick Reference</a></p></td></tr>
+</table></dd>
+</dl></div></dd>
+</dl></div>
+</div>
+<table xmlns:rev="http://www.cs.rpi.edu/~gregod/boost/tools/doc/revision" width="100%"><tr>
+<td align="left"></td>
+<td align="right"><div class="copyright-footer">Copyright © 2006 , 2007, 2008 John Maddock, Paul A. Bristow, Hubert
+      Holin, Xiaogang Zhang, Bruno Lalande and Gautam Sewani<p>
+        Distributed under the Boost Software License, Version 1.0. (See accompanying
+        file LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_0.txt)
+      </p>
+</div></td>
+</tr></table>
+<hr>
+<div class="spirit-nav">
+<a accesskey="p" href="s13.html"><img src="../../../doc/html/images/prev.png" alt="Prev"></a><a accesskey="u" href="../index.html"><img src="../../../doc/html/images/up.png" alt="Up"></a><a accesskey="h" href="../index.html"><img src="../../../doc/html/images/home.png" alt="Home"></a>
+</div>
+</body>
+</html>

Added: sandbox/tools/auto_index/example/math/doc/sf_and_dist/html/math_toolkit/backgrounders.html
==============================================================================
--- (empty file)
+++ sandbox/tools/auto_index/example/math/doc/sf_and_dist/html/math_toolkit/backgrounders.html	2008-11-28 05:25:28 EST (Fri, 28 Nov 2008)
@@ -0,0 +1,53 @@
+<html>
+<head>
+<meta http-equiv="Content-Type" content="text/html; charset=ISO-8859-1">
+<title>Backgrounders</title>
+<link rel="stylesheet" href="../boostbook.css" type="text/css">
+<meta name="generator" content="DocBook XSL Stylesheets Vsnapshot_8125">
+<link rel="home" href="../index.html" title="Math Toolkit">
+<link rel="up" href="../index.html" title="Math Toolkit">
+<link rel="prev" href="perf/perf_test_app.html" title="The Performance Test Application">
+<link rel="next" href="backgrounders/implementation.html" title="Additional Implementation Notes">
+</head>
+<body bgcolor="white" text="black" link="#0000FF" vlink="#840084" alink="#0000FF">
+<table cellpadding="2" width="100%"><tr>
+<td valign="top"><img alt="Boost C++ Libraries" width="277" height="86" src="../../../boost.png"></td>
+<td align="center">Home</td>
+<td align="center">Libraries</td>
+<td align="center">People</td>
+<td align="center">FAQ</td>
+<td align="center">More</td>
+</tr></table>
+<hr>
+<div class="spirit-nav">
+<a accesskey="p" href="perf/perf_test_app.html"><img src="../../../doc/html/images/prev.png" alt="Prev"></a><a accesskey="u" href="../index.html"><img src="../../../doc/html/images/up.png" alt="Up"></a><a accesskey="h" href="../index.html"><img src="../../../doc/html/images/home.png" alt="Home"></a><a accesskey="n" href="backgrounders/implementation.html"><img src="../../../doc/html/images/next.png" alt="Next"></a>
+</div>
+<div class="section" lang="en">
+<div class="titlepage"><div><div><h2 class="title" style="clear: both">
+<a name="math_toolkit.backgrounders"></a><a class="link" href="backgrounders.html" title="Backgrounders"> Backgrounders</a>
+</h2></div></div></div>
+<div class="toc"><dl>
+<dt><span class="section"><a href="backgrounders/implementation.html"> Additional
+      Implementation Notes</a></span></dt>
+<dt><span class="section"><a href="backgrounders/relative_error.html"> Relative
+      Error</a></span></dt>
+<dt><span class="section"> The Lanczos Approximation</span></dt>
+<dt><span class="section"> The Remez Method</span></dt>
+<dt><span class="section"> References</span></dt>
+</dl></div>
+</div>
+<table xmlns:rev="http://www.cs.rpi.edu/~gregod/boost/tools/doc/revision" width="100%"><tr>
+<td align="left"></td>
+<td align="right"><div class="copyright-footer">Copyright © 2006 , 2007, 2008 John Maddock, Paul A. Bristow, Hubert
+      Holin, Xiaogang Zhang, Bruno Lalande and Gautam Sewani<p>
+        Distributed under the Boost Software License, Version 1.0. (See accompanying
+        file LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_0.txt)
+      </p>
+</div></td>
+</tr></table>
+<hr>
+<div class="spirit-nav">
+<a accesskey="p" href="perf/perf_test_app.html"><img src="../../../doc/html/images/prev.png" alt="Prev"></a><a accesskey="u" href="../index.html"><img src="../../../doc/html/images/up.png" alt="Up"></a><a accesskey="h" href="../index.html"><img src="../../../doc/html/images/home.png" alt="Home"></a><a accesskey="n" href="backgrounders/implementation.html"><img src="../../../doc/html/images/next.png" alt="Next"></a>
+</div>
+</body>
+</html>

Added: sandbox/tools/auto_index/example/math/doc/sf_and_dist/html/math_toolkit/backgrounders/implementation.html
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+++ sandbox/tools/auto_index/example/math/doc/sf_and_dist/html/math_toolkit/backgrounders/implementation.html	2008-11-28 05:25:28 EST (Fri, 28 Nov 2008)
@@ -0,0 +1,758 @@
+<html>
+<head>
+<meta http-equiv="Content-Type" content="text/html; charset=ISO-8859-1">
+<title>Additional Implementation Notes</title>
+<link rel="stylesheet" href="../../boostbook.css" type="text/css">
+<meta name="generator" content="DocBook XSL Stylesheets Vsnapshot_8125">
+<link rel="home" href="../../index.html" title="Math Toolkit">
+<link rel="up" href="../backgrounders.html" title="Backgrounders">
+<link rel="prev" href="../backgrounders.html" title="Backgrounders">
+<link rel="next" href="relative_error.html" title="Relative Error">
+</head>
+<body bgcolor="white" text="black" link="#0000FF" vlink="#840084" alink="#0000FF">
+<table cellpadding="2" width="100%"><tr>
+<td valign="top"><img alt="Boost C++ Libraries" width="277" height="86" src="../../../../boost.png"></td>
+<td align="center">Home</td>
+<td align="center">Libraries</td>
+<td align="center">People</td>
+<td align="center">FAQ</td>
+<td align="center">More</td>
+</tr></table>
+<hr>
+<div class="spirit-nav">
+<a accesskey="p" href="../backgrounders.html"><img src="../../../../doc/html/images/prev.png" alt="Prev"></a><a accesskey="u" href="../backgrounders.html"><img src="../../../../doc/html/images/up.png" alt="Up"></a><a accesskey="h" href="../../index.html"><img src="../../../../doc/html/images/home.png" alt="Home"></a><a accesskey="n" href="relative_error.html"><img src="../../../../doc/html/images/next.png" alt="Next"></a>
+</div>
+<div class="section" lang="en">
+<div class="titlepage"><div><div><h3 class="title">
+<a name="math_toolkit.backgrounders.implementation"></a><a class="link" href="implementation.html" title="Additional Implementation Notes"> Additional
+      Implementation Notes</a>
+</h3></div></div></div>
+<p>
+        The majority of the implementation notes are included with the documentation
+        of each function or distribution. The notes here are of a more general nature,
+        and reflect more the general implementation philosophy used.
+      </p>
+<a name="math_toolkit.backgrounders.implementation.implemention_philosophy"></a><h5>
+<a name="id912054"></a>
+        <a class="link" href="implementation.html#math_toolkit.backgrounders.implementation.implemention_philosophy">Implemention
+        philosophy</a>
+      </h5>
+<p>
+        "First be right, then be fast."
+      </p>
+<p>
+        There will always be potential compromises to be made between speed and accuracy.
+        It may be possible to find faster methods, particularly for certain limited
+        ranges of arguments, but for most applications of math functions and distributions,
+        we judge that speed is rarely as important as accuracy.
+      </p>
+<p>
+        So our priority is accuracy.
+      </p>
+<p>
+        To permit evaluation of accuracy of the special functions, production of
+        extremely accurate tables of test values has received considerable effort.
+      </p>
+<p>
+        (It also required much CPU effort - there was some danger of molten plastic
+        dripping from the bottom of JM's laptop, so instead, PAB's Dual-core desktop
+        was kept 50% busy for <span class="bold"><strong>days</strong></span> calculating some
+        tables of test values!)
+      </p>
+<p>
+        For a specific RealType, say float or double, it may be possible to find
+        approximations for some functions that are simpler and thus faster, but less
+        accurate (perhaps because there are no refining iterations, for example,
+        when calculating inverse functions).
+      </p>
+<p>
+        If these prove accurate enough to be "fit for his purpose", then
+        a user may substitute his custom specialization.
+      </p>
+<p>
+        For example, there are approximations dating back from times when computation
+        was a <span class="bold"><strong>lot</strong></span> more expensive:
+      </p>
+<p>
+        H Goldberg and H Levine, Approximate formulas for percentage points and normalisation
+        of t and chi squared, Ann. Math. Stat., 17(4), 216 - 225 (Dec 1946).
+      </p>
+<p>
+        A H Carter, Approximations to percentage points of the z-distribution, Biometrika
+        34(2), 352 - 358 (Dec 1947).
+      </p>
+<p>
+        These could still provide sufficient accuracy for some speed-critical applications.
+      </p>
+<a name="math_toolkit.backgrounders.implementation.accuracy_and_representation_of_test_values"></a><h5>
+<a name="id912184"></a>
+        <a class="link" href="implementation.html#math_toolkit.backgrounders.implementation.accuracy_and_representation_of_test_values">Accuracy
+        and Representation of Test Values</a>
+      </h5>
+<p>
+        In order to be accurate enough for as many as possible real types, constant
+        values are given to 50 decimal digits if available (though many sources proved
+        only accurate near to 64-bit double precision). Values are specified as long
+        double types by appending L, unless they are exactly representable, for example
+        integers, or binary fractions like 0.125. This avoids the risk of loss of
+        accuracy converting from double, the default type. Values are used after
+        static_cast&lt;RealType&gt;(1.2345L) to provide the appropriate RealType
+        for spot tests.
+      </p>
+<p>
+        Functions that return constants values, like kurtosis for example, are written
+        as
+      </p>
+<p>
+        <code class="computeroutput"><span class="keyword">static_cast</span><span class="special">&lt;</span><span class="identifier">RealType</span><span class="special">&gt;(-</span><span class="number">3</span><span class="special">)</span> <span class="special">/</span>
+        <span class="number">5</span><span class="special">;</span></code>
+      </p>
+<p>
+        to provide the most accurate value that the compiler can compute for the
+        real type. (The denominator is an integer and so will be promoted exactly).
+      </p>
+<p>
+        So tests for one third, <span class="bold"><strong>not</strong></span> exactly representable
+        with radix two floating-point, (should) use, for example:
+      </p>
+<p>
+        <code class="computeroutput"><span class="keyword">static_cast</span><span class="special">&lt;</span><span class="identifier">RealType</span><span class="special">&gt;(</span><span class="number">1</span><span class="special">)</span> <span class="special">/</span>
+        <span class="number">3</span><span class="special">;</span></code>
+      </p>
+<p>
+        If a function is very sensitive to changes in input, specifying an inexact
+        value as input (such as 0.1) can throw the result off by a noticeable amount:
+        0.1f is "wrong" by ~1e-7 for example (because 0.1 has no exact
+        binary representation). That is why exact binary values - halves, quarters,
+        and eighths etc - are used in test code along with the occasional fraction
+        <code class="computeroutput"><span class="identifier">a</span><span class="special">/</span><span class="identifier">b</span></code> with <code class="computeroutput"><span class="identifier">b</span></code>
+        a power of two (in order to ensure that the result is an exactly representable
+        binary value).
+      </p>
+<a name="math_toolkit.backgrounders.implementation.tolerance_of_tests"></a><h5>
+<a name="id912427"></a>
+        <a class="link" href="implementation.html#math_toolkit.backgrounders.implementation.tolerance_of_tests">Tolerance
+        of Tests</a>
+      </h5>
+<p>
+        The tolerances need to be set to the maximum of:
+      </p>
+<div class="itemizedlist"><ul type="disc">
+<li>
+          Some epsilon value.
+        </li>
+<li>
+          The accuracy of the data (often only near 64-bit double).
+        </li>
+</ul></div>
+<p>
+        Otherwise when long double has more digits than the test data, then no amount
+        of tweaking an epsilon based tolerance will work.
+      </p>
+<p>
+        A common problem is when tolerances that are suitable for implementations
+        like Microsoft VS.NET where double and long double are the same size: tests
+        fail on other systems where long double is more accurate than double. Check
+        first that the suffix L is present, and then that the tolerance is big enough.
+      </p>
+<a name="math_toolkit.backgrounders.implementation.handling_unsuitable_arguments"></a><h5>
+<a name="id912500"></a>
+        <a class="link" href="implementation.html#math_toolkit.backgrounders.implementation.handling_unsuitable_arguments">Handling
+        Unsuitable Arguments</a>
+      </h5>
+<p>
+        In <a href="http://www.open-std.org/jtc1/sc22/wg21/docs/papers/2004/n1665.pdf" target="_top">Errors
+        in Mathematical Special Functions</a>, J. Marraffino &amp; M. Paterno
+        it is proposed that signalling a domain error is mandatory when the argument
+        would give an mathematically undefined result.
+      </p>
+<div class="itemizedlist"><ul type="disc"><li>
+          Guideline 1
+        </li></ul></div>
+<div class="blockquote"><blockquote class="blockquote">
+<p>
+          </p>
+<p>
+            A mathematical function is said to be defined at a point a = (a1, a2,
+            . . .) if the limits as x = (x1, x2, . . .) 'approaches a from all directions
+            agree'. The defined value may be any number, or +infinity, or -infinity.
+          </p>
+<p>
+        </p>
+</blockquote></div>
+<p>
+        Put crudely, if the function goes to + infinity and then emerges 'round-the-back'
+        with - infinity, it is NOT defined.
+      </p>
+<div class="blockquote"><blockquote class="blockquote">
+<p>
+          </p>
+<p>
+            The library function which approximates a mathematical function shall
+            signal a domain error whenever evaluated with argument values for which
+            the mathematical function is undefined.
+          </p>
+<p>
+        </p>
+</blockquote></div>
+<div class="itemizedlist"><ul type="disc"><li>
+          Guideline 2
+        </li></ul></div>
+<div class="blockquote"><blockquote class="blockquote">
+<p>
+          </p>
+<p>
+            The library function which approximates a mathematical function shall
+            signal a domain error whenever evaluated with argument values for which
+            the mathematical function obtains a non-real value.
+          </p>
+<p>
+        </p>
+</blockquote></div>
+<p>
+        This implementation is believed to follow these proposals and to assist compatibility
+        with <span class="emphasis"><em>ISO/IEC 9899:1999 Programming languages - C</em></span> and
+        with the <a href="http://www.open-std.org/jtc1/sc22/wg21/docs/papers/2005/n1836.pdf" target="_top">Draft
+        Technical Report on C++ Library Extensions, 2005-06-24, section 5.2.1, paragraph
+        5</a>. <a class="link" href="../main_overview/error_handling.html" title="Error Handling">See
+        also domain_error</a>.
+      </p>
+<p>
+        See <a class="link" href="../policy/pol_ref.html" title="Policy Reference">policy reference</a> for
+        details of the error handling policies that should allow a user to comply
+        with any of these recommendations, as well as other behaviour.
+      </p>
+<p>
+        See <a class="link" href="../main_overview/error_handling.html" title="Error Handling">error handling</a>
+        for a detailed explanation of the mechanism, and <a class="link" href="../dist/stat_tut/weg/error_eg.html" title="Error Handling Example">error_handling
+        example</a> and error_handling_example.cpp
+      </p>
+<div class="caution"><table border="0" summary="Caution">
+<tr>
+<td rowspan="2" align="center" valign="top" width="25"><img alt="[Caution]" src="../../../../doc/html/images/caution.png"></td>
+<th align="left">Caution</th>
+</tr>
+<tr><td align="left" valign="top"><p>
+          If you enable throw but do NOT have try &amp; catch block, then the program
+          will terminate with an uncaught exception and probably abort. Therefore
+          to get the benefit of helpful error messages, enabling <span class="bold"><strong>all</strong></span>
+          exceptions <span class="bold"><strong>and</strong></span> using try&amp;catch is
+          recommended for all applications. However, for simplicity, this is not
+          done for most examples.
+        </p></td></tr>
+</table></div>
+<a name="math_toolkit.backgrounders.implementation.handling_of_functions_that_are_not_mathematically_defined"></a><h5>
+<a name="id912732"></a>
+        <a class="link" href="implementation.html#math_toolkit.backgrounders.implementation.handling_of_functions_that_are_not_mathematically_defined">Handling
+        of Functions that are Not Mathematically defined</a>
+      </h5>
+<p>
+        Functions that are not mathematically defined, like the Cauchy mean, fail
+        to compile by default. <a class="link" href="../policy/pol_ref/assert_undefined.html" title="Mathematically Undefined Function Policies">A
+        policy</a> allows control of this.
+      </p>
+<p>
+        If the policy is to permit undefined functions, then calling them throws
+        a domain error, by default. But the error policy can be set to not throw,
+        and to return NaN instead. For example,
+      </p>
+<p>
+        <code class="computeroutput"><span class="preprocessor">#define</span> <span class="identifier">BOOST_MATH_DOMAIN_ERROR_POLICY</span>
+        <span class="identifier">ignore_error</span></code>
+      </p>
+<p>
+        appears before the first Boost include, then if the un-implemented function
+        is called, mean(cauchy&lt;&gt;()) will return std::numeric_limits&lt;T&gt;::quiet_NaN().
+      </p>
+<div class="warning"><table border="0" summary="Warning">
+<tr>
+<td rowspan="2" align="center" valign="top" width="25"><img alt="[Warning]" src="../../../../doc/html/images/warning.png"></td>
+<th align="left">Warning</th>
+</tr>
+<tr><td align="left" valign="top"><p>
+          If <code class="computeroutput"><span class="identifier">std</span><span class="special">::</span><span class="identifier">numeric_limits</span><span class="special">&lt;</span><span class="identifier">T</span><span class="special">&gt;::</span><span class="identifier">has_quiet_NaN</span></code> is false (for example T
+          is a User-defined type), then an exception will always be thrown when a
+          domain error occurs. Catching exceptions is therefore strongly recommended.
+        </p></td></tr>
+</table></div>
+<a name="math_toolkit.backgrounders.implementation.median_of_distributions"></a><h5>
+<a name="id912878"></a>
+        <a class="link" href="implementation.html#math_toolkit.backgrounders.implementation.median_of_distributions">Median
+        of distributions</a>
+      </h5>
+<p>
+        There are many distributions for which we have been unable to find an analytic
+        formula, and this has deterred us from implementing <a href="http://en.wikipedia.org/wiki/Median" target="_top">median
+        functions</a>, the mid-point in a list of values.
+      </p>
+<p>
+        However a useful median approximation for distribution <code class="computeroutput"><span class="identifier">dist</span></code>
+        may be available from
+      </p>
+<p>
+        <code class="computeroutput"><span class="identifier">quantile</span><span class="special">(</span><span class="identifier">dist</span><span class="special">,</span> <span class="number">0.5</span><span class="special">)</span></code>.
+      </p>
+<p>
+        <a href="http://www.amstat.org/publications/jse/v13n2/vonhippel.html" target="_top">Mean,
+        Median, and Skew, Paul T von Hippel</a>
+      </p>
+<p>
+        <a href="http://documents.wolfram.co.jp/teachersedition/MathematicaBook/24.5.html" target="_top">Descriptive
+        Statistics,</a>
+      </p>
+<p>
+        <a href="http://documents.wolfram.co.jp/v5/Add-onsLinks/StandardPackages/Statistics/DescriptiveStatistics.html" target="_top">and
+        </a>
+      </p>
+<p>
+        <a href="http://documents.wolfram.com/v5/TheMathematicaBook/AdvancedMathematicsInMathematica/NumericalOperationsOnData/3.8.1.html" target="_top">Mathematica
+        Basic Statistics.</a> give more detail, in particular for discrete distributions.
+      </p>
+<a name="math_toolkit.backgrounders.implementation.handling_of_floating_point_infinity"></a><h5>
+<a name="id913031"></a>
+        <a class="link" href="implementation.html#math_toolkit.backgrounders.implementation.handling_of_floating_point_infinity">Handling
+        of Floating-Point Infinity</a>
+      </h5>
+<p>
+        Some functions and distributions are well defined with + or - infinity as
+        argument(s), but after some experiments with handling infinite arguments
+        as special cases, we concluded that it was generally more useful to forbid
+        this, and instead to return the result of <a class="link" href="../main_overview/error_handling.html#domain_error">domain_error</a>.
+      </p>
+<p>
+        Handling infinity as special cases is additionally complicated because, unlike
+        built-in types on most - but not all - platforms, not all User-Defined Types
+        are specialized to provide <code class="computeroutput"><span class="identifier">std</span><span class="special">::</span><span class="identifier">numeric_limits</span><span class="special">&lt;</span><span class="identifier">RealType</span><span class="special">&gt;::</span><span class="identifier">infinity</span><span class="special">()</span></code> and would return zero rather than any representation
+        of infinity.
+      </p>
+<p>
+        The rationale is that non-finiteness may happen because of error or overflow
+        in the users code, and it will be more helpful for this to be diagnosed promptly
+        rather than just continuing. The code also became much more complicated,
+        more error-prone, much more work to test, and much less readable.
+      </p>
+<p>
+        However in a few cases, for example normal, where we felt it obvious, we
+        have permitted argument(s) to be infinity, provided infinity is implemented
+        for the realType on that implementation.
+      </p>
+<p>
+        Users who require special handling of infinity (or other specific value)
+        can, of course, always intercept this before calling a distribution or function
+        and return their own choice of value, or other behavior. This will often
+        be simpler than trying to handle the aftermath of the error policy.
+      </p>
+<p>
+        Overflow, underflow, denorm can be handled using <a class="link" href="../policy/pol_ref/error_handling_policies.html" title="Error Handling Policies">error
+        handling policies</a>.
+      </p>
+<p>
+        We have also tried to catch boundary cases where the mathematical specification
+        would result in divide by zero or overflow and signalling these similarly.
+        What happens at (and near), poles can be controlled through <a class="link" href="../policy/pol_ref/error_handling_policies.html" title="Error Handling Policies">error
+        handling policies</a>.
+      </p>
+<a name="math_toolkit.backgrounders.implementation.scale__shape_and_location"></a><h5>
+<a name="id913199"></a>
+        <a class="link" href="implementation.html#math_toolkit.backgrounders.implementation.scale__shape_and_location">Scale,
+        Shape and Location</a>
+      </h5>
+<p>
+        We considered adding location and scale to the list of functions, for example:
+      </p>
+<pre class="programlisting"><span class="keyword">template</span> <span class="special">&lt;</span><span class="keyword">class</span> <span class="identifier">RealType</span><span class="special">&gt;</span>
+<span class="keyword">inline</span> <span class="identifier">RealType</span> <span class="identifier">scale</span><span class="special">(</span><span class="keyword">const</span> <span class="identifier">triangular_distribution</span><span class="special">&lt;</span><span class="identifier">RealType</span><span class="special">&gt;&amp;</span> <span class="identifier">dist</span><span class="special">)</span>
+<span class="special">{</span>
+  <span class="identifier">RealType</span> <span class="identifier">lower</span> <span class="special">=</span> <span class="identifier">dist</span><span class="special">.</span><span class="identifier">lower</span><span class="special">();</span>
+  <span class="identifier">RealType</span> <span class="identifier">mode</span> <span class="special">=</span> <span class="identifier">dist</span><span class="special">.</span><span class="identifier">mode</span><span class="special">();</span>
+  <span class="identifier">RealType</span> <span class="identifier">upper</span> <span class="special">=</span> <span class="identifier">dist</span><span class="special">.</span><span class="identifier">upper</span><span class="special">();</span>
+  <span class="identifier">RealType</span> <span class="identifier">result</span><span class="special">;</span>  <span class="comment">// of checks.
+</span>  <span class="keyword">if</span><span class="special">(</span><span class="keyword">false</span> <span class="special">==</span> <span class="identifier">detail</span><span class="special">::</span><span class="identifier">check_triangular</span><span class="special">(</span><span class="identifier">BOOST_CURRENT_FUNCTION</span><span class="special">,</span> <span class="identifier">lower</span><span class="special">,</span> <span class="identifier">mode</span><span class="special">,</span> <span class="identifier">upper</span><span class="special">,</span> <span class="special">&amp;</span><span class="identifier">result</span><span class="special">))</span>
+  <span class="special">{</span>
+    <span class="keyword">return</span> <span class="identifier">result</span><span class="special">;</span>
+  <span class="special">}</span>
+  <span class="keyword">return</span> <span class="special">(</span><span class="identifier">upper</span> <span class="special">-</span> <span class="identifier">lower</span><span class="special">);</span>
+<span class="special">}</span>
+</pre>
+<p>
+        but found that these concepts are not defined (or their definition too contentious)
+        for too many distributions to be generally applicable. Because they are non-member
+        functions, they can be added if required.
+      </p>
+<a name="math_toolkit.backgrounders.implementation.notes_on_implementation_of_specific_functions__amp__distributions"></a><h5>
+<a name="id913669"></a>
+        <a class="link" href="implementation.html#math_toolkit.backgrounders.implementation.notes_on_implementation_of_specific_functions__amp__distributions">Notes
+        on Implementation of Specific Functions &amp; Distributions</a>
+      </h5>
+<div class="itemizedlist"><ul type="disc"><li>
+          Default parameters for the Triangular Distribution. We are uncertain about
+          the best default parameters. Some sources suggest that the Standard Triangular
+          Distribution has lower = 0, mode = half and upper = 1. However as a approximation
+          for the normal distribution, the most common usage, lower = -1, mode =
+          0 and upper = 1 would be more suitable.
+        </li></ul></div>
+<a name="math_toolkit.backgrounders.implementation.rational_approximations_used"></a><h5>
+<a name="id913718"></a>
+        <a class="link" href="implementation.html#math_toolkit.backgrounders.implementation.rational_approximations_used">Rational
+        Approximations Used</a>
+      </h5>
+<p>
+        Some of the special functions in this library are implemented via rational
+        approximations. These are either taken from the literature, or devised by
+        John Maddock using <a class="link" href="../toolkit/internals2/minimax.html" title="Minimax Approximations and the Remez Algorithm">our
+        Remez code</a>.
+      </p>
+<p>
+        Rational rather than Polynomial approximations are used to ensure accuracy:
+        polynomial approximations are often wonderful up to a certain level of accuracy,
+        but then quite often fail to provide much greater accuracy no matter how
+        many more terms are added.
+      </p>
+<p>
+        Our own approximations were devised either for added accuracy (to support
+        128-bit long doubles for example), or because literature methods were unavailable
+        or under non-BSL compatible license. Our Remez code is known to produce good
+        agreement with literature results in fairly simple "toy" cases.
+        All approximations were checked for convergence and to ensure that they were
+        not ill-conditioned (the coefficients can give a theoretically good solution,
+        but the resulting rational function may be un-computable at fixed precision).
+      </p>
+<p>
+        Recomputing using different Remez implementations may well produce differing
+        coefficients: the problem is well known to be ill conditioned in general,
+        and our Remez implementation often found a broad and ill-defined minima for
+        many of these approximations (of course for simple "toy" examples
+        like approximating <code class="computeroutput"><span class="identifier">exp</span></code> the
+        minima is well defined, and the coeffiecents should agree no matter whose
+        Remez implementation is used). This should not in general effect the validity
+        of the approximations: there's good literature supporting the idea that coefficients
+        can be "in error" without necessarily adversely effecting the result.
+        Note that "in error" has a special meaning in this context, see
+        <a href="http://front.math.ucdavis.edu/0101.5042" target="_top">"Approximate construction
+        of rational approximations and the effect of error autocorrection.",
+        Grigori Litvinov, eprint arXiv:math/0101042</a>. Therefore the coefficients
+        still need to be accurately calculated, even if they can be in error compared
+        to the "true" minimax solution.
+      </p>
+<a name="math_toolkit.backgrounders.implementation.representation_of_mathematical_constants"></a><h5>
+<a name="id913836"></a>
+        <a class="link" href="implementation.html#math_toolkit.backgrounders.implementation.representation_of_mathematical_constants">Representation
+        of Mathematical Constants</a>
+      </h5>
+<p>
+        A macro BOOST_DEFINE_MATH_CONSTANT in constants.hpp is used to provide high
+        accuracy constants to mathematical functions and distributions, since it
+        is important to provide values uniformly for both built-in float, double
+        and long double types, and for User Defined types like NTL::quad_float and
+        NTL::RR.
+      </p>
+<p>
+        To permit calculations in this Math ToolKit and its tests, (and elsewhere)
+        at about 100 decimal digits with NTL::RR type, it is obviously necessary
+        to define constants to this accuracy.
+      </p>
+<p>
+        However, some compilers do not accept decimal digits strings as long as this.
+        So the constant is split into two parts, with the 1st containing at least
+        long double precision, and the 2nd zero if not needed or known. The 3rd part
+        permits an exponent to be provided if necessary (use zero if none) - the
+        other two parameters may only contain decimal digits (and sign and decimal
+        point), and may NOT include an exponent like 1.234E99 (nor a trailing F or
+        L). The second digit string is only used if T is a User-Defined Type, when
+        the constant is converted to a long string literal and lexical_casted to
+        type T. (This is necessary because you can't use a numeric constant since
+        even a long double might not have enough digits).
+      </p>
+<p>
+        For example, pi is defined:
+      </p>
+<pre class="programlisting"><span class="identifier">BOOST_DEFINE_MATH_CONSTANT</span><span class="special">(</span><span class="identifier">pi</span><span class="special">,</span>
+  <span class="number">3.141592653589793238462643383279502884197169399375105820974944</span><span class="special">,</span>
+  <span class="number">5923078164062862089986280348253421170679821480865132823066470938446095505</span><span class="special">,</span>
+  <span class="number">0</span><span class="special">)</span>                                              
+</pre>
+<p>
+        And used thus:
+      </p>
+<pre class="programlisting"><span class="keyword">using</span> <span class="keyword">namespace</span> <span class="identifier">boost</span><span class="special">::</span><span class="identifier">math</span><span class="special">::</span><span class="identifier">constants</span><span class="special">;</span>
+
+<span class="keyword">double</span> <span class="identifier">diameter</span> <span class="special">=</span> <span class="number">1.</span><span class="special">;</span>
+<span class="keyword">double</span> <span class="identifier">radius</span> <span class="special">=</span> <span class="identifier">diameter</span> <span class="special">*</span> <span class="identifier">pi</span><span class="special">&lt;</span><span class="keyword">double</span><span class="special">&gt;();</span>
+
+<span class="keyword">or</span> <span class="identifier">boost</span><span class="special">::</span><span class="identifier">math</span><span class="special">::</span><span class="identifier">constants</span><span class="special">::</span><span class="identifier">pi</span><span class="special">&lt;</span><span class="identifier">NTL</span><span class="special">::</span><span class="identifier">RR</span><span class="special">&gt;()</span>
+</pre>
+<p>
+        Note that it is necessary (if inconvenient) to specify the type explicitly.
+      </p>
+<p>
+        So you cannot write
+      </p>
+<pre class="programlisting"><span class="keyword">double</span> <span class="identifier">p</span> <span class="special">=</span> <span class="identifier">boost</span><span class="special">::</span><span class="identifier">math</span><span class="special">::</span><span class="identifier">constants</span><span class="special">::</span><span class="identifier">pi</span><span class="special">&lt;&gt;();</span>  <span class="comment">// could not deduce template argument for 'T'  
+</span></pre>
+<p>
+        Neither can you write:
+      </p>
+<pre class="programlisting"><span class="keyword">double</span> <span class="identifier">p</span> <span class="special">=</span> <span class="identifier">boost</span><span class="special">::</span><span class="identifier">math</span><span class="special">::</span><span class="identifier">constants</span><span class="special">::</span><span class="identifier">pi</span><span class="special">;</span> <span class="comment">// Context does not allow for disambiguation of overloaded function     
+</span><span class="keyword">double</span> <span class="identifier">p</span> <span class="special">=</span> <span class="identifier">boost</span><span class="special">::</span><span class="identifier">math</span><span class="special">::</span><span class="identifier">constants</span><span class="special">::</span><span class="identifier">pi</span><span class="special">();</span> <span class="comment">// Context does not allow for disambiguation of overloaded function     
+</span></pre>
+<a name="math_toolkit.backgrounders.implementation.thread_safety"></a><h5>
+<a name="id914410"></a>
+        <a class="link" href="implementation.html#math_toolkit.backgrounders.implementation.thread_safety">Thread
+        safety</a>
+      </h5>
+<p>
+        Reporting of error by setting errno should be thread safe already (otherwise
+        none of the std lib math functions would be thread safe?). If you turn on
+        reporting of errors via exceptions, errno gets left unused anyway.
+      </p>
+<p>
+        Other than that, the code is intended to be thread safe <span class="bold"><strong>for
+        built in real-number types</strong></span> : so float, double and long double
+        are all thread safe.
+      </p>
+<p>
+        For non-built-in types - NTL::RR for example - initialisation of the various
+        constants used in the implementation is potentially <span class="bold"><strong>not</strong></span>
+        thread safe. This most undesiable, but it would be a signficant challenge
+        to fix it. Some compilers may offer the option of having static-constants
+        initialised in a thread safe manner (Commeau, and maybe others?), if that's
+        the case then the problem is solved. This is a topic of hot debate for the
+        next C++ std revision, so hopefully all compilers will be required to do
+        the right thing here at some point.
+      </p>
+<a name="math_toolkit.backgrounders.implementation.sources_of_test_data"></a><h5>
+<a name="id914487"></a>
+        <a class="link" href="implementation.html#math_toolkit.backgrounders.implementation.sources_of_test_data">Sources
+        of Test Data</a>
+      </h5>
+<p>
+        We found a large number of sources of test data. We have assumed that these
+        are <span class="emphasis"><em>"known good"</em></span> if they agree with the results
+        from our test and only consulted other sources for their <span class="emphasis"><em>'vote'</em></span>
+        in the case of serious disagreement. The accuracy, actual and claimed, vary
+        very widely. Only <a href="http://functions.wolfram.com/" target="_top">Wolfram Mathematica
+        functions</a> provided a higher accuracy than C++ double (64-bit floating-point)
+        and was regarded as the most-trusted source by far.
+      </p>
+<p>
+        A useful index of sources is: <a href="http://www.sal.hut.fi/Teaching/Resources/ProbStat/table.html" target="_top">Web-oriented
+        Teaching Resources in Probability and Statistics</a>
+      </p>
+<p>
+        Statlet:
+        Is a Javascript application that calculates and plots probability distributions,
+        and provides the most complete range of distributions:
+      </p>
+<div class="blockquote"><blockquote class="blockquote">
+<p>
+          </p>
+<p>
+            Bernoulli, Binomial, discrete uniform, geometric, hypergeometric, negative
+            binomial, Poisson, beta, Cauchy-Lorentz, chi-sequared, Erlang, exponential,
+            extreme value, Fisher, gamma, Laplace, logistic, lognormal, normal, Parteo,
+            Student's t, triangular, uniform, and Weibull.
+          </p>
+<p>
+        </p>
+</blockquote></div>
+<p>
+        It calculates pdf, cdf, survivor, log survivor, hazard, tail areas, &amp;
+        critical values for 5 tail values.
+      </p>
+<p>
+        It is also the only independent source found for the Weibull distribution;
+        unfortunately it appears to suffer from very poor accuracy in areas where
+        the underlying special function is known to be difficult to implement.
+      </p>
+<a name="math_toolkit.backgrounders.implementation.creating_and_managing_the_equations"></a><h5>
+<a name="id914609"></a>
+        <a class="link" href="implementation.html#math_toolkit.backgrounders.implementation.creating_and_managing_the_equations">Creating
+        and Managing the Equations</a>
+      </h5>
+<p>
+        The primary source for the equations is now MathML:
+        see the *.mml files in libs/math/doc/sf_and_dist/equations/.
+      </p>
+<p>
+        These are most easily edited by a GUI editor such as Mathcast,
+        please note that the equation editor supplied with Open Office currently
+        mangles these files and should not currently be used.
+      </p>
+<p>
+        Convertion to SVG was achieved using SVGMath
+        and a command line such as:
+      </p>
+<pre class="programlisting">$for file in *.mml; do 
+&gt;/cygdrive/c/Python25/python.exe 'C:\download\open\SVGMath-0.3.1\math2svg.py' \
+&gt;&gt;$file &gt; $(basename $file .mml).svg
+&gt;done
+</pre>
+<p>
+        Note that SVGMath requires that the mml files are <span class="bold"><strong>not</strong></span>
+        wrapped in an XHTML XML wrapper - this is added by Mathcast by default -
+        one workaround is to copy an existing mml file and then edit it with Mathcast:
+        the existing format should then be preserved. This is a bug in the XML parser
+        used by SVGMath which the author is aware of.
+      </p>
+<p>
+        If neccessary the XHTML wrapper can be removed with:
+      </p>
+<pre class="programlisting">cat filename | tr -d "\r\n" | sed -e 's/.*\(&lt;math[^&gt;]*&gt;.*&lt;/math&gt;\).*/\1/' &gt; newfile</pre>
+<p>
+        Setting up fonts for SVGMath is currently rather tricky, on a Windows XP
+        system JM's font setup is the same as the sample config file provided with
+        SVGMath but with:
+      </p>
+<pre class="programlisting">&lt;!-- Double-struck --&gt;
+    &lt;mathvariant name="double-struck" family="Mathematica7, Lucida Sans Unicode"/&gt;
+</pre>
+<p>
+        changed to:
+      </p>
+<pre class="programlisting">&lt;!-- Double-struck --&gt;
+    &lt;mathvariant name="double-struck" family="Lucida Sans Unicode"/&gt;
+</pre>
+<p>
+        Note that unlike the sample config file supplied with SVGMath, this does
+        not make use of the Mathematica 7 font as this lacks sufficient Unicode information
+        for it to be used with either SVGMath or XEP "as is".
+      </p>
+<p>
+        Also note that the SVG files in the repository are almost certainly Windows-specific
+        since they reference various Windows Fonts.
+      </p>
+<p>
+        PNG files can be created from the SVG's using Batik
+        and a command such as:
+      </p>
+<pre class="programlisting">java -jar 'C:\download\open\batik-1.7\batik-rasterizer.jar' -dpi 120 *.svg</pre>
+<p>
+        Or using Inkscape and a command such as:
+      </p>
+<pre class="programlisting">for file in *.svg; do 
+  /cygdrive/c/progra~1/Inkscape/inkscape -d 120 -e $(cygpath -a -w $(basename $file .svg).png) $(cygpath -a -w $file); 
+done</pre>
+<p>
+        Currently Inkscape seems to generate the better looking png's.
+      </p>
+<p>
+        The PDF is generated into \pdf\math.pdf using a command from a shell or command
+        window with current directory \math_toolkit\libs\math\doc\sf_and_dist, typically:
+      </p>
+<pre class="programlisting">bjam -a pdf</pre>
+<p>
+        Note that XEP will have to be configured to <span class="bold"><strong>use and
+        embed</strong></span> whatever fonts are used by the SVG equations (if necessary
+        editing the sample xep.xml provided by the XEP installation).
+      </p>
+<p>
+        (html is generated at math_toolkit\libs\math\doc\sf_and_dist\html\index.html
+        using just bjam -a).
+      </p>
+<p>
+        JM's XEP config file has the following font configuration section added:
+      </p>
+<pre class="programlisting">&lt;font-group xml:base="file:/C:/Windows/Fonts/" label="Windows TrueType" embed="true" subset="true"&gt; 
+      &lt;font-family name="Arial"&gt;
+        &lt;font&gt;&lt;font-data ttf="arial.ttf"/&gt;&lt;/font&gt;
+        &lt;font style="oblique"&gt;&lt;font-data ttf="ariali.ttf"/&gt;&lt;/font&gt;
+        &lt;font weight="bold"&gt;&lt;font-data ttf="arialbd.ttf"/&gt;&lt;/font&gt;
+        &lt;font weight="bold" style="oblique"&gt;&lt;font-data ttf="arialbi.ttf"/&gt;&lt;/font&gt;
+      &lt;/font-family&gt;
+
+      &lt;font-family name="Times New Roman" ligatures="&amp;#xFB01; &amp;#xFB02;"&gt;
+        &lt;font&gt;&lt;font-data ttf="times.ttf"/&gt;&lt;/font&gt;
+        &lt;font style="italic"&gt;&lt;font-data ttf="timesi.ttf"/&gt;&lt;/font&gt;
+        &lt;font weight="bold"&gt;&lt;font-data ttf="timesbd.ttf"/&gt;&lt;/font&gt;
+        &lt;font weight="bold" style="italic"&gt;&lt;font-data ttf="timesbi.ttf"/&gt;&lt;/font&gt;
+      &lt;/font-family&gt;
+
+      &lt;font-family name="Courier New"&gt;
+        &lt;font&gt;&lt;font-data ttf="cour.ttf"/&gt;&lt;/font&gt;
+        &lt;font style="oblique"&gt;&lt;font-data ttf="couri.ttf"/&gt;&lt;/font&gt;
+        &lt;font weight="bold"&gt;&lt;font-data ttf="courbd.ttf"/&gt;&lt;/font&gt;
+        &lt;font weight="bold" style="oblique"&gt;&lt;font-data ttf="courbi.ttf"/&gt;&lt;/font&gt;
+      &lt;/font-family&gt;
+
+      &lt;font-family name="Tahoma" embed="true"&gt;
+        &lt;font&gt;&lt;font-data ttf="tahoma.ttf"/&gt;&lt;/font&gt;
+        &lt;font weight="bold"&gt;&lt;font-data ttf="tahomabd.ttf"/&gt;&lt;/font&gt;
+      &lt;/font-family&gt;
+
+      &lt;font-family name="Verdana" embed="true"&gt;
+        &lt;font&gt;&lt;font-data ttf="verdana.ttf"/&gt;&lt;/font&gt;
+        &lt;font style="oblique"&gt;&lt;font-data ttf="verdanai.ttf"/&gt;&lt;/font&gt;
+        &lt;font weight="bold"&gt;&lt;font-data ttf="verdanab.ttf"/&gt;&lt;/font&gt;
+        &lt;font weight="bold" style="oblique"&gt;&lt;font-data ttf="verdanaz.ttf"/&gt;&lt;/font&gt;
+      &lt;/font-family&gt;
+
+      &lt;font-family name="Palatino" embed="true" ligatures="&amp;#xFB00; &amp;#xFB01; &amp;#xFB02; &amp;#xFB03; &amp;#xFB04;"&gt;
+        &lt;font&gt;&lt;font-data ttf="pala.ttf"/&gt;&lt;/font&gt;
+        &lt;font style="italic"&gt;&lt;font-data ttf="palai.ttf"/&gt;&lt;/font&gt;
+        &lt;font weight="bold"&gt;&lt;font-data ttf="palab.ttf"/&gt;&lt;/font&gt;
+        &lt;font weight="bold" style="italic"&gt;&lt;font-data ttf="palabi.ttf"/&gt;&lt;/font&gt;
+      &lt;/font-family&gt;
+      
+    &lt;font-family name="Lucida Sans Unicode"&gt;
+         &lt;font&gt;&lt;font-data ttf="lsansuni.ttf"/&gt;&lt;/font&gt;
+    &lt;/font-family&gt;
+</pre>
+<p>
+        PAB had to alter his because the Lucida Sans Unicode font had a different
+        name. Changes are very likely to be required if you are not using Windows.
+      </p>
+<p>
+        XZ authored his equations using the venerable Latex, JM converted these to
+        MathML using mxlatex.
+        This process is currently unreliable and required some manual intervention:
+        consequently Latex source is not considered a viable route for the automatic
+        production of SVG versions of equations.
+      </p>
+<p>
+        Equations are embedded in the quickbook source using the <span class="emphasis"><em>equation</em></span>
+        template defined in math.qbk. This outputs Docbook XML that looks like:
+      </p>
+<pre class="programlisting">&lt;inlinemediaobject&gt;
+&lt;imageobject role<code class="literal">"html"&gt;
+&lt;imagedata fileref</code>"../equations/myfile.png"&gt;&lt;/imagedata&gt;
+&lt;/imageobject&gt;
+&lt;imageobject role<code class="literal">"print"&gt;
+&lt;imagedata fileref</code>"../equations/myfile.svg"&gt;&lt;/imagedata&gt;
+&lt;/imageobject&gt;
+&lt;/inlinemediaobject&gt;
+</pre>
+<p>
+        MathML is not currently present in the Docbook output, or in the generated
+        HTML: this needs further investigation.
+      </p>
+<a name="math_toolkit.backgrounders.implementation.producing_graphs"></a><h5>
+<a name="id915028"></a>
+        <a class="link" href="implementation.html#math_toolkit.backgrounders.implementation.producing_graphs">Producing
+        Graphs</a>
+      </h5>
+<p>
+        Graphs were produced in SVG format and then converted to PNG's using the
+        same process as the equations.
+      </p>
+<p>
+        The programs /libs/math/doc/sf_and_dist/graphs/dist_graphs.cpp and /libs/math/doc/sf_and_dist/graphs<span class="emphasis"><em>sf_graphs.cpp
+        generate the SVG's directly using the [@http:</em></span>/code.google.com/soc/2007/boost/about.html
+        Google Summer of Code 2007] project of Jacob Voytko (whose work so far is
+        at .\boost-sandbox\SOC\2007\visualization).
+      </p>
+</div>
+<table xmlns:rev="http://www.cs.rpi.edu/~gregod/boost/tools/doc/revision" width="100%"><tr>
+<td align="left"></td>
+<td align="right"><div class="copyright-footer">Copyright © 2006 , 2007, 2008 John Maddock, Paul A. Bristow, Hubert
+      Holin, Xiaogang Zhang, Bruno Lalande and Gautam Sewani<p>
+        Distributed under the Boost Software License, Version 1.0. (See accompanying
+        file LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_0.txt)
+      </p>
+</div></td>
+</tr></table>
+<hr>
+<div class="spirit-nav">
+<a accesskey="p" href="../backgrounders.html"><img src="../../../../doc/html/images/prev.png" alt="Prev"></a><a accesskey="u" href="../backgrounders.html"><img src="../../../../doc/html/images/up.png" alt="Up"></a><a accesskey="h" href="../../index.html"><img src="../../../../doc/html/images/home.png" alt="Home"></a><a accesskey="n" href="relative_error.html"><img src="../../../../doc/html/images/next.png" alt="Next"></a>
+</div>
+</body>
+</html>

Added: sandbox/tools/auto_index/example/math/doc/sf_and_dist/html/math_toolkit/backgrounders/lanczos.html
==============================================================================
--- (empty file)
+++ sandbox/tools/auto_index/example/math/doc/sf_and_dist/html/math_toolkit/backgrounders/lanczos.html	2008-11-28 05:25:28 EST (Fri, 28 Nov 2008)
@@ -0,0 +1,576 @@
+<html>
+<head>
+<meta http-equiv="Content-Type" content="text/html; charset=ISO-8859-1">
+<title>The Lanczos Approximation</title>
+<link rel="stylesheet" href="../../boostbook.css" type="text/css">
+<meta name="generator" content="DocBook XSL Stylesheets Vsnapshot_8125">
+<link rel="home" href="../../index.html" title="Math Toolkit">
+<link rel="up" href="../backgrounders.html" title="Backgrounders">
+<link rel="prev" href="relative_error.html" title="Relative Error">
+<link rel="next" href="remez.html" title="The Remez Method">
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+<body bgcolor="white" text="black" link="#0000FF" vlink="#840084" alink="#0000FF">
+<table cellpadding="2" width="100%"><tr>
+<td valign="top"><img alt="Boost C++ Libraries" width="277" height="86" src="../../../../boost.png"></td>
+<td align="center">Home</td>
+<td align="center">Libraries</td>
+<td align="center">People</td>
+<td align="center">FAQ</td>
+<td align="center">More</td>
+</tr></table>
+<hr>
+<div class="spirit-nav">
+<a accesskey="p" href="relative_error.html"><img src="../../../../doc/html/images/prev.png" alt="Prev"></a><a accesskey="u" href="../backgrounders.html"><img src="../../../../doc/html/images/up.png" alt="Up"></a><a accesskey="h" href="../../index.html"><img src="../../../../doc/html/images/home.png" alt="Home"></a><a accesskey="n" href="remez.html"><img src="../../../../doc/html/images/next.png" alt="Next"></a>
+</div>
+<div class="section" lang="en">
+<div class="titlepage"><div><div><h3 class="title">
+<a name="math_toolkit.backgrounders.lanczos"></a><a class="link" href="lanczos.html" title="The Lanczos Approximation"> The Lanczos Approximation</a>
+</h3></div></div></div>
+<a name="math_toolkit.backgrounders.lanczos.motivation"></a><h5>
+<a name="id915453"></a>
+        <a class="link" href="lanczos.html#math_toolkit.backgrounders.lanczos.motivation">Motivation</a>
+      </h5>
+<p>
+        <span class="emphasis"><em>Why base gamma and gamma-like functions on the Lanczos approximation?</em></span>
+      </p>
+<p>
+        First of all I should make clear that for the gamma function over real numbers
+        (as opposed to complex ones) the Lanczos approximation (See <a href="http://en.wikipedia.org/wiki/Lanczos_approximation" target="_top">Wikipedia
+        or </a> Mathworld)
+        appears to offer no clear advantage over more traditional methods such as
+        <a href="http://en.wikipedia.org/wiki/Stirling_approximation" target="_top">Stirling's
+        approximation</a>. <a class="link" href="lanczos.html#pugh">Pugh</a> carried out an extensive
+        comparison of the various methods available and discovered that they were
+        all very similar in terms of complexity and relative error. However, the
+        Lanczos approximation does have a couple of properties that make it worthy
+        of further consideration:
+      </p>
+<div class="itemizedlist"><ul type="disc">
+<li>
+          The approximation has an easy to compute truncation error that holds for
+          all <span class="emphasis"><em>z &gt; 0</em></span>. In practice that means we can use the
+          same approximation for all <span class="emphasis"><em>z &gt; 0</em></span>, and be certain
+          that no matter how large or small <span class="emphasis"><em>z</em></span> is, the truncation
+          error will <span class="emphasis"><em>at worst</em></span> be bounded by some finite value.
+        </li>
+<li>
+          The approximation has a form that is particularly amenable to analytic
+          manipulation, in particular ratios of gamma or gamma-like functions are
+          particularly easy to compute without resorting to logarithms.
+        </li>
+</ul></div>
+<p>
+        It is the combination of these two properties that make the approximation
+        attractive: Stirling's approximation is highly accurate for large z, and
+        has some of the same analytic properties as the Lanczos approximation, but
+        can't easily be used across the whole range of z.
+      </p>
+<p>
+        As the simplest example, consider the ratio of two gamma functions: one could
+        compute the result via lgamma:
+      </p>
+<pre class="programlisting"><span class="identifier">exp</span><span class="special">(</span><span class="identifier">lgamma</span><span class="special">(</span><span class="identifier">a</span><span class="special">)</span> <span class="special">-</span> <span class="identifier">lgamma</span><span class="special">(</span><span class="identifier">b</span><span class="special">));</span>
+</pre>
+<p>
+        However, even if lgamma is uniformly accurate to 0.5ulp, the worst case relative
+        error in the above can easily be shown to be:
+      </p>
+<pre class="programlisting"><span class="identifier">Erel</span> <span class="special">&gt;</span> <span class="identifier">a</span> <span class="special">*</span> <span class="identifier">log</span><span class="special">(</span><span class="identifier">a</span><span class="special">)/</span><span class="number">2</span> <span class="special">+</span> <span class="identifier">b</span> <span class="special">*</span> <span class="identifier">log</span><span class="special">(</span><span class="identifier">b</span><span class="special">)/</span><span class="number">2</span>
+</pre>
+<p>
+        For small <span class="emphasis"><em>a</em></span> and <span class="emphasis"><em>b</em></span> that's not a
+        problem, but to put the relationship another way: <span class="emphasis"><em>each time a and
+        b increase in magnitude by a factor of 10, at least one decimal digit of
+        precision will be lost.</em></span>
+      </p>
+<p>
+        In contrast, by analytically combining like power terms in a ratio of Lanczos
+        approximation's, these errors can be virtually eliminated for small <span class="emphasis"><em>a</em></span>
+        and <span class="emphasis"><em>b</em></span>, and kept under control for very large (or very
+        small for that matter) <span class="emphasis"><em>a</em></span> and <span class="emphasis"><em>b</em></span>.
+        Of course, computing large powers is itself a notoriously hard problem, but
+        even so, analytic combinations of Lanczos approximations can make the difference
+        between obtaining a valid result, or simply garbage. Refer to the implementation
+        notes for the <a class="link" href="../special/sf_beta/beta_function.html" title="Beta">beta</a>
+        function for an example of this method in practice. The incomplete <a class="link" href="../special/sf_gamma/igamma.html" title="Incomplete Gamma Functions">gamma_p gamma</a> and
+        <a class="link" href="../special/sf_beta/ibeta_function.html" title="Incomplete Beta Functions">beta</a> functions
+        use similar analytic combinations of power terms, to combine gamma and beta
+        functions divided by large powers into single (simpler) expressions.
+      </p>
+<a name="math_toolkit.backgrounders.lanczos.the_approximation"></a><h5>
+<a name="id915863"></a>
+        <a class="link" href="lanczos.html#math_toolkit.backgrounders.lanczos.the_approximation">The
+        Approximation</a>
+      </h5>
+<p>
+        The Lanczos Approximation to the Gamma Function is given by:
+      </p>
+<p>
+        <span class="inlinemediaobject"><img src="../../../equations/lanczos0.png"></span>
+      </p>
+<p>
+        Where S<sub>g</sub>(z) is an infinite sum, that is convergent for all z &gt; 0, and
+        <span class="emphasis"><em>g</em></span> is an arbitrary parameter that controls the "shape"
+        of the terms in the sum which is given by:
+      </p>
+<p>
+        <span class="inlinemediaobject"><img src="../../../equations/lanczos0a.png"></span>
+      </p>
+<p>
+        With individual coefficients defined in closed form by:
+      </p>
+<p>
+        <span class="inlinemediaobject"><img src="../../../equations/lanczos0b.png"></span>
+      </p>
+<p>
+        However, evaluation of the sum in that form can lead to numerical instability
+        in the computation of the ratios of rising and falling factorials (effectively
+        we're multiplying by a series of numbers very close to 1, so roundoff errors
+        can accumulate quite rapidly).
+      </p>
+<p>
+        The Lanczos approximation is therefore often written in partial fraction
+        form with the leading constants absorbed by the coefficients in the sum:
+      </p>
+<p>
+        <span class="inlinemediaobject"><img src="../../../equations/lanczos1.png"></span>
+      </p>
+<p>
+        where:
+      </p>
+<p>
+        <span class="inlinemediaobject"><img src="../../../equations/lanczos2.png"></span>
+      </p>
+<p>
+        Again parameter <span class="emphasis"><em>g</em></span> is an arbitrarily chosen constant,
+        and <span class="emphasis"><em>N</em></span> is an arbitrarily chosen number of terms to evaluate
+        in the "Lanczos sum" part.
+      </p>
+<div class="note"><table border="0" summary="Note">
+<tr>
+<td rowspan="2" align="center" valign="top" width="25"><img alt="[Note]" src="../../../../doc/html/images/note.png"></td>
+<th align="left">Note</th>
+</tr>
+<tr><td align="left" valign="top"><p>
+          Some authors choose to define the sum from k=1 to N, and hence end up with
+          N+1 coefficients. This happens to confuse both the following discussion
+          and the code (since C++ deals with half open array ranges, rather than
+          the closed range of the sum). This convention is consistent with <a class="link" href="lanczos.html#godfrey">Godfrey</a>, but not <a class="link" href="lanczos.html#pugh">Pugh</a>,
+          so take care when referring to the literature in this field.
+        </p></td></tr>
+</table></div>
+<a name="math_toolkit.backgrounders.lanczos.computing_the_coefficients"></a><h5>
+<a name="id916135"></a>
+        <a class="link" href="lanczos.html#math_toolkit.backgrounders.lanczos.computing_the_coefficients">Computing
+        the Coefficients</a>
+      </h5>
+<p>
+        The coefficients C0..CN-1 need to be computed from <span class="emphasis"><em>N</em></span>
+        and <span class="emphasis"><em>g</em></span> at high precision, and then stored as part of
+        the program. Calculation of the coefficients is performed via the method
+        of <a class="link" href="lanczos.html#godfrey">Godfrey</a>; let the constants be contained
+        in a column vector P, then:
+      </p>
+<p>
+        P = B D C F
+      </p>
+<p>
+        where B is an NxN matrix:
+      </p>
+<p>
+        <span class="inlinemediaobject"><img src="../../../equations/lanczos4.png"></span>
+      </p>
+<p>
+        D is an NxN matrix:
+      </p>
+<p>
+        <span class="inlinemediaobject"><img src="../../../equations/lanczos3.png"></span>
+      </p>
+<p>
+        C is an NxN matrix:
+      </p>
+<p>
+        <span class="inlinemediaobject"><img src="../../../equations/lanczos5.png"></span>
+      </p>
+<p>
+        and F is an N element column vector:
+      </p>
+<p>
+        <span class="inlinemediaobject"><img src="../../../equations/lanczos6.png"></span>
+      </p>
+<p>
+        Note than the matrices B, D and C contain all integer terms and depend only
+        on <span class="emphasis"><em>N</em></span>, this product should be computed first, and then
+        multiplied by <span class="emphasis"><em>F</em></span> as the last step.
+      </p>
+<a name="math_toolkit.backgrounders.lanczos.choosing_the_right_parameters"></a><h5>
+<a name="id916351"></a>
+        <a class="link" href="lanczos.html#math_toolkit.backgrounders.lanczos.choosing_the_right_parameters">Choosing
+        the Right Parameters</a>
+      </h5>
+<p>
+        The trick is to choose <span class="emphasis"><em>N</em></span> and <span class="emphasis"><em>g</em></span>
+        to give the desired level of accuracy: choosing a small value for <span class="emphasis"><em>g</em></span>
+        leads to a strictly convergent series, but one which converges only slowly.
+        Choosing a larger value of <span class="emphasis"><em>g</em></span> causes the terms in the
+        series to be large and/or divergent for about the first <span class="emphasis"><em>g-1</em></span>
+        terms, and to then suddenly converge with a "crunch".
+      </p>
+<p>
+        <a class="link" href="lanczos.html#pugh">Pugh</a> has determined the optimal value of <span class="emphasis"><em>g</em></span>
+        for <span class="emphasis"><em>N</em></span> in the range <span class="emphasis"><em>1 &lt;= N &lt;= 60</em></span>:
+        unfortunately in practice choosing these values leads to cancellation errors
+        in the Lanczos sum as the largest term in the (alternating) series is approximately
+        1000 times larger than the result. These optimal values appear not to be
+        useful in practice unless the evaluation can be done with a number of guard
+        digits <span class="emphasis"><em>and</em></span> the coefficients are stored at higher precision
+        than that desired in the result. These values are best reserved for say,
+        computing to float precision with double precision arithmetic.
+      </p>
+<div class="table">
+<a name="id916444"></a><p class="title"><b>Table 53. Optimal choices for N and g when computing with
+      guard digits (source: Pugh)</b></p>
+<div class="table-contents"><table class="table" summary="Optimal choices for N and g when computing with
+      guard digits (source: Pugh)">
+<colgroup>
+<col>
+<col>
+<col>
+<col>
+</colgroup>
+<thead><tr>
+<th>
+            <p>
+              Significand Size
+            </p>
+            </th>
+<th>
+            <p>
+              N
+            </p>
+            </th>
+<th>
+            <p>
+              g
+            </p>
+            </th>
+<th>
+            <p>
+              Max Error
+            </p>
+            </th>
+</tr></thead>
+<tbody>
+<tr>
+<td>
+            <p>
+              24
+            </p>
+            </td>
+<td>
+            <p>
+              6
+            </p>
+            </td>
+<td>
+            <p>
+              5.581
+            </p>
+            </td>
+<td>
+            <p>
+              9.51e-12
+            </p>
+            </td>
+</tr>
+<tr>
+<td>
+            <p>
+              53
+            </p>
+            </td>
+<td>
+            <p>
+              13
+            </p>
+            </td>
+<td>
+            <p>
+              13.144565
+            </p>
+            </td>
+<td>
+            <p>
+              9.2213e-23
+            </p>
+            </td>
+</tr>
+</tbody>
+</table></div>
+</div>
+<br class="table-break"><p>
+        The alternative described by <a class="link" href="lanczos.html#godfrey">Godfrey</a> is to
+        perform an exhaustive search of the <span class="emphasis"><em>N</em></span> and <span class="emphasis"><em>g</em></span>
+        parameter space to determine the optimal combination for a given <span class="emphasis"><em>p</em></span>
+        digit floating-point type. Repeating this work found a good approximation
+        for double precision arithmetic (close to the one <a class="link" href="lanczos.html#godfrey">Godfrey</a>
+        found), but failed to find really good approximations for 80 or 128-bit long
+        doubles. Further it was observed that the approximations obtained tended
+        to optimised for the small values of z (1 &lt; z &lt; 200) used to test the
+        implementation against the factorials. Computing ratios of gamma functions
+        with large arguments were observed to suffer from error resulting from the
+        truncation of the Lancozos series.
+      </p>
+<p>
+        <a class="link" href="lanczos.html#pugh">Pugh</a> identified all the locations where the theoretical
+        error of the approximation were at a minimum, but unfortunately has published
+        only the largest of these minima. However, he makes the observation that
+        the minima coincide closely with the location where the first neglected term
+        (a<sub>N</sub>) in the Lanczos series S<sub>g</sub>(z) changes sign. These locations are quite
+        easy to locate, albeit with considerable computer time. These "sweet
+        spots" need only be computed once, tabulated, and then searched when
+        required for an approximation that delivers the required precision for some
+        fixed precision type.
+      </p>
+<p>
+        Unfortunately, following this path failed to find a really good approximation
+        for 128-bit long doubles, and those found for 64 and 80-bit reals required
+        an excessive number of terms. There are two competing issues here: high precision
+        requires a large value of <span class="emphasis"><em>g</em></span>, but avoiding cancellation
+        errors in the evaluation requires a small <span class="emphasis"><em>g</em></span>.
+      </p>
+<p>
+        At this point note that the Lanczos sum can be converted into rational form
+        (a ratio of two polynomials, obtained from the partial-fraction form using
+        polynomial arithmetic), and doing so changes the coefficients so that <span class="emphasis"><em>they
+        are all positive</em></span>. That means that the sum in rational form can
+        be evaluated without cancellation error, albeit with double the number of
+        coefficients for a given N. Repeating the search of the "sweet spots",
+        this time evaluating the Lanczos sum in rational form, and testing only those
+        "sweet spots" whose theoretical error is less than the machine
+        epsilon for the type being tested, yielded good approximations for all the
+        types tested. The optimal values found were quite close to the best cases
+        reported by <a class="link" href="lanczos.html#pugh">Pugh</a> (just slightly larger <span class="emphasis"><em>N</em></span>
+        and slightly smaller <span class="emphasis"><em>g</em></span> for a given precision than <a class="link" href="lanczos.html#pugh">Pugh</a> reports), and even though converting to rational
+        form doubles the number of stored coefficients, it should be noted that half
+        of them are integers (and therefore require less storage space) and the approximations
+        require a smaller <span class="emphasis"><em>N</em></span> than would otherwise be required,
+        so fewer floating point operations may be required overall.
+      </p>
+<p>
+        The following table shows the optimal values for <span class="emphasis"><em>N</em></span> and
+        <span class="emphasis"><em>g</em></span> when computing at fixed precision. These should be
+        taken as work in progress: there are no values for 106-bit significand machines
+        (Darwin long doubles &amp; NTL quad_float), and further optimisation of the
+        values of <span class="emphasis"><em>g</em></span> may be possible. Errors given in the table
+        are estimates of the error due to truncation of the Lanczos infinite series
+        to <span class="emphasis"><em>N</em></span> terms. They are calculated from the sum of the
+        first five neglected terms - and are known to be rather pessimistic estimates
+        - although it is noticeable that the best combinations of <span class="emphasis"><em>N</em></span>
+        and <span class="emphasis"><em>g</em></span> occurred when the estimated truncation error almost
+        exactly matches the machine epsilon for the type in question.
+      </p>
+<div class="table">
+<a name="id916801"></a><p class="title"><b>Table 54. Optimum value for N and g when computing at fixed
+      precision</b></p>
+<div class="table-contents"><table class="table" summary="Optimum value for N and g when computing at fixed
+      precision">
+<colgroup>
+<col>
+<col>
+<col>
+<col>
+<col>
+</colgroup>
+<thead><tr>
+<th>
+            <p>
+              Significand Size
+            </p>
+            </th>
+<th>
+            <p>
+              Platform/Compiler Used
+            </p>
+            </th>
+<th>
+            <p>
+              N
+            </p>
+            </th>
+<th>
+            <p>
+              g
+            </p>
+            </th>
+<th>
+            <p>
+              Max Truncation Error
+            </p>
+            </th>
+</tr></thead>
+<tbody>
+<tr>
+<td>
+            <p>
+              24
+            </p>
+            </td>
+<td>
+            <p>
+              Win32, VC++ 7.1
+            </p>
+            </td>
+<td>
+            <p>
+              6
+            </p>
+            </td>
+<td>
+            <p>
+              1.428456135094165802001953125
+            </p>
+            </td>
+<td>
+            <p>
+              9.41e-007
+            </p>
+            </td>
+</tr>
+<tr>
+<td>
+            <p>
+              53
+            </p>
+            </td>
+<td>
+            <p>
+              Win32, VC++ 7.1
+            </p>
+            </td>
+<td>
+            <p>
+              13
+            </p>
+            </td>
+<td>
+            <p>
+              6.024680040776729583740234375
+            </p>
+            </td>
+<td>
+            <p>
+              3.23e-016
+            </p>
+            </td>
+</tr>
+<tr>
+<td>
+            <p>
+              64
+            </p>
+            </td>
+<td>
+            <p>
+              Suse Linux 9 IA64, gcc-3.3.3
+            </p>
+            </td>
+<td>
+            <p>
+              17
+            </p>
+            </td>
+<td>
+            <p>
+              12.2252227365970611572265625
+            </p>
+            </td>
+<td>
+            <p>
+              2.34e-024
+            </p>
+            </td>
+</tr>
+<tr>
+<td>
+            <p>
+              116
+            </p>
+            </td>
+<td>
+            <p>
+              HP Tru64 Unix 5.1B / Alpha, Compaq C++ V7.1-006
+            </p>
+            </td>
+<td>
+            <p>
+              24
+            </p>
+            </td>
+<td>
+            <p>
+              20.3209821879863739013671875
+            </p>
+            </td>
+<td>
+            <p>
+              4.75e-035
+            </p>
+            </td>
+</tr>
+</tbody>
+</table></div>
+</div>
+<br class="table-break"><p>
+        Finally note that the Lanczos approximation can be written as follows by
+        removing a factor of exp(g) from the denominator, and then dividing all the
+        coefficients by exp(g):
+      </p>
+<p>
+        <span class="inlinemediaobject"><img src="../../../equations/lanczos7.png"></span>
+      </p>
+<p>
+        This form is more convenient for calculating lgamma, but for the gamma function
+        the division by <span class="emphasis"><em>e</em></span> turns a possibly exact quality into
+        an inexact value: this reduces accuracy in the common case that the input
+        is exact, and so isn't used for the gamma function.
+      </p>
+<a name="math_toolkit.backgrounders.lanczos.references"></a><h5>
+<a name="id917102"></a>
+        <a class="link" href="lanczos.html#math_toolkit.backgrounders.lanczos.references">References</a>
+      </h5>
+<a name="godfrey"></a><a name="pugh"></a><div class="orderedlist"><ol type="1">
+<li>
+          Paul Godfrey, <a href="http://my.fit.edu/~gabdo/gamma.txt" target="_top">"A note
+          on the computation of the convergent Lanczos complex Gamma approximation"</a>.
+        </li>
+<li>
+          Glendon Ralph Pugh, <a href="http://bh0.physics.ubc.ca/People/matt/Doc/ThesesOthers/Phd/pugh.pdf" target="_top">"An
+          Analysis of the Lanczos Gamma Approximation"</a>, PhD Thesis November
+          2004.
+        </li>
+<li>
+          Viktor T. Toth, <a href="http://www.rskey.org/gamma.htm" target="_top">"Calculators
+          and the Gamma Function"</a>.
+        </li>
+<li>
+          Mathworld, <a href="http://mathworld.wolfram.com/LanczosApproximation.html" target="_top">The
+          Lanczos Approximation</a>.
+        </li>
+</ol></div>
+</div>
+<table xmlns:rev="http://www.cs.rpi.edu/~gregod/boost/tools/doc/revision" width="100%"><tr>
+<td align="left"></td>
+<td align="right"><div class="copyright-footer">Copyright © 2006 , 2007, 2008 John Maddock, Paul A. Bristow, Hubert
+      Holin, Xiaogang Zhang, Bruno Lalande and Gautam Sewani<p>
+        Distributed under the Boost Software License, Version 1.0. (See accompanying
+        file LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_0.txt)
+      </p>
+</div></td>
+</tr></table>
+<hr>
+<div class="spirit-nav">
+<a accesskey="p" href="relative_error.html"><img src="../../../../doc/html/images/prev.png" alt="Prev"></a><a accesskey="u" href="../backgrounders.html"><img src="../../../../doc/html/images/up.png" alt="Up"></a><a accesskey="h" href="../../index.html"><img src="../../../../doc/html/images/home.png" alt="Home"></a><a accesskey="n" href="remez.html"><img src="../../../../doc/html/images/next.png" alt="Next"></a>
+</div>
+</body>
+</html>

Added: sandbox/tools/auto_index/example/math/doc/sf_and_dist/html/math_toolkit/backgrounders/refs.html
==============================================================================
--- (empty file)
+++ sandbox/tools/auto_index/example/math/doc/sf_and_dist/html/math_toolkit/backgrounders/refs.html	2008-11-28 05:25:28 EST (Fri, 28 Nov 2008)
@@ -0,0 +1,176 @@
+<html>
+<head>
+<meta http-equiv="Content-Type" content="text/html; charset=ISO-8859-1">
+<title>References</title>
+<link rel="stylesheet" href="../../boostbook.css" type="text/css">
+<meta name="generator" content="DocBook XSL Stylesheets Vsnapshot_8125">
+<link rel="home" href="../../index.html" title="Math Toolkit">
+<link rel="up" href="../backgrounders.html" title="Backgrounders">
+<link rel="prev" href="remez.html" title="The Remez Method">
+<link rel="next" href="../status.html" title="Library Status">
+</head>
+<body bgcolor="white" text="black" link="#0000FF" vlink="#840084" alink="#0000FF">
+<table cellpadding="2" width="100%"><tr>
+<td valign="top"><img alt="Boost C++ Libraries" width="277" height="86" src="../../../../boost.png"></td>
+<td align="center">Home</td>
+<td align="center">Libraries</td>
+<td align="center">People</td>
+<td align="center">FAQ</td>
+<td align="center">More</td>
+</tr></table>
+<hr>
+<div class="spirit-nav">
+<a accesskey="p" href="remez.html"><img src="../../../../doc/html/images/prev.png" alt="Prev"></a><a accesskey="u" href="../backgrounders.html"><img src="../../../../doc/html/images/up.png" alt="Up"></a><a accesskey="h" href="../../index.html"><img src="../../../../doc/html/images/home.png" alt="Home"></a><a accesskey="n" href="../status.html"><img src="../../../../doc/html/images/next.png" alt="Next"></a>
+</div>
+<div class="section" lang="en">
+<div class="titlepage"><div><div><h3 class="title">
+<a name="math_toolkit.backgrounders.refs"></a><a class="link" href="refs.html" title="References"> References</a>
+</h3></div></div></div>
+<a name="math_toolkit.backgrounders.refs.general_references"></a><h5>
+<a name="id918676"></a>
+        <a class="link" href="refs.html#math_toolkit.backgrounders.refs.general_references">General
+        references</a>
+      </h5>
+<p>
+        (Specific detailed sources for individual functions and distributions are
+        given at the end of each individual section).
+      </p>
+<p>
+        <a href="http://dlmf.nist.gov/about/" target="_top">DLMF (NIST Digital Library of Mathematical
+        Functions)</a> is intended to be a replacement for the legendary Abramowitz
+        and Stegun's Handbook of Mathematical Functions, now scheduled to be completed
+        in 2007.
+      </p>
+<p>
+        M. Abramowitz and I. A. Stegun (Eds.) (1964) Handbook of Mathematical Functions
+        with Formulas, Graphs, and Mathematical Tables, National Bureau of Standards
+        Applied Mathematics Series, U.S. Government Printing Office, Washington,
+        D.C..
+      </p>
+<p>
+        The Wolfram Functions Site
+        The Wolfram Functions Site - Providing the mathematical and scientific community
+        with the world's largest (and most authorititive) collection of formulas
+        and graphics about mathematical functions.
+      </p>
+<p>
+        <a href="http://www.itl.nist.gov/div898/handbook/index.htm" target="_top">NIST/SEMATECH
+        e-Handbook of Statistical Methods</a>
+      </p>
+<p>
+        <a href="http://documents.wolfram.com/mathematica/Add-onsLinks/StandardPackages/Statistics/DiscreteDistributions.html" target="_top">Mathematica
+        Documentation: DiscreteDistributions</a> The Wolfram Research Documentation
+        Center is a collection of online reference materials about Mathematica, CalculationCenter,
+        and other Wolfram Research products.
+      </p>
+<p>
+        <a href="http://documents.wolfram.com/mathematica/Add-onsLinks/StandardPackages/Statistics/ContinuousDistributions.html" target="_top">Mathematica
+        Documentation: ContinuousDistributions</a> The Wolfram Research Documentation
+        Center is a collection of online reference materials about Mathematica, CalculationCenter,
+        and other Wolfram Research products.
+      </p>
+<p>
+        Statistical Distributions (Wiley Series in Probability &amp; Statistics)
+        (Paperback) by N.A.J. Hastings, Brian Peacock, Merran Evans, ISBN: 0471371246,
+        Wiley 2000.
+      </p>
+<p>
+        <a href="http://www.worldscibooks.com/mathematics/p191.html" target="_top">EXTREME VALUE
+        DISTRIBUTIONS, Theory and Applications</a> Samuel Kotz &amp; Saralees
+        Nadarajah, ISBN 978-1-86094-224-2 &amp; 1-86094-224-5 Oct 2000, Chapter 1.2
+        discusses the various extreme value distributions.
+      </p>
+<p>
+        <a href="http://bh0.physics.ubc.ca/People/matt/Doc/ThesesOthers/Phd/pugh.pdf" target="_top">pugh.pdf
+        (application/pdf Object)</a> Pugh Msc Thesis on the Lanczos approximation
+        to the gamma function.
+      </p>
+<p>
+        <a href="http://www.open-std.org/jtc1/sc22/wg21/docs/papers/2003" target="_top">N1514,
+        03-0097, A Proposal to Add Mathematical Special Functions to the C++ Standard
+        Library (version 2), Walter E. Brown</a>
+      </p>
+<a name="math_toolkit.backgrounders.refs.calculators__that_we_found__and_used_to_cross_check___as_far_as_their_widely_varying_accuracy_allowed__"></a><h5>
+<a name="id918865"></a>
+        <a class="link" href="refs.html#math_toolkit.backgrounders.refs.calculators__that_we_found__and_used_to_cross_check___as_far_as_their_widely_varying_accuracy_allowed__">Calculators*
+        that we found (and used to cross-check - as far as their widely-varying accuracy
+        allowed).</a>
+      </h5>
+<p>
+        http://www.adsciengineering.combpdcalc
+        Binomial Probability Distribution Calculator.
+      </p>
+<a name="math_toolkit.backgrounders.refs.other_libraries"></a><h5>
+<a name="id918912"></a>
+        <a class="link" href="refs.html#math_toolkit.backgrounders.refs.other_libraries">Other Libraries</a>
+      </h5>
+<p>
+        Cephes library by Shephen
+        Moshier and his book:
+      </p>
+<p>
+        Methods and programs for mathematical functions, Stephen L B Moshier, Ellis
+        Horwood (1989) ISBN 0745802893 0470216093 provided inspiration.
+      </p>
+<p>
+        100-decimal digit calculator
+        provided some spot values.
+      </p>
+<p>
+        <a href="http://www.csit.fsu.edu/~burkardt/cpp_src/dcdflib/dcdflib.html" target="_top">C++
+        version</a>.
+      </p>
+<p>
+        <a href="http://lib.stat.cmu.edu/general/cdflib" target="_top">CDFLIB Library of Fortran
+        Routines for Cumulative Distribution functions.</a>
+      </p>
+<p>
+        <a href="http://www.csit.fsu.edu/~burkardt/f_src/dcdflib/dcdflib.html" target="_top">DCDFLIB
+        C++ version</a> DCDFLIB is a library of C++ routines, using double precision
+        arithmetic, for evaluating cumulative probability density functions.
+      </p>
+<p>
+        http://www.softintegration.com/docs/packagechnagstat
+      </p>
+<p>
+        NAG libraries.
+      </p>
+<p>
+        MathCAD
+      </p>
+<p>
+        <a href="http://www.vni.com/products/imsl/jmsl/v30/api/com/imsl/stat/Cdf.html" target="_top">JMSL
+        Numerical Library</a> (Java).
+      </p>
+<p>
+        John F Hart, Computer Approximations, (1978) ISBN 0 088275 642-7.
+      </p>
+<p>
+        William J Cody, Software Manual for the Elementary Functions, Prentice-Hall
+        (1980) ISBN 0138220646.
+      </p>
+<p>
+        Nico Temme, Special Functions, An Introduction to the Classical Functions
+        of Mathematical Physics, Wiley, ISBN: 0471-11313-1 (1996) who also gave valueable
+        advice.
+      </p>
+<p>
+        <a href="http://www.cas.lancs.ac.uk/glossary_v1.1/prob.html#probdistn" target="_top">Statistics
+        Glossary</a>, Valerie Easton and John H. McColl.
+      </p>
+</div>
+<table xmlns:rev="http://www.cs.rpi.edu/~gregod/boost/tools/doc/revision" width="100%"><tr>
+<td align="left"></td>
+<td align="right"><div class="copyright-footer">Copyright © 2006 , 2007, 2008 John Maddock, Paul A. Bristow, Hubert
+      Holin, Xiaogang Zhang, Bruno Lalande and Gautam Sewani<p>
+        Distributed under the Boost Software License, Version 1.0. (See accompanying
+        file LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_0.txt)
+      </p>
+</div></td>
+</tr></table>
+<hr>
+<div class="spirit-nav">
+<a accesskey="p" href="remez.html"><img src="../../../../doc/html/images/prev.png" alt="Prev"></a><a accesskey="u" href="../backgrounders.html"><img src="../../../../doc/html/images/up.png" alt="Up"></a><a accesskey="h" href="../../index.html"><img src="../../../../doc/html/images/home.png" alt="Home"></a><a accesskey="n" href="../status.html"><img src="../../../../doc/html/images/next.png" alt="Next"></a>
+</div>
+</body>
+</html>

Added: sandbox/tools/auto_index/example/math/doc/sf_and_dist/html/math_toolkit/backgrounders/relative_error.html
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+++ sandbox/tools/auto_index/example/math/doc/sf_and_dist/html/math_toolkit/backgrounders/relative_error.html	2008-11-28 05:25:28 EST (Fri, 28 Nov 2008)
@@ -0,0 +1,124 @@
+<html>
+<head>
+<meta http-equiv="Content-Type" content="text/html; charset=ISO-8859-1">
+<title>Relative Error</title>
+<link rel="stylesheet" href="../../boostbook.css" type="text/css">
+<meta name="generator" content="DocBook XSL Stylesheets Vsnapshot_8125">
+<link rel="home" href="../../index.html" title="Math Toolkit">
+<link rel="up" href="../backgrounders.html" title="Backgrounders">
+<link rel="prev" href="implementation.html" title="Additional Implementation Notes">
+<link rel="next" href="lanczos.html" title="The Lanczos Approximation">
+</head>
+<body bgcolor="white" text="black" link="#0000FF" vlink="#840084" alink="#0000FF">
+<table cellpadding="2" width="100%"><tr>
+<td valign="top"><img alt="Boost C++ Libraries" width="277" height="86" src="../../../../boost.png"></td>
+<td align="center">Home</td>
+<td align="center">Libraries</td>
+<td align="center">People</td>
+<td align="center">FAQ</td>
+<td align="center">More</td>
+</tr></table>
+<hr>
+<div class="spirit-nav">
+<a accesskey="p" href="implementation.html"><img src="../../../../doc/html/images/prev.png" alt="Prev"></a><a accesskey="u" href="../backgrounders.html"><img src="../../../../doc/html/images/up.png" alt="Up"></a><a accesskey="h" href="../../index.html"><img src="../../../../doc/html/images/home.png" alt="Home"></a><a accesskey="n" href="lanczos.html"><img src="../../../../doc/html/images/next.png" alt="Next"></a>
+</div>
+<div class="section" lang="en">
+<div class="titlepage"><div><div><h3 class="title">
+<a name="math_toolkit.backgrounders.relative_error"></a><a class="link" href="relative_error.html" title="Relative Error"> Relative
+      Error</a>
+</h3></div></div></div>
+<p>
+        Given an actual value <span class="emphasis"><em>a</em></span> and a found value <span class="emphasis"><em>v</em></span>
+        the relative error can be calculated from:
+      </p>
+<p>
+        <span class="inlinemediaobject"><img src="../../../equations/error2.png"></span>
+      </p>
+<p>
+        However the test programs in the library use the symmetrical form:
+      </p>
+<p>
+        <span class="inlinemediaobject"><img src="../../../equations/error1.png"></span>
+      </p>
+<p>
+        which measures <span class="emphasis"><em>relative difference</em></span> and happens to be
+        less error prone in use since we don't have to worry which value is the "true"
+        result, and which is the experimental one. It guarantees to return a value
+        at least as large as the relative error.
+      </p>
+<p>
+        Special care needs to be taken when one value is zero: we could either take
+        the absolute error in this case (but that's cheating as the absolute error
+        is likely to be very small), or we could assign a value of either 1 or infinity
+        to the relative error in this special case. In the test cases for the special
+        functions in this library, everything below a threshold is regarded as "effectively
+        zero", otherwise the relative error is assigned the value of 1 if only
+        one of the terms is zero. The threshold is currently set at <code class="computeroutput"><span class="identifier">std</span><span class="special">::</span><span class="identifier">numeric_limits</span><span class="special">&lt;&gt;::</span><span class="identifier">min</span><span class="special">()</span></code>: in other words all denormalised numbers
+        are regarded as a zero.
+      </p>
+<p>
+        All the test programs calculate <span class="emphasis"><em>quantized relative error</em></span>,
+        whereas the graphs in this manual are produced with the <span class="emphasis"><em>actual
+        error</em></span>. The difference is as follows: in the test programs, the
+        test data is rounded to the target real type under test when the program
+        is compiled, so the error observed will then be a whole number of <span class="emphasis"><em>units
+        in the last place</em></span> either rounded up from the actual error, or
+        rounded down (possibly to zero). In contrast the <span class="emphasis"><em>true error</em></span>
+        is obtained by extending the precision of the calculated value, and then
+        comparing to the actual value: in this case the calculated error may be some
+        fraction of <span class="emphasis"><em>units in the last place</em></span>.
+      </p>
+<p>
+        Note that throughout this manual and the test programs the relative error
+        is usually quoted in units of epsilon. However, remember that <span class="emphasis"><em>units
+        in the last place</em></span> more accurately reflect the number of contaminated
+        digits, and that relative error can <span class="emphasis"><em>"wobble"</em></span>
+        by a factor of 2 compared to <span class="emphasis"><em>units in the last place</em></span>.
+        In other words: two implementations of the same function, whose maximum relative
+        errors differ by a factor of 2, can actually be accurate to the same number
+        of binary digits. You have been warned!
+      </p>
+<a name="zero_error"></a><p>
+      </p>
+<a name="math_toolkit.backgrounders.relative_error.the_impossibility_of_zero_error"></a><h5>
+<a name="id915339"></a>
+        <a class="link" href="relative_error.html#math_toolkit.backgrounders.relative_error.the_impossibility_of_zero_error">The
+        Impossibility of Zero Error</a>
+      </h5>
+<p>
+        For many of the functions in this library, it is assumed that the error is
+        "effectively zero" if the computation can be done with a number
+        of guard digits. However it should be remembered that if the result is a
+        <span class="emphasis"><em>transcendental number</em></span> then as a point of principle we
+        can never be sure that the result is accurate to more than 1 ulp. This is
+        an example of <span class="emphasis"><em>the table makers dilemma</em></span>: consider what
+        happens if the first guard digit is a one, and the remaining guard digits
+        are all zero. Do we have a tie or not? Since the only thing we can tell about
+        a transcendental number is that its digits have no particular pattern, we
+        can never tell if we have a tie, no matter how many guard digits we have.
+        Therefore, we can never be completely sure that the result has been rounded
+        in the right direction. Of course, transcendental numbers that just happen
+        to be a tie - for however many guard digits we have - are extremely rare,
+        and get rarer the more guard digits we have, but even so....
+      </p>
+<p>
+        Refer to the classic text <a href="http://docs.sun.com/source/806-3568/ncg_goldberg.html" target="_top">What
+        Every Computer Scientist Should Know About Floating-Point Arithmetic</a>
+        for more information.
+      </p>
+</div>
+<table xmlns:rev="http://www.cs.rpi.edu/~gregod/boost/tools/doc/revision" width="100%"><tr>
+<td align="left"></td>
+<td align="right"><div class="copyright-footer">Copyright © 2006 , 2007, 2008 John Maddock, Paul A. Bristow, Hubert
+      Holin, Xiaogang Zhang, Bruno Lalande and Gautam Sewani<p>
+        Distributed under the Boost Software License, Version 1.0. (See accompanying
+        file LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_0.txt)
+      </p>
+</div></td>
+</tr></table>
+<hr>
+<div class="spirit-nav">
+<a accesskey="p" href="implementation.html"><img src="../../../../doc/html/images/prev.png" alt="Prev"></a><a accesskey="u" href="../backgrounders.html"><img src="../../../../doc/html/images/up.png" alt="Up"></a><a accesskey="h" href="../../index.html"><img src="../../../../doc/html/images/home.png" alt="Home"></a><a accesskey="n" href="lanczos.html"><img src="../../../../doc/html/images/next.png" alt="Next"></a>
+</div>
+</body>
+</html>

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+<div class="titlepage"><div><div><h3 class="title">
+<a name="math_toolkit.backgrounders.remez"></a><a class="link" href="remez.html" title="The Remez Method"> The Remez Method</a>
+</h3></div></div></div>
+<p>
+        The Remez algorithm
+        is a methodology for locating the minimax rational approximation to a function.
+        This short article gives a brief overview of the method, but it should not
+        be regarded as a thorough theoretical treatment, for that you should consult
+        your favorite textbook.
+      </p>
+<p>
+        Imagine that you want to approximate some function f(x) by way of a rational
+        function R(x), where R(x) may be either a polynomial P(x) or a ratio of two
+        polynomials P(x)/Q(x) (a rational function). Initially we'll concentrate
+        on the polynomial case, as it's by far the easier to deal with, later we'll
+        extend to the full rational function case.
+      </p>
+<p>
+        We want to find the "best" rational approximation, where "best"
+        is defined to be the approximation that has the least deviation from f(x).
+        We can measure the deviation by way of an error function:
+      </p>
+<p>
+        E<sub>abs</sub>(x) = f(x) - R(x)
+      </p>
+<p>
+        which is expressed in terms of absolute error, but we can equally use relative
+        error:
+      </p>
+<p>
+        E<sub>rel</sub>(x) = (f(x) - R(x)) / |f(x)|
+      </p>
+<p>
+        And indeed in general we can scale the error function in any way we want,
+        it makes no difference to the maths, although the two forms above cover almost
+        every practical case that you're likely to encounter.
+      </p>
+<p>
+        The minimax rational function R(x) is then defined to be the function that
+        yields the smallest maximal value of the error function. Chebyshev showed
+        that there is a unique minimax solution for R(x) that has the following properties:
+      </p>
+<div class="itemizedlist"><ul type="disc">
+<li>
+          If R(x) is a polynomial of degree N, then there are N+2 unknowns: the N+1
+          coefficients of the polynomial, and maximal value of the error function.
+        </li>
+<li>
+          The error function has N+1 roots, and N+2 extrema (minima and maxima).
+        </li>
+<li>
+          The extrema alternate in sign, and all have the same magnitude.
+        </li>
+</ul></div>
+<p>
+        That means that if we know the location of the extrema of the error function
+        then we can write N+2 simultaneous equations:
+      </p>
+<p>
+        R(x<sub>i</sub>) + (-1)<sup>i</sup>E = f(x<sub>i</sub>)
+      </p>
+<p>
+        where E is the maximal error term, and x<sub>i</sub> are the abscissa values of the N+2
+        extrema of the error function. It is then trivial to solve the simultaneous
+        equations to obtain the polynomial coefficients and the error term.
+      </p>
+<p>
+        <span class="emphasis"><em>Unfortunately we don't know where the extrema of the error function
+        are located!</em></span>
+      </p>
+<a name="math_toolkit.backgrounders.remez.the_remez_method"></a><h5>
+<a name="id917380"></a>
+        <a class="link" href="remez.html#math_toolkit.backgrounders.remez.the_remez_method">The Remez
+        Method</a>
+      </h5>
+<p>
+        The Remez method is an iterative technique which, given a broad range of
+        assumptions, will converge on the extrema of the error function, and therefore
+        the minimax solution.
+      </p>
+<p>
+        In the following discussion we'll use a concrete example to illustrate the
+        Remez method: an approximation to the function e<sup>x</sup> over the range [-1, 1].
+      </p>
+<p>
+        Before we can begin the Remez method, we must obtain an initial value for
+        the location of the extrema of the error function. We could "guess"
+        these, but a much closer first approximation can be obtained by first constructing
+        an interpolated polynomial approximation to f(x).
+      </p>
+<p>
+        In order to obtain the N+1 coefficients of the interpolated polynomial we
+        need N+1 points (x<sub>0</sub>...x<sub>N</sub>): with our interpolated form passing through each
+        of those points that yields N+1 simultaneous equations:
+      </p>
+<p>
+        f(x<sub>i</sub>) = P(x<sub>i</sub>) = c<sub>0</sub> + c<sub>1</sub>x<sub>i</sub> ... + c<sub>N</sub>x<sub>i</sub><sup>N</sup>
+      </p>
+<p>
+        Which can be solved for the coefficients c<sub>0</sub>...c<sub>N</sub> in P(x).
+      </p>
+<p>
+        Obviously this is not a minimax solution, indeed our only guarantee is that
+        f(x) and P(x) touch at N+1 locations, away from those points the error may
+        be arbitrarily large. However, we would clearly like this initial approximation
+        to be as close to f(x) as possible, and it turns out that using the zeros
+        of an orthogonal polynomial as the initial interpolation points is a good
+        choice. In our example we'll use the zeros of a Chebyshev polynomial as these
+        are particularly easy to calculate, interpolating for a polynomial of degree
+        4, and measuring <span class="emphasis"><em>relative error</em></span> we get the following
+        error function:
+      </p>
+<p>
+        <span class="inlinemediaobject"><img src="../../../graphs/remez-2.png" alt="remez-2"></span>
+      </p>
+<p>
+        Which has a peak relative error of 1.2x10<sup>-3</sup>.
+      </p>
+<p>
+        While this is a pretty good approximation already, judging by the shape of
+        the error function we can clearly do better. Before starting on the Remez
+        method propper, we have one more step to perform: locate all the extrema
+        of the error function, and store these locations as our initial <span class="emphasis"><em>Chebyshev
+        control points</em></span>.
+      </p>
+<div class="note"><table border="0" summary="Note">
+<tr>
+<td rowspan="2" align="center" valign="top" width="25"><img alt="[Note]" src="../../../../doc/html/images/note.png"></td>
+<th align="left">Note</th>
+</tr>
+<tr><td align="left" valign="top">
+<p>
+          In the simple case of a polynomial approximation, by interpolating through
+          the roots of a Chebyshev polynomial we have in fact created a <span class="emphasis"><em>Chebyshev
+          approximation</em></span> to the function: in terms of <span class="emphasis"><em>absolute
+          error</em></span> this is the best a priori choice for the interpolated
+          form we can achieve, and typically is very close to the minimax solution.
+        </p>
+<p>
+          However, if we want to optimise for <span class="emphasis"><em>relative error</em></span>,
+          or if the approximation is a rational function, then the initial Chebyshev
+          solution can be quite far from the ideal minimax solution.
+        </p>
+<p>
+          A more technical discussion of the theory involved can be found in this
+          <a href="http://math.fullerton.edu/mathews/n2003/ChebyshevPolyMod.html" target="_top">online
+          course</a>.
+        </p>
+</td></tr>
+</table></div>
+<a name="math_toolkit.backgrounders.remez.remez_step_1"></a><h5>
+<a name="id917619"></a>
+        <a class="link" href="remez.html#math_toolkit.backgrounders.remez.remez_step_1">Remez Step
+        1</a>
+      </h5>
+<p>
+        The first step in the Remez method, given our current set of N+2 Chebyshev
+        control points x<sub>i</sub>, is to solve the N+2 simultaneous equations:
+      </p>
+<p>
+        P(x<sub>i</sub>) + (-1)<sup>i</sup>E = f(x<sub>i</sub>)
+      </p>
+<p>
+        To obtain the error term E, and the coefficients of the polynomial P(x).
+      </p>
+<p>
+        This gives us a new approximation to f(x) that has the same error <span class="emphasis"><em>E</em></span>
+        at each of the control points, and whose error function <span class="emphasis"><em>alternates
+        in sign</em></span> at the control points. This is still not necessarily the
+        minimax solution though: since the control points may not be at the extrema
+        of the error function. After this first step here's what our approximation's
+        error function looks like:
+      </p>
+<p>
+        <span class="inlinemediaobject"><img src="../../../graphs/remez-3.png" alt="remez-3"></span>
+      </p>
+<p>
+        Clearly this is still not the minimax solution since the control points are
+        not located at the extrema, but the maximum relative error has now dropped
+        to 5.6x10<sup>-4</sup>.
+      </p>
+<a name="math_toolkit.backgrounders.remez.remez_step_2"></a><h5>
+<a name="id917731"></a>
+        <a class="link" href="remez.html#math_toolkit.backgrounders.remez.remez_step_2">Remez Step
+        2</a>
+      </h5>
+<p>
+        The second step is to locate the extrema of the new approximation, which
+        we do in two stages: first, since the error function changes sign at each
+        control point, we must have N+1 roots of the error function located between
+        each pair of N+2 control points. Once these roots are found by standard root
+        finding techniques, we know that N extrema are bracketed between each pair
+        of roots, plus two more between the endpoints of the range and the first
+        and last roots. The N+2 extrema can then be found using standard function
+        minimisation techniques.
+      </p>
+<p>
+        We now have a choice: multi-point exchange, or single point exchange.
+      </p>
+<p>
+        In single point exchange, we move the control point nearest to the largest
+        extrema to the absissa value of the extrema.
+      </p>
+<p>
+        In multi-point exchange we swap all the current control points, for the locations
+        of the extrema.
+      </p>
+<p>
+        In our example we perform multi-point exchange.
+      </p>
+<a name="math_toolkit.backgrounders.remez.iteration"></a><h5>
+<a name="id917802"></a>
+        <a class="link" href="remez.html#math_toolkit.backgrounders.remez.iteration">Iteration</a>
+      </h5>
+<p>
+        The Remez method then performs steps 1 and 2 above iteratively until the
+        control points are located at the extrema of the error function: this is
+        then the minimax solution.
+      </p>
+<p>
+        For our current example, two more iterations converges on a minimax solution
+        with a peak relative error of 5x10<sup>-4</sup> and an error function that looks like:
+      </p>
+<p>
+        <span class="inlinemediaobject"><img src="../../../graphs/remez-4.png" alt="remez-4"></span>
+      </p>
+<a name="math_toolkit.backgrounders.remez.rational_approximations"></a><h5>
+<a name="id917868"></a>
+        <a class="link" href="remez.html#math_toolkit.backgrounders.remez.rational_approximations">Rational
+        Approximations</a>
+      </h5>
+<p>
+        If we wish to extend the Remez method to a rational approximation of the
+        form
+      </p>
+<p>
+        f(x) = R(x) = P(x) / Q(x)
+      </p>
+<p>
+        where P(x) and Q(x) are polynomials, then we proceed as before, except that
+        now we have N+M+2 unknowns if P(x) is of order N and Q(x) is of order M.
+        This assumes that Q(x) is normalised so that it's leading coefficient is
+        1, giving N+M+1 polynomial coefficients in total, plus the error term E.
+      </p>
+<p>
+        The simultaneous equations to be solved are now:
+      </p>
+<p>
+        P(x<sub>i</sub>) / Q(x<sub>i</sub>) + (-1)<sup>i</sup>E = f(x<sub>i</sub>)
+      </p>
+<p>
+        Evaluated at the N+M+2 control points x<sub>i</sub>.
+      </p>
+<p>
+        Unfortunately these equations are non-linear in the error term E: we can
+        only solve them if we know E, and yet E is one of the unknowns!
+      </p>
+<p>
+        The method usually adopted to solve these equations is an iterative one:
+        we guess the value of E, solve the equations to obtain a new value for E
+        (as well as the polynomial coefficients), then use the new value of E as
+        the next guess. The method is repeated until E converges on a stable value.
+      </p>
+<p>
+        These complications extend the running time required for the development
+        of rational approximations quite considerably. It is often desirable to obtain
+        a rational rather than polynomial approximation none the less: rational approximations
+        will often match more difficult to approximate functions, to greater accuracy,
+        and with greater efficiency, than their polynomial alternatives. For example,
+        if we takes our previous example of an approximation to e<sup>x</sup>, we obtained 5x10<sup>-4</sup> accuracy
+        with an order 4 polynomial. If we move two of the unknowns into the denominator
+        to give a pair of order 2 polynomials, and re-minimise, then the peak relative
+        error drops to 8.7x10<sup>-5</sup>. That's a 5 fold increase in accuracy, for the same
+        number of terms overall.
+      </p>
+<a name="math_toolkit.backgrounders.remez.practical_considerations"></a><h5>
+<a name="id918027"></a>
+        <a class="link" href="remez.html#math_toolkit.backgrounders.remez.practical_considerations">Practical
+        Considerations</a>
+      </h5>
+<p>
+        Most treatises on approximation theory stop at this point. However, from
+        a practical point of view, most of the work involves finding the right approximating
+        form, and then persuading the Remez method to converge on a solution.
+      </p>
+<p>
+        So far we have used a direct approximation:
+      </p>
+<p>
+        f(x) = R(x)
+      </p>
+<p>
+        But this will converge to a useful approximation only if f(x) is smooth.
+        In addition round-off errors when evaluating the rational form mean that
+        this will never get closer than within a few epsilon of machine precision.
+        Therefore this form of direct approximation is often reserved for situations
+        where we want efficiency, rather than accuracy.
+      </p>
+<p>
+        The first step in improving the situation is generally to split f(x) into
+        a dominant part that we can compute accurately by another method, and a slowly
+        changing remainder which can be approximated by a rational approximation.
+        We might be tempted to write:
+      </p>
+<p>
+        f(x) = g(x) + R(x)
+      </p>
+<p>
+        where g(x) is the dominant part of f(x), but if f(x)/g(x) is approximately
+        constant over the interval of interest then:
+      </p>
+<p>
+        f(x) = g(x)(c + R(x))
+      </p>
+<p>
+        Will yield a much better solution: here <span class="emphasis"><em>c</em></span> is a constant
+        that is the approximate value of f(x)/g(x) and R(x) is typically tiny compared
+        to <span class="emphasis"><em>c</em></span>. In this situation if R(x) is optimised for absolute
+        error, then as long as its error is small compared to the constant <span class="emphasis"><em>c</em></span>,
+        that error will effectively get wiped out when R(x) is added to <span class="emphasis"><em>c</em></span>.
+      </p>
+<p>
+        The difficult part is obviously finding the right g(x) to extract from your
+        function: often the asymptotic behaviour of the function will give a clue,
+        so for example the function <a class="link" href="../special/sf_erf/error_function.html" title="Error Functions">erfc</a>
+        becomes proportional to e<sup>-x<sup>2</sup></sup>/x as x becomes large. Therefore using:
+      </p>
+<p>
+        erfc(z) = (C + R(x)) e<sup>-x<sup>2</sup></sup>/x
+      </p>
+<p>
+        as the approximating form seems like an obvious thing to try, and does indeed
+        yield a useful approximation.
+      </p>
+<p>
+        However, the difficulty then becomes one of converging the minimax solution.
+        Unfortunately, it is known that for some functions the Remez method can lead
+        to divergent behaviour, even when the initial starting approximation is quite
+        good. Furthermore, it is not uncommon for the solution obtained in the first
+        Remez step above to be a bad one: the equations to be solved are generally
+        "stiff", often very close to being singular, and assuming a solution
+        is found at all, round-off errors and a rapidly changing error function,
+        can lead to a situation where the error function does not in fact change
+        sign at each control point as required. If this occurs, it is fatal to the
+        Remez method. It is also possible to obtain solutions that are perfectly
+        valid mathematically, but which are quite useless computationally: either
+        because there is an unavoidable amount of roundoff error in the computation
+        of the rational function, or because the denominator has one or more roots
+        over the interval of the approximation. In the latter case while the approximation
+        may have the correct limiting value at the roots, the approximation is nonetheless
+        useless.
+      </p>
+<p>
+        Assuming that the approximation does not have any fatal errors, and that
+        the only issue is converging adequately on the minimax solution, the aim
+        is to get as close as possible to the minimax solution before beginning the
+        Remez method. Using the zeros of a Chebyshev polynomial for the initial interpolation
+        is a good start, but may not be ideal when dealing with relative errors and/or
+        rational (rather than polynomial) approximations. One approach is to skew
+        the initial interpolation points to one end: for example if we raise the
+        roots of the Chebyshev polynomial to a positive power greater than 1 then
+        the roots will be skewed towards the middle of the [-1,1] interval, while
+        a positive power less than one will skew them towards either end. More usefully,
+        if we initially rescale the points over [0,1] and then raise to a positive
+        power, we can skew them to the left or right. Returning to our example of
+        e<sup>x</sup> over [-1,1], the initial interpolated form was some way from the minimax
+        solution:
+      </p>
+<p>
+        <span class="inlinemediaobject"><img src="../../../graphs/remez-2.png" alt="remez-2"></span>
+      </p>
+<p>
+        However, if we first skew the interpolation points to the left (rescale them
+        to [0, 1], raise to the power 1.3, and then rescale back to [-1,1]) we reduce
+        the error from 1.3x10<sup>-3</sup>to 6x10<sup>-4</sup>:
+      </p>
+<p>
+        <span class="inlinemediaobject"><img src="../../../graphs/remez-5.png" alt="remez-5"></span>
+      </p>
+<p>
+        It's clearly still not ideal, but it is only a few percent away from our
+        desired minimax solution (5x10<sup>-4</sup>).
+      </p>
+<a name="math_toolkit.backgrounders.remez.remez_method_checklist"></a><h5>
+<a name="id918335"></a>
+        <a class="link" href="remez.html#math_toolkit.backgrounders.remez.remez_method_checklist">Remez
+        Method Checklist</a>
+      </h5>
+<p>
+        The following lists some of the things to check if the Remez method goes
+        wrong, it is by no means an exhaustive list, but is provided in the hopes
+        that it will prove useful.
+      </p>
+<div class="itemizedlist"><ul type="disc">
+<li>
+          Is the function smooth enough? Can it be better separated into a rapidly
+          changing part, and an asymptotic part?
+        </li>
+<li>
+          Does the function being approximated have any "blips" in it?
+          Check for problems as the function changes computation method, or if a
+          root, or an infinity has been divided out. The telltale sign is if there
+          is a narrow region where the Remez method will not converge.
+        </li>
+<li>
+          Check you have enough accuracy in your calculations: remember that the
+          Remez method works on the difference between the approximation and the
+          function being approximated: so you must have more digits of precision
+          available than the precision of the approximation being constructed. So
+          for example at double precision, you shouldn't expect to be able to get
+          better than a float precision approximation.
+        </li>
+<li>
+          Try skewing the initial interpolated approximation to minimise the error
+          before you begin the Remez steps.
+        </li>
+<li>
+          If the approximation won't converge or is ill-conditioned from one starting
+          location, try starting from a different location.
+        </li>
+<li>
+          If a rational function won't converge, one can minimise a polynomial (which
+          presents no problems), then rotate one term from the numerator to the denominator
+          and minimise again. In theory one can continue moving terms one at a time
+          from numerator to denominator, and then re-minimising, retaining the last
+          set of control points at each stage.
+        </li>
+<li>
+          Try using a smaller interval. It may also be possible to optimise over
+          one (small) interval, rescale the control points over a larger interval,
+          and then re-minimise.
+        </li>
+<li>
+          Keep absissa values small: use a change of variable to keep the abscissa
+          over, say [0, b], for some smallish value <span class="emphasis"><em>b</em></span>.
+        </li>
+</ul></div>
+<a name="math_toolkit.backgrounders.remez.references"></a><h5>
+<a name="id918471"></a>
+        <a class="link" href="remez.html#math_toolkit.backgrounders.remez.references">References</a>
+      </h5>
+<p>
+        The original references for the Remez Method and it's extension to rational
+        functions are unfortunately in Russian:
+      </p>
+<p>
+        Remez, E.Ya., <span class="emphasis"><em>Fundamentals of numerical methods for Chebyshev approximations</em></span>,
+        "Naukova Dumka", Kiev, 1969.
+      </p>
+<p>
+        Remez, E.Ya., Gavrilyuk, V.T., <span class="emphasis"><em>Computer development of certain
+        approaches to the approximate construction of solutions of Chebyshev problems
+        nonlinearly depending on parameters</em></span>, Ukr. Mat. Zh. 12 (1960),
+        324-338.
+      </p>
+<p>
+        Gavrilyuk, V.T., <span class="emphasis"><em>Generalization of the first polynomial algorithm
+        of E.Ya.Remez for the problem of constructing rational-fractional Chebyshev
+        approximations</em></span>, Ukr. Mat. Zh. 16 (1961), 575-585.
+      </p>
+<p>
+        Some English language sources include:
+      </p>
+<p>
+        Fraser, W., Hart, J.F., <span class="emphasis"><em>On the computation of rational approximations
+        to continuous functions</em></span>, Comm. of the ACM 5 (1962), 401-403, 414.
+      </p>
+<p>
+        Ralston, A., <span class="emphasis"><em>Rational Chebyshev approximation by Remes' algorithms</em></span>,
+        Numer.Math. 7 (1965), no. 4, 322-330.
+      </p>
+<p>
+        A. Ralston, <span class="emphasis"><em>Rational Chebyshev approximation, Mathematical Methods
+        for Digital Computers v. 2</em></span> (Ralston A., Wilf H., eds.), Wiley,
+        New York, 1967, pp. 264-284.
+      </p>
+<p>
+        Hart, J.F. e.a., <span class="emphasis"><em>Computer approximations</em></span>, Wiley, New
+        York a.o., 1968.
+      </p>
+<p>
+        Cody, W.J., Fraser, W., Hart, J.F., <span class="emphasis"><em>Rational Chebyshev approximation
+        using linear equations</em></span>, Numer.Math. 12 (1968), 242-251.
+      </p>
+<p>
+        Cody, W.J., <span class="emphasis"><em>A survey of practical rational and polynomial approximation
+        of functions</em></span>, SIAM Review 12 (1970), no. 3, 400-423.
+      </p>
+<p>
+        Barrar, R.B., Loeb, H.J., <span class="emphasis"><em>On the Remez algorithm for non-linear
+        families</em></span>, Numer.Math. 15 (1970), 382-391.
+      </p>
+<p>
+        Dunham, Ch.B., <span class="emphasis"><em>Convergence of the Fraser-Hart algorithm for rational
+        Chebyshev approximation</em></span>, Math. Comp. 29 (1975), no. 132, 1078-1082.
+      </p>
+<p>
+        G. L. Litvinov, <span class="emphasis"><em>Approximate construction of rational approximations
+        and the effect of error autocorrection</em></span>, Russian Journal of Mathematical
+        Physics, vol.1, No. 3, 1994.
+      </p>
+</div>
+<table xmlns:rev="http://www.cs.rpi.edu/~gregod/boost/tools/doc/revision" width="100%"><tr>
+<td align="left"></td>
+<td align="right"><div class="copyright-footer">Copyright © 2006 , 2007, 2008 John Maddock, Paul A. Bristow, Hubert
+      Holin, Xiaogang Zhang, Bruno Lalande and Gautam Sewani<p>
+        Distributed under the Boost Software License, Version 1.0. (See accompanying
+        file LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_0.txt)
+      </p>
+</div></td>
+</tr></table>
+<hr>
+<div class="spirit-nav">
+<a accesskey="p" href="lanczos.html"><img src="../../../../doc/html/images/prev.png" alt="Prev"></a><a accesskey="u" href="../backgrounders.html"><img src="../../../../doc/html/images/up.png" alt="Up"></a><a accesskey="h" href="../../index.html"><img src="../../../../doc/html/images/home.png" alt="Home"></a><a accesskey="n" href="refs.html"><img src="../../../../doc/html/images/next.png" alt="Next"></a>
+</div>
+</body>
+</html>

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==============================================================================
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+++ sandbox/tools/auto_index/example/math/doc/sf_and_dist/html/math_toolkit/dist.html	2008-11-28 05:25:28 EST (Fri, 28 Nov 2008)
@@ -0,0 +1,194 @@
+<html>
+<head>
+<meta http-equiv="Content-Type" content="text/html; charset=ISO-8859-1">
+<title>Statistical Distributions and Functions</title>
+<link rel="stylesheet" href="../boostbook.css" type="text/css">
+<meta name="generator" content="DocBook XSL Stylesheets Vsnapshot_8125">
+<link rel="home" href="../index.html" title="Math Toolkit">
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+<table cellpadding="2" width="100%"><tr>
+<td valign="top"><img alt="Boost C++ Libraries" width="277" height="86" src="../../../boost.png"></td>
+<td align="center">Home</td>
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+</div>
+<div class="section" lang="en">
+<div class="titlepage"><div><div><h2 class="title" style="clear: both">
+<a name="math_toolkit.dist"></a><a class="link" href="dist.html" title="Statistical Distributions and Functions"> Statistical Distributions and Functions</a>
+</h2></div></div></div>
+<div class="toc"><dl>
+<dt><span class="section"><a href="dist/stat_tut.html"> Statistical Distributions
+      Tutorial</a></span></dt>
+<dd><dl>
+<dt><span class="section"> Overview</span></dt>
+<dt><span class="section"> Worked Examples</span></dt>
+<dd><dl>
+<dt><span class="section"><a href="dist/stat_tut/weg/dist_construct_eg.html">
+          Distribution Construction Example</a></span></dt>
+<dt><span class="section"><a href="dist/stat_tut/weg/st_eg.html"> Student's
+          t Distribution Examples</a></span></dt>
+<dd><dl>
+<dt><span class="section"><a href="dist/stat_tut/weg/st_eg/tut_mean_intervals.html">
+            Calculating confidence intervals on the mean with the Students-t distribution</a></span></dt>
+<dt><span class="section"><a href="dist/stat_tut/weg/st_eg/tut_mean_test.html">
+            Testing a sample mean for difference from a "true" mean</a></span></dt>
+<dt><span class="section"><a href="dist/stat_tut/weg/st_eg/tut_mean_size.html">
+            Estimating how large a sample size would have to become in order to give
+            a significant Students-t test result with a single sample test</a></span></dt>
+<dt><span class="section"><a href="dist/stat_tut/weg/st_eg/two_sample_students_t.html">
+            Comparing the means of two samples with the Students-t test</a></span></dt>
+<dt><span class="section"><a href="dist/stat_tut/weg/st_eg/paired_st.html">
+            Comparing two paired samples with the Student's t distribution</a></span></dt>
+</dl></dd>
+<dt><span class="section"><a href="dist/stat_tut/weg/cs_eg.html"> Chi Squared
+          Distribution Examples</a></span></dt>
+<dd><dl>
+<dt><span class="section"><a href="dist/stat_tut/weg/cs_eg/chi_sq_intervals.html">
+            Confidence Intervals on the Standard Deviation</a></span></dt>
+<dt><span class="section"><a href="dist/stat_tut/weg/cs_eg/chi_sq_test.html">
+            Chi-Square Test for the Standard Deviation</a></span></dt>
+<dt><span class="section"><a href="dist/stat_tut/weg/cs_eg/chi_sq_size.html">
+            Estimating the Required Sample Sizes for a Chi-Square Test for the Standard
+            Deviation</a></span></dt>
+</dl></dd>
+<dt><span class="section"><a href="dist/stat_tut/weg/f_eg.html"> F Distribution
+          Examples</a></span></dt>
+<dt><span class="section"><a href="dist/stat_tut/weg/binom_eg.html"> Binomial
+          Distribution Examples</a></span></dt>
+<dd><dl>
+<dt><span class="section"><a href="dist/stat_tut/weg/binom_eg/binomial_coinflip_example.html">
+            Binomial Coin-Flipping Example</a></span></dt>
+<dt><span class="section"><a href="dist/stat_tut/weg/binom_eg/binomial_quiz_example.html">
+            Binomial Quiz Example</a></span></dt>
+<dt><span class="section"><a href="dist/stat_tut/weg/binom_eg/binom_conf.html">
+            Calculating Confidence Limits on the Frequency of Occurrence for a Binomial
+            Distribution</a></span></dt>
+<dt><span class="section"><a href="dist/stat_tut/weg/binom_eg/binom_size_eg.html">
+            Estimating Sample Sizes for a Binomial Distribution.</a></span></dt>
+</dl></dd>
+<dt><span class="section"><a href="dist/stat_tut/weg/neg_binom_eg.html"> Negative
+          Binomial Distribution Examples</a></span></dt>
+<dd><dl>
+<dt><span class="section"><a href="dist/stat_tut/weg/neg_binom_eg/neg_binom_conf.html">
+            Calculating Confidence Limits on the Frequency of Occurrence for the
+            Negative Binomial Distribution</a></span></dt>
+<dt><span class="section"><a href="dist/stat_tut/weg/neg_binom_eg/neg_binom_size_eg.html">
+            Estimating Sample Sizes for the Negative Binomial.</a></span></dt>
+<dt><span class="section"><a href="dist/stat_tut/weg/neg_binom_eg/negative_binomial_example1.html">
+            Negative Binomial Sales Quota Example.</a></span></dt>
+<dt><span class="section"><a href="dist/stat_tut/weg/neg_binom_eg/negative_binomial_example2.html">
+            Negative Binomial Table Printing Example.</a></span></dt>
+</dl></dd>
+<dt><span class="section"><a href="dist/stat_tut/weg/normal_example.html"> Normal
+          Distribution Examples</a></span></dt>
+<dd><dl><dt><span class="section"><a href="dist/stat_tut/weg/normal_example/normal_misc.html">
+            Some Miscellaneous Examples of the Normal (Gaussian) Distribution</a></span></dt></dl></dd>
+<dt><span class="section"><a href="dist/stat_tut/weg/nccs_eg.html"> Non Central
+          Chi Squared Example</a></span></dt>
+<dd><dl><dt><span class="section"><a href="dist/stat_tut/weg/nccs_eg/nccs_power_eg.html">
+            Tables of the power function of the &#967;<sup>2</sup> test.</a></span></dt></dl></dd>
+<dt><span class="section"><a href="dist/stat_tut/weg/error_eg.html"> Error Handling
+          Example</a></span></dt>
+<dt><span class="section"><a href="dist/stat_tut/weg/find_eg.html"> Find Location
+          and Scale Examples</a></span></dt>
+<dd><dl>
+<dt><span class="section"><a href="dist/stat_tut/weg/find_eg/find_location_eg.html">
+            Find Location (Mean) Example</a></span></dt>
+<dt><span class="section"><a href="dist/stat_tut/weg/find_eg/find_scale_eg.html">
+            Find Scale (Standard Deviation) Example</a></span></dt>
+<dt><span class="section"><a href="dist/stat_tut/weg/find_eg/find_mean_and_sd_eg.html">
+            Find mean and standard deviation example</a></span></dt>
+</dl></dd>
+<dt><span class="section"><a href="dist/stat_tut/weg/nag_library.html"> Comparison
+          with C, R, FORTRAN-style Free Functions</a></span></dt>
+</dl></dd>
+<dt><span class="section"><a href="dist/stat_tut/variates.html"> Random Variates
+        and Distribution Parameters</a></span></dt>
+<dt><span class="section"><a href="dist/stat_tut/dist_params.html"> Discrete Probability
+        Distributions</a></span></dt>
+</dl></dd>
+<dt><span class="section"><a href="dist/dist_ref.html"> Statistical Distributions
+      Reference</a></span></dt>
+<dd><dl>
+<dt><span class="section"> Non-Member Properties</span></dt>
+<dt><span class="section"> Distributions</span></dt>
+<dd><dl>
+<dt><span class="section"><a href="dist/dist_ref/dists/bernoulli_dist.html">
+          Bernoulli Distribution</a></span></dt>
+<dt><span class="section"><a href="dist/dist_ref/dists/beta_dist.html"> Beta
+          Distribution</a></span></dt>
+<dt><span class="section"><a href="dist/dist_ref/dists/binomial_dist.html">
+          Binomial Distribution</a></span></dt>
+<dt><span class="section"><a href="dist/dist_ref/dists/cauchy_dist.html"> Cauchy-Lorentz
+          Distribution</a></span></dt>
+<dt><span class="section"><a href="dist/dist_ref/dists/chi_squared_dist.html">
+          Chi Squared Distribution</a></span></dt>
+<dt><span class="section"><a href="dist/dist_ref/dists/exp_dist.html"> Exponential
+          Distribution</a></span></dt>
+<dt><span class="section"><a href="dist/dist_ref/dists/extreme_dist.html"> Extreme
+          Value Distribution</a></span></dt>
+<dt><span class="section"> F Distribution</span></dt>
+<dt><span class="section"><a href="dist/dist_ref/dists/gamma_dist.html"> Gamma
+          (and Erlang) Distribution</a></span></dt>
+<dt><span class="section"><a href="dist/dist_ref/dists/logistic_dist.html">
+          Logistic Distribution</a></span></dt>
+<dt><span class="section"><a href="dist/dist_ref/dists/lognormal_dist.html">
+          Log Normal Distribution</a></span></dt>
+<dt><span class="section"><a href="dist/dist_ref/dists/negative_binomial_dist.html">
+          Negative Binomial Distribution</a></span></dt>
+<dt><span class="section"><a href="dist/dist_ref/dists/nc_beta_dist.html"> Noncentral
+          Beta Distribution</a></span></dt>
+<dt><span class="section"><a href="dist/dist_ref/dists/nc_chi_squared_dist.html">
+          Noncentral Chi-Squared Distribution</a></span></dt>
+<dt><span class="section"><a href="dist/dist_ref/dists/nc_f_dist.html"> Noncentral
+          F Distribution</a></span></dt>
+<dt><span class="section"><a href="dist/dist_ref/dists/nc_t_dist.html"> Noncentral
+          T Distribution</a></span></dt>
+<dt><span class="section"><a href="dist/dist_ref/dists/normal_dist.html"> Normal
+          (Gaussian) Distribution</a></span></dt>
+<dt><span class="section"><a href="dist/dist_ref/dists/pareto.html"> Pareto
+          Distribution</a></span></dt>
+<dt><span class="section"><a href="dist/dist_ref/dists/poisson_dist.html"> Poisson
+          Distribution</a></span></dt>
+<dt><span class="section"><a href="dist/dist_ref/dists/rayleigh.html"> Rayleigh
+          Distribution</a></span></dt>
+<dt><span class="section"><a href="dist/dist_ref/dists/students_t_dist.html">
+          Students t Distribution</a></span></dt>
+<dt><span class="section"><a href="dist/dist_ref/dists/triangular_dist.html">
+          Triangular Distribution</a></span></dt>
+<dt><span class="section"><a href="dist/dist_ref/dists/weibull.html"> Weibull
+          Distribution</a></span></dt>
+<dt><span class="section"><a href="dist/dist_ref/dists/uniform_dist.html"> Uniform
+          Distribution</a></span></dt>
+</dl></dd>
+<dt><span class="section"><a href="dist/dist_ref/dist_algorithms.html"> Distribution
+        Algorithms</a></span></dt>
+</dl></dd>
+<dt><span class="section"> Extras/Future Directions</span></dt>
+</dl></div>
+</div>
+<table xmlns:rev="http://www.cs.rpi.edu/~gregod/boost/tools/doc/revision" width="100%"><tr>
+<td align="left"></td>
+<td align="right"><div class="copyright-footer">Copyright © 2006 , 2007, 2008 John Maddock, Paul A. Bristow, Hubert
+      Holin, Xiaogang Zhang, Bruno Lalande and Gautam Sewani<p>
+        Distributed under the Boost Software License, Version 1.0. (See accompanying
+        file LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_0.txt)
+      </p>
+</div></td>
+</tr></table>
+<hr>
+<div class="spirit-nav">
+<a accesskey="p" href="main_overview/contact.html"><img src="../../../doc/html/images/prev.png" alt="Prev"></a><a accesskey="u" href="../index.html"><img src="../../../doc/html/images/up.png" alt="Up"></a><a accesskey="h" href="../index.html"><img src="../../../doc/html/images/home.png" alt="Home"></a><a accesskey="n" href="dist/stat_tut.html"><img src="../../../doc/html/images/next.png" alt="Next"></a>
+</div>
+</body>
+</html>

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--- (empty file)
+++ sandbox/tools/auto_index/example/math/doc/sf_and_dist/html/math_toolkit/dist/dist_ref.html	2008-11-28 05:25:28 EST (Fri, 28 Nov 2008)
@@ -0,0 +1,100 @@
+<html>
+<head>
+<meta http-equiv="Content-Type" content="text/html; charset=ISO-8859-1">
+<title>Statistical Distributions Reference</title>
+<link rel="stylesheet" href="../../boostbook.css" type="text/css">
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+<link rel="prev" href="stat_tut/dist_params.html" title="Discrete Probability Distributions">
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+<table cellpadding="2" width="100%"><tr>
+<td valign="top"><img alt="Boost C++ Libraries" width="277" height="86" src="../../../../boost.png"></td>
+<td align="center">Home</td>
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+</div>
+<div class="section" lang="en">
+<div class="titlepage"><div><div><h3 class="title">
+<a name="math_toolkit.dist.dist_ref"></a><a class="link" href="dist_ref.html" title="Statistical Distributions Reference"> Statistical Distributions
+      Reference</a>
+</h3></div></div></div>
+<div class="toc"><dl>
+<dt><span class="section"> Non-Member Properties</span></dt>
+<dt><span class="section"> Distributions</span></dt>
+<dd><dl>
+<dt><span class="section"><a href="dist_ref/dists/bernoulli_dist.html">
+          Bernoulli Distribution</a></span></dt>
+<dt><span class="section"><a href="dist_ref/dists/beta_dist.html"> Beta
+          Distribution</a></span></dt>
+<dt><span class="section"><a href="dist_ref/dists/binomial_dist.html">
+          Binomial Distribution</a></span></dt>
+<dt><span class="section"><a href="dist_ref/dists/cauchy_dist.html"> Cauchy-Lorentz
+          Distribution</a></span></dt>
+<dt><span class="section"><a href="dist_ref/dists/chi_squared_dist.html">
+          Chi Squared Distribution</a></span></dt>
+<dt><span class="section"><a href="dist_ref/dists/exp_dist.html"> Exponential
+          Distribution</a></span></dt>
+<dt><span class="section"><a href="dist_ref/dists/extreme_dist.html"> Extreme
+          Value Distribution</a></span></dt>
+<dt><span class="section"> F Distribution</span></dt>
+<dt><span class="section"><a href="dist_ref/dists/gamma_dist.html"> Gamma
+          (and Erlang) Distribution</a></span></dt>
+<dt><span class="section"><a href="dist_ref/dists/logistic_dist.html">
+          Logistic Distribution</a></span></dt>
+<dt><span class="section"><a href="dist_ref/dists/lognormal_dist.html">
+          Log Normal Distribution</a></span></dt>
+<dt><span class="section"><a href="dist_ref/dists/negative_binomial_dist.html">
+          Negative Binomial Distribution</a></span></dt>
+<dt><span class="section"><a href="dist_ref/dists/nc_beta_dist.html"> Noncentral
+          Beta Distribution</a></span></dt>
+<dt><span class="section"><a href="dist_ref/dists/nc_chi_squared_dist.html">
+          Noncentral Chi-Squared Distribution</a></span></dt>
+<dt><span class="section"><a href="dist_ref/dists/nc_f_dist.html"> Noncentral
+          F Distribution</a></span></dt>
+<dt><span class="section"><a href="dist_ref/dists/nc_t_dist.html"> Noncentral
+          T Distribution</a></span></dt>
+<dt><span class="section"><a href="dist_ref/dists/normal_dist.html"> Normal
+          (Gaussian) Distribution</a></span></dt>
+<dt><span class="section"><a href="dist_ref/dists/pareto.html"> Pareto
+          Distribution</a></span></dt>
+<dt><span class="section"><a href="dist_ref/dists/poisson_dist.html"> Poisson
+          Distribution</a></span></dt>
+<dt><span class="section"><a href="dist_ref/dists/rayleigh.html"> Rayleigh
+          Distribution</a></span></dt>
+<dt><span class="section"><a href="dist_ref/dists/students_t_dist.html">
+          Students t Distribution</a></span></dt>
+<dt><span class="section"><a href="dist_ref/dists/triangular_dist.html">
+          Triangular Distribution</a></span></dt>
+<dt><span class="section"><a href="dist_ref/dists/weibull.html"> Weibull
+          Distribution</a></span></dt>
+<dt><span class="section"><a href="dist_ref/dists/uniform_dist.html"> Uniform
+          Distribution</a></span></dt>
+</dl></dd>
+<dt><span class="section"><a href="dist_ref/dist_algorithms.html"> Distribution
+        Algorithms</a></span></dt>
+</dl></div>
+</div>
+<table xmlns:rev="http://www.cs.rpi.edu/~gregod/boost/tools/doc/revision" width="100%"><tr>
+<td align="left"></td>
+<td align="right"><div class="copyright-footer">Copyright © 2006 , 2007, 2008 John Maddock, Paul A. Bristow, Hubert
+      Holin, Xiaogang Zhang, Bruno Lalande and Gautam Sewani<p>
+        Distributed under the Boost Software License, Version 1.0. (See accompanying
+        file LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_0.txt)
+      </p>
+</div></td>
+</tr></table>
+<hr>
+<div class="spirit-nav">
+<a accesskey="p" href="stat_tut/dist_params.html"><img src="../../../../doc/html/images/prev.png" alt="Prev"></a><a accesskey="u" href="../dist.html"><img src="../../../../doc/html/images/up.png" alt="Up"></a><a accesskey="h" href="../../index.html"><img src="../../../../doc/html/images/home.png" alt="Home"></a><a accesskey="n" href="dist_ref/nmp.html"><img src="../../../../doc/html/images/next.png" alt="Next"></a>
+</div>
+</body>
+</html>

Added: sandbox/tools/auto_index/example/math/doc/sf_and_dist/html/math_toolkit/dist/dist_ref/dist_algorithms.html
==============================================================================
--- (empty file)
+++ sandbox/tools/auto_index/example/math/doc/sf_and_dist/html/math_toolkit/dist/dist_ref/dist_algorithms.html	2008-11-28 05:25:28 EST (Fri, 28 Nov 2008)
@@ -0,0 +1,145 @@
+<html>
+<head>
+<meta http-equiv="Content-Type" content="text/html; charset=ISO-8859-1">
+<title>Distribution Algorithms</title>
+<link rel="stylesheet" href="../../../boostbook.css" type="text/css">
+<meta name="generator" content="DocBook XSL Stylesheets Vsnapshot_8125">
+<link rel="home" href="../../../index.html" title="Math Toolkit">
+<link rel="up" href="../dist_ref.html" title="Statistical Distributions Reference">
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+<body bgcolor="white" text="black" link="#0000FF" vlink="#840084" alink="#0000FF">
+<table cellpadding="2" width="100%"><tr>
+<td valign="top"><img alt="Boost C++ Libraries" width="277" height="86" src="../../../../../boost.png"></td>
+<td align="center">Home</td>
+<td align="center">Libraries</td>
+<td align="center">People</td>
+<td align="center">FAQ</td>
+<td align="center">More</td>
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+<hr>
+<div class="spirit-nav">
+<a accesskey="p" href="dists/uniform_dist.html"><img src="../../../../../doc/html/images/prev.png" alt="Prev"></a><a accesskey="u" href="../dist_ref.html"><img src="../../../../../doc/html/images/up.png" alt="Up"></a><a accesskey="h" href="../../../index.html"><img src="../../../../../doc/html/images/home.png" alt="Home"></a><a accesskey="n" href="../future.html"><img src="../../../../../doc/html/images/next.png" alt="Next"></a>
+</div>
+<div class="section" lang="en">
+<div class="titlepage"><div><div><h4 class="title">
+<a name="math_toolkit.dist.dist_ref.dist_algorithms"></a><a class="link" href="dist_algorithms.html" title="Distribution Algorithms"> Distribution
+        Algorithms</a>
+</h4></div></div></div>
+<a name="math_toolkit.dist.dist_ref.dist_algorithms.finding_the_location_and_scale_for_normal_and_similar_distributions"></a><h5>
+<a name="id695646"></a>
+          <a class="link" href="dist_algorithms.html#math_toolkit.dist.dist_ref.dist_algorithms.finding_the_location_and_scale_for_normal_and_similar_distributions">Finding
+          the Location and Scale for Normal and similar distributions</a>
+        </h5>
+<p>
+          Two functions aid finding location and scale of random variable z to give
+          probability p (given a scale or location). Only applies to distributions
+          like normal, lognormal, extreme value, Cauchy, (and symmetrical triangular),
+          that have scale and location properties.
+        </p>
+<p>
+          These functions are useful to predict the mean and/or standard deviation
+          that will be needed to meet a specified minimum weight or maximum dose.
+        </p>
+<p>
+          Complement versions are also provided, both with explicit and implicit
+          (default) policy.
+        </p>
+<pre class="programlisting"><span class="keyword">using</span> <span class="identifier">boost</span><span class="special">::</span><span class="identifier">math</span><span class="special">::</span><span class="identifier">policies</span><span class="special">::</span><span class="identifier">policy</span><span class="special">;</span> <span class="comment">// May be needed by users defining their own policies.
+</span><span class="keyword">using</span> <span class="identifier">boost</span><span class="special">::</span><span class="identifier">math</span><span class="special">::</span><span class="identifier">complement</span><span class="special">;</span> <span class="comment">// Will be needed by users who want to use complements.
+</span></pre>
+<a name="math_toolkit.dist.dist_ref.dist_algorithms.find_location_function"></a><h5>
+<a name="id695809"></a>
+          <a class="link" href="dist_algorithms.html#math_toolkit.dist.dist_ref.dist_algorithms.find_location_function">find_location
+          function</a>
+        </h5>
+<p>
+          
+</p>
+<pre class="programlisting"><span class="preprocessor">#include</span> <span class="special">&lt;</span><span class="identifier">boost</span><span class="special">/</span><span class="identifier">math</span><span class="special">/</span><span class="identifier">distributions</span><span class="special">/</span><span class="identifier">find_location</span><span class="special">.</span><span class="identifier">hpp</span><span class="special">&gt;</span></pre>
+<p>
+        </p>
+<pre class="programlisting"><span class="keyword">namespace</span> <span class="identifier">boost</span><span class="special">{</span> <span class="keyword">namespace</span> <span class="identifier">math</span><span class="special">{</span>
+
+<span class="keyword">template</span> <span class="special">&lt;</span><span class="keyword">class</span> <span class="identifier">Dist</span><span class="special">,</span> <span class="keyword">class</span> <a class="link" href="../../policy.html" title="Policies">Policy</a><span class="special">&gt;</span> <span class="comment">// explicit error handling policy
+</span>  <span class="keyword">typename</span> <span class="identifier">Dist</span><span class="special">::</span><span class="identifier">value_type</span> <span class="identifier">find_location</span><span class="special">(</span> <span class="comment">// For example, normal mean.
+</span>  <span class="keyword">typename</span> <span class="identifier">Dist</span><span class="special">::</span><span class="identifier">value_type</span> <span class="identifier">z</span><span class="special">,</span> <span class="comment">// location of random variable z to give probability, P(X &gt; z) == p.
+</span>  <span class="comment">// For example, a nominal minimum acceptable z, so that p * 100 % are &gt; z
+</span>  <span class="keyword">typename</span> <span class="identifier">Dist</span><span class="special">::</span><span class="identifier">value_type</span> <span class="identifier">p</span><span class="special">,</span> <span class="comment">// probability value desired at x, say 0.95 for 95% &gt; z.
+</span>  <span class="keyword">typename</span> <span class="identifier">Dist</span><span class="special">::</span><span class="identifier">value_type</span> <span class="identifier">scale</span><span class="special">,</span> <span class="comment">// scale parameter, for example, normal standard deviation.
+</span>  <span class="keyword">const</span> <a class="link" href="../../policy.html" title="Policies">Policy</a><span class="special">&amp;</span> <span class="identifier">pol</span><span class="special">);</span>
+
+<span class="keyword">template</span> <span class="special">&lt;</span><span class="keyword">class</span> <span class="identifier">Dist</span><span class="special">&gt;</span>  <span class="comment">// with default policy.
+</span>  <span class="keyword">typename</span> <span class="identifier">Dist</span><span class="special">::</span><span class="identifier">value_type</span> <span class="identifier">find_location</span><span class="special">(</span> <span class="comment">// For example, normal mean.
+</span>  <span class="keyword">typename</span> <span class="identifier">Dist</span><span class="special">::</span><span class="identifier">value_type</span> <span class="identifier">z</span><span class="special">,</span> <span class="comment">// location of random variable z to give probability, P(X &gt; z) == p.
+</span>  <span class="comment">// For example, a nominal minimum acceptable z, so that p * 100 % are &gt; z
+</span>  <span class="keyword">typename</span> <span class="identifier">Dist</span><span class="special">::</span><span class="identifier">value_type</span> <span class="identifier">p</span><span class="special">,</span> <span class="comment">// probability value desired at x, say 0.95 for 95% &gt; z.
+</span>  <span class="keyword">typename</span> <span class="identifier">Dist</span><span class="special">::</span><span class="identifier">value_type</span> <span class="identifier">scale</span><span class="special">);</span> <span class="comment">// scale parameter, for example, normal standard deviation.
+</span>
+  <span class="special">}}</span> <span class="comment">// namespaces
+</span></pre>
+<a name="math_toolkit.dist.dist_ref.dist_algorithms.find_scale_function"></a><h5>
+<a name="id696437"></a>
+          <a class="link" href="dist_algorithms.html#math_toolkit.dist.dist_ref.dist_algorithms.find_scale_function">find_scale
+          function</a>
+        </h5>
+<p>
+          
+</p>
+<pre class="programlisting"><span class="preprocessor">#include</span> <span class="special">&lt;</span><span class="identifier">boost</span><span class="special">/</span><span class="identifier">math</span><span class="special">/</span><span class="identifier">distributions</span><span class="special">/</span><span class="identifier">find_scale</span><span class="special">.</span><span class="identifier">hpp</span><span class="special">&gt;</span></pre>
+<p>
+        </p>
+<pre class="programlisting"><span class="keyword">namespace</span> <span class="identifier">boost</span><span class="special">{</span> <span class="keyword">namespace</span> <span class="identifier">math</span><span class="special">{</span> 
+
+<span class="keyword">template</span> <span class="special">&lt;</span><span class="keyword">class</span> <span class="identifier">Dist</span><span class="special">,</span> <span class="keyword">class</span> <a class="link" href="../../policy.html" title="Policies">Policy</a><span class="special">&gt;</span>
+  <span class="keyword">typename</span> <span class="identifier">Dist</span><span class="special">::</span><span class="identifier">value_type</span> <span class="identifier">find_scale</span><span class="special">(</span> <span class="comment">// For example, normal mean.
+</span>  <span class="keyword">typename</span> <span class="identifier">Dist</span><span class="special">::</span><span class="identifier">value_type</span> <span class="identifier">z</span><span class="special">,</span> <span class="comment">// location of random variable z to give probability, P(X &gt; z) == p.
+</span>  <span class="comment">// For example, a nominal minimum acceptable weight z, so that p * 100 % are &gt; z
+</span>  <span class="keyword">typename</span> <span class="identifier">Dist</span><span class="special">::</span><span class="identifier">value_type</span> <span class="identifier">p</span><span class="special">,</span> <span class="comment">// probability value desired at x, say 0.95 for 95% &gt; z.
+</span>  <span class="keyword">typename</span> <span class="identifier">Dist</span><span class="special">::</span><span class="identifier">value_type</span> <span class="identifier">location</span><span class="special">,</span> <span class="comment">// location parameter, for example, normal distribution mean.
+</span>  <span class="keyword">const</span> <a class="link" href="../../policy.html" title="Policies">Policy</a><span class="special">&amp;</span> <span class="identifier">pol</span><span class="special">);</span>
+
+ <span class="keyword">template</span> <span class="special">&lt;</span><span class="keyword">class</span> <span class="identifier">Dist</span><span class="special">&gt;</span> <span class="comment">// with default policy.
+</span>   <span class="keyword">typename</span> <span class="identifier">Dist</span><span class="special">::</span><span class="identifier">value_type</span> <span class="identifier">find_scale</span><span class="special">(</span> <span class="comment">// For example, normal mean.
+</span>   <span class="keyword">typename</span> <span class="identifier">Dist</span><span class="special">::</span><span class="identifier">value_type</span> <span class="identifier">z</span><span class="special">,</span> <span class="comment">// location of random variable z to give probability, P(X &gt; z) == p.
+</span>   <span class="comment">// For example, a nominal minimum acceptable z, so that p * 100 % are &gt; z
+</span>   <span class="keyword">typename</span> <span class="identifier">Dist</span><span class="special">::</span><span class="identifier">value_type</span> <span class="identifier">p</span><span class="special">,</span> <span class="comment">// probability value desired at x, say 0.95 for 95% &gt; z.
+</span>   <span class="keyword">typename</span> <span class="identifier">Dist</span><span class="special">::</span><span class="identifier">value_type</span> <span class="identifier">location</span><span class="special">)</span> <span class="comment">// location parameter, for example, normal distribution mean.
+</span><span class="special">}}</span> <span class="comment">// namespaces
+</span></pre>
+<p>
+          All argument must be finite, otherwise <a class="link" href="../../main_overview/error_handling.html#domain_error">domain_error</a>
+          is called.
+        </p>
+<p>
+          Probability arguments must be [0, 1], otherwise <a class="link" href="../../main_overview/error_handling.html#domain_error">domain_error</a>
+          is called.
+        </p>
+<p>
+          If the choice of arguments would give a negative scale, <a class="link" href="../../main_overview/error_handling.html#domain_error">domain_error</a>
+          is called, unless the policy is to ignore, when the negative (impossible)
+          value of scale is returned.
+        </p>
+<p>
+          <a class="link" href="../stat_tut/weg/find_eg.html" title="Find Location and Scale Examples">Find Mean and standard
+          deviation examples</a> gives simple examples of use of both find_scale
+          and find_location, and a longer example finding means and standard deviations
+          of normally distributed weights to meet a specification.
+        </p>
+</div>
+<table xmlns:rev="http://www.cs.rpi.edu/~gregod/boost/tools/doc/revision" width="100%"><tr>
+<td align="left"></td>
+<td align="right"><div class="copyright-footer">Copyright © 2006 , 2007, 2008 John Maddock, Paul A. Bristow, Hubert
+      Holin, Xiaogang Zhang, Bruno Lalande and Gautam Sewani<p>
+        Distributed under the Boost Software License, Version 1.0. (See accompanying
+        file LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_0.txt)
+      </p>
+</div></td>
+</tr></table>
+<hr>
+<div class="spirit-nav">
+<a accesskey="p" href="dists/uniform_dist.html"><img src="../../../../../doc/html/images/prev.png" alt="Prev"></a><a accesskey="u" href="../dist_ref.html"><img src="../../../../../doc/html/images/up.png" alt="Up"></a><a accesskey="h" href="../../../index.html"><img src="../../../../../doc/html/images/home.png" alt="Home"></a><a accesskey="n" href="../future.html"><img src="../../../../../doc/html/images/next.png" alt="Next"></a>
+</div>
+</body>
+</html>

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==============================================================================
--- (empty file)
+++ sandbox/tools/auto_index/example/math/doc/sf_and_dist/html/math_toolkit/dist/dist_ref/dists.html	2008-11-28 05:25:28 EST (Fri, 28 Nov 2008)
@@ -0,0 +1,93 @@
+<html>
+<head>
+<meta http-equiv="Content-Type" content="text/html; charset=ISO-8859-1">
+<title>Distributions</title>
+<link rel="stylesheet" href="../../../boostbook.css" type="text/css">
+<meta name="generator" content="DocBook XSL Stylesheets Vsnapshot_8125">
+<link rel="home" href="../../../index.html" title="Math Toolkit">
+<link rel="up" href="../dist_ref.html" title="Statistical Distributions Reference">
+<link rel="prev" href="nmp.html" title="Non-Member Properties">
+<link rel="next" href="dists/bernoulli_dist.html" title="Bernoulli Distribution">
+</head>
+<body bgcolor="white" text="black" link="#0000FF" vlink="#840084" alink="#0000FF">
+<table cellpadding="2" width="100%"><tr>
+<td valign="top"><img alt="Boost C++ Libraries" width="277" height="86" src="../../../../../boost.png"></td>
+<td align="center">Home</td>
+<td align="center">Libraries</td>
+<td align="center">People</td>
+<td align="center">FAQ</td>
+<td align="center">More</td>
+</tr></table>
+<hr>
+<div class="spirit-nav">
+<a accesskey="p" href="nmp.html"><img src="../../../../../doc/html/images/prev.png" alt="Prev"></a><a accesskey="u" href="../dist_ref.html"><img src="../../../../../doc/html/images/up.png" alt="Up"></a><a accesskey="h" href="../../../index.html"><img src="../../../../../doc/html/images/home.png" alt="Home"></a><a accesskey="n" href="dists/bernoulli_dist.html"><img src="../../../../../doc/html/images/next.png" alt="Next"></a>
+</div>
+<div class="section" lang="en">
+<div class="titlepage"><div><div><h4 class="title">
+<a name="math_toolkit.dist.dist_ref.dists"></a><a class="link" href="dists.html" title="Distributions"> Distributions</a>
+</h4></div></div></div>
+<div class="toc"><dl>
+<dt><span class="section"><a href="dists/bernoulli_dist.html">
+          Bernoulli Distribution</a></span></dt>
+<dt><span class="section"><a href="dists/beta_dist.html"> Beta
+          Distribution</a></span></dt>
+<dt><span class="section"><a href="dists/binomial_dist.html">
+          Binomial Distribution</a></span></dt>
+<dt><span class="section"><a href="dists/cauchy_dist.html"> Cauchy-Lorentz
+          Distribution</a></span></dt>
+<dt><span class="section"><a href="dists/chi_squared_dist.html">
+          Chi Squared Distribution</a></span></dt>
+<dt><span class="section"><a href="dists/exp_dist.html"> Exponential
+          Distribution</a></span></dt>
+<dt><span class="section"><a href="dists/extreme_dist.html"> Extreme
+          Value Distribution</a></span></dt>
+<dt><span class="section"> F Distribution</span></dt>
+<dt><span class="section"><a href="dists/gamma_dist.html"> Gamma
+          (and Erlang) Distribution</a></span></dt>
+<dt><span class="section"><a href="dists/logistic_dist.html">
+          Logistic Distribution</a></span></dt>
+<dt><span class="section"><a href="dists/lognormal_dist.html">
+          Log Normal Distribution</a></span></dt>
+<dt><span class="section"><a href="dists/negative_binomial_dist.html">
+          Negative Binomial Distribution</a></span></dt>
+<dt><span class="section"><a href="dists/nc_beta_dist.html"> Noncentral
+          Beta Distribution</a></span></dt>
+<dt><span class="section"><a href="dists/nc_chi_squared_dist.html">
+          Noncentral Chi-Squared Distribution</a></span></dt>
+<dt><span class="section"><a href="dists/nc_f_dist.html"> Noncentral
+          F Distribution</a></span></dt>
+<dt><span class="section"><a href="dists/nc_t_dist.html"> Noncentral
+          T Distribution</a></span></dt>
+<dt><span class="section"><a href="dists/normal_dist.html"> Normal
+          (Gaussian) Distribution</a></span></dt>
+<dt><span class="section"><a href="dists/pareto.html"> Pareto
+          Distribution</a></span></dt>
+<dt><span class="section"><a href="dists/poisson_dist.html"> Poisson
+          Distribution</a></span></dt>
+<dt><span class="section"><a href="dists/rayleigh.html"> Rayleigh
+          Distribution</a></span></dt>
+<dt><span class="section"><a href="dists/students_t_dist.html">
+          Students t Distribution</a></span></dt>
+<dt><span class="section"><a href="dists/triangular_dist.html">
+          Triangular Distribution</a></span></dt>
+<dt><span class="section"><a href="dists/weibull.html"> Weibull
+          Distribution</a></span></dt>
+<dt><span class="section"><a href="dists/uniform_dist.html"> Uniform
+          Distribution</a></span></dt>
+</dl></div>
+</div>
+<table xmlns:rev="http://www.cs.rpi.edu/~gregod/boost/tools/doc/revision" width="100%"><tr>
+<td align="left"></td>
+<td align="right"><div class="copyright-footer">Copyright © 2006 , 2007, 2008 John Maddock, Paul A. Bristow, Hubert
+      Holin, Xiaogang Zhang, Bruno Lalande and Gautam Sewani<p>
+        Distributed under the Boost Software License, Version 1.0. (See accompanying
+        file LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_0.txt)
+      </p>
+</div></td>
+</tr></table>
+<hr>
+<div class="spirit-nav">
+<a accesskey="p" href="nmp.html"><img src="../../../../../doc/html/images/prev.png" alt="Prev"></a><a accesskey="u" href="../dist_ref.html"><img src="../../../../../doc/html/images/up.png" alt="Up"></a><a accesskey="h" href="../../../index.html"><img src="../../../../../doc/html/images/home.png" alt="Home"></a><a accesskey="n" href="dists/bernoulli_dist.html"><img src="../../../../../doc/html/images/next.png" alt="Next"></a>
+</div>
+</body>
+</html>

Added: sandbox/tools/auto_index/example/math/doc/sf_and_dist/html/math_toolkit/dist/dist_ref/dists/bernoulli_dist.html
==============================================================================
--- (empty file)
+++ sandbox/tools/auto_index/example/math/doc/sf_and_dist/html/math_toolkit/dist/dist_ref/dists/bernoulli_dist.html	2008-11-28 05:25:28 EST (Fri, 28 Nov 2008)
@@ -0,0 +1,354 @@
+<html>
+<head>
+<meta http-equiv="Content-Type" content="text/html; charset=ISO-8859-1">
+<title>Bernoulli Distribution</title>
+<link rel="stylesheet" href="../../../../boostbook.css" type="text/css">
+<meta name="generator" content="DocBook XSL Stylesheets Vsnapshot_8125">
+<link rel="home" href="../../../../index.html" title="Math Toolkit">
+<link rel="up" href="../dists.html" title="Distributions">
+<link rel="prev" href="../dists.html" title="Distributions">
+<link rel="next" href="beta_dist.html" title="Beta Distribution">
+</head>
+<body bgcolor="white" text="black" link="#0000FF" vlink="#840084" alink="#0000FF">
+<table cellpadding="2" width="100%"><tr>
+<td valign="top"><img alt="Boost C++ Libraries" width="277" height="86" src="../../../../../../boost.png"></td>
+<td align="center">Home</td>
+<td align="center">Libraries</td>
+<td align="center">People</td>
+<td align="center">FAQ</td>
+<td align="center">More</td>
+</tr></table>
+<hr>
+<div class="spirit-nav">
+<a accesskey="p" href="../dists.html"><img src="../../../../../../doc/html/images/prev.png" alt="Prev"></a><a accesskey="u" href="../dists.html"><img src="../../../../../../doc/html/images/up.png" alt="Up"></a><a accesskey="h" href="../../../../index.html"><img src="../../../../../../doc/html/images/home.png" alt="Home"></a><a accesskey="n" href="beta_dist.html"><img src="../../../../../../doc/html/images/next.png" alt="Next"></a>
+</div>
+<div class="section" lang="en">
+<div class="titlepage"><div><div><h5 class="title">
+<a name="math_toolkit.dist.dist_ref.dists.bernoulli_dist"></a><a class="link" href="bernoulli_dist.html" title="Bernoulli Distribution">
+          Bernoulli Distribution</a>
+</h5></div></div></div>
+<p>
+            
+</p>
+<pre class="programlisting"><span class="preprocessor">#include</span> <span class="special">&lt;</span><span class="identifier">boost</span><span class="special">/</span><span class="identifier">math</span><span class="special">/</span><span class="identifier">distributions</span><span class="special">/</span><span class="identifier">bernoulli</span><span class="special">.</span><span class="identifier">hpp</span><span class="special">&gt;</span></pre>
+<p>
+          </p>
+<pre class="programlisting"><span class="keyword">namespace</span> <span class="identifier">boost</span><span class="special">{</span> <span class="keyword">namespace</span> <span class="identifier">math</span><span class="special">{</span>
+ <span class="keyword">template</span> <span class="special">&lt;</span><span class="keyword">class</span> <span class="identifier">RealType</span> <span class="special">=</span> <span class="keyword">double</span><span class="special">,</span> 
+           <span class="keyword">class</span> <a class="link" href="../../../policy.html" title="Policies">Policy</a>   <span class="special">=</span> <a class="link" href="../../../policy/pol_ref/pol_ref_ref.html" title="Policy Class Reference">policies::policy&lt;&gt;</a> <span class="special">&gt;</span>
+ <span class="keyword">class</span> <span class="identifier">bernoulli_distribution</span><span class="special">;</span>
+   
+ <span class="keyword">typedef</span> <span class="identifier">bernoulli_distribution</span><span class="special">&lt;&gt;</span> <span class="identifier">bernoulli</span><span class="special">;</span>
+
+ <span class="keyword">template</span> <span class="special">&lt;</span><span class="keyword">class</span> <span class="identifier">RealType</span><span class="special">,</span> <span class="keyword">class</span> <a class="link" href="../../../policy.html" title="Policies">Policy</a><span class="special">&gt;</span>
+ <span class="keyword">class</span> <span class="identifier">bernoulli_distribution</span>
+ <span class="special">{</span>
+ <span class="keyword">public</span><span class="special">:</span>
+    <span class="keyword">typedef</span> <span class="identifier">RealType</span>  <span class="identifier">value_type</span><span class="special">;</span>
+    <span class="keyword">typedef</span> <span class="identifier">Policy</span>    <span class="identifier">policy_type</span><span class="special">;</span>
+
+    <span class="identifier">bernoulli_distribution</span><span class="special">(</span><span class="identifier">RealType</span> <span class="identifier">p</span><span class="special">);</span> <span class="comment">// Constructor.
+</span>    <span class="comment">// Accessor function.
+</span>    <span class="identifier">RealType</span> <span class="identifier">success_fraction</span><span class="special">()</span> <span class="keyword">const</span>
+    <span class="comment">// Probability of success (as a fraction).
+</span> <span class="special">};</span> 
+<span class="special">}}</span> <span class="comment">// namespaces
+</span></pre>
+<p>
+            The Bernoulli distribution is a discrete distribution of the outcome
+            of a single trial with only two results, 0 (failure) or 1 (success),
+            with a probability of success p.
+          </p>
+<p>
+            The Bernoulli distribution is the simplest building block on which other
+            discrete distributions of sequences of independent Bernoulli trials can
+            be based.
+          </p>
+<p>
+            The Bernoulli is the binomial distribution (k = 1, p) with only one trial.
+          </p>
+<p>
+            <a href="http://en.wikipedia.org/wiki/Probability_density_function" target="_top">probability
+            density function pdf</a> f(0) = 1 - p, f(1) = p. <a href="http://en.wikipedia.org/wiki/Cumulative_Distribution_Function" target="_top">Cumulative
+            distribution function</a> D(k) = if (k == 0) 1 - p else 1.
+          </p>
+<p>
+            The following graph illustrates how the <a href="http://en.wikipedia.org/wiki/Probability_density_function" target="_top">probability
+            density function pdf</a> varies with the outcome of the single trial:
+          </p>
+<p>
+            <span class="inlinemediaobject"><img src="../../../../../graphs/bernoulli_pdf.png" align="middle"></span>
+          </p>
+<p>
+            and the <a href="http://en.wikipedia.org/wiki/Cumulative_Distribution_Function" target="_top">Cumulative
+            distribution function</a>
+          </p>
+<p>
+            <span class="inlinemediaobject"><img src="../../../../../graphs/bernoulli_cdf.png" align="middle"></span>
+          </p>
+<a name="math_toolkit.dist.dist_ref.dists.bernoulli_dist.member_functions"></a><h5>
+<a name="id645105"></a>
+            <a class="link" href="bernoulli_dist.html#math_toolkit.dist.dist_ref.dists.bernoulli_dist.member_functions">Member
+            Functions</a>
+          </h5>
+<pre class="programlisting"><span class="identifier">bernoulli_distribution</span><span class="special">(</span><span class="identifier">RealType</span> <span class="identifier">p</span><span class="special">);</span>
+</pre>
+<p>
+            Constructs a <a href="http://en.wikipedia.org/wiki/bernoulli_distribution" target="_top">bernoulli
+            distribution</a> with success_fraction <span class="emphasis"><em>p</em></span>.
+          </p>
+<pre class="programlisting"><span class="identifier">RealType</span> <span class="identifier">success_fraction</span><span class="special">()</span> <span class="keyword">const</span>
+</pre>
+<p>
+            Returns the <span class="emphasis"><em>success_fraction</em></span> parameter of this distribution.
+          </p>
+<a name="math_toolkit.dist.dist_ref.dists.bernoulli_dist.non_member_accessors"></a><h5>
+<a name="id645225"></a>
+            <a class="link" href="bernoulli_dist.html#math_toolkit.dist.dist_ref.dists.bernoulli_dist.non_member_accessors">Non-member
+            Accessors</a>
+          </h5>
+<p>
+            All the <a class="link" href="../nmp.html" title="Non-Member Properties">usual non-member
+            accessor functions</a> that are generic to all distributions are supported:
+            <a class="link" href="../nmp.html#math.dist.cdf">Cumulative Distribution Function</a>,
+            <a class="link" href="../nmp.html#math.dist.pdf">Probability Density Function</a>, <a class="link" href="../nmp.html#math.dist.quantile">Quantile</a>, <a class="link" href="../nmp.html#math.dist.hazard">Hazard
+            Function</a>, <a class="link" href="../nmp.html#math.dist.chf">Cumulative Hazard Function</a>,
+            <a class="link" href="../nmp.html#math.dist.mean">mean</a>, <a class="link" href="../nmp.html#math.dist.median">median</a>,
+            <a class="link" href="../nmp.html#math.dist.mode">mode</a>, <a class="link" href="../nmp.html#math.dist.variance">variance</a>,
+            <a class="link" href="../nmp.html#math.dist.sd">standard deviation</a>, <a class="link" href="../nmp.html#math.dist.skewness">skewness</a>,
+            <a class="link" href="../nmp.html#math.dist.kurtosis">kurtosis</a>, <a class="link" href="../nmp.html#math.dist.kurtosis_excess">kurtosis_excess</a>,
+            <a class="link" href="../nmp.html#math.dist.range">range</a> and <a class="link" href="../nmp.html#math.dist.support">support</a>.
+          </p>
+<p>
+            The domain of the random variable is 0 and 1, and the useful supported
+            range is only 0 or 1.
+          </p>
+<p>
+            Outside this range, functions are undefined, or may throw domain_error
+            exception and make an error message available.
+          </p>
+<a name="math_toolkit.dist.dist_ref.dists.bernoulli_dist.accuracy"></a><h5>
+<a name="id645410"></a>
+            <a class="link" href="bernoulli_dist.html#math_toolkit.dist.dist_ref.dists.bernoulli_dist.accuracy">Accuracy</a>
+          </h5>
+<p>
+            The Bernoulli distribution is implemented with simple arithmetic operators
+            and so should have errors within an epsilon or two.
+          </p>
+<a name="math_toolkit.dist.dist_ref.dists.bernoulli_dist.implementation"></a><h5>
+<a name="id645443"></a>
+            <a class="link" href="bernoulli_dist.html#math_toolkit.dist.dist_ref.dists.bernoulli_dist.implementation">Implementation</a>
+          </h5>
+<p>
+            In the following table <span class="emphasis"><em>p</em></span> is the probability of success
+            and <span class="emphasis"><em>q = 1-p</em></span>. <span class="emphasis"><em>k</em></span> is the random
+            variate, either 0 or 1.
+          </p>
+<div class="note"><table border="0" summary="Note">
+<tr>
+<td rowspan="2" align="center" valign="top" width="25"><img alt="[Note]" src="../../../../../../doc/html/images/note.png"></td>
+<th align="left">Note</th>
+</tr>
+<tr><td align="left" valign="top">
+<p>
+              The Bernoulli distribution is implemented here as a <span class="emphasis"><em>strict
+              discrete</em></span> distribution. If a generalised version, allowing
+              k to be any real, is required then the binomial distribution with a
+              single trial should be used, for example:
+            </p>
+<p>
+              <code class="computeroutput"><span class="identifier">binomial_distribution</span><span class="special">(</span><span class="number">1</span><span class="special">,</span>
+              <span class="number">0.25</span><span class="special">)</span></code>
+            </p>
+</td></tr>
+</table></div>
+<div class="informaltable"><table class="table">
+<colgroup>
+<col>
+<col>
+</colgroup>
+<thead><tr>
+<th>
+                  <p>
+                    Function
+                  </p>
+                  </th>
+<th>
+                  <p>
+                    Implementation Notes
+                  </p>
+                  </th>
+</tr></thead>
+<tbody>
+<tr>
+<td>
+                  <p>
+                    Supported range
+                  </p>
+                  </td>
+<td>
+                  <p>
+                    {0, 1}
+                  </p>
+                  </td>
+</tr>
+<tr>
+<td>
+                  <p>
+                    pdf
+                  </p>
+                  </td>
+<td>
+                  <p>
+                    Using the relation: pdf = 1 - p for k = 0, else p
+                  </p>
+                  </td>
+</tr>
+<tr>
+<td>
+                  <p>
+                    cdf
+                  </p>
+                  </td>
+<td>
+                  <p>
+                    Using the relation: cdf = 1 - p for k = 0, else 1
+                  </p>
+                  </td>
+</tr>
+<tr>
+<td>
+                  <p>
+                    cdf complement
+                  </p>
+                  </td>
+<td>
+                  <p>
+                    q = 1 - p
+                  </p>
+                  </td>
+</tr>
+<tr>
+<td>
+                  <p>
+                    quantile
+                  </p>
+                  </td>
+<td>
+                  <p>
+                    if x &lt;= (1-p) 0 else 1
+                  </p>
+                  </td>
+</tr>
+<tr>
+<td>
+                  <p>
+                    quantile from the complement
+                  </p>
+                  </td>
+<td>
+                  <p>
+                    if x &lt;= (1-p) 1 else 0
+                  </p>
+                  </td>
+</tr>
+<tr>
+<td>
+                  <p>
+                    mean
+                  </p>
+                  </td>
+<td>
+                  <p>
+                    p
+                  </p>
+                  </td>
+</tr>
+<tr>
+<td>
+                  <p>
+                    variance
+                  </p>
+                  </td>
+<td>
+                  <p>
+                    p * (1 - p)
+                  </p>
+                  </td>
+</tr>
+<tr>
+<td>
+                  <p>
+                    mode
+                  </p>
+                  </td>
+<td>
+                  <p>
+                    if (p &lt; 0.5) 0 else 1
+                  </p>
+                  </td>
+</tr>
+<tr>
+<td>
+                  <p>
+                    skewness
+                  </p>
+                  </td>
+<td>
+                  <p>
+                    (1 - 2 * p) / sqrt(p * q)
+                  </p>
+                  </td>
+</tr>
+<tr>
+<td>
+                  <p>
+                    kurtosis
+                  </p>
+                  </td>
+<td>
+                  <p>
+                    6 * p * p - 6 * p +1/ p * q
+                  </p>
+                  </td>
+</tr>
+<tr>
+<td>
+                  <p>
+                    kurtosis excess
+                  </p>
+                  </td>
+<td>
+                  <p>
+                    kurtosis -3
+                  </p>
+                  </td>
+</tr>
+</tbody>
+</table></div>
+<a name="math_toolkit.dist.dist_ref.dists.bernoulli_dist.references"></a><h5>
+<a name="id645835"></a>
+            <a class="link" href="bernoulli_dist.html#math_toolkit.dist.dist_ref.dists.bernoulli_dist.references">References</a>
+          </h5>
+<div class="itemizedlist"><ul type="disc">
+<li><a href="http://en.wikipedia.org/wiki/Bernoulli_distribution" target="_top">Wikpedia
+              Bernoulli distribution</a></li>
+<li><a href="../../../../" target="_top">Weisstein, Eric W. "Bernoulli Distribution."
+              From MathWorld--A Wolfram Web Resource.</a></li>
+</ul></div>
+</div>
+<table xmlns:rev="http://www.cs.rpi.edu/~gregod/boost/tools/doc/revision" width="100%"><tr>
+<td align="left"></td>
+<td align="right"><div class="copyright-footer">Copyright © 2006 , 2007, 2008 John Maddock, Paul A. Bristow, Hubert
+      Holin, Xiaogang Zhang, Bruno Lalande and Gautam Sewani<p>
+        Distributed under the Boost Software License, Version 1.0. (See accompanying
+        file LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_0.txt)
+      </p>
+</div></td>
+</tr></table>
+<hr>
+<div class="spirit-nav">
+<a accesskey="p" href="../dists.html"><img src="../../../../../../doc/html/images/prev.png" alt="Prev"></a><a accesskey="u" href="../dists.html"><img src="../../../../../../doc/html/images/up.png" alt="Up"></a><a accesskey="h" href="../../../../index.html"><img src="../../../../../../doc/html/images/home.png" alt="Home"></a><a accesskey="n" href="beta_dist.html"><img src="../../../../../../doc/html/images/next.png" alt="Next"></a>
+</div>
+</body>
+</html>

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+++ sandbox/tools/auto_index/example/math/doc/sf_and_dist/html/math_toolkit/dist/dist_ref/dists/beta_dist.html	2008-11-28 05:25:28 EST (Fri, 28 Nov 2008)
@@ -0,0 +1,630 @@
+<html>
+<head>
+<meta http-equiv="Content-Type" content="text/html; charset=ISO-8859-1">
+<title>Beta Distribution</title>
+<link rel="stylesheet" href="../../../../boostbook.css" type="text/css">
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+</div>
+<div class="section" lang="en">
+<div class="titlepage"><div><div><h5 class="title">
+<a name="math_toolkit.dist.dist_ref.dists.beta_dist"></a><a class="link" href="beta_dist.html" title="Beta Distribution"> Beta
+          Distribution</a>
+</h5></div></div></div>
+<p>
+            
+</p>
+<pre class="programlisting"><span class="preprocessor">#include</span> <span class="special">&lt;</span><span class="identifier">boost</span><span class="special">/</span><span class="identifier">math</span><span class="special">/</span><span class="identifier">distributions</span><span class="special">/</span><span class="identifier">beta</span><span class="special">.</span><span class="identifier">hpp</span><span class="special">&gt;</span></pre>
+<p>
+          </p>
+<pre class="programlisting"><span class="keyword">namespace</span> <span class="identifier">boost</span><span class="special">{</span> <span class="keyword">namespace</span> <span class="identifier">math</span><span class="special">{</span> 
+
+ <span class="keyword">template</span> <span class="special">&lt;</span><span class="keyword">class</span> <span class="identifier">RealType</span> <span class="special">=</span> <span class="keyword">double</span><span class="special">,</span> 
+           <span class="keyword">class</span> <a class="link" href="../../../policy.html" title="Policies">Policy</a>   <span class="special">=</span> <a class="link" href="../../../policy/pol_ref/pol_ref_ref.html" title="Policy Class Reference">policies::policy&lt;&gt;</a> <span class="special">&gt;</span>
+<span class="keyword">class</span> <span class="identifier">beta_distribution</span><span class="special">;</span>
+
+<span class="comment">// typedef beta_distribution&lt;double&gt; beta;
+</span><span class="comment">// Note that this is deliberately NOT provided,
+</span><span class="comment">// to avoid a clash with the function name beta.
+</span>
+<span class="keyword">template</span> <span class="special">&lt;</span><span class="keyword">class</span> <span class="identifier">RealType</span><span class="special">,</span> <span class="keyword">class</span> <a class="link" href="../../../policy.html" title="Policies">Policy</a><span class="special">&gt;</span>
+<span class="keyword">class</span> <span class="identifier">beta_distribution</span>
+<span class="special">{</span>
+<span class="keyword">public</span><span class="special">:</span>
+   <span class="keyword">typedef</span> <span class="identifier">RealType</span>  <span class="identifier">value_type</span><span class="special">;</span>
+   <span class="keyword">typedef</span> <span class="identifier">Policy</span>    <span class="identifier">policy_type</span><span class="special">;</span>
+   <span class="comment">// Constructor from two shape parameters, alpha &amp; beta:
+</span>   <span class="identifier">beta_distribution</span><span class="special">(</span><span class="identifier">RealType</span> <span class="identifier">a</span><span class="special">,</span> <span class="identifier">RealType</span> <span class="identifier">b</span><span class="special">);</span>
+   
+   <span class="comment">// Parameter accessors:
+</span>   <span class="identifier">RealType</span> <span class="identifier">alpha</span><span class="special">()</span> <span class="keyword">const</span><span class="special">;</span>
+   <span class="identifier">RealType</span> <span class="identifier">beta</span><span class="special">()</span> <span class="keyword">const</span><span class="special">;</span>
+   
+   <span class="comment">// Parameter estimators of alpha or beta from mean and variance.
+</span>   <span class="keyword">static</span> <span class="identifier">RealType</span> <span class="identifier">find_alpha</span><span class="special">(</span>
+     <span class="identifier">RealType</span> <span class="identifier">mean</span><span class="special">,</span> <span class="comment">// Expected value of mean.
+</span>     <span class="identifier">RealType</span> <span class="identifier">variance</span><span class="special">);</span> <span class="comment">// Expected value of variance.
+</span>   
+   <span class="keyword">static</span> <span class="identifier">RealType</span> <span class="identifier">find_beta</span><span class="special">(</span>
+     <span class="identifier">RealType</span> <span class="identifier">mean</span><span class="special">,</span> <span class="comment">// Expected value of mean.
+</span>     <span class="identifier">RealType</span> <span class="identifier">variance</span><span class="special">);</span> <span class="comment">// Expected value of variance.
+</span>
+   <span class="comment">// Parameter estimators from from
+</span>   <span class="comment">// either alpha or beta, and x and probability.
+</span>   
+   <span class="keyword">static</span> <span class="identifier">RealType</span> <span class="identifier">find_alpha</span><span class="special">(</span>
+     <span class="identifier">RealType</span> <span class="identifier">beta</span><span class="special">,</span> <span class="comment">// from beta.
+</span>     <span class="identifier">RealType</span> <span class="identifier">x</span><span class="special">,</span> <span class="comment">//  x.
+</span>     <span class="identifier">RealType</span> <span class="identifier">probability</span><span class="special">);</span> <span class="comment">// cdf
+</span>   
+   <span class="keyword">static</span> <span class="identifier">RealType</span> <span class="identifier">find_beta</span><span class="special">(</span>
+     <span class="identifier">RealType</span> <span class="identifier">alpha</span><span class="special">,</span> <span class="comment">// alpha.
+</span>     <span class="identifier">RealType</span> <span class="identifier">x</span><span class="special">,</span> <span class="comment">// probability x.
+</span>     <span class="identifier">RealType</span> <span class="identifier">probability</span><span class="special">);</span> <span class="comment">// probability cdf.
+</span><span class="special">};</span>
+
+<span class="special">}}</span> <span class="comment">// namespaces
+</span></pre>
+<p>
+            The class type <code class="computeroutput"><span class="identifier">beta_distribution</span></code>
+            represents a <a href="http://en.wikipedia.org/wiki/Beta_distribution" target="_top">beta
+            </a> <a href="http://en.wikipedia.org/wiki/Probability_distribution" target="_top">probability
+            distribution function</a>.
+          </p>
+<p>
+            The <a href="http://mathworld.wolfram.com/BetaDistribution.htm" target="_top">beta
+            distribution </a> is used as a <a href="http://en.wikipedia.org/wiki/Prior_distribution" target="_top">prior
+            distribution</a> for binomial proportions in <a href="http://mathworld.wolfram.com/BayesianAnalysis.html" target="_top">Bayesian
+            analysis</a>.
+          </p>
+<p>
+            See also: <a href="http://documents.wolfram.com/calculationcenter/v2/Functions/ListsMatrices/Statistics/BetaDistribution.html" target="_top">beta
+            distribution</a> and <a href="http://en.wikipedia.org/wiki/Bayesian_statistics" target="_top">Bayesian
+            statistics</a>.
+          </p>
+<p>
+            How the beta distribution is used for <a href="http://home.uchicago.edu/~grynav/bayes/ABSLec5.ppt" target="_top">Bayesian
+            analysis of one parameter models</a> is discussed by Jeff Grynaviski.
+          </p>
+<p>
+            The <a href="http://en.wikipedia.org/wiki/Probability_density_function" target="_top">probability
+            density function PDF</a> for the <a href="http://en.wikipedia.org/wiki/Beta_distribution" target="_top">beta
+            distribution</a> defined on the interval [0,1] is given by:
+          </p>
+<p>
+            f(x;&#945;,&#946;) = x<sup>&#945; - 1</sup> (1 - x)<sup>&#946; -1</sup> / B(&#945;, &#946;)
+          </p>
+<p>
+            where B(&#945;, &#946;) is the <a href="http://en.wikipedia.org/wiki/Beta_function" target="_top">beta
+            function</a>, implemented in this library as <a class="link" href="../../../special/sf_beta/beta_function.html" title="Beta">beta</a>.
+            Division by the beta function ensures that the pdf is normalized to the
+            range zero to unity.
+          </p>
+<p>
+            The following graph illustrates examples of the pdf for various values
+            of the shape parameters. Note the &#945; = &#946; = 2 (blue line) is dome-shaped, and
+            might be approximated by a symmetrical triangular distribution.
+          </p>
+<p>
+            <span class="inlinemediaobject"><img src="../../../../../graphs/beta_pdf.png" align="middle"></span>
+          </p>
+<p>
+            If &#945; = &#946; = 1, then it is a &#8203;
+<a href="http://en.wikipedia.org/wiki/Uniform_distribution_%28continuous%29" target="_top">uniform
+            distribution</a>, equal to unity in the entire interval x = 0 to
+            1. If &#945; &#8203; and &#946; &#8203; are &lt; 1, then the pdf is U-shaped. If &#945; != &#946;, then the shape
+            is asymmetric and could be approximated by a triangle whose apex is away
+            from the centre (where x = half).
+          </p>
+<a name="math_toolkit.dist.dist_ref.dists.beta_dist.member_functions"></a><h5>
+<a name="id646998"></a>
+            <a class="link" href="beta_dist.html#math_toolkit.dist.dist_ref.dists.beta_dist.member_functions">Member
+            Functions</a>
+          </h5>
+<a name="math_toolkit.dist.dist_ref.dists.beta_dist.constructor"></a><h6>
+<a name="id647025"></a>
+            <a class="link" href="beta_dist.html#math_toolkit.dist.dist_ref.dists.beta_dist.constructor">Constructor</a>
+          </h6>
+<pre class="programlisting"><span class="identifier">beta_distribution</span><span class="special">(</span><span class="identifier">RealType</span> <span class="identifier">alpha</span><span class="special">,</span> <span class="identifier">RealType</span> <span class="identifier">beta</span><span class="special">);</span>
+</pre>
+<p>
+            Constructs a beta distribution with shape parameters <span class="emphasis"><em>alpha</em></span>
+            and <span class="emphasis"><em>beta</em></span>.
+          </p>
+<p>
+            Requires alpha,beta &gt; 0,otherwise <a class="link" href="../../../main_overview/error_handling.html#domain_error">domain_error</a>
+            is called. Note that technically the beta distribution is defined for
+            alpha,beta &gt;= 0, but it's not clear whether any program can actually
+            make use of that latitude or how many of the non-member functions can
+            be usefully defined in that case. Therefore for now, we regard it as
+            an error if alpha or beta is zero.
+          </p>
+<p>
+            For example:
+          </p>
+<pre class="programlisting"><span class="identifier">beta_distribution</span><span class="special">&lt;&gt;</span> <span class="identifier">mybeta</span><span class="special">(</span><span class="number">2</span><span class="special">,</span> <span class="number">5</span><span class="special">);</span>
+</pre>
+<p>
+            Constructs a the beta distribution with alpha=2 and beta=5 (shown in
+            yellow in the graph above).
+          </p>
+<a name="math_toolkit.dist.dist_ref.dists.beta_dist.parameter_accessors"></a><h6>
+<a name="id647203"></a>
+            <a class="link" href="beta_dist.html#math_toolkit.dist.dist_ref.dists.beta_dist.parameter_accessors">Parameter
+            Accessors</a>
+          </h6>
+<pre class="programlisting"><span class="identifier">RealType</span> <span class="identifier">alpha</span><span class="special">()</span> <span class="keyword">const</span><span class="special">;</span>
+</pre>
+<p>
+            Returns the parameter <span class="emphasis"><em>alpha</em></span> from which this distribution
+            was constructed.
+          </p>
+<pre class="programlisting"><span class="identifier">RealType</span> <span class="identifier">beta</span><span class="special">()</span> <span class="keyword">const</span><span class="special">;</span>
+</pre>
+<p>
+            Returns the parameter <span class="emphasis"><em>beta</em></span> from which this distribution
+            was constructed.
+          </p>
+<p>
+            So for example:
+          </p>
+<pre class="programlisting"><span class="identifier">beta_distribution</span><span class="special">&lt;&gt;</span> <span class="identifier">mybeta</span><span class="special">(</span><span class="number">2</span><span class="special">,</span> <span class="number">5</span><span class="special">);</span>
+<span class="identifier">assert</span><span class="special">(</span><span class="identifier">mybeta</span><span class="special">.</span><span class="identifier">alpha</span><span class="special">()</span> <span class="special">==</span> <span class="number">2.</span><span class="special">);</span>  <span class="comment">// mybeta.alpha() returns 2
+</span><span class="identifier">assert</span><span class="special">(</span><span class="identifier">mybeta</span><span class="special">.</span><span class="identifier">beta</span><span class="special">()</span> <span class="special">==</span> <span class="number">5.</span><span class="special">);</span>   <span class="comment">// mybeta.beta()  returns 5
+</span></pre>
+<a name="math_toolkit.dist.dist_ref.dists.beta_dist.parameter_estimators"></a><h5>
+<a name="id647484"></a>
+            <a class="link" href="beta_dist.html#math_toolkit.dist.dist_ref.dists.beta_dist.parameter_estimators">Parameter
+            Estimators</a>
+          </h5>
+<p>
+            Two pairs of parameter estimators are provided.
+          </p>
+<p>
+            One estimates either &#945; &#8203; or &#946; &#8203; 
+from presumed-known mean and variance.
+          </p>
+<p>
+            The other pair estimates either &#945; &#8203; or &#946; &#8203; from the cdf and x.
+          </p>
+<p>
+            It is also possible to estimate &#945; &#8203; and &#946; &#8203; from 'known' mode &amp; quantile.
+            For example, calculators are provided by the <a href="http://www.ausvet.com.au/pprev/content.php?page=PPscript" target="_top">Pooled
+            Prevalence Calculator</a> and <a href="http://www.epi.ucdavis.edu/diagnostictests/betabuster.html" target="_top">Beta
+            Buster</a> but this is not yet implemented here.
+          </p>
+<pre class="programlisting"><span class="keyword">static</span> <span class="identifier">RealType</span> <span class="identifier">find_alpha</span><span class="special">(</span>
+  <span class="identifier">RealType</span> <span class="identifier">mean</span><span class="special">,</span> <span class="comment">// Expected value of mean.
+</span>  <span class="identifier">RealType</span> <span class="identifier">variance</span><span class="special">);</span> <span class="comment">// Expected value of variance.
+</span></pre>
+<p>
+            Returns the unique value of &#945; that corresponds to a beta distribution with
+            mean <span class="emphasis"><em>mean</em></span> and variance <span class="emphasis"><em>variance</em></span>.
+          </p>
+<pre class="programlisting"><span class="keyword">static</span> <span class="identifier">RealType</span> <span class="identifier">find_beta</span><span class="special">(</span>
+  <span class="identifier">RealType</span> <span class="identifier">mean</span><span class="special">,</span> <span class="comment">// Expected value of mean.
+</span>  <span class="identifier">RealType</span> <span class="identifier">variance</span><span class="special">);</span> <span class="comment">// Expected value of variance.
+</span></pre>
+<p>
+            Returns the unique value of &#946; that corresponds to a beta distribution with
+            mean <span class="emphasis"><em>mean</em></span> and variance <span class="emphasis"><em>variance</em></span>.
+          </p>
+<pre class="programlisting"><span class="keyword">static</span> <span class="identifier">RealType</span> <span class="identifier">find_alpha</span><span class="special">(</span>
+  <span class="identifier">RealType</span> <span class="identifier">beta</span><span class="special">,</span> <span class="comment">// from beta.
+</span>  <span class="identifier">RealType</span> <span class="identifier">x</span><span class="special">,</span> <span class="comment">//  x.
+</span>  <span class="identifier">RealType</span> <span class="identifier">probability</span><span class="special">);</span> <span class="comment">// probability cdf
+</span></pre>
+<p>
+            Returns the value of &#945; that gives: <code class="computeroutput"><span class="identifier">cdf</span><span class="special">(</span><span class="identifier">beta_distribution</span><span class="special">&lt;</span><span class="identifier">RealType</span><span class="special">&gt;(</span><span class="identifier">alpha</span><span class="special">,</span> <span class="identifier">beta</span><span class="special">),</span> <span class="identifier">x</span><span class="special">)</span> <span class="special">==</span> <span class="identifier">probability</span></code>.
+          </p>
+<pre class="programlisting"><span class="keyword">static</span> <span class="identifier">RealType</span> <span class="identifier">find_beta</span><span class="special">(</span>
+  <span class="identifier">RealType</span> <span class="identifier">alpha</span><span class="special">,</span> <span class="comment">// alpha.
+</span>  <span class="identifier">RealType</span> <span class="identifier">x</span><span class="special">,</span> <span class="comment">// probability x.
+</span>  <span class="identifier">RealType</span> <span class="identifier">probability</span><span class="special">);</span> <span class="comment">// probability cdf.
+</span></pre>
+<p>
+            Returns the value of &#946; that gives: <code class="computeroutput"><span class="identifier">cdf</span><span class="special">(</span><span class="identifier">beta_distribution</span><span class="special">&lt;</span><span class="identifier">RealType</span><span class="special">&gt;(</span><span class="identifier">alpha</span><span class="special">,</span> <span class="identifier">beta</span><span class="special">),</span> <span class="identifier">x</span><span class="special">)</span> <span class="special">==</span> <span class="identifier">probability</span></code>.
+          </p>
+<a name="math_toolkit.dist.dist_ref.dists.beta_dist.non_member_accessor_functions"></a><h5>
+<a name="id648131"></a>
+            <a class="link" href="beta_dist.html#math_toolkit.dist.dist_ref.dists.beta_dist.non_member_accessor_functions">Non-member
+            Accessor Functions</a>
+          </h5>
+<p>
+            All the <a class="link" href="../nmp.html" title="Non-Member Properties">usual non-member
+            accessor functions</a> that are generic to all distributions are supported:
+            <a class="link" href="../nmp.html#math.dist.cdf">Cumulative Distribution Function</a>,
+            <a class="link" href="../nmp.html#math.dist.pdf">Probability Density Function</a>, <a class="link" href="../nmp.html#math.dist.quantile">Quantile</a>, <a class="link" href="../nmp.html#math.dist.hazard">Hazard
+            Function</a>, <a class="link" href="../nmp.html#math.dist.chf">Cumulative Hazard Function</a>,
+            <a class="link" href="../nmp.html#math.dist.mean">mean</a>, <a class="link" href="../nmp.html#math.dist.median">median</a>,
+            <a class="link" href="../nmp.html#math.dist.mode">mode</a>, <a class="link" href="../nmp.html#math.dist.variance">variance</a>,
+            <a class="link" href="../nmp.html#math.dist.sd">standard deviation</a>, <a class="link" href="../nmp.html#math.dist.skewness">skewness</a>,
+            <a class="link" href="../nmp.html#math.dist.kurtosis">kurtosis</a>, <a class="link" href="../nmp.html#math.dist.kurtosis_excess">kurtosis_excess</a>,
+            <a class="link" href="../nmp.html#math.dist.range">range</a> and <a class="link" href="../nmp.html#math.dist.support">support</a>.
+          </p>
+<p>
+            The formulae for calculating these are shown in the table below, and
+            at <a href="http://mathworld.wolfram.com/BetaDistribution.html" target="_top">Wolfram
+            Mathworld</a>.
+          </p>
+<a name="math_toolkit.dist.dist_ref.dists.beta_dist.applications"></a><h5>
+<a name="id648316"></a>
+            <a class="link" href="beta_dist.html#math_toolkit.dist.dist_ref.dists.beta_dist.applications">Applications</a>
+          </h5>
+<p>
+            The beta distribution can be used to model events constrained to take
+            place within an interval defined by a minimum and maximum value: so it
+            is used in project management systems.
+          </p>
+<p>
+            It is also widely used in <a href="http://en.wikipedia.org/wiki/Bayesian_inference" target="_top">Bayesian
+            statistical inference</a>.
+          </p>
+<a name="math_toolkit.dist.dist_ref.dists.beta_dist.related_distributions"></a><h5>
+<a name="id648364"></a>
+            <a class="link" href="beta_dist.html#math_toolkit.dist.dist_ref.dists.beta_dist.related_distributions">Related
+            distributions</a>
+          </h5>
+<p>
+            The beta distribution with both &#945;  &#8203; and &#946; = 1 follows a <a href="http://en.wikipedia.org/wiki/Uniform_distribution_%28continuous%29" target="_top">uniform
+            distribution</a>.
+          </p>
+<p>
+            The triangular
+            is used when less precise information is available.
+          </p>
+<p>
+            The <a href="http://en.wikipedia.org/wiki/Binomial_distribution" target="_top">binomial
+            distribution</a> is closely related when &#945;  &#8203; and &#946;  &#8203; are integers.
+          </p>
+<p>
+            With integer values of &#945;  &#8203; and &#946;  &#8203; the distribution B(i, j) is that of the j-th
+            highest of a sample of i + j + 1 independent random variables uniformly
+            distributed between 0 and 1. The cumulative probability from 0 to x is
+            thus the probability that the j-th highest value is less than x. Or it
+            is the probability that that at least i of the random variables are less
+            than x, a probability given by summing over the <a class="link" href="binomial_dist.html" title="Binomial Distribution">Binomial
+            Distribution</a> with its p parameter set to x.
+          </p>
+<a name="math_toolkit.dist.dist_ref.dists.beta_dist.accuracy"></a><h5>
+<a name="id648458"></a>
+            <a class="link" href="beta_dist.html#math_toolkit.dist.dist_ref.dists.beta_dist.accuracy">Accuracy</a>
+          </h5>
+<p>
+            This distribution is implemented using the <a class="link" href="../../../special/sf_beta/beta_function.html" title="Beta">beta
+            functions</a> <a class="link" href="../../../special/sf_beta/beta_function.html" title="Beta">beta</a>
+            and <a class="link" href="../../../special/sf_beta/ibeta_function.html" title="Incomplete Beta Functions">incomplete
+            beta functions</a> <a class="link" href="../../../special/sf_beta/ibeta_function.html" title="Incomplete Beta Functions">ibeta</a>
+            and <a class="link" href="../../../special/sf_beta/ibeta_function.html" title="Incomplete Beta Functions">ibetac</a>;
+            please refer to these functions for information on accuracy.
+          </p>
+<a name="math_toolkit.dist.dist_ref.dists.beta_dist.implementation"></a><h5>
+<a name="id648540"></a>
+            <a class="link" href="beta_dist.html#math_toolkit.dist.dist_ref.dists.beta_dist.implementation">Implementation</a>
+          </h5>
+<p>
+            In the following table <span class="emphasis"><em>a</em></span> and <span class="emphasis"><em>b</em></span>
+            are the parameters &#945; and &#946;, <span class="emphasis"><em>x</em></span> is the random variable,
+            <span class="emphasis"><em>p</em></span> is the probability and <span class="emphasis"><em>q = 1-p</em></span>.
+          </p>
+<div class="informaltable"><table class="table">
+<colgroup>
+<col>
+<col>
+</colgroup>
+<thead><tr>
+<th>
+                  <p>
+                    Function
+                  </p>
+                  </th>
+<th>
+                  <p>
+                    Implementation Notes
+                  </p>
+                  </th>
+</tr></thead>
+<tbody>
+<tr>
+<td>
+                  <p>
+                    pdf
+                  </p>
+                  </td>
+<td>
+                  <p>
+                    f(x;&#945;,&#946;) = x<sup>&#945; - 1</sup> (1 - x)<sup>&#946; -1</sup> / B(&#945;, &#946;)
+                  </p>
+                  <p>
+                    Implemented using <a class="link" href="../../../special/sf_beta/beta_derivative.html" title="Derivative of the Incomplete Beta Function">ibeta_derivative</a>(a,
+                    b, x).
+                  </p>
+                  </td>
+</tr>
+<tr>
+<td>
+                  <p>
+                    cdf
+                  </p>
+                  </td>
+<td>
+                  <p>
+                    Using the incomplete beta function <a class="link" href="../../../special/sf_beta/ibeta_function.html" title="Incomplete Beta Functions">ibeta</a>(a,
+                    b, x)
+                  </p>
+                  </td>
+</tr>
+<tr>
+<td>
+                  <p>
+                    cdf complement
+                  </p>
+                  </td>
+<td>
+                  <p>
+                    <a class="link" href="../../../special/sf_beta/ibeta_function.html" title="Incomplete Beta Functions">ibetac</a>(a,
+                    b, x)
+                  </p>
+                  </td>
+</tr>
+<tr>
+<td>
+                  <p>
+                    quantile
+                  </p>
+                  </td>
+<td>
+                  <p>
+                    Using the inverse incomplete beta function <a class="link" href="../../../special/sf_beta/ibeta_inv_function.html" title="The Incomplete Beta Function Inverses">ibeta_inv</a>(a,
+                    b, p)
+                  </p>
+                  </td>
+</tr>
+<tr>
+<td>
+                  <p>
+                    quantile from the complement
+                  </p>
+                  </td>
+<td>
+                  <p>
+                    <a class="link" href="../../../special/sf_beta/ibeta_inv_function.html" title="The Incomplete Beta Function Inverses">ibetac_inv</a>(a,
+                    b, q)
+                  </p>
+                  </td>
+</tr>
+<tr>
+<td>
+                  <p>
+                    mean
+                  </p>
+                  </td>
+<td>
+                  <p>
+                    <code class="computeroutput"><span class="identifier">a</span><span class="special">/(</span><span class="identifier">a</span><span class="special">+</span><span class="identifier">b</span><span class="special">)</span></code>
+                  </p>
+                  </td>
+</tr>
+<tr>
+<td>
+                  <p>
+                    variance
+                  </p>
+                  </td>
+<td>
+                  <p>
+                    <code class="computeroutput"><span class="identifier">a</span> <span class="special">*</span>
+                    <span class="identifier">b</span> <span class="special">/</span>
+                    <span class="special">(</span><span class="identifier">a</span><span class="special">+</span><span class="identifier">b</span><span class="special">)^</span><span class="number">2</span> <span class="special">*</span> <span class="special">(</span><span class="identifier">a</span> <span class="special">+</span>
+                    <span class="identifier">b</span> <span class="special">+</span>
+                    <span class="number">1</span><span class="special">)</span></code>
+                  </p>
+                  </td>
+</tr>
+<tr>
+<td>
+                  <p>
+                    mode
+                  </p>
+                  </td>
+<td>
+                  <p>
+                    <code class="computeroutput"><span class="special">(</span><span class="identifier">a</span><span class="special">-</span><span class="number">1</span><span class="special">)</span> <span class="special">/</span>
+                    <span class="special">(</span><span class="identifier">a</span>
+                    <span class="special">+</span> <span class="identifier">b</span>
+                    <span class="special">-</span> <span class="number">2</span><span class="special">)</span></code>
+                  </p>
+                  </td>
+</tr>
+<tr>
+<td>
+                  <p>
+                    skewness
+                  </p>
+                  </td>
+<td>
+                  <p>
+                    <code class="computeroutput"><span class="number">2</span> <span class="special">(</span><span class="identifier">b</span><span class="special">-</span><span class="identifier">a</span><span class="special">)</span>
+                    <span class="identifier">sqrt</span><span class="special">(</span><span class="identifier">a</span><span class="special">+</span><span class="identifier">b</span><span class="special">+</span><span class="number">1</span><span class="special">)/(</span><span class="identifier">a</span><span class="special">+</span><span class="identifier">b</span><span class="special">+</span><span class="number">2</span><span class="special">)</span> <span class="special">*</span> <span class="identifier">sqrt</span><span class="special">(</span><span class="identifier">a</span>
+                    <span class="special">*</span> <span class="identifier">b</span><span class="special">)</span></code>
+                  </p>
+                  </td>
+</tr>
+<tr>
+<td>
+                  <p>
+                    kurtosis excess
+                  </p>
+                  </td>
+<td>
+                  <p>
+                    <span class="inlinemediaobject"><img src="../../../../../equations/beta_dist_kurtosis.png"></span>
+                  </p>
+                  </td>
+</tr>
+<tr>
+<td>
+                  <p>
+                    kurtosis
+                  </p>
+                  </td>
+<td>
+                  <p>
+                    <code class="computeroutput"><span class="identifier">kurtosis</span> <span class="special">+</span>
+                    <span class="number">3</span></code>
+                  </p>
+                  </td>
+</tr>
+<tr>
+<td>
+                  <p>
+                    parameter estimation
+                  </p>
+                  </td>
+<td>
+                  <p>
+                  </p>
+                  </td>
+</tr>
+<tr>
+<td>
+                  <p>
+                    alpha
+                  </p>
+                  <p>
+                    from mean and variance
+                  </p>
+                  </td>
+<td>
+                  <p>
+                    <code class="computeroutput"><span class="identifier">mean</span> <span class="special">*</span>
+                    <span class="special">((</span> <span class="special">(</span><span class="identifier">mean</span> <span class="special">*</span>
+                    <span class="special">(</span><span class="number">1</span>
+                    <span class="special">-</span> <span class="identifier">mean</span><span class="special">))</span> <span class="special">/</span>
+                    <span class="identifier">variance</span><span class="special">)-</span>
+                    <span class="number">1</span><span class="special">)</span></code>
+                  </p>
+                  </td>
+</tr>
+<tr>
+<td>
+                  <p>
+                    beta
+                  </p>
+                  <p>
+                    from mean and variance
+                  </p>
+                  </td>
+<td>
+                  <p>
+                    <code class="computeroutput"><span class="special">(</span><span class="number">1</span>
+                    <span class="special">-</span> <span class="identifier">mean</span><span class="special">)</span> <span class="special">*</span>
+                    <span class="special">(((</span><span class="identifier">mean</span>
+                    <span class="special">*</span> <span class="special">(</span><span class="number">1</span> <span class="special">-</span> <span class="identifier">mean</span><span class="special">))</span>
+                    <span class="special">/</span><span class="identifier">variance</span><span class="special">)-</span><span class="number">1</span><span class="special">)</span></code>
+                  </p>
+                  </td>
+</tr>
+<tr>
+<td>
+                  <p>
+                    The member functions <code class="computeroutput"><span class="identifier">find_alpha</span></code>
+                    and <code class="computeroutput"><span class="identifier">find_beta</span></code>
+                  </p>
+                  <p>
+                    from cdf and probability x
+                  </p>
+                  <p>
+                    and <span class="bold"><strong>either</strong></span> <code class="computeroutput"><span class="identifier">alpha</span></code>
+                    or <code class="computeroutput"><span class="identifier">beta</span></code>
+                  </p>
+                  </td>
+<td>
+                  <p>
+                    Implemented in terms of the inverse incomplete beta functions
+                  </p>
+                  <p>
+                    <a class="link" href="../../../special/sf_beta/ibeta_inv_function.html" title="The Incomplete Beta Function Inverses">ibeta_inva</a>,
+                    and <a class="link" href="../../../special/sf_beta/ibeta_inv_function.html" title="The Incomplete Beta Function Inverses">ibeta_invb</a>
+                    respectively.
+                  </p>
+                  </td>
+</tr>
+<tr>
+<td>
+                  <p>
+                    <code class="computeroutput"><span class="identifier">find_alpha</span></code>
+                  </p>
+                  </td>
+<td>
+                  <p>
+                    <code class="computeroutput"><span class="identifier">ibeta_inva</span><span class="special">(</span><span class="identifier">beta</span><span class="special">,</span>
+                    <span class="identifier">x</span><span class="special">,</span>
+                    <span class="identifier">probability</span><span class="special">)</span></code>
+                  </p>
+                  </td>
+</tr>
+<tr>
+<td>
+                  <p>
+                    <code class="computeroutput"><span class="identifier">find_beta</span></code>
+                  </p>
+                  </td>
+<td>
+                  <p>
+                    <code class="computeroutput"><span class="identifier">ibeta_invb</span><span class="special">(</span><span class="identifier">alpha</span><span class="special">,</span>
+                    <span class="identifier">x</span><span class="special">,</span>
+                    <span class="identifier">probability</span><span class="special">)</span></code>
+                  </p>
+                  </td>
+</tr>
+</tbody>
+</table></div>
+<a name="math_toolkit.dist.dist_ref.dists.beta_dist.references"></a><h5>
+<a name="id649857"></a>
+            <a class="link" href="beta_dist.html#math_toolkit.dist.dist_ref.dists.beta_dist.references">References</a>
+          </h5>
+<p>
+            <a href="http://en.wikipedia.org/wiki/Beta_distribution" target="_top">Wikipedia
+            Beta distribution</a>
+          </p>
+<p>
+            <a href="http://www.itl.nist.gov/div898/handbook/eda/section3/eda366h.htm" target="_top">NIST
+            Exploratory Data Analysis</a>
+          </p>
+<p>
+            <a href="http://mathworld.wolfram.com/BetaDistribution.html" target="_top">Wolfram
+            MathWorld</a>
+          </p>
+</div>
+<table xmlns:rev="http://www.cs.rpi.edu/~gregod/boost/tools/doc/revision" width="100%"><tr>
+<td align="left"></td>
+<td align="right"><div class="copyright-footer">Copyright © 2006 , 2007, 2008 John Maddock, Paul A. Bristow, Hubert
+      Holin, Xiaogang Zhang, Bruno Lalande and Gautam Sewani<p>
+        Distributed under the Boost Software License, Version 1.0. (See accompanying
+        file LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_0.txt)
+      </p>
+</div></td>
+</tr></table>
+<hr>
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@@ -0,0 +1,922 @@
+<html>
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+<meta http-equiv="Content-Type" content="text/html; charset=ISO-8859-1">
+<title>Binomial Distribution</title>
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+</div>
+<div class="section" lang="en">
+<div class="titlepage"><div><div><h5 class="title">
+<a name="math_toolkit.dist.dist_ref.dists.binomial_dist"></a><a class="link" href="binomial_dist.html" title="Binomial Distribution">
+          Binomial Distribution</a>
+</h5></div></div></div>
+<p>
+            
+</p>
+<pre class="programlisting"><span class="preprocessor">#include</span> <span class="special">&lt;</span><span class="identifier">boost</span><span class="special">/</span><span class="identifier">math</span><span class="special">/</span><span class="identifier">distributions</span><span class="special">/</span><span class="identifier">binomial</span><span class="special">.</span><span class="identifier">hpp</span><span class="special">&gt;</span></pre>
+<p>
+          </p>
+<pre class="programlisting"><span class="keyword">namespace</span> <span class="identifier">boost</span><span class="special">{</span> <span class="keyword">namespace</span> <span class="identifier">math</span><span class="special">{</span> 
+
+<span class="keyword">template</span> <span class="special">&lt;</span><span class="keyword">class</span> <span class="identifier">RealType</span> <span class="special">=</span> <span class="keyword">double</span><span class="special">,</span> 
+          <span class="keyword">class</span> <a class="link" href="../../../policy.html" title="Policies">Policy</a>   <span class="special">=</span> <a class="link" href="../../../policy/pol_ref/pol_ref_ref.html" title="Policy Class Reference">policies::policy&lt;&gt;</a> <span class="special">&gt;</span>
+<span class="keyword">class</span> <span class="identifier">binomial_distribution</span><span class="special">;</span>
+
+<span class="keyword">typedef</span> <span class="identifier">binomial_distribution</span><span class="special">&lt;&gt;</span> <span class="identifier">binomial</span><span class="special">;</span>
+
+<span class="keyword">template</span> <span class="special">&lt;</span><span class="keyword">class</span> <span class="identifier">RealType</span><span class="special">,</span> <span class="keyword">class</span> <a class="link" href="../../../policy.html" title="Policies">Policy</a><span class="special">&gt;</span>
+<span class="keyword">class</span> <span class="identifier">binomial_distribution</span>
+<span class="special">{</span>
+<span class="keyword">public</span><span class="special">:</span>
+   <span class="keyword">typedef</span> <span class="identifier">RealType</span>  <span class="identifier">value_type</span><span class="special">;</span>
+   <span class="keyword">typedef</span> <span class="identifier">Policy</span>    <span class="identifier">policy_type</span><span class="special">;</span>
+   
+   <span class="keyword">static</span> <span class="keyword">const</span> <span class="emphasis"><em>unspecified-type</em></span> <span class="identifier">cloppper_pearson_exact_interval</span><span class="special">;</span>
+   <span class="keyword">static</span> <span class="keyword">const</span> <span class="emphasis"><em>unspecified-type</em></span> <span class="identifier">jeffreys_prior_interval</span><span class="special">;</span>
+   
+   <span class="comment">// construct:
+</span>   <span class="identifier">binomial_distribution</span><span class="special">(</span><span class="identifier">RealType</span> <span class="identifier">n</span><span class="special">,</span> <span class="identifier">RealType</span> <span class="identifier">p</span><span class="special">);</span>
+   
+   <span class="comment">// parameter access::
+</span>   <span class="identifier">RealType</span> <span class="identifier">success_fraction</span><span class="special">()</span> <span class="keyword">const</span><span class="special">;</span>
+   <span class="identifier">RealType</span> <span class="identifier">trials</span><span class="special">()</span> <span class="keyword">const</span><span class="special">;</span>
+   
+   <span class="comment">// Bounds on success fraction:
+</span>   <span class="keyword">static</span> <span class="identifier">RealType</span> <span class="identifier">find_lower_bound_on_p</span><span class="special">(</span>
+      <span class="identifier">RealType</span> <span class="identifier">trials</span><span class="special">,</span> 
+      <span class="identifier">RealType</span> <span class="identifier">successes</span><span class="special">,</span>
+      <span class="identifier">RealType</span> <span class="identifier">probability</span><span class="special">,</span>
+      <span class="emphasis"><em>unspecified-type</em></span> <span class="identifier">method</span> <span class="special">=</span> <span class="identifier">clopper_pearson_exact_interval</span><span class="special">);</span>
+   <span class="keyword">static</span> <span class="identifier">RealType</span> <span class="identifier">find_upper_bound_on_p</span><span class="special">(</span>
+      <span class="identifier">RealType</span> <span class="identifier">trials</span><span class="special">,</span> 
+      <span class="identifier">RealType</span> <span class="identifier">successes</span><span class="special">,</span>
+      <span class="identifier">RealType</span> <span class="identifier">probability</span><span class="special">,</span>
+      <span class="emphasis"><em>unspecified-type</em></span> <span class="identifier">method</span> <span class="special">=</span> <span class="identifier">clopper_pearson_exact_interval</span><span class="special">);</span>
+      
+   <span class="comment">// estimate min/max number of trials:
+</span>   <span class="keyword">static</span> <span class="identifier">RealType</span> <span class="identifier">find_minimum_number_of_trials</span><span class="special">(</span>
+      <span class="identifier">RealType</span> <span class="identifier">k</span><span class="special">,</span>     <span class="comment">// number of events
+</span>      <span class="identifier">RealType</span> <span class="identifier">p</span><span class="special">,</span>     <span class="comment">// success fraction
+</span>      <span class="identifier">RealType</span> <span class="identifier">alpha</span><span class="special">);</span> <span class="comment">// risk level
+</span>      
+   <span class="keyword">static</span> <span class="identifier">RealType</span> <span class="identifier">find_maximum_number_of_trials</span><span class="special">(</span>
+      <span class="identifier">RealType</span> <span class="identifier">k</span><span class="special">,</span>     <span class="comment">// number of events
+</span>      <span class="identifier">RealType</span> <span class="identifier">p</span><span class="special">,</span>     <span class="comment">// success fraction
+</span>      <span class="identifier">RealType</span> <span class="identifier">alpha</span><span class="special">);</span> <span class="comment">// risk level
+</span><span class="special">};</span>
+
+<span class="special">}}</span> <span class="comment">// namespaces
+</span></pre>
+<p>
+            The class type <code class="computeroutput"><span class="identifier">binomial_distribution</span></code>
+            represents a <a href="http://mathworld.wolfram.com/BinomialDistribution.html" target="_top">binomial
+            distribution</a>: it is used when there are exactly two mutually
+            exclusive outcomes of a trial. These outcomes are labelled "success"
+            and "failure". The binomial distribution
+            is used to obtain the probability of observing k successes in N trials,
+            with the probability of success on a single trial denoted by p. The binomial
+            distribution assumes that p is fixed for all trials.
+          </p>
+<div class="note"><table border="0" summary="Note">
+<tr>
+<td rowspan="2" align="center" valign="top" width="25"><img alt="[Note]" src="../../../../../../doc/html/images/note.png"></td>
+<th align="left">Note</th>
+</tr>
+<tr><td align="left" valign="top"><p>
+              The random variable for the binomial distribution is the number of
+              successes, (the number of trials is a fixed property of the distribution)
+              whereas for the negative binomial, the random variable is the number
+              of trials, for a fixed number of successes.
+            </p></td></tr>
+</table></div>
+<p>
+            The PDF for the binomial distribution is given by:
+          </p>
+<p>
+            <span class="inlinemediaobject"><img src="../../../../../equations/binomial_ref2.png"></span>
+          </p>
+<p>
+            The following two graphs illustrate how the PDF changes depending upon
+            the distributions parameters, first we'll keep the success fraction
+            <span class="emphasis"><em>p</em></span> fixed at 0.5, and vary the sample size:
+          </p>
+<p>
+            <span class="inlinemediaobject"><img src="../../../../../graphs/binomial_pdf_1.png" align="middle"></span>
+          </p>
+<p>
+            Alternatively, we can keep the sample size fixed at N=20 and vary the
+            success fraction <span class="emphasis"><em>p</em></span>:
+          </p>
+<p>
+            <span class="inlinemediaobject"><img src="../../../../../graphs/binomial_pdf_2.png" align="middle"></span>
+          </p>
+<p>
+            </p>
+<div class="caution"><table border="0" summary="Caution">
+<tr>
+<td rowspan="2" align="center" valign="top" width="25"><img alt="[Caution]" src="../../../../../../doc/html/images/caution.png"></td>
+<th align="left">Caution</th>
+</tr>
+<tr><td align="left" valign="top">
+<p>
+                The Binomial distribution is a discrete distribution: internally
+                functions like the <code class="computeroutput"><span class="identifier">cdf</span></code>
+                and <code class="computeroutput"><span class="identifier">pdf</span></code> are treated
+                "as if" they are continuous functions, but in reality the
+                results returned from these functions only have meaning if an integer
+                value is provided for the random variate argument.
+              </p>
+<p>
+                The quantile function will by default return an integer result that
+                has been <span class="emphasis"><em>rounded outwards</em></span>. That is to say lower
+                quantiles (where the probability is less than 0.5) are rounded downward,
+                and upper quantiles (where the probability is greater than 0.5) are
+                rounded upwards. This behaviour ensures that if an X% quantile is
+                requested, then <span class="emphasis"><em>at least</em></span> the requested coverage
+                will be present in the central region, and <span class="emphasis"><em>no more than</em></span>
+                the requested coverage will be present in the tails.
+              </p>
+<p>
+                This behaviour can be changed so that the quantile functions are
+                rounded differently, or even return a real-valued result using <a class="link" href="../../../policy/pol_overview.html" title="Policy Overview">Policies</a>. It is
+                strongly recommended that you read the tutorial <a class="link" href="../../../policy/pol_tutorial/understand_dis_quant.html" title="Understanding Quantiles of Discrete Distributions">Understanding
+                Quantiles of Discrete Distributions</a> before using the quantile
+                function on the Binomial distribution. The <a class="link" href="../../../policy/pol_ref/discrete_quant_ref.html" title="Discrete Quantile Policies">reference
+                docs</a> describe how to change the rounding policy for these
+                distributions.
+              </p>
+</td></tr>
+</table></div>
+<p>
+          </p>
+<a name="math_toolkit.dist.dist_ref.dists.binomial_dist.member_functions"></a><h5>
+<a name="id651234"></a>
+            <a class="link" href="binomial_dist.html#math_toolkit.dist.dist_ref.dists.binomial_dist.member_functions">Member
+            Functions</a>
+          </h5>
+<a name="math_toolkit.dist.dist_ref.dists.binomial_dist.construct"></a><h6>
+<a name="id651259"></a>
+            <a class="link" href="binomial_dist.html#math_toolkit.dist.dist_ref.dists.binomial_dist.construct">Construct</a>
+          </h6>
+<pre class="programlisting"><span class="identifier">binomial_distribution</span><span class="special">(</span><span class="identifier">RealType</span> <span class="identifier">n</span><span class="special">,</span> <span class="identifier">RealType</span> <span class="identifier">p</span><span class="special">);</span>
+</pre>
+<p>
+            Constructor: <span class="emphasis"><em>n</em></span> is the total number of trials, <span class="emphasis"><em>p</em></span>
+            is the probability of success of a single trial.
+          </p>
+<p>
+            Requires <code class="computeroutput"><span class="number">0</span> <span class="special">&lt;=</span>
+            <span class="identifier">p</span> <span class="special">&lt;=</span>
+            <span class="number">1</span></code>, and <code class="computeroutput"><span class="identifier">n</span>
+            <span class="special">&gt;=</span> <span class="number">0</span></code>,
+            otherwise calls <a class="link" href="../../../main_overview/error_handling.html#domain_error">domain_error</a>.
+          </p>
+<a name="math_toolkit.dist.dist_ref.dists.binomial_dist.accessors"></a><h6>
+<a name="id651423"></a>
+            <a class="link" href="binomial_dist.html#math_toolkit.dist.dist_ref.dists.binomial_dist.accessors">Accessors</a>
+          </h6>
+<pre class="programlisting"><span class="identifier">RealType</span> <span class="identifier">success_fraction</span><span class="special">()</span> <span class="keyword">const</span><span class="special">;</span>
+</pre>
+<p>
+            Returns the parameter <span class="emphasis"><em>p</em></span> from which this distribution
+            was constructed.
+          </p>
+<pre class="programlisting"><span class="identifier">RealType</span> <span class="identifier">trials</span><span class="special">()</span> <span class="keyword">const</span><span class="special">;</span>
+</pre>
+<p>
+            Returns the parameter <span class="emphasis"><em>n</em></span> from which this distribution
+            was constructed.
+          </p>
+<a name="math_toolkit.dist.dist_ref.dists.binomial_dist.lower_bound_on_the_success_fraction"></a><h6>
+<a name="id651542"></a>
+            <a class="link" href="binomial_dist.html#math_toolkit.dist.dist_ref.dists.binomial_dist.lower_bound_on_the_success_fraction">Lower
+            Bound on the Success Fraction</a>
+          </h6>
+<pre class="programlisting"><span class="keyword">static</span> <span class="identifier">RealType</span> <span class="identifier">find_lower_bound_on_p</span><span class="special">(</span>
+   <span class="identifier">RealType</span> <span class="identifier">trials</span><span class="special">,</span> 
+   <span class="identifier">RealType</span> <span class="identifier">successes</span><span class="special">,</span>
+   <span class="identifier">RealType</span> <span class="identifier">alpha</span><span class="special">,</span>
+   <span class="emphasis"><em>unspecified-type</em></span> <span class="identifier">method</span> <span class="special">=</span> <span class="identifier">clopper_pearson_exact_interval</span><span class="special">);</span>
+</pre>
+<p>
+            Returns a lower bound on the success fraction:
+          </p>
+<div class="variablelist">
+<p class="title"><b></b></p>
+<dl>
+<dt><span class="term">trials</span></dt>
+<dd><p>
+                The total number of trials conducted.
+              </p></dd>
+<dt><span class="term">successes</span></dt>
+<dd><p>
+                The number of successes that occurred.
+              </p></dd>
+<dt><span class="term">alpha</span></dt>
+<dd><p>
+                The largest acceptable probability that the true value of the success
+                fraction is <span class="bold"><strong>less than</strong></span> the value
+                returned.
+              </p></dd>
+<dt><span class="term">method</span></dt>
+<dd><p>
+                An optional parameter that specifies the method to be used to compute
+                the interval (See below).
+              </p></dd>
+</dl>
+</div>
+<p>
+            For example, if you observe <span class="emphasis"><em>k</em></span> successes from <span class="emphasis"><em>n</em></span>
+            trials the best estimate for the success fraction is simply <span class="emphasis"><em>k/n</em></span>,
+            but if you want to be 95% sure that the true value is <span class="bold"><strong>greater
+            than</strong></span> some value, <span class="emphasis"><em>p<sub>min</sub></em></span>, then:
+          </p>
+<pre class="programlisting"><span class="identifier">p</span><sub>min</sub> <span class="special">=</span> <span class="identifier">binomial_distribution</span><span class="special">&lt;</span><span class="identifier">RealType</span><span class="special">&gt;::</span><span class="identifier">find_lower_bound_on_p</span><span class="special">(</span>
+                    <span class="identifier">n</span><span class="special">,</span> <span class="identifier">k</span><span class="special">,</span> <span class="number">0.05</span><span class="special">);</span>
+</pre>
+<p>
+            <a class="link" href="../../stat_tut/weg/binom_eg/binom_conf.html" title="Calculating Confidence Limits on the Frequency of Occurrence for a Binomial Distribution">See
+            worked example.</a>
+          </p>
+<p>
+            There are currently two possible values available for the <span class="emphasis"><em>method</em></span>
+            optional parameter: <span class="emphasis"><em>clopper_pearson_exact_interval</em></span>
+            or <span class="emphasis"><em>jeffreys_prior_interval</em></span>. These constants are
+            both members of class template <code class="computeroutput"><span class="identifier">binomial_distribution</span></code>,
+            so usage is for example:
+          </p>
+<pre class="programlisting"><span class="identifier">p</span> <span class="special">=</span> <span class="identifier">binomial_distribution</span><span class="special">&lt;</span><span class="identifier">RealType</span><span class="special">&gt;::</span><span class="identifier">find_lower_bound_on_p</span><span class="special">(</span>
+    <span class="identifier">n</span><span class="special">,</span> <span class="identifier">k</span><span class="special">,</span> <span class="number">0.05</span><span class="special">,</span> <span class="identifier">binomial_distribution</span><span class="special">&lt;</span><span class="identifier">RealType</span><span class="special">&gt;::</span><span class="identifier">jeffreys_prior_interval</span><span class="special">);</span>
+</pre>
+<p>
+            The default method if this parameter is not specified is the Clopper
+            Pearson "exact" interval. This produces an interval that guarantees
+            at least <code class="computeroutput"><span class="number">100</span><span class="special">(</span><span class="number">1</span><span class="special">-</span><span class="identifier">alpha</span><span class="special">)%</span></code> coverage, but which is known to be
+            overly conservative, sometimes producing intervals with much greater
+            than the requested coverage.
+          </p>
+<p>
+            The alternative calculation method produces a non-informative Jeffreys
+            Prior interval. It produces <code class="computeroutput"><span class="number">100</span><span class="special">(</span><span class="number">1</span><span class="special">-</span><span class="identifier">alpha</span><span class="special">)%</span></code>
+            coverage only <span class="emphasis"><em>in the average case</em></span>, though is typically
+            very close to the requested coverage level. It is one of the main methods
+            of calculation recommended in the review by Brown, Cai and DasGupta.
+          </p>
+<p>
+            Please note that the "textbook" calculation method using a
+            normal approximation (the Wald interval) is deliberately not provided:
+            it is known to produce consistently poor results, even when the sample
+            size is surprisingly large. Refer to Brown, Cai and DasGupta for a full
+            explanation. Many other methods of calculation are available, and may
+            be more appropriate for specific situations. Unfortunately there appears
+            to be no consensus amongst statisticians as to which is "best":
+            refer to the discussion at the end of Brown, Cai and DasGupta for examples.
+          </p>
+<p>
+            The two methods provided here were chosen principally because they can
+            be used for both one and two sided intervals. See also:
+          </p>
+<p>
+            Lawrence D. Brown, T. Tony Cai and Anirban DasGupta (2001), Interval
+            Estimation for a Binomial Proportion, Statistical Science, Vol. 16, No.
+            2, 101-133.
+          </p>
+<p>
+            T. Tony Cai (2005), One-sided confidence intervals in discrete distributions,
+            Journal of Statistical Planning and Inference 131, 63-88.
+          </p>
+<p>
+            Agresti, A. and Coull, B. A. (1998). Approximate is better than "exact"
+            for interval estimation of binomial proportions. Amer. Statist. 52 119-126.
+          </p>
+<p>
+            Clopper, C. J. and Pearson, E. S. (1934). The use of confidence or fiducial
+            limits illustrated in the case of the binomial. Biometrika 26 404-413.
+          </p>
+<a name="math_toolkit.dist.dist_ref.dists.binomial_dist.upper_bound_on_the_success_fraction"></a><h6>
+<a name="id652220"></a>
+            <a class="link" href="binomial_dist.html#math_toolkit.dist.dist_ref.dists.binomial_dist.upper_bound_on_the_success_fraction">Upper
+            Bound on the Success Fraction</a>
+          </h6>
+<pre class="programlisting"><span class="keyword">static</span> <span class="identifier">RealType</span> <span class="identifier">find_upper_bound_on_p</span><span class="special">(</span>
+   <span class="identifier">RealType</span> <span class="identifier">trials</span><span class="special">,</span> 
+   <span class="identifier">RealType</span> <span class="identifier">successes</span><span class="special">,</span>
+   <span class="identifier">RealType</span> <span class="identifier">alpha</span><span class="special">,</span>
+   <span class="emphasis"><em>unspecified-type</em></span> <span class="identifier">method</span> <span class="special">=</span> <span class="identifier">clopper_pearson_exact_interval</span><span class="special">);</span>
+</pre>
+<p>
+            Returns an upper bound on the success fraction:
+          </p>
+<div class="variablelist">
+<p class="title"><b></b></p>
+<dl>
+<dt><span class="term">trials</span></dt>
+<dd><p>
+                The total number of trials conducted.
+              </p></dd>
+<dt><span class="term">successes</span></dt>
+<dd><p>
+                The number of successes that occurred.
+              </p></dd>
+<dt><span class="term">alpha</span></dt>
+<dd><p>
+                The largest acceptable probability that the true value of the success
+                fraction is <span class="bold"><strong>greater than</strong></span> the value
+                returned.
+              </p></dd>
+<dt><span class="term">method</span></dt>
+<dd><p>
+                An optional parameter that specifies the method to be used to compute
+                the interval. Refer to the documentation for <code class="computeroutput"><span class="identifier">find_upper_bound_on_p</span></code>
+                above for the meaning of the method options.
+              </p></dd>
+</dl>
+</div>
+<p>
+            For example, if you observe <span class="emphasis"><em>k</em></span> successes from <span class="emphasis"><em>n</em></span>
+            trials the best estimate for the success fraction is simply <span class="emphasis"><em>k/n</em></span>,
+            but if you want to be 95% sure that the true value is <span class="bold"><strong>less
+            than</strong></span> some value, <span class="emphasis"><em>p<sub>max</sub></em></span>, then:
+          </p>
+<pre class="programlisting"><span class="identifier">p</span><sub>max</sub> <span class="special">=</span> <span class="identifier">binomial_distribution</span><span class="special">&lt;</span><span class="identifier">RealType</span><span class="special">&gt;::</span><span class="identifier">find_upper_bound_on_p</span><span class="special">(</span>
+                    <span class="identifier">n</span><span class="special">,</span> <span class="identifier">k</span><span class="special">,</span> <span class="number">0.05</span><span class="special">);</span>
+</pre>
+<p>
+            <a class="link" href="../../stat_tut/weg/binom_eg/binom_conf.html" title="Calculating Confidence Limits on the Frequency of Occurrence for a Binomial Distribution">See
+            worked example.</a>
+          </p>
+<div class="note"><table border="0" summary="Note">
+<tr>
+<td rowspan="2" align="center" valign="top" width="25"><img alt="[Note]" src="../../../../../../doc/html/images/note.png"></td>
+<th align="left">Note</th>
+</tr>
+<tr><td align="left" valign="top">
+<p>
+              In order to obtain a two sided bound on the success fraction, you call
+              both <code class="computeroutput"><span class="identifier">find_lower_bound_on_p</span></code>
+              <span class="bold"><strong>and</strong></span> <code class="computeroutput"><span class="identifier">find_upper_bound_on_p</span></code>
+              each with the same arguments.
+            </p>
+<p>
+              If the desired risk level that the true success fraction lies outside
+              the bounds is &#945;, then you pass &#945;/2 to these functions.
+            </p>
+<p>
+              So for example a two sided 95% confidence interval would be obtained
+              by passing &#945; = 0.025 to each of the functions.
+            </p>
+<p>
+              <a class="link" href="../../stat_tut/weg/binom_eg/binom_conf.html" title="Calculating Confidence Limits on the Frequency of Occurrence for a Binomial Distribution">See
+              worked example.</a>
+            </p>
+</td></tr>
+</table></div>
+<a name="math_toolkit.dist.dist_ref.dists.binomial_dist.estimating_the_number_of_trials_required_for_a_certain_number_of_successes"></a><h6>
+<a name="id652674"></a>
+            <a class="link" href="binomial_dist.html#math_toolkit.dist.dist_ref.dists.binomial_dist.estimating_the_number_of_trials_required_for_a_certain_number_of_successes">Estimating
+            the Number of Trials Required for a Certain Number of Successes</a>
+          </h6>
+<pre class="programlisting"><span class="keyword">static</span> <span class="identifier">RealType</span> <span class="identifier">find_minimum_number_of_trials</span><span class="special">(</span>
+   <span class="identifier">RealType</span> <span class="identifier">k</span><span class="special">,</span>     <span class="comment">// number of events
+</span>   <span class="identifier">RealType</span> <span class="identifier">p</span><span class="special">,</span>     <span class="comment">// success fraction
+</span>   <span class="identifier">RealType</span> <span class="identifier">alpha</span><span class="special">);</span> <span class="comment">// probability threshold
+</span></pre>
+<p>
+            This function estimates the minimum number of trials required to ensure
+            that more than k events is observed with a level of risk <span class="emphasis"><em>alpha</em></span>
+            that k or fewer events occur.
+          </p>
+<div class="variablelist">
+<p class="title"><b></b></p>
+<dl>
+<dt><span class="term">k</span></dt>
+<dd><p>
+                The number of success observed.
+              </p></dd>
+<dt><span class="term">p</span></dt>
+<dd><p>
+                The probability of success for each trial.
+              </p></dd>
+<dt><span class="term">alpha</span></dt>
+<dd><p>
+                The maximum acceptable probability that k events or fewer will be
+                observed.
+              </p></dd>
+</dl>
+</div>
+<p>
+            For example:
+          </p>
+<pre class="programlisting"><span class="identifier">binomial_distribution</span><span class="special">&lt;</span><span class="identifier">RealType</span><span class="special">&gt;::</span><span class="identifier">find_number_of_trials</span><span class="special">(</span><span class="number">10</span><span class="special">,</span> <span class="number">0.5</span><span class="special">,</span> <span class="number">0.05</span><span class="special">);</span>
+</pre>
+<p>
+            Returns the smallest number of trials we must conduct to be 95% sure
+            of seeing 10 events that occur with frequency one half.
+          </p>
+<a name="math_toolkit.dist.dist_ref.dists.binomial_dist.estimating_the_maximum_number_of_trials_to_ensure_no_more_than_a_certain_number_of_successes"></a><h6>
+<a name="id652964"></a>
+            <a class="link" href="binomial_dist.html#math_toolkit.dist.dist_ref.dists.binomial_dist.estimating_the_maximum_number_of_trials_to_ensure_no_more_than_a_certain_number_of_successes">Estimating
+            the Maximum Number of Trials to Ensure no more than a Certain Number
+            of Successes</a>
+          </h6>
+<pre class="programlisting"><span class="keyword">static</span> <span class="identifier">RealType</span> <span class="identifier">find_maximum_number_of_trials</span><span class="special">(</span>
+   <span class="identifier">RealType</span> <span class="identifier">k</span><span class="special">,</span>     <span class="comment">// number of events
+</span>   <span class="identifier">RealType</span> <span class="identifier">p</span><span class="special">,</span>     <span class="comment">// success fraction
+</span>   <span class="identifier">RealType</span> <span class="identifier">alpha</span><span class="special">);</span> <span class="comment">// probability threshold
+</span></pre>
+<p>
+            This function estimates the maximum number of trials we can conduct to
+            ensure that k successes or fewer are observed, with a risk <span class="emphasis"><em>alpha</em></span>
+            that more than k occur.
+          </p>
+<div class="variablelist">
+<p class="title"><b></b></p>
+<dl>
+<dt><span class="term">k</span></dt>
+<dd><p>
+                The number of success observed.
+              </p></dd>
+<dt><span class="term">p</span></dt>
+<dd><p>
+                The probability of success for each trial.
+              </p></dd>
+<dt><span class="term">alpha</span></dt>
+<dd><p>
+                The maximum acceptable probability that more than k events will be
+                observed.
+              </p></dd>
+</dl>
+</div>
+<p>
+            For example:
+          </p>
+<pre class="programlisting"><span class="identifier">binomial_distribution</span><span class="special">&lt;</span><span class="identifier">RealType</span><span class="special">&gt;::</span><span class="identifier">find_maximum_number_of_trials</span><span class="special">(</span><span class="number">0</span><span class="special">,</span> <span class="number">1e-6</span><span class="special">,</span> <span class="number">0.05</span><span class="special">);</span>
+</pre>
+<p>
+            Returns the largest number of trials we can conduct and still be 95%
+            certain of not observing any events that occur with one in a million
+            frequency. This is typically used in failure analysis.
+          </p>
+<p>
+            <a class="link" href="../../stat_tut/weg/binom_eg/binom_size_eg.html" title="Estimating Sample Sizes for a Binomial Distribution.">See
+            Worked Example.</a>
+          </p>
+<a name="math_toolkit.dist.dist_ref.dists.binomial_dist.non_member_accessors"></a><h5>
+<a name="id653268"></a>
+            <a class="link" href="binomial_dist.html#math_toolkit.dist.dist_ref.dists.binomial_dist.non_member_accessors">Non-member
+            Accessors</a>
+          </h5>
+<p>
+            All the <a class="link" href="../nmp.html" title="Non-Member Properties">usual non-member
+            accessor functions</a> that are generic to all distributions are supported:
+            <a class="link" href="../nmp.html#math.dist.cdf">Cumulative Distribution Function</a>,
+            <a class="link" href="../nmp.html#math.dist.pdf">Probability Density Function</a>, <a class="link" href="../nmp.html#math.dist.quantile">Quantile</a>, <a class="link" href="../nmp.html#math.dist.hazard">Hazard
+            Function</a>, <a class="link" href="../nmp.html#math.dist.chf">Cumulative Hazard Function</a>,
+            <a class="link" href="../nmp.html#math.dist.mean">mean</a>, <a class="link" href="../nmp.html#math.dist.median">median</a>,
+            <a class="link" href="../nmp.html#math.dist.mode">mode</a>, <a class="link" href="../nmp.html#math.dist.variance">variance</a>,
+            <a class="link" href="../nmp.html#math.dist.sd">standard deviation</a>, <a class="link" href="../nmp.html#math.dist.skewness">skewness</a>,
+            <a class="link" href="../nmp.html#math.dist.kurtosis">kurtosis</a>, <a class="link" href="../nmp.html#math.dist.kurtosis_excess">kurtosis_excess</a>,
+            <a class="link" href="../nmp.html#math.dist.range">range</a> and <a class="link" href="../nmp.html#math.dist.support">support</a>.
+          </p>
+<p>
+            The domain for the random variable <span class="emphasis"><em>k</em></span> is <code class="computeroutput"><span class="number">0</span> <span class="special">&lt;=</span> <span class="identifier">k</span> <span class="special">&lt;=</span> <span class="identifier">N</span></code>, otherwise a <a class="link" href="../../../main_overview/error_handling.html#domain_error">domain_error</a>
+            is returned.
+          </p>
+<p>
+            It's worth taking a moment to define what these accessors actually mean
+            in the context of this distribution:
+          </p>
+<div class="table">
+<a name="id653490"></a><p class="title"><b>Table 11. Meaning of the non-member accessors</b></p>
+<div class="table-contents"><table class="table" summary="Meaning of the non-member accessors">
+<colgroup>
+<col>
+<col>
+</colgroup>
+<thead><tr>
+<th>
+                <p>
+                  Function
+                </p>
+                </th>
+<th>
+                <p>
+                  Meaning
+                </p>
+                </th>
+</tr></thead>
+<tbody>
+<tr>
+<td>
+                <p>
+                  <a class="link" href="../nmp.html#math.dist.pdf">Probability Density Function</a>
+                </p>
+                </td>
+<td>
+                <p>
+                  The probability of obtaining <span class="bold"><strong>exactly k successes</strong></span>
+                  from n trials with success fraction p. For example:
+                </p>
+                <p>
+                  <code class="computeroutput"><span class="identifier">pdf</span><span class="special">(</span><span class="identifier">binomial</span><span class="special">(</span><span class="identifier">n</span><span class="special">,</span>
+                  <span class="identifier">p</span><span class="special">),</span>
+                  <span class="identifier">k</span><span class="special">)</span></code>
+                </p>
+                </td>
+</tr>
+<tr>
+<td>
+                <p>
+                  <a class="link" href="../nmp.html#math.dist.cdf">Cumulative Distribution Function</a>
+                </p>
+                </td>
+<td>
+                <p>
+                  The probability of obtaining <span class="bold"><strong>k successes
+                  or fewer</strong></span> from n trials with success fraction p. For
+                  example:
+                </p>
+                <p>
+                  <code class="computeroutput"><span class="identifier">cdf</span><span class="special">(</span><span class="identifier">binomial</span><span class="special">(</span><span class="identifier">n</span><span class="special">,</span>
+                  <span class="identifier">p</span><span class="special">),</span>
+                  <span class="identifier">k</span><span class="special">)</span></code>
+                </p>
+                </td>
+</tr>
+<tr>
+<td>
+                <p>
+                  <a class="link" href="../nmp.html#math.dist.ccdf">Complement of the Cumulative Distribution
+                  Function</a>
+                </p>
+                </td>
+<td>
+                <p>
+                  The probability of obtaining <span class="bold"><strong>more than k
+                  successes</strong></span> from n trials with success fraction p. For
+                  example:
+                </p>
+                <p>
+                  <code class="computeroutput"><span class="identifier">cdf</span><span class="special">(</span><span class="identifier">complement</span><span class="special">(</span><span class="identifier">binomial</span><span class="special">(</span><span class="identifier">n</span><span class="special">,</span>
+                  <span class="identifier">p</span><span class="special">),</span>
+                  <span class="identifier">k</span><span class="special">))</span></code>
+                </p>
+                </td>
+</tr>
+<tr>
+<td>
+                <p>
+                  <a class="link" href="../nmp.html#math.dist.quantile">Quantile</a>
+                </p>
+                </td>
+<td>
+                <p>
+                  The <span class="bold"><strong>greatest</strong></span> number of successes
+                  that may be observed from n trials with success fraction p, at
+                  probability P. Note that the value returned is a real-number, and
+                  not an integer. Depending on the use case you may want to take
+                  either the floor or ceiling of the result. For example:
+                </p>
+                <p>
+                  <code class="computeroutput"><span class="identifier">quantile</span><span class="special">(</span><span class="identifier">binomial</span><span class="special">(</span><span class="identifier">n</span><span class="special">,</span>
+                  <span class="identifier">p</span><span class="special">),</span>
+                  <span class="identifier">P</span><span class="special">)</span></code>
+                </p>
+                </td>
+</tr>
+<tr>
+<td>
+                <p>
+                  <a class="link" href="../nmp.html#math.dist.quantile_c">Quantile from the complement
+                  of the probability</a>
+                </p>
+                </td>
+<td>
+                <p>
+                  The <span class="bold"><strong>smallest</strong></span> number of successes
+                  that may be observed from n trials with success fraction p, at
+                  probability P. Note that the value returned is a real-number, and
+                  not an integer. Depending on the use case you may want to take
+                  either the floor or ceiling of the result. For example:
+                </p>
+                <p>
+                  <code class="computeroutput"><span class="identifier">quantile</span><span class="special">(</span><span class="identifier">complement</span><span class="special">(</span><span class="identifier">binomial</span><span class="special">(</span><span class="identifier">n</span><span class="special">,</span>
+                  <span class="identifier">p</span><span class="special">),</span>
+                  <span class="identifier">P</span><span class="special">))</span></code>`
+                </p>
+                </td>
+</tr>
+</tbody>
+</table></div>
+</div>
+<br class="table-break"><a name="math_toolkit.dist.dist_ref.dists.binomial_dist.examples"></a><h5>
+<a name="id654066"></a>
+            <a class="link" href="binomial_dist.html#math_toolkit.dist.dist_ref.dists.binomial_dist.examples">Examples</a>
+          </h5>
+<p>
+            Various <a class="link" href="../../stat_tut/weg/binom_eg.html" title="Binomial Distribution Examples">worked
+            examples</a> are available illustrating the use of the binomial distribution.
+          </p>
+<a name="math_toolkit.dist.dist_ref.dists.binomial_dist.accuracy"></a><h5>
+<a name="id654108"></a>
+            <a class="link" href="binomial_dist.html#math_toolkit.dist.dist_ref.dists.binomial_dist.accuracy">Accuracy</a>
+          </h5>
+<p>
+            This distribution is implemented using the incomplete beta functions
+            <a class="link" href="../../../special/sf_beta/ibeta_function.html" title="Incomplete Beta Functions">ibeta</a>
+            and <a class="link" href="../../../special/sf_beta/ibeta_function.html" title="Incomplete Beta Functions">ibetac</a>,
+            please refer to these functions for information on accuracy.
+          </p>
+<a name="math_toolkit.dist.dist_ref.dists.binomial_dist.implementation"></a><h5>
+<a name="id654160"></a>
+            <a class="link" href="binomial_dist.html#math_toolkit.dist.dist_ref.dists.binomial_dist.implementation">Implementation</a>
+          </h5>
+<p>
+            In the following table <span class="emphasis"><em>p</em></span> is the probability that
+            one trial will be successful (the success fraction), <span class="emphasis"><em>n</em></span>
+            is the number of trials, <span class="emphasis"><em>k</em></span> is the number of successes,
+            <span class="emphasis"><em>p</em></span> is the probability and <span class="emphasis"><em>q = 1-p</em></span>.
+          </p>
+<div class="informaltable"><table class="table">
+<colgroup>
+<col>
+<col>
+</colgroup>
+<thead><tr>
+<th>
+                  <p>
+                    Function
+                  </p>
+                  </th>
+<th>
+                  <p>
+                    Implementation Notes
+                  </p>
+                  </th>
+</tr></thead>
+<tbody>
+<tr>
+<td>
+                  <p>
+                    pdf
+                  </p>
+                  </td>
+<td>
+                  <p>
+                    Implementation is in terms of <a class="link" href="../../../special/sf_beta/beta_derivative.html" title="Derivative of the Incomplete Beta Function">ibeta_derivative</a>:
+                    if <sub>n</sub>C<sub>k </sub> is the binomial coefficient of a and b, then we have:
+                  </p>
+                  <p>
+                    <span class="inlinemediaobject"><img src="../../../../../equations/binomial_ref1.png"></span>
+                  </p>
+                  <p>
+                    Which can be evaluated as <code class="computeroutput"><span class="identifier">ibeta_derivative</span><span class="special">(</span><span class="identifier">k</span><span class="special">+</span><span class="number">1</span><span class="special">,</span> <span class="identifier">n</span><span class="special">-</span><span class="identifier">k</span><span class="special">+</span><span class="number">1</span><span class="special">,</span> <span class="identifier">p</span><span class="special">)</span> <span class="special">/</span>
+                    <span class="special">(</span><span class="identifier">n</span><span class="special">+</span><span class="number">1</span><span class="special">)</span></code>
+                  </p>
+                  <p>
+                    The function <a class="link" href="../../../special/sf_beta/beta_derivative.html" title="Derivative of the Incomplete Beta Function">ibeta_derivative</a>
+                    is used here, since it has already been optimised for the lowest
+                    possible error - indeed this is really just a thin wrapper around
+                    part of the internals of the incomplete beta function.
+                  </p>
+                  <p>
+                    There are also various special cases: refer to the code for details.
+                  </p>
+                  </td>
+</tr>
+<tr>
+<td>
+                  <p>
+                    cdf
+                  </p>
+                  </td>
+<td>
+                  <p>
+                    Using the relation:
+                  </p>
+                  <p>
+                    
+</p>
+<pre xmlns:rev="http://www.cs.rpi.edu/~gregod/boost/tools/doc/revision" class="table-programlisting"><span class="identifier">p</span> <span class="special">=</span> <span class="identifier">I</span><span class="special">[</span><span class="identifier">sub</span> <span class="number">1</span><span class="special">-</span><span class="identifier">p</span><span class="special">](</span><span class="identifier">n</span> <span class="special">-</span> <span class="identifier">k</span><span class="special">,</span> <span class="identifier">k</span> <span class="special">+</span> <span class="number">1</span><span class="special">)</span>
+  <span class="special">=</span> <span class="number">1</span> <span class="special">-</span> <span class="identifier">I</span><span class="special">[</span><span class="identifier">sub</span> <span class="identifier">p</span><span class="special">](</span><span class="identifier">k</span> <span class="special">+</span> <span class="number">1</span><span class="special">,</span> <span class="identifier">n</span> <span class="special">-</span> <span class="identifier">k</span><span class="special">)</span>
+  <span class="special">=</span> <a class="link" href="../../../special/sf_beta/ibeta_function.html" title="Incomplete Beta Functions">ibetac</a><span class="special">(</span><span class="identifier">k</span> <span class="special">+</span> <span class="number">1</span><span class="special">,</span> <span class="identifier">n</span> <span class="special">-</span> <span class="identifier">k</span><span class="special">,</span> <span class="identifier">p</span><span class="special">)</span></pre>
+<p>
+                  </p>
+                  <p>
+                    There are also various special cases: refer to the code for details.
+                  </p>
+                  </td>
+</tr>
+<tr>
+<td>
+                  <p>
+                    cdf complement
+                  </p>
+                  </td>
+<td>
+                  <p>
+                    Using the relation: q = <a class="link" href="../../../special/sf_beta/ibeta_function.html" title="Incomplete Beta Functions">ibeta</a>(k
+                    + 1, n - k, p)
+                  </p>
+                  <p>
+                    There are also various special cases: refer to the code for details.
+                  </p>
+                  </td>
+</tr>
+<tr>
+<td>
+                  <p>
+                    quantile
+                  </p>
+                  </td>
+<td>
+                  <p>
+                    Since the cdf is non-linear in variate <span class="emphasis"><em>k</em></span>
+                    none of the inverse incomplete beta functions can be used here.
+                    Instead the quantile is found numerically using a derivative
+                    free method (<a class="link" href="../../../toolkit/internals1/roots2.html" title="Root Finding Without Derivatives">TOMS
+                    Algorithm 748</a>).
+                  </p>
+                  </td>
+</tr>
+<tr>
+<td>
+                  <p>
+                    quantile from the complement
+                  </p>
+                  </td>
+<td>
+                  <p>
+                    Found numerically as above.
+                  </p>
+                  </td>
+</tr>
+<tr>
+<td>
+                  <p>
+                    mean
+                  </p>
+                  </td>
+<td>
+                  <p>
+                    <code class="computeroutput"><span class="identifier">p</span> <span class="special">*</span>
+                    <span class="identifier">n</span></code>
+                  </p>
+                  </td>
+</tr>
+<tr>
+<td>
+                  <p>
+                    variance
+                  </p>
+                  </td>
+<td>
+                  <p>
+                    <code class="computeroutput"><span class="identifier">p</span> <span class="special">*</span>
+                    <span class="identifier">n</span> <span class="special">*</span>
+                    <span class="special">(</span><span class="number">1</span><span class="special">-</span><span class="identifier">p</span><span class="special">)</span></code>
+                  </p>
+                  </td>
+</tr>
+<tr>
+<td>
+                  <p>
+                    mode
+                  </p>
+                  </td>
+<td>
+                  <p>
+                    <code class="computeroutput"><span class="identifier">floor</span><span class="special">(</span><span class="identifier">p</span> <span class="special">*</span>
+                    <span class="special">(</span><span class="identifier">n</span>
+                    <span class="special">+</span> <span class="number">1</span><span class="special">))</span></code>
+                  </p>
+                  </td>
+</tr>
+<tr>
+<td>
+                  <p>
+                    skewness
+                  </p>
+                  </td>
+<td>
+                  <p>
+                    <code class="computeroutput"><span class="special">(</span><span class="number">1</span>
+                    <span class="special">-</span> <span class="number">2</span>
+                    <span class="special">*</span> <span class="identifier">p</span><span class="special">)</span> <span class="special">/</span>
+                    <span class="identifier">sqrt</span><span class="special">(</span><span class="identifier">n</span> <span class="special">*</span>
+                    <span class="identifier">p</span> <span class="special">*</span>
+                    <span class="special">(</span><span class="number">1</span>
+                    <span class="special">-</span> <span class="identifier">p</span><span class="special">))</span></code>
+                  </p>
+                  </td>
+</tr>
+<tr>
+<td>
+                  <p>
+                    kurtosis
+                  </p>
+                  </td>
+<td>
+                  <p>
+                    <code class="computeroutput"><span class="number">3</span> <span class="special">-</span>
+                    <span class="special">(</span><span class="number">6</span>
+                    <span class="special">/</span> <span class="identifier">n</span><span class="special">)</span> <span class="special">+</span>
+                    <span class="special">(</span><span class="number">1</span>
+                    <span class="special">/</span> <span class="special">(</span><span class="identifier">n</span> <span class="special">*</span>
+                    <span class="identifier">p</span> <span class="special">*</span>
+                    <span class="special">(</span><span class="number">1</span>
+                    <span class="special">-</span> <span class="identifier">p</span><span class="special">)))</span></code>
+                  </p>
+                  </td>
+</tr>
+<tr>
+<td>
+                  <p>
+                    kurtosis excess
+                  </p>
+                  </td>
+<td>
+                  <p>
+                    <code class="computeroutput"><span class="special">(</span><span class="number">1</span>
+                    <span class="special">-</span> <span class="number">6</span>
+                    <span class="special">*</span> <span class="identifier">p</span>
+                    <span class="special">*</span> <span class="identifier">q</span><span class="special">)</span> <span class="special">/</span>
+                    <span class="special">(</span><span class="identifier">n</span>
+                    <span class="special">*</span> <span class="identifier">p</span>
+                    <span class="special">*</span> <span class="identifier">q</span><span class="special">)</span></code>
+                  </p>
+                  </td>
+</tr>
+<tr>
+<td>
+                  <p>
+                    parameter estimation
+                  </p>
+                  </td>
+<td>
+                  <p>
+                    The member functions <code class="computeroutput"><span class="identifier">find_upper_bound_on_p</span></code>
+                    <code class="computeroutput"><span class="identifier">find_lower_bound_on_p</span></code>
+                    and <code class="computeroutput"><span class="identifier">find_number_of_trials</span></code>
+                    are implemented in terms of the inverse incomplete beta functions
+                    <a class="link" href="../../../special/sf_beta/ibeta_inv_function.html" title="The Incomplete Beta Function Inverses">ibetac_inv</a>,
+                    <a class="link" href="../../../special/sf_beta/ibeta_inv_function.html" title="The Incomplete Beta Function Inverses">ibeta_inv</a>,
+                    and <a class="link" href="../../../special/sf_beta/ibeta_inv_function.html" title="The Incomplete Beta Function Inverses">ibetac_invb</a>
+                    respectively
+                  </p>
+                  </td>
+</tr>
+</tbody>
+</table></div>
+<a name="math_toolkit.dist.dist_ref.dists.binomial_dist.references"></a><h5>
+<a name="id655532"></a>
+            <a class="link" href="binomial_dist.html#math_toolkit.dist.dist_ref.dists.binomial_dist.references">References</a>
+          </h5>
+<div class="itemizedlist"><ul type="disc">
+<li>
+<a href="http://mathworld.wolfram.com/BinomialDistribution.html" target="_top">Weisstein,
+              Eric W. "Binomial Distribution." From MathWorld--A Wolfram
+              Web Resource</a>.
+            </li>
+<li>
+<a href="http://en.wikipedia.org/wiki/Beta_distribution" target="_top">Wikipedia
+              binomial distribution</a>.
+            </li>
+<li>
+<a href="http://www.itl.nist.gov/div898/handbook/eda/section3/eda366i.htm" target="_top">NIST
+              Explorary Data Analysis</a>.
+            </li>
+</ul></div>
+</div>
+<table xmlns:rev="http://www.cs.rpi.edu/~gregod/boost/tools/doc/revision" width="100%"><tr>
+<td align="left"></td>
+<td align="right"><div class="copyright-footer">Copyright © 2006 , 2007, 2008 John Maddock, Paul A. Bristow, Hubert
+      Holin, Xiaogang Zhang, Bruno Lalande and Gautam Sewani<p>
+        Distributed under the Boost Software License, Version 1.0. (See accompanying
+        file LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_0.txt)
+      </p>
+</div></td>
+</tr></table>
+<hr>
+<div class="spirit-nav">
+<a accesskey="p" href="beta_dist.html"><img src="../../../../../../doc/html/images/prev.png" alt="Prev"></a><a accesskey="u" href="../dists.html"><img src="../../../../../../doc/html/images/up.png" alt="Up"></a><a accesskey="h" href="../../../../index.html"><img src="../../../../../../doc/html/images/home.png" alt="Home"></a><a accesskey="n" href="cauchy_dist.html"><img src="../../../../../../doc/html/images/next.png" alt="Next"></a>
+</div>
+</body>
+</html>

Added: sandbox/tools/auto_index/example/math/doc/sf_and_dist/html/math_toolkit/dist/dist_ref/dists/cauchy_dist.html
==============================================================================
--- (empty file)
+++ sandbox/tools/auto_index/example/math/doc/sf_and_dist/html/math_toolkit/dist/dist_ref/dists/cauchy_dist.html	2008-11-28 05:25:28 EST (Fri, 28 Nov 2008)
@@ -0,0 +1,306 @@
+<html>
+<head>
+<meta http-equiv="Content-Type" content="text/html; charset=ISO-8859-1">
+<title>Cauchy-Lorentz Distribution</title>
+<link rel="stylesheet" href="../../../../boostbook.css" type="text/css">
+<meta name="generator" content="DocBook XSL Stylesheets Vsnapshot_8125">
+<link rel="home" href="../../../../index.html" title="Math Toolkit">
+<link rel="up" href="../dists.html" title="Distributions">
+<link rel="prev" href="binomial_dist.html" title="Binomial Distribution">
+<link rel="next" href="chi_squared_dist.html" title="Chi Squared Distribution">
+</head>
+<body bgcolor="white" text="black" link="#0000FF" vlink="#840084" alink="#0000FF">
+<table cellpadding="2" width="100%"><tr>
+<td valign="top"><img alt="Boost C++ Libraries" width="277" height="86" src="../../../../../../boost.png"></td>
+<td align="center">Home</td>
+<td align="center">Libraries</td>
+<td align="center">People</td>
+<td align="center">FAQ</td>
+<td align="center">More</td>
+</tr></table>
+<hr>
+<div class="spirit-nav">
+<a accesskey="p" href="binomial_dist.html"><img src="../../../../../../doc/html/images/prev.png" alt="Prev"></a><a accesskey="u" href="../dists.html"><img src="../../../../../../doc/html/images/up.png" alt="Up"></a><a accesskey="h" href="../../../../index.html"><img src="../../../../../../doc/html/images/home.png" alt="Home"></a><a accesskey="n" href="chi_squared_dist.html"><img src="../../../../../../doc/html/images/next.png" alt="Next"></a>
+</div>
+<div class="section" lang="en">
+<div class="titlepage"><div><div><h5 class="title">
+<a name="math_toolkit.dist.dist_ref.dists.cauchy_dist"></a><a class="link" href="cauchy_dist.html" title="Cauchy-Lorentz Distribution"> Cauchy-Lorentz
+          Distribution</a>
+</h5></div></div></div>
+<p>
+            
+</p>
+<pre class="programlisting"><span class="preprocessor">#include</span> <span class="special">&lt;</span><span class="identifier">boost</span><span class="special">/</span><span class="identifier">math</span><span class="special">/</span><span class="identifier">distributions</span><span class="special">/</span><span class="identifier">cauchy</span><span class="special">.</span><span class="identifier">hpp</span><span class="special">&gt;</span></pre>
+<p>
+          </p>
+<pre class="programlisting"><span class="keyword">template</span> <span class="special">&lt;</span><span class="keyword">class</span> <span class="identifier">RealType</span> <span class="special">=</span> <span class="keyword">double</span><span class="special">,</span> 
+          <span class="keyword">class</span> <a class="link" href="../../../policy.html" title="Policies">Policy</a>   <span class="special">=</span> <a class="link" href="../../../policy/pol_ref/pol_ref_ref.html" title="Policy Class Reference">policies::policy&lt;&gt;</a> <span class="special">&gt;</span>
+<span class="keyword">class</span> <span class="identifier">cauchy_distribution</span><span class="special">;</span>
+
+<span class="keyword">typedef</span> <span class="identifier">cauchy_distribution</span><span class="special">&lt;&gt;</span> <span class="identifier">cauchy</span><span class="special">;</span>
+
+<span class="keyword">template</span> <span class="special">&lt;</span><span class="keyword">class</span> <span class="identifier">RealType</span><span class="special">,</span> <span class="keyword">class</span> <a class="link" href="../../../policy.html" title="Policies">Policy</a><span class="special">&gt;</span>
+<span class="keyword">class</span> <span class="identifier">cauchy_distribution</span>
+<span class="special">{</span>
+<span class="keyword">public</span><span class="special">:</span>
+   <span class="keyword">typedef</span> <span class="identifier">RealType</span>  <span class="identifier">value_type</span><span class="special">;</span>
+   <span class="keyword">typedef</span> <span class="identifier">Policy</span>    <span class="identifier">policy_type</span><span class="special">;</span>
+
+   <span class="identifier">cauchy_distribution</span><span class="special">(</span><span class="identifier">RealType</span> <span class="identifier">location</span> <span class="special">=</span> <span class="number">0</span><span class="special">,</span> <span class="identifier">RealType</span> <span class="identifier">scale</span> <span class="special">=</span> <span class="number">1</span><span class="special">);</span>
+   
+   <span class="identifier">RealType</span> <span class="identifier">location</span><span class="special">()</span><span class="keyword">const</span><span class="special">;</span>
+   <span class="identifier">RealType</span> <span class="identifier">scale</span><span class="special">()</span><span class="keyword">const</span><span class="special">;</span>
+<span class="special">};</span>
+</pre>
+<p>
+            The <a href="http://en.wikipedia.org/wiki/Cauchy_distribution" target="_top">Cauchy-Lorentz
+            distribution</a> is named after Augustin Cauchy and Hendrik Lorentz.
+            It is a <a href="http://en.wikipedia.org/wiki/Probability_distribution" target="_top">continuous
+            probability distribution</a> with <a href="http://en.wikipedia.org/wiki/Probability_distribution" target="_top">probability
+            distribution function PDF</a> given by:
+          </p>
+<p>
+            <span class="inlinemediaobject"><img src="../../../../../equations/cauchy_ref1.png"></span>
+          </p>
+<p>
+            The location parameter x<sub>0</sub> is the location of the peak of the distribution
+            (the mode of the distribution), while the scale parameter &#947; specifies half
+            the width of the PDF at half the maximum height. If the location is zero,
+            and the scale 1, then the result is a standard Cauchy distribution.
+          </p>
+<p>
+            The distribution is important in physics as it is the solution to the
+            differential equation describing forced resonance, while in spectroscopy
+            it is the description of the line shape of spectral lines.
+          </p>
+<p>
+            The following graph shows how the distributions moves as the location
+            parameter changes:
+          </p>
+<p>
+            <span class="inlinemediaobject"><img src="../../../../../graphs/cauchy_pdf1.png" align="middle"></span>
+          </p>
+<p>
+            While the following graph shows how the shape (scale) parameter alters
+            the distribution:
+          </p>
+<p>
+            <span class="inlinemediaobject"><img src="../../../../../graphs/cauchy_pdf2.png" align="middle"></span>
+          </p>
+<a name="math_toolkit.dist.dist_ref.dists.cauchy_dist.member_functions"></a><h5>
+<a name="id656259"></a>
+            <a class="link" href="cauchy_dist.html#math_toolkit.dist.dist_ref.dists.cauchy_dist.member_functions">Member
+            Functions</a>
+          </h5>
+<pre class="programlisting"><span class="identifier">cauchy_distribution</span><span class="special">(</span><span class="identifier">RealType</span> <span class="identifier">location</span> <span class="special">=</span> <span class="number">0</span><span class="special">,</span> <span class="identifier">RealType</span> <span class="identifier">scale</span> <span class="special">=</span> <span class="number">1</span><span class="special">);</span>
+</pre>
+<p>
+            Constructs a Cauchy distribution, with location parameter <span class="emphasis"><em>location</em></span>
+            and scale parameter <span class="emphasis"><em>scale</em></span>. When these parameters
+            take their default values (location = 0, scale = 1) then the result is
+            a Standard Cauchy Distribution.
+          </p>
+<p>
+            Requires scale &gt; 0, otherwise calls <a class="link" href="../../../main_overview/error_handling.html#domain_error">domain_error</a>.
+          </p>
+<pre class="programlisting"><span class="identifier">RealType</span> <span class="identifier">location</span><span class="special">()</span><span class="keyword">const</span><span class="special">;</span>
+</pre>
+<p>
+            Returns the location parameter of the distribution.
+          </p>
+<pre class="programlisting"><span class="identifier">RealType</span> <span class="identifier">scale</span><span class="special">()</span><span class="keyword">const</span><span class="special">;</span>
+</pre>
+<p>
+            Returns the scale parameter of the distribution.
+          </p>
+<a name="math_toolkit.dist.dist_ref.dists.cauchy_dist.non_member_accessors"></a><h5>
+<a name="id656476"></a>
+            <a class="link" href="cauchy_dist.html#math_toolkit.dist.dist_ref.dists.cauchy_dist.non_member_accessors">Non-member
+            Accessors</a>
+          </h5>
+<p>
+            All the <a class="link" href="../nmp.html" title="Non-Member Properties">usual non-member
+            accessor functions</a> that are generic to all distributions are supported:
+            <a class="link" href="../nmp.html#math.dist.cdf">Cumulative Distribution Function</a>,
+            <a class="link" href="../nmp.html#math.dist.pdf">Probability Density Function</a>, <a class="link" href="../nmp.html#math.dist.quantile">Quantile</a>, <a class="link" href="../nmp.html#math.dist.hazard">Hazard
+            Function</a>, <a class="link" href="../nmp.html#math.dist.chf">Cumulative Hazard Function</a>,
+            <a class="link" href="../nmp.html#math.dist.mean">mean</a>, <a class="link" href="../nmp.html#math.dist.median">median</a>,
+            <a class="link" href="../nmp.html#math.dist.mode">mode</a>, <a class="link" href="../nmp.html#math.dist.variance">variance</a>,
+            <a class="link" href="../nmp.html#math.dist.sd">standard deviation</a>, <a class="link" href="../nmp.html#math.dist.skewness">skewness</a>,
+            <a class="link" href="../nmp.html#math.dist.kurtosis">kurtosis</a>, <a class="link" href="../nmp.html#math.dist.kurtosis_excess">kurtosis_excess</a>,
+            <a class="link" href="../nmp.html#math.dist.range">range</a> and <a class="link" href="../nmp.html#math.dist.support">support</a>.
+          </p>
+<p>
+            Note however that the Cauchy distribution does not have a mean, standard
+            deviation, etc. See <a class="link" href="../../../policy/pol_ref/assert_undefined.html" title="Mathematically Undefined Function Policies">mathematically
+            undefined function</a>
+          </p>
+<p>
+            to control whether these should fail to compile with a BOOST_STATIC_ASSERTION_FAILURE,
+            which is the default.
+          </p>
+<p>
+            Alternately, the functions <a class="link" href="../nmp.html#math.dist.mean">mean</a>,
+            <a class="link" href="../nmp.html#math.dist.sd">standard deviation</a>, <a class="link" href="../nmp.html#math.dist.variance">variance</a>,
+            <a class="link" href="../nmp.html#math.dist.skewness">skewness</a>, <a class="link" href="../nmp.html#math.dist.kurtosis">kurtosis</a>
+            and <a class="link" href="../nmp.html#math.dist.kurtosis_excess">kurtosis_excess</a>
+            will all return a <a class="link" href="../../../main_overview/error_handling.html#domain_error">domain_error</a> if
+            called.
+          </p>
+<p>
+            The domain of the random variable is [-[max_value], +[min_value]].
+          </p>
+<a name="math_toolkit.dist.dist_ref.dists.cauchy_dist.accuracy"></a><h5>
+<a name="id656743"></a>
+            <a class="link" href="cauchy_dist.html#math_toolkit.dist.dist_ref.dists.cauchy_dist.accuracy">Accuracy</a>
+          </h5>
+<p>
+            The Cauchy distribution is implemented in terms of the standard library
+            <code class="computeroutput"><span class="identifier">tan</span></code> and <code class="computeroutput"><span class="identifier">atan</span></code> functions, and as such should
+            have very low error rates.
+          </p>
+<a name="math_toolkit.dist.dist_ref.dists.cauchy_dist.implementation"></a><h5>
+<a name="id656801"></a>
+            <a class="link" href="cauchy_dist.html#math_toolkit.dist.dist_ref.dists.cauchy_dist.implementation">Implementation</a>
+          </h5>
+<p>
+            In the following table x<sub>0 </sub> is the location parameter of the distribution,
+            &#947; is its scale parameter, <span class="emphasis"><em>x</em></span> is the random variate,
+            <span class="emphasis"><em>p</em></span> is the probability and <span class="emphasis"><em>q = 1-p</em></span>.
+          </p>
+<div class="informaltable"><table class="table">
+<colgroup>
+<col>
+<col>
+</colgroup>
+<thead><tr>
+<th>
+                  <p>
+                    Function
+                  </p>
+                  </th>
+<th>
+                  <p>
+                    Implementation Notes
+                  </p>
+                  </th>
+</tr></thead>
+<tbody>
+<tr>
+<td>
+                  <p>
+                    pdf
+                  </p>
+                  </td>
+<td>
+                  <p>
+                    Using the relation: pdf = 1 / (&#960; * &#947; * (1 + ((x - x<sub>0 </sub>) / &#947;)<sup>2</sup>)
+                  </p>
+                  </td>
+</tr>
+<tr>
+<td>
+                  <p>
+                    cdf and its complement
+                  </p>
+                  </td>
+<td>
+                  <p>
+                    The cdf is normally given by:
+                  </p>
+                  <p>
+                    p = 0.5 + atan(x)/&#960;
+                  </p>
+                  <p>
+                    But that suffers from cancellation error as x -&gt; -&#8734;. So recall
+                    that for <code class="computeroutput"><span class="identifier">x</span> <span class="special">&lt;</span>
+                    <span class="number">0</span></code>:
+                  </p>
+                  <p>
+                    atan(x) = -&#960;/2 - atan(1/x)
+                  </p>
+                  <p>
+                    Substituting into the above we get:
+                  </p>
+                  <p>
+                    p = -atan(1/x) ; x &lt; 0
+                  </p>
+                  <p>
+                    So the procedure is to calculate the cdf for -fabs(x) using the
+                    above formula. Note that to factor in the location and scale
+                    parameters you must substitute (x - x<sub>0 </sub>) / &#947; for x in the above.
+                  </p>
+                  <p>
+                    This procedure yields the smaller of <span class="emphasis"><em>p</em></span> and
+                    <span class="emphasis"><em>q</em></span>, so the result may need subtracting from
+                    1 depending on whether we want the complement or not, and whether
+                    <span class="emphasis"><em>x</em></span> is less than x<sub>0 </sub> or not.
+                  </p>
+                  </td>
+</tr>
+<tr>
+<td>
+                  <p>
+                    quantile
+                  </p>
+                  </td>
+<td>
+                  <p>
+                    The same procedure is used irrespective of whether we're starting
+                    from the probability or it's complement. First the argument
+                    <span class="emphasis"><em>p</em></span> is reduced to the range [-0.5, 0.5], then
+                    the relation
+                  </p>
+                  <p>
+                    x = x<sub>0 </sub> ± &#947; / tan(&#960; * p)
+                  </p>
+                  <p>
+                    is used to obtain the result. Whether we're adding or subtracting
+                    from x<sub>0 </sub> is determined by whether we're starting from the complement
+                    or not.
+                  </p>
+                  </td>
+</tr>
+<tr>
+<td>
+                  <p>
+                    mode
+                  </p>
+                  </td>
+<td>
+                  <p>
+                    The location parameter.
+                  </p>
+                  </td>
+</tr>
+</tbody>
+</table></div>
+<a name="math_toolkit.dist.dist_ref.dists.cauchy_dist.references"></a><h5>
+<a name="id657109"></a>
+            <a class="link" href="cauchy_dist.html#math_toolkit.dist.dist_ref.dists.cauchy_dist.references">References</a>
+          </h5>
+<div class="itemizedlist"><ul type="disc">
+<li><a href="http://en.wikipedia.org/wiki/Cauchy_distribution" target="_top">Cauchy-Lorentz
+              distribution</a></li>
+<li><a href="http://www.itl.nist.gov/div898/handbook/eda/section3/eda3663.htm" target="_top">NIST
+              Exploratory Data Analysis</a></li>
+<li><a href="http://mathworld.wolfram.com/CauchyDistribution.html" target="_top">Weisstein,
+              Eric W. "Cauchy Distribution." From MathWorld--A Wolfram
+              Web Resource.</a></li>
+</ul></div>
+</div>
+<table xmlns:rev="http://www.cs.rpi.edu/~gregod/boost/tools/doc/revision" width="100%"><tr>
+<td align="left"></td>
+<td align="right"><div class="copyright-footer">Copyright © 2006 , 2007, 2008 John Maddock, Paul A. Bristow, Hubert
+      Holin, Xiaogang Zhang, Bruno Lalande and Gautam Sewani<p>
+        Distributed under the Boost Software License, Version 1.0. (See accompanying
+        file LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_0.txt)
+      </p>
+</div></td>
+</tr></table>
+<hr>
+<div class="spirit-nav">
+<a accesskey="p" href="binomial_dist.html"><img src="../../../../../../doc/html/images/prev.png" alt="Prev"></a><a accesskey="u" href="../dists.html"><img src="../../../../../../doc/html/images/up.png" alt="Up"></a><a accesskey="h" href="../../../../index.html"><img src="../../../../../../doc/html/images/home.png" alt="Home"></a><a accesskey="n" href="chi_squared_dist.html"><img src="../../../../../../doc/html/images/next.png" alt="Next"></a>
+</div>
+</body>
+</html>

Added: sandbox/tools/auto_index/example/math/doc/sf_and_dist/html/math_toolkit/dist/dist_ref/dists/chi_squared_dist.html
==============================================================================
--- (empty file)
+++ sandbox/tools/auto_index/example/math/doc/sf_and_dist/html/math_toolkit/dist/dist_ref/dists/chi_squared_dist.html	2008-11-28 05:25:28 EST (Fri, 28 Nov 2008)
@@ -0,0 +1,409 @@
+<html>
+<head>
+<meta http-equiv="Content-Type" content="text/html; charset=ISO-8859-1">
+<title>Chi Squared Distribution</title>
+<link rel="stylesheet" href="../../../../boostbook.css" type="text/css">
+<meta name="generator" content="DocBook XSL Stylesheets Vsnapshot_8125">
+<link rel="home" href="../../../../index.html" title="Math Toolkit">
+<link rel="up" href="../dists.html" title="Distributions">
+<link rel="prev" href="cauchy_dist.html" title="Cauchy-Lorentz Distribution">
+<link rel="next" href="exp_dist.html" title="Exponential Distribution">
+</head>
+<body bgcolor="white" text="black" link="#0000FF" vlink="#840084" alink="#0000FF">
+<table cellpadding="2" width="100%"><tr>
+<td valign="top"><img alt="Boost C++ Libraries" width="277" height="86" src="../../../../../../boost.png"></td>
+<td align="center">Home</td>
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+<hr>
+<div class="spirit-nav">
+<a accesskey="p" href="cauchy_dist.html"><img src="../../../../../../doc/html/images/prev.png" alt="Prev"></a><a accesskey="u" href="../dists.html"><img src="../../../../../../doc/html/images/up.png" alt="Up"></a><a accesskey="h" href="../../../../index.html"><img src="../../../../../../doc/html/images/home.png" alt="Home"></a><a accesskey="n" href="exp_dist.html"><img src="../../../../../../doc/html/images/next.png" alt="Next"></a>
+</div>
+<div class="section" lang="en">
+<div class="titlepage"><div><div><h5 class="title">
+<a name="math_toolkit.dist.dist_ref.dists.chi_squared_dist"></a><a class="link" href="chi_squared_dist.html" title="Chi Squared Distribution">
+          Chi Squared Distribution</a>
+</h5></div></div></div>
+<p>
+            
+</p>
+<pre class="programlisting"><span class="preprocessor">#include</span> <span class="special">&lt;</span><span class="identifier">boost</span><span class="special">/</span><span class="identifier">math</span><span class="special">/</span><span class="identifier">distributions</span><span class="special">/</span><span class="identifier">chi_squared</span><span class="special">.</span><span class="identifier">hpp</span><span class="special">&gt;</span></pre>
+<p>
+          </p>
+<pre class="programlisting"><span class="keyword">namespace</span> <span class="identifier">boost</span><span class="special">{</span> <span class="keyword">namespace</span> <span class="identifier">math</span><span class="special">{</span> 
+
+<span class="keyword">template</span> <span class="special">&lt;</span><span class="keyword">class</span> <span class="identifier">RealType</span> <span class="special">=</span> <span class="keyword">double</span><span class="special">,</span> 
+          <span class="keyword">class</span> <a class="link" href="../../../policy.html" title="Policies">Policy</a>   <span class="special">=</span> <a class="link" href="../../../policy/pol_ref/pol_ref_ref.html" title="Policy Class Reference">policies::policy&lt;&gt;</a> <span class="special">&gt;</span>
+<span class="keyword">class</span> <span class="identifier">chi_squared_distribution</span><span class="special">;</span>
+
+<span class="keyword">typedef</span> <span class="identifier">chi_squared_distribution</span><span class="special">&lt;&gt;</span> <span class="identifier">chi_squared</span><span class="special">;</span>
+
+<span class="keyword">template</span> <span class="special">&lt;</span><span class="keyword">class</span> <span class="identifier">RealType</span><span class="special">,</span> <span class="keyword">class</span> <a class="link" href="../../../policy.html" title="Policies">Policy</a><span class="special">&gt;</span>
+<span class="keyword">class</span> <span class="identifier">chi_squared_distribution</span>
+<span class="special">{</span>
+<span class="keyword">public</span><span class="special">:</span>
+   <span class="keyword">typedef</span> <span class="identifier">RealType</span>  <span class="identifier">value_type</span><span class="special">;</span>
+   <span class="keyword">typedef</span> <span class="identifier">Policy</span>    <span class="identifier">policy_type</span><span class="special">;</span>
+
+   <span class="comment">// Constructor:
+</span>   <span class="identifier">chi_squared_distribution</span><span class="special">(</span><span class="identifier">RealType</span> <span class="identifier">i</span><span class="special">);</span>
+
+   <span class="comment">// Accessor to parameter:
+</span>   <span class="identifier">RealType</span> <span class="identifier">degrees_of_freedom</span><span class="special">()</span><span class="keyword">const</span><span class="special">;</span>
+
+   <span class="comment">// Parameter estimation:
+</span>   <span class="keyword">static</span> <span class="identifier">RealType</span> <span class="identifier">find_degrees_of_freedom</span><span class="special">(</span>
+      <span class="identifier">RealType</span> <span class="identifier">difference_from_mean</span><span class="special">,</span>
+      <span class="identifier">RealType</span> <span class="identifier">alpha</span><span class="special">,</span>
+      <span class="identifier">RealType</span> <span class="identifier">beta</span><span class="special">,</span>
+      <span class="identifier">RealType</span> <span class="identifier">sd</span><span class="special">,</span>
+      <span class="identifier">RealType</span> <span class="identifier">hint</span> <span class="special">=</span> <span class="number">100</span><span class="special">);</span>
+<span class="special">};</span>
+
+<span class="special">}}</span> <span class="comment">// namespaces
+</span></pre>
+<p>
+            The Chi-Squared distribution is one of the most widely used distributions
+            in statistical tests. If &#967;<sub>i</sub> are &#957; 
+independent, normally distributed random
+            variables with means &#956;<sub>i</sub> and variances &#963;<sub>i</sub><sup>2</sup>, then the random variable:
+          </p>
+<p>
+            <span class="inlinemediaobject"><img src="../../../../../equations/chi_squ_ref1.png"></span>
+          </p>
+<p>
+            is distributed according to the Chi-Squared distribution.
+          </p>
+<p>
+            The Chi-Squared distribution is a special case of the gamma distribution
+            and has a single parameter &#957; that specifies the number of degrees of freedom.
+            The following graph illustrates how the distribution changes for different
+            values of &#957;:
+          </p>
+<p>
+            <span class="inlinemediaobject"><img src="../../../../../graphs/chi_squared_pdf.png" align="middle"></span>
+          </p>
+<a name="math_toolkit.dist.dist_ref.dists.chi_squared_dist.member_functions"></a><h5>
+<a name="id657898"></a>
+            <a class="link" href="chi_squared_dist.html#math_toolkit.dist.dist_ref.dists.chi_squared_dist.member_functions">Member
+            Functions</a>
+          </h5>
+<pre class="programlisting"><span class="identifier">chi_squared_distribution</span><span class="special">(</span><span class="identifier">RealType</span> <span class="identifier">v</span><span class="special">);</span>
+</pre>
+<p>
+            Constructs a Chi-Squared distribution with <span class="emphasis"><em>v</em></span> degrees
+            of freedom.
+          </p>
+<p>
+            Requires v &gt; 0, otherwise calls <a class="link" href="../../../main_overview/error_handling.html#domain_error">domain_error</a>.
+          </p>
+<pre class="programlisting"><span class="identifier">RealType</span> <span class="identifier">degrees_of_freedom</span><span class="special">()</span><span class="keyword">const</span><span class="special">;</span>
+</pre>
+<p>
+            Returns the parameter <span class="emphasis"><em>v</em></span> from which this object was
+            constructed.
+          </p>
+<pre class="programlisting"><span class="keyword">static</span> <span class="identifier">RealType</span> <span class="identifier">find_degrees_of_freedom</span><span class="special">(</span>
+   <span class="identifier">RealType</span> <span class="identifier">difference_from_variance</span><span class="special">,</span>
+   <span class="identifier">RealType</span> <span class="identifier">alpha</span><span class="special">,</span>
+   <span class="identifier">RealType</span> <span class="identifier">beta</span><span class="special">,</span>
+   <span class="identifier">RealType</span> <span class="identifier">variance</span><span class="special">,</span>
+   <span class="identifier">RealType</span> <span class="identifier">hint</span> <span class="special">=</span> <span class="number">100</span><span class="special">);</span>
+</pre>
+<p>
+            Estimates the sample size required to detect a difference from a nominal
+            variance in a Chi-Squared test for equal standard deviations.
+          </p>
+<div class="variablelist">
+<p class="title"><b></b></p>
+<dl>
+<dt><span class="term">difference_from_variance</span></dt>
+<dd><p>
+                The difference from the assumed nominal variance that is to be detected:
+                Note that the sign of this value is critical, see below.
+              </p></dd>
+<dt><span class="term">alpha</span></dt>
+<dd><p>
+                The maximum acceptable risk of rejecting the null hypothesis when
+                it is in fact true.
+              </p></dd>
+<dt><span class="term">beta</span></dt>
+<dd><p>
+                The maximum acceptable risk of falsely failing to reject the null
+                hypothesis.
+              </p></dd>
+<dt><span class="term">variance</span></dt>
+<dd><p>
+                The nominal variance being tested against.
+              </p></dd>
+<dt><span class="term">hint</span></dt>
+<dd><p>
+                An optional hint on where to start looking for a result: the current
+                sample size would be a good choice.
+              </p></dd>
+</dl>
+</div>
+<p>
+            Note that this calculation works with <span class="emphasis"><em>variances</em></span>
+            and not <span class="emphasis"><em>standard deviations</em></span>.
+          </p>
+<p>
+            The sign of the parameter <span class="emphasis"><em>difference_from_variance</em></span>
+            is important: the Chi Squared distribution is asymmetric, and the caller
+            must decide in advance whether they are testing for a variance greater
+            than a nominal value (positive <span class="emphasis"><em>difference_from_variance</em></span>)
+            or testing for a variance less than a nominal value (negative <span class="emphasis"><em>difference_from_variance</em></span>).
+            If the latter, then obviously it is a requirement that <code class="computeroutput"><span class="identifier">variance</span> <span class="special">+</span>
+            <span class="identifier">difference_from_variance</span> <span class="special">&gt;</span>
+            <span class="number">0</span></code>, since no sample can have a negative
+            variance!
+          </p>
+<p>
+            This procedure uses the method in Diamond, W. J. (1989). Practical Experiment
+            Designs, Van-Nostrand Reinhold, New York.
+          </p>
+<p>
+            See also section on Sample sizes required in <a href="http://www.itl.nist.gov/div898/handbook/prc/section2/prc232.htm" target="_top">the
+            NIST Engineering Statistics Handbook, Section 7.2.3.2</a>.
+          </p>
+<a name="math_toolkit.dist.dist_ref.dists.chi_squared_dist.non_member_accessors"></a><h5>
+<a name="id658367"></a>
+            <a class="link" href="chi_squared_dist.html#math_toolkit.dist.dist_ref.dists.chi_squared_dist.non_member_accessors">Non-member
+            Accessors</a>
+          </h5>
+<p>
+            All the <a class="link" href="../nmp.html" title="Non-Member Properties">usual non-member
+            accessor functions</a> that are generic to all distributions are supported:
+            <a class="link" href="../nmp.html#math.dist.cdf">Cumulative Distribution Function</a>,
+            <a class="link" href="../nmp.html#math.dist.pdf">Probability Density Function</a>, <a class="link" href="../nmp.html#math.dist.quantile">Quantile</a>, <a class="link" href="../nmp.html#math.dist.hazard">Hazard
+            Function</a>, <a class="link" href="../nmp.html#math.dist.chf">Cumulative Hazard Function</a>,
+            <a class="link" href="../nmp.html#math.dist.mean">mean</a>, <a class="link" href="../nmp.html#math.dist.median">median</a>,
+            <a class="link" href="../nmp.html#math.dist.mode">mode</a>, <a class="link" href="../nmp.html#math.dist.variance">variance</a>,
+            <a class="link" href="../nmp.html#math.dist.sd">standard deviation</a>, <a class="link" href="../nmp.html#math.dist.skewness">skewness</a>,
+            <a class="link" href="../nmp.html#math.dist.kurtosis">kurtosis</a>, <a class="link" href="../nmp.html#math.dist.kurtosis_excess">kurtosis_excess</a>,
+            <a class="link" href="../nmp.html#math.dist.range">range</a> and <a class="link" href="../nmp.html#math.dist.support">support</a>.
+          </p>
+<p>
+            (We have followed the usual restriction of the mode to degrees of freedom
+            &gt;= 2, but note that the maximum of the pdf is actually zero for degrees
+            of freedom from 2 down to 0, and provide an extended definition that
+            would avoid a discontinuity in the mode as alternative code in a comment).
+          </p>
+<p>
+            The domain of the random variable is [0, +&#8734;].
+          </p>
+<a name="math_toolkit.dist.dist_ref.dists.chi_squared_dist.examples"></a><h5>
+<a name="id658557"></a>
+            <a class="link" href="chi_squared_dist.html#math_toolkit.dist.dist_ref.dists.chi_squared_dist.examples">Examples</a>
+          </h5>
+<p>
+            Various <a class="link" href="../../stat_tut/weg/cs_eg.html" title="Chi Squared Distribution Examples">worked examples</a>
+            are available illustrating the use of the Chi Squared Distribution.
+          </p>
+<a name="math_toolkit.dist.dist_ref.dists.chi_squared_dist.accuracy"></a><h5>
+<a name="id658599"></a>
+            <a class="link" href="chi_squared_dist.html#math_toolkit.dist.dist_ref.dists.chi_squared_dist.accuracy">Accuracy</a>
+          </h5>
+<p>
+            The Chi-Squared distribution is implemented in terms of the <a class="link" href="../../../special/sf_gamma/igamma.html" title="Incomplete Gamma Functions">incomplete
+            gamma functions</a>: please refer to the accuracy data for those functions.
+          </p>
+<a name="math_toolkit.dist.dist_ref.dists.chi_squared_dist.implementation"></a><h5>
+<a name="id658642"></a>
+            <a class="link" href="chi_squared_dist.html#math_toolkit.dist.dist_ref.dists.chi_squared_dist.implementation">Implementation</a>
+          </h5>
+<p>
+            In the following table <span class="emphasis"><em>v</em></span> is the number of degrees
+            of freedom of the distribution, <span class="emphasis"><em>x</em></span> is the random
+            variate, <span class="emphasis"><em>p</em></span> is the probability, and <span class="emphasis"><em>q =
+            1-p</em></span>.
+          </p>
+<div class="informaltable"><table class="table">
+<colgroup>
+<col>
+<col>
+</colgroup>
+<thead><tr>
+<th>
+                  <p>
+                    Function
+                  </p>
+                  </th>
+<th>
+                  <p>
+                    Implementation Notes
+                  </p>
+                  </th>
+</tr></thead>
+<tbody>
+<tr>
+<td>
+                  <p>
+                    pdf
+                  </p>
+                  </td>
+<td>
+                  <p>
+                    Using the relation: pdf = <a class="link" href="../../../special/sf_gamma/gamma_derivatives.html" title="Derivative of the Incomplete Gamma Function">gamma_p_derivative</a>(v
+                    / 2, x / 2) / 2
+                  </p>
+                  </td>
+</tr>
+<tr>
+<td>
+                  <p>
+                    cdf
+                  </p>
+                  </td>
+<td>
+                  <p>
+                    Using the relation: p = <a class="link" href="../../../special/sf_gamma/igamma.html" title="Incomplete Gamma Functions">gamma_p</a>(v
+                    / 2, x / 2)
+                  </p>
+                  </td>
+</tr>
+<tr>
+<td>
+                  <p>
+                    cdf complement
+                  </p>
+                  </td>
+<td>
+                  <p>
+                    Using the relation: q = <a class="link" href="../../../special/sf_gamma/igamma.html" title="Incomplete Gamma Functions">gamma_q</a>(v
+                    / 2, x / 2)
+                  </p>
+                  </td>
+</tr>
+<tr>
+<td>
+                  <p>
+                    quantile
+                  </p>
+                  </td>
+<td>
+                  <p>
+                    Using the relation: x = 2 * <a class="link" href="../../../special/sf_gamma/igamma_inv.html" title="Incomplete Gamma Function Inverses">gamma_p_inv</a>(v
+                    / 2, p)
+                  </p>
+                  </td>
+</tr>
+<tr>
+<td>
+                  <p>
+                    quantile from the complement
+                  </p>
+                  </td>
+<td>
+                  <p>
+                    Using the relation: x = 2 * <a class="link" href="../../../special/sf_gamma/igamma_inv.html" title="Incomplete Gamma Function Inverses">gamma_q_inv</a>(v
+                    / 2, p)
+                  </p>
+                  </td>
+</tr>
+<tr>
+<td>
+                  <p>
+                    mean
+                  </p>
+                  </td>
+<td>
+                  <p>
+                    v
+                  </p>
+                  </td>
+</tr>
+<tr>
+<td>
+                  <p>
+                    variance
+                  </p>
+                  </td>
+<td>
+                  <p>
+                    2v
+                  </p>
+                  </td>
+</tr>
+<tr>
+<td>
+                  <p>
+                    mode
+                  </p>
+                  </td>
+<td>
+                  <p>
+                    v - 2 (if v &gt;= 2)
+                  </p>
+                  </td>
+</tr>
+<tr>
+<td>
+                  <p>
+                    skewness
+                  </p>
+                  </td>
+<td>
+                  <p>
+                    2 * sqrt(2 / v) == sqrt(8 / v)
+                  </p>
+                  </td>
+</tr>
+<tr>
+<td>
+                  <p>
+                    kurtosis
+                  </p>
+                  </td>
+<td>
+                  <p>
+                    3 + 12 / v
+                  </p>
+                  </td>
+</tr>
+<tr>
+<td>
+                  <p>
+                    kurtosis excess
+                  </p>
+                  </td>
+<td>
+                  <p>
+                    12 / v
+                  </p>
+                  </td>
+</tr>
+</tbody>
+</table></div>
+<a name="math_toolkit.dist.dist_ref.dists.chi_squared_dist.references"></a><h5>
+<a name="id659004"></a>
+            <a class="link" href="chi_squared_dist.html#math_toolkit.dist.dist_ref.dists.chi_squared_dist.references">References</a>
+          </h5>
+<div class="itemizedlist"><ul type="disc">
+<li><a href="http://www.itl.nist.gov/div898/handbook/eda/section3/eda3666.htm" target="_top">NIST
+              Exploratory Data Analysis</a></li>
+<li><a href="http://en.wikipedia.org/wiki/Chi-square_distribution" target="_top">Chi-square
+              distribution</a></li>
+<li><a href="http://mathworld.wolfram.com/Chi-SquaredDistribution.html" target="_top">Weisstein,
+              Eric W. "Chi-Squared Distribution." From MathWorld--A Wolfram
+              Web Resource.</a></li>
+</ul></div>
+</div>
+<table xmlns:rev="http://www.cs.rpi.edu/~gregod/boost/tools/doc/revision" width="100%"><tr>
+<td align="left"></td>
+<td align="right"><div class="copyright-footer">Copyright © 2006 , 2007, 2008 John Maddock, Paul A. Bristow, Hubert
+      Holin, Xiaogang Zhang, Bruno Lalande and Gautam Sewani<p>
+        Distributed under the Boost Software License, Version 1.0. (See accompanying
+        file LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_0.txt)
+      </p>
+</div></td>
+</tr></table>
+<hr>
+<div class="spirit-nav">
+<a accesskey="p" href="cauchy_dist.html"><img src="../../../../../../doc/html/images/prev.png" alt="Prev"></a><a accesskey="u" href="../dists.html"><img src="../../../../../../doc/html/images/up.png" alt="Up"></a><a accesskey="h" href="../../../../index.html"><img src="../../../../../../doc/html/images/home.png" alt="Home"></a><a accesskey="n" href="exp_dist.html"><img src="../../../../../../doc/html/images/next.png" alt="Next"></a>
+</div>
+</body>
+</html>

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@@ -0,0 +1,325 @@
+<html>
+<head>
+<meta http-equiv="Content-Type" content="text/html; charset=ISO-8859-1">
+<title>Exponential Distribution</title>
+<link rel="stylesheet" href="../../../../boostbook.css" type="text/css">
+<meta name="generator" content="DocBook XSL Stylesheets Vsnapshot_8125">
+<link rel="home" href="../../../../index.html" title="Math Toolkit">
+<link rel="up" href="../dists.html" title="Distributions">
+<link rel="prev" href="chi_squared_dist.html" title="Chi Squared Distribution">
+<link rel="next" href="extreme_dist.html" title="Extreme Value Distribution">
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+<body bgcolor="white" text="black" link="#0000FF" vlink="#840084" alink="#0000FF">
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+</div>
+<div class="section" lang="en">
+<div class="titlepage"><div><div><h5 class="title">
+<a name="math_toolkit.dist.dist_ref.dists.exp_dist"></a><a class="link" href="exp_dist.html" title="Exponential Distribution"> Exponential
+          Distribution</a>
+</h5></div></div></div>
+<p>
+            
+</p>
+<pre class="programlisting"><span class="preprocessor">#include</span> <span class="special">&lt;</span><span class="identifier">boost</span><span class="special">/</span><span class="identifier">math</span><span class="special">/</span><span class="identifier">distributions</span><span class="special">/</span><span class="identifier">exponential</span><span class="special">.</span><span class="identifier">hpp</span><span class="special">&gt;</span></pre>
+<p>
+          </p>
+<pre class="programlisting"><span class="keyword">template</span> <span class="special">&lt;</span><span class="keyword">class</span> <span class="identifier">RealType</span> <span class="special">=</span> <span class="keyword">double</span><span class="special">,</span> 
+          <span class="keyword">class</span> <a class="link" href="../../../policy.html" title="Policies">Policy</a>   <span class="special">=</span> <a class="link" href="../../../policy/pol_ref/pol_ref_ref.html" title="Policy Class Reference">policies::policy&lt;&gt;</a> <span class="special">&gt;</span>
+<span class="keyword">class</span> <span class="identifier">exponential_distribution</span><span class="special">;</span>
+
+<span class="keyword">typedef</span> <span class="identifier">exponential_distribution</span><span class="special">&lt;&gt;</span> <span class="identifier">exponential</span><span class="special">;</span>
+
+<span class="keyword">template</span> <span class="special">&lt;</span><span class="keyword">class</span> <span class="identifier">RealType</span><span class="special">,</span> <span class="keyword">class</span> <a class="link" href="../../../policy.html" title="Policies">Policy</a><span class="special">&gt;</span>
+<span class="keyword">class</span> <span class="identifier">exponential_distribution</span>
+<span class="special">{</span>
+<span class="keyword">public</span><span class="special">:</span>
+   <span class="keyword">typedef</span> <span class="identifier">RealType</span> <span class="identifier">value_type</span><span class="special">;</span>
+   <span class="keyword">typedef</span> <span class="identifier">Policy</span>   <span class="identifier">policy_type</span><span class="special">;</span>
+
+   <span class="identifier">exponential_distribution</span><span class="special">(</span><span class="identifier">RealType</span> <span class="identifier">lambda</span> <span class="special">=</span> <span class="number">1</span><span class="special">);</span>
+
+   <span class="identifier">RealType</span> <span class="identifier">lambda</span><span class="special">()</span><span class="keyword">const</span><span class="special">;</span>
+<span class="special">};</span>
+</pre>
+<p>
+            The <a href="http://en.wikipedia.org/wiki/Exponential_distribution" target="_top">exponential
+            distribution</a> is a <a href="http://en.wikipedia.org/wiki/Probability_distribution" target="_top">continuous
+            probability distribution</a> with PDF:
+          </p>
+<p>
+            <span class="inlinemediaobject"><img src="../../../../../equations/exponential_dist_ref1.png"></span>
+          </p>
+<p>
+            It is often used to model the time between independent events that happen
+            at a constant average rate.
+          </p>
+<p>
+            The following graph shows how the distribution changes for different
+            values of the rate parameter lambda:
+          </p>
+<p>
+            <span class="inlinemediaobject"><img src="../../../../../graphs/exponential_pdf.png" align="middle"></span>
+          </p>
+<a name="math_toolkit.dist.dist_ref.dists.exp_dist.member_functions"></a><h5>
+<a name="id659599"></a>
+            <a class="link" href="exp_dist.html#math_toolkit.dist.dist_ref.dists.exp_dist.member_functions">Member
+            Functions</a>
+          </h5>
+<pre class="programlisting"><span class="identifier">exponential_distribution</span><span class="special">(</span><span class="identifier">RealType</span> <span class="identifier">lambda</span> <span class="special">=</span> <span class="number">1</span><span class="special">);</span>
+</pre>
+<p>
+            Constructs an <a href="http://en.wikipedia.org/wiki/Exponential_distribution" target="_top">Exponential
+            distribution</a> with parameter <span class="emphasis"><em>lambda</em></span>. Lambda
+            is defined as the reciprocal of the scale parameter.
+          </p>
+<p>
+            Requires lambda &gt; 0, otherwise calls <a class="link" href="../../../main_overview/error_handling.html#domain_error">domain_error</a>.
+          </p>
+<pre class="programlisting"><span class="identifier">RealType</span> <span class="identifier">lambda</span><span class="special">()</span><span class="keyword">const</span><span class="special">;</span>
+</pre>
+<p>
+            Accessor function returns the lambda parameter of the distribution.
+          </p>
+<a name="math_toolkit.dist.dist_ref.dists.exp_dist.non_member_accessors"></a><h5>
+<a name="id659747"></a>
+            <a class="link" href="exp_dist.html#math_toolkit.dist.dist_ref.dists.exp_dist.non_member_accessors">Non-member
+            Accessors</a>
+          </h5>
+<p>
+            All the <a class="link" href="../nmp.html" title="Non-Member Properties">usual non-member
+            accessor functions</a> that are generic to all distributions are supported:
+            <a class="link" href="../nmp.html#math.dist.cdf">Cumulative Distribution Function</a>,
+            <a class="link" href="../nmp.html#math.dist.pdf">Probability Density Function</a>, <a class="link" href="../nmp.html#math.dist.quantile">Quantile</a>, <a class="link" href="../nmp.html#math.dist.hazard">Hazard
+            Function</a>, <a class="link" href="../nmp.html#math.dist.chf">Cumulative Hazard Function</a>,
+            <a class="link" href="../nmp.html#math.dist.mean">mean</a>, <a class="link" href="../nmp.html#math.dist.median">median</a>,
+            <a class="link" href="../nmp.html#math.dist.mode">mode</a>, <a class="link" href="../nmp.html#math.dist.variance">variance</a>,
+            <a class="link" href="../nmp.html#math.dist.sd">standard deviation</a>, <a class="link" href="../nmp.html#math.dist.skewness">skewness</a>,
+            <a class="link" href="../nmp.html#math.dist.kurtosis">kurtosis</a>, <a class="link" href="../nmp.html#math.dist.kurtosis_excess">kurtosis_excess</a>,
+            <a class="link" href="../nmp.html#math.dist.range">range</a> and <a class="link" href="../nmp.html#math.dist.support">support</a>.
+          </p>
+<p>
+            The domain of the random variable is [0, +&#8734;].
+          </p>
+<a name="math_toolkit.dist.dist_ref.dists.exp_dist.accuracy"></a><h5>
+<a name="id659923"></a>
+            <a class="link" href="exp_dist.html#math_toolkit.dist.dist_ref.dists.exp_dist.accuracy">Accuracy</a>
+          </h5>
+<p>
+            The exponential distribution is implemented in terms of the standard
+            library functions <code class="computeroutput"><span class="identifier">exp</span></code>,
+            <code class="computeroutput"><span class="identifier">log</span></code>, <code class="computeroutput"><span class="identifier">log1p</span></code>
+            and <code class="computeroutput"><span class="identifier">expm1</span></code> and as such
+            should have very low error rates.
+          </p>
+<a name="math_toolkit.dist.dist_ref.dists.exp_dist.implementation"></a><h5>
+<a name="id660003"></a>
+            <a class="link" href="exp_dist.html#math_toolkit.dist.dist_ref.dists.exp_dist.implementation">Implementation</a>
+          </h5>
+<p>
+            In the following table &#955; is the parameter lambda of the distribution,
+            <span class="emphasis"><em>x</em></span> is the random variate, <span class="emphasis"><em>p</em></span>
+            is the probability and <span class="emphasis"><em>q = 1-p</em></span>.
+          </p>
+<div class="informaltable"><table class="table">
+<colgroup>
+<col>
+<col>
+</colgroup>
+<thead><tr>
+<th>
+                  <p>
+                    Function
+                  </p>
+                  </th>
+<th>
+                  <p>
+                    Implementation Notes
+                  </p>
+                  </th>
+</tr></thead>
+<tbody>
+<tr>
+<td>
+                  <p>
+                    pdf
+                  </p>
+                  </td>
+<td>
+                  <p>
+                    Using the relation: pdf = &#955; * exp(-&#955; * x)
+                  </p>
+                  </td>
+</tr>
+<tr>
+<td>
+                  <p>
+                    cdf
+                  </p>
+                  </td>
+<td>
+                  <p>
+                    Using the relation: p = 1 - exp(-x * &#955;) = -expm1(-x * &#955;)
+                  </p>
+                  </td>
+</tr>
+<tr>
+<td>
+                  <p>
+                    cdf complement
+                  </p>
+                  </td>
+<td>
+                  <p>
+                    Using the relation: q = exp(-x * &#955;)
+                  </p>
+                  </td>
+</tr>
+<tr>
+<td>
+                  <p>
+                    quantile
+                  </p>
+                  </td>
+<td>
+                  <p>
+                    Using the relation: x = -log(1-p) / &#955; = -log1p(-p) / &#955;
+                  </p>
+                  </td>
+</tr>
+<tr>
+<td>
+                  <p>
+                    quantile from the complement
+                  </p>
+                  </td>
+<td>
+                  <p>
+                    Using the relation: x = -log(q) / &#955;
+                  </p>
+                  </td>
+</tr>
+<tr>
+<td>
+                  <p>
+                    mean
+                  </p>
+                  </td>
+<td>
+                  <p>
+                    1/&#955;
+                  </p>
+                  </td>
+</tr>
+<tr>
+<td>
+                  <p>
+                    standard deviation
+                  </p>
+                  </td>
+<td>
+                  <p>
+                    1/&#955;
+                  </p>
+                  </td>
+</tr>
+<tr>
+<td>
+                  <p>
+                    mode
+                  </p>
+                  </td>
+<td>
+                  <p>
+                    0
+                  </p>
+                  </td>
+</tr>
+<tr>
+<td>
+                  <p>
+                    skewness
+                  </p>
+                  </td>
+<td>
+                  <p>
+                    2
+                  </p>
+                  </td>
+</tr>
+<tr>
+<td>
+                  <p>
+                    kurtosis
+                  </p>
+                  </td>
+<td>
+                  <p>
+                    9
+                  </p>
+                  </td>
+</tr>
+<tr>
+<td>
+                  <p>
+                    kurtosis excess
+                  </p>
+                  </td>
+<td>
+                  <p>
+                    6
+                  </p>
+                  </td>
+</tr>
+</tbody>
+</table></div>
+<a name="math_toolkit.dist.dist_ref.dists.exp_dist.references"></a><h5>
+<a name="id660320"></a>
+            <a class="link" href="exp_dist.html#math_toolkit.dist.dist_ref.dists.exp_dist.references">references</a>
+          </h5>
+<div class="itemizedlist"><ul type="disc">
+<li><a href="http://mathworld.wolfram.com/ExponentialDistribution.html" target="_top">Weisstein,
+              Eric W. "Exponential Distribution." From MathWorld--A Wolfram
+              Web Resource</a></li>
+<li><a href="http://documents.wolfram.com/calccenter/Functions/ListsMatrices/Statistics/ExponentialDistribution.html" target="_top">Wolfram
+              Mathematica calculator</a></li>
+<li><a href="http://www.itl.nist.gov/div898/handbook/eda/section3/eda3667.htm" target="_top">NIST
+              Exploratory Data Analysis</a></li>
+<li><a href="http://en.wikipedia.org/wiki/Exponential_distribution" target="_top">Wikipedia
+              Exponential distribution</a></li>
+</ul></div>
+<p>
+            (See also the reference documentation for the related <a class="link" href="extreme_dist.html" title="Extreme Value Distribution">Extreme
+            Distributions</a>.)
+          </p>
+<div class="itemizedlist"><ul type="disc"><li>
+<a href="http://www.worldscibooks.com/mathematics/p191.html" target="_top">Extreme
+              Value Distributions, Theory and Applications Samuel Kotz &amp; Saralees
+              Nadarajah</a> discuss the relationship of the types of extreme
+              value distributions.
+            </li></ul></div>
+</div>
+<table xmlns:rev="http://www.cs.rpi.edu/~gregod/boost/tools/doc/revision" width="100%"><tr>
+<td align="left"></td>
+<td align="right"><div class="copyright-footer">Copyright © 2006 , 2007, 2008 John Maddock, Paul A. Bristow, Hubert
+      Holin, Xiaogang Zhang, Bruno Lalande and Gautam Sewani<p>
+        Distributed under the Boost Software License, Version 1.0. (See accompanying
+        file LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_0.txt)
+      </p>
+</div></td>
+</tr></table>
+<hr>
+<div class="spirit-nav">
+<a accesskey="p" href="chi_squared_dist.html"><img src="../../../../../../doc/html/images/prev.png" alt="Prev"></a><a accesskey="u" href="../dists.html"><img src="../../../../../../doc/html/images/up.png" alt="Up"></a><a accesskey="h" href="../../../../index.html"><img src="../../../../../../doc/html/images/home.png" alt="Home"></a><a accesskey="n" href="extreme_dist.html"><img src="../../../../../../doc/html/images/next.png" alt="Next"></a>
+</div>
+</body>
+</html>

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+++ sandbox/tools/auto_index/example/math/doc/sf_and_dist/html/math_toolkit/dist/dist_ref/dists/extreme_dist.html	2008-11-28 05:25:28 EST (Fri, 28 Nov 2008)
@@ -0,0 +1,335 @@
+<html>
+<head>
+<meta http-equiv="Content-Type" content="text/html; charset=ISO-8859-1">
+<title>Extreme Value Distribution</title>
+<link rel="stylesheet" href="../../../../boostbook.css" type="text/css">
+<meta name="generator" content="DocBook XSL Stylesheets Vsnapshot_8125">
+<link rel="home" href="../../../../index.html" title="Math Toolkit">
+<link rel="up" href="../dists.html" title="Distributions">
+<link rel="prev" href="exp_dist.html" title="Exponential Distribution">
+<link rel="next" href="f_dist.html" title="F Distribution">
+</head>
+<body bgcolor="white" text="black" link="#0000FF" vlink="#840084" alink="#0000FF">
+<table cellpadding="2" width="100%"><tr>
+<td valign="top"><img alt="Boost C++ Libraries" width="277" height="86" src="../../../../../../boost.png"></td>
+<td align="center">Home</td>
+<td align="center">Libraries</td>
+<td align="center">People</td>
+<td align="center">FAQ</td>
+<td align="center">More</td>
+</tr></table>
+<hr>
+<div class="spirit-nav">
+<a accesskey="p" href="exp_dist.html"><img src="../../../../../../doc/html/images/prev.png" alt="Prev"></a><a accesskey="u" href="../dists.html"><img src="../../../../../../doc/html/images/up.png" alt="Up"></a><a accesskey="h" href="../../../../index.html"><img src="../../../../../../doc/html/images/home.png" alt="Home"></a><a accesskey="n" href="f_dist.html"><img src="../../../../../../doc/html/images/next.png" alt="Next"></a>
+</div>
+<div class="section" lang="en">
+<div class="titlepage"><div><div><h5 class="title">
+<a name="math_toolkit.dist.dist_ref.dists.extreme_dist"></a><a class="link" href="extreme_dist.html" title="Extreme Value Distribution"> Extreme
+          Value Distribution</a>
+</h5></div></div></div>
+<p>
+            
+</p>
+<pre class="programlisting"><span class="preprocessor">#include</span> <span class="special">&lt;</span><span class="identifier">boost</span><span class="special">/</span><span class="identifier">math</span><span class="special">/</span><span class="identifier">distributions</span><span class="special">/</span><span class="identifier">extreme</span><span class="special">.</span><span class="identifier">hpp</span><span class="special">&gt;</span></pre>
+<p>
+          </p>
+<pre class="programlisting"><span class="keyword">template</span> <span class="special">&lt;</span><span class="keyword">class</span> <span class="identifier">RealType</span> <span class="special">=</span> <span class="keyword">double</span><span class="special">,</span> 
+          <span class="keyword">class</span> <a class="link" href="../../../policy.html" title="Policies">Policy</a>   <span class="special">=</span> <a class="link" href="../../../policy/pol_ref/pol_ref_ref.html" title="Policy Class Reference">policies::policy&lt;&gt;</a> <span class="special">&gt;</span>
+<span class="keyword">class</span> <span class="identifier">extreme_value_distribution</span><span class="special">;</span>
+
+<span class="keyword">typedef</span> <span class="identifier">extreme_value_distribution</span><span class="special">&lt;&gt;</span> <span class="identifier">extreme_value</span><span class="special">;</span>
+
+<span class="keyword">template</span> <span class="special">&lt;</span><span class="keyword">class</span> <span class="identifier">RealType</span><span class="special">,</span> <span class="keyword">class</span> <a class="link" href="../../../policy.html" title="Policies">Policy</a><span class="special">&gt;</span>
+<span class="keyword">class</span> <span class="identifier">extreme_value_distribution</span>
+<span class="special">{</span>
+<span class="keyword">public</span><span class="special">:</span>
+   <span class="keyword">typedef</span> <span class="identifier">RealType</span> <span class="identifier">value_type</span><span class="special">;</span>
+
+   <span class="identifier">extreme_value_distribution</span><span class="special">(</span><span class="identifier">RealType</span> <span class="identifier">location</span> <span class="special">=</span> <span class="number">0</span><span class="special">,</span> <span class="identifier">RealType</span> <span class="identifier">scale</span> <span class="special">=</span> <span class="number">1</span><span class="special">);</span>
+
+   <span class="identifier">RealType</span> <span class="identifier">scale</span><span class="special">()</span><span class="keyword">const</span><span class="special">;</span>
+   <span class="identifier">RealType</span> <span class="identifier">location</span><span class="special">()</span><span class="keyword">const</span><span class="special">;</span>
+<span class="special">};</span>
+</pre>
+<p>
+            There are various <a href="http://mathworld.wolfram.com/ExtremeValueDistribution.html" target="_top">extreme
+            value distributions</a> : this implementation represents the maximum
+            case, and is variously known as a Fisher-Tippett distribution, a log-Weibull
+            distribution or a Gumbel distribution.
+          </p>
+<p>
+            Extreme value theory is important for assessing risk for highly unusual
+            events, such as 100-year floods.
+          </p>
+<p>
+            More information can be found on the NIST,
+            Wikipedia,
+            Mathworld,
+            and <a href="http://en.wikipedia.org/wiki/Extreme_value_theory" target="_top">Extreme
+            value theory</a> websites.
+          </p>
+<p>
+            The relationship of the types of extreme value distributions, of which
+            this is but one, is discussed by <a href="http://www.worldscibooks.com/mathematics/p191.html" target="_top">Extreme
+            Value Distributions, Theory and Applications Samuel Kotz &amp; Saralees
+            Nadarajah</a>.
+          </p>
+<p>
+            The distribution has a PDF given by:
+          </p>
+<p>
+            f(x) = (1/scale) e<sup>-(x-location)/scale</sup> e<sup>-e<sup>-(x-location)/scale</sup></sup>
+          </p>
+<p>
+            Which in the standard case (scale = 1, location = 0) reduces to:
+          </p>
+<p>
+            f(x) = e<sup>-x</sup>e<sup>-e<sup>-x</sup></sup>
+          </p>
+<p>
+            The following graph illustrates how the PDF varies with the location
+            parameter:
+          </p>
+<p>
+            <span class="inlinemediaobject"><img src="../../../../../graphs/extreme_value_pdf1.png" align="middle"></span>
+          </p>
+<p>
+            And this graph illustrates how the PDF varies with the shape parameter:
+          </p>
+<p>
+            <span class="inlinemediaobject"><img src="../../../../../graphs/extreme_value_pdf2.png" align="middle"></span>
+          </p>
+<a name="math_toolkit.dist.dist_ref.dists.extreme_dist.member_functions"></a><h5>
+<a name="id661100"></a>
+            <a class="link" href="extreme_dist.html#math_toolkit.dist.dist_ref.dists.extreme_dist.member_functions">Member
+            Functions</a>
+          </h5>
+<pre class="programlisting"><span class="identifier">extreme_value_distribution</span><span class="special">(</span><span class="identifier">RealType</span> <span class="identifier">location</span> <span class="special">=</span> <span class="number">0</span><span class="special">,</span> <span class="identifier">RealType</span> <span class="identifier">scale</span> <span class="special">=</span> <span class="number">1</span><span class="special">);</span>
+</pre>
+<p>
+            Constructs an Extreme Value distribution with the specified location
+            and scale parameters.
+          </p>
+<p>
+            Requires <code class="computeroutput"><span class="identifier">scale</span> <span class="special">&gt;</span>
+            <span class="number">0</span></code>, otherwise calls <a class="link" href="../../../main_overview/error_handling.html#domain_error">domain_error</a>.
+          </p>
+<pre class="programlisting"><span class="identifier">RealType</span> <span class="identifier">location</span><span class="special">()</span><span class="keyword">const</span><span class="special">;</span>
+</pre>
+<p>
+            Returns the location parameter of the distribution.
+          </p>
+<pre class="programlisting"><span class="identifier">RealType</span> <span class="identifier">scale</span><span class="special">()</span><span class="keyword">const</span><span class="special">;</span>
+</pre>
+<p>
+            Returns the scale parameter of the distribution.
+          </p>
+<a name="math_toolkit.dist.dist_ref.dists.extreme_dist.non_member_accessors"></a><h5>
+<a name="id661331"></a>
+            <a class="link" href="extreme_dist.html#math_toolkit.dist.dist_ref.dists.extreme_dist.non_member_accessors">Non-member
+            Accessors</a>
+          </h5>
+<p>
+            All the <a class="link" href="../nmp.html" title="Non-Member Properties">usual non-member
+            accessor functions</a> that are generic to all distributions are supported:
+            <a class="link" href="../nmp.html#math.dist.cdf">Cumulative Distribution Function</a>,
+            <a class="link" href="../nmp.html#math.dist.pdf">Probability Density Function</a>, <a class="link" href="../nmp.html#math.dist.quantile">Quantile</a>, <a class="link" href="../nmp.html#math.dist.hazard">Hazard
+            Function</a>, <a class="link" href="../nmp.html#math.dist.chf">Cumulative Hazard Function</a>,
+            <a class="link" href="../nmp.html#math.dist.mean">mean</a>, <a class="link" href="../nmp.html#math.dist.median">median</a>,
+            <a class="link" href="../nmp.html#math.dist.mode">mode</a>, <a class="link" href="../nmp.html#math.dist.variance">variance</a>,
+            <a class="link" href="../nmp.html#math.dist.sd">standard deviation</a>, <a class="link" href="../nmp.html#math.dist.skewness">skewness</a>,
+            <a class="link" href="../nmp.html#math.dist.kurtosis">kurtosis</a>, <a class="link" href="../nmp.html#math.dist.kurtosis_excess">kurtosis_excess</a>,
+            <a class="link" href="../nmp.html#math.dist.range">range</a> and <a class="link" href="../nmp.html#math.dist.support">support</a>.
+          </p>
+<p>
+            The domain of the random parameter is [-&#8734;, +&#8734;].
+          </p>
+<a name="math_toolkit.dist.dist_ref.dists.extreme_dist.accuracy"></a><h5>
+<a name="id661508"></a>
+            <a class="link" href="extreme_dist.html#math_toolkit.dist.dist_ref.dists.extreme_dist.accuracy">Accuracy</a>
+          </h5>
+<p>
+            The extreme value distribution is implemented in terms of the standard
+            library <code class="computeroutput"><span class="identifier">exp</span></code> and <code class="computeroutput"><span class="identifier">log</span></code> functions and as such should have
+            very low error rates.
+          </p>
+<a name="math_toolkit.dist.dist_ref.dists.extreme_dist.implementation"></a><h5>
+<a name="id661564"></a>
+            <a class="link" href="extreme_dist.html#math_toolkit.dist.dist_ref.dists.extreme_dist.implementation">Implementation</a>
+          </h5>
+<p>
+            In the following table: <span class="emphasis"><em>a</em></span> is the location parameter,
+            <span class="emphasis"><em>b</em></span> is the scale parameter, <span class="emphasis"><em>x</em></span>
+            is the random variate, <span class="emphasis"><em>p</em></span> is the probability and
+            <span class="emphasis"><em>q = 1-p</em></span>.
+          </p>
+<div class="informaltable"><table class="table">
+<colgroup>
+<col>
+<col>
+</colgroup>
+<thead><tr>
+<th>
+                  <p>
+                    Function
+                  </p>
+                  </th>
+<th>
+                  <p>
+                    Implementation Notes
+                  </p>
+                  </th>
+</tr></thead>
+<tbody>
+<tr>
+<td>
+                  <p>
+                    pdf
+                  </p>
+                  </td>
+<td>
+                  <p>
+                    Using the relation: pdf = exp((a-x)/b) * exp(-exp((a-x)/b)) /
+                    b
+                  </p>
+                  </td>
+</tr>
+<tr>
+<td>
+                  <p>
+                    cdf
+                  </p>
+                  </td>
+<td>
+                  <p>
+                    Using the relation: p = exp(-exp((a-x)/b))
+                  </p>
+                  </td>
+</tr>
+<tr>
+<td>
+                  <p>
+                    cdf complement
+                  </p>
+                  </td>
+<td>
+                  <p>
+                    Using the relation: q = -expm1(-exp((a-x)/b))
+                  </p>
+                  </td>
+</tr>
+<tr>
+<td>
+                  <p>
+                    quantile
+                  </p>
+                  </td>
+<td>
+                  <p>
+                    Using the relation: a - log(-log(p)) * b
+                  </p>
+                  </td>
+</tr>
+<tr>
+<td>
+                  <p>
+                    quantile from the complement
+                  </p>
+                  </td>
+<td>
+                  <p>
+                    Using the relation: a - log(-log1p(-q)) * b
+                  </p>
+                  </td>
+</tr>
+<tr>
+<td>
+                  <p>
+                    mean
+                  </p>
+                  </td>
+<td>
+                  <p>
+                    a + Euler-Mascheroni-constant
+                    * b
+                  </p>
+                  </td>
+</tr>
+<tr>
+<td>
+                  <p>
+                    standard deviation
+                  </p>
+                  </td>
+<td>
+                  <p>
+                    pi * b / sqrt(6)
+                  </p>
+                  </td>
+</tr>
+<tr>
+<td>
+                  <p>
+                    mode
+                  </p>
+                  </td>
+<td>
+                  <p>
+                    The same as the location parameter <span class="emphasis"><em>a</em></span>.
+                  </p>
+                  </td>
+</tr>
+<tr>
+<td>
+                  <p>
+                    skewness
+                  </p>
+                  </td>
+<td>
+                  <p>
+                    12 * sqrt(6) * zeta(3) / pi<sup>3</sup>
+                  </p>
+                  </td>
+</tr>
+<tr>
+<td>
+                  <p>
+                    kurtosis
+                  </p>
+                  </td>
+<td>
+                  <p>
+                    27 / 5
+                  </p>
+                  </td>
+</tr>
+<tr>
+<td>
+                  <p>
+                    kurtosis excess
+                  </p>
+                  </td>
+<td>
+                  <p>
+                    kurtosis - 3 or 12 / 5
+                  </p>
+                  </td>
+</tr>
+</tbody>
+</table></div>
+</div>
+<table xmlns:rev="http://www.cs.rpi.edu/~gregod/boost/tools/doc/revision" width="100%"><tr>
+<td align="left"></td>
+<td align="right"><div class="copyright-footer">Copyright © 2006 , 2007, 2008 John Maddock, Paul A. Bristow, Hubert
+      Holin, Xiaogang Zhang, Bruno Lalande and Gautam Sewani<p>
+        Distributed under the Boost Software License, Version 1.0. (See accompanying
+        file LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_0.txt)
+      </p>
+</div></td>
+</tr></table>
+<hr>
+<div class="spirit-nav">
+<a accesskey="p" href="exp_dist.html"><img src="../../../../../../doc/html/images/prev.png" alt="Prev"></a><a accesskey="u" href="../dists.html"><img src="../../../../../../doc/html/images/up.png" alt="Up"></a><a accesskey="h" href="../../../../index.html"><img src="../../../../../../doc/html/images/home.png" alt="Home"></a><a accesskey="n" href="f_dist.html"><img src="../../../../../../doc/html/images/next.png" alt="Next"></a>
+</div>
+</body>
+</html>

Added: sandbox/tools/auto_index/example/math/doc/sf_and_dist/html/math_toolkit/dist/dist_ref/dists/f_dist.html
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+++ sandbox/tools/auto_index/example/math/doc/sf_and_dist/html/math_toolkit/dist/dist_ref/dists/f_dist.html	2008-11-28 05:25:28 EST (Fri, 28 Nov 2008)
@@ -0,0 +1,438 @@
+<html>
+<head>
+<meta http-equiv="Content-Type" content="text/html; charset=ISO-8859-1">
+<title>F Distribution</title>
+<link rel="stylesheet" href="../../../../boostbook.css" type="text/css">
+<meta name="generator" content="DocBook XSL Stylesheets Vsnapshot_8125">
+<link rel="home" href="../../../../index.html" title="Math Toolkit">
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+<td align="center">Home</td>
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+</div>
+<div class="section" lang="en">
+<div class="titlepage"><div><div><h5 class="title">
+<a name="math_toolkit.dist.dist_ref.dists.f_dist"></a><a class="link" href="f_dist.html" title="F Distribution"> F Distribution</a>
+</h5></div></div></div>
+<p>
+            
+</p>
+<pre class="programlisting"><span class="preprocessor">#include</span> <span class="special">&lt;</span><span class="identifier">boost</span><span class="special">/</span><span class="identifier">math</span><span class="special">/</span><span class="identifier">distributions</span><span class="special">/</span><span class="identifier">fisher_f</span><span class="special">.</span><span class="identifier">hpp</span><span class="special">&gt;</span></pre>
+<p>
+          </p>
+<pre class="programlisting"><span class="keyword">namespace</span> <span class="identifier">boost</span><span class="special">{</span> <span class="keyword">namespace</span> <span class="identifier">math</span><span class="special">{</span> 
+   
+<span class="keyword">template</span> <span class="special">&lt;</span><span class="keyword">class</span> <span class="identifier">RealType</span> <span class="special">=</span> <span class="keyword">double</span><span class="special">,</span> 
+          <span class="keyword">class</span> <a class="link" href="../../../policy.html" title="Policies">Policy</a>   <span class="special">=</span> <a class="link" href="../../../policy/pol_ref/pol_ref_ref.html" title="Policy Class Reference">policies::policy&lt;&gt;</a> <span class="special">&gt;</span>
+<span class="keyword">class</span> <span class="identifier">fisher_f_distribution</span><span class="special">;</span>
+
+<span class="keyword">typedef</span> <span class="identifier">fisher_f_distribution</span><span class="special">&lt;&gt;</span> <span class="identifier">fisher_f</span><span class="special">;</span>
+
+<span class="keyword">template</span> <span class="special">&lt;</span><span class="keyword">class</span> <span class="identifier">RealType</span><span class="special">,</span> <span class="keyword">class</span> <a class="link" href="../../../policy.html" title="Policies">Policy</a><span class="special">&gt;</span>
+<span class="keyword">class</span> <span class="identifier">fisher_f_distribution</span>
+<span class="special">{</span>
+<span class="keyword">public</span><span class="special">:</span>
+   <span class="keyword">typedef</span> <span class="identifier">RealType</span> <span class="identifier">value_type</span><span class="special">;</span>
+   
+   <span class="comment">// Construct:
+</span>   <span class="identifier">fisher_f_distribution</span><span class="special">(</span><span class="keyword">const</span> <span class="identifier">RealType</span><span class="special">&amp;</span> <span class="identifier">i</span><span class="special">,</span> <span class="keyword">const</span> <span class="identifier">RealType</span><span class="special">&amp;</span> <span class="identifier">j</span><span class="special">);</span>
+   
+   <span class="comment">// Accessors:
+</span>   <span class="identifier">RealType</span> <span class="identifier">degrees_of_freedom1</span><span class="special">()</span><span class="keyword">const</span><span class="special">;</span>
+   <span class="identifier">RealType</span> <span class="identifier">degrees_of_freedom2</span><span class="special">()</span><span class="keyword">const</span><span class="special">;</span>
+<span class="special">};</span>
+
+<span class="special">}}</span> <span class="comment">//namespaces
+</span></pre>
+<p>
+            The F distribution is a continuous distribution that arises when testing
+            whether two samples have the same variance. If &#967;<sup>2</sup><sub>m</sub> and &#967;<sup>2</sup><sub>n</sub> are independent
+            variates each distributed as Chi-Squared with <span class="emphasis"><em>m</em></span>
+            and <span class="emphasis"><em>n</em></span> degrees of freedom, then the test statistic:
+          </p>
+<p>
+            F<sub>n,m</sub> = (&#967;<sup>2</sup><sub>n</sub> / n) / (&#967;<sup>2</sup><sub>m</sub> / m)
+          </p>
+<p>
+            Is distributed over the range [0, &#8734;] with an F distribution, and has the
+            PDF:
+          </p>
+<p>
+            <span class="inlinemediaobject"><img src="../../../../../equations/fisher_pdf.png"></span>
+          </p>
+<p>
+            The following graph illustrates how the PDF varies depending on the two
+            degrees of freedom parameters.
+          </p>
+<p>
+            <span class="inlinemediaobject"><img src="../../../../../graphs/fisher_f_pdf.png" align="middle"></span>
+          </p>
+<a name="math_toolkit.dist.dist_ref.dists.f_dist.member_functions"></a><h5>
+<a name="id662554"></a>
+            <a class="link" href="f_dist.html#math_toolkit.dist.dist_ref.dists.f_dist.member_functions">Member
+            Functions</a>
+          </h5>
+<pre class="programlisting"><span class="identifier">fisher_f_distribution</span><span class="special">(</span><span class="keyword">const</span> <span class="identifier">RealType</span><span class="special">&amp;</span> <span class="identifier">df1</span><span class="special">,</span> <span class="keyword">const</span> <span class="identifier">RealType</span><span class="special">&amp;</span> <span class="identifier">df2</span><span class="special">);</span>
+</pre>
+<p>
+            Constructs an F-distribution with numerator degrees of freedom <span class="emphasis"><em>df1</em></span>
+            and denominator degrees of freedom <span class="emphasis"><em>df2</em></span>.
+          </p>
+<p>
+            Requires that <span class="emphasis"><em>df1</em></span> and <span class="emphasis"><em>df2</em></span> are
+            both greater than zero, otherwise <a class="link" href="../../../main_overview/error_handling.html#domain_error">domain_error</a>
+            is called.
+          </p>
+<pre class="programlisting"><span class="identifier">RealType</span> <span class="identifier">degrees_of_freedom1</span><span class="special">()</span><span class="keyword">const</span><span class="special">;</span>
+</pre>
+<p>
+            Returns the numerator degrees of freedom parameter of the distribution.
+          </p>
+<pre class="programlisting"><span class="identifier">RealType</span> <span class="identifier">degrees_of_freedom2</span><span class="special">()</span><span class="keyword">const</span><span class="special">;</span>
+</pre>
+<p>
+            Returns the denominator degrees of freedom parameter of the distribution.
+          </p>
+<a name="math_toolkit.dist.dist_ref.dists.f_dist.non_member_accessors"></a><h5>
+<a name="id662776"></a>
+            <a class="link" href="f_dist.html#math_toolkit.dist.dist_ref.dists.f_dist.non_member_accessors">Non-member
+            Accessors</a>
+          </h5>
+<p>
+            All the <a class="link" href="../nmp.html" title="Non-Member Properties">usual non-member
+            accessor functions</a> that are generic to all distributions are supported:
+            <a class="link" href="../nmp.html#math.dist.cdf">Cumulative Distribution Function</a>,
+            <a class="link" href="../nmp.html#math.dist.pdf">Probability Density Function</a>, <a class="link" href="../nmp.html#math.dist.quantile">Quantile</a>, <a class="link" href="../nmp.html#math.dist.hazard">Hazard
+            Function</a>, <a class="link" href="../nmp.html#math.dist.chf">Cumulative Hazard Function</a>,
+            <a class="link" href="../nmp.html#math.dist.mean">mean</a>, <a class="link" href="../nmp.html#math.dist.median">median</a>,
+            <a class="link" href="../nmp.html#math.dist.mode">mode</a>, <a class="link" href="../nmp.html#math.dist.variance">variance</a>,
+            <a class="link" href="../nmp.html#math.dist.sd">standard deviation</a>, <a class="link" href="../nmp.html#math.dist.skewness">skewness</a>,
+            <a class="link" href="../nmp.html#math.dist.kurtosis">kurtosis</a>, <a class="link" href="../nmp.html#math.dist.kurtosis_excess">kurtosis_excess</a>,
+            <a class="link" href="../nmp.html#math.dist.range">range</a> and <a class="link" href="../nmp.html#math.dist.support">support</a>.
+          </p>
+<p>
+            The domain of the random variable is [0, +&#8734;].
+          </p>
+<a name="math_toolkit.dist.dist_ref.dists.f_dist.examples"></a><h5>
+<a name="id662951"></a>
+            <a class="link" href="f_dist.html#math_toolkit.dist.dist_ref.dists.f_dist.examples">Examples</a>
+          </h5>
+<p>
+            Various <a class="link" href="../../stat_tut/weg/f_eg.html" title="F Distribution Examples">worked examples</a>
+            are available illustrating the use of the F Distribution.
+          </p>
+<a name="math_toolkit.dist.dist_ref.dists.f_dist.accuracy"></a><h5>
+<a name="id662992"></a>
+            <a class="link" href="f_dist.html#math_toolkit.dist.dist_ref.dists.f_dist.accuracy">Accuracy</a>
+          </h5>
+<p>
+            The normal distribution is implemented in terms of the <a class="link" href="../../../special/sf_beta/ibeta_function.html" title="Incomplete Beta Functions">incomplete
+            beta function</a> and it's <a class="link" href="../../../special/sf_beta/ibeta_inv_function.html" title="The Incomplete Beta Function Inverses">inverses</a>,
+            refer to those functions for accuracy data.
+          </p>
+<a name="math_toolkit.dist.dist_ref.dists.f_dist.implementation"></a><h5>
+<a name="id663042"></a>
+            <a class="link" href="f_dist.html#math_toolkit.dist.dist_ref.dists.f_dist.implementation">Implementation</a>
+          </h5>
+<p>
+            In the following table <span class="emphasis"><em>v1</em></span> and <span class="emphasis"><em>v2</em></span>
+            are the first and second degrees of freedom parameters of the distribution,
+            <span class="emphasis"><em>x</em></span> is the random variate, <span class="emphasis"><em>p</em></span>
+            is the probability, and <span class="emphasis"><em>q = 1-p</em></span>.
+          </p>
+<div class="informaltable"><table class="table">
+<colgroup>
+<col>
+<col>
+</colgroup>
+<thead><tr>
+<th>
+                  <p>
+                    Function
+                  </p>
+                  </th>
+<th>
+                  <p>
+                    Implementation Notes
+                  </p>
+                  </th>
+</tr></thead>
+<tbody>
+<tr>
+<td>
+                  <p>
+                    pdf
+                  </p>
+                  </td>
+<td>
+                  <p>
+                    The usual form of the PDF is given by:
+                  </p>
+                  <p>
+                    <span class="inlinemediaobject"><img src="../../../../../equations/fisher_pdf.png"></span>
+                  </p>
+                  <p>
+                    However, that form is hard to evaluate directly without incurring
+                    problems with either accuracy or numeric overflow.
+                  </p>
+                  <p>
+                    Direct differentiation of the CDF expressed in terms of the incomplete
+                    beta function
+                  </p>
+                  <p>
+                    led to the following two formulas:
+                  </p>
+                  <p>
+                    f<sub>v1,v2</sub>(x) = y * <a class="link" href="../../../special/sf_beta/beta_derivative.html" title="Derivative of the Incomplete Beta Function">ibeta_derivative</a>(v2
+                    / 2, v1 / 2, v2 / (v2 + v1 * x))
+                  </p>
+                  <p>
+                    with y = (v2 * v1) / ((v2 + v1 * x) * (v2 + v1 * x))
+                  </p>
+                  <p>
+                    and
+                  </p>
+                  <p>
+                    f<sub>v1,v2</sub>(x) = y * <a class="link" href="../../../special/sf_beta/beta_derivative.html" title="Derivative of the Incomplete Beta Function">ibeta_derivative</a>(v1
+                    / 2, v2 / 2, v1 * x / (v2 + v1 * x))
+                  </p>
+                  <p>
+                    with y = (z * v1 - x * v1 * v1) / z<sup>2</sup>
+                  </p>
+                  <p>
+                    and z = v2 + v1 * x
+                  </p>
+                  <p>
+                    The first of these is used for v1 * x &gt; v2, otherwise the
+                    second is used.
+                  </p>
+                  <p>
+                    The aim is to keep the <span class="emphasis"><em>x</em></span> argument to <a class="link" href="../../../special/sf_beta/beta_derivative.html" title="Derivative of the Incomplete Beta Function">ibeta_derivative</a>
+                    away from 1 to avoid rounding error.
+                  </p>
+                  </td>
+</tr>
+<tr>
+<td>
+                  <p>
+                    cdf
+                  </p>
+                  </td>
+<td>
+                  <p>
+                    Using the relations:
+                  </p>
+                  <p>
+                    p = <a class="link" href="../../../special/sf_beta/ibeta_function.html" title="Incomplete Beta Functions">ibeta</a>(v1
+                    / 2, v2 / 2, v1 * x / (v2 + v1 * x))
+                  </p>
+                  <p>
+                    and
+                  </p>
+                  <p>
+                    p = <a class="link" href="../../../special/sf_beta/ibeta_function.html" title="Incomplete Beta Functions">ibetac</a>(v2
+                    / 2, v1 / 2, v2 / (v2 + v1 * x))
+                  </p>
+                  <p>
+                    The first is used for v1 * x &gt; v2, otherwise the second is
+                    used.
+                  </p>
+                  <p>
+                    The aim is to keep the <span class="emphasis"><em>x</em></span> argument to <a class="link" href="../../../special/sf_beta/ibeta_function.html" title="Incomplete Beta Functions">ibeta</a>
+                    well away from 1 to avoid rounding error.
+                  </p>
+                  </td>
+</tr>
+<tr>
+<td>
+                  <p>
+                    cdf complement
+                  </p>
+                  </td>
+<td>
+                  <p>
+                    Using the relations:
+                  </p>
+                  <p>
+                    p = <a class="link" href="../../../special/sf_beta/ibeta_function.html" title="Incomplete Beta Functions">ibetac</a>(v1
+                    / 2, v2 / 2, v1 * x / (v2 + v1 * x))
+                  </p>
+                  <p>
+                    and
+                  </p>
+                  <p>
+                    p = <a class="link" href="../../../special/sf_beta/ibeta_function.html" title="Incomplete Beta Functions">ibeta</a>(v2
+                    / 2, v1 / 2, v2 / (v2 + v1 * x))
+                  </p>
+                  <p>
+                    The first is used for v1 * x &lt; v2, otherwise the second is
+                    used.
+                  </p>
+                  <p>
+                    The aim is to keep the <span class="emphasis"><em>x</em></span> argument to <a class="link" href="../../../special/sf_beta/ibeta_function.html" title="Incomplete Beta Functions">ibeta</a>
+                    well away from 1 to avoid rounding error.
+                  </p>
+                  </td>
+</tr>
+<tr>
+<td>
+                  <p>
+                    quantile
+                  </p>
+                  </td>
+<td>
+                  <p>
+                    Using the relation:
+                  </p>
+                  <p>
+                    x = v2 * a / (v1 * b)
+                  </p>
+                  <p>
+                    where:
+                  </p>
+                  <p>
+                    a = <a class="link" href="../../../special/sf_beta/ibeta_inv_function.html" title="The Incomplete Beta Function Inverses">ibeta_inv</a>(v1
+                    / 2, v2 / 2, p)
+                  </p>
+                  <p>
+                    and
+                  </p>
+                  <p>
+                    b = 1 - a
+                  </p>
+                  <p>
+                    Quantities <span class="emphasis"><em>a</em></span> and <span class="emphasis"><em>b</em></span>
+                    are both computed by <a class="link" href="../../../special/sf_beta/ibeta_inv_function.html" title="The Incomplete Beta Function Inverses">ibeta_inv</a>
+                    without the subtraction implied above.
+                  </p>
+                  </td>
+</tr>
+<tr>
+<td>
+                  <p>
+                    quantile
+                  </p>
+                  <p>
+                    from the complement
+                  </p>
+                  </td>
+<td>
+                  <p>
+                    Using the relation:
+                  </p>
+                  <p>
+                    x = v2 * a / (v1 * b)
+                  </p>
+                  <p>
+                    where
+                  </p>
+                  <p>
+                    a = <a class="link" href="../../../special/sf_beta/ibeta_inv_function.html" title="The Incomplete Beta Function Inverses">ibetac_inv</a>(v1
+                    / 2, v2 / 2, p)
+                  </p>
+                  <p>
+                    and
+                  </p>
+                  <p>
+                    b = 1 - a
+                  </p>
+                  <p>
+                    Quantities <span class="emphasis"><em>a</em></span> and <span class="emphasis"><em>b</em></span>
+                    are both computed by <a class="link" href="../../../special/sf_beta/ibeta_inv_function.html" title="The Incomplete Beta Function Inverses">ibetac_inv</a>
+                    without the subtraction implied above.
+                  </p>
+                  </td>
+</tr>
+<tr>
+<td>
+                  <p>
+                    mean
+                  </p>
+                  </td>
+<td>
+                  <p>
+                    v2 / (v2 - 2)
+                  </p>
+                  </td>
+</tr>
+<tr>
+<td>
+                  <p>
+                    variance
+                  </p>
+                  </td>
+<td>
+                  <p>
+                    2 * v2<sup>2 </sup> * (v1 + v2 - 2) / (v1 * (v2 - 2) * (v2 - 2) * (v2 - 4))
+                  </p>
+                  </td>
+</tr>
+<tr>
+<td>
+                  <p>
+                    mode
+                  </p>
+                  </td>
+<td>
+                  <p>
+                    v2 * (v1 - 2) / (v1 * (v2 + 2))
+                  </p>
+                  </td>
+</tr>
+<tr>
+<td>
+                  <p>
+                    skewness
+                  </p>
+                  </td>
+<td>
+                  <p>
+                    2 * (v2 + 2 * v1 - 2) * sqrt((2 * v2 - 8) / (v1 * (v2 + v1 -
+                    2))) / (v2 - 6)
+                  </p>
+                  </td>
+</tr>
+<tr>
+<td>
+                  <p>
+                    kurtosis and kurtosis excess
+                  </p>
+                  </td>
+<td>
+                  <p>
+                    Refer to, <a href="http://mathworld.wolfram.com/F-Distribution.html" target="_top">Weisstein,
+                    Eric W. "F-Distribution." From MathWorld--A Wolfram
+                    Web Resource.</a>
+                  </p>
+                  </td>
+</tr>
+</tbody>
+</table></div>
+</div>
+<table xmlns:rev="http://www.cs.rpi.edu/~gregod/boost/tools/doc/revision" width="100%"><tr>
+<td align="left"></td>
+<td align="right"><div class="copyright-footer">Copyright © 2006 , 2007, 2008 John Maddock, Paul A. Bristow, Hubert
+      Holin, Xiaogang Zhang, Bruno Lalande and Gautam Sewani<p>
+        Distributed under the Boost Software License, Version 1.0. (See accompanying
+        file LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_0.txt)
+      </p>
+</div></td>
+</tr></table>
+<hr>
+<div class="spirit-nav">
+<a accesskey="p" href="extreme_dist.html"><img src="../../../../../../doc/html/images/prev.png" alt="Prev"></a><a accesskey="u" href="../dists.html"><img src="../../../../../../doc/html/images/up.png" alt="Up"></a><a accesskey="h" href="../../../../index.html"><img src="../../../../../../doc/html/images/home.png" alt="Home"></a><a accesskey="n" href="gamma_dist.html"><img src="../../../../../../doc/html/images/next.png" alt="Next"></a>
+</div>
+</body>
+</html>

Added: sandbox/tools/auto_index/example/math/doc/sf_and_dist/html/math_toolkit/dist/dist_ref/dists/gamma_dist.html
==============================================================================
--- (empty file)
+++ sandbox/tools/auto_index/example/math/doc/sf_and_dist/html/math_toolkit/dist/dist_ref/dists/gamma_dist.html	2008-11-28 05:25:28 EST (Fri, 28 Nov 2008)
@@ -0,0 +1,378 @@
+<html>
+<head>
+<meta http-equiv="Content-Type" content="text/html; charset=ISO-8859-1">
+<title>Gamma (and Erlang) Distribution</title>
+<link rel="stylesheet" href="../../../../boostbook.css" type="text/css">
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+</div>
+<div class="section" lang="en">
+<div class="titlepage"><div><div><h5 class="title">
+<a name="math_toolkit.dist.dist_ref.dists.gamma_dist"></a><a class="link" href="gamma_dist.html" title="Gamma (and Erlang) Distribution"> Gamma
+          (and Erlang) Distribution</a>
+</h5></div></div></div>
+<p>
+            
+</p>
+<pre class="programlisting"><span class="preprocessor">#include</span> <span class="special">&lt;</span><span class="identifier">boost</span><span class="special">/</span><span class="identifier">math</span><span class="special">/</span><span class="identifier">distributions</span><span class="special">/</span><span class="identifier">gamma</span><span class="special">.</span><span class="identifier">hpp</span><span class="special">&gt;</span></pre>
+<p>
+          </p>
+<pre class="programlisting"><span class="keyword">namespace</span> <span class="identifier">boost</span><span class="special">{</span> <span class="keyword">namespace</span> <span class="identifier">math</span><span class="special">{</span> 
+   
+<span class="keyword">template</span> <span class="special">&lt;</span><span class="keyword">class</span> <span class="identifier">RealType</span> <span class="special">=</span> <span class="keyword">double</span><span class="special">,</span> 
+          <span class="keyword">class</span> <a class="link" href="../../../policy.html" title="Policies">Policy</a>   <span class="special">=</span> <a class="link" href="../../../policy/pol_ref/pol_ref_ref.html" title="Policy Class Reference">policies::policy&lt;&gt;</a> <span class="special">&gt;</span>
+<span class="keyword">class</span> <span class="identifier">gamma_distribution</span>
+<span class="special">{</span>
+<span class="keyword">public</span><span class="special">:</span>
+   <span class="keyword">typedef</span> <span class="identifier">RealType</span> <span class="identifier">value_type</span><span class="special">;</span>
+   <span class="keyword">typedef</span> <span class="identifier">Policy</span>   <span class="identifier">policy_type</span><span class="special">;</span>
+
+   <span class="identifier">gamma_distribution</span><span class="special">(</span><span class="identifier">RealType</span> <span class="identifier">shape</span><span class="special">,</span> <span class="identifier">RealType</span> <span class="identifier">scale</span> <span class="special">=</span> <span class="number">1</span><span class="special">)</span>
+
+   <span class="identifier">RealType</span> <span class="identifier">shape</span><span class="special">()</span><span class="keyword">const</span><span class="special">;</span>
+   <span class="identifier">RealType</span> <span class="identifier">scale</span><span class="special">()</span><span class="keyword">const</span><span class="special">;</span>
+<span class="special">};</span>
+
+<span class="special">}}</span> <span class="comment">// namespaces
+</span></pre>
+<p>
+            The gamma distribution is a continuous probability distribution. When
+            the shape parameter is an integer then it is known as the Erlang Distribution.
+            It is also closely related to the Poisson and Chi Squared Distributions.
+          </p>
+<p>
+            When the shape parameter has an integer value, the distribution is the
+            <a href="http://en.wikipedia.org/wiki/Erlang_distribution" target="_top">Erlang
+            distribution</a>. Since this can be produced by ensuring that the
+            shape parameter has an integer value &gt; 0, the Erlang distribution
+            is not separately implemented.
+          </p>
+<div class="note"><table border="0" summary="Note">
+<tr>
+<td rowspan="2" align="center" valign="top" width="25"><img alt="[Note]" src="../../../../../../doc/html/images/note.png"></td>
+<th align="left">Note</th>
+</tr>
+<tr><td align="left" valign="top">
+<p>
+              To avoid potential confusion with the gamma functions, this distribution
+              does not provide the typedef:
+            </p>
+<p>
+              
+</p>
+<pre class="programlisting"><span class="keyword">typedef</span> <span class="identifier">gamma_distibution</span><span class="special">&lt;</span><span class="keyword">double</span><span class="special">&gt;</span> <span class="identifier">gamma</span><span class="special">;</span></pre>
+<p>
+            </p>
+<p>
+              Instead if you want a double precision gamma distribution you can use
+            </p>
+<p>
+              
+</p>
+<pre class="programlisting"><span class="identifier">boost</span><span class="special">::</span><span class="identifier">gamma_distribution</span><span class="special">&lt;&gt;</span></pre>
+<p>
+            </p>
+</td></tr>
+</table></div>
+<p>
+            For shape parameter <span class="emphasis"><em>k</em></span> and scale parameter &#952; it is
+            defined by the probability density function:
+          </p>
+<p>
+            <span class="inlinemediaobject"><img src="../../../../../equations/gamma_dist_ref1.png"></span>
+          </p>
+<p>
+            Sometimes an alternative formulation is used: given parameters &#945;= k and
+            &#946;= 1 / &#952;, then the distribution can be defined by the PDF:
+          </p>
+<p>
+            <span class="inlinemediaobject"><img src="../../../../../equations/gamma_dist_ref2.png"></span>
+          </p>
+<p>
+            In this form the inverse scale parameter is called a <span class="emphasis"><em>rate parameter</em></span>.
+          </p>
+<p>
+            Both forms are in common usage: this library uses the first definition
+            throughout. Therefore to construct a Gamma Distribution from a <span class="emphasis"><em>rate
+            parameter</em></span>, you should pass the reciprocal of the rate as the
+            scale parameter.
+          </p>
+<p>
+            The following two graphs illustrate how the PDF of the gamma distribution
+            varies as the parameters vary:
+          </p>
+<p>
+            <span class="inlinemediaobject"><img src="../../../../../graphs/gamma1_pdf.png" align="middle"></span>
+          </p>
+<p>
+            <span class="inlinemediaobject"><img src="../../../../../graphs/gamma2_pdf.png" align="middle"></span>
+          </p>
+<p>
+            The <span class="bold"><strong>Erlang Distribution</strong></span> is the same
+            as the Gamma, but with the shape parameter an integer. It is often expressed
+            using a <span class="emphasis"><em>rate</em></span> rather than a <span class="emphasis"><em>scale</em></span>
+            as the second parameter (remember that the rate is the reciprocal of
+            the scale).
+          </p>
+<p>
+            Internally the functions used to implement the Gamma Distribution are
+            already optimised for small-integer arguments, so in general there should
+            be no great loss of performance from using a Gamma Distribution rather
+            than a dedicated Erlang Distribution.
+          </p>
+<a name="math_toolkit.dist.dist_ref.dists.gamma_dist.member_functions"></a><h5>
+<a name="id664532"></a>
+            <a class="link" href="gamma_dist.html#math_toolkit.dist.dist_ref.dists.gamma_dist.member_functions">Member
+            Functions</a>
+          </h5>
+<pre class="programlisting"><span class="identifier">gamma_distribution</span><span class="special">(</span><span class="identifier">RealType</span> <span class="identifier">shape</span><span class="special">,</span> <span class="identifier">RealType</span> <span class="identifier">scale</span> <span class="special">=</span> <span class="number">1</span><span class="special">);</span>
+</pre>
+<p>
+            Constructs a gamma distribution with shape <span class="emphasis"><em>shape</em></span>
+            and scale <span class="emphasis"><em>scale</em></span>.
+          </p>
+<p>
+            Requires that the shape and scale parameters are greater than zero, otherwise
+            calls <a class="link" href="../../../main_overview/error_handling.html#domain_error">domain_error</a>.
+          </p>
+<pre class="programlisting"><span class="identifier">RealType</span> <span class="identifier">shape</span><span class="special">()</span><span class="keyword">const</span><span class="special">;</span>
+</pre>
+<p>
+            Returns the <span class="emphasis"><em>shape</em></span> parameter of this distribution.
+          </p>
+<pre class="programlisting"><span class="identifier">RealType</span> <span class="identifier">scale</span><span class="special">()</span><span class="keyword">const</span><span class="special">;</span>
+</pre>
+<p>
+            Returns the <span class="emphasis"><em>scale</em></span> parameter of this distribution.
+          </p>
+<a name="math_toolkit.dist.dist_ref.dists.gamma_dist.non_member_accessors"></a><h5>
+<a name="id664743"></a>
+            <a class="link" href="gamma_dist.html#math_toolkit.dist.dist_ref.dists.gamma_dist.non_member_accessors">Non-member
+            Accessors</a>
+          </h5>
+<p>
+            All the <a class="link" href="../nmp.html" title="Non-Member Properties">usual non-member
+            accessor functions</a> that are generic to all distributions are supported:
+            <a class="link" href="../nmp.html#math.dist.cdf">Cumulative Distribution Function</a>,
+            <a class="link" href="../nmp.html#math.dist.pdf">Probability Density Function</a>, <a class="link" href="../nmp.html#math.dist.quantile">Quantile</a>, <a class="link" href="../nmp.html#math.dist.hazard">Hazard
+            Function</a>, <a class="link" href="../nmp.html#math.dist.chf">Cumulative Hazard Function</a>,
+            <a class="link" href="../nmp.html#math.dist.mean">mean</a>, <a class="link" href="../nmp.html#math.dist.median">median</a>,
+            <a class="link" href="../nmp.html#math.dist.mode">mode</a>, <a class="link" href="../nmp.html#math.dist.variance">variance</a>,
+            <a class="link" href="../nmp.html#math.dist.sd">standard deviation</a>, <a class="link" href="../nmp.html#math.dist.skewness">skewness</a>,
+            <a class="link" href="../nmp.html#math.dist.kurtosis">kurtosis</a>, <a class="link" href="../nmp.html#math.dist.kurtosis_excess">kurtosis_excess</a>,
+            <a class="link" href="../nmp.html#math.dist.range">range</a> and <a class="link" href="../nmp.html#math.dist.support">support</a>.
+          </p>
+<p>
+            The domain of the random variable is [0,+&#8734;].
+          </p>
+<a name="math_toolkit.dist.dist_ref.dists.gamma_dist.accuracy"></a><h5>
+<a name="id664920"></a>
+            <a class="link" href="gamma_dist.html#math_toolkit.dist.dist_ref.dists.gamma_dist.accuracy">Accuracy</a>
+          </h5>
+<p>
+            The lognormal distribution is implemented in terms of the incomplete
+            gamma functions <a class="link" href="../../../special/sf_gamma/igamma.html" title="Incomplete Gamma Functions">gamma_p</a>
+            and <a class="link" href="../../../special/sf_gamma/igamma.html" title="Incomplete Gamma Functions">gamma_q</a>
+            and their inverses <a class="link" href="../../../special/sf_gamma/igamma_inv.html" title="Incomplete Gamma Function Inverses">gamma_p_inv</a>
+            and <a class="link" href="../../../special/sf_gamma/igamma_inv.html" title="Incomplete Gamma Function Inverses">gamma_q_inv</a>:
+            refer to the accuracy data for those functions for more information.
+          </p>
+<a name="math_toolkit.dist.dist_ref.dists.gamma_dist.implementation"></a><h5>
+<a name="id664992"></a>
+            <a class="link" href="gamma_dist.html#math_toolkit.dist.dist_ref.dists.gamma_dist.implementation">Implementation</a>
+          </h5>
+<p>
+            In the following table <span class="emphasis"><em>k</em></span> is the shape parameter
+            of the distribution, &#952; is it's scale parameter, <span class="emphasis"><em>x</em></span>
+            is the random variate, <span class="emphasis"><em>p</em></span> is the probability and
+            <span class="emphasis"><em>q = 1-p</em></span>.
+          </p>
+<div class="informaltable"><table class="table">
+<colgroup>
+<col>
+<col>
+</colgroup>
+<thead><tr>
+<th>
+                  <p>
+                    Function
+                  </p>
+                  </th>
+<th>
+                  <p>
+                    Implementation Notes
+                  </p>
+                  </th>
+</tr></thead>
+<tbody>
+<tr>
+<td>
+                  <p>
+                    pdf
+                  </p>
+                  </td>
+<td>
+                  <p>
+                    Using the relation: pdf = <a class="link" href="../../../special/sf_gamma/gamma_derivatives.html" title="Derivative of the Incomplete Gamma Function">gamma_p_derivative</a>(k,
+                    x / &#952;) / &#952;
+                  </p>
+                  </td>
+</tr>
+<tr>
+<td>
+                  <p>
+                    cdf
+                  </p>
+                  </td>
+<td>
+                  <p>
+                    Using the relation: p = <a class="link" href="../../../special/sf_gamma/igamma.html" title="Incomplete Gamma Functions">gamma_p</a>(k,
+                    x / &#952;)
+                  </p>
+                  </td>
+</tr>
+<tr>
+<td>
+                  <p>
+                    cdf complement
+                  </p>
+                  </td>
+<td>
+                  <p>
+                    Using the relation: q = <a class="link" href="../../../special/sf_gamma/igamma.html" title="Incomplete Gamma Functions">gamma_q</a>(k,
+                    x / &#952;)
+                  </p>
+                  </td>
+</tr>
+<tr>
+<td>
+                  <p>
+                    quantile
+                  </p>
+                  </td>
+<td>
+                  <p>
+                    Using the relation: x = &#952;* <a class="link" href="../../../special/sf_gamma/igamma_inv.html" title="Incomplete Gamma Function Inverses">gamma_p_inv</a>(k,
+                    p)
+                  </p>
+                  </td>
+</tr>
+<tr>
+<td>
+                  <p>
+                    quantile from the complement
+                  </p>
+                  </td>
+<td>
+                  <p>
+                    Using the relation: x = &#952;* <a class="link" href="../../../special/sf_gamma/igamma_inv.html" title="Incomplete Gamma Function Inverses">gamma_q_inv</a>(k,
+                    p)
+                  </p>
+                  </td>
+</tr>
+<tr>
+<td>
+                  <p>
+                    mean
+                  </p>
+                  </td>
+<td>
+                  <p>
+                    k&#952;
+                  </p>
+                  </td>
+</tr>
+<tr>
+<td>
+                  <p>
+                    variance
+                  </p>
+                  </td>
+<td>
+                  <p>
+                    k&#952;<sup>2</sup>
+                  </p>
+                  </td>
+</tr>
+<tr>
+<td>
+                  <p>
+                    mode
+                  </p>
+                  </td>
+<td>
+                  <p>
+                    (k-1)&#952; for <span class="emphasis"><em>k&gt;1</em></span> otherwise a <a class="link" href="../../../main_overview/error_handling.html#domain_error">domain_error</a>
+                  </p>
+                  </td>
+</tr>
+<tr>
+<td>
+                  <p>
+                    skewness
+                  </p>
+                  </td>
+<td>
+                  <p>
+                    2 / sqrt(k)
+                  </p>
+                  </td>
+</tr>
+<tr>
+<td>
+                  <p>
+                    kurtosis
+                  </p>
+                  </td>
+<td>
+                  <p>
+                    3 + 6 / k
+                  </p>
+                  </td>
+</tr>
+<tr>
+<td>
+                  <p>
+                    kurtosis excess
+                  </p>
+                  </td>
+<td>
+                  <p>
+                    6 / k
+                  </p>
+                  </td>
+</tr>
+</tbody>
+</table></div>
+</div>
+<table xmlns:rev="http://www.cs.rpi.edu/~gregod/boost/tools/doc/revision" width="100%"><tr>
+<td align="left"></td>
+<td align="right"><div class="copyright-footer">Copyright © 2006 , 2007, 2008 John Maddock, Paul A. Bristow, Hubert
+      Holin, Xiaogang Zhang, Bruno Lalande and Gautam Sewani<p>
+        Distributed under the Boost Software License, Version 1.0. (See accompanying
+        file LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_0.txt)
+      </p>
+</div></td>
+</tr></table>
+<hr>
+<div class="spirit-nav">
+<a accesskey="p" href="f_dist.html"><img src="../../../../../../doc/html/images/prev.png" alt="Prev"></a><a accesskey="u" href="../dists.html"><img src="../../../../../../doc/html/images/up.png" alt="Up"></a><a accesskey="h" href="../../../../index.html"><img src="../../../../../../doc/html/images/home.png" alt="Home"></a><a accesskey="n" href="logistic_dist.html"><img src="../../../../../../doc/html/images/next.png" alt="Next"></a>
+</div>
+</body>
+</html>

Added: sandbox/tools/auto_index/example/math/doc/sf_and_dist/html/math_toolkit/dist/dist_ref/dists/logistic_dist.html
==============================================================================
--- (empty file)
+++ sandbox/tools/auto_index/example/math/doc/sf_and_dist/html/math_toolkit/dist/dist_ref/dists/logistic_dist.html	2008-11-28 05:25:28 EST (Fri, 28 Nov 2008)
@@ -0,0 +1,301 @@
+<html>
+<head>
+<meta http-equiv="Content-Type" content="text/html; charset=ISO-8859-1">
+<title>Logistic Distribution</title>
+<link rel="stylesheet" href="../../../../boostbook.css" type="text/css">
+<meta name="generator" content="DocBook XSL Stylesheets Vsnapshot_8125">
+<link rel="home" href="../../../../index.html" title="Math Toolkit">
+<link rel="up" href="../dists.html" title="Distributions">
+<link rel="prev" href="gamma_dist.html" title="Gamma (and Erlang) Distribution">
+<link rel="next" href="lognormal_dist.html" title="Log Normal Distribution">
+</head>
+<body bgcolor="white" text="black" link="#0000FF" vlink="#840084" alink="#0000FF">
+<table cellpadding="2" width="100%"><tr>
+<td valign="top"><img alt="Boost C++ Libraries" width="277" height="86" src="../../../../../../boost.png"></td>
+<td align="center">Home</td>
+<td align="center">Libraries</td>
+<td align="center">People</td>
+<td align="center">FAQ</td>
+<td align="center">More</td>
+</tr></table>
+<hr>
+<div class="spirit-nav">
+<a accesskey="p" href="gamma_dist.html"><img src="../../../../../../doc/html/images/prev.png" alt="Prev"></a><a accesskey="u" href="../dists.html"><img src="../../../../../../doc/html/images/up.png" alt="Up"></a><a accesskey="h" href="../../../../index.html"><img src="../../../../../../doc/html/images/home.png" alt="Home"></a><a accesskey="n" href="lognormal_dist.html"><img src="../../../../../../doc/html/images/next.png" alt="Next"></a>
+</div>
+<div class="section" lang="en">
+<div class="titlepage"><div><div><h5 class="title">
+<a name="math_toolkit.dist.dist_ref.dists.logistic_dist"></a><a class="link" href="logistic_dist.html" title="Logistic Distribution">
+          Logistic Distribution</a>
+</h5></div></div></div>
+<p>
+            
+</p>
+<pre class="programlisting"><span class="preprocessor">#include</span> <span class="special">&lt;</span><span class="identifier">boost</span><span class="special">/</span><span class="identifier">math</span><span class="special">/</span><span class="identifier">distributions</span><span class="special">/</span><span class="identifier">logistic</span><span class="special">.</span><span class="identifier">hpp</span><span class="special">&gt;</span></pre>
+<p>
+          </p>
+<pre class="programlisting"><span class="keyword">namespace</span> <span class="identifier">boost</span><span class="special">{</span> <span class="keyword">namespace</span> <span class="identifier">math</span><span class="special">{</span> 
+   
+<span class="keyword">template</span> <span class="special">&lt;</span><span class="keyword">class</span> <span class="identifier">RealType</span> <span class="special">=</span> <span class="keyword">double</span><span class="special">,</span> 
+          <span class="keyword">class</span> <a class="link" href="../../../policy.html" title="Policies">Policy</a>   <span class="special">=</span> <a class="link" href="../../../policy/pol_ref/pol_ref_ref.html" title="Policy Class Reference">policies::policy&lt;&gt;</a> <span class="special">&gt;</span>
+<span class="keyword">class</span> <span class="identifier">logistic_distribution</span><span class="special">;</span>
+
+<span class="keyword">template</span> <span class="special">&lt;</span><span class="keyword">class</span> <span class="identifier">RealType</span><span class="special">,</span> <span class="keyword">class</span> <span class="identifier">Policy</span><span class="special">&gt;</span>
+<span class="keyword">class</span> <span class="identifier">logistic_distribution</span>
+<span class="special">{</span>
+<span class="keyword">public</span><span class="special">:</span>
+   <span class="keyword">typedef</span> <span class="identifier">RealType</span> <span class="identifier">value_type</span><span class="special">;</span>
+   <span class="keyword">typedef</span> <span class="identifier">Policy</span>   <span class="identifier">policy_type</span><span class="special">;</span>
+   <span class="comment">// Construct:
+</span>   <span class="identifier">logistic_distribution</span><span class="special">(</span><span class="identifier">RealType</span> <span class="identifier">location</span> <span class="special">=</span> <span class="number">0</span><span class="special">,</span> <span class="identifier">RealType</span> <span class="identifier">scale</span> <span class="special">=</span> <span class="number">1</span><span class="special">);</span>
+   <span class="comment">// Accessors:
+</span>   <span class="identifier">RealType</span> <span class="identifier">location</span><span class="special">()</span><span class="keyword">const</span><span class="special">;</span> <span class="comment">// location.
+</span>   <span class="identifier">RealType</span> <span class="identifier">scale</span><span class="special">()</span><span class="keyword">const</span><span class="special">;</span> <span class="comment">// scale.
+</span>   
+<span class="special">};</span>
+
+<span class="keyword">typedef</span> <span class="identifier">logistic_distribution</span><span class="special">&lt;&gt;</span> <span class="identifier">logistic</span><span class="special">;</span>
+
+<span class="special">}}</span> <span class="comment">// namespaces
+</span></pre>
+<p>
+            The logistic distribution is a continous probability distribution. It
+            has two parameters - location and scale. The cumulative distribution
+            function of the logistic distribution appears in logistic regression
+            and feedforward neural networks. Among other applications, United State
+            Chess Federation and FIDE use it to calculate chess ratings.
+          </p>
+<p>
+            The following graph shows how the distribution changes as the parameters
+            change:
+          </p>
+<p>
+            <span class="inlinemediaobject"><img src="../../../../../graphs/logistic_pdf.png" align="middle"></span>
+          </p>
+<a name="math_toolkit.dist.dist_ref.dists.logistic_dist.member_functions"></a><h5>
+<a name="id665982"></a>
+            <a class="link" href="logistic_dist.html#math_toolkit.dist.dist_ref.dists.logistic_dist.member_functions">Member
+            Functions</a>
+          </h5>
+<pre class="programlisting"><span class="identifier">logistic_distribution</span><span class="special">(</span><span class="identifier">RealType</span> <span class="identifier">u</span> <span class="special">=</span> <span class="number">0</span><span class="special">,</span> <span class="identifier">RealType</span> <span class="identifier">s</span> <span class="special">=</span> <span class="number">1</span><span class="special">);</span>
+</pre>
+<p>
+            Constructs a logistic distribution with location <span class="emphasis"><em>u</em></span>
+            and scale <span class="emphasis"><em>s</em></span>.
+          </p>
+<p>
+            Requires <code class="computeroutput"><span class="identifier">scale</span> <span class="special">&gt;</span>
+            <span class="number">0</span></code>, otherwise a <a class="link" href="../../../main_overview/error_handling.html#domain_error">domain_error</a>
+            is raised.
+          </p>
+<pre class="programlisting"><span class="identifier">RealType</span> <span class="identifier">location</span><span class="special">()</span><span class="keyword">const</span><span class="special">;</span>   
+</pre>
+<p>
+            Returns the location of this distribution.
+          </p>
+<pre class="programlisting"><span class="identifier">RealType</span> <span class="identifier">scale</span><span class="special">()</span><span class="keyword">const</span><span class="special">;</span>
+</pre>
+<p>
+            Returns the scale of this distribution.
+          </p>
+<a name="math_toolkit.dist.dist_ref.dists.logistic_dist.non_member_accessors"></a><h5>
+<a name="id666218"></a>
+            <a class="link" href="logistic_dist.html#math_toolkit.dist.dist_ref.dists.logistic_dist.non_member_accessors">Non-member
+            Accessors</a>
+          </h5>
+<p>
+            All the <a class="link" href="../nmp.html" title="Non-Member Properties">usual non-member
+            accessor functions</a> that are generic to all distributions are supported:
+            <a class="link" href="../nmp.html#math.dist.cdf">Cumulative Distribution Function</a>,
+            <a class="link" href="../nmp.html#math.dist.pdf">Probability Density Function</a>, <a class="link" href="../nmp.html#math.dist.quantile">Quantile</a>, <a class="link" href="../nmp.html#math.dist.hazard">Hazard
+            Function</a>, <a class="link" href="../nmp.html#math.dist.chf">Cumulative Hazard Function</a>,
+            <a class="link" href="../nmp.html#math.dist.mean">mean</a>, <a class="link" href="../nmp.html#math.dist.median">median</a>,
+            <a class="link" href="../nmp.html#math.dist.mode">mode</a>, <a class="link" href="../nmp.html#math.dist.variance">variance</a>,
+            <a class="link" href="../nmp.html#math.dist.sd">standard deviation</a>, <a class="link" href="../nmp.html#math.dist.skewness">skewness</a>,
+            <a class="link" href="../nmp.html#math.dist.kurtosis">kurtosis</a>, <a class="link" href="../nmp.html#math.dist.kurtosis_excess">kurtosis_excess</a>,
+            <a class="link" href="../nmp.html#math.dist.range">range</a> and <a class="link" href="../nmp.html#math.dist.support">support</a>.
+          </p>
+<p>
+            The domain of the random variable is [-[max_value], +[min_value]]. However,
+            the pdf and cdf support inputs of +&#8734; and -&#8734;
+as special cases if RealType
+            permits.
+          </p>
+<p>
+            At <code class="computeroutput"><span class="identifier">p</span><span class="special">=</span><span class="number">1</span></code> and <code class="computeroutput"><span class="identifier">p</span><span class="special">=</span><span class="number">0</span></code>, the
+            quantile function returns the result of +<a class="link" href="../../../main_overview/error_handling.html#overflow_error">overflow_error</a>
+            and -<a class="link" href="../../../main_overview/error_handling.html#overflow_error">overflow_error</a>, while the
+            complement quantile function returns the result of -<a class="link" href="../../../main_overview/error_handling.html#overflow_error">overflow_error</a>
+            and +<a class="link" href="../../../main_overview/error_handling.html#overflow_error">overflow_error</a> respectively.
+          </p>
+<a name="math_toolkit.dist.dist_ref.dists.logistic_dist.accuracy"></a><h5>
+<a name="id666478"></a>
+            <a class="link" href="logistic_dist.html#math_toolkit.dist.dist_ref.dists.logistic_dist.accuracy">Accuracy</a>
+          </h5>
+<p>
+            The logistic distribution is implemented in terms of the <code class="computeroutput"><span class="identifier">std</span><span class="special">::</span><span class="identifier">exp</span></code> and the <code class="computeroutput"><span class="identifier">std</span><span class="special">::</span><span class="identifier">log</span></code>
+            functions, so its accuracy is related to the accurate implementations
+            of those functions on a given platform. While calculating the quantile
+            and the inverse quantile, some non-zero position values might cause catastrophic
+            cancellation errors. In such cases, only a low <span class="emphasis"><em>absolute error</em></span>
+            can be guarenteed.
+          </p>
+<a name="math_toolkit.dist.dist_ref.dists.logistic_dist.implementation"></a><h5>
+<a name="id666560"></a>
+            <a class="link" href="logistic_dist.html#math_toolkit.dist.dist_ref.dists.logistic_dist.implementation">Implementation</a>
+          </h5>
+<div class="informaltable"><table class="table">
+<colgroup>
+<col>
+<col>
+</colgroup>
+<thead><tr>
+<th>
+                  <p>
+                    Function
+                  </p>
+                  </th>
+<th>
+                  <p>
+                    Implementation Notes
+                  </p>
+                  </th>
+</tr></thead>
+<tbody>
+<tr>
+<td>
+                  <p>
+                    pdf
+                  </p>
+                  </td>
+<td>
+                  <p>
+                    Using the relation: pdf = e<sup>-(x-u)/s</sup> / (s*(1+e<sup>-(x-u)/s</sup>)<sup>2</sup>)
+                  </p>
+                  </td>
+</tr>
+<tr>
+<td>
+                  <p>
+                    cdf
+                  </p>
+                  </td>
+<td>
+                  <p>
+                    Using the relation: p = 1/(1+e<sup>-(x-u)/s</sup>)
+                  </p>
+                  </td>
+</tr>
+<tr>
+<td>
+                  <p>
+                    cdf complement
+                  </p>
+                  </td>
+<td>
+                  <p>
+                    Using the relation: q = 1/(1+e<sup>(x-u)/s</sup>)
+                  </p>
+                  </td>
+</tr>
+<tr>
+<td>
+                  <p>
+                    quantile
+                  </p>
+                  </td>
+<td>
+                  <p>
+                    Using the relation: x = u - s*log(1/p-1)
+                  </p>
+                  </td>
+</tr>
+<tr>
+<td>
+                  <p>
+                    quantile from the complement
+                  </p>
+                  </td>
+<td>
+                  <p>
+                    Using the relation: x = u + s*log(p/1-p)
+                  </p>
+                  </td>
+</tr>
+<tr>
+<td>
+                  <p>
+                    mean
+                  </p>
+                  </td>
+<td>
+                  <p>
+                    u
+                  </p>
+                  </td>
+</tr>
+<tr>
+<td>
+                  <p>
+                    mode
+                  </p>
+                  </td>
+<td>
+                  <p>
+                    The same as the mean.
+                  </p>
+                  </td>
+</tr>
+<tr>
+<td>
+                  <p>
+                    skewness
+                  </p>
+                  </td>
+<td>
+                  <p>
+                    0
+                  </p>
+                  </td>
+</tr>
+<tr>
+<td>
+                  <p>
+                    kurtosis excess
+                  </p>
+                  </td>
+<td>
+                  <p>
+                    6/5
+                  </p>
+                  </td>
+</tr>
+<tr>
+<td>
+                  <p>
+                    variance
+                  </p>
+                  </td>
+<td>
+                  <p>
+                    (&#960;*s)<sup>2</sup> / 3
+                  </p>
+                  </td>
+</tr>
+</tbody>
+</table></div>
+</div>
+<table xmlns:rev="http://www.cs.rpi.edu/~gregod/boost/tools/doc/revision" width="100%"><tr>
+<td align="left"></td>
+<td align="right"><div class="copyright-footer">Copyright © 2006 , 2007, 2008 John Maddock, Paul A. Bristow, Hubert
+      Holin, Xiaogang Zhang, Bruno Lalande and Gautam Sewani<p>
+        Distributed under the Boost Software License, Version 1.0. (See accompanying
+        file LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_0.txt)
+      </p>
+</div></td>
+</tr></table>
+<hr>
+<div class="spirit-nav">
+<a accesskey="p" href="gamma_dist.html"><img src="../../../../../../doc/html/images/prev.png" alt="Prev"></a><a accesskey="u" href="../dists.html"><img src="../../../../../../doc/html/images/up.png" alt="Up"></a><a accesskey="h" href="../../../../index.html"><img src="../../../../../../doc/html/images/home.png" alt="Home"></a><a accesskey="n" href="lognormal_dist.html"><img src="../../../../../../doc/html/images/next.png" alt="Next"></a>
+</div>
+</body>
+</html>

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==============================================================================
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+++ sandbox/tools/auto_index/example/math/doc/sf_and_dist/html/math_toolkit/dist/dist_ref/dists/lognormal_dist.html	2008-11-28 05:25:28 EST (Fri, 28 Nov 2008)
@@ -0,0 +1,333 @@
+<html>
+<head>
+<meta http-equiv="Content-Type" content="text/html; charset=ISO-8859-1">
+<title>Log Normal Distribution</title>
+<link rel="stylesheet" href="../../../../boostbook.css" type="text/css">
+<meta name="generator" content="DocBook XSL Stylesheets Vsnapshot_8125">
+<link rel="home" href="../../../../index.html" title="Math Toolkit">
+<link rel="up" href="../dists.html" title="Distributions">
+<link rel="prev" href="logistic_dist.html" title="Logistic Distribution">
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+<body bgcolor="white" text="black" link="#0000FF" vlink="#840084" alink="#0000FF">
+<table cellpadding="2" width="100%"><tr>
+<td valign="top"><img alt="Boost C++ Libraries" width="277" height="86" src="../../../../../../boost.png"></td>
+<td align="center">Home</td>
+<td align="center">Libraries</td>
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+<hr>
+<div class="spirit-nav">
+<a accesskey="p" href="logistic_dist.html"><img src="../../../../../../doc/html/images/prev.png" alt="Prev"></a><a accesskey="u" href="../dists.html"><img src="../../../../../../doc/html/images/up.png" alt="Up"></a><a accesskey="h" href="../../../../index.html"><img src="../../../../../../doc/html/images/home.png" alt="Home"></a><a accesskey="n" href="negative_binomial_dist.html"><img src="../../../../../../doc/html/images/next.png" alt="Next"></a>
+</div>
+<div class="section" lang="en">
+<div class="titlepage"><div><div><h5 class="title">
+<a name="math_toolkit.dist.dist_ref.dists.lognormal_dist"></a><a class="link" href="lognormal_dist.html" title="Log Normal Distribution">
+          Log Normal Distribution</a>
+</h5></div></div></div>
+<p>
+            
+</p>
+<pre class="programlisting"><span class="preprocessor">#include</span> <span class="special">&lt;</span><span class="identifier">boost</span><span class="special">/</span><span class="identifier">math</span><span class="special">/</span><span class="identifier">distributions</span><span class="special">/</span><span class="identifier">lognormal</span><span class="special">.</span><span class="identifier">hpp</span><span class="special">&gt;</span></pre>
+<p>
+          </p>
+<pre class="programlisting"><span class="keyword">namespace</span> <span class="identifier">boost</span><span class="special">{</span> <span class="keyword">namespace</span> <span class="identifier">math</span><span class="special">{</span> 
+   
+<span class="keyword">template</span> <span class="special">&lt;</span><span class="keyword">class</span> <span class="identifier">RealType</span> <span class="special">=</span> <span class="keyword">double</span><span class="special">,</span> 
+          <span class="keyword">class</span> <a class="link" href="../../../policy.html" title="Policies">Policy</a>   <span class="special">=</span> <a class="link" href="../../../policy/pol_ref/pol_ref_ref.html" title="Policy Class Reference">policies::policy&lt;&gt;</a> <span class="special">&gt;</span>
+<span class="keyword">class</span> <span class="identifier">lognormal_distribution</span><span class="special">;</span>
+
+<span class="keyword">typedef</span> <span class="identifier">lognormal_distribution</span><span class="special">&lt;&gt;</span> <span class="identifier">lognormal</span><span class="special">;</span>
+
+<span class="keyword">template</span> <span class="special">&lt;</span><span class="keyword">class</span> <span class="identifier">RealType</span><span class="special">,</span> <span class="keyword">class</span> <a class="link" href="../../../policy.html" title="Policies">Policy</a><span class="special">&gt;</span>
+<span class="keyword">class</span> <span class="identifier">lognormal_distribution</span>
+<span class="special">{</span>
+<span class="keyword">public</span><span class="special">:</span>
+   <span class="keyword">typedef</span> <span class="identifier">RealType</span> <span class="identifier">value_type</span><span class="special">;</span>
+   <span class="keyword">typedef</span> <span class="identifier">Policy</span>   <span class="identifier">policy_type</span><span class="special">;</span>
+   <span class="comment">// Construct:
+</span>   <span class="identifier">lognormal_distribution</span><span class="special">(</span><span class="identifier">RealType</span> <span class="identifier">location</span> <span class="special">=</span> <span class="number">0</span><span class="special">,</span> <span class="identifier">RealType</span> <span class="identifier">scale</span> <span class="special">=</span> <span class="number">1</span><span class="special">);</span>
+   <span class="comment">// Accessors:
+</span>   <span class="identifier">RealType</span> <span class="identifier">location</span><span class="special">()</span><span class="keyword">const</span><span class="special">;</span>
+   <span class="identifier">RealType</span> <span class="identifier">scale</span><span class="special">()</span><span class="keyword">const</span><span class="special">;</span>
+<span class="special">};</span>
+
+<span class="special">}}</span> <span class="comment">// namespaces
+</span></pre>
+<p>
+            The lognormal distribution is the distribution that arises when the logarithm
+            of the random variable is normally distributed. A lognormal distribution
+            results when the variable is the product of a large number of independent,
+            identically-distributed variables.
+          </p>
+<p>
+            For location and scale parameters <span class="emphasis"><em>m</em></span> and <span class="emphasis"><em>s</em></span>
+            it is defined by the probability density function:
+          </p>
+<p>
+            <span class="inlinemediaobject"><img src="../../../../../equations/lognormal_ref.png"></span>
+          </p>
+<p>
+            The location and scale parameters are equivalent to the mean and standard
+            deviation of the logarithm of the random variable.
+          </p>
+<p>
+            The following graph illustrates the effect of the location parameter
+            on the PDF, note that the range of the random variable remains [0,+&#8734;]
+            irrespective of the value of the location parameter:
+          </p>
+<p>
+            <span class="inlinemediaobject"><img src="../../../../../graphs/lognormal_pdf1.png" align="middle"></span>
+          </p>
+<p>
+            The next graph illustrates the effect of the scale parameter on the PDF:
+          </p>
+<p>
+            <span class="inlinemediaobject"><img src="../../../../../graphs/lognormal_pdf2.png" align="middle"></span>
+          </p>
+<a name="math_toolkit.dist.dist_ref.dists.lognormal_dist.member_functions"></a><h5>
+<a name="id667548"></a>
+            <a class="link" href="lognormal_dist.html#math_toolkit.dist.dist_ref.dists.lognormal_dist.member_functions">Member
+            Functions</a>
+          </h5>
+<pre class="programlisting"><span class="identifier">lognormal_distribution</span><span class="special">(</span><span class="identifier">RealType</span> <span class="identifier">location</span> <span class="special">=</span> <span class="number">0</span><span class="special">,</span> <span class="identifier">RealType</span> <span class="identifier">scale</span> <span class="special">=</span> <span class="number">1</span><span class="special">);</span>
+</pre>
+<p>
+            Constructs a lognormal distribution with location <span class="emphasis"><em>location</em></span>
+            and scale <span class="emphasis"><em>scale</em></span>.
+          </p>
+<p>
+            The location parameter is the same as the mean of the logarithm of the
+            random variate.
+          </p>
+<p>
+            The scale parameter is the same as the standard deviation of the logarithm
+            of the random variate.
+          </p>
+<p>
+            Requires that the scale parameter is greater than zero, otherwise calls
+            <a class="link" href="../../../main_overview/error_handling.html#domain_error">domain_error</a>.
+          </p>
+<pre class="programlisting"><span class="identifier">RealType</span> <span class="identifier">location</span><span class="special">()</span><span class="keyword">const</span><span class="special">;</span>
+</pre>
+<p>
+            Returns the <span class="emphasis"><em>location</em></span> parameter of this distribution.
+          </p>
+<pre class="programlisting"><span class="identifier">RealType</span> <span class="identifier">scale</span><span class="special">()</span><span class="keyword">const</span><span class="special">;</span>
+</pre>
+<p>
+            Returns the <span class="emphasis"><em>scale</em></span> parameter of this distribution.
+          </p>
+<a name="math_toolkit.dist.dist_ref.dists.lognormal_dist.non_member_accessors"></a><h5>
+<a name="id667784"></a>
+            <a class="link" href="lognormal_dist.html#math_toolkit.dist.dist_ref.dists.lognormal_dist.non_member_accessors">Non-member
+            Accessors</a>
+          </h5>
+<p>
+            All the <a class="link" href="../nmp.html" title="Non-Member Properties">usual non-member
+            accessor functions</a> that are generic to all distributions are supported:
+            <a class="link" href="../nmp.html#math.dist.cdf">Cumulative Distribution Function</a>,
+            <a class="link" href="../nmp.html#math.dist.pdf">Probability Density Function</a>, <a class="link" href="../nmp.html#math.dist.quantile">Quantile</a>, <a class="link" href="../nmp.html#math.dist.hazard">Hazard
+            Function</a>, <a class="link" href="../nmp.html#math.dist.chf">Cumulative Hazard Function</a>,
+            <a class="link" href="../nmp.html#math.dist.mean">mean</a>, <a class="link" href="../nmp.html#math.dist.median">median</a>,
+            <a class="link" href="../nmp.html#math.dist.mode">mode</a>, <a class="link" href="../nmp.html#math.dist.variance">variance</a>,
+            <a class="link" href="../nmp.html#math.dist.sd">standard deviation</a>, <a class="link" href="../nmp.html#math.dist.skewness">skewness</a>,
+            <a class="link" href="../nmp.html#math.dist.kurtosis">kurtosis</a>, <a class="link" href="../nmp.html#math.dist.kurtosis_excess">kurtosis_excess</a>,
+            <a class="link" href="../nmp.html#math.dist.range">range</a> and <a class="link" href="../nmp.html#math.dist.support">support</a>.
+          </p>
+<p>
+            The domain of the random variable is [0,+&#8734;].
+          </p>
+<a name="math_toolkit.dist.dist_ref.dists.lognormal_dist.accuracy"></a><h5>
+<a name="id667958"></a>
+            <a class="link" href="lognormal_dist.html#math_toolkit.dist.dist_ref.dists.lognormal_dist.accuracy">Accuracy</a>
+          </h5>
+<p>
+            The lognormal distribution is implemented in terms of the standard library
+            log and exp functions, plus the <a class="link" href="../../../special/sf_erf/error_function.html" title="Error Functions">error
+            function</a>, and as such should have very low error rates.
+          </p>
+<a name="math_toolkit.dist.dist_ref.dists.lognormal_dist.implementation"></a><h5>
+<a name="id668004"></a>
+            <a class="link" href="lognormal_dist.html#math_toolkit.dist.dist_ref.dists.lognormal_dist.implementation">Implementation</a>
+          </h5>
+<p>
+            In the following table <span class="emphasis"><em>m</em></span> is the location parameter
+            of the distribution, <span class="emphasis"><em>s</em></span> is it's scale parameter,
+            <span class="emphasis"><em>x</em></span> is the random variate, <span class="emphasis"><em>p</em></span>
+            is the probability and <span class="emphasis"><em>q = 1-p</em></span>.
+          </p>
+<div class="informaltable"><table class="table">
+<colgroup>
+<col>
+<col>
+</colgroup>
+<thead><tr>
+<th>
+                  <p>
+                    Function
+                  </p>
+                  </th>
+<th>
+                  <p>
+                    Implementation Notes
+                  </p>
+                  </th>
+</tr></thead>
+<tbody>
+<tr>
+<td>
+                  <p>
+                    pdf
+                  </p>
+                  </td>
+<td>
+                  <p>
+                    Using the relation: pdf = e<sup>-(ln(x) - m)<sup>2 </sup> / 2s<sup>2 </sup> </sup> / (x * s * sqrt(2pi))
+                  </p>
+                  </td>
+</tr>
+<tr>
+<td>
+                  <p>
+                    cdf
+                  </p>
+                  </td>
+<td>
+                  <p>
+                    Using the relation: p = cdf(normal_distribtion&lt;RealType&gt;(m,
+                    s), log(x))
+                  </p>
+                  </td>
+</tr>
+<tr>
+<td>
+                  <p>
+                    cdf complement
+                  </p>
+                  </td>
+<td>
+                  <p>
+                    Using the relation: q = cdf(complement(normal_distribtion&lt;RealType&gt;(m,
+                    s), log(x)))
+                  </p>
+                  </td>
+</tr>
+<tr>
+<td>
+                  <p>
+                    quantile
+                  </p>
+                  </td>
+<td>
+                  <p>
+                    Using the relation: x = exp(quantile(normal_distribtion&lt;RealType&gt;(m,
+                    s), p))
+                  </p>
+                  </td>
+</tr>
+<tr>
+<td>
+                  <p>
+                    quantile from the complement
+                  </p>
+                  </td>
+<td>
+                  <p>
+                    Using the relation: x = exp(quantile(complement(normal_distribtion&lt;RealType&gt;(m,
+                    s), q)))
+                  </p>
+                  </td>
+</tr>
+<tr>
+<td>
+                  <p>
+                    mean
+                  </p>
+                  </td>
+<td>
+                  <p>
+                    e<sup>m + s<sup>2 </sup> / 2 </sup>
+                  </p>
+                  </td>
+</tr>
+<tr>
+<td>
+                  <p>
+                    variance
+                  </p>
+                  </td>
+<td>
+                  <p>
+                    (e<sup>s<sup>2</sup> </sup> - 1) * e<sup>2m + s<sup>2 </sup> </sup>
+                  </p>
+                  </td>
+</tr>
+<tr>
+<td>
+                  <p>
+                    mode
+                  </p>
+                  </td>
+<td>
+                  <p>
+                    e<sup>m + s<sup>2 </sup> </sup>
+                  </p>
+                  </td>
+</tr>
+<tr>
+<td>
+                  <p>
+                    skewness
+                  </p>
+                  </td>
+<td>
+                  <p>
+                    sqrt(e<sup>s<sup>2</sup> </sup> - 1) * (2 + e<sup>s<sup>2</sup> </sup>)
+                  </p>
+                  </td>
+</tr>
+<tr>
+<td>
+                  <p>
+                    kurtosis
+                  </p>
+                  </td>
+<td>
+                  <p>
+                    e<sup>4s<sup>2</sup> </sup> + 2e<sup>3s<sup>2</sup> </sup> + 3e<sup>2s<sup>2</sup> </sup> - 3
+                  </p>
+                  </td>
+</tr>
+<tr>
+<td>
+                  <p>
+                    kurtosis excess
+                  </p>
+                  </td>
+<td>
+                  <p>
+                    e<sup>4s<sup>2</sup> </sup> + 2e<sup>3s<sup>2</sup> </sup> + 3e<sup>2s<sup>2</sup> </sup> - 6
+                  </p>
+                  </td>
+</tr>
+</tbody>
+</table></div>
+</div>
+<table xmlns:rev="http://www.cs.rpi.edu/~gregod/boost/tools/doc/revision" width="100%"><tr>
+<td align="left"></td>
+<td align="right"><div class="copyright-footer">Copyright © 2006 , 2007, 2008 John Maddock, Paul A. Bristow, Hubert
+      Holin, Xiaogang Zhang, Bruno Lalande and Gautam Sewani<p>
+        Distributed under the Boost Software License, Version 1.0. (See accompanying
+        file LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_0.txt)
+      </p>
+</div></td>
+</tr></table>
+<hr>
+<div class="spirit-nav">
+<a accesskey="p" href="logistic_dist.html"><img src="../../../../../../doc/html/images/prev.png" alt="Prev"></a><a accesskey="u" href="../dists.html"><img src="../../../../../../doc/html/images/up.png" alt="Up"></a><a accesskey="h" href="../../../../index.html"><img src="../../../../../../doc/html/images/home.png" alt="Home"></a><a accesskey="n" href="negative_binomial_dist.html"><img src="../../../../../../doc/html/images/next.png" alt="Next"></a>
+</div>
+</body>
+</html>

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+++ sandbox/tools/auto_index/example/math/doc/sf_and_dist/html/math_toolkit/dist/dist_ref/dists/nc_beta_dist.html	2008-11-28 05:25:28 EST (Fri, 28 Nov 2008)
@@ -0,0 +1,413 @@
+<html>
+<head>
+<meta http-equiv="Content-Type" content="text/html; charset=ISO-8859-1">
+<title>Noncentral Beta Distribution</title>
+<link rel="stylesheet" href="../../../../boostbook.css" type="text/css">
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+<link rel="next" href="nc_chi_squared_dist.html" title="Noncentral Chi-Squared Distribution">
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+</div>
+<div class="section" lang="en">
+<div class="titlepage"><div><div><h5 class="title">
+<a name="math_toolkit.dist.dist_ref.dists.nc_beta_dist"></a><a class="link" href="nc_beta_dist.html" title="Noncentral Beta Distribution"> Noncentral
+          Beta Distribution</a>
+</h5></div></div></div>
+<p>
+            
+</p>
+<pre class="programlisting"><span class="preprocessor">#include</span> <span class="special">&lt;</span><span class="identifier">boost</span><span class="special">/</span><span class="identifier">math</span><span class="special">/</span><span class="identifier">distributions</span><span class="special">/</span><span class="identifier">non_central_beta</span><span class="special">.</span><span class="identifier">hpp</span><span class="special">&gt;</span></pre>
+<p>
+          </p>
+<pre class="programlisting"><span class="keyword">namespace</span> <span class="identifier">boost</span><span class="special">{</span> <span class="keyword">namespace</span> <span class="identifier">math</span><span class="special">{</span> 
+
+<span class="keyword">template</span> <span class="special">&lt;</span><span class="keyword">class</span> <span class="identifier">RealType</span> <span class="special">=</span> <span class="keyword">double</span><span class="special">,</span> 
+          <span class="keyword">class</span> <a class="link" href="../../../policy.html" title="Policies">Policy</a>   <span class="special">=</span> <a class="link" href="../../../policy/pol_ref/pol_ref_ref.html" title="Policy Class Reference">policies::policy&lt;&gt;</a> <span class="special">&gt;</span>
+<span class="keyword">class</span> <span class="identifier">non_central_beta_distribution</span><span class="special">;</span>
+
+<span class="keyword">typedef</span> <span class="identifier">non_central_beta_distribution</span><span class="special">&lt;&gt;</span> <span class="identifier">non_central_beta</span><span class="special">;</span>
+
+<span class="keyword">template</span> <span class="special">&lt;</span><span class="keyword">class</span> <span class="identifier">RealType</span><span class="special">,</span> <span class="keyword">class</span> <a class="link" href="../../../policy.html" title="Policies">Policy</a><span class="special">&gt;</span>
+<span class="keyword">class</span> <span class="identifier">non_central_beta_distribution</span>
+<span class="special">{</span>
+<span class="keyword">public</span><span class="special">:</span>
+   <span class="keyword">typedef</span> <span class="identifier">RealType</span>  <span class="identifier">value_type</span><span class="special">;</span>
+   <span class="keyword">typedef</span> <span class="identifier">Policy</span>    <span class="identifier">policy_type</span><span class="special">;</span>
+
+   <span class="comment">// Constructor:
+</span>   <span class="identifier">non_central_beta_distribution</span><span class="special">(</span><span class="identifier">RealType</span> <span class="identifier">alpha</span><span class="special">,</span> <span class="identifier">RealType</span> <span class="identifier">beta</span><span class="special">,</span> <span class="identifier">RealType</span> <span class="identifier">lambda</span><span class="special">);</span>
+
+   <span class="comment">// Accessor to shape parameters:
+</span>   <span class="identifier">RealType</span> <span class="identifier">alpha</span><span class="special">()</span><span class="keyword">const</span><span class="special">;</span>
+   <span class="identifier">RealType</span> <span class="identifier">beta</span><span class="special">()</span><span class="keyword">const</span><span class="special">;</span>
+
+   <span class="comment">// Accessor to non-centrality parameter lambda:
+</span>   <span class="identifier">RealType</span> <span class="identifier">non_centrality</span><span class="special">()</span><span class="keyword">const</span><span class="special">;</span>
+<span class="special">};</span>
+
+<span class="special">}}</span> <span class="comment">// namespaces
+</span></pre>
+<p>
+            The noncentral beta distribution is a generalization of the <a class="link" href="beta_dist.html" title="Beta Distribution">Beta
+            Distribution</a>.
+          </p>
+<p>
+            It is defined as the ratio X = &#967;<sub>m</sub><sup>2</sup>(&#955;) / (&#967;<sub>m</sub><sup>2</sup>(&#955;) + &#967;<sub>n</sub><sup>2</sup>) where &#967;<sub>m</sub><sup>2</sup>(&#955;) is a noncentral
+            &#967;<sup>2</sup>
+random variable with <span class="emphasis"><em>m</em></span> degrees of freedom, and
+            &#967;<sub>n</sub><sup>2</sup>
+is a central &#967;<sup>2</sup> random variable with <span class="emphasis"><em>n</em></span> degrees of
+            freedom.
+          </p>
+<p>
+            This gives a PDF that can be expressed as a Poisson mixture of beta distribution
+            PDFs:
+          </p>
+<p>
+            <span class="inlinemediaobject"><img src="../../../../../equations/nc_beta_ref1.png"></span>
+          </p>
+<p>
+            where P(i;&#955;/2) is the discrete Poisson probablity at <span class="emphasis"><em>i</em></span>,
+            with mean &#955;/2, and I<sub>x</sub><sup>'</sup>(&#945;, &#946;) is the derivative of the incomplete beta function.
+            This leads to the usual form of the CDF as:
+          </p>
+<p>
+            <span class="inlinemediaobject"><img src="../../../../../equations/nc_beta_ref2.png"></span>
+          </p>
+<p>
+            The following graph illustrates how the distribution changes for different
+            values of &#955;:
+          </p>
+<p>
+            <span class="inlinemediaobject"><img src="../../../../../graphs/nc_beta_pdf.png" align="middle"></span>
+          </p>
+<a name="math_toolkit.dist.dist_ref.dists.nc_beta_dist.member_functions"></a><h5>
+<a name="id674113"></a>
+            <a class="link" href="nc_beta_dist.html#math_toolkit.dist.dist_ref.dists.nc_beta_dist.member_functions">Member
+            Functions</a>
+          </h5>
+<pre class="programlisting"><span class="identifier">non_central_beta_distribution</span><span class="special">(</span><span class="identifier">RealType</span> <span class="identifier">a</span><span class="special">,</span> <span class="identifier">RealType</span> <span class="identifier">b</span><span class="special">,</span> <span class="identifier">RealType</span> <span class="identifier">lambda</span><span class="special">);</span>
+</pre>
+<p>
+            Constructs a noncentral beta distribution with shape parameters <span class="emphasis"><em>a</em></span>
+            and <span class="emphasis"><em>b</em></span> and non-centrality parameter <span class="emphasis"><em>lambda</em></span>.
+          </p>
+<p>
+            Requires a &gt; 0, b &gt; 0 and lambda &gt;= 0, otherwise calls <a class="link" href="../../../main_overview/error_handling.html#domain_error">domain_error</a>.
+          </p>
+<pre class="programlisting"><span class="identifier">RealType</span> <span class="identifier">alpha</span><span class="special">()</span><span class="keyword">const</span><span class="special">;</span>
+</pre>
+<p>
+            Returns the parameter <span class="emphasis"><em>a</em></span> from which this object was
+            constructed.
+          </p>
+<pre class="programlisting"><span class="identifier">RealType</span> <span class="identifier">beta</span><span class="special">()</span><span class="keyword">const</span><span class="special">;</span>
+</pre>
+<p>
+            Returns the parameter <span class="emphasis"><em>b</em></span> from which this object was
+            constructed.
+          </p>
+<pre class="programlisting"><span class="identifier">RealType</span> <span class="identifier">non_centrality</span><span class="special">()</span><span class="keyword">const</span><span class="special">;</span>
+</pre>
+<p>
+            Returns the parameter <span class="emphasis"><em>lambda</em></span> from which this object
+            was constructed.
+          </p>
+<a name="math_toolkit.dist.dist_ref.dists.nc_beta_dist.non_member_accessors"></a><h5>
+<a name="id674376"></a>
+            <a class="link" href="nc_beta_dist.html#math_toolkit.dist.dist_ref.dists.nc_beta_dist.non_member_accessors">Non-member
+            Accessors</a>
+          </h5>
+<p>
+            Most of the <a class="link" href="../nmp.html" title="Non-Member Properties">usual non-member
+            accessor functions</a> are supported: <a class="link" href="../nmp.html#math.dist.cdf">Cumulative
+            Distribution Function</a>, <a class="link" href="../nmp.html#math.dist.pdf">Probability
+            Density Function</a>, <a class="link" href="../nmp.html#math.dist.quantile">Quantile</a>,
+            <a class="link" href="../nmp.html#math.dist.median">median</a>, <a class="link" href="../nmp.html#math.dist.mode">mode</a>,
+            <a class="link" href="../nmp.html#math.dist.hazard">Hazard Function</a>, <a class="link" href="../nmp.html#math.dist.chf">Cumulative
+            Hazard Function</a>, <a class="link" href="../nmp.html#math.dist.range">range</a>
+            and <a class="link" href="../nmp.html#math.dist.support">support</a>.
+          </p>
+<p>
+            However, the following are not currently implemented: <a class="link" href="../nmp.html#math.dist.mean">mean</a>,
+            <a class="link" href="../nmp.html#math.dist.variance">variance</a>, <a class="link" href="../nmp.html#math.dist.sd">standard
+            deviation</a>, <a class="link" href="../nmp.html#math.dist.skewness">skewness</a>,
+            <a class="link" href="../nmp.html#math.dist.kurtosis">kurtosis</a> and <a class="link" href="../nmp.html#math.dist.kurtosis_excess">kurtosis_excess</a>.
+          </p>
+<p>
+            The domain of the random variable is [0, 1].
+          </p>
+<a name="math_toolkit.dist.dist_ref.dists.nc_beta_dist.accuracy"></a><h5>
+<a name="id674556"></a>
+            <a class="link" href="nc_beta_dist.html#math_toolkit.dist.dist_ref.dists.nc_beta_dist.accuracy">Accuracy</a>
+          </h5>
+<p>
+            The following table shows the peak errors (in units of epsilon)
+            found on various platforms with various floating point types. No comparison
+            to the R-2.5.1 Math library,
+            or to the FORTRAN implementations of AS226 or AS310 are given since these
+            appear to only guarantee absolute error: this would causes our test harness
+            to assign an <span class="emphasis"><em>"infinite"</em></span> error to these
+            libraries for some of our test values when measuring <span class="emphasis"><em>relative
+            error</em></span>. Unless otherwise specified any floating-point type
+            that is narrower than the one shown will have <a class="link" href="../../../backgrounders/relative_error.html#zero_error">effectively
+            zero error</a>.
+          </p>
+<div class="table">
+<a name="id674627"></a><p class="title"><b>Table 13. Errors In CDF of the Noncentral Beta</b></p>
+<div class="table-contents"><table class="table" summary="Errors In CDF of the Noncentral Beta">
+<colgroup>
+<col>
+<col>
+<col>
+<col>
+</colgroup>
+<thead><tr>
+<th>
+                <p>
+                  Significand Size
+                </p>
+                </th>
+<th>
+                <p>
+                  Platform and Compiler
+                </p>
+                </th>
+<th>
+                <p>
+                  &#945;, &#946;,&#955; &lt; 200
+                </p>
+                </th>
+<th>
+                <p>
+                  &#945;,&#946;,&#955; &gt; 200
+                </p>
+                </th>
+</tr></thead>
+<tbody>
+<tr>
+<td>
+                <p>
+                  53
+                </p>
+                </td>
+<td>
+                <p>
+                  Win32, Visual C++ 8
+                </p>
+                </td>
+<td>
+                <p>
+                  Peak=620 Mean=22
+                </p>
+                </td>
+<td>
+                <p>
+                  Peak=8670 Mean=1040
+                </p>
+                </td>
+</tr>
+<tr>
+<td>
+                <p>
+                  64
+                </p>
+                </td>
+<td>
+                <p>
+                  RedHat Linux IA32, gcc-4.1.1
+                </p>
+                </td>
+<td>
+                <p>
+                  Peak=825 Mean=50
+                </p>
+                </td>
+<td>
+                <p>
+                  Peak=2.5x10<sup>4</sup> Mean=4000
+                </p>
+                </td>
+</tr>
+<tr>
+<td>
+                <p>
+                  64
+                </p>
+                </td>
+<td>
+                <p>
+                  Redhat Linux IA64, gcc-3.4.4
+                </p>
+                </td>
+<td>
+                <p>
+                  Peak=825 Mean=30
+                </p>
+                </td>
+<td>
+                <p>
+                  Peak=1.7x10<sup>4</sup> Mean=2500
+                </p>
+                </td>
+</tr>
+<tr>
+<td>
+                <p>
+                  113
+                </p>
+                </td>
+<td>
+                <p>
+                  HPUX IA64, aCC A.06.06
+                </p>
+                </td>
+<td>
+                <p>
+                  Peak=420 Mean=50
+                </p>
+                </td>
+<td>
+                <p>
+                  Peak=9200 Mean=1200
+                </p>
+                </td>
+</tr>
+</tbody>
+</table></div>
+</div>
+<br class="table-break"><p>
+            Error rates for the PDF, the complement of the CDF and for the quantile
+            functions are broadly similar.
+          </p>
+<a name="math_toolkit.dist.dist_ref.dists.nc_beta_dist.tests"></a><h5>
+<a name="id674854"></a>
+            <a class="link" href="nc_beta_dist.html#math_toolkit.dist.dist_ref.dists.nc_beta_dist.tests">Tests</a>
+          </h5>
+<p>
+            There are two sets of test data used to verify this implementation: firstly
+            we can compare with a few sample values generated by the <a href="http://www.r-project.org/" target="_top">R
+            library</a>. Secondly, we have tables of test data, computed with
+            this implementation and using interval arithmetic - this data should
+            be accurate to at least 50 decimal digits - and is the used for our accuracy
+            tests.
+          </p>
+<a name="math_toolkit.dist.dist_ref.dists.nc_beta_dist.implementation"></a><h5>
+<a name="id674900"></a>
+            <a class="link" href="nc_beta_dist.html#math_toolkit.dist.dist_ref.dists.nc_beta_dist.implementation">Implementation</a>
+          </h5>
+<p>
+            The CDF and its complement are evaluated as follows:
+          </p>
+<p>
+            First we determine which of the two values (the CDF or its complement)
+            is likely to be the smaller, the crossover point is taken to be the mean
+            of the distribution: for this we use the approximation due to: R. Chattamvelli
+            and R. Shanmugam, "Algorithm AS 310: Computing the Non-Central Beta
+            Distribution Function", Applied Statistics, Vol. 46, No. 1. (1997),
+            pp. 146-156.
+          </p>
+<p>
+            <span class="inlinemediaobject"><img src="../../../../../equations/nc_beta_ref3.png"></span>
+          </p>
+<p>
+            Then either the CDF or its complement is computed using the relations:
+          </p>
+<p>
+            <span class="inlinemediaobject"><img src="../../../../../equations/nc_beta_ref4.png"></span>
+          </p>
+<p>
+            The summation is performed by starting at i = &#955;/2, and then recursing
+            in both directions, using the usual recurrence relations for the Poisson
+            PDF and incomplete beta functions. This is the "Method 2" described
+            by:
+          </p>
+<p>
+            Denise Benton and K. Krishnamoorthy, "Computing discrete mixtures
+            of continuous distributions: noncentral chisquare, noncentral t and the
+            distribution of the square of the sample multiple correlation coefficient",
+            Computational Statistics &amp; Data Analysis 43 (2003) 249-267.
+          </p>
+<p>
+            Specific applications of the above formulae to the noncentral beta distribution
+            can be found in:
+          </p>
+<p>
+            Russell V. Lenth, "Algorithm AS 226: Computing Noncentral Beta Probabilities",
+            Applied Statistics, Vol. 36, No. 2. (1987), pp. 241-244.
+          </p>
+<p>
+            H. Frick, "Algorithm AS R84: A Remark on Algorithm AS 226: Computing
+            Non-Central Beta Probabilities", Applied Statistics, Vol. 39, No.
+            2. (1990), pp. 311-312.
+          </p>
+<p>
+            Ming Long Lam, "Remark AS R95: A Remark on Algorithm AS 226: Computing
+            Non-Central Beta Probabilities", Applied Statistics, Vol. 44, No.
+            4. (1995), pp. 551-552.
+          </p>
+<p>
+            Harry O. Posten, "An Effective Algorithm for the Noncentral Beta
+            Distribution Function", The American Statistician, Vol. 47, No.
+            2. (May, 1993), pp. 129-131.
+          </p>
+<p>
+            R. Chattamvelli, "A Note on the Noncentral Beta Distribution Function",
+            The American Statistician, Vol. 49, No. 2. (May, 1995), pp. 231-234.
+          </p>
+<p>
+            Of these, the Posten reference provides the most complete overview, and
+            includes the modification starting iteration at &#955;/2.
+          </p>
+<p>
+            The main difference between this implementation and the above references
+            is the direct computation of the complement when most efficient to do
+            so, and the accumulation of the sum to -1 rather than subtracting the
+            result from 1 at the end: this can substantially reduce the number of
+            iterations required when the result is near 1.
+          </p>
+<p>
+            The PDF is computed using the methodology of Benton and Krishnamoorthy
+            and the relation:
+          </p>
+<p>
+            <span class="inlinemediaobject"><img src="../../../../../equations/nc_beta_ref1.png"></span>
+          </p>
+<p>
+            Quantiles are computed using a specially modified version of <a class="link" href="../../../toolkit/internals1/roots2.html" title="Root Finding Without Derivatives">bracket_and_solve_root</a>,
+            starting the search for the root at the mean of the distribution. (A
+            Cornish-Fisher type expansion was also tried, but while this gets quite
+            close to the root in many cases, when it is wrong it tends to introduce
+            quite pathological behaviour: more investigation in this area is probably
+            warranted).
+          </p>
+</div>
+<table xmlns:rev="http://www.cs.rpi.edu/~gregod/boost/tools/doc/revision" width="100%"><tr>
+<td align="left"></td>
+<td align="right"><div class="copyright-footer">Copyright © 2006 , 2007, 2008 John Maddock, Paul A. Bristow, Hubert
+      Holin, Xiaogang Zhang, Bruno Lalande and Gautam Sewani<p>
+        Distributed under the Boost Software License, Version 1.0. (See accompanying
+        file LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_0.txt)
+      </p>
+</div></td>
+</tr></table>
+<hr>
+<div class="spirit-nav">
+<a accesskey="p" href="negative_binomial_dist.html"><img src="../../../../../../doc/html/images/prev.png" alt="Prev"></a><a accesskey="u" href="../dists.html"><img src="../../../../../../doc/html/images/up.png" alt="Up"></a><a accesskey="h" href="../../../../index.html"><img src="../../../../../../doc/html/images/home.png" alt="Home"></a><a accesskey="n" href="nc_chi_squared_dist.html"><img src="../../../../../../doc/html/images/next.png" alt="Next"></a>
+</div>
+</body>
+</html>

Added: sandbox/tools/auto_index/example/math/doc/sf_and_dist/html/math_toolkit/dist/dist_ref/dists/nc_chi_squared_dist.html
==============================================================================
--- (empty file)
+++ sandbox/tools/auto_index/example/math/doc/sf_and_dist/html/math_toolkit/dist/dist_ref/dists/nc_chi_squared_dist.html	2008-11-28 05:25:28 EST (Fri, 28 Nov 2008)
@@ -0,0 +1,515 @@
+<html>
+<head>
+<meta http-equiv="Content-Type" content="text/html; charset=ISO-8859-1">
+<title>Noncentral Chi-Squared Distribution</title>
+<link rel="stylesheet" href="../../../../boostbook.css" type="text/css">
+<meta name="generator" content="DocBook XSL Stylesheets Vsnapshot_8125">
+<link rel="home" href="../../../../index.html" title="Math Toolkit">
+<link rel="up" href="../dists.html" title="Distributions">
+<link rel="prev" href="nc_beta_dist.html" title="Noncentral Beta Distribution">
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+<a accesskey="p" href="nc_beta_dist.html"><img src="../../../../../../doc/html/images/prev.png" alt="Prev"></a><a accesskey="u" href="../dists.html"><img src="../../../../../../doc/html/images/up.png" alt="Up"></a><a accesskey="h" href="../../../../index.html"><img src="../../../../../../doc/html/images/home.png" alt="Home"></a><a accesskey="n" href="nc_f_dist.html"><img src="../../../../../../doc/html/images/next.png" alt="Next"></a>
+</div>
+<div class="section" lang="en">
+<div class="titlepage"><div><div><h5 class="title">
+<a name="math_toolkit.dist.dist_ref.dists.nc_chi_squared_dist"></a><a class="link" href="nc_chi_squared_dist.html" title="Noncentral Chi-Squared Distribution">
+          Noncentral Chi-Squared Distribution</a>
+</h5></div></div></div>
+<p>
+            
+</p>
+<pre class="programlisting"><span class="preprocessor">#include</span> <span class="special">&lt;</span><span class="identifier">boost</span><span class="special">/</span><span class="identifier">math</span><span class="special">/</span><span class="identifier">distributions</span><span class="special">/</span><span class="identifier">non_central_chi_squared</span><span class="special">.</span><span class="identifier">hpp</span><span class="special">&gt;</span></pre>
+<p>
+          </p>
+<pre class="programlisting"><span class="keyword">namespace</span> <span class="identifier">boost</span><span class="special">{</span> <span class="keyword">namespace</span> <span class="identifier">math</span><span class="special">{</span> 
+
+<span class="keyword">template</span> <span class="special">&lt;</span><span class="keyword">class</span> <span class="identifier">RealType</span> <span class="special">=</span> <span class="keyword">double</span><span class="special">,</span> 
+          <span class="keyword">class</span> <a class="link" href="../../../policy.html" title="Policies">Policy</a>   <span class="special">=</span> <a class="link" href="../../../policy/pol_ref/pol_ref_ref.html" title="Policy Class Reference">policies::policy&lt;&gt;</a> <span class="special">&gt;</span>
+<span class="keyword">class</span> <span class="identifier">non_central_chi_squared_distribution</span><span class="special">;</span>
+
+<span class="keyword">typedef</span> <span class="identifier">non_central_chi_squared_distribution</span><span class="special">&lt;&gt;</span> <span class="identifier">non_central_chi_squared</span><span class="special">;</span>
+
+<span class="keyword">template</span> <span class="special">&lt;</span><span class="keyword">class</span> <span class="identifier">RealType</span><span class="special">,</span> <span class="keyword">class</span> <a class="link" href="../../../policy.html" title="Policies">Policy</a><span class="special">&gt;</span>
+<span class="keyword">class</span> <span class="identifier">non_central_chi_squared_distribution</span>
+<span class="special">{</span>
+<span class="keyword">public</span><span class="special">:</span>
+   <span class="keyword">typedef</span> <span class="identifier">RealType</span>  <span class="identifier">value_type</span><span class="special">;</span>
+   <span class="keyword">typedef</span> <span class="identifier">Policy</span>    <span class="identifier">policy_type</span><span class="special">;</span>
+
+   <span class="comment">// Constructor:
+</span>   <span class="identifier">non_central_chi_squared_distribution</span><span class="special">(</span><span class="identifier">RealType</span> <span class="identifier">v</span><span class="special">,</span> <span class="identifier">RealType</span> <span class="identifier">lambda</span><span class="special">);</span>
+
+   <span class="comment">// Accessor to degrees of freedom parameter v:
+</span>   <span class="identifier">RealType</span> <span class="identifier">degrees_of_freedom</span><span class="special">()</span><span class="keyword">const</span><span class="special">;</span>
+
+   <span class="comment">// Accessor to non centrality parameter lambda:
+</span>   <span class="identifier">RealType</span> <span class="identifier">non_centrality</span><span class="special">()</span><span class="keyword">const</span><span class="special">;</span>
+
+   <span class="comment">// Parameter finders:
+</span>   <span class="keyword">static</span> <span class="identifier">RealType</span> <span class="identifier">find_degrees_of_freedom</span><span class="special">(</span><span class="identifier">RealType</span> <span class="identifier">lambda</span><span class="special">,</span> <span class="identifier">RealType</span> <span class="identifier">x</span><span class="special">,</span> <span class="identifier">RealType</span> <span class="identifier">p</span><span class="special">);</span>
+   <span class="keyword">template</span> <span class="special">&lt;</span><span class="keyword">class</span> <span class="identifier">A</span><span class="special">,</span> <span class="keyword">class</span> <span class="identifier">B</span><span class="special">,</span> <span class="keyword">class</span> <span class="identifier">C</span><span class="special">&gt;</span>
+   <span class="keyword">static</span> <span class="identifier">RealType</span> <span class="identifier">find_degrees_of_freedom</span><span class="special">(</span><span class="keyword">const</span> <span class="identifier">complemented3_type</span><span class="special">&lt;</span><span class="identifier">A</span><span class="special">,</span><span class="identifier">B</span><span class="special">,</span><span class="identifier">C</span><span class="special">&gt;&amp;</span> <span class="identifier">c</span><span class="special">);</span>
+   
+   <span class="keyword">static</span> <span class="identifier">RealType</span> <span class="identifier">find_non_centrality</span><span class="special">(</span><span class="identifier">RealType</span> <span class="identifier">v</span><span class="special">,</span> <span class="identifier">RealType</span> <span class="identifier">x</span><span class="special">,</span> <span class="identifier">RealType</span> <span class="identifier">p</span><span class="special">);</span>
+   <span class="keyword">template</span> <span class="special">&lt;</span><span class="keyword">class</span> <span class="identifier">A</span><span class="special">,</span> <span class="keyword">class</span> <span class="identifier">B</span><span class="special">,</span> <span class="keyword">class</span> <span class="identifier">C</span><span class="special">&gt;</span>
+   <span class="keyword">static</span> <span class="identifier">RealType</span> <span class="identifier">find_non_centrality</span><span class="special">(</span><span class="keyword">const</span> <span class="identifier">complemented3_type</span><span class="special">&lt;</span><span class="identifier">A</span><span class="special">,</span><span class="identifier">B</span><span class="special">,</span><span class="identifier">C</span><span class="special">&gt;&amp;</span> <span class="identifier">c</span><span class="special">);</span>
+<span class="special">};</span>
+
+<span class="special">}}</span> <span class="comment">// namespaces
+</span></pre>
+<p>
+            The noncentral chi-squared distribution is a generalization of the <a class="link" href="chi_squared_dist.html" title="Chi Squared Distribution">Chi Squared
+            Distribution</a>. If X<sub>i</sub> are &#957; independent, normally distributed random
+            variables with means &#956;<sub>i</sub> and variances &#963;<sub>i</sub><sup>2</sup>, then the random variable
+          </p>
+<p>
+            <span class="inlinemediaobject"><img src="../../../../../equations/nc_chi_squ_ref1.png"></span>
+          </p>
+<p>
+            is distributed according to the noncentral chi-squared distribution.
+          </p>
+<p>
+            The noncentral chi-squared distribution has two parameters: &#957; which specifies
+            the number of degrees of freedom (i.e. the number of X<sub>i</sub>), and &#955; which is
+            related to the mean of the random variables X<sub>i</sub> by:
+          </p>
+<p>
+            <span class="inlinemediaobject"><img src="../../../../../equations/nc_chi_squ_ref2.png"></span>
+          </p>
+<p>
+            (Note that some references define &#955; as one half of the above sum).
+          </p>
+<p>
+            This leads to a PDF of:
+          </p>
+<p>
+            <span class="inlinemediaobject"><img src="../../../../../equations/nc_chi_squ_ref3.png"></span>
+          </p>
+<p>
+            where <span class="emphasis"><em>f(x;k)</em></span> is the central chi-squared distribution
+            PDF, and <span class="emphasis"><em>I<sub>v</sub>(x)</em></span> is a modified Bessel function of
+            the first kind.
+          </p>
+<p>
+            The following graph illustrates how the distribution changes for different
+            values of &#955;:
+          </p>
+<p>
+            <span class="inlinemediaobject"><img src="../../../../../graphs/nccs_pdf.png" align="middle"></span>
+          </p>
+<a name="math_toolkit.dist.dist_ref.dists.nc_chi_squared_dist.member_functions"></a><h5>
+<a name="id676386"></a>
+            <a class="link" href="nc_chi_squared_dist.html#math_toolkit.dist.dist_ref.dists.nc_chi_squared_dist.member_functions">Member
+            Functions</a>
+          </h5>
+<pre class="programlisting"><span class="identifier">non_central_chi_squared_distribution</span><span class="special">(</span><span class="identifier">RealType</span> <span class="identifier">v</span><span class="special">,</span> <span class="identifier">RealType</span> <span class="identifier">lambda</span><span class="special">);</span>
+</pre>
+<p>
+            Constructs a Chi-Squared distribution with <span class="emphasis"><em>v</em></span> degrees
+            of freedom and non-centrality parameter <span class="emphasis"><em>lambda</em></span>.
+          </p>
+<p>
+            Requires v &gt; 0 and lambda &gt;= 0, otherwise calls <a class="link" href="../../../main_overview/error_handling.html#domain_error">domain_error</a>.
+          </p>
+<pre class="programlisting"><span class="identifier">RealType</span> <span class="identifier">degrees_of_freedom</span><span class="special">()</span><span class="keyword">const</span><span class="special">;</span>
+</pre>
+<p>
+            Returns the parameter <span class="emphasis"><em>v</em></span> from which this object was
+            constructed.
+          </p>
+<pre class="programlisting"><span class="identifier">RealType</span> <span class="identifier">non_centrality</span><span class="special">()</span><span class="keyword">const</span><span class="special">;</span>
+</pre>
+<p>
+            Returns the parameter <span class="emphasis"><em>lambda</em></span> from which this object
+            was constructed.
+          </p>
+<pre class="programlisting"><span class="keyword">static</span> <span class="identifier">RealType</span> <span class="identifier">find_degrees_of_freedom</span><span class="special">(</span><span class="identifier">RealType</span> <span class="identifier">lambda</span><span class="special">,</span> <span class="identifier">RealType</span> <span class="identifier">x</span><span class="special">,</span> <span class="identifier">RealType</span> <span class="identifier">p</span><span class="special">);</span>
+</pre>
+<p>
+            This function returns the number of degrees of freedom <span class="emphasis"><em>v</em></span>
+            such that: <code class="computeroutput"><span class="identifier">cdf</span><span class="special">(</span><span class="identifier">non_central_chi_squared</span><span class="special">&lt;</span><span class="identifier">RealType</span><span class="special">,</span>
+            <span class="identifier">Policy</span><span class="special">&gt;(</span><span class="identifier">v</span><span class="special">,</span> <span class="identifier">lambda</span><span class="special">),</span>
+            <span class="identifier">x</span><span class="special">)</span>
+            <span class="special">==</span> <span class="identifier">p</span></code>
+          </p>
+<pre class="programlisting"><span class="keyword">template</span> <span class="special">&lt;</span><span class="keyword">class</span> <span class="identifier">A</span><span class="special">,</span> <span class="keyword">class</span> <span class="identifier">B</span><span class="special">,</span> <span class="keyword">class</span> <span class="identifier">C</span><span class="special">&gt;</span>
+<span class="keyword">static</span> <span class="identifier">RealType</span> <span class="identifier">find_degrees_of_freedom</span><span class="special">(</span><span class="keyword">const</span> <span class="identifier">complemented3_type</span><span class="special">&lt;</span><span class="identifier">A</span><span class="special">,</span><span class="identifier">B</span><span class="special">,</span><span class="identifier">C</span><span class="special">&gt;&amp;</span> <span class="identifier">c</span><span class="special">);</span>
+</pre>
+<p>
+            When called with argument <code class="computeroutput"><span class="identifier">boost</span><span class="special">::</span><span class="identifier">math</span><span class="special">::</span><span class="identifier">complement</span><span class="special">(</span><span class="identifier">lambda</span><span class="special">,</span> <span class="identifier">x</span><span class="special">,</span> <span class="identifier">q</span><span class="special">)</span></code> this function returns the number of
+            degrees of freedom <span class="emphasis"><em>v</em></span> such that:
+          </p>
+<p>
+            <code class="computeroutput"><span class="identifier">cdf</span><span class="special">(</span><span class="identifier">complement</span><span class="special">(</span><span class="identifier">non_central_chi_squared</span><span class="special">&lt;</span><span class="identifier">RealType</span><span class="special">,</span>
+            <span class="identifier">Policy</span><span class="special">&gt;(</span><span class="identifier">v</span><span class="special">,</span> <span class="identifier">lambda</span><span class="special">),</span>
+            <span class="identifier">x</span><span class="special">))</span>
+            <span class="special">==</span> <span class="identifier">q</span></code>.
+          </p>
+<pre class="programlisting"><span class="keyword">static</span> <span class="identifier">RealType</span> <span class="identifier">find_non_centrality</span><span class="special">(</span><span class="identifier">RealType</span> <span class="identifier">v</span><span class="special">,</span> <span class="identifier">RealType</span> <span class="identifier">x</span><span class="special">,</span> <span class="identifier">RealType</span> <span class="identifier">p</span><span class="special">);</span>
+</pre>
+<p>
+            This function returns the non centrality parameter <span class="emphasis"><em>lambda</em></span>
+            such that:
+          </p>
+<p>
+            <code class="computeroutput"><span class="identifier">cdf</span><span class="special">(</span><span class="identifier">non_central_chi_squared</span><span class="special">&lt;</span><span class="identifier">RealType</span><span class="special">,</span>
+            <span class="identifier">Policy</span><span class="special">&gt;(</span><span class="identifier">v</span><span class="special">,</span> <span class="identifier">lambda</span><span class="special">),</span>
+            <span class="identifier">x</span><span class="special">)</span>
+            <span class="special">==</span> <span class="identifier">p</span></code>
+          </p>
+<pre class="programlisting"><span class="keyword">template</span> <span class="special">&lt;</span><span class="keyword">class</span> <span class="identifier">A</span><span class="special">,</span> <span class="keyword">class</span> <span class="identifier">B</span><span class="special">,</span> <span class="keyword">class</span> <span class="identifier">C</span><span class="special">&gt;</span>
+<span class="keyword">static</span> <span class="identifier">RealType</span> <span class="identifier">find_non_centrality</span><span class="special">(</span><span class="keyword">const</span> <span class="identifier">complemented3_type</span><span class="special">&lt;</span><span class="identifier">A</span><span class="special">,</span><span class="identifier">B</span><span class="special">,</span><span class="identifier">C</span><span class="special">&gt;&amp;</span> <span class="identifier">c</span><span class="special">);</span>
+</pre>
+<p>
+            When called with argument <code class="computeroutput"><span class="identifier">boost</span><span class="special">::</span><span class="identifier">math</span><span class="special">::</span><span class="identifier">complement</span><span class="special">(</span><span class="identifier">v</span><span class="special">,</span> <span class="identifier">x</span><span class="special">,</span> <span class="identifier">q</span><span class="special">)</span></code> this function returns the non centrality
+            parameter <span class="emphasis"><em>lambda</em></span> such that:
+          </p>
+<p>
+            <code class="computeroutput"><span class="identifier">cdf</span><span class="special">(</span><span class="identifier">complement</span><span class="special">(</span><span class="identifier">non_central_chi_squared</span><span class="special">&lt;</span><span class="identifier">RealType</span><span class="special">,</span>
+            <span class="identifier">Policy</span><span class="special">&gt;(</span><span class="identifier">v</span><span class="special">,</span> <span class="identifier">lambda</span><span class="special">),</span>
+            <span class="identifier">x</span><span class="special">))</span>
+            <span class="special">==</span> <span class="identifier">q</span></code>.
+          </p>
+<a name="math_toolkit.dist.dist_ref.dists.nc_chi_squared_dist.non_member_accessors"></a><h5>
+<a name="id677635"></a>
+            <a class="link" href="nc_chi_squared_dist.html#math_toolkit.dist.dist_ref.dists.nc_chi_squared_dist.non_member_accessors">Non-member
+            Accessors</a>
+          </h5>
+<p>
+            All the <a class="link" href="../nmp.html" title="Non-Member Properties">usual non-member
+            accessor functions</a> that are generic to all distributions are supported:
+            <a class="link" href="../nmp.html#math.dist.cdf">Cumulative Distribution Function</a>,
+            <a class="link" href="../nmp.html#math.dist.pdf">Probability Density Function</a>, <a class="link" href="../nmp.html#math.dist.quantile">Quantile</a>, <a class="link" href="../nmp.html#math.dist.hazard">Hazard
+            Function</a>, <a class="link" href="../nmp.html#math.dist.chf">Cumulative Hazard Function</a>,
+            <a class="link" href="../nmp.html#math.dist.mean">mean</a>, <a class="link" href="../nmp.html#math.dist.median">median</a>,
+            <a class="link" href="../nmp.html#math.dist.mode">mode</a>, <a class="link" href="../nmp.html#math.dist.variance">variance</a>,
+            <a class="link" href="../nmp.html#math.dist.sd">standard deviation</a>, <a class="link" href="../nmp.html#math.dist.skewness">skewness</a>,
+            <a class="link" href="../nmp.html#math.dist.kurtosis">kurtosis</a>, <a class="link" href="../nmp.html#math.dist.kurtosis_excess">kurtosis_excess</a>,
+            <a class="link" href="../nmp.html#math.dist.range">range</a> and <a class="link" href="../nmp.html#math.dist.support">support</a>.
+          </p>
+<p>
+            The domain of the random variable is [0, +&#8734;].
+          </p>
+<a name="math_toolkit.dist.dist_ref.dists.nc_chi_squared_dist.examples"></a><h5>
+<a name="id677811"></a>
+            <a class="link" href="nc_chi_squared_dist.html#math_toolkit.dist.dist_ref.dists.nc_chi_squared_dist.examples">Examples</a>
+          </h5>
+<p>
+            There is a <a class="link" href="../../stat_tut/weg/nccs_eg.html" title="Non Central Chi Squared Example">worked
+            example</a> for the noncentral chi-squared distribution.
+          </p>
+<a name="math_toolkit.dist.dist_ref.dists.nc_chi_squared_dist.accuracy"></a><h5>
+<a name="id677852"></a>
+            <a class="link" href="nc_chi_squared_dist.html#math_toolkit.dist.dist_ref.dists.nc_chi_squared_dist.accuracy">Accuracy</a>
+          </h5>
+<p>
+            The following table shows the peak errors (in units of epsilon)
+            found on various platforms with various floating-point types, along with
+            comparisons to the <a href="http://www.r-project.org/" target="_top">R-2.5.1 Math
+            library</a>. Unless otherwise specified, any floating-point type
+            that is narrower than the one shown will have <a class="link" href="../../../backgrounders/relative_error.html#zero_error">effectively
+            zero error</a>.
+          </p>
+<div class="table">
+<a name="id677906"></a><p class="title"><b>Table 14. Errors In CDF of the Noncentral Chi-Squared</b></p>
+<div class="table-contents"><table class="table" summary="Errors In CDF of the Noncentral Chi-Squared">
+<colgroup>
+<col>
+<col>
+<col>
+<col>
+</colgroup>
+<thead><tr>
+<th>
+                <p>
+                  Significand Size
+                </p>
+                </th>
+<th>
+                <p>
+                  Platform and Compiler
+                </p>
+                </th>
+<th>
+                <p>
+                  &#957;,&#955; &lt; 200
+                </p>
+                </th>
+<th>
+                <p>
+                  &#957;,&#955; &gt; 200
+                </p>
+                </th>
+</tr></thead>
+<tbody>
+<tr>
+<td>
+                <p>
+                  53
+                </p>
+                </td>
+<td>
+                <p>
+                  Win32, Visual C++ 8
+                </p>
+                </td>
+<td>
+                <p>
+                  Peak=50 Mean=9.9
+                </p>
+                <p>
+                  R Peak=685 Mean=109
+                </p>
+                </td>
+<td>
+                <p>
+                  Peak=9780 Mean=718
+                </p>
+                <p>
+                  R Peak=3x10<sup>8</sup> Mean=2x10<sup>7</sup>
+                </p>
+                </td>
+</tr>
+<tr>
+<td>
+                <p>
+                  64
+                </p>
+                </td>
+<td>
+                <p>
+                  RedHat Linux IA32, gcc-4.1.1
+                </p>
+                </td>
+<td>
+                <p>
+                  Peak=270 Mean=27
+                </p>
+                </td>
+<td>
+                <p>
+                  Peak=7900 Mean=900
+                </p>
+                </td>
+</tr>
+<tr>
+<td>
+                <p>
+                  64
+                </p>
+                </td>
+<td>
+                <p>
+                  Redhat Linux IA64, gcc-3.4.4
+                </p>
+                </td>
+<td>
+                <p>
+                  Peak=107 Mean=17
+                </p>
+                </td>
+<td>
+                <p>
+                  Peak=5000 Mean=630
+                </p>
+                </td>
+</tr>
+<tr>
+<td>
+                <p>
+                  113
+                </p>
+                </td>
+<td>
+                <p>
+                  HPUX IA64, aCC A.06.06
+                </p>
+                </td>
+<td>
+                <p>
+                  Peak=270 Mean=20
+                </p>
+                </td>
+<td>
+                <p>
+                  Peak=4600 Mean=560
+                </p>
+                </td>
+</tr>
+</tbody>
+</table></div>
+</div>
+<br class="table-break"><p>
+            Error rates for the complement of the CDF and for the quantile functions
+            are broadly similar. Special mention should go to the <code class="computeroutput"><span class="identifier">mode</span></code>
+            function: there is no closed form for this function, so it is evaluated
+            numerically by finding the maxima of the PDF: in principal this can not
+            produce an accuracy greater than the square root of the machine epsilon.
+          </p>
+<a name="math_toolkit.dist.dist_ref.dists.nc_chi_squared_dist.tests"></a><h5>
+<a name="id678161"></a>
+            <a class="link" href="nc_chi_squared_dist.html#math_toolkit.dist.dist_ref.dists.nc_chi_squared_dist.tests">Tests</a>
+          </h5>
+<p>
+            There are two sets of test data used to verify this implementation: firstly
+            we can compare with published data, for example with Table 6 of "Self-Validating
+            Computations of Probabilities for Selected Central and Noncentral Univariate
+            Probability Functions", Morgan C. Wang and William J. Kennedy, Journal
+            of the American Statistical Association, Vol. 89, No. 427. (Sep., 1994),
+            pp. 878-887. Secondly, we have tables of test data, computed with this
+            implementation and using interval arithmetic - this data should be accurate
+            to at least 50 decimal digits - and is the used for our accuracy tests.
+          </p>
+<a name="math_toolkit.dist.dist_ref.dists.nc_chi_squared_dist.implementation"></a><h5>
+<a name="id678206"></a>
+            <a class="link" href="nc_chi_squared_dist.html#math_toolkit.dist.dist_ref.dists.nc_chi_squared_dist.implementation">Implementation</a>
+          </h5>
+<p>
+            The CDF and its complement are evaluated as follows:
+          </p>
+<p>
+            First we determine which of the two values (the CDF or its complement)
+            is likely to be the smaller: for this we can use the relation due to
+            Temme (see "Asymptotic and Numerical Aspects of the Noncentral Chi-Square
+            Distribution", N. M. Temme, Computers Math. Applic. Vol 25, No.
+            5, 55-63, 1993) that:
+          </p>
+<p>
+            F(&#957;,&#955;;&#957;+&#955;) &#8776; 0.5
+          </p>
+<p>
+            and so compute the CDF when the random variable is less than &#957;+&#955;, and its
+            complement when the random variable is greater than &#957;+&#955;. If necessary the
+            computed result is then subtracted from 1 to give the desired result
+            (the CDF or its complement).
+          </p>
+<p>
+            For small values of the non centrality parameter, the CDF is computed
+            using the method of Ding (see "Algorithm AS 275: Computing the Non-Central
+            #2 Distribution Function", Cherng G. Ding, Applied Statistics, Vol.
+            41, No. 2. (1992), pp. 478-482). This uses the following series representation:
+          </p>
+<p>
+            <span class="inlinemediaobject"><img src="../../../../../equations/nc_chi_squ_ref4.png"></span>
+          </p>
+<p>
+            which requires just one call to <a class="link" href="../../../special/sf_gamma/gamma_derivatives.html" title="Derivative of the Incomplete Gamma Function">gamma_p_derivative</a>
+            with the subsequent terms being computed by recursion as shown above.
+          </p>
+<p>
+            For larger values of the non-centrality parameter, Ding's method can
+            take an unreasonable number of terms before convergence is achieved.
+            Furthermore, the largest term is not the first term, so in extreme cases
+            the first term may be zero, leading to a zero result, even though the
+            true value may be non-zero.
+          </p>
+<p>
+            Therefore, when the non-centrality parameter is greater than 200, the
+            method due to Krishnamoorthy (see "Computing discrete mixtures of
+            continuous distributions: noncentral chisquare, noncentral t and the
+            distribution of the square of the sample multiple correlation coefficient",
+            Denise Benton and K. Krishnamoorthy, Computational Statistics &amp; Data
+            Analysis, 43, (2003), 249-267) is used.
+          </p>
+<p>
+            This method uses the well known sum:
+          </p>
+<p>
+            <span class="inlinemediaobject"><img src="../../../../../equations/nc_chi_squ_ref5.png"></span>
+          </p>
+<p>
+            Where P<sub>a</sub>(x) is the incomplete gamma function.
+          </p>
+<p>
+            The method starts at the &#955;th term, which is where the Poisson weighting
+            function achieves its maximum value, although this is not necessarily
+            the largest overall term. Subsequent terms are calculated via the normal
+            recurrence relations for the incomplete gamma function, and iteration
+            proceeds both forwards and backwards until sufficient precision has been
+            achieved. It should be noted that recurrence in the forwards direction
+            of P<sub>a</sub>(x) is numerically unstable. However, since we always start <span class="emphasis"><em>after</em></span>
+            the largest term in the series, numeric instability is introduced more
+            slowly than the series converges.
+          </p>
+<p>
+            Computation of the complement of the CDF uses an extension of Krishnamoorthy's
+            method, given that:
+          </p>
+<p>
+            <span class="inlinemediaobject"><img src="../../../../../equations/nc_chi_squ_ref6.png"></span>
+          </p>
+<p>
+            we can again start at the &#955;'th term and proceed in both directions from
+            there until the required precision is achieved. This time it is backwards
+            recursion on the incomplete gamma function Q<sub>a</sub>(x) which is unstable. However,
+            as long as we start well <span class="emphasis"><em>before</em></span> the largest term,
+            this is not an issue in practice.
+          </p>
+<p>
+            The PDF is computed directly using the relation:
+          </p>
+<p>
+            <span class="inlinemediaobject"><img src="../../../../../equations/nc_chi_squ_ref3.png"></span>
+          </p>
+<p>
+            Where <span class="emphasis"><em>f(x; v)</em></span> is the PDF of the central <a class="link" href="chi_squared_dist.html" title="Chi Squared Distribution">Chi
+            Squared Distribution</a> and <span class="emphasis"><em>I<sub>v</sub>(x)</em></span> is a modified
+            Bessel function, see <a class="link" href="../../../special/bessel/mbessel.html" title="Modified Bessel Functions of the First and Second Kinds">cyl_bessel_i</a>.
+            For small values of the non-centrality parameter the relation in terms
+            of <a class="link" href="../../../special/bessel/mbessel.html" title="Modified Bessel Functions of the First and Second Kinds">cyl_bessel_i</a>
+            is used. However, this method fails for large values of the non-centrality
+            parameter, so in that case the infinite sum is evaluated using the method
+            of Benton and Krishnamoorthy, and the usual recurrence relations for
+            successive terms.
+          </p>
+<p>
+            The quantile functions are computed by numeric inversion of the CDF.
+          </p>
+<p>
+            There is no <a href="http://en.wikipedia.org/wiki/Closed_form" target="_top">closed
+            form</a> for the mode of the noncentral chi-squared distribution:
+            it is computed numerically by finding the maximum of the PDF. Likewise,
+            the median is computed numerically via the quantile.
+          </p>
+<p>
+            The remaining non-member functions use the following formulas:
+          </p>
+<p>
+            <span class="inlinemediaobject"><img src="../../../../../equations/nc_chi_squ_ref7.png"></span>
+          </p>
+<p>
+            Some analytic properties of noncentral distributions (particularly unimodality,
+            and monotonicity of their modes) are surveyed and summarized by:
+          </p>
+<p>
+            Andrea van Aubel &amp; Wolfgang Gawronski, Applied Mathematics and Computation,
+            141 (2003) 3-12.
+          </p>
+</div>
+<table xmlns:rev="http://www.cs.rpi.edu/~gregod/boost/tools/doc/revision" width="100%"><tr>
+<td align="left"></td>
+<td align="right"><div class="copyright-footer">Copyright © 2006 , 2007, 2008 John Maddock, Paul A. Bristow, Hubert
+      Holin, Xiaogang Zhang, Bruno Lalande and Gautam Sewani<p>
+        Distributed under the Boost Software License, Version 1.0. (See accompanying
+        file LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_0.txt)
+      </p>
+</div></td>
+</tr></table>
+<hr>
+<div class="spirit-nav">
+<a accesskey="p" href="nc_beta_dist.html"><img src="../../../../../../doc/html/images/prev.png" alt="Prev"></a><a accesskey="u" href="../dists.html"><img src="../../../../../../doc/html/images/up.png" alt="Up"></a><a accesskey="h" href="../../../../index.html"><img src="../../../../../../doc/html/images/home.png" alt="Home"></a><a accesskey="n" href="nc_f_dist.html"><img src="../../../../../../doc/html/images/next.png" alt="Next"></a>
+</div>
+</body>
+</html>

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@@ -0,0 +1,422 @@
+<html>
+<head>
+<meta http-equiv="Content-Type" content="text/html; charset=ISO-8859-1">
+<title>Noncentral F Distribution</title>
+<link rel="stylesheet" href="../../../../boostbook.css" type="text/css">
+<meta name="generator" content="DocBook XSL Stylesheets Vsnapshot_8125">
+<link rel="home" href="../../../../index.html" title="Math Toolkit">
+<link rel="up" href="../dists.html" title="Distributions">
+<link rel="prev" href="nc_chi_squared_dist.html" title="Noncentral Chi-Squared Distribution">
+<link rel="next" href="nc_t_dist.html" title="Noncentral T Distribution">
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+<body bgcolor="white" text="black" link="#0000FF" vlink="#840084" alink="#0000FF">
+<table cellpadding="2" width="100%"><tr>
+<td valign="top"><img alt="Boost C++ Libraries" width="277" height="86" src="../../../../../../boost.png"></td>
+<td align="center">Home</td>
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+<hr>
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+<a accesskey="p" href="nc_chi_squared_dist.html"><img src="../../../../../../doc/html/images/prev.png" alt="Prev"></a><a accesskey="u" href="../dists.html"><img src="../../../../../../doc/html/images/up.png" alt="Up"></a><a accesskey="h" href="../../../../index.html"><img src="../../../../../../doc/html/images/home.png" alt="Home"></a><a accesskey="n" href="nc_t_dist.html"><img src="../../../../../../doc/html/images/next.png" alt="Next"></a>
+</div>
+<div class="section" lang="en">
+<div class="titlepage"><div><div><h5 class="title">
+<a name="math_toolkit.dist.dist_ref.dists.nc_f_dist"></a><a class="link" href="nc_f_dist.html" title="Noncentral F Distribution"> Noncentral
+          F Distribution</a>
+</h5></div></div></div>
+<p>
+            
+</p>
+<pre class="programlisting"><span class="preprocessor">#include</span> <span class="special">&lt;</span><span class="identifier">boost</span><span class="special">/</span><span class="identifier">math</span><span class="special">/</span><span class="identifier">distributions</span><span class="special">/</span><span class="identifier">non_central_f</span><span class="special">.</span><span class="identifier">hpp</span><span class="special">&gt;</span></pre>
+<p>
+          </p>
+<pre class="programlisting"><span class="keyword">namespace</span> <span class="identifier">boost</span><span class="special">{</span> <span class="keyword">namespace</span> <span class="identifier">math</span><span class="special">{</span> 
+
+<span class="keyword">template</span> <span class="special">&lt;</span><span class="keyword">class</span> <span class="identifier">RealType</span> <span class="special">=</span> <span class="keyword">double</span><span class="special">,</span> 
+          <span class="keyword">class</span> <a class="link" href="../../../policy.html" title="Policies">Policy</a>   <span class="special">=</span> <a class="link" href="../../../policy/pol_ref/pol_ref_ref.html" title="Policy Class Reference">policies::policy&lt;&gt;</a> <span class="special">&gt;</span>
+<span class="keyword">class</span> <span class="identifier">non_central_f_distribution</span><span class="special">;</span>
+
+<span class="keyword">typedef</span> <span class="identifier">non_central_f_distribution</span><span class="special">&lt;&gt;</span> <span class="identifier">non_central_f</span><span class="special">;</span>
+
+<span class="keyword">template</span> <span class="special">&lt;</span><span class="keyword">class</span> <span class="identifier">RealType</span><span class="special">,</span> <span class="keyword">class</span> <a class="link" href="../../../policy.html" title="Policies">Policy</a><span class="special">&gt;</span>
+<span class="keyword">class</span> <span class="identifier">non_central_f_distribution</span>
+<span class="special">{</span>
+<span class="keyword">public</span><span class="special">:</span>
+   <span class="keyword">typedef</span> <span class="identifier">RealType</span>  <span class="identifier">value_type</span><span class="special">;</span>
+   <span class="keyword">typedef</span> <span class="identifier">Policy</span>    <span class="identifier">policy_type</span><span class="special">;</span>
+
+   <span class="comment">// Constructor:
+</span>   <span class="identifier">non_central_f_distribution</span><span class="special">(</span><span class="identifier">RealType</span> <span class="identifier">v1</span><span class="special">,</span> <span class="identifier">RealType</span> <span class="identifier">v2</span><span class="special">,</span> <span class="identifier">RealType</span> <span class="identifier">lambda</span><span class="special">);</span>
+
+   <span class="comment">// Accessor to degrees_of_freedom parameters v1 &amp; v2:
+</span>   <span class="identifier">RealType</span> <span class="identifier">degrees_of_freedom1</span><span class="special">()</span><span class="keyword">const</span><span class="special">;</span>
+   <span class="identifier">RealType</span> <span class="identifier">degrees_of_freedom2</span><span class="special">()</span><span class="keyword">const</span><span class="special">;</span>
+
+   <span class="comment">// Accessor to non-centrality parameter lambda:
+</span>   <span class="identifier">RealType</span> <span class="identifier">non_centrality</span><span class="special">()</span><span class="keyword">const</span><span class="special">;</span>
+<span class="special">};</span>
+
+<span class="special">}}</span> <span class="comment">// namespaces
+</span></pre>
+<p>
+            The noncentral F distribution is a generalization of the <a class="link" href="f_dist.html" title="F Distribution">Fisher
+            F Distribution</a>. It is defined as the ratio
+          </p>
+<pre class="programlisting"><span class="identifier">F</span> <span class="special">=</span> <span class="special">(</span><span class="identifier">X</span><span class="special">/</span><span class="identifier">v1</span><span class="special">)</span> <span class="special">/</span> <span class="special">(</span><span class="identifier">Y</span><span class="special">/</span><span class="identifier">v2</span><span class="special">)</span>
+</pre>
+<p>
+            where X is a noncentral &#967;<sup>2</sup>
+random variable with <span class="emphasis"><em>v1</em></span>
+            degrees of freedom and non-centrality parameter &#955;, and Y is a central
+            &#967;<sup>2</sup> random variable with <span class="emphasis"><em>v2</em></span> degrees of freedom.
+          </p>
+<p>
+            This gives the following PDF:
+          </p>
+<p>
+            <span class="inlinemediaobject"><img src="../../../../../equations/nc_f_ref1.png"></span>
+          </p>
+<p>
+            where L<sub>a</sub><sup>b</sup>(c) is a generalised Laguerre polynomial and B(a,b) is the
+            <a class="link" href="../../../special/sf_beta/beta_function.html" title="Beta">beta</a>
+            function, or
+          </p>
+<p>
+            <span class="inlinemediaobject"><img src="../../../../../equations/nc_f_ref2.png"></span>
+          </p>
+<p>
+            The following graph illustrates how the distribution changes for different
+            values of &#955;:
+          </p>
+<p>
+            <span class="inlinemediaobject"><img src="../../../../../graphs/nc_f_pdf.png" align="middle"></span>
+          </p>
+<a name="math_toolkit.dist.dist_ref.dists.nc_f_dist.member_functions"></a><h5>
+<a name="id679488"></a>
+            <a class="link" href="nc_f_dist.html#math_toolkit.dist.dist_ref.dists.nc_f_dist.member_functions">Member
+            Functions</a>
+          </h5>
+<pre class="programlisting"><span class="identifier">non_central_f_distribution</span><span class="special">(</span><span class="identifier">RealType</span> <span class="identifier">v1</span><span class="special">,</span> <span class="identifier">RealType</span> <span class="identifier">v2</span><span class="special">,</span> <span class="identifier">RealType</span> <span class="identifier">lambda</span><span class="special">);</span>
+</pre>
+<p>
+            Constructs a non-central beta distribution with parameters <span class="emphasis"><em>v1</em></span>
+            and <span class="emphasis"><em>v2</em></span> and non-centrality parameter <span class="emphasis"><em>lambda</em></span>.
+          </p>
+<p>
+            Requires v1 &gt; 0, v2 &gt; 0 and lambda &gt;= 0, otherwise calls <a class="link" href="../../../main_overview/error_handling.html#domain_error">domain_error</a>.
+          </p>
+<pre class="programlisting"><span class="identifier">RealType</span> <span class="identifier">degrees_of_freedom1</span><span class="special">()</span><span class="keyword">const</span><span class="special">;</span>
+</pre>
+<p>
+            Returns the parameter <span class="emphasis"><em>v1</em></span> from which this object
+            was constructed.
+          </p>
+<pre class="programlisting"><span class="identifier">RealType</span> <span class="identifier">degrees_of_freedom2</span><span class="special">()</span><span class="keyword">const</span><span class="special">;</span>
+</pre>
+<p>
+            Returns the parameter <span class="emphasis"><em>v2</em></span> from which this object
+            was constructed.
+          </p>
+<pre class="programlisting"><span class="identifier">RealType</span> <span class="identifier">non_centrality</span><span class="special">()</span><span class="keyword">const</span><span class="special">;</span>
+</pre>
+<p>
+            Returns the non-centrality parameter <span class="emphasis"><em>lambda</em></span> from
+            which this object was constructed.
+          </p>
+<a name="math_toolkit.dist.dist_ref.dists.nc_f_dist.non_member_accessors"></a><h5>
+<a name="id679750"></a>
+            <a class="link" href="nc_f_dist.html#math_toolkit.dist.dist_ref.dists.nc_f_dist.non_member_accessors">Non-member
+            Accessors</a>
+          </h5>
+<p>
+            All the <a class="link" href="../nmp.html" title="Non-Member Properties">usual non-member
+            accessor functions</a> that are generic to all distributions are supported:
+            <a class="link" href="../nmp.html#math.dist.cdf">Cumulative Distribution Function</a>,
+            <a class="link" href="../nmp.html#math.dist.pdf">Probability Density Function</a>, <a class="link" href="../nmp.html#math.dist.quantile">Quantile</a>, <a class="link" href="../nmp.html#math.dist.hazard">Hazard
+            Function</a>, <a class="link" href="../nmp.html#math.dist.chf">Cumulative Hazard Function</a>,
+            <a class="link" href="../nmp.html#math.dist.mean">mean</a>, <a class="link" href="../nmp.html#math.dist.median">median</a>,
+            <a class="link" href="../nmp.html#math.dist.mode">mode</a>, <a class="link" href="../nmp.html#math.dist.variance">variance</a>,
+            <a class="link" href="../nmp.html#math.dist.sd">standard deviation</a>, <a class="link" href="../nmp.html#math.dist.skewness">skewness</a>,
+            <a class="link" href="../nmp.html#math.dist.kurtosis">kurtosis</a>, <a class="link" href="../nmp.html#math.dist.kurtosis_excess">kurtosis_excess</a>,
+            <a class="link" href="../nmp.html#math.dist.range">range</a> and <a class="link" href="../nmp.html#math.dist.support">support</a>.
+          </p>
+<p>
+            The domain of the random variable is [0, +&#8734;].
+          </p>
+<a name="math_toolkit.dist.dist_ref.dists.nc_f_dist.accuracy"></a><h5>
+<a name="id679926"></a>
+            <a class="link" href="nc_f_dist.html#math_toolkit.dist.dist_ref.dists.nc_f_dist.accuracy">Accuracy</a>
+          </h5>
+<p>
+            This distribution is implemented in terms of the <a class="link" href="nc_beta_dist.html" title="Noncentral Beta Distribution">noncentral
+            beta distribution</a>: refer to that distribution for accuracy data.
+          </p>
+<a name="math_toolkit.dist.dist_ref.dists.nc_f_dist.tests"></a><h5>
+<a name="id679968"></a>
+            <a class="link" href="nc_f_dist.html#math_toolkit.dist.dist_ref.dists.nc_f_dist.tests">Tests</a>
+          </h5>
+<p>
+            Since this distribution is implemented by adapting another distribution,
+            the tests consist of basic sanity checks computed by the <a href="http://www.r-project.org/" target="_top">R-2.5.1
+            Math library statistical package</a> and its pbeta and dbeta functions.
+          </p>
+<a name="math_toolkit.dist.dist_ref.dists.nc_f_dist.implementation"></a><h5>
+<a name="id680011"></a>
+            <a class="link" href="nc_f_dist.html#math_toolkit.dist.dist_ref.dists.nc_f_dist.implementation">Implementation</a>
+          </h5>
+<p>
+            In the following table <span class="emphasis"><em>v1</em></span> and <span class="emphasis"><em>v2</em></span>
+            are the first and second degrees of freedom parameters of the distribution,
+            &#955;
+is the non-centrality parameter, <span class="emphasis"><em>x</em></span> is the random
+            variate, <span class="emphasis"><em>p</em></span> is the probability, and <span class="emphasis"><em>q =
+            1-p</em></span>.
+          </p>
+<div class="informaltable"><table class="table">
+<colgroup>
+<col>
+<col>
+</colgroup>
+<thead><tr>
+<th>
+                  <p>
+                    Function
+                  </p>
+                  </th>
+<th>
+                  <p>
+                    Implementation Notes
+                  </p>
+                  </th>
+</tr></thead>
+<tbody>
+<tr>
+<td>
+                  <p>
+                    pdf
+                  </p>
+                  </td>
+<td>
+                  <p>
+                    Implemented in terms of the non-central beta PDF using the relation:
+                  </p>
+                  <p>
+                    f(x;v1,v2;&#955;) = (v1/v2) / ((1+y)*(1+y)) * g(y/(1+y);v1/2,v2/2;&#955;)
+                  </p>
+                  <p>
+                    where g(x; a, b; &#955;) is the non central beta PDF, and:
+                  </p>
+                  <p>
+                    y = x * v1 / v2
+                  </p>
+                  </td>
+</tr>
+<tr>
+<td>
+                  <p>
+                    cdf
+                  </p>
+                  </td>
+<td>
+                  <p>
+                    Using the relation:
+                  </p>
+                  <p>
+                    p = B<sub>y</sub>(v1/2, v2/2; &#955;)
+                  </p>
+                  <p>
+                    where B<sub>x</sub>(a, b; &#955;) is the noncentral beta distribution CDF and
+                  </p>
+                  <p>
+                    y = x * v1 / v2
+                  </p>
+                  <p>
+                  </p>
+                  </td>
+</tr>
+<tr>
+<td>
+                  <p>
+                    cdf complement
+                  </p>
+                  </td>
+<td>
+                  <p>
+                    Using the relation:
+                  </p>
+                  <p>
+                    q = 1 - B<sub>y</sub>(v1/2, v2/2; &#955;)
+                  </p>
+                  <p>
+                    where 1 - B<sub>x</sub>(a, b; &#955;) is the complement of the noncentral beta
+                    distribution CDF and
+                  </p>
+                  <p>
+                    y = x * v1 / v2
+                  </p>
+                  <p>
+                  </p>
+                  </td>
+</tr>
+<tr>
+<td>
+                  <p>
+                    quantile
+                  </p>
+                  </td>
+<td>
+                  <p>
+                    Using the relation:
+                  </p>
+                  <p>
+                    x = (bx / (1-bx)) * (v1 / v2)
+                  </p>
+                  <p>
+                    where
+                  </p>
+                  <p>
+                    bx = Q<sub>p</sub><sup>-1</sup>(v1/2, v2/2; &#955;)
+                  </p>
+                  <p>
+                    and
+                  </p>
+                  <p>
+                    Q<sub>p</sub><sup>-1</sup>(v1/2, v2/2; &#955;)
+                  </p>
+                  <p>
+                    is the noncentral beta quantile.
+                  </p>
+                  <p>
+                  </p>
+                  </td>
+</tr>
+<tr>
+<td>
+                  <p>
+                    quantile
+                  </p>
+                  <p>
+                    from the complement
+                  </p>
+                  </td>
+<td>
+                  <p>
+                    Using the relation:
+                  </p>
+                  <p>
+                    x = (bx / (1-bx)) * (v1 / v2)
+                  </p>
+                  <p>
+                    where
+                  </p>
+                  <p>
+                    bx = QC<sub>q</sub><sup>-1</sup>(v1/2, v2/2; &#955;)
+                  </p>
+                  <p>
+                    and
+                  </p>
+                  <p>
+                    QC<sub>q</sub><sup>-1</sup>(v1/2, v2/2; &#955;)
+                  </p>
+                  <p>
+                    is the noncentral beta quantile from the complement.
+                  </p>
+                  </td>
+</tr>
+<tr>
+<td>
+                  <p>
+                    mean
+                  </p>
+                  </td>
+<td>
+                  <p>
+                    v2 * (v1 + l) / (v1 * (v2 - 2))
+                  </p>
+                  </td>
+</tr>
+<tr>
+<td>
+                  <p>
+                    mode
+                  </p>
+                  </td>
+<td>
+                  <p>
+                    By numeric maximalisation of the PDF.
+                  </p>
+                  </td>
+</tr>
+<tr>
+<td>
+                  <p>
+                    variance
+                  </p>
+                  </td>
+<td>
+                  <p>
+                    Refer to, <a href="http://mathworld.wolfram.com/NoncentralF-Distribution.html" target="_top">Weisstein,
+                    Eric W. "Noncentral F-Distribution." From MathWorld--A
+                    Wolfram Web Resource.</a>
+                  </p>
+                  </td>
+</tr>
+<tr>
+<td>
+                  <p>
+                    skewness
+                  </p>
+                  </td>
+<td>
+                  <p>
+                    Refer to, <a href="http://mathworld.wolfram.com/NoncentralF-Distribution.html" target="_top">Weisstein,
+                    Eric W. "Noncentral F-Distribution." From MathWorld--A
+                    Wolfram Web Resource.</a>, and to the <a href="http://reference.wolfram.com/mathematica/ref/NoncentralFRatioDistribution.html" target="_top">Mathematica
+                    documentation</a>
+                  </p>
+                  </td>
+</tr>
+<tr>
+<td>
+                  <p>
+                    kurtosis and kurtosis excess
+                  </p>
+                  </td>
+<td>
+                  <p>
+                    Refer to, <a href="http://mathworld.wolfram.com/NoncentralF-Distribution.html" target="_top">Weisstein,
+                    Eric W. "Noncentral F-Distribution." From MathWorld--A
+                    Wolfram Web Resource.</a>, and to the <a href="http://reference.wolfram.com/mathematica/ref/NoncentralFRatioDistribution.html" target="_top">Mathematica
+                    documentation</a>
+                  </p>
+                  </td>
+</tr>
+</tbody>
+</table></div>
+<p>
+            Some analytic properties of noncentral distributions (particularly unimodality,
+            and monotonicity of their modes) are surveyed and summarized by:
+          </p>
+<p>
+            Andrea van Aubel &amp; Wolfgang Gawronski, Applied Mathematics and Computation,
+            141 (2003) 3-12.
+          </p>
+</div>
+<table xmlns:rev="http://www.cs.rpi.edu/~gregod/boost/tools/doc/revision" width="100%"><tr>
+<td align="left"></td>
+<td align="right"><div class="copyright-footer">Copyright © 2006 , 2007, 2008 John Maddock, Paul A. Bristow, Hubert
+      Holin, Xiaogang Zhang, Bruno Lalande and Gautam Sewani<p>
+        Distributed under the Boost Software License, Version 1.0. (See accompanying
+        file LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_0.txt)
+      </p>
+</div></td>
+</tr></table>
+<hr>
+<div class="spirit-nav">
+<a accesskey="p" href="nc_chi_squared_dist.html"><img src="../../../../../../doc/html/images/prev.png" alt="Prev"></a><a accesskey="u" href="../dists.html"><img src="../../../../../../doc/html/images/up.png" alt="Up"></a><a accesskey="h" href="../../../../index.html"><img src="../../../../../../doc/html/images/home.png" alt="Home"></a><a accesskey="n" href="nc_t_dist.html"><img src="../../../../../../doc/html/images/next.png" alt="Next"></a>
+</div>
+</body>
+</html>

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+++ sandbox/tools/auto_index/example/math/doc/sf_and_dist/html/math_toolkit/dist/dist_ref/dists/nc_t_dist.html	2008-11-28 05:25:28 EST (Fri, 28 Nov 2008)
@@ -0,0 +1,366 @@
+<html>
+<head>
+<meta http-equiv="Content-Type" content="text/html; charset=ISO-8859-1">
+<title>Noncentral T Distribution</title>
+<link rel="stylesheet" href="../../../../boostbook.css" type="text/css">
+<meta name="generator" content="DocBook XSL Stylesheets Vsnapshot_8125">
+<link rel="home" href="../../../../index.html" title="Math Toolkit">
+<link rel="up" href="../dists.html" title="Distributions">
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+</div>
+<div class="section" lang="en">
+<div class="titlepage"><div><div><h5 class="title">
+<a name="math_toolkit.dist.dist_ref.dists.nc_t_dist"></a><a class="link" href="nc_t_dist.html" title="Noncentral T Distribution"> Noncentral
+          T Distribution</a>
+</h5></div></div></div>
+<p>
+            
+</p>
+<pre class="programlisting"><span class="preprocessor">#include</span> <span class="special">&lt;</span><span class="identifier">boost</span><span class="special">/</span><span class="identifier">math</span><span class="special">/</span><span class="identifier">distributions</span><span class="special">/</span><span class="identifier">non_central_t</span><span class="special">.</span><span class="identifier">hpp</span><span class="special">&gt;</span></pre>
+<p>
+          </p>
+<pre class="programlisting"><span class="keyword">namespace</span> <span class="identifier">boost</span><span class="special">{</span> <span class="keyword">namespace</span> <span class="identifier">math</span><span class="special">{</span> 
+
+<span class="keyword">template</span> <span class="special">&lt;</span><span class="keyword">class</span> <span class="identifier">RealType</span> <span class="special">=</span> <span class="keyword">double</span><span class="special">,</span> 
+          <span class="keyword">class</span> <a class="link" href="../../../policy.html" title="Policies">Policy</a>   <span class="special">=</span> <a class="link" href="../../../policy/pol_ref/pol_ref_ref.html" title="Policy Class Reference">policies::policy&lt;&gt;</a> <span class="special">&gt;</span>
+<span class="keyword">class</span> <span class="identifier">non_central_t_distribution</span><span class="special">;</span>
+
+<span class="keyword">typedef</span> <span class="identifier">non_central_t_distribution</span><span class="special">&lt;&gt;</span> <span class="identifier">non_central_t</span><span class="special">;</span>
+
+<span class="keyword">template</span> <span class="special">&lt;</span><span class="keyword">class</span> <span class="identifier">RealType</span><span class="special">,</span> <span class="keyword">class</span> <a class="link" href="../../../policy.html" title="Policies">Policy</a><span class="special">&gt;</span>
+<span class="keyword">class</span> <span class="identifier">non_central_t_distribution</span>
+<span class="special">{</span>
+<span class="keyword">public</span><span class="special">:</span>
+   <span class="keyword">typedef</span> <span class="identifier">RealType</span>  <span class="identifier">value_type</span><span class="special">;</span>
+   <span class="keyword">typedef</span> <span class="identifier">Policy</span>    <span class="identifier">policy_type</span><span class="special">;</span>
+
+   <span class="comment">// Constructor:
+</span>   <span class="identifier">non_central_t_distribution</span><span class="special">(</span><span class="identifier">RealType</span> <span class="identifier">v</span><span class="special">,</span> <span class="identifier">RealType</span> <span class="identifier">delta</span><span class="special">);</span>
+
+   <span class="comment">// Accessor to degrees_of_freedom parameter v:
+</span>   <span class="identifier">RealType</span> <span class="identifier">degrees_of_freedom</span><span class="special">()</span><span class="keyword">const</span><span class="special">;</span>
+
+   <span class="comment">// Accessor to non-centrality parameter lambda:
+</span>   <span class="identifier">RealType</span> <span class="identifier">non_centrality</span><span class="special">()</span><span class="keyword">const</span><span class="special">;</span>
+<span class="special">};</span>
+
+<span class="special">}}</span> <span class="comment">// namespaces
+</span></pre>
+<p>
+            The noncentral T distribution is a generalization of the <a class="link" href="students_t_dist.html" title="Students t Distribution">Students
+            t Distribution</a>. Let X have a normal distribution with mean &#948; and
+            variance 1, and let &#957; S<sup>2</sup> have a chi-squared distribution with degrees of
+            freedom &#957;. Assume that X and S<sup>2</sup> are independent. The distribution of t<sub>&#957;</sub>(&#948;)=X/S
+            is called a noncentral t distribution with degrees of freedom &#957; and noncentrality
+            parameter &#948;.
+          </p>
+<p>
+            This gives the following PDF:
+          </p>
+<p>
+            <span class="inlinemediaobject"><img src="../../../../../equations/nc_t_ref1.png"></span>
+          </p>
+<p>
+            where <sub>1</sub>F<sub>1</sub>(a;b;x) is a confluent hypergeometric function.
+          </p>
+<p>
+            The following graph illustrates how the distribution changes for different
+            values of &#948;:
+          </p>
+<p>
+            <span class="inlinemediaobject"><img src="../../../../../graphs/nc_t_pdf.png" align="middle"></span>
+          </p>
+<a name="math_toolkit.dist.dist_ref.dists.nc_t_dist.member_functions"></a><h5>
+<a name="id681219"></a>
+            <a class="link" href="nc_t_dist.html#math_toolkit.dist.dist_ref.dists.nc_t_dist.member_functions">Member
+            Functions</a>
+          </h5>
+<pre class="programlisting"><span class="identifier">non_central_t_distribution</span><span class="special">(</span><span class="identifier">RealType</span> <span class="identifier">v</span><span class="special">,</span> <span class="identifier">RealType</span> <span class="identifier">lambda</span><span class="special">);</span>
+</pre>
+<p>
+            Constructs a non-central t distribution with degrees of freedom parameter
+            <span class="emphasis"><em>v</em></span> and non-centrality parameter <span class="emphasis"><em>delta</em></span>.
+          </p>
+<p>
+            Requires v &gt; 0 and finite delta, otherwise calls <a class="link" href="../../../main_overview/error_handling.html#domain_error">domain_error</a>.
+          </p>
+<pre class="programlisting"><span class="identifier">RealType</span> <span class="identifier">degrees_of_freedom</span><span class="special">()</span><span class="keyword">const</span><span class="special">;</span>
+</pre>
+<p>
+            Returns the parameter <span class="emphasis"><em>v</em></span> from which this object was
+            constructed.
+          </p>
+<pre class="programlisting"><span class="identifier">RealType</span> <span class="identifier">non_centrality</span><span class="special">()</span><span class="keyword">const</span><span class="special">;</span>
+</pre>
+<p>
+            Returns the non-centrality parameter <span class="emphasis"><em>delta</em></span> from
+            which this object was constructed.
+          </p>
+<a name="math_toolkit.dist.dist_ref.dists.nc_t_dist.non_member_accessors"></a><h5>
+<a name="id681418"></a>
+            <a class="link" href="nc_t_dist.html#math_toolkit.dist.dist_ref.dists.nc_t_dist.non_member_accessors">Non-member
+            Accessors</a>
+          </h5>
+<p>
+            All the <a class="link" href="../nmp.html" title="Non-Member Properties">usual non-member
+            accessor functions</a> that are generic to all distributions are supported:
+            <a class="link" href="../nmp.html#math.dist.cdf">Cumulative Distribution Function</a>,
+            <a class="link" href="../nmp.html#math.dist.pdf">Probability Density Function</a>, <a class="link" href="../nmp.html#math.dist.quantile">Quantile</a>, <a class="link" href="../nmp.html#math.dist.hazard">Hazard
+            Function</a>, <a class="link" href="../nmp.html#math.dist.chf">Cumulative Hazard Function</a>,
+            <a class="link" href="../nmp.html#math.dist.mean">mean</a>, <a class="link" href="../nmp.html#math.dist.median">median</a>,
+            <a class="link" href="../nmp.html#math.dist.mode">mode</a>, <a class="link" href="../nmp.html#math.dist.variance">variance</a>,
+            <a class="link" href="../nmp.html#math.dist.sd">standard deviation</a>, <a class="link" href="../nmp.html#math.dist.skewness">skewness</a>,
+            <a class="link" href="../nmp.html#math.dist.kurtosis">kurtosis</a>, <a class="link" href="../nmp.html#math.dist.kurtosis_excess">kurtosis_excess</a>,
+            <a class="link" href="../nmp.html#math.dist.range">range</a> and <a class="link" href="../nmp.html#math.dist.support">support</a>.
+          </p>
+<p>
+            The domain of the random variable is [-&#8734;, +&#8734;].
+          </p>
+<a name="math_toolkit.dist.dist_ref.dists.nc_t_dist.accuracy"></a><h5>
+<a name="id681594"></a>
+            <a class="link" href="nc_t_dist.html#math_toolkit.dist.dist_ref.dists.nc_t_dist.accuracy">Accuracy</a>
+          </h5>
+<p>
+            The following table shows the peak errors (in units of epsilon)
+            found on various platforms with various floating-point types. Unless
+            otherwise specified, any floating-point type that is narrower than the
+            one shown will have <a class="link" href="../../../backgrounders/relative_error.html#zero_error">effectively zero error</a>.
+          </p>
+<div class="table">
+<a name="id681639"></a><p class="title"><b>Table 15. Errors In CDF of the Noncentral T Distribution</b></p>
+<div class="table-contents"><table class="table" summary="Errors In CDF of the Noncentral T Distribution">
+<colgroup>
+<col>
+<col>
+<col>
+</colgroup>
+<thead><tr>
+<th>
+                <p>
+                  Significand Size
+                </p>
+                </th>
+<th>
+                <p>
+                  Platform and Compiler
+                </p>
+                </th>
+<th>
+                <p>
+                  &#957;,&#948; &lt; 600
+                </p>
+                </th>
+</tr></thead>
+<tbody>
+<tr>
+<td>
+                <p>
+                  53
+                </p>
+                </td>
+<td>
+                <p>
+                  Win32, Visual C++ 8
+                </p>
+                </td>
+<td>
+                <p>
+                  Peak=120 Mean=26
+                </p>
+                </td>
+</tr>
+<tr>
+<td>
+                <p>
+                  64
+                </p>
+                </td>
+<td>
+                <p>
+                  RedHat Linux IA32, gcc-4.1.1
+                </p>
+                </td>
+<td>
+                <p>
+                  Peak=121 Mean=26
+                </p>
+                </td>
+</tr>
+<tr>
+<td>
+                <p>
+                  64
+                </p>
+                </td>
+<td>
+                <p>
+                  Redhat Linux IA64, gcc-3.4.4
+                </p>
+                </td>
+<td>
+                <p>
+                  Peak=122 Mean=25
+                </p>
+                </td>
+</tr>
+<tr>
+<td>
+                <p>
+                  113
+                </p>
+                </td>
+<td>
+                <p>
+                  HPUX IA64, aCC A.06.06
+                </p>
+                </td>
+<td>
+                <p>
+                  Peak=115 Mean=24
+                </p>
+                </td>
+</tr>
+</tbody>
+</table></div>
+</div>
+<br class="table-break"><div class="caution"><table border="0" summary="Caution">
+<tr>
+<td rowspan="2" align="center" valign="top" width="25"><img alt="[Caution]" src="../../../../../../doc/html/images/caution.png"></td>
+<th align="left">Caution</th>
+</tr>
+<tr><td align="left" valign="top"><p>
+              The complexity of the current algorithm is dependent upon &#948;<sup>2</sup>: consequently
+              the time taken to evaluate the CDF increases rapidly for &#948; &gt; 500,
+              likewise the accuracy decreases rapidly for very large &#948;.
+            </p></td></tr>
+</table></div>
+<p>
+            Accuracy for the quantile and PDF functions should be broadly similar,
+            note however that the <span class="emphasis"><em>mode</em></span> is determined numerically
+            and can not in principal be more accurate than the square root of machine
+            epsilon.
+          </p>
+<a name="math_toolkit.dist.dist_ref.dists.nc_t_dist.tests"></a><h5>
+<a name="id681848"></a>
+            <a class="link" href="nc_t_dist.html#math_toolkit.dist.dist_ref.dists.nc_t_dist.tests">Tests</a>
+          </h5>
+<p>
+            There are two sets of tests of this distribution: basic sanity checks
+            compare this implementation to the test values given in "Computing
+            discrete mixtures of continuous distributions: noncentral chisquare,
+            noncentral t and the distribution of the square of the sample multiple
+            correlation coefficient." Denise Benton, K. Krishnamoorthy, Computational
+            Statistics &amp; Data Analysis 43 (2003) 249-267. While accuracy checks
+            use test data computed with this implementation and arbitary precision
+            interval arithmetic: this test data is believed to be accurate to at
+            least 50 decimal places.
+          </p>
+<a name="math_toolkit.dist.dist_ref.dists.nc_t_dist.implementation"></a><h5>
+<a name="id681890"></a>
+            <a class="link" href="nc_t_dist.html#math_toolkit.dist.dist_ref.dists.nc_t_dist.implementation">Implementation</a>
+          </h5>
+<p>
+            The CDF is computed using a modification of the method described in "Computing
+            discrete mixtures of continuous distributions: noncentral chisquare,
+            noncentral t and the distribution of the square of the sample multiple
+            correlation coefficient." Denise Benton, K. Krishnamoorthy, Computational
+            Statistics &amp; Data Analysis 43 (2003) 249-267.
+          </p>
+<p>
+            This uses the following formula for the CDF:
+          </p>
+<p>
+            <span class="inlinemediaobject"><img src="../../../../../equations/nc_t_ref2.png"></span>
+          </p>
+<p>
+            Where I<sub>x</sub>(a,b) is the incomplete beta function, and &#934;(x) is the normal
+            CDF at x.
+          </p>
+<p>
+            Iteration starts at the largest of the Poisson weighting terms (at i
+            = &#948;<sup>2</sup> / 2) and then proceeds in both directions as per Benton and Krishnamoorthy's
+            paper.
+          </p>
+<p>
+            Alternatively, by considering what happens when t = &#8734;, we have x = 1,
+            and therefore I<sub>x</sub>(a,b) = 1 and:
+          </p>
+<p>
+            <span class="inlinemediaobject"><img src="../../../../../equations/nc_t_ref3.png"></span>
+          </p>
+<p>
+            From this we can easily show that:
+          </p>
+<p>
+            <span class="inlinemediaobject"><img src="../../../../../equations/nc_t_ref4.png"></span>
+          </p>
+<p>
+            and therefore we have a means to compute either the probability or its
+            complement directly without the risk of cancellation error. The crossover
+            criterion for choosing whether to calculate the CDF or it's complement
+            is the same as for the <a class="link" href="nc_beta_dist.html" title="Noncentral Beta Distribution">noncentral
+            beta distribution</a>.
+          </p>
+<p>
+            The PDF can be computed by a very similar method using:
+          </p>
+<p>
+            <span class="inlinemediaobject"><img src="../../../../../equations/nc_t_ref5.png"></span>
+          </p>
+<p>
+            Where I<sub>x</sub><sup>'</sup>(a,b) is the derivative of the incomplete beta function.
+          </p>
+<p>
+            The quantile is calculated via the usual <a class="link" href="../../../toolkit/internals1/roots2.html" title="Root Finding Without Derivatives">derivative-free
+            root-finding techniques</a>, with the initial guess taken as the quantile
+            of a normal approximation to the noncentral T.
+          </p>
+<p>
+            There is no closed form for the mode, so this is computed via functional
+            maximisation of the PDF.
+          </p>
+<p>
+            The remaining functions (mean, variance etc) are implemented using the
+            formulas given in Weisstein, Eric W. "Noncentral Student's t-Distribution."
+            From MathWorld--A Wolfram Web Resource. http://mathworld.wolfram.com/NoncentralStudentst-Distribution.html
+            and in the <a href="http://reference.wolfram.com/mathematica/ref/NoncentralStudentTDistribution.html" target="_top">Mathematica
+            documentation</a>.
+          </p>
+<p>
+            Some analytic properties of noncentral distributions (particularly unimodality,
+            and monotonicity of their modes) are surveyed and summarized by:
+          </p>
+<p>
+            Andrea van Aubel &amp; Wolfgang Gawronski, Applied Mathematics and Computation,
+            141 (2003) 3-12.
+          </p>
+</div>
+<table xmlns:rev="http://www.cs.rpi.edu/~gregod/boost/tools/doc/revision" width="100%"><tr>
+<td align="left"></td>
+<td align="right"><div class="copyright-footer">Copyright © 2006 , 2007, 2008 John Maddock, Paul A. Bristow, Hubert
+      Holin, Xiaogang Zhang, Bruno Lalande and Gautam Sewani<p>
+        Distributed under the Boost Software License, Version 1.0. (See accompanying
+        file LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_0.txt)
+      </p>
+</div></td>
+</tr></table>
+<hr>
+<div class="spirit-nav">
+<a accesskey="p" href="nc_f_dist.html"><img src="../../../../../../doc/html/images/prev.png" alt="Prev"></a><a accesskey="u" href="../dists.html"><img src="../../../../../../doc/html/images/up.png" alt="Up"></a><a accesskey="h" href="../../../../index.html"><img src="../../../../../../doc/html/images/home.png" alt="Home"></a><a accesskey="n" href="normal_dist.html"><img src="../../../../../../doc/html/images/next.png" alt="Next"></a>
+</div>
+</body>
+</html>

Added: sandbox/tools/auto_index/example/math/doc/sf_and_dist/html/math_toolkit/dist/dist_ref/dists/negative_binomial_dist.html
==============================================================================
--- (empty file)
+++ sandbox/tools/auto_index/example/math/doc/sf_and_dist/html/math_toolkit/dist/dist_ref/dists/negative_binomial_dist.html	2008-11-28 05:25:28 EST (Fri, 28 Nov 2008)
@@ -0,0 +1,909 @@
+<html>
+<head>
+<meta http-equiv="Content-Type" content="text/html; charset=ISO-8859-1">
+<title>Negative Binomial Distribution</title>
+<link rel="stylesheet" href="../../../../boostbook.css" type="text/css">
+<meta name="generator" content="DocBook XSL Stylesheets Vsnapshot_8125">
+<link rel="home" href="../../../../index.html" title="Math Toolkit">
+<link rel="up" href="../dists.html" title="Distributions">
+<link rel="prev" href="lognormal_dist.html" title="Log Normal Distribution">
+<link rel="next" href="nc_beta_dist.html" title="Noncentral Beta Distribution">
+</head>
+<body bgcolor="white" text="black" link="#0000FF" vlink="#840084" alink="#0000FF">
+<table cellpadding="2" width="100%"><tr>
+<td valign="top"><img alt="Boost C++ Libraries" width="277" height="86" src="../../../../../../boost.png"></td>
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+<hr>
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+<a accesskey="p" href="lognormal_dist.html"><img src="../../../../../../doc/html/images/prev.png" alt="Prev"></a><a accesskey="u" href="../dists.html"><img src="../../../../../../doc/html/images/up.png" alt="Up"></a><a accesskey="h" href="../../../../index.html"><img src="../../../../../../doc/html/images/home.png" alt="Home"></a><a accesskey="n" href="nc_beta_dist.html"><img src="../../../../../../doc/html/images/next.png" alt="Next"></a>
+</div>
+<div class="section" lang="en">
+<div class="titlepage"><div><div><h5 class="title">
+<a name="math_toolkit.dist.dist_ref.dists.negative_binomial_dist"></a><a class="link" href="negative_binomial_dist.html" title="Negative Binomial Distribution">
+          Negative Binomial Distribution</a>
+</h5></div></div></div>
+<p>
+            
+</p>
+<pre class="programlisting"><span class="preprocessor">#include</span> <span class="special">&lt;</span><span class="identifier">boost</span><span class="special">/</span><span class="identifier">math</span><span class="special">/</span><span class="identifier">distributions</span><span class="special">/</span><span class="identifier">negative_binomial</span><span class="special">.</span><span class="identifier">hpp</span><span class="special">&gt;</span></pre>
+<p>
+          </p>
+<pre class="programlisting"><span class="keyword">namespace</span> <span class="identifier">boost</span><span class="special">{</span> <span class="keyword">namespace</span> <span class="identifier">math</span><span class="special">{</span> 
+
+<span class="keyword">template</span> <span class="special">&lt;</span><span class="keyword">class</span> <span class="identifier">RealType</span> <span class="special">=</span> <span class="keyword">double</span><span class="special">,</span> 
+          <span class="keyword">class</span> <a class="link" href="../../../policy.html" title="Policies">Policy</a>   <span class="special">=</span> <a class="link" href="../../../policy/pol_ref/pol_ref_ref.html" title="Policy Class Reference">policies::policy&lt;&gt;</a> <span class="special">&gt;</span>
+<span class="keyword">class</span> <span class="identifier">negative_binomial_distribution</span><span class="special">;</span>
+
+<span class="keyword">typedef</span> <span class="identifier">negative_binomial_distribution</span><span class="special">&lt;&gt;</span> <span class="identifier">negative_binomial</span><span class="special">;</span>
+
+<span class="keyword">template</span> <span class="special">&lt;</span><span class="keyword">class</span> <span class="identifier">RealType</span><span class="special">,</span> <span class="keyword">class</span> <a class="link" href="../../../policy.html" title="Policies">Policy</a><span class="special">&gt;</span>
+<span class="keyword">class</span> <span class="identifier">negative_binomial_distribution</span>
+<span class="special">{</span>
+<span class="keyword">public</span><span class="special">:</span>
+   <span class="keyword">typedef</span> <span class="identifier">RealType</span> <span class="identifier">value_type</span><span class="special">;</span>
+   <span class="keyword">typedef</span> <span class="identifier">Policy</span>   <span class="identifier">policy_type</span><span class="special">;</span>
+   <span class="comment">// Constructor from successes and success_fraction:
+</span>   <span class="identifier">negative_binomial_distribution</span><span class="special">(</span><span class="identifier">RealType</span> <span class="identifier">r</span><span class="special">,</span> <span class="identifier">RealType</span> <span class="identifier">p</span><span class="special">);</span>
+   
+   <span class="comment">// Parameter accessors:
+</span>   <span class="identifier">RealType</span> <span class="identifier">success_fraction</span><span class="special">()</span> <span class="keyword">const</span><span class="special">;</span>
+   <span class="identifier">RealType</span> <span class="identifier">successes</span><span class="special">()</span> <span class="keyword">const</span><span class="special">;</span>
+   
+   <span class="comment">// Bounds on success fraction:
+</span>   <span class="keyword">static</span> <span class="identifier">RealType</span> <span class="identifier">find_lower_bound_on_p</span><span class="special">(</span>
+      <span class="identifier">RealType</span> <span class="identifier">trials</span><span class="special">,</span> 
+      <span class="identifier">RealType</span> <span class="identifier">successes</span><span class="special">,</span>
+      <span class="identifier">RealType</span> <span class="identifier">probability</span><span class="special">);</span> <span class="comment">// alpha
+</span>   <span class="keyword">static</span> <span class="identifier">RealType</span> <span class="identifier">find_upper_bound_on_p</span><span class="special">(</span>
+      <span class="identifier">RealType</span> <span class="identifier">trials</span><span class="special">,</span> 
+      <span class="identifier">RealType</span> <span class="identifier">successes</span><span class="special">,</span>
+      <span class="identifier">RealType</span> <span class="identifier">probability</span><span class="special">);</span> <span class="comment">// alpha
+</span>      
+   <span class="comment">// Estimate min/max number of trials:
+</span>   <span class="keyword">static</span> <span class="identifier">RealType</span> <span class="identifier">find_minimum_number_of_trials</span><span class="special">(</span>
+      <span class="identifier">RealType</span> <span class="identifier">k</span><span class="special">,</span>     <span class="comment">// Number of failures.
+</span>      <span class="identifier">RealType</span> <span class="identifier">p</span><span class="special">,</span>     <span class="comment">// Success fraction.
+</span>      <span class="identifier">RealType</span> <span class="identifier">probability</span><span class="special">);</span> <span class="comment">// Probability threshold alpha.
+</span>   <span class="keyword">static</span> <span class="identifier">RealType</span> <span class="identifier">find_maximum_number_of_trials</span><span class="special">(</span>
+      <span class="identifier">RealType</span> <span class="identifier">k</span><span class="special">,</span>     <span class="comment">// Number of failures.
+</span>      <span class="identifier">RealType</span> <span class="identifier">p</span><span class="special">,</span>     <span class="comment">// Success fraction.
+</span>      <span class="identifier">RealType</span> <span class="identifier">probability</span><span class="special">);</span> <span class="comment">// Probability threshold alpha.
+</span><span class="special">};</span>
+
+<span class="special">}}</span> <span class="comment">// namespaces
+</span></pre>
+<p>
+            The class type <code class="computeroutput"><span class="identifier">negative_binomial_distribution</span></code>
+            represents a <a href="http://en.wikipedia.org/wiki/Negative_binomial_distribution" target="_top">negative_binomial
+            distribution</a>: it is used when there are exactly two mutually
+            exclusive outcomes of a <a href="http://en.wikipedia.org/wiki/Bernoulli_trial" target="_top">Bernoulli
+            trial</a>: these outcomes are labelled "success" and "failure".
+          </p>
+<p>
+            For k + r Bernoulli trials each with success fraction p, the negative_binomial
+            distribution gives the probability of observing k failures and r successes
+            with success on the last trial. The negative_binomial distribution assumes
+            that success_fraction p is fixed for all (k + r) trials.
+          </p>
+<div class="note"><table border="0" summary="Note">
+<tr>
+<td rowspan="2" align="center" valign="top" width="25"><img alt="[Note]" src="../../../../../../doc/html/images/note.png"></td>
+<th align="left">Note</th>
+</tr>
+<tr><td align="left" valign="top"><p>
+              The random variable for the negative binomial distribution is the number
+              of trials, (the number of successes is a fixed property of the distribution)
+              whereas for the binomial, the random variable is the number of successes,
+              for a fixed number of trials.
+            </p></td></tr>
+</table></div>
+<p>
+            It has the PDF:
+          </p>
+<p>
+            <span class="inlinemediaobject"><img src="../../../../../equations/neg_binomial_ref.png"></span>
+          </p>
+<p>
+            The following graph illustrate how the PDF varies as the success fraction
+            <span class="emphasis"><em>p</em></span> changes:
+          </p>
+<p>
+            <span class="inlinemediaobject"><img src="../../../../../graphs/negative_binomial_pdf_1.png" align="middle"></span>
+          </p>
+<p>
+            Alternatively, this graph shows how the shape of the PDF varies as the
+            number of successes changes:
+          </p>
+<p>
+            <span class="inlinemediaobject"><img src="../../../../../graphs/negative_binomial_pdf_2.png" align="middle"></span>
+          </p>
+<a name="math_toolkit.dist.dist_ref.dists.negative_binomial_dist.related_distributions"></a><h5>
+<a name="id669518"></a>
+            <a class="link" href="negative_binomial_dist.html#math_toolkit.dist.dist_ref.dists.negative_binomial_dist.related_distributions">Related
+            Distributions</a>
+          </h5>
+<p>
+            The name negative binomial distribution is reserved by some to the case
+            where the successes parameter r is an integer. This integer version is
+            also called the <a href="http://mathworld.wolfram.com/PascalDistribution.html" target="_top">Pascal
+            distribution</a>.
+          </p>
+<p>
+            This implementation uses real numbers for the computation throughout
+            (because it uses the <span class="bold"><strong>real-valued</strong></span> incomplete
+            beta function family of functions). This real-valued version is also
+            called the Polya Distribution.
+          </p>
+<p>
+            The Poisson distribution is a generalization of the Pascal distribution,
+            where the success parameter r is an integer: to obtain the Pascal distribution
+            you must ensure that an integer value is provided for r, and take integer
+            values (floor or ceiling) from functions that return a number of successes.
+          </p>
+<p>
+            For large values of r (successes), the negative binomial distribution
+            converges to the Poisson distribution.
+          </p>
+<p>
+            The geometric distribution is a special case where the successes parameter
+            r = 1, so only a first and only success is required. geometric(p) = negative_binomial(1,
+            p).
+          </p>
+<p>
+            The Poisson distribution is a special case for large successes
+          </p>
+<p>
+            poisson(&#955;) = lim <sub>r &#8594; &#8734;</sub>  negative_binomial(r, r / (&#955; + r)))
+          </p>
+<p>
+            </p>
+<div class="caution"><table border="0" summary="Caution">
+<tr>
+<td rowspan="2" align="center" valign="top" width="25"><img alt="[Caution]" src="../../../../../../doc/html/images/caution.png"></td>
+<th align="left">Caution</th>
+</tr>
+<tr><td align="left" valign="top">
+<p>
+                The Negative Binomial distribution is a discrete distribution: internally
+                functions like the <code class="computeroutput"><span class="identifier">cdf</span></code>
+                and <code class="computeroutput"><span class="identifier">pdf</span></code> are treated
+                "as if" they are continuous functions, but in reality the
+                results returned from these functions only have meaning if an integer
+                value is provided for the random variate argument.
+              </p>
+<p>
+                The quantile function will by default return an integer result that
+                has been <span class="emphasis"><em>rounded outwards</em></span>. That is to say lower
+                quantiles (where the probability is less than 0.5) are rounded downward,
+                and upper quantiles (where the probability is greater than 0.5) are
+                rounded upwards. This behaviour ensures that if an X% quantile is
+                requested, then <span class="emphasis"><em>at least</em></span> the requested coverage
+                will be present in the central region, and <span class="emphasis"><em>no more than</em></span>
+                the requested coverage will be present in the tails.
+              </p>
+<p>
+                This behaviour can be changed so that the quantile functions are
+                rounded differently, or even return a real-valued result using <a class="link" href="../../../policy/pol_overview.html" title="Policy Overview">Policies</a>. It is
+                strongly recommended that you read the tutorial <a class="link" href="../../../policy/pol_tutorial/understand_dis_quant.html" title="Understanding Quantiles of Discrete Distributions">Understanding
+                Quantiles of Discrete Distributions</a> before using the quantile
+                function on the Negative Binomial distribution. The <a class="link" href="../../../policy/pol_ref/discrete_quant_ref.html" title="Discrete Quantile Policies">reference
+                docs</a> describe how to change the rounding policy for these
+                distributions.
+              </p>
+</td></tr>
+</table></div>
+<p>
+          </p>
+<a name="math_toolkit.dist.dist_ref.dists.negative_binomial_dist.member_functions"></a><h5>
+<a name="id669765"></a>
+            <a class="link" href="negative_binomial_dist.html#math_toolkit.dist.dist_ref.dists.negative_binomial_dist.member_functions">Member
+            Functions</a>
+          </h5>
+<a name="math_toolkit.dist.dist_ref.dists.negative_binomial_dist.construct"></a><h6>
+<a name="id669792"></a>
+            <a class="link" href="negative_binomial_dist.html#math_toolkit.dist.dist_ref.dists.negative_binomial_dist.construct">Construct</a>
+          </h6>
+<pre class="programlisting"><span class="identifier">negative_binomial_distribution</span><span class="special">(</span><span class="identifier">RealType</span> <span class="identifier">r</span><span class="special">,</span> <span class="identifier">RealType</span> <span class="identifier">p</span><span class="special">);</span>
+</pre>
+<p>
+            Constructor: <span class="emphasis"><em>r</em></span> is the total number of successes,
+            <span class="emphasis"><em>p</em></span> is the probability of success of a single trial.
+          </p>
+<p>
+            Requires: <code class="computeroutput"><span class="identifier">r</span> <span class="special">&gt;</span>
+            <span class="number">0</span></code> and <code class="computeroutput"><span class="number">0</span>
+            <span class="special">&lt;=</span> <span class="identifier">p</span>
+            <span class="special">&lt;=</span> <span class="number">1</span></code>.
+          </p>
+<a name="math_toolkit.dist.dist_ref.dists.negative_binomial_dist.accessors"></a><h6>
+<a name="id669949"></a>
+            <a class="link" href="negative_binomial_dist.html#math_toolkit.dist.dist_ref.dists.negative_binomial_dist.accessors">Accessors</a>
+          </h6>
+<pre class="programlisting"><span class="identifier">RealType</span> <span class="identifier">success_fraction</span><span class="special">()</span> <span class="keyword">const</span><span class="special">;</span> <span class="comment">// successes / trials (0 &lt;= p &lt;= 1)
+</span></pre>
+<p>
+            Returns the parameter <span class="emphasis"><em>p</em></span> from which this distribution
+            was constructed.
+          </p>
+<pre class="programlisting"><span class="identifier">RealType</span> <span class="identifier">successes</span><span class="special">()</span> <span class="keyword">const</span><span class="special">;</span> <span class="comment">// required successes (r &gt; 0)
+</span></pre>
+<p>
+            Returns the parameter <span class="emphasis"><em>r</em></span> from which this distribution
+            was constructed.
+          </p>
+<a name="math_toolkit.dist.dist_ref.dists.negative_binomial_dist.lower_bound_on_parameter_p"></a><h6>
+<a name="id670078"></a>
+            <a class="link" href="negative_binomial_dist.html#math_toolkit.dist.dist_ref.dists.negative_binomial_dist.lower_bound_on_parameter_p">Lower
+            Bound on Parameter p</a>
+          </h6>
+<pre class="programlisting"><span class="keyword">static</span> <span class="identifier">RealType</span> <span class="identifier">find_lower_bound_on_p</span><span class="special">(</span>
+  <span class="identifier">RealType</span> <span class="identifier">failures</span><span class="special">,</span> 
+  <span class="identifier">RealType</span> <span class="identifier">successes</span><span class="special">,</span>
+  <span class="identifier">RealType</span> <span class="identifier">probability</span><span class="special">)</span> <span class="comment">// (0 &lt;= alpha &lt;= 1), 0.05 equivalent to 95% confidence.
+</span></pre>
+<p>
+            Returns a <span class="bold"><strong>lower bound</strong></span> on the success
+            fraction:
+          </p>
+<div class="variablelist">
+<p class="title"><b></b></p>
+<dl>
+<dt><span class="term">failures</span></dt>
+<dd><p>
+                The total number of failures before the r th success.
+              </p></dd>
+<dt><span class="term">successes</span></dt>
+<dd><p>
+                The number of successes required.
+              </p></dd>
+<dt><span class="term">alpha</span></dt>
+<dd><p>
+                The largest acceptable probability that the true value of the success
+                fraction is <span class="bold"><strong>less than</strong></span> the value
+                returned.
+              </p></dd>
+</dl>
+</div>
+<p>
+            For example, if you observe <span class="emphasis"><em>k</em></span> failures and <span class="emphasis"><em>r</em></span>
+            successes from <span class="emphasis"><em>n</em></span> = k + r trials the best estimate
+            for the success fraction is simply <span class="emphasis"><em>r/n</em></span>, but if you
+            want to be 95% sure that the true value is <span class="bold"><strong>greater
+            than</strong></span> some value, <span class="emphasis"><em>p<sub>min</sub></em></span>, then:
+          </p>
+<pre class="programlisting"><span class="identifier">p</span><sub>min</sub> <span class="special">=</span> <span class="identifier">negative_binomial_distribution</span><span class="special">&lt;</span><span class="identifier">RealType</span><span class="special">&gt;::</span><span class="identifier">find_lower_bound_on_p</span><span class="special">(</span>
+                    <span class="identifier">failures</span><span class="special">,</span> <span class="identifier">successes</span><span class="special">,</span> <span class="number">0.05</span><span class="special">);</span>
+</pre>
+<p>
+            <a class="link" href="../../stat_tut/weg/neg_binom_eg/neg_binom_conf.html" title="Calculating Confidence Limits on the Frequency of Occurrence for the Negative Binomial Distribution">See
+            negative binomial confidence interval example.</a>
+          </p>
+<p>
+            This function uses the Clopper-Pearson method of computing the lower
+            bound on the success fraction, whilst many texts refer to this method
+            as giving an "exact" result in practice it produces an interval
+            that guarantees <span class="emphasis"><em>at least</em></span> the coverage required,
+            and may produce pessimistic estimates for some combinations of <span class="emphasis"><em>failures</em></span>
+            and <span class="emphasis"><em>successes</em></span>. See:
+          </p>
+<p>
+            <a href="http://www.ucs.louisiana.edu/~kxk4695/Discrete_new.pdf" target="_top">Yong
+            Cai and K. Krishnamoorthy, A Simple Improved Inferential Method for Some
+            Discrete Distributions. Computational statistics and data analysis, 2005,
+            vol. 48, no3, 605-621</a>.
+          </p>
+<a name="math_toolkit.dist.dist_ref.dists.negative_binomial_dist.upper_bound_on_parameter_p"></a><h6>
+<a name="id670463"></a>
+            <a class="link" href="negative_binomial_dist.html#math_toolkit.dist.dist_ref.dists.negative_binomial_dist.upper_bound_on_parameter_p">Upper
+            Bound on Parameter p</a>
+          </h6>
+<pre class="programlisting"><span class="keyword">static</span> <span class="identifier">RealType</span> <span class="identifier">find_upper_bound_on_p</span><span class="special">(</span>
+   <span class="identifier">RealType</span> <span class="identifier">trials</span><span class="special">,</span> 
+   <span class="identifier">RealType</span> <span class="identifier">successes</span><span class="special">,</span>
+   <span class="identifier">RealType</span> <span class="identifier">alpha</span><span class="special">);</span> <span class="comment">// (0 &lt;= alpha &lt;= 1), 0.05 equivalent to 95% confidence.
+</span></pre>
+<p>
+            Returns an <span class="bold"><strong>upper bound</strong></span> on the success
+            fraction:
+          </p>
+<div class="variablelist">
+<p class="title"><b></b></p>
+<dl>
+<dt><span class="term">trials</span></dt>
+<dd><p>
+                The total number of trials conducted.
+              </p></dd>
+<dt><span class="term">successes</span></dt>
+<dd><p>
+                The number of successes that occurred.
+              </p></dd>
+<dt><span class="term">alpha</span></dt>
+<dd><p>
+                The largest acceptable probability that the true value of the success
+                fraction is <span class="bold"><strong>greater than</strong></span> the value
+                returned.
+              </p></dd>
+</dl>
+</div>
+<p>
+            For example, if you observe <span class="emphasis"><em>k</em></span> successes from <span class="emphasis"><em>n</em></span>
+            trials the best estimate for the success fraction is simply <span class="emphasis"><em>k/n</em></span>,
+            but if you want to be 95% sure that the true value is <span class="bold"><strong>less
+            than</strong></span> some value, <span class="emphasis"><em>p<sub>max</sub></em></span>, then:
+          </p>
+<pre class="programlisting"><span class="identifier">p</span><sub>max</sub> <span class="special">=</span> <span class="identifier">negative_binomial_distribution</span><span class="special">&lt;</span><span class="identifier">RealType</span><span class="special">&gt;::</span><span class="identifier">find_upper_bound_on_p</span><span class="special">(</span>
+                    <span class="identifier">r</span><span class="special">,</span> <span class="identifier">k</span><span class="special">,</span> <span class="number">0.05</span><span class="special">);</span>
+</pre>
+<p>
+            <a class="link" href="../../stat_tut/weg/neg_binom_eg/neg_binom_conf.html" title="Calculating Confidence Limits on the Frequency of Occurrence for the Negative Binomial Distribution">See
+            negative binomial confidence interval example.</a>
+          </p>
+<p>
+            This function uses the Clopper-Pearson method of computing the lower
+            bound on the success fraction, whilst many texts refer to this method
+            as giving an "exact" result in practice it produces an interval
+            that guarantees <span class="emphasis"><em>at least</em></span> the coverage required,
+            and may produce pessimistic estimates for some combinations of <span class="emphasis"><em>failures</em></span>
+            and <span class="emphasis"><em>successes</em></span>. See:
+          </p>
+<p>
+            <a href="http://www.ucs.louisiana.edu/~kxk4695/Discrete_new.pdf" target="_top">Yong
+            Cai and K. Krishnamoorthy, A Simple Improved Inferential Method for Some
+            Discrete Distributions. Computational statistics and data analysis, 2005,
+            vol. 48, no3, 605-621</a>.
+          </p>
+<a name="math_toolkit.dist.dist_ref.dists.negative_binomial_dist.estimating_number_of_trials_to_ensure_at_least_a_certain_number_of_failures"></a><h6>
+<a name="id670842"></a>
+            <a class="link" href="negative_binomial_dist.html#math_toolkit.dist.dist_ref.dists.negative_binomial_dist.estimating_number_of_trials_to_ensure_at_least_a_certain_number_of_failures">Estimating
+            Number of Trials to Ensure at Least a Certain Number of Failures</a>
+          </h6>
+<pre class="programlisting"><span class="keyword">static</span> <span class="identifier">RealType</span> <span class="identifier">find_minimum_number_of_trials</span><span class="special">(</span>
+   <span class="identifier">RealType</span> <span class="identifier">k</span><span class="special">,</span>     <span class="comment">// number of failures.
+</span>   <span class="identifier">RealType</span> <span class="identifier">p</span><span class="special">,</span>     <span class="comment">// success fraction.
+</span>   <span class="identifier">RealType</span> <span class="identifier">alpha</span><span class="special">);</span> <span class="comment">// probability threshold (0.05 equivalent to 95%).
+</span></pre>
+<p>
+            This functions estimates the number of trials required to achieve a certain
+            probability that <span class="bold"><strong>more than k failures will be observed</strong></span>.
+          </p>
+<div class="variablelist">
+<p class="title"><b></b></p>
+<dl>
+<dt><span class="term">k</span></dt>
+<dd><p>
+                The target number of failures to be observed.
+              </p></dd>
+<dt><span class="term">p</span></dt>
+<dd><p>
+                The probability of <span class="emphasis"><em>success</em></span> for each trial.
+              </p></dd>
+<dt><span class="term">alpha</span></dt>
+<dd><p>
+                The maximum acceptable risk that only k failures or fewer will be
+                observed.
+              </p></dd>
+</dl>
+</div>
+<p>
+            For example:
+          </p>
+<pre class="programlisting"><span class="identifier">negative_binomial_distribution</span><span class="special">&lt;</span><span class="identifier">RealType</span><span class="special">&gt;::</span><span class="identifier">find_minimum_number_of_trials</span><span class="special">(</span><span class="number">10</span><span class="special">,</span> <span class="number">0.5</span><span class="special">,</span> <span class="number">0.05</span><span class="special">);</span>
+</pre>
+<p>
+            Returns the smallest number of trials we must conduct to be 95% sure
+            of seeing 10 failures that occur with frequency one half.
+          </p>
+<p>
+            <a class="link" href="../../stat_tut/weg/neg_binom_eg/neg_binom_size_eg.html" title="Estimating Sample Sizes for the Negative Binomial.">Worked
+            Example.</a>
+          </p>
+<p>
+            This function uses numeric inversion of the negative binomial distribution
+            to obtain the result: another interpretation of the result, is that it
+            finds the number of trials (success+failures) that will lead to an <span class="emphasis"><em>alpha</em></span>
+            probability of observing k failures or fewer.
+          </p>
+<a name="math_toolkit.dist.dist_ref.dists.negative_binomial_dist.estimating_number_of_trials_to_ensure_a_maximum_number_of_failures_or_less"></a><h6>
+<a name="id671167"></a>
+            <a class="link" href="negative_binomial_dist.html#math_toolkit.dist.dist_ref.dists.negative_binomial_dist.estimating_number_of_trials_to_ensure_a_maximum_number_of_failures_or_less">Estimating
+            Number of Trials to Ensure a Maximum Number of Failures or Less</a>
+          </h6>
+<pre class="programlisting"><span class="keyword">static</span> <span class="identifier">RealType</span> <span class="identifier">find_maximum_number_of_trials</span><span class="special">(</span>
+   <span class="identifier">RealType</span> <span class="identifier">k</span><span class="special">,</span>     <span class="comment">// number of failures.
+</span>   <span class="identifier">RealType</span> <span class="identifier">p</span><span class="special">,</span>     <span class="comment">// success fraction.
+</span>   <span class="identifier">RealType</span> <span class="identifier">alpha</span><span class="special">);</span> <span class="comment">// probability threshold (0.05 equivalent to 95%).
+</span></pre>
+<p>
+            This functions estimates the maximum number of trials we can conduct
+            and achieve a certain probability that <span class="bold"><strong>k failures
+            or fewer will be observed</strong></span>.
+          </p>
+<div class="variablelist">
+<p class="title"><b></b></p>
+<dl>
+<dt><span class="term">k</span></dt>
+<dd><p>
+                The maximum number of failures to be observed.
+              </p></dd>
+<dt><span class="term">p</span></dt>
+<dd><p>
+                The probability of <span class="emphasis"><em>success</em></span> for each trial.
+              </p></dd>
+<dt><span class="term">alpha</span></dt>
+<dd><p>
+                The maximum acceptable <span class="emphasis"><em>risk</em></span> that more than k
+                failures will be observed.
+              </p></dd>
+</dl>
+</div>
+<p>
+            For example:
+          </p>
+<pre class="programlisting"><span class="identifier">negative_binomial_distribution</span><span class="special">&lt;</span><span class="identifier">RealType</span><span class="special">&gt;::</span><span class="identifier">find_maximum_number_of_trials</span><span class="special">(</span><span class="number">0</span><span class="special">,</span> <span class="number">1.0</span><span class="special">-</span><span class="number">1.0</span><span class="special">/</span><span class="number">1000000</span><span class="special">,</span> <span class="number">0.05</span><span class="special">);</span>
+</pre>
+<p>
+            Returns the largest number of trials we can conduct and still be 95%
+            sure of seeing no failures that occur with frequency one in one million.
+          </p>
+<p>
+            This function uses numeric inversion of the negative binomial distribution
+            to obtain the result: another interpretation of the result, is that it
+            finds the number of trials (success+failures) that will lead to an <span class="emphasis"><em>alpha</em></span>
+            probability of observing more than k failures.
+          </p>
+<a name="math_toolkit.dist.dist_ref.dists.negative_binomial_dist.non_member_accessors"></a><h5>
+<a name="id671502"></a>
+            <a class="link" href="negative_binomial_dist.html#math_toolkit.dist.dist_ref.dists.negative_binomial_dist.non_member_accessors">Non-member
+            Accessors</a>
+          </h5>
+<p>
+            All the <a class="link" href="../nmp.html" title="Non-Member Properties">usual non-member
+            accessor functions</a> that are generic to all distributions are supported:
+            <a class="link" href="../nmp.html#math.dist.cdf">Cumulative Distribution Function</a>,
+            <a class="link" href="../nmp.html#math.dist.pdf">Probability Density Function</a>, <a class="link" href="../nmp.html#math.dist.quantile">Quantile</a>, <a class="link" href="../nmp.html#math.dist.hazard">Hazard
+            Function</a>, <a class="link" href="../nmp.html#math.dist.chf">Cumulative Hazard Function</a>,
+            <a class="link" href="../nmp.html#math.dist.mean">mean</a>, <a class="link" href="../nmp.html#math.dist.median">median</a>,
+            <a class="link" href="../nmp.html#math.dist.mode">mode</a>, <a class="link" href="../nmp.html#math.dist.variance">variance</a>,
+            <a class="link" href="../nmp.html#math.dist.sd">standard deviation</a>, <a class="link" href="../nmp.html#math.dist.skewness">skewness</a>,
+            <a class="link" href="../nmp.html#math.dist.kurtosis">kurtosis</a>, <a class="link" href="../nmp.html#math.dist.kurtosis_excess">kurtosis_excess</a>,
+            <a class="link" href="../nmp.html#math.dist.range">range</a> and <a class="link" href="../nmp.html#math.dist.support">support</a>.
+          </p>
+<p>
+            However it's worth taking a moment to define what these actually mean
+            in the context of this distribution:
+          </p>
+<div class="table">
+<a name="id671672"></a><p class="title"><b>Table 12. Meaning of the non-member accessors.</b></p>
+<div class="table-contents"><table class="table" summary="Meaning of the non-member accessors.">
+<colgroup>
+<col>
+<col>
+</colgroup>
+<thead><tr>
+<th>
+                <p>
+                  Function
+                </p>
+                </th>
+<th>
+                <p>
+                  Meaning
+                </p>
+                </th>
+</tr></thead>
+<tbody>
+<tr>
+<td>
+                <p>
+                  <a class="link" href="../nmp.html#math.dist.pdf">Probability Density Function</a>
+                </p>
+                </td>
+<td>
+                <p>
+                  The probability of obtaining <span class="bold"><strong>exactly k failures</strong></span>
+                  from k+r trials with success fraction p. For example:
+                </p>
+                <p>
+                  
+</p>
+<pre class="programlisting"><span class="identifier">pdf</span><span class="special">(</span><span class="identifier">negative_binomial</span><span class="special">(</span><span class="identifier">r</span><span class="special">,</span> <span class="identifier">p</span><span class="special">),</span> <span class="identifier">k</span><span class="special">)</span></pre>
+<p>
+                </p>
+                </td>
+</tr>
+<tr>
+<td>
+                <p>
+                  <a class="link" href="../nmp.html#math.dist.cdf">Cumulative Distribution Function</a>
+                </p>
+                </td>
+<td>
+                <p>
+                  The probability of obtaining <span class="bold"><strong>k failures or
+                  fewer</strong></span> from k+r trials with success fraction p and success
+                  on the last trial. For example:
+                </p>
+                <p>
+                  
+</p>
+<pre class="programlisting"><span class="identifier">cdf</span><span class="special">(</span><span class="identifier">negative_binomial</span><span class="special">(</span><span class="identifier">r</span><span class="special">,</span> <span class="identifier">p</span><span class="special">),</span> <span class="identifier">k</span><span class="special">)</span></pre>
+<p>
+                </p>
+                </td>
+</tr>
+<tr>
+<td>
+                <p>
+                  <a class="link" href="../nmp.html#math.dist.ccdf">Complement of the Cumulative Distribution
+                  Function</a>
+                </p>
+                </td>
+<td>
+                <p>
+                  The probability of obtaining <span class="bold"><strong>more than k
+                  failures</strong></span> from k+r trials with success fraction p and
+                  success on the last trial. For example:
+                </p>
+                <p>
+                  
+</p>
+<pre class="programlisting"><span class="identifier">cdf</span><span class="special">(</span><span class="identifier">complement</span><span class="special">(</span><span class="identifier">negative_binomial</span><span class="special">(</span><span class="identifier">r</span><span class="special">,</span> <span class="identifier">p</span><span class="special">),</span> <span class="identifier">k</span><span class="special">))</span></pre>
+<p>
+                </p>
+                </td>
+</tr>
+<tr>
+<td>
+                <p>
+                  <a class="link" href="../nmp.html#math.dist.quantile">Quantile</a>
+                </p>
+                </td>
+<td>
+                <p>
+                  The <span class="bold"><strong>greatest</strong></span> number of failures
+                  k expected to be observed from k+r trials with success fraction
+                  p, at probability P. Note that the value returned is a real-number,
+                  and not an integer. Depending on the use case you may want to take
+                  either the floor or ceiling of the real result. For example:
+                </p>
+                <p>
+                  
+</p>
+<pre class="programlisting"><span class="identifier">quantile</span><span class="special">(</span><span class="identifier">negative_binomial</span><span class="special">(</span><span class="identifier">r</span><span class="special">,</span> <span class="identifier">p</span><span class="special">),</span> <span class="identifier">P</span><span class="special">)</span></pre>
+<p>
+                </p>
+                </td>
+</tr>
+<tr>
+<td>
+                <p>
+                  <a class="link" href="../nmp.html#math.dist.quantile_c">Quantile from the complement
+                  of the probability</a>
+                </p>
+                </td>
+<td>
+                <p>
+                  The <span class="bold"><strong>smallest</strong></span> number of failures
+                  k expected to be observed from k+r trials with success fraction
+                  p, at probability P. Note that the value returned is a real-number,
+                  and not an integer. Depending on the use case you may want to take
+                  either the floor or ceiling of the real result. For example: 
+</p>
+<pre class="programlisting"><span class="identifier">quantile</span><span class="special">(</span><span class="identifier">complement</span><span class="special">(</span><span class="identifier">negative_binomial</span><span class="special">(</span><span class="identifier">r</span><span class="special">,</span> <span class="identifier">p</span><span class="special">),</span> <span class="identifier">P</span><span class="special">))</span></pre>
+<p>
+                </p>
+                </td>
+</tr>
+</tbody>
+</table></div>
+</div>
+<br class="table-break"><a name="math_toolkit.dist.dist_ref.dists.negative_binomial_dist.accuracy"></a><h5>
+<a name="id672247"></a>
+            <a class="link" href="negative_binomial_dist.html#math_toolkit.dist.dist_ref.dists.negative_binomial_dist.accuracy">Accuracy</a>
+          </h5>
+<p>
+            This distribution is implemented using the incomplete beta functions
+            <a class="link" href="../../../special/sf_beta/ibeta_function.html" title="Incomplete Beta Functions">ibeta</a>
+            and <a class="link" href="../../../special/sf_beta/ibeta_function.html" title="Incomplete Beta Functions">ibetac</a>:
+            please refer to these functions for information on accuracy.
+          </p>
+<a name="math_toolkit.dist.dist_ref.dists.negative_binomial_dist.implementation"></a><h5>
+<a name="id672299"></a>
+            <a class="link" href="negative_binomial_dist.html#math_toolkit.dist.dist_ref.dists.negative_binomial_dist.implementation">Implementation</a>
+          </h5>
+<p>
+            In the following table, <span class="emphasis"><em>p</em></span> is the probability that
+            any one trial will be successful (the success fraction), <span class="emphasis"><em>r</em></span>
+            is the number of successes, <span class="emphasis"><em>k</em></span> is the number of failures,
+            <span class="emphasis"><em>p</em></span> is the probability and <span class="emphasis"><em>q = 1-p</em></span>.
+          </p>
+<div class="informaltable"><table class="table">
+<colgroup>
+<col>
+<col>
+</colgroup>
+<thead><tr>
+<th>
+                  <p>
+                    Function
+                  </p>
+                  </th>
+<th>
+                  <p>
+                    Implementation Notes
+                  </p>
+                  </th>
+</tr></thead>
+<tbody>
+<tr>
+<td>
+                  <p>
+                    pdf
+                  </p>
+                  </td>
+<td>
+                  <p>
+                    pdf = exp(lgamma(r + k) - lgamma(r) - lgamma(k+1)) * pow(p, r)
+                    * pow((1-p), k)
+                  </p>
+                  <p>
+                    Implementation is in terms of <a class="link" href="../../../special/sf_beta/beta_derivative.html" title="Derivative of the Incomplete Beta Function">ibeta_derivative</a>:
+                  </p>
+                  <p>
+                    (p/(r + k)) * ibeta_derivative(r, static_cast&lt;RealType&gt;(k+1),
+                    p) The function <a class="link" href="../../../special/sf_beta/beta_derivative.html" title="Derivative of the Incomplete Beta Function">ibeta_derivative</a>
+                    is used here, since it has already been optimised for the lowest
+                    possible error - indeed this is really just a thin wrapper around
+                    part of the internals of the incomplete beta function.
+                  </p>
+                  </td>
+</tr>
+<tr>
+<td>
+                  <p>
+                    cdf
+                  </p>
+                  </td>
+<td>
+                  <p>
+                    Using the relation:
+                  </p>
+                  <p>
+                    cdf = I<sub>p</sub>(r, k+1) = ibeta(r, k+1, p)
+                  </p>
+                  <p>
+                    = ibeta(r, static_cast&lt;RealType&gt;(k+1), p)
+                  </p>
+                  </td>
+</tr>
+<tr>
+<td>
+                  <p>
+                    cdf complement
+                  </p>
+                  </td>
+<td>
+                  <p>
+                    Using the relation:
+                  </p>
+                  <p>
+                    1 - cdf = I<sub>p</sub>(k+1, r)
+                  </p>
+                  <p>
+                    = ibetac(r, static_cast&lt;RealType&gt;(k+1), p)
+                  </p>
+                  </td>
+</tr>
+<tr>
+<td>
+                  <p>
+                    quantile
+                  </p>
+                  </td>
+<td>
+                  <p>
+                    ibeta_invb(r, p, P) - 1
+                  </p>
+                  </td>
+</tr>
+<tr>
+<td>
+                  <p>
+                    quantile from the complement
+                  </p>
+                  </td>
+<td>
+                  <p>
+                    ibetac_invb(r, p, Q) -1)
+                  </p>
+                  </td>
+</tr>
+<tr>
+<td>
+                  <p>
+                    mean
+                  </p>
+                  </td>
+<td>
+                  <p>
+                    <code class="computeroutput"><span class="identifier">r</span><span class="special">(</span><span class="number">1</span><span class="special">-</span><span class="identifier">p</span><span class="special">)/</span><span class="identifier">p</span></code>
+                  </p>
+                  </td>
+</tr>
+<tr>
+<td>
+                  <p>
+                    variance
+                  </p>
+                  </td>
+<td>
+                  <p>
+                    <code class="computeroutput"><span class="identifier">r</span> <span class="special">(</span><span class="number">1</span><span class="special">-</span><span class="identifier">p</span><span class="special">)</span>
+                    <span class="special">/</span> <span class="identifier">p</span>
+                    <span class="special">*</span> <span class="identifier">p</span></code>
+                  </p>
+                  </td>
+</tr>
+<tr>
+<td>
+                  <p>
+                    mode
+                  </p>
+                  </td>
+<td>
+                  <p>
+                    <code class="computeroutput"><span class="identifier">floor</span><span class="special">((</span><span class="identifier">r</span><span class="special">-</span><span class="number">1</span><span class="special">)</span> <span class="special">*</span> <span class="special">(</span><span class="number">1</span> <span class="special">-</span> <span class="identifier">p</span><span class="special">)/</span><span class="identifier">p</span><span class="special">)</span></code>
+                  </p>
+                  </td>
+</tr>
+<tr>
+<td>
+                  <p>
+                    skewness
+                  </p>
+                  </td>
+<td>
+                  <p>
+                    <code class="computeroutput"><span class="special">(</span><span class="number">2</span>
+                    <span class="special">-</span> <span class="identifier">p</span><span class="special">)</span> <span class="special">/</span>
+                    <span class="identifier">sqrt</span><span class="special">(</span><span class="identifier">r</span> <span class="special">*</span>
+                    <span class="special">(</span><span class="number">1</span>
+                    <span class="special">-</span> <span class="identifier">p</span><span class="special">))</span></code>
+                  </p>
+                  </td>
+</tr>
+<tr>
+<td>
+                  <p>
+                    kurtosis
+                  </p>
+                  </td>
+<td>
+                  <p>
+                    <code class="computeroutput"><span class="number">6</span> <span class="special">/</span>
+                    <span class="identifier">r</span> <span class="special">+</span>
+                    <span class="special">(</span><span class="identifier">p</span>
+                    <span class="special">*</span> <span class="identifier">p</span><span class="special">)</span> <span class="special">/</span>
+                    <span class="identifier">r</span> <span class="special">*</span>
+                    <span class="special">(</span><span class="number">1</span>
+                    <span class="special">-</span> <span class="identifier">p</span>
+                    <span class="special">)</span></code>
+                  </p>
+                  </td>
+</tr>
+<tr>
+<td>
+                  <p>
+                    kurtosis excess
+                  </p>
+                  </td>
+<td>
+                  <p>
+                    <code class="computeroutput"><span class="number">6</span> <span class="special">/</span>
+                    <span class="identifier">r</span> <span class="special">+</span>
+                    <span class="special">(</span><span class="identifier">p</span>
+                    <span class="special">*</span> <span class="identifier">p</span><span class="special">)</span> <span class="special">/</span>
+                    <span class="identifier">r</span> <span class="special">*</span>
+                    <span class="special">(</span><span class="number">1</span>
+                    <span class="special">-</span> <span class="identifier">p</span>
+                    <span class="special">)</span> <span class="special">-</span><span class="number">3</span></code>
+                  </p>
+                  </td>
+</tr>
+<tr>
+<td>
+                  <p>
+                    parameter estimation member functions
+                  </p>
+                  </td>
+<td>
+                  <p>
+                  </p>
+                  </td>
+</tr>
+<tr>
+<td>
+                  <p>
+                    <code class="computeroutput"><span class="identifier">find_lower_bound_on_p</span></code>
+                  </p>
+                  </td>
+<td>
+                  <p>
+                    ibeta_inv(successes, failures + 1, alpha)
+                  </p>
+                  </td>
+</tr>
+<tr>
+<td>
+                  <p>
+                    <code class="computeroutput"><span class="identifier">find_upper_bound_on_p</span></code>
+                  </p>
+                  </td>
+<td>
+                  <p>
+                    ibetac_inv(successes, failures, alpha) plus see comments in code.
+                  </p>
+                  </td>
+</tr>
+<tr>
+<td>
+                  <p>
+                    <code class="computeroutput"><span class="identifier">find_minimum_number_of_trials</span></code>
+                  </p>
+                  </td>
+<td>
+                  <p>
+                    ibeta_inva(k + 1, p, alpha)
+                  </p>
+                  </td>
+</tr>
+<tr>
+<td>
+                  <p>
+                    <code class="computeroutput"><span class="identifier">find_maximum_number_of_trials</span></code>
+                  </p>
+                  </td>
+<td>
+                  <p>
+                    ibetac_inva(k + 1, p, alpha)
+                  </p>
+                  </td>
+</tr>
+</tbody>
+</table></div>
+<p>
+            Implementation notes:
+          </p>
+<div class="itemizedlist"><ul type="disc">
+<li>
+              The real concept type (that deliberately lacks the Lanczos approximation),
+              was found to take several minutes to evaluate some extreme test values,
+              so the test has been disabled for this type.
+            </li>
+<li>
+              Much greater speed, and perhaps greater accuracy, might be achieved
+              for extreme values by using a normal approximation. This is NOT been
+              tested or implemented.
+            </li>
+</ul></div>
+</div>
+<table xmlns:rev="http://www.cs.rpi.edu/~gregod/boost/tools/doc/revision" width="100%"><tr>
+<td align="left"></td>
+<td align="right"><div class="copyright-footer">Copyright © 2006 , 2007, 2008 John Maddock, Paul A. Bristow, Hubert
+      Holin, Xiaogang Zhang, Bruno Lalande and Gautam Sewani<p>
+        Distributed under the Boost Software License, Version 1.0. (See accompanying
+        file LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_0.txt)
+      </p>
+</div></td>
+</tr></table>
+<hr>
+<div class="spirit-nav">
+<a accesskey="p" href="lognormal_dist.html"><img src="../../../../../../doc/html/images/prev.png" alt="Prev"></a><a accesskey="u" href="../dists.html"><img src="../../../../../../doc/html/images/up.png" alt="Up"></a><a accesskey="h" href="../../../../index.html"><img src="../../../../../../doc/html/images/home.png" alt="Home"></a><a accesskey="n" href="nc_beta_dist.html"><img src="../../../../../../doc/html/images/next.png" alt="Next"></a>
+</div>
+</body>
+</html>

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+++ sandbox/tools/auto_index/example/math/doc/sf_and_dist/html/math_toolkit/dist/dist_ref/dists/normal_dist.html	2008-11-28 05:25:28 EST (Fri, 28 Nov 2008)
@@ -0,0 +1,304 @@
+<html>
+<head>
+<meta http-equiv="Content-Type" content="text/html; charset=ISO-8859-1">
+<title>Normal (Gaussian) Distribution</title>
+<link rel="stylesheet" href="../../../../boostbook.css" type="text/css">
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+</tr></table>
+<hr>
+<div class="spirit-nav">
+<a accesskey="p" href="nc_t_dist.html"><img src="../../../../../../doc/html/images/prev.png" alt="Prev"></a><a accesskey="u" href="../dists.html"><img src="../../../../../../doc/html/images/up.png" alt="Up"></a><a accesskey="h" href="../../../../index.html"><img src="../../../../../../doc/html/images/home.png" alt="Home"></a><a accesskey="n" href="pareto.html"><img src="../../../../../../doc/html/images/next.png" alt="Next"></a>
+</div>
+<div class="section" lang="en">
+<div class="titlepage"><div><div><h5 class="title">
+<a name="math_toolkit.dist.dist_ref.dists.normal_dist"></a><a class="link" href="normal_dist.html" title="Normal (Gaussian) Distribution"> Normal
+          (Gaussian) Distribution</a>
+</h5></div></div></div>
+<p>
+            
+</p>
+<pre class="programlisting"><span class="preprocessor">#include</span> <span class="special">&lt;</span><span class="identifier">boost</span><span class="special">/</span><span class="identifier">math</span><span class="special">/</span><span class="identifier">distributions</span><span class="special">/</span><span class="identifier">normal</span><span class="special">.</span><span class="identifier">hpp</span><span class="special">&gt;</span></pre>
+<p>
+          </p>
+<pre class="programlisting"><span class="keyword">namespace</span> <span class="identifier">boost</span><span class="special">{</span> <span class="keyword">namespace</span> <span class="identifier">math</span><span class="special">{</span> 
+   
+<span class="keyword">template</span> <span class="special">&lt;</span><span class="keyword">class</span> <span class="identifier">RealType</span> <span class="special">=</span> <span class="keyword">double</span><span class="special">,</span> 
+          <span class="keyword">class</span> <a class="link" href="../../../policy.html" title="Policies">Policy</a>   <span class="special">=</span> <a class="link" href="../../../policy/pol_ref/pol_ref_ref.html" title="Policy Class Reference">policies::policy&lt;&gt;</a> <span class="special">&gt;</span>
+<span class="keyword">class</span> <span class="identifier">normal_distribution</span><span class="special">;</span>
+
+<span class="keyword">typedef</span> <span class="identifier">normal_distribution</span><span class="special">&lt;&gt;</span> <span class="identifier">normal</span><span class="special">;</span>
+
+<span class="keyword">template</span> <span class="special">&lt;</span><span class="keyword">class</span> <span class="identifier">RealType</span><span class="special">,</span> <span class="keyword">class</span> <a class="link" href="../../../policy.html" title="Policies">Policy</a><span class="special">&gt;</span>
+<span class="keyword">class</span> <span class="identifier">normal_distribution</span>
+<span class="special">{</span>
+<span class="keyword">public</span><span class="special">:</span>
+   <span class="keyword">typedef</span> <span class="identifier">RealType</span> <span class="identifier">value_type</span><span class="special">;</span>
+   <span class="keyword">typedef</span> <span class="identifier">Policy</span>   <span class="identifier">policy_type</span><span class="special">;</span>
+   <span class="comment">// Construct:
+</span>   <span class="identifier">normal_distribution</span><span class="special">(</span><span class="identifier">RealType</span> <span class="identifier">mean</span> <span class="special">=</span> <span class="number">0</span><span class="special">,</span> <span class="identifier">RealType</span> <span class="identifier">sd</span> <span class="special">=</span> <span class="number">1</span><span class="special">);</span>
+   <span class="comment">// Accessors:
+</span>   <span class="identifier">RealType</span> <span class="identifier">mean</span><span class="special">()</span><span class="keyword">const</span><span class="special">;</span> <span class="comment">// location.
+</span>   <span class="identifier">RealType</span> <span class="identifier">standard_deviation</span><span class="special">()</span><span class="keyword">const</span><span class="special">;</span> <span class="comment">// scale.
+</span>   <span class="comment">// Synonyms, provided to allow generic use of find_location and find_scale.
+</span>   <span class="identifier">RealType</span> <span class="identifier">location</span><span class="special">()</span><span class="keyword">const</span><span class="special">;</span>
+   <span class="identifier">RealType</span> <span class="identifier">scale</span><span class="special">()</span><span class="keyword">const</span><span class="special">;</span>
+<span class="special">};</span>
+
+<span class="special">}}</span> <span class="comment">// namespaces
+</span></pre>
+<p>
+            The normal distribution is probably the most well known statistical distribution:
+            it is also known as the Gaussian Distribution. A normal distribution
+            with mean zero and standard deviation one is known as the <span class="emphasis"><em>Standard
+            Normal Distribution</em></span>.
+          </p>
+<p>
+            Given mean &#956; and standard deviation &#963; it has the PDF:
+          </p>
+<p>
+            <span class="inlinemediaobject"><img src="../../../../../equations/normal_ref1.png"></span>
+          </p>
+<p>
+            The variation the PDF with its parameters is illustrated in the following
+            graph:
+          </p>
+<p>
+            <span class="inlinemediaobject"><img src="../../../../../graphs/normal_pdf.png" align="middle"></span>
+          </p>
+<a name="math_toolkit.dist.dist_ref.dists.normal_dist.member_functions"></a><h5>
+<a name="id682927"></a>
+            <a class="link" href="normal_dist.html#math_toolkit.dist.dist_ref.dists.normal_dist.member_functions">Member
+            Functions</a>
+          </h5>
+<pre class="programlisting"><span class="identifier">normal_distribution</span><span class="special">(</span><span class="identifier">RealType</span> <span class="identifier">mean</span> <span class="special">=</span> <span class="number">0</span><span class="special">,</span> <span class="identifier">RealType</span> <span class="identifier">sd</span> <span class="special">=</span> <span class="number">1</span><span class="special">);</span>
+</pre>
+<p>
+            Constructs a normal distribution with mean <span class="emphasis"><em>mean</em></span>
+            and standard deviation <span class="emphasis"><em>sd</em></span>.
+          </p>
+<p>
+            Requires sd &gt; 0, otherwise <a class="link" href="../../../main_overview/error_handling.html#domain_error">domain_error</a>
+            is called.
+          </p>
+<pre class="programlisting"><span class="identifier">RealType</span> <span class="identifier">mean</span><span class="special">()</span><span class="keyword">const</span><span class="special">;</span>
+<span class="identifier">RealType</span> <span class="identifier">location</span><span class="special">()</span><span class="keyword">const</span><span class="special">;</span>   
+</pre>
+<p>
+            both return the <span class="emphasis"><em>mean</em></span> of this distribution.
+          </p>
+<pre class="programlisting"><span class="identifier">RealType</span> <span class="identifier">standard_deviation</span><span class="special">()</span><span class="keyword">const</span><span class="special">;</span>
+<span class="identifier">RealType</span> <span class="identifier">scale</span><span class="special">()</span><span class="keyword">const</span><span class="special">;</span>
+</pre>
+<p>
+            both return the <span class="emphasis"><em>standard deviation</em></span> of this distribution.
+            (Redundant location and scale function are provided to match other similar
+            distributions, allowing the functions find_location and find_scale to
+            be used generically).
+          </p>
+<a name="math_toolkit.dist.dist_ref.dists.normal_dist.non_member_accessors"></a><h5>
+<a name="id683209"></a>
+            <a class="link" href="normal_dist.html#math_toolkit.dist.dist_ref.dists.normal_dist.non_member_accessors">Non-member
+            Accessors</a>
+          </h5>
+<p>
+            All the <a class="link" href="../nmp.html" title="Non-Member Properties">usual non-member
+            accessor functions</a> that are generic to all distributions are supported:
+            <a class="link" href="../nmp.html#math.dist.cdf">Cumulative Distribution Function</a>,
+            <a class="link" href="../nmp.html#math.dist.pdf">Probability Density Function</a>, <a class="link" href="../nmp.html#math.dist.quantile">Quantile</a>, <a class="link" href="../nmp.html#math.dist.hazard">Hazard
+            Function</a>, <a class="link" href="../nmp.html#math.dist.chf">Cumulative Hazard Function</a>,
+            <a class="link" href="../nmp.html#math.dist.mean">mean</a>, <a class="link" href="../nmp.html#math.dist.median">median</a>,
+            <a class="link" href="../nmp.html#math.dist.mode">mode</a>, <a class="link" href="../nmp.html#math.dist.variance">variance</a>,
+            <a class="link" href="../nmp.html#math.dist.sd">standard deviation</a>, <a class="link" href="../nmp.html#math.dist.skewness">skewness</a>,
+            <a class="link" href="../nmp.html#math.dist.kurtosis">kurtosis</a>, <a class="link" href="../nmp.html#math.dist.kurtosis_excess">kurtosis_excess</a>,
+            <a class="link" href="../nmp.html#math.dist.range">range</a> and <a class="link" href="../nmp.html#math.dist.support">support</a>.
+          </p>
+<p>
+            The domain of the random variable is [-[max_value], +[min_value]]. However,
+            the pdf of +&#8734; and -&#8734; = 0 is also supported, and cdf at -&#8734; = 0, cdf at +&#8734; = 1,
+            and complement cdf -&#8734; = 1 and +&#8734; = 0, if RealType permits.
+          </p>
+<a name="math_toolkit.dist.dist_ref.dists.normal_dist.accuracy"></a><h5>
+<a name="id683396"></a>
+            <a class="link" href="normal_dist.html#math_toolkit.dist.dist_ref.dists.normal_dist.accuracy">Accuracy</a>
+          </h5>
+<p>
+            The normal distribution is implemented in terms of the <a class="link" href="../../../special/sf_erf/error_function.html" title="Error Functions">error
+            function</a>, and as such should have very low error rates.
+          </p>
+<a name="math_toolkit.dist.dist_ref.dists.normal_dist.implementation"></a><h5>
+<a name="id683437"></a>
+            <a class="link" href="normal_dist.html#math_toolkit.dist.dist_ref.dists.normal_dist.implementation">Implementation</a>
+          </h5>
+<p>
+            In the following table <span class="emphasis"><em>m</em></span> is the mean of the distribution,
+            and <span class="emphasis"><em>s</em></span> is its standard deviation.
+          </p>
+<div class="informaltable"><table class="table">
+<colgroup>
+<col>
+<col>
+</colgroup>
+<thead><tr>
+<th>
+                  <p>
+                    Function
+                  </p>
+                  </th>
+<th>
+                  <p>
+                    Implementation Notes
+                  </p>
+                  </th>
+</tr></thead>
+<tbody>
+<tr>
+<td>
+                  <p>
+                    pdf
+                  </p>
+                  </td>
+<td>
+                  <p>
+                    Using the relation: pdf = e<sup>-(x-m)<sup>2</sup>/(2s<sup>2</sup>)</sup> / (s * sqrt(2*pi))
+                  </p>
+                  </td>
+</tr>
+<tr>
+<td>
+                  <p>
+                    cdf
+                  </p>
+                  </td>
+<td>
+                  <p>
+                    Using the relation: p = 0.5 * <a class="link" href="../../../special/sf_erf/error_function.html" title="Error Functions">erfc</a>(-(x-m)/(s*sqrt(2)))
+                  </p>
+                  </td>
+</tr>
+<tr>
+<td>
+                  <p>
+                    cdf complement
+                  </p>
+                  </td>
+<td>
+                  <p>
+                    Using the relation: q = 0.5 * <a class="link" href="../../../special/sf_erf/error_function.html" title="Error Functions">erfc</a>((x-m)/(s*sqrt(2)))
+                  </p>
+                  </td>
+</tr>
+<tr>
+<td>
+                  <p>
+                    quantile
+                  </p>
+                  </td>
+<td>
+                  <p>
+                    Using the relation: x = m - s * sqrt(2) * <a class="link" href="../../../special/sf_erf/error_inv.html" title="Error Function Inverses">erfc_inv</a>(2*p)
+                  </p>
+                  </td>
+</tr>
+<tr>
+<td>
+                  <p>
+                    quantile from the complement
+                  </p>
+                  </td>
+<td>
+                  <p>
+                    Using the relation: x = m + s * sqrt(2) * <a class="link" href="../../../special/sf_erf/error_inv.html" title="Error Function Inverses">erfc_inv</a>(2*p)
+                  </p>
+                  </td>
+</tr>
+<tr>
+<td>
+                  <p>
+                    mean and standard deviation
+                  </p>
+                  </td>
+<td>
+                  <p>
+                    The same as <code class="computeroutput"><span class="identifier">dist</span><span class="special">.</span><span class="identifier">mean</span><span class="special">()</span></code> and <code class="computeroutput"><span class="identifier">dist</span><span class="special">.</span><span class="identifier">standard_deviation</span><span class="special">()</span></code>
+                  </p>
+                  </td>
+</tr>
+<tr>
+<td>
+                  <p>
+                    mode
+                  </p>
+                  </td>
+<td>
+                  <p>
+                    The same as the mean.
+                  </p>
+                  </td>
+</tr>
+<tr>
+<td>
+                  <p>
+                    skewness
+                  </p>
+                  </td>
+<td>
+                  <p>
+                    0
+                  </p>
+                  </td>
+</tr>
+<tr>
+<td>
+                  <p>
+                    kurtosis
+                  </p>
+                  </td>
+<td>
+                  <p>
+                    3
+                  </p>
+                  </td>
+</tr>
+<tr>
+<td>
+                  <p>
+                    kurtosis excess
+                  </p>
+                  </td>
+<td>
+                  <p>
+                    0
+                  </p>
+                  </td>
+</tr>
+</tbody>
+</table></div>
+</div>
+<table xmlns:rev="http://www.cs.rpi.edu/~gregod/boost/tools/doc/revision" width="100%"><tr>
+<td align="left"></td>
+<td align="right"><div class="copyright-footer">Copyright © 2006 , 2007, 2008 John Maddock, Paul A. Bristow, Hubert
+      Holin, Xiaogang Zhang, Bruno Lalande and Gautam Sewani<p>
+        Distributed under the Boost Software License, Version 1.0. (See accompanying
+        file LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_0.txt)
+      </p>
+</div></td>
+</tr></table>
+<hr>
+<div class="spirit-nav">
+<a accesskey="p" href="nc_t_dist.html"><img src="../../../../../../doc/html/images/prev.png" alt="Prev"></a><a accesskey="u" href="../dists.html"><img src="../../../../../../doc/html/images/up.png" alt="Up"></a><a accesskey="h" href="../../../../index.html"><img src="../../../../../../doc/html/images/home.png" alt="Home"></a><a accesskey="n" href="pareto.html"><img src="../../../../../../doc/html/images/next.png" alt="Next"></a>
+</div>
+</body>
+</html>

Added: sandbox/tools/auto_index/example/math/doc/sf_and_dist/html/math_toolkit/dist/dist_ref/dists/pareto.html
==============================================================================
--- (empty file)
+++ sandbox/tools/auto_index/example/math/doc/sf_and_dist/html/math_toolkit/dist/dist_ref/dists/pareto.html	2008-11-28 05:25:28 EST (Fri, 28 Nov 2008)
@@ -0,0 +1,343 @@
+<html>
+<head>
+<meta http-equiv="Content-Type" content="text/html; charset=ISO-8859-1">
+<title>Pareto Distribution</title>
+<link rel="stylesheet" href="../../../../boostbook.css" type="text/css">
+<meta name="generator" content="DocBook XSL Stylesheets Vsnapshot_8125">
+<link rel="home" href="../../../../index.html" title="Math Toolkit">
+<link rel="up" href="../dists.html" title="Distributions">
+<link rel="prev" href="normal_dist.html" title="Normal (Gaussian) Distribution">
+<link rel="next" href="poisson_dist.html" title="Poisson Distribution">
+</head>
+<body bgcolor="white" text="black" link="#0000FF" vlink="#840084" alink="#0000FF">
+<table cellpadding="2" width="100%"><tr>
+<td valign="top"><img alt="Boost C++ Libraries" width="277" height="86" src="../../../../../../boost.png"></td>
+<td align="center">Home</td>
+<td align="center">Libraries</td>
+<td align="center">People</td>
+<td align="center">FAQ</td>
+<td align="center">More</td>
+</tr></table>
+<hr>
+<div class="spirit-nav">
+<a accesskey="p" href="normal_dist.html"><img src="../../../../../../doc/html/images/prev.png" alt="Prev"></a><a accesskey="u" href="../dists.html"><img src="../../../../../../doc/html/images/up.png" alt="Up"></a><a accesskey="h" href="../../../../index.html"><img src="../../../../../../doc/html/images/home.png" alt="Home"></a><a accesskey="n" href="poisson_dist.html"><img src="../../../../../../doc/html/images/next.png" alt="Next"></a>
+</div>
+<div class="section" lang="en">
+<div class="titlepage"><div><div><h5 class="title">
+<a name="math_toolkit.dist.dist_ref.dists.pareto"></a><a class="link" href="pareto.html" title="Pareto Distribution"> Pareto
+          Distribution</a>
+</h5></div></div></div>
+<p>
+            
+</p>
+<pre class="programlisting"><span class="preprocessor">#include</span> <span class="special">&lt;</span><span class="identifier">boost</span><span class="special">/</span><span class="identifier">math</span><span class="special">/</span><span class="identifier">distributions</span><span class="special">/</span><span class="identifier">pareto</span><span class="special">.</span><span class="identifier">hpp</span><span class="special">&gt;</span></pre>
+<p>
+          </p>
+<pre class="programlisting"><span class="keyword">namespace</span> <span class="identifier">boost</span><span class="special">{</span> <span class="keyword">namespace</span> <span class="identifier">math</span><span class="special">{</span> 
+   
+<span class="keyword">template</span> <span class="special">&lt;</span><span class="keyword">class</span> <span class="identifier">RealType</span> <span class="special">=</span> <span class="keyword">double</span><span class="special">,</span> 
+          <span class="keyword">class</span> <a class="link" href="../../../policy.html" title="Policies">Policy</a>   <span class="special">=</span> <a class="link" href="../../../policy/pol_ref/pol_ref_ref.html" title="Policy Class Reference">policies::policy&lt;&gt;</a> <span class="special">&gt;</span>
+<span class="keyword">class</span> <span class="identifier">pareto_distribution</span><span class="special">;</span>
+
+<span class="keyword">typedef</span> <span class="identifier">pareto_distribution</span><span class="special">&lt;&gt;</span> <span class="identifier">pareto</span><span class="special">;</span>
+
+<span class="keyword">template</span> <span class="special">&lt;</span><span class="keyword">class</span> <span class="identifier">RealType</span><span class="special">,</span> <span class="keyword">class</span> <a class="link" href="../../../policy.html" title="Policies">Policy</a><span class="special">&gt;</span>
+<span class="keyword">class</span> <span class="identifier">pareto_distribution</span>
+<span class="special">{</span>
+<span class="keyword">public</span><span class="special">:</span>
+   <span class="keyword">typedef</span> <span class="identifier">RealType</span> <span class="identifier">value_type</span><span class="special">;</span>
+   <span class="comment">// Constructor:
+</span>   <span class="identifier">pareto_distribution</span><span class="special">(</span><span class="identifier">RealType</span> <span class="identifier">location</span> <span class="special">=</span> <span class="number">1</span><span class="special">,</span> <span class="identifier">RealType</span> <span class="identifier">shape</span> <span class="special">=</span> <span class="number">1</span><span class="special">)</span>
+   <span class="comment">// Accessors:
+</span>   <span class="identifier">RealType</span> <span class="identifier">location</span><span class="special">()</span><span class="keyword">const</span><span class="special">;</span>
+   <span class="identifier">RealType</span> <span class="identifier">shape</span><span class="special">()</span><span class="keyword">const</span><span class="special">;</span>
+<span class="special">};</span>
+
+<span class="special">}}</span> <span class="comment">// namespaces
+</span></pre>
+<p>
+            The <a href="http://en.wikipedia.org/wiki/pareto_distribution" target="_top">Pareto
+            distribution</a> is a continuous distribution with the <a href="http://en.wikipedia.org/wiki/Probability_density_function" target="_top">probability
+            density function (pdf)</a>:
+          </p>
+<p>
+            f(x; &#945;, &#946;) = &#945;&#946;<sup>&#945;</sup> / x<sup>&#945;+ 1</sup>
+          </p>
+<p>
+            For shape parameter &#945; &gt; 0, and location parameter &#946; &gt; 0, and &#945; &gt; 0.
+          </p>
+<p>
+            The <a href="http://mathworld.wolfram.com/paretoDistribution.html" target="_top">Pareto
+            distribution</a> often describes the larger compared to the smaller.
+            A classic example is that 80% of the wealth is owned by 20% of the population.
+          </p>
+<p>
+            The following graph illustrates how the PDF varies with the location
+            parameter &#946;:
+          </p>
+<p>
+            <span class="inlinemediaobject"><img src="../../../../../graphs/pareto_pdf1.png" align="middle"></span>
+          </p>
+<p>
+            And this graph illustrates how the PDF varies with the shape parameter
+            &#945;:
+          </p>
+<p>
+            <span class="inlinemediaobject"><img src="../../../../../graphs/pareto_pdf2.png" align="middle"></span>
+          </p>
+<a name="math_toolkit.dist.dist_ref.dists.pareto.related_distributions"></a><h5>
+<a name="id684485"></a>
+            <a class="link" href="pareto.html#math_toolkit.dist.dist_ref.dists.pareto.related_distributions">Related
+            distributions</a>
+          </h5>
+<a name="math_toolkit.dist.dist_ref.dists.pareto.member_functions"></a><h5>
+<a name="id684510"></a>
+            <a class="link" href="pareto.html#math_toolkit.dist.dist_ref.dists.pareto.member_functions">Member
+            Functions</a>
+          </h5>
+<pre class="programlisting"><span class="identifier">pareto_distribution</span><span class="special">(</span><span class="identifier">RealType</span> <span class="identifier">location</span> <span class="special">=</span> <span class="number">1</span><span class="special">,</span> <span class="identifier">RealType</span> <span class="identifier">shape</span> <span class="special">=</span> <span class="number">1</span><span class="special">);</span>
+</pre>
+<p>
+            Constructs a <a href="http://en.wikipedia.org/wiki/pareto_distribution" target="_top">pareto
+            distribution</a> with shape <span class="emphasis"><em>shape</em></span> and scale
+            <span class="emphasis"><em>scale</em></span>.
+          </p>
+<p>
+            Requires that the <span class="emphasis"><em>shape</em></span> and <span class="emphasis"><em>scale</em></span>
+            parameters are both greater than zero, otherwise calls <a class="link" href="../../../main_overview/error_handling.html#domain_error">domain_error</a>.
+          </p>
+<pre class="programlisting"><span class="identifier">RealType</span> <span class="identifier">location</span><span class="special">()</span><span class="keyword">const</span><span class="special">;</span>
+</pre>
+<p>
+            Returns the <span class="emphasis"><em>location</em></span> parameter of this distribution.
+          </p>
+<pre class="programlisting"><span class="identifier">RealType</span> <span class="identifier">shape</span><span class="special">()</span><span class="keyword">const</span><span class="special">;</span>
+</pre>
+<p>
+            Returns the <span class="emphasis"><em>shape</em></span> parameter of this distribution.
+          </p>
+<a name="math_toolkit.dist.dist_ref.dists.pareto.non_member_accessors"></a><h5>
+<a name="id684747"></a>
+            <a class="link" href="pareto.html#math_toolkit.dist.dist_ref.dists.pareto.non_member_accessors">Non-member
+            Accessors</a>
+          </h5>
+<p>
+            All the <a class="link" href="../nmp.html" title="Non-Member Properties">usual non-member
+            accessor functions</a> that are generic to all distributions are supported:
+            <a class="link" href="../nmp.html#math.dist.cdf">Cumulative Distribution Function</a>,
+            <a class="link" href="../nmp.html#math.dist.pdf">Probability Density Function</a>, <a class="link" href="../nmp.html#math.dist.quantile">Quantile</a>, <a class="link" href="../nmp.html#math.dist.hazard">Hazard
+            Function</a>, <a class="link" href="../nmp.html#math.dist.chf">Cumulative Hazard Function</a>,
+            <a class="link" href="../nmp.html#math.dist.mean">mean</a>, <a class="link" href="../nmp.html#math.dist.median">median</a>,
+            <a class="link" href="../nmp.html#math.dist.mode">mode</a>, <a class="link" href="../nmp.html#math.dist.variance">variance</a>,
+            <a class="link" href="../nmp.html#math.dist.sd">standard deviation</a>, <a class="link" href="../nmp.html#math.dist.skewness">skewness</a>,
+            <a class="link" href="../nmp.html#math.dist.kurtosis">kurtosis</a>, <a class="link" href="../nmp.html#math.dist.kurtosis_excess">kurtosis_excess</a>,
+            <a class="link" href="../nmp.html#math.dist.range">range</a> and <a class="link" href="../nmp.html#math.dist.support">support</a>.
+          </p>
+<p>
+            The supported domain of the random variable is [location, &#8734;].
+          </p>
+<a name="math_toolkit.dist.dist_ref.dists.pareto.accuracy"></a><h5>
+<a name="id684924"></a>
+            <a class="link" href="pareto.html#math_toolkit.dist.dist_ref.dists.pareto.accuracy">Accuracy</a>
+          </h5>
+<p>
+            The pareto distribution is implemented in terms of the standard library
+            <code class="computeroutput"><span class="identifier">exp</span></code> functions plus <a class="link" href="../../../special/powers/expm1.html" title="expm1">expm1</a> and as such
+            should have very low error rates except when probability is very close
+            to unity.
+          </p>
+<a name="math_toolkit.dist.dist_ref.dists.pareto.implementation"></a><h5>
+<a name="id684980"></a>
+            <a class="link" href="pareto.html#math_toolkit.dist.dist_ref.dists.pareto.implementation">Implementation</a>
+          </h5>
+<p>
+            In the following table &#945; is the shape parameter of the distribution, and
+            &#946; is its location parameter, <span class="emphasis"><em>x</em></span> is the random variate,
+            <span class="emphasis"><em>p</em></span> is the probability and its complement <span class="emphasis"><em>q
+            = 1-p</em></span>.
+          </p>
+<div class="informaltable"><table class="table">
+<colgroup>
+<col>
+<col>
+</colgroup>
+<thead><tr>
+<th>
+                  <p>
+                    Function
+                  </p>
+                  </th>
+<th>
+                  <p>
+                    Implementation Notes
+                  </p>
+                  </th>
+</tr></thead>
+<tbody>
+<tr>
+<td>
+                  <p>
+                    pdf
+                  </p>
+                  </td>
+<td>
+                  <p>
+                    Using the relation: pdf p = &#945;&#946;<sup>&#945;</sup>/x<sup>&#945; +1</sup>
+                  </p>
+                  </td>
+</tr>
+<tr>
+<td>
+                  <p>
+                    cdf
+                  </p>
+                  </td>
+<td>
+                  <p>
+                    Using the relation: cdf p = 1 - (&#946; / x)<sup>&#945;</sup>
+                  </p>
+                  </td>
+</tr>
+<tr>
+<td>
+                  <p>
+                    cdf complement
+                  </p>
+                  </td>
+<td>
+                  <p>
+                    Using the relation: q = 1 - p = -(&#946; / x)<sup>&#945;</sup>
+                  </p>
+                  </td>
+</tr>
+<tr>
+<td>
+                  <p>
+                    quantile
+                  </p>
+                  </td>
+<td>
+                  <p>
+                    Using the relation: x = &#945; / (1 - p)<sup>1/&#946;</sup>
+                  </p>
+                  </td>
+</tr>
+<tr>
+<td>
+                  <p>
+                    quantile from the complement
+                  </p>
+                  </td>
+<td>
+                  <p>
+                    Using the relation: x = &#945; / (q)<sup>1/&#946;</sup>
+                  </p>
+                  </td>
+</tr>
+<tr>
+<td>
+                  <p>
+                    mean
+                  </p>
+                  </td>
+<td>
+                  <p>
+                    &#945;&#946; / (&#946; - 1)
+                  </p>
+                  </td>
+</tr>
+<tr>
+<td>
+                  <p>
+                    variance
+                  </p>
+                  </td>
+<td>
+                  <p>
+                    &#946;&#945;<sup>2</sup> / (&#946; - 1)<sup>2</sup> (&#946; - 2)
+                  </p>
+                  </td>
+</tr>
+<tr>
+<td>
+                  <p>
+                    mode
+                  </p>
+                  </td>
+<td>
+                  <p>
+                    &#945;
+                  </p>
+                  </td>
+</tr>
+<tr>
+<td>
+                  <p>
+                    skewness
+                  </p>
+                  </td>
+<td>
+                  <p>
+                    Refer to <a href="http://mathworld.wolfram.com/paretoDistribution.html" target="_top">Weisstein,
+                    Eric W. "Pareto Distribution." From MathWorld--A Wolfram
+                    Web Resource.</a>
+                  </p>
+                  </td>
+</tr>
+<tr>
+<td>
+                  <p>
+                    kurtosis
+                  </p>
+                  </td>
+<td>
+                  <p>
+                    Refer to <a href="http://mathworld.wolfram.com/paretoDistribution.html" target="_top">Weisstein,
+                    Eric W. "Pareto Distribution." From MathWorld--A Wolfram
+                    Web Resource.</a>
+                  </p>
+                  </td>
+</tr>
+<tr>
+<td>
+                  <p>
+                    kurtosis excess
+                  </p>
+                  </td>
+<td>
+                  <p>
+                    Refer to <a href="http://mathworld.wolfram.com/paretoDistribution.html" target="_top">Weisstein,
+                    Eric W. "pareto Distribution." From MathWorld--A Wolfram
+                    Web Resource.</a>
+                  </p>
+                  </td>
+</tr>
+</tbody>
+</table></div>
+<a name="math_toolkit.dist.dist_ref.dists.pareto.references"></a><h5>
+<a name="id685351"></a>
+            <a class="link" href="pareto.html#math_toolkit.dist.dist_ref.dists.pareto.references">References</a>
+          </h5>
+<div class="itemizedlist"><ul type="disc">
+<li><a href="http://en.wikipedia.org/wiki/pareto_distribution" target="_top">Pareto
+              Distribution</a></li>
+<li><a href="http://mathworld.wolfram.com/paretoDistribution.html" target="_top">Weisstein,
+              Eric W. "Pareto Distribution." From MathWorld--A Wolfram
+              Web Resource.</a></li>
+</ul></div>
+</div>
+<table xmlns:rev="http://www.cs.rpi.edu/~gregod/boost/tools/doc/revision" width="100%"><tr>
+<td align="left"></td>
+<td align="right"><div class="copyright-footer">Copyright © 2006 , 2007, 2008 John Maddock, Paul A. Bristow, Hubert
+      Holin, Xiaogang Zhang, Bruno Lalande and Gautam Sewani<p>
+        Distributed under the Boost Software License, Version 1.0. (See accompanying
+        file LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_0.txt)
+      </p>
+</div></td>
+</tr></table>
+<hr>
+<div class="spirit-nav">
+<a accesskey="p" href="normal_dist.html"><img src="../../../../../../doc/html/images/prev.png" alt="Prev"></a><a accesskey="u" href="../dists.html"><img src="../../../../../../doc/html/images/up.png" alt="Up"></a><a accesskey="h" href="../../../../index.html"><img src="../../../../../../doc/html/images/home.png" alt="Home"></a><a accesskey="n" href="poisson_dist.html"><img src="../../../../../../doc/html/images/next.png" alt="Next"></a>
+</div>
+</body>
+</html>

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+++ sandbox/tools/auto_index/example/math/doc/sf_and_dist/html/math_toolkit/dist/dist_ref/dists/poisson_dist.html	2008-11-28 05:25:28 EST (Fri, 28 Nov 2008)
@@ -0,0 +1,341 @@
+<html>
+<head>
+<meta http-equiv="Content-Type" content="text/html; charset=ISO-8859-1">
+<title>Poisson Distribution</title>
+<link rel="stylesheet" href="../../../../boostbook.css" type="text/css">
+<meta name="generator" content="DocBook XSL Stylesheets Vsnapshot_8125">
+<link rel="home" href="../../../../index.html" title="Math Toolkit">
+<link rel="up" href="../dists.html" title="Distributions">
+<link rel="prev" href="pareto.html" title="Pareto Distribution">
+<link rel="next" href="rayleigh.html" title="Rayleigh Distribution">
+</head>
+<body bgcolor="white" text="black" link="#0000FF" vlink="#840084" alink="#0000FF">
+<table cellpadding="2" width="100%"><tr>
+<td valign="top"><img alt="Boost C++ Libraries" width="277" height="86" src="../../../../../../boost.png"></td>
+<td align="center">Home</td>
+<td align="center">Libraries</td>
+<td align="center">People</td>
+<td align="center">FAQ</td>
+<td align="center">More</td>
+</tr></table>
+<hr>
+<div class="spirit-nav">
+<a accesskey="p" href="pareto.html"><img src="../../../../../../doc/html/images/prev.png" alt="Prev"></a><a accesskey="u" href="../dists.html"><img src="../../../../../../doc/html/images/up.png" alt="Up"></a><a accesskey="h" href="../../../../index.html"><img src="../../../../../../doc/html/images/home.png" alt="Home"></a><a accesskey="n" href="rayleigh.html"><img src="../../../../../../doc/html/images/next.png" alt="Next"></a>
+</div>
+<div class="section" lang="en">
+<div class="titlepage"><div><div><h5 class="title">
+<a name="math_toolkit.dist.dist_ref.dists.poisson_dist"></a><a class="link" href="poisson_dist.html" title="Poisson Distribution"> Poisson
+          Distribution</a>
+</h5></div></div></div>
+<p>
+            
+</p>
+<pre class="programlisting"><span class="preprocessor">#include</span> <span class="special">&lt;</span><span class="identifier">boost</span><span class="special">/</span><span class="identifier">math</span><span class="special">/</span><span class="identifier">distributions</span><span class="special">/</span><span class="identifier">poisson</span><span class="special">.</span><span class="identifier">hpp</span><span class="special">&gt;</span></pre>
+<p>
+          </p>
+<pre class="programlisting"><span class="keyword">namespace</span> <span class="identifier">boost</span> <span class="special">{</span> <span class="keyword">namespace</span> <span class="identifier">math</span> <span class="special">{</span>
+
+<span class="keyword">template</span> <span class="special">&lt;</span><span class="keyword">class</span> <span class="identifier">RealType</span> <span class="special">=</span> <span class="keyword">double</span><span class="special">,</span> 
+          <span class="keyword">class</span> <a class="link" href="../../../policy.html" title="Policies">Policy</a>   <span class="special">=</span> <a class="link" href="../../../policy/pol_ref/pol_ref_ref.html" title="Policy Class Reference">policies::policy&lt;&gt;</a> <span class="special">&gt;</span>
+<span class="keyword">class</span> <span class="identifier">poisson_distribution</span><span class="special">;</span>
+
+<span class="keyword">typedef</span> <span class="identifier">poisson_distribution</span><span class="special">&lt;&gt;</span> <span class="identifier">poisson</span><span class="special">;</span>
+
+<span class="keyword">template</span> <span class="special">&lt;</span><span class="keyword">class</span> <span class="identifier">RealType</span><span class="special">,</span> <span class="keyword">class</span> <a class="link" href="../../../policy.html" title="Policies">Policy</a><span class="special">&gt;</span>
+<span class="keyword">class</span> <span class="identifier">poisson_distribution</span>
+<span class="special">{</span> 
+<span class="keyword">public</span><span class="special">:</span>
+  <span class="keyword">typedef</span> <span class="identifier">RealType</span> <span class="identifier">value_type</span><span class="special">;</span>
+  <span class="keyword">typedef</span> <span class="identifier">Policy</span>   <span class="identifier">policy_type</span><span class="special">;</span>
+  
+  <span class="identifier">poisson_distribution</span><span class="special">(</span><span class="identifier">RealType</span> <span class="identifier">mean</span> <span class="special">=</span> <span class="number">1</span><span class="special">);</span> <span class="comment">// Constructor.
+</span>  <span class="identifier">RealType</span> <span class="identifier">mean</span><span class="special">()</span><span class="keyword">const</span><span class="special">;</span> <span class="comment">// Accessor.
+</span><span class="special">}</span>
+ 
+<span class="special">}}</span> <span class="comment">// namespaces boost::math
+</span></pre>
+<p>
+            The <a href="http://en.wikipedia.org/wiki/Poisson_distribution" target="_top">Poisson
+            distribution</a> is a well-known statistical discrete distribution.
+            It expresses the probability of a number of events (or failures, arrivals,
+            occurrences ...) occurring in a fixed period of time, provided these
+            events occur with a known mean rate &#955;
+(events/time), and are independent
+            of the time since the last event.
+          </p>
+<p>
+            The distribution was discovered by Simé on-Denis Poisson (1781 to 1840).
+          </p>
+<p>
+            It has the Probability Mass Function:
+          </p>
+<p>
+            <span class="inlinemediaobject"><img src="../../../../../equations/poisson_ref1.png"></span>
+          </p>
+<p>
+            for k events, with an expected number of events &#955;.
+          </p>
+<p>
+            The following graph illustrates how the PDF varies with the parameter
+            &#955;:
+          </p>
+<p>
+            <span class="inlinemediaobject"><img src="../../../../../graphs/poisson_pdf_1.png" align="middle"></span>
+          </p>
+<p>
+            </p>
+<div class="caution"><table border="0" summary="Caution">
+<tr>
+<td rowspan="2" align="center" valign="top" width="25"><img alt="[Caution]" src="../../../../../../doc/html/images/caution.png"></td>
+<th align="left">Caution</th>
+</tr>
+<tr><td align="left" valign="top">
+<p>
+                The Poisson distribution is a discrete distribution: internally functions
+                like the <code class="computeroutput"><span class="identifier">cdf</span></code> and
+                <code class="computeroutput"><span class="identifier">pdf</span></code> are treated "as
+                if" they are continuous functions, but in reality the results
+                returned from these functions only have meaning if an integer value
+                is provided for the random variate argument.
+              </p>
+<p>
+                The quantile function will by default return an integer result that
+                has been <span class="emphasis"><em>rounded outwards</em></span>. That is to say lower
+                quantiles (where the probability is less than 0.5) are rounded downward,
+                and upper quantiles (where the probability is greater than 0.5) are
+                rounded upwards. This behaviour ensures that if an X% quantile is
+                requested, then <span class="emphasis"><em>at least</em></span> the requested coverage
+                will be present in the central region, and <span class="emphasis"><em>no more than</em></span>
+                the requested coverage will be present in the tails.
+              </p>
+<p>
+                This behaviour can be changed so that the quantile functions are
+                rounded differently, or even return a real-valued result using <a class="link" href="../../../policy/pol_overview.html" title="Policy Overview">Policies</a>. It is
+                strongly recommended that you read the tutorial <a class="link" href="../../../policy/pol_tutorial/understand_dis_quant.html" title="Understanding Quantiles of Discrete Distributions">Understanding
+                Quantiles of Discrete Distributions</a> before using the quantile
+                function on the Poisson distribution. The <a class="link" href="../../../policy/pol_ref/discrete_quant_ref.html" title="Discrete Quantile Policies">reference
+                docs</a> describe how to change the rounding policy for these
+                distributions.
+              </p>
+</td></tr>
+</table></div>
+<p>
+          </p>
+<a name="math_toolkit.dist.dist_ref.dists.poisson_dist.member_functions"></a><h5>
+<a name="id686138"></a>
+            <a class="link" href="poisson_dist.html#math_toolkit.dist.dist_ref.dists.poisson_dist.member_functions">Member
+            Functions</a>
+          </h5>
+<pre class="programlisting"><span class="identifier">poisson_distribution</span><span class="special">(</span><span class="identifier">RealType</span> <span class="identifier">mean</span> <span class="special">=</span> <span class="number">1</span><span class="special">);</span>
+</pre>
+<p>
+            Constructs a poisson distribution with mean <span class="emphasis"><em>mean</em></span>.
+          </p>
+<pre class="programlisting"><span class="identifier">RealType</span> <span class="identifier">mean</span><span class="special">()</span><span class="keyword">const</span><span class="special">;</span>
+</pre>
+<p>
+            Returns the <span class="emphasis"><em>mean</em></span> of this distribution.
+          </p>
+<a name="math_toolkit.dist.dist_ref.dists.poisson_dist.non_member_accessors"></a><h5>
+<a name="id686266"></a>
+            <a class="link" href="poisson_dist.html#math_toolkit.dist.dist_ref.dists.poisson_dist.non_member_accessors">Non-member
+            Accessors</a>
+          </h5>
+<p>
+            All the <a class="link" href="../nmp.html" title="Non-Member Properties">usual non-member
+            accessor functions</a> that are generic to all distributions are supported:
+            <a class="link" href="../nmp.html#math.dist.cdf">Cumulative Distribution Function</a>,
+            <a class="link" href="../nmp.html#math.dist.pdf">Probability Density Function</a>, <a class="link" href="../nmp.html#math.dist.quantile">Quantile</a>, <a class="link" href="../nmp.html#math.dist.hazard">Hazard
+            Function</a>, <a class="link" href="../nmp.html#math.dist.chf">Cumulative Hazard Function</a>,
+            <a class="link" href="../nmp.html#math.dist.mean">mean</a>, <a class="link" href="../nmp.html#math.dist.median">median</a>,
+            <a class="link" href="../nmp.html#math.dist.mode">mode</a>, <a class="link" href="../nmp.html#math.dist.variance">variance</a>,
+            <a class="link" href="../nmp.html#math.dist.sd">standard deviation</a>, <a class="link" href="../nmp.html#math.dist.skewness">skewness</a>,
+            <a class="link" href="../nmp.html#math.dist.kurtosis">kurtosis</a>, <a class="link" href="../nmp.html#math.dist.kurtosis_excess">kurtosis_excess</a>,
+            <a class="link" href="../nmp.html#math.dist.range">range</a> and <a class="link" href="../nmp.html#math.dist.support">support</a>.
+          </p>
+<p>
+            The domain of the random variable is [0, &#8734;].
+          </p>
+<a name="math_toolkit.dist.dist_ref.dists.poisson_dist.accuracy"></a><h5>
+<a name="id686440"></a>
+            <a class="link" href="poisson_dist.html#math_toolkit.dist.dist_ref.dists.poisson_dist.accuracy">Accuracy</a>
+          </h5>
+<p>
+            The Poisson distribution is implemented in terms of the incomplete gamma
+            functions <a class="link" href="../../../special/sf_gamma/igamma.html" title="Incomplete Gamma Functions">gamma_p</a>
+            and <a class="link" href="../../../special/sf_gamma/igamma.html" title="Incomplete Gamma Functions">gamma_q</a>
+            and as such should have low error rates: but refer to the documentation
+            of those functions for more information. The quantile and its complement
+            use the inverse gamma functions and are therefore probably slightly less
+            accurate: this is because the inverse gamma functions are implemented
+            using an iterative method with a lower tolerance to avoid excessive computation.
+          </p>
+<a name="math_toolkit.dist.dist_ref.dists.poisson_dist.implementation"></a><h5>
+<a name="id686496"></a>
+            <a class="link" href="poisson_dist.html#math_toolkit.dist.dist_ref.dists.poisson_dist.implementation">Implementation</a>
+          </h5>
+<p>
+            In the following table &#955; is the mean of the distribution, <span class="emphasis"><em>k</em></span>
+            is the random variable, <span class="emphasis"><em>p</em></span> is the probability and
+            <span class="emphasis"><em>q = 1-p</em></span>.
+          </p>
+<div class="informaltable"><table class="table">
+<colgroup>
+<col>
+<col>
+</colgroup>
+<thead><tr>
+<th>
+                  <p>
+                    Function
+                  </p>
+                  </th>
+<th>
+                  <p>
+                    Implementation Notes
+                  </p>
+                  </th>
+</tr></thead>
+<tbody>
+<tr>
+<td>
+                  <p>
+                    pdf
+                  </p>
+                  </td>
+<td>
+                  <p>
+                    Using the relation: pdf = e<sup>-&#955;</sup> &#955;<sup>k</sup> / k!
+                  </p>
+                  </td>
+</tr>
+<tr>
+<td>
+                  <p>
+                    cdf
+                  </p>
+                  </td>
+<td>
+                  <p>
+                    Using the relation: p = &#915;(k+1, &#955;) / k! = <a class="link" href="../../../special/sf_gamma/igamma.html" title="Incomplete Gamma Functions">gamma_q</a>(k+1,
+                    &#955;)
+                  </p>
+                  </td>
+</tr>
+<tr>
+<td>
+                  <p>
+                    cdf complement
+                  </p>
+                  </td>
+<td>
+                  <p>
+                    Using the relation: q = <a class="link" href="../../../special/sf_gamma/igamma.html" title="Incomplete Gamma Functions">gamma_p</a>(k+1,
+                    &#955;)
+                  </p>
+                  </td>
+</tr>
+<tr>
+<td>
+                  <p>
+                    quantile
+                  </p>
+                  </td>
+<td>
+                  <p>
+                    Using the relation: k = <a class="link" href="../../../special/sf_gamma/igamma_inv.html" title="Incomplete Gamma Function Inverses">gamma_q_inva</a>(&#955;,
+                    p) - 1
+                  </p>
+                  </td>
+</tr>
+<tr>
+<td>
+                  <p>
+                    quantile from the complement
+                  </p>
+                  </td>
+<td>
+                  <p>
+                    Using the relation: k = <a class="link" href="../../../special/sf_gamma/igamma_inv.html" title="Incomplete Gamma Function Inverses">gamma_p_inva</a>(&#955;,
+                    q) - 1
+                  </p>
+                  </td>
+</tr>
+<tr>
+<td>
+                  <p>
+                    mean
+                  </p>
+                  </td>
+<td>
+                  <p>
+                    &#955;
+                  </p>
+                  </td>
+</tr>
+<tr>
+<td>
+                  <p>
+                    mode
+                  </p>
+                  </td>
+<td>
+                  <p>
+                    floor (&#955;) or &#8970;&#955;&#8971;
+                  </p>
+                  </td>
+</tr>
+<tr>
+<td>
+                  <p>
+                    skewness
+                  </p>
+                  </td>
+<td>
+                  <p>
+                    1/&#8730;&#955;
+                  </p>
+                  </td>
+</tr>
+<tr>
+<td>
+                  <p>
+                    kurtosis
+                  </p>
+                  </td>
+<td>
+                  <p>
+                    3 + 1/&#955;
+                  </p>
+                  </td>
+</tr>
+<tr>
+<td>
+                  <p>
+                    kurtosis excess
+                  </p>
+                  </td>
+<td>
+                  <p>
+                    1/&#955;
+                  </p>
+                  </td>
+</tr>
+</tbody>
+</table></div>
+</div>
+<table xmlns:rev="http://www.cs.rpi.edu/~gregod/boost/tools/doc/revision" width="100%"><tr>
+<td align="left"></td>
+<td align="right"><div class="copyright-footer">Copyright © 2006 , 2007, 2008 John Maddock, Paul A. Bristow, Hubert
+      Holin, Xiaogang Zhang, Bruno Lalande and Gautam Sewani<p>
+        Distributed under the Boost Software License, Version 1.0. (See accompanying
+        file LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_0.txt)
+      </p>
+</div></td>
+</tr></table>
+<hr>
+<div class="spirit-nav">
+<a accesskey="p" href="pareto.html"><img src="../../../../../../doc/html/images/prev.png" alt="Prev"></a><a accesskey="u" href="../dists.html"><img src="../../../../../../doc/html/images/up.png" alt="Up"></a><a accesskey="h" href="../../../../index.html"><img src="../../../../../../doc/html/images/home.png" alt="Home"></a><a accesskey="n" href="rayleigh.html"><img src="../../../../../../doc/html/images/next.png" alt="Next"></a>
+</div>
+</body>
+</html>

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+++ sandbox/tools/auto_index/example/math/doc/sf_and_dist/html/math_toolkit/dist/dist_ref/dists/rayleigh.html	2008-11-28 05:25:28 EST (Fri, 28 Nov 2008)
@@ -0,0 +1,347 @@
+<html>
+<head>
+<meta http-equiv="Content-Type" content="text/html; charset=ISO-8859-1">
+<title>Rayleigh Distribution</title>
+<link rel="stylesheet" href="../../../../boostbook.css" type="text/css">
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+<link rel="home" href="../../../../index.html" title="Math Toolkit">
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+</div>
+<div class="section" lang="en">
+<div class="titlepage"><div><div><h5 class="title">
+<a name="math_toolkit.dist.dist_ref.dists.rayleigh"></a><a class="link" href="rayleigh.html" title="Rayleigh Distribution"> Rayleigh
+          Distribution</a>
+</h5></div></div></div>
+<p>
+            
+</p>
+<pre class="programlisting"><span class="preprocessor">#include</span> <span class="special">&lt;</span><span class="identifier">boost</span><span class="special">/</span><span class="identifier">math</span><span class="special">/</span><span class="identifier">distributions</span><span class="special">/</span><span class="identifier">rayleigh</span><span class="special">.</span><span class="identifier">hpp</span><span class="special">&gt;</span></pre>
+<p>
+          </p>
+<pre class="programlisting"><span class="keyword">namespace</span> <span class="identifier">boost</span><span class="special">{</span> <span class="keyword">namespace</span> <span class="identifier">math</span><span class="special">{</span> 
+   
+<span class="keyword">template</span> <span class="special">&lt;</span><span class="keyword">class</span> <span class="identifier">RealType</span> <span class="special">=</span> <span class="keyword">double</span><span class="special">,</span> 
+          <span class="keyword">class</span> <a class="link" href="../../../policy.html" title="Policies">Policy</a>   <span class="special">=</span> <a class="link" href="../../../policy/pol_ref/pol_ref_ref.html" title="Policy Class Reference">policies::policy&lt;&gt;</a> <span class="special">&gt;</span>
+<span class="keyword">class</span> <span class="identifier">rayleigh_distribution</span><span class="special">;</span>
+
+<span class="keyword">typedef</span> <span class="identifier">rayleigh_distribution</span><span class="special">&lt;&gt;</span> <span class="identifier">rayleigh</span><span class="special">;</span>
+
+<span class="keyword">template</span> <span class="special">&lt;</span><span class="keyword">class</span> <span class="identifier">RealType</span><span class="special">,</span> <span class="keyword">class</span> <a class="link" href="../../../policy.html" title="Policies">Policy</a><span class="special">&gt;</span>
+<span class="keyword">class</span> <span class="identifier">rayleigh_distribution</span>
+<span class="special">{</span>
+<span class="keyword">public</span><span class="special">:</span>
+   <span class="keyword">typedef</span> <span class="identifier">RealType</span> <span class="identifier">value_type</span><span class="special">;</span>
+   <span class="keyword">typedef</span> <span class="identifier">Policy</span>   <span class="identifier">policy_type</span><span class="special">;</span>
+   <span class="comment">// Construct:
+</span>   <span class="identifier">rayleigh_distribution</span><span class="special">(</span><span class="identifier">RealType</span> <span class="identifier">sigma</span> <span class="special">=</span> <span class="number">1</span><span class="special">)</span>
+   <span class="comment">// Accessors:
+</span>   <span class="identifier">RealType</span> <span class="identifier">sigma</span><span class="special">()</span><span class="keyword">const</span><span class="special">;</span>
+<span class="special">};</span>
+
+<span class="special">}}</span> <span class="comment">// namespaces
+</span></pre>
+<p>
+            The <a href="http://en.wikipedia.org/wiki/Rayleigh_distribution" target="_top">Rayleigh
+            distribution</a> is a continuous distribution with the <a href="http://en.wikipedia.org/wiki/Probability_density_function" target="_top">probability
+            density function</a>:
+          </p>
+<p>
+            f(x; sigma) = x * exp(-x<sup>2</sup>/2 &#963;<sup>2</sup>) / &#963;<sup>2</sup>
+          </p>
+<p>
+            For sigma parameter &#963; &gt; 0, and x &gt; 0.
+          </p>
+<p>
+            The Rayleigh distribution is often used where two orthogonal components
+            have an absolute value, for example, wind velocity and direction may
+            be combined to yield a wind speed, or real and imaginary components may
+            have absolute values that are Rayleigh distributed.
+          </p>
+<p>
+            The following graph illustrates how the Probability density Function(pdf)
+            varies with the shape parameter &#963;:
+          </p>
+<p>
+            <span class="inlinemediaobject"><img src="../../../../../graphs/rayleigh_pdf.png" align="middle"></span>
+          </p>
+<p>
+            and the Cumulative Distribution Function (cdf)
+          </p>
+<p>
+            <span class="inlinemediaobject"><img src="../../../../../graphs/rayleigh_cdf.png" align="middle"></span>
+          </p>
+<a name="math_toolkit.dist.dist_ref.dists.rayleigh.related_distributions"></a><h5>
+<a name="id687452"></a>
+            <a class="link" href="rayleigh.html#math_toolkit.dist.dist_ref.dists.rayleigh.related_distributions">Related
+            distributions</a>
+          </h5>
+<p>
+            The absolute value of two independent normal distributions X and Y, &#8730; (X<sup>2</sup> +
+            Y<sup>2</sup>) is a Rayleigh distribution.
+          </p>
+<p>
+            The Chi,
+            Rice
+            and Weibull
+            distributions are generalizations of the <a href="http://en.wikipedia.org/wiki/Rayleigh_distribution" target="_top">Rayleigh
+            distribution</a>.
+          </p>
+<a name="math_toolkit.dist.dist_ref.dists.rayleigh.member_functions"></a><h5>
+<a name="id687530"></a>
+            <a class="link" href="rayleigh.html#math_toolkit.dist.dist_ref.dists.rayleigh.member_functions">Member
+            Functions</a>
+          </h5>
+<pre class="programlisting"><span class="identifier">rayleigh_distribution</span><span class="special">(</span><span class="identifier">RealType</span> <span class="identifier">sigma</span> <span class="special">=</span> <span class="number">1</span><span class="special">);</span>
+</pre>
+<p>
+            Constructs a <a href="http://en.wikipedia.org/wiki/Rayleigh_distribution" target="_top">Rayleigh
+            distribution</a> with &#963; <span class="emphasis"><em>sigma</em></span>.
+          </p>
+<p>
+            Requires that the &#963; parameter is greater than zero, otherwise calls <a class="link" href="../../../main_overview/error_handling.html#domain_error">domain_error</a>.
+          </p>
+<pre class="programlisting"><span class="identifier">RealType</span> <span class="identifier">sigma</span><span class="special">()</span><span class="keyword">const</span><span class="special">;</span>
+</pre>
+<p>
+            Returns the <span class="emphasis"><em>sigma</em></span> parameter of this distribution.
+          </p>
+<a name="math_toolkit.dist.dist_ref.dists.rayleigh.non_member_accessors"></a><h5>
+<a name="id687680"></a>
+            <a class="link" href="rayleigh.html#math_toolkit.dist.dist_ref.dists.rayleigh.non_member_accessors">Non-member
+            Accessors</a>
+          </h5>
+<p>
+            All the <a class="link" href="../nmp.html" title="Non-Member Properties">usual non-member
+            accessor functions</a> that are generic to all distributions are supported:
+            <a class="link" href="../nmp.html#math.dist.cdf">Cumulative Distribution Function</a>,
+            <a class="link" href="../nmp.html#math.dist.pdf">Probability Density Function</a>, <a class="link" href="../nmp.html#math.dist.quantile">Quantile</a>, <a class="link" href="../nmp.html#math.dist.hazard">Hazard
+            Function</a>, <a class="link" href="../nmp.html#math.dist.chf">Cumulative Hazard Function</a>,
+            <a class="link" href="../nmp.html#math.dist.mean">mean</a>, <a class="link" href="../nmp.html#math.dist.median">median</a>,
+            <a class="link" href="../nmp.html#math.dist.mode">mode</a>, <a class="link" href="../nmp.html#math.dist.variance">variance</a>,
+            <a class="link" href="../nmp.html#math.dist.sd">standard deviation</a>, <a class="link" href="../nmp.html#math.dist.skewness">skewness</a>,
+            <a class="link" href="../nmp.html#math.dist.kurtosis">kurtosis</a>, <a class="link" href="../nmp.html#math.dist.kurtosis_excess">kurtosis_excess</a>,
+            <a class="link" href="../nmp.html#math.dist.range">range</a> and <a class="link" href="../nmp.html#math.dist.support">support</a>.
+          </p>
+<p>
+            The domain of the random variable is [0, max_value].
+          </p>
+<a name="math_toolkit.dist.dist_ref.dists.rayleigh.accuracy"></a><h5>
+<a name="id687857"></a>
+            <a class="link" href="rayleigh.html#math_toolkit.dist.dist_ref.dists.rayleigh.accuracy">Accuracy</a>
+          </h5>
+<p>
+            The Rayleigh distribution is implemented in terms of the standard library
+            <code class="computeroutput"><span class="identifier">sqrt</span></code> and <code class="computeroutput"><span class="identifier">exp</span></code> and as such should have very low
+            error rates. Some constants such as skewness and kurtosis were calculated
+            using NTL RR type with 150-bit accuracy, about 50 decimal digits.
+          </p>
+<a name="math_toolkit.dist.dist_ref.dists.rayleigh.implementation"></a><h5>
+<a name="id687916"></a>
+            <a class="link" href="rayleigh.html#math_toolkit.dist.dist_ref.dists.rayleigh.implementation">Implementation</a>
+          </h5>
+<p>
+            In the following table &#963; is the sigma parameter of the distribution, <span class="emphasis"><em>x</em></span>
+            is the random variate, <span class="emphasis"><em>p</em></span> is the probability and
+            <span class="emphasis"><em>q = 1-p</em></span>.
+          </p>
+<div class="informaltable"><table class="table">
+<colgroup>
+<col>
+<col>
+</colgroup>
+<thead><tr>
+<th>
+                  <p>
+                    Function
+                  </p>
+                  </th>
+<th>
+                  <p>
+                    Implementation Notes
+                  </p>
+                  </th>
+</tr></thead>
+<tbody>
+<tr>
+<td>
+                  <p>
+                    pdf
+                  </p>
+                  </td>
+<td>
+                  <p>
+                    Using the relation: pdf = x * exp(-x<sup>2</sup>)/2 &#963;<sup>2</sup>
+                  </p>
+                  </td>
+</tr>
+<tr>
+<td>
+                  <p>
+                    cdf
+                  </p>
+                  </td>
+<td>
+                  <p>
+                    Using the relation: p = 1 - exp(-x<sup>2</sup>/2) &#963;<sup>2</sup> = -<a class="link" href="../../../special/powers/expm1.html" title="expm1">expm1</a>(-x<sup>2</sup>/2)
+                    &#963;<sup>2</sup>
+                  </p>
+                  </td>
+</tr>
+<tr>
+<td>
+                  <p>
+                    cdf complement
+                  </p>
+                  </td>
+<td>
+                  <p>
+                    Using the relation: q = exp(-x<sup>2</sup>/ 2) * &#963;<sup>2</sup>
+                  </p>
+                  </td>
+</tr>
+<tr>
+<td>
+                  <p>
+                    quantile
+                  </p>
+                  </td>
+<td>
+                  <p>
+                    Using the relation: x = sqrt(-2 * &#963; <sup>2</sup>) * log(1 - p)) = sqrt(-2
+                    * &#963; <sup>2</sup>) * <a class="link" href="../../../special/powers/log1p.html" title="log1p">log1p</a>(-p))
+                  </p>
+                  </td>
+</tr>
+<tr>
+<td>
+                  <p>
+                    quantile from the complement
+                  </p>
+                  </td>
+<td>
+                  <p>
+                    Using the relation: x = sqrt(-2 * &#963; <sup>2</sup>) * log(q))
+                  </p>
+                  </td>
+</tr>
+<tr>
+<td>
+                  <p>
+                    mean
+                  </p>
+                  </td>
+<td>
+                  <p>
+                    &#963; * sqrt(&#960;/2)
+                  </p>
+                  </td>
+</tr>
+<tr>
+<td>
+                  <p>
+                    variance
+                  </p>
+                  </td>
+<td>
+                  <p>
+                    &#963;<sup>2</sup> * (4 - &#960;/2)
+                  </p>
+                  </td>
+</tr>
+<tr>
+<td>
+                  <p>
+                    mode
+                  </p>
+                  </td>
+<td>
+                  <p>
+                    &#963;
+                  </p>
+                  </td>
+</tr>
+<tr>
+<td>
+                  <p>
+                    skewness
+                  </p>
+                  </td>
+<td>
+                  <p>
+                    Constant from <a href="http://mathworld.wolfram.com/RayleighDistribution.html" target="_top">Weisstein,
+                    Eric W. "Weibull Distribution." From MathWorld--A Wolfram
+                    Web Resource.</a>
+                  </p>
+                  </td>
+</tr>
+<tr>
+<td>
+                  <p>
+                    kurtosis
+                  </p>
+                  </td>
+<td>
+                  <p>
+                    Constant from <a href="http://mathworld.wolfram.com/RayleighDistribution.html" target="_top">Weisstein,
+                    Eric W. "Weibull Distribution." From MathWorld--A Wolfram
+                    Web Resource.</a>
+                  </p>
+                  </td>
+</tr>
+<tr>
+<td>
+                  <p>
+                    kurtosis excess
+                  </p>
+                  </td>
+<td>
+                  <p>
+                    Constant from <a href="http://mathworld.wolfram.com/RayleighDistribution.html" target="_top">Weisstein,
+                    Eric W. "Weibull Distribution." From MathWorld--A Wolfram
+                    Web Resource.</a>
+                  </p>
+                  </td>
+</tr>
+</tbody>
+</table></div>
+<a name="math_toolkit.dist.dist_ref.dists.rayleigh.references"></a><h5>
+<a name="id688321"></a>
+            <a class="link" href="rayleigh.html#math_toolkit.dist.dist_ref.dists.rayleigh.references">References</a>
+          </h5>
+<div class="itemizedlist"><ul type="disc">
+<li>http://en.wikipedia.org/wiki/Rayleigh_distribution</li>
+<li><a href="http://mathworld.wolfram.com/RayleighDistribution.html" target="_top">Weisstein,
+              Eric W. "Rayleigh Distribution." From MathWorld--A Wolfram
+              Web Resource.</a></li>
+</ul></div>
+</div>
+<table xmlns:rev="http://www.cs.rpi.edu/~gregod/boost/tools/doc/revision" width="100%"><tr>
+<td align="left"></td>
+<td align="right"><div class="copyright-footer">Copyright © 2006 , 2007, 2008 John Maddock, Paul A. Bristow, Hubert
+      Holin, Xiaogang Zhang, Bruno Lalande and Gautam Sewani<p>
+        Distributed under the Boost Software License, Version 1.0. (See accompanying
+        file LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_0.txt)
+      </p>
+</div></td>
+</tr></table>
+<hr>
+<div class="spirit-nav">
+<a accesskey="p" href="poisson_dist.html"><img src="../../../../../../doc/html/images/prev.png" alt="Prev"></a><a accesskey="u" href="../dists.html"><img src="../../../../../../doc/html/images/up.png" alt="Up"></a><a accesskey="h" href="../../../../index.html"><img src="../../../../../../doc/html/images/home.png" alt="Home"></a><a accesskey="n" href="students_t_dist.html"><img src="../../../../../../doc/html/images/next.png" alt="Next"></a>
+</div>
+</body>
+</html>

Added: sandbox/tools/auto_index/example/math/doc/sf_and_dist/html/math_toolkit/dist/dist_ref/dists/students_t_dist.html
==============================================================================
--- (empty file)
+++ sandbox/tools/auto_index/example/math/doc/sf_and_dist/html/math_toolkit/dist/dist_ref/dists/students_t_dist.html	2008-11-28 05:25:28 EST (Fri, 28 Nov 2008)
@@ -0,0 +1,423 @@
+<html>
+<head>
+<meta http-equiv="Content-Type" content="text/html; charset=ISO-8859-1">
+<title>Students t Distribution</title>
+<link rel="stylesheet" href="../../../../boostbook.css" type="text/css">
+<meta name="generator" content="DocBook XSL Stylesheets Vsnapshot_8125">
+<link rel="home" href="../../../../index.html" title="Math Toolkit">
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+<link rel="next" href="triangular_dist.html" title="Triangular Distribution">
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+<table cellpadding="2" width="100%"><tr>
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+<td align="center">Home</td>
+<td align="center">Libraries</td>
+<td align="center">People</td>
+<td align="center">FAQ</td>
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+</tr></table>
+<hr>
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+<a accesskey="p" href="rayleigh.html"><img src="../../../../../../doc/html/images/prev.png" alt="Prev"></a><a accesskey="u" href="../dists.html"><img src="../../../../../../doc/html/images/up.png" alt="Up"></a><a accesskey="h" href="../../../../index.html"><img src="../../../../../../doc/html/images/home.png" alt="Home"></a><a accesskey="n" href="triangular_dist.html"><img src="../../../../../../doc/html/images/next.png" alt="Next"></a>
+</div>
+<div class="section" lang="en">
+<div class="titlepage"><div><div><h5 class="title">
+<a name="math_toolkit.dist.dist_ref.dists.students_t_dist"></a><a class="link" href="students_t_dist.html" title="Students t Distribution">
+          Students t Distribution</a>
+</h5></div></div></div>
+<p>
+            
+</p>
+<pre class="programlisting"><span class="preprocessor">#include</span> <span class="special">&lt;</span><span class="identifier">boost</span><span class="special">/</span><span class="identifier">math</span><span class="special">/</span><span class="identifier">distributions</span><span class="special">/</span><span class="identifier">students_t</span><span class="special">.</span><span class="identifier">hpp</span><span class="special">&gt;</span></pre>
+<p>
+          </p>
+<pre class="programlisting"><span class="keyword">namespace</span> <span class="identifier">boost</span><span class="special">{</span> <span class="keyword">namespace</span> <span class="identifier">math</span><span class="special">{</span> 
+   
+<span class="keyword">template</span> <span class="special">&lt;</span><span class="keyword">class</span> <span class="identifier">RealType</span> <span class="special">=</span> <span class="keyword">double</span><span class="special">,</span> 
+          <span class="keyword">class</span> <a class="link" href="../../../policy.html" title="Policies">Policy</a>   <span class="special">=</span> <a class="link" href="../../../policy/pol_ref/pol_ref_ref.html" title="Policy Class Reference">policies::policy&lt;&gt;</a> <span class="special">&gt;</span>
+<span class="keyword">class</span> <span class="identifier">students_t_distribution</span><span class="special">;</span>
+
+<span class="keyword">typedef</span> <span class="identifier">students_t_distribution</span><span class="special">&lt;&gt;</span> <span class="identifier">students_t</span><span class="special">;</span>
+
+<span class="keyword">template</span> <span class="special">&lt;</span><span class="keyword">class</span> <span class="identifier">RealType</span><span class="special">,</span> <span class="keyword">class</span> <a class="link" href="../../../policy.html" title="Policies">Policy</a><span class="special">&gt;</span>
+<span class="keyword">class</span> <span class="identifier">students_t_distribution</span>
+<span class="special">{</span>
+   <span class="keyword">typedef</span> <span class="identifier">RealType</span> <span class="identifier">value_type</span><span class="special">;</span>
+   <span class="keyword">typedef</span> <span class="identifier">Policy</span>   <span class="identifier">policy_type</span><span class="special">;</span>
+   
+   <span class="comment">// Construct:
+</span>   <span class="identifier">students_t_distribution</span><span class="special">(</span><span class="keyword">const</span> <span class="identifier">RealType</span><span class="special">&amp;</span> <span class="identifier">v</span><span class="special">);</span>
+   
+   <span class="comment">// Accessor:
+</span>   <span class="identifier">RealType</span> <span class="identifier">degrees_of_freedom</span><span class="special">()</span><span class="keyword">const</span><span class="special">;</span>
+   
+   <span class="comment">// degrees of freedom estimation:
+</span>   <span class="keyword">static</span> <span class="identifier">RealType</span> <span class="identifier">find_degrees_of_freedom</span><span class="special">(</span>
+      <span class="identifier">RealType</span> <span class="identifier">difference_from_mean</span><span class="special">,</span>
+      <span class="identifier">RealType</span> <span class="identifier">alpha</span><span class="special">,</span>
+      <span class="identifier">RealType</span> <span class="identifier">beta</span><span class="special">,</span>
+      <span class="identifier">RealType</span> <span class="identifier">sd</span><span class="special">,</span>
+      <span class="identifier">RealType</span> <span class="identifier">hint</span> <span class="special">=</span> <span class="number">100</span><span class="special">);</span>
+<span class="special">};</span>
+
+<span class="special">}}</span> <span class="comment">// namespaces
+</span></pre>
+<p>
+            A statistical distribution published by William Gosset in 1908. His employer,
+            Guinness Breweries, required him to publish under a pseudonym, so he
+            chose "Student". Given N independent measurements, let
+          </p>
+<p>
+            <span class="inlinemediaobject"><img src="../../../../../equations/students_t_dist.png"></span>
+          </p>
+<p>
+            where <span class="emphasis"><em>M</em></span> is the population mean,<span class="emphasis"><em>&#956;</em></span>
+            is the sample mean, and <span class="emphasis"><em>s</em></span> is the sample variance.
+          </p>
+<p>
+            Student's t-distribution is defined as the distribution of the random
+            variable t which is - very loosely - the "best" that we can
+            do not knowing the true standard deviation of the sample. It has the
+            PDF:
+          </p>
+<p>
+            <span class="inlinemediaobject"><img src="../../../../../equations/students_t_ref1.png"></span>
+          </p>
+<p>
+            The Student's t-distribution takes a single parameter: the number of
+            degrees of freedom of the sample. When the degrees of freedom is <span class="emphasis"><em>one</em></span>
+            then this distribution is the same as the Cauchy-distribution. As the
+            number of degrees of freedom tends towards infinity, then this distribution
+            approaches the normal-distribution. The following graph illustrates how
+            the PDF varies with the degrees of freedom &#957;:
+          </p>
+<p>
+            <span class="inlinemediaobject"><img src="../../../../../graphs/students_t_pdf.png" align="middle"></span>
+          </p>
+<a name="math_toolkit.dist.dist_ref.dists.students_t_dist.member_functions"></a><h5>
+<a name="id689125"></a>
+            <a class="link" href="students_t_dist.html#math_toolkit.dist.dist_ref.dists.students_t_dist.member_functions">Member
+            Functions</a>
+          </h5>
+<pre class="programlisting"><span class="identifier">students_t_distribution</span><span class="special">(</span><span class="keyword">const</span> <span class="identifier">RealType</span><span class="special">&amp;</span> <span class="identifier">v</span><span class="special">);</span>
+</pre>
+<p>
+            Constructs a Student's t-distribution with <span class="emphasis"><em>v</em></span> degrees
+            of freedom.
+          </p>
+<p>
+            Requires v &gt; 0, otherwise calls <a class="link" href="../../../main_overview/error_handling.html#domain_error">domain_error</a>.
+            Note that non-integral degrees of freedom are supported, and meaningful
+            under certain circumstances.
+          </p>
+<pre class="programlisting"><span class="identifier">RealType</span> <span class="identifier">degrees_of_freedom</span><span class="special">()</span><span class="keyword">const</span><span class="special">;</span>
+</pre>
+<p>
+            Returns the number of degrees of freedom of this distribution.
+          </p>
+<pre class="programlisting"><span class="keyword">static</span> <span class="identifier">RealType</span> <span class="identifier">find_degrees_of_freedom</span><span class="special">(</span>
+   <span class="identifier">RealType</span> <span class="identifier">difference_from_mean</span><span class="special">,</span>
+   <span class="identifier">RealType</span> <span class="identifier">alpha</span><span class="special">,</span>
+   <span class="identifier">RealType</span> <span class="identifier">beta</span><span class="special">,</span>
+   <span class="identifier">RealType</span> <span class="identifier">sd</span><span class="special">,</span>
+   <span class="identifier">RealType</span> <span class="identifier">hint</span> <span class="special">=</span> <span class="number">100</span><span class="special">);</span>
+</pre>
+<p>
+            Returns the number of degrees of freedom required to observe a significant
+            result in the Student's t test when the mean differs from the "true"
+            mean by <span class="emphasis"><em>difference_from_mean</em></span>.
+          </p>
+<div class="variablelist">
+<p class="title"><b></b></p>
+<dl>
+<dt><span class="term">difference_from_mean</span></dt>
+<dd><p>
+                The difference between the true mean and the sample mean that we
+                wish to show is significant.
+              </p></dd>
+<dt><span class="term">alpha</span></dt>
+<dd><p>
+                The maximum acceptable probability of rejecting the null hypothesis
+                when it is in fact true.
+              </p></dd>
+<dt><span class="term">beta</span></dt>
+<dd><p>
+                The maximum acceptable probability of failing to reject the null
+                hypothesis when it is in fact false.
+              </p></dd>
+<dt><span class="term">sd</span></dt>
+<dd><p>
+                The sample standard deviation.
+              </p></dd>
+<dt><span class="term">hint</span></dt>
+<dd><p>
+                A hint for the location to start looking for the result, a good choice
+                for this would be the sample size of a previous borderline Student's
+                t test.
+              </p></dd>
+</dl>
+</div>
+<div class="note"><table border="0" summary="Note">
+<tr>
+<td rowspan="2" align="center" valign="top" width="25"><img alt="[Note]" src="../../../../../../doc/html/images/note.png"></td>
+<th align="left">Note</th>
+</tr>
+<tr><td align="left" valign="top"><p>
+              Remember that for a two-sided test, you must divide alpha by two before
+              calling this function.
+            </p></td></tr>
+</table></div>
+<p>
+            For more information on this function see the <a href="http://www.itl.nist.gov/div898/handbook/prc/section2/prc222.htm" target="_top">NIST
+            Engineering Statistics Handbook</a>.
+          </p>
+<a name="math_toolkit.dist.dist_ref.dists.students_t_dist.non_member_accessors"></a><h5>
+<a name="id689525"></a>
+            <a class="link" href="students_t_dist.html#math_toolkit.dist.dist_ref.dists.students_t_dist.non_member_accessors">Non-member
+            Accessors</a>
+          </h5>
+<p>
+            All the <a class="link" href="../nmp.html" title="Non-Member Properties">usual non-member
+            accessor functions</a> that are generic to all distributions are supported:
+            <a class="link" href="../nmp.html#math.dist.cdf">Cumulative Distribution Function</a>,
+            <a class="link" href="../nmp.html#math.dist.pdf">Probability Density Function</a>, <a class="link" href="../nmp.html#math.dist.quantile">Quantile</a>, <a class="link" href="../nmp.html#math.dist.hazard">Hazard
+            Function</a>, <a class="link" href="../nmp.html#math.dist.chf">Cumulative Hazard Function</a>,
+            <a class="link" href="../nmp.html#math.dist.mean">mean</a>, <a class="link" href="../nmp.html#math.dist.median">median</a>,
+            <a class="link" href="../nmp.html#math.dist.mode">mode</a>, <a class="link" href="../nmp.html#math.dist.variance">variance</a>,
+            <a class="link" href="../nmp.html#math.dist.sd">standard deviation</a>, <a class="link" href="../nmp.html#math.dist.skewness">skewness</a>,
+            <a class="link" href="../nmp.html#math.dist.kurtosis">kurtosis</a>, <a class="link" href="../nmp.html#math.dist.kurtosis_excess">kurtosis_excess</a>,
+            <a class="link" href="../nmp.html#math.dist.range">range</a> and <a class="link" href="../nmp.html#math.dist.support">support</a>.
+          </p>
+<p>
+            The domain of the random variable is [-&#8734;, +&#8734;].
+          </p>
+<a name="math_toolkit.dist.dist_ref.dists.students_t_dist.examples"></a><h5>
+<a name="id689701"></a>
+            <a class="link" href="students_t_dist.html#math_toolkit.dist.dist_ref.dists.students_t_dist.examples">Examples</a>
+          </h5>
+<p>
+            Various <a class="link" href="../../stat_tut/weg/st_eg.html" title="Student's t Distribution Examples">worked examples</a>
+            are available illustrating the use of the Student's t distribution.
+          </p>
+<a name="math_toolkit.dist.dist_ref.dists.students_t_dist.accuracy"></a><h5>
+<a name="id689743"></a>
+            <a class="link" href="students_t_dist.html#math_toolkit.dist.dist_ref.dists.students_t_dist.accuracy">Accuracy</a>
+          </h5>
+<p>
+            The normal distribution is implemented in terms of the <a class="link" href="../../../special/sf_beta/ibeta_function.html" title="Incomplete Beta Functions">incomplete
+            beta function</a> and <a class="link" href="../../../special/sf_beta/ibeta_inv_function.html" title="The Incomplete Beta Function Inverses">it's
+            inverses</a>, refer to accuracy data on those functions for more information.
+          </p>
+<a name="math_toolkit.dist.dist_ref.dists.students_t_dist.implementation"></a><h5>
+<a name="id689794"></a>
+            <a class="link" href="students_t_dist.html#math_toolkit.dist.dist_ref.dists.students_t_dist.implementation">Implementation</a>
+          </h5>
+<p>
+            In the following table <span class="emphasis"><em>v</em></span> is the degrees of freedom
+            of the distribution, <span class="emphasis"><em>t</em></span> is the random variate, <span class="emphasis"><em>p</em></span>
+            is the probability and <span class="emphasis"><em>q = 1-p</em></span>.
+          </p>
+<div class="informaltable"><table class="table">
+<colgroup>
+<col>
+<col>
+</colgroup>
+<thead><tr>
+<th>
+                  <p>
+                    Function
+                  </p>
+                  </th>
+<th>
+                  <p>
+                    Implementation Notes
+                  </p>
+                  </th>
+</tr></thead>
+<tbody>
+<tr>
+<td>
+                  <p>
+                    pdf
+                  </p>
+                  </td>
+<td>
+                  <p>
+                    Using the relation: pdf = (v / (v + t<sup>2</sup>))<sup>(1+v)/2 </sup> / (sqrt(v) *
+                    <a class="link" href="../../../special/sf_beta/beta_function.html" title="Beta">beta</a>(v/2,
+                    0.5))
+                  </p>
+                  </td>
+</tr>
+<tr>
+<td>
+                  <p>
+                    cdf
+                  </p>
+                  </td>
+<td>
+                  <p>
+                    Using the relations:
+                  </p>
+                  <p>
+                    p = 1 - z <span class="emphasis"><em>iff t &gt; 0</em></span>
+                  </p>
+                  <p>
+                    p = z <span class="emphasis"><em>otherwise</em></span>
+                  </p>
+                  <p>
+                    where z is given by:
+                  </p>
+                  <p>
+                    <a class="link" href="../../../special/sf_beta/ibeta_function.html" title="Incomplete Beta Functions">ibeta</a>(v
+                    / 2, 0.5, v / (v + t<sup>2</sup>)) / 2 <span class="emphasis"><em>iff v &lt; 2t<sup>2</sup></em></span>
+                  </p>
+                  <p>
+                    <a class="link" href="../../../special/sf_beta/ibeta_function.html" title="Incomplete Beta Functions">ibetac</a>(0.5,
+                    v / 2, t<sup>2 </sup> / (v + t<sup>2</sup>) / 2 <span class="emphasis"><em>otherwise</em></span>
+                  </p>
+                  </td>
+</tr>
+<tr>
+<td>
+                  <p>
+                    cdf complement
+                  </p>
+                  </td>
+<td>
+                  <p>
+                    Using the relation: q = cdf(-t)
+                  </p>
+                  </td>
+</tr>
+<tr>
+<td>
+                  <p>
+                    quantile
+                  </p>
+                  </td>
+<td>
+                  <p>
+                    Using the relation: t = sign(p - 0.5) * sqrt(v * y / x)
+                  </p>
+                  <p>
+                    where:
+                  </p>
+                  <p>
+                    x = <a class="link" href="../../../special/sf_beta/ibeta_inv_function.html" title="The Incomplete Beta Function Inverses">ibeta_inv</a>(v
+                    / 2, 0.5, 2 * min(p, q))
+                  </p>
+                  <p>
+                    y = 1 - x
+                  </p>
+                  <p>
+                    The quantities <span class="emphasis"><em>x</em></span> and <span class="emphasis"><em>y</em></span>
+                    are both returned by <a class="link" href="../../../special/sf_beta/ibeta_inv_function.html" title="The Incomplete Beta Function Inverses">ibeta_inv</a>
+                    without the subtraction implied above.
+                  </p>
+                  </td>
+</tr>
+<tr>
+<td>
+                  <p>
+                    quantile from the complement
+                  </p>
+                  </td>
+<td>
+                  <p>
+                    Using the relation: t = -quantile(q)
+                  </p>
+                  </td>
+</tr>
+<tr>
+<td>
+                  <p>
+                    mean
+                  </p>
+                  </td>
+<td>
+                  <p>
+                    0
+                  </p>
+                  </td>
+</tr>
+<tr>
+<td>
+                  <p>
+                    variance
+                  </p>
+                  </td>
+<td>
+                  <p>
+                    v / (v - 2)
+                  </p>
+                  </td>
+</tr>
+<tr>
+<td>
+                  <p>
+                    mode
+                  </p>
+                  </td>
+<td>
+                  <p>
+                    0
+                  </p>
+                  </td>
+</tr>
+<tr>
+<td>
+                  <p>
+                    skewness
+                  </p>
+                  </td>
+<td>
+                  <p>
+                    0
+                  </p>
+                  </td>
+</tr>
+<tr>
+<td>
+                  <p>
+                    kurtosis
+                  </p>
+                  </td>
+<td>
+                  <p>
+                    3 * (v - 2) / (v - 4)
+                  </p>
+                  </td>
+</tr>
+<tr>
+<td>
+                  <p>
+                    kurtosis excess
+                  </p>
+                  </td>
+<td>
+                  <p>
+                    6 / (df - 4)
+                  </p>
+                  </td>
+</tr>
+</tbody>
+</table></div>
+</div>
+<table xmlns:rev="http://www.cs.rpi.edu/~gregod/boost/tools/doc/revision" width="100%"><tr>
+<td align="left"></td>
+<td align="right"><div class="copyright-footer">Copyright © 2006 , 2007, 2008 John Maddock, Paul A. Bristow, Hubert
+      Holin, Xiaogang Zhang, Bruno Lalande and Gautam Sewani<p>
+        Distributed under the Boost Software License, Version 1.0. (See accompanying
+        file LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_0.txt)
+      </p>
+</div></td>
+</tr></table>
+<hr>
+<div class="spirit-nav">
+<a accesskey="p" href="rayleigh.html"><img src="../../../../../../doc/html/images/prev.png" alt="Prev"></a><a accesskey="u" href="../dists.html"><img src="../../../../../../doc/html/images/up.png" alt="Up"></a><a accesskey="h" href="../../../../index.html"><img src="../../../../../../doc/html/images/home.png" alt="Home"></a><a accesskey="n" href="triangular_dist.html"><img src="../../../../../../doc/html/images/next.png" alt="Next"></a>
+</div>
+</body>
+</html>

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--- (empty file)
+++ sandbox/tools/auto_index/example/math/doc/sf_and_dist/html/math_toolkit/dist/dist_ref/dists/triangular_dist.html	2008-11-28 05:25:28 EST (Fri, 28 Nov 2008)
@@ -0,0 +1,419 @@
+<html>
+<head>
+<meta http-equiv="Content-Type" content="text/html; charset=ISO-8859-1">
+<title>Triangular Distribution</title>
+<link rel="stylesheet" href="../../../../boostbook.css" type="text/css">
+<meta name="generator" content="DocBook XSL Stylesheets Vsnapshot_8125">
+<link rel="home" href="../../../../index.html" title="Math Toolkit">
+<link rel="up" href="../dists.html" title="Distributions">
+<link rel="prev" href="students_t_dist.html" title="Students t Distribution">
+<link rel="next" href="weibull.html" title="Weibull Distribution">
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+</div>
+<div class="section" lang="en">
+<div class="titlepage"><div><div><h5 class="title">
+<a name="math_toolkit.dist.dist_ref.dists.triangular_dist"></a><a class="link" href="triangular_dist.html" title="Triangular Distribution">
+          Triangular Distribution</a>
+</h5></div></div></div>
+<p>
+            
+</p>
+<pre class="programlisting"><span class="preprocessor">#include</span> <span class="special">&lt;</span><span class="identifier">boost</span><span class="special">/</span><span class="identifier">math</span><span class="special">/</span><span class="identifier">distributions</span><span class="special">/</span><span class="identifier">triangular</span><span class="special">.</span><span class="identifier">hpp</span><span class="special">&gt;</span></pre>
+<p>
+          </p>
+<pre class="programlisting"><span class="keyword">namespace</span> <span class="identifier">boost</span><span class="special">{</span> <span class="keyword">namespace</span> <span class="identifier">math</span><span class="special">{</span>
+ <span class="keyword">template</span> <span class="special">&lt;</span><span class="keyword">class</span> <span class="identifier">RealType</span> <span class="special">=</span> <span class="keyword">double</span><span class="special">,</span> 
+           <span class="keyword">class</span> <a class="link" href="../../../policy.html" title="Policies">Policy</a>   <span class="special">=</span> <a class="link" href="../../../policy/pol_ref/pol_ref_ref.html" title="Policy Class Reference">policies::policy&lt;&gt;</a> <span class="special">&gt;</span>
+ <span class="keyword">class</span> <span class="identifier">triangular_distribution</span><span class="special">;</span>
+   
+ <span class="keyword">typedef</span> <span class="identifier">triangular_distribution</span><span class="special">&lt;&gt;</span> <span class="identifier">triangular</span><span class="special">;</span>
+
+ <span class="keyword">template</span> <span class="special">&lt;</span><span class="keyword">class</span> <span class="identifier">RealType</span><span class="special">,</span> <span class="keyword">class</span> <a class="link" href="../../../policy.html" title="Policies">Policy</a><span class="special">&gt;</span>
+ <span class="keyword">class</span> <span class="identifier">triangular_distribution</span>
+ <span class="special">{</span>
+ <span class="keyword">public</span><span class="special">:</span>
+    <span class="keyword">typedef</span> <span class="identifier">RealType</span> <span class="identifier">value_type</span><span class="special">;</span>
+    <span class="keyword">typedef</span> <span class="identifier">Policy</span>   <span class="identifier">policy_type</span><span class="special">;</span>
+
+    <span class="identifier">triangular_distribution</span><span class="special">(</span><span class="identifier">RealType</span> <span class="identifier">lower</span> <span class="special">=</span> <span class="special">-</span><span class="number">1</span><span class="special">,</span> <span class="identifier">RealType</span> <span class="identifier">mode</span> <span class="special">=</span> <span class="number">0</span><span class="special">)</span> <span class="identifier">RealType</span> <span class="identifier">upper</span> <span class="special">=</span> <span class="number">1</span><span class="special">);</span> <span class="comment">// Constructor.
+</span>       <span class="special">:</span> <span class="identifier">m_lower</span><span class="special">(</span><span class="identifier">lower</span><span class="special">),</span> <span class="identifier">m_mode</span><span class="special">(</span><span class="identifier">mode</span><span class="special">),</span> <span class="identifier">m_upper</span><span class="special">(</span><span class="identifier">upper</span><span class="special">)</span> <span class="comment">// Default is -1, 0, +1 triangular distribution.
+</span>    <span class="comment">// Accessor functions.
+</span>    <span class="identifier">RealType</span> <span class="identifier">lower</span><span class="special">()</span><span class="keyword">const</span><span class="special">;</span>
+    <span class="identifier">RealType</span> <span class="identifier">mode</span><span class="special">()</span><span class="keyword">const</span><span class="special">;</span>
+    <span class="identifier">RealType</span> <span class="identifier">upper</span><span class="special">()</span><span class="keyword">const</span><span class="special">;</span>
+ <span class="special">};</span> <span class="comment">// class triangular_distribution
+</span>
+<span class="special">}}</span> <span class="comment">// namespaces
+</span></pre>
+<p>
+            The <a href="http://en.wikipedia.org/wiki/Triangular_distribution" target="_top">triangular
+            distribution</a> is a continuous
+            <a href="http://en.wikipedia.org/wiki/Probability_distribution" target="_top">probability
+            distribution</a> with a lower limit a, <a href="http://en.wikipedia.org/wiki/Mode_%28statistics%29" target="_top">mode
+            c</a>, and upper limit b.
+          </p>
+<p>
+            The triangular distribution is often used where the distribution is only
+            vaguely known, but, like the <a href="http://en.wikipedia.org/wiki/Uniform_distribution_%28continuous%29" target="_top">uniform
+            distribution</a>, upper and limits are 'known', but a 'best guess',
+            the mode or center point, is also added. It has been recommended as a
+            <a href="http://www.worldscibooks.com/mathematics/etextbook/5720/5720_chap1.pdf" target="_top">proxy
+            for the beta distribution.</a> The distribution is used in business
+            decision making and project planning.
+          </p>
+<p>
+            The <a href="http://en.wikipedia.org/wiki/Triangular_distribution" target="_top">triangular
+            distribution</a> is a distribution with the <a href="http://en.wikipedia.org/wiki/Probability_density_function" target="_top">probability
+            density function</a>:
+          </p>
+<p>
+            f(x) =
+          </p>
+<div class="itemizedlist"><ul type="disc">
+<li>
+              2(x-a)/(b-a) (c-a) for a &lt;= x &lt;= c
+            </li>
+<li>
+              2(b-x)/(b-a)(b-c) for c &lt; x &lt;= b
+            </li>
+</ul></div>
+<p>
+            Parameter a (lower) can be any finite value. Parameter b (upper) can
+            be any finite value &gt; a (lower). Parameter c (mode) a &lt;= c &lt;=
+            b. This is the most probable value.
+          </p>
+<p>
+            The random variate
+            x must also be finite, and is supported lower &lt;= x &lt;= upper.
+          </p>
+<p>
+            The triangular distribution may be appropriate when an assumption of
+            a normal distribution is unjustified because uncertainty is caused by
+            rounding and quantization from analog to digital conversion. Upper and
+            lower limits are known, and the most probable value lies midway.
+          </p>
+<p>
+            The distribution simplifies when the 'best guess' is either the lower
+            or upper limit - a 90 degree angle triangle. The default chosen is the
+            001 triangular distribution which expresses an estimate that the lowest
+            value is the most likely; for example, you believe that the next-day
+            quoted delivery date is most likely (knowing that a quicker delivery
+            is impossible - the postman only comes once a day), and that longer delays
+            are decreasingly likely, and delivery is assumed to never take more than
+            your upper limit.
+          </p>
+<p>
+            The following graph illustrates how the <a href="http://en.wikipedia.org/wiki/Probability_density_function" target="_top">probability
+            density function PDF</a> varies with the various parameters:
+          </p>
+<p>
+            <span class="inlinemediaobject"><img src="../../../../../graphs/triangular_pdf.png" align="middle"></span>
+          </p>
+<p>
+            and cumulative distribution function
+          </p>
+<p>
+            <span class="inlinemediaobject"><img src="../../../../../graphs/triangular_cdf.png" align="middle"></span>
+          </p>
+<a name="math_toolkit.dist.dist_ref.dists.triangular_dist.member_functions"></a><h5>
+<a name="id691195"></a>
+            <a class="link" href="triangular_dist.html#math_toolkit.dist.dist_ref.dists.triangular_dist.member_functions">Member
+            Functions</a>
+          </h5>
+<pre class="programlisting"><span class="identifier">triangular_distribution</span><span class="special">(</span><span class="identifier">RealType</span> <span class="identifier">lower</span> <span class="special">=</span> <span class="number">0</span><span class="special">,</span> <span class="identifier">RealType</span> <span class="identifier">mode</span> <span class="special">=</span> <span class="number">0</span> <span class="identifier">RealType</span> <span class="identifier">upper</span> <span class="special">=</span> <span class="number">1</span><span class="special">);</span>
+</pre>
+<p>
+            Constructs a <a href="http://en.wikipedia.org/wiki/triangular_distribution" target="_top">triangular
+            distribution</a> with lower <span class="emphasis"><em>lower</em></span> (a) and upper
+            <span class="emphasis"><em>upper</em></span> (b).
+          </p>
+<p>
+            Requires that the <span class="emphasis"><em>lower</em></span>, <span class="emphasis"><em>mode</em></span>
+            and <span class="emphasis"><em>upper</em></span> parameters are all finite, otherwise calls
+            <a class="link" href="../../../main_overview/error_handling.html#domain_error">domain_error</a>.
+          </p>
+<pre class="programlisting"><span class="identifier">RealType</span> <span class="identifier">lower</span><span class="special">()</span><span class="keyword">const</span><span class="special">;</span>
+</pre>
+<p>
+            Returns the <span class="emphasis"><em>lower</em></span> parameter of this distribution
+            (default -1).
+          </p>
+<pre class="programlisting"><span class="identifier">RealType</span> <span class="identifier">mode</span><span class="special">()</span><span class="keyword">const</span><span class="special">;</span>
+</pre>
+<p>
+            Returns the <span class="emphasis"><em>mode</em></span> parameter of this distribution
+            (default 0).
+          </p>
+<pre class="programlisting"><span class="identifier">RealType</span> <span class="identifier">upper</span><span class="special">()</span><span class="keyword">const</span><span class="special">;</span>
+</pre>
+<p>
+            Returns the <span class="emphasis"><em>upper</em></span> parameter of this distribution
+            (default+1).
+          </p>
+<a name="math_toolkit.dist.dist_ref.dists.triangular_dist.non_member_accessors"></a><h5>
+<a name="id691508"></a>
+            <a class="link" href="triangular_dist.html#math_toolkit.dist.dist_ref.dists.triangular_dist.non_member_accessors">Non-member
+            Accessors</a>
+          </h5>
+<p>
+            All the <a class="link" href="../nmp.html" title="Non-Member Properties">usual non-member
+            accessor functions</a> that are generic to all distributions are supported:
+            <a class="link" href="../nmp.html#math.dist.cdf">Cumulative Distribution Function</a>,
+            <a class="link" href="../nmp.html#math.dist.pdf">Probability Density Function</a>, <a class="link" href="../nmp.html#math.dist.quantile">Quantile</a>, <a class="link" href="../nmp.html#math.dist.hazard">Hazard
+            Function</a>, <a class="link" href="../nmp.html#math.dist.chf">Cumulative Hazard Function</a>,
+            <a class="link" href="../nmp.html#math.dist.mean">mean</a>, <a class="link" href="../nmp.html#math.dist.median">median</a>,
+            <a class="link" href="../nmp.html#math.dist.mode">mode</a>, <a class="link" href="../nmp.html#math.dist.variance">variance</a>,
+            <a class="link" href="../nmp.html#math.dist.sd">standard deviation</a>, <a class="link" href="../nmp.html#math.dist.skewness">skewness</a>,
+            <a class="link" href="../nmp.html#math.dist.kurtosis">kurtosis</a>, <a class="link" href="../nmp.html#math.dist.kurtosis_excess">kurtosis_excess</a>,
+            <a class="link" href="../nmp.html#math.dist.range">range</a> and <a class="link" href="../nmp.html#math.dist.support">support</a>.
+          </p>
+<p>
+            The domain of the random variable is \lowerto \upper, and the supported
+            range is lower &lt;= x &lt;= upper.
+          </p>
+<a name="math_toolkit.dist.dist_ref.dists.triangular_dist.accuracy"></a><h5>
+<a name="id691686"></a>
+            <a class="link" href="triangular_dist.html#math_toolkit.dist.dist_ref.dists.triangular_dist.accuracy">Accuracy</a>
+          </h5>
+<p>
+            The triangular distribution is implemented with simple arithmetic operators
+            and so should have errors within an epsilon or two, except quantiles
+            with arguments nearing the extremes of zero and unity.
+          </p>
+<a name="math_toolkit.dist.dist_ref.dists.triangular_dist.implementation"></a><h5>
+<a name="id691720"></a>
+            <a class="link" href="triangular_dist.html#math_toolkit.dist.dist_ref.dists.triangular_dist.implementation">Implementation</a>
+          </h5>
+<p>
+            In the following table, a is the <span class="emphasis"><em>lower</em></span> parameter
+            of the distribution, c is the <span class="emphasis"><em>mode</em></span> parameter, b
+            is the <span class="emphasis"><em>upper</em></span> parameter, <span class="emphasis"><em>x</em></span> is
+            the random variate, <span class="emphasis"><em>p</em></span> is the probability and <span class="emphasis"><em>q
+            = 1-p</em></span>.
+          </p>
+<div class="informaltable"><table class="table">
+<colgroup>
+<col>
+<col>
+</colgroup>
+<thead><tr>
+<th>
+                  <p>
+                    Function
+                  </p>
+                  </th>
+<th>
+                  <p>
+                    Implementation Notes
+                  </p>
+                  </th>
+</tr></thead>
+<tbody>
+<tr>
+<td>
+                  <p>
+                    pdf
+                  </p>
+                  </td>
+<td>
+                  <p>
+                    Using the relation: pdf = 0 for x &lt; mode, 2(x-a)/(b-a)(c-a)
+                    else 2*(b-x)/((b-a)(b-c))
+                  </p>
+                  </td>
+</tr>
+<tr>
+<td>
+                  <p>
+                    cdf
+                  </p>
+                  </td>
+<td>
+                  <p>
+                    Using the relation: cdf = 0 for x &lt; mode (x-a)<sup>2</sup>/((b-a)(c-a))
+                    else 1 - (b-x)<sup>2</sup>/((b-a)(b-c))
+                  </p>
+                  </td>
+</tr>
+<tr>
+<td>
+                  <p>
+                    cdf complement
+                  </p>
+                  </td>
+<td>
+                  <p>
+                    Using the relation: q = 1 - p
+                  </p>
+                  </td>
+</tr>
+<tr>
+<td>
+                  <p>
+                    quantile
+                  </p>
+                  </td>
+<td>
+                  <p>
+                    let p0 = (c-a)/(b-a) the point of inflection on the cdf, then
+                    given probability p and q = 1-p:
+                  </p>
+                  <p>
+                    x = sqrt((b-a)(c-a)p) + a ; for p &lt; p0
+                  </p>
+                  <p>
+                    x = c ; for p == p0
+                  </p>
+                  <p>
+                    x = b - sqrt((b-a)(b-c)q) ; for p &gt; p0
+                  </p>
+                  <p>
+                    (See /boost/math/distributions/triangular.hpp
+                    for details.)
+                  </p>
+                  </td>
+</tr>
+<tr>
+<td>
+                  <p>
+                    quantile from the complement
+                  </p>
+                  </td>
+<td>
+                  <p>
+                    As quantile (See /boost/math/distributions/triangular.hpp
+                    for details.)
+                  </p>
+                  </td>
+</tr>
+<tr>
+<td>
+                  <p>
+                    mean
+                  </p>
+                  </td>
+<td>
+                  <p>
+                    (a + b + 3) / 3
+                  </p>
+                  </td>
+</tr>
+<tr>
+<td>
+                  <p>
+                    variance
+                  </p>
+                  </td>
+<td>
+                  <p>
+                    (a<sup>2</sup>+b<sup>2</sup>+c<sup>2</sup> - ab - ac - bc)/18
+                  </p>
+                  </td>
+</tr>
+<tr>
+<td>
+                  <p>
+                    mode
+                  </p>
+                  </td>
+<td>
+                  <p>
+                    c
+                  </p>
+                  </td>
+</tr>
+<tr>
+<td>
+                  <p>
+                    skewness
+                  </p>
+                  </td>
+<td>
+                  <p>
+                    (See /boost/math/distributions/triangular.hpp
+                    for details).
+                  </p>
+                  </td>
+</tr>
+<tr>
+<td>
+                  <p>
+                    kurtosis
+                  </p>
+                  </td>
+<td>
+                  <p>
+                    12/5
+                  </p>
+                  </td>
+</tr>
+<tr>
+<td>
+                  <p>
+                    kurtosis excess
+                  </p>
+                  </td>
+<td>
+                  <p>
+                    -3/5
+                  </p>
+                  </td>
+</tr>
+</tbody>
+</table></div>
+<p>
+            Some 'known good' test values were obtained from <a href="http://espse.ed.psu.edu/edpsych/faculty/rhale/hale/507Mat/statlets/free/pdist.htm" target="_top">Statlet:
+            Calculate and plot probability distributions</a>
+          </p>
+<a name="math_toolkit.dist.dist_ref.dists.triangular_dist.references"></a><h5>
+<a name="id692134"></a>
+            <a class="link" href="triangular_dist.html#math_toolkit.dist.dist_ref.dists.triangular_dist.references">References</a>
+          </h5>
+<div class="itemizedlist"><ul type="disc">
+<li><a href="http://en.wikipedia.org/wiki/Triangular_distribution" target="_top">Wikpedia
+              triangular distribution</a></li>
+<li><a href="http://mathworld.wolfram.com/TriangularDistribution.html" target="_top">Weisstein,
+              Eric W. "Triangular Distribution." From MathWorld--A Wolfram
+              Web Resource.</a></li>
+<li>
+              Evans, M.; Hastings, N.; and Peacock, B. "Triangular Distribution."
+              Ch. 40 in Statistical Distributions, 3rd ed. New York: Wiley, pp. 187-188,
+              2000, ISBN - 0471371246]
+            </li>
+<li><a href="http://www.brighton-webs.co.uk/distributions/triangular.asp" target="_top">Brighton
+              Webs Ltd. BW D-Calc 1.0 Distribution Calculator</a></li>
+<li><a href="http://www.worldscibooks.com/mathematics/etextbook/5720/5720_chap1.pdf" target="_top">The
+              Triangular Distribution including its history.</a></li>
+<li><a href="http://www.measurement.sk/2002/S1/Wimmer2.pdf" target="_top">Gejza Wimmer,
+              Viktor Witkovsky and Tomas Duby, Measurement Science Review, Volume
+              2, Section 1, 2002, Proper Rounding Of The Measurement Results Under
+              The Assumption Of Triangular Distribution.</a></li>
+</ul></div>
+</div>
+<table xmlns:rev="http://www.cs.rpi.edu/~gregod/boost/tools/doc/revision" width="100%"><tr>
+<td align="left"></td>
+<td align="right"><div class="copyright-footer">Copyright © 2006 , 2007, 2008 John Maddock, Paul A. Bristow, Hubert
+      Holin, Xiaogang Zhang, Bruno Lalande and Gautam Sewani<p>
+        Distributed under the Boost Software License, Version 1.0. (See accompanying
+        file LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_0.txt)
+      </p>
+</div></td>
+</tr></table>
+<hr>
+<div class="spirit-nav">
+<a accesskey="p" href="students_t_dist.html"><img src="../../../../../../doc/html/images/prev.png" alt="Prev"></a><a accesskey="u" href="../dists.html"><img src="../../../../../../doc/html/images/up.png" alt="Up"></a><a accesskey="h" href="../../../../index.html"><img src="../../../../../../doc/html/images/home.png" alt="Home"></a><a accesskey="n" href="weibull.html"><img src="../../../../../../doc/html/images/next.png" alt="Next"></a>
+</div>
+</body>
+</html>

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+++ sandbox/tools/auto_index/example/math/doc/sf_and_dist/html/math_toolkit/dist/dist_ref/dists/uniform_dist.html	2008-11-28 05:25:28 EST (Fri, 28 Nov 2008)
@@ -0,0 +1,366 @@
+<html>
+<head>
+<meta http-equiv="Content-Type" content="text/html; charset=ISO-8859-1">
+<title>Uniform Distribution</title>
+<link rel="stylesheet" href="../../../../boostbook.css" type="text/css">
+<meta name="generator" content="DocBook XSL Stylesheets Vsnapshot_8125">
+<link rel="home" href="../../../../index.html" title="Math Toolkit">
+<link rel="up" href="../dists.html" title="Distributions">
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+<td align="center">Home</td>
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+<a accesskey="p" href="weibull.html"><img src="../../../../../../doc/html/images/prev.png" alt="Prev"></a><a accesskey="u" href="../dists.html"><img src="../../../../../../doc/html/images/up.png" alt="Up"></a><a accesskey="h" href="../../../../index.html"><img src="../../../../../../doc/html/images/home.png" alt="Home"></a><a accesskey="n" href="../dist_algorithms.html"><img src="../../../../../../doc/html/images/next.png" alt="Next"></a>
+</div>
+<div class="section" lang="en">
+<div class="titlepage"><div><div><h5 class="title">
+<a name="math_toolkit.dist.dist_ref.dists.uniform_dist"></a><a class="link" href="uniform_dist.html" title="Uniform Distribution"> Uniform
+          Distribution</a>
+</h5></div></div></div>
+<p>
+            
+</p>
+<pre class="programlisting"><span class="preprocessor">#include</span> <span class="special">&lt;</span><span class="identifier">boost</span><span class="special">/</span><span class="identifier">math</span><span class="special">/</span><span class="identifier">distributions</span><span class="special">/</span><span class="identifier">uniform</span><span class="special">.</span><span class="identifier">hpp</span><span class="special">&gt;</span></pre>
+<p>
+          </p>
+<pre class="programlisting"><span class="keyword">namespace</span> <span class="identifier">boost</span><span class="special">{</span> <span class="keyword">namespace</span> <span class="identifier">math</span><span class="special">{</span>
+ <span class="keyword">template</span> <span class="special">&lt;</span><span class="keyword">class</span> <span class="identifier">RealType</span> <span class="special">=</span> <span class="keyword">double</span><span class="special">,</span> 
+           <span class="keyword">class</span> <a class="link" href="../../../policy.html" title="Policies">Policy</a>   <span class="special">=</span> <a class="link" href="../../../policy/pol_ref/pol_ref_ref.html" title="Policy Class Reference">policies::policy&lt;&gt;</a> <span class="special">&gt;</span>
+ <span class="keyword">class</span> <span class="identifier">uniform_distribution</span><span class="special">;</span>
+   
+ <span class="keyword">typedef</span> <span class="identifier">uniform_distribution</span><span class="special">&lt;&gt;</span> <span class="identifier">uniform</span><span class="special">;</span>
+
+ <span class="keyword">template</span> <span class="special">&lt;</span><span class="keyword">class</span> <span class="identifier">RealType</span><span class="special">,</span> <span class="keyword">class</span> <a class="link" href="../../../policy.html" title="Policies">Policy</a><span class="special">&gt;</span>
+ <span class="keyword">class</span> <span class="identifier">uniform_distribution</span>
+ <span class="special">{</span>
+ <span class="keyword">public</span><span class="special">:</span>
+    <span class="keyword">typedef</span> <span class="identifier">RealType</span> <span class="identifier">value_type</span><span class="special">;</span>
+
+    <span class="identifier">uniform_distribution</span><span class="special">(</span><span class="identifier">RealType</span> <span class="identifier">lower</span> <span class="special">=</span> <span class="number">0</span><span class="special">,</span> <span class="identifier">RealType</span> <span class="identifier">upper</span> <span class="special">=</span> <span class="number">1</span><span class="special">);</span> <span class="comment">// Constructor.
+</span>       <span class="special">:</span> <span class="identifier">m_lower</span><span class="special">(</span><span class="identifier">lower</span><span class="special">),</span> <span class="identifier">m_upper</span><span class="special">(</span><span class="identifier">upper</span><span class="special">)</span> <span class="comment">// Default is standard uniform distribution.
+</span>    <span class="comment">// Accessor functions.
+</span>    <span class="identifier">RealType</span> <span class="identifier">lower</span><span class="special">()</span><span class="keyword">const</span><span class="special">;</span>
+    <span class="identifier">RealType</span> <span class="identifier">upper</span><span class="special">()</span><span class="keyword">const</span><span class="special">;</span>
+ <span class="special">};</span> <span class="comment">// class uniform_distribution
+</span>
+<span class="special">}}</span> <span class="comment">// namespaces
+</span></pre>
+<p>
+            The uniform distribution, also known as a rectangular distribution, is
+            a probability distribution that has constant probability.
+          </p>
+<p>
+            The <a href="http://en.wikipedia.org/wiki/Uniform_distribution_%28continuous%29" target="_top">continuous
+            uniform distribution</a> is a distribution with the <a href="http://en.wikipedia.org/wiki/Probability_density_function" target="_top">probability
+            density function</a>:
+          </p>
+<p>
+            f(x) =
+          </p>
+<div class="itemizedlist"><ul type="disc">
+<li>
+              1 / (upper - lower) for lower &lt; x &lt; upper
+            </li>
+<li>
+              zero for x &lt; lower or x &gt; upper
+            </li>
+</ul></div>
+<p>
+            and in this implementation:
+          </p>
+<div class="itemizedlist"><ul type="disc"><li>
+              1 / (upper - lower) for x = lower or x = upper
+            </li></ul></div>
+<p>
+            The choice of x = lower or x = upper is made because statistical use
+            of this distribution judged is most likely: the method of maximum likelihood
+            uses this definition.
+          </p>
+<p>
+            There is also a discrete uniform distribution.
+          </p>
+<p>
+            Parameters lower and upper can be any finite value.
+          </p>
+<p>
+            The random variate
+            x must also be finite, and is supported lower &lt;= x &lt;= upper.
+          </p>
+<p>
+            The lower parameter is also called the <a href="http://www.itl.nist.gov/div898/handbook/eda/section3/eda364.htm" target="_top">location
+            parameter</a>, <a href="http://en.wikipedia.org/wiki/Location_parameter" target="_top">that
+            is where the origin of a plot will lie</a>, and (upper - lower) is
+            also called the <a href="http://en.wikipedia.org/wiki/Scale_parameter" target="_top">scale
+            parameter</a>.
+          </p>
+<p>
+            The following graph illustrates how the <a href="http://en.wikipedia.org/wiki/Probability_density_function" target="_top">probability
+            density function PDF</a> varies with the shape parameter:
+          </p>
+<p>
+            <span class="inlinemediaobject"><img src="../../../../../graphs/uniform_pdf.png" align="middle"></span>
+          </p>
+<p>
+            Likewise for the CDF:
+          </p>
+<p>
+            <span class="inlinemediaobject"><img src="../../../../../graphs/uniform_cdf.png" align="middle"></span>
+          </p>
+<a name="math_toolkit.dist.dist_ref.dists.uniform_dist.member_functions"></a><h5>
+<a name="id694767"></a>
+            <a class="link" href="uniform_dist.html#math_toolkit.dist.dist_ref.dists.uniform_dist.member_functions">Member
+            Functions</a>
+          </h5>
+<pre class="programlisting"><span class="identifier">uniform_distribution</span><span class="special">(</span><span class="identifier">RealType</span> <span class="identifier">lower</span> <span class="special">=</span> <span class="number">0</span><span class="special">,</span> <span class="identifier">RealType</span> <span class="identifier">upper</span> <span class="special">=</span> <span class="number">1</span><span class="special">);</span>
+</pre>
+<p>
+            Constructs a <a href="http://en.wikipedia.org/wiki/uniform_distribution" target="_top">uniform
+            distribution</a> with lower <span class="emphasis"><em>lower</em></span> (a) and upper
+            <span class="emphasis"><em>upper</em></span> (b).
+          </p>
+<p>
+            Requires that the <span class="emphasis"><em>lower</em></span> and <span class="emphasis"><em>upper</em></span>
+            parameters are both finite; otherwise if infinity or NaN then calls
+            <a class="link" href="../../../main_overview/error_handling.html#domain_error">domain_error</a>.
+          </p>
+<pre class="programlisting"><span class="identifier">RealType</span> <span class="identifier">lower</span><span class="special">()</span><span class="keyword">const</span><span class="special">;</span>
+</pre>
+<p>
+            Returns the <span class="emphasis"><em>lower</em></span> parameter of this distribution.
+          </p>
+<pre class="programlisting"><span class="identifier">RealType</span> <span class="identifier">upper</span><span class="special">()</span><span class="keyword">const</span><span class="special">;</span>
+</pre>
+<p>
+            Returns the <span class="emphasis"><em>upper</em></span> parameter of this distribution.
+          </p>
+<a name="math_toolkit.dist.dist_ref.dists.uniform_dist.non_member_accessors"></a><h5>
+<a name="id695007"></a>
+            <a class="link" href="uniform_dist.html#math_toolkit.dist.dist_ref.dists.uniform_dist.non_member_accessors">Non-member
+            Accessors</a>
+          </h5>
+<p>
+            All the <a class="link" href="../nmp.html" title="Non-Member Properties">usual non-member
+            accessor functions</a> that are generic to all distributions are supported:
+            <a class="link" href="../nmp.html#math.dist.cdf">Cumulative Distribution Function</a>,
+            <a class="link" href="../nmp.html#math.dist.pdf">Probability Density Function</a>, <a class="link" href="../nmp.html#math.dist.quantile">Quantile</a>, <a class="link" href="../nmp.html#math.dist.hazard">Hazard
+            Function</a>, <a class="link" href="../nmp.html#math.dist.chf">Cumulative Hazard Function</a>,
+            <a class="link" href="../nmp.html#math.dist.mean">mean</a>, <a class="link" href="../nmp.html#math.dist.median">median</a>,
+            <a class="link" href="../nmp.html#math.dist.mode">mode</a>, <a class="link" href="../nmp.html#math.dist.variance">variance</a>,
+            <a class="link" href="../nmp.html#math.dist.sd">standard deviation</a>, <a class="link" href="../nmp.html#math.dist.skewness">skewness</a>,
+            <a class="link" href="../nmp.html#math.dist.kurtosis">kurtosis</a>, <a class="link" href="../nmp.html#math.dist.kurtosis_excess">kurtosis_excess</a>,
+            <a class="link" href="../nmp.html#math.dist.range">range</a> and <a class="link" href="../nmp.html#math.dist.support">support</a>.
+          </p>
+<p>
+            The domain of the random variable is any finite value, but the supported
+            range is only <span class="emphasis"><em>lower</em></span> &lt;= x &lt;= <span class="emphasis"><em>upper</em></span>.
+          </p>
+<a name="math_toolkit.dist.dist_ref.dists.uniform_dist.accuracy"></a><h5>
+<a name="id695192"></a>
+            <a class="link" href="uniform_dist.html#math_toolkit.dist.dist_ref.dists.uniform_dist.accuracy">Accuracy</a>
+          </h5>
+<p>
+            The uniform distribution is implemented with simple arithmetic operators
+            and so should have errors within an epsilon or two.
+          </p>
+<a name="math_toolkit.dist.dist_ref.dists.uniform_dist.implementation"></a><h5>
+<a name="id695226"></a>
+            <a class="link" href="uniform_dist.html#math_toolkit.dist.dist_ref.dists.uniform_dist.implementation">Implementation</a>
+          </h5>
+<p>
+            In the following table a is the <span class="emphasis"><em>lower</em></span> parameter
+            of the distribution, b is the <span class="emphasis"><em>upper</em></span> parameter,
+            <span class="emphasis"><em>x</em></span> is the random variate, <span class="emphasis"><em>p</em></span>
+            is the probability and <span class="emphasis"><em>q = 1-p</em></span>.
+          </p>
+<div class="informaltable"><table class="table">
+<colgroup>
+<col>
+<col>
+</colgroup>
+<thead><tr>
+<th>
+                  <p>
+                    Function
+                  </p>
+                  </th>
+<th>
+                  <p>
+                    Implementation Notes
+                  </p>
+                  </th>
+</tr></thead>
+<tbody>
+<tr>
+<td>
+                  <p>
+                    pdf
+                  </p>
+                  </td>
+<td>
+                  <p>
+                    Using the relation: pdf = 0 for x &lt; a, 1 / (b - a) for a &lt;=
+                    x &lt;= b, 0 for x &gt; b
+                  </p>
+                  </td>
+</tr>
+<tr>
+<td>
+                  <p>
+                    cdf
+                  </p>
+                  </td>
+<td>
+                  <p>
+                    Using the relation: cdf = 0 for x &lt; a, (x - a) / (b - a) for
+                    a &lt;= x &lt;= b, 1 for x &gt; b
+                  </p>
+                  </td>
+</tr>
+<tr>
+<td>
+                  <p>
+                    cdf complement
+                  </p>
+                  </td>
+<td>
+                  <p>
+                    Using the relation: q = 1 - p, (b - x) / (b - a)
+                  </p>
+                  </td>
+</tr>
+<tr>
+<td>
+                  <p>
+                    quantile
+                  </p>
+                  </td>
+<td>
+                  <p>
+                    Using the relation: x = p * (b - a) + a;
+                  </p>
+                  </td>
+</tr>
+<tr>
+<td>
+                  <p>
+                    quantile from the complement
+                  </p>
+                  </td>
+<td>
+                  <p>
+                    x = -q * (b - a) + b
+                  </p>
+                  </td>
+</tr>
+<tr>
+<td>
+                  <p>
+                    mean
+                  </p>
+                  </td>
+<td>
+                  <p>
+                    (a + b) / 2
+                  </p>
+                  </td>
+</tr>
+<tr>
+<td>
+                  <p>
+                    variance
+                  </p>
+                  </td>
+<td>
+                  <p>
+                    (b - a) <sup>2</sup> / 12
+                  </p>
+                  </td>
+</tr>
+<tr>
+<td>
+                  <p>
+                    mode
+                  </p>
+                  </td>
+<td>
+                  <p>
+                    any value in [a, b] but a is chosen. (Would NaN be better?)
+                  </p>
+                  </td>
+</tr>
+<tr>
+<td>
+                  <p>
+                    skewness
+                  </p>
+                  </td>
+<td>
+                  <p>
+                    0
+                  </p>
+                  </td>
+</tr>
+<tr>
+<td>
+                  <p>
+                    kurtosis excess
+                  </p>
+                  </td>
+<td>
+                  <p>
+                    -6/5 = -1.2 exactly. (kurtosis - 3)
+                  </p>
+                  </td>
+</tr>
+<tr>
+<td>
+                  <p>
+                    kurtosis
+                  </p>
+                  </td>
+<td>
+                  <p>
+                    9/5
+                  </p>
+                  </td>
+</tr>
+</tbody>
+</table></div>
+<a name="math_toolkit.dist.dist_ref.dists.uniform_dist.references"></a><h5>
+<a name="id695557"></a>
+            <a class="link" href="uniform_dist.html#math_toolkit.dist.dist_ref.dists.uniform_dist.references">References</a>
+          </h5>
+<div class="itemizedlist"><ul type="disc">
+<li><a href="http://en.wikipedia.org/wiki/Uniform_distribution_%28continuous%29" target="_top">Wikpedia
+              continuous uniform distribution</a></li>
+<li><a href="http://mathworld.wolfram.com/UniformDistribution.html" target="_top">Weisstein,
+              Weisstein, Eric W. "Uniform Distribution." From MathWorld--A
+              Wolfram Web Resource.</a></li>
+<li>http://www.itl.nist.gov/div898/handbook/eda/section3/eda3662.htm</li>
+</ul></div>
+</div>
+<table xmlns:rev="http://www.cs.rpi.edu/~gregod/boost/tools/doc/revision" width="100%"><tr>
+<td align="left"></td>
+<td align="right"><div class="copyright-footer">Copyright © 2006 , 2007, 2008 John Maddock, Paul A. Bristow, Hubert
+      Holin, Xiaogang Zhang, Bruno Lalande and Gautam Sewani<p>
+        Distributed under the Boost Software License, Version 1.0. (See accompanying
+        file LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_0.txt)
+      </p>
+</div></td>
+</tr></table>
+<hr>
+<div class="spirit-nav">
+<a accesskey="p" href="weibull.html"><img src="../../../../../../doc/html/images/prev.png" alt="Prev"></a><a accesskey="u" href="../dists.html"><img src="../../../../../../doc/html/images/up.png" alt="Up"></a><a accesskey="h" href="../../../../index.html"><img src="../../../../../../doc/html/images/home.png" alt="Home"></a><a accesskey="n" href="../dist_algorithms.html"><img src="../../../../../../doc/html/images/next.png" alt="Next"></a>
+</div>
+</body>
+</html>

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+++ sandbox/tools/auto_index/example/math/doc/sf_and_dist/html/math_toolkit/dist/dist_ref/dists/weibull.html	2008-11-28 05:25:28 EST (Fri, 28 Nov 2008)
@@ -0,0 +1,366 @@
+<html>
+<head>
+<meta http-equiv="Content-Type" content="text/html; charset=ISO-8859-1">
+<title>Weibull Distribution</title>
+<link rel="stylesheet" href="../../../../boostbook.css" type="text/css">
+<meta name="generator" content="DocBook XSL Stylesheets Vsnapshot_8125">
+<link rel="home" href="../../../../index.html" title="Math Toolkit">
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+<link rel="next" href="uniform_dist.html" title="Uniform Distribution">
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+<table cellpadding="2" width="100%"><tr>
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+<td align="center">Home</td>
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+<a accesskey="p" href="triangular_dist.html"><img src="../../../../../../doc/html/images/prev.png" alt="Prev"></a><a accesskey="u" href="../dists.html"><img src="../../../../../../doc/html/images/up.png" alt="Up"></a><a accesskey="h" href="../../../../index.html"><img src="../../../../../../doc/html/images/home.png" alt="Home"></a><a accesskey="n" href="uniform_dist.html"><img src="../../../../../../doc/html/images/next.png" alt="Next"></a>
+</div>
+<div class="section" lang="en">
+<div class="titlepage"><div><div><h5 class="title">
+<a name="math_toolkit.dist.dist_ref.dists.weibull"></a><a class="link" href="weibull.html" title="Weibull Distribution"> Weibull
+          Distribution</a>
+</h5></div></div></div>
+<p>
+            
+</p>
+<pre class="programlisting"><span class="preprocessor">#include</span> <span class="special">&lt;</span><span class="identifier">boost</span><span class="special">/</span><span class="identifier">math</span><span class="special">/</span><span class="identifier">distributions</span><span class="special">/</span><span class="identifier">weibull</span><span class="special">.</span><span class="identifier">hpp</span><span class="special">&gt;</span></pre>
+<p>
+          </p>
+<pre class="programlisting"><span class="keyword">namespace</span> <span class="identifier">boost</span><span class="special">{</span> <span class="keyword">namespace</span> <span class="identifier">math</span><span class="special">{</span> 
+   
+<span class="keyword">template</span> <span class="special">&lt;</span><span class="keyword">class</span> <span class="identifier">RealType</span> <span class="special">=</span> <span class="keyword">double</span><span class="special">,</span> 
+          <span class="keyword">class</span> <a class="link" href="../../../policy.html" title="Policies">Policy</a>   <span class="special">=</span> <a class="link" href="../../../policy/pol_ref/pol_ref_ref.html" title="Policy Class Reference">policies::policy&lt;&gt;</a> <span class="special">&gt;</span>
+<span class="keyword">class</span> <span class="identifier">weibull_distribution</span><span class="special">;</span>
+
+<span class="keyword">typedef</span> <span class="identifier">weibull_distribution</span><span class="special">&lt;&gt;</span> <span class="identifier">weibull</span><span class="special">;</span>
+
+<span class="keyword">template</span> <span class="special">&lt;</span><span class="keyword">class</span> <span class="identifier">RealType</span><span class="special">,</span> <span class="keyword">class</span> <a class="link" href="../../../policy.html" title="Policies">Policy</a><span class="special">&gt;</span>
+<span class="keyword">class</span> <span class="identifier">weibull_distribution</span>
+<span class="special">{</span>
+<span class="keyword">public</span><span class="special">:</span>
+   <span class="keyword">typedef</span> <span class="identifier">RealType</span> <span class="identifier">value_type</span><span class="special">;</span>
+   <span class="keyword">typedef</span> <span class="identifier">Policy</span>   <span class="identifier">policy_type</span><span class="special">;</span>
+   <span class="comment">// Construct:
+</span>   <span class="identifier">weibull_distribution</span><span class="special">(</span><span class="identifier">RealType</span> <span class="identifier">shape</span><span class="special">,</span> <span class="identifier">RealType</span> <span class="identifier">scale</span> <span class="special">=</span> <span class="number">1</span><span class="special">)</span>
+   <span class="comment">// Accessors:
+</span>   <span class="identifier">RealType</span> <span class="identifier">shape</span><span class="special">()</span><span class="keyword">const</span><span class="special">;</span>
+   <span class="identifier">RealType</span> <span class="identifier">scale</span><span class="special">()</span><span class="keyword">const</span><span class="special">;</span>
+<span class="special">};</span>
+
+<span class="special">}}</span> <span class="comment">// namespaces
+</span></pre>
+<p>
+            The <a href="http://en.wikipedia.org/wiki/Weibull_distribution" target="_top">Weibull
+            distribution</a> is a continuous distribution with the <a href="http://en.wikipedia.org/wiki/Probability_density_function" target="_top">probability
+            density function</a>:
+          </p>
+<p>
+            f(x; &#945;, &#946;) = (&#945;/&#946;) * (x / &#946;)<sup>&#945; - 1</sup> * e<sup>-(x/&#946;)<sup>&#945;</sup></sup>
+          </p>
+<p>
+            For shape parameter &#945; &gt; 0, and scale parameter &#946; &gt; 0, and x &gt; 0.
+          </p>
+<p>
+            The Weibull distribution is often used in the field of failure analysis;
+            in particular it can mimic distributions where the failure rate varies
+            over time. If the failure rate is:
+          </p>
+<div class="itemizedlist"><ul type="disc">
+<li>
+              constant over time, then &#945; = 1, suggests that items are failing from
+              random events.
+            </li>
+<li>
+              decreases over time, then &#945; &lt; 1, suggesting "infant mortality".
+            </li>
+<li>
+              increases over time, then &#945; &gt; 1, suggesting "wear out" -
+              more likely to fail as time goes by.
+            </li>
+</ul></div>
+<p>
+            The following graph illustrates how the PDF varies with the shape parameter
+            &#945;:
+          </p>
+<p>
+            <span class="inlinemediaobject"><img src="../../../../../graphs/weibull_pdf1.png" align="middle"></span>
+          </p>
+<p>
+            While this graph illustrates how the PDF varies with the scale parameter
+            &#946;:
+          </p>
+<p>
+            <span class="inlinemediaobject"><img src="../../../../../graphs/weibull_pdf2.png" align="middle"></span>
+          </p>
+<a name="math_toolkit.dist.dist_ref.dists.weibull.related_distributions"></a><h5>
+<a name="id692938"></a>
+            <a class="link" href="weibull.html#math_toolkit.dist.dist_ref.dists.weibull.related_distributions">Related
+            distributions</a>
+          </h5>
+<p>
+            When &#945; = 3, the <a href="http://en.wikipedia.org/wiki/Weibull_distribution" target="_top">Weibull
+            distribution</a> appears similar to the <a href="http://en.wikipedia.org/wiki/Normal_distribution" target="_top">normal
+            distribution</a>. When &#945; = 1, the Weibull distribution reduces to the
+            <a href="http://en.wikipedia.org/wiki/Exponential_distribution" target="_top">exponential
+            distribution</a>. The relationship of the types of extreme value
+            distributions, of which the Weibull is but one, is discussed by <a href="http://www.worldscibooks.com/mathematics/p191.html" target="_top">Extreme Value
+            Distributions, Theory and Applications Samuel Kotz &amp; Saralees Nadarajah</a>.
+          </p>
+<a name="math_toolkit.dist.dist_ref.dists.weibull.member_functions"></a><h5>
+<a name="id693010"></a>
+            <a class="link" href="weibull.html#math_toolkit.dist.dist_ref.dists.weibull.member_functions">Member
+            Functions</a>
+          </h5>
+<pre class="programlisting"><span class="identifier">weibull_distribution</span><span class="special">(</span><span class="identifier">RealType</span> <span class="identifier">shape</span><span class="special">,</span> <span class="identifier">RealType</span> <span class="identifier">scale</span> <span class="special">=</span> <span class="number">1</span><span class="special">);</span>
+</pre>
+<p>
+            Constructs a <a href="http://en.wikipedia.org/wiki/Weibull_distribution" target="_top">Weibull
+            distribution</a> with shape <span class="emphasis"><em>shape</em></span> and scale
+            <span class="emphasis"><em>scale</em></span>.
+          </p>
+<p>
+            Requires that the <span class="emphasis"><em>shape</em></span> and <span class="emphasis"><em>scale</em></span>
+            parameters are both greater than zero, otherwise calls <a class="link" href="../../../main_overview/error_handling.html#domain_error">domain_error</a>.
+          </p>
+<pre class="programlisting"><span class="identifier">RealType</span> <span class="identifier">shape</span><span class="special">()</span><span class="keyword">const</span><span class="special">;</span>
+</pre>
+<p>
+            Returns the <span class="emphasis"><em>shape</em></span> parameter of this distribution.
+          </p>
+<pre class="programlisting"><span class="identifier">RealType</span> <span class="identifier">scale</span><span class="special">()</span><span class="keyword">const</span><span class="special">;</span>
+</pre>
+<p>
+            Returns the <span class="emphasis"><em>scale</em></span> parameter of this distribution.
+          </p>
+<a name="math_toolkit.dist.dist_ref.dists.weibull.non_member_accessors"></a><h5>
+<a name="id693235"></a>
+            <a class="link" href="weibull.html#math_toolkit.dist.dist_ref.dists.weibull.non_member_accessors">Non-member
+            Accessors</a>
+          </h5>
+<p>
+            All the <a class="link" href="../nmp.html" title="Non-Member Properties">usual non-member
+            accessor functions</a> that are generic to all distributions are supported:
+            <a class="link" href="../nmp.html#math.dist.cdf">Cumulative Distribution Function</a>,
+            <a class="link" href="../nmp.html#math.dist.pdf">Probability Density Function</a>, <a class="link" href="../nmp.html#math.dist.quantile">Quantile</a>, <a class="link" href="../nmp.html#math.dist.hazard">Hazard
+            Function</a>, <a class="link" href="../nmp.html#math.dist.chf">Cumulative Hazard Function</a>,
+            <a class="link" href="../nmp.html#math.dist.mean">mean</a>, <a class="link" href="../nmp.html#math.dist.median">median</a>,
+            <a class="link" href="../nmp.html#math.dist.mode">mode</a>, <a class="link" href="../nmp.html#math.dist.variance">variance</a>,
+            <a class="link" href="../nmp.html#math.dist.sd">standard deviation</a>, <a class="link" href="../nmp.html#math.dist.skewness">skewness</a>,
+            <a class="link" href="../nmp.html#math.dist.kurtosis">kurtosis</a>, <a class="link" href="../nmp.html#math.dist.kurtosis_excess">kurtosis_excess</a>,
+            <a class="link" href="../nmp.html#math.dist.range">range</a> and <a class="link" href="../nmp.html#math.dist.support">support</a>.
+          </p>
+<p>
+            The domain of the random variable is [0, &#8734;].
+          </p>
+<a name="math_toolkit.dist.dist_ref.dists.weibull.accuracy"></a><h5>
+<a name="id693410"></a>
+            <a class="link" href="weibull.html#math_toolkit.dist.dist_ref.dists.weibull.accuracy">Accuracy</a>
+          </h5>
+<p>
+            The Weibull distribution is implemented in terms of the standard library
+            <code class="computeroutput"><span class="identifier">log</span></code> and <code class="computeroutput"><span class="identifier">exp</span></code> functions plus <a class="link" href="../../../special/powers/expm1.html" title="expm1">expm1</a>
+            and <a class="link" href="../../../special/powers/log1p.html" title="log1p">log1p</a> and
+            as such should have very low error rates.
+          </p>
+<a name="math_toolkit.dist.dist_ref.dists.weibull.implementation"></a><h5>
+<a name="id693485"></a>
+            <a class="link" href="weibull.html#math_toolkit.dist.dist_ref.dists.weibull.implementation">Implementation</a>
+          </h5>
+<p>
+            In the following table &#945; is the shape parameter of the distribution, &#946; is
+            it's scale parameter, <span class="emphasis"><em>x</em></span> is the random variate,
+            <span class="emphasis"><em>p</em></span> is the probability and <span class="emphasis"><em>q = 1-p</em></span>.
+          </p>
+<div class="informaltable"><table class="table">
+<colgroup>
+<col>
+<col>
+</colgroup>
+<thead><tr>
+<th>
+                  <p>
+                    Function
+                  </p>
+                  </th>
+<th>
+                  <p>
+                    Implementation Notes
+                  </p>
+                  </th>
+</tr></thead>
+<tbody>
+<tr>
+<td>
+                  <p>
+                    pdf
+                  </p>
+                  </td>
+<td>
+                  <p>
+                    Using the relation: pdf = &#945;&#946;<sup>-&#945; </sup>x<sup>&#945; - 1</sup> e<sup>-(x/beta)<sup>alpha</sup></sup>
+                  </p>
+                  </td>
+</tr>
+<tr>
+<td>
+                  <p>
+                    cdf
+                  </p>
+                  </td>
+<td>
+                  <p>
+                    Using the relation: p = -<a class="link" href="../../../special/powers/expm1.html" title="expm1">expm1</a>(-(x/&#946;)<sup>&#945;</sup>)
+                  </p>
+                  </td>
+</tr>
+<tr>
+<td>
+                  <p>
+                    cdf complement
+                  </p>
+                  </td>
+<td>
+                  <p>
+                    Using the relation: q = e<sup>-(x/&#946;)<sup>&#945;</sup></sup>
+                  </p>
+                  </td>
+</tr>
+<tr>
+<td>
+                  <p>
+                    quantile
+                  </p>
+                  </td>
+<td>
+                  <p>
+                    Using the relation: x = &#946; * (-<a class="link" href="../../../special/powers/log1p.html" title="log1p">log1p</a>(-p))<sup>1/&#945;</sup>
+                  </p>
+                  </td>
+</tr>
+<tr>
+<td>
+                  <p>
+                    quantile from the complement
+                  </p>
+                  </td>
+<td>
+                  <p>
+                    Using the relation: x = &#946; * (-log(q))<sup>1/&#945;</sup>
+                  </p>
+                  </td>
+</tr>
+<tr>
+<td>
+                  <p>
+                    mean
+                  </p>
+                  </td>
+<td>
+                  <p>
+                    &#946; * &#915;(1 + 1/&#945;)
+                  </p>
+                  </td>
+</tr>
+<tr>
+<td>
+                  <p>
+                    variance
+                  </p>
+                  </td>
+<td>
+                  <p>
+                    &#946;<sup>2</sup>(&#915;(1 + 2/&#945;) - &#915;<sup>2</sup>(1 + 1/&#945;))
+                  </p>
+                  </td>
+</tr>
+<tr>
+<td>
+                  <p>
+                    mode
+                  </p>
+                  </td>
+<td>
+                  <p>
+                    &#946;((&#945; - 1) / &#945;)<sup>1/&#945;</sup>
+                  </p>
+                  </td>
+</tr>
+<tr>
+<td>
+                  <p>
+                    skewness
+                  </p>
+                  </td>
+<td>
+                  <p>
+                    Refer to <a href="http://mathworld.wolfram.com/WeibullDistribution.html" target="_top">Weisstein,
+                    Eric W. "Weibull Distribution." From MathWorld--A Wolfram
+                    Web Resource.</a>
+                  </p>
+                  </td>
+</tr>
+<tr>
+<td>
+                  <p>
+                    kurtosis
+                  </p>
+                  </td>
+<td>
+                  <p>
+                    Refer to <a href="http://mathworld.wolfram.com/WeibullDistribution.html" target="_top">Weisstein,
+                    Eric W. "Weibull Distribution." From MathWorld--A Wolfram
+                    Web Resource.</a>
+                  </p>
+                  </td>
+</tr>
+<tr>
+<td>
+                  <p>
+                    kurtosis excess
+                  </p>
+                  </td>
+<td>
+                  <p>
+                    Refer to <a href="http://mathworld.wolfram.com/WeibullDistribution.html" target="_top">Weisstein,
+                    Eric W. "Weibull Distribution." From MathWorld--A Wolfram
+                    Web Resource.</a>
+                  </p>
+                  </td>
+</tr>
+</tbody>
+</table></div>
+<a name="math_toolkit.dist.dist_ref.dists.weibull.references"></a><h5>
+<a name="id693886"></a>
+            <a class="link" href="weibull.html#math_toolkit.dist.dist_ref.dists.weibull.references">References</a>
+          </h5>
+<div class="itemizedlist"><ul type="disc">
+<li>http://en.wikipedia.org/wiki/Weibull_distribution</li>
+<li><a href="http://mathworld.wolfram.com/WeibullDistribution.html" target="_top">Weisstein,
+              Eric W. "Weibull Distribution." From MathWorld--A Wolfram
+              Web Resource.</a></li>
+<li><a href="http://www.itl.nist.gov/div898/handbook/eda/section3/eda3668.htm" target="_top">Weibull
+              in NIST Exploratory Data Analysis</a></li>
+</ul></div>
+</div>
+<table xmlns:rev="http://www.cs.rpi.edu/~gregod/boost/tools/doc/revision" width="100%"><tr>
+<td align="left"></td>
+<td align="right"><div class="copyright-footer">Copyright © 2006 , 2007, 2008 John Maddock, Paul A. Bristow, Hubert
+      Holin, Xiaogang Zhang, Bruno Lalande and Gautam Sewani<p>
+        Distributed under the Boost Software License, Version 1.0. (See accompanying
+        file LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_0.txt)
+      </p>
+</div></td>
+</tr></table>
+<hr>
+<div class="spirit-nav">
+<a accesskey="p" href="triangular_dist.html"><img src="../../../../../../doc/html/images/prev.png" alt="Prev"></a><a accesskey="u" href="../dists.html"><img src="../../../../../../doc/html/images/up.png" alt="Up"></a><a accesskey="h" href="../../../../index.html"><img src="../../../../../../doc/html/images/home.png" alt="Home"></a><a accesskey="n" href="uniform_dist.html"><img src="../../../../../../doc/html/images/next.png" alt="Next"></a>
+</div>
+</body>
+</html>

Added: sandbox/tools/auto_index/example/math/doc/sf_and_dist/html/math_toolkit/dist/dist_ref/nmp.html
==============================================================================
--- (empty file)
+++ sandbox/tools/auto_index/example/math/doc/sf_and_dist/html/math_toolkit/dist/dist_ref/nmp.html	2008-11-28 05:25:28 EST (Fri, 28 Nov 2008)
@@ -0,0 +1,682 @@
+<html>
+<head>
+<meta http-equiv="Content-Type" content="text/html; charset=ISO-8859-1">
+<title>Non-Member Properties</title>
+<link rel="stylesheet" href="../../../boostbook.css" type="text/css">
+<meta name="generator" content="DocBook XSL Stylesheets Vsnapshot_8125">
+<link rel="home" href="../../../index.html" title="Math Toolkit">
+<link rel="up" href="../dist_ref.html" title="Statistical Distributions Reference">
+<link rel="prev" href="../dist_ref.html" title="Statistical Distributions Reference">
+<link rel="next" href="dists.html" title="Distributions">
+</head>
+<body bgcolor="white" text="black" link="#0000FF" vlink="#840084" alink="#0000FF">
+<table cellpadding="2" width="100%"><tr>
+<td valign="top"><img alt="Boost C++ Libraries" width="277" height="86" src="../../../../../boost.png"></td>
+<td align="center">Home</td>
+<td align="center">Libraries</td>
+<td align="center">People</td>
+<td align="center">FAQ</td>
+<td align="center">More</td>
+</tr></table>
+<hr>
+<div class="spirit-nav">
+<a accesskey="p" href="../dist_ref.html"><img src="../../../../../doc/html/images/prev.png" alt="Prev"></a><a accesskey="u" href="../dist_ref.html"><img src="../../../../../doc/html/images/up.png" alt="Up"></a><a accesskey="h" href="../../../index.html"><img src="../../../../../doc/html/images/home.png" alt="Home"></a><a accesskey="n" href="dists.html"><img src="../../../../../doc/html/images/next.png" alt="Next"></a>
+</div>
+<div class="section" lang="en">
+<div class="titlepage"><div><div><h4 class="title">
+<a name="math_toolkit.dist.dist_ref.nmp"></a><a class="link" href="nmp.html" title="Non-Member Properties"> Non-Member Properties</a>
+</h4></div></div></div>
+<p>
+          Properties that are common to all distributions are accessed via non-member
+          getter functions. This allows more of these functions to be added over
+          time as the need arises. Unfortunately the literature uses many different
+          and confusing names to refer to a rather small number of actual concepts;
+          refer to the <a class="link" href="nmp.html#concept_index">concept index</a> to find
+          the property you want by the name you are most familiar with. Or use the
+          <a class="link" href="nmp.html#function_index">function index</a> to go straight to
+          the function you want if you already know its name.
+        </p>
+<a name="function_index"></a><a name="math_toolkit.dist.dist_ref.nmp.function_index"></a><h5>
+<a name="id639139"></a>
+          <a class="link" href="nmp.html#math_toolkit.dist.dist_ref.nmp.function_index">Function
+          Index</a>
+        </h5>
+<div class="itemizedlist"><ul type="disc">
+<li>
+<a class="link" href="nmp.html#math.dist.cdf">cdf</a>.
+          </li>
+<li>
+<a class="link" href="nmp.html#math.dist.ccdf">cdf complement</a>.
+          </li>
+<li>
+<a class="link" href="nmp.html#math.dist.chf">chf</a>.
+          </li>
+<li>
+<a class="link" href="nmp.html#math.dist.hazard">hazard</a>.
+          </li>
+<li>
+<a class="link" href="nmp.html#math.dist.kurtosis">kurtosis</a>.
+          </li>
+<li><a class="link" href="nmp.html#math.dist.kurtosis_excess">kurtosis_excess</a></li>
+<li>
+<a class="link" href="nmp.html#math.dist.mean">mean</a>.
+          </li>
+<li>
+<a class="link" href="nmp.html#math.dist.median">median</a>.
+          </li>
+<li>
+<a class="link" href="nmp.html#math.dist.mode">mode</a>.
+          </li>
+<li>
+<a class="link" href="nmp.html#math.dist.pdf">pdf</a>.
+          </li>
+<li>
+<a class="link" href="nmp.html#math.dist.range">range</a>.
+          </li>
+<li>
+<a class="link" href="nmp.html#math.dist.quantile">quantile</a>.
+          </li>
+<li>
+<a class="link" href="nmp.html#math.dist.quantile_c">quantile from the complement</a>.
+          </li>
+<li>
+<a class="link" href="nmp.html#math.dist.skewness">skewness</a>.
+          </li>
+<li>
+<a class="link" href="nmp.html#math.dist.sd">standard_deviation</a>.
+          </li>
+<li>
+<a class="link" href="nmp.html#math.dist.support">support</a>.
+          </li>
+<li>
+<a class="link" href="nmp.html#math.dist.variance">variance</a>.
+          </li>
+</ul></div>
+<a name="concept_index"></a><a name="math_toolkit.dist.dist_ref.nmp.conceptual_index"></a><h5>
+<a name="id639401"></a>
+          <a class="link" href="nmp.html#math_toolkit.dist.dist_ref.nmp.conceptual_index">Conceptual
+          Index</a>
+        </h5>
+<div class="itemizedlist"><ul type="disc">
+<li>
+<a class="link" href="nmp.html#math.dist.ccdf">Complement of the Cumulative Distribution
+            Function</a>.
+          </li>
+<li>
+<a class="link" href="nmp.html#math.dist.cdf">Cumulative Distribution Function</a>.
+          </li>
+<li>
+<a class="link" href="nmp.html#math.dist.chf">Cumulative Hazard Function</a>.
+          </li>
+<li>
+<a class="link" href="nmp.html#cdf_inv">Inverse Cumulative Distribution Function</a>.
+          </li>
+<li>
+<a class="link" href="nmp.html#survival_inv">Inverse Survival Function</a>.
+          </li>
+<li><a class="link" href="nmp.html#math.dist.hazard">Hazard Function</a></li>
+<li>
+<a class="link" href="nmp.html#lower_critical">Lower Critical Value</a>.
+          </li>
+<li>
+<a class="link" href="nmp.html#math.dist.kurtosis">kurtosis</a>.
+          </li>
+<li><a class="link" href="nmp.html#math.dist.kurtosis_excess">kurtosis_excess</a></li>
+<li>
+<a class="link" href="nmp.html#math.dist.mean">mean</a>.
+          </li>
+<li>
+<a class="link" href="nmp.html#math.dist.median">median</a>.
+          </li>
+<li>
+<a class="link" href="nmp.html#math.dist.mode">mode</a>.
+          </li>
+<li>
+<a class="link" href="nmp.html#cdfPQ">P</a>.
+          </li>
+<li>
+<a class="link" href="nmp.html#percent">Percent Point Function</a>.
+          </li>
+<li>
+<a class="link" href="nmp.html#math.dist.pdf">Probability Density Function</a>.
+          </li>
+<li>
+<a class="link" href="nmp.html#pmf">Probability Mass Function</a>.
+          </li>
+<li>
+<a class="link" href="nmp.html#math.dist.range">range</a>.
+          </li>
+<li>
+<a class="link" href="nmp.html#cdfPQ">Q</a>.
+          </li>
+<li>
+<a class="link" href="nmp.html#math.dist.quantile">Quantile</a>.
+          </li>
+<li>
+<a class="link" href="nmp.html#math.dist.quantile_c">Quantile from the complement of
+            the probability</a>.
+          </li>
+<li>
+<a class="link" href="nmp.html#math.dist.skewness">skewness</a>.
+          </li>
+<li><a class="link" href="nmp.html#math.dist.sd">standard deviation</a></li>
+<li>
+<a class="link" href="nmp.html#survival">Survival Function</a>.
+          </li>
+<li>
+<a class="link" href="nmp.html#math.dist.support">support</a>.
+          </li>
+<li>
+<a class="link" href="nmp.html#upper_critical">Upper Critical Value</a>.
+          </li>
+<li>
+<a class="link" href="nmp.html#math.dist.variance">variance</a>.
+          </li>
+</ul></div>
+<a name="math.dist.cdf"></a><a name="math_toolkit.dist.dist_ref.nmp.cumulative_distribution_function"></a><h5>
+<a name="id639765"></a>
+          <a class="link" href="nmp.html#math_toolkit.dist.dist_ref.nmp.cumulative_distribution_function">Cumulative
+          Distribution Function</a>
+        </h5>
+<pre class="programlisting"><span class="keyword">template</span> <span class="special">&lt;</span><span class="keyword">class</span> <span class="identifier">RealType</span><span class="special">,</span> <span class="keyword">class</span> <a class="link" href="../../policy.html" title="Policies">Policy</a><span class="special">&gt;</span>
+<span class="identifier">RealType</span> <span class="identifier">cdf</span><span class="special">(</span><span class="keyword">const</span> <span class="emphasis"><em>Distribution-Type</em></span><span class="special">&lt;</span><span class="identifier">RealType</span><span class="special">,</span> <a class="link" href="../../policy.html" title="Policies">Policy</a><span class="special">&gt;&amp;</span> <span class="identifier">dist</span><span class="special">,</span> <span class="keyword">const</span> <span class="identifier">RealType</span><span class="special">&amp;</span> <span class="identifier">x</span><span class="special">);</span>
+</pre>
+<p>
+          The <a class="link" href="nmp.html#math.dist.cdf">Cumulative Distribution Function</a>
+          is the probability that the variable takes a value less than or equal to
+          x. It is equivalent to the integral from -infinity to x of the <a class="link" href="nmp.html#math.dist.pdf">Probability
+          Density Function</a>.
+        </p>
+<p>
+          This function may return a <a class="link" href="../../main_overview/error_handling.html#domain_error">domain_error</a>
+          if the random variable is outside the defined range for the distribution.
+        </p>
+<p>
+          For example the following graph shows the cdf for the normal distribution:
+        </p>
+<p>
+          <span class="inlinemediaobject"><img src="../../../../graphs/cdf.png" alt="cdf"></span>
+        </p>
+<a name="math.dist.ccdf"></a><a name="math_toolkit.dist.dist_ref.nmp.complement_of_the_cumulative_distribution_function"></a><h5>
+<a name="id640020"></a>
+          <a class="link" href="nmp.html#math_toolkit.dist.dist_ref.nmp.complement_of_the_cumulative_distribution_function">Complement
+          of the Cumulative Distribution Function</a>
+        </h5>
+<pre class="programlisting"><span class="keyword">template</span> <span class="special">&lt;</span><span class="keyword">class</span> <span class="identifier">Distribution</span><span class="special">,</span> <span class="keyword">class</span> <span class="identifier">RealType</span><span class="special">&gt;</span>
+<span class="identifier">RealType</span> <span class="identifier">cdf</span><span class="special">(</span><span class="keyword">const</span> <span class="emphasis"><em>Unspecified-Complement-Type</em></span><span class="special">&lt;</span><span class="identifier">Distribution</span><span class="special">,</span> <span class="identifier">RealType</span><span class="special">&gt;&amp;</span> <span class="identifier">comp</span><span class="special">);</span>
+</pre>
+<p>
+          The complement of the <a class="link" href="nmp.html#math.dist.cdf">Cumulative Distribution
+          Function</a> is the probability that the variable takes a value greater
+          than x. It is equivalent to the integral from x to infinity of the <a class="link" href="nmp.html#math.dist.pdf">Probability Density Function</a>, or 1 minus
+          the <a class="link" href="nmp.html#math.dist.cdf">Cumulative Distribution Function</a>
+          of x.
+        </p>
+<p>
+          This is also known as the survival function.
+        </p>
+<p>
+          This function may return a <a class="link" href="../../main_overview/error_handling.html#domain_error">domain_error</a>
+          if the random variable is outside the defined range for the distribution.
+        </p>
+<p>
+          In this library, it is obtained by wrapping the arguments to the <code class="computeroutput"><span class="identifier">cdf</span></code> function in a call to <code class="computeroutput"><span class="identifier">complement</span></code>, for example:
+        </p>
+<pre class="programlisting"><span class="comment">// standard normal distribution object:
+</span><span class="identifier">boost</span><span class="special">::</span><span class="identifier">math</span><span class="special">::</span><span class="identifier">normal</span> <span class="identifier">norm</span><span class="special">;</span>
+<span class="comment">// print survival function for x=2.0:
+</span><span class="identifier">std</span><span class="special">::</span><span class="identifier">cout</span> <span class="special">&lt;&lt;</span> <span class="identifier">cdf</span><span class="special">(</span><span class="identifier">complement</span><span class="special">(</span><span class="identifier">norm</span><span class="special">,</span> <span class="number">2.0</span><span class="special">))</span> <span class="special">&lt;&lt;</span> <span class="identifier">std</span><span class="special">::</span><span class="identifier">endl</span><span class="special">;</span>
+</pre>
+<p>
+          For example the following graph shows the __complement of the cdf for the
+          normal distribution:
+        </p>
+<p>
+          <span class="inlinemediaobject"><img src="../../../../graphs/survival.png" alt="survival"></span>
+        </p>
+<p>
+          See <a class="link" href="../stat_tut/overview.html#why_complements">why complements?</a> for why the
+          complement is useful and when it should be used.
+        </p>
+<a name="math.dist.hazard"></a><a name="math_toolkit.dist.dist_ref.nmp.hazard_function"></a><h5>
+<a name="id640450"></a>
+          <a class="link" href="nmp.html#math_toolkit.dist.dist_ref.nmp.hazard_function">Hazard Function</a>
+        </h5>
+<pre class="programlisting"><span class="keyword">template</span> <span class="special">&lt;</span><span class="keyword">class</span> <span class="identifier">RealType</span><span class="special">,</span> <span class="keyword">class</span> <a class="link" href="../../policy.html" title="Policies">Policy</a><span class="special">&gt;</span>
+<span class="identifier">RealType</span> <span class="identifier">hazard</span><span class="special">(</span><span class="keyword">const</span> <span class="emphasis"><em>Distribution-Type</em></span><span class="special">&lt;</span><span class="identifier">RealType</span><span class="special">,</span> <a class="link" href="../../policy.html" title="Policies">Policy</a><span class="special">&gt;&amp;</span> <span class="identifier">dist</span><span class="special">,</span> <span class="keyword">const</span> <span class="identifier">RealType</span><span class="special">&amp;</span> <span class="identifier">x</span><span class="special">);</span>
+</pre>
+<p>
+          Returns the <a class="link" href="nmp.html#math.dist.hazard">Hazard Function</a> of
+          <span class="emphasis"><em>x</em></span> and distibution <span class="emphasis"><em>dist</em></span>.
+        </p>
+<p>
+          This function may return a <a class="link" href="../../main_overview/error_handling.html#domain_error">domain_error</a>
+          if the random variable is outside the defined range for the distribution.
+        </p>
+<p>
+          <span class="inlinemediaobject"><img src="../../../../equations/hazard.png"></span>
+        </p>
+<div class="caution"><table border="0" summary="Caution">
+<tr>
+<td rowspan="2" align="center" valign="top" width="25"><img alt="[Caution]" src="../../../../../doc/html/images/caution.png"></td>
+<th align="left">Caution</th>
+</tr>
+<tr><td align="left" valign="top"><p>
+            Some authors refer to this as the conditional failure density function
+            rather than the hazard function.
+          </p></td></tr>
+</table></div>
+<a name="math.dist.chf"></a><a name="math_toolkit.dist.dist_ref.nmp.cumulative_hazard_function"></a><h5>
+<a name="id640708"></a>
+          <a class="link" href="nmp.html#math_toolkit.dist.dist_ref.nmp.cumulative_hazard_function">Cumulative
+          Hazard Function</a>
+        </h5>
+<pre class="programlisting"><span class="keyword">template</span> <span class="special">&lt;</span><span class="keyword">class</span> <span class="identifier">RealType</span><span class="special">,</span> <span class="keyword">class</span> <a class="link" href="../../policy.html" title="Policies">Policy</a><span class="special">&gt;</span>
+<span class="identifier">RealType</span> <span class="identifier">chf</span><span class="special">(</span><span class="keyword">const</span> <span class="emphasis"><em>Distribution-Type</em></span><span class="special">&lt;</span><span class="identifier">RealType</span><span class="special">,</span> <a class="link" href="../../policy.html" title="Policies">Policy</a><span class="special">&gt;&amp;</span> <span class="identifier">dist</span><span class="special">,</span> <span class="keyword">const</span> <span class="identifier">RealType</span><span class="special">&amp;</span> <span class="identifier">x</span><span class="special">);</span>
+</pre>
+<p>
+          Returns the <a class="link" href="nmp.html#math.dist.chf">Cumulative Hazard Function</a>
+          of <span class="emphasis"><em>x</em></span> and distibution <span class="emphasis"><em>dist</em></span>.
+        </p>
+<p>
+          This function may return a <a class="link" href="../../main_overview/error_handling.html#domain_error">domain_error</a>
+          if the random variable is outside the defined range for the distribution.
+        </p>
+<p>
+          <span class="inlinemediaobject"><img src="../../../../equations/chf.png"></span>
+        </p>
+<div class="caution"><table border="0" summary="Caution">
+<tr>
+<td rowspan="2" align="center" valign="top" width="25"><img alt="[Caution]" src="../../../../../doc/html/images/caution.png"></td>
+<th align="left">Caution</th>
+</tr>
+<tr><td align="left" valign="top"><p>
+            Some authors refer to this as simply the "Hazard Function".
+          </p></td></tr>
+</table></div>
+<a name="math.dist.mean"></a><a name="math_toolkit.dist.dist_ref.nmp.mean"></a><h5>
+<a name="id640966"></a>
+          <a class="link" href="nmp.html#math_toolkit.dist.dist_ref.nmp.mean">mean</a>
+        </h5>
+<pre class="programlisting"><span class="keyword">template</span><span class="special">&lt;</span><span class="keyword">class</span> <span class="identifier">RealType</span><span class="special">,</span> <span class="keyword">class</span> <a class="link" href="../../policy.html" title="Policies">Policy</a><span class="special">&gt;</span>
+<span class="identifier">RealType</span> <span class="identifier">mean</span><span class="special">(</span><span class="keyword">const</span> <span class="emphasis"><em>Distribution-Type</em></span><span class="special">&lt;</span><span class="identifier">RealType</span><span class="special">,</span> <a class="link" href="../../policy.html" title="Policies">Policy</a><span class="special">&gt;&amp;</span> <span class="identifier">dist</span><span class="special">);</span>
+</pre>
+<p>
+          Returns the mean of the distribution <span class="emphasis"><em>dist</em></span>.
+        </p>
+<p>
+          This function may return a <a class="link" href="../../main_overview/error_handling.html#domain_error">domain_error</a>
+          if the distribution does not have a defined mean (for example the Cauchy
+          distribution).
+        </p>
+<a name="math.dist.median"></a><a name="math_toolkit.dist.dist_ref.nmp.median"></a><h5>
+<a name="id641142"></a>
+          <a class="link" href="nmp.html#math_toolkit.dist.dist_ref.nmp.median">median</a>
+        </h5>
+<pre class="programlisting"><span class="keyword">template</span><span class="special">&lt;</span><span class="keyword">class</span> <span class="identifier">RealType</span><span class="special">,</span> <span class="keyword">class</span> <a class="link" href="../../policy.html" title="Policies">Policy</a><span class="special">&gt;</span>
+<span class="identifier">RealType</span> <span class="identifier">median</span><span class="special">(</span><span class="keyword">const</span> <span class="emphasis"><em>Distribution-Type</em></span><span class="special">&lt;</span><span class="identifier">RealType</span><span class="special">,</span> <a class="link" href="../../policy.html" title="Policies">Policy</a><span class="special">&gt;&amp;</span> <span class="identifier">dist</span><span class="special">);</span>
+</pre>
+<p>
+          Returns the median of the distribution <span class="emphasis"><em>dist</em></span>.
+        </p>
+<a name="math.dist.mode"></a><a name="math_toolkit.dist.dist_ref.nmp.mode"></a><h5>
+<a name="id641300"></a>
+          <a class="link" href="nmp.html#math_toolkit.dist.dist_ref.nmp.mode">mode</a>
+        </h5>
+<pre class="programlisting"><span class="keyword">template</span><span class="special">&lt;</span><span class="keyword">class</span> <span class="identifier">RealType</span><span class="special">,</span> <a class="link" href="../../policy.html" title="Policies">Policy</a><span class="special">&gt;</span>
+<span class="identifier">RealType</span> <span class="identifier">mode</span><span class="special">(</span><span class="keyword">const</span> <span class="emphasis"><em>Distribution-Type</em></span><span class="special">&lt;</span><span class="identifier">RealType</span><span class="special">,</span> <a class="link" href="../../policy.html" title="Policies">Policy</a><span class="special">&gt;&amp;</span> <span class="identifier">dist</span><span class="special">);</span>
+</pre>
+<p>
+          Returns the mode of the distribution <span class="emphasis"><em>dist</em></span>.
+        </p>
+<p>
+          This function may return a <a class="link" href="../../main_overview/error_handling.html#domain_error">domain_error</a>
+          if the distribution does not have a defined mode.
+        </p>
+<a name="math.dist.pdf"></a><a name="math_toolkit.dist.dist_ref.nmp.probability_density_function"></a><h5>
+<a name="id641467"></a>
+          <a class="link" href="nmp.html#math_toolkit.dist.dist_ref.nmp.probability_density_function">Probability
+          Density Function</a>
+        </h5>
+<pre class="programlisting"><span class="keyword">template</span> <span class="special">&lt;</span><span class="keyword">class</span> <span class="identifier">RealType</span><span class="special">,</span> <span class="keyword">class</span> <a class="link" href="../../policy.html" title="Policies">Policy</a><span class="special">&gt;</span>
+<span class="identifier">RealType</span> <span class="identifier">pdf</span><span class="special">(</span><span class="keyword">const</span> <span class="emphasis"><em>Distribution-Type</em></span><span class="special">&lt;</span><span class="identifier">RealType</span><span class="special">,</span> <a class="link" href="../../policy.html" title="Policies">Policy</a><span class="special">&gt;&amp;</span> <span class="identifier">dist</span><span class="special">,</span> <span class="keyword">const</span> <span class="identifier">RealType</span><span class="special">&amp;</span> <span class="identifier">x</span><span class="special">);</span>
+</pre>
+<p>
+          For a continuous function, the probability density function (pdf) returns
+          the probability that the variate has the value x. Since for continuous
+          distributions the probability at a single point is actually zero, the probability
+          is better expressed as the integral of the pdf between two points: see
+          the <a class="link" href="nmp.html#math.dist.cdf">Cumulative Distribution Function</a>.
+        </p>
+<p>
+          For a discrete distribution, the pdf is the probability that the variate
+          takes the value x.
+        </p>
+<p>
+          This function may return a <a class="link" href="../../main_overview/error_handling.html#domain_error">domain_error</a>
+          if the random variable is outside the defined range for the distribution.
+        </p>
+<p>
+          For example for a standard normal distribution the pdf looks like this:
+        </p>
+<p>
+          <span class="inlinemediaobject"><img src="../../../../graphs/pdf.png" alt="pdf"></span>
+        </p>
+<a name="math.dist.range"></a><a name="math_toolkit.dist.dist_ref.nmp.range"></a><h5>
+<a name="id641724"></a>
+          <a class="link" href="nmp.html#math_toolkit.dist.dist_ref.nmp.range">range</a>
+        </h5>
+<pre class="programlisting"><span class="keyword">template</span><span class="special">&lt;</span><span class="keyword">class</span> <span class="identifier">RealType</span><span class="special">,</span> <span class="keyword">class</span> <a class="link" href="../../policy.html" title="Policies">Policy</a><span class="special">&gt;</span>
+<span class="identifier">std</span><span class="special">::</span><span class="identifier">pair</span><span class="special">&lt;</span><span class="identifier">RealType</span><span class="special">,</span> <span class="identifier">RealType</span><span class="special">&gt;</span> <span class="identifier">range</span><span class="special">(</span><span class="keyword">const</span> <span class="emphasis"><em>Distribution-Type</em></span><span class="special">&lt;</span><span class="identifier">RealType</span><span class="special">,</span> <a class="link" href="../../policy.html" title="Policies">Policy</a><span class="special">&gt;&amp;</span> <span class="identifier">dist</span><span class="special">);</span>
+</pre>
+<p>
+          Returns the valid range of the random variable over distribution <span class="emphasis"><em>dist</em></span>.
+        </p>
+<a name="math.dist.quantile"></a><a name="math_toolkit.dist.dist_ref.nmp.quantile"></a><h5>
+<a name="id641920"></a>
+          <a class="link" href="nmp.html#math_toolkit.dist.dist_ref.nmp.quantile">Quantile</a>
+        </h5>
+<pre class="programlisting"><span class="keyword">template</span> <span class="special">&lt;</span><span class="keyword">class</span> <span class="identifier">RealType</span><span class="special">,</span> <span class="keyword">class</span> <a class="link" href="../../policy.html" title="Policies">Policy</a><span class="special">&gt;</span>
+<span class="identifier">RealType</span> <span class="identifier">quantile</span><span class="special">(</span><span class="keyword">const</span> <span class="emphasis"><em>Distribution-Type</em></span><span class="special">&lt;</span><span class="identifier">RealType</span><span class="special">,</span> <a class="link" href="../../policy.html" title="Policies">Policy</a><span class="special">&gt;&amp;</span> <span class="identifier">dist</span><span class="special">,</span> <span class="keyword">const</span> <span class="identifier">RealType</span><span class="special">&amp;</span> <span class="identifier">p</span><span class="special">);</span>
+</pre>
+<p>
+          The quantile is best viewed as the inverse of the <a class="link" href="nmp.html#math.dist.cdf">Cumulative
+          Distribution Function</a>, it returns a value <span class="emphasis"><em>x</em></span>
+          such that <code class="computeroutput"><span class="identifier">cdf</span><span class="special">(</span><span class="identifier">dist</span><span class="special">,</span> <span class="identifier">x</span><span class="special">)</span> <span class="special">==</span>
+          <span class="identifier">p</span></code>.
+        </p>
+<p>
+          This is also known as the <span class="emphasis"><em>percent point function</em></span>,
+          or a <span class="emphasis"><em>percentile</em></span>, it is also the same as calculating
+          the <span class="emphasis"><em>lower critical value</em></span> of a distribution.
+        </p>
+<p>
+          This function returns a <a class="link" href="../../main_overview/error_handling.html#domain_error">domain_error</a>
+          if the probability lies outside [0,1]. The function may return an <a class="link" href="../../main_overview/error_handling.html#overflow_error">overflow_error</a> if there is no finite value
+          that has the specified probability.
+        </p>
+<p>
+          The following graph shows the quantile function for a standard normal distribution:
+        </p>
+<p>
+          <span class="inlinemediaobject"><img src="../../../../graphs/quantile.png" alt="quantile"></span>
+        </p>
+<a name="math.dist.quantile_c"></a><a name="math_toolkit.dist.dist_ref.nmp.quantile_from_the_complement_of_the_probability_"></a><h5>
+<a name="id642241"></a>
+          <a class="link" href="nmp.html#math_toolkit.dist.dist_ref.nmp.quantile_from_the_complement_of_the_probability_">Quantile
+          from the complement of the probability.</a>
+        </h5>
+<p>
+          <a class="link" href="../stat_tut/overview.html#complements">complements</a>
+        </p>
+<pre class="programlisting"><span class="keyword">template</span> <span class="special">&lt;</span><span class="keyword">class</span> <span class="identifier">Distribution</span><span class="special">,</span> <span class="keyword">class</span> <span class="identifier">RealType</span><span class="special">&gt;</span>
+<span class="identifier">RealType</span> <span class="identifier">quantile</span><span class="special">(</span><span class="keyword">const</span> <span class="emphasis"><em>Unspecified-Complement-Type</em></span><span class="special">&lt;</span><span class="identifier">Distribution</span><span class="special">,</span> <span class="identifier">RealType</span><span class="special">&gt;&amp;</span> <span class="identifier">comp</span><span class="special">);</span>
+</pre>
+<p>
+          This is the inverse of the <a class="link" href="nmp.html#math.dist.ccdf">Complement of
+          the Cumulative Distribution Function</a>. It is calculated by wrapping
+          the arguments in a call to the quantile function in a call to <span class="emphasis"><em>complement</em></span>.
+          For example:
+        </p>
+<pre class="programlisting"><span class="comment">// define a standard normal distribution:
+</span><span class="identifier">boost</span><span class="special">::</span><span class="identifier">math</span><span class="special">::</span><span class="identifier">normal</span> <span class="identifier">norm</span><span class="special">;</span>
+<span class="comment">// print the value of x for which the complement
+</span><span class="comment">// of the probability is 0.05:
+</span><span class="identifier">std</span><span class="special">::</span><span class="identifier">cout</span> <span class="special">&lt;&lt;</span> <span class="identifier">quantile</span><span class="special">(</span><span class="identifier">complement</span><span class="special">(</span><span class="identifier">norm</span><span class="special">,</span> <span class="number">0.05</span><span class="special">))</span> <span class="special">&lt;&lt;</span> <span class="identifier">std</span><span class="special">::</span><span class="identifier">endl</span><span class="special">;</span>
+</pre>
+<p>
+          The function computes a value <span class="emphasis"><em>x</em></span> such that <code class="computeroutput"><span class="identifier">cdf</span><span class="special">(</span><span class="identifier">complement</span><span class="special">(</span><span class="identifier">dist</span><span class="special">,</span> <span class="identifier">x</span><span class="special">))</span> <span class="special">==</span> <span class="identifier">q</span></code>
+          where <span class="emphasis"><em>q</em></span> is complement of the probability.
+        </p>
+<p>
+          <a class="link" href="../stat_tut/overview.html#why_complements">Why complements?</a>
+        </p>
+<p>
+          This function is also called the inverse survival function, and is the
+          same as calculating the <span class="emphasis"><em>upper critical value</em></span> of a
+          distribution.
+        </p>
+<p>
+          This function returns a <a class="link" href="../../main_overview/error_handling.html#domain_error">domain_error</a>
+          if the probablity lies outside [0,1]. The function may return an <a class="link" href="../../main_overview/error_handling.html#overflow_error">overflow_error</a> if there is no finite value
+          that has the specified probability.
+        </p>
+<p>
+          The following graph show the inverse survival function for the normal distribution:
+        </p>
+<p>
+          <span class="inlinemediaobject"><img src="../../../../graphs/survival_inv.png" alt="survival_inv"></span>
+        </p>
+<a name="math.dist.sd"></a><a name="math_toolkit.dist.dist_ref.nmp.standard_deviation"></a><h5>
+<a name="id642732"></a>
+          <a class="link" href="nmp.html#math_toolkit.dist.dist_ref.nmp.standard_deviation">Standard
+          Deviation</a>
+        </h5>
+<pre class="programlisting"><span class="keyword">template</span> <span class="special">&lt;</span><span class="keyword">class</span> <span class="identifier">RealType</span><span class="special">,</span> <span class="keyword">class</span> <a class="link" href="../../policy.html" title="Policies">Policy</a><span class="special">&gt;</span>
+<span class="identifier">RealType</span> <span class="identifier">standard_deviation</span><span class="special">(</span><span class="keyword">const</span> <span class="emphasis"><em>Distribution-Type</em></span><span class="special">&lt;</span><span class="identifier">RealType</span><span class="special">,</span> <a class="link" href="../../policy.html" title="Policies">Policy</a><span class="special">&gt;&amp;</span> <span class="identifier">dist</span><span class="special">);</span>
+</pre>
+<p>
+          Returns the standard deviation of distribution <span class="emphasis"><em>dist</em></span>.
+        </p>
+<p>
+          This function may return a <a class="link" href="../../main_overview/error_handling.html#domain_error">domain_error</a>
+          if the distribution does not have a defined standard deviation.
+        </p>
+<a name="math.dist.support"></a><a name="math_toolkit.dist.dist_ref.nmp.support"></a><h5>
+<a name="id642911"></a>
+          <a class="link" href="nmp.html#math_toolkit.dist.dist_ref.nmp.support">support</a>
+        </h5>
+<pre class="programlisting"><span class="keyword">template</span><span class="special">&lt;</span><span class="keyword">class</span> <span class="identifier">RealType</span><span class="special">,</span> <span class="keyword">class</span> <a class="link" href="../../policy.html" title="Policies">Policy</a><span class="special">&gt;</span>
+<span class="identifier">std</span><span class="special">::</span><span class="identifier">pair</span><span class="special">&lt;</span><span class="identifier">RealType</span><span class="special">,</span> <span class="identifier">RealType</span><span class="special">&gt;</span> <span class="identifier">support</span><span class="special">(</span><span class="keyword">const</span> <span class="emphasis"><em>Distribution-Type</em></span><span class="special">&lt;</span><span class="identifier">RealType</span><span class="special">,</span> <a class="link" href="../../policy.html" title="Policies">Policy</a><span class="special">&gt;&amp;</span> <span class="identifier">dist</span><span class="special">);</span>
+</pre>
+<p>
+          Returns the supported range of random variable over the distribution <span class="emphasis"><em>dist</em></span>.
+        </p>
+<p>
+          The distribution is said to be 'supported' over a range that is <a href="http://en.wikipedia.org/wiki/Probability_distribution" target="_top">"the smallest
+          closed set whose complement has probability zero"</a>. Non-mathematicians
+          might say it means the 'interesting' smallest range of random variate x
+          that has the cdf going from zero to unity. Outside are uninteresting zones
+          where the pdf is zero, and the cdf zero or unity.
+        </p>
+<a name="math.dist.variance"></a><a name="math_toolkit.dist.dist_ref.nmp.variance"></a><h5>
+<a name="id643129"></a>
+          <a class="link" href="nmp.html#math_toolkit.dist.dist_ref.nmp.variance">Variance</a>
+        </h5>
+<pre class="programlisting"><span class="keyword">template</span> <span class="special">&lt;</span><span class="keyword">class</span> <span class="identifier">RealType</span><span class="special">,</span> <span class="keyword">class</span> <a class="link" href="../../policy.html" title="Policies">Policy</a><span class="special">&gt;</span>
+<span class="identifier">RealType</span> <span class="identifier">variance</span><span class="special">(</span><span class="keyword">const</span> <span class="emphasis"><em>Distribution-Type</em></span><span class="special">&lt;</span><span class="identifier">RealType</span><span class="special">,</span> <a class="link" href="../../policy.html" title="Policies">Policy</a><span class="special">&gt;&amp;</span> <span class="identifier">dist</span><span class="special">);</span>
+</pre>
+<p>
+          Returns the variance of the distribution <span class="emphasis"><em>dist</em></span>.
+        </p>
+<p>
+          This function may return a <a class="link" href="../../main_overview/error_handling.html#domain_error">domain_error</a>
+          if the distribution does not have a defined variance.
+        </p>
+<a name="math.dist.skewness"></a><a name="math_toolkit.dist.dist_ref.nmp.skewness"></a><h5>
+<a name="id643304"></a>
+          <a class="link" href="nmp.html#math_toolkit.dist.dist_ref.nmp.skewness">Skewness</a>
+        </h5>
+<pre class="programlisting"><span class="keyword">template</span> <span class="special">&lt;</span><span class="keyword">class</span> <span class="identifier">RealType</span><span class="special">,</span> <span class="keyword">class</span> <a class="link" href="../../policy.html" title="Policies">Policy</a><span class="special">&gt;</span>
+<span class="identifier">RealType</span> <span class="identifier">skewness</span><span class="special">(</span><span class="keyword">const</span> <span class="emphasis"><em>Distribution-Type</em></span><span class="special">&lt;</span><span class="identifier">RealType</span><span class="special">,</span> <a class="link" href="../../policy.html" title="Policies">Policy</a><span class="special">&gt;&amp;</span> <span class="identifier">dist</span><span class="special">);</span>
+</pre>
+<p>
+          Returns the skewness of the distribution <span class="emphasis"><em>dist</em></span>.
+        </p>
+<p>
+          This function may return a <a class="link" href="../../main_overview/error_handling.html#domain_error">domain_error</a>
+          if the distribution does not have a defined skewness.
+        </p>
+<a name="math.dist.kurtosis"></a><a name="math_toolkit.dist.dist_ref.nmp.kurtosis"></a><h5>
+<a name="id643480"></a>
+          <a class="link" href="nmp.html#math_toolkit.dist.dist_ref.nmp.kurtosis">Kurtosis</a>
+        </h5>
+<pre class="programlisting"><span class="keyword">template</span> <span class="special">&lt;</span><span class="keyword">class</span> <span class="identifier">RealType</span><span class="special">,</span> <span class="keyword">class</span> <a class="link" href="../../policy.html" title="Policies">Policy</a><span class="special">&gt;</span>
+<span class="identifier">RealType</span> <span class="identifier">kurtosis</span><span class="special">(</span><span class="keyword">const</span> <span class="emphasis"><em>Distribution-Type</em></span><span class="special">&lt;</span><span class="identifier">RealType</span><span class="special">,</span> <a class="link" href="../../policy.html" title="Policies">Policy</a><span class="special">&gt;&amp;</span> <span class="identifier">dist</span><span class="special">);</span>
+</pre>
+<p>
+          Returns the 'proper' kurtosis (normalized fourth moment) of the distribution
+          <span class="emphasis"><em>dist</em></span>.
+        </p>
+<p>
+          kertosis = &#946;<sub>2</sub>= &#956;<sub>4</sub> / &#956;<sub>2</sub><sup>2</sup>
+        </p>
+<p>
+          Where &#956;<sub>i</sub> is the i'th central moment of the distribution, and in particular
+          &#956;<sub>2</sub> is the variance of the distribution.
+        </p>
+<p>
+          The kurtosis is a measure of the "peakedness" of a distribution.
+        </p>
+<p>
+          Note that the literature definition of kurtosis is confusing. The definition
+          used here is that used by for example <a href="http://mathworld.wolfram.com/Kurtosis.html" target="_top">Wolfram
+          MathWorld</a> (that includes a table of formulae for kurtosis excess
+          for various distributions) but NOT the definition of <a href="http://en.wikipedia.org/wiki/Kurtosis" target="_top">kurtosis
+          used by Wikipedia</a> which treats "kurtosis" and "kurtosis
+          excess" as the same quantity.
+        </p>
+<pre class="programlisting"><span class="identifier">kurtosis_excess</span> <span class="special">=</span> <span class="char">'proper'</span> <span class="identifier">kurtosis</span> <span class="special">-</span> <span class="number">3</span>
+</pre>
+<p>
+          This subtraction of 3 is convenient so that the <span class="emphasis"><em>kurtosis excess</em></span>
+          of a normal distribution is zero.
+        </p>
+<p>
+          This function may return a <a class="link" href="../../main_overview/error_handling.html#domain_error">domain_error</a>
+          if the distribution does not have a defined kurtosis.
+        </p>
+<p>
+          'Proper' kurtosis can have a value from zero to + infinity.
+        </p>
+<a name="math.dist.kurtosis_excess"></a><a name="math_toolkit.dist.dist_ref.nmp.kurtosis_excess"></a><h5>
+<a name="id643794"></a>
+          <a class="link" href="nmp.html#math_toolkit.dist.dist_ref.nmp.kurtosis_excess">Kurtosis
+          excess</a>
+        </h5>
+<pre class="programlisting"><span class="keyword">template</span> <span class="special">&lt;</span><span class="keyword">class</span> <span class="identifier">RealType</span><span class="special">,</span> <a class="link" href="../../policy.html" title="Policies">Policy</a><span class="special">&gt;</span>
+<span class="identifier">RealType</span> <span class="identifier">kurtosis_excess</span><span class="special">(</span><span class="keyword">const</span> <span class="emphasis"><em>Distribution-Type</em></span><span class="special">&lt;</span><span class="identifier">RealType</span><span class="special">,</span> <a class="link" href="../../policy.html" title="Policies">Policy</a><span class="special">&gt;&amp;</span> <span class="identifier">dist</span><span class="special">);</span>
+</pre>
+<p>
+          Returns the kurtosis excess of the distribution <span class="emphasis"><em>dist</em></span>.
+        </p>
+<p>
+          kurtosis excess = &#947;<sub>2</sub>= &#956;<sub>4</sub> / &#956;<sub>2</sub><sup>2</sup>- 3 = kurtosis - 3
+        </p>
+<p>
+          Where &#956;<sub>i</sub> is the i'th central moment of the distribution, and in particular
+          &#956;<sub>2</sub> is the variance of the distribution.
+        </p>
+<p>
+          The kurtosis excess is a measure of the "peakedness" of a distribution,
+          and is more widely used than the "kurtosis proper". It is defined
+          so that the kurtosis excess of a normal distribution is zero.
+        </p>
+<p>
+          This function may return a <a class="link" href="../../main_overview/error_handling.html#domain_error">domain_error</a>
+          if the distribution does not have a defined kurtosis excess.
+        </p>
+<p>
+          Kurtosis excess can have a value from -2 to + infinity.
+        </p>
+<pre class="programlisting"><span class="identifier">kurtosis</span> <span class="special">=</span> <span class="identifier">kurtosis_excess</span> <span class="special">+</span><span class="number">3</span><span class="special">;</span>
+</pre>
+<p>
+          The kurtosis excess of a normal distribution is zero.
+        </p>
+<a name="cdfPQ"></a><a name="math_toolkit.dist.dist_ref.nmp.p_and_q"></a><h5>
+<a name="id644061"></a>
+          <a class="link" href="nmp.html#math_toolkit.dist.dist_ref.nmp.p_and_q">P and Q</a>
+        </h5>
+<p>
+          The terms P and Q are sometimes used to refer to the <a class="link" href="nmp.html#math.dist.cdf">Cumulative
+          Distribution Function</a> and its <a class="link" href="nmp.html#math.dist.ccdf">complement</a>
+          respectively. Lowercase p and q are sometimes used to refer to the values
+          returned by these functions.
+        </p>
+<a name="percent"></a><a name="math_toolkit.dist.dist_ref.nmp.percent_point_function"></a><h5>
+<a name="id644118"></a>
+          <a class="link" href="nmp.html#math_toolkit.dist.dist_ref.nmp.percent_point_function">Percent
+          Point Function</a>
+        </h5>
+<p>
+          The percent point function, also known as the percentile, is the same as
+          the <a class="link" href="nmp.html#math.dist.quantile">Quantile</a>.
+        </p>
+<a name="cdf_inv"></a><a name="math_toolkit.dist.dist_ref.nmp.inverse_cdf_function_"></a><h5>
+<a name="id644165"></a>
+          <a class="link" href="nmp.html#math_toolkit.dist.dist_ref.nmp.inverse_cdf_function_">Inverse
+          CDF Function.</a>
+        </h5>
+<p>
+          The inverse of the cumulative distribution function, is the same as the
+          <a class="link" href="nmp.html#math.dist.quantile">Quantile</a>.
+        </p>
+<a name="survival_inv"></a><a name="math_toolkit.dist.dist_ref.nmp.inverse_survival_function_"></a><h5>
+<a name="id644212"></a>
+          <a class="link" href="nmp.html#math_toolkit.dist.dist_ref.nmp.inverse_survival_function_">Inverse
+          Survival Function.</a>
+        </h5>
+<p>
+          The inverse of the survival function, is the same as computing the <a class="link" href="nmp.html#math.dist.quantile_c">quantile from the complement of the probability</a>.
+        </p>
+<a name="pmf"></a><a name="math_toolkit.dist.dist_ref.nmp.probability_mass_function"></a><h5>
+<a name="id644259"></a>
+          <a class="link" href="nmp.html#math_toolkit.dist.dist_ref.nmp.probability_mass_function">Probability
+          Mass Function</a>
+        </h5>
+<p>
+          The Probability Mass Function is the same as the <a class="link" href="nmp.html#math.dist.pdf">Probability
+          Density Function</a>.
+        </p>
+<p>
+          The term Mass Function is usually applied to discrete distributions, while
+          the term <a class="link" href="nmp.html#math.dist.pdf">Probability Density Function</a>
+          applies to continuous distributions.
+        </p>
+<a name="lower_critical"></a><a name="math_toolkit.dist.dist_ref.nmp.lower_critical_value_"></a><h5>
+<a name="id644322"></a>
+          <a class="link" href="nmp.html#math_toolkit.dist.dist_ref.nmp.lower_critical_value_">Lower
+          Critical Value.</a>
+        </h5>
+<p>
+          The lower critical value calculates the value of the random variable given
+          the area under the left tail of the distribution. It is equivalent to calculating
+          the <a class="link" href="nmp.html#math.dist.quantile">Quantile</a>.
+        </p>
+<a name="upper_critical"></a><a name="math_toolkit.dist.dist_ref.nmp.upper_critical_value_"></a><h5>
+<a name="id644371"></a>
+          <a class="link" href="nmp.html#math_toolkit.dist.dist_ref.nmp.upper_critical_value_">Upper
+          Critical Value.</a>
+        </h5>
+<p>
+          The upper critical value calculates the value of the random variable given
+          the area under the right tail of the distribution. It is equivalent to
+          calculating the <a class="link" href="nmp.html#math.dist.quantile_c">quantile from the
+          complement of the probability</a>.
+        </p>
+<a name="survival"></a><a name="math_toolkit.dist.dist_ref.nmp.survival_function"></a><h5>
+<a name="id644420"></a>
+          <a class="link" href="nmp.html#math_toolkit.dist.dist_ref.nmp.survival_function">Survival
+          Function</a>
+        </h5>
+<p>
+          Refer to the <a class="link" href="nmp.html#math.dist.ccdf">Complement of the Cumulative
+          Distribution Function</a>.
+        </p>
+</div>
+<table xmlns:rev="http://www.cs.rpi.edu/~gregod/boost/tools/doc/revision" width="100%"><tr>
+<td align="left"></td>
+<td align="right"><div class="copyright-footer">Copyright © 2006 , 2007, 2008 John Maddock, Paul A. Bristow, Hubert
+      Holin, Xiaogang Zhang, Bruno Lalande and Gautam Sewani<p>
+        Distributed under the Boost Software License, Version 1.0. (See accompanying
+        file LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_0.txt)
+      </p>
+</div></td>
+</tr></table>
+<hr>
+<div class="spirit-nav">
+<a accesskey="p" href="../dist_ref.html"><img src="../../../../../doc/html/images/prev.png" alt="Prev"></a><a accesskey="u" href="../dist_ref.html"><img src="../../../../../doc/html/images/up.png" alt="Up"></a><a accesskey="h" href="../../../index.html"><img src="../../../../../doc/html/images/home.png" alt="Home"></a><a accesskey="n" href="dists.html"><img src="../../../../../doc/html/images/next.png" alt="Next"></a>
+</div>
+</body>
+</html>

Added: sandbox/tools/auto_index/example/math/doc/sf_and_dist/html/math_toolkit/dist/future.html
==============================================================================
--- (empty file)
+++ sandbox/tools/auto_index/example/math/doc/sf_and_dist/html/math_toolkit/dist/future.html	2008-11-28 05:25:28 EST (Fri, 28 Nov 2008)
@@ -0,0 +1,141 @@
+<html>
+<head>
+<meta http-equiv="Content-Type" content="text/html; charset=ISO-8859-1">
+<title>Extras/Future Directions</title>
+<link rel="stylesheet" href="../../boostbook.css" type="text/css">
+<meta name="generator" content="DocBook XSL Stylesheets Vsnapshot_8125">
+<link rel="home" href="../../index.html" title="Math Toolkit">
+<link rel="up" href="../dist.html" title="Statistical Distributions and Functions">
+<link rel="prev" href="dist_ref/dist_algorithms.html" title="Distribution Algorithms">
+<link rel="next" href="../special.html" title="Special Functions">
+</head>
+<body bgcolor="white" text="black" link="#0000FF" vlink="#840084" alink="#0000FF">
+<table cellpadding="2" width="100%"><tr>
+<td valign="top"><img alt="Boost C++ Libraries" width="277" height="86" src="../../../../boost.png"></td>
+<td align="center">Home</td>
+<td align="center">Libraries</td>
+<td align="center">People</td>
+<td align="center">FAQ</td>
+<td align="center">More</td>
+</tr></table>
+<hr>
+<div class="spirit-nav">
+<a accesskey="p" href="dist_ref/dist_algorithms.html"><img src="../../../../doc/html/images/prev.png" alt="Prev"></a><a accesskey="u" href="../dist.html"><img src="../../../../doc/html/images/up.png" alt="Up"></a><a accesskey="h" href="../../index.html"><img src="../../../../doc/html/images/home.png" alt="Home"></a><a accesskey="n" href="../special.html"><img src="../../../../doc/html/images/next.png" alt="Next"></a>
+</div>
+<div class="section" lang="en">
+<div class="titlepage"><div><div><h3 class="title">
+<a name="math_toolkit.dist.future"></a><a class="link" href="future.html" title="Extras/Future Directions"> Extras/Future Directions</a>
+</h3></div></div></div>
+<a name="math_toolkit.dist.future.adding_additional_location_and_scale_parameters"></a><h5>
+<a name="id697141"></a>
+        <a class="link" href="future.html#math_toolkit.dist.future.adding_additional_location_and_scale_parameters">Adding
+        Additional Location and Scale Parameters</a>
+      </h5>
+<p>
+        In some modelling applications we require a distribution with a specific
+        location and scale: often this equates to a specific mean and standard deviation,
+        although for many distributions the relationship between these properties
+        and the location and scale parameters are non-trivial. See http://www.itl.nist.gov/div898/handbook/eda/section3/eda364.htm
+        for more information.
+      </p>
+<p>
+        The obvious way to handle this is via an adapter template:
+      </p>
+<pre class="programlisting"><span class="keyword">template</span> <span class="special">&lt;</span><span class="keyword">class</span> <span class="identifier">Dist</span><span class="special">&gt;</span>
+<span class="keyword">class</span> <span class="identifier">scaled_distribution</span>
+<span class="special">{</span>
+   <span class="identifier">scaled_distribution</span><span class="special">(</span>
+     <span class="keyword">const</span> <span class="identifier">Dist</span> <span class="identifier">dist</span><span class="special">,</span> 
+     <span class="keyword">typename</span> <span class="identifier">Dist</span><span class="special">::</span><span class="identifier">value_type</span> <span class="identifier">location</span><span class="special">,</span>
+     <span class="keyword">typename</span> <span class="identifier">Dist</span><span class="special">::</span><span class="identifier">value_type</span> <span class="identifier">scale</span> <span class="special">=</span> <span class="number">0</span><span class="special">);</span>
+<span class="special">};</span>
+</pre>
+<p>
+        Which would then have its own set of overloads for the non-member accessor
+        functions.
+      </p>
+<a name="math_toolkit.dist.future.an__quot_any_distribution_quot__class"></a><h5>
+<a name="id697378"></a>
+        <a class="link" href="future.html#math_toolkit.dist.future.an__quot_any_distribution_quot__class">An
+        "any_distribution" class</a>
+      </h5>
+<p>
+        It would be fairly trivial to add a distribution object that virtualises
+        the actual type of the distribution, and can therefore hold "any"
+        object that conforms to the conceptual requirements of a distribution:
+      </p>
+<pre class="programlisting"><span class="keyword">template</span> <span class="special">&lt;</span><span class="keyword">class</span> <span class="identifier">RealType</span><span class="special">&gt;</span>
+<span class="keyword">class</span> <span class="identifier">any_distribution</span>
+<span class="special">{</span>
+<span class="keyword">public</span><span class="special">:</span>
+   <span class="keyword">template</span> <span class="special">&lt;</span><span class="keyword">class</span> <span class="identifier">Distribution</span><span class="special">&gt;</span>
+   <span class="identifier">any_distribution</span><span class="special">(</span><span class="keyword">const</span> <span class="identifier">Distribution</span><span class="special">&amp;</span> <span class="identifier">d</span><span class="special">);</span>
+<span class="special">};</span>
+
+<span class="comment">// Get the cdf of the underlying distribution:
+</span><span class="keyword">template</span> <span class="special">&lt;</span><span class="keyword">class</span> <span class="identifier">RealType</span><span class="special">&gt;</span>
+<span class="identifier">RealType</span> <span class="identifier">cdf</span><span class="special">(</span><span class="keyword">const</span> <span class="identifier">any_distribution</span><span class="special">&lt;</span><span class="identifier">RealType</span><span class="special">&gt;&amp;</span> <span class="identifier">d</span><span class="special">,</span> <span class="identifier">RealType</span> <span class="identifier">x</span><span class="special">);</span>
+<span class="comment">// etc....
+</span></pre>
+<p>
+        Such a class would facilitate the writing of non-template code that can function
+        with any distribution type. It's not clear yet whether there is a compelling
+        use case though. Possibly tests for goodness of fit might provide such a
+        use case: this needs more investigation.
+      </p>
+<a name="math_toolkit.dist.future.higher_level_hypothesis_tests"></a><h5>
+<a name="id697679"></a>
+        <a class="link" href="future.html#math_toolkit.dist.future.higher_level_hypothesis_tests">Higher
+        Level Hypothesis Tests</a>
+      </h5>
+<p>
+        Higher-level tests roughly corresponding to the <a href="http://documents.wolfram.com/mathematica/Add-onsLinks/StandardPackages/Statistics/HypothesisTests.html" target="_top">Mathematica
+        Hypothesis Tests</a> package could be added reasonably easily, for example:
+      </p>
+<pre class="programlisting"><span class="keyword">template</span> <span class="special">&lt;</span><span class="keyword">class</span> <span class="identifier">InputIterator</span><span class="special">&gt;</span>
+<span class="keyword">typename</span> <span class="identifier">std</span><span class="special">::</span><span class="identifier">iterator_traits</span><span class="special">&lt;</span><span class="identifier">InputIterator</span><span class="special">&gt;::</span><span class="identifier">value_type</span>
+   <span class="identifier">test_equal_mean</span><span class="special">(</span>
+     <span class="identifier">InputIterator</span> <span class="identifier">a</span><span class="special">,</span>
+     <span class="identifier">InputIterator</span> <span class="identifier">b</span><span class="special">,</span>
+     <span class="keyword">typename</span> <span class="identifier">std</span><span class="special">::</span><span class="identifier">iterator_traits</span><span class="special">&lt;</span><span class="identifier">InputIterator</span><span class="special">&gt;::</span><span class="identifier">value_type</span> <span class="identifier">expected_mean</span><span class="special">);</span>
+</pre>
+<p>
+        Returns the probability that the data in the sequence [a,b) has the mean
+        <span class="emphasis"><em>expected_mean</em></span>.
+      </p>
+<a name="math_toolkit.dist.future.integration_with_statistical_accumulators"></a><h5>
+<a name="id697915"></a>
+        <a class="link" href="future.html#math_toolkit.dist.future.integration_with_statistical_accumulators">Integration
+        With Statistical Accumulators</a>
+      </h5>
+<p>
+        <a href="http://boost-sandbox.sourceforge.net/libs/accumulators/doc/html/index.html" target="_top">Eric
+        Niebler's accumulator framework</a> - also work in progress - provides
+        the means to calculate various statistical properties from experimental data.
+        There is an opportunity to integrate the statistical tests with this framework
+        at some later date:
+      </p>
+<pre class="programlisting"><span class="comment">// Define an accumulator, all required statistics to calculate the test
+</span><span class="comment">// are calculated automatically:
+</span><span class="identifier">accumulator_set</span><span class="special">&lt;</span><span class="keyword">double</span><span class="special">,</span> <span class="identifier">features</span><span class="special">&lt;</span><span class="identifier">tag</span><span class="special">::</span><span class="identifier">test_expected_mean</span><span class="special">&gt;</span> <span class="special">&gt;</span> <span class="identifier">acc</span><span class="special">(</span><span class="identifier">expected_mean</span><span class="special">=</span><span class="number">4</span><span class="special">);</span>
+<span class="comment">// Pass our data to the accumulator:
+</span><span class="identifier">acc</span> <span class="special">=</span> <span class="identifier">std</span><span class="special">::</span><span class="identifier">for_each</span><span class="special">(</span><span class="identifier">mydata</span><span class="special">.</span><span class="identifier">begin</span><span class="special">(),</span> <span class="identifier">mydata</span><span class="special">.</span><span class="identifier">end</span><span class="special">(),</span> <span class="identifier">acc</span><span class="special">);</span>
+<span class="comment">// Extract the result:
+</span><span class="keyword">double</span> <span class="identifier">p</span> <span class="special">=</span> <span class="identifier">probability</span><span class="special">(</span><span class="identifier">acc</span><span class="special">);</span>
+</pre>
+</div>
+<table xmlns:rev="http://www.cs.rpi.edu/~gregod/boost/tools/doc/revision" width="100%"><tr>
+<td align="left"></td>
+<td align="right"><div class="copyright-footer">Copyright © 2006 , 2007, 2008 John Maddock, Paul A. Bristow, Hubert
+      Holin, Xiaogang Zhang, Bruno Lalande and Gautam Sewani<p>
+        Distributed under the Boost Software License, Version 1.0. (See accompanying
+        file LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_0.txt)
+      </p>
+</div></td>
+</tr></table>
+<hr>
+<div class="spirit-nav">
+<a accesskey="p" href="dist_ref/dist_algorithms.html"><img src="../../../../doc/html/images/prev.png" alt="Prev"></a><a accesskey="u" href="../dist.html"><img src="../../../../doc/html/images/up.png" alt="Up"></a><a accesskey="h" href="../../index.html"><img src="../../../../doc/html/images/home.png" alt="Home"></a><a accesskey="n" href="../special.html"><img src="../../../../doc/html/images/next.png" alt="Next"></a>
+</div>
+</body>
+</html>

Added: sandbox/tools/auto_index/example/math/doc/sf_and_dist/html/math_toolkit/dist/stat_tut.html
==============================================================================
--- (empty file)
+++ sandbox/tools/auto_index/example/math/doc/sf_and_dist/html/math_toolkit/dist/stat_tut.html	2008-11-28 05:25:28 EST (Fri, 28 Nov 2008)
@@ -0,0 +1,138 @@
+<html>
+<head>
+<meta http-equiv="Content-Type" content="text/html; charset=ISO-8859-1">
+<title>Statistical Distributions Tutorial</title>
+<link rel="stylesheet" href="../../boostbook.css" type="text/css">
+<meta name="generator" content="DocBook XSL Stylesheets Vsnapshot_8125">
+<link rel="home" href="../../index.html" title="Math Toolkit">
+<link rel="up" href="../dist.html" title="Statistical Distributions and Functions">
+<link rel="prev" href="../dist.html" title="Statistical Distributions and Functions">
+<link rel="next" href="stat_tut/overview.html" title="Overview">
+</head>
+<body bgcolor="white" text="black" link="#0000FF" vlink="#840084" alink="#0000FF">
+<table cellpadding="2" width="100%"><tr>
+<td valign="top"><img alt="Boost C++ Libraries" width="277" height="86" src="../../../../boost.png"></td>
+<td align="center">Home</td>
+<td align="center">Libraries</td>
+<td align="center">People</td>
+<td align="center">FAQ</td>
+<td align="center">More</td>
+</tr></table>
+<hr>
+<div class="spirit-nav">
+<a accesskey="p" href="../dist.html"><img src="../../../../doc/html/images/prev.png" alt="Prev"></a><a accesskey="u" href="../dist.html"><img src="../../../../doc/html/images/up.png" alt="Up"></a><a accesskey="h" href="../../index.html"><img src="../../../../doc/html/images/home.png" alt="Home"></a><a accesskey="n" href="stat_tut/overview.html"><img src="../../../../doc/html/images/next.png" alt="Next"></a>
+</div>
+<div class="section" lang="en">
+<div class="titlepage"><div><div><h3 class="title">
+<a name="math_toolkit.dist.stat_tut"></a><a class="link" href="stat_tut.html" title="Statistical Distributions Tutorial"> Statistical Distributions
+      Tutorial</a>
+</h3></div></div></div>
+<div class="toc"><dl>
+<dt><span class="section"> Overview</span></dt>
+<dt><span class="section"> Worked Examples</span></dt>
+<dd><dl>
+<dt><span class="section"><a href="stat_tut/weg/dist_construct_eg.html">
+          Distribution Construction Example</a></span></dt>
+<dt><span class="section"><a href="stat_tut/weg/st_eg.html"> Student's
+          t Distribution Examples</a></span></dt>
+<dd><dl>
+<dt><span class="section"><a href="stat_tut/weg/st_eg/tut_mean_intervals.html">
+            Calculating confidence intervals on the mean with the Students-t distribution</a></span></dt>
+<dt><span class="section"><a href="stat_tut/weg/st_eg/tut_mean_test.html">
+            Testing a sample mean for difference from a "true" mean</a></span></dt>
+<dt><span class="section"><a href="stat_tut/weg/st_eg/tut_mean_size.html">
+            Estimating how large a sample size would have to become in order to give
+            a significant Students-t test result with a single sample test</a></span></dt>
+<dt><span class="section"><a href="stat_tut/weg/st_eg/two_sample_students_t.html">
+            Comparing the means of two samples with the Students-t test</a></span></dt>
+<dt><span class="section"><a href="stat_tut/weg/st_eg/paired_st.html">
+            Comparing two paired samples with the Student's t distribution</a></span></dt>
+</dl></dd>
+<dt><span class="section"><a href="stat_tut/weg/cs_eg.html"> Chi Squared
+          Distribution Examples</a></span></dt>
+<dd><dl>
+<dt><span class="section"><a href="stat_tut/weg/cs_eg/chi_sq_intervals.html">
+            Confidence Intervals on the Standard Deviation</a></span></dt>
+<dt><span class="section"><a href="stat_tut/weg/cs_eg/chi_sq_test.html">
+            Chi-Square Test for the Standard Deviation</a></span></dt>
+<dt><span class="section"><a href="stat_tut/weg/cs_eg/chi_sq_size.html">
+            Estimating the Required Sample Sizes for a Chi-Square Test for the Standard
+            Deviation</a></span></dt>
+</dl></dd>
+<dt><span class="section"><a href="stat_tut/weg/f_eg.html"> F Distribution
+          Examples</a></span></dt>
+<dt><span class="section"><a href="stat_tut/weg/binom_eg.html"> Binomial
+          Distribution Examples</a></span></dt>
+<dd><dl>
+<dt><span class="section"><a href="stat_tut/weg/binom_eg/binomial_coinflip_example.html">
+            Binomial Coin-Flipping Example</a></span></dt>
+<dt><span class="section"><a href="stat_tut/weg/binom_eg/binomial_quiz_example.html">
+            Binomial Quiz Example</a></span></dt>
+<dt><span class="section"><a href="stat_tut/weg/binom_eg/binom_conf.html">
+            Calculating Confidence Limits on the Frequency of Occurrence for a Binomial
+            Distribution</a></span></dt>
+<dt><span class="section"><a href="stat_tut/weg/binom_eg/binom_size_eg.html">
+            Estimating Sample Sizes for a Binomial Distribution.</a></span></dt>
+</dl></dd>
+<dt><span class="section"><a href="stat_tut/weg/neg_binom_eg.html"> Negative
+          Binomial Distribution Examples</a></span></dt>
+<dd><dl>
+<dt><span class="section"><a href="stat_tut/weg/neg_binom_eg/neg_binom_conf.html">
+            Calculating Confidence Limits on the Frequency of Occurrence for the
+            Negative Binomial Distribution</a></span></dt>
+<dt><span class="section"><a href="stat_tut/weg/neg_binom_eg/neg_binom_size_eg.html">
+            Estimating Sample Sizes for the Negative Binomial.</a></span></dt>
+<dt><span class="section"><a href="stat_tut/weg/neg_binom_eg/negative_binomial_example1.html">
+            Negative Binomial Sales Quota Example.</a></span></dt>
+<dt><span class="section"><a href="stat_tut/weg/neg_binom_eg/negative_binomial_example2.html">
+            Negative Binomial Table Printing Example.</a></span></dt>
+</dl></dd>
+<dt><span class="section"><a href="stat_tut/weg/normal_example.html"> Normal
+          Distribution Examples</a></span></dt>
+<dd><dl><dt><span class="section"><a href="stat_tut/weg/normal_example/normal_misc.html">
+            Some Miscellaneous Examples of the Normal (Gaussian) Distribution</a></span></dt></dl></dd>
+<dt><span class="section"><a href="stat_tut/weg/nccs_eg.html"> Non Central
+          Chi Squared Example</a></span></dt>
+<dd><dl><dt><span class="section"><a href="stat_tut/weg/nccs_eg/nccs_power_eg.html">
+            Tables of the power function of the &#967;<sup>2</sup> test.</a></span></dt></dl></dd>
+<dt><span class="section"><a href="stat_tut/weg/error_eg.html"> Error Handling
+          Example</a></span></dt>
+<dt><span class="section"><a href="stat_tut/weg/find_eg.html"> Find Location
+          and Scale Examples</a></span></dt>
+<dd><dl>
+<dt><span class="section"><a href="stat_tut/weg/find_eg/find_location_eg.html">
+            Find Location (Mean) Example</a></span></dt>
+<dt><span class="section"><a href="stat_tut/weg/find_eg/find_scale_eg.html">
+            Find Scale (Standard Deviation) Example</a></span></dt>
+<dt><span class="section"><a href="stat_tut/weg/find_eg/find_mean_and_sd_eg.html">
+            Find mean and standard deviation example</a></span></dt>
+</dl></dd>
+<dt><span class="section"><a href="stat_tut/weg/nag_library.html"> Comparison
+          with C, R, FORTRAN-style Free Functions</a></span></dt>
+</dl></dd>
+<dt><span class="section"><a href="stat_tut/variates.html"> Random Variates
+        and Distribution Parameters</a></span></dt>
+<dt><span class="section"><a href="stat_tut/dist_params.html"> Discrete Probability
+        Distributions</a></span></dt>
+</dl></div>
+<p>
+        This library is centred around statistical distributions, this tutorial will
+        give you an overview of what they are, how they can be used, and provides
+        a few worked examples of applying the library to statistical tests.
+      </p>
+</div>
+<table xmlns:rev="http://www.cs.rpi.edu/~gregod/boost/tools/doc/revision" width="100%"><tr>
+<td align="left"></td>
+<td align="right"><div class="copyright-footer">Copyright © 2006 , 2007, 2008 John Maddock, Paul A. Bristow, Hubert
+      Holin, Xiaogang Zhang, Bruno Lalande and Gautam Sewani<p>
+        Distributed under the Boost Software License, Version 1.0. (See accompanying
+        file LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_0.txt)
+      </p>
+</div></td>
+</tr></table>
+<hr>
+<div class="spirit-nav">
+<a accesskey="p" href="../dist.html"><img src="../../../../doc/html/images/prev.png" alt="Prev"></a><a accesskey="u" href="../dist.html"><img src="../../../../doc/html/images/up.png" alt="Up"></a><a accesskey="h" href="../../index.html"><img src="../../../../doc/html/images/home.png" alt="Home"></a><a accesskey="n" href="stat_tut/overview.html"><img src="../../../../doc/html/images/next.png" alt="Next"></a>
+</div>
+</body>
+</html>

Added: sandbox/tools/auto_index/example/math/doc/sf_and_dist/html/math_toolkit/dist/stat_tut/dist_params.html
==============================================================================
--- (empty file)
+++ sandbox/tools/auto_index/example/math/doc/sf_and_dist/html/math_toolkit/dist/stat_tut/dist_params.html	2008-11-28 05:25:28 EST (Fri, 28 Nov 2008)
@@ -0,0 +1,98 @@
+<html>
+<head>
+<meta http-equiv="Content-Type" content="text/html; charset=ISO-8859-1">
+<title>Discrete Probability Distributions</title>
+<link rel="stylesheet" href="../../../boostbook.css" type="text/css">
+<meta name="generator" content="DocBook XSL Stylesheets Vsnapshot_8125">
+<link rel="home" href="../../../index.html" title="Math Toolkit">
+<link rel="up" href="../stat_tut.html" title="Statistical Distributions Tutorial">
+<link rel="prev" href="variates.html" title="Random Variates and Distribution Parameters">
+<link rel="next" href="../dist_ref.html" title="Statistical Distributions Reference">
+</head>
+<body bgcolor="white" text="black" link="#0000FF" vlink="#840084" alink="#0000FF">
+<table cellpadding="2" width="100%"><tr>
+<td valign="top"><img alt="Boost C++ Libraries" width="277" height="86" src="../../../../../boost.png"></td>
+<td align="center">Home</td>
+<td align="center">Libraries</td>
+<td align="center">People</td>
+<td align="center">FAQ</td>
+<td align="center">More</td>
+</tr></table>
+<hr>
+<div class="spirit-nav">
+<a accesskey="p" href="variates.html"><img src="../../../../../doc/html/images/prev.png" alt="Prev"></a><a accesskey="u" href="../stat_tut.html"><img src="../../../../../doc/html/images/up.png" alt="Up"></a><a accesskey="h" href="../../../index.html"><img src="../../../../../doc/html/images/home.png" alt="Home"></a><a accesskey="n" href="../dist_ref.html"><img src="../../../../../doc/html/images/next.png" alt="Next"></a>
+</div>
+<div class="section" lang="en">
+<div class="titlepage"><div><div><h4 class="title">
+<a name="math_toolkit.dist.stat_tut.dist_params"></a><a class="link" href="dist_params.html" title="Discrete Probability Distributions"> Discrete Probability
+        Distributions</a>
+</h4></div></div></div>
+<p>
+          Note that the <a href="http://en.wikipedia.org/wiki/Discrete_probability_distribution" target="_top">discrete
+          distributions</a>, including the binomial, negative binomial, Poisson
+          &amp; Bernoulli, are all mathematically defined as discrete functions:
+          only integral values of the random variate are envisaged and the functions
+          are only defined at these integral values. However because the method of
+          calculation often uses continuous functions, it is convenient to treat
+          them as if they were continuous functions, and permit non-integral values
+          of their parameters.
+        </p>
+<p>
+          To enforce a strict mathematical model, users may use floor or ceil functions
+          on the random variate, prior to calling the distribution function, to enforce
+          integral values.
+        </p>
+<p>
+          For similar reasons, in continuous distributions, parameters like degrees
+          of freedom that might appear to be integral, are treated as real values
+          (and are promoted from integer to floating-point if necessary). In this
+          case however, that there are a small number of situations where non-integral
+          degrees of freedom do have a genuine meaning.
+        </p>
+<p>
+          Generally speaking there is no loss of performance from allowing real-values
+          parameters: the underlying special functions contain optimizations for
+          integer-valued arguments when applicable.
+        </p>
+<div class="caution"><table border="0" summary="Caution">
+<tr>
+<td rowspan="2" align="center" valign="top" width="25"><img alt="[Caution]" src="../../../../../doc/html/images/caution.png"></td>
+<th align="left">Caution</th>
+</tr>
+<tr><td align="left" valign="top">
+<p>
+            The quantile function of a discrete distribution will by default return
+            an integer result that has been <span class="emphasis"><em>rounded outwards</em></span>.
+            That is to say lower quantiles (where the probability is less than 0.5)
+            are rounded downward, and upper quantiles (where the probability is greater
+            than 0.5) are rounded upwards. This behaviour ensures that if an X% quantile
+            is requested, then <span class="emphasis"><em>at least</em></span> the requested coverage
+            will be present in the central region, and <span class="emphasis"><em>no more than</em></span>
+            the requested coverage will be present in the tails.
+          </p>
+<p>
+            This behaviour can be changed so that the quantile functions are rounded
+            differently, or even return a real-valued result using <a class="link" href="../../policy/pol_overview.html" title="Policy Overview">Policies</a>.
+            It is strongly recommended that you read the tutorial <a class="link" href="../../policy/pol_tutorial/understand_dis_quant.html" title="Understanding Quantiles of Discrete Distributions">Understanding
+            Quantiles of Discrete Distributions</a> before using the quantile
+            function on a discrete distribution. The <a class="link" href="../../policy/pol_ref/discrete_quant_ref.html" title="Discrete Quantile Policies">reference
+            docs</a> describe how to change the rounding policy for these distributions.
+          </p>
+</td></tr>
+</table></div>
+</div>
+<table xmlns:rev="http://www.cs.rpi.edu/~gregod/boost/tools/doc/revision" width="100%"><tr>
+<td align="left"></td>
+<td align="right"><div class="copyright-footer">Copyright © 2006 , 2007, 2008 John Maddock, Paul A. Bristow, Hubert
+      Holin, Xiaogang Zhang, Bruno Lalande and Gautam Sewani<p>
+        Distributed under the Boost Software License, Version 1.0. (See accompanying
+        file LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_0.txt)
+      </p>
+</div></td>
+</tr></table>
+<hr>
+<div class="spirit-nav">
+<a accesskey="p" href="variates.html"><img src="../../../../../doc/html/images/prev.png" alt="Prev"></a><a accesskey="u" href="../stat_tut.html"><img src="../../../../../doc/html/images/up.png" alt="Up"></a><a accesskey="h" href="../../../index.html"><img src="../../../../../doc/html/images/home.png" alt="Home"></a><a accesskey="n" href="../dist_ref.html"><img src="../../../../../doc/html/images/next.png" alt="Next"></a>
+</div>
+</body>
+</html>

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@@ -0,0 +1,541 @@
+<html>
+<head>
+<meta http-equiv="Content-Type" content="text/html; charset=ISO-8859-1">
+<title>Overview</title>
+<link rel="stylesheet" href="../../../boostbook.css" type="text/css">
+<meta name="generator" content="DocBook XSL Stylesheets Vsnapshot_8125">
+<link rel="home" href="../../../index.html" title="Math Toolkit">
+<link rel="up" href="../stat_tut.html" title="Statistical Distributions Tutorial">
+<link rel="prev" href="../stat_tut.html" title="Statistical Distributions Tutorial">
+<link rel="next" href="weg.html" title="Worked Examples">
+</head>
+<body bgcolor="white" text="black" link="#0000FF" vlink="#840084" alink="#0000FF">
+<table cellpadding="2" width="100%"><tr>
+<td valign="top"><img alt="Boost C++ Libraries" width="277" height="86" src="../../../../../boost.png"></td>
+<td align="center">Home</td>
+<td align="center">Libraries</td>
+<td align="center">People</td>
+<td align="center">FAQ</td>
+<td align="center">More</td>
+</tr></table>
+<hr>
+<div class="spirit-nav">
+<a accesskey="p" href="../stat_tut.html"><img src="../../../../../doc/html/images/prev.png" alt="Prev"></a><a accesskey="u" href="../stat_tut.html"><img src="../../../../../doc/html/images/up.png" alt="Up"></a><a accesskey="h" href="../../../index.html"><img src="../../../../../doc/html/images/home.png" alt="Home"></a><a accesskey="n" href="weg.html"><img src="../../../../../doc/html/images/next.png" alt="Next"></a>
+</div>
+<div class="section" lang="en">
+<div class="titlepage"><div><div><h4 class="title">
+<a name="math_toolkit.dist.stat_tut.overview"></a><a class="link" href="overview.html" title="Overview"> Overview</a>
+</h4></div></div></div>
+<a name="math_toolkit.dist.stat_tut.overview.headers_and_namespaces"></a><h5>
+<a name="id559920"></a>
+          <a class="link" href="overview.html#math_toolkit.dist.stat_tut.overview.headers_and_namespaces">Headers
+          and Namespaces</a>
+        </h5>
+<p>
+          All the code in this library is inside namespace boost::math.
+        </p>
+<p>
+          In order to use a distribution <span class="emphasis"><em>my_distribution</em></span> you
+          will need to include either the header &lt;boost/math/distributions/my_distribution.hpp&gt;
+          or the "include everything" header: &lt;boost/math/distributions.hpp&gt;.
+        </p>
+<p>
+          For example, to use the Students-t distribution include either &lt;boost/math/distributions/students_t.hpp&gt;
+          or &lt;boost/math/distributions.hpp&gt;
+        </p>
+<a name="math_toolkit.dist.stat_tut.overview.distributions_are_objects"></a><h5>
+<a name="id559970"></a>
+          <a class="link" href="overview.html#math_toolkit.dist.stat_tut.overview.distributions_are_objects">Distributions
+          are Objects</a>
+        </h5>
+<p>
+          Each kind of distribution in this library is a class type.
+        </p>
+<p>
+          <a class="link" href="../../policy.html" title="Policies">Policies</a> provide fine-grained
+          control of the behaviour of these classes, allowing the user to customise
+          behaviour such as how errors are handled, or how the quantiles of discrete
+          distribtions behave.
+        </p>
+<div class="tip"><table border="0" summary="Tip">
+<tr>
+<td rowspan="2" align="center" valign="top" width="25"><img alt="[Tip]" src="../../../../../doc/html/images/tip.png"></td>
+<th align="left">Tip</th>
+</tr>
+<tr><td align="left" valign="top"><p>
+            If you are familiar with statistics libraries using functions, and 'Distributions
+            as Objects' seem alien, see <a class="link" href="weg/nag_library.html" title="Comparison with C, R, FORTRAN-style Free Functions">the
+            comparison to other statistics libraries.</a>
+          </p></td></tr>
+</table></div>
+<p>
+          Making distributions class types does two things:
+        </p>
+<div class="itemizedlist"><ul type="disc">
+<li>
+            It encapsulates the kind of distribution in the C++ type system; so,
+            for example, Students-t distributions are always a different C++ type
+            from Chi-Squared distributions.
+          </li>
+<li>
+            The distribution objects store any parameters associated with the distribution:
+            for example, the Students-t distribution has a <span class="emphasis"><em>degrees of freedom</em></span>
+            parameter that controls the shape of the distribution. This <span class="emphasis"><em>degrees
+            of freedom</em></span> parameter has to be provided to the Students-t
+            object when it is constructed.
+          </li>
+</ul></div>
+<p>
+          Although the distribution classes in this library are templates, there
+          are typedefs on type <span class="emphasis"><em>double</em></span> that mostly take the usual
+          name of the distribution (except where there is a clash with a function
+          of the same name: beta and gamma, in which case using the default template
+          arguments - <code class="computeroutput"><span class="identifier">RealType</span> <span class="special">=</span>
+          <span class="keyword">double</span></code> - is nearly as convenient).
+          Probably 95% of uses are covered by these typedefs:
+        </p>
+<pre class="programlisting"><span class="keyword">using</span> <span class="keyword">namespace</span> <span class="identifier">boost</span><span class="special">::</span><span class="identifier">math</span><span class="special">;</span>
+
+<span class="comment">// Construct a students_t distribution with 4 degrees of freedom:
+</span><span class="identifier">students_t</span> <span class="identifier">d1</span><span class="special">(</span><span class="number">4</span><span class="special">);</span>
+
+<span class="comment">// Construct a double-precision beta distribution 
+</span><span class="comment">// with parameters a = 10, b = 20
+</span><span class="identifier">beta_distribution</span><span class="special">&lt;&gt;</span> <span class="identifier">d2</span><span class="special">(</span><span class="number">10</span><span class="special">,</span> <span class="number">20</span><span class="special">);</span> <span class="comment">// Note: _distribution&lt;&gt; suffix !
+</span></pre>
+<p>
+          If you need to use the distributions with a type other than <code class="computeroutput"><span class="keyword">double</span></code>, then you can instantiate the template
+          directly: the names of the templates are the same as the <code class="computeroutput"><span class="keyword">double</span></code> typedef but with <code class="computeroutput"><span class="identifier">_distribution</span></code>
+          appended, for example: <a class="link" href="../dist_ref/dists/students_t_dist.html" title="Students t Distribution">Students
+          t Distribution</a> or <a class="link" href="../dist_ref/dists/binomial_dist.html" title="Binomial Distribution">Binomial
+          Distribution</a>:
+        </p>
+<pre class="programlisting"><span class="comment">// Construct a students_t distribution, of float type,
+</span><span class="comment">// with 4 degrees of freedom:
+</span><span class="identifier">students_t_distribution</span><span class="special">&lt;</span><span class="keyword">float</span><span class="special">&gt;</span> <span class="identifier">d3</span><span class="special">(</span><span class="number">4</span><span class="special">);</span>
+
+<span class="comment">// Construct a binomial distribution, of long double type,
+</span><span class="comment">// with probability of success 0.3
+</span><span class="comment">// and 20 trials in total:
+</span><span class="identifier">binomial_distribution</span><span class="special">&lt;</span><span class="keyword">long</span> <span class="keyword">double</span><span class="special">&gt;</span> <span class="identifier">d4</span><span class="special">(</span><span class="number">20</span><span class="special">,</span> <span class="number">0.3</span><span class="special">);</span>
+</pre>
+<p>
+          The parameters passed to the distributions can be accessed via getter member
+          functions:
+        </p>
+<pre class="programlisting"><span class="identifier">d1</span><span class="special">.</span><span class="identifier">degrees_of_freedom</span><span class="special">();</span>  <span class="comment">// returns 4.0 
+</span></pre>
+<p>
+          This is all well and good, but not very useful so far. What we often want
+          is to be able to calculate the <span class="emphasis"><em>cumulative distribution functions</em></span>
+          and <span class="emphasis"><em>quantiles</em></span> etc for these distributions.
+        </p>
+<a name="math_toolkit.dist.stat_tut.overview.generic_operations_common_to_all_distributions_are_non_member_functions"></a><h5>
+<a name="id560488"></a>
+          <a class="link" href="overview.html#math_toolkit.dist.stat_tut.overview.generic_operations_common_to_all_distributions_are_non_member_functions">Generic
+          operations common to all distributions are non-member functions</a>
+        </h5>
+<p>
+          Want to calculate the PDF (Probability Density Function) of a distribution?
+          No problem, just use:
+        </p>
+<pre class="programlisting"><span class="identifier">pdf</span><span class="special">(</span><span class="identifier">my_dist</span><span class="special">,</span> <span class="identifier">x</span><span class="special">);</span>  <span class="comment">// Returns PDF (density) at point x of distribution my_dist.
+</span></pre>
+<p>
+          Or how about the CDF (Cumulative Distribution Function):
+        </p>
+<pre class="programlisting"><span class="identifier">cdf</span><span class="special">(</span><span class="identifier">my_dist</span><span class="special">,</span> <span class="identifier">x</span><span class="special">);</span>  <span class="comment">// Returns CDF (integral from -infinity to point x)
+</span>                  <span class="comment">// of distribution my_dist.
+</span></pre>
+<p>
+          And quantiles are just the same:
+        </p>
+<pre class="programlisting"><span class="identifier">quantile</span><span class="special">(</span><span class="identifier">my_dist</span><span class="special">,</span> <span class="identifier">p</span><span class="special">);</span>  <span class="comment">// Returns the value of the random variable x
+</span>                       <span class="comment">// such that cdf(my_dist, x) == p.
+</span></pre>
+<p>
+          If you're wondering why these aren't member functions, it's to make the
+          library more easily extensible: if you want to add additional generic operations
+          - let's say the <span class="emphasis"><em>n'th moment</em></span> - then all you have to
+          do is add the appropriate non-member functions, overloaded for each implemented
+          distribution type.
+        </p>
+<div class="tip"><table border="0" summary="Tip">
+<tr>
+<td rowspan="2" align="center" valign="top" width="25"><img alt="[Tip]" src="../../../../../doc/html/images/tip.png"></td>
+<th align="left">Tip</th>
+</tr>
+<tr><td align="left" valign="top">
+<p>
+          </p>
+<p>
+            <span class="bold"><strong>Random numbers that approximate Quantiles of Distributions</strong></span>
+          </p>
+<p>
+            If you want random numbers that are distributed in a specific way, for
+            example in a uniform, normal or triangular, see Boost.Random.
+          </p>
+<p>
+            Whilst in principal there's nothing to prevent you from using the quantile
+            function to convert a uniformly distributed random number to another
+            distribution, in practice there are much more efficient algorithms available
+            that are specific to random number generation.
+          </p>
+</td></tr>
+</table></div>
+<p>
+          For example, the binomial distribution has two parameters: n (the number
+          of trials) and p (the probability of success on one trial).
+        </p>
+<p>
+          The <code class="computeroutput"><span class="identifier">binomial_distribution</span></code>
+          constructor therefore has two parameters:
+        </p>
+<p>
+          <code class="computeroutput"><span class="identifier">binomial_distribution</span><span class="special">(</span><span class="identifier">RealType</span> <span class="identifier">n</span><span class="special">,</span> <span class="identifier">RealType</span>
+          <span class="identifier">p</span><span class="special">);</span></code>
+        </p>
+<p>
+          For this distribution the random variate is k: the number of successes
+          observed. The probability density/mass function (pdf) is therefore written
+          as <span class="emphasis"><em>f(k; n, p)</em></span>.
+        </p>
+<div class="note"><table border="0" summary="Note">
+<tr>
+<td rowspan="2" align="center" valign="top" width="25"><img alt="[Note]" src="../../../../../doc/html/images/note.png"></td>
+<th align="left">Note</th>
+</tr>
+<tr><td align="left" valign="top">
+<p>
+          </p>
+<p>
+            <span class="bold"><strong>Random Variates and Distribution Parameters</strong></span>
+          </p>
+<p>
+            Random variates
+            and <a href="http://en.wikipedia.org/wiki/Parameter" target="_top">distribution
+            parameters</a> are conventionally distinguished (for example in Wikipedia
+            and Wolfram MathWorld by placing a semi-colon (or sometimes vertical
+            bar) after the random variate (whose value you 'choose'), to separate
+            the variate from the parameter(s) that defines the shape of the distribution.
+          </p>
+</td></tr>
+</table></div>
+<p>
+          As noted above the non-member function <code class="computeroutput"><span class="identifier">pdf</span></code>
+          has one parameter for the distribution object, and a second for the random
+          variate. So taking our binomial distribution example, we would write:
+        </p>
+<p>
+          <code class="computeroutput"><span class="identifier">pdf</span><span class="special">(</span><span class="identifier">binomial_distribution</span><span class="special">&lt;</span><span class="identifier">RealType</span><span class="special">&gt;(</span><span class="identifier">n</span><span class="special">,</span> <span class="identifier">p</span><span class="special">),</span> <span class="identifier">k</span><span class="special">);</span></code>
+        </p>
+<p>
+          The ranges of random variate values that are permitted and are supported
+          can be tested by using two functions <code class="computeroutput"><span class="identifier">range</span></code>
+          and <code class="computeroutput"><span class="identifier">support</span></code>.
+        </p>
+<p>
+          The distribution (effectively the random variate) is said to be 'supported'
+          over a range that is <a href="http://en.wikipedia.org/wiki/Probability_distribution" target="_top">"the
+          smallest closed set whose complement has probability zero"</a>.
+          MathWorld uses the word 'defined' for this range. Non-mathematicians might
+          say it means the 'interesting' smallest range of random variate x that
+          has the cdf going from zero to unity. Outside are uninteresting zones where
+          the pdf is zero, and the cdf zero or unity.
+        </p>
+<p>
+          For most distributions, with probability distribution functions one might
+          describe as 'well-behaved', we have decided that it is most useful for
+          the supported range to exclude random variate values like exact zero <span class="bold"><strong>if the end point is discontinuous</strong></span>. For example,
+          the Weibull (scale 1, shape 1) distribution smoothly heads for unity as
+          the random variate x declines towards zero. But at x = zero, the value
+          of the pdf is suddenly exactly zero, by definition. If you are plotting
+          the PDF, or otherwise calculating, zero is not the most useful value for
+          the lower limit of supported, as we discovered. So for this, and similar
+          distributions, we have decided it is most numerically useful to use the
+          closest value to zero, min_value, for the limit of the supported range.
+          (The <code class="computeroutput"><span class="identifier">range</span></code> remains from
+          zero, so you will still get <code class="computeroutput"><span class="identifier">pdf</span><span class="special">(</span><span class="identifier">weibull</span><span class="special">,</span> <span class="number">0</span><span class="special">)</span>
+          <span class="special">==</span> <span class="number">0</span></code>).
+          (Exponential and gamma distributions have similarly discontinuous functions).
+        </p>
+<p>
+          Mathematically, the functions may make sense with an (+ or -) infinite
+          value, but except for a few special cases (in the Normal and Cauchy distributions)
+          this implementation limits random variates to finite values from the <code class="computeroutput"><span class="identifier">max</span></code> to <code class="computeroutput"><span class="identifier">min</span></code>
+          for the <code class="computeroutput"><span class="identifier">RealType</span></code>. (See
+          <a class="link" href="../../backgrounders/implementation.html#math_toolkit.backgrounders.implementation.handling_of_floating_point_infinity">Handling
+          of Floating-Point Infinity</a> for rationale).
+        </p>
+<div class="note"><table border="0" summary="Note">
+<tr>
+<td rowspan="2" align="center" valign="top" width="25"><img alt="[Note]" src="../../../../../doc/html/images/note.png"></td>
+<th align="left">Note</th>
+</tr>
+<tr><td align="left" valign="top">
+<p>
+          </p>
+<p>
+            <span class="bold"><strong>Discrete Probability Distributions</strong></span>
+          </p>
+<p>
+            Note that the <a href="http://en.wikipedia.org/wiki/Discrete_probability_distribution" target="_top">discrete
+            distributions</a>, including the binomial, negative binomial, Poisson
+            &amp; Bernoulli, are all mathematically defined as discrete functions:
+            that is to say the functions <code class="computeroutput"><span class="identifier">cdf</span></code>
+            and <code class="computeroutput"><span class="identifier">pdf</span></code> are only defined
+            for integral values of the random variate.
+          </p>
+<p>
+            However, because the method of calculation often uses continuous functions
+            it is convenient to treat them as if they were continuous functions,
+            and permit non-integral values of their parameters.
+          </p>
+<p>
+            Users wanting to enforce a strict mathematical model may use <code class="computeroutput"><span class="identifier">floor</span></code> or <code class="computeroutput"><span class="identifier">ceil</span></code>
+            functions on the random variate prior to calling the distribution function.
+          </p>
+<p>
+            The quantile functions for these distributions are hard to specify in
+            a manner that will satisfy everyone all of the time. The default behaviour
+            is to return an integer result, that has been rounded <span class="emphasis"><em>outwards</em></span>:
+            that is to say, lower quantiles - where the probablity is less than 0.5
+            are rounded down, while upper quantiles - where the probability is greater
+            than 0.5 - are rounded up. This behaviour ensures that if an X% quantile
+            is requested, then <span class="emphasis"><em>at least</em></span> the requested coverage
+            will be present in the central region, and <span class="emphasis"><em>no more than</em></span>
+            the requested coverage will be present in the tails.
+          </p>
+<p>
+            This behaviour can be changed so that the quantile functions are rounded
+            differently, or return a real-valued result using <a class="link" href="../../policy/pol_overview.html" title="Policy Overview">Policies</a>.
+            It is strongly recommended that you read the tutorial <a class="link" href="../../policy/pol_tutorial/understand_dis_quant.html" title="Understanding Quantiles of Discrete Distributions">Understanding
+            Quantiles of Discrete Distributions</a> before using the quantile
+            function on a discrete distribtion. The <a class="link" href="../../policy/pol_ref/discrete_quant_ref.html" title="Discrete Quantile Policies">reference
+            docs</a> describe how to change the rounding policy for these distributions.
+          </p>
+<p>
+            For similar reasons continuous distributions with parameters like "degrees
+            of freedom" that might appear to be integral, are treated as real
+            values (and are promoted from integer to floating-point if necessary).
+            In this case however, there are a small number of situations where non-integral
+            degrees of freedom do have a genuine meaning.
+          </p>
+</td></tr>
+</table></div>
+<a name="complements"></a><p>
+        </p>
+<a name="math_toolkit.dist.stat_tut.overview.complements_are_supported_too"></a><h5>
+<a name="id561397"></a>
+          <a class="link" href="overview.html#math_toolkit.dist.stat_tut.overview.complements_are_supported_too">Complements
+          are supported too</a>
+        </h5>
+<p>
+          Often you don't want the value of the CDF, but its complement, which is
+          to say <code class="computeroutput"><span class="number">1</span><span class="special">-</span><span class="identifier">p</span></code> rather than <code class="computeroutput"><span class="identifier">p</span></code>.
+          You could calculate the CDF and subtract it from <code class="computeroutput"><span class="number">1</span></code>,
+          but if <code class="computeroutput"><span class="identifier">p</span></code> is very close
+          to <code class="computeroutput"><span class="number">1</span></code> then cancellation error
+          will cause you to lose significant digits. In extreme cases, <code class="computeroutput"><span class="identifier">p</span></code> may actually be equal to <code class="computeroutput"><span class="number">1</span></code>, even though the true value of the complement
+          is non-zero.
+        </p>
+<p>
+          <a class="link" href="overview.html#why_complements">See also <span class="emphasis"><em>"Why complements?"</em></span></a>
+        </p>
+<p>
+          In this library, whenever you want to receive a complement, just wrap all
+          the function arguments in a call to <code class="computeroutput"><span class="identifier">complement</span><span class="special">(...)</span></code>, for example:
+        </p>
+<pre class="programlisting"><span class="identifier">students_t</span> <span class="identifier">dist</span><span class="special">(</span><span class="number">5</span><span class="special">);</span>
+<span class="identifier">cout</span> <span class="special">&lt;&lt;</span> <span class="string">"CDF at t = 1 is "</span> <span class="special">&lt;&lt;</span> <span class="identifier">cdf</span><span class="special">(</span><span class="identifier">dist</span><span class="special">,</span> <span class="number">1.0</span><span class="special">)</span> <span class="special">&lt;&lt;</span> <span class="identifier">endl</span><span class="special">;</span>
+<span class="identifier">cout</span> <span class="special">&lt;&lt;</span> <span class="string">"Complement of CDF at t = 1 is "</span> <span class="special">&lt;&lt;</span> <span class="identifier">cdf</span><span class="special">(</span><span class="identifier">complement</span><span class="special">(</span><span class="identifier">dist</span><span class="special">,</span> <span class="number">1.0</span><span class="special">))</span> <span class="special">&lt;&lt;</span> <span class="identifier">endl</span><span class="special">;</span>
+</pre>
+<p>
+          But wait, now that we have a complement, we have to be able to use it as
+          well. Any function that accepts a probability as an argument can also accept
+          a complement by wrapping all of its arguments in a call to <code class="computeroutput"><span class="identifier">complement</span><span class="special">(...)</span></code>,
+          for example:
+        </p>
+<pre class="programlisting"><span class="identifier">students_t</span> <span class="identifier">dist</span><span class="special">(</span><span class="number">5</span><span class="special">);</span>
+
+<span class="keyword">for</span><span class="special">(</span><span class="keyword">double</span> <span class="identifier">i</span> <span class="special">=</span> <span class="number">10</span><span class="special">;</span> <span class="identifier">i</span> <span class="special">&lt;</span> <span class="number">1e10</span><span class="special">;</span> <span class="identifier">i</span> <span class="special">*=</span> <span class="number">10</span><span class="special">)</span>
+<span class="special">{</span>
+   <span class="comment">// Calculate the quantile for a 1 in i chance:
+</span>   <span class="keyword">double</span> <span class="identifier">t</span> <span class="special">=</span> <span class="identifier">quantile</span><span class="special">(</span><span class="identifier">complement</span><span class="special">(</span><span class="identifier">dist</span><span class="special">,</span> <span class="number">1</span><span class="special">/</span><span class="identifier">i</span><span class="special">));</span>
+   <span class="comment">// Print it out:
+</span>   <span class="identifier">cout</span> <span class="special">&lt;&lt;</span> <span class="string">"Quantile of students-t with 5 degrees of freedom\n"</span>
+           <span class="string">"for a 1 in "</span> <span class="special">&lt;&lt;</span> <span class="identifier">i</span> <span class="special">&lt;&lt;</span> <span class="string">" chance is "</span> <span class="special">&lt;&lt;</span> <span class="identifier">t</span> <span class="special">&lt;&lt;</span> <span class="identifier">endl</span><span class="special">;</span>
+<span class="special">}</span>
+</pre>
+<div class="tip"><table border="0" summary="Tip">
+<tr>
+<td rowspan="2" align="center" valign="top" width="25"><img alt="[Tip]" src="../../../../../doc/html/images/tip.png"></td>
+<th align="left">Tip</th>
+</tr>
+<tr><td align="left" valign="top">
+<p>
+          </p>
+<p>
+            <span class="bold"><strong>Critical values are just quantiles</strong></span>
+          </p>
+<p>
+            Some texts talk about quantiles, others about critical values, the basic
+            rule is:
+          </p>
+<p>
+            <span class="emphasis"><em>Lower critical values</em></span> are the same as the quantile.
+          </p>
+<p>
+            <span class="emphasis"><em>Upper critical values</em></span> are the same as the quantile
+            from the complement of the probability.
+          </p>
+<p>
+            For example, suppose we have a Bernoulli process, giving rise to a binomial
+            distribution with success ratio 0.1 and 100 trials in total. The <span class="emphasis"><em>lower
+            critical value</em></span> for a probability of 0.05 is given by:
+          </p>
+<p>
+            <code class="computeroutput"><span class="identifier">quantile</span><span class="special">(</span><span class="identifier">binomial</span><span class="special">(</span><span class="number">100</span><span class="special">,</span> <span class="number">0.1</span><span class="special">),</span> <span class="number">0.05</span><span class="special">)</span></code>
+          </p>
+<p>
+            and the <span class="emphasis"><em>upper critical value</em></span> is given by:
+          </p>
+<p>
+            <code class="computeroutput"><span class="identifier">quantile</span><span class="special">(</span><span class="identifier">complement</span><span class="special">(</span><span class="identifier">binomial</span><span class="special">(</span><span class="number">100</span><span class="special">,</span> <span class="number">0.1</span><span class="special">),</span> <span class="number">0.05</span><span class="special">))</span></code>
+          </p>
+<p>
+            which return 4.82 and 14.63 respectively.
+          </p>
+</td></tr>
+</table></div>
+<a name="why_complements"></a><p>
+        </p>
+<div class="tip"><table border="0" summary="Tip">
+<tr>
+<td rowspan="2" align="center" valign="top" width="25"><img alt="[Tip]" src="../../../../../doc/html/images/tip.png"></td>
+<th align="left">Tip</th>
+</tr>
+<tr><td align="left" valign="top">
+<p>
+          </p>
+<p>
+            <span class="bold"><strong>Why bother with complements anyway?</strong></span>
+          </p>
+<p>
+            It's very tempting to dispense with complements, and simply subtract
+            the probability from 1 when required. However, consider what happens
+            when the probability is very close to 1: let's say the probability expressed
+            at float precision is <code class="computeroutput"><span class="number">0.999999940f</span></code>,
+            then <code class="computeroutput"><span class="number">1</span> <span class="special">-</span>
+            <span class="number">0.999999940f</span> <span class="special">=</span>
+            <span class="number">5.96046448e-008</span></code>, but the result
+            is actually accurate to just <span class="emphasis"><em>one single bit</em></span>: the
+            only bit that didn't cancel out!
+          </p>
+<p>
+            Or to look at this another way: consider that we want the risk of falsely
+            rejecting the null-hypothesis in the Student's t test to be 1 in 1 billion,
+            for a sample size of 10,000. This gives a probability of 1 - 10<sup>-9</sup>, which
+            is exactly 1 when calculated at float precision. In this case calculating
+            the quantile from the complement neatly solves the problem, so for example:
+          </p>
+<p>
+            <code class="computeroutput"><span class="identifier">quantile</span><span class="special">(</span><span class="identifier">complement</span><span class="special">(</span><span class="identifier">students_t</span><span class="special">(</span><span class="number">10000</span><span class="special">),</span> <span class="number">1e-9</span><span class="special">))</span></code>
+          </p>
+<p>
+            returns the expected t-statistic <code class="computeroutput"><span class="number">6.00336</span></code>,
+            where as:
+          </p>
+<p>
+            <code class="computeroutput"><span class="identifier">quantile</span><span class="special">(</span><span class="identifier">students_t</span><span class="special">(</span><span class="number">10000</span><span class="special">),</span> <span class="number">1</span><span class="special">-</span><span class="number">1e-9f</span><span class="special">)</span></code>
+          </p>
+<p>
+            raises an overflow error, since it is the same as:
+          </p>
+<p>
+            <code class="computeroutput"><span class="identifier">quantile</span><span class="special">(</span><span class="identifier">students_t</span><span class="special">(</span><span class="number">10000</span><span class="special">),</span> <span class="number">1</span><span class="special">)</span></code>
+          </p>
+<p>
+            Which has no finite result.
+          </p>
+</td></tr>
+</table></div>
+<a name="math_toolkit.dist.stat_tut.overview.parameters_can_be_calculated"></a><h5>
+<a name="id562607"></a>
+          <a class="link" href="overview.html#math_toolkit.dist.stat_tut.overview.parameters_can_be_calculated">Parameters
+          can be calculated</a>
+        </h5>
+<p>
+          Sometimes it's the parameters that define the distribution that you need
+          to find. Suppose, for example, you have conducted a Students-t test for
+          equal means and the result is borderline. Maybe your two samples differ
+          from each other, or maybe they don't; based on the result of the test you
+          can't be sure. A legitimate question to ask then is "How many more
+          measurements would I have to take before I would get an X% probability
+          that the difference is real?" Parameter finders can answer questions
+          like this, and are necessarily different for each distribution. They are
+          implemented as static member functions of the distributions, for example:
+        </p>
+<pre class="programlisting"><span class="identifier">students_t</span><span class="special">::</span><span class="identifier">find_degrees_of_freedom</span><span class="special">(</span>
+   <span class="number">1.3</span><span class="special">,</span>        <span class="comment">// difference from true mean to detect
+</span>   <span class="number">0.05</span><span class="special">,</span>       <span class="comment">// maximum risk of falsely rejecting the null-hypothesis.
+</span>   <span class="number">0.1</span><span class="special">,</span>        <span class="comment">// maximum risk of falsely failing to reject the null-hypothesis.
+</span>   <span class="number">0.13</span><span class="special">);</span>      <span class="comment">// sample standard deviation
+</span></pre>
+<p>
+          Returns the number of degrees of freedom required to obtain a 95% probability
+          that the observed differences in means is not down to chance alone. In
+          the case that a borderline Students-t test result was previously obtained,
+          this can be used to estimate how large the sample size would have to become
+          before the observed difference was considered significant. It assumes,
+          of course, that the sample mean and standard deviation are invariant with
+          sample size.
+        </p>
+<a name="math_toolkit.dist.stat_tut.overview.summary"></a><h5>
+<a name="id562772"></a>
+          <a class="link" href="overview.html#math_toolkit.dist.stat_tut.overview.summary">Summary</a>
+        </h5>
+<div class="itemizedlist"><ul type="disc">
+<li>
+            Distributions are objects, which are constructed from whatever parameters
+            the distribution may have.
+          </li>
+<li>
+            Member functions allow you to retrieve the parameters of a distribution.
+          </li>
+<li>
+            Generic non-member functions provide access to the properties that are
+            common to all the distributions (PDF, CDF, quantile etc).
+          </li>
+<li>
+            Complements of probabilities are calculated by wrapping the function's
+            arguments in a call to <code class="computeroutput"><span class="identifier">complement</span><span class="special">(...)</span></code>.
+          </li>
+<li>
+            Functions that accept a probability can accept a complement of the probability
+            as well, by wrapping the function's arguments in a call to <code class="computeroutput"><span class="identifier">complement</span><span class="special">(...)</span></code>.
+          </li>
+<li>
+            Static member functions allow the parameters of a distribution to be
+            found from other information.
+          </li>
+</ul></div>
+<p>
+          Now that you have the basics, the next section looks at some worked examples.
+        </p>
+</div>
+<table xmlns:rev="http://www.cs.rpi.edu/~gregod/boost/tools/doc/revision" width="100%"><tr>
+<td align="left"></td>
+<td align="right"><div class="copyright-footer">Copyright © 2006 , 2007, 2008 John Maddock, Paul A. Bristow, Hubert
+      Holin, Xiaogang Zhang, Bruno Lalande and Gautam Sewani<p>
+        Distributed under the Boost Software License, Version 1.0. (See accompanying
+        file LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_0.txt)
+      </p>
+</div></td>
+</tr></table>
+<hr>
+<div class="spirit-nav">
+<a accesskey="p" href="../stat_tut.html"><img src="../../../../../doc/html/images/prev.png" alt="Prev"></a><a accesskey="u" href="../stat_tut.html"><img src="../../../../../doc/html/images/up.png" alt="Up"></a><a accesskey="h" href="../../../index.html"><img src="../../../../../doc/html/images/home.png" alt="Home"></a><a accesskey="n" href="weg.html"><img src="../../../../../doc/html/images/next.png" alt="Next"></a>
+</div>
+</body>
+</html>

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@@ -0,0 +1,74 @@
+<html>
+<head>
+<meta http-equiv="Content-Type" content="text/html; charset=ISO-8859-1">
+<title>Random Variates and Distribution Parameters</title>
+<link rel="stylesheet" href="../../../boostbook.css" type="text/css">
+<meta name="generator" content="DocBook XSL Stylesheets Vsnapshot_8125">
+<link rel="home" href="../../../index.html" title="Math Toolkit">
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+<link rel="prev" href="weg/nag_library.html" title="Comparison with C, R, FORTRAN-style Free Functions">
+<link rel="next" href="dist_params.html" title="Discrete Probability Distributions">
+</head>
+<body bgcolor="white" text="black" link="#0000FF" vlink="#840084" alink="#0000FF">
+<table cellpadding="2" width="100%"><tr>
+<td valign="top"><img alt="Boost C++ Libraries" width="277" height="86" src="../../../../../boost.png"></td>
+<td align="center">Home</td>
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+<td align="center">People</td>
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+<td align="center">More</td>
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+<hr>
+<div class="spirit-nav">
+<a accesskey="p" href="weg/nag_library.html"><img src="../../../../../doc/html/images/prev.png" alt="Prev"></a><a accesskey="u" href="../stat_tut.html"><img src="../../../../../doc/html/images/up.png" alt="Up"></a><a accesskey="h" href="../../../index.html"><img src="../../../../../doc/html/images/home.png" alt="Home"></a><a accesskey="n" href="dist_params.html"><img src="../../../../../doc/html/images/next.png" alt="Next"></a>
+</div>
+<div class="section" lang="en">
+<div class="titlepage"><div><div><h4 class="title">
+<a name="math_toolkit.dist.stat_tut.variates"></a><a class="link" href="variates.html" title="Random Variates and Distribution Parameters"> Random Variates
+        and Distribution Parameters</a>
+</h4></div></div></div>
+<p>
+          Random variates
+          and distribution parameters
+          are conventionally distinguished (for example in Wikipedia and Wolfram
+          MathWorld by placing a semi-colon after the random variate (whose value
+          you 'choose'), to separate the variate from the parameter(s) that defines
+          the shape of the distribution.
+        </p>
+<p>
+          For example, the binomial distribution has two parameters: n (the number
+          of trials) and p (the probability of success on one trial). It also has
+          the random variate <span class="emphasis"><em>k</em></span>: the number of successes observed.
+          This means the probability density/mass function (pdf) is written as <span class="emphasis"><em>f(k;
+          n, p)</em></span>.
+        </p>
+<p>
+          Translating this into code the <code class="computeroutput"><span class="identifier">binomial_distribution</span></code>
+          constructor therefore has two parameters:
+        </p>
+<pre class="programlisting"><span class="identifier">binomial_distribution</span><span class="special">(</span><span class="identifier">RealType</span> <span class="identifier">n</span><span class="special">,</span> <span class="identifier">RealType</span> <span class="identifier">p</span><span class="special">);</span>
+</pre>
+<p>
+          While the function <code class="computeroutput"><span class="identifier">pdf</span></code>
+          has one argument specifying the distribution type (which includes it's
+          parameters, if any), and a second argument for the random variate. So taking
+          our binomial distribution example, we would write:
+        </p>
+<pre class="programlisting"><span class="identifier">pdf</span><span class="special">(</span><span class="identifier">binomial_distribution</span><span class="special">&lt;</span><span class="identifier">RealType</span><span class="special">&gt;(</span><span class="identifier">n</span><span class="special">,</span> <span class="identifier">p</span><span class="special">),</span> <span class="identifier">k</span><span class="special">);</span>
+</pre>
+</div>
+<table xmlns:rev="http://www.cs.rpi.edu/~gregod/boost/tools/doc/revision" width="100%"><tr>
+<td align="left"></td>
+<td align="right"><div class="copyright-footer">Copyright © 2006 , 2007, 2008 John Maddock, Paul A. Bristow, Hubert
+      Holin, Xiaogang Zhang, Bruno Lalande and Gautam Sewani<p>
+        Distributed under the Boost Software License, Version 1.0. (See accompanying
+        file LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_0.txt)
+      </p>
+</div></td>
+</tr></table>
+<hr>
+<div class="spirit-nav">
+<a accesskey="p" href="weg/nag_library.html"><img src="../../../../../doc/html/images/prev.png" alt="Prev"></a><a accesskey="u" href="../stat_tut.html"><img src="../../../../../doc/html/images/up.png" alt="Up"></a><a accesskey="h" href="../../../index.html"><img src="../../../../../doc/html/images/home.png" alt="Home"></a><a accesskey="n" href="dist_params.html"><img src="../../../../../doc/html/images/next.png" alt="Next"></a>
+</div>
+</body>
+</html>

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@@ -0,0 +1,128 @@
+<html>
+<head>
+<meta http-equiv="Content-Type" content="text/html; charset=ISO-8859-1">
+<title>Worked Examples</title>
+<link rel="stylesheet" href="../../../boostbook.css" type="text/css">
+<meta name="generator" content="DocBook XSL Stylesheets Vsnapshot_8125">
+<link rel="home" href="../../../index.html" title="Math Toolkit">
+<link rel="up" href="../stat_tut.html" title="Statistical Distributions Tutorial">
+<link rel="prev" href="overview.html" title="Overview">
+<link rel="next" href="weg/dist_construct_eg.html" title="Distribution Construction Example">
+</head>
+<body bgcolor="white" text="black" link="#0000FF" vlink="#840084" alink="#0000FF">
+<table cellpadding="2" width="100%"><tr>
+<td valign="top"><img alt="Boost C++ Libraries" width="277" height="86" src="../../../../../boost.png"></td>
+<td align="center">Home</td>
+<td align="center">Libraries</td>
+<td align="center">People</td>
+<td align="center">FAQ</td>
+<td align="center">More</td>
+</tr></table>
+<hr>
+<div class="spirit-nav">
+<a accesskey="p" href="overview.html"><img src="../../../../../doc/html/images/prev.png" alt="Prev"></a><a accesskey="u" href="../stat_tut.html"><img src="../../../../../doc/html/images/up.png" alt="Up"></a><a accesskey="h" href="../../../index.html"><img src="../../../../../doc/html/images/home.png" alt="Home"></a><a accesskey="n" href="weg/dist_construct_eg.html"><img src="../../../../../doc/html/images/next.png" alt="Next"></a>
+</div>
+<div class="section" lang="en">
+<div class="titlepage"><div><div><h4 class="title">
+<a name="math_toolkit.dist.stat_tut.weg"></a><a class="link" href="weg.html" title="Worked Examples"> Worked Examples</a>
+</h4></div></div></div>
+<div class="toc"><dl>
+<dt><span class="section"><a href="weg/dist_construct_eg.html">
+          Distribution Construction Example</a></span></dt>
+<dt><span class="section"><a href="weg/st_eg.html"> Student's
+          t Distribution Examples</a></span></dt>
+<dd><dl>
+<dt><span class="section"><a href="weg/st_eg/tut_mean_intervals.html">
+            Calculating confidence intervals on the mean with the Students-t distribution</a></span></dt>
+<dt><span class="section"><a href="weg/st_eg/tut_mean_test.html">
+            Testing a sample mean for difference from a "true" mean</a></span></dt>
+<dt><span class="section"><a href="weg/st_eg/tut_mean_size.html">
+            Estimating how large a sample size would have to become in order to give
+            a significant Students-t test result with a single sample test</a></span></dt>
+<dt><span class="section"><a href="weg/st_eg/two_sample_students_t.html">
+            Comparing the means of two samples with the Students-t test</a></span></dt>
+<dt><span class="section"><a href="weg/st_eg/paired_st.html">
+            Comparing two paired samples with the Student's t distribution</a></span></dt>
+</dl></dd>
+<dt><span class="section"><a href="weg/cs_eg.html"> Chi Squared
+          Distribution Examples</a></span></dt>
+<dd><dl>
+<dt><span class="section"><a href="weg/cs_eg/chi_sq_intervals.html">
+            Confidence Intervals on the Standard Deviation</a></span></dt>
+<dt><span class="section"><a href="weg/cs_eg/chi_sq_test.html">
+            Chi-Square Test for the Standard Deviation</a></span></dt>
+<dt><span class="section"><a href="weg/cs_eg/chi_sq_size.html">
+            Estimating the Required Sample Sizes for a Chi-Square Test for the Standard
+            Deviation</a></span></dt>
+</dl></dd>
+<dt><span class="section"><a href="weg/f_eg.html"> F Distribution
+          Examples</a></span></dt>
+<dt><span class="section"><a href="weg/binom_eg.html"> Binomial
+          Distribution Examples</a></span></dt>
+<dd><dl>
+<dt><span class="section"><a href="weg/binom_eg/binomial_coinflip_example.html">
+            Binomial Coin-Flipping Example</a></span></dt>
+<dt><span class="section"><a href="weg/binom_eg/binomial_quiz_example.html">
+            Binomial Quiz Example</a></span></dt>
+<dt><span class="section"><a href="weg/binom_eg/binom_conf.html">
+            Calculating Confidence Limits on the Frequency of Occurrence for a Binomial
+            Distribution</a></span></dt>
+<dt><span class="section"><a href="weg/binom_eg/binom_size_eg.html">
+            Estimating Sample Sizes for a Binomial Distribution.</a></span></dt>
+</dl></dd>
+<dt><span class="section"><a href="weg/neg_binom_eg.html"> Negative
+          Binomial Distribution Examples</a></span></dt>
+<dd><dl>
+<dt><span class="section"><a href="weg/neg_binom_eg/neg_binom_conf.html">
+            Calculating Confidence Limits on the Frequency of Occurrence for the
+            Negative Binomial Distribution</a></span></dt>
+<dt><span class="section"><a href="weg/neg_binom_eg/neg_binom_size_eg.html">
+            Estimating Sample Sizes for the Negative Binomial.</a></span></dt>
+<dt><span class="section"><a href="weg/neg_binom_eg/negative_binomial_example1.html">
+            Negative Binomial Sales Quota Example.</a></span></dt>
+<dt><span class="section"><a href="weg/neg_binom_eg/negative_binomial_example2.html">
+            Negative Binomial Table Printing Example.</a></span></dt>
+</dl></dd>
+<dt><span class="section"><a href="weg/normal_example.html"> Normal
+          Distribution Examples</a></span></dt>
+<dd><dl><dt><span class="section"><a href="weg/normal_example/normal_misc.html">
+            Some Miscellaneous Examples of the Normal (Gaussian) Distribution</a></span></dt></dl></dd>
+<dt><span class="section"><a href="weg/nccs_eg.html"> Non Central
+          Chi Squared Example</a></span></dt>
+<dd><dl><dt><span class="section"><a href="weg/nccs_eg/nccs_power_eg.html">
+            Tables of the power function of the &#967;<sup>2</sup> test.</a></span></dt></dl></dd>
+<dt><span class="section"><a href="weg/error_eg.html"> Error Handling
+          Example</a></span></dt>
+<dt><span class="section"><a href="weg/find_eg.html"> Find Location
+          and Scale Examples</a></span></dt>
+<dd><dl>
+<dt><span class="section"><a href="weg/find_eg/find_location_eg.html">
+            Find Location (Mean) Example</a></span></dt>
+<dt><span class="section"><a href="weg/find_eg/find_scale_eg.html">
+            Find Scale (Standard Deviation) Example</a></span></dt>
+<dt><span class="section"><a href="weg/find_eg/find_mean_and_sd_eg.html">
+            Find mean and standard deviation example</a></span></dt>
+</dl></dd>
+<dt><span class="section"><a href="weg/nag_library.html"> Comparison
+          with C, R, FORTRAN-style Free Functions</a></span></dt>
+</dl></div>
+<p>
+        </p>
+<p>
+        </p>
+</div>
+<table xmlns:rev="http://www.cs.rpi.edu/~gregod/boost/tools/doc/revision" width="100%"><tr>
+<td align="left"></td>
+<td align="right"><div class="copyright-footer">Copyright © 2006 , 2007, 2008 John Maddock, Paul A. Bristow, Hubert
+      Holin, Xiaogang Zhang, Bruno Lalande and Gautam Sewani<p>
+        Distributed under the Boost Software License, Version 1.0. (See accompanying
+        file LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_0.txt)
+      </p>
+</div></td>
+</tr></table>
+<hr>
+<div class="spirit-nav">
+<a accesskey="p" href="overview.html"><img src="../../../../../doc/html/images/prev.png" alt="Prev"></a><a accesskey="u" href="../stat_tut.html"><img src="../../../../../doc/html/images/up.png" alt="Up"></a><a accesskey="h" href="../../../index.html"><img src="../../../../../doc/html/images/home.png" alt="Home"></a><a accesskey="n" href="weg/dist_construct_eg.html"><img src="../../../../../doc/html/images/next.png" alt="Next"></a>
+</div>
+</body>
+</html>

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+++ sandbox/tools/auto_index/example/math/doc/sf_and_dist/html/math_toolkit/dist/stat_tut/weg/binom_eg.html	2008-11-28 05:25:28 EST (Fri, 28 Nov 2008)
@@ -0,0 +1,60 @@
+<html>
+<head>
+<meta http-equiv="Content-Type" content="text/html; charset=ISO-8859-1">
+<title>Binomial Distribution Examples</title>
+<link rel="stylesheet" href="../../../../boostbook.css" type="text/css">
+<meta name="generator" content="DocBook XSL Stylesheets Vsnapshot_8125">
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+<link rel="next" href="binom_eg/binomial_coinflip_example.html" title="Binomial Coin-Flipping Example">
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+</div>
+<div class="section" lang="en">
+<div class="titlepage"><div><div><h5 class="title">
+<a name="math_toolkit.dist.stat_tut.weg.binom_eg"></a><a class="link" href="binom_eg.html" title="Binomial Distribution Examples"> Binomial
+          Distribution Examples</a>
+</h5></div></div></div>
+<div class="toc"><dl>
+<dt><span class="section"><a href="binom_eg/binomial_coinflip_example.html">
+            Binomial Coin-Flipping Example</a></span></dt>
+<dt><span class="section"><a href="binom_eg/binomial_quiz_example.html">
+            Binomial Quiz Example</a></span></dt>
+<dt><span class="section"><a href="binom_eg/binom_conf.html">
+            Calculating Confidence Limits on the Frequency of Occurrence for a Binomial
+            Distribution</a></span></dt>
+<dt><span class="section"><a href="binom_eg/binom_size_eg.html">
+            Estimating Sample Sizes for a Binomial Distribution.</a></span></dt>
+</dl></div>
+<p>
+            See also the reference documentation for the <a class="link" href="../../dist_ref/dists/binomial_dist.html" title="Binomial Distribution">Binomial
+            Distribution</a>.
+          </p>
+</div>
+<table xmlns:rev="http://www.cs.rpi.edu/~gregod/boost/tools/doc/revision" width="100%"><tr>
+<td align="left"></td>
+<td align="right"><div class="copyright-footer">Copyright © 2006 , 2007, 2008 John Maddock, Paul A. Bristow, Hubert
+      Holin, Xiaogang Zhang, Bruno Lalande and Gautam Sewani<p>
+        Distributed under the Boost Software License, Version 1.0. (See accompanying
+        file LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_0.txt)
+      </p>
+</div></td>
+</tr></table>
+<hr>
+<div class="spirit-nav">
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+</div>
+</body>
+</html>

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+++ sandbox/tools/auto_index/example/math/doc/sf_and_dist/html/math_toolkit/dist/stat_tut/weg/binom_eg/binom_conf.html	2008-11-28 05:25:28 EST (Fri, 28 Nov 2008)
@@ -0,0 +1,242 @@
+<html>
+<head>
+<meta http-equiv="Content-Type" content="text/html; charset=ISO-8859-1">
+<title>Calculating Confidence Limits on the Frequency of Occurrence for a Binomial Distribution</title>
+<link rel="stylesheet" href="../../../../../boostbook.css" type="text/css">
+<meta name="generator" content="DocBook XSL Stylesheets Vsnapshot_8125">
+<link rel="home" href="../../../../../index.html" title="Math Toolkit">
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+<link rel="prev" href="binomial_quiz_example.html" title="Binomial Quiz Example">
+<link rel="next" href="binom_size_eg.html" title="Estimating Sample Sizes for a Binomial Distribution.">
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+</div>
+<div class="section" lang="en">
+<div class="titlepage"><div><div><h6 class="title">
+<a name="math_toolkit.dist.stat_tut.weg.binom_eg.binom_conf"></a><a class="link" href="binom_conf.html" title="Calculating Confidence Limits on the Frequency of Occurrence for a Binomial Distribution">
+            Calculating Confidence Limits on the Frequency of Occurrence for a Binomial
+            Distribution</a>
+</h6></div></div></div>
+<p>
+              Imagine you have a process that follows a binomial distribution: for
+              each trial conducted, an event either occurs or does it does not, referred
+              to as "successes" and "failures". If, by experiment,
+              you want to measure the frequency with which successes occur, the best
+              estimate is given simply by <span class="emphasis"><em>k</em></span> / <span class="emphasis"><em>N</em></span>,
+              for <span class="emphasis"><em>k</em></span> successes out of <span class="emphasis"><em>N</em></span>
+              trials. However our confidence in that estimate will be shaped by how
+              many trials were conducted, and how many successes were observed. The
+              static member functions <code class="computeroutput"><span class="identifier">binomial_distribution</span><span class="special">&lt;&gt;::</span><span class="identifier">find_lower_bound_on_p</span></code>
+              and <code class="computeroutput"><span class="identifier">binomial_distribution</span><span class="special">&lt;&gt;::</span><span class="identifier">find_upper_bound_on_p</span></code>
+              allow you to calculate the confidence intervals for your estimate of
+              the occurrence frequency.
+            </p>
+<p>
+              The sample program binomial_confidence_limits.cpp
+              illustrates their use. It begins by defining a procedure that will
+              print a table of confidence limits for various degrees of certainty:
+            </p>
+<pre class="programlisting"><span class="preprocessor">#include</span> <span class="special">&lt;</span><span class="identifier">iostream</span><span class="special">&gt;</span>
+<span class="preprocessor">#include</span> <span class="special">&lt;</span><span class="identifier">iomanip</span><span class="special">&gt;</span>
+<span class="preprocessor">#include</span> <span class="special">&lt;</span><span class="identifier">boost</span><span class="special">/</span><span class="identifier">math</span><span class="special">/</span><span class="identifier">distributions</span><span class="special">/</span><span class="identifier">binomial</span><span class="special">.</span><span class="identifier">hpp</span><span class="special">&gt;</span>
+
+<span class="keyword">void</span> <span class="identifier">confidence_limits_on_frequency</span><span class="special">(</span><span class="keyword">unsigned</span> <span class="identifier">trials</span><span class="special">,</span> <span class="keyword">unsigned</span> <span class="identifier">successes</span><span class="special">)</span>
+<span class="special">{</span>
+   <span class="comment">//
+</span>   <span class="comment">// trials = Total number of trials.
+</span>   <span class="comment">// successes = Total number of observed successes.
+</span>   <span class="comment">//
+</span>   <span class="comment">// Calculate confidence limits for an observed
+</span>   <span class="comment">// frequency of occurrence that follows a binomial
+</span>   <span class="comment">// distribution.
+</span>   <span class="comment">//
+</span>   <span class="keyword">using</span> <span class="keyword">namespace</span> <span class="identifier">std</span><span class="special">;</span>
+   <span class="keyword">using</span> <span class="keyword">namespace</span> <span class="identifier">boost</span><span class="special">::</span><span class="identifier">math</span><span class="special">;</span>
+
+   <span class="comment">// Print out general info:
+</span>   <span class="identifier">cout</span> <span class="special">&lt;&lt;</span>
+      <span class="string">"___________________________________________\n"</span>
+      <span class="string">"2-Sided Confidence Limits For Success Ratio\n"</span>
+      <span class="string">"___________________________________________\n\n"</span><span class="special">;</span>
+   <span class="identifier">cout</span> <span class="special">&lt;&lt;</span> <span class="identifier">setprecision</span><span class="special">(</span><span class="number">7</span><span class="special">);</span>
+   <span class="identifier">cout</span> <span class="special">&lt;&lt;</span> <span class="identifier">setw</span><span class="special">(</span><span class="number">40</span><span class="special">)</span> <span class="special">&lt;&lt;</span> <span class="identifier">left</span> <span class="special">&lt;&lt;</span> <span class="string">"Number of Observations"</span> <span class="special">&lt;&lt;</span> <span class="string">"=  "</span> <span class="special">&lt;&lt;</span> <span class="identifier">trials</span> <span class="special">&lt;&lt;</span> <span class="string">"\n"</span><span class="special">;</span>
+   <span class="identifier">cout</span> <span class="special">&lt;&lt;</span> <span class="identifier">setw</span><span class="special">(</span><span class="number">40</span><span class="special">)</span> <span class="special">&lt;&lt;</span> <span class="identifier">left</span> <span class="special">&lt;&lt;</span> <span class="string">"Number of successes"</span> <span class="special">&lt;&lt;</span> <span class="string">"=  "</span> <span class="special">&lt;&lt;</span> <span class="identifier">successes</span> <span class="special">&lt;&lt;</span> <span class="string">"\n"</span><span class="special">;</span>
+   <span class="identifier">cout</span> <span class="special">&lt;&lt;</span> <span class="identifier">setw</span><span class="special">(</span><span class="number">40</span><span class="special">)</span> <span class="special">&lt;&lt;</span> <span class="identifier">left</span> <span class="special">&lt;&lt;</span> <span class="string">"Sample frequency of occurrence"</span> <span class="special">&lt;&lt;</span> <span class="string">"=  "</span> <span class="special">&lt;&lt;</span> <span class="keyword">double</span><span class="special">(</span><span class="identifier">successes</span><span class="special">)</span> <span class="special">/</span> <span class="identifier">trials</span> <span class="special">&lt;&lt;</span> <span class="string">"\n"</span><span class="special">;</span>
+</pre>
+<p>
+              The procedure now defines a table of significance levels: these are
+              the probabilities that the true occurrence frequency lies outside the
+              calculated interval:
+            </p>
+<pre class="programlisting"><span class="keyword">double</span> <span class="identifier">alpha</span><span class="special">[]</span> <span class="special">=</span> <span class="special">{</span> <span class="number">0.5</span><span class="special">,</span> <span class="number">0.25</span><span class="special">,</span> <span class="number">0.1</span><span class="special">,</span> <span class="number">0.05</span><span class="special">,</span> <span class="number">0.01</span><span class="special">,</span> <span class="number">0.001</span><span class="special">,</span> <span class="number">0.0001</span><span class="special">,</span> <span class="number">0.00001</span> <span class="special">};</span>
+</pre>
+<p>
+              Some pretty printing of the table header follows:
+            </p>
+<pre class="programlisting"><span class="identifier">cout</span> <span class="special">&lt;&lt;</span> <span class="string">"\n\n"</span>
+        <span class="string">"_______________________________________________________________________\n"</span>
+        <span class="string">"Confidence        Lower CP       Upper CP       Lower JP       Upper JP\n"</span>
+        <span class="string">" Value (%)        Limit          Limit          Limit          Limit\n"</span>
+        <span class="string">"_______________________________________________________________________\n"</span><span class="special">;</span>
+</pre>
+<p>
+              And now for the important part - the intervals themselves - for each
+              value of <span class="emphasis"><em>alpha</em></span>, we call <code class="computeroutput"><span class="identifier">find_lower_bound_on_p</span></code>
+              and <code class="computeroutput"><span class="identifier">find_lower_upper_on_p</span></code>
+              to obtain lower and upper bounds respectively. Note that since we are
+              calculating a two-sided interval, we must divide the value of alpha
+              in two.
+            </p>
+<p>
+              Please note that calculating two separate <span class="emphasis"><em>single sided bounds</em></span>,
+              each with risk level &#945;is not the same thing as calculating a two sided
+              interval. Had we calculate two single-sided intervals each with a risk
+              that the true value is outside the interval of &#945;, then:
+            </p>
+<div class="itemizedlist"><ul type="disc"><li>
+                The risk that it is less than the lower bound is &#945;.
+              </li></ul></div>
+<p>
+              and
+            </p>
+<div class="itemizedlist"><ul type="disc"><li>
+                The risk that it is greater than the upper bound is also &#945;.
+              </li></ul></div>
+<p>
+              So the risk it is outside <span class="bold"><strong>upper or lower bound</strong></span>,
+              is <span class="bold"><strong>twice</strong></span> alpha, and the probability
+              that it is inside the bounds is therefore not nearly as high as one
+              might have thought. This is why &#945;/2 must be used in the calculations
+              below.
+            </p>
+<p>
+              In contrast, had we been calculating a single-sided interval, for example:
+              <span class="emphasis"><em>"Calculate a lower bound so that we are P% sure that
+              the true occurrence frequency is greater than some value"</em></span>
+              then we would <span class="bold"><strong>not</strong></span> have divided by
+              two.
+            </p>
+<p>
+              Finally note that <code class="computeroutput"><span class="identifier">binomial_distribution</span></code>
+              provides a choice of two methods for the calculation, we print out
+              the results from both methods in this example:
+            </p>
+<pre class="programlisting">   <span class="keyword">for</span><span class="special">(</span><span class="keyword">unsigned</span> <span class="identifier">i</span> <span class="special">=</span> <span class="number">0</span><span class="special">;</span> <span class="identifier">i</span> <span class="special">&lt;</span> <span class="keyword">sizeof</span><span class="special">(</span><span class="identifier">alpha</span><span class="special">)/</span><span class="keyword">sizeof</span><span class="special">(</span><span class="identifier">alpha</span><span class="special">[</span><span class="number">0</span><span class="special">]);</span> <span class="special">++</span><span class="identifier">i</span><span class="special">)</span>
+   <span class="special">{</span>
+      <span class="comment">// Confidence value:
+</span>      <span class="identifier">cout</span> <span class="special">&lt;&lt;</span> <span class="identifier">fixed</span> <span class="special">&lt;&lt;</span> <span class="identifier">setprecision</span><span class="special">(</span><span class="number">3</span><span class="special">)</span> <span class="special">&lt;&lt;</span> <span class="identifier">setw</span><span class="special">(</span><span class="number">10</span><span class="special">)</span> <span class="special">&lt;&lt;</span> <span class="identifier">right</span> <span class="special">&lt;&lt;</span> <span class="number">100</span> <span class="special">*</span> <span class="special">(</span><span class="number">1</span><span class="special">-</span><span class="identifier">alpha</span><span class="special">[</span><span class="identifier">i</span><span class="special">]);</span>
+      <span class="comment">// Calculate Clopper Pearson bounds:
+</span>      <span class="keyword">double</span> <span class="identifier">l</span> <span class="special">=</span> <span class="identifier">binomial_distribution</span><span class="special">&lt;&gt;::</span><span class="identifier">find_lower_bound_on_p</span><span class="special">(</span>
+                     <span class="identifier">trials</span><span class="special">,</span> <span class="identifier">successes</span><span class="special">,</span> <span class="identifier">alpha</span><span class="special">[</span><span class="identifier">i</span><span class="special">]/</span><span class="number">2</span><span class="special">);</span>
+      <span class="keyword">double</span> <span class="identifier">u</span> <span class="special">=</span> <span class="identifier">binomial_distribution</span><span class="special">&lt;&gt;::</span><span class="identifier">find_upper_bound_on_p</span><span class="special">(</span>
+                     <span class="identifier">trials</span><span class="special">,</span> <span class="identifier">successes</span><span class="special">,</span> <span class="identifier">alpha</span><span class="special">[</span><span class="identifier">i</span><span class="special">]/</span><span class="number">2</span><span class="special">);</span>
+      <span class="comment">// Print Clopper Pearson Limits:
+</span>      <span class="identifier">cout</span> <span class="special">&lt;&lt;</span> <span class="identifier">fixed</span> <span class="special">&lt;&lt;</span> <span class="identifier">setprecision</span><span class="special">(</span><span class="number">5</span><span class="special">)</span> <span class="special">&lt;&lt;</span> <span class="identifier">setw</span><span class="special">(</span><span class="number">15</span><span class="special">)</span> <span class="special">&lt;&lt;</span> <span class="identifier">right</span> <span class="special">&lt;&lt;</span> <span class="identifier">l</span><span class="special">;</span>
+      <span class="identifier">cout</span> <span class="special">&lt;&lt;</span> <span class="identifier">fixed</span> <span class="special">&lt;&lt;</span> <span class="identifier">setprecision</span><span class="special">(</span><span class="number">5</span><span class="special">)</span> <span class="special">&lt;&lt;</span> <span class="identifier">setw</span><span class="special">(</span><span class="number">15</span><span class="special">)</span> <span class="special">&lt;&lt;</span> <span class="identifier">right</span> <span class="special">&lt;&lt;</span> <span class="identifier">u</span><span class="special">;</span>
+      <span class="comment">// Calculate Jeffreys Prior Bounds:
+</span>      <span class="identifier">l</span> <span class="special">=</span> <span class="identifier">binomial_distribution</span><span class="special">&lt;&gt;::</span><span class="identifier">find_lower_bound_on_p</span><span class="special">(</span>
+            <span class="identifier">trials</span><span class="special">,</span> <span class="identifier">successes</span><span class="special">,</span> <span class="identifier">alpha</span><span class="special">[</span><span class="identifier">i</span><span class="special">]/</span><span class="number">2</span><span class="special">,</span> 
+            <span class="identifier">binomial_distribution</span><span class="special">&lt;&gt;::</span><span class="identifier">jeffreys_prior_interval</span><span class="special">);</span>
+      <span class="identifier">u</span> <span class="special">=</span> <span class="identifier">binomial_distribution</span><span class="special">&lt;&gt;::</span><span class="identifier">find_upper_bound_on_p</span><span class="special">(</span>
+            <span class="identifier">trials</span><span class="special">,</span> <span class="identifier">successes</span><span class="special">,</span> <span class="identifier">alpha</span><span class="special">[</span><span class="identifier">i</span><span class="special">]/</span><span class="number">2</span><span class="special">,</span> 
+            <span class="identifier">binomial_distribution</span><span class="special">&lt;&gt;::</span><span class="identifier">jeffreys_prior_interval</span><span class="special">);</span>
+      <span class="comment">// Print Jeffreys Prior Limits:
+</span>      <span class="identifier">cout</span> <span class="special">&lt;&lt;</span> <span class="identifier">fixed</span> <span class="special">&lt;&lt;</span> <span class="identifier">setprecision</span><span class="special">(</span><span class="number">5</span><span class="special">)</span> <span class="special">&lt;&lt;</span> <span class="identifier">setw</span><span class="special">(</span><span class="number">15</span><span class="special">)</span> <span class="special">&lt;&lt;</span> <span class="identifier">right</span> <span class="special">&lt;&lt;</span> <span class="identifier">l</span><span class="special">;</span>
+      <span class="identifier">cout</span> <span class="special">&lt;&lt;</span> <span class="identifier">fixed</span> <span class="special">&lt;&lt;</span> <span class="identifier">setprecision</span><span class="special">(</span><span class="number">5</span><span class="special">)</span> <span class="special">&lt;&lt;</span> <span class="identifier">setw</span><span class="special">(</span><span class="number">15</span><span class="special">)</span> <span class="special">&lt;&lt;</span> <span class="identifier">right</span> <span class="special">&lt;&lt;</span> <span class="identifier">u</span> <span class="special">&lt;&lt;</span> <span class="identifier">std</span><span class="special">::</span><span class="identifier">endl</span><span class="special">;</span>
+   <span class="special">}</span>
+   <span class="identifier">cout</span> <span class="special">&lt;&lt;</span> <span class="identifier">endl</span><span class="special">;</span>
+<span class="special">}</span>
+</pre>
+<p>
+              And that's all there is to it. Let's see some sample output for a 2
+              in 10 success ratio, first for 20 trials:
+            </p>
+<pre class="programlisting">___________________________________________
+2-Sided Confidence Limits For Success Ratio
+___________________________________________
+
+Number of Observations                  =  20
+Number of successes                     =  4
+Sample frequency of occurrence          =  0.2
+
+
+_______________________________________________________________________
+Confidence        Lower CP       Upper CP       Lower JP       Upper JP
+ Value (%)        Limit          Limit          Limit          Limit
+_______________________________________________________________________
+    50.000        0.12840        0.29588        0.14974        0.26916
+    75.000        0.09775        0.34633        0.11653        0.31861
+    90.000        0.07135        0.40103        0.08734        0.37274
+    95.000        0.05733        0.43661        0.07152        0.40823
+    99.000        0.03576        0.50661        0.04655        0.47859
+    99.900        0.01905        0.58632        0.02634        0.55960
+    99.990        0.01042        0.64997        0.01530        0.62495
+    99.999        0.00577        0.70216        0.00901        0.67897
+</pre>
+<p>
+              As you can see, even at the 95% confidence level the bounds are really
+              quite wide (this example is chosen to be easily compared to the one
+              in the <a href="http://www.itl.nist.gov/div898/handbook/" target="_top">NIST/SEMATECH
+              e-Handbook of Statistical Methods.</a> here).
+              Note also that the Clopper-Pearson calculation method (CP above) produces
+              quite noticeably more pessimistic estimates than the Jeffreys Prior
+              method (JP above).
+            </p>
+<p>
+              Compare that with the program output for 2000 trials:
+            </p>
+<pre class="programlisting">___________________________________________
+2-Sided Confidence Limits For Success Ratio
+___________________________________________
+
+Number of Observations                  =  2000
+Number of successes                     =  400
+Sample frequency of occurrence          =  0.2000000
+
+
+_______________________________________________________________________
+Confidence        Lower CP       Upper CP       Lower JP       Upper JP
+ Value (%)        Limit          Limit          Limit          Limit
+_______________________________________________________________________
+    50.000        0.19382        0.20638        0.19406        0.20613
+    75.000        0.18965        0.21072        0.18990        0.21047
+    90.000        0.18537        0.21528        0.18561        0.21503
+    95.000        0.18267        0.21821        0.18291        0.21796
+    99.000        0.17745        0.22400        0.17769        0.22374
+    99.900        0.17150        0.23079        0.17173        0.23053
+    99.990        0.16658        0.23657        0.16681        0.23631
+    99.999        0.16233        0.24169        0.16256        0.24143
+</pre>
+<p>
+              Now even when the confidence level is very high, the limits are really
+              quite close to the experimentally calculated value of 0.2. Furthermore
+              the difference between the two calculation methods is now really quite
+              small.
+            </p>
+</div>
+<table xmlns:rev="http://www.cs.rpi.edu/~gregod/boost/tools/doc/revision" width="100%"><tr>
+<td align="left"></td>
+<td align="right"><div class="copyright-footer">Copyright © 2006 , 2007, 2008 John Maddock, Paul A. Bristow, Hubert
+      Holin, Xiaogang Zhang, Bruno Lalande and Gautam Sewani<p>
+        Distributed under the Boost Software License, Version 1.0. (See accompanying
+        file LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_0.txt)
+      </p>
+</div></td>
+</tr></table>
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@@ -0,0 +1,158 @@
+<html>
+<head>
+<meta http-equiv="Content-Type" content="text/html; charset=ISO-8859-1">
+<title>Estimating Sample Sizes for a Binomial Distribution.</title>
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+</div>
+<div class="section" lang="en">
+<div class="titlepage"><div><div><h6 class="title">
+<a name="math_toolkit.dist.stat_tut.weg.binom_eg.binom_size_eg"></a><a class="link" href="binom_size_eg.html" title="Estimating Sample Sizes for a Binomial Distribution.">
+            Estimating Sample Sizes for a Binomial Distribution.</a>
+</h6></div></div></div>
+<p>
+              Imagine you have a critical component that you know will fail in 1
+              in N "uses" (for some suitable definition of "use").
+              You may want to schedule routine replacement of the component so that
+              its chance of failure between routine replacements is less than P%.
+              If the failures follow a binomial distribution (each time the component
+              is "used" it either fails or does not) then the static member
+              function <code class="computeroutput"><span class="identifier">binomial_distibution</span><span class="special">&lt;&gt;::</span><span class="identifier">find_maximum_number_of_trials</span></code>
+              can be used to estimate the maximum number of "uses" of that
+              component for some acceptable risk level <span class="emphasis"><em>alpha</em></span>.
+            </p>
+<p>
+              The example program binomial_sample_sizes.cpp
+              demonstrates its usage. It centres on a routine that prints out a table
+              of maximum sample sizes for various probability thresholds:
+            </p>
+<pre class="programlisting"><span class="keyword">void</span> <span class="identifier">find_max_sample_size</span><span class="special">(</span>
+   <span class="keyword">double</span> <span class="identifier">p</span><span class="special">,</span>              <span class="comment">// success ratio.
+</span>   <span class="keyword">unsigned</span> <span class="identifier">successes</span><span class="special">)</span>    <span class="comment">// Total number of observed successes permitted.
+</span><span class="special">{</span>
+</pre>
+<p>
+              The routine then declares a table of probability thresholds: these
+              are the maximum acceptable probability that <span class="emphasis"><em>successes</em></span>
+              or fewer events will be observed. In our example, <span class="emphasis"><em>successes</em></span>
+              will be always zero, since we want no component failures, but in other
+              situations non-zero values may well make sense.
+            </p>
+<pre class="programlisting"><span class="keyword">double</span> <span class="identifier">alpha</span><span class="special">[]</span> <span class="special">=</span> <span class="special">{</span> <span class="number">0.5</span><span class="special">,</span> <span class="number">0.25</span><span class="special">,</span> <span class="number">0.1</span><span class="special">,</span> <span class="number">0.05</span><span class="special">,</span> <span class="number">0.01</span><span class="special">,</span> <span class="number">0.001</span><span class="special">,</span> <span class="number">0.0001</span><span class="special">,</span> <span class="number">0.00001</span> <span class="special">};</span>
+</pre>
+<p>
+              Much of the rest of the program is pretty-printing, the important part
+              is in the calculation of maximum number of permitted trials for each
+              value of alpha:
+            </p>
+<pre class="programlisting"><span class="keyword">for</span><span class="special">(</span><span class="keyword">unsigned</span> <span class="identifier">i</span> <span class="special">=</span> <span class="number">0</span><span class="special">;</span> <span class="identifier">i</span> <span class="special">&lt;</span> <span class="keyword">sizeof</span><span class="special">(</span><span class="identifier">alpha</span><span class="special">)/</span><span class="keyword">sizeof</span><span class="special">(</span><span class="identifier">alpha</span><span class="special">[</span><span class="number">0</span><span class="special">]);</span> <span class="special">++</span><span class="identifier">i</span><span class="special">)</span>
+<span class="special">{</span>
+   <span class="comment">// Confidence value:
+</span>   <span class="identifier">cout</span> <span class="special">&lt;&lt;</span> <span class="identifier">fixed</span> <span class="special">&lt;&lt;</span> <span class="identifier">setprecision</span><span class="special">(</span><span class="number">3</span><span class="special">)</span> <span class="special">&lt;&lt;</span> <span class="identifier">setw</span><span class="special">(</span><span class="number">10</span><span class="special">)</span> <span class="special">&lt;&lt;</span> <span class="identifier">right</span> <span class="special">&lt;&lt;</span> <span class="number">100</span> <span class="special">*</span> <span class="special">(</span><span class="number">1</span><span class="special">-</span><span class="identifier">alpha</span><span class="special">[</span><span class="identifier">i</span><span class="special">]);</span>
+   <span class="comment">// calculate trials:
+</span>   <span class="keyword">double</span> <span class="identifier">t</span> <span class="special">=</span> <span class="identifier">binomial</span><span class="special">::</span><span class="identifier">find_maximum_number_of_trials</span><span class="special">(</span>
+                  <span class="identifier">successes</span><span class="special">,</span> <span class="identifier">p</span><span class="special">,</span> <span class="identifier">alpha</span><span class="special">[</span><span class="identifier">i</span><span class="special">]);</span>
+   <span class="identifier">t</span> <span class="special">=</span> <span class="identifier">floor</span><span class="special">(</span><span class="identifier">t</span><span class="special">);</span>
+   <span class="comment">// Print Trials:
+</span>   <span class="identifier">cout</span> <span class="special">&lt;&lt;</span> <span class="identifier">fixed</span> <span class="special">&lt;&lt;</span> <span class="identifier">setprecision</span><span class="special">(</span><span class="number">5</span><span class="special">)</span> <span class="special">&lt;&lt;</span> <span class="identifier">setw</span><span class="special">(</span><span class="number">15</span><span class="special">)</span> <span class="special">&lt;&lt;</span> <span class="identifier">right</span> <span class="special">&lt;&lt;</span> <span class="identifier">t</span> <span class="special">&lt;&lt;</span> <span class="identifier">endl</span><span class="special">;</span>
+<span class="special">}</span>
+</pre>
+<p>
+              Note that since we're calculating the maximum number of trials permitted,
+              we'll err on the safe side and take the floor of the result. Had we
+              been calculating the <span class="emphasis"><em>minimum</em></span> number of trials
+              required to observe a certain number of <span class="emphasis"><em>successes</em></span>
+              using <code class="computeroutput"><span class="identifier">find_minimum_number_of_trials</span></code>
+              we would have taken the ceiling instead.
+            </p>
+<p>
+              We'll finish off by looking at some sample output, firstly for a 1
+              in 1000 chance of component failure with each use:
+            </p>
+<pre class="programlisting">________________________
+Maximum Number of Trials
+________________________
+
+Success ratio                           =  0.001
+Maximum Number of "successes" permitted =  0
+
+
+____________________________
+Confidence        Max Number
+ Value (%)        Of Trials
+____________________________
+    50.000            692
+    75.000            287
+    90.000            105
+    95.000             51
+    99.000             10
+    99.900              0
+    99.990              0
+    99.999              0
+</pre>
+<p>
+              So 51 "uses" of the component would yield a 95% chance that
+              no component failures would be observed.
+            </p>
+<p>
+              Compare that with a 1 in 1 million chance of component failure:
+            </p>
+<pre class="programlisting">________________________
+Maximum Number of Trials
+________________________
+
+Success ratio                           =  0.0000010
+Maximum Number of "successes" permitted =  0
+
+
+____________________________
+Confidence        Max Number
+ Value (%)        Of Trials
+____________________________
+    50.000         693146
+    75.000         287681
+    90.000         105360
+    95.000          51293
+    99.000          10050
+    99.900           1000
+    99.990            100
+    99.999             10
+</pre>
+<p>
+              In this case, even 1000 uses of the component would still yield a less
+              than 1 in 1000 chance of observing a component failure (i.e. a 99.9%
+              chance of no failure).
+            </p>
+</div>
+<table xmlns:rev="http://www.cs.rpi.edu/~gregod/boost/tools/doc/revision" width="100%"><tr>
+<td align="left"></td>
+<td align="right"><div class="copyright-footer">Copyright © 2006 , 2007, 2008 John Maddock, Paul A. Bristow, Hubert
+      Holin, Xiaogang Zhang, Bruno Lalande and Gautam Sewani<p>
+        Distributed under the Boost Software License, Version 1.0. (See accompanying
+        file LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_0.txt)
+      </p>
+</div></td>
+</tr></table>
+<hr>
+<div class="spirit-nav">
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+</div>
+</body>
+</html>

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+++ sandbox/tools/auto_index/example/math/doc/sf_and_dist/html/math_toolkit/dist/stat_tut/weg/binom_eg/binomial_coinflip_example.html	2008-11-28 05:25:28 EST (Fri, 28 Nov 2008)
@@ -0,0 +1,406 @@
+<html>
+<head>
+<meta http-equiv="Content-Type" content="text/html; charset=ISO-8859-1">
+<title>Binomial Coin-Flipping Example</title>
+<link rel="stylesheet" href="../../../../../boostbook.css" type="text/css">
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+<link rel="home" href="../../../../../index.html" title="Math Toolkit">
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+<td align="center">Home</td>
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+</div>
+<div class="section" lang="en">
+<div class="titlepage"><div><div><h6 class="title">
+<a name="math_toolkit.dist.stat_tut.weg.binom_eg.binomial_coinflip_example"></a><a class="link" href="binomial_coinflip_example.html" title="Binomial Coin-Flipping Example">
+            Binomial Coin-Flipping Example</a>
+</h6></div></div></div>
+<p>
+              </p>
+<p>
+                An example of a <a href="http://en.wikipedia.org/wiki/Bernoulli_process" target="_top">Bernoulli
+                process</a> is coin flipping. A variable in such a sequence may
+                be called a Bernoulli variable.
+              </p>
+<p>
+              </p>
+<p>
+                This example shows using the Binomial distribution to predict the
+                probability of heads and tails when throwing a coin.
+              </p>
+<p>
+              </p>
+<p>
+                The number of correct answers (say heads), X, is distributed as a
+                binomial random variable with binomial distribution parameters number
+                of trials (flips) n = 10 and probability (success_fraction) of getting
+                a head p = 0.5 (a 'fair' coin).
+              </p>
+<p>
+              </p>
+<p>
+                (Our coin is assumed fair, but we could easily change the success_fraction
+                parameter p from 0.5 to some other value to simulate an unfair coin,
+                say 0.6 for one with chewing gum on the tail, so it is more likely
+                to fall tails down and heads up).
+              </p>
+<p>
+              </p>
+<p>
+                First we need some includes and using statements to be able to use
+                the binomial distribution, some std input and output, and get started:
+              </p>
+<p>
+              </p>
+<p>
+                
+</p>
+<pre class="programlisting"><span class="preprocessor">#include</span> <span class="special">&lt;</span><span class="identifier">boost</span><span class="special">/</span><span class="identifier">math</span><span class="special">/</span><span class="identifier">distributions</span><span class="special">/</span><span class="identifier">binomial</span><span class="special">.</span><span class="identifier">hpp</span><span class="special">&gt;</span>
+  <span class="keyword">using</span> <span class="identifier">boost</span><span class="special">::</span><span class="identifier">math</span><span class="special">::</span><span class="identifier">binomial</span><span class="special">;</span>
+
+<span class="preprocessor">#include</span> <span class="special">&lt;</span><span class="identifier">iostream</span><span class="special">&gt;</span>
+  <span class="keyword">using</span> <span class="identifier">std</span><span class="special">::</span><span class="identifier">cout</span><span class="special">;</span>  <span class="keyword">using</span> <span class="identifier">std</span><span class="special">::</span><span class="identifier">endl</span><span class="special">;</span>  <span class="keyword">using</span> <span class="identifier">std</span><span class="special">::</span><span class="identifier">left</span><span class="special">;</span>
+<span class="preprocessor">#include</span> <span class="special">&lt;</span><span class="identifier">iomanip</span><span class="special">&gt;</span>
+  <span class="keyword">using</span> <span class="identifier">std</span><span class="special">::</span><span class="identifier">setw</span><span class="special">;</span>
+
+<span class="keyword">int</span> <span class="identifier">main</span><span class="special">()</span>
+<span class="special">{</span>
+  <span class="identifier">cout</span> <span class="special">&lt;&lt;</span> <span class="string">"Using Binomial distribution to predict how many heads and tails."</span> <span class="special">&lt;&lt;</span> <span class="identifier">endl</span><span class="special">;</span>
+  <span class="keyword">try</span>
+  <span class="special">{</span></pre>
+<p>
+              </p>
+<p>
+              </p>
+<p>
+                See note <a class="link" href="binomial_coinflip_example.html#coinflip_eg_catch">with the catch block</a>
+                about why a try and catch block is always a good idea.
+              </p>
+<p>
+              </p>
+<p>
+                First, construct a binomial distribution with parameters success_fraction
+                1/2, and how many flips.
+              </p>
+<p>
+              </p>
+<p>
+                
+</p>
+<pre class="programlisting"><span class="keyword">const</span> <span class="keyword">double</span> <span class="identifier">success_fraction</span> <span class="special">=</span> <span class="number">0.5</span><span class="special">;</span> <span class="comment">// = 50% = 1/2 for a 'fair' coin.
+</span><span class="keyword">int</span> <span class="identifier">flips</span> <span class="special">=</span> <span class="number">10</span><span class="special">;</span>
+<span class="identifier">binomial</span> <span class="identifier">flip</span><span class="special">(</span><span class="identifier">flips</span><span class="special">,</span> <span class="identifier">success_fraction</span><span class="special">);</span>
+
+<span class="identifier">cout</span><span class="special">.</span><span class="identifier">precision</span><span class="special">(</span><span class="number">4</span><span class="special">);</span></pre>
+<p>
+              </p>
+<p>
+              </p>
+<p>
+                Then some examples of using Binomial moments (and echoing the parameters).
+              </p>
+<p>
+              </p>
+<p>
+                
+</p>
+<pre class="programlisting"><span class="identifier">cout</span> <span class="special">&lt;&lt;</span> <span class="string">"From "</span> <span class="special">&lt;&lt;</span> <span class="identifier">flips</span> <span class="special">&lt;&lt;</span> <span class="string">" one can expect to get on average "</span>
+  <span class="special">&lt;&lt;</span> <span class="identifier">mean</span><span class="special">(</span><span class="identifier">flip</span><span class="special">)</span> <span class="special">&lt;&lt;</span> <span class="string">" heads (or tails)."</span> <span class="special">&lt;&lt;</span> <span class="identifier">endl</span><span class="special">;</span>
+<span class="identifier">cout</span> <span class="special">&lt;&lt;</span> <span class="string">"Mode is "</span> <span class="special">&lt;&lt;</span> <span class="identifier">mode</span><span class="special">(</span><span class="identifier">flip</span><span class="special">)</span> <span class="special">&lt;&lt;</span> <span class="identifier">endl</span><span class="special">;</span>
+<span class="identifier">cout</span> <span class="special">&lt;&lt;</span> <span class="string">"Standard deviation is "</span> <span class="special">&lt;&lt;</span> <span class="identifier">standard_deviation</span><span class="special">(</span><span class="identifier">flip</span><span class="special">)</span> <span class="special">&lt;&lt;</span> <span class="identifier">endl</span><span class="special">;</span>
+<span class="identifier">cout</span> <span class="special">&lt;&lt;</span> <span class="string">"So about 2/3 will lie within 1 standard deviation and get between "</span>
+  <span class="special">&lt;&lt;</span>  <span class="identifier">ceil</span><span class="special">(</span><span class="identifier">mean</span><span class="special">(</span><span class="identifier">flip</span><span class="special">)</span> <span class="special">-</span> <span class="identifier">standard_deviation</span><span class="special">(</span><span class="identifier">flip</span><span class="special">))</span>  <span class="special">&lt;&lt;</span> <span class="string">" and "</span>
+  <span class="special">&lt;&lt;</span> <span class="identifier">floor</span><span class="special">(</span><span class="identifier">mean</span><span class="special">(</span><span class="identifier">flip</span><span class="special">)</span> <span class="special">+</span> <span class="identifier">standard_deviation</span><span class="special">(</span><span class="identifier">flip</span><span class="special">))</span> <span class="special">&lt;&lt;</span> <span class="string">" correct."</span> <span class="special">&lt;&lt;</span> <span class="identifier">endl</span><span class="special">;</span>
+<span class="identifier">cout</span> <span class="special">&lt;&lt;</span> <span class="string">"Skewness is "</span> <span class="special">&lt;&lt;</span> <span class="identifier">skewness</span><span class="special">(</span><span class="identifier">flip</span><span class="special">)</span> <span class="special">&lt;&lt;</span> <span class="identifier">endl</span><span class="special">;</span>
+<span class="comment">// Skewness of binomial distributions is only zero (symmetrical)
+</span><span class="comment">// if success_fraction is exactly one half,
+</span><span class="comment">// for example, when flipping 'fair' coins.
+</span><span class="identifier">cout</span> <span class="special">&lt;&lt;</span> <span class="string">"Skewness if success_fraction is "</span> <span class="special">&lt;&lt;</span> <span class="identifier">flip</span><span class="special">.</span><span class="identifier">success_fraction</span><span class="special">()</span>
+  <span class="special">&lt;&lt;</span> <span class="string">" is "</span> <span class="special">&lt;&lt;</span> <span class="identifier">skewness</span><span class="special">(</span><span class="identifier">flip</span><span class="special">)</span> <span class="special">&lt;&lt;</span> <span class="identifier">endl</span> <span class="special">&lt;&lt;</span> <span class="identifier">endl</span><span class="special">;</span> <span class="comment">// Expect zero for a 'fair' coin.</span></pre>
+<p>
+              </p>
+<p>
+              </p>
+<p>
+                Now we show a variety of predictions on the probability of heads:
+              </p>
+<p>
+              </p>
+<p>
+                
+</p>
+<pre class="programlisting"><span class="identifier">cout</span> <span class="special">&lt;&lt;</span> <span class="string">"For "</span> <span class="special">&lt;&lt;</span> <span class="identifier">flip</span><span class="special">.</span><span class="identifier">trials</span><span class="special">()</span> <span class="special">&lt;&lt;</span> <span class="string">" coin flips: "</span> <span class="special">&lt;&lt;</span> <span class="identifier">endl</span><span class="special">;</span>
+<span class="identifier">cout</span> <span class="special">&lt;&lt;</span> <span class="string">"Probability of getting no heads is "</span> <span class="special">&lt;&lt;</span> <span class="identifier">pdf</span><span class="special">(</span><span class="identifier">flip</span><span class="special">,</span> <span class="number">0</span><span class="special">)</span> <span class="special">&lt;&lt;</span> <span class="identifier">endl</span><span class="special">;</span>
+<span class="identifier">cout</span> <span class="special">&lt;&lt;</span> <span class="string">"Probability of getting at least one head is "</span> <span class="special">&lt;&lt;</span> <span class="number">1.</span> <span class="special">-</span> <span class="identifier">pdf</span><span class="special">(</span><span class="identifier">flip</span><span class="special">,</span> <span class="number">0</span><span class="special">)</span> <span class="special">&lt;&lt;</span> <span class="identifier">endl</span><span class="special">;</span></pre>
+<p>
+              </p>
+<p>
+              </p>
+<p>
+                When we want to calculate the probability for a range or values we
+                can sum the PDF's:
+              </p>
+<p>
+              </p>
+<p>
+                
+</p>
+<pre class="programlisting"><span class="identifier">cout</span> <span class="special">&lt;&lt;</span> <span class="string">"Probability of getting 0 or 1 heads is "</span>
+  <span class="special">&lt;&lt;</span> <span class="identifier">pdf</span><span class="special">(</span><span class="identifier">flip</span><span class="special">,</span> <span class="number">0</span><span class="special">)</span> <span class="special">+</span> <span class="identifier">pdf</span><span class="special">(</span><span class="identifier">flip</span><span class="special">,</span> <span class="number">1</span><span class="special">)</span> <span class="special">&lt;&lt;</span> <span class="identifier">endl</span><span class="special">;</span> <span class="comment">// sum of exactly == probabilities</span></pre>
+<p>
+              </p>
+<p>
+              </p>
+<p>
+                Or we can use the cdf.
+              </p>
+<p>
+              </p>
+<p>
+                
+</p>
+<pre class="programlisting"><span class="identifier">cout</span> <span class="special">&lt;&lt;</span> <span class="string">"Probability of getting 0 or 1 (&lt;= 1) heads is "</span> <span class="special">&lt;&lt;</span> <span class="identifier">cdf</span><span class="special">(</span><span class="identifier">flip</span><span class="special">,</span> <span class="number">1</span><span class="special">)</span> <span class="special">&lt;&lt;</span> <span class="identifier">endl</span><span class="special">;</span>
+<span class="identifier">cout</span> <span class="special">&lt;&lt;</span> <span class="string">"Probability of getting 9 or 10 heads is "</span> <span class="special">&lt;&lt;</span> <span class="identifier">pdf</span><span class="special">(</span><span class="identifier">flip</span><span class="special">,</span> <span class="number">9</span><span class="special">)</span> <span class="special">+</span> <span class="identifier">pdf</span><span class="special">(</span><span class="identifier">flip</span><span class="special">,</span> <span class="number">10</span><span class="special">)</span> <span class="special">&lt;&lt;</span> <span class="identifier">endl</span><span class="special">;</span></pre>
+<p>
+              </p>
+<p>
+              </p>
+<p>
+                Note that using
+              </p>
+<p>
+              </p>
+<p>
+                
+</p>
+<pre class="programlisting"><span class="identifier">cout</span> <span class="special">&lt;&lt;</span> <span class="string">"Probability of getting 9 or 10 heads is "</span> <span class="special">&lt;&lt;</span> <span class="number">1.</span> <span class="special">-</span> <span class="identifier">cdf</span><span class="special">(</span><span class="identifier">flip</span><span class="special">,</span> <span class="number">8</span><span class="special">)</span> <span class="special">&lt;&lt;</span> <span class="identifier">endl</span><span class="special">;</span></pre>
+<p>
+              </p>
+<p>
+              </p>
+<p>
+                is less accurate than using the complement
+              </p>
+<p>
+              </p>
+<p>
+                
+</p>
+<pre class="programlisting"><span class="identifier">cout</span> <span class="special">&lt;&lt;</span> <span class="string">"Probability of getting 9 or 10 heads is "</span> <span class="special">&lt;&lt;</span> <span class="identifier">cdf</span><span class="special">(</span><span class="identifier">complement</span><span class="special">(</span><span class="identifier">flip</span><span class="special">,</span> <span class="number">8</span><span class="special">))</span> <span class="special">&lt;&lt;</span> <span class="identifier">endl</span><span class="special">;</span></pre>
+<p>
+              </p>
+<p>
+              </p>
+<p>
+                Since the subtraction may involve <a href="http://docs.sun.com/source/806-3568/ncg_goldberg.html" target="_top">cancellation
+                error</a>, where as <code class="computeroutput"><span class="identifier">cdf</span><span class="special">(</span><span class="identifier">complement</span><span class="special">(</span><span class="identifier">flip</span><span class="special">,</span> <span class="number">8</span><span class="special">))</span></code> does not use such a subtraction
+                internally, and so does not exhibit the problem.
+              </p>
+<p>
+              </p>
+<p>
+                To get the probability for a range of heads, we can either add the
+                pdfs for each number of heads
+              </p>
+<p>
+              </p>
+<p>
+                
+</p>
+<pre class="programlisting"><span class="identifier">cout</span> <span class="special">&lt;&lt;</span> <span class="string">"Probability of between 4 and 6 heads (4 or 5 or 6) is "</span>
+  <span class="comment">//  P(X == 4) + P(X == 5) + P(X == 6)
+</span>  <span class="special">&lt;&lt;</span> <span class="identifier">pdf</span><span class="special">(</span><span class="identifier">flip</span><span class="special">,</span> <span class="number">4</span><span class="special">)</span> <span class="special">+</span> <span class="identifier">pdf</span><span class="special">(</span><span class="identifier">flip</span><span class="special">,</span> <span class="number">5</span><span class="special">)</span> <span class="special">+</span> <span class="identifier">pdf</span><span class="special">(</span><span class="identifier">flip</span><span class="special">,</span> <span class="number">6</span><span class="special">)</span> <span class="special">&lt;&lt;</span> <span class="identifier">endl</span><span class="special">;</span></pre>
+<p>
+              </p>
+<p>
+              </p>
+<p>
+                But this is probably less efficient than using the cdf
+              </p>
+<p>
+              </p>
+<p>
+                
+</p>
+<pre class="programlisting"><span class="identifier">cout</span> <span class="special">&lt;&lt;</span> <span class="string">"Probability of between 4 and 6 heads (4 or 5 or 6) is "</span>
+  <span class="comment">// P(X &lt;= 6) - P(X &lt;= 3) == P(X &lt; 4)
+</span>  <span class="special">&lt;&lt;</span> <span class="identifier">cdf</span><span class="special">(</span><span class="identifier">flip</span><span class="special">,</span> <span class="number">6</span><span class="special">)</span> <span class="special">-</span> <span class="identifier">cdf</span><span class="special">(</span><span class="identifier">flip</span><span class="special">,</span> <span class="number">3</span><span class="special">)</span> <span class="special">&lt;&lt;</span> <span class="identifier">endl</span><span class="special">;</span></pre>
+<p>
+              </p>
+<p>
+              </p>
+<p>
+                Certainly for a bigger range like, 3 to 7
+              </p>
+<p>
+              </p>
+<p>
+                
+</p>
+<pre class="programlisting"><span class="identifier">cout</span> <span class="special">&lt;&lt;</span> <span class="string">"Probability of between 3 and 7 heads (3, 4, 5, 6 or 7) is "</span>
+  <span class="comment">// P(X &lt;= 7) - P(X &lt;= 2) == P(X &lt; 3)
+</span>  <span class="special">&lt;&lt;</span> <span class="identifier">cdf</span><span class="special">(</span><span class="identifier">flip</span><span class="special">,</span> <span class="number">7</span><span class="special">)</span> <span class="special">-</span> <span class="identifier">cdf</span><span class="special">(</span><span class="identifier">flip</span><span class="special">,</span> <span class="number">2</span><span class="special">)</span> <span class="special">&lt;&lt;</span> <span class="identifier">endl</span><span class="special">;</span>
+<span class="identifier">cout</span> <span class="special">&lt;&lt;</span> <span class="identifier">endl</span><span class="special">;</span></pre>
+<p>
+              </p>
+<p>
+              </p>
+<p>
+                Finally, print two tables of probability for the <span class="emphasis"><em>exactly</em></span>
+                and <span class="emphasis"><em>at least</em></span> a number of heads.
+              </p>
+<p>
+              </p>
+<p>
+                
+</p>
+<pre class="programlisting"><span class="comment">// Print a table of probability for the exactly a number of heads.
+</span><span class="identifier">cout</span> <span class="special">&lt;&lt;</span> <span class="string">"Probability of getting exactly (==) heads"</span> <span class="special">&lt;&lt;</span> <span class="identifier">endl</span><span class="special">;</span>
+<span class="keyword">for</span> <span class="special">(</span><span class="keyword">int</span> <span class="identifier">successes</span> <span class="special">=</span> <span class="number">0</span><span class="special">;</span> <span class="identifier">successes</span> <span class="special">&lt;=</span> <span class="identifier">flips</span><span class="special">;</span> <span class="identifier">successes</span><span class="special">++)</span>
+<span class="special">{</span> <span class="comment">// Say success means getting a head (or equally success means getting a tail).
+</span>  <span class="keyword">double</span> <span class="identifier">probability</span> <span class="special">=</span> <span class="identifier">pdf</span><span class="special">(</span><span class="identifier">flip</span><span class="special">,</span> <span class="identifier">successes</span><span class="special">);</span>
+  <span class="identifier">cout</span> <span class="special">&lt;&lt;</span> <span class="identifier">left</span> <span class="special">&lt;&lt;</span> <span class="identifier">setw</span><span class="special">(</span><span class="number">2</span><span class="special">)</span> <span class="special">&lt;&lt;</span> <span class="identifier">successes</span> <span class="special">&lt;&lt;</span> <span class="string">"     "</span> <span class="special">&lt;&lt;</span> <span class="identifier">setw</span><span class="special">(</span><span class="number">10</span><span class="special">)</span>
+    <span class="special">&lt;&lt;</span> <span class="identifier">probability</span> <span class="special">&lt;&lt;</span> <span class="string">" or 1 in "</span> <span class="special">&lt;&lt;</span> <span class="number">1.</span> <span class="special">/</span> <span class="identifier">probability</span>
+    <span class="special">&lt;&lt;</span> <span class="string">", or "</span> <span class="special">&lt;&lt;</span> <span class="identifier">probability</span> <span class="special">*</span> <span class="number">100.</span> <span class="special">&lt;&lt;</span> <span class="string">"%"</span> <span class="special">&lt;&lt;</span> <span class="identifier">endl</span><span class="special">;</span>
+<span class="special">}</span> <span class="comment">// for i
+</span><span class="identifier">cout</span> <span class="special">&lt;&lt;</span> <span class="identifier">endl</span><span class="special">;</span>
+
+<span class="comment">// Tabulate the probability of getting between zero heads and 0 upto 10 heads.
+</span><span class="identifier">cout</span> <span class="special">&lt;&lt;</span> <span class="string">"Probability of getting upto (&lt;=) heads"</span> <span class="special">&lt;&lt;</span> <span class="identifier">endl</span><span class="special">;</span>
+<span class="keyword">for</span> <span class="special">(</span><span class="keyword">int</span> <span class="identifier">successes</span> <span class="special">=</span> <span class="number">0</span><span class="special">;</span> <span class="identifier">successes</span> <span class="special">&lt;=</span> <span class="identifier">flips</span><span class="special">;</span> <span class="identifier">successes</span><span class="special">++)</span>
+<span class="special">{</span> <span class="comment">// Say success means getting a head
+</span>  <span class="comment">// (equally success could mean getting a tail).
+</span>  <span class="keyword">double</span> <span class="identifier">probability</span> <span class="special">=</span> <span class="identifier">cdf</span><span class="special">(</span><span class="identifier">flip</span><span class="special">,</span> <span class="identifier">successes</span><span class="special">);</span> <span class="comment">// P(X &lt;= heads)
+</span>  <span class="identifier">cout</span> <span class="special">&lt;&lt;</span> <span class="identifier">setw</span><span class="special">(</span><span class="number">2</span><span class="special">)</span> <span class="special">&lt;&lt;</span> <span class="identifier">successes</span> <span class="special">&lt;&lt;</span> <span class="string">"        "</span> <span class="special">&lt;&lt;</span> <span class="identifier">setw</span><span class="special">(</span><span class="number">10</span><span class="special">)</span> <span class="special">&lt;&lt;</span> <span class="identifier">left</span>
+    <span class="special">&lt;&lt;</span> <span class="identifier">probability</span> <span class="special">&lt;&lt;</span> <span class="string">" or 1 in "</span> <span class="special">&lt;&lt;</span> <span class="number">1.</span> <span class="special">/</span> <span class="identifier">probability</span> <span class="special">&lt;&lt;</span> <span class="string">", or "</span>
+    <span class="special">&lt;&lt;</span> <span class="identifier">probability</span> <span class="special">*</span> <span class="number">100.</span> <span class="special">&lt;&lt;</span> <span class="string">"%"</span><span class="special">&lt;&lt;</span> <span class="identifier">endl</span><span class="special">;</span>
+<span class="special">}</span> <span class="comment">// for i</span></pre>
+<p>
+              </p>
+<p>
+              </p>
+<p>
+                The last (0 to 10 heads) must, of course, be 100% probability.
+              </p>
+<p>
+              </p>
+<p>
+                
+</p>
+<pre class="programlisting"><span class="special">}</span>
+<span class="keyword">catch</span><span class="special">(</span><span class="keyword">const</span> <span class="identifier">std</span><span class="special">::</span><span class="identifier">exception</span><span class="special">&amp;</span> <span class="identifier">e</span><span class="special">)</span>
+<span class="special">{</span>
+  <span class="comment">//</span></pre>
+<p>
+              </p>
+<p>
+              <a name="coinflip_eg_catch"></a>
+              </p>
+<p>
+                It is always essential to include try &amp; catch blocks because
+                default policies are to throw exceptions on arguments that are out
+                of domain or cause errors like numeric-overflow.
+              </p>
+<p>
+              </p>
+<p>
+                Lacking try &amp; catch blocks, the program will abort, whereas the
+                message below from the thrown exception will give some helpful clues
+                as to the cause of the problem.
+              </p>
+<p>
+              </p>
+<p>
+                
+</p>
+<pre class="programlisting">  <span class="identifier">std</span><span class="special">::</span><span class="identifier">cout</span> <span class="special">&lt;&lt;</span>
+    <span class="string">"\n"</span><span class="string">"Message from thrown exception was:\n   "</span> <span class="special">&lt;&lt;</span> <span class="identifier">e</span><span class="special">.</span><span class="identifier">what</span><span class="special">()</span> <span class="special">&lt;&lt;</span> <span class="identifier">std</span><span class="special">::</span><span class="identifier">endl</span><span class="special">;</span>
+<span class="special">}</span>
+</pre>
+<p>
+              </p>
+<p>
+            </p>
+<p>
+              See binomial_coinflip_example.cpp
+              for full source code, the program output looks like this:
+            </p>
+<p>
+              
+</p>
+<pre class="programlisting">Using Binomial distribution to predict how many heads and tails.
+From 10 one can expect to get on average 5 heads (or tails).
+Mode is 5
+Standard deviation is 1.581
+So about 2/3 will lie within 1 standard deviation and get between 4 and 6 correct.
+Skewness is 0
+Skewness if success_fraction is 0.5 is 0
+
+For 10 coin flips:
+Probability of getting no heads is 0.0009766
+Probability of getting at least one head is 0.999
+Probability of getting 0 or 1 heads is 0.01074
+Probability of getting 0 or 1 (&lt;= 1) heads is 0.01074
+Probability of getting 9 or 10 heads is 0.01074
+Probability of getting 9 or 10 heads is 0.01074
+Probability of getting 9 or 10 heads is 0.01074
+Probability of between 4 and 6 heads (4 or 5 or 6) is 0.6562
+Probability of between 4 and 6 heads (4 or 5 or 6) is 0.6563
+Probability of between 3 and 7 heads (3, 4, 5, 6 or 7) is 0.8906
+
+Probability of getting exactly (<code class="literal">=) heads
+0      0.0009766  or 1 in 1024, or 0.09766%
+1      0.009766   or 1 in 102.4, or 0.9766%
+2      0.04395    or 1 in 22.76, or 4.395%
+3      0.1172     or 1 in 8.533, or 11.72%
+4      0.2051     or 1 in 4.876, or 20.51%
+5      0.2461     or 1 in 4.063, or 24.61%
+6      0.2051     or 1 in 4.876, or 20.51%
+7      0.1172     or 1 in 8.533, or 11.72%
+8      0.04395    or 1 in 22.76, or 4.395%
+9      0.009766   or 1 in 102.4, or 0.9766%
+10     0.0009766  or 1 in 1024, or 0.09766%
+
+Probability of getting upto (&lt;</code>) heads
+0         0.0009766  or 1 in 1024, or 0.09766%
+1         0.01074    or 1 in 93.09, or 1.074%
+2         0.05469    or 1 in 18.29, or 5.469%
+3         0.1719     or 1 in 5.818, or 17.19%
+4         0.377      or 1 in 2.653, or 37.7%
+5         0.623      or 1 in 1.605, or 62.3%
+6         0.8281     or 1 in 1.208, or 82.81%
+7         0.9453     or 1 in 1.058, or 94.53%
+8         0.9893     or 1 in 1.011, or 98.93%
+9         0.999      or 1 in 1.001, or 99.9%
+10        1          or 1 in 1, or 100%
+</pre>
+<p>
+            </p>
+</div>
+<table xmlns:rev="http://www.cs.rpi.edu/~gregod/boost/tools/doc/revision" width="100%"><tr>
+<td align="left"></td>
+<td align="right"><div class="copyright-footer">Copyright © 2006 , 2007, 2008 John Maddock, Paul A. Bristow, Hubert
+      Holin, Xiaogang Zhang, Bruno Lalande and Gautam Sewani<p>
+        Distributed under the Boost Software License, Version 1.0. (See accompanying
+        file LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_0.txt)
+      </p>
+</div></td>
+</tr></table>
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+</div>
+<div class="section" lang="en">
+<div class="titlepage"><div><div><h6 class="title">
+<a name="math_toolkit.dist.stat_tut.weg.binom_eg.binomial_quiz_example"></a><a class="link" href="binomial_quiz_example.html" title="Binomial Quiz Example">
+            Binomial Quiz Example</a>
+</h6></div></div></div>
+<p>
+              </p>
+<p>
+                A multiple choice test has four possible answers to each of 16 questions.
+                A student guesses the answer to each question, so the probability
+                of getting a correct answer on any given question is one in four,
+                a quarter, 1/4, 25% or fraction 0.25. The conditions of the binomial
+                experiment are assumed to be met: n = 16 questions constitute the
+                trials; each question results in one of two possible outcomes (correct
+                or incorrect); the probability of being correct is 0.25 and is constant
+                if no knowledge about the subject is assumed; the questions are answered
+                independently if the student's answer to a question in no way influences
+                his/her answer to another question.
+              </p>
+<p>
+              </p>
+<p>
+                First, we need to be able to use the binomial distribution constructor
+                (and some std input/output, of course).
+              </p>
+<p>
+              </p>
+<p>
+                
+</p>
+<pre class="programlisting"><span class="preprocessor">#include</span> <span class="special">&lt;</span><span class="identifier">boost</span><span class="special">/</span><span class="identifier">math</span><span class="special">/</span><span class="identifier">distributions</span><span class="special">/</span><span class="identifier">binomial</span><span class="special">.</span><span class="identifier">hpp</span><span class="special">&gt;</span>
+  <span class="keyword">using</span> <span class="identifier">boost</span><span class="special">::</span><span class="identifier">math</span><span class="special">::</span><span class="identifier">binomial</span><span class="special">;</span>
+
+<span class="preprocessor">#include</span> <span class="special">&lt;</span><span class="identifier">iostream</span><span class="special">&gt;</span>
+  <span class="keyword">using</span> <span class="identifier">std</span><span class="special">::</span><span class="identifier">cout</span><span class="special">;</span> <span class="keyword">using</span> <span class="identifier">std</span><span class="special">::</span><span class="identifier">endl</span><span class="special">;</span>
+  <span class="keyword">using</span> <span class="identifier">std</span><span class="special">::</span><span class="identifier">ios</span><span class="special">;</span> <span class="keyword">using</span> <span class="identifier">std</span><span class="special">::</span><span class="identifier">flush</span><span class="special">;</span> <span class="keyword">using</span> <span class="identifier">std</span><span class="special">::</span><span class="identifier">left</span><span class="special">;</span> <span class="keyword">using</span> <span class="identifier">std</span><span class="special">::</span><span class="identifier">right</span><span class="special">;</span> <span class="keyword">using</span> <span class="identifier">std</span><span class="special">::</span><span class="identifier">fixed</span><span class="special">;</span>
+<span class="preprocessor">#include</span> <span class="special">&lt;</span><span class="identifier">iomanip</span><span class="special">&gt;</span>
+  <span class="keyword">using</span> <span class="identifier">std</span><span class="special">::</span><span class="identifier">setw</span><span class="special">;</span> <span class="keyword">using</span> <span class="identifier">std</span><span class="special">::</span><span class="identifier">setprecision</span><span class="special">;</span>
+</pre>
+<p>
+              </p>
+<p>
+              </p>
+<p>
+                The number of correct answers, X, is distributed as a binomial random
+                variable with binomial distribution parameters: questions n = 16
+                and success fraction probability p = 0.25. So we construct a binomial
+                distribution:
+              </p>
+<p>
+              </p>
+<p>
+                
+</p>
+<pre class="programlisting"><span class="keyword">int</span> <span class="identifier">questions</span> <span class="special">=</span> <span class="number">16</span><span class="special">;</span> <span class="comment">// All the questions in the quiz.
+</span><span class="keyword">int</span> <span class="identifier">answers</span> <span class="special">=</span> <span class="number">4</span><span class="special">;</span> <span class="comment">// Possible answers to each question.
+</span><span class="keyword">double</span> <span class="identifier">success_fraction</span> <span class="special">=</span> <span class="special">(</span><span class="keyword">double</span><span class="special">)</span><span class="identifier">answers</span> <span class="special">/</span> <span class="special">(</span><span class="keyword">double</span><span class="special">)</span><span class="identifier">questions</span><span class="special">;</span> <span class="comment">// If a random guess.
+</span><span class="comment">// Caution:  = answers / questions would be zero (because they are integers)!
+</span><span class="identifier">binomial</span> <span class="identifier">quiz</span><span class="special">(</span><span class="identifier">questions</span><span class="special">,</span> <span class="identifier">success_fraction</span><span class="special">);</span></pre>
+<p>
+              </p>
+<p>
+              </p>
+<p>
+                and display the distribution parameters we used thus:
+              </p>
+<p>
+              </p>
+<p>
+                
+</p>
+<pre class="programlisting"><span class="identifier">cout</span> <span class="special">&lt;&lt;</span> <span class="string">"In a quiz with "</span> <span class="special">&lt;&lt;</span> <span class="identifier">quiz</span><span class="special">.</span><span class="identifier">trials</span><span class="special">()</span>
+  <span class="special">&lt;&lt;</span> <span class="string">" questions and with a probability of guessing right of "</span>
+  <span class="special">&lt;&lt;</span> <span class="identifier">quiz</span><span class="special">.</span><span class="identifier">success_fraction</span><span class="special">()</span> <span class="special">*</span> <span class="number">100</span> <span class="special">&lt;&lt;</span> <span class="string">" %"</span> 
+  <span class="special">&lt;&lt;</span> <span class="string">" or 1 in "</span> <span class="special">&lt;&lt;</span> <span class="keyword">static_cast</span><span class="special">&lt;</span><span class="keyword">int</span><span class="special">&gt;(</span><span class="number">1.</span> <span class="special">/</span> <span class="identifier">quiz</span><span class="special">.</span><span class="identifier">success_fraction</span><span class="special">())</span> <span class="special">&lt;&lt;</span> <span class="identifier">endl</span><span class="special">;</span></pre>
+<p>
+              </p>
+<p>
+              </p>
+<p>
+                Show a few probabilities of just guessing:
+              </p>
+<p>
+              </p>
+<p>
+                
+</p>
+<pre class="programlisting"><span class="identifier">cout</span> <span class="special">&lt;&lt;</span> <span class="string">"Probability of getting none right is "</span> <span class="special">&lt;&lt;</span> <span class="identifier">pdf</span><span class="special">(</span><span class="identifier">quiz</span><span class="special">,</span> <span class="number">0</span><span class="special">)</span> <span class="special">&lt;&lt;</span> <span class="identifier">endl</span><span class="special">;</span> <span class="comment">// 0.010023
+</span><span class="identifier">cout</span> <span class="special">&lt;&lt;</span> <span class="string">"Probability of getting exactly one right is "</span> <span class="special">&lt;&lt;</span> <span class="identifier">pdf</span><span class="special">(</span><span class="identifier">quiz</span><span class="special">,</span> <span class="number">1</span><span class="special">)</span> <span class="special">&lt;&lt;</span> <span class="identifier">endl</span><span class="special">;</span>
+<span class="identifier">cout</span> <span class="special">&lt;&lt;</span> <span class="string">"Probability of getting exactly two right is "</span> <span class="special">&lt;&lt;</span> <span class="identifier">pdf</span><span class="special">(</span><span class="identifier">quiz</span><span class="special">,</span> <span class="number">2</span><span class="special">)</span> <span class="special">&lt;&lt;</span> <span class="identifier">endl</span><span class="special">;</span>
+<span class="keyword">int</span> <span class="identifier">pass_score</span> <span class="special">=</span> <span class="number">11</span><span class="special">;</span>
+<span class="identifier">cout</span> <span class="special">&lt;&lt;</span> <span class="string">"Probability of getting exactly "</span> <span class="special">&lt;&lt;</span> <span class="identifier">pass_score</span> <span class="special">&lt;&lt;</span> <span class="string">" answers right by chance is "</span> 
+  <span class="special">&lt;&lt;</span> <span class="identifier">pdf</span><span class="special">(</span><span class="identifier">quiz</span><span class="special">,</span> <span class="identifier">questions</span><span class="special">)</span> <span class="special">&lt;&lt;</span> <span class="identifier">endl</span><span class="special">;</span></pre>
+<p>
+              </p>
+<p>
+              
+</p>
+<pre class="programlisting">Probability of getting none right is 0.0100226
+Probability of getting exactly one right is 0.0534538
+Probability of getting exactly two right is 0.133635
+Probability of getting exactly 11 answers right by chance is 2.32831e-010
+</pre>
+<p>
+              </p>
+<p>
+                These don't give any encouragement to guessers!
+              </p>
+<p>
+              </p>
+<p>
+                We can tabulate the 'getting exactly right' ( == ) probabilities
+                thus:
+              </p>
+<p>
+              </p>
+<p>
+                
+</p>
+<pre class="programlisting"><span class="identifier">cout</span> <span class="special">&lt;&lt;</span> <span class="string">"\n"</span> <span class="string">"Guessed Probability"</span> <span class="special">&lt;&lt;</span> <span class="identifier">right</span> <span class="special">&lt;&lt;</span> <span class="identifier">endl</span><span class="special">;</span>
+<span class="keyword">for</span> <span class="special">(</span><span class="keyword">int</span> <span class="identifier">successes</span> <span class="special">=</span> <span class="number">0</span><span class="special">;</span> <span class="identifier">successes</span> <span class="special">&lt;=</span> <span class="identifier">questions</span><span class="special">;</span> <span class="identifier">successes</span><span class="special">++)</span>
+<span class="special">{</span>
+  <span class="keyword">double</span> <span class="identifier">probability</span> <span class="special">=</span> <span class="identifier">pdf</span><span class="special">(</span><span class="identifier">quiz</span><span class="special">,</span> <span class="identifier">successes</span><span class="special">);</span>
+  <span class="identifier">cout</span> <span class="special">&lt;&lt;</span> <span class="identifier">setw</span><span class="special">(</span><span class="number">2</span><span class="special">)</span> <span class="special">&lt;&lt;</span> <span class="identifier">successes</span> <span class="special">&lt;&lt;</span> <span class="string">"      "</span> <span class="special">&lt;&lt;</span> <span class="identifier">probability</span> <span class="special">&lt;&lt;</span> <span class="identifier">endl</span><span class="special">;</span>
+<span class="special">}</span>
+<span class="identifier">cout</span> <span class="special">&lt;&lt;</span> <span class="identifier">endl</span><span class="special">;</span></pre>
+<p>
+              </p>
+<p>
+              
+</p>
+<pre class="programlisting">Guessed Probability
+ 0      0.0100226
+ 1      0.0534538
+ 2      0.133635
+ 3      0.207876
+ 4      0.225199
+ 5      0.180159
+ 6      0.110097
+ 7      0.0524273
+ 8      0.0196602
+ 9      0.00582526
+10      0.00135923
+11      0.000247132
+12      3.43239e-005
+13      3.5204e-006
+14      2.51457e-007
+15      1.11759e-008
+16      2.32831e-010
+</pre>
+<p>
+              </p>
+<p>
+                Then we can add the probabilities of some 'exactly right' like this:
+              </p>
+<p>
+              </p>
+<p>
+                
+</p>
+<pre class="programlisting"><span class="identifier">cout</span> <span class="special">&lt;&lt;</span> <span class="string">"Probability of getting none or one right is "</span> <span class="special">&lt;&lt;</span> <span class="identifier">pdf</span><span class="special">(</span><span class="identifier">quiz</span><span class="special">,</span> <span class="number">0</span><span class="special">)</span> <span class="special">+</span> <span class="identifier">pdf</span><span class="special">(</span><span class="identifier">quiz</span><span class="special">,</span> <span class="number">1</span><span class="special">)</span> <span class="special">&lt;&lt;</span> <span class="identifier">endl</span><span class="special">;</span></pre>
+<p>
+              </p>
+<p>
+              
+</p>
+<pre class="programlisting">Probability of getting none or one right is 0.0634764
+</pre>
+<p>
+              </p>
+<p>
+                But if more than a couple of scores are involved, it is more convenient
+                (and may be more accurate) to use the Cumulative Distribution Function
+                (cdf) instead:
+              </p>
+<p>
+              </p>
+<p>
+                
+</p>
+<pre class="programlisting"><span class="identifier">cout</span> <span class="special">&lt;&lt;</span> <span class="string">"Probability of getting none or one right is "</span> <span class="special">&lt;&lt;</span> <span class="identifier">cdf</span><span class="special">(</span><span class="identifier">quiz</span><span class="special">,</span> <span class="number">1</span><span class="special">)</span> <span class="special">&lt;&lt;</span> <span class="identifier">endl</span><span class="special">;</span></pre>
+<p>
+              </p>
+<p>
+              
+</p>
+<pre class="programlisting">Probability of getting none or one right is 0.0634764
+</pre>
+<p>
+              </p>
+<p>
+                Since the cdf is inclusive, we can get the probability of getting
+                up to 10 right ( &lt;= )
+              </p>
+<p>
+              </p>
+<p>
+                
+</p>
+<pre class="programlisting"><span class="identifier">cout</span> <span class="special">&lt;&lt;</span> <span class="string">"Probability of getting &lt;= 10 right (to fail) is "</span> <span class="special">&lt;&lt;</span> <span class="identifier">cdf</span><span class="special">(</span><span class="identifier">quiz</span><span class="special">,</span> <span class="number">10</span><span class="special">)</span> <span class="special">&lt;&lt;</span> <span class="identifier">endl</span><span class="special">;</span></pre>
+<p>
+              </p>
+<p>
+              
+</p>
+<pre class="programlisting">Probability of getting &lt;= 10 right (to fail) is 0.999715
+</pre>
+<p>
+              </p>
+<p>
+                To get the probability of getting 11 or more right (to pass), it
+                is tempting to use 
+</p>
+<pre class="programlisting"><span class="number">1</span> <span class="special">-</span> <span class="identifier">cdf</span><span class="special">(</span><span class="identifier">quiz</span><span class="special">,</span> <span class="number">10</span><span class="special">)</span></pre>
+<p>
+                to get the probability of &gt; 10
+              </p>
+<p>
+              </p>
+<p>
+                
+</p>
+<pre class="programlisting"><span class="identifier">cout</span> <span class="special">&lt;&lt;</span> <span class="string">"Probability of getting &gt; 10 right (to pass) is "</span> <span class="special">&lt;&lt;</span> <span class="number">1</span> <span class="special">-</span> <span class="identifier">cdf</span><span class="special">(</span><span class="identifier">quiz</span><span class="special">,</span> <span class="number">10</span><span class="special">)</span> <span class="special">&lt;&lt;</span> <span class="identifier">endl</span><span class="special">;</span></pre>
+<p>
+              </p>
+<p>
+              
+</p>
+<pre class="programlisting">Probability of getting &gt; 10 right (to pass) is 0.000285239
+</pre>
+<p>
+              </p>
+<p>
+                But this should be resisted in favor of using the complement function.
+                <a class="link" href="../../overview.html#why_complements">Why complements?</a>
+              </p>
+<p>
+              </p>
+<p>
+                
+</p>
+<pre class="programlisting"><span class="identifier">cout</span> <span class="special">&lt;&lt;</span> <span class="string">"Probability of getting &gt; 10 right (to pass) is "</span> <span class="special">&lt;&lt;</span> <span class="identifier">cdf</span><span class="special">(</span><span class="identifier">complement</span><span class="special">(</span><span class="identifier">quiz</span><span class="special">,</span> <span class="number">10</span><span class="special">))</span> <span class="special">&lt;&lt;</span> <span class="identifier">endl</span><span class="special">;</span></pre>
+<p>
+              </p>
+<p>
+              
+</p>
+<pre class="programlisting">Probability of getting &gt; 10 right (to pass) is 0.000285239
+</pre>
+<p>
+              </p>
+<p>
+                And we can check that these two, &lt;= 10 and &gt; 10, add up to
+                unity.
+              </p>
+<p>
+              </p>
+<p>
+                
+</p>
+<pre class="programlisting"><span class="identifier">BOOST_ASSERT</span><span class="special">((</span><span class="identifier">cdf</span><span class="special">(</span><span class="identifier">quiz</span><span class="special">,</span> <span class="number">10</span><span class="special">)</span> <span class="special">+</span> <span class="identifier">cdf</span><span class="special">(</span><span class="identifier">complement</span><span class="special">(</span><span class="identifier">quiz</span><span class="special">,</span> <span class="number">10</span><span class="special">)))</span> <span class="special">==</span> <span class="number">1.</span><span class="special">);</span></pre>
+<p>
+              </p>
+<p>
+              </p>
+<p>
+                If we want a &lt; rather than a &lt;= test, because the CDF is inclusive,
+                we must subtract one from the score.
+              </p>
+<p>
+              </p>
+<p>
+                
+</p>
+<pre class="programlisting"><span class="identifier">cout</span> <span class="special">&lt;&lt;</span> <span class="string">"Probability of getting less than "</span> <span class="special">&lt;&lt;</span> <span class="identifier">pass_score</span>
+  <span class="special">&lt;&lt;</span> <span class="string">" (&lt; "</span> <span class="special">&lt;&lt;</span> <span class="identifier">pass_score</span> <span class="special">&lt;&lt;</span> <span class="string">") answers right by guessing is "</span>
+  <span class="special">&lt;&lt;</span> <span class="identifier">cdf</span><span class="special">(</span><span class="identifier">quiz</span><span class="special">,</span> <span class="identifier">pass_score</span> <span class="special">-</span><span class="number">1</span><span class="special">)</span> <span class="special">&lt;&lt;</span> <span class="identifier">endl</span><span class="special">;</span></pre>
+<p>
+              </p>
+<p>
+              
+</p>
+<pre class="programlisting">Probability of getting less than 11 (&lt; 11) answers right by guessing is 0.999715
+</pre>
+<p>
+              </p>
+<p>
+                and similarly to get a &gt;= rather than a &gt; test we also need
+                to subtract one from the score (and can again check the sum is unity).
+                This is because if the cdf is <span class="emphasis"><em>inclusive</em></span>, then
+                its complement must be <span class="emphasis"><em>exclusive</em></span> otherwise there
+                would be one possible outcome counted twice!
+              </p>
+<p>
+              </p>
+<p>
+                
+</p>
+<pre class="programlisting"><span class="identifier">cout</span> <span class="special">&lt;&lt;</span> <span class="string">"Probability of getting at least "</span> <span class="special">&lt;&lt;</span> <span class="identifier">pass_score</span> 
+  <span class="special">&lt;&lt;</span> <span class="string">"(&gt;= "</span> <span class="special">&lt;&lt;</span> <span class="identifier">pass_score</span> <span class="special">&lt;&lt;</span> <span class="string">") answers right by guessing is "</span>
+  <span class="special">&lt;&lt;</span> <span class="identifier">cdf</span><span class="special">(</span><span class="identifier">complement</span><span class="special">(</span><span class="identifier">quiz</span><span class="special">,</span> <span class="identifier">pass_score</span><span class="special">-</span><span class="number">1</span><span class="special">))</span>
+  <span class="special">&lt;&lt;</span> <span class="string">", only 1 in "</span> <span class="special">&lt;&lt;</span> <span class="number">1</span><span class="special">/</span><span class="identifier">cdf</span><span class="special">(</span><span class="identifier">complement</span><span class="special">(</span><span class="identifier">quiz</span><span class="special">,</span> <span class="identifier">pass_score</span><span class="special">-</span><span class="number">1</span><span class="special">))</span> <span class="special">&lt;&lt;</span> <span class="identifier">endl</span><span class="special">;</span>
+
+<span class="identifier">BOOST_ASSERT</span><span class="special">((</span><span class="identifier">cdf</span><span class="special">(</span><span class="identifier">quiz</span><span class="special">,</span> <span class="identifier">pass_score</span> <span class="special">-</span><span class="number">1</span><span class="special">)</span> <span class="special">+</span> <span class="identifier">cdf</span><span class="special">(</span><span class="identifier">complement</span><span class="special">(</span><span class="identifier">quiz</span><span class="special">,</span> <span class="identifier">pass_score</span><span class="special">-</span><span class="number">1</span><span class="special">)))</span> <span class="special">==</span> <span class="number">1</span><span class="special">);</span></pre>
+<p>
+              </p>
+<p>
+              
+</p>
+<pre class="programlisting">Probability of getting at least 11 (&gt;= 11) answers right by guessing is 0.000285239, only 1 in 3505.83
+</pre>
+<p>
+              </p>
+<p>
+                Finally we can tabulate some probabilities:
+              </p>
+<p>
+              </p>
+<p>
+                
+</p>
+<pre class="programlisting"><span class="identifier">cout</span> <span class="special">&lt;&lt;</span> <span class="string">"\n"</span> <span class="string">"At most (&lt;=)"</span><span class="string">"\n"</span><span class="string">"Guessed OK   Probability"</span> <span class="special">&lt;&lt;</span> <span class="identifier">right</span> <span class="special">&lt;&lt;</span> <span class="identifier">endl</span><span class="special">;</span>
+<span class="keyword">for</span> <span class="special">(</span><span class="keyword">int</span> <span class="identifier">score</span> <span class="special">=</span> <span class="number">0</span><span class="special">;</span> <span class="identifier">score</span> <span class="special">&lt;=</span> <span class="identifier">questions</span><span class="special">;</span> <span class="identifier">score</span><span class="special">++)</span>
+<span class="special">{</span>
+  <span class="identifier">cout</span> <span class="special">&lt;&lt;</span> <span class="identifier">setw</span><span class="special">(</span><span class="number">2</span><span class="special">)</span> <span class="special">&lt;&lt;</span> <span class="identifier">score</span> <span class="special">&lt;&lt;</span> <span class="string">"           "</span> <span class="special">&lt;&lt;</span> <span class="identifier">setprecision</span><span class="special">(</span><span class="number">10</span><span class="special">)</span>
+    <span class="special">&lt;&lt;</span> <span class="identifier">cdf</span><span class="special">(</span><span class="identifier">quiz</span><span class="special">,</span> <span class="identifier">score</span><span class="special">)</span> <span class="special">&lt;&lt;</span> <span class="identifier">endl</span><span class="special">;</span>
+<span class="special">}</span>
+<span class="identifier">cout</span> <span class="special">&lt;&lt;</span> <span class="identifier">endl</span><span class="special">;</span></pre>
+<p>
+              </p>
+<p>
+              
+</p>
+<pre class="programlisting">At most (&lt;=)
+Guessed OK   Probability
+ 0           0.01002259576
+ 1           0.0634764398
+ 2           0.1971110499
+ 3           0.4049871101
+ 4           0.6301861752
+ 5           0.8103454274
+ 6           0.9204427481
+ 7           0.9728700437
+ 8           0.9925302796
+ 9           0.9983555346
+10           0.9997147608
+11           0.9999618928
+12           0.9999962167
+13           0.9999997371
+14           0.9999999886
+15           0.9999999998
+16           1
+</pre>
+<p>
+              </p>
+<p>
+                
+</p>
+<pre class="programlisting"><span class="identifier">cout</span> <span class="special">&lt;&lt;</span> <span class="string">"\n"</span> <span class="string">"At least (&gt;)"</span><span class="string">"\n"</span><span class="string">"Guessed OK   Probability"</span> <span class="special">&lt;&lt;</span> <span class="identifier">right</span> <span class="special">&lt;&lt;</span> <span class="identifier">endl</span><span class="special">;</span>
+<span class="keyword">for</span> <span class="special">(</span><span class="keyword">int</span> <span class="identifier">score</span> <span class="special">=</span> <span class="number">0</span><span class="special">;</span> <span class="identifier">score</span> <span class="special">&lt;=</span> <span class="identifier">questions</span><span class="special">;</span> <span class="identifier">score</span><span class="special">++)</span>
+<span class="special">{</span>
+  <span class="identifier">cout</span> <span class="special">&lt;&lt;</span> <span class="identifier">setw</span><span class="special">(</span><span class="number">2</span><span class="special">)</span> <span class="special">&lt;&lt;</span> <span class="identifier">score</span> <span class="special">&lt;&lt;</span> <span class="string">"           "</span>  <span class="special">&lt;&lt;</span> <span class="identifier">setprecision</span><span class="special">(</span><span class="number">10</span><span class="special">)</span>
+    <span class="special">&lt;&lt;</span> <span class="identifier">cdf</span><span class="special">(</span><span class="identifier">complement</span><span class="special">(</span><span class="identifier">quiz</span><span class="special">,</span> <span class="identifier">score</span><span class="special">))</span> <span class="special">&lt;&lt;</span> <span class="identifier">endl</span><span class="special">;</span>
+<span class="special">}</span></pre>
+<p>
+              </p>
+<p>
+              
+</p>
+<pre class="programlisting">At least (&gt;)
+Guessed OK   Probability
+ 0           0.9899774042
+ 1           0.9365235602
+ 2           0.8028889501
+ 3           0.5950128899
+ 4           0.3698138248
+ 5           0.1896545726
+ 6           0.07955725188
+ 7           0.02712995629
+ 8           0.00746972044
+ 9           0.001644465374
+10           0.0002852391917
+11           3.810715862e-005
+12           3.783265129e-006
+13           2.628657967e-007
+14           1.140870154e-008
+15           2.328306437e-010
+16           0
+</pre>
+<p>
+              </p>
+<p>
+                We now consider the probabilities of <span class="bold"><strong>ranges</strong></span>
+                of correct guesses.
+              </p>
+<p>
+              </p>
+<p>
+                First, calculate the probability of getting a range of guesses right,
+                by adding the exact probabilities of each from low ... high.
+              </p>
+<p>
+              </p>
+<p>
+                
+</p>
+<pre class="programlisting"><span class="keyword">int</span> <span class="identifier">low</span> <span class="special">=</span> <span class="number">3</span><span class="special">;</span> <span class="comment">// Getting at least 3 right.
+</span><span class="keyword">int</span> <span class="identifier">high</span> <span class="special">=</span> <span class="number">5</span><span class="special">;</span> <span class="comment">// Getting as most 5 right.
+</span><span class="keyword">double</span> <span class="identifier">sum</span> <span class="special">=</span> <span class="number">0.</span><span class="special">;</span>
+<span class="keyword">for</span> <span class="special">(</span><span class="keyword">int</span> <span class="identifier">i</span> <span class="special">=</span> <span class="identifier">low</span><span class="special">;</span> <span class="identifier">i</span> <span class="special">&lt;=</span> <span class="identifier">high</span><span class="special">;</span> <span class="identifier">i</span><span class="special">++)</span>
+<span class="special">{</span>
+  <span class="identifier">sum</span> <span class="special">+=</span> <span class="identifier">pdf</span><span class="special">(</span><span class="identifier">quiz</span><span class="special">,</span> <span class="identifier">i</span><span class="special">);</span>
+<span class="special">}</span>
+<span class="identifier">cout</span><span class="special">.</span><span class="identifier">precision</span><span class="special">(</span><span class="number">4</span><span class="special">);</span>
+<span class="identifier">cout</span> <span class="special">&lt;&lt;</span> <span class="string">"Probability of getting between "</span>
+  <span class="special">&lt;&lt;</span> <span class="identifier">low</span> <span class="special">&lt;&lt;</span> <span class="string">" and "</span> <span class="special">&lt;&lt;</span> <span class="identifier">high</span> <span class="special">&lt;&lt;</span> <span class="string">" answers right by guessing is "</span>
+  <span class="special">&lt;&lt;</span> <span class="identifier">sum</span>  <span class="special">&lt;&lt;</span> <span class="identifier">endl</span><span class="special">;</span> <span class="comment">// 0.61323</span></pre>
+<p>
+              </p>
+<p>
+              
+</p>
+<pre class="programlisting">Probability of getting between 3 and 5 answers right by guessing is 0.6132
+</pre>
+<p>
+              </p>
+<p>
+                Or, usually better, we can use the difference of cdfs instead:
+              </p>
+<p>
+              </p>
+<p>
+                
+</p>
+<pre class="programlisting"><span class="identifier">cout</span> <span class="special">&lt;&lt;</span> <span class="string">"Probability of getting between "</span> <span class="special">&lt;&lt;</span> <span class="identifier">low</span> <span class="special">&lt;&lt;</span> <span class="string">" and "</span> <span class="special">&lt;&lt;</span> <span class="identifier">high</span> <span class="special">&lt;&lt;</span> <span class="string">" answers right by guessing is "</span>
+  <span class="special">&lt;&lt;</span>  <span class="identifier">cdf</span><span class="special">(</span><span class="identifier">quiz</span><span class="special">,</span> <span class="identifier">high</span><span class="special">)</span> <span class="special">-</span> <span class="identifier">cdf</span><span class="special">(</span><span class="identifier">quiz</span><span class="special">,</span> <span class="identifier">low</span> <span class="special">-</span> <span class="number">1</span><span class="special">)</span> <span class="special">&lt;&lt;</span> <span class="identifier">endl</span><span class="special">;</span> <span class="comment">// 0.61323</span></pre>
+<p>
+              </p>
+<p>
+              
+</p>
+<pre class="programlisting">Probability of getting between 3 and 5 answers right by guessing is 0.6132
+</pre>
+<p>
+              </p>
+<p>
+                And we can also try a few more combinations of high and low choices:
+              </p>
+<p>
+              </p>
+<p>
+                
+</p>
+<pre class="programlisting"><span class="identifier">low</span> <span class="special">=</span> <span class="number">1</span><span class="special">;</span> <span class="identifier">high</span> <span class="special">=</span> <span class="number">6</span><span class="special">;</span> 
+<span class="identifier">cout</span> <span class="special">&lt;&lt;</span> <span class="string">"Probability of getting between "</span> <span class="special">&lt;&lt;</span> <span class="identifier">low</span> <span class="special">&lt;&lt;</span> <span class="string">" and "</span> <span class="special">&lt;&lt;</span> <span class="identifier">high</span> <span class="special">&lt;&lt;</span> <span class="string">" answers right by guessing is "</span>
+  <span class="special">&lt;&lt;</span>  <span class="identifier">cdf</span><span class="special">(</span><span class="identifier">quiz</span><span class="special">,</span> <span class="identifier">high</span><span class="special">)</span> <span class="special">-</span> <span class="identifier">cdf</span><span class="special">(</span><span class="identifier">quiz</span><span class="special">,</span> <span class="identifier">low</span> <span class="special">-</span> <span class="number">1</span><span class="special">)</span> <span class="special">&lt;&lt;</span> <span class="identifier">endl</span><span class="special">;</span> <span class="comment">// 1 and 6 P= 0.91042
+</span><span class="identifier">low</span> <span class="special">=</span> <span class="number">1</span><span class="special">;</span> <span class="identifier">high</span> <span class="special">=</span> <span class="number">8</span><span class="special">;</span> 
+<span class="identifier">cout</span> <span class="special">&lt;&lt;</span> <span class="string">"Probability of getting between "</span> <span class="special">&lt;&lt;</span> <span class="identifier">low</span> <span class="special">&lt;&lt;</span> <span class="string">" and "</span> <span class="special">&lt;&lt;</span> <span class="identifier">high</span> <span class="special">&lt;&lt;</span> <span class="string">" answers right by guessing is "</span>
+  <span class="special">&lt;&lt;</span>  <span class="identifier">cdf</span><span class="special">(</span><span class="identifier">quiz</span><span class="special">,</span> <span class="identifier">high</span><span class="special">)</span> <span class="special">-</span> <span class="identifier">cdf</span><span class="special">(</span><span class="identifier">quiz</span><span class="special">,</span> <span class="identifier">low</span> <span class="special">-</span> <span class="number">1</span><span class="special">)</span> <span class="special">&lt;&lt;</span> <span class="identifier">endl</span><span class="special">;</span> <span class="comment">// 1 &lt;= x 8 P = 0.9825
+</span><span class="identifier">low</span> <span class="special">=</span> <span class="number">4</span><span class="special">;</span> <span class="identifier">high</span> <span class="special">=</span> <span class="number">4</span><span class="special">;</span> 
+<span class="identifier">cout</span> <span class="special">&lt;&lt;</span> <span class="string">"Probability of getting between "</span> <span class="special">&lt;&lt;</span> <span class="identifier">low</span> <span class="special">&lt;&lt;</span> <span class="string">" and "</span> <span class="special">&lt;&lt;</span> <span class="identifier">high</span> <span class="special">&lt;&lt;</span> <span class="string">" answers right by guessing is "</span>
+  <span class="special">&lt;&lt;</span>  <span class="identifier">cdf</span><span class="special">(</span><span class="identifier">quiz</span><span class="special">,</span> <span class="identifier">high</span><span class="special">)</span> <span class="special">-</span> <span class="identifier">cdf</span><span class="special">(</span><span class="identifier">quiz</span><span class="special">,</span> <span class="identifier">low</span> <span class="special">-</span> <span class="number">1</span><span class="special">)</span> <span class="special">&lt;&lt;</span> <span class="identifier">endl</span><span class="special">;</span> <span class="comment">// 4 &lt;= x 4 P = 0.22520</span></pre>
+<p>
+              </p>
+<p>
+              
+</p>
+<pre class="programlisting">Probability of getting between 1 and 6 answers right by guessing is 0.9104
+Probability of getting between 1 and 8 answers right by guessing is 0.9825
+Probability of getting between 4 and 4 answers right by guessing is 0.2252
+</pre>
+<p>
+              <a name="math_toolkit.dist.stat_tut.weg.binom_eg.binomial_quiz_example.using_binomial_distribution_moments"></a>
+              </p>
+<h5>
+<a name="id591585"></a>
+                <a class="link" href="binomial_quiz_example.html#math_toolkit.dist.stat_tut.weg.binom_eg.binomial_quiz_example.using_binomial_distribution_moments">Using
+                Binomial distribution moments</a>
+              </h5>
+<p>
+              </p>
+<p>
+                Using moments of the distribution, we can say more about the spread
+                of results from guessing.
+              </p>
+<p>
+              </p>
+<p>
+                
+</p>
+<pre class="programlisting"><span class="identifier">cout</span> <span class="special">&lt;&lt;</span> <span class="string">"By guessing, on average, one can expect to get "</span> <span class="special">&lt;&lt;</span> <span class="identifier">mean</span><span class="special">(</span><span class="identifier">quiz</span><span class="special">)</span> <span class="special">&lt;&lt;</span> <span class="string">" correct answers."</span> <span class="special">&lt;&lt;</span> <span class="identifier">endl</span><span class="special">;</span>
+<span class="identifier">cout</span> <span class="special">&lt;&lt;</span> <span class="string">"Standard deviation is "</span> <span class="special">&lt;&lt;</span> <span class="identifier">standard_deviation</span><span class="special">(</span><span class="identifier">quiz</span><span class="special">)</span> <span class="special">&lt;&lt;</span> <span class="identifier">endl</span><span class="special">;</span>
+<span class="identifier">cout</span> <span class="special">&lt;&lt;</span> <span class="string">"So about 2/3 will lie within 1 standard deviation and get between "</span>
+  <span class="special">&lt;&lt;</span>  <span class="identifier">ceil</span><span class="special">(</span><span class="identifier">mean</span><span class="special">(</span><span class="identifier">quiz</span><span class="special">)</span> <span class="special">-</span> <span class="identifier">standard_deviation</span><span class="special">(</span><span class="identifier">quiz</span><span class="special">))</span>  <span class="special">&lt;&lt;</span> <span class="string">" and "</span>
+  <span class="special">&lt;&lt;</span> <span class="identifier">floor</span><span class="special">(</span><span class="identifier">mean</span><span class="special">(</span><span class="identifier">quiz</span><span class="special">)</span> <span class="special">+</span> <span class="identifier">standard_deviation</span><span class="special">(</span><span class="identifier">quiz</span><span class="special">))</span> <span class="special">&lt;&lt;</span> <span class="string">" correct."</span> <span class="special">&lt;&lt;</span> <span class="identifier">endl</span><span class="special">;</span> 
+<span class="identifier">cout</span> <span class="special">&lt;&lt;</span> <span class="string">"Mode (the most frequent) is "</span> <span class="special">&lt;&lt;</span> <span class="identifier">mode</span><span class="special">(</span><span class="identifier">quiz</span><span class="special">)</span> <span class="special">&lt;&lt;</span> <span class="identifier">endl</span><span class="special">;</span>
+<span class="identifier">cout</span> <span class="special">&lt;&lt;</span> <span class="string">"Skewness is "</span> <span class="special">&lt;&lt;</span> <span class="identifier">skewness</span><span class="special">(</span><span class="identifier">quiz</span><span class="special">)</span> <span class="special">&lt;&lt;</span> <span class="identifier">endl</span><span class="special">;</span></pre>
+<p>
+              </p>
+<p>
+              
+</p>
+<pre class="programlisting">By guessing, on average, one can expect to get 4 correct answers.
+Standard deviation is 1.732
+So about 2/3 will lie within 1 standard deviation and get between 3 and 5 correct.
+Mode (the most frequent) is 4
+Skewness is 0.2887
+</pre>
+<p>
+              <a name="math_toolkit.dist.stat_tut.weg.binom_eg.binomial_quiz_example.quantiles"></a>
+              </p>
+<h5>
+<a name="id592111"></a>
+                <a class="link" href="binomial_quiz_example.html#math_toolkit.dist.stat_tut.weg.binom_eg.binomial_quiz_example.quantiles">Quantiles</a>
+              </h5>
+<p>
+              </p>
+<p>
+                The quantiles (percentiles or percentage points) for a few probability
+                levels:
+              </p>
+<p>
+              </p>
+<p>
+                
+</p>
+<pre class="programlisting"><span class="identifier">cout</span> <span class="special">&lt;&lt;</span> <span class="string">"Quartiles "</span> <span class="special">&lt;&lt;</span> <span class="identifier">quantile</span><span class="special">(</span><span class="identifier">quiz</span><span class="special">,</span> <span class="number">0.25</span><span class="special">)</span> <span class="special">&lt;&lt;</span> <span class="string">" to "</span>
+  <span class="special">&lt;&lt;</span> <span class="identifier">quantile</span><span class="special">(</span><span class="identifier">complement</span><span class="special">(</span><span class="identifier">quiz</span><span class="special">,</span> <span class="number">0.25</span><span class="special">))</span> <span class="special">&lt;&lt;</span> <span class="identifier">endl</span><span class="special">;</span> <span class="comment">// Quartiles 
+</span><span class="identifier">cout</span> <span class="special">&lt;&lt;</span> <span class="string">"1 standard deviation "</span> <span class="special">&lt;&lt;</span> <span class="identifier">quantile</span><span class="special">(</span><span class="identifier">quiz</span><span class="special">,</span> <span class="number">0.33</span><span class="special">)</span> <span class="special">&lt;&lt;</span> <span class="string">" to "</span> 
+  <span class="special">&lt;&lt;</span> <span class="identifier">quantile</span><span class="special">(</span><span class="identifier">quiz</span><span class="special">,</span> <span class="number">0.67</span><span class="special">)</span> <span class="special">&lt;&lt;</span> <span class="identifier">endl</span><span class="special">;</span> <span class="comment">// 1 sd 
+</span><span class="identifier">cout</span> <span class="special">&lt;&lt;</span> <span class="string">"Deciles "</span> <span class="special">&lt;&lt;</span> <span class="identifier">quantile</span><span class="special">(</span><span class="identifier">quiz</span><span class="special">,</span> <span class="number">0.1</span><span class="special">)</span>  <span class="special">&lt;&lt;</span> <span class="string">" to "</span>
+  <span class="special">&lt;&lt;</span> <span class="identifier">quantile</span><span class="special">(</span><span class="identifier">complement</span><span class="special">(</span><span class="identifier">quiz</span><span class="special">,</span> <span class="number">0.1</span><span class="special">))&lt;&lt;</span> <span class="identifier">endl</span><span class="special">;</span> <span class="comment">// Deciles 
+</span><span class="identifier">cout</span> <span class="special">&lt;&lt;</span> <span class="string">"5 to 95% "</span> <span class="special">&lt;&lt;</span> <span class="identifier">quantile</span><span class="special">(</span><span class="identifier">quiz</span><span class="special">,</span> <span class="number">0.05</span><span class="special">)</span>  <span class="special">&lt;&lt;</span> <span class="string">" to "</span>
+  <span class="special">&lt;&lt;</span> <span class="identifier">quantile</span><span class="special">(</span><span class="identifier">complement</span><span class="special">(</span><span class="identifier">quiz</span><span class="special">,</span> <span class="number">0.05</span><span class="special">))&lt;&lt;</span> <span class="identifier">endl</span><span class="special">;</span> <span class="comment">// 5 to 95%
+</span><span class="identifier">cout</span> <span class="special">&lt;&lt;</span> <span class="string">"2.5 to 97.5% "</span> <span class="special">&lt;&lt;</span> <span class="identifier">quantile</span><span class="special">(</span><span class="identifier">quiz</span><span class="special">,</span> <span class="number">0.025</span><span class="special">)</span> <span class="special">&lt;&lt;</span> <span class="string">" to "</span>
+  <span class="special">&lt;&lt;</span>  <span class="identifier">quantile</span><span class="special">(</span><span class="identifier">complement</span><span class="special">(</span><span class="identifier">quiz</span><span class="special">,</span> <span class="number">0.025</span><span class="special">))</span> <span class="special">&lt;&lt;</span> <span class="identifier">endl</span><span class="special">;</span> <span class="comment">// 2.5 to 97.5% 
+</span><span class="identifier">cout</span> <span class="special">&lt;&lt;</span> <span class="string">"2 to 98% "</span> <span class="special">&lt;&lt;</span> <span class="identifier">quantile</span><span class="special">(</span><span class="identifier">quiz</span><span class="special">,</span> <span class="number">0.02</span><span class="special">)</span>  <span class="special">&lt;&lt;</span> <span class="string">" to "</span>
+  <span class="special">&lt;&lt;</span> <span class="identifier">quantile</span><span class="special">(</span><span class="identifier">complement</span><span class="special">(</span><span class="identifier">quiz</span><span class="special">,</span> <span class="number">0.02</span><span class="special">))</span> <span class="special">&lt;&lt;</span> <span class="identifier">endl</span><span class="special">;</span> <span class="comment">//  2 to 98%
+</span>
+<span class="identifier">cout</span> <span class="special">&lt;&lt;</span> <span class="string">"If guessing then percentiles 1 to 99% will get "</span> <span class="special">&lt;&lt;</span> <span class="identifier">quantile</span><span class="special">(</span><span class="identifier">quiz</span><span class="special">,</span> <span class="number">0.01</span><span class="special">)</span> 
+  <span class="special">&lt;&lt;</span> <span class="string">" to "</span> <span class="special">&lt;&lt;</span> <span class="identifier">quantile</span><span class="special">(</span><span class="identifier">complement</span><span class="special">(</span><span class="identifier">quiz</span><span class="special">,</span> <span class="number">0.01</span><span class="special">))</span> <span class="special">&lt;&lt;</span> <span class="string">" right."</span> <span class="special">&lt;&lt;</span> <span class="identifier">endl</span><span class="special">;</span></pre>
+<p>
+              </p>
+<p>
+              </p>
+<p>
+                Notice that these output integral values because the default policy
+                is <code class="computeroutput"><span class="identifier">integer_round_outwards</span></code>.
+              </p>
+<p>
+              
+</p>
+<pre class="programlisting">Quartiles 2 to 5
+1 standard deviation 2 to 5
+Deciles 1 to 6
+5 to 95% 0 to 7
+2.5 to 97.5% 0 to 8
+2 to 98% 0 to 8
+</pre>
+<p>
+              </p>
+<p>
+                Quantiles values are controlled by the <a class="link" href="../../../../policy/pol_ref/discrete_quant_ref.html" title="Discrete Quantile Policies">discrete
+                quantile policy</a> chosen. The default is <code class="computeroutput"><span class="identifier">integer_round_outwards</span></code>,
+                so the lower quantile is rounded down, and the upper quantile is
+                rounded up.
+              </p>
+<p>
+              </p>
+<p>
+                But we might believe that the real values tell us a little more -
+                see <a class="link" href="../../../../policy/pol_tutorial/understand_dis_quant.html" title="Understanding Quantiles of Discrete Distributions">Understanding
+                Discrete Quantile Policy</a>.
+              </p>
+<p>
+              </p>
+<p>
+                We could control the policy for <span class="bold"><strong>all</strong></span>
+                distributions by
+              </p>
+<p>
+              
+</p>
+<pre class="programlisting"><span class="preprocessor">#define</span> <span class="identifier">BOOST_MATH_DISCRETE_QUANTILE_POLICY</span> <span class="identifier">real</span>
+
+<span class="identifier">at</span> <span class="identifier">the</span> <span class="identifier">head</span> <span class="identifier">of</span> <span class="identifier">the</span> <span class="identifier">program</span> <span class="identifier">would</span> <span class="identifier">make</span> <span class="keyword">this</span> <span class="identifier">policy</span> <span class="identifier">apply</span>
+</pre>
+<p>
+              </p>
+<p>
+                #define BOOST_MATH_DISCRETE_QUANTILE_POLICY real
+              </p>
+<p>
+              
+</p>
+<pre class="programlisting"><span class="identifier">at</span> <span class="identifier">the</span> <span class="identifier">head</span> <span class="identifier">of</span> <span class="identifier">the</span> <span class="identifier">program</span> <span class="identifier">would</span> <span class="identifier">make</span> <span class="keyword">this</span> <span class="identifier">policy</span> <span class="identifier">apply</span>
+</pre>
+<p>
+              </p>
+<p>
+                at the head of the program would make this policy apply to this
+                <span class="bold"><strong>one, and only</strong></span>, translation unit.
+              </p>
+<p>
+              </p>
+<p>
+                Or we can now create a (typedef for) policy that has discrete quantiles
+                real (here avoiding any 'using namespaces ...' statements):
+              </p>
+<p>
+              </p>
+<p>
+                
+</p>
+<pre class="programlisting"><span class="keyword">using</span> <span class="identifier">boost</span><span class="special">::</span><span class="identifier">math</span><span class="special">::</span><span class="identifier">policies</span><span class="special">::</span><span class="identifier">policy</span><span class="special">;</span>
+<span class="keyword">using</span> <span class="identifier">boost</span><span class="special">::</span><span class="identifier">math</span><span class="special">::</span><span class="identifier">policies</span><span class="special">::</span><span class="identifier">discrete_quantile</span><span class="special">;</span>
+<span class="keyword">using</span> <span class="identifier">boost</span><span class="special">::</span><span class="identifier">math</span><span class="special">::</span><span class="identifier">policies</span><span class="special">::</span><span class="identifier">real</span><span class="special">;</span>
+<span class="keyword">using</span> <span class="identifier">boost</span><span class="special">::</span><span class="identifier">math</span><span class="special">::</span><span class="identifier">policies</span><span class="special">::</span><span class="identifier">integer_round_outwards</span><span class="special">;</span> <span class="comment">// Default.
+</span><span class="keyword">typedef</span> <span class="identifier">boost</span><span class="special">::</span><span class="identifier">math</span><span class="special">::</span><span class="identifier">policies</span><span class="special">::</span><span class="identifier">policy</span><span class="special">&lt;</span><span class="identifier">discrete_quantile</span><span class="special">&lt;</span><span class="identifier">real</span><span class="special">&gt;</span> <span class="special">&gt;</span> <span class="identifier">real_quantile_policy</span><span class="special">;</span></pre>
+<p>
+              </p>
+<p>
+              </p>
+<p>
+                Add a custom binomial distribution called 
+</p>
+<pre class="programlisting"><span class="identifier">real_quantile_binomial</span></pre>
+<p>
+                that uses 
+</p>
+<pre class="programlisting"><span class="identifier">real_quantile_policy</span></pre>
+<p>
+              </p>
+<p>
+              </p>
+<p>
+                
+</p>
+<pre class="programlisting"><span class="keyword">using</span> <span class="identifier">boost</span><span class="special">::</span><span class="identifier">math</span><span class="special">::</span><span class="identifier">binomial_distribution</span><span class="special">;</span>
+<span class="keyword">typedef</span> <span class="identifier">binomial_distribution</span><span class="special">&lt;</span><span class="keyword">double</span><span class="special">,</span> <span class="identifier">real_quantile_policy</span><span class="special">&gt;</span> <span class="identifier">real_quantile_binomial</span><span class="special">;</span></pre>
+<p>
+              </p>
+<p>
+              </p>
+<p>
+                Construct an object of this custom distribution:
+              </p>
+<p>
+              </p>
+<p>
+                
+</p>
+<pre class="programlisting"><span class="identifier">real_quantile_binomial</span> <span class="identifier">quiz_real</span><span class="special">(</span><span class="identifier">questions</span><span class="special">,</span> <span class="identifier">success_fraction</span><span class="special">);</span></pre>
+<p>
+              </p>
+<p>
+              </p>
+<p>
+                And use this to show some quantiles - that now have real rather than
+                integer values.
+              </p>
+<p>
+              </p>
+<p>
+                
+</p>
+<pre class="programlisting"><span class="identifier">cout</span> <span class="special">&lt;&lt;</span> <span class="string">"Quartiles "</span> <span class="special">&lt;&lt;</span> <span class="identifier">quantile</span><span class="special">(</span><span class="identifier">quiz</span><span class="special">,</span> <span class="number">0.25</span><span class="special">)</span> <span class="special">&lt;&lt;</span> <span class="string">" to "</span>
+  <span class="special">&lt;&lt;</span> <span class="identifier">quantile</span><span class="special">(</span><span class="identifier">complement</span><span class="special">(</span><span class="identifier">quiz_real</span><span class="special">,</span> <span class="number">0.25</span><span class="special">))</span> <span class="special">&lt;&lt;</span> <span class="identifier">endl</span><span class="special">;</span> <span class="comment">// Quartiles 2 to 4.6212
+</span><span class="identifier">cout</span> <span class="special">&lt;&lt;</span> <span class="string">"1 standard deviation "</span> <span class="special">&lt;&lt;</span> <span class="identifier">quantile</span><span class="special">(</span><span class="identifier">quiz_real</span><span class="special">,</span> <span class="number">0.33</span><span class="special">)</span> <span class="special">&lt;&lt;</span> <span class="string">" to "</span> 
+  <span class="special">&lt;&lt;</span> <span class="identifier">quantile</span><span class="special">(</span><span class="identifier">quiz_real</span><span class="special">,</span> <span class="number">0.67</span><span class="special">)</span> <span class="special">&lt;&lt;</span> <span class="identifier">endl</span><span class="special">;</span> <span class="comment">// 1 sd 2.6654 4.194
+</span><span class="identifier">cout</span> <span class="special">&lt;&lt;</span> <span class="string">"Deciles "</span> <span class="special">&lt;&lt;</span> <span class="identifier">quantile</span><span class="special">(</span><span class="identifier">quiz_real</span><span class="special">,</span> <span class="number">0.1</span><span class="special">)</span>  <span class="special">&lt;&lt;</span> <span class="string">" to "</span>
+  <span class="special">&lt;&lt;</span> <span class="identifier">quantile</span><span class="special">(</span><span class="identifier">complement</span><span class="special">(</span><span class="identifier">quiz_real</span><span class="special">,</span> <span class="number">0.1</span><span class="special">))&lt;&lt;</span> <span class="identifier">endl</span><span class="special">;</span> <span class="comment">// Deciles 1.3487 5.7583
+</span><span class="identifier">cout</span> <span class="special">&lt;&lt;</span> <span class="string">"5 to 95% "</span> <span class="special">&lt;&lt;</span> <span class="identifier">quantile</span><span class="special">(</span><span class="identifier">quiz_real</span><span class="special">,</span> <span class="number">0.05</span><span class="special">)</span>  <span class="special">&lt;&lt;</span> <span class="string">" to "</span>
+  <span class="special">&lt;&lt;</span> <span class="identifier">quantile</span><span class="special">(</span><span class="identifier">complement</span><span class="special">(</span><span class="identifier">quiz_real</span><span class="special">,</span> <span class="number">0.05</span><span class="special">))&lt;&lt;</span> <span class="identifier">endl</span><span class="special">;</span> <span class="comment">// 5 to 95% 0.83739 6.4559
+</span><span class="identifier">cout</span> <span class="special">&lt;&lt;</span> <span class="string">"2.5 to 97.5% "</span> <span class="special">&lt;&lt;</span> <span class="identifier">quantile</span><span class="special">(</span><span class="identifier">quiz_real</span><span class="special">,</span> <span class="number">0.025</span><span class="special">)</span> <span class="special">&lt;&lt;</span> <span class="string">" to "</span>
+  <span class="special">&lt;&lt;</span>  <span class="identifier">quantile</span><span class="special">(</span><span class="identifier">complement</span><span class="special">(</span><span class="identifier">quiz_real</span><span class="special">,</span> <span class="number">0.025</span><span class="special">))</span> <span class="special">&lt;&lt;</span> <span class="identifier">endl</span><span class="special">;</span> <span class="comment">// 2.5 to 97.5% 0.42806 7.0688
+</span><span class="identifier">cout</span> <span class="special">&lt;&lt;</span> <span class="string">"2 to 98% "</span> <span class="special">&lt;&lt;</span> <span class="identifier">quantile</span><span class="special">(</span><span class="identifier">quiz_real</span><span class="special">,</span> <span class="number">0.02</span><span class="special">)</span>  <span class="special">&lt;&lt;</span> <span class="string">" to "</span>
+  <span class="special">&lt;&lt;</span> <span class="identifier">quantile</span><span class="special">(</span><span class="identifier">complement</span><span class="special">(</span><span class="identifier">quiz_real</span><span class="special">,</span> <span class="number">0.02</span><span class="special">))</span> <span class="special">&lt;&lt;</span> <span class="identifier">endl</span><span class="special">;</span> <span class="comment">//  2 to 98% 0.31311 7.7880
+</span>
+<span class="identifier">cout</span> <span class="special">&lt;&lt;</span> <span class="string">"If guessing, then percentiles 1 to 99% will get "</span> <span class="special">&lt;&lt;</span> <span class="identifier">quantile</span><span class="special">(</span><span class="identifier">quiz_real</span><span class="special">,</span> <span class="number">0.01</span><span class="special">)</span> 
+  <span class="special">&lt;&lt;</span> <span class="string">" to "</span> <span class="special">&lt;&lt;</span> <span class="identifier">quantile</span><span class="special">(</span><span class="identifier">complement</span><span class="special">(</span><span class="identifier">quiz_real</span><span class="special">,</span> <span class="number">0.01</span><span class="special">))</span> <span class="special">&lt;&lt;</span> <span class="string">" right."</span> <span class="special">&lt;&lt;</span> <span class="identifier">endl</span><span class="special">;</span></pre>
+<p>
+              </p>
+<p>
+              
+</p>
+<pre class="programlisting">Real Quantiles
+Quartiles 2 to 4.621
+1 standard deviation 2.665 to 4.194
+Deciles 1.349 to 5.758
+5 to 95% 0.8374 to 6.456
+2.5 to 97.5% 0.4281 to 7.069
+2 to 98% 0.3131 to 7.252
+If guessing then percentiles 1 to 99% will get 0 to 7.788 right.
+</pre>
+<p>
+            </p>
+<p>
+              See binomial_quiz_example.cpp
+              for full source code and output.
+            </p>
+</div>
+<table xmlns:rev="http://www.cs.rpi.edu/~gregod/boost/tools/doc/revision" width="100%"><tr>
+<td align="left"></td>
+<td align="right"><div class="copyright-footer">Copyright © 2006 , 2007, 2008 John Maddock, Paul A. Bristow, Hubert
+      Holin, Xiaogang Zhang, Bruno Lalande and Gautam Sewani<p>
+        Distributed under the Boost Software License, Version 1.0. (See accompanying
+        file LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_0.txt)
+      </p>
+</div></td>
+</tr></table>
+<hr>
+<div class="spirit-nav">
+<a accesskey="p" href="binomial_coinflip_example.html"><img src="../../../../../../../doc/html/images/prev.png" alt="Prev"></a><a accesskey="u" href="../binom_eg.html"><img src="../../../../../../../doc/html/images/up.png" alt="Up"></a><a accesskey="h" href="../../../../../index.html"><img src="../../../../../../../doc/html/images/home.png" alt="Home"></a><a accesskey="n" href="binom_conf.html"><img src="../../../../../../../doc/html/images/next.png" alt="Next"></a>
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+</div>
+<div class="section" lang="en">
+<div class="titlepage"><div><div><h5 class="title">
+<a name="math_toolkit.dist.stat_tut.weg.cs_eg"></a><a class="link" href="cs_eg.html" title="Chi Squared Distribution Examples"> Chi Squared
+          Distribution Examples</a>
+</h5></div></div></div>
+<div class="toc"><dl>
+<dt><span class="section"><a href="cs_eg/chi_sq_intervals.html">
+            Confidence Intervals on the Standard Deviation</a></span></dt>
+<dt><span class="section"><a href="cs_eg/chi_sq_test.html">
+            Chi-Square Test for the Standard Deviation</a></span></dt>
+<dt><span class="section"><a href="cs_eg/chi_sq_size.html">
+            Estimating the Required Sample Sizes for a Chi-Square Test for the Standard
+            Deviation</a></span></dt>
+</dl></div>
+</div>
+<table xmlns:rev="http://www.cs.rpi.edu/~gregod/boost/tools/doc/revision" width="100%"><tr>
+<td align="left"></td>
+<td align="right"><div class="copyright-footer">Copyright © 2006 , 2007, 2008 John Maddock, Paul A. Bristow, Hubert
+      Holin, Xiaogang Zhang, Bruno Lalande and Gautam Sewani<p>
+        Distributed under the Boost Software License, Version 1.0. (See accompanying
+        file LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_0.txt)
+      </p>
+</div></td>
+</tr></table>
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@@ -0,0 +1,235 @@
+<html>
+<head>
+<meta http-equiv="Content-Type" content="text/html; charset=ISO-8859-1">
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+<link rel="stylesheet" href="../../../../../boostbook.css" type="text/css">
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+</div>
+<div class="section" lang="en">
+<div class="titlepage"><div><div><h6 class="title">
+<a name="math_toolkit.dist.stat_tut.weg.cs_eg.chi_sq_intervals"></a><a class="link" href="chi_sq_intervals.html" title="Confidence Intervals on the Standard Deviation">
+            Confidence Intervals on the Standard Deviation</a>
+</h6></div></div></div>
+<p>
+              Once you have calculated the standard deviation for your data, a legitimate
+              question to ask is "How reliable is the calculated standard deviation?".
+              For this situation the Chi Squared distribution can be used to calculate
+              confidence intervals for the standard deviation.
+            </p>
+<p>
+              The full example code &amp; sample output is in chi_square_std_deviation_test.cpp.
+            </p>
+<p>
+              We'll begin by defining the procedure that will calculate and print
+              out the confidence intervals:
+            </p>
+<pre class="programlisting"><span class="keyword">void</span> <span class="identifier">confidence_limits_on_std_deviation</span><span class="special">(</span>
+     <span class="keyword">double</span> <span class="identifier">Sd</span><span class="special">,</span>    <span class="comment">// Sample Standard Deviation
+</span>     <span class="keyword">unsigned</span> <span class="identifier">N</span><span class="special">)</span>   <span class="comment">// Sample size
+</span><span class="special">{</span>
+</pre>
+<p>
+              We'll begin by printing out some general information:
+            </p>
+<pre class="programlisting"><span class="identifier">cout</span> <span class="special">&lt;&lt;</span>
+   <span class="string">"________________________________________________\n"</span>
+   <span class="string">"2-Sided Confidence Limits For Standard Deviation\n"</span>
+   <span class="string">"________________________________________________\n\n"</span><span class="special">;</span>
+<span class="identifier">cout</span> <span class="special">&lt;&lt;</span> <span class="identifier">setprecision</span><span class="special">(</span><span class="number">7</span><span class="special">);</span>
+<span class="identifier">cout</span> <span class="special">&lt;&lt;</span> <span class="identifier">setw</span><span class="special">(</span><span class="number">40</span><span class="special">)</span> <span class="special">&lt;&lt;</span> <span class="identifier">left</span> <span class="special">&lt;&lt;</span> <span class="string">"Number of Observations"</span> <span class="special">&lt;&lt;</span> <span class="string">"=  "</span> <span class="special">&lt;&lt;</span> <span class="identifier">N</span> <span class="special">&lt;&lt;</span> <span class="string">"\n"</span><span class="special">;</span>
+<span class="identifier">cout</span> <span class="special">&lt;&lt;</span> <span class="identifier">setw</span><span class="special">(</span><span class="number">40</span><span class="special">)</span> <span class="special">&lt;&lt;</span> <span class="identifier">left</span> <span class="special">&lt;&lt;</span> <span class="string">"Standard Deviation"</span> <span class="special">&lt;&lt;</span> <span class="string">"=  "</span> <span class="special">&lt;&lt;</span> <span class="identifier">Sd</span> <span class="special">&lt;&lt;</span> <span class="string">"\n"</span><span class="special">;</span>
+</pre>
+<p>
+              and then define a table of significance levels for which we'll calculate
+              intervals:
+            </p>
+<pre class="programlisting"><span class="keyword">double</span> <span class="identifier">alpha</span><span class="special">[]</span> <span class="special">=</span> <span class="special">{</span> <span class="number">0.5</span><span class="special">,</span> <span class="number">0.25</span><span class="special">,</span> <span class="number">0.1</span><span class="special">,</span> <span class="number">0.05</span><span class="special">,</span> <span class="number">0.01</span><span class="special">,</span> <span class="number">0.001</span><span class="special">,</span> <span class="number">0.0001</span><span class="special">,</span> <span class="number">0.00001</span> <span class="special">};</span>
+</pre>
+<p>
+              The distribution we'll need to calculate the confidence intervals is
+              a Chi Squared distribution, with N-1 degrees of freedom:
+            </p>
+<pre class="programlisting"><span class="identifier">chi_squared</span> <span class="identifier">dist</span><span class="special">(</span><span class="identifier">N</span> <span class="special">-</span> <span class="number">1</span><span class="special">);</span>
+</pre>
+<p>
+              For each value of alpha, the formula for the confidence interval is
+              given by:
+            </p>
+<p>
+              <span class="inlinemediaobject"><img src="../../../../../../equations/chi_squ_tut1.png"></span>
+            </p>
+<p>
+              Where <span class="inlinemediaobject"><img src="../../../../../../equations/chi_squ_tut2.png"></span> is the upper critical value, and <span class="inlinemediaobject"><img src="../../../../../../equations/chi_squ_tut3.png"></span> is
+              the lower critical value of the Chi Squared distribution.
+            </p>
+<p>
+              In code we begin by printing out a table header:
+            </p>
+<pre class="programlisting"><span class="identifier">cout</span> <span class="special">&lt;&lt;</span> <span class="string">"\n\n"</span>
+        <span class="string">"_____________________________________________\n"</span>
+        <span class="string">"Confidence          Lower          Upper\n"</span>
+        <span class="string">" Value (%)          Limit          Limit\n"</span>
+        <span class="string">"_____________________________________________\n"</span><span class="special">;</span>
+</pre>
+<p>
+              and then loop over the values of alpha and calculate the intervals
+              for each: remember that the lower critical value is the same as the
+              quantile, and the upper critical value is the same as the quantile
+              from the complement of the probability:
+            </p>
+<pre class="programlisting"><span class="keyword">for</span><span class="special">(</span><span class="keyword">unsigned</span> <span class="identifier">i</span> <span class="special">=</span> <span class="number">0</span><span class="special">;</span> <span class="identifier">i</span> <span class="special">&lt;</span> <span class="keyword">sizeof</span><span class="special">(</span><span class="identifier">alpha</span><span class="special">)/</span><span class="keyword">sizeof</span><span class="special">(</span><span class="identifier">alpha</span><span class="special">[</span><span class="number">0</span><span class="special">]);</span> <span class="special">++</span><span class="identifier">i</span><span class="special">)</span>
+<span class="special">{</span>
+   <span class="comment">// Confidence value:
+</span>   <span class="identifier">cout</span> <span class="special">&lt;&lt;</span> <span class="identifier">fixed</span> <span class="special">&lt;&lt;</span> <span class="identifier">setprecision</span><span class="special">(</span><span class="number">3</span><span class="special">)</span> <span class="special">&lt;&lt;</span> <span class="identifier">setw</span><span class="special">(</span><span class="number">10</span><span class="special">)</span> <span class="special">&lt;&lt;</span> <span class="identifier">right</span> <span class="special">&lt;&lt;</span> <span class="number">100</span> <span class="special">*</span> <span class="special">(</span><span class="number">1</span><span class="special">-</span><span class="identifier">alpha</span><span class="special">[</span><span class="identifier">i</span><span class="special">]);</span>
+   <span class="comment">// Calculate limits:
+</span>   <span class="keyword">double</span> <span class="identifier">lower_limit</span> <span class="special">=</span> <span class="identifier">sqrt</span><span class="special">((</span><span class="identifier">N</span> <span class="special">-</span> <span class="number">1</span><span class="special">)</span> <span class="special">*</span> <span class="identifier">Sd</span> <span class="special">*</span> <span class="identifier">Sd</span> <span class="special">/</span> <span class="identifier">quantile</span><span class="special">(</span><span class="identifier">complement</span><span class="special">(</span><span class="identifier">dist</span><span class="special">,</span> <span class="identifier">alpha</span><span class="special">[</span><span class="identifier">i</span><span class="special">]</span> <span class="special">/</span> <span class="number">2</span><span class="special">)));</span>
+   <span class="keyword">double</span> <span class="identifier">upper_limit</span> <span class="special">=</span> <span class="identifier">sqrt</span><span class="special">((</span><span class="identifier">N</span> <span class="special">-</span> <span class="number">1</span><span class="special">)</span> <span class="special">*</span> <span class="identifier">Sd</span> <span class="special">*</span> <span class="identifier">Sd</span> <span class="special">/</span> <span class="identifier">quantile</span><span class="special">(</span><span class="identifier">dist</span><span class="special">,</span> <span class="identifier">alpha</span><span class="special">[</span><span class="identifier">i</span><span class="special">]</span> <span class="special">/</span> <span class="number">2</span><span class="special">));</span>
+   <span class="comment">// Print Limits:
+</span>   <span class="identifier">cout</span> <span class="special">&lt;&lt;</span> <span class="identifier">fixed</span> <span class="special">&lt;&lt;</span> <span class="identifier">setprecision</span><span class="special">(</span><span class="number">5</span><span class="special">)</span> <span class="special">&lt;&lt;</span> <span class="identifier">setw</span><span class="special">(</span><span class="number">15</span><span class="special">)</span> <span class="special">&lt;&lt;</span> <span class="identifier">right</span> <span class="special">&lt;&lt;</span> <span class="identifier">lower_limit</span><span class="special">;</span>
+   <span class="identifier">cout</span> <span class="special">&lt;&lt;</span> <span class="identifier">fixed</span> <span class="special">&lt;&lt;</span> <span class="identifier">setprecision</span><span class="special">(</span><span class="number">5</span><span class="special">)</span> <span class="special">&lt;&lt;</span> <span class="identifier">setw</span><span class="special">(</span><span class="number">15</span><span class="special">)</span> <span class="special">&lt;&lt;</span> <span class="identifier">right</span> <span class="special">&lt;&lt;</span> <span class="identifier">upper_limit</span> <span class="special">&lt;&lt;</span> <span class="identifier">endl</span><span class="special">;</span>
+<span class="special">}</span>
+<span class="identifier">cout</span> <span class="special">&lt;&lt;</span> <span class="identifier">endl</span><span class="special">;</span>
+</pre>
+<p>
+              To see some example output we'll use the <a href="http://www.itl.nist.gov/div898/handbook/eda/section3/eda3581.htm" target="_top">gear
+              data</a> from the <a href="http://www.itl.nist.gov/div898/handbook/" target="_top">NIST/SEMATECH
+              e-Handbook of Statistical Methods.</a>. The data represents measurements
+              of gear diameter from a manufacturing process.
+            </p>
+<pre class="programlisting">________________________________________________
+2-Sided Confidence Limits For Standard Deviation
+________________________________________________
+
+Number of Observations                  =  100
+Standard Deviation                      =  0.006278908
+
+
+_____________________________________________
+Confidence          Lower          Upper
+ Value (%)          Limit          Limit
+_____________________________________________
+    50.000        0.00601        0.00662
+    75.000        0.00582        0.00685
+    90.000        0.00563        0.00712
+    95.000        0.00551        0.00729
+    99.000        0.00530        0.00766
+    99.900        0.00507        0.00812
+    99.990        0.00489        0.00855
+    99.999        0.00474        0.00895
+</pre>
+<p>
+              So at the 95% confidence level we conclude that the standard deviation
+              is between 0.00551 and 0.00729.
+            </p>
+<a name="math_toolkit.dist.stat_tut.weg.cs_eg.chi_sq_intervals.confidence_intervals_as_a_function_of_the_number_of_observations"></a><h5>
+<a name="id574898"></a>
+              <a class="link" href="chi_sq_intervals.html#math_toolkit.dist.stat_tut.weg.cs_eg.chi_sq_intervals.confidence_intervals_as_a_function_of_the_number_of_observations">Confidence
+              intervals as a function of the number of observations</a>
+            </h5>
+<p>
+              Similarly, we can also list the confidence intervals for the standard
+              deviation for the common confidence levels 95%, for increasing numbers
+              of observations.
+            </p>
+<p>
+              The standard deviation used to compute these values is unity, so the
+              limits listed are <span class="bold"><strong>multipliers</strong></span> for
+              any particular standard deviation. For example, given a standard deviation
+              of 0.0062789 as in the example above; for 100 observations the multiplier
+              is 0.8780 giving the lower confidence limit of 0.8780 * 0.006728 =
+              0.00551.
+            </p>
+<pre class="programlisting">____________________________________________________
+Confidence level (two-sided)            =  0.0500000
+Standard Deviation                      =  1.0000000
+________________________________________
+Observations        Lower          Upper
+                    Limit          Limit
+________________________________________
+         2         0.4461        31.9102
+         3         0.5207         6.2847
+         4         0.5665         3.7285
+         5         0.5991         2.8736
+         6         0.6242         2.4526
+         7         0.6444         2.2021
+         8         0.6612         2.0353
+         9         0.6755         1.9158
+        10         0.6878         1.8256
+        15         0.7321         1.5771
+        20         0.7605         1.4606
+        30         0.7964         1.3443
+        40         0.8192         1.2840
+        50         0.8353         1.2461
+        60         0.8476         1.2197
+       100         0.8780         1.1617
+       120         0.8875         1.1454
+      1000         0.9580         1.0459
+     10000         0.9863         1.0141
+     50000         0.9938         1.0062
+    100000         0.9956         1.0044
+   1000000         0.9986         1.0014
+</pre>
+<p>
+              With just 2 observations the limits are from <span class="bold"><strong>0.445</strong></span>
+              up to to <span class="bold"><strong>31.9</strong></span>, so the standard deviation
+              might be about <span class="bold"><strong>half</strong></span> the observed value
+              up to <span class="bold"><strong>30 times</strong></span> the observed value!
+            </p>
+<p>
+              Estimating a standard deviation with just a handful of values leaves
+              a very great uncertainty, especially the upper limit. Note especially
+              how far the upper limit is skewed from the most likely standard deviation.
+            </p>
+<p>
+              Even for 10 observations, normally considered a reasonable number,
+              the range is still from 0.69 to 1.8, about a range of 0.7 to 2, and
+              is still highly skewed with an upper limit <span class="bold"><strong>twice</strong></span>
+              the median.
+            </p>
+<p>
+              When we have 1000 observations, the estimate of the standard deviation
+              is starting to look convincing, with a range from 0.95 to 1.05 - now
+              near symmetrical, but still about + or - 5%.
+            </p>
+<p>
+              Only when we have 10000 or more repeated observations can we start
+              to be reasonably confident (provided we are sure that other factors
+              like drift are not creeping in).
+            </p>
+<p>
+              For 10000 observations, the interval is 0.99 to 1.1 - finally a really
+              convincing + or -1% confidence.
+            </p>
+</div>
+<table xmlns:rev="http://www.cs.rpi.edu/~gregod/boost/tools/doc/revision" width="100%"><tr>
+<td align="left"></td>
+<td align="right"><div class="copyright-footer">Copyright © 2006 , 2007, 2008 John Maddock, Paul A. Bristow, Hubert
+      Holin, Xiaogang Zhang, Bruno Lalande and Gautam Sewani<p>
+        Distributed under the Boost Software License, Version 1.0. (See accompanying
+        file LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_0.txt)
+      </p>
+</div></td>
+</tr></table>
+<hr>
+<div class="spirit-nav">
+<a accesskey="p" href="../cs_eg.html"><img src="../../../../../../../doc/html/images/prev.png" alt="Prev"></a><a accesskey="u" href="../cs_eg.html"><img src="../../../../../../../doc/html/images/up.png" alt="Up"></a><a accesskey="h" href="../../../../../index.html"><img src="../../../../../../../doc/html/images/home.png" alt="Home"></a><a accesskey="n" href="chi_sq_test.html"><img src="../../../../../../../doc/html/images/next.png" alt="Next"></a>
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+<a name="math_toolkit.dist.stat_tut.weg.cs_eg.chi_sq_size"></a><a class="link" href="chi_sq_size.html" title="Estimating the Required Sample Sizes for a Chi-Square Test for the Standard Deviation">
+            Estimating the Required Sample Sizes for a Chi-Square Test for the Standard
+            Deviation</a>
+</h6></div></div></div>
+<p>
+              Suppose we conduct a Chi Squared test for standard deviation and the
+              result is borderline, a legitimate question to ask is "How large
+              would the sample size have to be in order to produce a definitive result?"
+            </p>
+<p>
+              The class template <a class="link" href="../../../dist_ref/dists/chi_squared_dist.html" title="Chi Squared Distribution">chi_squared_distribution</a>
+              has a static method <code class="computeroutput"><span class="identifier">find_degrees_of_freedom</span></code>
+              that will calculate this value for some acceptable risk of type I failure
+              <span class="emphasis"><em>alpha</em></span>, type II failure <span class="emphasis"><em>beta</em></span>,
+              and difference from the standard deviation <span class="emphasis"><em>diff</em></span>.
+              Please note that the method used works on variance, and not standard
+              deviation as is usual for the Chi Squared Test.
+            </p>
+<p>
+              The code for this example is located in chi_square_std_dev_test.cpp.
+            </p>
+<p>
+              We begin by defining a procedure to print out the sample sizes required
+              for various risk levels:
+            </p>
+<pre class="programlisting"><span class="keyword">void</span> <span class="identifier">chi_squared_sample_sized</span><span class="special">(</span>
+     <span class="keyword">double</span> <span class="identifier">diff</span><span class="special">,</span>      <span class="comment">// difference from variance to detect
+</span>     <span class="keyword">double</span> <span class="identifier">variance</span><span class="special">)</span>  <span class="comment">// true variance
+</span><span class="special">{</span>
+</pre>
+<p>
+              The procedure begins by printing out the input data:
+            </p>
+<pre class="programlisting"><span class="keyword">using</span> <span class="keyword">namespace</span> <span class="identifier">std</span><span class="special">;</span>
+<span class="keyword">using</span> <span class="keyword">namespace</span> <span class="identifier">boost</span><span class="special">::</span><span class="identifier">math</span><span class="special">;</span>
+
+<span class="comment">// Print out general info:
+</span><span class="identifier">cout</span> <span class="special">&lt;&lt;</span>
+   <span class="string">"_____________________________________________________________\n"</span>
+   <span class="string">"Estimated sample sizes required for various confidence levels\n"</span>
+   <span class="string">"_____________________________________________________________\n\n"</span><span class="special">;</span>
+<span class="identifier">cout</span> <span class="special">&lt;&lt;</span> <span class="identifier">setprecision</span><span class="special">(</span><span class="number">5</span><span class="special">);</span>
+<span class="identifier">cout</span> <span class="special">&lt;&lt;</span> <span class="identifier">setw</span><span class="special">(</span><span class="number">40</span><span class="special">)</span> <span class="special">&lt;&lt;</span> <span class="identifier">left</span> <span class="special">&lt;&lt;</span> <span class="string">"True Variance"</span> <span class="special">&lt;&lt;</span> <span class="string">"=  "</span> <span class="special">&lt;&lt;</span> <span class="identifier">variance</span> <span class="special">&lt;&lt;</span> <span class="string">"\n"</span><span class="special">;</span>
+<span class="identifier">cout</span> <span class="special">&lt;&lt;</span> <span class="identifier">setw</span><span class="special">(</span><span class="number">40</span><span class="special">)</span> <span class="special">&lt;&lt;</span> <span class="identifier">left</span> <span class="special">&lt;&lt;</span> <span class="string">"Difference to detect"</span> <span class="special">&lt;&lt;</span> <span class="string">"=  "</span> <span class="special">&lt;&lt;</span> <span class="identifier">diff</span> <span class="special">&lt;&lt;</span> <span class="string">"\n"</span><span class="special">;</span>
+</pre>
+<p>
+              And defines a table of significance levels for which we'll calculate
+              sample sizes:
+            </p>
+<pre class="programlisting"><span class="keyword">double</span> <span class="identifier">alpha</span><span class="special">[]</span> <span class="special">=</span> <span class="special">{</span> <span class="number">0.5</span><span class="special">,</span> <span class="number">0.25</span><span class="special">,</span> <span class="number">0.1</span><span class="special">,</span> <span class="number">0.05</span><span class="special">,</span> <span class="number">0.01</span><span class="special">,</span> <span class="number">0.001</span><span class="special">,</span> <span class="number">0.0001</span><span class="special">,</span> <span class="number">0.00001</span> <span class="special">};</span>
+</pre>
+<p>
+              For each value of alpha we can calculate two sample sizes: one where
+              the sample variance is less than the true value by <span class="emphasis"><em>diff</em></span>
+              and one where it is greater than the true value by <span class="emphasis"><em>diff</em></span>.
+              Thanks to the asymmetric nature of the Chi Squared distribution these
+              two values will not be the same, the difference in their calculation
+              differs only in the sign of <span class="emphasis"><em>diff</em></span> that's passed
+              to <code class="computeroutput"><span class="identifier">find_degrees_of_freedom</span></code>.
+              Finally in this example we'll simply things, and let risk level <span class="emphasis"><em>beta</em></span>
+              be the same as <span class="emphasis"><em>alpha</em></span>:
+            </p>
+<pre class="programlisting"><span class="identifier">cout</span> <span class="special">&lt;&lt;</span> <span class="string">"\n\n"</span>
+        <span class="string">"_______________________________________________________________\n"</span>
+        <span class="string">"Confidence       Estimated          Estimated\n"</span>
+        <span class="string">" Value (%)      Sample Size        Sample Size\n"</span>
+        <span class="string">"                (lower one         (upper one\n"</span>
+        <span class="string">"                 sided test)        sided test)\n"</span>
+        <span class="string">"_______________________________________________________________\n"</span><span class="special">;</span>
+<span class="comment">//
+</span><span class="comment">// Now print out the data for the table rows.
+</span><span class="comment">//
+</span><span class="keyword">for</span><span class="special">(</span><span class="keyword">unsigned</span> <span class="identifier">i</span> <span class="special">=</span> <span class="number">0</span><span class="special">;</span> <span class="identifier">i</span> <span class="special">&lt;</span> <span class="keyword">sizeof</span><span class="special">(</span><span class="identifier">alpha</span><span class="special">)/</span><span class="keyword">sizeof</span><span class="special">(</span><span class="identifier">alpha</span><span class="special">[</span><span class="number">0</span><span class="special">]);</span> <span class="special">++</span><span class="identifier">i</span><span class="special">)</span>
+<span class="special">{</span>
+   <span class="comment">// Confidence value:
+</span>   <span class="identifier">cout</span> <span class="special">&lt;&lt;</span> <span class="identifier">fixed</span> <span class="special">&lt;&lt;</span> <span class="identifier">setprecision</span><span class="special">(</span><span class="number">3</span><span class="special">)</span> <span class="special">&lt;&lt;</span> <span class="identifier">setw</span><span class="special">(</span><span class="number">10</span><span class="special">)</span> <span class="special">&lt;&lt;</span> <span class="identifier">right</span> <span class="special">&lt;&lt;</span> <span class="number">100</span> <span class="special">*</span> <span class="special">(</span><span class="number">1</span><span class="special">-</span><span class="identifier">alpha</span><span class="special">[</span><span class="identifier">i</span><span class="special">]);</span>
+   <span class="comment">// calculate df for a lower single sided test:
+</span>   <span class="keyword">double</span> <span class="identifier">df</span> <span class="special">=</span> <span class="identifier">chi_squared</span><span class="special">::</span><span class="identifier">find_degrees_of_freedom</span><span class="special">(</span>
+      <span class="special">-</span><span class="identifier">diff</span><span class="special">,</span> <span class="identifier">alpha</span><span class="special">[</span><span class="identifier">i</span><span class="special">],</span> <span class="identifier">alpha</span><span class="special">[</span><span class="identifier">i</span><span class="special">],</span> <span class="identifier">variance</span><span class="special">);</span>
+   <span class="comment">// convert to sample size:
+</span>   <span class="keyword">double</span> <span class="identifier">size</span> <span class="special">=</span> <span class="identifier">ceil</span><span class="special">(</span><span class="identifier">df</span><span class="special">)</span> <span class="special">+</span> <span class="number">1</span><span class="special">;</span>
+   <span class="comment">// Print size:
+</span>   <span class="identifier">cout</span> <span class="special">&lt;&lt;</span> <span class="identifier">fixed</span> <span class="special">&lt;&lt;</span> <span class="identifier">setprecision</span><span class="special">(</span><span class="number">0</span><span class="special">)</span> <span class="special">&lt;&lt;</span> <span class="identifier">setw</span><span class="special">(</span><span class="number">16</span><span class="special">)</span> <span class="special">&lt;&lt;</span> <span class="identifier">right</span> <span class="special">&lt;&lt;</span> <span class="identifier">size</span><span class="special">;</span>
+   <span class="comment">// calculate df for an upper single sided test:
+</span>   <span class="identifier">df</span> <span class="special">=</span> <span class="identifier">chi_squared</span><span class="special">::</span><span class="identifier">find_degrees_of_freedom</span><span class="special">(</span>
+      <span class="identifier">diff</span><span class="special">,</span> <span class="identifier">alpha</span><span class="special">[</span><span class="identifier">i</span><span class="special">],</span> <span class="identifier">alpha</span><span class="special">[</span><span class="identifier">i</span><span class="special">],</span> <span class="identifier">variance</span><span class="special">);</span>
+   <span class="comment">// convert to sample size:
+</span>   <span class="identifier">size</span> <span class="special">=</span> <span class="identifier">ceil</span><span class="special">(</span><span class="identifier">df</span><span class="special">)</span> <span class="special">+</span> <span class="number">1</span><span class="special">;</span>
+   <span class="comment">// Print size:
+</span>   <span class="identifier">cout</span> <span class="special">&lt;&lt;</span> <span class="identifier">fixed</span> <span class="special">&lt;&lt;</span> <span class="identifier">setprecision</span><span class="special">(</span><span class="number">0</span><span class="special">)</span> <span class="special">&lt;&lt;</span> <span class="identifier">setw</span><span class="special">(</span><span class="number">16</span><span class="special">)</span> <span class="special">&lt;&lt;</span> <span class="identifier">right</span> <span class="special">&lt;&lt;</span> <span class="identifier">size</span> <span class="special">&lt;&lt;</span> <span class="identifier">endl</span><span class="special">;</span>
+<span class="special">}</span>
+<span class="identifier">cout</span> <span class="special">&lt;&lt;</span> <span class="identifier">endl</span><span class="special">;</span>
+</pre>
+<p>
+              For some example output, consider the <a href="http://www.itl.nist.gov/div898/handbook/prc/section2/prc23.htm" target="_top">silicon
+              wafer data</a> from the <a href="http://www.itl.nist.gov/div898/handbook/" target="_top">NIST/SEMATECH
+              e-Handbook of Statistical Methods.</a>. In this scenario a supplier
+              of 100 ohm.cm silicon wafers claims that his fabrication process can
+              produce wafers with sufficient consistency so that the standard deviation
+              of resistivity for the lot does not exceed 10 ohm.cm. A sample of N
+              = 10 wafers taken from the lot has a standard deviation of 13.97 ohm.cm,
+              and the question we ask ourselves is "How large would our sample
+              have to be to reliably detect this difference?".
+            </p>
+<p>
+              To use our procedure above, we have to convert the standard deviations
+              to variance (square them), after which the program output looks like
+              this:
+            </p>
+<pre class="programlisting">_____________________________________________________________
+Estimated sample sizes required for various confidence levels
+_____________________________________________________________
+
+True Variance                           =  100.00000
+Difference to detect                    =  95.16090
+
+
+_______________________________________________________________
+Confidence       Estimated          Estimated
+ Value (%)      Sample Size        Sample Size
+                (lower one         (upper one
+                 sided test)        sided test)
+_______________________________________________________________
+    50.000               2               2
+    75.000               2              10
+    90.000               4              32
+    95.000               5              51
+    99.000               7              99
+    99.900              11             174
+    99.990              15             251
+    99.999              20             330
+</pre>
+<p>
+              In this case we are interested in a upper single sided test. So for
+              example, if the maximum acceptable risk of falsely rejecting the null-hypothesis
+              is 0.05 (Type I error), and the maximum acceptable risk of failing
+              to reject the null-hypothesis is also 0.05 (Type II error), we estimate
+              that we would need a sample size of 51.
+            </p>
+</div>
+<table xmlns:rev="http://www.cs.rpi.edu/~gregod/boost/tools/doc/revision" width="100%"><tr>
+<td align="left"></td>
+<td align="right"><div class="copyright-footer">Copyright © 2006 , 2007, 2008 John Maddock, Paul A. Bristow, Hubert
+      Holin, Xiaogang Zhang, Bruno Lalande and Gautam Sewani<p>
+        Distributed under the Boost Software License, Version 1.0. (See accompanying
+        file LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_0.txt)
+      </p>
+</div></td>
+</tr></table>
+<hr>
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+<title>Chi-Square Test for the Standard Deviation</title>
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+<a name="math_toolkit.dist.stat_tut.weg.cs_eg.chi_sq_test"></a><a class="link" href="chi_sq_test.html" title="Chi-Square Test for the Standard Deviation">
+            Chi-Square Test for the Standard Deviation</a>
+</h6></div></div></div>
+<p>
+              We use this test to determine whether the standard deviation of a sample
+              differs from a specified value. Typically this occurs in process change
+              situations where we wish to compare the standard deviation of a new
+              process to an established one.
+            </p>
+<p>
+              The code for this example is contained in chi_square_std_dev_test.cpp,
+              and we'll begin by defining the procedure that will print out the test
+              statistics:
+            </p>
+<pre class="programlisting"><span class="keyword">void</span> <span class="identifier">chi_squared_test</span><span class="special">(</span>
+    <span class="keyword">double</span> <span class="identifier">Sd</span><span class="special">,</span>     <span class="comment">// Sample std deviation
+</span>    <span class="keyword">double</span> <span class="identifier">D</span><span class="special">,</span>      <span class="comment">// True std deviation
+</span>    <span class="keyword">unsigned</span> <span class="identifier">N</span><span class="special">,</span>    <span class="comment">// Sample size
+</span>    <span class="keyword">double</span> <span class="identifier">alpha</span><span class="special">)</span>  <span class="comment">// Significance level
+</span><span class="special">{</span>
+</pre>
+<p>
+              The procedure begins by printing a summary of the input data:
+            </p>
+<pre class="programlisting"><span class="keyword">using</span> <span class="keyword">namespace</span> <span class="identifier">std</span><span class="special">;</span>
+<span class="keyword">using</span> <span class="keyword">namespace</span> <span class="identifier">boost</span><span class="special">::</span><span class="identifier">math</span><span class="special">;</span>
+
+<span class="comment">// Print header:
+</span><span class="identifier">cout</span> <span class="special">&lt;&lt;</span>
+   <span class="string">"______________________________________________\n"</span>
+   <span class="string">"Chi Squared test for sample standard deviation\n"</span>
+   <span class="string">"______________________________________________\n\n"</span><span class="special">;</span>
+<span class="identifier">cout</span> <span class="special">&lt;&lt;</span> <span class="identifier">setprecision</span><span class="special">(</span><span class="number">5</span><span class="special">);</span>
+<span class="identifier">cout</span> <span class="special">&lt;&lt;</span> <span class="identifier">setw</span><span class="special">(</span><span class="number">55</span><span class="special">)</span> <span class="special">&lt;&lt;</span> <span class="identifier">left</span> <span class="special">&lt;&lt;</span> <span class="string">"Number of Observations"</span> <span class="special">&lt;&lt;</span> <span class="string">"=  "</span> <span class="special">&lt;&lt;</span> <span class="identifier">N</span> <span class="special">&lt;&lt;</span> <span class="string">"\n"</span><span class="special">;</span>
+<span class="identifier">cout</span> <span class="special">&lt;&lt;</span> <span class="identifier">setw</span><span class="special">(</span><span class="number">55</span><span class="special">)</span> <span class="special">&lt;&lt;</span> <span class="identifier">left</span> <span class="special">&lt;&lt;</span> <span class="string">"Sample Standard Deviation"</span> <span class="special">&lt;&lt;</span> <span class="string">"=  "</span> <span class="special">&lt;&lt;</span> <span class="identifier">Sd</span> <span class="special">&lt;&lt;</span> <span class="string">"\n"</span><span class="special">;</span>
+<span class="identifier">cout</span> <span class="special">&lt;&lt;</span> <span class="identifier">setw</span><span class="special">(</span><span class="number">55</span><span class="special">)</span> <span class="special">&lt;&lt;</span> <span class="identifier">left</span> <span class="special">&lt;&lt;</span> <span class="string">"Expected True Standard Deviation"</span> <span class="special">&lt;&lt;</span> <span class="string">"=  "</span> <span class="special">&lt;&lt;</span> <span class="identifier">D</span> <span class="special">&lt;&lt;</span> <span class="string">"\n\n"</span><span class="special">;</span>
+</pre>
+<p>
+              The test statistic (T) is simply the ratio of the sample and "true"
+              standard deviations squared, multiplied by the number of degrees of
+              freedom (the sample size less one):
+            </p>
+<pre class="programlisting"><span class="keyword">double</span> <span class="identifier">t_stat</span> <span class="special">=</span> <span class="special">(</span><span class="identifier">N</span> <span class="special">-</span> <span class="number">1</span><span class="special">)</span> <span class="special">*</span> <span class="special">(</span><span class="identifier">Sd</span> <span class="special">/</span> <span class="identifier">D</span><span class="special">)</span> <span class="special">*</span> <span class="special">(</span><span class="identifier">Sd</span> <span class="special">/</span> <span class="identifier">D</span><span class="special">);</span>
+<span class="identifier">cout</span> <span class="special">&lt;&lt;</span> <span class="identifier">setw</span><span class="special">(</span><span class="number">55</span><span class="special">)</span> <span class="special">&lt;&lt;</span> <span class="identifier">left</span> <span class="special">&lt;&lt;</span> <span class="string">"Test Statistic"</span> <span class="special">&lt;&lt;</span> <span class="string">"=  "</span> <span class="special">&lt;&lt;</span> <span class="identifier">t_stat</span> <span class="special">&lt;&lt;</span> <span class="string">"\n"</span><span class="special">;</span>
+</pre>
+<p>
+              The distribution we need to use, is a Chi Squared distribution with
+              N-1 degrees of freedom:
+            </p>
+<pre class="programlisting"><span class="identifier">chi_squared</span> <span class="identifier">dist</span><span class="special">(</span><span class="identifier">N</span> <span class="special">-</span> <span class="number">1</span><span class="special">);</span>
+</pre>
+<p>
+              The various hypothesis that can be tested are summarised in the following
+              table:
+            </p>
+<div class="informaltable"><table class="table">
+<colgroup>
+<col>
+<col>
+</colgroup>
+<thead><tr>
+<th>
+                    <p>
+                      Hypothesis
+                    </p>
+                    </th>
+<th>
+                    <p>
+                      Test
+                    </p>
+                    </th>
+</tr></thead>
+<tbody>
+<tr>
+<td>
+                    <p>
+                      The null-hypothesis: there is no difference in standard deviation
+                      from the specified value
+                    </p>
+                    </td>
+<td>
+                    <p>
+                      Reject if T &lt; &#967;<sup>2</sup><sub>(1-alpha/2; N-1)</sub> or T &gt; &#967;<sup>2</sup><sub>(alpha/2; N-1)</sub>
+                    </p>
+                    </td>
+</tr>
+<tr>
+<td>
+                    <p>
+                      The alternative hypothesis: there is a difference in standard
+                      deviation from the specified value
+                    </p>
+                    </td>
+<td>
+                    <p>
+                      Reject if &#967;<sup>2</sup><sub>(1-alpha/2; N-1)</sub> &gt;= T &gt;= &#967;<sup>2</sup><sub>(alpha/2; N-1)</sub>
+                    </p>
+                    </td>
+</tr>
+<tr>
+<td>
+                    <p>
+                      The alternative hypothesis: the standard deviation is less
+                      than the specified value
+                    </p>
+                    </td>
+<td>
+                    <p>
+                      Reject if &#967;<sup>2</sup><sub>(1-alpha; N-1)</sub> &lt;= T
+                    </p>
+                    </td>
+</tr>
+<tr>
+<td>
+                    <p>
+                      The alternative hypothesis: the standard deviation is greater
+                      than the specified value
+                    </p>
+                    </td>
+<td>
+                    <p>
+                      Reject if &#967;<sup>2</sup><sub>(alpha; N-1)</sub> &gt;= T
+                    </p>
+                    </td>
+</tr>
+</tbody>
+</table></div>
+<p>
+              Where &#967;<sup>2</sup><sub>(alpha; N-1)</sub> is the upper critical value of the Chi Squared distribution,
+              and &#967;<sup>2</sup><sub>(1-alpha; N-1)</sub> is the lower critical value.
+            </p>
+<p>
+              Recall that the lower critical value is the same as the quantile, and
+              the upper critical value is the same as the quantile from the complement
+              of the probability, that gives us the following code to calculate the
+              critical values:
+            </p>
+<pre class="programlisting"><span class="keyword">double</span> <span class="identifier">ucv</span> <span class="special">=</span> <span class="identifier">quantile</span><span class="special">(</span><span class="identifier">complement</span><span class="special">(</span><span class="identifier">dist</span><span class="special">,</span> <span class="identifier">alpha</span><span class="special">));</span>
+<span class="keyword">double</span> <span class="identifier">ucv2</span> <span class="special">=</span> <span class="identifier">quantile</span><span class="special">(</span><span class="identifier">complement</span><span class="special">(</span><span class="identifier">dist</span><span class="special">,</span> <span class="identifier">alpha</span> <span class="special">/</span> <span class="number">2</span><span class="special">));</span>
+<span class="keyword">double</span> <span class="identifier">lcv</span> <span class="special">=</span> <span class="identifier">quantile</span><span class="special">(</span><span class="identifier">dist</span><span class="special">,</span> <span class="identifier">alpha</span><span class="special">);</span>
+<span class="keyword">double</span> <span class="identifier">lcv2</span> <span class="special">=</span> <span class="identifier">quantile</span><span class="special">(</span><span class="identifier">dist</span><span class="special">,</span> <span class="identifier">alpha</span> <span class="special">/</span> <span class="number">2</span><span class="special">);</span>
+<span class="identifier">cout</span> <span class="special">&lt;&lt;</span> <span class="identifier">setw</span><span class="special">(</span><span class="number">55</span><span class="special">)</span> <span class="special">&lt;&lt;</span> <span class="identifier">left</span> <span class="special">&lt;&lt;</span> <span class="string">"Upper Critical Value at alpha: "</span> <span class="special">&lt;&lt;</span> <span class="string">"=  "</span>
+   <span class="special">&lt;&lt;</span> <span class="identifier">setprecision</span><span class="special">(</span><span class="number">3</span><span class="special">)</span> <span class="special">&lt;&lt;</span> <span class="identifier">scientific</span> <span class="special">&lt;&lt;</span> <span class="identifier">ucv</span> <span class="special">&lt;&lt;</span> <span class="string">"\n"</span><span class="special">;</span>
+<span class="identifier">cout</span> <span class="special">&lt;&lt;</span> <span class="identifier">setw</span><span class="special">(</span><span class="number">55</span><span class="special">)</span> <span class="special">&lt;&lt;</span> <span class="identifier">left</span> <span class="special">&lt;&lt;</span> <span class="string">"Upper Critical Value at alpha/2: "</span> <span class="special">&lt;&lt;</span> <span class="string">"=  "</span>
+   <span class="special">&lt;&lt;</span> <span class="identifier">setprecision</span><span class="special">(</span><span class="number">3</span><span class="special">)</span> <span class="special">&lt;&lt;</span> <span class="identifier">scientific</span> <span class="special">&lt;&lt;</span> <span class="identifier">ucv2</span> <span class="special">&lt;&lt;</span> <span class="string">"\n"</span><span class="special">;</span>
+<span class="identifier">cout</span> <span class="special">&lt;&lt;</span> <span class="identifier">setw</span><span class="special">(</span><span class="number">55</span><span class="special">)</span> <span class="special">&lt;&lt;</span> <span class="identifier">left</span> <span class="special">&lt;&lt;</span> <span class="string">"Lower Critical Value at alpha: "</span> <span class="special">&lt;&lt;</span> <span class="string">"=  "</span>
+   <span class="special">&lt;&lt;</span> <span class="identifier">setprecision</span><span class="special">(</span><span class="number">3</span><span class="special">)</span> <span class="special">&lt;&lt;</span> <span class="identifier">scientific</span> <span class="special">&lt;&lt;</span> <span class="identifier">lcv</span> <span class="special">&lt;&lt;</span> <span class="string">"\n"</span><span class="special">;</span>
+<span class="identifier">cout</span> <span class="special">&lt;&lt;</span> <span class="identifier">setw</span><span class="special">(</span><span class="number">55</span><span class="special">)</span> <span class="special">&lt;&lt;</span> <span class="identifier">left</span> <span class="special">&lt;&lt;</span> <span class="string">"Lower Critical Value at alpha/2: "</span> <span class="special">&lt;&lt;</span> <span class="string">"=  "</span>
+   <span class="special">&lt;&lt;</span> <span class="identifier">setprecision</span><span class="special">(</span><span class="number">3</span><span class="special">)</span> <span class="special">&lt;&lt;</span> <span class="identifier">scientific</span> <span class="special">&lt;&lt;</span> <span class="identifier">lcv2</span> <span class="special">&lt;&lt;</span> <span class="string">"\n\n"</span><span class="special">;</span>
+</pre>
+<p>
+              Now that we have the critical values, we can compare these to our test
+              statistic, and print out the result of each hypothesis and test:
+            </p>
+<pre class="programlisting"><span class="identifier">cout</span> <span class="special">&lt;&lt;</span> <span class="identifier">setw</span><span class="special">(</span><span class="number">55</span><span class="special">)</span> <span class="special">&lt;&lt;</span> <span class="identifier">left</span> <span class="special">&lt;&lt;</span>
+   <span class="string">"Results for Alternative Hypothesis and alpha"</span> <span class="special">&lt;&lt;</span> <span class="string">"=  "</span>
+   <span class="special">&lt;&lt;</span> <span class="identifier">setprecision</span><span class="special">(</span><span class="number">4</span><span class="special">)</span> <span class="special">&lt;&lt;</span> <span class="identifier">fixed</span> <span class="special">&lt;&lt;</span> <span class="identifier">alpha</span> <span class="special">&lt;&lt;</span> <span class="string">"\n\n"</span><span class="special">;</span>
+<span class="identifier">cout</span> <span class="special">&lt;&lt;</span> <span class="string">"Alternative Hypothesis              Conclusion\n"</span><span class="special">;</span>
+
+<span class="identifier">cout</span> <span class="special">&lt;&lt;</span> <span class="string">"Standard Deviation != "</span> <span class="special">&lt;&lt;</span> <span class="identifier">setprecision</span><span class="special">(</span><span class="number">3</span><span class="special">)</span> <span class="special">&lt;&lt;</span> <span class="identifier">fixed</span> <span class="special">&lt;&lt;</span> <span class="identifier">D</span> <span class="special">&lt;&lt;</span> <span class="string">"            "</span><span class="special">;</span>
+<span class="keyword">if</span><span class="special">((</span><span class="identifier">ucv2</span> <span class="special">&lt;</span> <span class="identifier">t_stat</span><span class="special">)</span> <span class="special">||</span> <span class="special">(</span><span class="identifier">lcv2</span> <span class="special">&gt;</span> <span class="identifier">t_stat</span><span class="special">))</span>
+   <span class="identifier">cout</span> <span class="special">&lt;&lt;</span> <span class="string">"ACCEPTED\n"</span><span class="special">;</span>
+<span class="keyword">else</span>
+   <span class="identifier">cout</span> <span class="special">&lt;&lt;</span> <span class="string">"REJECTED\n"</span><span class="special">;</span>
+
+<span class="identifier">cout</span> <span class="special">&lt;&lt;</span> <span class="string">"Standard Deviation  &lt; "</span> <span class="special">&lt;&lt;</span> <span class="identifier">setprecision</span><span class="special">(</span><span class="number">3</span><span class="special">)</span> <span class="special">&lt;&lt;</span> <span class="identifier">fixed</span> <span class="special">&lt;&lt;</span> <span class="identifier">D</span> <span class="special">&lt;&lt;</span> <span class="string">"            "</span><span class="special">;</span>
+<span class="keyword">if</span><span class="special">(</span><span class="identifier">lcv</span> <span class="special">&gt;</span> <span class="identifier">t_stat</span><span class="special">)</span>
+   <span class="identifier">cout</span> <span class="special">&lt;&lt;</span> <span class="string">"ACCEPTED\n"</span><span class="special">;</span>
+<span class="keyword">else</span>
+   <span class="identifier">cout</span> <span class="special">&lt;&lt;</span> <span class="string">"REJECTED\n"</span><span class="special">;</span>
+
+<span class="identifier">cout</span> <span class="special">&lt;&lt;</span> <span class="string">"Standard Deviation  &gt; "</span> <span class="special">&lt;&lt;</span> <span class="identifier">setprecision</span><span class="special">(</span><span class="number">3</span><span class="special">)</span> <span class="special">&lt;&lt;</span> <span class="identifier">fixed</span> <span class="special">&lt;&lt;</span> <span class="identifier">D</span> <span class="special">&lt;&lt;</span> <span class="string">"            "</span><span class="special">;</span>
+<span class="keyword">if</span><span class="special">(</span><span class="identifier">ucv</span> <span class="special">&lt;</span> <span class="identifier">t_stat</span><span class="special">)</span>
+   <span class="identifier">cout</span> <span class="special">&lt;&lt;</span> <span class="string">"ACCEPTED\n"</span><span class="special">;</span>
+<span class="keyword">else</span>
+   <span class="identifier">cout</span> <span class="special">&lt;&lt;</span> <span class="string">"REJECTED\n"</span><span class="special">;</span>
+<span class="identifier">cout</span> <span class="special">&lt;&lt;</span> <span class="identifier">endl</span> <span class="special">&lt;&lt;</span> <span class="identifier">endl</span><span class="special">;</span>
+</pre>
+<p>
+              To see some example output we'll use the <a href="http://www.itl.nist.gov/div898/handbook/eda/section3/eda3581.htm" target="_top">gear
+              data</a> from the <a href="http://www.itl.nist.gov/div898/handbook/" target="_top">NIST/SEMATECH
+              e-Handbook of Statistical Methods.</a>. The data represents measurements
+              of gear diameter from a manufacturing process. The program output is
+              deliberately designed to mirror the DATAPLOT output shown in the <a href="http://www.itl.nist.gov/div898/handbook/eda/section3/eda358.htm" target="_top">NIST
+              Handbook Example</a>.
+            </p>
+<pre class="programlisting">______________________________________________
+Chi Squared test for sample standard deviation
+______________________________________________
+
+Number of Observations                                 =  100
+Sample Standard Deviation                              =  0.00628
+Expected True Standard Deviation                       =  0.10000
+
+Test Statistic                                         =  0.39030
+CDF of test statistic:                                 =  1.438e-099
+Upper Critical Value at alpha:                         =  1.232e+002
+Upper Critical Value at alpha/2:                       =  1.284e+002
+Lower Critical Value at alpha:                         =  7.705e+001
+Lower Critical Value at alpha/2:                       =  7.336e+001
+
+Results for Alternative Hypothesis and alpha           =  0.0500
+
+Alternative Hypothesis              Conclusion
+Standard Deviation != 0.100            ACCEPTED
+Standard Deviation  &lt; 0.100            ACCEPTED
+Standard Deviation  &gt; 0.100            REJECTED
+</pre>
+<p>
+              In this case we are testing whether the sample standard deviation is
+              0.1, and the null-hypothesis is rejected, so we conclude that the standard
+              deviation <span class="emphasis"><em>is not</em></span> 0.1.
+            </p>
+<p>
+              For an alternative example, consider the <a href="http://www.itl.nist.gov/div898/handbook/prc/section2/prc23.htm" target="_top">silicon
+              wafer data</a> again from the <a href="http://www.itl.nist.gov/div898/handbook/" target="_top">NIST/SEMATECH
+              e-Handbook of Statistical Methods.</a>. In this scenario a supplier
+              of 100 ohm.cm silicon wafers claims that his fabrication process can
+              produce wafers with sufficient consistency so that the standard deviation
+              of resistivity for the lot does not exceed 10 ohm.cm. A sample of N
+              = 10 wafers taken from the lot has a standard deviation of 13.97 ohm.cm,
+              and the question we ask ourselves is "Is the suppliers claim correct?".
+            </p>
+<p>
+              The program output now looks like this:
+            </p>
+<pre class="programlisting">______________________________________________
+Chi Squared test for sample standard deviation
+______________________________________________
+
+Number of Observations                                 =  10
+Sample Standard Deviation                              =  13.97000
+Expected True Standard Deviation                       =  10.00000
+
+Test Statistic                                         =  17.56448
+CDF of test statistic:                                 =  9.594e-001
+Upper Critical Value at alpha:                         =  1.692e+001
+Upper Critical Value at alpha/2:                       =  1.902e+001
+Lower Critical Value at alpha:                         =  3.325e+000
+Lower Critical Value at alpha/2:                       =  2.700e+000
+
+Results for Alternative Hypothesis and alpha           =  0.0500
+
+Alternative Hypothesis              Conclusion
+Standard Deviation != 10.000            REJECTED
+Standard Deviation  &lt; 10.000            REJECTED
+Standard Deviation  &gt; 10.000            ACCEPTED
+</pre>
+<p>
+              In this case, our null-hypothesis is that the standard deviation of
+              the sample is less than 10: this hypothesis is rejected in the analysis
+              above, and so we reject the manufacturers claim.
+            </p>
+</div>
+<table xmlns:rev="http://www.cs.rpi.edu/~gregod/boost/tools/doc/revision" width="100%"><tr>
+<td align="left"></td>
+<td align="right"><div class="copyright-footer">Copyright © 2006 , 2007, 2008 John Maddock, Paul A. Bristow, Hubert
+      Holin, Xiaogang Zhang, Bruno Lalande and Gautam Sewani<p>
+        Distributed under the Boost Software License, Version 1.0. (See accompanying
+        file LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_0.txt)
+      </p>
+</div></td>
+</tr></table>
+<hr>
+<div class="spirit-nav">
+<a accesskey="p" href="chi_sq_intervals.html"><img src="../../../../../../../doc/html/images/prev.png" alt="Prev"></a><a accesskey="u" href="../cs_eg.html"><img src="../../../../../../../doc/html/images/up.png" alt="Up"></a><a accesskey="h" href="../../../../../index.html"><img src="../../../../../../../doc/html/images/home.png" alt="Home"></a><a accesskey="n" href="chi_sq_size.html"><img src="../../../../../../../doc/html/images/next.png" alt="Next"></a>
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@@ -0,0 +1,411 @@
+<html>
+<head>
+<meta http-equiv="Content-Type" content="text/html; charset=ISO-8859-1">
+<title>Distribution Construction Example</title>
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+</div>
+<div class="section" lang="en">
+<div class="titlepage"><div><div><h5 class="title">
+<a name="math_toolkit.dist.stat_tut.weg.dist_construct_eg"></a><a class="link" href="dist_construct_eg.html" title="Distribution Construction Example">
+          Distribution Construction Example</a>
+</h5></div></div></div>
+<p>
+            See distribution_construction.cpp
+            for full source code.
+          </p>
+<p>
+            </p>
+<p>
+              The structure of distributions is rather different from some other
+              statistical libraries, for example in less object-oriented language
+              like FORTRAN and C, that provide a few arguments to each free function.
+              This library provides each distribution as a template C++ class. A
+              distribution is constructed with a few arguments, and then member and
+              non-member functions are used to find values of the distribution, often
+              a function of a random variate.
+            </p>
+<p>
+            </p>
+<p>
+              First we need some includes to access the negative binomial distribution
+              (and the binomial, beta and gamma too).
+            </p>
+<p>
+            </p>
+<p>
+              
+</p>
+<pre class="programlisting"><span class="preprocessor">#include</span> <span class="special">&lt;</span><span class="identifier">boost</span><span class="special">/</span><span class="identifier">math</span><span class="special">/</span><span class="identifier">distributions</span><span class="special">/</span><span class="identifier">negative_binomial</span><span class="special">.</span><span class="identifier">hpp</span><span class="special">&gt;</span> <span class="comment">// for negative_binomial_distribution
+</span>  <span class="keyword">using</span> <span class="identifier">boost</span><span class="special">::</span><span class="identifier">math</span><span class="special">::</span><span class="identifier">negative_binomial_distribution</span><span class="special">;</span> <span class="comment">// default type is double.
+</span>  <span class="keyword">using</span> <span class="identifier">boost</span><span class="special">::</span><span class="identifier">math</span><span class="special">::</span><span class="identifier">negative_binomial</span><span class="special">;</span> <span class="comment">// typedef provides default type is double.
+</span><span class="preprocessor">#include</span> <span class="special">&lt;</span><span class="identifier">boost</span><span class="special">/</span><span class="identifier">math</span><span class="special">/</span><span class="identifier">distributions</span><span class="special">/</span><span class="identifier">binomial</span><span class="special">.</span><span class="identifier">hpp</span><span class="special">&gt;</span> <span class="comment">// for binomial_distribution.
+</span><span class="preprocessor">#include</span> <span class="special">&lt;</span><span class="identifier">boost</span><span class="special">/</span><span class="identifier">math</span><span class="special">/</span><span class="identifier">distributions</span><span class="special">/</span><span class="identifier">beta</span><span class="special">.</span><span class="identifier">hpp</span><span class="special">&gt;</span> <span class="comment">// for beta_distribution.
+</span><span class="preprocessor">#include</span> <span class="special">&lt;</span><span class="identifier">boost</span><span class="special">/</span><span class="identifier">math</span><span class="special">/</span><span class="identifier">distributions</span><span class="special">/</span><span class="identifier">gamma</span><span class="special">.</span><span class="identifier">hpp</span><span class="special">&gt;</span> <span class="comment">// for gamma_distribution.
+</span><span class="preprocessor">#include</span> <span class="special">&lt;</span><span class="identifier">boost</span><span class="special">/</span><span class="identifier">math</span><span class="special">/</span><span class="identifier">distributions</span><span class="special">/</span><span class="identifier">normal</span><span class="special">.</span><span class="identifier">hpp</span><span class="special">&gt;</span> <span class="comment">// for normal_distribution.</span></pre>
+<p>
+            </p>
+<p>
+            </p>
+<p>
+              Several examples of constructing distributions follow:
+            </p>
+<p>
+            </p>
+<p>
+              First, a negative binomial distribution with 8 successes and a success
+              fraction 0.25, 25% or 1 in 4, is constructed like this:
+            </p>
+<p>
+            </p>
+<p>
+              
+</p>
+<pre class="programlisting"><span class="identifier">boost</span><span class="special">::</span><span class="identifier">math</span><span class="special">::</span><span class="identifier">negative_binomial_distribution</span><span class="special">&lt;</span><span class="keyword">double</span><span class="special">&gt;</span> <span class="identifier">mydist0</span><span class="special">(</span><span class="number">8.</span><span class="special">,</span> <span class="number">0.25</span><span class="special">);</span></pre>
+<p>
+            </p>
+<p>
+            </p>
+<p>
+              But this is inconveniently long, so by writing
+            </p>
+<p>
+            </p>
+<p>
+              
+</p>
+<pre class="programlisting"><span class="keyword">using</span> <span class="keyword">namespace</span> <span class="identifier">boost</span><span class="special">::</span><span class="identifier">math</span><span class="special">;</span></pre>
+<p>
+            </p>
+<p>
+            </p>
+<p>
+              or
+            </p>
+<p>
+            </p>
+<p>
+              
+</p>
+<pre class="programlisting"><span class="keyword">using</span> <span class="identifier">boost</span><span class="special">::</span><span class="identifier">math</span><span class="special">::</span><span class="identifier">negative_binomial_distribution</span><span class="special">;</span></pre>
+<p>
+            </p>
+<p>
+            </p>
+<p>
+              we can reduce typing.
+            </p>
+<p>
+            </p>
+<p>
+              Since the vast majority of applications use will be using double precision,
+              the template argument to the distribution (RealType) defaults to type
+              double, so we can also write:
+            </p>
+<p>
+            </p>
+<p>
+              
+</p>
+<pre class="programlisting"><span class="identifier">negative_binomial_distribution</span><span class="special">&lt;&gt;</span> <span class="identifier">mydist9</span><span class="special">(</span><span class="number">8.</span><span class="special">,</span> <span class="number">0.25</span><span class="special">);</span> <span class="comment">// Uses default RealType = double.</span></pre>
+<p>
+            </p>
+<p>
+            </p>
+<p>
+              But the name "negative_binomial_distribution" is still inconveniently
+              long, so for most distributions, a convenience typedef is provided,
+              for example:
+            </p>
+<p>
+            
+</p>
+<pre class="programlisting"><span class="keyword">typedef</span> <span class="identifier">negative_binomial_distribution</span><span class="special">&lt;</span><span class="keyword">double</span><span class="special">&gt;</span> <span class="identifier">negative_binomial</span><span class="special">;</span> <span class="comment">// Reserved name of type double.
+</span></pre>
+<p>
+            </p>
+<div class="caution"><table border="0" summary="Caution">
+<tr>
+<td rowspan="2" align="center" valign="top" width="25"><img alt="[Caution]" src="../../../../../../doc/html/images/caution.png"></td>
+<th align="left">Caution</th>
+</tr>
+<tr><td align="left" valign="top"><p>
+                This convenience typedef is <span class="emphasis"><em>not</em></span> provided if
+                a clash would occur with the name of a function: currently only "beta"
+                and "gamma" fall into this category.
+              </p></td></tr>
+</table></div>
+<p>
+            </p>
+<p>
+              So, after a using statement,
+            </p>
+<p>
+            </p>
+<p>
+              
+</p>
+<pre class="programlisting"><span class="keyword">using</span> <span class="identifier">boost</span><span class="special">::</span><span class="identifier">math</span><span class="special">::</span><span class="identifier">negative_binomial</span><span class="special">;</span></pre>
+<p>
+            </p>
+<p>
+            </p>
+<p>
+              we have a convenient typedef to <code class="computeroutput"><span class="identifier">negative_binomial_distribution</span><span class="special">&lt;</span><span class="keyword">double</span><span class="special">&gt;</span></code>:
+            </p>
+<p>
+            </p>
+<p>
+              
+</p>
+<pre class="programlisting"><span class="identifier">negative_binomial</span> <span class="identifier">mydist</span><span class="special">(</span><span class="number">8.</span><span class="special">,</span> <span class="number">0.25</span><span class="special">);</span></pre>
+<p>
+            </p>
+<p>
+            </p>
+<p>
+              Some more examples using the convenience typedef:
+            </p>
+<p>
+            </p>
+<p>
+              
+</p>
+<pre class="programlisting"><span class="identifier">negative_binomial</span> <span class="identifier">mydist10</span><span class="special">(</span><span class="number">5.</span><span class="special">,</span> <span class="number">0.4</span><span class="special">);</span> <span class="comment">// Both arguments double.</span></pre>
+<p>
+            </p>
+<p>
+            </p>
+<p>
+              And automatic conversion takes place, so you can use integers and floats:
+            </p>
+<p>
+            </p>
+<p>
+              
+</p>
+<pre class="programlisting"><span class="identifier">negative_binomial</span> <span class="identifier">mydist11</span><span class="special">(</span><span class="number">5</span><span class="special">,</span> <span class="number">0.4</span><span class="special">);</span> <span class="comment">// Using provided typedef double, int and double arguments.</span></pre>
+<p>
+            </p>
+<p>
+            </p>
+<p>
+              This is probably the most common usage.
+            </p>
+<p>
+            </p>
+<p>
+              
+</p>
+<pre class="programlisting"><span class="identifier">negative_binomial</span> <span class="identifier">mydist12</span><span class="special">(</span><span class="number">5.</span><span class="special">,</span> <span class="number">0.4F</span><span class="special">);</span> <span class="comment">// Double and float arguments.
+</span><span class="identifier">negative_binomial</span> <span class="identifier">mydist13</span><span class="special">(</span><span class="number">5</span><span class="special">,</span> <span class="number">1</span><span class="special">);</span> <span class="comment">// Both arguments integer.</span></pre>
+<p>
+            </p>
+<p>
+            </p>
+<p>
+              Similarly for most other distributions like the binomial.
+            </p>
+<p>
+            </p>
+<p>
+              
+</p>
+<pre class="programlisting"><span class="identifier">binomial</span> <span class="identifier">mybinomial</span><span class="special">(</span><span class="number">1</span><span class="special">,</span> <span class="number">0.5</span><span class="special">);</span> <span class="comment">// is more concise than
+</span><span class="identifier">binomial_distribution</span><span class="special">&lt;&gt;</span> <span class="identifier">mybinomd1</span><span class="special">(</span><span class="number">1</span><span class="special">,</span> <span class="number">0.5</span><span class="special">);</span></pre>
+<p>
+            </p>
+<p>
+            </p>
+<p>
+              For cases when the typdef distribution name would clash with a math
+              special function (currently only beta and gamma) the typedef is deliberately
+              not provided, and the longer version of the name must be used. For
+              example do not use:
+            </p>
+<p>
+            
+</p>
+<pre class="programlisting"><span class="keyword">using</span> <span class="identifier">boost</span><span class="special">::</span><span class="identifier">math</span><span class="special">::</span><span class="identifier">beta</span><span class="special">;</span>
+<span class="identifier">beta</span> <span class="identifier">mybetad0</span><span class="special">(</span><span class="number">1</span><span class="special">,</span> <span class="number">0.5</span><span class="special">);</span> <span class="comment">// Error beta is a math FUNCTION!
+</span></pre>
+<p>
+            </p>
+<p>
+              Which produces the error messages:
+            </p>
+<p>
+            
+</p>
+<pre class="programlisting">error C2146: syntax error : missing ';' before identifier 'mybetad0'
+warning C4551: function call missing argument list
+error C3861: 'mybetad0': identifier not found
+</pre>
+<p>
+            </p>
+<p>
+              Instead you should use:
+            </p>
+<p>
+            </p>
+<p>
+              
+</p>
+<pre class="programlisting"><span class="keyword">using</span> <span class="identifier">boost</span><span class="special">::</span><span class="identifier">math</span><span class="special">::</span><span class="identifier">beta_distribution</span><span class="special">;</span>
+<span class="identifier">beta_distribution</span><span class="special">&lt;&gt;</span> <span class="identifier">mybetad1</span><span class="special">(</span><span class="number">1</span><span class="special">,</span> <span class="number">0.5</span><span class="special">);</span></pre>
+<p>
+            </p>
+<p>
+            </p>
+<p>
+              or for the gamma distribution:
+            </p>
+<p>
+            </p>
+<p>
+              
+</p>
+<pre class="programlisting"><span class="identifier">gamma_distribution</span><span class="special">&lt;&gt;</span> <span class="identifier">mygammad1</span><span class="special">(</span><span class="number">1</span><span class="special">,</span> <span class="number">0.5</span><span class="special">);</span></pre>
+<p>
+            </p>
+<p>
+            </p>
+<p>
+              We can, of course, still provide the type explicitly thus:
+            </p>
+<p>
+            </p>
+<p>
+              
+</p>
+<pre class="programlisting"><span class="comment">// Explicit double precision:
+</span><span class="identifier">negative_binomial_distribution</span><span class="special">&lt;</span><span class="keyword">double</span><span class="special">&gt;</span>        <span class="identifier">mydist1</span><span class="special">(</span><span class="number">8.</span><span class="special">,</span> <span class="number">0.25</span><span class="special">);</span> 
+
+<span class="comment">// Explicit float precision, double arguments are truncated to float:
+</span><span class="identifier">negative_binomial_distribution</span><span class="special">&lt;</span><span class="keyword">float</span><span class="special">&gt;</span>         <span class="identifier">mydist2</span><span class="special">(</span><span class="number">8.</span><span class="special">,</span> <span class="number">0.25</span><span class="special">);</span>
+
+<span class="comment">// Explicit float precision, integer &amp; double arguments converted to float.
+</span><span class="identifier">negative_binomial_distribution</span><span class="special">&lt;</span><span class="keyword">float</span><span class="special">&gt;</span>         <span class="identifier">mydist3</span><span class="special">(</span><span class="number">8</span><span class="special">,</span> <span class="number">0.25</span><span class="special">);</span> 
+
+<span class="comment">// Explicit float precision, float arguments, so no conversion:
+</span><span class="identifier">negative_binomial_distribution</span><span class="special">&lt;</span><span class="keyword">float</span><span class="special">&gt;</span>         <span class="identifier">mydist4</span><span class="special">(</span><span class="number">8.F</span><span class="special">,</span> <span class="number">0.25F</span><span class="special">);</span> 
+
+<span class="comment">// Explicit float precision, integer arguments promoted to float.
+</span><span class="identifier">negative_binomial_distribution</span><span class="special">&lt;</span><span class="keyword">float</span><span class="special">&gt;</span>         <span class="identifier">mydist5</span><span class="special">(</span><span class="number">8</span><span class="special">,</span> <span class="number">1</span><span class="special">);</span> 
+
+<span class="comment">// Explicit double precision:
+</span><span class="identifier">negative_binomial_distribution</span><span class="special">&lt;</span><span class="keyword">double</span><span class="special">&gt;</span>        <span class="identifier">mydist6</span><span class="special">(</span><span class="number">8.</span><span class="special">,</span> <span class="number">0.25</span><span class="special">);</span> 
+
+<span class="comment">// Explicit long double precision:
+</span><span class="identifier">negative_binomial_distribution</span><span class="special">&lt;</span><span class="keyword">long</span> <span class="keyword">double</span><span class="special">&gt;</span>   <span class="identifier">mydist7</span><span class="special">(</span><span class="number">8.</span><span class="special">,</span> <span class="number">0.25</span><span class="special">);</span></pre>
+<p>
+            </p>
+<p>
+            </p>
+<p>
+              And if you have your own RealType called MyFPType, for example NTL
+              RR (an arbitrary precision type), then we can write:
+            </p>
+<p>
+            
+</p>
+<pre class="programlisting"><span class="identifier">negative_binomial_distribution</span><span class="special">&lt;</span><span class="identifier">MyFPType</span><span class="special">&gt;</span>  <span class="identifier">mydist6</span><span class="special">(</span><span class="number">8</span><span class="special">,</span> <span class="number">1</span><span class="special">);</span> <span class="comment">// Integer arguments -&gt; MyFPType.
+</span></pre>
+<p>
+            <a name="math_toolkit.dist.stat_tut.weg.dist_construct_eg.default_arguments_to_distribution_constructors_"></a>
+            </p>
+<h6>
+<a name="id565023"></a>
+              <a class="link" href="dist_construct_eg.html#math_toolkit.dist.stat_tut.weg.dist_construct_eg.default_arguments_to_distribution_constructors_">Default
+              arguments to distribution constructors.</a>
+            </h6>
+<p>
+            </p>
+<p>
+              Note that default constructor arguments are only provided for some
+              distributions. So if you wrongly assume a default argument you will
+              get an error message, for example:
+            </p>
+<p>
+            
+</p>
+<pre class="programlisting"><span class="identifier">negative_binomial_distribution</span><span class="special">&lt;&gt;</span> <span class="identifier">mydist8</span><span class="special">;</span>
+</pre>
+<p>
+            
+</p>
+<pre class="programlisting">error C2512 no appropriate default constructor available.</pre>
+<p>
+            </p>
+<p>
+              No default constructors are provided for the negative binomial, because
+              it is difficult to chose any sensible default values for this distribution.
+              For other distributions, like the normal distribution, it is obviously
+              very useful to provide 'standard' defaults for the mean and standard
+              deviation thus:
+            </p>
+<p>
+            
+</p>
+<pre class="programlisting"><span class="identifier">normal_distribution</span><span class="special">(</span><span class="identifier">RealType</span> <span class="identifier">mean</span> <span class="special">=</span> <span class="number">0</span><span class="special">,</span> <span class="identifier">RealType</span> <span class="identifier">sd</span> <span class="special">=</span> <span class="number">1</span><span class="special">);</span>
+</pre>
+<p>
+            </p>
+<p>
+              So in this case we can write:
+            </p>
+<p>
+            </p>
+<p>
+              
+</p>
+<pre class="programlisting">  <span class="keyword">using</span> <span class="identifier">boost</span><span class="special">::</span><span class="identifier">math</span><span class="special">::</span><span class="identifier">normal</span><span class="special">;</span>
+  
+  <span class="identifier">normal</span> <span class="identifier">norm1</span><span class="special">;</span>       <span class="comment">// Standard normal distribution.
+</span>  <span class="identifier">normal</span> <span class="identifier">norm2</span><span class="special">(</span><span class="number">2</span><span class="special">);</span>    <span class="comment">// Mean = 2, std deviation = 1.
+</span>  <span class="identifier">normal</span> <span class="identifier">norm3</span><span class="special">(</span><span class="number">2</span><span class="special">,</span> <span class="number">3</span><span class="special">);</span> <span class="comment">// Mean = 2, std deviation = 3.
+</span>
+  <span class="keyword">return</span> <span class="number">0</span><span class="special">;</span>
+<span class="special">}</span>  <span class="comment">// int main()</span></pre>
+<p>
+            </p>
+<p>
+            </p>
+<p>
+              There is no useful output from this program, of course.
+            </p>
+<p>
+          </p>
+</div>
+<table xmlns:rev="http://www.cs.rpi.edu/~gregod/boost/tools/doc/revision" width="100%"><tr>
+<td align="left"></td>
+<td align="right"><div class="copyright-footer">Copyright © 2006 , 2007, 2008 John Maddock, Paul A. Bristow, Hubert
+      Holin, Xiaogang Zhang, Bruno Lalande and Gautam Sewani<p>
+        Distributed under the Boost Software License, Version 1.0. (See accompanying
+        file LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_0.txt)
+      </p>
+</div></td>
+</tr></table>
+<hr>
+<div class="spirit-nav">
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@@ -0,0 +1,265 @@
+<html>
+<head>
+<meta http-equiv="Content-Type" content="text/html; charset=ISO-8859-1">
+<title>Error Handling Example</title>
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+</div>
+<div class="section" lang="en">
+<div class="titlepage"><div><div><h5 class="title">
+<a name="math_toolkit.dist.stat_tut.weg.error_eg"></a><a class="link" href="error_eg.html" title="Error Handling Example"> Error Handling
+          Example</a>
+</h5></div></div></div>
+<p>
+            See <a class="link" href="../../../main_overview/error_handling.html" title="Error Handling">error handling
+            documentation</a> for a detailed explanation of the mechanism of handling
+            errors, including the common "bad" arguments to distributions
+            and functions, and how to use <a class="link" href="../../../policy.html" title="Policies">Policies</a>
+            to control it.
+          </p>
+<p>
+            But, by default, <span class="bold"><strong>exceptions will be raised</strong></span>,
+            for domain errors, pole errors, numeric overflow, and internal evaluation
+            errors. To avoid the exceptions from getting thrown and instead get an
+            appropriate value returned, usually a NaN (domain errors pole errors
+            or internal errors), or infinity (from overflow), you need to change
+            the policy.
+          </p>
+<p>
+            </p>
+<p>
+              The following example demonstrates the effect of setting the macro
+              BOOST_MATH_DOMAIN_ERROR_POLICY when an invalid argument is encountered.
+              For the purposes of this example, we'll pass a negative degrees of
+              freedom parameter to the student's t distribution.
+            </p>
+<p>
+            </p>
+<p>
+              Since we know that this is a single file program we could just add:
+            </p>
+<p>
+            
+</p>
+<pre class="programlisting"><span class="preprocessor">#define</span> <span class="identifier">BOOST_MATH_DOMAIN_ERROR_POLICY</span> <span class="identifier">ignore_error</span>
+</pre>
+<p>
+            </p>
+<p>
+              to the top of the source file to change the default policy to one that
+              simply returns a NaN when a domain error occurs. Alternatively we could
+              use:
+            </p>
+<p>
+            
+</p>
+<pre class="programlisting"><span class="preprocessor">#define</span> <span class="identifier">BOOST_MATH_DOMAIN_ERROR_POLICY</span> <span class="identifier">errno_on_error</span>
+</pre>
+<p>
+            </p>
+<p>
+              To ensure the <code class="computeroutput"><span class="special">::</span><span class="identifier">errno</span></code>
+              is set when a domain error occurs as well as returning a NaN.
+            </p>
+<p>
+            </p>
+<p>
+              This is safe provided the program consists of a single translation
+              unit <span class="emphasis"><em>and</em></span> we place the define <span class="emphasis"><em>before</em></span>
+              any #includes. Note that should we add the define after the includes
+              then it will have no effect! A warning such as:
+            </p>
+<p>
+            
+</p>
+<pre class="programlisting">warning C4005: 'BOOST_MATH_OVERFLOW_ERROR_POLICY' : macro redefinition</pre>
+<p>
+            </p>
+<p>
+              is a certain sign that it will <span class="emphasis"><em>not</em></span> have the desired
+              effect.
+            </p>
+<p>
+            </p>
+<p>
+              We'll begin our sample program with the needed includes:
+            </p>
+<p>
+            </p>
+<p>
+              
+</p>
+<pre class="programlisting"><span class="comment">// Boost
+</span><span class="preprocessor">#include</span> <span class="special">&lt;</span><span class="identifier">boost</span><span class="special">/</span><span class="identifier">math</span><span class="special">/</span><span class="identifier">distributions</span><span class="special">/</span><span class="identifier">students_t</span><span class="special">.</span><span class="identifier">hpp</span><span class="special">&gt;</span>
+   <span class="keyword">using</span> <span class="identifier">boost</span><span class="special">::</span><span class="identifier">math</span><span class="special">::</span><span class="identifier">students_t</span><span class="special">;</span>  <span class="comment">// Probability of students_t(df, t).
+</span>
+<span class="comment">// std
+</span><span class="preprocessor">#include</span> <span class="special">&lt;</span><span class="identifier">iostream</span><span class="special">&gt;</span>
+   <span class="keyword">using</span> <span class="identifier">std</span><span class="special">::</span><span class="identifier">cout</span><span class="special">;</span>
+   <span class="keyword">using</span> <span class="identifier">std</span><span class="special">::</span><span class="identifier">endl</span><span class="special">;</span>
+
+<span class="preprocessor">#include</span> <span class="special">&lt;</span><span class="identifier">stdexcept</span><span class="special">&gt;</span>
+   <span class="keyword">using</span> <span class="identifier">std</span><span class="special">::</span><span class="identifier">exception</span><span class="special">;</span></pre>
+<p>
+            </p>
+<p>
+            </p>
+<p>
+              Next we'll define the program's main() to call the student's t distribution
+              with an invalid degrees of freedom parameter, the program is set up
+              to handle either an exception or a NaN:
+            </p>
+<p>
+            </p>
+<p>
+              
+</p>
+<pre class="programlisting"><span class="keyword">int</span> <span class="identifier">main</span><span class="special">()</span>
+<span class="special">{</span>
+   <span class="identifier">cout</span> <span class="special">&lt;&lt;</span> <span class="string">"Example error handling using Student's t function. "</span> <span class="special">&lt;&lt;</span> <span class="identifier">endl</span><span class="special">;</span>
+   <span class="identifier">cout</span> <span class="special">&lt;&lt;</span> <span class="string">"BOOST_MATH_DOMAIN_ERROR_POLICY is set to: "</span>
+      <span class="special">&lt;&lt;</span> <span class="identifier">BOOST_STRINGIZE</span><span class="special">(</span><span class="identifier">BOOST_MATH_DOMAIN_ERROR_POLICY</span><span class="special">)</span> <span class="special">&lt;&lt;</span> <span class="identifier">endl</span><span class="special">;</span>
+
+   <span class="keyword">double</span> <span class="identifier">degrees_of_freedom</span> <span class="special">=</span> <span class="special">-</span><span class="number">1</span><span class="special">;</span> <span class="comment">// A bad argument!
+</span>   <span class="keyword">double</span> <span class="identifier">t</span> <span class="special">=</span> <span class="number">10</span><span class="special">;</span>
+
+   <span class="keyword">try</span>
+   <span class="special">{</span>
+      <span class="identifier">errno</span> <span class="special">=</span> <span class="number">0</span><span class="special">;</span>
+      <span class="identifier">students_t</span> <span class="identifier">dist</span><span class="special">(</span><span class="identifier">degrees_of_freedom</span><span class="special">);</span> <span class="comment">// exception is thrown here if enabled
+</span>      <span class="keyword">double</span> <span class="identifier">p</span> <span class="special">=</span> <span class="identifier">cdf</span><span class="special">(</span><span class="identifier">dist</span><span class="special">,</span> <span class="identifier">t</span><span class="special">);</span>
+      <span class="comment">// test for error reported by other means:
+</span>      <span class="keyword">if</span><span class="special">((</span><span class="identifier">boost</span><span class="special">::</span><span class="identifier">math</span><span class="special">::</span><span class="identifier">isnan</span><span class="special">)(</span><span class="identifier">p</span><span class="special">))</span>
+      <span class="special">{</span>
+         <span class="identifier">cout</span> <span class="special">&lt;&lt;</span> <span class="string">"cdf returned a NaN!"</span> <span class="special">&lt;&lt;</span> <span class="identifier">endl</span><span class="special">;</span>
+         <span class="identifier">cout</span> <span class="special">&lt;&lt;</span> <span class="string">"errno is set to: "</span> <span class="special">&lt;&lt;</span> <span class="identifier">errno</span> <span class="special">&lt;&lt;</span> <span class="identifier">endl</span><span class="special">;</span>
+      <span class="special">}</span>
+      <span class="keyword">else</span>
+         <span class="identifier">cout</span> <span class="special">&lt;&lt;</span> <span class="string">"Probability of Student's t is "</span> <span class="special">&lt;&lt;</span> <span class="identifier">p</span> <span class="special">&lt;&lt;</span> <span class="identifier">endl</span><span class="special">;</span>
+   <span class="special">}</span>
+   <span class="keyword">catch</span><span class="special">(</span><span class="keyword">const</span> <span class="identifier">std</span><span class="special">::</span><span class="identifier">exception</span><span class="special">&amp;</span> <span class="identifier">e</span><span class="special">)</span>
+   <span class="special">{</span>
+      <span class="identifier">std</span><span class="special">::</span><span class="identifier">cout</span> <span class="special">&lt;&lt;</span>
+         <span class="string">"\n"</span><span class="string">"Message from thrown exception was:\n   "</span> <span class="special">&lt;&lt;</span> <span class="identifier">e</span><span class="special">.</span><span class="identifier">what</span><span class="special">()</span> <span class="special">&lt;&lt;</span> <span class="identifier">std</span><span class="special">::</span><span class="identifier">endl</span><span class="special">;</span>
+   <span class="special">}</span>
+
+   <span class="keyword">return</span> <span class="number">0</span><span class="special">;</span>
+<span class="special">}</span> <span class="comment">// int main()</span></pre>
+<p>
+            </p>
+<p>
+            </p>
+<p>
+              Here's what the program output looks like with a default build (one
+              that does throw exceptions):
+            </p>
+<p>
+            
+</p>
+<pre class="programlisting">Example error handling using Student's t function.
+BOOST_MATH_DOMAIN_ERROR_POLICY is set to: throw_on_error
+
+Message from thrown exception was:
+   Error in function boost::math::students_t_distribution&lt;double&gt;::students_t_distribution:
+   Degrees of freedom argument is -1, but must be &gt; 0 !
+</pre>
+<p>
+            </p>
+<p>
+              Alternatively let's build with:
+            </p>
+<p>
+            
+</p>
+<pre class="programlisting"><span class="preprocessor">#define</span> <span class="identifier">BOOST_MATH_DOMAIN_ERROR_POLICY</span> <span class="identifier">ignore_error</span>
+</pre>
+<p>
+            </p>
+<p>
+              Now the program output is:
+            </p>
+<p>
+            
+</p>
+<pre class="programlisting">Example error handling using Student's t function.
+BOOST_MATH_DOMAIN_ERROR_POLICY is set to: ignore_error
+cdf returned a NaN!
+errno is set to: 0
+</pre>
+<p>
+            </p>
+<p>
+              And finally let's build with:
+            </p>
+<p>
+            
+</p>
+<pre class="programlisting"><span class="preprocessor">#define</span> <span class="identifier">BOOST_MATH_DOMAIN_ERROR_POLICY</span> <span class="identifier">errno_on_error</span>
+</pre>
+<p>
+            </p>
+<p>
+              Which gives the output:
+            </p>
+<p>
+            
+</p>
+<pre class="programlisting">Example error handling using Student's t function.
+BOOST_MATH_DOMAIN_ERROR_POLICY is set to: errno_on_error
+cdf returned a NaN!
+errno is set to: 33
+</pre>
+<p>
+          </p>
+<div class="caution"><table border="0" summary="Caution">
+<tr>
+<td rowspan="2" align="center" valign="top" width="25"><img alt="[Caution]" src="../../../../../../doc/html/images/caution.png"></td>
+<th align="left">Caution</th>
+</tr>
+<tr><td align="left" valign="top">
+<p>
+              If throwing of exceptions is enabled (the default) but you do <span class="bold"><strong>not</strong></span> have try &amp; catch block, then the program
+              will terminate with an uncaught exception and probably abort.
+            </p>
+<p>
+              Therefore to get the benefit of helpful error messages, enabling <span class="bold"><strong>all exceptions and using try &amp; catch</strong></span> is
+              recommended for most applications.
+            </p>
+<p>
+              However, for simplicity, the is not done for most examples.
+            </p>
+</td></tr>
+</table></div>
+</div>
+<table xmlns:rev="http://www.cs.rpi.edu/~gregod/boost/tools/doc/revision" width="100%"><tr>
+<td align="left"></td>
+<td align="right"><div class="copyright-footer">Copyright © 2006 , 2007, 2008 John Maddock, Paul A. Bristow, Hubert
+      Holin, Xiaogang Zhang, Bruno Lalande and Gautam Sewani<p>
+        Distributed under the Boost Software License, Version 1.0. (See accompanying
+        file LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_0.txt)
+      </p>
+</div></td>
+</tr></table>
+<hr>
+<div class="spirit-nav">
+<a accesskey="p" href="nccs_eg/nccs_power_eg.html"><img src="../../../../../../doc/html/images/prev.png" alt="Prev"></a><a accesskey="u" href="../weg.html"><img src="../../../../../../doc/html/images/up.png" alt="Up"></a><a accesskey="h" href="../../../../index.html"><img src="../../../../../../doc/html/images/home.png" alt="Home"></a><a accesskey="n" href="find_eg.html"><img src="../../../../../../doc/html/images/next.png" alt="Next"></a>
+</div>
+</body>
+</html>

Added: sandbox/tools/auto_index/example/math/doc/sf_and_dist/html/math_toolkit/dist/stat_tut/weg/f_eg.html
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--- (empty file)
+++ sandbox/tools/auto_index/example/math/doc/sf_and_dist/html/math_toolkit/dist/stat_tut/weg/f_eg.html	2008-11-28 05:25:28 EST (Fri, 28 Nov 2008)
@@ -0,0 +1,330 @@
+<html>
+<head>
+<meta http-equiv="Content-Type" content="text/html; charset=ISO-8859-1">
+<title>F Distribution Examples</title>
+<link rel="stylesheet" href="../../../../boostbook.css" type="text/css">
+<meta name="generator" content="DocBook XSL Stylesheets Vsnapshot_8125">
+<link rel="home" href="../../../../index.html" title="Math Toolkit">
+<link rel="up" href="../weg.html" title="Worked Examples">
+<link rel="prev" href="cs_eg/chi_sq_size.html" title="Estimating the Required Sample Sizes for a Chi-Square Test for the Standard Deviation">
+<link rel="next" href="binom_eg.html" title="Binomial Distribution Examples">
+</head>
+<body bgcolor="white" text="black" link="#0000FF" vlink="#840084" alink="#0000FF">
+<table cellpadding="2" width="100%"><tr>
+<td valign="top"><img alt="Boost C++ Libraries" width="277" height="86" src="../../../../../../boost.png"></td>
+<td align="center">Home</td>
+<td align="center">Libraries</td>
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+<td align="center">More</td>
+</tr></table>
+<hr>
+<div class="spirit-nav">
+<a accesskey="p" href="cs_eg/chi_sq_size.html"><img src="../../../../../../doc/html/images/prev.png" alt="Prev"></a><a accesskey="u" href="../weg.html"><img src="../../../../../../doc/html/images/up.png" alt="Up"></a><a accesskey="h" href="../../../../index.html"><img src="../../../../../../doc/html/images/home.png" alt="Home"></a><a accesskey="n" href="binom_eg.html"><img src="../../../../../../doc/html/images/next.png" alt="Next"></a>
+</div>
+<div class="section" lang="en">
+<div class="titlepage"><div><div><h5 class="title">
+<a name="math_toolkit.dist.stat_tut.weg.f_eg"></a><a class="link" href="f_eg.html" title="F Distribution Examples"> F Distribution
+          Examples</a>
+</h5></div></div></div>
+<p>
+            Imagine that you want to compare the standard deviations of two sample
+            to determine if they differ in any significant way, in this situation
+            you use the F distribution and perform an F-test. This situation commonly
+            occurs when conducting a process change comparison: "is a new process
+            more consistent that the old one?".
+          </p>
+<p>
+            In this example we'll be using the data for ceramic strength from http://www.itl.nist.gov/div898/handbook/eda/section4/eda42a1.htm.
+            The data for this case study were collected by Said Jahanmir of the NIST
+            Ceramics Division in 1996 in connection with a NIST/industry ceramics
+            consortium for strength optimization of ceramic strength.
+          </p>
+<p>
+            The example program is f_test.cpp,
+            program output has been deliberately made as similar as possible to the
+            DATAPLOT output in the corresponding <a href="http://www.itl.nist.gov/div898/handbook/eda/section3/eda359.htm" target="_top">NIST
+            EngineeringStatistics Handbook example</a>.
+          </p>
+<p>
+            We'll begin by defining the procedure to conduct the test:
+          </p>
+<pre class="programlisting"><span class="keyword">void</span> <span class="identifier">f_test</span><span class="special">(</span>
+    <span class="keyword">double</span> <span class="identifier">sd1</span><span class="special">,</span>     <span class="comment">// Sample 1 std deviation
+</span>    <span class="keyword">double</span> <span class="identifier">sd2</span><span class="special">,</span>     <span class="comment">// Sample 2 std deviation
+</span>    <span class="keyword">double</span> <span class="identifier">N1</span><span class="special">,</span>      <span class="comment">// Sample 1 size
+</span>    <span class="keyword">double</span> <span class="identifier">N2</span><span class="special">,</span>      <span class="comment">// Sample 2 size
+</span>    <span class="keyword">double</span> <span class="identifier">alpha</span><span class="special">)</span>  <span class="comment">// Significance level
+</span><span class="special">{</span>
+</pre>
+<p>
+            The procedure begins by printing out a summary of our input data:
+          </p>
+<pre class="programlisting"><span class="keyword">using</span> <span class="keyword">namespace</span> <span class="identifier">std</span><span class="special">;</span>
+<span class="keyword">using</span> <span class="keyword">namespace</span> <span class="identifier">boost</span><span class="special">::</span><span class="identifier">math</span><span class="special">;</span>
+
+<span class="comment">// Print header:
+</span><span class="identifier">cout</span> <span class="special">&lt;&lt;</span>
+   <span class="string">"____________________________________\n"</span>
+   <span class="string">"F test for equal standard deviations\n"</span>
+   <span class="string">"____________________________________\n\n"</span><span class="special">;</span>
+<span class="identifier">cout</span> <span class="special">&lt;&lt;</span> <span class="identifier">setprecision</span><span class="special">(</span><span class="number">5</span><span class="special">);</span>
+<span class="identifier">cout</span> <span class="special">&lt;&lt;</span> <span class="string">"Sample 1:\n"</span><span class="special">;</span>
+<span class="identifier">cout</span> <span class="special">&lt;&lt;</span> <span class="identifier">setw</span><span class="special">(</span><span class="number">55</span><span class="special">)</span> <span class="special">&lt;&lt;</span> <span class="identifier">left</span> <span class="special">&lt;&lt;</span> <span class="string">"Number of Observations"</span> <span class="special">&lt;&lt;</span> <span class="string">"=  "</span> <span class="special">&lt;&lt;</span> <span class="identifier">N1</span> <span class="special">&lt;&lt;</span> <span class="string">"\n"</span><span class="special">;</span>
+<span class="identifier">cout</span> <span class="special">&lt;&lt;</span> <span class="identifier">setw</span><span class="special">(</span><span class="number">55</span><span class="special">)</span> <span class="special">&lt;&lt;</span> <span class="identifier">left</span> <span class="special">&lt;&lt;</span> <span class="string">"Sample Standard Deviation"</span> <span class="special">&lt;&lt;</span> <span class="string">"=  "</span> <span class="special">&lt;&lt;</span> <span class="identifier">sd1</span> <span class="special">&lt;&lt;</span> <span class="string">"\n\n"</span><span class="special">;</span>
+<span class="identifier">cout</span> <span class="special">&lt;&lt;</span> <span class="string">"Sample 2:\n"</span><span class="special">;</span>
+<span class="identifier">cout</span> <span class="special">&lt;&lt;</span> <span class="identifier">setw</span><span class="special">(</span><span class="number">55</span><span class="special">)</span> <span class="special">&lt;&lt;</span> <span class="identifier">left</span> <span class="special">&lt;&lt;</span> <span class="string">"Number of Observations"</span> <span class="special">&lt;&lt;</span> <span class="string">"=  "</span> <span class="special">&lt;&lt;</span> <span class="identifier">N2</span> <span class="special">&lt;&lt;</span> <span class="string">"\n"</span><span class="special">;</span>
+<span class="identifier">cout</span> <span class="special">&lt;&lt;</span> <span class="identifier">setw</span><span class="special">(</span><span class="number">55</span><span class="special">)</span> <span class="special">&lt;&lt;</span> <span class="identifier">left</span> <span class="special">&lt;&lt;</span> <span class="string">"Sample Standard Deviation"</span> <span class="special">&lt;&lt;</span> <span class="string">"=  "</span> <span class="special">&lt;&lt;</span> <span class="identifier">sd2</span> <span class="special">&lt;&lt;</span> <span class="string">"\n\n"</span><span class="special">;</span>
+</pre>
+<p>
+            The test statistic for an F-test is simply the ratio of the square of
+            the two standard deviations:
+          </p>
+<p>
+            F = s<sub>1</sub><sup>2</sup> / s<sub>2</sub><sup>2</sup>
+          </p>
+<p>
+            where s<sub>1</sub> is the standard deviation of the first sample and s<sub>2</sub>
+is the standard
+            deviation of the second sample. Or in code:
+          </p>
+<pre class="programlisting"><span class="keyword">double</span> <span class="identifier">F</span> <span class="special">=</span> <span class="special">(</span><span class="identifier">sd1</span> <span class="special">/</span> <span class="identifier">sd2</span><span class="special">);</span>
+<span class="identifier">F</span> <span class="special">*=</span> <span class="identifier">F</span><span class="special">;</span>
+<span class="identifier">cout</span> <span class="special">&lt;&lt;</span> <span class="identifier">setw</span><span class="special">(</span><span class="number">55</span><span class="special">)</span> <span class="special">&lt;&lt;</span> <span class="identifier">left</span> <span class="special">&lt;&lt;</span> <span class="string">"Test Statistic"</span> <span class="special">&lt;&lt;</span> <span class="string">"=  "</span> <span class="special">&lt;&lt;</span> <span class="identifier">F</span> <span class="special">&lt;&lt;</span> <span class="string">"\n\n"</span><span class="special">;</span>
+</pre>
+<p>
+            At this point a word of caution: the F distribution is asymmetric, so
+            we have to be careful how we compute the tests, the following table summarises
+            the options available:
+          </p>
+<div class="informaltable"><table class="table">
+<colgroup>
+<col>
+<col>
+</colgroup>
+<thead><tr>
+<th>
+                  <p>
+                    Hypothesis
+                  </p>
+                  </th>
+<th>
+                  <p>
+                    Test
+                  </p>
+                  </th>
+</tr></thead>
+<tbody>
+<tr>
+<td>
+                  <p>
+                    The null-hypothesis: there is no difference in standard deviations
+                    (two sided test)
+                  </p>
+                  </td>
+<td>
+                  <p>
+                    Reject if F &lt;= F<sub>(1-alpha/2; N1-1, N2-1)</sub> or F &gt;= F<sub>(alpha/2;
+                    N1-1, N2-1)</sub>
+                  </p>
+                  </td>
+</tr>
+<tr>
+<td>
+                  <p>
+                    The alternative hypothesis: there is a difference in means (two
+                    sided test)
+                  </p>
+                  </td>
+<td>
+                  <p>
+                    Reject if F<sub>(1-alpha/2; N1-1, N2-1)</sub> &lt;= F &lt;= F<sub>(alpha/2; N1-1,
+                    N2-1)</sub>
+                  </p>
+                  </td>
+</tr>
+<tr>
+<td>
+                  <p>
+                    The alternative hypothesis: Standard deviation of sample 1 is
+                    greater than that of sample 2
+                  </p>
+                  </td>
+<td>
+                  <p>
+                    Reject if F &lt; F<sub>(alpha; N1-1, N2-1)</sub>
+                  </p>
+                  </td>
+</tr>
+<tr>
+<td>
+                  <p>
+                    The alternative hypothesis: Standard deviation of sample 1 is
+                    less than that of sample 2
+                  </p>
+                  </td>
+<td>
+                  <p>
+                    Reject if F &gt; F<sub>(1-alpha; N1-1, N2-1)</sub>
+                  </p>
+                  </td>
+</tr>
+</tbody>
+</table></div>
+<p>
+            Where F<sub>(1-alpha; N1-1, N2-1)</sub> is the lower critical value of the F distribution
+            with degrees of freedom N1-1 and N2-1, and F<sub>(alpha; N1-1, N2-1)</sub> is the
+            upper critical value of the F distribution with degrees of freedom N1-1
+            and N2-1.
+          </p>
+<p>
+            The upper and lower critical values can be computed using the quantile
+            function:
+          </p>
+<p>
+            F<sub>(1-alpha; N1-1, N2-1)</sub> = <code class="computeroutput"><span class="identifier">quantile</span><span class="special">(</span><span class="identifier">fisher_f</span><span class="special">(</span><span class="identifier">N1</span><span class="special">-</span><span class="number">1</span><span class="special">,</span>
+            <span class="identifier">N2</span><span class="special">-</span><span class="number">1</span><span class="special">),</span> <span class="identifier">alpha</span><span class="special">)</span></code>
+          </p>
+<p>
+            F<sub>(alpha; N1-1, N2-1)</sub> = <code class="computeroutput"><span class="identifier">quantile</span><span class="special">(</span><span class="identifier">complement</span><span class="special">(</span><span class="identifier">fisher_f</span><span class="special">(</span><span class="identifier">N1</span><span class="special">-</span><span class="number">1</span><span class="special">,</span>
+            <span class="identifier">N2</span><span class="special">-</span><span class="number">1</span><span class="special">),</span> <span class="identifier">alpha</span><span class="special">))</span></code>
+          </p>
+<p>
+            In our example program we need both upper and lower critical values for
+            alpha and for alpha/2:
+          </p>
+<pre class="programlisting"><span class="keyword">double</span> <span class="identifier">ucv</span> <span class="special">=</span> <span class="identifier">quantile</span><span class="special">(</span><span class="identifier">complement</span><span class="special">(</span><span class="identifier">dist</span><span class="special">,</span> <span class="identifier">alpha</span><span class="special">));</span>
+<span class="keyword">double</span> <span class="identifier">ucv2</span> <span class="special">=</span> <span class="identifier">quantile</span><span class="special">(</span><span class="identifier">complement</span><span class="special">(</span><span class="identifier">dist</span><span class="special">,</span> <span class="identifier">alpha</span> <span class="special">/</span> <span class="number">2</span><span class="special">));</span>
+<span class="keyword">double</span> <span class="identifier">lcv</span> <span class="special">=</span> <span class="identifier">quantile</span><span class="special">(</span><span class="identifier">dist</span><span class="special">,</span> <span class="identifier">alpha</span><span class="special">);</span>
+<span class="keyword">double</span> <span class="identifier">lcv2</span> <span class="special">=</span> <span class="identifier">quantile</span><span class="special">(</span><span class="identifier">dist</span><span class="special">,</span> <span class="identifier">alpha</span> <span class="special">/</span> <span class="number">2</span><span class="special">);</span>
+<span class="identifier">cout</span> <span class="special">&lt;&lt;</span> <span class="identifier">setw</span><span class="special">(</span><span class="number">55</span><span class="special">)</span> <span class="special">&lt;&lt;</span> <span class="identifier">left</span> <span class="special">&lt;&lt;</span> <span class="string">"Upper Critical Value at alpha: "</span> <span class="special">&lt;&lt;</span> <span class="string">"=  "</span>
+   <span class="special">&lt;&lt;</span> <span class="identifier">setprecision</span><span class="special">(</span><span class="number">3</span><span class="special">)</span> <span class="special">&lt;&lt;</span> <span class="identifier">scientific</span> <span class="special">&lt;&lt;</span> <span class="identifier">ucv</span> <span class="special">&lt;&lt;</span> <span class="string">"\n"</span><span class="special">;</span>
+<span class="identifier">cout</span> <span class="special">&lt;&lt;</span> <span class="identifier">setw</span><span class="special">(</span><span class="number">55</span><span class="special">)</span> <span class="special">&lt;&lt;</span> <span class="identifier">left</span> <span class="special">&lt;&lt;</span> <span class="string">"Upper Critical Value at alpha/2: "</span> <span class="special">&lt;&lt;</span> <span class="string">"=  "</span>
+   <span class="special">&lt;&lt;</span> <span class="identifier">setprecision</span><span class="special">(</span><span class="number">3</span><span class="special">)</span> <span class="special">&lt;&lt;</span> <span class="identifier">scientific</span> <span class="special">&lt;&lt;</span> <span class="identifier">ucv2</span> <span class="special">&lt;&lt;</span> <span class="string">"\n"</span><span class="special">;</span>
+<span class="identifier">cout</span> <span class="special">&lt;&lt;</span> <span class="identifier">setw</span><span class="special">(</span><span class="number">55</span><span class="special">)</span> <span class="special">&lt;&lt;</span> <span class="identifier">left</span> <span class="special">&lt;&lt;</span> <span class="string">"Lower Critical Value at alpha: "</span> <span class="special">&lt;&lt;</span> <span class="string">"=  "</span>
+   <span class="special">&lt;&lt;</span> <span class="identifier">setprecision</span><span class="special">(</span><span class="number">3</span><span class="special">)</span> <span class="special">&lt;&lt;</span> <span class="identifier">scientific</span> <span class="special">&lt;&lt;</span> <span class="identifier">lcv</span> <span class="special">&lt;&lt;</span> <span class="string">"\n"</span><span class="special">;</span>
+<span class="identifier">cout</span> <span class="special">&lt;&lt;</span> <span class="identifier">setw</span><span class="special">(</span><span class="number">55</span><span class="special">)</span> <span class="special">&lt;&lt;</span> <span class="identifier">left</span> <span class="special">&lt;&lt;</span> <span class="string">"Lower Critical Value at alpha/2: "</span> <span class="special">&lt;&lt;</span> <span class="string">"=  "</span>
+   <span class="special">&lt;&lt;</span> <span class="identifier">setprecision</span><span class="special">(</span><span class="number">3</span><span class="special">)</span> <span class="special">&lt;&lt;</span> <span class="identifier">scientific</span> <span class="special">&lt;&lt;</span> <span class="identifier">lcv2</span> <span class="special">&lt;&lt;</span> <span class="string">"\n\n"</span><span class="special">;</span>
+</pre>
+<p>
+            The final step is to perform the comparisons given above, and print out
+            whether the hypothesis is rejected or not:
+          </p>
+<pre class="programlisting"><span class="identifier">cout</span> <span class="special">&lt;&lt;</span> <span class="identifier">setw</span><span class="special">(</span><span class="number">55</span><span class="special">)</span> <span class="special">&lt;&lt;</span> <span class="identifier">left</span> <span class="special">&lt;&lt;</span>
+   <span class="string">"Results for Alternative Hypothesis and alpha"</span> <span class="special">&lt;&lt;</span> <span class="string">"=  "</span>
+   <span class="special">&lt;&lt;</span> <span class="identifier">setprecision</span><span class="special">(</span><span class="number">4</span><span class="special">)</span> <span class="special">&lt;&lt;</span> <span class="identifier">fixed</span> <span class="special">&lt;&lt;</span> <span class="identifier">alpha</span> <span class="special">&lt;&lt;</span> <span class="string">"\n\n"</span><span class="special">;</span>
+<span class="identifier">cout</span> <span class="special">&lt;&lt;</span> <span class="string">"Alternative Hypothesis                                    Conclusion\n"</span><span class="special">;</span>
+
+<span class="identifier">cout</span> <span class="special">&lt;&lt;</span> <span class="string">"Standard deviations are unequal (two sided test)          "</span><span class="special">;</span>
+<span class="keyword">if</span><span class="special">((</span><span class="identifier">ucv2</span> <span class="special">&lt;</span> <span class="identifier">F</span><span class="special">)</span> <span class="special">||</span> <span class="special">(</span><span class="identifier">lcv2</span> <span class="special">&gt;</span> <span class="identifier">F</span><span class="special">))</span>
+   <span class="identifier">cout</span> <span class="special">&lt;&lt;</span> <span class="string">"ACCEPTED\n"</span><span class="special">;</span>
+<span class="keyword">else</span>
+   <span class="identifier">cout</span> <span class="special">&lt;&lt;</span> <span class="string">"REJECTED\n"</span><span class="special">;</span>
+
+<span class="identifier">cout</span> <span class="special">&lt;&lt;</span> <span class="string">"Standard deviation 1 is less than standard deviation 2    "</span><span class="special">;</span>
+<span class="keyword">if</span><span class="special">(</span><span class="identifier">lcv</span> <span class="special">&gt;</span> <span class="identifier">F</span><span class="special">)</span>
+   <span class="identifier">cout</span> <span class="special">&lt;&lt;</span> <span class="string">"ACCEPTED\n"</span><span class="special">;</span>
+<span class="keyword">else</span>
+   <span class="identifier">cout</span> <span class="special">&lt;&lt;</span> <span class="string">"REJECTED\n"</span><span class="special">;</span>
+
+<span class="identifier">cout</span> <span class="special">&lt;&lt;</span> <span class="string">"Standard deviation 1 is greater than standard deviation 2 "</span><span class="special">;</span>
+<span class="keyword">if</span><span class="special">(</span><span class="identifier">ucv</span> <span class="special">&lt;</span> <span class="identifier">F</span><span class="special">)</span>
+   <span class="identifier">cout</span> <span class="special">&lt;&lt;</span> <span class="string">"ACCEPTED\n"</span><span class="special">;</span>
+<span class="keyword">else</span>
+   <span class="identifier">cout</span> <span class="special">&lt;&lt;</span> <span class="string">"REJECTED\n"</span><span class="special">;</span>
+<span class="identifier">cout</span> <span class="special">&lt;&lt;</span> <span class="identifier">endl</span> <span class="special">&lt;&lt;</span> <span class="identifier">endl</span><span class="special">;</span>
+</pre>
+<p>
+            Using the ceramic strength data as an example we get the following output:
+          </p>
+<pre class="programlisting">F test for equal standard deviations
+____________________________________
+
+Sample 1:
+Number of Observations                                 =  240
+Sample Standard Deviation                              =  65.549
+
+Sample 2:
+Number of Observations                                 =  240
+Sample Standard Deviation                              =  61.854
+
+Test Statistic                                         =  1.123
+
+CDF of test statistic:                                 =  8.148e-001
+Upper Critical Value at alpha:                         =  1.238e+000
+Upper Critical Value at alpha/2:                       =  1.289e+000
+Lower Critical Value at alpha:                         =  8.080e-001
+Lower Critical Value at alpha/2:                       =  7.756e-001
+
+Results for Alternative Hypothesis and alpha           =  0.0500
+
+Alternative Hypothesis                                    Conclusion
+Standard deviations are unequal (two sided test)          REJECTED
+Standard deviation 1 is less than standard deviation 2    REJECTED
+Standard deviation 1 is greater than standard deviation 2 REJECTED
+</pre>
+<p>
+            In this case we are unable to reject the null-hypothesis, and must instead
+            reject the alternative hypothesis.
+          </p>
+<p>
+            By contrast let's see what happens when we use some different <a href="http://www.itl.nist.gov/div898/handbook/prc/section3/prc32.htm" target="_top">sample
+            data</a>:, once again from the NIST Engineering Statistics Handbook:
+            A new procedure to assemble a device is introduced and tested for possible
+            improvement in time of assembly. The question being addressed is whether
+            the standard deviation of the new assembly process (sample 2) is better
+            (i.e., smaller) than the standard deviation for the old assembly process
+            (sample 1).
+          </p>
+<pre class="programlisting">____________________________________
+F test for equal standard deviations
+____________________________________
+
+Sample 1:
+Number of Observations                                 =  11.00000
+Sample Standard Deviation                              =  4.90820
+
+Sample 2:
+Number of Observations                                 =  9.00000
+Sample Standard Deviation                              =  2.58740
+
+Test Statistic                                         =  3.59847
+
+CDF of test statistic:                                 =  9.589e-001
+Upper Critical Value at alpha:                         =  3.347e+000
+Upper Critical Value at alpha/2:                       =  4.295e+000
+Lower Critical Value at alpha:                         =  3.256e-001
+Lower Critical Value at alpha/2:                       =  2.594e-001
+
+Results for Alternative Hypothesis and alpha           =  0.0500
+
+Alternative Hypothesis                                    Conclusion
+Standard deviations are unequal (two sided test)          REJECTED
+Standard deviation 1 is less than standard deviation 2    REJECTED
+Standard deviation 1 is greater than standard deviation 2 ACCEPTED
+</pre>
+<p>
+            In this case we take our null hypothesis as "standard deviation
+            1 is less than or equal to standard deviation 2", since this represents
+            the "no change" situation. So we want to compare the upper
+            critical value at <span class="emphasis"><em>alpha</em></span> (a one sided test) with
+            the test statistic, and since 3.35 &lt; 3.6 this hypothesis must be rejected.
+            We therefore conclude that there is a change for the better in our standard
+            deviation.
+          </p>
+</div>
+<table xmlns:rev="http://www.cs.rpi.edu/~gregod/boost/tools/doc/revision" width="100%"><tr>
+<td align="left"></td>
+<td align="right"><div class="copyright-footer">Copyright © 2006 , 2007, 2008 John Maddock, Paul A. Bristow, Hubert
+      Holin, Xiaogang Zhang, Bruno Lalande and Gautam Sewani<p>
+        Distributed under the Boost Software License, Version 1.0. (See accompanying
+        file LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_0.txt)
+      </p>
+</div></td>
+</tr></table>
+<hr>
+<div class="spirit-nav">
+<a accesskey="p" href="cs_eg/chi_sq_size.html"><img src="../../../../../../doc/html/images/prev.png" alt="Prev"></a><a accesskey="u" href="../weg.html"><img src="../../../../../../doc/html/images/up.png" alt="Up"></a><a accesskey="h" href="../../../../index.html"><img src="../../../../../../doc/html/images/home.png" alt="Home"></a><a accesskey="n" href="binom_eg.html"><img src="../../../../../../doc/html/images/next.png" alt="Next"></a>
+</div>
+</body>
+</html>

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+<td align="center">Home</td>
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+</div>
+<div class="section" lang="en">
+<div class="titlepage"><div><div><h5 class="title">
+<a name="math_toolkit.dist.stat_tut.weg.find_eg"></a><a class="link" href="find_eg.html" title="Find Location and Scale Examples"> Find Location
+          and Scale Examples</a>
+</h5></div></div></div>
+<div class="toc"><dl>
+<dt><span class="section"><a href="find_eg/find_location_eg.html">
+            Find Location (Mean) Example</a></span></dt>
+<dt><span class="section"><a href="find_eg/find_scale_eg.html">
+            Find Scale (Standard Deviation) Example</a></span></dt>
+<dt><span class="section"><a href="find_eg/find_mean_and_sd_eg.html">
+            Find mean and standard deviation example</a></span></dt>
+</dl></div>
+</div>
+<table xmlns:rev="http://www.cs.rpi.edu/~gregod/boost/tools/doc/revision" width="100%"><tr>
+<td align="left"></td>
+<td align="right"><div class="copyright-footer">Copyright © 2006 , 2007, 2008 John Maddock, Paul A. Bristow, Hubert
+      Holin, Xiaogang Zhang, Bruno Lalande and Gautam Sewani<p>
+        Distributed under the Boost Software License, Version 1.0. (See accompanying
+        file LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_0.txt)
+      </p>
+</div></td>
+</tr></table>
+<hr>
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@@ -0,0 +1,283 @@
+<html>
+<head>
+<meta http-equiv="Content-Type" content="text/html; charset=ISO-8859-1">
+<title>Find Location (Mean) Example</title>
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+</div>
+<div class="section" lang="en">
+<div class="titlepage"><div><div><h6 class="title">
+<a name="math_toolkit.dist.stat_tut.weg.find_eg.find_location_eg"></a><a class="link" href="find_location_eg.html" title="Find Location (Mean) Example">
+            Find Location (Mean) Example</a>
+</h6></div></div></div>
+<p>
+              </p>
+<p>
+                First we need some includes to access the normal distribution, the
+                algorithms to find location (and some std output of course).
+              </p>
+<p>
+              </p>
+<p>
+                
+</p>
+<pre class="programlisting"><span class="preprocessor">#include</span> <span class="special">&lt;</span><span class="identifier">boost</span><span class="special">/</span><span class="identifier">math</span><span class="special">/</span><span class="identifier">distributions</span><span class="special">/</span><span class="identifier">normal</span><span class="special">.</span><span class="identifier">hpp</span><span class="special">&gt;</span> <span class="comment">// for normal_distribution
+</span>  <span class="keyword">using</span> <span class="identifier">boost</span><span class="special">::</span><span class="identifier">math</span><span class="special">::</span><span class="identifier">normal</span><span class="special">;</span> <span class="comment">// typedef provides default type is double.
+</span><span class="preprocessor">#include</span> <span class="special">&lt;</span><span class="identifier">boost</span><span class="special">/</span><span class="identifier">math</span><span class="special">/</span><span class="identifier">distributions</span><span class="special">/</span><span class="identifier">cauchy</span><span class="special">.</span><span class="identifier">hpp</span><span class="special">&gt;</span> <span class="comment">// for cauchy_distribution
+</span>  <span class="keyword">using</span> <span class="identifier">boost</span><span class="special">::</span><span class="identifier">math</span><span class="special">::</span><span class="identifier">cauchy</span><span class="special">;</span> <span class="comment">// typedef provides default type is double.
+</span><span class="preprocessor">#include</span> <span class="special">&lt;</span><span class="identifier">boost</span><span class="special">/</span><span class="identifier">math</span><span class="special">/</span><span class="identifier">distributions</span><span class="special">/</span><span class="identifier">find_location</span><span class="special">.</span><span class="identifier">hpp</span><span class="special">&gt;</span>
+  <span class="keyword">using</span> <span class="identifier">boost</span><span class="special">::</span><span class="identifier">math</span><span class="special">::</span><span class="identifier">find_location</span><span class="special">;</span> <span class="comment">// for mean
+</span><span class="preprocessor">#include</span> <span class="special">&lt;</span><span class="identifier">boost</span><span class="special">/</span><span class="identifier">math</span><span class="special">/</span><span class="identifier">distributions</span><span class="special">/</span><span class="identifier">find_scale</span><span class="special">.</span><span class="identifier">hpp</span><span class="special">&gt;</span>
+  <span class="keyword">using</span> <span class="identifier">boost</span><span class="special">::</span><span class="identifier">math</span><span class="special">::</span><span class="identifier">find_scale</span><span class="special">;</span> <span class="comment">// for standard devation
+</span>  <span class="keyword">using</span> <span class="identifier">boost</span><span class="special">::</span><span class="identifier">math</span><span class="special">::</span><span class="identifier">complement</span><span class="special">;</span> <span class="comment">// Needed if you want to use the complement version.
+</span>  <span class="keyword">using</span> <span class="identifier">boost</span><span class="special">::</span><span class="identifier">math</span><span class="special">::</span><span class="identifier">policies</span><span class="special">::</span><span class="identifier">policy</span><span class="special">;</span>
+
+<span class="preprocessor">#include</span> <span class="special">&lt;</span><span class="identifier">iostream</span><span class="special">&gt;</span>
+  <span class="keyword">using</span> <span class="identifier">std</span><span class="special">::</span><span class="identifier">cout</span><span class="special">;</span> <span class="keyword">using</span> <span class="identifier">std</span><span class="special">::</span><span class="identifier">endl</span><span class="special">;</span>
+<span class="preprocessor">#include</span> <span class="special">&lt;</span><span class="identifier">iomanip</span><span class="special">&gt;</span>
+  <span class="keyword">using</span> <span class="identifier">std</span><span class="special">::</span><span class="identifier">setw</span><span class="special">;</span> <span class="keyword">using</span> <span class="identifier">std</span><span class="special">::</span><span class="identifier">setprecision</span><span class="special">;</span>
+<span class="preprocessor">#include</span> <span class="special">&lt;</span><span class="identifier">limits</span><span class="special">&gt;</span>
+  <span class="keyword">using</span> <span class="identifier">std</span><span class="special">::</span><span class="identifier">numeric_limits</span><span class="special">;</span>
+</pre>
+<p>
+              </p>
+<p>
+              </p>
+<p>
+                For this example, we will use the standard normal distribution, with
+                mean (location) zero and standard deviation (scale) unity. This is
+                also the default for this implementation.
+              </p>
+<p>
+              </p>
+<p>
+                
+</p>
+<pre class="programlisting"><span class="identifier">normal</span> <span class="identifier">N01</span><span class="special">;</span>  <span class="comment">// Default 'standard' normal distribution with zero mean and 
+</span><span class="keyword">double</span> <span class="identifier">sd</span> <span class="special">=</span> <span class="number">1.</span><span class="special">;</span> <span class="comment">// normal default standard deviation is 1.</span></pre>
+<p>
+              </p>
+<p>
+              </p>
+<p>
+                Suppose we want to find a different normal distribution whose mean
+                is shifted so that only fraction p (here 0.001 or 0.1%) are below
+                a certain chosen limit (here -2, two standard deviations).
+              </p>
+<p>
+              </p>
+<p>
+                
+</p>
+<pre class="programlisting"><span class="keyword">double</span> <span class="identifier">z</span> <span class="special">=</span> <span class="special">-</span><span class="number">2.</span><span class="special">;</span> <span class="comment">// z to give prob p
+</span><span class="keyword">double</span> <span class="identifier">p</span> <span class="special">=</span> <span class="number">0.001</span><span class="special">;</span> <span class="comment">// only 0.1% below z
+</span>
+<span class="identifier">cout</span> <span class="special">&lt;&lt;</span> <span class="string">"Normal distribution with mean = "</span> <span class="special">&lt;&lt;</span> <span class="identifier">N01</span><span class="special">.</span><span class="identifier">location</span><span class="special">()</span>
+  <span class="special">&lt;&lt;</span> <span class="string">", standard deviation "</span> <span class="special">&lt;&lt;</span> <span class="identifier">N01</span><span class="special">.</span><span class="identifier">scale</span><span class="special">()</span>
+  <span class="special">&lt;&lt;</span> <span class="string">", has "</span> <span class="special">&lt;&lt;</span> <span class="string">"fraction &lt;= "</span> <span class="special">&lt;&lt;</span> <span class="identifier">z</span> 
+  <span class="special">&lt;&lt;</span> <span class="string">", p = "</span>  <span class="special">&lt;&lt;</span> <span class="identifier">cdf</span><span class="special">(</span><span class="identifier">N01</span><span class="special">,</span> <span class="identifier">z</span><span class="special">)</span> <span class="special">&lt;&lt;</span> <span class="identifier">endl</span><span class="special">;</span>
+<span class="identifier">cout</span> <span class="special">&lt;&lt;</span> <span class="string">"Normal distribution with mean = "</span> <span class="special">&lt;&lt;</span> <span class="identifier">N01</span><span class="special">.</span><span class="identifier">location</span><span class="special">()</span>
+  <span class="special">&lt;&lt;</span> <span class="string">", standard deviation "</span> <span class="special">&lt;&lt;</span> <span class="identifier">N01</span><span class="special">.</span><span class="identifier">scale</span><span class="special">()</span>
+  <span class="special">&lt;&lt;</span> <span class="string">", has "</span> <span class="special">&lt;&lt;</span> <span class="string">"fraction &gt; "</span> <span class="special">&lt;&lt;</span> <span class="identifier">z</span>
+  <span class="special">&lt;&lt;</span> <span class="string">", p = "</span>  <span class="special">&lt;&lt;</span> <span class="identifier">cdf</span><span class="special">(</span><span class="identifier">complement</span><span class="special">(</span><span class="identifier">N01</span><span class="special">,</span> <span class="identifier">z</span><span class="special">))</span> <span class="special">&lt;&lt;</span> <span class="identifier">endl</span><span class="special">;</span> <span class="comment">// Note: uses complement.</span></pre>
+<p>
+              </p>
+<p>
+              
+</p>
+<pre class="programlisting">Normal distribution with mean = 0, standard deviation 1, has fraction &lt;= -2, p = 0.0227501
+Normal distribution with mean = 0, standard deviation 1, has fraction &gt; -2, p = 0.97725
+</pre>
+<p>
+              </p>
+<p>
+                We can now use ''find_location'' to give a new offset mean.
+              </p>
+<p>
+              </p>
+<p>
+                
+</p>
+<pre class="programlisting"><span class="keyword">double</span> <span class="identifier">l</span> <span class="special">=</span> <span class="identifier">find_location</span><span class="special">&lt;</span><span class="identifier">normal</span><span class="special">&gt;(</span><span class="identifier">z</span><span class="special">,</span> <span class="identifier">p</span><span class="special">,</span> <span class="identifier">sd</span><span class="special">);</span>
+<span class="identifier">cout</span> <span class="special">&lt;&lt;</span> <span class="string">"offset location (mean) = "</span> <span class="special">&lt;&lt;</span> <span class="identifier">l</span> <span class="special">&lt;&lt;</span> <span class="identifier">endl</span><span class="special">;</span></pre>
+<p>
+              </p>
+<p>
+              </p>
+<p>
+                that outputs:
+              </p>
+<p>
+              
+</p>
+<pre class="programlisting">offset location (mean) = 1.09023
+</pre>
+<p>
+              </p>
+<p>
+                showing that we need to shift the mean just over one standard deviation
+                from its previous value of zero.
+              </p>
+<p>
+              </p>
+<p>
+                Then we can check that we have achieved our objective by constructing
+                a new distribution with the offset mean (but same standard deviation):
+              </p>
+<p>
+              </p>
+<p>
+                
+</p>
+<pre class="programlisting"><span class="identifier">normal</span> <span class="identifier">np001pc</span><span class="special">(</span><span class="identifier">l</span><span class="special">,</span> <span class="identifier">sd</span><span class="special">);</span> <span class="comment">// Same standard_deviation (scale) but with mean (location) shifted.</span></pre>
+<p>
+              </p>
+<p>
+              </p>
+<p>
+                And re-calculating the fraction below our chosen limit.
+              </p>
+<p>
+              </p>
+<p>
+                
+</p>
+<pre class="programlisting"><span class="identifier">cout</span> <span class="special">&lt;&lt;</span> <span class="string">"Normal distribution with mean = "</span> <span class="special">&lt;&lt;</span> <span class="identifier">l</span> 
+    <span class="special">&lt;&lt;</span> <span class="string">" has "</span> <span class="special">&lt;&lt;</span> <span class="string">"fraction &lt;= "</span> <span class="special">&lt;&lt;</span> <span class="identifier">z</span> 
+    <span class="special">&lt;&lt;</span> <span class="string">", p = "</span>  <span class="special">&lt;&lt;</span> <span class="identifier">cdf</span><span class="special">(</span><span class="identifier">np001pc</span><span class="special">,</span> <span class="identifier">z</span><span class="special">)</span> <span class="special">&lt;&lt;</span> <span class="identifier">endl</span><span class="special">;</span>
+  <span class="identifier">cout</span> <span class="special">&lt;&lt;</span> <span class="string">"Normal distribution with mean = "</span> <span class="special">&lt;&lt;</span> <span class="identifier">l</span> 
+    <span class="special">&lt;&lt;</span> <span class="string">" has "</span> <span class="special">&lt;&lt;</span> <span class="string">"fraction &gt; "</span> <span class="special">&lt;&lt;</span> <span class="identifier">z</span> 
+    <span class="special">&lt;&lt;</span> <span class="string">", p = "</span>  <span class="special">&lt;&lt;</span> <span class="identifier">cdf</span><span class="special">(</span><span class="identifier">complement</span><span class="special">(</span><span class="identifier">np001pc</span><span class="special">,</span> <span class="identifier">z</span><span class="special">))</span> <span class="special">&lt;&lt;</span> <span class="identifier">endl</span><span class="special">;</span></pre>
+<p>
+              </p>
+<p>
+              
+</p>
+<pre class="programlisting">Normal distribution with mean = 1.09023 has fraction &lt;= -2, p = 0.001
+Normal distribution with mean = 1.09023 has fraction &gt; -2, p = 0.999
+</pre>
+<p>
+              <a name="math_toolkit.dist.stat_tut.weg.find_eg.find_location_eg.controlling_error_handling_from_find_location"></a>
+              </p>
+<h5>
+<a name="id626993"></a>
+                <a class="link" href="find_location_eg.html#math_toolkit.dist.stat_tut.weg.find_eg.find_location_eg.controlling_error_handling_from_find_location">Controlling
+                Error Handling from find_location</a>
+              </h5>
+<p>
+              </p>
+<p>
+                We can also control the policy for handling various errors. For example,
+                we can define a new (possibly unwise) policy to ignore domain errors
+                ('bad' arguments).
+              </p>
+<p>
+              </p>
+<p>
+                Unless we are using the boost::math namespace, we will need:
+              </p>
+<p>
+              </p>
+<p>
+                
+</p>
+<pre class="programlisting"><span class="keyword">using</span> <span class="identifier">boost</span><span class="special">::</span><span class="identifier">math</span><span class="special">::</span><span class="identifier">policies</span><span class="special">::</span><span class="identifier">policy</span><span class="special">;</span>
+<span class="keyword">using</span> <span class="identifier">boost</span><span class="special">::</span><span class="identifier">math</span><span class="special">::</span><span class="identifier">policies</span><span class="special">::</span><span class="identifier">domain_error</span><span class="special">;</span>
+<span class="keyword">using</span> <span class="identifier">boost</span><span class="special">::</span><span class="identifier">math</span><span class="special">::</span><span class="identifier">policies</span><span class="special">::</span><span class="identifier">ignore_error</span><span class="special">;</span></pre>
+<p>
+              </p>
+<p>
+              </p>
+<p>
+                Using a typedef is often convenient, especially if it is re-used,
+                although it is not required, as the various examples below show.
+              </p>
+<p>
+              </p>
+<p>
+                
+</p>
+<pre class="programlisting"><span class="keyword">typedef</span> <span class="identifier">policy</span><span class="special">&lt;</span><span class="identifier">domain_error</span><span class="special">&lt;</span><span class="identifier">ignore_error</span><span class="special">&gt;</span> <span class="special">&gt;</span> <span class="identifier">ignore_domain_policy</span><span class="special">;</span>
+<span class="comment">// find_location with new policy, using typedef.
+</span><span class="identifier">l</span> <span class="special">=</span> <span class="identifier">find_location</span><span class="special">&lt;</span><span class="identifier">normal</span><span class="special">&gt;(</span><span class="identifier">z</span><span class="special">,</span> <span class="identifier">p</span><span class="special">,</span> <span class="identifier">sd</span><span class="special">,</span> <span class="identifier">ignore_domain_policy</span><span class="special">());</span>
+<span class="comment">// Default policy policy&lt;&gt;, needs "using boost::math::policies::policy;"
+</span><span class="identifier">l</span> <span class="special">=</span> <span class="identifier">find_location</span><span class="special">&lt;</span><span class="identifier">normal</span><span class="special">&gt;(</span><span class="identifier">z</span><span class="special">,</span> <span class="identifier">p</span><span class="special">,</span> <span class="identifier">sd</span><span class="special">,</span> <span class="identifier">policy</span><span class="special">&lt;&gt;());</span>
+<span class="comment">// Default policy, fully specified.
+</span><span class="identifier">l</span> <span class="special">=</span> <span class="identifier">find_location</span><span class="special">&lt;</span><span class="identifier">normal</span><span class="special">&gt;(</span><span class="identifier">z</span><span class="special">,</span> <span class="identifier">p</span><span class="special">,</span> <span class="identifier">sd</span><span class="special">,</span> <span class="identifier">boost</span><span class="special">::</span><span class="identifier">math</span><span class="special">::</span><span class="identifier">policies</span><span class="special">::</span><span class="identifier">policy</span><span class="special">&lt;&gt;());</span>
+<span class="comment">// A new policy, ignoring domain errors, without using a typedef.
+</span><span class="identifier">l</span> <span class="special">=</span> <span class="identifier">find_location</span><span class="special">&lt;</span><span class="identifier">normal</span><span class="special">&gt;(</span><span class="identifier">z</span><span class="special">,</span> <span class="identifier">p</span><span class="special">,</span> <span class="identifier">sd</span><span class="special">,</span> <span class="identifier">policy</span><span class="special">&lt;</span><span class="identifier">domain_error</span><span class="special">&lt;</span><span class="identifier">ignore_error</span><span class="special">&gt;</span> <span class="special">&gt;());</span></pre>
+<p>
+              </p>
+<p>
+              </p>
+<p>
+                If we want to use a probability that is the <a class="link" href="../../overview.html#complements">complement
+                of our probability</a>, we should not even think of writing <code class="computeroutput"><span class="identifier">find_location</span><span class="special">&lt;</span><span class="identifier">normal</span><span class="special">&gt;(</span><span class="identifier">z</span><span class="special">,</span> <span class="number">1</span> <span class="special">-</span> <span class="identifier">p</span><span class="special">,</span> <span class="identifier">sd</span><span class="special">)</span></code>,
+                but, <a class="link" href="../../overview.html#why_complements">to avoid loss of accuracy</a>,
+                use the complement version.
+              </p>
+<p>
+              </p>
+<p>
+                
+</p>
+<pre class="programlisting"><span class="identifier">z</span> <span class="special">=</span> <span class="number">2.</span><span class="special">;</span>
+<span class="keyword">double</span> <span class="identifier">q</span> <span class="special">=</span> <span class="number">0.95</span><span class="special">;</span> <span class="comment">// = 1 - p; // complement.
+</span><span class="identifier">l</span> <span class="special">=</span> <span class="identifier">find_location</span><span class="special">&lt;</span><span class="identifier">normal</span><span class="special">&gt;(</span><span class="identifier">complement</span><span class="special">(</span><span class="identifier">z</span><span class="special">,</span> <span class="identifier">q</span><span class="special">,</span> <span class="identifier">sd</span><span class="special">));</span>
+
+<span class="identifier">normal</span> <span class="identifier">np95pc</span><span class="special">(</span><span class="identifier">l</span><span class="special">,</span> <span class="identifier">sd</span><span class="special">);</span> <span class="comment">// Same standard_deviation (scale) but with mean(location) shifted
+</span><span class="identifier">cout</span> <span class="special">&lt;&lt;</span> <span class="string">"Normal distribution with mean = "</span> <span class="special">&lt;&lt;</span> <span class="identifier">l</span> <span class="special">&lt;&lt;</span> <span class="string">" has "</span> 
+  <span class="special">&lt;&lt;</span> <span class="string">"fraction &lt;= "</span> <span class="special">&lt;&lt;</span> <span class="identifier">z</span> <span class="special">&lt;&lt;</span> <span class="string">" = "</span>  <span class="special">&lt;&lt;</span> <span class="identifier">cdf</span><span class="special">(</span><span class="identifier">np95pc</span><span class="special">,</span> <span class="identifier">z</span><span class="special">)</span> <span class="special">&lt;&lt;</span> <span class="identifier">endl</span><span class="special">;</span>
+<span class="identifier">cout</span> <span class="special">&lt;&lt;</span> <span class="string">"Normal distribution with mean = "</span> <span class="special">&lt;&lt;</span> <span class="identifier">l</span> <span class="special">&lt;&lt;</span> <span class="string">" has "</span> 
+  <span class="special">&lt;&lt;</span> <span class="string">"fraction &gt; "</span> <span class="special">&lt;&lt;</span> <span class="identifier">z</span> <span class="special">&lt;&lt;</span> <span class="string">" = "</span>  <span class="special">&lt;&lt;</span> <span class="identifier">cdf</span><span class="special">(</span><span class="identifier">complement</span><span class="special">(</span><span class="identifier">np95pc</span><span class="special">,</span> <span class="identifier">z</span><span class="special">))</span> <span class="special">&lt;&lt;</span> <span class="identifier">endl</span><span class="special">;</span>
+</pre>
+<p>
+              </p>
+<p>
+              See find_location_example.cpp
+              for full source code: the program output looks like this: 
+</p>
+<pre class="programlisting">Example: Find location (mean).
+Normal distribution with mean = 0, standard deviation 1, has fraction &lt;= -2, p = 0.0227501
+Normal distribution with mean = 0, standard deviation 1, has fraction &gt; -2, p = 0.97725
+offset location (mean) = 1.09023
+Normal distribution with mean = 1.09023 has fraction &lt;= -2, p = 0.001
+Normal distribution with mean = 1.09023 has fraction &gt; -2, p = 0.999
+Normal distribution with mean = 0.355146 has fraction &lt;= 2 = 0.95
+Normal distribution with mean = 0.355146 has fraction &gt; 2 = 0.05
+</pre>
+<p>
+            </p>
+</div>
+<table xmlns:rev="http://www.cs.rpi.edu/~gregod/boost/tools/doc/revision" width="100%"><tr>
+<td align="left"></td>
+<td align="right"><div class="copyright-footer">Copyright © 2006 , 2007, 2008 John Maddock, Paul A. Bristow, Hubert
+      Holin, Xiaogang Zhang, Bruno Lalande and Gautam Sewani<p>
+        Distributed under the Boost Software License, Version 1.0. (See accompanying
+        file LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_0.txt)
+      </p>
+</div></td>
+</tr></table>
+<hr>
+<div class="spirit-nav">
+<a accesskey="p" href="../find_eg.html"><img src="../../../../../../../doc/html/images/prev.png" alt="Prev"></a><a accesskey="u" href="../find_eg.html"><img src="../../../../../../../doc/html/images/up.png" alt="Up"></a><a accesskey="h" href="../../../../../index.html"><img src="../../../../../../../doc/html/images/home.png" alt="Home"></a><a accesskey="n" href="find_scale_eg.html"><img src="../../../../../../../doc/html/images/next.png" alt="Next"></a>
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+<a accesskey="p" href="find_scale_eg.html"><img src="../../../../../../../doc/html/images/prev.png" alt="Prev"></a><a accesskey="u" href="../find_eg.html"><img src="../../../../../../../doc/html/images/up.png" alt="Up"></a><a accesskey="h" href="../../../../../index.html"><img src="../../../../../../../doc/html/images/home.png" alt="Home"></a><a accesskey="n" href="../nag_library.html"><img src="../../../../../../../doc/html/images/next.png" alt="Next"></a>
+</div>
+<div class="section" lang="en">
+<div class="titlepage"><div><div><h6 class="title">
+<a name="math_toolkit.dist.stat_tut.weg.find_eg.find_mean_and_sd_eg"></a><a class="link" href="find_mean_and_sd_eg.html" title="Find mean and standard deviation example">
+            Find mean and standard deviation example</a>
+</h6></div></div></div>
+<p>
+              </p>
+<p>
+                First we need some includes to access the normal distribution, the
+                algorithms to find location and scale (and some std output of course).
+              </p>
+<p>
+              </p>
+<p>
+                
+</p>
+<pre class="programlisting"><span class="preprocessor">#include</span> <span class="special">&lt;</span><span class="identifier">boost</span><span class="special">/</span><span class="identifier">math</span><span class="special">/</span><span class="identifier">distributions</span><span class="special">/</span><span class="identifier">normal</span><span class="special">.</span><span class="identifier">hpp</span><span class="special">&gt;</span> <span class="comment">// for normal_distribution
+</span>  <span class="keyword">using</span> <span class="identifier">boost</span><span class="special">::</span><span class="identifier">math</span><span class="special">::</span><span class="identifier">normal</span><span class="special">;</span> <span class="comment">// typedef provides default type is double.
+</span><span class="preprocessor">#include</span> <span class="special">&lt;</span><span class="identifier">boost</span><span class="special">/</span><span class="identifier">math</span><span class="special">/</span><span class="identifier">distributions</span><span class="special">/</span><span class="identifier">cauchy</span><span class="special">.</span><span class="identifier">hpp</span><span class="special">&gt;</span> <span class="comment">// for cauchy_distribution
+</span>  <span class="keyword">using</span> <span class="identifier">boost</span><span class="special">::</span><span class="identifier">math</span><span class="special">::</span><span class="identifier">cauchy</span><span class="special">;</span> <span class="comment">// typedef provides default type is double.
+</span><span class="preprocessor">#include</span> <span class="special">&lt;</span><span class="identifier">boost</span><span class="special">/</span><span class="identifier">math</span><span class="special">/</span><span class="identifier">distributions</span><span class="special">/</span><span class="identifier">find_location</span><span class="special">.</span><span class="identifier">hpp</span><span class="special">&gt;</span>
+  <span class="keyword">using</span> <span class="identifier">boost</span><span class="special">::</span><span class="identifier">math</span><span class="special">::</span><span class="identifier">find_location</span><span class="special">;</span>
+<span class="preprocessor">#include</span> <span class="special">&lt;</span><span class="identifier">boost</span><span class="special">/</span><span class="identifier">math</span><span class="special">/</span><span class="identifier">distributions</span><span class="special">/</span><span class="identifier">find_scale</span><span class="special">.</span><span class="identifier">hpp</span><span class="special">&gt;</span>
+  <span class="keyword">using</span> <span class="identifier">boost</span><span class="special">::</span><span class="identifier">math</span><span class="special">::</span><span class="identifier">find_scale</span><span class="special">;</span>
+  <span class="keyword">using</span> <span class="identifier">boost</span><span class="special">::</span><span class="identifier">math</span><span class="special">::</span><span class="identifier">complement</span><span class="special">;</span>
+  <span class="keyword">using</span> <span class="identifier">boost</span><span class="special">::</span><span class="identifier">math</span><span class="special">::</span><span class="identifier">policies</span><span class="special">::</span><span class="identifier">policy</span><span class="special">;</span>
+
+<span class="preprocessor">#include</span> <span class="special">&lt;</span><span class="identifier">iostream</span><span class="special">&gt;</span>
+  <span class="keyword">using</span> <span class="identifier">std</span><span class="special">::</span><span class="identifier">cout</span><span class="special">;</span> <span class="keyword">using</span> <span class="identifier">std</span><span class="special">::</span><span class="identifier">endl</span><span class="special">;</span> <span class="keyword">using</span> <span class="identifier">std</span><span class="special">::</span><span class="identifier">left</span><span class="special">;</span> <span class="keyword">using</span> <span class="identifier">std</span><span class="special">::</span><span class="identifier">showpoint</span><span class="special">;</span> <span class="keyword">using</span> <span class="identifier">std</span><span class="special">::</span><span class="identifier">noshowpoint</span><span class="special">;</span>
+<span class="preprocessor">#include</span> <span class="special">&lt;</span><span class="identifier">iomanip</span><span class="special">&gt;</span>
+  <span class="keyword">using</span> <span class="identifier">std</span><span class="special">::</span><span class="identifier">setw</span><span class="special">;</span> <span class="keyword">using</span> <span class="identifier">std</span><span class="special">::</span><span class="identifier">setprecision</span><span class="special">;</span>
+<span class="preprocessor">#include</span> <span class="special">&lt;</span><span class="identifier">limits</span><span class="special">&gt;</span>
+  <span class="keyword">using</span> <span class="identifier">std</span><span class="special">::</span><span class="identifier">numeric_limits</span><span class="special">;</span>
+</pre>
+<p>
+              </p>
+<p>
+              <a name="math_toolkit.dist.stat_tut.weg.find_eg.find_mean_and_sd_eg.using_find_location_and_find_scale_to_meet_dispensing_and_measurement_specifications"></a>
+              </p>
+<h5>
+<a name="id632238"></a>
+                <a class="link" href="find_mean_and_sd_eg.html#math_toolkit.dist.stat_tut.weg.find_eg.find_mean_and_sd_eg.using_find_location_and_find_scale_to_meet_dispensing_and_measurement_specifications">Using
+                find_location and find_scale to meet dispensing and measurement specifications</a>
+              </h5>
+<p>
+              </p>
+<p>
+                Consider an example from K Krishnamoorthy, Handbook of Statistical
+                Distributions with Applications, ISBN 1-58488-635-8, (2006) p 126,
+                example 10.3.7.
+              </p>
+<p>
+              </p>
+<p>
+                "A machine is set to pack 3 kg of ground beef per pack. Over
+                a long period of time it is found that the average packed was 3 kg
+                with a standard deviation of 0.1 kg. Assume the packing is normally
+                distributed."
+              </p>
+<p>
+              </p>
+<p>
+                We start by constructing a normal distribution with the given parameters:
+              </p>
+<p>
+              </p>
+<p>
+                
+</p>
+<pre class="programlisting"><span class="keyword">double</span> <span class="identifier">mean</span> <span class="special">=</span> <span class="number">3.</span><span class="special">;</span> <span class="comment">// kg
+</span><span class="keyword">double</span> <span class="identifier">standard_deviation</span> <span class="special">=</span> <span class="number">0.1</span><span class="special">;</span> <span class="comment">// kg
+</span><span class="identifier">normal</span> <span class="identifier">packs</span><span class="special">(</span><span class="identifier">mean</span><span class="special">,</span> <span class="identifier">standard_deviation</span><span class="special">);</span></pre>
+<p>
+              </p>
+<p>
+              </p>
+<p>
+                We can then find the fraction (or %) of packages that weigh more
+                than 3.1 kg.
+              </p>
+<p>
+              </p>
+<p>
+                
+</p>
+<pre class="programlisting"><span class="keyword">double</span> <span class="identifier">max_weight</span> <span class="special">=</span> <span class="number">3.1</span><span class="special">;</span> <span class="comment">// kg
+</span><span class="identifier">cout</span> <span class="special">&lt;&lt;</span> <span class="string">"Percentage of packs &gt; "</span> <span class="special">&lt;&lt;</span> <span class="identifier">max_weight</span> <span class="special">&lt;&lt;</span> <span class="string">" is "</span>
+<span class="special">&lt;&lt;</span> <span class="identifier">cdf</span><span class="special">(</span><span class="identifier">complement</span><span class="special">(</span><span class="identifier">packs</span><span class="special">,</span> <span class="identifier">max_weight</span><span class="special">))</span> <span class="special">*</span> <span class="number">100.</span> <span class="special">&lt;&lt;</span> <span class="identifier">endl</span><span class="special">;</span> <span class="comment">// P(X &gt; 3.1)</span></pre>
+<p>
+              </p>
+<p>
+              </p>
+<p>
+                We might want to ensure that 95% of packs are over a minimum weight
+                specification, then we want the value of the mean such that P(X &lt;
+                2.9) = 0.05.
+              </p>
+<p>
+              </p>
+<p>
+                Using the mean of 3 kg, we can estimate the fraction of packs that
+                fail to meet the specification of 2.9 kg.
+              </p>
+<p>
+              </p>
+<p>
+                
+</p>
+<pre class="programlisting"><span class="keyword">double</span> <span class="identifier">minimum_weight</span> <span class="special">=</span> <span class="number">2.9</span><span class="special">;</span>
+<span class="identifier">cout</span> <span class="special">&lt;&lt;</span><span class="string">"Fraction of packs &lt;= "</span> <span class="special">&lt;&lt;</span> <span class="identifier">minimum_weight</span> <span class="special">&lt;&lt;</span> <span class="string">" with a mean of "</span> <span class="special">&lt;&lt;</span> <span class="identifier">mean</span>
+  <span class="special">&lt;&lt;</span> <span class="string">" is "</span> <span class="special">&lt;&lt;</span> <span class="identifier">cdf</span><span class="special">(</span><span class="identifier">complement</span><span class="special">(</span><span class="identifier">packs</span><span class="special">,</span> <span class="identifier">minimum_weight</span><span class="special">))</span> <span class="special">&lt;&lt;</span> <span class="identifier">endl</span><span class="special">;</span>
+<span class="comment">// fraction of packs &lt;= 2.9 with a mean of 3 is 0.841345</span></pre>
+<p>
+              </p>
+<p>
+              </p>
+<p>
+                This is 0.84 - more than the target fraction of 0.95. If we want
+                95% to be over the minimum weight, what should we set the mean weight
+                to be?
+              </p>
+<p>
+              </p>
+<p>
+                Using the KK StatCalc program supplied with the book and the method
+                given on page 126 gives 3.06449.
+              </p>
+<p>
+              </p>
+<p>
+                We can confirm this by constructing a new distribution which we call
+                'xpacks' with a safety margin mean of 3.06449 thus:
+              </p>
+<p>
+              </p>
+<p>
+                
+</p>
+<pre class="programlisting"><span class="keyword">double</span> <span class="identifier">over_mean</span> <span class="special">=</span> <span class="number">3.06449</span><span class="special">;</span>
+<span class="identifier">normal</span> <span class="identifier">xpacks</span><span class="special">(</span><span class="identifier">over_mean</span><span class="special">,</span> <span class="identifier">standard_deviation</span><span class="special">);</span>
+<span class="identifier">cout</span> <span class="special">&lt;&lt;</span> <span class="string">"Fraction of packs &gt;= "</span> <span class="special">&lt;&lt;</span> <span class="identifier">minimum_weight</span>
+<span class="special">&lt;&lt;</span> <span class="string">" with a mean of "</span> <span class="special">&lt;&lt;</span> <span class="identifier">xpacks</span><span class="special">.</span><span class="identifier">mean</span><span class="special">()</span>
+  <span class="special">&lt;&lt;</span> <span class="string">" is "</span> <span class="special">&lt;&lt;</span> <span class="identifier">cdf</span><span class="special">(</span><span class="identifier">complement</span><span class="special">(</span><span class="identifier">xpacks</span><span class="special">,</span> <span class="identifier">minimum_weight</span><span class="special">))</span> <span class="special">&lt;&lt;</span> <span class="identifier">endl</span><span class="special">;</span>
+<span class="comment">// fraction of packs &gt;= 2.9 with a mean of 3.06449 is 0.950005</span></pre>
+<p>
+              </p>
+<p>
+              </p>
+<p>
+                Using this Math Toolkit, we can calculate the required mean directly
+                thus:
+              </p>
+<p>
+              </p>
+<p>
+                
+</p>
+<pre class="programlisting"><span class="keyword">double</span> <span class="identifier">under_fraction</span> <span class="special">=</span> <span class="number">0.05</span><span class="special">;</span>  <span class="comment">// so 95% are above the minimum weight mean - sd = 2.9
+</span><span class="keyword">double</span> <span class="identifier">low_limit</span> <span class="special">=</span> <span class="identifier">standard_deviation</span><span class="special">;</span>
+<span class="keyword">double</span> <span class="identifier">offset</span> <span class="special">=</span> <span class="identifier">mean</span> <span class="special">-</span> <span class="identifier">low_limit</span> <span class="special">-</span> <span class="identifier">quantile</span><span class="special">(</span><span class="identifier">packs</span><span class="special">,</span> <span class="identifier">under_fraction</span><span class="special">);</span>
+<span class="keyword">double</span> <span class="identifier">nominal_mean</span> <span class="special">=</span> <span class="identifier">mean</span> <span class="special">+</span> <span class="identifier">offset</span><span class="special">;</span>
+<span class="comment">// mean + (mean - low_limit - quantile(packs, under_fraction));
+</span>
+<span class="identifier">normal</span> <span class="identifier">nominal_packs</span><span class="special">(</span><span class="identifier">nominal_mean</span><span class="special">,</span> <span class="identifier">standard_deviation</span><span class="special">);</span>
+<span class="identifier">cout</span> <span class="special">&lt;&lt;</span> <span class="string">"Setting the packer to "</span> <span class="special">&lt;&lt;</span> <span class="identifier">nominal_mean</span> <span class="special">&lt;&lt;</span> <span class="string">" will mean that "</span>
+  <span class="special">&lt;&lt;</span> <span class="string">"fraction of packs &gt;= "</span> <span class="special">&lt;&lt;</span> <span class="identifier">minimum_weight</span>
+  <span class="special">&lt;&lt;</span> <span class="string">" is "</span> <span class="special">&lt;&lt;</span> <span class="identifier">cdf</span><span class="special">(</span><span class="identifier">complement</span><span class="special">(</span><span class="identifier">nominal_packs</span><span class="special">,</span> <span class="identifier">minimum_weight</span><span class="special">))</span> <span class="special">&lt;&lt;</span> <span class="identifier">endl</span><span class="special">;</span>
+<span class="comment">// Setting the packer to 3.06449 will mean that fraction of packs &gt;= 2.9 is 0.95</span></pre>
+<p>
+              </p>
+<p>
+              </p>
+<p>
+                This calculation is generalized as the free function called <a class="link" href="../../../dist_ref/dist_algorithms.html" title="Distribution Algorithms">find_location</a>.
+              </p>
+<p>
+              </p>
+<p>
+                To use this we will need to
+              </p>
+<p>
+              </p>
+<p>
+                
+</p>
+<pre class="programlisting"><span class="preprocessor">#include</span> <span class="special">&lt;</span><span class="identifier">boost</span><span class="special">/</span><span class="identifier">math</span><span class="special">/</span><span class="identifier">distributions</span><span class="special">/</span><span class="identifier">find_location</span><span class="special">.</span><span class="identifier">hpp</span><span class="special">&gt;</span>
+  <span class="keyword">using</span> <span class="identifier">boost</span><span class="special">::</span><span class="identifier">math</span><span class="special">::</span><span class="identifier">find_location</span><span class="special">;</span></pre>
+<p>
+              </p>
+<p>
+              </p>
+<p>
+                and then use find_location function to find safe_mean, &amp; construct
+                a new normal distribution called 'goodpacks'.
+              </p>
+<p>
+              </p>
+<p>
+                
+</p>
+<pre class="programlisting"><span class="keyword">double</span> <span class="identifier">safe_mean</span> <span class="special">=</span> <span class="identifier">find_location</span><span class="special">&lt;</span><span class="identifier">normal</span><span class="special">&gt;(</span><span class="identifier">minimum_weight</span><span class="special">,</span> <span class="identifier">under_fraction</span><span class="special">,</span> <span class="identifier">standard_deviation</span><span class="special">);</span>
+<span class="identifier">normal</span> <span class="identifier">good_packs</span><span class="special">(</span><span class="identifier">safe_mean</span><span class="special">,</span> <span class="identifier">standard_deviation</span><span class="special">);</span></pre>
+<p>
+              </p>
+<p>
+              </p>
+<p>
+                with the same confirmation as before:
+              </p>
+<p>
+              </p>
+<p>
+                
+</p>
+<pre class="programlisting"><span class="identifier">cout</span> <span class="special">&lt;&lt;</span> <span class="string">"Setting the packer to "</span> <span class="special">&lt;&lt;</span> <span class="identifier">nominal_mean</span> <span class="special">&lt;&lt;</span> <span class="string">" will mean that "</span>
+  <span class="special">&lt;&lt;</span> <span class="string">"fraction of packs &gt;= "</span> <span class="special">&lt;&lt;</span> <span class="identifier">minimum_weight</span>
+  <span class="special">&lt;&lt;</span> <span class="string">" is "</span> <span class="special">&lt;&lt;</span> <span class="identifier">cdf</span><span class="special">(</span><span class="identifier">complement</span><span class="special">(</span><span class="identifier">good_packs</span><span class="special">,</span> <span class="identifier">minimum_weight</span><span class="special">))</span> <span class="special">&lt;&lt;</span> <span class="identifier">endl</span><span class="special">;</span>
+<span class="comment">// Setting the packer to 3.06449 will mean that fraction of packs &gt;= 2.9 is 0.95</span></pre>
+<p>
+              </p>
+<p>
+              <a name="math_toolkit.dist.stat_tut.weg.find_eg.find_mean_and_sd_eg.using_cauchy_lorentz_instead_of_normal_distribution"></a>
+              </p>
+<h5>
+<a name="id633908"></a>
+                <a class="link" href="find_mean_and_sd_eg.html#math_toolkit.dist.stat_tut.weg.find_eg.find_mean_and_sd_eg.using_cauchy_lorentz_instead_of_normal_distribution">Using
+                Cauchy-Lorentz instead of normal distribution</a>
+              </h5>
+<p>
+              </p>
+<p>
+                After examining the weight distribution of a large number of packs,
+                we might decide that, after all, the assumption of a normal distribution
+                is not really justified. We might find that the fit is better to
+                a <a class="link" href="../../../dist_ref/dists/cauchy_dist.html" title="Cauchy-Lorentz Distribution">Cauchy
+                Distribution</a>. This distribution has wider 'wings', so that
+                whereas most of the values are closer to the mean than the normal,
+                there are also more values than 'normal' that lie further from the
+                mean than the normal.
+              </p>
+<p>
+              </p>
+<p>
+                This might happen because a larger than normal lump of meat is either
+                included or excluded.
+              </p>
+<p>
+              </p>
+<p>
+                We first create a <a class="link" href="../../../dist_ref/dists/cauchy_dist.html" title="Cauchy-Lorentz Distribution">Cauchy
+                Distribution</a> with the original mean and standard deviation,
+                and estimate the fraction that lie below our minimum weight specification.
+              </p>
+<p>
+              </p>
+<p>
+                
+</p>
+<pre class="programlisting"><span class="identifier">cauchy</span> <span class="identifier">cpacks</span><span class="special">(</span><span class="identifier">mean</span><span class="special">,</span> <span class="identifier">standard_deviation</span><span class="special">);</span>
+<span class="identifier">cout</span> <span class="special">&lt;&lt;</span> <span class="string">"Cauchy Setting the packer to "</span> <span class="special">&lt;&lt;</span> <span class="identifier">mean</span> <span class="special">&lt;&lt;</span> <span class="string">" will mean that "</span>
+  <span class="special">&lt;&lt;</span> <span class="string">"fraction of packs &gt;= "</span> <span class="special">&lt;&lt;</span> <span class="identifier">minimum_weight</span>
+  <span class="special">&lt;&lt;</span> <span class="string">" is "</span> <span class="special">&lt;&lt;</span> <span class="identifier">cdf</span><span class="special">(</span><span class="identifier">complement</span><span class="special">(</span><span class="identifier">cpacks</span><span class="special">,</span> <span class="identifier">minimum_weight</span><span class="special">))</span> <span class="special">&lt;&lt;</span> <span class="identifier">endl</span><span class="special">;</span>
+<span class="comment">// Cauchy Setting the packer to 3 will mean that fraction of packs &gt;= 2.9 is 0.75</span></pre>
+<p>
+              </p>
+<p>
+              </p>
+<p>
+                Note that far fewer of the packs meet the specification, only 75%
+                instead of 95%. Now we can repeat the find_location, using the cauchy
+                distribution as template parameter, in place of the normal used above.
+              </p>
+<p>
+              </p>
+<p>
+                
+</p>
+<pre class="programlisting"><span class="keyword">double</span> <span class="identifier">lc</span> <span class="special">=</span> <span class="identifier">find_location</span><span class="special">&lt;</span><span class="identifier">cauchy</span><span class="special">&gt;(</span><span class="identifier">minimum_weight</span><span class="special">,</span> <span class="identifier">under_fraction</span><span class="special">,</span> <span class="identifier">standard_deviation</span><span class="special">);</span>
+<span class="identifier">cout</span> <span class="special">&lt;&lt;</span> <span class="string">"find_location&lt;cauchy&gt;(minimum_weight, over fraction, standard_deviation); "</span> <span class="special">&lt;&lt;</span> <span class="identifier">lc</span> <span class="special">&lt;&lt;</span> <span class="identifier">endl</span><span class="special">;</span>
+<span class="comment">// find_location&lt;cauchy&gt;(minimum_weight, over fraction, packs.standard_deviation()); 3.53138</span></pre>
+<p>
+              </p>
+<p>
+              </p>
+<p>
+                Note that the safe_mean setting needs to be much higher, 3.53138
+                instead of 3.06449, so we will make rather less profit.
+              </p>
+<p>
+              </p>
+<p>
+                And again confirm that the fraction meeting specification is as expected.
+              </p>
+<p>
+              </p>
+<p>
+                
+</p>
+<pre class="programlisting"><span class="identifier">cauchy</span> <span class="identifier">goodcpacks</span><span class="special">(</span><span class="identifier">lc</span><span class="special">,</span> <span class="identifier">standard_deviation</span><span class="special">);</span>
+<span class="identifier">cout</span> <span class="special">&lt;&lt;</span> <span class="string">"Cauchy Setting the packer to "</span> <span class="special">&lt;&lt;</span> <span class="identifier">lc</span> <span class="special">&lt;&lt;</span> <span class="string">" will mean that "</span>
+  <span class="special">&lt;&lt;</span> <span class="string">"fraction of packs &gt;= "</span> <span class="special">&lt;&lt;</span> <span class="identifier">minimum_weight</span>
+  <span class="special">&lt;&lt;</span> <span class="string">" is "</span> <span class="special">&lt;&lt;</span> <span class="identifier">cdf</span><span class="special">(</span><span class="identifier">complement</span><span class="special">(</span><span class="identifier">goodcpacks</span><span class="special">,</span> <span class="identifier">minimum_weight</span><span class="special">))</span> <span class="special">&lt;&lt;</span> <span class="identifier">endl</span><span class="special">;</span>
+<span class="comment">// Cauchy Setting the packer to 3.53138 will mean that fraction of packs &gt;= 2.9 is 0.95</span></pre>
+<p>
+              </p>
+<p>
+              </p>
+<p>
+                Finally we could estimate the effect of a much tighter specification,
+                that 99% of packs met the specification.
+              </p>
+<p>
+              </p>
+<p>
+                
+</p>
+<pre class="programlisting"><span class="identifier">cout</span> <span class="special">&lt;&lt;</span> <span class="string">"Cauchy Setting the packer to "</span>
+  <span class="special">&lt;&lt;</span> <span class="identifier">find_location</span><span class="special">&lt;</span><span class="identifier">cauchy</span><span class="special">&gt;(</span><span class="identifier">minimum_weight</span><span class="special">,</span> <span class="number">0.99</span><span class="special">,</span> <span class="identifier">standard_deviation</span><span class="special">)</span>
+  <span class="special">&lt;&lt;</span> <span class="string">" will mean that "</span>
+  <span class="special">&lt;&lt;</span> <span class="string">"fraction of packs &gt;= "</span> <span class="special">&lt;&lt;</span> <span class="identifier">minimum_weight</span>
+  <span class="special">&lt;&lt;</span> <span class="string">" is "</span> <span class="special">&lt;&lt;</span> <span class="identifier">cdf</span><span class="special">(</span><span class="identifier">complement</span><span class="special">(</span><span class="identifier">goodcpacks</span><span class="special">,</span> <span class="identifier">minimum_weight</span><span class="special">))</span> <span class="special">&lt;&lt;</span> <span class="identifier">endl</span><span class="special">;</span></pre>
+<p>
+              </p>
+<p>
+              </p>
+<p>
+                Setting the packer to 3.13263 will mean that fraction of packs &gt;=
+                2.9 is 0.99, but will more than double the mean loss from 0.0644
+                to 0.133 kg per pack.
+              </p>
+<p>
+              </p>
+<p>
+                Of course, this calculation is not limited to packs of meat, it applies
+                to dispensing anything, and it also applies to a 'virtual' material
+                like any measurement.
+              </p>
+<p>
+              </p>
+<p>
+                The only caveat is that the calculation assumes that the standard
+                deviation (scale) is known with a reasonably low uncertainty, something
+                that is not so easy to ensure in practice. And that the distribution
+                is well defined, <a class="link" href="../../../dist_ref/dists/normal_dist.html" title="Normal (Gaussian) Distribution">Normal
+                Distribution</a> or <a class="link" href="../../../dist_ref/dists/cauchy_dist.html" title="Cauchy-Lorentz Distribution">Cauchy
+                Distribution</a>, or some other.
+              </p>
+<p>
+              </p>
+<p>
+                If one is simply dispensing a very large number of packs, then it
+                may be feasible to measure the weight of hundreds or thousands of
+                packs. With a healthy 'degrees of freedom', the confidence intervals
+                for the standard deviation are not too wide, typically about + and
+                - 10% for hundreds of observations.
+              </p>
+<p>
+              </p>
+<p>
+                For other applications, where it is more difficult or expensive to
+                make many observations, the confidence intervals are depressingly
+                wide.
+              </p>
+<p>
+              </p>
+<p>
+                See <a class="link" href="../cs_eg/chi_sq_intervals.html" title="Confidence Intervals on the Standard Deviation">Confidence
+                Intervals on the standard deviation</a> for a worked example
+                chi_square_std_dev_test.cpp
+                of estimating these intervals.
+              </p>
+<p>
+              <a name="math_toolkit.dist.stat_tut.weg.find_eg.find_mean_and_sd_eg.changing_the_scale_or_standard_deviation"></a>
+              </p>
+<h5>
+<a name="id634900"></a>
+                <a class="link" href="find_mean_and_sd_eg.html#math_toolkit.dist.stat_tut.weg.find_eg.find_mean_and_sd_eg.changing_the_scale_or_standard_deviation">Changing
+                the scale or standard deviation</a>
+              </h5>
+<p>
+              </p>
+<p>
+                Alternatively, we could invest in a better (more precise) packer
+                (or measuring device) with a lower standard deviation, or scale.
+              </p>
+<p>
+              </p>
+<p>
+                This might cost more, but would reduce the amount we have to 'give
+                away' in order to meet the specification.
+              </p>
+<p>
+              </p>
+<p>
+                To estimate how much better (how much smaller standard deviation)
+                it would have to be, we need to get the 5% quantile to be located
+                at the under_weight limit, 2.9
+              </p>
+<p>
+              </p>
+<p>
+                
+</p>
+<pre class="programlisting"><span class="keyword">double</span> <span class="identifier">p</span> <span class="special">=</span> <span class="number">0.05</span><span class="special">;</span> <span class="comment">// wanted p th quantile.
+</span><span class="identifier">cout</span> <span class="special">&lt;&lt;</span> <span class="string">"Quantile of "</span> <span class="special">&lt;&lt;</span> <span class="identifier">p</span> <span class="special">&lt;&lt;</span> <span class="string">" = "</span> <span class="special">&lt;&lt;</span> <span class="identifier">quantile</span><span class="special">(</span><span class="identifier">packs</span><span class="special">,</span> <span class="identifier">p</span><span class="special">)</span>
+  <span class="special">&lt;&lt;</span> <span class="string">", mean = "</span> <span class="special">&lt;&lt;</span> <span class="identifier">packs</span><span class="special">.</span><span class="identifier">mean</span><span class="special">()</span> <span class="special">&lt;&lt;</span> <span class="string">", sd = "</span> <span class="special">&lt;&lt;</span> <span class="identifier">packs</span><span class="special">.</span><span class="identifier">standard_deviation</span><span class="special">()</span> <span class="special">&lt;&lt;</span> <span class="identifier">endl</span><span class="special">;</span></pre>
+<p>
+              </p>
+<p>
+              </p>
+<p>
+                Quantile of 0.05 = 2.83551, mean = 3, sd = 0.1
+              </p>
+<p>
+              </p>
+<p>
+                With the current packer (mean = 3, sd = 0.1), the 5% quantile is
+                at 2.8551 kg, a little below our target of 2.9 kg. So we know that
+                the standard deviation is going to have to be smaller.
+              </p>
+<p>
+              </p>
+<p>
+                Let's start by guessing that it (now 0.1) needs to be halved, to
+                a standard deviation of 0.05 kg.
+              </p>
+<p>
+              </p>
+<p>
+                
+</p>
+<pre class="programlisting"><span class="identifier">normal</span> <span class="identifier">pack05</span><span class="special">(</span><span class="identifier">mean</span><span class="special">,</span> <span class="number">0.05</span><span class="special">);</span>
+<span class="identifier">cout</span> <span class="special">&lt;&lt;</span> <span class="string">"Quantile of "</span> <span class="special">&lt;&lt;</span> <span class="identifier">p</span> <span class="special">&lt;&lt;</span> <span class="string">" = "</span> <span class="special">&lt;&lt;</span> <span class="identifier">quantile</span><span class="special">(</span><span class="identifier">pack05</span><span class="special">,</span> <span class="identifier">p</span><span class="special">)</span>
+  <span class="special">&lt;&lt;</span> <span class="string">", mean = "</span> <span class="special">&lt;&lt;</span> <span class="identifier">pack05</span><span class="special">.</span><span class="identifier">mean</span><span class="special">()</span> <span class="special">&lt;&lt;</span> <span class="string">", sd = "</span> <span class="special">&lt;&lt;</span> <span class="identifier">pack05</span><span class="special">.</span><span class="identifier">standard_deviation</span><span class="special">()</span> <span class="special">&lt;&lt;</span> <span class="identifier">endl</span><span class="special">;</span>
+<span class="comment">// Quantile of 0.05 = 2.91776, mean = 3, sd = 0.05
+</span>
+<span class="identifier">cout</span> <span class="special">&lt;&lt;</span><span class="string">"Fraction of packs &gt;= "</span> <span class="special">&lt;&lt;</span> <span class="identifier">minimum_weight</span> <span class="special">&lt;&lt;</span> <span class="string">" with a mean of "</span> <span class="special">&lt;&lt;</span> <span class="identifier">mean</span>
+  <span class="special">&lt;&lt;</span> <span class="string">" and standard deviation of "</span> <span class="special">&lt;&lt;</span> <span class="identifier">pack05</span><span class="special">.</span><span class="identifier">standard_deviation</span><span class="special">()</span>
+  <span class="special">&lt;&lt;</span> <span class="string">" is "</span> <span class="special">&lt;&lt;</span> <span class="identifier">cdf</span><span class="special">(</span><span class="identifier">complement</span><span class="special">(</span><span class="identifier">pack05</span><span class="special">,</span> <span class="identifier">minimum_weight</span><span class="special">))</span> <span class="special">&lt;&lt;</span> <span class="identifier">endl</span><span class="special">;</span>
+<span class="comment">// Fraction of packs &gt;= 2.9 with a mean of 3 and standard deviation of 0.05 is 0.97725</span></pre>
+<p>
+              </p>
+<p>
+              </p>
+<p>
+                So 0.05 was quite a good guess, but we are a little over the 2.9
+                target, so the standard deviation could be a tiny bit more. So we
+                could do some more guessing to get closer, say by increasing standard
+                deviation to 0.06 kg, constructing another new distribution called
+                pack06.
+              </p>
+<p>
+              </p>
+<p>
+                
+</p>
+<pre class="programlisting"><span class="identifier">normal</span> <span class="identifier">pack06</span><span class="special">(</span><span class="identifier">mean</span><span class="special">,</span> <span class="number">0.06</span><span class="special">);</span>
+<span class="identifier">cout</span> <span class="special">&lt;&lt;</span> <span class="string">"Quantile of "</span> <span class="special">&lt;&lt;</span> <span class="identifier">p</span> <span class="special">&lt;&lt;</span> <span class="string">" = "</span> <span class="special">&lt;&lt;</span> <span class="identifier">quantile</span><span class="special">(</span><span class="identifier">pack06</span><span class="special">,</span> <span class="identifier">p</span><span class="special">)</span>
+  <span class="special">&lt;&lt;</span> <span class="string">", mean = "</span> <span class="special">&lt;&lt;</span> <span class="identifier">pack06</span><span class="special">.</span><span class="identifier">mean</span><span class="special">()</span> <span class="special">&lt;&lt;</span> <span class="string">", sd = "</span> <span class="special">&lt;&lt;</span> <span class="identifier">pack06</span><span class="special">.</span><span class="identifier">standard_deviation</span><span class="special">()</span> <span class="special">&lt;&lt;</span> <span class="identifier">endl</span><span class="special">;</span>
+<span class="comment">// Quantile of 0.05 = 2.90131, mean = 3, sd = 0.06
+</span>
+<span class="identifier">cout</span> <span class="special">&lt;&lt;</span><span class="string">"Fraction of packs &gt;= "</span> <span class="special">&lt;&lt;</span> <span class="identifier">minimum_weight</span> <span class="special">&lt;&lt;</span> <span class="string">" with a mean of "</span> <span class="special">&lt;&lt;</span> <span class="identifier">mean</span>
+  <span class="special">&lt;&lt;</span> <span class="string">" and standard deviation of "</span> <span class="special">&lt;&lt;</span> <span class="identifier">pack06</span><span class="special">.</span><span class="identifier">standard_deviation</span><span class="special">()</span>
+  <span class="special">&lt;&lt;</span> <span class="string">" is "</span> <span class="special">&lt;&lt;</span> <span class="identifier">cdf</span><span class="special">(</span><span class="identifier">complement</span><span class="special">(</span><span class="identifier">pack06</span><span class="special">,</span> <span class="identifier">minimum_weight</span><span class="special">))</span> <span class="special">&lt;&lt;</span> <span class="identifier">endl</span><span class="special">;</span>
+<span class="comment">// Fraction of packs &gt;= 2.9 with a mean of 3 and standard deviation of 0.06 is 0.95221</span></pre>
+<p>
+              </p>
+<p>
+              </p>
+<p>
+                Now we are getting really close, but to do the job properly, we might
+                need to use root finding method, for example the tools provided,
+                and used elsewhere, in the Math Toolkit, see <a class="link" href="../../../../toolkit/internals1/roots2.html" title="Root Finding Without Derivatives">Root
+                Finding Without Derivatives</a>.
+              </p>
+<p>
+              </p>
+<p>
+                But in this (normal) distribution case, we can and should be even
+                smarter and make a direct calculation.
+              </p>
+<p>
+              </p>
+<p>
+                Our required limit is minimum_weight = 2.9 kg, often called the random
+                variate z. For a standard normal distribution, then probability p
+                = N((minimum_weight - mean) / sd).
+              </p>
+<p>
+              </p>
+<p>
+                We want to find the standard deviation that would be required to
+                meet this limit, so that the p th quantile is located at z (minimum_weight).
+                In this case, the 0.05 (5%) quantile is at 2.9 kg pack weight, when
+                the mean is 3 kg, ensuring that 0.95 (95%) of packs are above the
+                minimum weight.
+              </p>
+<p>
+              </p>
+<p>
+                Rearranging, we can directly calculate the required standard deviation:
+              </p>
+<p>
+              </p>
+<p>
+                
+</p>
+<pre class="programlisting"><span class="identifier">normal</span> <span class="identifier">N01</span><span class="special">;</span> <span class="comment">// standard normal distribution with meamn zero and unit standard deviation.
+</span><span class="identifier">p</span> <span class="special">=</span> <span class="number">0.05</span><span class="special">;</span>
+<span class="keyword">double</span> <span class="identifier">qp</span> <span class="special">=</span> <span class="identifier">quantile</span><span class="special">(</span><span class="identifier">N01</span><span class="special">,</span> <span class="identifier">p</span><span class="special">);</span>
+<span class="keyword">double</span> <span class="identifier">sd95</span> <span class="special">=</span> <span class="special">(</span><span class="identifier">minimum_weight</span> <span class="special">-</span> <span class="identifier">mean</span><span class="special">)</span> <span class="special">/</span> <span class="identifier">qp</span><span class="special">;</span>
+
+<span class="identifier">cout</span> <span class="special">&lt;&lt;</span> <span class="string">"For the "</span><span class="special">&lt;&lt;</span> <span class="identifier">p</span> <span class="special">&lt;&lt;</span> <span class="string">"th quantile to be located at "</span>
+  <span class="special">&lt;&lt;</span> <span class="identifier">minimum_weight</span> <span class="special">&lt;&lt;</span> <span class="string">", would need a standard deviation of "</span> <span class="special">&lt;&lt;</span> <span class="identifier">sd95</span> <span class="special">&lt;&lt;</span> <span class="identifier">endl</span><span class="special">;</span>
+<span class="comment">// For the 0.05th quantile to be located at 2.9, would need a standard deviation of 0.0607957</span></pre>
+<p>
+              </p>
+<p>
+              </p>
+<p>
+                We can now construct a new (normal) distribution pack95 for the 'better'
+                packer, and check that our distribution will meet the specification.
+              </p>
+<p>
+              </p>
+<p>
+                
+</p>
+<pre class="programlisting"><span class="identifier">normal</span> <span class="identifier">pack95</span><span class="special">(</span><span class="identifier">mean</span><span class="special">,</span> <span class="identifier">sd95</span><span class="special">);</span>
+<span class="identifier">cout</span> <span class="special">&lt;&lt;</span><span class="string">"Fraction of packs &gt;= "</span> <span class="special">&lt;&lt;</span> <span class="identifier">minimum_weight</span> <span class="special">&lt;&lt;</span> <span class="string">" with a mean of "</span> <span class="special">&lt;&lt;</span> <span class="identifier">mean</span>
+  <span class="special">&lt;&lt;</span> <span class="string">" and standard deviation of "</span> <span class="special">&lt;&lt;</span> <span class="identifier">pack95</span><span class="special">.</span><span class="identifier">standard_deviation</span><span class="special">()</span>
+  <span class="special">&lt;&lt;</span> <span class="string">" is "</span> <span class="special">&lt;&lt;</span> <span class="identifier">cdf</span><span class="special">(</span><span class="identifier">complement</span><span class="special">(</span><span class="identifier">pack95</span><span class="special">,</span> <span class="identifier">minimum_weight</span><span class="special">))</span> <span class="special">&lt;&lt;</span> <span class="identifier">endl</span><span class="special">;</span>
+<span class="comment">// Fraction of packs &gt;= 2.9 with a mean of 3 and standard deviation of 0.0607957 is 0.95</span></pre>
+<p>
+              </p>
+<p>
+              </p>
+<p>
+                This calculation is generalized in the free function find_scale,
+                as shown below, giving the same standard deviation.
+              </p>
+<p>
+              </p>
+<p>
+                
+</p>
+<pre class="programlisting"><span class="keyword">double</span> <span class="identifier">ss</span> <span class="special">=</span> <span class="identifier">find_scale</span><span class="special">&lt;</span><span class="identifier">normal</span><span class="special">&gt;(</span><span class="identifier">minimum_weight</span><span class="special">,</span> <span class="identifier">under_fraction</span><span class="special">,</span> <span class="identifier">packs</span><span class="special">.</span><span class="identifier">mean</span><span class="special">());</span>
+<span class="identifier">cout</span> <span class="special">&lt;&lt;</span> <span class="string">"find_scale&lt;normal&gt;(minimum_weight, under_fraction, packs.mean()); "</span> <span class="special">&lt;&lt;</span> <span class="identifier">ss</span> <span class="special">&lt;&lt;</span> <span class="identifier">endl</span><span class="special">;</span>
+<span class="comment">// find_scale&lt;normal&gt;(minimum_weight, under_fraction, packs.mean()); 0.0607957</span></pre>
+<p>
+              </p>
+<p>
+              </p>
+<p>
+                If we had defined an over_fraction, or percentage that must pass
+                specification
+              </p>
+<p>
+              </p>
+<p>
+                
+</p>
+<pre class="programlisting"><span class="keyword">double</span> <span class="identifier">over_fraction</span> <span class="special">=</span> <span class="number">0.95</span><span class="special">;</span></pre>
+<p>
+              </p>
+<p>
+              </p>
+<p>
+                And (wrongly) written
+              </p>
+<p>
+              
+</p>
+<pre class="programlisting"><span class="keyword">double</span> <span class="identifier">sso</span> <span class="special">=</span> <span class="identifier">find_scale</span><span class="special">&lt;</span><span class="identifier">normal</span><span class="special">&gt;(</span><span class="identifier">minimum_weight</span><span class="special">,</span> <span class="identifier">over_fraction</span><span class="special">,</span> <span class="identifier">packs</span><span class="special">.</span><span class="identifier">mean</span><span class="special">());</span>
+</pre>
+<p>
+              </p>
+<p>
+                With the default policy, we would get a message like
+              </p>
+<p>
+              
+</p>
+<pre class="programlisting">Message from thrown exception was:
+   Error in function boost::math::find_scale&lt;Dist, Policy&gt;(double, double, double, Policy):
+   Computed scale (-0.060795683191176959) is &lt;= 0! Was the complement intended?
+</pre>
+<p>
+              </p>
+<p>
+                But this would return a <span class="bold"><strong>negative</strong></span>
+                standard deviation - obviously impossible. The probability should
+                be 1 - over_fraction, not over_fraction, thus:
+              </p>
+<p>
+              </p>
+<p>
+                
+</p>
+<pre class="programlisting"><span class="keyword">double</span> <span class="identifier">ss1o</span> <span class="special">=</span> <span class="identifier">find_scale</span><span class="special">&lt;</span><span class="identifier">normal</span><span class="special">&gt;(</span><span class="identifier">minimum_weight</span><span class="special">,</span> <span class="number">1</span> <span class="special">-</span> <span class="identifier">over_fraction</span><span class="special">,</span> <span class="identifier">packs</span><span class="special">.</span><span class="identifier">mean</span><span class="special">());</span>
+<span class="identifier">cout</span> <span class="special">&lt;&lt;</span> <span class="string">"find_scale&lt;normal&gt;(minimum_weight, under_fraction, packs.mean()); "</span> <span class="special">&lt;&lt;</span> <span class="identifier">ss1o</span> <span class="special">&lt;&lt;</span> <span class="identifier">endl</span><span class="special">;</span>
+<span class="comment">// find_scale&lt;normal&gt;(minimum_weight, under_fraction, packs.mean()); 0.0607957</span></pre>
+<p>
+              </p>
+<p>
+              </p>
+<p>
+                But notice that using '1 - over_fraction' - will lead to a <a class="link" href="../../overview.html#why_complements">loss of accuracy, especially if over_fraction
+                was close to unity.</a> In this (very common) case, we should
+                instead use the <a class="link" href="../../overview.html#complements">complements</a>, giving
+                the most accurate result.
+              </p>
+<p>
+              </p>
+<p>
+                
+</p>
+<pre class="programlisting"><span class="keyword">double</span> <span class="identifier">ssc</span> <span class="special">=</span> <span class="identifier">find_scale</span><span class="special">&lt;</span><span class="identifier">normal</span><span class="special">&gt;(</span><span class="identifier">complement</span><span class="special">(</span><span class="identifier">minimum_weight</span><span class="special">,</span> <span class="identifier">over_fraction</span><span class="special">,</span> <span class="identifier">packs</span><span class="special">.</span><span class="identifier">mean</span><span class="special">()));</span>
+<span class="identifier">cout</span> <span class="special">&lt;&lt;</span> <span class="string">"find_scale&lt;normal&gt;(complement(minimum_weight, over_fraction, packs.mean())); "</span> <span class="special">&lt;&lt;</span> <span class="identifier">ssc</span> <span class="special">&lt;&lt;</span> <span class="identifier">endl</span><span class="special">;</span>
+<span class="comment">// find_scale&lt;normal&gt;(complement(minimum_weight, over_fraction, packs.mean())); 0.0607957</span></pre>
+<p>
+              </p>
+<p>
+              </p>
+<p>
+                Note that our guess of 0.06 was close to the accurate value of 0.060795683191176959.
+              </p>
+<p>
+              </p>
+<p>
+                We can again confirm our prediction thus:
+              </p>
+<p>
+              </p>
+<p>
+                
+</p>
+<pre class="programlisting"><span class="identifier">normal</span> <span class="identifier">pack95c</span><span class="special">(</span><span class="identifier">mean</span><span class="special">,</span> <span class="identifier">ssc</span><span class="special">);</span>
+<span class="identifier">cout</span> <span class="special">&lt;&lt;</span><span class="string">"Fraction of packs &gt;= "</span> <span class="special">&lt;&lt;</span> <span class="identifier">minimum_weight</span> <span class="special">&lt;&lt;</span> <span class="string">" with a mean of "</span> <span class="special">&lt;&lt;</span> <span class="identifier">mean</span>
+  <span class="special">&lt;&lt;</span> <span class="string">" and standard deviation of "</span> <span class="special">&lt;&lt;</span> <span class="identifier">pack95c</span><span class="special">.</span><span class="identifier">standard_deviation</span><span class="special">()</span>
+  <span class="special">&lt;&lt;</span> <span class="string">" is "</span> <span class="special">&lt;&lt;</span> <span class="identifier">cdf</span><span class="special">(</span><span class="identifier">complement</span><span class="special">(</span><span class="identifier">pack95c</span><span class="special">,</span> <span class="identifier">minimum_weight</span><span class="special">))</span> <span class="special">&lt;&lt;</span> <span class="identifier">endl</span><span class="special">;</span>
+<span class="comment">// Fraction of packs &gt;= 2.9 with a mean of 3 and standard deviation of 0.0607957 is 0.95</span></pre>
+<p>
+              </p>
+<p>
+              </p>
+<p>
+                Notice that these two deceptively simple questions:
+              </p>
+<p>
+              </p>
+<div class="itemizedlist"><ul type="disc"><li>
+                  Do we over-fill to make sure we meet a minimum specification (or
+                  under-fill to avoid an overdose)?
+                </li></ul></div>
+<p>
+              </p>
+<p>
+                and/or
+              </p>
+<p>
+              </p>
+<div class="itemizedlist"><ul type="disc"><li>
+                  Do we measure better?
+                </li></ul></div>
+<p>
+              </p>
+<p>
+                are actually extremely common.
+              </p>
+<p>
+              </p>
+<p>
+                The weight of beef might be replaced by a measurement of more or
+                less anything, from drug tablet content, Apollo landing rocket firing,
+                X-ray treatment doses...
+              </p>
+<p>
+              </p>
+<p>
+                The scale can be variation in dispensing or uncertainty in measurement.
+              </p>
+<p>
+              See find_mean_and_sd_normal.cpp
+              for full source code &amp; appended program output.
+            </p>
+</div>
+<table xmlns:rev="http://www.cs.rpi.edu/~gregod/boost/tools/doc/revision" width="100%"><tr>
+<td align="left"></td>
+<td align="right"><div class="copyright-footer">Copyright © 2006 , 2007, 2008 John Maddock, Paul A. Bristow, Hubert
+      Holin, Xiaogang Zhang, Bruno Lalande and Gautam Sewani<p>
+        Distributed under the Boost Software License, Version 1.0. (See accompanying
+        file LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_0.txt)
+      </p>
+</div></td>
+</tr></table>
+<hr>
+<div class="spirit-nav">
+<a accesskey="p" href="find_scale_eg.html"><img src="../../../../../../../doc/html/images/prev.png" alt="Prev"></a><a accesskey="u" href="../find_eg.html"><img src="../../../../../../../doc/html/images/up.png" alt="Up"></a><a accesskey="h" href="../../../../../index.html"><img src="../../../../../../../doc/html/images/home.png" alt="Home"></a><a accesskey="n" href="../nag_library.html"><img src="../../../../../../../doc/html/images/next.png" alt="Next"></a>
+</div>
+</body>
+</html>

Added: sandbox/tools/auto_index/example/math/doc/sf_and_dist/html/math_toolkit/dist/stat_tut/weg/find_eg/find_scale_eg.html
==============================================================================
--- (empty file)
+++ sandbox/tools/auto_index/example/math/doc/sf_and_dist/html/math_toolkit/dist/stat_tut/weg/find_eg/find_scale_eg.html	2008-11-28 05:25:28 EST (Fri, 28 Nov 2008)
@@ -0,0 +1,306 @@
+<html>
+<head>
+<meta http-equiv="Content-Type" content="text/html; charset=ISO-8859-1">
+<title>Find Scale (Standard Deviation) Example</title>
+<link rel="stylesheet" href="../../../../../boostbook.css" type="text/css">
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+<link rel="home" href="../../../../../index.html" title="Math Toolkit">
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+</div>
+<div class="section" lang="en">
+<div class="titlepage"><div><div><h6 class="title">
+<a name="math_toolkit.dist.stat_tut.weg.find_eg.find_scale_eg"></a><a class="link" href="find_scale_eg.html" title="Find Scale (Standard Deviation) Example">
+            Find Scale (Standard Deviation) Example</a>
+</h6></div></div></div>
+<p>
+              </p>
+<p>
+                First we need some includes to access the <a class="link" href="../../../dist_ref/dists/normal_dist.html" title="Normal (Gaussian) Distribution">Normal
+                Distribution</a>, the algorithms to find scale (and some std output
+                of course).
+              </p>
+<p>
+              </p>
+<p>
+                
+</p>
+<pre class="programlisting"><span class="preprocessor">#include</span> <span class="special">&lt;</span><span class="identifier">boost</span><span class="special">/</span><span class="identifier">math</span><span class="special">/</span><span class="identifier">distributions</span><span class="special">/</span><span class="identifier">normal</span><span class="special">.</span><span class="identifier">hpp</span><span class="special">&gt;</span> <span class="comment">// for normal_distribution
+</span>  <span class="keyword">using</span> <span class="identifier">boost</span><span class="special">::</span><span class="identifier">math</span><span class="special">::</span><span class="identifier">normal</span><span class="special">;</span> <span class="comment">// typedef provides default type is double.
+</span><span class="preprocessor">#include</span> <span class="special">&lt;</span><span class="identifier">boost</span><span class="special">/</span><span class="identifier">math</span><span class="special">/</span><span class="identifier">distributions</span><span class="special">/</span><span class="identifier">find_scale</span><span class="special">.</span><span class="identifier">hpp</span><span class="special">&gt;</span>
+  <span class="keyword">using</span> <span class="identifier">boost</span><span class="special">::</span><span class="identifier">math</span><span class="special">::</span><span class="identifier">find_scale</span><span class="special">;</span> 
+  <span class="keyword">using</span> <span class="identifier">boost</span><span class="special">::</span><span class="identifier">math</span><span class="special">::</span><span class="identifier">complement</span><span class="special">;</span> <span class="comment">// Needed if you want to use the complement version.
+</span>  <span class="keyword">using</span> <span class="identifier">boost</span><span class="special">::</span><span class="identifier">math</span><span class="special">::</span><span class="identifier">policies</span><span class="special">::</span><span class="identifier">policy</span><span class="special">;</span> <span class="comment">// Needed to specify the error handling policy.
+</span>
+<span class="preprocessor">#include</span> <span class="special">&lt;</span><span class="identifier">iostream</span><span class="special">&gt;</span>
+  <span class="keyword">using</span> <span class="identifier">std</span><span class="special">::</span><span class="identifier">cout</span><span class="special">;</span> <span class="keyword">using</span> <span class="identifier">std</span><span class="special">::</span><span class="identifier">endl</span><span class="special">;</span>
+<span class="preprocessor">#include</span> <span class="special">&lt;</span><span class="identifier">iomanip</span><span class="special">&gt;</span>
+  <span class="keyword">using</span> <span class="identifier">std</span><span class="special">::</span><span class="identifier">setw</span><span class="special">;</span> <span class="keyword">using</span> <span class="identifier">std</span><span class="special">::</span><span class="identifier">setprecision</span><span class="special">;</span>
+<span class="preprocessor">#include</span> <span class="special">&lt;</span><span class="identifier">limits</span><span class="special">&gt;</span>
+  <span class="keyword">using</span> <span class="identifier">std</span><span class="special">::</span><span class="identifier">numeric_limits</span><span class="special">;</span>
+</pre>
+<p>
+              </p>
+<p>
+              </p>
+<p>
+                For this example, we will use the standard <a class="link" href="../../../dist_ref/dists/normal_dist.html" title="Normal (Gaussian) Distribution">Normal
+                Distribution</a>, with location (mean) zero and standard deviation
+                (scale) unity. Conveniently, this is also the default for this implementation's
+                constructor.
+              </p>
+<p>
+              </p>
+<p>
+                
+</p>
+<pre class="programlisting"><span class="identifier">normal</span> <span class="identifier">N01</span><span class="special">;</span>  <span class="comment">// Default 'standard' normal distribution with zero mean
+</span><span class="keyword">double</span> <span class="identifier">sd</span> <span class="special">=</span> <span class="number">1.</span><span class="special">;</span> <span class="comment">// and standard deviation is 1.</span></pre>
+<p>
+              </p>
+<p>
+              </p>
+<p>
+                Suppose we want to find a different normal distribution with standard
+                deviation so that only fraction p (here 0.001 or 0.1%) are below
+                a certain chosen limit (here -2. standard deviations).
+              </p>
+<p>
+              </p>
+<p>
+                
+</p>
+<pre class="programlisting"><span class="keyword">double</span> <span class="identifier">z</span> <span class="special">=</span> <span class="special">-</span><span class="number">2.</span><span class="special">;</span> <span class="comment">// z to give prob p
+</span><span class="keyword">double</span> <span class="identifier">p</span> <span class="special">=</span> <span class="number">0.001</span><span class="special">;</span> <span class="comment">// only 0.1% below z = -2
+</span>
+<span class="identifier">cout</span> <span class="special">&lt;&lt;</span> <span class="string">"Normal distribution with mean = "</span> <span class="special">&lt;&lt;</span> <span class="identifier">N01</span><span class="special">.</span><span class="identifier">location</span><span class="special">()</span>  <span class="comment">// aka N01.mean()
+</span>  <span class="special">&lt;&lt;</span> <span class="string">", standard deviation "</span> <span class="special">&lt;&lt;</span> <span class="identifier">N01</span><span class="special">.</span><span class="identifier">scale</span><span class="special">()</span> <span class="comment">// aka N01.standard_deviation()
+</span>  <span class="special">&lt;&lt;</span> <span class="string">", has "</span> <span class="special">&lt;&lt;</span> <span class="string">"fraction &lt;= "</span> <span class="special">&lt;&lt;</span> <span class="identifier">z</span> 
+  <span class="special">&lt;&lt;</span> <span class="string">", p = "</span>  <span class="special">&lt;&lt;</span> <span class="identifier">cdf</span><span class="special">(</span><span class="identifier">N01</span><span class="special">,</span> <span class="identifier">z</span><span class="special">)</span> <span class="special">&lt;&lt;</span> <span class="identifier">endl</span><span class="special">;</span>
+<span class="identifier">cout</span> <span class="special">&lt;&lt;</span> <span class="string">"Normal distribution with mean = "</span> <span class="special">&lt;&lt;</span> <span class="identifier">N01</span><span class="special">.</span><span class="identifier">location</span><span class="special">()</span>
+  <span class="special">&lt;&lt;</span> <span class="string">", standard deviation "</span> <span class="special">&lt;&lt;</span> <span class="identifier">N01</span><span class="special">.</span><span class="identifier">scale</span><span class="special">()</span>
+  <span class="special">&lt;&lt;</span> <span class="string">", has "</span> <span class="special">&lt;&lt;</span> <span class="string">"fraction &gt; "</span> <span class="special">&lt;&lt;</span> <span class="identifier">z</span>
+  <span class="special">&lt;&lt;</span> <span class="string">", p = "</span>  <span class="special">&lt;&lt;</span> <span class="identifier">cdf</span><span class="special">(</span><span class="identifier">complement</span><span class="special">(</span><span class="identifier">N01</span><span class="special">,</span> <span class="identifier">z</span><span class="special">))</span> <span class="special">&lt;&lt;</span> <span class="identifier">endl</span><span class="special">;</span> <span class="comment">// Note: uses complement.</span></pre>
+<p>
+              </p>
+<p>
+              
+</p>
+<pre class="programlisting">Normal distribution with mean = 0 has fraction &lt;= -2, p = 0.0227501
+Normal distribution with mean = 0 has fraction &gt; -2, p = 0.97725
+</pre>
+<p>
+              </p>
+<p>
+                Noting that p = 0.02 instead of our target of 0.001, we can now use
+                <code class="computeroutput"><span class="identifier">find_scale</span></code> to give
+                a new standard deviation.
+              </p>
+<p>
+              </p>
+<p>
+                
+</p>
+<pre class="programlisting"><span class="keyword">double</span> <span class="identifier">l</span> <span class="special">=</span> <span class="identifier">N01</span><span class="special">.</span><span class="identifier">location</span><span class="special">();</span>
+<span class="keyword">double</span> <span class="identifier">s</span> <span class="special">=</span> <span class="identifier">find_scale</span><span class="special">&lt;</span><span class="identifier">normal</span><span class="special">&gt;(</span><span class="identifier">z</span><span class="special">,</span> <span class="identifier">p</span><span class="special">,</span> <span class="identifier">l</span><span class="special">);</span>
+<span class="identifier">cout</span> <span class="special">&lt;&lt;</span> <span class="string">"scale (standard deviation) = "</span> <span class="special">&lt;&lt;</span> <span class="identifier">s</span> <span class="special">&lt;&lt;</span> <span class="identifier">endl</span><span class="special">;</span></pre>
+<p>
+              </p>
+<p>
+              </p>
+<p>
+                that outputs:
+              </p>
+<p>
+              
+</p>
+<pre class="programlisting">scale (standard deviation) = 0.647201
+</pre>
+<p>
+              </p>
+<p>
+                showing that we need to reduce the standard deviation from 1. to
+                0.65.
+              </p>
+<p>
+              </p>
+<p>
+                Then we can check that we have achieved our objective by constructing
+                a new distribution with the new standard deviation (but same zero
+                mean):
+              </p>
+<p>
+              </p>
+<p>
+                
+</p>
+<pre class="programlisting"><span class="identifier">normal</span> <span class="identifier">np001pc</span><span class="special">(</span><span class="identifier">N01</span><span class="special">.</span><span class="identifier">location</span><span class="special">(),</span> <span class="identifier">s</span><span class="special">);</span></pre>
+<p>
+              </p>
+<p>
+              </p>
+<p>
+                And re-calculating the fraction below (and above) our chosen limit.
+              </p>
+<p>
+              </p>
+<p>
+                
+</p>
+<pre class="programlisting"><span class="identifier">cout</span> <span class="special">&lt;&lt;</span> <span class="string">"Normal distribution with mean = "</span> <span class="special">&lt;&lt;</span> <span class="identifier">l</span> 
+  <span class="special">&lt;&lt;</span> <span class="string">" has "</span> <span class="special">&lt;&lt;</span> <span class="string">"fraction &lt;= "</span> <span class="special">&lt;&lt;</span> <span class="identifier">z</span> 
+  <span class="special">&lt;&lt;</span> <span class="string">", p = "</span>  <span class="special">&lt;&lt;</span> <span class="identifier">cdf</span><span class="special">(</span><span class="identifier">np001pc</span><span class="special">,</span> <span class="identifier">z</span><span class="special">)</span> <span class="special">&lt;&lt;</span> <span class="identifier">endl</span><span class="special">;</span>
+<span class="identifier">cout</span> <span class="special">&lt;&lt;</span> <span class="string">"Normal distribution with mean = "</span> <span class="special">&lt;&lt;</span> <span class="identifier">l</span> 
+  <span class="special">&lt;&lt;</span> <span class="string">" has "</span> <span class="special">&lt;&lt;</span> <span class="string">"fraction &gt; "</span> <span class="special">&lt;&lt;</span> <span class="identifier">z</span> 
+  <span class="special">&lt;&lt;</span> <span class="string">", p = "</span>  <span class="special">&lt;&lt;</span> <span class="identifier">cdf</span><span class="special">(</span><span class="identifier">complement</span><span class="special">(</span><span class="identifier">np001pc</span><span class="special">,</span> <span class="identifier">z</span><span class="special">))</span> <span class="special">&lt;&lt;</span> <span class="identifier">endl</span><span class="special">;</span></pre>
+<p>
+              </p>
+<p>
+              
+</p>
+<pre class="programlisting">Normal distribution with mean = 0 has fraction &lt;= -2, p = 0.001
+Normal distribution with mean = 0 has fraction &gt; -2, p = 0.999
+</pre>
+<p>
+              <a name="math_toolkit.dist.stat_tut.weg.find_eg.find_scale_eg.controlling_how_errors_from_find_scale_are_handled"></a>
+              </p>
+<h5>
+<a name="id630055"></a>
+                <a class="link" href="find_scale_eg.html#math_toolkit.dist.stat_tut.weg.find_eg.find_scale_eg.controlling_how_errors_from_find_scale_are_handled">Controlling
+                how Errors from find_scale are handled</a>
+              </h5>
+<p>
+              </p>
+<p>
+                We can also control the policy for handling various errors. For example,
+                we can define a new (possibly unwise) policy to ignore domain errors
+                ('bad' arguments).
+              </p>
+<p>
+              </p>
+<p>
+                Unless we are using the boost::math namespace, we will need:
+              </p>
+<p>
+              </p>
+<p>
+                
+</p>
+<pre class="programlisting"><span class="keyword">using</span> <span class="identifier">boost</span><span class="special">::</span><span class="identifier">math</span><span class="special">::</span><span class="identifier">policies</span><span class="special">::</span><span class="identifier">policy</span><span class="special">;</span>
+<span class="keyword">using</span> <span class="identifier">boost</span><span class="special">::</span><span class="identifier">math</span><span class="special">::</span><span class="identifier">policies</span><span class="special">::</span><span class="identifier">domain_error</span><span class="special">;</span>
+<span class="keyword">using</span> <span class="identifier">boost</span><span class="special">::</span><span class="identifier">math</span><span class="special">::</span><span class="identifier">policies</span><span class="special">::</span><span class="identifier">ignore_error</span><span class="special">;</span></pre>
+<p>
+              </p>
+<p>
+              </p>
+<p>
+                Using a typedef is convenient, especially if it is re-used, although
+                it is not required, as the various examples below show.
+              </p>
+<p>
+              </p>
+<p>
+                
+</p>
+<pre class="programlisting"><span class="keyword">typedef</span> <span class="identifier">policy</span><span class="special">&lt;</span><span class="identifier">domain_error</span><span class="special">&lt;</span><span class="identifier">ignore_error</span><span class="special">&gt;</span> <span class="special">&gt;</span> <span class="identifier">ignore_domain_policy</span><span class="special">;</span>
+<span class="comment">// find_scale with new policy, using typedef.
+</span><span class="identifier">l</span> <span class="special">=</span> <span class="identifier">find_scale</span><span class="special">&lt;</span><span class="identifier">normal</span><span class="special">&gt;(</span><span class="identifier">z</span><span class="special">,</span> <span class="identifier">p</span><span class="special">,</span> <span class="identifier">l</span><span class="special">,</span> <span class="identifier">ignore_domain_policy</span><span class="special">());</span>
+<span class="comment">// Default policy policy&lt;&gt;, needs using boost::math::policies::policy;
+</span>
+<span class="identifier">l</span> <span class="special">=</span> <span class="identifier">find_scale</span><span class="special">&lt;</span><span class="identifier">normal</span><span class="special">&gt;(</span><span class="identifier">z</span><span class="special">,</span> <span class="identifier">p</span><span class="special">,</span> <span class="identifier">l</span><span class="special">,</span> <span class="identifier">policy</span><span class="special">&lt;&gt;());</span>
+<span class="comment">// Default policy, fully specified.
+</span><span class="identifier">l</span> <span class="special">=</span> <span class="identifier">find_scale</span><span class="special">&lt;</span><span class="identifier">normal</span><span class="special">&gt;(</span><span class="identifier">z</span><span class="special">,</span> <span class="identifier">p</span><span class="special">,</span> <span class="identifier">l</span><span class="special">,</span> <span class="identifier">boost</span><span class="special">::</span><span class="identifier">math</span><span class="special">::</span><span class="identifier">policies</span><span class="special">::</span><span class="identifier">policy</span><span class="special">&lt;&gt;());</span>
+<span class="comment">// New policy, without typedef.
+</span><span class="identifier">l</span> <span class="special">=</span> <span class="identifier">find_scale</span><span class="special">&lt;</span><span class="identifier">normal</span><span class="special">&gt;(</span><span class="identifier">z</span><span class="special">,</span> <span class="identifier">p</span><span class="special">,</span> <span class="identifier">l</span><span class="special">,</span> <span class="identifier">policy</span><span class="special">&lt;</span><span class="identifier">domain_error</span><span class="special">&lt;</span><span class="identifier">ignore_error</span><span class="special">&gt;</span> <span class="special">&gt;());</span></pre>
+<p>
+              </p>
+<p>
+              </p>
+<p>
+                If we want to express a probability, say 0.999, that is a complement,
+                <code class="computeroutput"><span class="number">1</span> <span class="special">-</span>
+                <span class="identifier">p</span></code> we should not even think
+                of writing <code class="computeroutput"><span class="identifier">find_scale</span><span class="special">&lt;</span><span class="identifier">normal</span><span class="special">&gt;(</span><span class="identifier">z</span><span class="special">,</span> <span class="number">1</span> <span class="special">-</span> <span class="identifier">p</span><span class="special">,</span> <span class="identifier">l</span><span class="special">)</span></code>, but <a class="link" href="../../overview.html#why_complements">instead</a>,
+                use the <a class="link" href="../../overview.html#complements">complements</a> version.
+              </p>
+<p>
+              </p>
+<p>
+                
+</p>
+<pre class="programlisting"><span class="identifier">z</span> <span class="special">=</span> <span class="special">-</span><span class="number">2.</span><span class="special">;</span>
+<span class="keyword">double</span> <span class="identifier">q</span> <span class="special">=</span> <span class="number">0.999</span><span class="special">;</span> <span class="comment">// = 1 - p; // complement of 0.001.
+</span><span class="identifier">sd</span> <span class="special">=</span> <span class="identifier">find_scale</span><span class="special">&lt;</span><span class="identifier">normal</span><span class="special">&gt;(</span><span class="identifier">complement</span><span class="special">(</span><span class="identifier">z</span><span class="special">,</span> <span class="identifier">q</span><span class="special">,</span> <span class="identifier">l</span><span class="special">));</span>
+
+<span class="identifier">normal</span> <span class="identifier">np95pc</span><span class="special">(</span><span class="identifier">l</span><span class="special">,</span> <span class="identifier">sd</span><span class="special">);</span> <span class="comment">// Same standard_deviation (scale) but with mean(scale) shifted
+</span><span class="identifier">cout</span> <span class="special">&lt;&lt;</span> <span class="string">"Normal distribution with mean = "</span> <span class="special">&lt;&lt;</span> <span class="identifier">l</span> <span class="special">&lt;&lt;</span> <span class="string">" has "</span> 
+  <span class="special">&lt;&lt;</span> <span class="string">"fraction &lt;= "</span> <span class="special">&lt;&lt;</span> <span class="identifier">z</span> <span class="special">&lt;&lt;</span> <span class="string">" = "</span>  <span class="special">&lt;&lt;</span> <span class="identifier">cdf</span><span class="special">(</span><span class="identifier">np95pc</span><span class="special">,</span> <span class="identifier">z</span><span class="special">)</span> <span class="special">&lt;&lt;</span> <span class="identifier">endl</span><span class="special">;</span>
+<span class="identifier">cout</span> <span class="special">&lt;&lt;</span> <span class="string">"Normal distribution with mean = "</span> <span class="special">&lt;&lt;</span> <span class="identifier">l</span> <span class="special">&lt;&lt;</span> <span class="string">" has "</span> 
+  <span class="special">&lt;&lt;</span> <span class="string">"fraction &gt; "</span> <span class="special">&lt;&lt;</span> <span class="identifier">z</span> <span class="special">&lt;&lt;</span> <span class="string">" = "</span>  <span class="special">&lt;&lt;</span> <span class="identifier">cdf</span><span class="special">(</span><span class="identifier">complement</span><span class="special">(</span><span class="identifier">np95pc</span><span class="special">,</span> <span class="identifier">z</span><span class="special">))</span> <span class="special">&lt;&lt;</span> <span class="identifier">endl</span><span class="special">;</span></pre>
+<p>
+              </p>
+<p>
+              </p>
+<p>
+                Sadly, it is all too easy to get probabilities the wrong way round,
+                when you may get a warning like this:
+              </p>
+<p>
+              
+</p>
+<pre class="programlisting">Message from thrown exception was:
+   Error in function boost::math::find_scale&lt;Dist, Policy&gt;(complement(double, double, double, Policy)):
+   Computed scale (-0.48043523852179076) is &lt;= 0! Was the complement intended?
+</pre>
+<p>
+              </p>
+<p>
+                The default error handling policy is to throw an exception with this
+                message, but if you chose a policy to ignore the error, the (impossible)
+                negative scale is quietly returned.
+              </p>
+<p>
+              See find_scale_example.cpp
+              for full source code: the program output looks like this: 
+</p>
+<pre class="programlisting">Example: Find scale (standard deviation).
+Normal distribution with mean = 0, standard deviation 1, has fraction &lt;= -2, p = 0.0227501
+Normal distribution with mean = 0, standard deviation 1, has fraction &gt; -2, p = 0.97725
+scale (standard deviation) = 0.647201
+Normal distribution with mean = 0 has fraction &lt;= -2, p = 0.001
+Normal distribution with mean = 0 has fraction &gt; -2, p = 0.999
+Normal distribution with mean = 0.946339 has fraction &lt;= -2 = 0.001
+Normal distribution with mean = 0.946339 has fraction &gt; -2 = 0.999
+</pre>
+<p>
+            </p>
+</div>
+<table xmlns:rev="http://www.cs.rpi.edu/~gregod/boost/tools/doc/revision" width="100%"><tr>
+<td align="left"></td>
+<td align="right"><div class="copyright-footer">Copyright © 2006 , 2007, 2008 John Maddock, Paul A. Bristow, Hubert
+      Holin, Xiaogang Zhang, Bruno Lalande and Gautam Sewani<p>
+        Distributed under the Boost Software License, Version 1.0. (See accompanying
+        file LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_0.txt)
+      </p>
+</div></td>
+</tr></table>
+<hr>
+<div class="spirit-nav">
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+</div>
+</body>
+</html>

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@@ -0,0 +1,114 @@
+<html>
+<head>
+<meta http-equiv="Content-Type" content="text/html; charset=ISO-8859-1">
+<title>Comparison with C, R, FORTRAN-style Free Functions</title>
+<link rel="stylesheet" href="../../../../boostbook.css" type="text/css">
+<meta name="generator" content="DocBook XSL Stylesheets Vsnapshot_8125">
+<link rel="home" href="../../../../index.html" title="Math Toolkit">
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+<link rel="next" href="../variates.html" title="Random Variates and Distribution Parameters">
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+<table cellpadding="2" width="100%"><tr>
+<td valign="top"><img alt="Boost C++ Libraries" width="277" height="86" src="../../../../../../boost.png"></td>
+<td align="center">Home</td>
+<td align="center">Libraries</td>
+<td align="center">People</td>
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+</div>
+<div class="section" lang="en">
+<div class="titlepage"><div><div><h5 class="title">
+<a name="math_toolkit.dist.stat_tut.weg.nag_library"></a><a class="link" href="nag_library.html" title="Comparison with C, R, FORTRAN-style Free Functions"> Comparison
+          with C, R, FORTRAN-style Free Functions</a>
+</h5></div></div></div>
+<p>
+            You are probably familiar with a statistics library that has free functions,
+            for example the classic <a href="http://nag.com/numeric/CL/CLdescription.asp" target="_top">NAG
+            C library</a> and matching <a href="http://nag.com/numeric/FL/FLdescription.asp" target="_top">NAG
+            FORTRAN Library</a>, <a href="http://office.microsoft.com/en-us/excel/HP052090051033.aspx" target="_top">Microsoft
+            Excel BINOMDIST(number_s,trials,probability_s,cumulative)</a>, R, <a href="http://www.ptc.com/products/mathcad/mathcad14/mathcad_func_chart.htm" target="_top">MathCAD
+            pbinom</a> and many others.
+          </p>
+<p>
+            If so, you may find 'Distributions as Objects' unfamiliar, if not alien.
+          </p>
+<p>
+            However, <span class="bold"><strong>do not panic</strong></span>, both definition
+            and usage are not really very different.
+          </p>
+<p>
+            A very simple example of generating the same values as the <a href="http://nag.com/numeric/CL/CLdescription.asp" target="_top">NAG
+            C library</a> for the binomial distribution follows. (If you find
+            slightly different values, the Boost C++ version, using double or better,
+            is very likely to be the more accurate. Of course, accuracy is not usually
+            a concern for most applications of this function).
+          </p>
+<p>
+            The <a href="http://www.nag.co.uk/numeric/cl/manual/pdf/G01/g01bjc.pdf" target="_top">NAG
+            function specification</a> is
+          </p>
+<pre class="programlisting"><span class="keyword">void</span> <span class="identifier">nag_binomial_dist</span><span class="special">(</span><span class="identifier">Integer</span> <span class="identifier">n</span><span class="special">,</span> <span class="keyword">double</span> <span class="identifier">p</span><span class="special">,</span> <span class="identifier">Integer</span> <span class="identifier">k</span><span class="special">,</span>
+<span class="keyword">double</span> <span class="special">*</span><span class="identifier">plek</span><span class="special">,</span> <span class="keyword">double</span> <span class="special">*</span><span class="identifier">pgtk</span><span class="special">,</span> <span class="keyword">double</span> <span class="special">*</span><span class="identifier">peqk</span><span class="special">,</span> <span class="identifier">NagError</span> <span class="special">*</span><span class="identifier">fail</span><span class="special">)</span>
+</pre>
+<p>
+            and is called
+          </p>
+<pre class="programlisting"><span class="identifier">g01bjc</span><span class="special">(</span><span class="identifier">n</span><span class="special">,</span> <span class="identifier">p</span><span class="special">,</span> <span class="identifier">k</span><span class="special">,</span> <span class="special">&amp;</span><span class="identifier">plek</span><span class="special">,</span> <span class="special">&amp;</span><span class="identifier">pgtk</span><span class="special">,</span> <span class="special">&amp;</span><span class="identifier">peqk</span><span class="special">,</span> <span class="identifier">NAGERR_DEFAULT</span><span class="special">);</span>
+</pre>
+<p>
+            The equivalent using this Boost C++ library is:
+          </p>
+<pre class="programlisting"><span class="keyword">using</span> <span class="keyword">namespace</span> <span class="identifier">boost</span><span class="special">::</span><span class="identifier">math</span><span class="special">;</span>  <span class="comment">// Using declaration avoids very long names.
+</span><span class="identifier">binomial</span> <span class="identifier">my_dist</span><span class="special">(</span><span class="number">4</span><span class="special">,</span> <span class="number">0.5</span><span class="special">);</span> <span class="comment">// c.f. NAG n = 4, p = 0.5
+</span></pre>
+<p>
+            and values can be output thus:
+          </p>
+<pre class="programlisting"><span class="identifier">cout</span>
+  <span class="special">&lt;&lt;</span> <span class="identifier">my_dist</span><span class="special">.</span><span class="identifier">trials</span><span class="special">()</span> <span class="special">&lt;&lt;</span> <span class="string">" "</span>             <span class="comment">// Echo the NAG input n = 4 trials.
+</span>  <span class="special">&lt;&lt;</span> <span class="identifier">my_dist</span><span class="special">.</span><span class="identifier">success_fraction</span><span class="special">()</span> <span class="special">&lt;&lt;</span> <span class="string">" "</span>   <span class="comment">// Echo the NAG input p = 0.5
+</span>  <span class="special">&lt;&lt;</span> <span class="identifier">cdf</span><span class="special">(</span><span class="identifier">my_dist</span><span class="special">,</span> <span class="number">2</span><span class="special">)</span> <span class="special">&lt;&lt;</span> <span class="string">"  "</span>             <span class="comment">// NAG plek with k = 2
+</span>  <span class="special">&lt;&lt;</span> <span class="identifier">cdf</span><span class="special">(</span><span class="identifier">complement</span><span class="special">(</span><span class="identifier">my_dist</span><span class="special">,</span> <span class="number">2</span><span class="special">))</span> <span class="special">&lt;&lt;</span> <span class="string">"  "</span> <span class="comment">// NAG pgtk with k = 2
+</span>  <span class="special">&lt;&lt;</span> <span class="identifier">pdf</span><span class="special">(</span><span class="identifier">my_dist</span><span class="special">,</span> <span class="number">2</span><span class="special">)</span> <span class="special">&lt;&lt;</span> <span class="identifier">endl</span><span class="special">;</span>            <span class="comment">// NAG peqk with k = 2
+</span></pre>
+<p>
+            <code class="computeroutput"><span class="identifier">cdf</span><span class="special">(</span><span class="identifier">dist</span><span class="special">,</span> <span class="identifier">k</span><span class="special">)</span></code>
+            is equivalent to NAG library <code class="computeroutput"><span class="identifier">plek</span></code>,
+            lower tail probability of &lt;= k
+          </p>
+<p>
+            <code class="computeroutput"><span class="identifier">cdf</span><span class="special">(</span><span class="identifier">complement</span><span class="special">(</span><span class="identifier">dist</span><span class="special">,</span> <span class="identifier">k</span><span class="special">))</span></code>
+            is equivalent to NAG library <code class="computeroutput"><span class="identifier">pgtk</span></code>,
+            upper tail probability of &gt; k
+          </p>
+<p>
+            <code class="computeroutput"><span class="identifier">pdf</span><span class="special">(</span><span class="identifier">dist</span><span class="special">,</span> <span class="identifier">k</span><span class="special">)</span></code>
+            is equivalent to NAG library <code class="computeroutput"><span class="identifier">peqk</span></code>,
+            point probability of == k
+          </p>
+<p>
+            See binomial_example_nag.cpp
+            for details.
+          </p>
+</div>
+<table xmlns:rev="http://www.cs.rpi.edu/~gregod/boost/tools/doc/revision" width="100%"><tr>
+<td align="left"></td>
+<td align="right"><div class="copyright-footer">Copyright © 2006 , 2007, 2008 John Maddock, Paul A. Bristow, Hubert
+      Holin, Xiaogang Zhang, Bruno Lalande and Gautam Sewani<p>
+        Distributed under the Boost Software License, Version 1.0. (See accompanying
+        file LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_0.txt)
+      </p>
+</div></td>
+</tr></table>
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+</div>
+</body>
+</html>

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@@ -0,0 +1,51 @@
+<html>
+<head>
+<meta http-equiv="Content-Type" content="text/html; charset=ISO-8859-1">
+<title>Non Central Chi Squared Example</title>
+<link rel="stylesheet" href="../../../../boostbook.css" type="text/css">
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+<link rel="next" href="nccs_eg/nccs_power_eg.html" title="Tables of the power function of the &#967;2 test.">
+</head>
+<body bgcolor="white" text="black" link="#0000FF" vlink="#840084" alink="#0000FF">
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+</div>
+<div class="section" lang="en">
+<div class="titlepage"><div><div><h5 class="title">
+<a name="math_toolkit.dist.stat_tut.weg.nccs_eg"></a><a class="link" href="nccs_eg.html" title="Non Central Chi Squared Example"> Non Central
+          Chi Squared Example</a>
+</h5></div></div></div>
+<div class="toc"><dl><dt><span class="section"><a href="nccs_eg/nccs_power_eg.html">
+            Tables of the power function of the &#967;<sup>2</sup> test.</a></span></dt></dl></div>
+<p>
+            (See also the reference documentation for the <a class="link" href="../../dist_ref/dists/nc_chi_squared_dist.html" title="Noncentral Chi-Squared Distribution">Non
+            Central Chi Squared</a>.)
+          </p>
+</div>
+<table xmlns:rev="http://www.cs.rpi.edu/~gregod/boost/tools/doc/revision" width="100%"><tr>
+<td align="left"></td>
+<td align="right"><div class="copyright-footer">Copyright © 2006 , 2007, 2008 John Maddock, Paul A. Bristow, Hubert
+      Holin, Xiaogang Zhang, Bruno Lalande and Gautam Sewani<p>
+        Distributed under the Boost Software License, Version 1.0. (See accompanying
+        file LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_0.txt)
+      </p>
+</div></td>
+</tr></table>
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+<title>Tables of the power function of the &#967;2 test.</title>
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+</div>
+<div class="section" lang="en">
+<div class="titlepage"><div><div><h6 class="title">
+<a name="math_toolkit.dist.stat_tut.weg.nccs_eg.nccs_power_eg"></a><a class="link" href="nccs_power_eg.html" title="Tables of the power function of the &#967;2 test.">
+            Tables of the power function of the &#967;<sup>2</sup> test.</a>
+</h6></div></div></div>
+<p>
+              </p>
+<p>
+                This example computes a table of the power of the &#967;<sup>2</sup>
+test at the 5%
+                significance level, for various degrees of freedom and non-centrality
+                parameters. The table is deliberately the same as Table 6 from "The
+                Non-Central &#967;<sup>2</sup> and F-Distributions and their applications.", P.
+                B. Patnaik, Biometrika, Vol. 36, No. 1/2 (June 1949), 202-232.
+              </p>
+<p>
+              </p>
+<p>
+                First we need some includes to access the non-central chi squared
+                distribution (and some basic std output of course).
+              </p>
+<p>
+              </p>
+<p>
+                
+</p>
+<pre class="programlisting"><span class="preprocessor">#include</span> <span class="special">&lt;</span><span class="identifier">boost</span><span class="special">/</span><span class="identifier">math</span><span class="special">/</span><span class="identifier">distributions</span><span class="special">/</span><span class="identifier">non_central_chi_squared</span><span class="special">.</span><span class="identifier">hpp</span><span class="special">&gt;</span>
+<span class="preprocessor">#include</span> <span class="special">&lt;</span><span class="identifier">iostream</span><span class="special">&gt;</span>
+
+<span class="keyword">int</span> <span class="identifier">main</span><span class="special">()</span>
+<span class="special">{</span></pre>
+<p>
+              </p>
+<p>
+              </p>
+<p>
+                Create a table of the power of the &#967;<sup>2</sup> test at 5% significance level,
+                start with a table header:
+              </p>
+<p>
+              </p>
+<p>
+                
+</p>
+<pre class="programlisting"><span class="identifier">std</span><span class="special">::</span><span class="identifier">cout</span> <span class="special">&lt;&lt;</span> <span class="string">"[table\n[[[nu]]"</span><span class="special">;</span>
+<span class="keyword">for</span><span class="special">(</span><span class="keyword">int</span> <span class="identifier">lam</span> <span class="special">=</span> <span class="number">2</span><span class="special">;</span> <span class="identifier">lam</span> <span class="special">&lt;=</span> <span class="number">20</span><span class="special">;</span> <span class="identifier">lam</span> <span class="special">+=</span> <span class="number">2</span><span class="special">)</span>
+<span class="special">{</span>
+   <span class="identifier">std</span><span class="special">::</span><span class="identifier">cout</span> <span class="special">&lt;&lt;</span> <span class="string">"[[lambda]="</span> <span class="special">&lt;&lt;</span> <span class="identifier">lam</span> <span class="special">&lt;&lt;</span> <span class="string">"]"</span><span class="special">;</span>
+<span class="special">}</span>
+<span class="identifier">std</span><span class="special">::</span><span class="identifier">cout</span> <span class="special">&lt;&lt;</span> <span class="string">"]\n"</span><span class="special">;</span></pre>
+<p>
+              </p>
+<p>
+              </p>
+<p>
+                (Note: the enclosing [] brackets are to format as a table in Boost.Quickbook).
+              </p>
+<p>
+              </p>
+<p>
+                Enumerate the rows and columns and print the power of the test for
+                each table cell:
+              </p>
+<p>
+              </p>
+<p>
+                
+</p>
+<pre class="programlisting"><span class="keyword">for</span><span class="special">(</span><span class="keyword">int</span> <span class="identifier">n</span> <span class="special">=</span> <span class="number">2</span><span class="special">;</span> <span class="identifier">n</span> <span class="special">&lt;=</span> <span class="number">20</span><span class="special">;</span> <span class="special">++</span><span class="identifier">n</span><span class="special">)</span>
+<span class="special">{</span>
+   <span class="identifier">std</span><span class="special">::</span><span class="identifier">cout</span> <span class="special">&lt;&lt;</span> <span class="string">"[["</span> <span class="special">&lt;&lt;</span> <span class="identifier">n</span> <span class="special">&lt;&lt;</span> <span class="string">"]"</span><span class="special">;</span>
+   <span class="keyword">for</span><span class="special">(</span><span class="keyword">int</span> <span class="identifier">lam</span> <span class="special">=</span> <span class="number">2</span><span class="special">;</span> <span class="identifier">lam</span> <span class="special">&lt;=</span> <span class="number">20</span><span class="special">;</span> <span class="identifier">lam</span> <span class="special">+=</span> <span class="number">2</span><span class="special">)</span>
+   <span class="special">{</span></pre>
+<p>
+              </p>
+<p>
+              </p>
+<p>
+                Calculate the &#967;<sup>2</sup> statistic for a 5% significance:
+              </p>
+<p>
+              </p>
+<p>
+                
+</p>
+<pre class="programlisting"><span class="keyword">double</span> <span class="identifier">cs</span> <span class="special">=</span> <span class="identifier">quantile</span><span class="special">(</span><span class="identifier">complement</span><span class="special">(</span><span class="identifier">boost</span><span class="special">::</span><span class="identifier">math</span><span class="special">::</span><span class="identifier">chi_squared</span><span class="special">(</span><span class="identifier">n</span><span class="special">),</span> <span class="number">0.05</span><span class="special">));</span></pre>
+<p>
+              </p>
+<p>
+              </p>
+<p>
+                The power of the test is given by the complement of the CDF of the
+                non-central &#967;<sup>2</sup> distribution:
+              </p>
+<p>
+              </p>
+<p>
+                
+</p>
+<pre class="programlisting"><span class="keyword">double</span> <span class="identifier">beta</span> <span class="special">=</span> <span class="identifier">cdf</span><span class="special">(</span><span class="identifier">complement</span><span class="special">(</span><span class="identifier">boost</span><span class="special">::</span><span class="identifier">math</span><span class="special">::</span><span class="identifier">non_central_chi_squared</span><span class="special">(</span><span class="identifier">n</span><span class="special">,</span> <span class="identifier">lam</span><span class="special">),</span> <span class="identifier">cs</span><span class="special">));</span></pre>
+<p>
+              </p>
+<p>
+              </p>
+<p>
+                Then output the cell value:
+              </p>
+<p>
+              </p>
+<p>
+                
+</p>
+<pre class="programlisting">         <span class="identifier">std</span><span class="special">::</span><span class="identifier">cout</span> <span class="special">&lt;&lt;</span> <span class="string">"["</span> <span class="special">&lt;&lt;</span> <span class="identifier">std</span><span class="special">::</span><span class="identifier">setprecision</span><span class="special">(</span><span class="number">3</span><span class="special">)</span> <span class="special">&lt;&lt;</span> <span class="identifier">beta</span> <span class="special">&lt;&lt;</span> <span class="string">"]"</span><span class="special">;</span>
+      <span class="special">}</span>
+      <span class="identifier">std</span><span class="special">::</span><span class="identifier">cout</span> <span class="special">&lt;&lt;</span> <span class="string">"]"</span> <span class="special">&lt;&lt;</span> <span class="identifier">std</span><span class="special">::</span><span class="identifier">endl</span><span class="special">;</span>
+   <span class="special">}</span>
+   <span class="identifier">std</span><span class="special">::</span><span class="identifier">cout</span> <span class="special">&lt;&lt;</span> <span class="string">"]"</span> <span class="special">&lt;&lt;</span> <span class="identifier">std</span><span class="special">::</span><span class="identifier">endl</span><span class="special">;</span>
+<span class="special">}</span></pre>
+<p>
+              </p>
+<p>
+              </p>
+<p>
+                The output from this program is a table in Boost.Quickbook format
+                as shown below.
+              </p>
+<p>
+              </p>
+<p>
+                We can interpret this as follows - for example if &#957;=10 and &#955;=10 then
+                the power of the test is 0.542 - so we have only a 54% chance of
+                correctly detecting that our null hypothesis is false, and a 46%
+                chance of incurring a type II error (failing to reject the null hypothesis
+                when it is in fact false):
+              </p>
+<p>
+              </p>
+<div class="informaltable"><table class="table">
+<colgroup>
+<col>
+<col>
+<col>
+<col>
+<col>
+<col>
+<col>
+<col>
+<col>
+<col>
+<col>
+</colgroup>
+<thead><tr>
+<th>
+                      <p>
+                        &#957;
+                      </p>
+                      </th>
+<th>
+                      <p>
+                        &#955;=2
+                      </p>
+                      </th>
+<th>
+                      <p>
+                        &#955;=4
+                      </p>
+                      </th>
+<th>
+                      <p>
+                        &#955;=6
+                      </p>
+                      </th>
+<th>
+                      <p>
+                        &#955;=8
+                      </p>
+                      </th>
+<th>
+                      <p>
+                        &#955;=10
+                      </p>
+                      </th>
+<th>
+                      <p>
+                        &#955;=12
+                      </p>
+                      </th>
+<th>
+                      <p>
+                        &#955;=14
+                      </p>
+                      </th>
+<th>
+                      <p>
+                        &#955;=16
+                      </p>
+                      </th>
+<th>
+                      <p>
+                        &#955;=18
+                      </p>
+                      </th>
+<th>
+                      <p>
+                        &#955;=20
+                      </p>
+                      </th>
+</tr></thead>
+<tbody>
+<tr>
+<td>
+                      <p>
+                        2
+                      </p>
+                      </td>
+<td>
+                      <p>
+                        0.226
+                      </p>
+                      </td>
+<td>
+                      <p>
+                        0.415
+                      </p>
+                      </td>
+<td>
+                      <p>
+                        0.584
+                      </p>
+                      </td>
+<td>
+                      <p>
+                        0.718
+                      </p>
+                      </td>
+<td>
+                      <p>
+                        0.815
+                      </p>
+                      </td>
+<td>
+                      <p>
+                        0.883
+                      </p>
+                      </td>
+<td>
+                      <p>
+                        0.928
+                      </p>
+                      </td>
+<td>
+                      <p>
+                        0.957
+                      </p>
+                      </td>
+<td>
+                      <p>
+                        0.974
+                      </p>
+                      </td>
+<td>
+                      <p>
+                        0.985
+                      </p>
+                      </td>
+</tr>
+<tr>
+<td>
+                      <p>
+                        3
+                      </p>
+                      </td>
+<td>
+                      <p>
+                        0.192
+                      </p>
+                      </td>
+<td>
+                      <p>
+                        0.359
+                      </p>
+                      </td>
+<td>
+                      <p>
+                        0.518
+                      </p>
+                      </td>
+<td>
+                      <p>
+                        0.654
+                      </p>
+                      </td>
+<td>
+                      <p>
+                        0.761
+                      </p>
+                      </td>
+<td>
+                      <p>
+                        0.84
+                      </p>
+                      </td>
+<td>
+                      <p>
+                        0.896
+                      </p>
+                      </td>
+<td>
+                      <p>
+                        0.934
+                      </p>
+                      </td>
+<td>
+                      <p>
+                        0.959
+                      </p>
+                      </td>
+<td>
+                      <p>
+                        0.975
+                      </p>
+                      </td>
+</tr>
+<tr>
+<td>
+                      <p>
+                        4
+                      </p>
+                      </td>
+<td>
+                      <p>
+                        0.171
+                      </p>
+                      </td>
+<td>
+                      <p>
+                        0.32
+                      </p>
+                      </td>
+<td>
+                      <p>
+                        0.47
+                      </p>
+                      </td>
+<td>
+                      <p>
+                        0.605
+                      </p>
+                      </td>
+<td>
+                      <p>
+                        0.716
+                      </p>
+                      </td>
+<td>
+                      <p>
+                        0.802
+                      </p>
+                      </td>
+<td>
+                      <p>
+                        0.866
+                      </p>
+                      </td>
+<td>
+                      <p>
+                        0.912
+                      </p>
+                      </td>
+<td>
+                      <p>
+                        0.943
+                      </p>
+                      </td>
+<td>
+                      <p>
+                        0.964
+                      </p>
+                      </td>
+</tr>
+<tr>
+<td>
+                      <p>
+                        5
+                      </p>
+                      </td>
+<td>
+                      <p>
+                        0.157
+                      </p>
+                      </td>
+<td>
+                      <p>
+                        0.292
+                      </p>
+                      </td>
+<td>
+                      <p>
+                        0.433
+                      </p>
+                      </td>
+<td>
+                      <p>
+                        0.564
+                      </p>
+                      </td>
+<td>
+                      <p>
+                        0.677
+                      </p>
+                      </td>
+<td>
+                      <p>
+                        0.769
+                      </p>
+                      </td>
+<td>
+                      <p>
+                        0.839
+                      </p>
+                      </td>
+<td>
+                      <p>
+                        0.89
+                      </p>
+                      </td>
+<td>
+                      <p>
+                        0.927
+                      </p>
+                      </td>
+<td>
+                      <p>
+                        0.952
+                      </p>
+                      </td>
+</tr>
+<tr>
+<td>
+                      <p>
+                        6
+                      </p>
+                      </td>
+<td>
+                      <p>
+                        0.146
+                      </p>
+                      </td>
+<td>
+                      <p>
+                        0.27
+                      </p>
+                      </td>
+<td>
+                      <p>
+                        0.403
+                      </p>
+                      </td>
+<td>
+                      <p>
+                        0.531
+                      </p>
+                      </td>
+<td>
+                      <p>
+                        0.644
+                      </p>
+                      </td>
+<td>
+                      <p>
+                        0.738
+                      </p>
+                      </td>
+<td>
+                      <p>
+                        0.813
+                      </p>
+                      </td>
+<td>
+                      <p>
+                        0.869
+                      </p>
+                      </td>
+<td>
+                      <p>
+                        0.911
+                      </p>
+                      </td>
+<td>
+                      <p>
+                        0.94
+                      </p>
+                      </td>
+</tr>
+<tr>
+<td>
+                      <p>
+                        7
+                      </p>
+                      </td>
+<td>
+                      <p>
+                        0.138
+                      </p>
+                      </td>
+<td>
+                      <p>
+                        0.252
+                      </p>
+                      </td>
+<td>
+                      <p>
+                        0.378
+                      </p>
+                      </td>
+<td>
+                      <p>
+                        0.502
+                      </p>
+                      </td>
+<td>
+                      <p>
+                        0.614
+                      </p>
+                      </td>
+<td>
+                      <p>
+                        0.71
+                      </p>
+                      </td>
+<td>
+                      <p>
+                        0.788
+                      </p>
+                      </td>
+<td>
+                      <p>
+                        0.849
+                      </p>
+                      </td>
+<td>
+                      <p>
+                        0.895
+                      </p>
+                      </td>
+<td>
+                      <p>
+                        0.928
+                      </p>
+                      </td>
+</tr>
+<tr>
+<td>
+                      <p>
+                        8
+                      </p>
+                      </td>
+<td>
+                      <p>
+                        0.131
+                      </p>
+                      </td>
+<td>
+                      <p>
+                        0.238
+                      </p>
+                      </td>
+<td>
+                      <p>
+                        0.357
+                      </p>
+                      </td>
+<td>
+                      <p>
+                        0.477
+                      </p>
+                      </td>
+<td>
+                      <p>
+                        0.588
+                      </p>
+                      </td>
+<td>
+                      <p>
+                        0.685
+                      </p>
+                      </td>
+<td>
+                      <p>
+                        0.765
+                      </p>
+                      </td>
+<td>
+                      <p>
+                        0.829
+                      </p>
+                      </td>
+<td>
+                      <p>
+                        0.879
+                      </p>
+                      </td>
+<td>
+                      <p>
+                        0.915
+                      </p>
+                      </td>
+</tr>
+<tr>
+<td>
+                      <p>
+                        9
+                      </p>
+                      </td>
+<td>
+                      <p>
+                        0.125
+                      </p>
+                      </td>
+<td>
+                      <p>
+                        0.225
+                      </p>
+                      </td>
+<td>
+                      <p>
+                        0.339
+                      </p>
+                      </td>
+<td>
+                      <p>
+                        0.454
+                      </p>
+                      </td>
+<td>
+                      <p>
+                        0.564
+                      </p>
+                      </td>
+<td>
+                      <p>
+                        0.661
+                      </p>
+                      </td>
+<td>
+                      <p>
+                        0.744
+                      </p>
+                      </td>
+<td>
+                      <p>
+                        0.811
+                      </p>
+                      </td>
+<td>
+                      <p>
+                        0.863
+                      </p>
+                      </td>
+<td>
+                      <p>
+                        0.903
+                      </p>
+                      </td>
+</tr>
+<tr>
+<td>
+                      <p>
+                        10
+                      </p>
+                      </td>
+<td>
+                      <p>
+                        0.121
+                      </p>
+                      </td>
+<td>
+                      <p>
+                        0.215
+                      </p>
+                      </td>
+<td>
+                      <p>
+                        0.323
+                      </p>
+                      </td>
+<td>
+                      <p>
+                        0.435
+                      </p>
+                      </td>
+<td>
+                      <p>
+                        0.542
+                      </p>
+                      </td>
+<td>
+                      <p>
+                        0.64
+                      </p>
+                      </td>
+<td>
+                      <p>
+                        0.723
+                      </p>
+                      </td>
+<td>
+                      <p>
+                        0.793
+                      </p>
+                      </td>
+<td>
+                      <p>
+                        0.848
+                      </p>
+                      </td>
+<td>
+                      <p>
+                        0.891
+                      </p>
+                      </td>
+</tr>
+<tr>
+<td>
+                      <p>
+                        11
+                      </p>
+                      </td>
+<td>
+                      <p>
+                        0.117
+                      </p>
+                      </td>
+<td>
+                      <p>
+                        0.206
+                      </p>
+                      </td>
+<td>
+                      <p>
+                        0.309
+                      </p>
+                      </td>
+<td>
+                      <p>
+                        0.417
+                      </p>
+                      </td>
+<td>
+                      <p>
+                        0.523
+                      </p>
+                      </td>
+<td>
+                      <p>
+                        0.62
+                      </p>
+                      </td>
+<td>
+                      <p>
+                        0.704
+                      </p>
+                      </td>
+<td>
+                      <p>
+                        0.775
+                      </p>
+                      </td>
+<td>
+                      <p>
+                        0.833
+                      </p>
+                      </td>
+<td>
+                      <p>
+                        0.878
+                      </p>
+                      </td>
+</tr>
+<tr>
+<td>
+                      <p>
+                        12
+                      </p>
+                      </td>
+<td>
+                      <p>
+                        0.113
+                      </p>
+                      </td>
+<td>
+                      <p>
+                        0.198
+                      </p>
+                      </td>
+<td>
+                      <p>
+                        0.297
+                      </p>
+                      </td>
+<td>
+                      <p>
+                        0.402
+                      </p>
+                      </td>
+<td>
+                      <p>
+                        0.505
+                      </p>
+                      </td>
+<td>
+                      <p>
+                        0.601
+                      </p>
+                      </td>
+<td>
+                      <p>
+                        0.686
+                      </p>
+                      </td>
+<td>
+                      <p>
+                        0.759
+                      </p>
+                      </td>
+<td>
+                      <p>
+                        0.818
+                      </p>
+                      </td>
+<td>
+                      <p>
+                        0.866
+                      </p>
+                      </td>
+</tr>
+<tr>
+<td>
+                      <p>
+                        13
+                      </p>
+                      </td>
+<td>
+                      <p>
+                        0.11
+                      </p>
+                      </td>
+<td>
+                      <p>
+                        0.191
+                      </p>
+                      </td>
+<td>
+                      <p>
+                        0.286
+                      </p>
+                      </td>
+<td>
+                      <p>
+                        0.387
+                      </p>
+                      </td>
+<td>
+                      <p>
+                        0.488
+                      </p>
+                      </td>
+<td>
+                      <p>
+                        0.584
+                      </p>
+                      </td>
+<td>
+                      <p>
+                        0.669
+                      </p>
+                      </td>
+<td>
+                      <p>
+                        0.743
+                      </p>
+                      </td>
+<td>
+                      <p>
+                        0.804
+                      </p>
+                      </td>
+<td>
+                      <p>
+                        0.854
+                      </p>
+                      </td>
+</tr>
+<tr>
+<td>
+                      <p>
+                        14
+                      </p>
+                      </td>
+<td>
+                      <p>
+                        0.108
+                      </p>
+                      </td>
+<td>
+                      <p>
+                        0.185
+                      </p>
+                      </td>
+<td>
+                      <p>
+                        0.276
+                      </p>
+                      </td>
+<td>
+                      <p>
+                        0.374
+                      </p>
+                      </td>
+<td>
+                      <p>
+                        0.473
+                      </p>
+                      </td>
+<td>
+                      <p>
+                        0.567
+                      </p>
+                      </td>
+<td>
+                      <p>
+                        0.653
+                      </p>
+                      </td>
+<td>
+                      <p>
+                        0.728
+                      </p>
+                      </td>
+<td>
+                      <p>
+                        0.791
+                      </p>
+                      </td>
+<td>
+                      <p>
+                        0.842
+                      </p>
+                      </td>
+</tr>
+<tr>
+<td>
+                      <p>
+                        15
+                      </p>
+                      </td>
+<td>
+                      <p>
+                        0.105
+                      </p>
+                      </td>
+<td>
+                      <p>
+                        0.179
+                      </p>
+                      </td>
+<td>
+                      <p>
+                        0.267
+                      </p>
+                      </td>
+<td>
+                      <p>
+                        0.362
+                      </p>
+                      </td>
+<td>
+                      <p>
+                        0.459
+                      </p>
+                      </td>
+<td>
+                      <p>
+                        0.552
+                      </p>
+                      </td>
+<td>
+                      <p>
+                        0.638
+                      </p>
+                      </td>
+<td>
+                      <p>
+                        0.713
+                      </p>
+                      </td>
+<td>
+                      <p>
+                        0.777
+                      </p>
+                      </td>
+<td>
+                      <p>
+                        0.83
+                      </p>
+                      </td>
+</tr>
+<tr>
+<td>
+                      <p>
+                        16
+                      </p>
+                      </td>
+<td>
+                      <p>
+                        0.103
+                      </p>
+                      </td>
+<td>
+                      <p>
+                        0.174
+                      </p>
+                      </td>
+<td>
+                      <p>
+                        0.259
+                      </p>
+                      </td>
+<td>
+                      <p>
+                        0.351
+                      </p>
+                      </td>
+<td>
+                      <p>
+                        0.446
+                      </p>
+                      </td>
+<td>
+                      <p>
+                        0.538
+                      </p>
+                      </td>
+<td>
+                      <p>
+                        0.623
+                      </p>
+                      </td>
+<td>
+                      <p>
+                        0.699
+                      </p>
+                      </td>
+<td>
+                      <p>
+                        0.764
+                      </p>
+                      </td>
+<td>
+                      <p>
+                        0.819
+                      </p>
+                      </td>
+</tr>
+<tr>
+<td>
+                      <p>
+                        17
+                      </p>
+                      </td>
+<td>
+                      <p>
+                        0.101
+                      </p>
+                      </td>
+<td>
+                      <p>
+                        0.169
+                      </p>
+                      </td>
+<td>
+                      <p>
+                        0.251
+                      </p>
+                      </td>
+<td>
+                      <p>
+                        0.341
+                      </p>
+                      </td>
+<td>
+                      <p>
+                        0.434
+                      </p>
+                      </td>
+<td>
+                      <p>
+                        0.525
+                      </p>
+                      </td>
+<td>
+                      <p>
+                        0.609
+                      </p>
+                      </td>
+<td>
+                      <p>
+                        0.686
+                      </p>
+                      </td>
+<td>
+                      <p>
+                        0.752
+                      </p>
+                      </td>
+<td>
+                      <p>
+                        0.807
+                      </p>
+                      </td>
+</tr>
+<tr>
+<td>
+                      <p>
+                        18
+                      </p>
+                      </td>
+<td>
+                      <p>
+                        0.0992
+                      </p>
+                      </td>
+<td>
+                      <p>
+                        0.165
+                      </p>
+                      </td>
+<td>
+                      <p>
+                        0.244
+                      </p>
+                      </td>
+<td>
+                      <p>
+                        0.332
+                      </p>
+                      </td>
+<td>
+                      <p>
+                        0.423
+                      </p>
+                      </td>
+<td>
+                      <p>
+                        0.512
+                      </p>
+                      </td>
+<td>
+                      <p>
+                        0.596
+                      </p>
+                      </td>
+<td>
+                      <p>
+                        0.673
+                      </p>
+                      </td>
+<td>
+                      <p>
+                        0.74
+                      </p>
+                      </td>
+<td>
+                      <p>
+                        0.796
+                      </p>
+                      </td>
+</tr>
+<tr>
+<td>
+                      <p>
+                        19
+                      </p>
+                      </td>
+<td>
+                      <p>
+                        0.0976
+                      </p>
+                      </td>
+<td>
+                      <p>
+                        0.161
+                      </p>
+                      </td>
+<td>
+                      <p>
+                        0.238
+                      </p>
+                      </td>
+<td>
+                      <p>
+                        0.323
+                      </p>
+                      </td>
+<td>
+                      <p>
+                        0.412
+                      </p>
+                      </td>
+<td>
+                      <p>
+                        0.5
+                      </p>
+                      </td>
+<td>
+                      <p>
+                        0.584
+                      </p>
+                      </td>
+<td>
+                      <p>
+                        0.66
+                      </p>
+                      </td>
+<td>
+                      <p>
+                        0.728
+                      </p>
+                      </td>
+<td>
+                      <p>
+                        0.786
+                      </p>
+                      </td>
+</tr>
+<tr>
+<td>
+                      <p>
+                        20
+                      </p>
+                      </td>
+<td>
+                      <p>
+                        0.0961
+                      </p>
+                      </td>
+<td>
+                      <p>
+                        0.158
+                      </p>
+                      </td>
+<td>
+                      <p>
+                        0.232
+                      </p>
+                      </td>
+<td>
+                      <p>
+                        0.315
+                      </p>
+                      </td>
+<td>
+                      <p>
+                        0.402
+                      </p>
+                      </td>
+<td>
+                      <p>
+                        0.489
+                      </p>
+                      </td>
+<td>
+                      <p>
+                        0.572
+                      </p>
+                      </td>
+<td>
+                      <p>
+                        0.648
+                      </p>
+                      </td>
+<td>
+                      <p>
+                        0.716
+                      </p>
+                      </td>
+<td>
+                      <p>
+                        0.775
+                      </p>
+                      </td>
+</tr>
+</tbody>
+</table></div>
+<p>
+              </p>
+<p>
+                See nc_chi_sq_example.cpp
+                for the full C++ source code.
+              </p>
+<p>
+            </p>
+</div>
+<table xmlns:rev="http://www.cs.rpi.edu/~gregod/boost/tools/doc/revision" width="100%"><tr>
+<td align="left"></td>
+<td align="right"><div class="copyright-footer">Copyright © 2006 , 2007, 2008 John Maddock, Paul A. Bristow, Hubert
+      Holin, Xiaogang Zhang, Bruno Lalande and Gautam Sewani<p>
+        Distributed under the Boost Software License, Version 1.0. (See accompanying
+        file LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_0.txt)
+      </p>
+</div></td>
+</tr></table>
+<hr>
+<div class="spirit-nav">
+<a accesskey="p" href="../nccs_eg.html"><img src="../../../../../../../doc/html/images/prev.png" alt="Prev"></a><a accesskey="u" href="../nccs_eg.html"><img src="../../../../../../../doc/html/images/up.png" alt="Up"></a><a accesskey="h" href="../../../../../index.html"><img src="../../../../../../../doc/html/images/home.png" alt="Home"></a><a accesskey="n" href="../error_eg.html"><img src="../../../../../../../doc/html/images/next.png" alt="Next"></a>
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+<title>Negative Binomial Distribution Examples</title>
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+</div>
+<div class="section" lang="en">
+<div class="titlepage"><div><div><h5 class="title">
+<a name="math_toolkit.dist.stat_tut.weg.neg_binom_eg"></a><a class="link" href="neg_binom_eg.html" title="Negative Binomial Distribution Examples"> Negative
+          Binomial Distribution Examples</a>
+</h5></div></div></div>
+<div class="toc"><dl>
+<dt><span class="section"><a href="neg_binom_eg/neg_binom_conf.html">
+            Calculating Confidence Limits on the Frequency of Occurrence for the
+            Negative Binomial Distribution</a></span></dt>
+<dt><span class="section"><a href="neg_binom_eg/neg_binom_size_eg.html">
+            Estimating Sample Sizes for the Negative Binomial.</a></span></dt>
+<dt><span class="section"><a href="neg_binom_eg/negative_binomial_example1.html">
+            Negative Binomial Sales Quota Example.</a></span></dt>
+<dt><span class="section"><a href="neg_binom_eg/negative_binomial_example2.html">
+            Negative Binomial Table Printing Example.</a></span></dt>
+</dl></div>
+<p>
+            (See also the reference documentation for the <a class="link" href="../../dist_ref/dists/negative_binomial_dist.html" title="Negative Binomial Distribution">Negative
+            Binomial Distribution</a>.)
+          </p>
+</div>
+<table xmlns:rev="http://www.cs.rpi.edu/~gregod/boost/tools/doc/revision" width="100%"><tr>
+<td align="left"></td>
+<td align="right"><div class="copyright-footer">Copyright © 2006 , 2007, 2008 John Maddock, Paul A. Bristow, Hubert
+      Holin, Xiaogang Zhang, Bruno Lalande and Gautam Sewani<p>
+        Distributed under the Boost Software License, Version 1.0. (See accompanying
+        file LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_0.txt)
+      </p>
+</div></td>
+</tr></table>
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+++ sandbox/tools/auto_index/example/math/doc/sf_and_dist/html/math_toolkit/dist/stat_tut/weg/neg_binom_eg/neg_binom_conf.html	2008-11-28 05:25:28 EST (Fri, 28 Nov 2008)
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+<head>
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+<title>Calculating Confidence Limits on the Frequency of Occurrence for the Negative Binomial Distribution</title>
+<link rel="stylesheet" href="../../../../../boostbook.css" type="text/css">
+<meta name="generator" content="DocBook XSL Stylesheets Vsnapshot_8125">
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+</div>
+<div class="section" lang="en">
+<div class="titlepage"><div><div><h6 class="title">
+<a name="math_toolkit.dist.stat_tut.weg.neg_binom_eg.neg_binom_conf"></a><a class="link" href="neg_binom_conf.html" title="Calculating Confidence Limits on the Frequency of Occurrence for the Negative Binomial Distribution">
+            Calculating Confidence Limits on the Frequency of Occurrence for the
+            Negative Binomial Distribution</a>
+</h6></div></div></div>
+<p>
+              Imagine you have a process that follows a negative binomial distribution:
+              for each trial conducted, an event either occurs or does it does not,
+              referred to as "successes" and "failures". The
+              frequency with which successes occur is variously referred to as the
+              success fraction, success ratio, success percentage, occurrence frequency,
+              or probability of occurrence.
+            </p>
+<p>
+              If, by experiment, you want to measure the the best estimate of success
+              fraction is given simply by <span class="emphasis"><em>k</em></span> / <span class="emphasis"><em>N</em></span>,
+              for <span class="emphasis"><em>k</em></span> successes out of <span class="emphasis"><em>N</em></span>
+              trials.
+            </p>
+<p>
+              However our confidence in that estimate will be shaped by how many
+              trials were conducted, and how many successes were observed. The static
+              member functions <code class="computeroutput"><span class="identifier">negative_binomial_distribution</span><span class="special">&lt;&gt;::</span><span class="identifier">find_lower_bound_on_p</span></code>
+              and <code class="computeroutput"><span class="identifier">negative_binomial_distribution</span><span class="special">&lt;&gt;::</span><span class="identifier">find_upper_bound_on_p</span></code>
+              allow you to calculate the confidence intervals for your estimate of
+              the success fraction.
+            </p>
+<p>
+              The sample program neg_binom_confidence_limits.cpp
+              illustrates their use.
+            </p>
+<p>
+              </p>
+<p>
+                First we need some includes to access the negative binomial distribution
+                (and some basic std output of course).
+              </p>
+<p>
+              </p>
+<p>
+                
+</p>
+<pre class="programlisting"><span class="preprocessor">#include</span> <span class="special">&lt;</span><span class="identifier">boost</span><span class="special">/</span><span class="identifier">math</span><span class="special">/</span><span class="identifier">distributions</span><span class="special">/</span><span class="identifier">negative_binomial</span><span class="special">.</span><span class="identifier">hpp</span><span class="special">&gt;</span>
+<span class="keyword">using</span> <span class="identifier">boost</span><span class="special">::</span><span class="identifier">math</span><span class="special">::</span><span class="identifier">negative_binomial</span><span class="special">;</span>
+
+<span class="preprocessor">#include</span> <span class="special">&lt;</span><span class="identifier">iostream</span><span class="special">&gt;</span>
+<span class="keyword">using</span> <span class="identifier">std</span><span class="special">::</span><span class="identifier">cout</span><span class="special">;</span> <span class="keyword">using</span> <span class="identifier">std</span><span class="special">::</span><span class="identifier">endl</span><span class="special">;</span>
+<span class="preprocessor">#include</span> <span class="special">&lt;</span><span class="identifier">iomanip</span><span class="special">&gt;</span>
+<span class="keyword">using</span> <span class="identifier">std</span><span class="special">::</span><span class="identifier">setprecision</span><span class="special">;</span>
+<span class="keyword">using</span> <span class="identifier">std</span><span class="special">::</span><span class="identifier">setw</span><span class="special">;</span> <span class="keyword">using</span> <span class="identifier">std</span><span class="special">::</span><span class="identifier">left</span><span class="special">;</span> <span class="keyword">using</span> <span class="identifier">std</span><span class="special">::</span><span class="identifier">fixed</span><span class="special">;</span> <span class="keyword">using</span> <span class="identifier">std</span><span class="special">::</span><span class="identifier">right</span><span class="special">;</span></pre>
+<p>
+              </p>
+<p>
+              </p>
+<p>
+                First define a table of significance levels: these are the probabilities
+                that the true occurrence frequency lies outside the calculated interval:
+              </p>
+<p>
+              </p>
+<p>
+                
+</p>
+<pre class="programlisting"><span class="keyword">double</span> <span class="identifier">alpha</span><span class="special">[]</span> <span class="special">=</span> <span class="special">{</span> <span class="number">0.5</span><span class="special">,</span> <span class="number">0.25</span><span class="special">,</span> <span class="number">0.1</span><span class="special">,</span> <span class="number">0.05</span><span class="special">,</span> <span class="number">0.01</span><span class="special">,</span> <span class="number">0.001</span><span class="special">,</span> <span class="number">0.0001</span><span class="special">,</span> <span class="number">0.00001</span> <span class="special">};</span></pre>
+<p>
+              </p>
+<p>
+              </p>
+<p>
+                Confidence value as % is (1 - alpha) * 100, so alpha 0.05 == 95%
+                confidence that the true occurence frequency lies <span class="bold"><strong>inside</strong></span>
+                the calculated interval.
+              </p>
+<p>
+              </p>
+<p>
+                We need a function to calculate and print confidence limits for an
+                observed frequency of occurrence that follows a negative binomial
+                distribution.
+              </p>
+<p>
+              </p>
+<p>
+                
+</p>
+<pre class="programlisting"><span class="keyword">void</span> <span class="identifier">confidence_limits_on_frequency</span><span class="special">(</span><span class="keyword">unsigned</span> <span class="identifier">trials</span><span class="special">,</span> <span class="keyword">unsigned</span> <span class="identifier">successes</span><span class="special">)</span>
+<span class="special">{</span>
+   <span class="comment">// trials = Total number of trials.
+</span>   <span class="comment">// successes = Total number of observed successes.
+</span>   <span class="comment">// failures = trials - successes.
+</span>   <span class="comment">// success_fraction = successes /trials.
+</span>   <span class="comment">// Print out general info:
+</span>   <span class="identifier">cout</span> <span class="special">&lt;&lt;</span>
+      <span class="string">"______________________________________________\n"</span>
+      <span class="string">"2-Sided Confidence Limits For Success Fraction\n"</span>
+      <span class="string">"______________________________________________\n\n"</span><span class="special">;</span>
+   <span class="identifier">cout</span> <span class="special">&lt;&lt;</span> <span class="identifier">setprecision</span><span class="special">(</span><span class="number">7</span><span class="special">);</span>
+   <span class="identifier">cout</span> <span class="special">&lt;&lt;</span> <span class="identifier">setw</span><span class="special">(</span><span class="number">40</span><span class="special">)</span> <span class="special">&lt;&lt;</span> <span class="identifier">left</span> <span class="special">&lt;&lt;</span> <span class="string">"Number of trials"</span> <span class="special">&lt;&lt;</span> <span class="string">" =  "</span> <span class="special">&lt;&lt;</span> <span class="identifier">trials</span> <span class="special">&lt;&lt;</span> <span class="string">"\n"</span><span class="special">;</span>
+   <span class="identifier">cout</span> <span class="special">&lt;&lt;</span> <span class="identifier">setw</span><span class="special">(</span><span class="number">40</span><span class="special">)</span> <span class="special">&lt;&lt;</span> <span class="identifier">left</span> <span class="special">&lt;&lt;</span> <span class="string">"Number of successes"</span> <span class="special">&lt;&lt;</span> <span class="string">" =  "</span> <span class="special">&lt;&lt;</span> <span class="identifier">successes</span> <span class="special">&lt;&lt;</span> <span class="string">"\n"</span><span class="special">;</span>
+   <span class="identifier">cout</span> <span class="special">&lt;&lt;</span> <span class="identifier">setw</span><span class="special">(</span><span class="number">40</span><span class="special">)</span> <span class="special">&lt;&lt;</span> <span class="identifier">left</span> <span class="special">&lt;&lt;</span> <span class="string">"Number of failures"</span> <span class="special">&lt;&lt;</span> <span class="string">" =  "</span> <span class="special">&lt;&lt;</span> <span class="identifier">trials</span> <span class="special">-</span> <span class="identifier">successes</span> <span class="special">&lt;&lt;</span> <span class="string">"\n"</span><span class="special">;</span>
+   <span class="identifier">cout</span> <span class="special">&lt;&lt;</span> <span class="identifier">setw</span><span class="special">(</span><span class="number">40</span><span class="special">)</span> <span class="special">&lt;&lt;</span> <span class="identifier">left</span> <span class="special">&lt;&lt;</span> <span class="string">"Observed frequency of occurrence"</span> <span class="special">&lt;&lt;</span> <span class="string">" =  "</span> <span class="special">&lt;&lt;</span> <span class="keyword">double</span><span class="special">(</span><span class="identifier">successes</span><span class="special">)</span> <span class="special">/</span> <span class="identifier">trials</span> <span class="special">&lt;&lt;</span> <span class="string">"\n"</span><span class="special">;</span>
+
+   <span class="comment">// Print table header:
+</span>   <span class="identifier">cout</span> <span class="special">&lt;&lt;</span> <span class="string">"\n\n"</span>
+           <span class="string">"___________________________________________\n"</span>
+           <span class="string">"Confidence        Lower          Upper\n"</span>
+           <span class="string">" Value (%)        Limit          Limit\n"</span>
+           <span class="string">"___________________________________________\n"</span><span class="special">;</span></pre>
+<p>
+              </p>
+<p>
+              </p>
+<p>
+                And now for the important part - the bounds themselves. For each
+                value of <span class="emphasis"><em>alpha</em></span>, we call <code class="computeroutput"><span class="identifier">find_lower_bound_on_p</span></code>
+                and <code class="computeroutput"><span class="identifier">find_upper_bound_on_p</span></code>
+                to obtain lower and upper bounds respectively. Note that since we
+                are calculating a two-sided interval, we must divide the value of
+                alpha in two. Had we been calculating a single-sided interval, for
+                example: <span class="emphasis"><em>"Calculate a lower bound so that we are P%
+                sure that the true occurrence frequency is greater than some value"</em></span>
+                then we would <span class="bold"><strong>not</strong></span> have divided by
+                two.
+              </p>
+<p>
+              </p>
+<p>
+                
+</p>
+<pre class="programlisting">   <span class="comment">// Now print out the upper and lower limits for the alpha table values.
+</span>   <span class="keyword">for</span><span class="special">(</span><span class="keyword">unsigned</span> <span class="identifier">i</span> <span class="special">=</span> <span class="number">0</span><span class="special">;</span> <span class="identifier">i</span> <span class="special">&lt;</span> <span class="keyword">sizeof</span><span class="special">(</span><span class="identifier">alpha</span><span class="special">)/</span><span class="keyword">sizeof</span><span class="special">(</span><span class="identifier">alpha</span><span class="special">[</span><span class="number">0</span><span class="special">]);</span> <span class="special">++</span><span class="identifier">i</span><span class="special">)</span>
+   <span class="special">{</span>
+      <span class="comment">// Confidence value:
+</span>      <span class="identifier">cout</span> <span class="special">&lt;&lt;</span> <span class="identifier">fixed</span> <span class="special">&lt;&lt;</span> <span class="identifier">setprecision</span><span class="special">(</span><span class="number">3</span><span class="special">)</span> <span class="special">&lt;&lt;</span> <span class="identifier">setw</span><span class="special">(</span><span class="number">10</span><span class="special">)</span> <span class="special">&lt;&lt;</span> <span class="identifier">right</span> <span class="special">&lt;&lt;</span> <span class="number">100</span> <span class="special">*</span> <span class="special">(</span><span class="number">1</span><span class="special">-</span><span class="identifier">alpha</span><span class="special">[</span><span class="identifier">i</span><span class="special">]);</span>
+      <span class="comment">// Calculate bounds:
+</span>      <span class="keyword">double</span> <span class="identifier">lower</span> <span class="special">=</span> <span class="identifier">negative_binomial</span><span class="special">::</span><span class="identifier">find_lower_bound_on_p</span><span class="special">(</span><span class="identifier">trials</span><span class="special">,</span> <span class="identifier">successes</span><span class="special">,</span> <span class="identifier">alpha</span><span class="special">[</span><span class="identifier">i</span><span class="special">]/</span><span class="number">2</span><span class="special">);</span>
+      <span class="keyword">double</span> <span class="identifier">upper</span> <span class="special">=</span> <span class="identifier">negative_binomial</span><span class="special">::</span><span class="identifier">find_upper_bound_on_p</span><span class="special">(</span><span class="identifier">trials</span><span class="special">,</span> <span class="identifier">successes</span><span class="special">,</span> <span class="identifier">alpha</span><span class="special">[</span><span class="identifier">i</span><span class="special">]/</span><span class="number">2</span><span class="special">);</span>
+      <span class="comment">// Print limits:
+</span>      <span class="identifier">cout</span> <span class="special">&lt;&lt;</span> <span class="identifier">fixed</span> <span class="special">&lt;&lt;</span> <span class="identifier">setprecision</span><span class="special">(</span><span class="number">5</span><span class="special">)</span> <span class="special">&lt;&lt;</span> <span class="identifier">setw</span><span class="special">(</span><span class="number">15</span><span class="special">)</span> <span class="special">&lt;&lt;</span> <span class="identifier">right</span> <span class="special">&lt;&lt;</span> <span class="identifier">lower</span><span class="special">;</span>
+      <span class="identifier">cout</span> <span class="special">&lt;&lt;</span> <span class="identifier">fixed</span> <span class="special">&lt;&lt;</span> <span class="identifier">setprecision</span><span class="special">(</span><span class="number">5</span><span class="special">)</span> <span class="special">&lt;&lt;</span> <span class="identifier">setw</span><span class="special">(</span><span class="number">15</span><span class="special">)</span> <span class="special">&lt;&lt;</span> <span class="identifier">right</span> <span class="special">&lt;&lt;</span> <span class="identifier">upper</span> <span class="special">&lt;&lt;</span> <span class="identifier">endl</span><span class="special">;</span>
+   <span class="special">}</span>
+   <span class="identifier">cout</span> <span class="special">&lt;&lt;</span> <span class="identifier">endl</span><span class="special">;</span>
+<span class="special">}</span> <span class="comment">// void confidence_limits_on_frequency(unsigned trials, unsigned successes)</span></pre>
+<p>
+              </p>
+<p>
+              </p>
+<p>
+                And then call confidence_limits_on_frequency with increasing numbers
+                of trials, but always the same success fraction 0.1, or 1 in 10.
+              </p>
+<p>
+              </p>
+<p>
+                
+</p>
+<pre class="programlisting"><span class="keyword">int</span> <span class="identifier">main</span><span class="special">()</span>
+<span class="special">{</span>
+  <span class="identifier">confidence_limits_on_frequency</span><span class="special">(</span><span class="number">20</span><span class="special">,</span> <span class="number">2</span><span class="special">);</span> <span class="comment">// 20 trials, 2 successes, 2 in 20, = 1 in 10 = 0.1 success fraction.
+</span>  <span class="identifier">confidence_limits_on_frequency</span><span class="special">(</span><span class="number">200</span><span class="special">,</span> <span class="number">20</span><span class="special">);</span> <span class="comment">// More trials, but same 0.1 success fraction.
+</span>  <span class="identifier">confidence_limits_on_frequency</span><span class="special">(</span><span class="number">2000</span><span class="special">,</span> <span class="number">200</span><span class="special">);</span> <span class="comment">// Many more trials, but same 0.1 success fraction.
+</span>
+  <span class="keyword">return</span> <span class="number">0</span><span class="special">;</span>
+<span class="special">}</span> <span class="comment">// int main()
+</span>
+</pre>
+<p>
+              </p>
+<p>
+              Let's see some sample output for a 1 in 10 success ratio, first for
+              a mere 20 trials:
+            </p>
+<pre class="programlisting">______________________________________________
+2-Sided Confidence Limits For Success Fraction
+______________________________________________
+Number of trials                         =  20
+Number of successes                      =  2
+Number of failures                       =  18
+Observed frequency of occurrence         =  0.1
+___________________________________________
+Confidence        Lower          Upper
+ Value (%)        Limit          Limit
+___________________________________________
+    50.000        0.04812        0.13554
+    75.000        0.03078        0.17727
+    90.000        0.01807        0.22637
+    95.000        0.01235        0.26028
+    99.000        0.00530        0.33111
+    99.900        0.00164        0.41802
+    99.990        0.00051        0.49202
+    99.999        0.00016        0.55574
+</pre>
+<p>
+              As you can see, even at the 95% confidence level the bounds (0.012
+              to 0.26) are really very wide, and very asymmetric about the observed
+              value 0.1.
+            </p>
+<p>
+              Compare that with the program output for a mass 2000 trials:
+            </p>
+<pre class="programlisting">______________________________________________
+2-Sided Confidence Limits For Success Fraction
+______________________________________________
+Number of trials                         =  2000
+Number of successes                      =  200
+Number of failures                       =  1800
+Observed frequency of occurrence         =  0.1
+___________________________________________
+Confidence        Lower          Upper
+ Value (%)        Limit          Limit
+___________________________________________
+    50.000        0.09536        0.10445
+    75.000        0.09228        0.10776
+    90.000        0.08916        0.11125
+    95.000        0.08720        0.11352
+    99.000        0.08344        0.11802
+    99.900        0.07921        0.12336
+    99.990        0.07577        0.12795
+    99.999        0.07282        0.13206
+</pre>
+<p>
+              Now even when the confidence level is very high, the limits (at 99.999%,
+              0.07 to 0.13) are really quite close and nearly symmetric to the observed
+              value of 0.1.
+            </p>
+</div>
+<table xmlns:rev="http://www.cs.rpi.edu/~gregod/boost/tools/doc/revision" width="100%"><tr>
+<td align="left"></td>
+<td align="right"><div class="copyright-footer">Copyright © 2006 , 2007, 2008 John Maddock, Paul A. Bristow, Hubert
+      Holin, Xiaogang Zhang, Bruno Lalande and Gautam Sewani<p>
+        Distributed under the Boost Software License, Version 1.0. (See accompanying
+        file LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_0.txt)
+      </p>
+</div></td>
+</tr></table>
+<hr>
+<div class="spirit-nav">
+<a accesskey="p" href="../neg_binom_eg.html"><img src="../../../../../../../doc/html/images/prev.png" alt="Prev"></a><a accesskey="u" href="../neg_binom_eg.html"><img src="../../../../../../../doc/html/images/up.png" alt="Up"></a><a accesskey="h" href="../../../../../index.html"><img src="../../../../../../../doc/html/images/home.png" alt="Home"></a><a accesskey="n" href="neg_binom_size_eg.html"><img src="../../../../../../../doc/html/images/next.png" alt="Next"></a>
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+<title>Estimating Sample Sizes for the Negative Binomial.</title>
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+<div class="titlepage"><div><div><h6 class="title">
+<a name="math_toolkit.dist.stat_tut.weg.neg_binom_eg.neg_binom_size_eg"></a><a class="link" href="neg_binom_size_eg.html" title="Estimating Sample Sizes for the Negative Binomial.">
+            Estimating Sample Sizes for the Negative Binomial.</a>
+</h6></div></div></div>
+<p>
+              Imagine you have an event (let's call it a "failure" - though
+              we could equally well call it a success if we felt it was a 'good'
+              event) that you know will occur in 1 in N trials. You may want to know
+              how many trials you need to conduct to be P% sure of observing at least
+              k such failures. If the failure events follow a negative binomial distribution
+              (each trial either succeeds or fails) then the static member function
+              <code class="computeroutput"><span class="identifier">negative_binomial_distibution</span><span class="special">&lt;&gt;::</span><span class="identifier">find_minimum_number_of_trials</span></code>
+              can be used to estimate the minimum number of trials required to be
+              P% sure of observing the desired number of failures.
+            </p>
+<p>
+              The example program neg_binomial_sample_sizes.cpp
+              demonstrates its usage.
+            </p>
+<p>
+              </p>
+<p>
+                It centres around a routine that prints out a table of minimum sample
+                sizes for various probability thresholds:
+              </p>
+<p>
+              </p>
+<p>
+                
+</p>
+<pre class="programlisting"><span class="keyword">void</span> <span class="identifier">find_number_of_trials</span><span class="special">(</span><span class="keyword">double</span> <span class="identifier">failures</span><span class="special">,</span> <span class="keyword">double</span> <span class="identifier">p</span><span class="special">);</span></pre>
+<p>
+              </p>
+<p>
+              </p>
+<p>
+                First define a table of significance levels: these are the maximum
+                acceptable probability that <span class="emphasis"><em>failure</em></span> or fewer
+                events will be observed.
+              </p>
+<p>
+              </p>
+<p>
+                
+</p>
+<pre class="programlisting"><span class="keyword">double</span> <span class="identifier">alpha</span><span class="special">[]</span> <span class="special">=</span> <span class="special">{</span> <span class="number">0.5</span><span class="special">,</span> <span class="number">0.25</span><span class="special">,</span> <span class="number">0.1</span><span class="special">,</span> <span class="number">0.05</span><span class="special">,</span> <span class="number">0.01</span><span class="special">,</span> <span class="number">0.001</span><span class="special">,</span> <span class="number">0.0001</span><span class="special">,</span> <span class="number">0.00001</span> <span class="special">};</span></pre>
+<p>
+              </p>
+<p>
+              </p>
+<p>
+                Confidence value as % is (1 - alpha) * 100, so alpha 0.05 == 95%
+                confidence that the desired number of failures will be observed.
+              </p>
+<p>
+              </p>
+<p>
+                Much of the rest of the program is pretty-printing, the important
+                part is in the calculation of minimum number of trials required for
+                each value of alpha using:
+              </p>
+<p>
+              
+</p>
+<pre class="programlisting"><span class="special">(</span><span class="keyword">int</span><span class="special">)</span><span class="identifier">ceil</span><span class="special">(</span><span class="identifier">negative_binomial</span><span class="special">::</span><span class="identifier">find_minimum_number_of_trials</span><span class="special">(</span><span class="identifier">failures</span><span class="special">,</span> <span class="identifier">p</span><span class="special">,</span> <span class="identifier">alpha</span><span class="special">[</span><span class="identifier">i</span><span class="special">]);</span>
+</pre>
+<p>
+              </p>
+<p>
+                find_minimum_number_of_trials returns a double, so ceil rounds this
+                up to ensure we have an integral minimum number of trials.
+              </p>
+<p>
+              </p>
+<p>
+                
+</p>
+<pre class="programlisting">  
+<span class="keyword">void</span> <span class="identifier">find_number_of_trials</span><span class="special">(</span><span class="keyword">double</span> <span class="identifier">failures</span><span class="special">,</span> <span class="keyword">double</span> <span class="identifier">p</span><span class="special">)</span>
+<span class="special">{</span>
+   <span class="comment">// trials = number of trials
+</span>   <span class="comment">// failures = number of failures before achieving required success(es).
+</span>   <span class="comment">// p        = success fraction (0 &lt;= p &lt;= 1.).
+</span>   <span class="comment">//
+</span>   <span class="comment">// Calculate how many trials we need to ensure the
+</span>   <span class="comment">// required number of failures DOES exceed "failures".
+</span>
+  <span class="identifier">cout</span> <span class="special">&lt;&lt;</span> <span class="string">"\n"</span><span class="string">"Target number of failures = "</span> <span class="special">&lt;&lt;</span> <span class="identifier">failures</span><span class="special">;</span>
+  <span class="identifier">cout</span> <span class="special">&lt;&lt;</span> <span class="string">",   Success fraction = "</span> <span class="special">&lt;&lt;</span> <span class="number">100</span> <span class="special">*</span> <span class="identifier">p</span> <span class="special">&lt;&lt;</span> <span class="string">"%"</span> <span class="special">&lt;&lt;</span> <span class="identifier">endl</span><span class="special">;</span>
+   <span class="comment">// Print table header:
+</span>   <span class="identifier">cout</span> <span class="special">&lt;&lt;</span> <span class="string">"\n\n"</span>
+           <span class="string">"____________________________\n"</span>
+           <span class="string">"Confidence        Min Number\n"</span>
+           <span class="string">" Value (%)        Of Trials \n"</span>
+           <span class="string">"____________________________\n"</span><span class="special">;</span>
+   <span class="comment">// Now print out the data for the alpha table values.
+</span>  <span class="keyword">for</span><span class="special">(</span><span class="keyword">unsigned</span> <span class="identifier">i</span> <span class="special">=</span> <span class="number">0</span><span class="special">;</span> <span class="identifier">i</span> <span class="special">&lt;</span> <span class="keyword">sizeof</span><span class="special">(</span><span class="identifier">alpha</span><span class="special">)/</span><span class="keyword">sizeof</span><span class="special">(</span><span class="identifier">alpha</span><span class="special">[</span><span class="number">0</span><span class="special">]);</span> <span class="special">++</span><span class="identifier">i</span><span class="special">)</span>
+   <span class="special">{</span> <span class="comment">// Confidence values %:
+</span>      <span class="identifier">cout</span> <span class="special">&lt;&lt;</span> <span class="identifier">fixed</span> <span class="special">&lt;&lt;</span> <span class="identifier">setprecision</span><span class="special">(</span><span class="number">3</span><span class="special">)</span> <span class="special">&lt;&lt;</span> <span class="identifier">setw</span><span class="special">(</span><span class="number">10</span><span class="special">)</span> <span class="special">&lt;&lt;</span> <span class="identifier">right</span> <span class="special">&lt;&lt;</span> <span class="number">100</span> <span class="special">*</span> <span class="special">(</span><span class="number">1</span><span class="special">-</span><span class="identifier">alpha</span><span class="special">[</span><span class="identifier">i</span><span class="special">])</span> <span class="special">&lt;&lt;</span> <span class="string">"      "</span>
+      <span class="comment">// find_minimum_number_of_trials
+</span>      <span class="special">&lt;&lt;</span> <span class="identifier">setw</span><span class="special">(</span><span class="number">6</span><span class="special">)</span> <span class="special">&lt;&lt;</span> <span class="identifier">right</span>
+      <span class="special">&lt;&lt;</span> <span class="special">(</span><span class="keyword">int</span><span class="special">)</span><span class="identifier">ceil</span><span class="special">(</span><span class="identifier">negative_binomial</span><span class="special">::</span><span class="identifier">find_minimum_number_of_trials</span><span class="special">(</span><span class="identifier">failures</span><span class="special">,</span> <span class="identifier">p</span><span class="special">,</span> <span class="identifier">alpha</span><span class="special">[</span><span class="identifier">i</span><span class="special">]))</span>
+      <span class="special">&lt;&lt;</span> <span class="identifier">endl</span><span class="special">;</span>
+   <span class="special">}</span>
+   <span class="identifier">cout</span> <span class="special">&lt;&lt;</span> <span class="identifier">endl</span><span class="special">;</span>
+<span class="special">}</span> <span class="comment">// void find_number_of_trials(double failures, double p)</span></pre>
+<p>
+              </p>
+<p>
+              </p>
+<p>
+                finally we can produce some tables of minimum trials for the chosen
+                confidence levels:
+              </p>
+<p>
+              </p>
+<p>
+                
+</p>
+<pre class="programlisting"><span class="keyword">int</span> <span class="identifier">main</span><span class="special">()</span>
+<span class="special">{</span>
+    <span class="identifier">find_number_of_trials</span><span class="special">(</span><span class="number">5</span><span class="special">,</span> <span class="number">0.5</span><span class="special">);</span>
+    <span class="identifier">find_number_of_trials</span><span class="special">(</span><span class="number">50</span><span class="special">,</span> <span class="number">0.5</span><span class="special">);</span>
+    <span class="identifier">find_number_of_trials</span><span class="special">(</span><span class="number">500</span><span class="special">,</span> <span class="number">0.5</span><span class="special">);</span>
+    <span class="identifier">find_number_of_trials</span><span class="special">(</span><span class="number">50</span><span class="special">,</span> <span class="number">0.1</span><span class="special">);</span>
+    <span class="identifier">find_number_of_trials</span><span class="special">(</span><span class="number">500</span><span class="special">,</span> <span class="number">0.1</span><span class="special">);</span>
+    <span class="identifier">find_number_of_trials</span><span class="special">(</span><span class="number">5</span><span class="special">,</span> <span class="number">0.9</span><span class="special">);</span>
+
+    <span class="keyword">return</span> <span class="number">0</span><span class="special">;</span>
+<span class="special">}</span> <span class="comment">// int main()
+</span>
+</pre>
+<p>
+              </p>
+<p>
+            </p>
+<div class="note"><table border="0" summary="Note">
+<tr>
+<td rowspan="2" align="center" valign="top" width="25"><img alt="[Note]" src="../../../../../../../doc/html/images/note.png"></td>
+<th align="left">Note</th>
+</tr>
+<tr><td align="left" valign="top">
+<p>
+                Since we're calculating the <span class="emphasis"><em>minimum</em></span> number of
+                trials required, we'll err on the safe side and take the ceiling
+                of the result. Had we been calculating the <span class="emphasis"><em>maximum</em></span>
+                number of trials permitted to observe less than a certain number
+                of <span class="emphasis"><em>failures</em></span> then we would have taken the floor
+                instead. We would also have called <code class="computeroutput"><span class="identifier">find_minimum_number_of_trials</span></code>
+                like this: 
+</p>
+<pre class="programlisting"><span class="identifier">floor</span><span class="special">(</span><span class="identifier">negative_binomial</span><span class="special">::</span><span class="identifier">find_minimum_number_of_trials</span><span class="special">(</span><span class="identifier">failures</span><span class="special">,</span> <span class="identifier">p</span><span class="special">,</span> <span class="identifier">alpha</span><span class="special">[</span><span class="identifier">i</span><span class="special">]))</span>
+</pre>
+<p>
+                which would give us the largest number of trials we could conduct
+                and still be P% sure of observing <span class="emphasis"><em>failures or less</em></span>
+                failure events, when the probability of success is <span class="emphasis"><em>p</em></span>.
+              </p>
+</td></tr>
+</table></div>
+<p>
+              We'll finish off by looking at some sample output, firstly suppose
+              we wish to observe at least 5 "failures" with a 50/50 (0.5)
+              chance of success or failure:
+            </p>
+<pre class="programlisting">Target number of failures = 5,   Success fraction = 50%
+
+____________________________
+Confidence        Min Number
+ Value (%)        Of Trials
+____________________________
+    50.000          11
+    75.000          14
+    90.000          17
+    95.000          18
+    99.000          22
+    99.900          27
+    99.990          31
+    99.999          36
+
+</pre>
+<p>
+              So 18 trials or more would yield a 95% chance that at least our 5 required
+              failures would be observed.
+            </p>
+<p>
+              Compare that to what happens if the success ratio is 90%:
+            </p>
+<pre class="programlisting">Target number of failures = 5.000,   Success fraction = 90.000%
+
+____________________________
+Confidence        Min Number
+ Value (%)        Of Trials
+____________________________
+    50.000          57
+    75.000          73
+    90.000          91
+    95.000         103
+    99.000         127
+    99.900         159
+    99.990         189
+    99.999         217
+</pre>
+<p>
+              So now 103 trials are required to observe at least 5 failures with
+              95% certainty.
+            </p>
+</div>
+<table xmlns:rev="http://www.cs.rpi.edu/~gregod/boost/tools/doc/revision" width="100%"><tr>
+<td align="left"></td>
+<td align="right"><div class="copyright-footer">Copyright © 2006 , 2007, 2008 John Maddock, Paul A. Bristow, Hubert
+      Holin, Xiaogang Zhang, Bruno Lalande and Gautam Sewani<p>
+        Distributed under the Boost Software License, Version 1.0. (See accompanying
+        file LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_0.txt)
+      </p>
+</div></td>
+</tr></table>
+<hr>
+<div class="spirit-nav">
+<a accesskey="p" href="neg_binom_conf.html"><img src="../../../../../../../doc/html/images/prev.png" alt="Prev"></a><a accesskey="u" href="../neg_binom_eg.html"><img src="../../../../../../../doc/html/images/up.png" alt="Up"></a><a accesskey="h" href="../../../../../index.html"><img src="../../../../../../../doc/html/images/home.png" alt="Home"></a><a accesskey="n" href="negative_binomial_example1.html"><img src="../../../../../../../doc/html/images/next.png" alt="Next"></a>
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+<a name="math_toolkit.dist.stat_tut.weg.neg_binom_eg.negative_binomial_example1"></a><a class="link" href="negative_binomial_example1.html" title="Negative Binomial Sales Quota Example.">
+            Negative Binomial Sales Quota Example.</a>
+</h6></div></div></div>
+<p>
+              This example program <a href="../../../../../../../../example/negative_binomial_example1.cpp" target="_top">negative_binomial_example1.cpp
+              (full source code)</a> demonstrates a simple use to find the probability
+              of meeting a sales quota.
+            </p>
+<p>
+              </p>
+<p>
+                Based on <a href="http://en.wikipedia.org/wiki/Negative_binomial_distribution" target="_top">a
+                problem by Dr. Diane Evans, Professor of Mathematics at Rose-Hulman
+                Institute of Technology</a>.
+              </p>
+<p>
+              </p>
+<p>
+                Pat is required to sell candy bars to raise money for the 6th grade
+                field trip. There are thirty houses in the neighborhood, and Pat
+                is not supposed to return home until five candy bars have been sold.
+                So the child goes door to door, selling candy bars. At each house,
+                there is a 0.4 probability (40%) of selling one candy bar and a 0.6
+                probability (60%) of selling nothing.
+              </p>
+<p>
+              </p>
+<p>
+                What is the probability mass (density) function (pdf) for selling
+                the last (fifth) candy bar at the nth house?
+              </p>
+<p>
+              </p>
+<p>
+                The Negative Binomial(r, p) distribution describes the probability
+                of k failures and r successes in k+r Bernoulli(p) trials with success
+                on the last trial. (A <a href="http://en.wikipedia.org/wiki/Bernoulli_distribution" target="_top">Bernoulli
+                trial</a> is one with only two possible outcomes, success of
+                failure, and p is the probability of success). See also <a href="../../../../../" target="_top">http://en.wikipedia.org/wiki/Bernoulli_distribution
+                Bernoulli distribution</a> and <a href="http://www.math.uah.edu/stat/bernoulli/Introduction.xhtml" target="_top">Bernoulli
+                applications</a>.
+              </p>
+<p>
+              </p>
+<p>
+                In this example, we will deliberately produce a variety of calculations
+                and outputs to demonstrate the ways that the negative binomial distribution
+                can be implemented with this library: it is also deliberately over-commented.
+              </p>
+<p>
+              </p>
+<p>
+                First we need to #define macros to control the error and discrete
+                handling policies. For this simple example, we want to avoid throwing
+                an exception (the default policy) and just return infinity. We want
+                to treat the distribution as if it was continuous, so we choose a
+                discrete_quantile policy of real, rather than the default policy
+                integer_round_outwards.
+              </p>
+<p>
+              </p>
+<p>
+                
+</p>
+<pre class="programlisting"><span class="preprocessor">#define</span> <span class="identifier">BOOST_MATH_OVERFLOW_ERROR_POLICY</span> <span class="identifier">ignore_error</span>
+<span class="preprocessor">#define</span> <span class="identifier">BOOST_MATH_DISCRETE_QUANTILE_POLICY</span> <span class="identifier">real</span></pre>
+<p>
+              </p>
+<p>
+              </p>
+<p>
+                After that we need some includes to provide easy access to the negative
+                binomial distribution,
+              </p>
+<p>
+              </p>
+<div class="caution"><table border="0" summary="Caution">
+<tr>
+<td rowspan="2" align="center" valign="top" width="25"><img alt="[Caution]" src="../../../../../../../doc/html/images/caution.png"></td>
+<th align="left">Caution</th>
+</tr>
+<tr><td align="left" valign="top"><p>
+                  It is vital to #include distributions etc <span class="bold"><strong>after</strong></span>
+                  the above #defines
+                </p></td></tr>
+</table></div>
+<p>
+              </p>
+<p>
+                and we need some std library iostream, of course.
+              </p>
+<p>
+              </p>
+<p>
+                
+</p>
+<pre class="programlisting"><span class="preprocessor">#include</span> <span class="special">&lt;</span><span class="identifier">boost</span><span class="special">/</span><span class="identifier">math</span><span class="special">/</span><span class="identifier">distributions</span><span class="special">/</span><span class="identifier">negative_binomial</span><span class="special">.</span><span class="identifier">hpp</span><span class="special">&gt;</span>
+  <span class="comment">// for negative_binomial_distribution
+</span>  <span class="keyword">using</span> <span class="identifier">boost</span><span class="special">::</span><span class="identifier">math</span><span class="special">::</span><span class="identifier">negative_binomial</span><span class="special">;</span> <span class="comment">// typedef provides default type is double.
+</span>  <span class="keyword">using</span>  <span class="special">::</span><span class="identifier">boost</span><span class="special">::</span><span class="identifier">math</span><span class="special">::</span><span class="identifier">pdf</span><span class="special">;</span> <span class="comment">// Probability mass function.
+</span>  <span class="keyword">using</span>  <span class="special">::</span><span class="identifier">boost</span><span class="special">::</span><span class="identifier">math</span><span class="special">::</span><span class="identifier">cdf</span><span class="special">;</span> <span class="comment">// Cumulative density function.
+</span>  <span class="keyword">using</span>  <span class="special">::</span><span class="identifier">boost</span><span class="special">::</span><span class="identifier">math</span><span class="special">::</span><span class="identifier">quantile</span><span class="special">;</span>
+
+<span class="preprocessor">#include</span> <span class="special">&lt;</span><span class="identifier">iostream</span><span class="special">&gt;</span>
+  <span class="keyword">using</span> <span class="identifier">std</span><span class="special">::</span><span class="identifier">cout</span><span class="special">;</span> <span class="keyword">using</span> <span class="identifier">std</span><span class="special">::</span><span class="identifier">endl</span><span class="special">;</span>
+  <span class="keyword">using</span> <span class="identifier">std</span><span class="special">::</span><span class="identifier">noshowpoint</span><span class="special">;</span> <span class="keyword">using</span> <span class="identifier">std</span><span class="special">::</span><span class="identifier">fixed</span><span class="special">;</span> <span class="keyword">using</span> <span class="identifier">std</span><span class="special">::</span><span class="identifier">right</span><span class="special">;</span> <span class="keyword">using</span> <span class="identifier">std</span><span class="special">::</span><span class="identifier">left</span><span class="special">;</span>
+<span class="preprocessor">#include</span> <span class="special">&lt;</span><span class="identifier">iomanip</span><span class="special">&gt;</span>
+  <span class="keyword">using</span> <span class="identifier">std</span><span class="special">::</span><span class="identifier">setprecision</span><span class="special">;</span> <span class="keyword">using</span> <span class="identifier">std</span><span class="special">::</span><span class="identifier">setw</span><span class="special">;</span> 
+
+<span class="preprocessor">#include</span> <span class="special">&lt;</span><span class="identifier">limits</span><span class="special">&gt;</span>
+  <span class="keyword">using</span> <span class="identifier">std</span><span class="special">::</span><span class="identifier">numeric_limits</span><span class="special">;</span>
+</pre>
+<p>
+              </p>
+<p>
+              </p>
+<p>
+                It is always sensible to use try and catch blocks because defaults
+                policies are to throw an exception if anything goes wrong.
+              </p>
+<p>
+              </p>
+<p>
+                A simple catch block (see below) will ensure that you get a helpful
+                error message instead of an abrupt program abort.
+              </p>
+<p>
+              </p>
+<p>
+                
+</p>
+<pre class="programlisting"><span class="keyword">try</span>
+<span class="special">{</span></pre>
+<p>
+              </p>
+<p>
+              </p>
+<p>
+                Selling five candy bars means getting five successes, so successes
+                r = 5. The total number of trials (n, in this case, houses visited)
+                this takes is therefore = sucesses + failures or k + r = k + 5.
+              </p>
+<p>
+              </p>
+<p>
+                
+</p>
+<pre class="programlisting"><span class="keyword">double</span> <span class="identifier">sales_quota</span> <span class="special">=</span> <span class="number">5</span><span class="special">;</span> <span class="comment">// Pat's sales quota - successes (r).</span></pre>
+<p>
+              </p>
+<p>
+              </p>
+<p>
+                At each house, there is a 0.4 probability (40%) of selling one candy
+                bar and a 0.6 probability (60%) of selling nothing.
+              </p>
+<p>
+              </p>
+<p>
+                
+</p>
+<pre class="programlisting"><span class="keyword">double</span> <span class="identifier">success_fraction</span> <span class="special">=</span> <span class="number">0.4</span><span class="special">;</span> <span class="comment">// success_fraction (p) - so failure_fraction is 0.6.</span></pre>
+<p>
+              </p>
+<p>
+              </p>
+<p>
+                The Negative Binomial(r, p) distribution describes the probability
+                of k failures and r successes in k+r Bernoulli(p) trials with success
+                on the last trial. (A <a href="http://en.wikipedia.org/wiki/Bernoulli_distribution" target="_top">Bernoulli
+                trial</a> is one with only two possible outcomes, success of
+                failure, and p is the probability of success).
+              </p>
+<p>
+              </p>
+<p>
+                We therefore start by constructing a negative binomial distribution
+                with parameters sales_quota (required successes) and probability
+                of success.
+              </p>
+<p>
+              </p>
+<p>
+                
+</p>
+<pre class="programlisting"><span class="identifier">negative_binomial</span> <span class="identifier">nb</span><span class="special">(</span><span class="identifier">sales_quota</span><span class="special">,</span> <span class="identifier">success_fraction</span><span class="special">);</span> <span class="comment">// type double by default.</span></pre>
+<p>
+              </p>
+<p>
+              </p>
+<p>
+                To confirm, display the success_fraction &amp; successes parameters
+                of the distribution.
+              </p>
+<p>
+              </p>
+<p>
+                
+</p>
+<pre class="programlisting"><span class="identifier">cout</span> <span class="special">&lt;&lt;</span> <span class="string">"Pat has a sales per house success rate of "</span> <span class="special">&lt;&lt;</span> <span class="identifier">success_fraction</span>
+  <span class="special">&lt;&lt;</span> <span class="string">".\nTherefore he would, on average, sell "</span> <span class="special">&lt;&lt;</span> <span class="identifier">nb</span><span class="special">.</span><span class="identifier">success_fraction</span><span class="special">()</span> <span class="special">*</span> <span class="number">100</span>
+  <span class="special">&lt;&lt;</span> <span class="string">" bars after trying 100 houses."</span> <span class="special">&lt;&lt;</span> <span class="identifier">endl</span><span class="special">;</span>
+
+<span class="keyword">int</span> <span class="identifier">all_houses</span> <span class="special">=</span> <span class="number">30</span><span class="special">;</span> <span class="comment">// The number of houses on the estate.
+</span>
+<span class="identifier">cout</span> <span class="special">&lt;&lt;</span> <span class="string">"With a success rate of "</span> <span class="special">&lt;&lt;</span> <span class="identifier">nb</span><span class="special">.</span><span class="identifier">success_fraction</span><span class="special">()</span> 
+  <span class="special">&lt;&lt;</span> <span class="string">", he might expect, on average,\n"</span>
+    <span class="string">"to need to visit about "</span> <span class="special">&lt;&lt;</span> <span class="identifier">success_fraction</span> <span class="special">*</span> <span class="identifier">all_houses</span>
+    <span class="special">&lt;&lt;</span> <span class="string">" houses in order to sell all "</span> <span class="special">&lt;&lt;</span> <span class="identifier">nb</span><span class="special">.</span><span class="identifier">successes</span><span class="special">()</span> <span class="special">&lt;&lt;</span> <span class="string">" bars. "</span> <span class="special">&lt;&lt;</span> <span class="identifier">endl</span><span class="special">;</span></pre>
+<p>
+              </p>
+<p>
+              
+</p>
+<pre class="programlisting">Pat has a sales per house success rate of 0.4.
+Therefore he would, on average, sell 40 bars after trying 100 houses.
+With a success rate of 0.4, he might expect, on average,
+to need to visit about 12 houses in order to sell all 5 bars. 
+</pre>
+<p>
+              </p>
+<p>
+                The random variable of interest is the number of houses that must
+                be visited to sell five candy bars, so we substitute k = n - 5 into
+                a negative_binomial(5, 0.4) and obtain the <a class="link" href="../../../dist_ref/nmp.html#math.dist.pdf">probability
+                mass (density) function (pdf or pmf)</a> of the distribution of
+                houses visited. Obviously, the best possible case is that Pat makes
+                sales on all the first five houses.
+              </p>
+<p>
+              </p>
+<p>
+                We calculate this using the pdf function:
+              </p>
+<p>
+              </p>
+<p>
+                
+</p>
+<pre class="programlisting"><span class="identifier">cout</span> <span class="special">&lt;&lt;</span> <span class="string">"Probability that Pat finishes on the "</span> <span class="special">&lt;&lt;</span> <span class="identifier">sales_quota</span> <span class="special">&lt;&lt;</span> <span class="string">"th house is "</span>
+  <span class="special">&lt;&lt;</span> <span class="identifier">pdf</span><span class="special">(</span><span class="identifier">nb</span><span class="special">,</span> <span class="number">5</span> <span class="special">-</span> <span class="identifier">sales_quota</span><span class="special">)</span> <span class="special">&lt;&lt;</span> <span class="identifier">endl</span><span class="special">;</span> <span class="comment">// == pdf(nb, 0)</span></pre>
+<p>
+              </p>
+<p>
+              </p>
+<p>
+                Of course, he could not finish on fewer than 5 houses because he
+                must sell 5 candy bars. So the 5th house is the first that he could
+                possibly finish on.
+              </p>
+<p>
+              </p>
+<p>
+                To finish on or before the 8th house, Pat must finish at the 5th,
+                6th, 7th or 8th house. The probability that he will finish on <span class="bold"><strong>exactly</strong></span> ( == ) on any house is the Probability
+                Density Function (pdf).
+              </p>
+<p>
+              </p>
+<p>
+                
+</p>
+<pre class="programlisting"><span class="identifier">cout</span> <span class="special">&lt;&lt;</span> <span class="string">"Probability that Pat finishes on the 6th house is "</span>
+  <span class="special">&lt;&lt;</span> <span class="identifier">pdf</span><span class="special">(</span><span class="identifier">nb</span><span class="special">,</span> <span class="number">6</span> <span class="special">-</span> <span class="identifier">sales_quota</span><span class="special">)</span> <span class="special">&lt;&lt;</span> <span class="identifier">endl</span><span class="special">;</span>
+<span class="identifier">cout</span> <span class="special">&lt;&lt;</span> <span class="string">"Probability that Pat finishes on the 7th house is "</span>
+  <span class="special">&lt;&lt;</span> <span class="identifier">pdf</span><span class="special">(</span><span class="identifier">nb</span><span class="special">,</span> <span class="number">7</span> <span class="special">-</span> <span class="identifier">sales_quota</span><span class="special">)</span> <span class="special">&lt;&lt;</span> <span class="identifier">endl</span><span class="special">;</span>
+<span class="identifier">cout</span> <span class="special">&lt;&lt;</span> <span class="string">"Probability that Pat finishes on the 8th house is "</span>
+  <span class="special">&lt;&lt;</span> <span class="identifier">pdf</span><span class="special">(</span><span class="identifier">nb</span><span class="special">,</span> <span class="number">8</span> <span class="special">-</span> <span class="identifier">sales_quota</span><span class="special">)</span> <span class="special">&lt;&lt;</span> <span class="identifier">endl</span><span class="special">;</span></pre>
+<p>
+              </p>
+<p>
+              
+</p>
+<pre class="programlisting">Probability that Pat finishes on the 6th house is 0.03072
+Probability that Pat finishes on the 7th house is 0.055296
+Probability that Pat finishes on the 8th house is 0.077414
+</pre>
+<p>
+              </p>
+<p>
+                The sum of the probabilities for these houses is the Cumulative Distribution
+                Function (cdf). We can calculate it by adding the individual probabilities.
+              </p>
+<p>
+              </p>
+<p>
+                
+</p>
+<pre class="programlisting"><span class="identifier">cout</span> <span class="special">&lt;&lt;</span> <span class="string">"Probability that Pat finishes on or before the 8th house is sum "</span>
+  <span class="string">"\n"</span> <span class="special">&lt;&lt;</span> <span class="string">"pdf(sales_quota) + pdf(6) + pdf(7) + pdf(8) = "</span>
+  <span class="comment">// Sum each of the mass/density probabilities for houses sales_quota = 5, 6, 7, &amp; 8.
+</span>  <span class="special">&lt;&lt;</span> <span class="identifier">pdf</span><span class="special">(</span><span class="identifier">nb</span><span class="special">,</span> <span class="number">5</span> <span class="special">-</span> <span class="identifier">sales_quota</span><span class="special">)</span> <span class="comment">// 0 failures.
+</span>    <span class="special">+</span> <span class="identifier">pdf</span><span class="special">(</span><span class="identifier">nb</span><span class="special">,</span> <span class="number">6</span> <span class="special">-</span> <span class="identifier">sales_quota</span><span class="special">)</span> <span class="comment">// 1 failure.
+</span>    <span class="special">+</span> <span class="identifier">pdf</span><span class="special">(</span><span class="identifier">nb</span><span class="special">,</span> <span class="number">7</span> <span class="special">-</span> <span class="identifier">sales_quota</span><span class="special">)</span> <span class="comment">// 2 failures.
+</span>    <span class="special">+</span> <span class="identifier">pdf</span><span class="special">(</span><span class="identifier">nb</span><span class="special">,</span> <span class="number">8</span> <span class="special">-</span> <span class="identifier">sales_quota</span><span class="special">)</span> <span class="comment">// 3 failures.
+</span>  <span class="special">&lt;&lt;</span> <span class="identifier">endl</span><span class="special">;</span></pre>
+<p>
+              </p>
+<p>
+              
+</p>
+<pre class="programlisting">pdf(sales_quota) + pdf(6) + pdf(7) + pdf(8) = 0.17367
+</pre>
+<p>
+              </p>
+<p>
+                Or, usually better, by using the negative binomial <span class="bold"><strong>cumulative</strong></span>
+                distribution function.
+              </p>
+<p>
+              </p>
+<p>
+                
+</p>
+<pre class="programlisting"><span class="identifier">cout</span> <span class="special">&lt;&lt;</span> <span class="string">"\nProbability of selling his quota of "</span> <span class="special">&lt;&lt;</span> <span class="identifier">sales_quota</span>
+  <span class="special">&lt;&lt;</span> <span class="string">" bars\non or before the "</span> <span class="special">&lt;&lt;</span> <span class="number">8</span> <span class="special">&lt;&lt;</span> <span class="string">"th house is "</span>
+  <span class="special">&lt;&lt;</span> <span class="identifier">cdf</span><span class="special">(</span><span class="identifier">nb</span><span class="special">,</span> <span class="number">8</span> <span class="special">-</span> <span class="identifier">sales_quota</span><span class="special">)</span> <span class="special">&lt;&lt;</span> <span class="identifier">endl</span><span class="special">;</span></pre>
+<p>
+              </p>
+<p>
+              
+</p>
+<pre class="programlisting">Probability of selling his quota of 5 bars on or before the 8th house is 0.17367
+</pre>
+<p>
+              </p>
+<p>
+                
+</p>
+<pre class="programlisting"><span class="identifier">cout</span> <span class="special">&lt;&lt;</span> <span class="string">"\nProbability that Pat finishes exactly on the 10th house is "</span>
+  <span class="special">&lt;&lt;</span> <span class="identifier">pdf</span><span class="special">(</span><span class="identifier">nb</span><span class="special">,</span> <span class="number">10</span> <span class="special">-</span> <span class="identifier">sales_quota</span><span class="special">)</span> <span class="special">&lt;&lt;</span> <span class="identifier">endl</span><span class="special">;</span>
+<span class="identifier">cout</span> <span class="special">&lt;&lt;</span> <span class="string">"\nProbability of selling his quota of "</span> <span class="special">&lt;&lt;</span> <span class="identifier">sales_quota</span>
+  <span class="special">&lt;&lt;</span> <span class="string">" bars\non or before the "</span> <span class="special">&lt;&lt;</span> <span class="number">10</span> <span class="special">&lt;&lt;</span> <span class="string">"th house is "</span>
+  <span class="special">&lt;&lt;</span> <span class="identifier">cdf</span><span class="special">(</span><span class="identifier">nb</span><span class="special">,</span> <span class="number">10</span> <span class="special">-</span> <span class="identifier">sales_quota</span><span class="special">)</span> <span class="special">&lt;&lt;</span> <span class="identifier">endl</span><span class="special">;</span></pre>
+<p>
+              </p>
+<p>
+              
+</p>
+<pre class="programlisting">Probability that Pat finishes exactly on the 10th house is 0.10033
+Probability of selling his quota of 5 bars on or before the 10th house is 0.3669
+</pre>
+<p>
+              </p>
+<p>
+                
+</p>
+<pre class="programlisting"><span class="identifier">cout</span> <span class="special">&lt;&lt;</span> <span class="string">"Probability that Pat finishes exactly on the 11th house is "</span>
+  <span class="special">&lt;&lt;</span> <span class="identifier">pdf</span><span class="special">(</span><span class="identifier">nb</span><span class="special">,</span> <span class="number">11</span> <span class="special">-</span> <span class="identifier">sales_quota</span><span class="special">)</span> <span class="special">&lt;&lt;</span> <span class="identifier">endl</span><span class="special">;</span>
+<span class="identifier">cout</span> <span class="special">&lt;&lt;</span> <span class="string">"\nProbability of selling his quota of "</span> <span class="special">&lt;&lt;</span> <span class="identifier">sales_quota</span>
+  <span class="special">&lt;&lt;</span> <span class="string">" bars\non or before the "</span> <span class="special">&lt;&lt;</span> <span class="number">11</span> <span class="special">&lt;&lt;</span> <span class="string">"th house is "</span>
+  <span class="special">&lt;&lt;</span> <span class="identifier">cdf</span><span class="special">(</span><span class="identifier">nb</span><span class="special">,</span> <span class="number">11</span> <span class="special">-</span> <span class="identifier">sales_quota</span><span class="special">)</span> <span class="special">&lt;&lt;</span> <span class="identifier">endl</span><span class="special">;</span></pre>
+<p>
+              </p>
+<p>
+              
+</p>
+<pre class="programlisting">Probability that Pat finishes on the 11th house is 0.10033
+Probability of selling his quota of 5 candy bars
+on or before the 11th house is 0.46723
+</pre>
+<p>
+              </p>
+<p>
+                
+</p>
+<pre class="programlisting"><span class="identifier">cout</span> <span class="special">&lt;&lt;</span> <span class="string">"Probability that Pat finishes exactly on the 12th house is "</span>
+  <span class="special">&lt;&lt;</span> <span class="identifier">pdf</span><span class="special">(</span><span class="identifier">nb</span><span class="special">,</span> <span class="number">12</span> <span class="special">-</span> <span class="identifier">sales_quota</span><span class="special">)</span> <span class="special">&lt;&lt;</span> <span class="identifier">endl</span><span class="special">;</span>
+
+<span class="identifier">cout</span> <span class="special">&lt;&lt;</span> <span class="string">"\nProbability of selling his quota of "</span> <span class="special">&lt;&lt;</span> <span class="identifier">sales_quota</span>
+  <span class="special">&lt;&lt;</span> <span class="string">" bars\non or before the "</span> <span class="special">&lt;&lt;</span> <span class="number">12</span> <span class="special">&lt;&lt;</span> <span class="string">"th house is "</span>
+  <span class="special">&lt;&lt;</span> <span class="identifier">cdf</span><span class="special">(</span><span class="identifier">nb</span><span class="special">,</span> <span class="number">12</span> <span class="special">-</span> <span class="identifier">sales_quota</span><span class="special">)</span> <span class="special">&lt;&lt;</span> <span class="identifier">endl</span><span class="special">;</span></pre>
+<p>
+              </p>
+<p>
+              
+</p>
+<pre class="programlisting">Probability that Pat finishes on the 12th house is 0.094596
+Probability of selling his quota of 5 candy bars
+on or before the 12th house is 0.56182
+</pre>
+<p>
+              </p>
+<p>
+                Finally consider the risk of Pat not selling his quota of 5 bars
+                even after visiting all the houses. Calculate the probability that
+                he <span class="emphasis"><em>will</em></span> sell on or before the last house: Calculate
+                the probability that he would sell all his quota on the very last
+                house.
+              </p>
+<p>
+              </p>
+<p>
+                
+</p>
+<pre class="programlisting"><span class="identifier">cout</span> <span class="special">&lt;&lt;</span> <span class="string">"Probability that Pat finishes on the "</span> <span class="special">&lt;&lt;</span> <span class="identifier">all_houses</span>
+  <span class="special">&lt;&lt;</span> <span class="string">" house is "</span> <span class="special">&lt;&lt;</span> <span class="identifier">pdf</span><span class="special">(</span><span class="identifier">nb</span><span class="special">,</span> <span class="identifier">all_houses</span> <span class="special">-</span> <span class="identifier">sales_quota</span><span class="special">)</span> <span class="special">&lt;&lt;</span> <span class="identifier">endl</span><span class="special">;</span></pre>
+<p>
+              </p>
+<p>
+              </p>
+<p>
+                Probability of selling his quota of 5 bars on the 30th house is
+              </p>
+<p>
+              
+</p>
+<pre class="programlisting">Probability that Pat finishes on the 30 house is 0.00069145
+</pre>
+<p>
+              </p>
+<p>
+                when he'd be very unlucky indeed!
+              </p>
+<p>
+              </p>
+<p>
+                What is the probability that Pat exhausts all 30 houses in the neighborhood,
+                and <span class="bold"><strong>still</strong></span> doesn't sell the required
+                5 candy bars?
+              </p>
+<p>
+              </p>
+<p>
+                
+</p>
+<pre class="programlisting"><span class="identifier">cout</span> <span class="special">&lt;&lt;</span> <span class="string">"\nProbability of selling his quota of "</span> <span class="special">&lt;&lt;</span> <span class="identifier">sales_quota</span>
+  <span class="special">&lt;&lt;</span> <span class="string">" bars\non or before the "</span> <span class="special">&lt;&lt;</span> <span class="identifier">all_houses</span> <span class="special">&lt;&lt;</span> <span class="string">"th house is "</span>
+  <span class="special">&lt;&lt;</span> <span class="identifier">cdf</span><span class="special">(</span><span class="identifier">nb</span><span class="special">,</span> <span class="identifier">all_houses</span> <span class="special">-</span> <span class="identifier">sales_quota</span><span class="special">)</span> <span class="special">&lt;&lt;</span> <span class="identifier">endl</span><span class="special">;</span></pre>
+<p>
+              </p>
+<p>
+              
+</p>
+<pre class="programlisting">Probability of selling his quota of 5 bars
+on or before the 30th house is 0.99849
+</pre>
+<p>
+              </p>
+<p>
+                /*<code class="computeroutput"><span class="identifier">So</span> <span class="identifier">the</span>
+                <span class="identifier">risk</span> <span class="identifier">of</span>
+                <span class="identifier">failing</span> <span class="identifier">even</span>
+                <span class="identifier">after</span> <span class="identifier">visiting</span>
+                <span class="identifier">all</span> <span class="identifier">the</span>
+                <span class="identifier">houses</span> <span class="identifier">is</span>
+                <span class="number">1</span> <span class="special">-</span>
+                <span class="keyword">this</span> <span class="identifier">probability</span><span class="special">,</span> </code><code class="computeroutput"><span class="number">1</span>
+                <span class="special">-</span> <span class="identifier">cdf</span><span class="special">(</span><span class="identifier">nb</span><span class="special">,</span> <span class="identifier">all_houses</span>
+                <span class="special">-</span> <span class="identifier">sales_quota</span></code><code class="computeroutput">
+                <span class="identifier">But</span> <span class="keyword">using</span>
+                <span class="keyword">this</span> <span class="identifier">expression</span>
+                <span class="identifier">may</span> <span class="identifier">cause</span>
+                <span class="identifier">serious</span> <span class="identifier">inaccuracy</span><span class="special">,</span> <span class="identifier">so</span>
+                <span class="identifier">it</span> <span class="identifier">would</span>
+                <span class="identifier">be</span> <span class="identifier">much</span>
+                <span class="identifier">better</span> <span class="identifier">to</span>
+                <span class="identifier">use</span> <span class="identifier">the</span>
+                <span class="identifier">complement</span> <span class="identifier">of</span>
+                <span class="identifier">the</span> <span class="identifier">cdf</span><span class="special">:</span> <span class="identifier">So</span>
+                <span class="identifier">the</span> <span class="identifier">risk</span>
+                <span class="identifier">of</span> <span class="identifier">failing</span>
+                <span class="identifier">even</span> <span class="identifier">at</span><span class="special">,</span> <span class="keyword">or</span> <span class="identifier">after</span><span class="special">,</span>
+                <span class="identifier">the</span> <span class="number">31</span><span class="identifier">th</span> <span class="special">(</span><span class="identifier">non</span><span class="special">-</span><span class="identifier">existent</span><span class="special">)</span>
+                <span class="identifier">houses</span> <span class="identifier">is</span>
+                <span class="number">1</span> <span class="special">-</span>
+                <span class="keyword">this</span> <span class="identifier">probability</span><span class="special">,</span> </code><code class="computeroutput"><span class="number">1</span>
+                <span class="special">-</span> <span class="identifier">cdf</span><span class="special">(</span><span class="identifier">nb</span><span class="special">,</span> <span class="identifier">all_houses</span>
+                <span class="special">-</span> <span class="identifier">sales_quota</span><span class="special">)</span></code>` But using this expression may cause
+                serious inaccuracy. So it would be much better to use the complement
+                of the cdf. <a class="link" href="../../overview.html#why_complements">Why complements?</a>
+              </p>
+<p>
+              </p>
+<p>
+                
+</p>
+<pre class="programlisting"><span class="identifier">cout</span> <span class="special">&lt;&lt;</span> <span class="string">"\nProbability of failing to sell his quota of "</span> <span class="special">&lt;&lt;</span> <span class="identifier">sales_quota</span>
+  <span class="special">&lt;&lt;</span> <span class="string">" bars\neven after visiting all "</span> <span class="special">&lt;&lt;</span> <span class="identifier">all_houses</span> <span class="special">&lt;&lt;</span> <span class="string">" houses is "</span>
+  <span class="special">&lt;&lt;</span> <span class="identifier">cdf</span><span class="special">(</span><span class="identifier">complement</span><span class="special">(</span><span class="identifier">nb</span><span class="special">,</span> <span class="identifier">all_houses</span> <span class="special">-</span> <span class="identifier">sales_quota</span><span class="special">))</span> <span class="special">&lt;&lt;</span> <span class="identifier">endl</span><span class="special">;</span></pre>
+<p>
+              </p>
+<p>
+              
+</p>
+<pre class="programlisting">Probability of failing to sell his quota of 5 bars
+even after visiting all 30 houses is 0.0015101
+</pre>
+<p>
+              </p>
+<p>
+                We can also use the quantile (percentile), the inverse of the cdf,
+                to predict which house Pat will finish on. So for the 8th house:
+              </p>
+<p>
+              </p>
+<p>
+                
+</p>
+<pre class="programlisting"><span class="keyword">double</span> <span class="identifier">p</span> <span class="special">=</span> <span class="identifier">cdf</span><span class="special">(</span><span class="identifier">nb</span><span class="special">,</span> <span class="special">(</span><span class="number">8</span> <span class="special">-</span> <span class="identifier">sales_quota</span><span class="special">));</span> 
+<span class="identifier">cout</span> <span class="special">&lt;&lt;</span> <span class="string">"Probability of meeting sales quota on or before 8th house is "</span><span class="special">&lt;&lt;</span> <span class="identifier">p</span> <span class="special">&lt;&lt;</span> <span class="identifier">endl</span><span class="special">;</span></pre>
+<p>
+              </p>
+<p>
+              
+</p>
+<pre class="programlisting">Probability of meeting sales quota on or before 8th house is 0.174
+</pre>
+<p>
+              </p>
+<p>
+                
+</p>
+<pre class="programlisting"><span class="identifier">cout</span> <span class="special">&lt;&lt;</span> <span class="string">"If the confidence of meeting sales quota is "</span> <span class="special">&lt;&lt;</span> <span class="identifier">p</span>
+    <span class="special">&lt;&lt;</span> <span class="string">", then the finishing house is "</span> <span class="special">&lt;&lt;</span> <span class="identifier">quantile</span><span class="special">(</span><span class="identifier">nb</span><span class="special">,</span> <span class="identifier">p</span><span class="special">)</span> <span class="special">+</span> <span class="identifier">sales_quota</span> <span class="special">&lt;&lt;</span> <span class="identifier">endl</span><span class="special">;</span>
+
+<span class="identifier">cout</span><span class="special">&lt;&lt;</span> <span class="string">" quantile(nb, p) = "</span> <span class="special">&lt;&lt;</span> <span class="identifier">quantile</span><span class="special">(</span><span class="identifier">nb</span><span class="special">,</span> <span class="identifier">p</span><span class="special">)</span> <span class="special">&lt;&lt;</span> <span class="identifier">endl</span><span class="special">;</span></pre>
+<p>
+              </p>
+<p>
+              
+</p>
+<pre class="programlisting">If the confidence of meeting sales quota is 0.17367, then the finishing house is 8
+</pre>
+<p>
+              </p>
+<p>
+                Demanding absolute certainty that all 5 will be sold, implies an
+                infinite number of trials. (Of course, there are only 30 houses on
+                the estate, so he can't ever be <span class="bold"><strong>certain</strong></span>
+                of selling his quota).
+              </p>
+<p>
+              </p>
+<p>
+                
+</p>
+<pre class="programlisting"><span class="identifier">cout</span> <span class="special">&lt;&lt;</span> <span class="string">"If the confidence of meeting sales quota is "</span> <span class="special">&lt;&lt;</span> <span class="number">1.</span>
+    <span class="special">&lt;&lt;</span> <span class="string">", then the finishing house is "</span> <span class="special">&lt;&lt;</span> <span class="identifier">quantile</span><span class="special">(</span><span class="identifier">nb</span><span class="special">,</span> <span class="number">1</span><span class="special">)</span> <span class="special">+</span> <span class="identifier">sales_quota</span> <span class="special">&lt;&lt;</span> <span class="identifier">endl</span><span class="special">;</span>
+<span class="comment">//  1.#INF == infinity.</span></pre>
+<p>
+              </p>
+<p>
+              
+</p>
+<pre class="programlisting">If the confidence of meeting sales quota is 1, then the finishing house is 1.#INF
+</pre>
+<p>
+              </p>
+<p>
+                And similarly for a few other probabilities:
+              </p>
+<p>
+              </p>
+<p>
+                
+</p>
+<pre class="programlisting"><span class="identifier">cout</span> <span class="special">&lt;&lt;</span> <span class="string">"If the confidence of meeting sales quota is "</span> <span class="special">&lt;&lt;</span> <span class="number">0.</span>
+    <span class="special">&lt;&lt;</span> <span class="string">", then the finishing house is "</span> <span class="special">&lt;&lt;</span> <span class="identifier">quantile</span><span class="special">(</span><span class="identifier">nb</span><span class="special">,</span> <span class="number">0.</span><span class="special">)</span> <span class="special">+</span> <span class="identifier">sales_quota</span> <span class="special">&lt;&lt;</span> <span class="identifier">endl</span><span class="special">;</span>
+
+<span class="identifier">cout</span> <span class="special">&lt;&lt;</span> <span class="string">"If the confidence of meeting sales quota is "</span> <span class="special">&lt;&lt;</span> <span class="number">0.5</span>
+    <span class="special">&lt;&lt;</span> <span class="string">", then the finishing house is "</span> <span class="special">&lt;&lt;</span> <span class="identifier">quantile</span><span class="special">(</span><span class="identifier">nb</span><span class="special">,</span> <span class="number">0.5</span><span class="special">)</span> <span class="special">+</span> <span class="identifier">sales_quota</span> <span class="special">&lt;&lt;</span> <span class="identifier">endl</span><span class="special">;</span>
+
+<span class="identifier">cout</span> <span class="special">&lt;&lt;</span> <span class="string">"If the confidence of meeting sales quota is "</span> <span class="special">&lt;&lt;</span> <span class="number">1</span> <span class="special">-</span> <span class="number">0.00151</span> <span class="comment">// 30 th
+</span>    <span class="special">&lt;&lt;</span> <span class="string">", then the finishing house is "</span> <span class="special">&lt;&lt;</span> <span class="identifier">quantile</span><span class="special">(</span><span class="identifier">nb</span><span class="special">,</span> <span class="number">1</span> <span class="special">-</span> <span class="number">0.00151</span><span class="special">)</span> <span class="special">+</span> <span class="identifier">sales_quota</span> <span class="special">&lt;&lt;</span> <span class="identifier">endl</span><span class="special">;</span></pre>
+<p>
+              </p>
+<p>
+              
+</p>
+<pre class="programlisting">If the confidence of meeting sales quota is 0, then the finishing house is 5
+If the confidence of meeting sales quota is 0.5, then the finishing house is 11.337
+If the confidence of meeting sales quota is 0.99849, then the finishing house is 30
+</pre>
+<p>
+              </p>
+<p>
+                Notice that because we chose a discrete quantile policy of real,
+                the result can be an 'unreal' fractional house.
+              </p>
+<p>
+              </p>
+<p>
+                If the opposite is true, we don't want to assume any confidence,
+                then this is tantamount to assuming that all the first sales_quota
+                trials will be successful sales.
+              </p>
+<p>
+              </p>
+<p>
+                
+</p>
+<pre class="programlisting"><span class="identifier">cout</span> <span class="special">&lt;&lt;</span> <span class="string">"If confidence of meeting quota is zero\n(we assume all houses are successful sales)"</span> 
+  <span class="string">", then finishing house is "</span> <span class="special">&lt;&lt;</span> <span class="identifier">sales_quota</span> <span class="special">&lt;&lt;</span> <span class="identifier">endl</span><span class="special">;</span></pre>
+<p>
+              </p>
+<p>
+              
+</p>
+<pre class="programlisting">If confidence of meeting quota is zero (we assume all houses are successful sales), then finishing house is 5
+If confidence of meeting quota is 0, then finishing house is 5
+</pre>
+<p>
+              </p>
+<p>
+                We can list quantiles for a few probabilities:
+              </p>
+<p>
+              </p>
+<p>
+                
+</p>
+<pre class="programlisting"> <span class="keyword">double</span> <span class="identifier">ps</span><span class="special">[]</span> <span class="special">=</span> <span class="special">{</span><span class="number">0.</span><span class="special">,</span> <span class="number">0.001</span><span class="special">,</span> <span class="number">0.01</span><span class="special">,</span> <span class="number">0.05</span><span class="special">,</span> <span class="number">0.1</span><span class="special">,</span> <span class="number">0.5</span><span class="special">,</span> <span class="number">0.9</span><span class="special">,</span> <span class="number">0.95</span><span class="special">,</span> <span class="number">0.99</span><span class="special">,</span> <span class="number">0.999</span><span class="special">,</span> <span class="number">1.</span><span class="special">};</span>
+ <span class="comment">// Confidence as fraction = 1-alpha, as percent =  100 * (1-alpha[i]) %
+</span> <span class="identifier">cout</span><span class="special">.</span><span class="identifier">precision</span><span class="special">(</span><span class="number">3</span><span class="special">);</span>
+ <span class="keyword">for</span> <span class="special">(</span><span class="keyword">int</span> <span class="identifier">i</span> <span class="special">=</span> <span class="number">0</span><span class="special">;</span> <span class="identifier">i</span> <span class="special">&lt;</span> <span class="keyword">sizeof</span><span class="special">(</span><span class="identifier">ps</span><span class="special">)/</span><span class="keyword">sizeof</span><span class="special">(</span><span class="identifier">ps</span><span class="special">[</span><span class="number">0</span><span class="special">]);</span> <span class="identifier">i</span><span class="special">++)</span>
+ <span class="special">{</span>
+   <span class="identifier">cout</span> <span class="special">&lt;&lt;</span> <span class="string">"If confidence of meeting quota is "</span> <span class="special">&lt;&lt;</span> <span class="identifier">ps</span><span class="special">[</span><span class="identifier">i</span><span class="special">]</span>
+     <span class="special">&lt;&lt;</span> <span class="string">", then finishing house is "</span> <span class="special">&lt;&lt;</span> <span class="identifier">quantile</span><span class="special">(</span><span class="identifier">nb</span><span class="special">,</span> <span class="identifier">ps</span><span class="special">[</span><span class="identifier">i</span><span class="special">])</span> <span class="special">+</span> <span class="identifier">sales_quota</span>
+     <span class="special">&lt;&lt;</span> <span class="identifier">endl</span><span class="special">;</span>
+<span class="special">}</span></pre>
+<p>
+              </p>
+<p>
+              
+</p>
+<pre class="programlisting">If confidence of meeting quota is 0, then finishing house is 5
+If confidence of meeting quota is 0.001, then finishing house is 5
+If confidence of meeting quota is 0.01, then finishing house is 5
+If confidence of meeting quota is 0.05, then finishing house is 6.2
+If confidence of meeting quota is 0.1, then finishing house is 7.06
+If confidence of meeting quota is 0.5, then finishing house is 11.3
+If confidence of meeting quota is 0.9, then finishing house is 17.8
+If confidence of meeting quota is 0.95, then finishing house is 20.1
+If confidence of meeting quota is 0.99, then finishing house is 24.8
+If confidence of meeting quota is 0.999, then finishing house is 31.1
+If confidence of meeting quota is 1, then finishing house is 1.#INF
+</pre>
+<p>
+              </p>
+<p>
+                We could have applied a ceil function to obtain a 'worst case' integer
+                value for house. 
+</p>
+<pre class="programlisting"><span class="identifier">ceil</span><span class="special">(</span><span class="identifier">quantile</span><span class="special">(</span><span class="identifier">nb</span><span class="special">,</span> <span class="identifier">ps</span><span class="special">[</span><span class="identifier">i</span><span class="special">]))</span></pre>
+<p>
+              </p>
+<p>
+              </p>
+<p>
+                Or, if we had used the default discrete quantile policy, integer_outside,
+                by omitting 
+</p>
+<pre class="programlisting"><span class="preprocessor">#define</span> <span class="identifier">BOOST_MATH_DISCRETE_QUANTILE_POLICY</span> <span class="identifier">real</span></pre>
+<p>
+                we would have achieved the same effect.
+              </p>
+<p>
+              </p>
+<p>
+                The real result gives some suggestion which house is most likely.
+                For example, compare the real and integer_outside for 95% confidence.
+              </p>
+<p>
+              
+</p>
+<pre class="programlisting">If confidence of meeting quota is 0.95, then finishing house is 20.1
+If confidence of meeting quota is 0.95, then finishing house is 21
+</pre>
+<p>
+              </p>
+<p>
+                The real value 20.1 is much closer to 20 than 21, so integer_outside
+                is pessimistic. We could also use integer_round_nearest policy to
+                suggest that 20 is more likely.
+              </p>
+<p>
+              </p>
+<p>
+                Finally, we can tabulate the probability for the last sale being
+                exactly on each house.
+              </p>
+<p>
+              </p>
+<p>
+                
+</p>
+<pre class="programlisting"><span class="identifier">cout</span> <span class="special">&lt;&lt;</span> <span class="string">"\nHouse for "</span> <span class="special">&lt;&lt;</span> <span class="identifier">sales_quota</span> <span class="special">&lt;&lt;</span> <span class="string">"th (last) sale.  Probability (%)"</span> <span class="special">&lt;&lt;</span> <span class="identifier">endl</span><span class="special">;</span>
+<span class="identifier">cout</span><span class="special">.</span><span class="identifier">precision</span><span class="special">(</span><span class="number">5</span><span class="special">);</span>
+<span class="keyword">for</span> <span class="special">(</span><span class="keyword">int</span> <span class="identifier">i</span> <span class="special">=</span> <span class="special">(</span><span class="keyword">int</span><span class="special">)</span><span class="identifier">sales_quota</span><span class="special">;</span> <span class="identifier">i</span> <span class="special">&lt;</span> <span class="identifier">all_houses</span><span class="special">+</span><span class="number">1</span><span class="special">;</span> <span class="identifier">i</span><span class="special">++)</span>
+<span class="special">{</span>
+  <span class="identifier">cout</span> <span class="special">&lt;&lt;</span> <span class="identifier">left</span> <span class="special">&lt;&lt;</span> <span class="identifier">setw</span><span class="special">(</span><span class="number">3</span><span class="special">)</span> <span class="special">&lt;&lt;</span> <span class="identifier">i</span> <span class="special">&lt;&lt;</span> <span class="string">"                             "</span> <span class="special">&lt;&lt;</span> <span class="identifier">setw</span><span class="special">(</span><span class="number">8</span><span class="special">)</span> <span class="special">&lt;&lt;</span> <span class="identifier">cdf</span><span class="special">(</span><span class="identifier">nb</span><span class="special">,</span> <span class="identifier">i</span> <span class="special">-</span> <span class="identifier">sales_quota</span><span class="special">)</span>  <span class="special">&lt;&lt;</span> <span class="identifier">endl</span><span class="special">;</spa
n>
+<span class="special">}</span>
+<span class="identifier">cout</span> <span class="special">&lt;&lt;</span> <span class="identifier">endl</span><span class="special">;</span></pre>
+<p>
+              </p>
+<p>
+              
+</p>
+<pre class="programlisting">House for 5 th (last) sale.  Probability (%)
+5                               0.01024 
+6                               0.04096 
+7                               0.096256
+8                               0.17367 
+9                               0.26657 
+10                              0.3669  
+11                              0.46723 
+12                              0.56182 
+13                              0.64696 
+14                              0.72074 
+15                              0.78272 
+16                              0.83343 
+17                              0.874   
+18                              0.90583 
+19                              0.93039 
+20                              0.94905 
+21                              0.96304 
+22                              0.97342 
+23                              0.98103 
+24                              0.98655 
+25                              0.99053 
+26                              0.99337 
+27                              0.99539 
+28                              0.99681 
+29                              0.9978  
+30                              0.99849
+</pre>
+<p>
+              </p>
+<p>
+                As noted above, using a catch block is always a good idea, even if
+                you do not expect to use it.
+              </p>
+<p>
+              </p>
+<p>
+                
+</p>
+<pre class="programlisting"><span class="special">}</span>
+<span class="keyword">catch</span><span class="special">(</span><span class="keyword">const</span> <span class="identifier">std</span><span class="special">::</span><span class="identifier">exception</span><span class="special">&amp;</span> <span class="identifier">e</span><span class="special">)</span>
+<span class="special">{</span> <span class="comment">// Since we have set an overflow policy of ignore_error,
+</span>  <span class="comment">// an overflow exception should never be thrown.
+</span>   <span class="identifier">std</span><span class="special">::</span><span class="identifier">cout</span> <span class="special">&lt;&lt;</span> <span class="string">"\nMessage from thrown exception was:\n "</span> <span class="special">&lt;&lt;</span> <span class="identifier">e</span><span class="special">.</span><span class="identifier">what</span><span class="special">()</span> <span class="special">&lt;&lt;</span> <span class="identifier">std</span><span class="special">::</span><span class="identifier">endl</span><span class="special">;</span></pre>
+<p>
+              </p>
+<p>
+              </p>
+<p>
+                For example, without a ignore domain error policy, if we asked for
+                
+</p>
+<pre class="programlisting"><span class="identifier">pdf</span><span class="special">(</span><span class="identifier">nb</span><span class="special">,</span> <span class="special">-</span><span class="number">1</span><span class="special">)</span></pre>
+<p>
+                for example, we would get:
+              </p>
+<p>
+              
+</p>
+<pre class="programlisting">Message from thrown exception was:
+ Error in function boost::math::pdf(const negative_binomial_distribution&lt;double&gt;&amp;, double):
+ Number of failures argument is -1, but must be &gt;= 0 !
+</pre>
+<p>
+            </p>
+</div>
+<table xmlns:rev="http://www.cs.rpi.edu/~gregod/boost/tools/doc/revision" width="100%"><tr>
+<td align="left"></td>
+<td align="right"><div class="copyright-footer">Copyright © 2006 , 2007, 2008 John Maddock, Paul A. Bristow, Hubert
+      Holin, Xiaogang Zhang, Bruno Lalande and Gautam Sewani<p>
+        Distributed under the Boost Software License, Version 1.0. (See accompanying
+        file LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_0.txt)
+      </p>
+</div></td>
+</tr></table>
+<hr>
+<div class="spirit-nav">
+<a accesskey="p" href="neg_binom_size_eg.html"><img src="../../../../../../../doc/html/images/prev.png" alt="Prev"></a><a accesskey="u" href="../neg_binom_eg.html"><img src="../../../../../../../doc/html/images/up.png" alt="Up"></a><a accesskey="h" href="../../../../../index.html"><img src="../../../../../../../doc/html/images/home.png" alt="Home"></a><a accesskey="n" href="negative_binomial_example2.html"><img src="../../../../../../../doc/html/images/next.png" alt="Next"></a>
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@@ -0,0 +1,150 @@
+<html>
+<head>
+<meta http-equiv="Content-Type" content="text/html; charset=ISO-8859-1">
+<title>Negative Binomial Table Printing Example.</title>
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+<div class="section" lang="en">
+<div class="titlepage"><div><div><h6 class="title">
+<a name="math_toolkit.dist.stat_tut.weg.neg_binom_eg.negative_binomial_example2"></a><a class="link" href="negative_binomial_example2.html" title="Negative Binomial Table Printing Example.">
+            Negative Binomial Table Printing Example.</a>
+</h6></div></div></div>
+<p>
+              Example program showing output of a table of values of cdf and pdf
+              for various k failures.
+            </p>
+<p>
+              </p>
+<p>
+                
+</p>
+<pre class="programlisting"><span class="comment">// Print a table of values that can be used to plot
+</span><span class="comment">// using Excel, or some other superior graphical display tool.
+</span>
+<span class="identifier">cout</span><span class="special">.</span><span class="identifier">precision</span><span class="special">(</span><span class="number">17</span><span class="special">);</span> <span class="comment">// Use max_digits10 precision, the maximum available for a reference table.
+</span><span class="identifier">cout</span> <span class="special">&lt;&lt;</span> <span class="identifier">showpoint</span> <span class="special">&lt;&lt;</span> <span class="identifier">endl</span><span class="special">;</span> <span class="comment">// include trailing zeros.
+</span><span class="comment">// This is a maximum possible precision for the type (here double) to suit a reference table.
+</span><span class="keyword">int</span> <span class="identifier">maxk</span> <span class="special">=</span> <span class="keyword">static_cast</span><span class="special">&lt;</span><span class="keyword">int</span><span class="special">&gt;(</span><span class="number">2.</span> <span class="special">*</span> <span class="identifier">mynbdist</span><span class="special">.</span><span class="identifier">successes</span><span class="special">()</span> <span class="special">/</span>  <span class="identifier">mynbdist</span><span class="special">.</span><span class="identifier">success_fraction</span><span class="special">());</span>
+<span class="comment">// This maxk shows most of the range of interest, probability about 0.0001 to 0.999.
+</span><span class="identifier">cout</span> <span class="special">&lt;&lt;</span> <span class="string">"\n"</span><span class="string">" k            pdf                      cdf"</span><span class="string">"\n"</span> <span class="special">&lt;&lt;</span> <span class="identifier">endl</span><span class="special">;</span>
+<span class="keyword">for</span> <span class="special">(</span><span class="keyword">int</span> <span class="identifier">k</span> <span class="special">=</span> <span class="number">0</span><span class="special">;</span> <span class="identifier">k</span> <span class="special">&lt;</span> <span class="identifier">maxk</span><span class="special">;</span> <span class="identifier">k</span><span class="special">++)</span>
+<span class="special">{</span>
+  <span class="identifier">cout</span> <span class="special">&lt;&lt;</span> <span class="identifier">right</span> <span class="special">&lt;&lt;</span> <span class="identifier">setprecision</span><span class="special">(</span><span class="number">17</span><span class="special">)</span> <span class="special">&lt;&lt;</span> <span class="identifier">showpoint</span>
+    <span class="special">&lt;&lt;</span> <span class="identifier">right</span> <span class="special">&lt;&lt;</span> <span class="identifier">setw</span><span class="special">(</span><span class="number">3</span><span class="special">)</span> <span class="special">&lt;&lt;</span> <span class="identifier">k</span>  <span class="special">&lt;&lt;</span> <span class="string">", "</span>
+    <span class="special">&lt;&lt;</span> <span class="identifier">left</span> <span class="special">&lt;&lt;</span> <span class="identifier">setw</span><span class="special">(</span><span class="number">25</span><span class="special">)</span> <span class="special">&lt;&lt;</span> <span class="identifier">pdf</span><span class="special">(</span><span class="identifier">mynbdist</span><span class="special">,</span> <span class="keyword">static_cast</span><span class="special">&lt;</span><span class="keyword">double</span><span class="special">&gt;(</span><span class="identifier">k</span><span class="special">))</span>
+    <span class="special">&lt;&lt;</span> <span class="identifier">left</span> <span class="special">&lt;&lt;</span> <span class="identifier">setw</span><span class="special">(</span><span class="number">25</span><span class="special">)</span> <span class="special">&lt;&lt;</span> <span class="identifier">cdf</span><span class="special">(</span><span class="identifier">mynbdist</span><span class="special">,</span> <span class="keyword">static_cast</span><span class="special">&lt;</span><span class="keyword">double</span><span class="special">&gt;(</span><span class="identifier">k</span><span class="special">))</span>
+    <span class="special">&lt;&lt;</span> <span class="identifier">endl</span><span class="special">;</span>
+<span class="special">}</span>
+<span class="identifier">cout</span> <span class="special">&lt;&lt;</span> <span class="identifier">endl</span><span class="special">;</span>
+</pre>
+<p>
+              </p>
+<p>
+              </p>
+<p>
+                
+</p>
+<pre class="programlisting"><span class="identifier">k</span>            <span class="identifier">pdf</span>                      <span class="identifier">cdf</span>
+ <span class="number">0</span><span class="special">,</span> <span class="number">1.5258789062500000e-005</span>  <span class="number">1.5258789062500003e-005</span>  
+ <span class="number">1</span><span class="special">,</span> <span class="number">9.1552734375000000e-005</span>  <span class="number">0.00010681152343750000</span>   
+ <span class="number">2</span><span class="special">,</span> <span class="number">0.00030899047851562522</span>   <span class="number">0.00041580200195312500</span>   
+ <span class="number">3</span><span class="special">,</span> <span class="number">0.00077247619628906272</span>   <span class="number">0.0011882781982421875</span>    
+ <span class="number">4</span><span class="special">,</span> <span class="number">0.0015932321548461918</span>    <span class="number">0.0027815103530883789</span>    
+ <span class="number">5</span><span class="special">,</span> <span class="number">0.0028678178787231476</span>    <span class="number">0.0056493282318115234</span>    
+ <span class="number">6</span><span class="special">,</span> <span class="number">0.0046602040529251142</span>    <span class="number">0.010309532284736633</span>     
+ <span class="number">7</span><span class="special">,</span> <span class="number">0.0069903060793876605</span>    <span class="number">0.017299838364124298</span>     
+ <span class="number">8</span><span class="special">,</span> <span class="number">0.0098301179241389001</span>    <span class="number">0.027129956288263202</span>     
+ <span class="number">9</span><span class="special">,</span> <span class="number">0.013106823898851871</span>     <span class="number">0.040236780187115073</span>     
+<span class="number">10</span><span class="special">,</span> <span class="number">0.016711200471036140</span>     <span class="number">0.056947980658151209</span>     
+<span class="number">11</span><span class="special">,</span> <span class="number">0.020509200578089786</span>     <span class="number">0.077457181236241013</span>     
+<span class="number">12</span><span class="special">,</span> <span class="number">0.024354675686481652</span>     <span class="number">0.10181185692272265</span>      
+<span class="number">13</span><span class="special">,</span> <span class="number">0.028101548869017230</span>     <span class="number">0.12991340579173993</span>      
+<span class="number">14</span><span class="special">,</span> <span class="number">0.031614242477644432</span>     <span class="number">0.16152764826938440</span>      
+<span class="number">15</span><span class="special">,</span> <span class="number">0.034775666725408917</span>     <span class="number">0.19630331499479325</span>      
+<span class="number">16</span><span class="special">,</span> <span class="number">0.037492515688331451</span>     <span class="number">0.23379583068312471</span>      
+<span class="number">17</span><span class="special">,</span> <span class="number">0.039697957787645101</span>     <span class="number">0.27349378847076977</span>      
+<span class="number">18</span><span class="special">,</span> <span class="number">0.041352039362130305</span>     <span class="number">0.31484582783290005</span>      
+<span class="number">19</span><span class="special">,</span> <span class="number">0.042440250924291580</span>     <span class="number">0.35728607875719176</span>      
+<span class="number">20</span><span class="special">,</span> <span class="number">0.042970754060845245</span>     <span class="number">0.40025683281803687</span>      
+<span class="number">21</span><span class="special">,</span> <span class="number">0.042970754060845225</span>     <span class="number">0.44322758687888220</span>      
+<span class="number">22</span><span class="special">,</span> <span class="number">0.042482450037426581</span>     <span class="number">0.48571003691630876</span>      
+<span class="number">23</span><span class="special">,</span> <span class="number">0.041558918514873783</span>     <span class="number">0.52726895543118257</span>      
+<span class="number">24</span><span class="special">,</span> <span class="number">0.040260202311284021</span>     <span class="number">0.56752915774246648</span>      
+<span class="number">25</span><span class="special">,</span> <span class="number">0.038649794218832620</span>     <span class="number">0.60617895196129912</span>      
+<span class="number">26</span><span class="special">,</span> <span class="number">0.036791631035234917</span>     <span class="number">0.64297058299653398</span>      
+<span class="number">27</span><span class="special">,</span> <span class="number">0.034747651533277427</span>     <span class="number">0.67771823452981139</span>      
+<span class="number">28</span><span class="special">,</span> <span class="number">0.032575923312447595</span>     <span class="number">0.71029415784225891</span>      
+<span class="number">29</span><span class="special">,</span> <span class="number">0.030329307911589130</span>     <span class="number">0.74062346575384819</span>      
+<span class="number">30</span><span class="special">,</span> <span class="number">0.028054609818219924</span>     <span class="number">0.76867807557206813</span>      
+<span class="number">31</span><span class="special">,</span> <span class="number">0.025792141284492545</span>     <span class="number">0.79447021685656061</span>      
+<span class="number">32</span><span class="special">,</span> <span class="number">0.023575629142856460</span>     <span class="number">0.81804584599941710</span>      
+<span class="number">33</span><span class="special">,</span> <span class="number">0.021432390129869489</span>     <span class="number">0.83947823612928651</span>      
+<span class="number">34</span><span class="special">,</span> <span class="number">0.019383705779220189</span>     <span class="number">0.85886194190850684</span>      
+<span class="number">35</span><span class="special">,</span> <span class="number">0.017445335201298231</span>     <span class="number">0.87630727710980494</span>      
+<span class="number">36</span><span class="special">,</span> <span class="number">0.015628112784496322</span>     <span class="number">0.89193538989430121</span>      
+<span class="number">37</span><span class="special">,</span> <span class="number">0.013938587078064250</span>     <span class="number">0.90587397697236549</span>      
+<span class="number">38</span><span class="special">,</span> <span class="number">0.012379666154859701</span>     <span class="number">0.91825364312722524</span>      
+<span class="number">39</span><span class="special">,</span> <span class="number">0.010951243136991251</span>     <span class="number">0.92920488626421649</span>      
+<span class="number">40</span><span class="special">,</span> <span class="number">0.0096507830144735539</span>    <span class="number">0.93885566927869002</span>      
+<span class="number">41</span><span class="special">,</span> <span class="number">0.0084738582566109364</span>    <span class="number">0.94732952753530097</span>      
+<span class="number">42</span><span class="special">,</span> <span class="number">0.0074146259745345548</span>    <span class="number">0.95474415350983555</span>      
+<span class="number">43</span><span class="special">,</span> <span class="number">0.0064662435824429246</span>    <span class="number">0.96121039709227851</span>      
+<span class="number">44</span><span class="special">,</span> <span class="number">0.0056212231142827853</span>    <span class="number">0.96683162020656122</span>      
+<span class="number">45</span><span class="special">,</span> <span class="number">0.0048717266990450708</span>    <span class="number">0.97170334690560634</span>      
+<span class="number">46</span><span class="special">,</span> <span class="number">0.0042098073105878630</span>    <span class="number">0.97591315421619418</span>      
+<span class="number">47</span><span class="special">,</span> <span class="number">0.0036275999165703964</span>    <span class="number">0.97954075413276465</span>      
+<span class="number">48</span><span class="special">,</span> <span class="number">0.0031174686783026818</span>    <span class="number">0.98265822281106729</span>      
+<span class="number">49</span><span class="special">,</span> <span class="number">0.0026721160099737302</span>    <span class="number">0.98533033882104104</span>      
+<span class="number">50</span><span class="special">,</span> <span class="number">0.0022846591885275322</span>    <span class="number">0.98761499800956853</span>      
+<span class="number">51</span><span class="special">,</span> <span class="number">0.0019486798960970148</span>    <span class="number">0.98956367790566557</span>      
+<span class="number">52</span><span class="special">,</span> <span class="number">0.0016582516423517923</span>    <span class="number">0.99122192954801736</span>      
+<span class="number">53</span><span class="special">,</span> <span class="number">0.0014079495076571762</span>    <span class="number">0.99262987905567457</span>      
+<span class="number">54</span><span class="special">,</span> <span class="number">0.0011928461106539983</span>    <span class="number">0.99382272516632852</span>      
+<span class="number">55</span><span class="special">,</span> <span class="number">0.0010084971662802015</span>    <span class="number">0.99483122233260868</span>      
+<span class="number">56</span><span class="special">,</span> <span class="number">0.00085091948404891532</span>   <span class="number">0.99568214181665760</span>      
+<span class="number">57</span><span class="special">,</span> <span class="number">0.00071656377604119542</span>   <span class="number">0.99639870559269883</span>      
+<span class="number">58</span><span class="special">,</span> <span class="number">0.00060228420831048650</span>   <span class="number">0.99700098980100937</span>      
+<span class="number">59</span><span class="special">,</span> <span class="number">0.00050530624256557675</span>   <span class="number">0.99750629604357488</span>      
+<span class="number">60</span><span class="special">,</span> <span class="number">0.00042319397814867202</span>   <span class="number">0.99792949002172360</span>      
+<span class="number">61</span><span class="special">,</span> <span class="number">0.00035381791615708398</span>   <span class="number">0.99828330793788067</span>      
+<span class="number">62</span><span class="special">,</span> <span class="number">0.00029532382517950324</span>   <span class="number">0.99857863176306016</span>      
+<span class="number">63</span><span class="special">,</span> <span class="number">0.00024610318764958566</span>   <span class="number">0.99882473495070978</span>      
+</pre>
+<p>
+              </p>
+<p>
+            </p>
+</div>
+<table xmlns:rev="http://www.cs.rpi.edu/~gregod/boost/tools/doc/revision" width="100%"><tr>
+<td align="left"></td>
+<td align="right"><div class="copyright-footer">Copyright © 2006 , 2007, 2008 John Maddock, Paul A. Bristow, Hubert
+      Holin, Xiaogang Zhang, Bruno Lalande and Gautam Sewani<p>
+        Distributed under the Boost Software License, Version 1.0. (See accompanying
+        file LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_0.txt)
+      </p>
+</div></td>
+</tr></table>
+<hr>
+<div class="spirit-nav">
+<a accesskey="p" href="negative_binomial_example1.html"><img src="../../../../../../../doc/html/images/prev.png" alt="Prev"></a><a accesskey="u" href="../neg_binom_eg.html"><img src="../../../../../../../doc/html/images/up.png" alt="Up"></a><a accesskey="h" href="../../../../../index.html"><img src="../../../../../../../doc/html/images/home.png" alt="Home"></a><a accesskey="n" href="../normal_example.html"><img src="../../../../../../../doc/html/images/next.png" alt="Next"></a>
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@@ -0,0 +1,51 @@
+<html>
+<head>
+<meta http-equiv="Content-Type" content="text/html; charset=ISO-8859-1">
+<title>Normal Distribution Examples</title>
+<link rel="stylesheet" href="../../../../boostbook.css" type="text/css">
+<meta name="generator" content="DocBook XSL Stylesheets Vsnapshot_8125">
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+<link rel="up" href="../weg.html" title="Worked Examples">
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+<link rel="next" href="normal_example/normal_misc.html" title="Some Miscellaneous Examples of the Normal (Gaussian) Distribution">
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+</div>
+<div class="section" lang="en">
+<div class="titlepage"><div><div><h5 class="title">
+<a name="math_toolkit.dist.stat_tut.weg.normal_example"></a><a class="link" href="normal_example.html" title="Normal Distribution Examples"> Normal
+          Distribution Examples</a>
+</h5></div></div></div>
+<div class="toc"><dl><dt><span class="section"><a href="normal_example/normal_misc.html">
+            Some Miscellaneous Examples of the Normal (Gaussian) Distribution</a></span></dt></dl></div>
+<p>
+            (See also the reference documentation for the <a class="link" href="../../dist_ref/dists/normal_dist.html" title="Normal (Gaussian) Distribution">Normal
+            Distribution</a>.)
+          </p>
+</div>
+<table xmlns:rev="http://www.cs.rpi.edu/~gregod/boost/tools/doc/revision" width="100%"><tr>
+<td align="left"></td>
+<td align="right"><div class="copyright-footer">Copyright © 2006 , 2007, 2008 John Maddock, Paul A. Bristow, Hubert
+      Holin, Xiaogang Zhang, Bruno Lalande and Gautam Sewani<p>
+        Distributed under the Boost Software License, Version 1.0. (See accompanying
+        file LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_0.txt)
+      </p>
+</div></td>
+</tr></table>
+<hr>
+<div class="spirit-nav">
+<a accesskey="p" href="neg_binom_eg/negative_binomial_example2.html"><img src="../../../../../../doc/html/images/prev.png" alt="Prev"></a><a accesskey="u" href="../weg.html"><img src="../../../../../../doc/html/images/up.png" alt="Up"></a><a accesskey="h" href="../../../../index.html"><img src="../../../../../../doc/html/images/home.png" alt="Home"></a><a accesskey="n" href="normal_example/normal_misc.html"><img src="../../../../../../doc/html/images/next.png" alt="Next"></a>
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@@ -0,0 +1,759 @@
+<html>
+<head>
+<meta http-equiv="Content-Type" content="text/html; charset=ISO-8859-1">
+<title>Some Miscellaneous Examples of the Normal (Gaussian) Distribution</title>
+<link rel="stylesheet" href="../../../../../boostbook.css" type="text/css">
+<meta name="generator" content="DocBook XSL Stylesheets Vsnapshot_8125">
+<link rel="home" href="../../../../../index.html" title="Math Toolkit">
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+<link rel="prev" href="../normal_example.html" title="Normal Distribution Examples">
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+<table cellpadding="2" width="100%"><tr>
+<td valign="top"><img alt="Boost C++ Libraries" width="277" height="86" src="../../../../../../../boost.png"></td>
+<td align="center">Home</td>
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+</div>
+<div class="section" lang="en">
+<div class="titlepage"><div><div><h6 class="title">
+<a name="math_toolkit.dist.stat_tut.weg.normal_example.normal_misc"></a><a class="link" href="normal_misc.html" title="Some Miscellaneous Examples of the Normal (Gaussian) Distribution">
+            Some Miscellaneous Examples of the Normal (Gaussian) Distribution</a>
+</h6></div></div></div>
+<p>
+              The sample program normal_misc_examples.cpp
+              illustrates their use.
+            </p>
+<a name="math_toolkit.dist.stat_tut.weg.normal_example.normal_misc.traditional_tables"></a><h5>
+<a name="id611492"></a>
+              <a class="link" href="normal_misc.html#math_toolkit.dist.stat_tut.weg.normal_example.normal_misc.traditional_tables">Traditional
+              Tables</a>
+            </h5>
+<p>
+              </p>
+<p>
+                First we need some includes to access the normal distribution (and
+                some std output of course).
+              </p>
+<p>
+              </p>
+<p>
+                
+</p>
+<pre class="programlisting"><span class="preprocessor">#include</span> <span class="special">&lt;</span><span class="identifier">boost</span><span class="special">/</span><span class="identifier">math</span><span class="special">/</span><span class="identifier">distributions</span><span class="special">/</span><span class="identifier">normal</span><span class="special">.</span><span class="identifier">hpp</span><span class="special">&gt;</span> <span class="comment">// for normal_distribution
+</span>  <span class="keyword">using</span> <span class="identifier">boost</span><span class="special">::</span><span class="identifier">math</span><span class="special">::</span><span class="identifier">normal</span><span class="special">;</span> <span class="comment">// typedef provides default type is double.
+</span>
+<span class="preprocessor">#include</span> <span class="special">&lt;</span><span class="identifier">iostream</span><span class="special">&gt;</span>
+  <span class="keyword">using</span> <span class="identifier">std</span><span class="special">::</span><span class="identifier">cout</span><span class="special">;</span> <span class="keyword">using</span> <span class="identifier">std</span><span class="special">::</span><span class="identifier">endl</span><span class="special">;</span> <span class="keyword">using</span> <span class="identifier">std</span><span class="special">::</span><span class="identifier">left</span><span class="special">;</span> <span class="keyword">using</span> <span class="identifier">std</span><span class="special">::</span><span class="identifier">showpoint</span><span class="special">;</span> <span class="keyword">using</span> <span class="identifier">std</span><span class="special">::</span><span class="identifier">noshowpoint</span><span class="special">;</span>
+<span class="preprocessor">#include</span> <span class="special">&lt;</span><span class="identifier">iomanip</span><span class="special">&gt;</span>
+  <span class="keyword">using</span> <span class="identifier">std</span><span class="special">::</span><span class="identifier">setw</span><span class="special">;</span> <span class="keyword">using</span> <span class="identifier">std</span><span class="special">::</span><span class="identifier">setprecision</span><span class="special">;</span>
+<span class="preprocessor">#include</span> <span class="special">&lt;</span><span class="identifier">limits</span><span class="special">&gt;</span>
+  <span class="keyword">using</span> <span class="identifier">std</span><span class="special">::</span><span class="identifier">numeric_limits</span><span class="special">;</span>
+
+<span class="keyword">int</span> <span class="identifier">main</span><span class="special">()</span>
+<span class="special">{</span>
+  <span class="identifier">cout</span> <span class="special">&lt;&lt;</span> <span class="string">"Example: Normal distribution, Miscellaneous Applications."</span><span class="special">;</span>
+
+  <span class="keyword">try</span>
+  <span class="special">{</span>
+    <span class="special">{</span> <span class="comment">// Traditional tables and values.</span></pre>
+<p>
+              </p>
+<p>
+              </p>
+<p>
+                Let's start by printing some traditional tables.
+              </p>
+<p>
+              </p>
+<p>
+                
+</p>
+<pre class="programlisting"><span class="keyword">double</span> <span class="identifier">step</span> <span class="special">=</span> <span class="number">1.</span><span class="special">;</span> <span class="comment">// in z 
+</span><span class="keyword">double</span> <span class="identifier">range</span> <span class="special">=</span> <span class="number">4</span><span class="special">;</span> <span class="comment">// min and max z = -range to +range.
+</span><span class="keyword">int</span> <span class="identifier">precision</span> <span class="special">=</span> <span class="number">17</span><span class="special">;</span> <span class="comment">// traditional tables are only computed to much lower precision.
+</span>
+<span class="comment">// Construct a standard normal distribution s
+</span>  <span class="identifier">normal</span> <span class="identifier">s</span><span class="special">;</span> <span class="comment">// (default mean = zero, and standard deviation = unity)
+</span>  <span class="identifier">cout</span> <span class="special">&lt;&lt;</span> <span class="string">"Standard normal distribution, mean = "</span><span class="special">&lt;&lt;</span> <span class="identifier">s</span><span class="special">.</span><span class="identifier">mean</span><span class="special">()</span>
+    <span class="special">&lt;&lt;</span> <span class="string">", standard deviation = "</span> <span class="special">&lt;&lt;</span> <span class="identifier">s</span><span class="special">.</span><span class="identifier">standard_deviation</span><span class="special">()</span> <span class="special">&lt;&lt;</span> <span class="identifier">endl</span><span class="special">;</span></pre>
+<p>
+              </p>
+<p>
+              </p>
+<p>
+                First the probability distribution function (pdf).
+              </p>
+<p>
+              </p>
+<p>
+                
+</p>
+<pre class="programlisting"><span class="identifier">cout</span> <span class="special">&lt;&lt;</span> <span class="string">"Probability distribution function values"</span> <span class="special">&lt;&lt;</span> <span class="identifier">endl</span><span class="special">;</span>
+<span class="identifier">cout</span> <span class="special">&lt;&lt;</span> <span class="string">"  z "</span> <span class="string">"      pdf "</span> <span class="special">&lt;&lt;</span> <span class="identifier">endl</span><span class="special">;</span>
+<span class="identifier">cout</span><span class="special">.</span><span class="identifier">precision</span><span class="special">(</span><span class="number">5</span><span class="special">);</span>
+<span class="keyword">for</span> <span class="special">(</span><span class="keyword">double</span> <span class="identifier">z</span> <span class="special">=</span> <span class="special">-</span><span class="identifier">range</span><span class="special">;</span> <span class="identifier">z</span> <span class="special">&lt;</span> <span class="identifier">range</span> <span class="special">+</span> <span class="identifier">step</span><span class="special">;</span> <span class="identifier">z</span> <span class="special">+=</span> <span class="identifier">step</span><span class="special">)</span>
+<span class="special">{</span>
+  <span class="identifier">cout</span> <span class="special">&lt;&lt;</span> <span class="identifier">left</span> <span class="special">&lt;&lt;</span> <span class="identifier">setprecision</span><span class="special">(</span><span class="number">3</span><span class="special">)</span> <span class="special">&lt;&lt;</span> <span class="identifier">setw</span><span class="special">(</span><span class="number">6</span><span class="special">)</span> <span class="special">&lt;&lt;</span> <span class="identifier">z</span> <span class="special">&lt;&lt;</span> <span class="string">" "</span> 
+    <span class="special">&lt;&lt;</span> <span class="identifier">setprecision</span><span class="special">(</span><span class="identifier">precision</span><span class="special">)</span> <span class="special">&lt;&lt;</span> <span class="identifier">setw</span><span class="special">(</span><span class="number">12</span><span class="special">)</span> <span class="special">&lt;&lt;</span> <span class="identifier">pdf</span><span class="special">(</span><span class="identifier">s</span><span class="special">,</span> <span class="identifier">z</span><span class="special">)</span> <span class="special">&lt;&lt;</span> <span class="identifier">endl</span><span class="special">;</span>
+<span class="special">}</span>
+<span class="identifier">cout</span><span class="special">.</span><span class="identifier">precision</span><span class="special">(</span><span class="number">6</span><span class="special">);</span> <span class="comment">// default</span></pre>
+<p>
+              </p>
+<p>
+              </p>
+<p>
+                And the area under the normal curve from -&#8734; up to z, the cumulative
+                distribution function (cdf).
+              </p>
+<p>
+              </p>
+<p>
+                
+</p>
+<pre class="programlisting"><span class="comment">// For a standard normal distribution 
+</span><span class="identifier">cout</span> <span class="special">&lt;&lt;</span> <span class="string">"Standard normal mean = "</span><span class="special">&lt;&lt;</span> <span class="identifier">s</span><span class="special">.</span><span class="identifier">mean</span><span class="special">()</span>
+  <span class="special">&lt;&lt;</span> <span class="string">", standard deviation = "</span> <span class="special">&lt;&lt;</span> <span class="identifier">s</span><span class="special">.</span><span class="identifier">standard_deviation</span><span class="special">()</span> <span class="special">&lt;&lt;</span> <span class="identifier">endl</span><span class="special">;</span>
+<span class="identifier">cout</span> <span class="special">&lt;&lt;</span> <span class="string">"Integral (area under the curve) from - infinity up to z "</span> <span class="special">&lt;&lt;</span> <span class="identifier">endl</span><span class="special">;</span>
+<span class="identifier">cout</span> <span class="special">&lt;&lt;</span> <span class="string">"  z "</span> <span class="string">"      cdf "</span> <span class="special">&lt;&lt;</span> <span class="identifier">endl</span><span class="special">;</span>
+<span class="keyword">for</span> <span class="special">(</span><span class="keyword">double</span> <span class="identifier">z</span> <span class="special">=</span> <span class="special">-</span><span class="identifier">range</span><span class="special">;</span> <span class="identifier">z</span> <span class="special">&lt;</span> <span class="identifier">range</span> <span class="special">+</span> <span class="identifier">step</span><span class="special">;</span> <span class="identifier">z</span> <span class="special">+=</span> <span class="identifier">step</span><span class="special">)</span>
+<span class="special">{</span>
+  <span class="identifier">cout</span> <span class="special">&lt;&lt;</span> <span class="identifier">left</span> <span class="special">&lt;&lt;</span> <span class="identifier">setprecision</span><span class="special">(</span><span class="number">3</span><span class="special">)</span> <span class="special">&lt;&lt;</span> <span class="identifier">setw</span><span class="special">(</span><span class="number">6</span><span class="special">)</span> <span class="special">&lt;&lt;</span> <span class="identifier">z</span> <span class="special">&lt;&lt;</span> <span class="string">" "</span> 
+    <span class="special">&lt;&lt;</span> <span class="identifier">setprecision</span><span class="special">(</span><span class="identifier">precision</span><span class="special">)</span> <span class="special">&lt;&lt;</span> <span class="identifier">setw</span><span class="special">(</span><span class="number">12</span><span class="special">)</span> <span class="special">&lt;&lt;</span> <span class="identifier">cdf</span><span class="special">(</span><span class="identifier">s</span><span class="special">,</span> <span class="identifier">z</span><span class="special">)</span> <span class="special">&lt;&lt;</span> <span class="identifier">endl</span><span class="special">;</span>
+<span class="special">}</span>
+<span class="identifier">cout</span><span class="special">.</span><span class="identifier">precision</span><span class="special">(</span><span class="number">6</span><span class="special">);</span> <span class="comment">// default</span></pre>
+<p>
+              </p>
+<p>
+              </p>
+<p>
+                And all this you can do with a nanoscopic amount of work compared
+                to the team of <span class="bold"><strong>human computers</strong></span> toiling
+                with Milton Abramovitz and Irene Stegen at the US National Bureau
+                of Standards (now NIST).
+                Starting in 1938, their "Handbook of Mathematical Functions
+                with Formulas, Graphs and Mathematical Tables", was eventually
+                published in 1964, and has been reprinted numerous times since. (A
+                major replacement is planned at <a href="http://dlmf.nist.gov" target="_top">Digital
+                Library of Mathematical Functions</a>).
+              </p>
+<p>
+              </p>
+<p>
+                Pretty-printing a traditional 2-dimensional table is left as an exercise
+                for the student, but why bother now that the Math Toolkit lets you
+                write
+              </p>
+<p>
+              </p>
+<p>
+                
+</p>
+<pre class="programlisting"><span class="keyword">double</span> <span class="identifier">z</span> <span class="special">=</span> <span class="number">2.</span><span class="special">;</span> 
+<span class="identifier">cout</span> <span class="special">&lt;&lt;</span> <span class="string">"Area for z = "</span> <span class="special">&lt;&lt;</span> <span class="identifier">z</span> <span class="special">&lt;&lt;</span> <span class="string">" is "</span> <span class="special">&lt;&lt;</span> <span class="identifier">cdf</span><span class="special">(</span><span class="identifier">s</span><span class="special">,</span> <span class="identifier">z</span><span class="special">)</span> <span class="special">&lt;&lt;</span> <span class="identifier">endl</span><span class="special">;</span> <span class="comment">// to get the area for z.</span></pre>
+<p>
+              </p>
+<p>
+              </p>
+<p>
+                Correspondingly, we can obtain the traditional 'critical' values
+                for significance levels. For the 95% confidence level, the significance
+                level usually called alpha, is 0.05 = 1 - 0.95 (for a one-sided test),
+                so we can write
+              </p>
+<p>
+              </p>
+<p>
+                
+</p>
+<pre class="programlisting">  <span class="identifier">cout</span> <span class="special">&lt;&lt;</span> <span class="string">"95% of area has a z below "</span> <span class="special">&lt;&lt;</span> <span class="identifier">quantile</span><span class="special">(</span><span class="identifier">s</span><span class="special">,</span> <span class="number">0.95</span><span class="special">)</span> <span class="special">&lt;&lt;</span> <span class="identifier">endl</span><span class="special">;</span>
+<span class="comment">// 95% of area has a z below 1.64485</span></pre>
+<p>
+              </p>
+<p>
+              </p>
+<p>
+                and a two-sided test (a comparison between two levels, rather than
+                a one-sided test)
+              </p>
+<p>
+              </p>
+<p>
+                
+</p>
+<pre class="programlisting">  <span class="identifier">cout</span> <span class="special">&lt;&lt;</span> <span class="string">"95% of area has a z between "</span> <span class="special">&lt;&lt;</span> <span class="identifier">quantile</span><span class="special">(</span><span class="identifier">s</span><span class="special">,</span> <span class="number">0.975</span><span class="special">)</span>
+    <span class="special">&lt;&lt;</span> <span class="string">" and "</span> <span class="special">&lt;&lt;</span> <span class="special">-</span><span class="identifier">quantile</span><span class="special">(</span><span class="identifier">s</span><span class="special">,</span> <span class="number">0.975</span><span class="special">)</span> <span class="special">&lt;&lt;</span> <span class="identifier">endl</span><span class="special">;</span>
+<span class="comment">// 95% of area has a z between 1.95996 and -1.95996</span></pre>
+<p>
+              </p>
+<p>
+              </p>
+<p>
+                First, define a table of significance levels: these are the probabilities
+                that the true occurrence frequency lies outside the calculated interval.
+              </p>
+<p>
+              </p>
+<p>
+                It is convenient to have an alpha level for the probability that
+                z lies outside just one standard deviation. This will not be some
+                nice neat number like 0.05, but we can easily calculate it,
+              </p>
+<p>
+              </p>
+<p>
+                
+</p>
+<pre class="programlisting"><span class="keyword">double</span> <span class="identifier">alpha1</span> <span class="special">=</span> <span class="identifier">cdf</span><span class="special">(</span><span class="identifier">s</span><span class="special">,</span> <span class="special">-</span><span class="number">1</span><span class="special">)</span> <span class="special">*</span> <span class="number">2</span><span class="special">;</span> <span class="comment">// 0.3173105078629142
+</span><span class="identifier">cout</span> <span class="special">&lt;&lt;</span> <span class="identifier">setprecision</span><span class="special">(</span><span class="number">17</span><span class="special">)</span> <span class="special">&lt;&lt;</span> <span class="string">"Significance level for z == 1 is "</span> <span class="special">&lt;&lt;</span> <span class="identifier">alpha1</span> <span class="special">&lt;&lt;</span> <span class="identifier">endl</span><span class="special">;</span></pre>
+<p>
+              </p>
+<p>
+              </p>
+<p>
+                and place in our array of favorite alpha values.
+              </p>
+<p>
+              </p>
+<p>
+                
+</p>
+<pre class="programlisting"><span class="keyword">double</span> <span class="identifier">alpha</span><span class="special">[]</span> <span class="special">=</span> <span class="special">{</span><span class="number">0.3173105078629142</span><span class="special">,</span> <span class="comment">// z for 1 standard deviation.
+</span>  <span class="number">0.20</span><span class="special">,</span> <span class="number">0.1</span><span class="special">,</span> <span class="number">0.05</span><span class="special">,</span> <span class="number">0.01</span><span class="special">,</span> <span class="number">0.001</span><span class="special">,</span> <span class="number">0.0001</span><span class="special">,</span> <span class="number">0.00001</span> <span class="special">};</span></pre>
+<p>
+              </p>
+<p>
+              </p>
+<p>
+                Confidence value as % is (1 - alpha) * 100 (so alpha 0.05 == 95%
+                confidence) that the true occurrence frequency lies <span class="bold"><strong>inside</strong></span>
+                the calculated interval.
+              </p>
+<p>
+              </p>
+<p>
+                
+</p>
+<pre class="programlisting"><span class="identifier">cout</span> <span class="special">&lt;&lt;</span> <span class="string">"level of significance (alpha)"</span> <span class="special">&lt;&lt;</span> <span class="identifier">setprecision</span><span class="special">(</span><span class="number">4</span><span class="special">)</span> <span class="special">&lt;&lt;</span> <span class="identifier">endl</span><span class="special">;</span>
+<span class="identifier">cout</span> <span class="special">&lt;&lt;</span> <span class="string">"2-sided       1 -sided          z(alpha) "</span> <span class="special">&lt;&lt;</span> <span class="identifier">endl</span><span class="special">;</span>
+<span class="keyword">for</span> <span class="special">(</span><span class="keyword">int</span> <span class="identifier">i</span> <span class="special">=</span> <span class="number">0</span><span class="special">;</span> <span class="identifier">i</span> <span class="special">&lt;</span> <span class="keyword">sizeof</span><span class="special">(</span><span class="identifier">alpha</span><span class="special">)/</span><span class="keyword">sizeof</span><span class="special">(</span><span class="identifier">alpha</span><span class="special">[</span><span class="number">0</span><span class="special">]);</span> <span class="special">++</span><span class="identifier">i</span><span class="special">)</span>
+<span class="special">{</span>
+  <span class="identifier">cout</span> <span class="special">&lt;&lt;</span> <span class="identifier">setw</span><span class="special">(</span><span class="number">15</span><span class="special">)</span> <span class="special">&lt;&lt;</span> <span class="identifier">alpha</span><span class="special">[</span><span class="identifier">i</span><span class="special">]</span> <span class="special">&lt;&lt;</span> <span class="identifier">setw</span><span class="special">(</span><span class="number">15</span><span class="special">)</span> <span class="special">&lt;&lt;</span> <span class="identifier">alpha</span><span class="special">[</span><span class="identifier">i</span><span class="special">]</span> <span class="special">/</span><span class="number">2</span> <span class="special">&lt;&lt;</span> <span class="identifier">setw</span><span class="special">(</span><span class="number">10</span><span class="special">)</span> <span class="special">&lt;&lt;</span> <span class="identifier">quantile</span><span class=
"special">(</span><span class="identifier">complement</span><span class="special">(</span><span class="identifier">s</span><span class="special">,</span>  <span class="identifier">alpha</span><span class="special">[</span><span class="identifier">i</span><span class="special">]/</span><span class="number">2</span><span class="special">))</span> <span class="special">&lt;&lt;</span> <span class="identifier">endl</span><span class="special">;</span>
+  <span class="comment">// Use quantile(complement(s, alpha[i]/2)) to avoid potential loss of accuracy from quantile(s,  1 - alpha[i]/2) 
+</span><span class="special">}</span>
+<span class="identifier">cout</span> <span class="special">&lt;&lt;</span> <span class="identifier">endl</span><span class="special">;</span></pre>
+<p>
+              </p>
+<p>
+              </p>
+<p>
+                Notice the distinction between one-sided (also called one-tailed)
+                where we are using a &gt; <span class="bold"><strong>or</strong></span> &lt;
+                test (and not both) and considering the area of the tail (integral)
+                from z up to +&#8734;, and a two-sided test where we are using two &gt;
+                <span class="bold"><strong>and</strong></span> &lt; tests, and thus considering
+                two tails, from -&#8734; up to z low and z high up to +&#8734;.
+              </p>
+<p>
+              </p>
+<p>
+                So the 2-sided values alpha[i] are calculated using alpha[i]/2.
+              </p>
+<p>
+              </p>
+<p>
+                If we consider a simple example of alpha = 0.05, then for a two-sided
+                test, the lower tail area from -&#8734; up to -1.96 is 0.025 (alpha/2) and
+                the upper tail area from +z up to +1.96 is also 0.025 (alpha/2),
+                and the area between -1.96 up to 12.96 is alpha = 0.95. and the sum
+                of the two tails is 0.025 + 0.025 = 0.05,
+              </p>
+<p>
+            </p>
+<a name="math_toolkit.dist.stat_tut.weg.normal_example.normal_misc.standard_deviations_either_side_of_the_mean"></a><h5>
+<a name="id614708"></a>
+              <a class="link" href="normal_misc.html#math_toolkit.dist.stat_tut.weg.normal_example.normal_misc.standard_deviations_either_side_of_the_mean">Standard
+              deviations either side of the Mean</a>
+            </h5>
+<p>
+              </p>
+<p>
+                Armed with the cumulative distribution function, we can easily calculate
+                the easy to remember proportion of values that lie within 1, 2 and
+                3 standard deviations from the mean.
+              </p>
+<p>
+              </p>
+<p>
+                
+</p>
+<pre class="programlisting"><span class="identifier">cout</span><span class="special">.</span><span class="identifier">precision</span><span class="special">(</span><span class="number">3</span><span class="special">);</span>
+<span class="identifier">cout</span> <span class="special">&lt;&lt;</span> <span class="identifier">showpoint</span> <span class="special">&lt;&lt;</span> <span class="string">"cdf(s, s.standard_deviation()) = "</span>
+  <span class="special">&lt;&lt;</span> <span class="identifier">cdf</span><span class="special">(</span><span class="identifier">s</span><span class="special">,</span> <span class="identifier">s</span><span class="special">.</span><span class="identifier">standard_deviation</span><span class="special">())</span> <span class="special">&lt;&lt;</span> <span class="identifier">endl</span><span class="special">;</span>  <span class="comment">// from -infinity to 1 sd
+</span><span class="identifier">cout</span> <span class="special">&lt;&lt;</span> <span class="string">"cdf(complement(s, s.standard_deviation())) = "</span>
+  <span class="special">&lt;&lt;</span> <span class="identifier">cdf</span><span class="special">(</span><span class="identifier">complement</span><span class="special">(</span><span class="identifier">s</span><span class="special">,</span> <span class="identifier">s</span><span class="special">.</span><span class="identifier">standard_deviation</span><span class="special">()))</span> <span class="special">&lt;&lt;</span> <span class="identifier">endl</span><span class="special">;</span>
+<span class="identifier">cout</span> <span class="special">&lt;&lt;</span> <span class="string">"Fraction 1 standard deviation within either side of mean is "</span>
+  <span class="special">&lt;&lt;</span> <span class="number">1</span> <span class="special">-</span>  <span class="identifier">cdf</span><span class="special">(</span><span class="identifier">complement</span><span class="special">(</span><span class="identifier">s</span><span class="special">,</span> <span class="identifier">s</span><span class="special">.</span><span class="identifier">standard_deviation</span><span class="special">()))</span> <span class="special">*</span> <span class="number">2</span> <span class="special">&lt;&lt;</span> <span class="identifier">endl</span><span class="special">;</span>
+<span class="identifier">cout</span> <span class="special">&lt;&lt;</span> <span class="string">"Fraction 2 standard deviations within either side of mean is "</span>
+  <span class="special">&lt;&lt;</span> <span class="number">1</span> <span class="special">-</span>  <span class="identifier">cdf</span><span class="special">(</span><span class="identifier">complement</span><span class="special">(</span><span class="identifier">s</span><span class="special">,</span> <span class="number">2</span> <span class="special">*</span> <span class="identifier">s</span><span class="special">.</span><span class="identifier">standard_deviation</span><span class="special">()))</span> <span class="special">*</span> <span class="number">2</span> <span class="special">&lt;&lt;</span> <span class="identifier">endl</span><span class="special">;</span>
+<span class="identifier">cout</span> <span class="special">&lt;&lt;</span> <span class="string">"Fraction 3 standard deviations within either side of mean is "</span>
+  <span class="special">&lt;&lt;</span> <span class="number">1</span> <span class="special">-</span>  <span class="identifier">cdf</span><span class="special">(</span><span class="identifier">complement</span><span class="special">(</span><span class="identifier">s</span><span class="special">,</span> <span class="number">3</span> <span class="special">*</span> <span class="identifier">s</span><span class="special">.</span><span class="identifier">standard_deviation</span><span class="special">()))</span> <span class="special">*</span> <span class="number">2</span> <span class="special">&lt;&lt;</span> <span class="identifier">endl</span><span class="special">;</span></pre>
+<p>
+              </p>
+<p>
+              </p>
+<p>
+                To a useful precision, the 1, 2 &amp; 3 percentages are 68, 95 and
+                99.7, and these are worth memorising as useful 'rules of thumb',
+                as, for example, in <a href="http://en.wikipedia.org/wiki/Standard_deviation" target="_top">standard
+                deviation</a>:
+              </p>
+<p>
+              
+</p>
+<pre class="programlisting">Fraction 1 standard deviation within either side of mean is 0.683
+Fraction 2 standard deviations within either side of mean is 0.954
+Fraction 3 standard deviations within either side of mean is 0.997
+</pre>
+<p>
+              </p>
+<p>
+                We could of course get some really accurate values for these <a href="http://en.wikipedia.org/wiki/Confidence_interval" target="_top">confidence
+                intervals</a> by using cout.precision(15);
+              </p>
+<p>
+              
+</p>
+<pre class="programlisting">Fraction 1 standard deviation within either side of mean is 0.682689492137086
+Fraction 2 standard deviations within either side of mean is 0.954499736103642
+Fraction 3 standard deviations within either side of mean is 0.997300203936740
+</pre>
+<p>
+              </p>
+<p>
+                But before you get too excited about this impressive precision, don't
+                forget that the <span class="bold"><strong>confidence intervals of the
+                standard deviation</strong></span> are surprisingly wide, especially if
+                you have estimated the standard deviation from only a few measurements.
+              </p>
+<p>
+            </p>
+<a name="math_toolkit.dist.stat_tut.weg.normal_example.normal_misc.some_simple_examples"></a><h5>
+<a name="id615454"></a>
+              <a class="link" href="normal_misc.html#math_toolkit.dist.stat_tut.weg.normal_example.normal_misc.some_simple_examples">Some
+              simple examples</a>
+            </h5>
+<a name="math_toolkit.dist.stat_tut.weg.normal_example.normal_misc.life_of_light_bulbs"></a><h5>
+<a name="id615481"></a>
+              <a class="link" href="normal_misc.html#math_toolkit.dist.stat_tut.weg.normal_example.normal_misc.life_of_light_bulbs">Life
+              of light bulbs</a>
+            </h5>
+<p>
+              </p>
+<p>
+                Examples from K. Krishnamoorthy, Handbook of Statistical Distributions
+                with Applications, ISBN 1 58488 635 8, page 125... implemented using
+                the Math Toolkit library.
+              </p>
+<p>
+              </p>
+<p>
+                A few very simple examples are shown here:
+              </p>
+<p>
+              </p>
+<p>
+                
+</p>
+<pre class="programlisting"><span class="comment">// K. Krishnamoorthy, Handbook of Statistical Distributions with Applications,
+</span> <span class="comment">// ISBN 1 58488 635 8, page 125, example 10.3.5</span></pre>
+<p>
+              </p>
+<p>
+              </p>
+<p>
+                Mean lifespan of 100 W bulbs is 1100 h with standard deviation of
+                100 h. Assuming, perhaps with little evidence and much faith, that
+                the distribution is normal, we construct a normal distribution called
+                <span class="emphasis"><em>bulbs</em></span> with these values:
+              </p>
+<p>
+              </p>
+<p>
+                
+</p>
+<pre class="programlisting"><span class="keyword">double</span> <span class="identifier">mean_life</span> <span class="special">=</span> <span class="number">1100.</span><span class="special">;</span>
+<span class="keyword">double</span> <span class="identifier">life_standard_deviation</span> <span class="special">=</span> <span class="number">100.</span><span class="special">;</span>
+<span class="identifier">normal</span> <span class="identifier">bulbs</span><span class="special">(</span><span class="identifier">mean_life</span><span class="special">,</span> <span class="identifier">life_standard_deviation</span><span class="special">);</span> 
+<span class="keyword">double</span> <span class="identifier">expected_life</span> <span class="special">=</span> <span class="number">1000.</span><span class="special">;</span></pre>
+<p>
+              </p>
+<p>
+              </p>
+<p>
+                The we can use the Cumulative distribution function to predict fractions
+                (or percentages, if * 100) that will last various lifetimes.
+              </p>
+<p>
+              </p>
+<p>
+                
+</p>
+<pre class="programlisting"><span class="identifier">cout</span> <span class="special">&lt;&lt;</span> <span class="string">"Fraction of bulbs that will last at best (&lt;=) "</span> <span class="comment">// P(X &lt;= 1000)
+</span>  <span class="special">&lt;&lt;</span> <span class="identifier">expected_life</span> <span class="special">&lt;&lt;</span> <span class="string">" is "</span><span class="special">&lt;&lt;</span> <span class="identifier">cdf</span><span class="special">(</span><span class="identifier">bulbs</span><span class="special">,</span> <span class="identifier">expected_life</span><span class="special">)</span> <span class="special">&lt;&lt;</span> <span class="identifier">endl</span><span class="special">;</span>
+<span class="identifier">cout</span> <span class="special">&lt;&lt;</span> <span class="string">"Fraction of bulbs that will last at least (&gt;) "</span> <span class="comment">// P(X &gt; 1000)
+</span>  <span class="special">&lt;&lt;</span> <span class="identifier">expected_life</span> <span class="special">&lt;&lt;</span> <span class="string">" is "</span><span class="special">&lt;&lt;</span> <span class="identifier">cdf</span><span class="special">(</span><span class="identifier">complement</span><span class="special">(</span><span class="identifier">bulbs</span><span class="special">,</span> <span class="identifier">expected_life</span><span class="special">))</span> <span class="special">&lt;&lt;</span> <span class="identifier">endl</span><span class="special">;</span>
+<span class="keyword">double</span> <span class="identifier">min_life</span> <span class="special">=</span> <span class="number">900</span><span class="special">;</span>
+<span class="keyword">double</span> <span class="identifier">max_life</span> <span class="special">=</span> <span class="number">1200</span><span class="special">;</span>
+<span class="identifier">cout</span> <span class="special">&lt;&lt;</span> <span class="string">"Fraction of bulbs that will last between "</span>
+  <span class="special">&lt;&lt;</span> <span class="identifier">min_life</span> <span class="special">&lt;&lt;</span> <span class="string">" and "</span> <span class="special">&lt;&lt;</span> <span class="identifier">max_life</span> <span class="special">&lt;&lt;</span> <span class="string">" is "</span>
+  <span class="special">&lt;&lt;</span> <span class="identifier">cdf</span><span class="special">(</span><span class="identifier">bulbs</span><span class="special">,</span> <span class="identifier">max_life</span><span class="special">)</span>  <span class="comment">// P(X &lt;= 1200)
+</span>   <span class="special">-</span> <span class="identifier">cdf</span><span class="special">(</span><span class="identifier">bulbs</span><span class="special">,</span> <span class="identifier">min_life</span><span class="special">)</span> <span class="special">&lt;&lt;</span> <span class="identifier">endl</span><span class="special">;</span> <span class="comment">// P(X &lt;= 900)</span></pre>
+<p>
+              </p>
+<p>
+              </p>
+<div class="note"><table border="0" summary="Note">
+<tr>
+<td rowspan="2" align="center" valign="top" width="25"><img alt="[Note]" src="../../../../../../../doc/html/images/note.png"></td>
+<th align="left">Note</th>
+</tr>
+<tr><td align="left" valign="top"><p>
+                  Real-life failures are often very ab-normal, with a significant
+                  number that 'dead-on-arrival' or suffer failure very early in their
+                  life: the lifetime of the survivors of 'early mortality' may be
+                  well described by the normal distribution.
+                </p></td></tr>
+</table></div>
+<p>
+            </p>
+<a name="math_toolkit.dist.stat_tut.weg.normal_example.normal_misc.how_many_onions_"></a><h5>
+<a name="id616199"></a>
+              <a class="link" href="normal_misc.html#math_toolkit.dist.stat_tut.weg.normal_example.normal_misc.how_many_onions_">How
+              many onions?</a>
+            </h5>
+<p>
+              </p>
+<p>
+                Weekly demand for 5 lb sacks of onions at a store is normally distributed
+                with mean 140 sacks and standard deviation 10.
+              </p>
+<p>
+              </p>
+<p>
+                
+</p>
+<pre class="programlisting"><span class="keyword">double</span> <span class="identifier">mean</span> <span class="special">=</span> <span class="number">140.</span><span class="special">;</span> <span class="comment">// sacks per week.
+</span><span class="keyword">double</span> <span class="identifier">standard_deviation</span> <span class="special">=</span> <span class="number">10</span><span class="special">;</span> 
+<span class="identifier">normal</span> <span class="identifier">sacks</span><span class="special">(</span><span class="identifier">mean</span><span class="special">,</span> <span class="identifier">standard_deviation</span><span class="special">);</span>
+
+<span class="keyword">double</span> <span class="identifier">stock</span> <span class="special">=</span> <span class="number">160.</span><span class="special">;</span> <span class="comment">// per week.
+</span><span class="identifier">cout</span> <span class="special">&lt;&lt;</span> <span class="string">"Percentage of weeks overstocked "</span>
+  <span class="special">&lt;&lt;</span> <span class="identifier">cdf</span><span class="special">(</span><span class="identifier">sacks</span><span class="special">,</span> <span class="identifier">stock</span><span class="special">)</span> <span class="special">*</span> <span class="number">100.</span> <span class="special">&lt;&lt;</span> <span class="identifier">endl</span><span class="special">;</span> <span class="comment">// P(X &lt;=160)
+</span><span class="comment">// Percentage of weeks overstocked 97.7</span></pre>
+<p>
+              </p>
+<p>
+              </p>
+<p>
+                So there will be lots of mouldy onions! So we should be able to say
+                what stock level will meet demand 95% of the weeks.
+              </p>
+<p>
+              </p>
+<p>
+                
+</p>
+<pre class="programlisting"><span class="keyword">double</span> <span class="identifier">stock_95</span> <span class="special">=</span> <span class="identifier">quantile</span><span class="special">(</span><span class="identifier">sacks</span><span class="special">,</span> <span class="number">0.95</span><span class="special">);</span>
+<span class="identifier">cout</span> <span class="special">&lt;&lt;</span> <span class="string">"Store should stock "</span> <span class="special">&lt;&lt;</span> <span class="keyword">int</span><span class="special">(</span><span class="identifier">stock_95</span><span class="special">)</span> <span class="special">&lt;&lt;</span> <span class="string">" sacks to meet 95% of demands."</span> <span class="special">&lt;&lt;</span> <span class="identifier">endl</span><span class="special">;</span></pre>
+<p>
+              </p>
+<p>
+              </p>
+<p>
+                And it is easy to estimate how to meet 80% of demand, and waste even
+                less.
+              </p>
+<p>
+              </p>
+<p>
+                
+</p>
+<pre class="programlisting"><span class="keyword">double</span> <span class="identifier">stock_80</span> <span class="special">=</span> <span class="identifier">quantile</span><span class="special">(</span><span class="identifier">sacks</span><span class="special">,</span> <span class="number">0.80</span><span class="special">);</span>
+<span class="identifier">cout</span> <span class="special">&lt;&lt;</span> <span class="string">"Store should stock "</span> <span class="special">&lt;&lt;</span> <span class="keyword">int</span><span class="special">(</span><span class="identifier">stock_80</span><span class="special">)</span> <span class="special">&lt;&lt;</span> <span class="string">" sacks to meet 8 out of 10 demands."</span> <span class="special">&lt;&lt;</span> <span class="identifier">endl</span><span class="special">;</span>
+</pre>
+<p>
+              </p>
+<p>
+            </p>
+<a name="math_toolkit.dist.stat_tut.weg.normal_example.normal_misc.packing_beef"></a><h5>
+<a name="id616780"></a>
+              <a class="link" href="normal_misc.html#math_toolkit.dist.stat_tut.weg.normal_example.normal_misc.packing_beef">Packing
+              beef</a>
+            </h5>
+<p>
+              </p>
+<p>
+                A machine is set to pack 3 kg of ground beef per pack. Over a long
+                period of time it is found that the average packed was 3 kg with
+                a standard deviation of 0.1 kg. Assuming the packing is normally
+                distributed, we can find the fraction (or %) of packages that weigh
+                more than 3.1 kg.
+              </p>
+<p>
+              </p>
+<p>
+                
+</p>
+<pre class="programlisting"><span class="keyword">double</span> <span class="identifier">mean</span> <span class="special">=</span> <span class="number">3.</span><span class="special">;</span> <span class="comment">// kg
+</span><span class="keyword">double</span> <span class="identifier">standard_deviation</span> <span class="special">=</span> <span class="number">0.1</span><span class="special">;</span> <span class="comment">// kg
+</span><span class="identifier">normal</span> <span class="identifier">packs</span><span class="special">(</span><span class="identifier">mean</span><span class="special">,</span> <span class="identifier">standard_deviation</span><span class="special">);</span>
+
+<span class="keyword">double</span> <span class="identifier">max_weight</span> <span class="special">=</span> <span class="number">3.1</span><span class="special">;</span> <span class="comment">// kg
+</span><span class="identifier">cout</span> <span class="special">&lt;&lt;</span> <span class="string">"Percentage of packs &gt; "</span> <span class="special">&lt;&lt;</span> <span class="identifier">max_weight</span> <span class="special">&lt;&lt;</span> <span class="string">" is "</span>
+<span class="special">&lt;&lt;</span> <span class="identifier">cdf</span><span class="special">(</span><span class="identifier">complement</span><span class="special">(</span><span class="identifier">packs</span><span class="special">,</span> <span class="identifier">max_weight</span><span class="special">))</span> <span class="special">&lt;&lt;</span> <span class="identifier">endl</span><span class="special">;</span> <span class="comment">// P(X &gt; 3.1)
+</span>
+<span class="keyword">double</span> <span class="identifier">under_weight</span> <span class="special">=</span> <span class="number">2.9</span><span class="special">;</span>
+<span class="identifier">cout</span> <span class="special">&lt;&lt;</span><span class="string">"fraction of packs &lt;= "</span> <span class="special">&lt;&lt;</span> <span class="identifier">under_weight</span> <span class="special">&lt;&lt;</span> <span class="string">" with a mean of "</span> <span class="special">&lt;&lt;</span> <span class="identifier">mean</span> 
+  <span class="special">&lt;&lt;</span> <span class="string">" is "</span> <span class="special">&lt;&lt;</span> <span class="identifier">cdf</span><span class="special">(</span><span class="identifier">complement</span><span class="special">(</span><span class="identifier">packs</span><span class="special">,</span> <span class="identifier">under_weight</span><span class="special">))</span> <span class="special">&lt;&lt;</span> <span class="identifier">endl</span><span class="special">;</span>
+<span class="comment">// fraction of packs &lt;= 2.9 with a mean of 3 is 0.841345
+</span><span class="comment">// This is 0.84 - more than the target 0.95
+</span><span class="comment">// Want 95% to be over this weight, so what should we set the mean weight to be?
+</span><span class="comment">// KK StatCalc says:
+</span><span class="keyword">double</span> <span class="identifier">over_mean</span> <span class="special">=</span> <span class="number">3.0664</span><span class="special">;</span>
+<span class="identifier">normal</span> <span class="identifier">xpacks</span><span class="special">(</span><span class="identifier">over_mean</span><span class="special">,</span> <span class="identifier">standard_deviation</span><span class="special">);</span>
+<span class="identifier">cout</span> <span class="special">&lt;&lt;</span> <span class="string">"fraction of packs &gt;= "</span> <span class="special">&lt;&lt;</span> <span class="identifier">under_weight</span>
+<span class="special">&lt;&lt;</span> <span class="string">" with a mean of "</span> <span class="special">&lt;&lt;</span> <span class="identifier">xpacks</span><span class="special">.</span><span class="identifier">mean</span><span class="special">()</span> 
+  <span class="special">&lt;&lt;</span> <span class="string">" is "</span> <span class="special">&lt;&lt;</span> <span class="identifier">cdf</span><span class="special">(</span><span class="identifier">complement</span><span class="special">(</span><span class="identifier">xpacks</span><span class="special">,</span> <span class="identifier">under_weight</span><span class="special">))</span> <span class="special">&lt;&lt;</span> <span class="identifier">endl</span><span class="special">;</span>
+<span class="comment">// fraction of packs &gt;= 2.9 with a mean of 3.06449 is 0.950005
+</span><span class="keyword">double</span> <span class="identifier">under_fraction</span> <span class="special">=</span> <span class="number">0.05</span><span class="special">;</span>  <span class="comment">// so 95% are above the minimum weight mean - sd = 2.9
+</span><span class="keyword">double</span> <span class="identifier">low_limit</span> <span class="special">=</span> <span class="identifier">standard_deviation</span><span class="special">;</span>
+<span class="keyword">double</span> <span class="identifier">offset</span> <span class="special">=</span> <span class="identifier">mean</span> <span class="special">-</span> <span class="identifier">low_limit</span> <span class="special">-</span> <span class="identifier">quantile</span><span class="special">(</span><span class="identifier">packs</span><span class="special">,</span> <span class="identifier">under_fraction</span><span class="special">);</span>
+<span class="keyword">double</span> <span class="identifier">nominal_mean</span> <span class="special">=</span> <span class="identifier">mean</span> <span class="special">+</span> <span class="identifier">offset</span><span class="special">;</span>
+
+<span class="identifier">normal</span> <span class="identifier">nominal_packs</span><span class="special">(</span><span class="identifier">nominal_mean</span><span class="special">,</span> <span class="identifier">standard_deviation</span><span class="special">);</span>
+<span class="identifier">cout</span> <span class="special">&lt;&lt;</span> <span class="string">"Setting the packer to "</span> <span class="special">&lt;&lt;</span> <span class="identifier">nominal_mean</span> <span class="special">&lt;&lt;</span> <span class="string">" will mean that "</span>
+  <span class="special">&lt;&lt;</span> <span class="string">"fraction of packs &gt;= "</span> <span class="special">&lt;&lt;</span> <span class="identifier">under_weight</span> 
+  <span class="special">&lt;&lt;</span> <span class="string">" is "</span> <span class="special">&lt;&lt;</span> <span class="identifier">cdf</span><span class="special">(</span><span class="identifier">complement</span><span class="special">(</span><span class="identifier">nominal_packs</span><span class="special">,</span> <span class="identifier">under_weight</span><span class="special">))</span> <span class="special">&lt;&lt;</span> <span class="identifier">endl</span><span class="special">;</span></pre>
+<p>
+              </p>
+<p>
+              </p>
+<p>
+                Setting the packer to 3.06449 will mean that fraction of packs &gt;=
+                2.9 is 0.95.
+              </p>
+<p>
+              </p>
+<p>
+                Setting the packer to 3.13263 will mean that fraction of packs &gt;=
+                2.9 is 0.99, but will more than double the mean loss from 0.0644
+                to 0.133.
+              </p>
+<p>
+              </p>
+<p>
+                Alternatively, we could invest in a better (more precise) packer
+                with a lower standard deviation.
+              </p>
+<p>
+              </p>
+<p>
+                To estimate how much better (how much smaller standard deviation)
+                it would have to be, we need to get the 5% quantile to be located
+                at the under_weight limit, 2.9
+              </p>
+<p>
+              </p>
+<p>
+                
+</p>
+<pre class="programlisting"><span class="keyword">double</span> <span class="identifier">p</span> <span class="special">=</span> <span class="number">0.05</span><span class="special">;</span> <span class="comment">// wanted p th quantile.
+</span><span class="identifier">cout</span> <span class="special">&lt;&lt;</span> <span class="string">"Quantile of "</span> <span class="special">&lt;&lt;</span> <span class="identifier">p</span> <span class="special">&lt;&lt;</span> <span class="string">" = "</span> <span class="special">&lt;&lt;</span> <span class="identifier">quantile</span><span class="special">(</span><span class="identifier">packs</span><span class="special">,</span> <span class="identifier">p</span><span class="special">)</span>
+  <span class="special">&lt;&lt;</span> <span class="string">", mean = "</span> <span class="special">&lt;&lt;</span> <span class="identifier">packs</span><span class="special">.</span><span class="identifier">mean</span><span class="special">()</span> <span class="special">&lt;&lt;</span> <span class="string">", sd = "</span> <span class="special">&lt;&lt;</span> <span class="identifier">packs</span><span class="special">.</span><span class="identifier">standard_deviation</span><span class="special">()</span> <span class="special">&lt;&lt;</span> <span class="identifier">endl</span><span class="special">;</span> <span class="comment">//</span></pre>
+<p>
+              </p>
+<p>
+              </p>
+<p>
+                Quantile of 0.05 = 2.83551, mean = 3, sd = 0.1
+              </p>
+<p>
+              </p>
+<p>
+                With the current packer (mean = 3, sd = 0.1), the 5% quantile is
+                at 2.8551 kg, a little below our target of 2.9 kg. So we know that
+                the standard deviation is going to have to be smaller.
+              </p>
+<p>
+              </p>
+<p>
+                Let's start by guessing that it (now 0.1) needs to be halved, to
+                a standard deviation of 0.05
+              </p>
+<p>
+              </p>
+<p>
+                
+</p>
+<pre class="programlisting"><span class="identifier">normal</span> <span class="identifier">pack05</span><span class="special">(</span><span class="identifier">mean</span><span class="special">,</span> <span class="number">0.05</span><span class="special">);</span> 
+<span class="identifier">cout</span> <span class="special">&lt;&lt;</span> <span class="string">"Quantile of "</span> <span class="special">&lt;&lt;</span> <span class="identifier">p</span> <span class="special">&lt;&lt;</span> <span class="string">" = "</span> <span class="special">&lt;&lt;</span> <span class="identifier">quantile</span><span class="special">(</span><span class="identifier">pack05</span><span class="special">,</span> <span class="identifier">p</span><span class="special">)</span> 
+  <span class="special">&lt;&lt;</span> <span class="string">", mean = "</span> <span class="special">&lt;&lt;</span> <span class="identifier">pack05</span><span class="special">.</span><span class="identifier">mean</span><span class="special">()</span> <span class="special">&lt;&lt;</span> <span class="string">", sd = "</span> <span class="special">&lt;&lt;</span> <span class="identifier">pack05</span><span class="special">.</span><span class="identifier">standard_deviation</span><span class="special">()</span> <span class="special">&lt;&lt;</span> <span class="identifier">endl</span><span class="special">;</span>
+
+<span class="identifier">cout</span> <span class="special">&lt;&lt;</span><span class="string">"Fraction of packs &gt;= "</span> <span class="special">&lt;&lt;</span> <span class="identifier">under_weight</span> <span class="special">&lt;&lt;</span> <span class="string">" with a mean of "</span> <span class="special">&lt;&lt;</span> <span class="identifier">mean</span> 
+  <span class="special">&lt;&lt;</span> <span class="string">" and standard deviation of "</span> <span class="special">&lt;&lt;</span> <span class="identifier">pack05</span><span class="special">.</span><span class="identifier">standard_deviation</span><span class="special">()</span>
+  <span class="special">&lt;&lt;</span> <span class="string">" is "</span> <span class="special">&lt;&lt;</span> <span class="identifier">cdf</span><span class="special">(</span><span class="identifier">complement</span><span class="special">(</span><span class="identifier">pack05</span><span class="special">,</span> <span class="identifier">under_weight</span><span class="special">))</span> <span class="special">&lt;&lt;</span> <span class="identifier">endl</span><span class="special">;</span>
+<span class="comment">//</span></pre>
+<p>
+              </p>
+<p>
+              </p>
+<p>
+                Fraction of packs &gt;= 2.9 with a mean of 3 and standard deviation
+                of 0.05 is 0.9772
+              </p>
+<p>
+              </p>
+<p>
+                So 0.05 was quite a good guess, but we are a little over the 2.9
+                target, so the standard deviation could be a tiny bit more. So we
+                could do some more guessing to get closer, say by increasing to 0.06
+              </p>
+<p>
+              </p>
+<p>
+                
+</p>
+<pre class="programlisting"><span class="identifier">normal</span> <span class="identifier">pack06</span><span class="special">(</span><span class="identifier">mean</span><span class="special">,</span> <span class="number">0.06</span><span class="special">);</span> 
+<span class="identifier">cout</span> <span class="special">&lt;&lt;</span> <span class="string">"Quantile of "</span> <span class="special">&lt;&lt;</span> <span class="identifier">p</span> <span class="special">&lt;&lt;</span> <span class="string">" = "</span> <span class="special">&lt;&lt;</span> <span class="identifier">quantile</span><span class="special">(</span><span class="identifier">pack06</span><span class="special">,</span> <span class="identifier">p</span><span class="special">)</span> 
+  <span class="special">&lt;&lt;</span> <span class="string">", mean = "</span> <span class="special">&lt;&lt;</span> <span class="identifier">pack06</span><span class="special">.</span><span class="identifier">mean</span><span class="special">()</span> <span class="special">&lt;&lt;</span> <span class="string">", sd = "</span> <span class="special">&lt;&lt;</span> <span class="identifier">pack06</span><span class="special">.</span><span class="identifier">standard_deviation</span><span class="special">()</span> <span class="special">&lt;&lt;</span> <span class="identifier">endl</span><span class="special">;</span>
+
+<span class="identifier">cout</span> <span class="special">&lt;&lt;</span><span class="string">"Fraction of packs &gt;= "</span> <span class="special">&lt;&lt;</span> <span class="identifier">under_weight</span> <span class="special">&lt;&lt;</span> <span class="string">" with a mean of "</span> <span class="special">&lt;&lt;</span> <span class="identifier">mean</span> 
+  <span class="special">&lt;&lt;</span> <span class="string">" and standard deviation of "</span> <span class="special">&lt;&lt;</span> <span class="identifier">pack06</span><span class="special">.</span><span class="identifier">standard_deviation</span><span class="special">()</span>
+  <span class="special">&lt;&lt;</span> <span class="string">" is "</span> <span class="special">&lt;&lt;</span> <span class="identifier">cdf</span><span class="special">(</span><span class="identifier">complement</span><span class="special">(</span><span class="identifier">pack06</span><span class="special">,</span> <span class="identifier">under_weight</span><span class="special">))</span> <span class="special">&lt;&lt;</span> <span class="identifier">endl</span><span class="special">;</span></pre>
+<p>
+              </p>
+<p>
+              </p>
+<p>
+                Fraction of packs &gt;= 2.9 with a mean of 3 and standard deviation
+                of 0.06 is 0.9522
+              </p>
+<p>
+              </p>
+<p>
+                Now we are getting really close, but to do the job properly, we could
+                use root finding method, for example the tools provided, and used
+                elsewhere, in the Math Toolkit, see <a class="link" href="../../../../toolkit/internals1/roots2.html" title="Root Finding Without Derivatives">Root
+                Finding Without Derivatives</a>.
+              </p>
+<p>
+              </p>
+<p>
+                But in this normal distribution case, we could be even smarter and
+                make a direct calculation.
+              </p>
+<p>
+              </p>
+<p>
+                
+</p>
+<pre class="programlisting"><span class="identifier">normal</span> <span class="identifier">s</span><span class="special">;</span> <span class="comment">// For standard normal distribution, 
+</span><span class="keyword">double</span> <span class="identifier">sd</span> <span class="special">=</span> <span class="number">0.1</span><span class="special">;</span>
+<span class="keyword">double</span> <span class="identifier">x</span> <span class="special">=</span> <span class="number">2.9</span><span class="special">;</span> <span class="comment">// Our required limit.
+</span><span class="comment">// then probability p = N((x - mean) / sd)
+</span><span class="comment">// So if we want to find the standard deviation that would be required to meet this limit,
+</span><span class="comment">// so that the p th quantile is located at x,
+</span><span class="comment">// in this case the 0.95 (95%) quantile at 2.9 kg pack weight, when the mean is 3 kg.
+</span>
+<span class="keyword">double</span> <span class="identifier">prob</span> <span class="special">=</span>  <span class="identifier">pdf</span><span class="special">(</span><span class="identifier">s</span><span class="special">,</span> <span class="special">(</span><span class="identifier">x</span> <span class="special">-</span> <span class="identifier">mean</span><span class="special">)</span> <span class="special">/</span> <span class="identifier">sd</span><span class="special">);</span>
+<span class="keyword">double</span> <span class="identifier">qp</span> <span class="special">=</span> <span class="identifier">quantile</span><span class="special">(</span><span class="identifier">s</span><span class="special">,</span> <span class="number">0.95</span><span class="special">);</span>
+<span class="identifier">cout</span> <span class="special">&lt;&lt;</span> <span class="string">"prob = "</span> <span class="special">&lt;&lt;</span> <span class="identifier">prob</span> <span class="special">&lt;&lt;</span> <span class="string">", quantile(p) "</span> <span class="special">&lt;&lt;</span> <span class="identifier">qp</span> <span class="special">&lt;&lt;</span> <span class="identifier">endl</span><span class="special">;</span> <span class="comment">// p = 0.241971, quantile(p) 1.64485
+</span><span class="comment">// Rearranging, we can directly calculate the required standard deviation:
+</span><span class="keyword">double</span> <span class="identifier">sd95</span> <span class="special">=</span> <span class="identifier">abs</span><span class="special">((</span><span class="identifier">x</span> <span class="special">-</span> <span class="identifier">mean</span><span class="special">))</span> <span class="special">/</span> <span class="identifier">qp</span><span class="special">;</span>
+
+<span class="identifier">cout</span> <span class="special">&lt;&lt;</span> <span class="string">"If we want the "</span><span class="special">&lt;&lt;</span> <span class="identifier">p</span> <span class="special">&lt;&lt;</span> <span class="string">" th quantile to be located at "</span>  
+  <span class="special">&lt;&lt;</span> <span class="identifier">x</span> <span class="special">&lt;&lt;</span> <span class="string">", would need a standard deviation of "</span> <span class="special">&lt;&lt;</span> <span class="identifier">sd95</span> <span class="special">&lt;&lt;</span> <span class="identifier">endl</span><span class="special">;</span>
+
+<span class="identifier">normal</span> <span class="identifier">pack95</span><span class="special">(</span><span class="identifier">mean</span><span class="special">,</span> <span class="identifier">sd95</span><span class="special">);</span>  <span class="comment">// Distribution of the 'ideal better' packer.
+</span><span class="identifier">cout</span> <span class="special">&lt;&lt;</span><span class="string">"Fraction of packs &gt;= "</span> <span class="special">&lt;&lt;</span> <span class="identifier">under_weight</span> <span class="special">&lt;&lt;</span> <span class="string">" with a mean of "</span> <span class="special">&lt;&lt;</span> <span class="identifier">mean</span> 
+  <span class="special">&lt;&lt;</span> <span class="string">" and standard deviation of "</span> <span class="special">&lt;&lt;</span> <span class="identifier">pack95</span><span class="special">.</span><span class="identifier">standard_deviation</span><span class="special">()</span>
+  <span class="special">&lt;&lt;</span> <span class="string">" is "</span> <span class="special">&lt;&lt;</span> <span class="identifier">cdf</span><span class="special">(</span><span class="identifier">complement</span><span class="special">(</span><span class="identifier">pack95</span><span class="special">,</span> <span class="identifier">under_weight</span><span class="special">))</span> <span class="special">&lt;&lt;</span> <span class="identifier">endl</span><span class="special">;</span>
+
+<span class="comment">// Fraction of packs &gt;= 2.9 with a mean of 3 and standard deviation of 0.0608 is 0.95</span></pre>
+<p>
+              </p>
+<p>
+              </p>
+<p>
+                Notice that these two deceptively simple questions (do we over-fill
+                or measure better) are actually very common. The weight of beef might
+                be replaced by a measurement of more or less anything. But the calculations
+                rely on the accuracy of the standard deviation - something that is
+                almost always less good than we might wish, especially if based on
+                a few measurements.
+              </p>
+<p>
+            </p>
+<a name="math_toolkit.dist.stat_tut.weg.normal_example.normal_misc.length_of_bolts"></a><h5>
+<a name="id619823"></a>
+              <a class="link" href="normal_misc.html#math_toolkit.dist.stat_tut.weg.normal_example.normal_misc.length_of_bolts">Length
+              of bolts</a>
+            </h5>
+<p>
+              </p>
+<p>
+                A bolt is usable if between 3.9 and 4.1 long. From a large batch
+                of bolts, a sample of 50 show a mean length of 3.95 with standard
+                deviation 0.1. Assuming a normal distribution, what proportion is
+                usable? The true sample mean is unknown, but we can use the sample
+                mean and standard deviation to find approximate solutions.
+              </p>
+<p>
+              </p>
+<p>
+                
+</p>
+<pre class="programlisting">    <span class="identifier">normal</span> <span class="identifier">bolts</span><span class="special">(</span><span class="number">3.95</span><span class="special">,</span> <span class="number">0.1</span><span class="special">);</span>
+    <span class="keyword">double</span> <span class="identifier">top</span> <span class="special">=</span> <span class="number">4.1</span><span class="special">;</span>
+    <span class="keyword">double</span> <span class="identifier">bottom</span> <span class="special">=</span> <span class="number">3.9</span><span class="special">;</span> 
+
+<span class="identifier">cout</span> <span class="special">&lt;&lt;</span> <span class="string">"Fraction long enough [ P(X &lt;= "</span> <span class="special">&lt;&lt;</span> <span class="identifier">top</span> <span class="special">&lt;&lt;</span> <span class="string">") ] is "</span> <span class="special">&lt;&lt;</span> <span class="identifier">cdf</span><span class="special">(</span><span class="identifier">bolts</span><span class="special">,</span> <span class="identifier">top</span><span class="special">)</span> <span class="special">&lt;&lt;</span> <span class="identifier">endl</span><span class="special">;</span>
+<span class="identifier">cout</span> <span class="special">&lt;&lt;</span> <span class="string">"Fraction too short [ P(X &lt;= "</span> <span class="special">&lt;&lt;</span> <span class="identifier">bottom</span> <span class="special">&lt;&lt;</span> <span class="string">") ] is "</span> <span class="special">&lt;&lt;</span> <span class="identifier">cdf</span><span class="special">(</span><span class="identifier">bolts</span><span class="special">,</span> <span class="identifier">bottom</span><span class="special">)</span> <span class="special">&lt;&lt;</span> <span class="identifier">endl</span><span class="special">;</span>
+<span class="identifier">cout</span> <span class="special">&lt;&lt;</span> <span class="string">"Fraction OK  -between "</span> <span class="special">&lt;&lt;</span> <span class="identifier">bottom</span> <span class="special">&lt;&lt;</span> <span class="string">" and "</span> <span class="special">&lt;&lt;</span> <span class="identifier">top</span>
+  <span class="special">&lt;&lt;</span> <span class="string">"[ P(X &lt;= "</span> <span class="special">&lt;&lt;</span> <span class="identifier">top</span>  <span class="special">&lt;&lt;</span> <span class="string">") - P(X&lt;= "</span> <span class="special">&lt;&lt;</span> <span class="identifier">bottom</span> <span class="special">&lt;&lt;</span> <span class="string">" ) ] is "</span>
+  <span class="special">&lt;&lt;</span> <span class="identifier">cdf</span><span class="special">(</span><span class="identifier">bolts</span><span class="special">,</span> <span class="identifier">top</span><span class="special">)</span> <span class="special">-</span> <span class="identifier">cdf</span><span class="special">(</span><span class="identifier">bolts</span><span class="special">,</span> <span class="identifier">bottom</span><span class="special">)</span> <span class="special">&lt;&lt;</span> <span class="identifier">endl</span><span class="special">;</span>
+
+<span class="identifier">cout</span> <span class="special">&lt;&lt;</span> <span class="string">"Fraction too long [ P(X &gt; "</span> <span class="special">&lt;&lt;</span> <span class="identifier">top</span> <span class="special">&lt;&lt;</span> <span class="string">") ] is "</span>
+  <span class="special">&lt;&lt;</span> <span class="identifier">cdf</span><span class="special">(</span><span class="identifier">complement</span><span class="special">(</span><span class="identifier">bolts</span><span class="special">,</span> <span class="identifier">top</span><span class="special">))</span> <span class="special">&lt;&lt;</span> <span class="identifier">endl</span><span class="special">;</span>
+
+<span class="identifier">cout</span> <span class="special">&lt;&lt;</span> <span class="string">"95% of bolts are shorter than "</span> <span class="special">&lt;&lt;</span> <span class="identifier">quantile</span><span class="special">(</span><span class="identifier">bolts</span><span class="special">,</span> <span class="number">0.95</span><span class="special">)</span> <span class="special">&lt;&lt;</span> <span class="identifier">endl</span><span class="special">;</span>
+ 
+</pre>
+<p>
+              </p>
+<p>
+            </p>
+</div>
+<table xmlns:rev="http://www.cs.rpi.edu/~gregod/boost/tools/doc/revision" width="100%"><tr>
+<td align="left"></td>
+<td align="right"><div class="copyright-footer">Copyright © 2006 , 2007, 2008 John Maddock, Paul A. Bristow, Hubert
+      Holin, Xiaogang Zhang, Bruno Lalande and Gautam Sewani<p>
+        Distributed under the Boost Software License, Version 1.0. (See accompanying
+        file LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_0.txt)
+      </p>
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+<a name="math_toolkit.dist.stat_tut.weg.st_eg"></a><a class="link" href="st_eg.html" title="Student's t Distribution Examples"> Student's
+          t Distribution Examples</a>
+</h5></div></div></div>
+<div class="toc"><dl>
+<dt><span class="section"><a href="st_eg/tut_mean_intervals.html">
+            Calculating confidence intervals on the mean with the Students-t distribution</a></span></dt>
+<dt><span class="section"><a href="st_eg/tut_mean_test.html">
+            Testing a sample mean for difference from a "true" mean</a></span></dt>
+<dt><span class="section"><a href="st_eg/tut_mean_size.html">
+            Estimating how large a sample size would have to become in order to give
+            a significant Students-t test result with a single sample test</a></span></dt>
+<dt><span class="section"><a href="st_eg/two_sample_students_t.html">
+            Comparing the means of two samples with the Students-t test</a></span></dt>
+<dt><span class="section"><a href="st_eg/paired_st.html">
+            Comparing two paired samples with the Student's t distribution</a></span></dt>
+</dl></div>
+</div>
+<table xmlns:rev="http://www.cs.rpi.edu/~gregod/boost/tools/doc/revision" width="100%"><tr>
+<td align="left"></td>
+<td align="right"><div class="copyright-footer">Copyright © 2006 , 2007, 2008 John Maddock, Paul A. Bristow, Hubert
+      Holin, Xiaogang Zhang, Bruno Lalande and Gautam Sewani<p>
+        Distributed under the Boost Software License, Version 1.0. (See accompanying
+        file LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_0.txt)
+      </p>
+</div></td>
+</tr></table>
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+<div class="titlepage"><div><div><h6 class="title">
+<a name="math_toolkit.dist.stat_tut.weg.st_eg.paired_st"></a><a class="link" href="paired_st.html" title="Comparing two paired samples with the Student's t distribution">
+            Comparing two paired samples with the Student's t distribution</a>
+</h6></div></div></div>
+<p>
+              Imagine that we have a before and after reading for each item in the
+              sample: for example we might have measured blood pressure before and
+              after administration of a new drug. We can't pool the results and compare
+              the means before and after the change, because each patient will have
+              a different baseline reading. Instead we calculate the difference between
+              before and after measurements in each patient, and calculate the mean
+              and standard deviation of the differences. To test whether a significant
+              change has taken place, we can then test the null-hypothesis that the
+              true mean is zero using the same procedure we used in the single sample
+              cases previously discussed.
+            </p>
+<p>
+              That means we can:
+            </p>
+<div class="itemizedlist"><ul type="disc">
+<li>
+<a class="link" href="tut_mean_intervals.html" title="Calculating confidence intervals on the mean with the Students-t distribution">Calculate
+                confidence intervals of the mean</a>. If the endpoints of the
+                interval differ in sign then we are unable to reject the null-hypothesis
+                that there is no change.
+              </li>
+<li>
+<a class="link" href="tut_mean_test.html" title='Testing a sample mean for difference from a "true" mean'>Test
+                whether the true mean is zero</a>. If the result is consistent
+                with a true mean of zero, then we are unable to reject the null-hypothesis
+                that there is no change.
+              </li>
+<li>
+<a class="link" href="tut_mean_size.html" title="Estimating how large a sample size would have to become in order to give a significant Students-t test result with a single sample test">Calculate
+                how many pairs of readings we would need in order to obtain a significant
+                result</a>.
+              </li>
+</ul></div>
+</div>
+<table xmlns:rev="http://www.cs.rpi.edu/~gregod/boost/tools/doc/revision" width="100%"><tr>
+<td align="left"></td>
+<td align="right"><div class="copyright-footer">Copyright © 2006 , 2007, 2008 John Maddock, Paul A. Bristow, Hubert
+      Holin, Xiaogang Zhang, Bruno Lalande and Gautam Sewani<p>
+        Distributed under the Boost Software License, Version 1.0. (See accompanying
+        file LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_0.txt)
+      </p>
+</div></td>
+</tr></table>
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+</div>
+<div class="section" lang="en">
+<div class="titlepage"><div><div><h6 class="title">
+<a name="math_toolkit.dist.stat_tut.weg.st_eg.tut_mean_intervals"></a><a class="link" href="tut_mean_intervals.html" title="Calculating confidence intervals on the mean with the Students-t distribution">
+            Calculating confidence intervals on the mean with the Students-t distribution</a>
+</h6></div></div></div>
+<p>
+              Let's say you have a sample mean, you may wish to know what confidence
+              intervals you can place on that mean. Colloquially: "I want an
+              interval that I can be P% sure contains the true mean". (On a
+              technical point, note that the interval either contains the true mean
+              or it does not: the meaning of the confidence level is subtly different
+              from this colloquialism. More background information can be found on
+              the <a href="http://www.itl.nist.gov/div898/handbook/eda/section3/eda352.htm" target="_top">NIST
+              site</a>).
+            </p>
+<p>
+              The formula for the interval can be expressed as:
+            </p>
+<p>
+              <span class="inlinemediaobject"><img src="../../../../../../equations/dist_tutorial4.png"></span>
+            </p>
+<p>
+              Where, <span class="emphasis"><em>Y<sub>s</sub></em></span> is the sample mean, <span class="emphasis"><em>s</em></span>
+              is the sample standard deviation, <span class="emphasis"><em>N</em></span> is the sample
+              size, <span class="emphasis"><em>[alpha]</em></span> is the desired significance level
+              and <span class="emphasis"><em>t<sub>(&#945;/2,N-1)</sub></em></span> is the upper critical value of the
+              Students-t distribution with <span class="emphasis"><em>N-1</em></span> degrees of freedom.
+            </p>
+<div class="note"><table border="0" summary="Note">
+<tr>
+<td rowspan="2" align="center" valign="top" width="25"><img alt="[Note]" src="../../../../../../../doc/html/images/note.png"></td>
+<th align="left">Note</th>
+</tr>
+<tr><td align="left" valign="top">
+<p>
+                The quantity &#945; is the maximum acceptable risk of falsely rejecting
+                the null-hypothesis. The smaller the value of &#945; the greater the strength
+                of the test.
+              </p>
+<p>
+                The confidence level of the test is defined as 1 - &#945;, and often expressed
+                as a percentage. So for example a significance level of 0.05, is
+                equivalent to a 95% confidence level. Refer to <a href="http://www.itl.nist.gov/div898/handbook/prc/section1/prc14.htm" target="_top">"What
+                are confidence intervals?"</a> in <a href="http://www.itl.nist.gov/div898/handbook/" target="_top">NIST/SEMATECH
+                e-Handbook of Statistical Methods.</a> for more information.
+              </p>
+</td></tr>
+</table></div>
+<div class="note"><table border="0" summary="Note">
+<tr>
+<td rowspan="2" align="center" valign="top" width="25"><img alt="[Note]" src="../../../../../../../doc/html/images/note.png"></td>
+<th align="left">Note</th>
+</tr>
+<tr><td align="left" valign="top"><p>
+                The usual assumptions of <a href="http://en.wikipedia.org/wiki/Independent_and_identically-distributed_random_variables" target="_top">independent
+                and identically distributed (i.i.d.)</a> variables and normal distribution
+                of course apply here, as they do in other examples.
+              </p></td></tr>
+</table></div>
+<p>
+              From the formula, it should be clear that:
+            </p>
+<div class="itemizedlist"><ul type="disc">
+<li>
+                The width of the confidence interval decreases as the sample size
+                increases.
+              </li>
+<li>
+                The width increases as the standard deviation increases.
+              </li>
+<li>
+                The width increases as the <span class="emphasis"><em>confidence level increases</em></span>
+                (0.5 towards 0.99999 - stronger).
+              </li>
+<li>
+                The width increases as the <span class="emphasis"><em>significance level decreases</em></span>
+                (0.5 towards 0.00000...01 - stronger).
+              </li>
+</ul></div>
+<p>
+              The following example code is taken from the example program students_t_single_sample.cpp.
+            </p>
+<p>
+              We'll begin by defining a procedure to calculate intervals for various
+              confidence levels; the procedure will print these out as a table:
+            </p>
+<pre class="programlisting"><span class="comment">// Needed includes:
+</span><span class="preprocessor">#include</span> <span class="special">&lt;</span><span class="identifier">boost</span><span class="special">/</span><span class="identifier">math</span><span class="special">/</span><span class="identifier">distributions</span><span class="special">/</span><span class="identifier">students_t</span><span class="special">.</span><span class="identifier">hpp</span><span class="special">&gt;</span>
+<span class="preprocessor">#include</span> <span class="special">&lt;</span><span class="identifier">iostream</span><span class="special">&gt;</span>
+<span class="preprocessor">#include</span> <span class="special">&lt;</span><span class="identifier">iomanip</span><span class="special">&gt;</span>
+<span class="comment">// Bring everything into global namespace for ease of use:
+</span><span class="keyword">using</span> <span class="keyword">namespace</span> <span class="identifier">boost</span><span class="special">::</span><span class="identifier">math</span><span class="special">;</span>
+<span class="keyword">using</span> <span class="keyword">namespace</span> <span class="identifier">std</span><span class="special">;</span>   
+
+<span class="keyword">void</span> <span class="identifier">confidence_limits_on_mean</span><span class="special">(</span>
+   <span class="keyword">double</span> <span class="identifier">Sm</span><span class="special">,</span>           <span class="comment">// Sm = Sample Mean.
+</span>   <span class="keyword">double</span> <span class="identifier">Sd</span><span class="special">,</span>           <span class="comment">// Sd = Sample Standard Deviation.
+</span>   <span class="keyword">unsigned</span> <span class="identifier">Sn</span><span class="special">)</span>         <span class="comment">// Sn = Sample Size.
+</span><span class="special">{</span>
+   <span class="keyword">using</span> <span class="keyword">namespace</span> <span class="identifier">std</span><span class="special">;</span>
+   <span class="keyword">using</span> <span class="keyword">namespace</span> <span class="identifier">boost</span><span class="special">::</span><span class="identifier">math</span><span class="special">;</span>
+
+   <span class="comment">// Print out general info:
+</span>   <span class="identifier">cout</span> <span class="special">&lt;&lt;</span> 
+      <span class="string">"__________________________________\n"</span>
+      <span class="string">"2-Sided Confidence Limits For Mean\n"</span>
+      <span class="string">"__________________________________\n\n"</span><span class="special">;</span>
+   <span class="identifier">cout</span> <span class="special">&lt;&lt;</span> <span class="identifier">setprecision</span><span class="special">(</span><span class="number">7</span><span class="special">);</span>
+   <span class="identifier">cout</span> <span class="special">&lt;&lt;</span> <span class="identifier">setw</span><span class="special">(</span><span class="number">40</span><span class="special">)</span> <span class="special">&lt;&lt;</span> <span class="identifier">left</span> <span class="special">&lt;&lt;</span> <span class="string">"Number of Observations"</span> <span class="special">&lt;&lt;</span> <span class="string">"=  "</span> <span class="special">&lt;&lt;</span> <span class="identifier">Sn</span> <span class="special">&lt;&lt;</span> <span class="string">"\n"</span><span class="special">;</span>
+   <span class="identifier">cout</span> <span class="special">&lt;&lt;</span> <span class="identifier">setw</span><span class="special">(</span><span class="number">40</span><span class="special">)</span> <span class="special">&lt;&lt;</span> <span class="identifier">left</span> <span class="special">&lt;&lt;</span> <span class="string">"Mean"</span> <span class="special">&lt;&lt;</span> <span class="string">"=  "</span> <span class="special">&lt;&lt;</span> <span class="identifier">Sm</span> <span class="special">&lt;&lt;</span> <span class="string">"\n"</span><span class="special">;</span>
+   <span class="identifier">cout</span> <span class="special">&lt;&lt;</span> <span class="identifier">setw</span><span class="special">(</span><span class="number">40</span><span class="special">)</span> <span class="special">&lt;&lt;</span> <span class="identifier">left</span> <span class="special">&lt;&lt;</span> <span class="string">"Standard Deviation"</span> <span class="special">&lt;&lt;</span> <span class="string">"=  "</span> <span class="special">&lt;&lt;</span> <span class="identifier">Sd</span> <span class="special">&lt;&lt;</span> <span class="string">"\n"</span><span class="special">;</span>
+</pre>
+<p>
+              We'll define a table of significance/risk levels for which we'll compute
+              intervals:
+            </p>
+<pre class="programlisting"><span class="keyword">double</span> <span class="identifier">alpha</span><span class="special">[]</span> <span class="special">=</span> <span class="special">{</span> <span class="number">0.5</span><span class="special">,</span> <span class="number">0.25</span><span class="special">,</span> <span class="number">0.1</span><span class="special">,</span> <span class="number">0.05</span><span class="special">,</span> <span class="number">0.01</span><span class="special">,</span> <span class="number">0.001</span><span class="special">,</span> <span class="number">0.0001</span><span class="special">,</span> <span class="number">0.00001</span> <span class="special">};</span>
+</pre>
+<p>
+              Note that these are the complements of the confidence/probability levels:
+              0.5, 0.75, 0.9 .. 0.99999).
+            </p>
+<p>
+              Next we'll declare the distribution object we'll need, note that the
+              <span class="emphasis"><em>degrees of freedom</em></span> parameter is the sample size
+              less one:
+            </p>
+<pre class="programlisting"><span class="identifier">students_t</span> <span class="identifier">dist</span><span class="special">(</span><span class="identifier">Sn</span> <span class="special">-</span> <span class="number">1</span><span class="special">);</span>
+</pre>
+<p>
+              Most of what follows in the program is pretty printing, so let's focus
+              on the calculation of the interval. First we need the t-statistic,
+              computed using the <span class="emphasis"><em>quantile</em></span> function and our significance
+              level. Note that since the significance levels are the complement of
+              the probability, we have to wrap the arguments in a call to <span class="emphasis"><em>complement(...)</em></span>:
+            </p>
+<pre class="programlisting"><span class="keyword">double</span> <span class="identifier">T</span> <span class="special">=</span> <span class="identifier">quantile</span><span class="special">(</span><span class="identifier">complement</span><span class="special">(</span><span class="identifier">dist</span><span class="special">,</span> <span class="identifier">alpha</span><span class="special">[</span><span class="identifier">i</span><span class="special">]</span> <span class="special">/</span> <span class="number">2</span><span class="special">));</span>
+</pre>
+<p>
+              Note that alpha was divided by two, since we'll be calculating both
+              the upper and lower bounds: had we been interested in a single sided
+              interval then we would have omitted this step.
+            </p>
+<p>
+              Now to complete the picture, we'll get the (one-sided) width of the
+              interval from the t-statistic by multiplying by the standard deviation,
+              and dividing by the square root of the sample size:
+            </p>
+<pre class="programlisting"><span class="keyword">double</span> <span class="identifier">w</span> <span class="special">=</span> <span class="identifier">T</span> <span class="special">*</span> <span class="identifier">Sd</span> <span class="special">/</span> <span class="identifier">sqrt</span><span class="special">(</span><span class="keyword">double</span><span class="special">(</span><span class="identifier">Sn</span><span class="special">));</span>
+</pre>
+<p>
+              The two-sided interval is then the sample mean plus and minus this
+              width.
+            </p>
+<p>
+              And apart from some more pretty-printing that completes the procedure.
+            </p>
+<p>
+              Let's take a look at some sample output, first using the <a href="http://www.itl.nist.gov/div898/handbook/eda/section4/eda428.htm" target="_top">Heat
+              flow data</a> from the NIST site. The data set was collected by
+              Bob Zarr of NIST in January, 1990 from a heat flow meter calibration
+              and stability analysis. The corresponding dataplot output for this
+              test can be found in <a href="http://www.itl.nist.gov/div898/handbook/eda/section3/eda352.htm" target="_top">section
+              3.5.2</a> of the <a href="http://www.itl.nist.gov/div898/handbook/" target="_top">NIST/SEMATECH
+              e-Handbook of Statistical Methods.</a>.
+            </p>
+<pre class="programlisting">   __________________________________
+   2-Sided Confidence Limits For Mean
+   __________________________________
+
+   Number of Observations                  =  195
+   Mean                                    =  9.26146
+   Standard Deviation                      =  0.02278881
+
+
+   ___________________________________________________________________
+   Confidence       T           Interval          Lower          Upper
+    Value (%)     Value          Width            Limit          Limit
+   ___________________________________________________________________
+       50.000     0.676       1.103e-003        9.26036        9.26256
+       75.000     1.154       1.883e-003        9.25958        9.26334
+       90.000     1.653       2.697e-003        9.25876        9.26416
+       95.000     1.972       3.219e-003        9.25824        9.26468
+       99.000     2.601       4.245e-003        9.25721        9.26571
+       99.900     3.341       5.453e-003        9.25601        9.26691
+       99.990     3.973       6.484e-003        9.25498        9.26794
+       99.999     4.537       7.404e-003        9.25406        9.26886
+</pre>
+<p>
+              As you can see the large sample size (195) and small standard deviation
+              (0.023) have combined to give very small intervals, indeed we can be
+              very confident that the true mean is 9.2.
+            </p>
+<p>
+              For comparison the next example data output is taken from <span class="emphasis"><em>P.K.Hou,
+              O. W. Lau &amp; M.C. Wong, Analyst (1983) vol. 108, p 64. and from
+              Statistics for Analytical Chemistry, 3rd ed. (1994), pp 54-55 J. C.
+              Miller and J. N. Miller, Ellis Horwood ISBN 0 13 0309907.</em></span>
+              The values result from the determination of mercury by cold-vapour
+              atomic absorption.
+            </p>
+<pre class="programlisting">   __________________________________
+   2-Sided Confidence Limits For Mean
+   __________________________________
+
+   Number of Observations                  =  3
+   Mean                                    =  37.8000000
+   Standard Deviation                      =  0.9643650
+
+
+   ___________________________________________________________________
+   Confidence       T           Interval          Lower          Upper
+    Value (%)     Value          Width            Limit          Limit
+   ___________________________________________________________________
+       50.000     0.816            0.455       37.34539       38.25461
+       75.000     1.604            0.893       36.90717       38.69283
+       90.000     2.920            1.626       36.17422       39.42578
+       95.000     4.303            2.396       35.40438       40.19562
+       99.000     9.925            5.526       32.27408       43.32592
+       99.900    31.599           17.594       20.20639       55.39361
+       99.990    99.992           55.673      -17.87346       93.47346
+       99.999   316.225          176.067     -138.26683      213.86683
+</pre>
+<p>
+              This time the fact that there are only three measurements leads to
+              much wider intervals, indeed such large intervals that it's hard to
+              be very confident in the location of the mean.
+            </p>
+</div>
+<table xmlns:rev="http://www.cs.rpi.edu/~gregod/boost/tools/doc/revision" width="100%"><tr>
+<td align="left"></td>
+<td align="right"><div class="copyright-footer">Copyright © 2006 , 2007, 2008 John Maddock, Paul A. Bristow, Hubert
+      Holin, Xiaogang Zhang, Bruno Lalande and Gautam Sewani<p>
+        Distributed under the Boost Software License, Version 1.0. (See accompanying
+        file LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_0.txt)
+      </p>
+</div></td>
+</tr></table>
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+<a name="math_toolkit.dist.stat_tut.weg.st_eg.tut_mean_size"></a><a class="link" href="tut_mean_size.html" title="Estimating how large a sample size would have to become in order to give a significant Students-t test result with a single sample test">
+            Estimating how large a sample size would have to become in order to give
+            a significant Students-t test result with a single sample test</a>
+</h6></div></div></div>
+<p>
+              Imagine you have conducted a Students-t test on a single sample in
+              order to check for systematic errors in your measurements. Imagine
+              that the result is borderline. At this point one might go off and collect
+              more data, but it might be prudent to first ask the question "How
+              much more?". The parameter estimators of the students_t_distribution
+              class can provide this information.
+            </p>
+<p>
+              This section is based on the example code in students_t_single_sample.cpp
+              and we begin by defining a procedure that will print out a table of
+              estimated sample sizes for various confidence levels:
+            </p>
+<pre class="programlisting"><span class="comment">// Needed includes:
+</span><span class="preprocessor">#include</span> <span class="special">&lt;</span><span class="identifier">boost</span><span class="special">/</span><span class="identifier">math</span><span class="special">/</span><span class="identifier">distributions</span><span class="special">/</span><span class="identifier">students_t</span><span class="special">.</span><span class="identifier">hpp</span><span class="special">&gt;</span>
+<span class="preprocessor">#include</span> <span class="special">&lt;</span><span class="identifier">iostream</span><span class="special">&gt;</span>
+<span class="preprocessor">#include</span> <span class="special">&lt;</span><span class="identifier">iomanip</span><span class="special">&gt;</span>
+<span class="comment">// Bring everything into global namespace for ease of use:
+</span><span class="keyword">using</span> <span class="keyword">namespace</span> <span class="identifier">boost</span><span class="special">::</span><span class="identifier">math</span><span class="special">;</span>
+<span class="keyword">using</span> <span class="keyword">namespace</span> <span class="identifier">std</span><span class="special">;</span>   
+
+<span class="keyword">void</span> <span class="identifier">single_sample_find_df</span><span class="special">(</span>
+   <span class="keyword">double</span> <span class="identifier">M</span><span class="special">,</span>          <span class="comment">// M = true mean.
+</span>   <span class="keyword">double</span> <span class="identifier">Sm</span><span class="special">,</span>         <span class="comment">// Sm = Sample Mean.
+</span>   <span class="keyword">double</span> <span class="identifier">Sd</span><span class="special">)</span>         <span class="comment">// Sd = Sample Standard Deviation.
+</span><span class="special">{</span>
+</pre>
+<p>
+              Next we define a table of significance levels:
+            </p>
+<pre class="programlisting"><span class="keyword">double</span> <span class="identifier">alpha</span><span class="special">[]</span> <span class="special">=</span> <span class="special">{</span> <span class="number">0.5</span><span class="special">,</span> <span class="number">0.25</span><span class="special">,</span> <span class="number">0.1</span><span class="special">,</span> <span class="number">0.05</span><span class="special">,</span> <span class="number">0.01</span><span class="special">,</span> <span class="number">0.001</span><span class="special">,</span> <span class="number">0.0001</span><span class="special">,</span> <span class="number">0.00001</span> <span class="special">};</span>
+</pre>
+<p>
+              Printing out the table of sample sizes required for various confidence
+              levels begins with the table header:
+            </p>
+<pre class="programlisting"><span class="identifier">cout</span> <span class="special">&lt;&lt;</span> <span class="string">"\n\n"</span>
+        <span class="string">"_______________________________________________________________\n"</span>
+        <span class="string">"Confidence       Estimated          Estimated\n"</span>
+        <span class="string">" Value (%)      Sample Size        Sample Size\n"</span>
+        <span class="string">"              (one sided test)    (two sided test)\n"</span>
+        <span class="string">"_______________________________________________________________\n"</span><span class="special">;</span>
+</pre>
+<p>
+              And now the important part: the sample sizes required. Class <code class="computeroutput"><span class="identifier">students_t_distribution</span></code> has a static
+              member function <code class="computeroutput"><span class="identifier">find_degrees_of_freedom</span></code>
+              that will calculate how large a sample size needs to be in order to
+              give a definitive result.
+            </p>
+<p>
+              The first argument is the difference between the means that you wish
+              to be able to detect, here it's the absolute value of the difference
+              between the sample mean, and the true mean.
+            </p>
+<p>
+              Then come two probability values: alpha and beta. Alpha is the maximum
+              acceptable risk of rejecting the null-hypothesis when it is in fact
+              true. Beta is the maximum acceptable risk of failing to reject the
+              null-hypothesis when in fact it is false. Also note that for a two-sided
+              test, alpha must be divided by 2.
+            </p>
+<p>
+              The final parameter of the function is the standard deviation of the
+              sample.
+            </p>
+<p>
+              In this example, we assume that alpha and beta are the same, and call
+              <code class="computeroutput"><span class="identifier">find_degrees_of_freedom</span></code>
+              twice: once with alpha for a one-sided test, and once with alpha/2
+              for a two-sided test.
+            </p>
+<pre class="programlisting">   <span class="keyword">for</span><span class="special">(</span><span class="keyword">unsigned</span> <span class="identifier">i</span> <span class="special">=</span> <span class="number">0</span><span class="special">;</span> <span class="identifier">i</span> <span class="special">&lt;</span> <span class="keyword">sizeof</span><span class="special">(</span><span class="identifier">alpha</span><span class="special">)/</span><span class="keyword">sizeof</span><span class="special">(</span><span class="identifier">alpha</span><span class="special">[</span><span class="number">0</span><span class="special">]);</span> <span class="special">++</span><span class="identifier">i</span><span class="special">)</span>
+   <span class="special">{</span>
+      <span class="comment">// Confidence value:
+</span>      <span class="identifier">cout</span> <span class="special">&lt;&lt;</span> <span class="identifier">fixed</span> <span class="special">&lt;&lt;</span> <span class="identifier">setprecision</span><span class="special">(</span><span class="number">3</span><span class="special">)</span> <span class="special">&lt;&lt;</span> <span class="identifier">setw</span><span class="special">(</span><span class="number">10</span><span class="special">)</span> <span class="special">&lt;&lt;</span> <span class="identifier">right</span> <span class="special">&lt;&lt;</span> <span class="number">100</span> <span class="special">*</span> <span class="special">(</span><span class="number">1</span><span class="special">-</span><span class="identifier">alpha</span><span class="special">[</span><span class="identifier">i</span><span class="special">]);</span>
+      <span class="comment">// calculate df for single sided test:
+</span>      <span class="keyword">double</span> <span class="identifier">df</span> <span class="special">=</span> <span class="identifier">students_t</span><span class="special">::</span><span class="identifier">find_degrees_of_freedom</span><span class="special">(</span>
+         <span class="identifier">fabs</span><span class="special">(</span><span class="identifier">M</span> <span class="special">-</span> <span class="identifier">Sm</span><span class="special">),</span> <span class="identifier">alpha</span><span class="special">[</span><span class="identifier">i</span><span class="special">],</span> <span class="identifier">alpha</span><span class="special">[</span><span class="identifier">i</span><span class="special">],</span> <span class="identifier">Sd</span><span class="special">);</span>
+      <span class="comment">// convert to sample size:
+</span>      <span class="keyword">double</span> <span class="identifier">size</span> <span class="special">=</span> <span class="identifier">ceil</span><span class="special">(</span><span class="identifier">df</span><span class="special">)</span> <span class="special">+</span> <span class="number">1</span><span class="special">;</span>
+      <span class="comment">// Print size:
+</span>      <span class="identifier">cout</span> <span class="special">&lt;&lt;</span> <span class="identifier">fixed</span> <span class="special">&lt;&lt;</span> <span class="identifier">setprecision</span><span class="special">(</span><span class="number">0</span><span class="special">)</span> <span class="special">&lt;&lt;</span> <span class="identifier">setw</span><span class="special">(</span><span class="number">16</span><span class="special">)</span> <span class="special">&lt;&lt;</span> <span class="identifier">right</span> <span class="special">&lt;&lt;</span> <span class="identifier">size</span><span class="special">;</span>
+      <span class="comment">// calculate df for two sided test:
+</span>      <span class="identifier">df</span> <span class="special">=</span> <span class="identifier">students_t</span><span class="special">::</span><span class="identifier">find_degrees_of_freedom</span><span class="special">(</span>
+         <span class="identifier">fabs</span><span class="special">(</span><span class="identifier">M</span> <span class="special">-</span> <span class="identifier">Sm</span><span class="special">),</span> <span class="identifier">alpha</span><span class="special">[</span><span class="identifier">i</span><span class="special">]/</span><span class="number">2</span><span class="special">,</span> <span class="identifier">alpha</span><span class="special">[</span><span class="identifier">i</span><span class="special">],</span> <span class="identifier">Sd</span><span class="special">);</span>
+      <span class="comment">// convert to sample size:
+</span>      <span class="identifier">size</span> <span class="special">=</span> <span class="identifier">ceil</span><span class="special">(</span><span class="identifier">df</span><span class="special">)</span> <span class="special">+</span> <span class="number">1</span><span class="special">;</span>
+      <span class="comment">// Print size:
+</span>      <span class="identifier">cout</span> <span class="special">&lt;&lt;</span> <span class="identifier">fixed</span> <span class="special">&lt;&lt;</span> <span class="identifier">setprecision</span><span class="special">(</span><span class="number">0</span><span class="special">)</span> <span class="special">&lt;&lt;</span> <span class="identifier">setw</span><span class="special">(</span><span class="number">16</span><span class="special">)</span> <span class="special">&lt;&lt;</span> <span class="identifier">right</span> <span class="special">&lt;&lt;</span> <span class="identifier">size</span> <span class="special">&lt;&lt;</span> <span class="identifier">endl</span><span class="special">;</span>
+   <span class="special">}</span>
+   <span class="identifier">cout</span> <span class="special">&lt;&lt;</span> <span class="identifier">endl</span><span class="special">;</span>
+<span class="special">}</span>
+</pre>
+<p>
+              Let's now look at some sample output using data taken from <span class="emphasis"><em>P.K.Hou,
+              O. W. Lau &amp; M.C. Wong, Analyst (1983) vol. 108, p 64. and from
+              Statistics for Analytical Chemistry, 3rd ed. (1994), pp 54-55 J. C.
+              Miller and J. N. Miller, Ellis Horwood ISBN 0 13 0309907.</em></span>
+              The values result from the determination of mercury by cold-vapour
+              atomic absorption.
+            </p>
+<p>
+              Only three measurements were made, and the Students-t test above gave
+              a borderline result, so this example will show us how many samples
+              would need to be collected:
+            </p>
+<pre class="programlisting">_____________________________________________________________
+Estimated sample sizes required for various confidence levels
+_____________________________________________________________
+
+True Mean                               =  38.90000
+Sample Mean                             =  37.80000
+Sample Standard Deviation               =  0.96437
+
+
+_______________________________________________________________
+Confidence       Estimated          Estimated
+ Value (%)      Sample Size        Sample Size
+              (one sided test)    (two sided test)
+_______________________________________________________________
+    75.000               3               4
+    90.000               7               9
+    95.000              11              13
+    99.000              20              22
+    99.900              35              37
+    99.990              50              53
+    99.999              66              68
+</pre>
+<p>
+              So in this case, many more measurements would have had to be made,
+              for example at the 95% level, 14 measurements in total for a two-sided
+              test.
+            </p>
+</div>
+<table xmlns:rev="http://www.cs.rpi.edu/~gregod/boost/tools/doc/revision" width="100%"><tr>
+<td align="left"></td>
+<td align="right"><div class="copyright-footer">Copyright © 2006 , 2007, 2008 John Maddock, Paul A. Bristow, Hubert
+      Holin, Xiaogang Zhang, Bruno Lalande and Gautam Sewani<p>
+        Distributed under the Boost Software License, Version 1.0. (See accompanying
+        file LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_0.txt)
+      </p>
+</div></td>
+</tr></table>
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+</div>
+<div class="section" lang="en">
+<div class="titlepage"><div><div><h6 class="title">
+<a name="math_toolkit.dist.stat_tut.weg.st_eg.tut_mean_test"></a><a class="link" href="tut_mean_test.html" title='Testing a sample mean for difference from a "true" mean'>
+            Testing a sample mean for difference from a "true" mean</a>
+</h6></div></div></div>
+<p>
+              When calibrating or comparing a scientific instrument or measurement
+              method of some kind, we want to be answer the question "Does an
+              observed sample mean differ from the "true" mean in any significant
+              way?". If it does, then we have evidence of a systematic difference.
+              This question can be answered with a Students-t test: more information
+              can be found <a href="http://www.itl.nist.gov/div898/handbook/eda/section3/eda352.htm" target="_top">on
+              the NIST site</a>.
+            </p>
+<p>
+              Of course, the assignment of "true" to one mean may be quite
+              arbitrary, often this is simply a "traditional" method of
+              measurement.
+            </p>
+<p>
+              The following example code is taken from the example program students_t_single_sample.cpp.
+            </p>
+<p>
+              We'll begin by defining a procedure to determine which of the possible
+              hypothesis are rejected or not-rejected at a given significance level:
+            </p>
+<div class="note"><table border="0" summary="Note">
+<tr>
+<td rowspan="2" align="center" valign="top" width="25"><img alt="[Note]" src="../../../../../../../doc/html/images/note.png"></td>
+<th align="left">Note</th>
+</tr>
+<tr><td align="left" valign="top"><p>
+                Non-statisticians might say 'not-rejected' means 'accepted', (often
+                of the null-hypothesis) implying, wrongly, that there really <span class="bold"><strong>IS</strong></span> no difference, but statisticans eschew
+                this to avoid implying that there is positive evidence of 'no difference'.
+                'Not-rejected' here means there is <span class="bold"><strong>no evidence</strong></span>
+                of difference, but there still might well be a difference. For example,
+                see <a href="http://en.wikipedia.org/wiki/Argument_from_ignorance" target="_top">argument
+                from ignorance</a> and <a href="http://www.bmj.com/cgi/content/full/311/7003/485" target="_top">Absence
+                of evidence does not constitute evidence of absence.</a>
+              </p></td></tr>
+</table></div>
+<pre class="programlisting"><span class="comment">// Needed includes:
+</span><span class="preprocessor">#include</span> <span class="special">&lt;</span><span class="identifier">boost</span><span class="special">/</span><span class="identifier">math</span><span class="special">/</span><span class="identifier">distributions</span><span class="special">/</span><span class="identifier">students_t</span><span class="special">.</span><span class="identifier">hpp</span><span class="special">&gt;</span>
+<span class="preprocessor">#include</span> <span class="special">&lt;</span><span class="identifier">iostream</span><span class="special">&gt;</span>
+<span class="preprocessor">#include</span> <span class="special">&lt;</span><span class="identifier">iomanip</span><span class="special">&gt;</span>
+<span class="comment">// Bring everything into global namespace for ease of use:
+</span><span class="keyword">using</span> <span class="keyword">namespace</span> <span class="identifier">boost</span><span class="special">::</span><span class="identifier">math</span><span class="special">;</span>
+<span class="keyword">using</span> <span class="keyword">namespace</span> <span class="identifier">std</span><span class="special">;</span>   
+
+<span class="keyword">void</span> <span class="identifier">single_sample_t_test</span><span class="special">(</span><span class="keyword">double</span> <span class="identifier">M</span><span class="special">,</span> <span class="keyword">double</span> <span class="identifier">Sm</span><span class="special">,</span> <span class="keyword">double</span> <span class="identifier">Sd</span><span class="special">,</span> <span class="keyword">unsigned</span> <span class="identifier">Sn</span><span class="special">,</span> <span class="keyword">double</span> <span class="identifier">alpha</span><span class="special">)</span>
+<span class="special">{</span>
+   <span class="comment">//
+</span>   <span class="comment">// M = true mean.
+</span>   <span class="comment">// Sm = Sample Mean.
+</span>   <span class="comment">// Sd = Sample Standard Deviation.
+</span>   <span class="comment">// Sn = Sample Size.
+</span>   <span class="comment">// alpha = Significance Level.
+</span></pre>
+<p>
+              Most of the procedure is pretty-printing, so let's just focus on the
+              calculation, we begin by calculating the t-statistic:
+            </p>
+<pre class="programlisting"><span class="comment">// Difference in means:
+</span><span class="keyword">double</span> <span class="identifier">diff</span> <span class="special">=</span> <span class="identifier">Sm</span> <span class="special">-</span> <span class="identifier">M</span><span class="special">;</span>
+<span class="comment">// Degrees of freedom:
+</span><span class="keyword">unsigned</span> <span class="identifier">v</span> <span class="special">=</span> <span class="identifier">Sn</span> <span class="special">-</span> <span class="number">1</span><span class="special">;</span>
+<span class="comment">// t-statistic:
+</span><span class="keyword">double</span> <span class="identifier">t_stat</span> <span class="special">=</span> <span class="identifier">diff</span> <span class="special">*</span> <span class="identifier">sqrt</span><span class="special">(</span><span class="keyword">double</span><span class="special">(</span><span class="identifier">Sn</span><span class="special">))</span> <span class="special">/</span> <span class="identifier">Sd</span><span class="special">;</span>
+</pre>
+<p>
+              Finally calculate the probability from the t-statistic. If we're interested
+              in simply whether there is a difference (either less or greater) or
+              not, we don't care about the sign of the t-statistic, and we take the
+              complement of the probability for comparison to the significance level:
+            </p>
+<pre class="programlisting"><span class="identifier">students_t</span> <span class="identifier">dist</span><span class="special">(</span><span class="identifier">v</span><span class="special">);</span>
+<span class="keyword">double</span> <span class="identifier">q</span> <span class="special">=</span> <span class="identifier">cdf</span><span class="special">(</span><span class="identifier">complement</span><span class="special">(</span><span class="identifier">dist</span><span class="special">,</span> <span class="identifier">fabs</span><span class="special">(</span><span class="identifier">t_stat</span><span class="special">)));</span>
+</pre>
+<p>
+              The procedure then prints out the results of the various tests that
+              can be done, these can be summarised in the following table:
+            </p>
+<div class="informaltable"><table class="table">
+<colgroup>
+<col>
+<col>
+</colgroup>
+<thead><tr>
+<th>
+                    <p>
+                      Hypothesis
+                    </p>
+                    </th>
+<th>
+                    <p>
+                      Test
+                    </p>
+                    </th>
+</tr></thead>
+<tbody>
+<tr>
+<td>
+                    <p>
+                      The Null-hypothesis: there is <span class="bold"><strong>no difference</strong></span>
+                      in means
+                    </p>
+                    </td>
+<td>
+                    <p>
+                      Reject if complement of CDF for |t| &lt; significance level
+                      / 2:
+                    </p>
+                    <p>
+                      <code class="computeroutput"><span class="identifier">cdf</span><span class="special">(</span><span class="identifier">complement</span><span class="special">(</span><span class="identifier">dist</span><span class="special">,</span>
+                      <span class="identifier">fabs</span><span class="special">(</span><span class="identifier">t</span><span class="special">)))</span>
+                      <span class="special">&lt;</span> <span class="identifier">alpha</span>
+                      <span class="special">/</span> <span class="number">2</span></code>
+                    </p>
+                    </td>
+</tr>
+<tr>
+<td>
+                    <p>
+                      The Alternative-hypothesis: there <span class="bold"><strong>is
+                      difference</strong></span> in means
+                    </p>
+                    </td>
+<td>
+                    <p>
+                      Reject if complement of CDF for |t| &gt; significance level
+                      / 2:
+                    </p>
+                    <p>
+                      <code class="computeroutput"><span class="identifier">cdf</span><span class="special">(</span><span class="identifier">complement</span><span class="special">(</span><span class="identifier">dist</span><span class="special">,</span>
+                      <span class="identifier">fabs</span><span class="special">(</span><span class="identifier">t</span><span class="special">)))</span>
+                      <span class="special">&gt;</span> <span class="identifier">alpha</span>
+                      <span class="special">/</span> <span class="number">2</span></code>
+                    </p>
+                    </td>
+</tr>
+<tr>
+<td>
+                    <p>
+                      The Alternative-hypothesis: the sample mean <span class="bold"><strong>is
+                      less</strong></span> than the true mean.
+                    </p>
+                    </td>
+<td>
+                    <p>
+                      Reject if CDF of t &gt; significance level:
+                    </p>
+                    <p>
+                      <code class="computeroutput"><span class="identifier">cdf</span><span class="special">(</span><span class="identifier">dist</span><span class="special">,</span>
+                      <span class="identifier">t</span><span class="special">)</span>
+                      <span class="special">&gt;</span> <span class="identifier">alpha</span></code>
+                    </p>
+                    </td>
+</tr>
+<tr>
+<td>
+                    <p>
+                      The Alternative-hypothesis: the sample mean <span class="bold"><strong>is
+                      greater</strong></span> than the true mean.
+                    </p>
+                    </td>
+<td>
+                    <p>
+                      Reject if complement of CDF of t &gt; significance level:
+                    </p>
+                    <p>
+                      <code class="computeroutput"><span class="identifier">cdf</span><span class="special">(</span><span class="identifier">complement</span><span class="special">(</span><span class="identifier">dist</span><span class="special">,</span>
+                      <span class="identifier">t</span><span class="special">))</span>
+                      <span class="special">&gt;</span> <span class="identifier">alpha</span></code>
+                    </p>
+                    </td>
+</tr>
+</tbody>
+</table></div>
+<div class="note"><table border="0" summary="Note">
+<tr>
+<td rowspan="2" align="center" valign="top" width="25"><img alt="[Note]" src="../../../../../../../doc/html/images/note.png"></td>
+<th align="left">Note</th>
+</tr>
+<tr><td align="left" valign="top"><p>
+                Notice that the comparisons are against <code class="computeroutput"><span class="identifier">alpha</span>
+                <span class="special">/</span> <span class="number">2</span></code>
+                for a two-sided test and against <code class="computeroutput"><span class="identifier">alpha</span></code>
+                for a one-sided test
+              </p></td></tr>
+</table></div>
+<p>
+              Now that we have all the parts in place, let's take a look at some
+              sample output, first using the <a href="http://www.itl.nist.gov/div898/handbook/eda/section4/eda428.htm" target="_top">Heat
+              flow data</a> from the NIST site. The data set was collected by
+              Bob Zarr of NIST in January, 1990 from a heat flow meter calibration
+              and stability analysis. The corresponding dataplot output for this
+              test can be found in <a href="http://www.itl.nist.gov/div898/handbook/eda/section3/eda352.htm" target="_top">section
+              3.5.2</a> of the <a href="http://www.itl.nist.gov/div898/handbook/" target="_top">NIST/SEMATECH
+              e-Handbook of Statistical Methods.</a>.
+            </p>
+<pre class="programlisting">   __________________________________
+   Student t test for a single sample
+   __________________________________
+
+   Number of Observations                                 =  195
+   Sample Mean                                            =  9.26146
+   Sample Standard Deviation                              =  0.02279
+   Expected True Mean                                     =  5.00000
+
+   Sample Mean - Expected Test Mean                       =  4.26146
+   Degrees of Freedom                                     =  194
+   T Statistic                                            =  2611.28380
+   Probability that difference is due to chance           =  0.000e+000
+
+   Results for Alternative Hypothesis and alpha           =  0.0500
+
+   Alternative Hypothesis     Conclusion
+   Mean != 5.000              NOT REJECTED
+   Mean  &lt; 5.000              REJECTED
+   Mean  &gt; 5.000              NOT REJECTED
+</pre>
+<p>
+              You will note the line that says the probability that the difference
+              is due to chance is zero. From a philosophical point of view, of course,
+              the probability can never reach zero. However, in this case the calculated
+              probability is smaller than the smallest representable double precision
+              number, hence the appearance of a zero here. Whatever its "true"
+              value is, we know it must be extraordinarily small, so the alternative
+              hypothesis - that there is a difference in means - is not rejected.
+            </p>
+<p>
+              For comparison the next example data output is taken from <span class="emphasis"><em>P.K.Hou,
+              O. W. Lau &amp; M.C. Wong, Analyst (1983) vol. 108, p 64. and from
+              Statistics for Analytical Chemistry, 3rd ed. (1994), pp 54-55 J. C.
+              Miller and J. N. Miller, Ellis Horwood ISBN 0 13 0309907.</em></span>
+              The values result from the determination of mercury by cold-vapour
+              atomic absorption.
+            </p>
+<pre class="programlisting">   __________________________________
+   Student t test for a single sample
+   __________________________________
+
+   Number of Observations                                 =  3
+   Sample Mean                                            =  37.80000
+   Sample Standard Deviation                              =  0.96437
+   Expected True Mean                                     =  38.90000
+
+   Sample Mean - Expected Test Mean                       =  -1.10000
+   Degrees of Freedom                                     =  2
+   T Statistic                                            =  -1.97566
+   Probability that difference is due to chance           =  1.869e-001
+
+   Results for Alternative Hypothesis and alpha           =  0.0500
+
+   Alternative Hypothesis     Conclusion
+   Mean != 38.900             REJECTED
+   Mean  &lt; 38.900             REJECTED
+   Mean  &gt; 38.900             REJECTED
+</pre>
+<p>
+              As you can see the small number of measurements (3) has led to a large
+              uncertainty in the location of the true mean. So even though there
+              appears to be a difference between the sample mean and the expected
+              true mean, we conclude that there is no significant difference, and
+              are unable to reject the null hypothesis. However, if we were to lower
+              the bar for acceptance down to alpha = 0.1 (a 90% confidence level)
+              we see a different output:
+            </p>
+<pre class="programlisting">__________________________________
+Student t test for a single sample
+__________________________________
+
+Number of Observations                                 =  3
+Sample Mean                                            =  37.80000
+Sample Standard Deviation                              =  0.96437
+Expected True Mean                                     =  38.90000
+
+Sample Mean - Expected Test Mean                       =  -1.10000
+Degrees of Freedom                                     =  2
+T Statistic                                            =  -1.97566
+Probability that difference is due to chance           =  1.869e-001
+
+Results for Alternative Hypothesis and alpha           =  0.1000
+
+Alternative Hypothesis     Conclusion
+Mean != 38.900            REJECTED
+Mean  &lt; 38.900            NOT REJECTED
+Mean  &gt; 38.900            REJECTED
+</pre>
+<p>
+              In this case, we really have a borderline result, and more data (and/or
+              more accurate data), is needed for a more convincing conclusion.
+            </p>
+</div>
+<table xmlns:rev="http://www.cs.rpi.edu/~gregod/boost/tools/doc/revision" width="100%"><tr>
+<td align="left"></td>
+<td align="right"><div class="copyright-footer">Copyright © 2006 , 2007, 2008 John Maddock, Paul A. Bristow, Hubert
+      Holin, Xiaogang Zhang, Bruno Lalande and Gautam Sewani<p>
+        Distributed under the Boost Software License, Version 1.0. (See accompanying
+        file LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_0.txt)
+      </p>
+</div></td>
+</tr></table>
+<hr>
+<div class="spirit-nav">
+<a accesskey="p" href="tut_mean_intervals.html"><img src="../../../../../../../doc/html/images/prev.png" alt="Prev"></a><a accesskey="u" href="../st_eg.html"><img src="../../../../../../../doc/html/images/up.png" alt="Up"></a><a accesskey="h" href="../../../../../index.html"><img src="../../../../../../../doc/html/images/home.png" alt="Home"></a><a accesskey="n" href="tut_mean_size.html"><img src="../../../../../../../doc/html/images/next.png" alt="Next"></a>
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+<title>Comparing the means of two samples with the Students-t test</title>
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+<div class="titlepage"><div><div><h6 class="title">
+<a name="math_toolkit.dist.stat_tut.weg.st_eg.two_sample_students_t"></a><a class="link" href="two_sample_students_t.html" title="Comparing the means of two samples with the Students-t test">
+            Comparing the means of two samples with the Students-t test</a>
+</h6></div></div></div>
+<p>
+              Imagine that we have two samples, and we wish to determine whether
+              their means are different or not. This situation often arises when
+              determining whether a new process or treatment is better than an old
+              one.
+            </p>
+<p>
+              In this example, we'll be using the <a href="http://www.itl.nist.gov/div898/handbook/eda/section3/eda3531.htm" target="_top">Car
+              Mileage sample data</a> from the <a href="http://www.itl.nist.gov" target="_top">NIST
+              website</a>. The data compares miles per gallon of US cars with
+              miles per gallon of Japanese cars.
+            </p>
+<p>
+              The sample code is in students_t_two_samples.cpp.
+            </p>
+<p>
+              There are two ways in which this test can be conducted: we can assume
+              that the true standard deviations of the two samples are equal or not.
+              If the standard deviations are assumed to be equal, then the calculation
+              of the t-statistic is greatly simplified, so we'll examine that case
+              first. In real life we should verify whether this assumption is valid
+              with a Chi-Squared test for equal variances.
+            </p>
+<p>
+              We begin by defining a procedure that will conduct our test assuming
+              equal variances:
+            </p>
+<pre class="programlisting"><span class="comment">// Needed headers:
+</span><span class="preprocessor">#include</span> <span class="special">&lt;</span><span class="identifier">boost</span><span class="special">/</span><span class="identifier">math</span><span class="special">/</span><span class="identifier">distributions</span><span class="special">/</span><span class="identifier">students_t</span><span class="special">.</span><span class="identifier">hpp</span><span class="special">&gt;</span>
+<span class="preprocessor">#include</span> <span class="special">&lt;</span><span class="identifier">iostream</span><span class="special">&gt;</span>
+<span class="preprocessor">#include</span> <span class="special">&lt;</span><span class="identifier">iomanip</span><span class="special">&gt;</span>
+<span class="comment">// Simplify usage:
+</span><span class="keyword">using</span> <span class="keyword">namespace</span> <span class="identifier">boost</span><span class="special">::</span><span class="identifier">math</span><span class="special">;</span>
+<span class="keyword">using</span> <span class="keyword">namespace</span> <span class="identifier">std</span><span class="special">;</span>
+
+<span class="keyword">void</span> <span class="identifier">two_samples_t_test_equal_sd</span><span class="special">(</span>
+        <span class="keyword">double</span> <span class="identifier">Sm1</span><span class="special">,</span>       <span class="comment">// Sm1 = Sample 1 Mean.
+</span>        <span class="keyword">double</span> <span class="identifier">Sd1</span><span class="special">,</span>       <span class="comment">// Sd1 = Sample 1 Standard Deviation.
+</span>        <span class="keyword">unsigned</span> <span class="identifier">Sn1</span><span class="special">,</span>     <span class="comment">// Sn1 = Sample 1 Size.
+</span>        <span class="keyword">double</span> <span class="identifier">Sm2</span><span class="special">,</span>       <span class="comment">// Sm2 = Sample 2 Mean.
+</span>        <span class="keyword">double</span> <span class="identifier">Sd2</span><span class="special">,</span>       <span class="comment">// Sd2 = Sample 2 Standard Deviation.
+</span>        <span class="keyword">unsigned</span> <span class="identifier">Sn2</span><span class="special">,</span>     <span class="comment">// Sn2 = Sample 2 Size.
+</span>        <span class="keyword">double</span> <span class="identifier">alpha</span><span class="special">)</span>     <span class="comment">// alpha = Significance Level.
+</span><span class="special">{</span>
+</pre>
+<p>
+              Our procedure will begin by calculating the t-statistic, assuming equal
+              variances the needed formulae are:
+            </p>
+<p>
+              <span class="inlinemediaobject"><img src="../../../../../../equations/dist_tutorial1.png"></span>
+            </p>
+<p>
+              where Sp is the "pooled" standard deviation of the two samples,
+              and <span class="emphasis"><em>v</em></span> is the number of degrees of freedom of the
+              two combined samples. We can now write the code to calculate the t-statistic:
+            </p>
+<pre class="programlisting"><span class="comment">// Degrees of freedom:
+</span><span class="keyword">double</span> <span class="identifier">v</span> <span class="special">=</span> <span class="identifier">Sn1</span> <span class="special">+</span> <span class="identifier">Sn2</span> <span class="special">-</span> <span class="number">2</span><span class="special">;</span>
+<span class="identifier">cout</span> <span class="special">&lt;&lt;</span> <span class="identifier">setw</span><span class="special">(</span><span class="number">55</span><span class="special">)</span> <span class="special">&lt;&lt;</span> <span class="identifier">left</span> <span class="special">&lt;&lt;</span> <span class="string">"Degrees of Freedom"</span> <span class="special">&lt;&lt;</span> <span class="string">"=  "</span> <span class="special">&lt;&lt;</span> <span class="identifier">v</span> <span class="special">&lt;&lt;</span> <span class="string">"\n"</span><span class="special">;</span>
+<span class="comment">// Pooled variance:
+</span><span class="keyword">double</span> <span class="identifier">sp</span> <span class="special">=</span> <span class="identifier">sqrt</span><span class="special">(((</span><span class="identifier">Sn1</span><span class="special">-</span><span class="number">1</span><span class="special">)</span> <span class="special">*</span> <span class="identifier">Sd1</span> <span class="special">*</span> <span class="identifier">Sd1</span> <span class="special">+</span> <span class="special">(</span><span class="identifier">Sn2</span><span class="special">-</span><span class="number">1</span><span class="special">)</span> <span class="special">*</span> <span class="identifier">Sd2</span> <span class="special">*</span> <span class="identifier">Sd2</span><span class="special">)</span> <span class="special">/</span> <span class="identifier">v</span><span class="special">);</span>
+<span class="identifier">cout</span> <span class="special">&lt;&lt;</span> <span class="identifier">setw</span><span class="special">(</span><span class="number">55</span><span class="special">)</span> <span class="special">&lt;&lt;</span> <span class="identifier">left</span> <span class="special">&lt;&lt;</span> <span class="string">"Pooled Standard Deviation"</span> <span class="special">&lt;&lt;</span> <span class="string">"=  "</span> <span class="special">&lt;&lt;</span> <span class="identifier">v</span> <span class="special">&lt;&lt;</span> <span class="string">"\n"</span><span class="special">;</span>
+<span class="comment">// t-statistic:
+</span><span class="keyword">double</span> <span class="identifier">t_stat</span> <span class="special">=</span> <span class="special">(</span><span class="identifier">Sm1</span> <span class="special">-</span> <span class="identifier">Sm2</span><span class="special">)</span> <span class="special">/</span> <span class="special">(</span><span class="identifier">sp</span> <span class="special">*</span> <span class="identifier">sqrt</span><span class="special">(</span><span class="number">1.0</span> <span class="special">/</span> <span class="identifier">Sn1</span> <span class="special">+</span> <span class="number">1.0</span> <span class="special">/</span> <span class="identifier">Sn2</span><span class="special">));</span>
+<span class="identifier">cout</span> <span class="special">&lt;&lt;</span> <span class="identifier">setw</span><span class="special">(</span><span class="number">55</span><span class="special">)</span> <span class="special">&lt;&lt;</span> <span class="identifier">left</span> <span class="special">&lt;&lt;</span> <span class="string">"T Statistic"</span> <span class="special">&lt;&lt;</span> <span class="string">"=  "</span> <span class="special">&lt;&lt;</span> <span class="identifier">t_stat</span> <span class="special">&lt;&lt;</span> <span class="string">"\n"</span><span class="special">;</span>
+</pre>
+<p>
+              The next step is to define our distribution object, and calculate the
+              complement of the probability:
+            </p>
+<pre class="programlisting"><span class="identifier">students_t</span> <span class="identifier">dist</span><span class="special">(</span><span class="identifier">v</span><span class="special">);</span>
+<span class="keyword">double</span> <span class="identifier">q</span> <span class="special">=</span> <span class="identifier">cdf</span><span class="special">(</span><span class="identifier">complement</span><span class="special">(</span><span class="identifier">dist</span><span class="special">,</span> <span class="identifier">fabs</span><span class="special">(</span><span class="identifier">t_stat</span><span class="special">)));</span>
+<span class="identifier">cout</span> <span class="special">&lt;&lt;</span> <span class="identifier">setw</span><span class="special">(</span><span class="number">55</span><span class="special">)</span> <span class="special">&lt;&lt;</span> <span class="identifier">left</span> <span class="special">&lt;&lt;</span> <span class="string">"Probability that difference is due to chance"</span> <span class="special">&lt;&lt;</span> <span class="string">"=  "</span> 
+   <span class="special">&lt;&lt;</span> <span class="identifier">setprecision</span><span class="special">(</span><span class="number">3</span><span class="special">)</span> <span class="special">&lt;&lt;</span> <span class="identifier">scientific</span> <span class="special">&lt;&lt;</span> <span class="number">2</span> <span class="special">*</span> <span class="identifier">q</span> <span class="special">&lt;&lt;</span> <span class="string">"\n\n"</span><span class="special">;</span>
+</pre>
+<p>
+              Here we've used the absolute value of the t-statistic, because we initially
+              want to know simply whether there is a difference or not (a two-sided
+              test). However, we can also test whether the mean of the second sample
+              is greater or is less (one-sided test) than that of the first: all
+              the possible tests are summed up in the following table:
+            </p>
+<div class="informaltable"><table class="table">
+<colgroup>
+<col>
+<col>
+</colgroup>
+<thead><tr>
+<th>
+                    <p>
+                      Hypothesis
+                    </p>
+                    </th>
+<th>
+                    <p>
+                      Test
+                    </p>
+                    </th>
+</tr></thead>
+<tbody>
+<tr>
+<td>
+                    <p>
+                      The Null-hypothesis: there is <span class="bold"><strong>no difference</strong></span>
+                      in means
+                    </p>
+                    </td>
+<td>
+                    <p>
+                      Reject if complement of CDF for |t| &lt; significance level
+                      / 2:
+                    </p>
+                    <p>
+                      <code class="computeroutput"><span class="identifier">cdf</span><span class="special">(</span><span class="identifier">complement</span><span class="special">(</span><span class="identifier">dist</span><span class="special">,</span>
+                      <span class="identifier">fabs</span><span class="special">(</span><span class="identifier">t</span><span class="special">)))</span>
+                      <span class="special">&lt;</span> <span class="identifier">alpha</span>
+                      <span class="special">/</span> <span class="number">2</span></code>
+                    </p>
+                    </td>
+</tr>
+<tr>
+<td>
+                    <p>
+                      The Alternative-hypothesis: there is a <span class="bold"><strong>difference</strong></span>
+                      in means
+                    </p>
+                    </td>
+<td>
+                    <p>
+                      Reject if complement of CDF for |t| &gt; significance level
+                      / 2:
+                    </p>
+                    <p>
+                      <code class="computeroutput"><span class="identifier">cdf</span><span class="special">(</span><span class="identifier">complement</span><span class="special">(</span><span class="identifier">dist</span><span class="special">,</span>
+                      <span class="identifier">fabs</span><span class="special">(</span><span class="identifier">t</span><span class="special">)))</span>
+                      <span class="special">&lt;</span> <span class="identifier">alpha</span>
+                      <span class="special">/</span> <span class="number">2</span></code>
+                    </p>
+                    </td>
+</tr>
+<tr>
+<td>
+                    <p>
+                      The Alternative-hypothesis: Sample 1 Mean is <span class="bold"><strong>less</strong></span>
+                      than Sample 2 Mean.
+                    </p>
+                    </td>
+<td>
+                    <p>
+                      Reject if CDF of t &gt; significance level:
+                    </p>
+                    <p>
+                      <code class="computeroutput"><span class="identifier">cdf</span><span class="special">(</span><span class="identifier">dist</span><span class="special">,</span>
+                      <span class="identifier">t</span><span class="special">)</span>
+                      <span class="special">&gt;</span> <span class="identifier">alpha</span></code>
+                    </p>
+                    </td>
+</tr>
+<tr>
+<td>
+                    <p>
+                      The Alternative-hypothesis: Sample 1 Mean is <span class="bold"><strong>greater</strong></span>
+                      than Sample 2 Mean.
+                    </p>
+                    </td>
+<td>
+                    <p>
+                      Reject if complement of CDF of t &gt; significance level:
+                    </p>
+                    <p>
+                      <code class="computeroutput"><span class="identifier">cdf</span><span class="special">(</span><span class="identifier">complement</span><span class="special">(</span><span class="identifier">dist</span><span class="special">,</span>
+                      <span class="identifier">t</span><span class="special">))</span>
+                      <span class="special">&gt;</span> <span class="identifier">alpha</span></code>
+                    </p>
+                    </td>
+</tr>
+</tbody>
+</table></div>
+<div class="note"><table border="0" summary="Note">
+<tr>
+<td rowspan="2" align="center" valign="top" width="25"><img alt="[Note]" src="../../../../../../../doc/html/images/note.png"></td>
+<th align="left">Note</th>
+</tr>
+<tr><td align="left" valign="top"><p>
+                For a two-sided test we must compare against alpha / 2 and not alpha.
+              </p></td></tr>
+</table></div>
+<p>
+              Most of the rest of the sample program is pretty-printing, so we'll
+              skip over that, and take a look at the sample output for alpha=0.05
+              (a 95% probability level). For comparison the dataplot output for the
+              same data is in <a href="http://www.itl.nist.gov/div898/handbook/eda/section3/eda353.htm" target="_top">section
+              1.3.5.3</a> of the <a href="http://www.itl.nist.gov/div898/handbook/" target="_top">NIST/SEMATECH
+              e-Handbook of Statistical Methods.</a>.
+            </p>
+<pre class="programlisting">   ________________________________________________
+   Student t test for two samples (equal variances)
+   ________________________________________________
+
+   Number of Observations (Sample 1)                      =  249
+   Sample 1 Mean                                          =  20.14458
+   Sample 1 Standard Deviation                            =  6.41470
+   Number of Observations (Sample 2)                      =  79
+   Sample 2 Mean                                          =  30.48101
+   Sample 2 Standard Deviation                            =  6.10771
+   Degrees of Freedom                                     =  326.00000
+   Pooled Standard Deviation                              =  326.00000
+   T Statistic                                            =  -12.62059
+   Probability that difference is due to chance           =  5.273e-030
+
+   Results for Alternative Hypothesis and alpha           =  0.0500
+
+   Alternative Hypothesis              Conclusion
+   Sample 1 Mean != Sample 2 Mean       NOT REJECTED
+   Sample 1 Mean &lt;  Sample 2 Mean       NOT REJECTED
+   Sample 1 Mean &gt;  Sample 2 Mean       REJECTED
+</pre>
+<p>
+              So with a probability that the difference is due to chance of just
+              5.273e-030, we can safely conclude that there is indeed a difference.
+            </p>
+<p>
+              The tests on the alternative hypothesis show that we must also reject
+              the hypothesis that Sample 1 Mean is greater than that for Sample 2:
+              in this case Sample 1 represents the miles per gallon for Japanese
+              cars, and Sample 2 the miles per gallon for US cars, so we conclude
+              that Japanese cars are on average more fuel efficient.
+            </p>
+<p>
+              Now that we have the simple case out of the way, let's look for a moment
+              at the more complex one: that the standard deviations of the two samples
+              are not equal. In this case the formula for the t-statistic becomes:
+            </p>
+<p>
+              <span class="inlinemediaobject"><img src="../../../../../../equations/dist_tutorial2.png"></span>
+            </p>
+<p>
+              And for the combined degrees of freedom we use the Welch-Satterthwaite
+              approximation:
+            </p>
+<p>
+              <span class="inlinemediaobject"><img src="../../../../../../equations/dist_tutorial3.png"></span>
+            </p>
+<p>
+              Note that this is one of the rare situations where the degrees-of-freedom
+              parameter to the Student's t distribution is a real number, and not
+              an integer value.
+            </p>
+<div class="note"><table border="0" summary="Note">
+<tr>
+<td rowspan="2" align="center" valign="top" width="25"><img alt="[Note]" src="../../../../../../../doc/html/images/note.png"></td>
+<th align="left">Note</th>
+</tr>
+<tr><td align="left" valign="top"><p>
+                Some statistical packages truncate the effective degrees of freedom
+                to an integer value: this may be necessary if you are relying on
+                lookup tables, but since our code fully supports non-integer degrees
+                of freedom there is no need to truncate in this case. Also note that
+                when the degrees of freedom is small then the Welch-Satterthwaite
+                approximation may be a significant source of error.
+              </p></td></tr>
+</table></div>
+<p>
+              Putting these formulae into code we get:
+            </p>
+<pre class="programlisting"><span class="comment">// Degrees of freedom:
+</span><span class="keyword">double</span> <span class="identifier">v</span> <span class="special">=</span> <span class="identifier">Sd1</span> <span class="special">*</span> <span class="identifier">Sd1</span> <span class="special">/</span> <span class="identifier">Sn1</span> <span class="special">+</span> <span class="identifier">Sd2</span> <span class="special">*</span> <span class="identifier">Sd2</span> <span class="special">/</span> <span class="identifier">Sn2</span><span class="special">;</span>
+<span class="identifier">v</span> <span class="special">*=</span> <span class="identifier">v</span><span class="special">;</span>
+<span class="keyword">double</span> <span class="identifier">t1</span> <span class="special">=</span> <span class="identifier">Sd1</span> <span class="special">*</span> <span class="identifier">Sd1</span> <span class="special">/</span> <span class="identifier">Sn1</span><span class="special">;</span>
+<span class="identifier">t1</span> <span class="special">*=</span> <span class="identifier">t1</span><span class="special">;</span>
+<span class="identifier">t1</span> <span class="special">/=</span>  <span class="special">(</span><span class="identifier">Sn1</span> <span class="special">-</span> <span class="number">1</span><span class="special">);</span>
+<span class="keyword">double</span> <span class="identifier">t2</span> <span class="special">=</span> <span class="identifier">Sd2</span> <span class="special">*</span> <span class="identifier">Sd2</span> <span class="special">/</span> <span class="identifier">Sn2</span><span class="special">;</span>
+<span class="identifier">t2</span> <span class="special">*=</span> <span class="identifier">t2</span><span class="special">;</span>
+<span class="identifier">t2</span> <span class="special">/=</span> <span class="special">(</span><span class="identifier">Sn2</span> <span class="special">-</span> <span class="number">1</span><span class="special">);</span>
+<span class="identifier">v</span> <span class="special">/=</span> <span class="special">(</span><span class="identifier">t1</span> <span class="special">+</span> <span class="identifier">t2</span><span class="special">);</span>
+<span class="identifier">cout</span> <span class="special">&lt;&lt;</span> <span class="identifier">setw</span><span class="special">(</span><span class="number">55</span><span class="special">)</span> <span class="special">&lt;&lt;</span> <span class="identifier">left</span> <span class="special">&lt;&lt;</span> <span class="string">"Degrees of Freedom"</span> <span class="special">&lt;&lt;</span> <span class="string">"=  "</span> <span class="special">&lt;&lt;</span> <span class="identifier">v</span> <span class="special">&lt;&lt;</span> <span class="string">"\n"</span><span class="special">;</span>
+<span class="comment">// t-statistic:
+</span><span class="keyword">double</span> <span class="identifier">t_stat</span> <span class="special">=</span> <span class="special">(</span><span class="identifier">Sm1</span> <span class="special">-</span> <span class="identifier">Sm2</span><span class="special">)</span> <span class="special">/</span> <span class="identifier">sqrt</span><span class="special">(</span><span class="identifier">Sd1</span> <span class="special">*</span> <span class="identifier">Sd1</span> <span class="special">/</span> <span class="identifier">Sn1</span> <span class="special">+</span> <span class="identifier">Sd2</span> <span class="special">*</span> <span class="identifier">Sd2</span> <span class="special">/</span> <span class="identifier">Sn2</span><span class="special">);</span>
+<span class="identifier">cout</span> <span class="special">&lt;&lt;</span> <span class="identifier">setw</span><span class="special">(</span><span class="number">55</span><span class="special">)</span> <span class="special">&lt;&lt;</span> <span class="identifier">left</span> <span class="special">&lt;&lt;</span> <span class="string">"T Statistic"</span> <span class="special">&lt;&lt;</span> <span class="string">"=  "</span> <span class="special">&lt;&lt;</span> <span class="identifier">t_stat</span> <span class="special">&lt;&lt;</span> <span class="string">"\n"</span><span class="special">;</span>
+</pre>
+<p>
+              Thereafter the code and the tests are performed the same as before.
+              Using are car mileage data again, here's what the output looks like:
+            </p>
+<pre class="programlisting">   __________________________________________________
+   Student t test for two samples (unequal variances)
+   __________________________________________________
+
+   Number of Observations (Sample 1)                      =  249
+   Sample 1 Mean                                          =  20.145
+   Sample 1 Standard Deviation                            =  6.4147
+   Number of Observations (Sample 2)                      =  79
+   Sample 2 Mean                                          =  30.481
+   Sample 2 Standard Deviation                            =  6.1077
+   Degrees of Freedom                                     =  136.87
+   T Statistic                                            =  -12.946
+   Probability that difference is due to chance           =  1.571e-025
+
+   Results for Alternative Hypothesis and alpha           =  0.0500
+
+   Alternative Hypothesis              Conclusion
+   Sample 1 Mean != Sample 2 Mean       NOT REJECTED
+   Sample 1 Mean &lt;  Sample 2 Mean       NOT REJECTED
+   Sample 1 Mean &gt;  Sample 2 Mean       REJECTED
+</pre>
+<p>
+              This time allowing the variances in the two samples to differ has yielded
+              a higher likelihood that the observed difference is down to chance
+              alone (1.571e-025 compared to 5.273e-030 when equal variances were
+              assumed). However, the conclusion remains the same: US cars are less
+              fuel efficient than Japanese models.
+            </p>
+</div>
+<table xmlns:rev="http://www.cs.rpi.edu/~gregod/boost/tools/doc/revision" width="100%"><tr>
+<td align="left"></td>
+<td align="right"><div class="copyright-footer">Copyright © 2006 , 2007, 2008 John Maddock, Paul A. Bristow, Hubert
+      Holin, Xiaogang Zhang, Bruno Lalande and Gautam Sewani<p>
+        Distributed under the Boost Software License, Version 1.0. (See accompanying
+        file LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_0.txt)
+      </p>
+</div></td>
+</tr></table>
+<hr>
+<div class="spirit-nav">
+<a accesskey="p" href="tut_mean_size.html"><img src="../../../../../../../doc/html/images/prev.png" alt="Prev"></a><a accesskey="u" href="../st_eg.html"><img src="../../../../../../../doc/html/images/up.png" alt="Up"></a><a accesskey="h" href="../../../../../index.html"><img src="../../../../../../../doc/html/images/home.png" alt="Home"></a><a accesskey="n" href="paired_st.html"><img src="../../../../../../../doc/html/images/next.png" alt="Next"></a>
+</div>
+</body>
+</html>

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==============================================================================
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+++ sandbox/tools/auto_index/example/math/doc/sf_and_dist/html/math_toolkit/main_overview.html	2008-11-28 05:25:28 EST (Fri, 28 Nov 2008)
@@ -0,0 +1,70 @@
+<html>
+<head>
+<meta http-equiv="Content-Type" content="text/html; charset=ISO-8859-1">
+<title>Overview</title>
+<link rel="stylesheet" href="../boostbook.css" type="text/css">
+<meta name="generator" content="DocBook XSL Stylesheets Vsnapshot_8125">
+<link rel="home" href="../index.html" title="Math Toolkit">
+<link rel="up" href="../index.html" title="Math Toolkit">
+<link rel="prev" href="../index.html" title="Math Toolkit">
+<link rel="next" href="main_overview/intro.html" title="About the Math Toolkit">
+</head>
+<body bgcolor="white" text="black" link="#0000FF" vlink="#840084" alink="#0000FF">
+<table cellpadding="2" width="100%"><tr>
+<td valign="top"><img alt="Boost C++ Libraries" width="277" height="86" src="../../../boost.png"></td>
+<td align="center">Home</td>
+<td align="center">Libraries</td>
+<td align="center">People</td>
+<td align="center">FAQ</td>
+<td align="center">More</td>
+</tr></table>
+<hr>
+<div class="spirit-nav">
+<a accesskey="p" href="../index.html"><img src="../../../doc/html/images/prev.png" alt="Prev"></a><a accesskey="u" href="../index.html"><img src="../../../doc/html/images/up.png" alt="Up"></a><a accesskey="h" href="../index.html"><img src="../../../doc/html/images/home.png" alt="Home"></a><a accesskey="n" href="main_overview/intro.html"><img src="../../../doc/html/images/next.png" alt="Next"></a>
+</div>
+<div class="section" lang="en">
+<div class="titlepage"><div><div><h2 class="title" style="clear: both">
+<a name="math_toolkit.main_overview"></a><a class="link" href="main_overview.html" title="Overview"> Overview</a>
+</h2></div></div></div>
+<div class="toc"><dl>
+<dt><span class="section"> About the Math Toolkit</span></dt>
+<dt><span class="section"> Navigation</span></dt>
+<dt><span class="section"><a href="main_overview/directories.html"> Directory and
+      File Structure</a></span></dt>
+<dt><span class="section"> Namespaces</span></dt>
+<dt><span class="section"><a href="main_overview/result_type.html"> Calculation
+      of the Type of the Result</a></span></dt>
+<dt><span class="section"> Error Handling</span></dt>
+<dt><span class="section"> Compilers</span></dt>
+<dt><span class="section"><a href="main_overview/pol_overview.html"> Configuration
+      and Policies</a></span></dt>
+<dt><span class="section"> Thread Safety</span></dt>
+<dt><span class="section"> Performance</span></dt>
+<dt><span class="section"><a href="main_overview/building.html"> If and How to Build
+      the Library and its Examples and Tests</a></span></dt>
+<dt><span class="section"><a href="main_overview/history1.html"> History and What's
+      New</a></span></dt>
+<dt><span class="section"> C99 and TR1 C Functions</span></dt>
+<dt><span class="section"><a href="main_overview/contact.html"> Contact Info and
+      Support</a></span></dt>
+</dl></div>
+<p>
+    </p>
+<p>
+    </p>
+</div>
+<table xmlns:rev="http://www.cs.rpi.edu/~gregod/boost/tools/doc/revision" width="100%"><tr>
+<td align="left"></td>
+<td align="right"><div class="copyright-footer">Copyright © 2006 , 2007, 2008 John Maddock, Paul A. Bristow, Hubert
+      Holin, Xiaogang Zhang, Bruno Lalande and Gautam Sewani<p>
+        Distributed under the Boost Software License, Version 1.0. (See accompanying
+        file LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_0.txt)
+      </p>
+</div></td>
+</tr></table>
+<hr>
+<div class="spirit-nav">
+<a accesskey="p" href="../index.html"><img src="../../../doc/html/images/prev.png" alt="Prev"></a><a accesskey="u" href="../index.html"><img src="../../../doc/html/images/up.png" alt="Up"></a><a accesskey="h" href="../index.html"><img src="../../../doc/html/images/home.png" alt="Home"></a><a accesskey="n" href="main_overview/intro.html"><img src="../../../doc/html/images/next.png" alt="Next"></a>
+</div>
+</body>
+</html>

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@@ -0,0 +1,154 @@
+<html>
+<head>
+<meta http-equiv="Content-Type" content="text/html; charset=ISO-8859-1">
+<title>If and How to Build the Library and its Examples and Tests</title>
+<link rel="stylesheet" href="../../boostbook.css" type="text/css">
+<meta name="generator" content="DocBook XSL Stylesheets Vsnapshot_8125">
+<link rel="home" href="../../index.html" title="Math Toolkit">
+<link rel="up" href="../main_overview.html" title="Overview">
+<link rel="prev" href="perf_over.html" title="Performance">
+<link rel="next" href="history1.html" title="History and What's New">
+</head>
+<body bgcolor="white" text="black" link="#0000FF" vlink="#840084" alink="#0000FF">
+<table cellpadding="2" width="100%"><tr>
+<td valign="top"><img alt="Boost C++ Libraries" width="277" height="86" src="../../../../boost.png"></td>
+<td align="center">Home</td>
+<td align="center">Libraries</td>
+<td align="center">People</td>
+<td align="center">FAQ</td>
+<td align="center">More</td>
+</tr></table>
+<hr>
+<div class="spirit-nav">
+<a accesskey="p" href="perf_over.html"><img src="../../../../doc/html/images/prev.png" alt="Prev"></a><a accesskey="u" href="../main_overview.html"><img src="../../../../doc/html/images/up.png" alt="Up"></a><a accesskey="h" href="../../index.html"><img src="../../../../doc/html/images/home.png" alt="Home"></a><a accesskey="n" href="history1.html"><img src="../../../../doc/html/images/next.png" alt="Next"></a>
+</div>
+<div class="section" lang="en">
+<div class="titlepage"><div><div><h3 class="title">
+<a name="math_toolkit.main_overview.building"></a><a class="link" href="building.html" title="If and How to Build the Library and its Examples and Tests"> If and How to Build
+      the Library and its Examples and Tests</a>
+</h3></div></div></div>
+<a name="math_toolkit.main_overview.building.building_the_library"></a><h5>
+<a name="id548790"></a>
+        <a class="link" href="building.html#math_toolkit.main_overview.building.building_the_library">Building
+        the Library</a>
+      </h5>
+<p>
+        The first thing you need to ask yourself is "Do I need to build anything
+        at all?" as the bulk of this library is header only: meaning you can
+        use it just by #including the necessary header(s). (The library includes
+        everything, so if you only use a few components, your total executables size
+        will be <span class="bold"><strong>much</strong></span> greater).
+      </p>
+<p>
+        The <span class="emphasis"><em>only</em></span> time you need to build the library is if you
+        want to use the <code class="computeroutput"><span class="keyword">extern</span> <span class="string">"C"</span></code>
+        functions declared in <code class="computeroutput"><span class="special">&lt;</span><span class="identifier">boost</span><span class="special">/</span><span class="identifier">math</span><span class="special">/</span><span class="identifier">tr1</span><span class="special">.</span><span class="identifier">hpp</span><span class="special">&gt;</span></code>. To build this using Boost.Build, from
+        a commandline boost-root directory issue a command like:
+      </p>
+<pre class="programlisting"><span class="identifier">bjam</span> <span class="identifier">toolset</span><span class="special">=</span><span class="identifier">gcc</span> <span class="special">--</span><span class="identifier">with</span><span class="special">-</span><span class="identifier">math</span> <span class="identifier">install</span>
+</pre>
+<p>
+        will do the job on Linux, while:
+      </p>
+<pre class="programlisting"><span class="identifier">bjam</span> <span class="identifier">toolset</span><span class="special">=</span><span class="identifier">msvc</span> <span class="special">--</span><span class="identifier">with</span><span class="special">-</span><span class="identifier">math</span> <span class="special">--</span><span class="identifier">build</span><span class="special">-</span><span class="identifier">type</span><span class="special">=</span><span class="identifier">complete</span> <span class="identifier">stage</span>
+</pre>
+<p>
+        will work better on Windows (leaving libraries built in sub-folder <code class="computeroutput"><span class="special">/</span><span class="identifier">stage</span></code>
+        below your Boost root directory). Either way you should consult the <a href="http://www.boost.org/doc/libs/release/more/getting_started/index.html" target="_top">getting
+        started guide</a> for more information.
+      </p>
+<p>
+        You can also build the libraries from your favourite IDE or command line
+        tool: each <code class="computeroutput"><span class="keyword">extern</span> <span class="string">"C"</span></code>
+        function declared in <code class="computeroutput"><span class="special">&lt;</span><span class="identifier">boost</span><span class="special">/</span><span class="identifier">math</span><span class="special">/</span><span class="identifier">tr1</span><span class="special">.</span><span class="identifier">hpp</span><span class="special">&gt;</span></code> has its own source file with the same
+        name in <code class="computeroutput"><span class="identifier">libs</span><span class="special">/</span><span class="identifier">math</span><span class="special">/</span><span class="identifier">src</span><span class="special">/</span><span class="identifier">tr1</span></code>. Just
+        select the sources corresponding to the functions you are using and build
+        them into a library, or else add them directly to your project. Note that
+        the directory <code class="computeroutput"><span class="identifier">libs</span><span class="special">/</span><span class="identifier">math</span><span class="special">/</span><span class="identifier">src</span><span class="special">/</span><span class="identifier">tr1</span></code> will
+        need to be in your compiler's #include path as well as the boost-root directory
+        (MSVC Tools, Options, Projects and Solutions, VC++ Directories, Include files).
+      </p>
+<div class="note"><table border="0" summary="Note">
+<tr>
+<td rowspan="2" align="center" valign="top" width="25"><img alt="[Note]" src="../../../../doc/html/images/note.png"></td>
+<th align="left">Note</th>
+</tr>
+<tr><td align="left" valign="top"><p>
+          If you are using a Windows compiler that supports auto-linking and you
+          have built the sources yourself (or added them directly to your project)
+          then you will need to prevent <code class="computeroutput"><span class="special">&lt;</span><span class="identifier">boost</span><span class="special">/</span><span class="identifier">math</span><span class="special">/</span><span class="identifier">tr1</span><span class="special">.</span><span class="identifier">hpp</span><span class="special">&gt;</span></code>
+          from trying to auto-link to the binaries that Boost.Build generates. You
+          can do this by defining either BOOST_MATH_NO_LIB or BOOST_ALL_NO_LIB at
+          project level (so the defines get passed to each compiler invocation).
+        </p></td></tr>
+</table></div>
+<p>
+        Optionally the sources in <code class="computeroutput"><span class="identifier">libs</span><span class="special">/</span><span class="identifier">math</span><span class="special">/</span><span class="identifier">src</span><span class="special">/</span><span class="identifier">tr1</span></code>
+        have support for using <code class="computeroutput"><span class="identifier">libs</span><span class="special">/</span><span class="identifier">math</span><span class="special">/</span><span class="identifier">src</span><span class="special">/</span><span class="identifier">tr1</span><span class="special">/</span><span class="identifier">pch</span><span class="special">.</span><span class="identifier">hpp</span></code> as a precompiled header <span class="emphasis"><em>if
+        your compiler supports precompiled headers.</em></span> Note that normally
+        this header is a do-nothing include: to activate the header so that it #includes
+        everything required by all the sources you will need to define BOOST_BUILD_PCH_ENABLED
+        on the command line, both when building the pre-compiled header and when
+        building the sources. Boost.Build will do this automatically when appropriate.
+      </p>
+<a name="math_toolkit.main_overview.building.building_the_examples"></a><h5>
+<a name="id549414"></a>
+        <a class="link" href="building.html#math_toolkit.main_overview.building.building_the_examples">Building
+        the Examples</a>
+      </h5>
+<p>
+        The examples are all located in <code class="computeroutput"><span class="identifier">libs</span><span class="special">/</span><span class="identifier">math</span><span class="special">/</span><span class="identifier">example</span></code>, they can all be built without
+        reference to any external libraries, either with Boost.Build using the supplied
+        Jamfile, or from your compiler's command line. The only requirement is that
+        the Boost headers are in your compilers #include search path.
+      </p>
+<a name="math_toolkit.main_overview.building.building_the_tests"></a><h5>
+<a name="id549480"></a>
+        <a class="link" href="building.html#math_toolkit.main_overview.building.building_the_tests">Building
+        the Tests</a>
+      </h5>
+<p>
+        The tests are located in <code class="computeroutput"><span class="identifier">libs</span><span class="special">/</span><span class="identifier">math</span><span class="special">/</span><span class="identifier">test</span></code> and are best built using Boost.Build
+        and the supplied Jamfile. If you plan to build them separately from your
+        favourite IDE then you will need to add <code class="computeroutput"><span class="identifier">libs</span><span class="special">/</span><span class="identifier">math</span><span class="special">/</span><span class="identifier">test</span></code> to the list of your compiler's search
+        paths.
+      </p>
+<p>
+        You will also need to build and link to the Boost.Regex library for many
+        of the tests: this can built from the command line by following the <a href="http://www.boost.org/doc/libs/release/more/getting_started/index.html" target="_top">getting
+        started guide</a>, using a command such as:
+      </p>
+<pre class="programlisting"><span class="identifier">bjam</span> <span class="identifier">toolset</span><span class="special">=</span><span class="identifier">gcc</span> <span class="special">--</span><span class="identifier">with</span><span class="special">-</span><span class="identifier">regex</span> <span class="identifier">install</span>
+</pre>
+<p>
+        or
+      </p>
+<pre class="programlisting"><span class="identifier">bjam</span> <span class="identifier">toolset</span><span class="special">=</span><span class="identifier">msvc</span> <span class="special">--</span><span class="identifier">with</span><span class="special">-</span><span class="identifier">regex</span> <span class="special">--</span><span class="identifier">build</span><span class="special">-</span><span class="identifier">type</span><span class="special">=</span><span class="identifier">complete</span> <span class="identifier">stage</span>
+</pre>
+<p>
+        depending on whether you are on Linux or Windows.
+      </p>
+<p>
+        Many of the tests have optional precompiled header support using the header
+        <code class="computeroutput"><span class="identifier">libs</span><span class="special">/</span><span class="identifier">math</span><span class="special">/</span><span class="identifier">test</span><span class="special">/</span><span class="identifier">pch</span><span class="special">.</span><span class="identifier">hpp</span></code>. Note that normally this header is
+        a do-nothing include: to activate the header so that it #includes everything
+        required by all the sources you will need to define BOOST_BUILD_PCH_ENABLED
+        on the command line, both when building the pre-compiled header and when
+        building the sources. Boost.Build will do this automatically when appropriate.
+      </p>
+</div>
+<table xmlns:rev="http://www.cs.rpi.edu/~gregod/boost/tools/doc/revision" width="100%"><tr>
+<td align="left"></td>
+<td align="right"><div class="copyright-footer">Copyright © 2006 , 2007, 2008 John Maddock, Paul A. Bristow, Hubert
+      Holin, Xiaogang Zhang, Bruno Lalande and Gautam Sewani<p>
+        Distributed under the Boost Software License, Version 1.0. (See accompanying
+        file LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_0.txt)
+      </p>
+</div></td>
+</tr></table>
+<hr>
+<div class="spirit-nav">
+<a accesskey="p" href="perf_over.html"><img src="../../../../doc/html/images/prev.png" alt="Prev"></a><a accesskey="u" href="../main_overview.html"><img src="../../../../doc/html/images/up.png" alt="Up"></a><a accesskey="h" href="../../index.html"><img src="../../../../doc/html/images/home.png" alt="Home"></a><a accesskey="n" href="history1.html"><img src="../../../../doc/html/images/next.png" alt="Next"></a>
+</div>
+</body>
+</html>

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==============================================================================
--- (empty file)
+++ sandbox/tools/auto_index/example/math/doc/sf_and_dist/html/math_toolkit/main_overview/compilers_overview.html	2008-11-28 05:25:28 EST (Fri, 28 Nov 2008)
@@ -0,0 +1,629 @@
+<html>
+<head>
+<meta http-equiv="Content-Type" content="text/html; charset=ISO-8859-1">
+<title>Compilers</title>
+<link rel="stylesheet" href="../../boostbook.css" type="text/css">
+<meta name="generator" content="DocBook XSL Stylesheets Vsnapshot_8125">
+<link rel="home" href="../../index.html" title="Math Toolkit">
+<link rel="up" href="../main_overview.html" title="Overview">
+<link rel="prev" href="error_handling.html" title="Error Handling">
+<link rel="next" href="pol_overview.html" title="Configuration and Policies">
+</head>
+<body bgcolor="white" text="black" link="#0000FF" vlink="#840084" alink="#0000FF">
+<table cellpadding="2" width="100%"><tr>
+<td valign="top"><img alt="Boost C++ Libraries" width="277" height="86" src="../../../../boost.png"></td>
+<td align="center">Home</td>
+<td align="center">Libraries</td>
+<td align="center">People</td>
+<td align="center">FAQ</td>
+<td align="center">More</td>
+</tr></table>
+<hr>
+<div class="spirit-nav">
+<a accesskey="p" href="error_handling.html"><img src="../../../../doc/html/images/prev.png" alt="Prev"></a><a accesskey="u" href="../main_overview.html"><img src="../../../../doc/html/images/up.png" alt="Up"></a><a accesskey="h" href="../../index.html"><img src="../../../../doc/html/images/home.png" alt="Home"></a><a accesskey="n" href="pol_overview.html"><img src="../../../../doc/html/images/next.png" alt="Next"></a>
+</div>
+<div class="section" lang="en">
+<div class="titlepage"><div><div><h3 class="title">
+<a name="math_toolkit.main_overview.compilers_overview"></a><a class="link" href="compilers_overview.html" title="Compilers"> Compilers</a>
+</h3></div></div></div>
+<p>
+        </p>
+<p>
+          This section contains some information about how various compilers work
+          with this library. It is not comprehensive and updated experiences are
+          always welcome. Some effort has been made to suppress unhelpful warnings
+          but it is difficult to achieve this on all systems.
+        </p>
+<p>
+        </p>
+<div class="table">
+<a name="id547094"></a><p class="title"><b>Table 9. Supported/Tested Compilers</b></p>
+<div class="table-contents"><table class="table" summary="Supported/Tested Compilers">
+<colgroup>
+<col>
+<col>
+<col>
+<col>
+</colgroup>
+<thead><tr>
+<th>
+              <p>
+                Platform
+              </p>
+              </th>
+<th>
+              <p>
+                Compiler
+              </p>
+              </th>
+<th>
+              <p>
+                Has long double support
+              </p>
+              </th>
+<th>
+              <p>
+                Notes
+              </p>
+              </th>
+</tr></thead>
+<tbody>
+<tr>
+<td>
+              <p>
+                Windows
+              </p>
+              </td>
+<td>
+              <p>
+                MSVC 7.1 and later
+              </p>
+              </td>
+<td>
+              <p>
+                Yes
+              </p>
+              </td>
+<td>
+              <p>
+                All tests OK.
+              </p>
+              <p>
+                We aim to keep our headers warning free at level 4 with this compiler.
+              </p>
+              </td>
+</tr>
+<tr>
+<td>
+              <p>
+                Windows
+              </p>
+              </td>
+<td>
+              <p>
+                Intel 8.1 and later
+              </p>
+              </td>
+<td>
+              <p>
+                Yes
+              </p>
+              </td>
+<td>
+              <p>
+                All tests OK.
+              </p>
+              <p>
+                We aim to keep our headers warning free at level 4 with this compiler.
+                However, The tests cases tend to generate a lot of warnings relating
+                to numeric underflow of the test data: these are harmless.
+              </p>
+              </td>
+</tr>
+<tr>
+<td>
+              <p>
+                Windows
+              </p>
+              </td>
+<td>
+              <p>
+                GNU Mingw32 C++
+              </p>
+              </td>
+<td>
+              <p>
+                Yes
+              </p>
+              </td>
+<td>
+              <p>
+                All tests OK.
+              </p>
+              <p>
+                We aim to keep our headers warning free with -Wall with this compiler.
+              </p>
+              </td>
+</tr>
+<tr>
+<td>
+              <p>
+                Windows
+              </p>
+              </td>
+<td>
+              <p>
+                GNU Cygwin C++
+              </p>
+              </td>
+<td>
+              <p>
+                No
+              </p>
+              </td>
+<td>
+              <p>
+                All tests OK.
+              </p>
+              <p>
+                We aim to keep our headers warning free with -Wall with this compiler.
+              </p>
+              <p>
+                Long double support has been disabled because there are no native
+                long double C std library functions available.
+              </p>
+              </td>
+</tr>
+<tr>
+<td>
+              <p>
+                Windows
+              </p>
+              </td>
+<td>
+              <p>
+                Borland C++ 5.8.2 (Developer studio 2006)
+              </p>
+              </td>
+<td>
+              <p>
+                No
+              </p>
+              </td>
+<td>
+              <p>
+                We have only partial compatability with this compiler:
+              </p>
+              <p>
+                Long double support has been disabled because the native long double
+                C standard library functions really only forward to the double versions.
+                This can result in unpredictable behaviour when using the long double
+                overloads: for example <code class="computeroutput"><span class="identifier">sqrtl</span></code>
+                applied to a finite value, can result in an infinite result.
+              </p>
+              <p>
+                Some functions still fail to compile, there are no known workarounds
+                at present.
+              </p>
+              </td>
+</tr>
+<tr>
+<td>
+              <p>
+                Linux
+              </p>
+              </td>
+<td>
+              <p>
+                GNU C++ 3.4 and later
+              </p>
+              </td>
+<td>
+              <p>
+                Yes
+              </p>
+              </td>
+<td>
+              <p>
+                All tests OK.
+              </p>
+              <p>
+                We aim to keep our headers warning free with -Wall with this compiler.
+              </p>
+              </td>
+</tr>
+<tr>
+<td>
+              <p>
+                Linux
+              </p>
+              </td>
+<td>
+              <p>
+                Intel C++ 10.0 and later
+              </p>
+              </td>
+<td>
+              <p>
+                Yes
+              </p>
+              </td>
+<td>
+              <p>
+                All tests OK.
+              </p>
+              <p>
+                We aim to keep our headers warning free with -Wall with this compiler.
+                However, The tests cases tend to generate a lot of warnings relating
+                to numeric underflow of the test data: these are harmless.
+              </p>
+              </td>
+</tr>
+<tr>
+<td>
+              <p>
+                Linux
+              </p>
+              </td>
+<td>
+              <p>
+                Intel C++ 8.1 and 9.1
+              </p>
+              </td>
+<td>
+              <p>
+                No
+              </p>
+              </td>
+<td>
+              <p>
+                All tests OK.
+              </p>
+              <p>
+                Long double support has been disabled with these compiler releases
+                because calling the standard library long double math functions can
+                result in a segfault. The issue is Linux distribution and glibc version
+                specific and is Intel bug report #409291. Fully up to date releases
+                of Intel 9.1 (post version l_cc_c_9.1.046) shouldn't have this problem.
+                If you need long double support with this compiler, then comment
+                out the define of BOOST_MATH_NO_LONG_DOUBLE_MATH_FUNCTIONS at line
+                55 of boost/math/tools/config.hpp.
+              </p>
+              <p>
+                We aim to keep our headers warning free with -Wall with this compiler.
+                However, The tests cases tend to generate a lot of warnings relating
+                to numeric underflow of the test data: these are harmless.
+              </p>
+              </td>
+</tr>
+<tr>
+<td>
+              <p>
+                Linux
+              </p>
+              </td>
+<td>
+              <p>
+                QLogic PathScale 3.0
+              </p>
+              </td>
+<td>
+              <p>
+                Yes
+              </p>
+              </td>
+<td>
+              <p>
+                Some tests involving conceptual checks fail to build, otherwise there
+                appear to be no issues.
+              </p>
+              </td>
+</tr>
+<tr>
+<td>
+              <p>
+                Linux
+              </p>
+              </td>
+<td>
+              <p>
+                Sun Studio 12
+              </p>
+              </td>
+<td>
+              <p>
+                Yes
+              </p>
+              </td>
+<td>
+              <p>
+                Some tests involving function overload resolution fail to build,
+                these issues should be rairly encountered in practice.
+              </p>
+              </td>
+</tr>
+<tr>
+<td>
+              <p>
+                Solaris
+              </p>
+              </td>
+<td>
+              <p>
+                Sun Studio 12
+              </p>
+              </td>
+<td>
+              <p>
+                Yes
+              </p>
+              </td>
+<td>
+              <p>
+                Some tests involving function overload resolution fail to build,
+                these issues should be rairly encountered in practice.
+              </p>
+              </td>
+</tr>
+<tr>
+<td>
+              <p>
+                Solaris
+              </p>
+              </td>
+<td>
+              <p>
+                GNU C++ 4.x
+              </p>
+              </td>
+<td>
+              <p>
+                Yes
+              </p>
+              </td>
+<td>
+              <p>
+                All tests OK.
+              </p>
+              <p>
+                We aim to keep our headers warning free with -Wall with this compiler.
+              </p>
+              </td>
+</tr>
+<tr>
+<td>
+              <p>
+                HP Tru64
+              </p>
+              </td>
+<td>
+              <p>
+                Compaq C++ 7.1
+              </p>
+              </td>
+<td>
+              <p>
+                Yes
+              </p>
+              </td>
+<td>
+              <p>
+                All tests OK.
+              </p>
+              </td>
+</tr>
+<tr>
+<td>
+              <p>
+                HP-UX Itanium
+              </p>
+              </td>
+<td>
+              <p>
+                HP aCC 6.x
+              </p>
+              </td>
+<td>
+              <p>
+                Yes
+              </p>
+              </td>
+<td>
+              <p>
+                All tests OK.
+              </p>
+              <p>
+                Unfortunately this compiler emits quite a few warnings from libraries
+                upon which we depend (TR1, Array etc).
+              </p>
+              </td>
+</tr>
+<tr>
+<td>
+              <p>
+                HP-UX PA-RISC
+              </p>
+              </td>
+<td>
+              <p>
+                GNU C++ 3.4
+              </p>
+              </td>
+<td>
+              <p>
+                No
+              </p>
+              </td>
+<td>
+              <p>
+                All tests OK.
+              </p>
+              </td>
+</tr>
+<tr>
+<td>
+              <p>
+                Apple Mac OS X, Intel
+              </p>
+              </td>
+<td>
+              <p>
+                Darwin/GNU C++ 4.x
+              </p>
+              </td>
+<td>
+              <p>
+                Yes
+              </p>
+              </td>
+<td>
+              <p>
+                All tests OK.
+              </p>
+              </td>
+</tr>
+<tr>
+<td>
+              <p>
+                Apple Mac OS X, PowerPC
+              </p>
+              </td>
+<td>
+              <p>
+                Darwin/GNU C++ 4.x
+              </p>
+              </td>
+<td>
+              <p>
+                No
+              </p>
+              </td>
+<td>
+              <p>
+                All tests OK.
+              </p>
+              <p>
+                Long double support has been disabled on this platform due to the
+                rather strange nature of Darwin's 106-bit long double implementation.
+                It should be possible to make this work if someone is prepared to
+                offer assistance.
+              </p>
+              </td>
+</tr>
+<tr>
+<td>
+              <p>
+                IMB AIX
+              </p>
+              </td>
+<td>
+              <p>
+                IBM xlc 5.3
+              </p>
+              </td>
+<td>
+              <p>
+                Yes
+              </p>
+              </td>
+<td>
+              <p>
+                All tests pass except for our fpclassify tests which fail due to
+                a bug in <code class="computeroutput"><span class="identifier">std</span><span class="special">::</span><span class="identifier">numeric_limits</span></code>, the bug effects
+                the test code, not fpclassify itself. The IBM compiler group are
+                aware of the problem.
+              </p>
+              </td>
+</tr>
+</tbody>
+</table></div>
+</div>
+<p><br class="table-break"> </p>
+<div class="table">
+<a name="id548103"></a><p class="title"><b>Table 10. Unsupported Compilers</b></p>
+<div class="table-contents"><table class="table" summary="Unsupported Compilers">
+<colgroup>
+<col>
+<col>
+</colgroup>
+<thead><tr>
+<th>
+              <p>
+                Platform
+              </p>
+              </th>
+<th>
+              <p>
+                Compiler
+              </p>
+              </th>
+</tr></thead>
+<tbody>
+<tr>
+<td>
+              <p>
+                Windows
+              </p>
+              </td>
+<td>
+              <p>
+                Borland C++ 5.9.2 (Borland Developer Studio 2007)
+              </p>
+              </td>
+</tr>
+<tr>
+<td>
+              <p>
+                Windows
+              </p>
+              </td>
+<td>
+              <p>
+                MSVC 6 and 7
+              </p>
+              </td>
+</tr>
+</tbody>
+</table></div>
+</div>
+<p><br class="table-break">
+        </p>
+<p>
+          If you're compiler or platform is not listed above, please try running
+          the regression tests: cd into boost-root/libs/math/test and do a:
+        </p>
+<p>
+        
+</p>
+<pre class="programlisting"><span class="identifier">bjam</span> <span class="identifier">mytoolset</span>
+</pre>
+<p>
+        </p>
+<p>
+          where "mytoolset" is the name of the Boost.Build
+          toolset used for your compiler. The chances are that <span class="bold"><strong>many
+          of the accuracy tests will fail at this stage</strong></span> - don't panic
+          - the default acceptable error tolerances are quite tight, especially for
+          long double types with an extended exponent range (these cause more extreme
+          test cases to be executed for some functions). You will need to cast an
+          eye over the output from the failing tests and make a judgement as to whether
+          the error rates are acceptable or not.
+        </p>
+<p>
+      </p>
+</div>
+<table xmlns:rev="http://www.cs.rpi.edu/~gregod/boost/tools/doc/revision" width="100%"><tr>
+<td align="left"></td>
+<td align="right"><div class="copyright-footer">Copyright © 2006 , 2007, 2008 John Maddock, Paul A. Bristow, Hubert
+      Holin, Xiaogang Zhang, Bruno Lalande and Gautam Sewani<p>
+        Distributed under the Boost Software License, Version 1.0. (See accompanying
+        file LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_0.txt)
+      </p>
+</div></td>
+</tr></table>
+<hr>
+<div class="spirit-nav">
+<a accesskey="p" href="error_handling.html"><img src="../../../../doc/html/images/prev.png" alt="Prev"></a><a accesskey="u" href="../main_overview.html"><img src="../../../../doc/html/images/up.png" alt="Up"></a><a accesskey="h" href="../../index.html"><img src="../../../../doc/html/images/home.png" alt="Home"></a><a accesskey="n" href="pol_overview.html"><img src="../../../../doc/html/images/next.png" alt="Next"></a>
+</div>
+</body>
+</html>

Added: sandbox/tools/auto_index/example/math/doc/sf_and_dist/html/math_toolkit/main_overview/contact.html
==============================================================================
--- (empty file)
+++ sandbox/tools/auto_index/example/math/doc/sf_and_dist/html/math_toolkit/main_overview/contact.html	2008-11-28 05:25:28 EST (Fri, 28 Nov 2008)
@@ -0,0 +1,62 @@
+<html>
+<head>
+<meta http-equiv="Content-Type" content="text/html; charset=ISO-8859-1">
+<title>Contact Info and Support</title>
+<link rel="stylesheet" href="../../boostbook.css" type="text/css">
+<meta name="generator" content="DocBook XSL Stylesheets Vsnapshot_8125">
+<link rel="home" href="../../index.html" title="Math Toolkit">
+<link rel="up" href="../main_overview.html" title="Overview">
+<link rel="prev" href="tr1.html" title="C99 and TR1 C Functions">
+<link rel="next" href="../dist.html" title="Statistical Distributions and Functions">
+</head>
+<body bgcolor="white" text="black" link="#0000FF" vlink="#840084" alink="#0000FF">
+<table cellpadding="2" width="100%"><tr>
+<td valign="top"><img alt="Boost C++ Libraries" width="277" height="86" src="../../../../boost.png"></td>
+<td align="center">Home</td>
+<td align="center">Libraries</td>
+<td align="center">People</td>
+<td align="center">FAQ</td>
+<td align="center">More</td>
+</tr></table>
+<hr>
+<div class="spirit-nav">
+<a accesskey="p" href="tr1.html"><img src="../../../../doc/html/images/prev.png" alt="Prev"></a><a accesskey="u" href="../main_overview.html"><img src="../../../../doc/html/images/up.png" alt="Up"></a><a accesskey="h" href="../../index.html"><img src="../../../../doc/html/images/home.png" alt="Home"></a><a accesskey="n" href="../dist.html"><img src="../../../../doc/html/images/next.png" alt="Next"></a>
+</div>
+<div class="section" lang="en">
+<div class="titlepage"><div><div><h3 class="title">
+<a name="math_toolkit.main_overview.contact"></a><a class="link" href="contact.html" title="Contact Info and Support"> Contact Info and
+      Support</a>
+</h3></div></div></div>
+<p>
+        The main support for this library is via the Boost mailing lists:
+      </p>
+<div class="itemizedlist"><ul type="disc">
+<li>
+          Use the <a href="http://www.boost.org/more/mailing_lists.htm#users" target="_top">boost-user
+          list</a> for general support questions.
+        </li>
+<li>
+          Use the <a href="http://www.boost.org/more/mailing_lists.htm#main" target="_top">boost-developer
+          list</a> for discussion about implementation and or submission of extensions.
+        </li>
+</ul></div>
+<p>
+        You can also find JM at john - at - johnmaddock.co.uk and PAB at pbristow
+        - at - hetp.u-net.com.
+      </p>
+</div>
+<table xmlns:rev="http://www.cs.rpi.edu/~gregod/boost/tools/doc/revision" width="100%"><tr>
+<td align="left"></td>
+<td align="right"><div class="copyright-footer">Copyright © 2006 , 2007, 2008 John Maddock, Paul A. Bristow, Hubert
+      Holin, Xiaogang Zhang, Bruno Lalande and Gautam Sewani<p>
+        Distributed under the Boost Software License, Version 1.0. (See accompanying
+        file LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_0.txt)
+      </p>
+</div></td>
+</tr></table>
+<hr>
+<div class="spirit-nav">
+<a accesskey="p" href="tr1.html"><img src="../../../../doc/html/images/prev.png" alt="Prev"></a><a accesskey="u" href="../main_overview.html"><img src="../../../../doc/html/images/up.png" alt="Up"></a><a accesskey="h" href="../../index.html"><img src="../../../../doc/html/images/home.png" alt="Home"></a><a accesskey="n" href="../dist.html"><img src="../../../../doc/html/images/next.png" alt="Next"></a>
+</div>
+</body>
+</html>

Added: sandbox/tools/auto_index/example/math/doc/sf_and_dist/html/math_toolkit/main_overview/directories.html
==============================================================================
--- (empty file)
+++ sandbox/tools/auto_index/example/math/doc/sf_and_dist/html/math_toolkit/main_overview/directories.html	2008-11-28 05:25:28 EST (Fri, 28 Nov 2008)
@@ -0,0 +1,124 @@
+<html>
+<head>
+<meta http-equiv="Content-Type" content="text/html; charset=ISO-8859-1">
+<title>Directory and File Structure</title>
+<link rel="stylesheet" href="../../boostbook.css" type="text/css">
+<meta name="generator" content="DocBook XSL Stylesheets Vsnapshot_8125">
+<link rel="home" href="../../index.html" title="Math Toolkit">
+<link rel="up" href="../main_overview.html" title="Overview">
+<link rel="prev" href="navigation.html" title="Navigation">
+<link rel="next" href="namespaces.html" title="Namespaces">
+</head>
+<body bgcolor="white" text="black" link="#0000FF" vlink="#840084" alink="#0000FF">
+<table cellpadding="2" width="100%"><tr>
+<td valign="top"><img alt="Boost C++ Libraries" width="277" height="86" src="../../../../boost.png"></td>
+<td align="center">Home</td>
+<td align="center">Libraries</td>
+<td align="center">People</td>
+<td align="center">FAQ</td>
+<td align="center">More</td>
+</tr></table>
+<hr>
+<div class="spirit-nav">
+<a accesskey="p" href="navigation.html"><img src="../../../../doc/html/images/prev.png" alt="Prev"></a><a accesskey="u" href="../main_overview.html"><img src="../../../../doc/html/images/up.png" alt="Up"></a><a accesskey="h" href="../../index.html"><img src="../../../../doc/html/images/home.png" alt="Home"></a><a accesskey="n" href="namespaces.html"><img src="../../../../doc/html/images/next.png" alt="Next"></a>
+</div>
+<div class="section" lang="en">
+<div class="titlepage"><div><div><h3 class="title">
+<a name="math_toolkit.main_overview.directories"></a><a class="link" href="directories.html" title="Directory and File Structure"> Directory and
+      File Structure</a>
+</h3></div></div></div>
+<a name="math_toolkit.main_overview.directories.boost_math"></a><h5>
+<a name="id475210"></a>
+        <a class="link" href="directories.html#math_toolkit.main_overview.directories.boost_math">boost/math</a>
+      </h5>
+<div class="variablelist">
+<p class="title"><b></b></p>
+<dl>
+<dt><span class="term">/concepts/</span></dt>
+<dd><p>
+            Prototype defining the <span class="bold"><strong>essential</strong></span> features
+            of a RealType class (see real_concept.hpp). Most applications will use
+            <code class="computeroutput"><span class="keyword">double</span></code> as the RealType (and
+            short <code class="computeroutput"><span class="keyword">typedef</span></code> names of distributions
+            are reserved for this type where possible), a few will use <code class="computeroutput"><span class="keyword">float</span></code> or <code class="computeroutput"><span class="keyword">long</span>
+            <span class="keyword">double</span></code>, but it is also possible
+            to use higher precision types like NTL::RR
+            that conform to the requirements specified by real_concept.
+          </p></dd>
+<dt><span class="term">/constants/</span></dt>
+<dd><p>
+            Templated definition of some highly accurate math constants (in constants.hpp).
+          </p></dd>
+<dt><span class="term">/distributions/</span></dt>
+<dd><p>
+            Distributions used in mathematics and, especially, statistics: Gaussian,
+            Students-t, Fisher, Binomial etc
+          </p></dd>
+<dt><span class="term">/policies/</span></dt>
+<dd><p>
+            Policy framework, for handling user requested behaviour modifications.
+          </p></dd>
+<dt><span class="term">/special_functions/</span></dt>
+<dd><p>
+            Math functions generally regarded as 'special', like beta, cbrt, erf,
+            gamma, lgamma, tgamma ... (Some of these are specified in C++, and C99/TR1,
+            and perhaps TR2).
+          </p></dd>
+<dt><span class="term">/tools/</span></dt>
+<dd><p>
+            Tools used by functions, like evaluating polynomials, continued fractions,
+            root finding, precision and limits, and by tests. Some will find application
+            outside this package.
+          </p></dd>
+</dl>
+</div>
+<a name="math_toolkit.main_overview.directories.boost_libs"></a><h5>
+<a name="id485575"></a>
+        <a class="link" href="directories.html#math_toolkit.main_overview.directories.boost_libs">boost/libs</a>
+      </h5>
+<div class="variablelist">
+<p class="title"><b></b></p>
+<dl>
+<dt><span class="term">/doc/</span></dt>
+<dd><p>
+            Documentation source files in Quickbook format processed into html and
+            pdf formats.
+          </p></dd>
+<dt><span class="term">/examples/</span></dt>
+<dd><p>
+            Examples and demos of using math functions and distributions.
+          </p></dd>
+<dt><span class="term">/performance/</span></dt>
+<dd><p>
+            Performance testing and tuning program.
+          </p></dd>
+<dt><span class="term">/test/</span></dt>
+<dd><p>
+            Test files, in various .cpp files, most using Boost.Test (some with test
+            data as .ipp files, usually generated using NTL RR type with ample precision
+            for the type, often for precisions suitable for up to 256-bit significand
+            real types).
+          </p></dd>
+<dt><span class="term">/tools/</span></dt>
+<dd><p>
+            Programs used to generate test data. Also changes to the NTL
+            released package to provide a few additional (and vital) extra features.
+          </p></dd>
+</dl>
+</div>
+</div>
+<table xmlns:rev="http://www.cs.rpi.edu/~gregod/boost/tools/doc/revision" width="100%"><tr>
+<td align="left"></td>
+<td align="right"><div class="copyright-footer">Copyright © 2006 , 2007, 2008 John Maddock, Paul A. Bristow, Hubert
+      Holin, Xiaogang Zhang, Bruno Lalande and Gautam Sewani<p>
+        Distributed under the Boost Software License, Version 1.0. (See accompanying
+        file LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_0.txt)
+      </p>
+</div></td>
+</tr></table>
+<hr>
+<div class="spirit-nav">
+<a accesskey="p" href="navigation.html"><img src="../../../../doc/html/images/prev.png" alt="Prev"></a><a accesskey="u" href="../main_overview.html"><img src="../../../../doc/html/images/up.png" alt="Up"></a><a accesskey="h" href="../../index.html"><img src="../../../../doc/html/images/home.png" alt="Home"></a><a accesskey="n" href="namespaces.html"><img src="../../../../doc/html/images/next.png" alt="Next"></a>
+</div>
+</body>
+</html>

Added: sandbox/tools/auto_index/example/math/doc/sf_and_dist/html/math_toolkit/main_overview/error_handling.html
==============================================================================
--- (empty file)
+++ sandbox/tools/auto_index/example/math/doc/sf_and_dist/html/math_toolkit/main_overview/error_handling.html	2008-11-28 05:25:28 EST (Fri, 28 Nov 2008)
@@ -0,0 +1,1124 @@
+<html>
+<head>
+<meta http-equiv="Content-Type" content="text/html; charset=ISO-8859-1">
+<title>Error Handling</title>
+<link rel="stylesheet" href="../../boostbook.css" type="text/css">
+<meta name="generator" content="DocBook XSL Stylesheets Vsnapshot_8125">
+<link rel="home" href="../../index.html" title="Math Toolkit">
+<link rel="up" href="../main_overview.html" title="Overview">
+<link rel="prev" href="result_type.html" title="Calculation of the Type of the Result">
+<link rel="next" href="compilers_overview.html" title="Compilers">
+</head>
+<body bgcolor="white" text="black" link="#0000FF" vlink="#840084" alink="#0000FF">
+<table cellpadding="2" width="100%"><tr>
+<td valign="top"><img alt="Boost C++ Libraries" width="277" height="86" src="../../../../boost.png"></td>
+<td align="center">Home</td>
+<td align="center">Libraries</td>
+<td align="center">People</td>
+<td align="center">FAQ</td>
+<td align="center">More</td>
+</tr></table>
+<hr>
+<div class="spirit-nav">
+<a accesskey="p" href="result_type.html"><img src="../../../../doc/html/images/prev.png" alt="Prev"></a><a accesskey="u" href="../main_overview.html"><img src="../../../../doc/html/images/up.png" alt="Up"></a><a accesskey="h" href="../../index.html"><img src="../../../../doc/html/images/home.png" alt="Home"></a><a accesskey="n" href="compilers_overview.html"><img src="../../../../doc/html/images/next.png" alt="Next"></a>
+</div>
+<div class="section" lang="en">
+<div class="titlepage"><div><div><h3 class="title">
+<a name="math_toolkit.main_overview.error_handling"></a><a class="link" href="error_handling.html" title="Error Handling"> Error Handling</a>
+</h3></div></div></div>
+<a name="math_toolkit.main_overview.error_handling.quick_reference"></a><h5>
+<a name="id542219"></a>
+        <a class="link" href="error_handling.html#math_toolkit.main_overview.error_handling.quick_reference">Quick
+        Reference</a>
+      </h5>
+<p>
+        Handling of errors by this library is split into two orthogonal parts:
+      </p>
+<div class="itemizedlist"><ul type="disc">
+<li>
+          What kind of error has been raised?
+        </li>
+<li>
+          What should be done when the error is raised?
+        </li>
+</ul></div>
+<p>
+        The kinds of errors that can be raised are:
+      </p>
+<div class="variablelist">
+<p class="title"><b></b></p>
+<dl>
+<dt><span class="term">Domain Error</span></dt>
+<dd><p>
+            Occurs when one or more arguments to a function are out of range.
+          </p></dd>
+<dt><span class="term">Pole Error</span></dt>
+<dd><p>
+            Occurs when the particular arguments cause the function to be evaluated
+            at a pole with no well defined residual value. For example if <a class="link" href="../special/sf_gamma/tgamma.html" title="Gamma">tgamma</a>
+            is evaluated at exactly -2, the function approaches different limiting
+            values depending upon whether you approach from just above or just below
+            -2. Hence the function has no well defined value at this point and a
+            Pole Error will be raised.
+          </p></dd>
+<dt><span class="term">Overflow Error</span></dt>
+<dd><p>
+            Occurs when the result is either infinite, or too large to represent
+            in the numeric type being returned by the function.
+          </p></dd>
+<dt><span class="term">Underflow Error</span></dt>
+<dd><p>
+            Occurs when the result is not zero, but is too small to be represented
+            by any other value in the type being returned by the function.
+          </p></dd>
+<dt><span class="term">Denormalisation Error</span></dt>
+<dd><p>
+            Occurs when the returned result would be a denormalised value.
+          </p></dd>
+<dt><span class="term">Rounding Error</span></dt>
+<dd><p>
+            Occurs when the argument to one of the rounding functions <a class="link" href="../special/rounding/trunc.html" title="Truncation Functions">trunc</a>,
+            <a class="link" href="../special/rounding/round.html" title="Rounding Functions">round</a> and
+            <a class="link" href="../special/rounding/modf.html" title="Integer and Fractional Part Splitting (modf)">modf</a> can not
+            be represented as an integer type, is is outide the range of the result
+            type.
+          </p></dd>
+<dt><span class="term">Evaluation Error</span></dt>
+<dd><p>
+            Occurs when an internal error occured that prevented the result from
+            being evaluated: this should never occur, but if it does, then it's likely
+            to be due to an iterative method not converging fast enough.
+          </p></dd>
+<dt><span class="term">Indeterminate Result Error</span></dt>
+<dd><p>
+            Occurs when the result of a function is not defined for the values that
+            were passed to it.
+          </p></dd>
+</dl>
+</div>
+<p>
+        The action undertaken by each error condition is determined by the current
+        <a class="link" href="../policy.html" title="Policies">Policy</a> in effect. This can be
+        changed program-wide by setting some configuration macros, or at namespace
+        scope, or at the call site (by specifying a specific policy in the function
+        call).
+      </p>
+<p>
+        The available actions are:
+      </p>
+<div class="variablelist">
+<p class="title"><b></b></p>
+<dl>
+<dt><span class="term">throw_on_error</span></dt>
+<dd><p>
+            Throws the exception most appropriate to the error condition.
+          </p></dd>
+<dt><span class="term">errno_on_error</span></dt>
+<dd><p>
+            Sets ::errno to an appropriate value, and then returns the most appropriate
+            result
+          </p></dd>
+<dt><span class="term">ignore_error</span></dt>
+<dd><p>
+            Ignores the error and simply the returns the most appropriate result.
+          </p></dd>
+<dt><span class="term">user_error</span></dt>
+<dd><p>
+            Calls a <a class="link" href="../policy/pol_tutorial/user_def_err_pol.html" title="Calling User Defined Error Handlers">user-supplied
+            error handler</a>.
+          </p></dd>
+</dl>
+</div>
+<p>
+        The following tables show all the permutations of errors and actions, with
+        the default action for each error shown in bold:
+      </p>
+<div class="table">
+<a name="id542548"></a><p class="title"><b>Table 1. Possible Actions for Domain Errors</b></p>
+<div class="table-contents"><table class="table" summary="Possible Actions for Domain Errors">
+<colgroup>
+<col>
+<col>
+</colgroup>
+<thead><tr>
+<th>
+            <p>
+              Action
+            </p>
+            </th>
+<th>
+            <p>
+              Behaviour
+            </p>
+            </th>
+</tr></thead>
+<tbody>
+<tr>
+<td>
+            <p>
+              throw_on_error
+            </p>
+            </td>
+<td>
+            <p>
+              <span class="bold"><strong>Throws <code class="computeroutput"><span class="identifier">std</span><span class="special">::</span><span class="identifier">domain_error</span></code></strong></span>
+            </p>
+            </td>
+</tr>
+<tr>
+<td>
+            <p>
+              errno_on_error
+            </p>
+            </td>
+<td>
+            <p>
+              Sets <code class="computeroutput"><span class="special">::</span><span class="identifier">errno</span></code>
+              to <code class="computeroutput"><span class="identifier">EDOM</span></code> and returns
+              <code class="computeroutput"><span class="identifier">std</span><span class="special">::</span><span class="identifier">numeric_limits</span><span class="special">&lt;</span><span class="identifier">T</span><span class="special">&gt;::</span><span class="identifier">quiet_NaN</span><span class="special">()</span></code>
+            </p>
+            </td>
+</tr>
+<tr>
+<td>
+            <p>
+              ignore_error
+            </p>
+            </td>
+<td>
+            <p>
+              Returns <code class="computeroutput"><span class="identifier">std</span><span class="special">::</span><span class="identifier">numeric_limits</span><span class="special">&lt;</span><span class="identifier">T</span><span class="special">&gt;::</span><span class="identifier">quiet_NaN</span><span class="special">()</span></code>
+            </p>
+            </td>
+</tr>
+<tr>
+<td>
+            <p>
+              user_error
+            </p>
+            </td>
+<td>
+            <p>
+              Returns the result of <code class="computeroutput"><span class="identifier">boost</span><span class="special">::</span><span class="identifier">math</span><span class="special">::</span><span class="identifier">policies</span><span class="special">::</span><span class="identifier">user_domain_error</span></code>:
+              <a class="link" href="../policy/pol_tutorial/user_def_err_pol.html" title="Calling User Defined Error Handlers">this
+              function must be defined by the user</a>.
+            </p>
+            </td>
+</tr>
+</tbody>
+</table></div>
+</div>
+<br class="table-break"><div class="table">
+<a name="id542845"></a><p class="title"><b>Table 2. Possible Actions for Pole Errors</b></p>
+<div class="table-contents"><table class="table" summary="Possible Actions for Pole Errors">
+<colgroup>
+<col>
+<col>
+</colgroup>
+<thead><tr>
+<th>
+            <p>
+              Action
+            </p>
+            </th>
+<th>
+            <p>
+              Behaviour
+            </p>
+            </th>
+</tr></thead>
+<tbody>
+<tr>
+<td>
+            <p>
+              throw_on_error
+            </p>
+            </td>
+<td>
+            <p>
+              <span class="bold"><strong>Throws <code class="computeroutput"><span class="identifier">std</span><span class="special">::</span><span class="identifier">domain_error</span></code></strong></span>
+            </p>
+            </td>
+</tr>
+<tr>
+<td>
+            <p>
+              errno_on_error
+            </p>
+            </td>
+<td>
+            <p>
+              Sets <code class="computeroutput"><span class="special">::</span><span class="identifier">errno</span></code>
+              to <code class="computeroutput"><span class="identifier">EDOM</span></code> and returns
+              <code class="computeroutput"><span class="identifier">std</span><span class="special">::</span><span class="identifier">numeric_limits</span><span class="special">&lt;</span><span class="identifier">T</span><span class="special">&gt;::</span><span class="identifier">quiet_NaN</span><span class="special">()</span></code>
+            </p>
+            </td>
+</tr>
+<tr>
+<td>
+            <p>
+              ignore_error
+            </p>
+            </td>
+<td>
+            <p>
+              Returns <code class="computeroutput"><span class="identifier">std</span><span class="special">::</span><span class="identifier">numeric_limits</span><span class="special">&lt;</span><span class="identifier">T</span><span class="special">&gt;::</span><span class="identifier">quiet_NaN</span><span class="special">()</span></code>
+            </p>
+            </td>
+</tr>
+<tr>
+<td>
+            <p>
+              user_error
+            </p>
+            </td>
+<td>
+            <p>
+              Returns the result of <code class="computeroutput"><span class="identifier">boost</span><span class="special">::</span><span class="identifier">math</span><span class="special">::</span><span class="identifier">policies</span><span class="special">::</span><span class="identifier">user_pole_error</span></code>:
+              <a class="link" href="../policy/pol_tutorial/user_def_err_pol.html" title="Calling User Defined Error Handlers">this
+              function must be defined by the user</a>.
+            </p>
+            </td>
+</tr>
+</tbody>
+</table></div>
+</div>
+<br class="table-break"><div class="table">
+<a name="id543140"></a><p class="title"><b>Table 3. Possible Actions for Overflow Errors</b></p>
+<div class="table-contents"><table class="table" summary="Possible Actions for Overflow Errors">
+<colgroup>
+<col>
+<col>
+</colgroup>
+<thead><tr>
+<th>
+            <p>
+              Action
+            </p>
+            </th>
+<th>
+            <p>
+              Behaviour
+            </p>
+            </th>
+</tr></thead>
+<tbody>
+<tr>
+<td>
+            <p>
+              throw_on_error
+            </p>
+            </td>
+<td>
+            <p>
+              <span class="bold"><strong>Throws <code class="computeroutput"><span class="identifier">std</span><span class="special">::</span><span class="identifier">overflow_error</span></code></strong></span>
+            </p>
+            </td>
+</tr>
+<tr>
+<td>
+            <p>
+              errno_on_error
+            </p>
+            </td>
+<td>
+            <p>
+              Sets <code class="computeroutput"><span class="special">::</span><span class="identifier">errno</span></code>
+              to <code class="computeroutput"><span class="identifier">ERANGE</span></code> and returns
+              <code class="computeroutput"><span class="identifier">std</span><span class="special">::</span><span class="identifier">numeric_limits</span><span class="special">&lt;</span><span class="identifier">T</span><span class="special">&gt;::</span><span class="identifier">infinity</span><span class="special">()</span></code>
+            </p>
+            </td>
+</tr>
+<tr>
+<td>
+            <p>
+              ignore_error
+            </p>
+            </td>
+<td>
+            <p>
+              Returns <code class="computeroutput"><span class="identifier">std</span><span class="special">::</span><span class="identifier">numeric_limits</span><span class="special">&lt;</span><span class="identifier">T</span><span class="special">&gt;::</span><span class="identifier">infinity</span><span class="special">()</span></code>
+            </p>
+            </td>
+</tr>
+<tr>
+<td>
+            <p>
+              user_error
+            </p>
+            </td>
+<td>
+            <p>
+              Returns the result of <code class="computeroutput"><span class="identifier">boost</span><span class="special">::</span><span class="identifier">math</span><span class="special">::</span><span class="identifier">policies</span><span class="special">::</span><span class="identifier">user_overflow_error</span></code>:
+              <a class="link" href="../policy/pol_tutorial/user_def_err_pol.html" title="Calling User Defined Error Handlers">this
+              function must be defined by the user</a>.
+            </p>
+            </td>
+</tr>
+</tbody>
+</table></div>
+</div>
+<br class="table-break"><div class="table">
+<a name="id543437"></a><p class="title"><b>Table 4. Possible Actions for Underflow Errors</b></p>
+<div class="table-contents"><table class="table" summary="Possible Actions for Underflow Errors">
+<colgroup>
+<col>
+<col>
+</colgroup>
+<thead><tr>
+<th>
+            <p>
+              Action
+            </p>
+            </th>
+<th>
+            <p>
+              Behaviour
+            </p>
+            </th>
+</tr></thead>
+<tbody>
+<tr>
+<td>
+            <p>
+              throw_on_error
+            </p>
+            </td>
+<td>
+            <p>
+              Throws <code class="computeroutput"><span class="identifier">std</span><span class="special">::</span><span class="identifier">underflow_error</span></code>
+            </p>
+            </td>
+</tr>
+<tr>
+<td>
+            <p>
+              errno_on_error
+            </p>
+            </td>
+<td>
+            <p>
+              Sets <code class="computeroutput"><span class="special">::</span><span class="identifier">errno</span></code>
+              to <code class="computeroutput"><span class="identifier">ERANGE</span></code> and returns
+              0.
+            </p>
+            </td>
+</tr>
+<tr>
+<td>
+            <p>
+              ignore_error
+            </p>
+            </td>
+<td>
+            <p>
+              <span class="bold"><strong>Returns 0</strong></span>
+            </p>
+            </td>
+</tr>
+<tr>
+<td>
+            <p>
+              user_error
+            </p>
+            </td>
+<td>
+            <p>
+              Returns the result of <code class="computeroutput"><span class="identifier">boost</span><span class="special">::</span><span class="identifier">math</span><span class="special">::</span><span class="identifier">policies</span><span class="special">::</span><span class="identifier">user_underflow_error</span></code>:
+              <a class="link" href="../policy/pol_tutorial/user_def_err_pol.html" title="Calling User Defined Error Handlers">this
+              function must be defined by the user</a>.
+            </p>
+            </td>
+</tr>
+</tbody>
+</table></div>
+</div>
+<br class="table-break"><div class="table">
+<a name="id543652"></a><p class="title"><b>Table 5. Possible Actions for Denorm Errors</b></p>
+<div class="table-contents"><table class="table" summary="Possible Actions for Denorm Errors">
+<colgroup>
+<col>
+<col>
+</colgroup>
+<thead><tr>
+<th>
+            <p>
+              Action
+            </p>
+            </th>
+<th>
+            <p>
+              Behaviour
+            </p>
+            </th>
+</tr></thead>
+<tbody>
+<tr>
+<td>
+            <p>
+              throw_on_error
+            </p>
+            </td>
+<td>
+            <p>
+              Throws <code class="computeroutput"><span class="identifier">std</span><span class="special">::</span><span class="identifier">underflow_error</span></code>
+            </p>
+            </td>
+</tr>
+<tr>
+<td>
+            <p>
+              errno_on_error
+            </p>
+            </td>
+<td>
+            <p>
+              Sets <code class="computeroutput"><span class="special">::</span><span class="identifier">errno</span></code>
+              to <code class="computeroutput"><span class="identifier">ERANGE</span></code> and returns
+              the denormalised value.
+            </p>
+            </td>
+</tr>
+<tr>
+<td>
+            <p>
+              ignore_error
+            </p>
+            </td>
+<td>
+            <p>
+              <span class="bold"><strong>Returns the denormalised value.</strong></span>
+            </p>
+            </td>
+</tr>
+<tr>
+<td>
+            <p>
+              user_error
+            </p>
+            </td>
+<td>
+            <p>
+              Returns the result of <code class="computeroutput"><span class="identifier">boost</span><span class="special">::</span><span class="identifier">math</span><span class="special">::</span><span class="identifier">policies</span><span class="special">::</span><span class="identifier">user_denorm_error</span></code>:
+              <a class="link" href="../policy/pol_tutorial/user_def_err_pol.html" title="Calling User Defined Error Handlers">this
+              function must be defined by the user</a>.
+            </p>
+            </td>
+</tr>
+</tbody>
+</table></div>
+</div>
+<br class="table-break"><div class="table">
+<a name="id543868"></a><p class="title"><b>Table 6. Possible Actions for Rounding Errors</b></p>
+<div class="table-contents"><table class="table" summary="Possible Actions for Rounding Errors">
+<colgroup>
+<col>
+<col>
+</colgroup>
+<thead><tr>
+<th>
+            <p>
+              Action
+            </p>
+            </th>
+<th>
+            <p>
+              Behaviour
+            </p>
+            </th>
+</tr></thead>
+<tbody>
+<tr>
+<td>
+            <p>
+              throw_on_error
+            </p>
+            </td>
+<td>
+            <p>
+              Throws <code class="computeroutput"><span class="identifier">boost</span><span class="special">::</span><span class="identifier">math</span><span class="special">::</span><span class="identifier">rounding_error</span></code>
+            </p>
+            </td>
+</tr>
+<tr>
+<td>
+            <p>
+              errno_on_error
+            </p>
+            </td>
+<td>
+            <p>
+              Sets <code class="computeroutput"><span class="special">::</span><span class="identifier">errno</span></code>
+              to <code class="computeroutput"><span class="identifier">ERANGE</span></code> and returns
+              an unspecified value.
+            </p>
+            </td>
+</tr>
+<tr>
+<td>
+            <p>
+              ignore_error
+            </p>
+            </td>
+<td>
+            <p>
+              <span class="bold"><strong>Returns the an unspecified value.</strong></span>
+            </p>
+            </td>
+</tr>
+<tr>
+<td>
+            <p>
+              user_error
+            </p>
+            </td>
+<td>
+            <p>
+              Returns the result of <code class="computeroutput"><span class="identifier">boost</span><span class="special">::</span><span class="identifier">math</span><span class="special">::</span><span class="identifier">policies</span><span class="special">::</span><span class="identifier">user_rounding_error</span></code>:
+              <a class="link" href="../policy/pol_tutorial/user_def_err_pol.html" title="Calling User Defined Error Handlers">this
+              function must be defined by the user</a>.
+            </p>
+            </td>
+</tr>
+</tbody>
+</table></div>
+</div>
+<br class="table-break"><div class="table">
+<a name="id544094"></a><p class="title"><b>Table 7. Possible Actions for Internal Evaluation
+      Errors</b></p>
+<div class="table-contents"><table class="table" summary="Possible Actions for Internal Evaluation
+      Errors">
+<colgroup>
+<col>
+<col>
+</colgroup>
+<thead><tr>
+<th>
+            <p>
+              Action
+            </p>
+            </th>
+<th>
+            <p>
+              Behaviour
+            </p>
+            </th>
+</tr></thead>
+<tbody>
+<tr>
+<td>
+            <p>
+              throw_on_error
+            </p>
+            </td>
+<td>
+            <p>
+              <span class="bold"><strong>Throws <code class="computeroutput"><span class="identifier">boost</span><span class="special">::</span><span class="identifier">math</span><span class="special">::</span><span class="identifier">evaluation_error</span></code></strong></span>
+            </p>
+            </td>
+</tr>
+<tr>
+<td>
+            <p>
+              errno_on_error
+            </p>
+            </td>
+<td>
+            <p>
+              Sets <code class="computeroutput"><span class="special">::</span><span class="identifier">errno</span></code>
+              to <code class="computeroutput"><span class="identifier">EDOM</span></code> and returns
+              the closest approximation found.
+            </p>
+            </td>
+</tr>
+<tr>
+<td>
+            <p>
+              ignore_error
+            </p>
+            </td>
+<td>
+            <p>
+              Returns the closest approximation found.
+            </p>
+            </td>
+</tr>
+<tr>
+<td>
+            <p>
+              user_error
+            </p>
+            </td>
+<td>
+            <p>
+              Returns the result of <code class="computeroutput"><span class="identifier">boost</span><span class="special">::</span><span class="identifier">math</span><span class="special">::</span><span class="identifier">policies</span><span class="special">::</span><span class="identifier">user_evaluation_error</span></code>:
+              <a class="link" href="../policy/pol_tutorial/user_def_err_pol.html" title="Calling User Defined Error Handlers">this
+              function must be defined by the user</a>.
+            </p>
+            </td>
+</tr>
+</tbody>
+</table></div>
+</div>
+<br class="table-break"><div class="table">
+<a name="id544319"></a><p class="title"><b>Table 8. Possible Actions for Indeterminate Result
+      Errors</b></p>
+<div class="table-contents"><table class="table" summary="Possible Actions for Indeterminate Result
+      Errors">
+<colgroup>
+<col>
+<col>
+</colgroup>
+<thead><tr>
+<th>
+            <p>
+              Action
+            </p>
+            </th>
+<th>
+            <p>
+              Behaviour
+            </p>
+            </th>
+</tr></thead>
+<tbody>
+<tr>
+<td>
+            <p>
+              throw_on_error
+            </p>
+            </td>
+<td>
+            <p>
+              Throws <code class="computeroutput"><span class="identifier">std</span><span class="special">::</span><span class="identifier">domain_error</span></code>
+            </p>
+            </td>
+</tr>
+<tr>
+<td>
+            <p>
+              errno_on_error
+            </p>
+            </td>
+<td>
+            <p>
+              Sets <code class="computeroutput"><span class="special">::</span><span class="identifier">errno</span></code>
+              to <code class="computeroutput"><span class="identifier">EDOM</span></code> and returns
+              the same value as <code class="computeroutput"><span class="identifier">ignore_error</span></code>.
+            </p>
+            </td>
+</tr>
+<tr>
+<td>
+            <p>
+              ignore_error
+            </p>
+            </td>
+<td>
+            <p>
+              <span class="bold"><strong>Returns a default result that depends on the
+              function where the error occurred.</strong></span>
+            </p>
+            </td>
+</tr>
+<tr>
+<td>
+            <p>
+              user_error
+            </p>
+            </td>
+<td>
+            <p>
+              Returns the result of <code class="computeroutput"><span class="identifier">boost</span><span class="special">::</span><span class="identifier">math</span><span class="special">::</span><span class="identifier">policies</span><span class="special">::</span><span class="identifier">user_indeterminate_result_error</span></code>:
+              <a class="link" href="../policy/pol_tutorial/user_def_err_pol.html" title="Calling User Defined Error Handlers">this
+              function must be defined by the user</a>.
+            </p>
+            </td>
+</tr>
+</tbody>
+</table></div>
+</div>
+<br class="table-break"><a name="math_toolkit.main_overview.error_handling.rationale"></a><h5>
+<a name="id544557"></a>
+        <a class="link" href="error_handling.html#math_toolkit.main_overview.error_handling.rationale">Rationale</a>
+      </h5>
+<p>
+        The flexibility of the current implementation should be reasonably obvious,
+        the default behaviours were chosen based on feedback during the formal review
+        of this library. It was felt that:
+      </p>
+<div class="itemizedlist"><ul type="disc">
+<li>
+          Genuine errors should be flagged with exceptions rather than following
+          C-compatible behaviour and setting ::errno.
+        </li>
+<li>
+          Numeric underflow and denormalised results were not considered to be fatal
+          errors in most cases, so it was felt that these should be ignored.
+        </li>
+</ul></div>
+<a name="math_toolkit.main_overview.error_handling.finding_more_information"></a><h5>
+<a name="id544610"></a>
+        <a class="link" href="error_handling.html#math_toolkit.main_overview.error_handling.finding_more_information">Finding
+        More Information</a>
+      </h5>
+<p>
+        There are some pre-processor macro defines that can be used to <a class="link" href="../policy/pol_ref/policy_defaults.html" title="Using macros to Change the Policy Defaults">change
+        the policy defaults</a>. See also the <a class="link" href="../policy.html" title="Policies">policy
+        section</a>.
+      </p>
+<p>
+        An example is at the Policy tutorial in <a class="link" href="../policy/pol_tutorial/changing_policy_defaults.html" title="Changing the Policy Defaults">Changing
+        the Policy Defaults</a>.
+      </p>
+<p>
+        Full source code of this typical example of passing a 'bad' argument (negative
+        degrees of freedom) to Student's t distribution is <a class="link" href="../dist/stat_tut/weg/error_eg.html" title="Error Handling Example">in
+        the error handling example</a>.
+      </p>
+<p>
+        The various kind of errors are described in more detail below.
+      </p>
+<a name="domain_error"></a><a name="math_toolkit.main_overview.error_handling.domain_errors"></a><h5>
+<a name="id544694"></a>
+        <a class="link" href="error_handling.html#math_toolkit.main_overview.error_handling.domain_errors">Domain
+        Errors</a>
+      </h5>
+<p>
+        When a special function is passed an argument that is outside the range of
+        values for which that function is defined, then the function returns the
+        result of:
+      </p>
+<pre class="programlisting"><span class="identifier">boost</span><span class="special">::</span><span class="identifier">math</span><span class="special">::</span><span class="identifier">policies</span><span class="special">::</span><span class="identifier">raise_domain_error</span><span class="special">&lt;</span><span class="identifier">T</span><span class="special">&gt;(</span><span class="identifier">FunctionName</span><span class="special">,</span> <span class="identifier">Message</span><span class="special">,</span> <span class="identifier">Val</span><span class="special">,</span> <a class="link" href="../policy.html" title="Policies">Policy</a><span class="special">);</span>
+</pre>
+<p>
+        Where <code class="computeroutput"><span class="identifier">T</span></code> is the floating-point
+        type passed to the function, <code class="computeroutput"><span class="identifier">FunctionName</span></code>
+        is the name of the function, <code class="computeroutput"><span class="identifier">Message</span></code>
+        is an error message describing the problem, Val is the value that was out
+        of range, and <a class="link" href="../policy.html" title="Policies">Policy</a> is the current
+        policy in use for the function that was called.
+      </p>
+<p>
+        The default policy behaviour of this function is to throw a std::domain_error
+        C++ exception. But if the <a class="link" href="../policy.html" title="Policies">Policy</a>
+        is to ignore the error, or set global ::errno, then a NaN will be returned.
+      </p>
+<p>
+        This behaviour is chosen to assist compatibility with the behaviour of <span class="emphasis"><em>ISO/IEC
+        9899:1999 Programming languages - C</em></span> and with the <a href="http://www.open-std.org/jtc1/sc22/wg21/docs/papers/2005/n1836.pdf" target="_top">Draft
+        Technical Report on C++ Library Extensions, 2005-06-24, section 5.2.1, paragraph
+        6</a>:
+      </p>
+<div class="blockquote"><blockquote class="blockquote">
+<p>
+          </p>
+<p>
+            <span class="emphasis"><em>"Each of the functions declared above shall return a NaN
+            (Not a Number) if any argument value is a NaN, but it shall not report
+            a domain error. Otherwise, each of the functions declared above shall
+            report a domain error for just those argument values for which:</em></span>
+          </p>
+<p>
+        </p>
+</blockquote></div>
+<div class="blockquote"><blockquote class="blockquote">
+<p>
+          </p>
+<p>
+            <span class="emphasis"><em>"the function description's Returns clause explicitly
+            specifies a domain, and those arguments fall outside the specified domain;
+            or</em></span>
+          </p>
+<p>
+          </p>
+<p>
+            <span class="emphasis"><em>"the corresponding mathematical function value has a non-zero
+            imaginary component; or</em></span>
+          </p>
+<p>
+          </p>
+<p>
+            <span class="emphasis"><em>"the corresponding mathematical function is not mathematically
+            defined.</em></span>
+          </p>
+<p>
+        </p>
+</blockquote></div>
+<div class="blockquote"><blockquote class="blockquote">
+<p>
+          </p>
+<p>
+            <span class="emphasis"><em>"Note 2: A mathematical function is mathematically defined
+            for a given set of argument values if it is explicitly defined for that
+            set of argument values or if its limiting value exists and does not depend
+            on the direction of approach."</em></span>
+          </p>
+<p>
+        </p>
+</blockquote></div>
+<p>
+        Note that in order to support information-rich error messages when throwing
+        exceptions, <code class="computeroutput"><span class="identifier">Message</span></code> must
+        contain a Boost.Format
+        recognised format specifier: the argument <code class="computeroutput"><span class="identifier">Val</span></code>
+        is inserted into the error message according to the specifier used.
+      </p>
+<p>
+        For example if <code class="computeroutput"><span class="identifier">Message</span></code> contains
+        a "%1%" then it is replaced by the value of <code class="computeroutput"><span class="identifier">Val</span></code>
+        to the full precision of T, where as "%.3g" would contain the value
+        of <code class="computeroutput"><span class="identifier">Val</span></code> to 3 digits. See the
+        Boost.Format documentation
+        for more details.
+      </p>
+<a name="pole_error"></a><a name="math_toolkit.main_overview.error_handling.evaluation_at_a_pole"></a><h5>
+<a name="id545071"></a>
+        <a class="link" href="error_handling.html#math_toolkit.main_overview.error_handling.evaluation_at_a_pole">Evaluation
+        at a pole</a>
+      </h5>
+<p>
+        When a special function is passed an argument that is at a pole without a
+        well defined residual value, then the function returns the result of:
+      </p>
+<pre class="programlisting"><span class="identifier">boost</span><span class="special">::</span><span class="identifier">math</span><span class="special">::</span><span class="identifier">policies</span><span class="special">::</span><span class="identifier">raise_pole_error</span><span class="special">&lt;</span><span class="identifier">T</span><span class="special">&gt;(</span><span class="identifier">FunctionName</span><span class="special">,</span> <span class="identifier">Message</span><span class="special">,</span> <span class="identifier">Val</span><span class="special">,</span> <a class="link" href="../policy.html" title="Policies">Policy</a><span class="special">);</span>
+</pre>
+<p>
+        Where <code class="computeroutput"><span class="identifier">T</span></code> is the floating point
+        type passed to the function, <code class="computeroutput"><span class="identifier">FunctionName</span></code>
+        is the name of the function, <code class="computeroutput"><span class="identifier">Message</span></code>
+        is an error message describing the problem, <code class="computeroutput"><span class="identifier">Val</span></code>
+        is the value of the argument that is at a pole, and <a class="link" href="../policy.html" title="Policies">Policy</a>
+        is the current policy in use for the function that was called.
+      </p>
+<p>
+        The default behaviour of this function is to throw a std::domain_error exception.
+        But <a class="link" href="../policy/pol_ref/error_handling_policies.html" title="Error Handling Policies">error
+        handling policies</a> can be used to change this, for example to <code class="computeroutput"><span class="identifier">ignore_error</span></code> and return NaN.
+      </p>
+<p>
+        Note that in order to support information-rich error messages when throwing
+        exceptions, <code class="computeroutput"><span class="identifier">Message</span></code> must
+        contain a Boost.Format
+        recognised format specifier: the argument <code class="computeroutput"><span class="identifier">val</span></code>
+        is inserted into the error message according to the specifier used.
+      </p>
+<p>
+        For example if <code class="computeroutput"><span class="identifier">Message</span></code> contains
+        a "%1%" then it is replaced by the value of <code class="computeroutput"><span class="identifier">val</span></code>
+        to the full precision of T, where as "%.3g" would contain the value
+        of <code class="computeroutput"><span class="identifier">val</span></code> to 3 digits. See the
+        Boost.Format documentation
+        for more details.
+      </p>
+<a name="overflow_error"></a><a name="math_toolkit.main_overview.error_handling.numeric_overflow"></a><h5>
+<a name="id545366"></a>
+        <a class="link" href="error_handling.html#math_toolkit.main_overview.error_handling.numeric_overflow">Numeric
+        Overflow</a>
+      </h5>
+<p>
+        When the result of a special function is too large to fit in the argument
+        floating-point type, then the function returns the result of:
+      </p>
+<pre class="programlisting"><span class="identifier">boost</span><span class="special">::</span><span class="identifier">math</span><span class="special">::</span><span class="identifier">policies</span><span class="special">::</span><span class="identifier">raise_overflow_error</span><span class="special">&lt;</span><span class="identifier">T</span><span class="special">&gt;(</span><span class="identifier">FunctionName</span><span class="special">,</span> <span class="identifier">Message</span><span class="special">,</span> <a class="link" href="../policy.html" title="Policies">Policy</a><span class="special">);</span>
+</pre>
+<p>
+        Where <code class="computeroutput"><span class="identifier">T</span></code> is the floating-point
+        type passed to the function, <code class="computeroutput"><span class="identifier">FunctionName</span></code>
+        is the name of the function, <code class="computeroutput"><span class="identifier">Message</span></code>
+        is an error message describing the problem, and <a class="link" href="../policy.html" title="Policies">Policy</a>
+        is the current policy in use for the function that was called.
+      </p>
+<p>
+        The default policy for this function is that <code class="computeroutput"><span class="identifier">std</span><span class="special">::</span><span class="identifier">overflow_error</span></code>
+        C++ exception is thrown. But if, for example, an <code class="computeroutput"><span class="identifier">ignore_error</span></code>
+        policy is used, then returns <code class="computeroutput"><span class="identifier">std</span><span class="special">::</span><span class="identifier">numeric_limits</span><span class="special">&lt;</span><span class="identifier">T</span><span class="special">&gt;::</span><span class="identifier">infinity</span><span class="special">()</span></code>.
+        In this situation if the type <code class="computeroutput"><span class="identifier">T</span></code>
+        doesn't support infinities, the maximum value for the type is returned.
+      </p>
+<a name="underflow_error"></a><a name="math_toolkit.main_overview.error_handling.numeric_underflow"></a><h5>
+<a name="id545620"></a>
+        <a class="link" href="error_handling.html#math_toolkit.main_overview.error_handling.numeric_underflow">Numeric
+        Underflow</a>
+      </h5>
+<p>
+        If the result of a special function is known to be non-zero, but the calculated
+        result underflows to zero, then the function returns the result of:
+      </p>
+<pre class="programlisting"><span class="identifier">boost</span><span class="special">::</span><span class="identifier">math</span><span class="special">::</span><span class="identifier">policies</span><span class="special">::</span><span class="identifier">raise_underflow_error</span><span class="special">&lt;</span><span class="identifier">T</span><span class="special">&gt;(</span><span class="identifier">FunctionName</span><span class="special">,</span> <span class="identifier">Message</span><span class="special">,</span> <a class="link" href="../policy.html" title="Policies">Policy</a><span class="special">);</span>
+</pre>
+<p>
+        Where <code class="computeroutput"><span class="identifier">T</span></code> is the floating point
+        type passed to the function, <code class="computeroutput"><span class="identifier">FunctionName</span></code>
+        is the name of the function, <code class="computeroutput"><span class="identifier">Message</span></code>
+        is an error message describing the problem, and <a class="link" href="../policy.html" title="Policies">Policy</a>
+        is the current policy in use for the called function.
+      </p>
+<p>
+        The default version of this function returns zero. But with another policy,
+        like <code class="computeroutput"><span class="identifier">throw_on_error</span></code>, throws
+        an <code class="computeroutput"><span class="identifier">std</span><span class="special">::</span><span class="identifier">underflow_error</span></code> C++ exception.
+      </p>
+<a name="denorm_error"></a><a name="math_toolkit.main_overview.error_handling.denormalisation_errors"></a><h5>
+<a name="id545821"></a>
+        <a class="link" href="error_handling.html#math_toolkit.main_overview.error_handling.denormalisation_errors">Denormalisation
+        Errors</a>
+      </h5>
+<p>
+        If the result of a special function is a denormalised value <span class="emphasis"><em>z</em></span>
+        then the function returns the result of:
+      </p>
+<pre class="programlisting"><span class="identifier">boost</span><span class="special">::</span><span class="identifier">math</span><span class="special">::</span><span class="identifier">policies</span><span class="special">::</span><span class="identifier">raise_denorm_error</span><span class="special">&lt;</span><span class="identifier">T</span><span class="special">&gt;(</span><span class="identifier">z</span><span class="special">,</span> <span class="identifier">FunctionName</span><span class="special">,</span> <span class="identifier">Message</span><span class="special">,</span> <a class="link" href="../policy.html" title="Policies">Policy</a><span class="special">);</span>
+</pre>
+<p>
+        Where <code class="computeroutput"><span class="identifier">T</span></code> is the floating point
+        type passed to the function, <code class="computeroutput"><span class="identifier">FunctionName</span></code>
+        is the name of the function, <code class="computeroutput"><span class="identifier">Message</span></code>
+        is an error message describing the problem, and <a class="link" href="../policy.html" title="Policies">Policy</a>
+        is the current policy in use for the called function.
+      </p>
+<p>
+        The default version of this function returns <span class="emphasis"><em>z</em></span>. But
+        with another policy, like <code class="computeroutput"><span class="identifier">throw_on_error</span></code>
+        throws an <code class="computeroutput"><span class="identifier">std</span><span class="special">::</span><span class="identifier">underflow_error</span></code> C++ exception.
+      </p>
+<a name="evaluation_error"></a><a name="math_toolkit.main_overview.error_handling.evaluation_errors"></a><h5>
+<a name="id546034"></a>
+        <a class="link" href="error_handling.html#math_toolkit.main_overview.error_handling.evaluation_errors">Evaluation
+        Errors</a>
+      </h5>
+<p>
+        When a special function calculates a result that is known to be erroneous,
+        or where the result is incalculable then it calls:
+      </p>
+<pre class="programlisting"><span class="identifier">boost</span><span class="special">::</span><span class="identifier">math</span><span class="special">::</span><span class="identifier">policies</span><span class="special">::</span><span class="identifier">raise_evaluation_error</span><span class="special">&lt;</span><span class="identifier">T</span><span class="special">&gt;(</span><span class="identifier">FunctionName</span><span class="special">,</span> <span class="identifier">Message</span><span class="special">,</span> <span class="identifier">Val</span><span class="special">,</span> <a class="link" href="../policy.html" title="Policies">Policy</a><span class="special">);</span>
+</pre>
+<p>
+        Where <code class="computeroutput"><span class="identifier">T</span></code> is the floating point
+        type passed to the function, <code class="computeroutput"><span class="identifier">FunctionName</span></code>
+        is the name of the function, <code class="computeroutput"><span class="identifier">Message</span></code>
+        is an error message describing the problem, <code class="computeroutput"><span class="identifier">Val</span></code>
+        is the erroneous value, and <a class="link" href="../policy.html" title="Policies">Policy</a>
+        is the current policy in use for the called function.
+      </p>
+<p>
+        The default behaviour of this function is to throw a <code class="computeroutput"><span class="identifier">boost</span><span class="special">::</span><span class="identifier">math</span><span class="special">::</span><span class="identifier">evaluation_error</span></code>.
+      </p>
+<p>
+        Note that in order to support information rich error messages when throwing
+        exceptions, <code class="computeroutput"><span class="identifier">Message</span></code> must
+        contain a Boost.Format
+        recognised format specifier: the argument <code class="computeroutput"><span class="identifier">val</span></code>
+        is inserted into the error message according to the specifier used.
+      </p>
+<p>
+        For example if <code class="computeroutput"><span class="identifier">Message</span></code> contains
+        a "%1%" then it is replaced by the value of <code class="computeroutput"><span class="identifier">val</span></code>
+        to the full precision of T, where as "%.3g" would contain the value
+        of <code class="computeroutput"><span class="identifier">val</span></code> to 3 digits. See the
+        Boost.Format documentation
+        for more details.
+      </p>
+<a name="indeterminate_result_error"></a><a name="math_toolkit.main_overview.error_handling.indeterminate_result_errors"></a><h5>
+<a name="id546339"></a>
+        <a class="link" href="error_handling.html#math_toolkit.main_overview.error_handling.indeterminate_result_errors">Indeterminate
+        Result Errors</a>
+      </h5>
+<p>
+        When the result of a special function is indeterminate for the value that
+        was passed to it, then the function returns the result of:
+      </p>
+<pre class="programlisting"><span class="identifier">boost</span><span class="special">::</span><span class="identifier">math</span><span class="special">::</span><span class="identifier">policies</span><span class="special">::</span><span class="identifier">raise_overflow_error</span><span class="special">&lt;</span><span class="identifier">T</span><span class="special">&gt;(</span><span class="identifier">FunctionName</span><span class="special">,</span> <span class="identifier">Message</span><span class="special">,</span> <span class="identifier">Val</span><span class="special">,</span> <span class="identifier">Default</span><span class="special">,</span> <a class="link" href="../policy.html" title="Policies">Policy</a><span class="special">);</span>
+</pre>
+<p>
+        Where <code class="computeroutput"><span class="identifier">T</span></code> is the floating-point
+        type passed to the function, <code class="computeroutput"><span class="identifier">FunctionName</span></code>
+        is the name of the function, <code class="computeroutput"><span class="identifier">Message</span></code>
+        is an error message describing the problem, Val is the value for which the
+        result is indeterminate, Default is an alternative default result that must
+        be returned for ignore_error and errno_on_error policies, and <a class="link" href="../policy.html" title="Policies">Policy</a>
+        is the current policy in use for the function that was called.
+      </p>
+<p>
+        The default policy for this function is <code class="computeroutput"><span class="identifier">ignore_error</span></code>:
+        note that this error type is reserved for situations where the result is
+        mathematically undefined or indeterminate, but there is none the less a convention
+        for what the result should be: for example the C99 standard specifies that
+        the result of 0<sup>0</sup> is 1, even though the result is actually mathematically indeterminate.
+      </p>
+<a name="rounding_error"></a><a name="math_toolkit.main_overview.error_handling.rounding_errors"></a><h5>
+<a name="id546555"></a>
+        <a class="link" href="error_handling.html#math_toolkit.main_overview.error_handling.rounding_errors">Rounding
+        Errors</a>
+      </h5>
+<p>
+        When one of the rounding functions <a class="link" href="../special/rounding/round.html" title="Rounding Functions">round</a>,
+        <a class="link" href="../special/rounding/trunc.html" title="Truncation Functions">trunc</a> or <a class="link" href="../special/rounding/modf.html" title="Integer and Fractional Part Splitting (modf)">modf</a> is called with an
+        argument that has no integer representation, or is too large to be represented
+        in the result type then the value returned is the result of a call to:
+      </p>
+<pre class="programlisting"><span class="identifier">boost</span><span class="special">::</span><span class="identifier">math</span><span class="special">::</span><span class="identifier">policies</span><span class="special">::</span><span class="identifier">raise_rounding_error</span><span class="special">&lt;</span><span class="identifier">T</span><span class="special">&gt;(</span><span class="identifier">FunctionName</span><span class="special">,</span> <span class="identifier">Message</span><span class="special">,</span> <span class="identifier">Val</span><span class="special">,</span> <a class="link" href="../policy.html" title="Policies">Policy</a><span class="special">);</span>
+</pre>
+<p>
+        Where <code class="computeroutput"><span class="identifier">T</span></code> is the floating point
+        type passed to the function, <code class="computeroutput"><span class="identifier">FunctionName</span></code>
+        is the name of the function, <code class="computeroutput"><span class="identifier">Message</span></code>
+        is an error message describing the problem, <code class="computeroutput"><span class="identifier">Val</span></code>
+        is the erroneous argument, and <a class="link" href="../policy.html" title="Policies">Policy</a>
+        is the current policy in use for the called function.
+      </p>
+<p>
+        The default behaviour of this function is to throw a <code class="computeroutput"><span class="identifier">boost</span><span class="special">::</span><span class="identifier">math</span><span class="special">::</span><span class="identifier">rounding_error</span></code>.
+      </p>
+<p>
+        Note that in order to support information rich error messages when throwing
+        exceptions, <code class="computeroutput"><span class="identifier">Message</span></code> must
+        contain a Boost.Format
+        recognised format specifier: the argument <code class="computeroutput"><span class="identifier">val</span></code>
+        is inserted into the error message according to the specifier used.
+      </p>
+<p>
+        For example if <code class="computeroutput"><span class="identifier">Message</span></code> contains
+        a "%1%" then it is replaced by the value of <code class="computeroutput"><span class="identifier">val</span></code>
+        to the full precision of T, where as "%.3g" would contain the value
+        of <code class="computeroutput"><span class="identifier">val</span></code> to 3 digits. See the
+        Boost.Format documentation
+        for more details.
+      </p>
+<a name="checked_narrowing_cast"></a><a name="math_toolkit.main_overview.error_handling.errors_from_typecasts"></a><h5>
+<a name="id546878"></a>
+        <a class="link" href="error_handling.html#math_toolkit.main_overview.error_handling.errors_from_typecasts">Errors
+        from typecasts</a>
+      </h5>
+<p>
+        Many special functions evaluate their results at a higher precision than
+        their arguments in order to ensure full machine precision in the result:
+        for example, a function passed a float argument may evaluate its result using
+        double precision internally. Many of the errors listed above may therefore
+        occur not during evaluation, but when converting the result to the narrower
+        result type. The function:
+      </p>
+<pre class="programlisting"><span class="keyword">template</span> <span class="special">&lt;</span><span class="keyword">class</span> <span class="identifier">T</span><span class="special">,</span> <span class="keyword">class</span> <a class="link" href="../policy.html" title="Policies">Policy</a><span class="special">,</span> <span class="keyword">class</span> <span class="identifier">U</span><span class="special">&gt;</span>
+<span class="identifier">T</span> <span class="identifier">checked_narrowing_cast</span><span class="special">(</span><span class="identifier">U</span> <span class="keyword">const</span><span class="special">&amp;</span> <span class="identifier">val</span><span class="special">,</span> <span class="keyword">const</span> <span class="keyword">char</span><span class="special">*</span> <span class="identifier">function</span><span class="special">);</span>
+</pre>
+<p>
+        Is used to perform these conversions, and will call the error handlers listed
+        above on <a class="link" href="error_handling.html#overflow_error">overflow</a>, <a class="link" href="error_handling.html#underflow_error">underflow</a>
+        or <a class="link" href="error_handling.html#denorm_error">denormalisation</a>.
+      </p>
+</div>
+<table xmlns:rev="http://www.cs.rpi.edu/~gregod/boost/tools/doc/revision" width="100%"><tr>
+<td align="left"></td>
+<td align="right"><div class="copyright-footer">Copyright © 2006 , 2007, 2008 John Maddock, Paul A. Bristow, Hubert
+      Holin, Xiaogang Zhang, Bruno Lalande and Gautam Sewani<p>
+        Distributed under the Boost Software License, Version 1.0. (See accompanying
+        file LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_0.txt)
+      </p>
+</div></td>
+</tr></table>
+<hr>
+<div class="spirit-nav">
+<a accesskey="p" href="result_type.html"><img src="../../../../doc/html/images/prev.png" alt="Prev"></a><a accesskey="u" href="../main_overview.html"><img src="../../../../doc/html/images/up.png" alt="Up"></a><a accesskey="h" href="../../index.html"><img src="../../../../doc/html/images/home.png" alt="Home"></a><a accesskey="n" href="compilers_overview.html"><img src="../../../../doc/html/images/next.png" alt="Next"></a>
+</div>
+</body>
+</html>

Added: sandbox/tools/auto_index/example/math/doc/sf_and_dist/html/math_toolkit/main_overview/history1.html
==============================================================================
--- (empty file)
+++ sandbox/tools/auto_index/example/math/doc/sf_and_dist/html/math_toolkit/main_overview/history1.html	2008-11-28 05:25:28 EST (Fri, 28 Nov 2008)
@@ -0,0 +1,287 @@
+<html>
+<head>
+<meta http-equiv="Content-Type" content="text/html; charset=ISO-8859-1">
+<title>History and What's New</title>
+<link rel="stylesheet" href="../../boostbook.css" type="text/css">
+<meta name="generator" content="DocBook XSL Stylesheets Vsnapshot_8125">
+<link rel="home" href="../../index.html" title="Math Toolkit">
+<link rel="up" href="../main_overview.html" title="Overview">
+<link rel="prev" href="building.html" title="If and How to Build the Library and its Examples and Tests">
+<link rel="next" href="tr1.html" title="C99 and TR1 C Functions">
+</head>
+<body bgcolor="white" text="black" link="#0000FF" vlink="#840084" alink="#0000FF">
+<table cellpadding="2" width="100%"><tr>
+<td valign="top"><img alt="Boost C++ Libraries" width="277" height="86" src="../../../../boost.png"></td>
+<td align="center">Home</td>
+<td align="center">Libraries</td>
+<td align="center">People</td>
+<td align="center">FAQ</td>
+<td align="center">More</td>
+</tr></table>
+<hr>
+<div class="spirit-nav">
+<a accesskey="p" href="building.html"><img src="../../../../doc/html/images/prev.png" alt="Prev"></a><a accesskey="u" href="../main_overview.html"><img src="../../../../doc/html/images/up.png" alt="Up"></a><a accesskey="h" href="../../index.html"><img src="../../../../doc/html/images/home.png" alt="Home"></a><a accesskey="n" href="tr1.html"><img src="../../../../doc/html/images/next.png" alt="Next"></a>
+</div>
+<div class="section" lang="en">
+<div class="titlepage"><div><div><h3 class="title">
+<a name="math_toolkit.main_overview.history1"></a><a class="link" href="history1.html" title="History and What's New"> History and What's
+      New</a>
+</h3></div></div></div>
+<p>
+        <a name="math_toolkit.main_overview.history1.boost_1_38_0"></a>
+        </p>
+<h5>
+<a name="id549811"></a>
+          <a class="link" href="history1.html#math_toolkit.main_overview.history1.boost_1_38_0">Boost-1.38.0</a>
+        </h5>
+<p>
+        </p>
+<div class="itemizedlist"><ul type="disc">
+<li>
+            Added support for MPFR as a bignum type.
+          </li>
+<li>
+            Added some full specializations of the policy classes to reduce compile
+            times.
+          </li>
+<li>
+            Added logistic distribution, from Gautam Sewani's Google Summer of Code
+            project.
+          </li>
+</ul></div>
+<p>
+        <a name="math_toolkit.main_overview.history1.boost_1_37_0"></a>
+        </p>
+<h5>
+<a name="id549855"></a>
+          <a class="link" href="history1.html#math_toolkit.main_overview.history1.boost_1_37_0">Boost-1.37.0</a>
+        </h5>
+<p>
+        </p>
+<div class="itemizedlist"><ul type="disc"><li>
+            Improved accuracy and testing of the inverse hypergeometric functions.
+          </li></ul></div>
+<p>
+        <a name="math_toolkit.main_overview.history1.boost_1_36_0"></a>
+        </p>
+<h5>
+<a name="id549886"></a>
+          <a class="link" href="history1.html#math_toolkit.main_overview.history1.boost_1_36_0">Boost-1.36.0</a>
+        </h5>
+<p>
+        </p>
+<div class="itemizedlist"><ul type="disc">
+<li>
+            Added Noncentral Chi Squared Distribution.
+          </li>
+<li>
+            Added Noncentral Beta Distribution.
+          </li>
+<li>
+            Added Noncentral F Distribution.
+          </li>
+<li>
+            Added Noncentral T Distribution.
+          </li>
+<li>
+            Added Exponential Integral Functions.
+          </li>
+<li>
+            Added Zeta Function.
+          </li>
+<li>
+            Added Rounding and Truncation functions.
+          </li>
+<li>
+            Added Compile time powers of runtime bases.
+          </li>
+</ul></div>
+<p>
+        <a name="math_toolkit.main_overview.history1.boost_1_35_0__post_review_first_official_release"></a>
+        </p>
+<h5>
+<a name="id549959"></a>
+          <a class="link" href="history1.html#math_toolkit.main_overview.history1.boost_1_35_0__post_review_first_official_release">Boost-1.35.0:
+          Post Review First Official Release</a>
+        </h5>
+<p>
+        </p>
+<div class="itemizedlist"><ul type="disc">
+<li>
+            Added Policy based framework that allows fine grained control over function
+            behaviour.
+          </li>
+<li>
+<span class="bold"><strong>Breaking change:</strong></span> Changed default behaviour
+            for domain, pole and overflow errors to throw an exception (based on
+            review feedback), this behaviour can be customised using <a class="link" href="../policy.html" title="Policies">Policy</a>'s.
+          </li>
+<li>
+<span class="bold"><strong>Breaking change:</strong></span> Changed exception thrown
+            when an internal evaluation error occurs to boost::math::evaluation_error.
+          </li>
+<li>
+<span class="bold"><strong>Breaking change:</strong></span> Changed discrete quantiles
+            to return an integer result: this is anything up to 20 times faster than
+            finding the true root, this behaviour can be customised using <a class="link" href="../policy.html" title="Policies">Policy</a>'s.
+          </li>
+<li>
+            Polynomial/rational function evaluation is now customisable and hopefully
+            faster than before.
+          </li>
+<li>
+            Added performance test program.
+          </li>
+</ul></div>
+<p>
+        <a name="math_toolkit.main_overview.history1.milestone_4__second_review_candidate__1st_march_2007_"></a>
+        </p>
+<h5>
+<a name="id550058"></a>
+          <a class="link" href="history1.html#math_toolkit.main_overview.history1.milestone_4__second_review_candidate__1st_march_2007_">Milestone
+          4: Second Review Candidate (1st March 2007)</a>
+        </h5>
+<p>
+        </p>
+<div class="itemizedlist"><ul type="disc">
+<li>
+            Moved Xiaogang Zhang's Bessel Functions code into the library, and brought
+            them into line with the rest of the code.
+          </li>
+<li>
+            Added C# "Distribution Explorer" demo application.
+          </li>
+</ul></div>
+<p>
+        <a name="math_toolkit.main_overview.history1.milestone_3__first_review_candidate__31st_dec_2006_"></a>
+        </p>
+<h5>
+<a name="id550102"></a>
+          <a class="link" href="history1.html#math_toolkit.main_overview.history1.milestone_3__first_review_candidate__31st_dec_2006_">Milestone
+          3: First Review Candidate (31st Dec 2006)</a>
+        </h5>
+<p>
+        </p>
+<div class="itemizedlist"><ul type="disc">
+<li>
+            Implemented the main probability distribution and density functions.
+          </li>
+<li>
+            Implemented digamma.
+          </li>
+<li>
+            Added more factorial functions.
+          </li>
+<li>
+            Implemented the Hermite, Legendre and Laguerre polynomials plus the spherical
+            harmonic functions from TR1.
+          </li>
+<li>
+            Moved Xiaogang Zhang's elliptic integral code into the library, and brought
+            them into line with the rest of the code.
+          </li>
+<li>
+            Moved Hubert Holin's existing Boost.Math special functions into this
+            library and brought them into line with the rest of the code.
+          </li>
+</ul></div>
+<p>
+        <a name="math_toolkit.main_overview.history1.milestone_2__released_september_10th_2006"></a>
+        </p>
+<h5>
+<a name="id550168"></a>
+          <a class="link" href="history1.html#math_toolkit.main_overview.history1.milestone_2__released_september_10th_2006">Milestone
+          2: Released September 10th 2006</a>
+        </h5>
+<p>
+        </p>
+<div class="itemizedlist"><ul type="disc">
+<li>
+            Implement preview release of the statistical distributions.
+          </li>
+<li>
+            Added statistical distributions tutorial.
+          </li>
+<li>
+            Implemented root finding algorithms.
+          </li>
+<li>
+            Implemented the inverses of the incomplete gamma and beta functions.
+          </li>
+<li>
+            Rewrite erf/erfc as rational approximations (valid to 128-bit precision).
+          </li>
+<li>
+            Integrated the statistical results generated from the test data with
+            Boost.Test: uses a database of expected results, indexed by test, floating
+            point type, platform, and compiler.
+          </li>
+<li>
+            Improved lgamma near 1 and 2 (rational approximations).
+          </li>
+<li>
+            Improved erf/erfc inverses (rational approximations).
+          </li>
+<li>
+            Implemented Rational function generation (the Remez method).
+          </li>
+</ul></div>
+<p>
+        <a name="math_toolkit.main_overview.history1.milestone_1__released_march_31st_2006"></a>
+        </p>
+<h5>
+<a name="id550248"></a>
+          <a class="link" href="history1.html#math_toolkit.main_overview.history1.milestone_1__released_march_31st_2006">Milestone
+          1: Released March 31st 2006</a>
+        </h5>
+<p>
+        </p>
+<div class="itemizedlist"><ul type="disc">
+<li>
+            Implement gamma/beta/erf functions along with their incomplete counterparts.
+          </li>
+<li>
+            Generate high quality test data, against which future improvements can
+            be judged.
+          </li>
+<li>
+            Provide tools for the evaluation of infinite series, continued fractions,
+            and rational functions.
+          </li>
+<li>
+            Provide tools for testing against tabulated test data, and collecting
+            statistics on error rates.
+          </li>
+<li>
+            Provide sufficient docs for people to be able to find their way around
+            the library.
+          </li>
+</ul></div>
+<p>
+        </p>
+<p>
+          SVN Revisions:
+        </p>
+<p>
+        </p>
+<p>
+          Sandbox and trunk last synchonised at revision: 48300.
+        </p>
+<p>
+      </p>
+</div>
+<table xmlns:rev="http://www.cs.rpi.edu/~gregod/boost/tools/doc/revision" width="100%"><tr>
+<td align="left"></td>
+<td align="right"><div class="copyright-footer">Copyright © 2006 , 2007, 2008 John Maddock, Paul A. Bristow, Hubert
+      Holin, Xiaogang Zhang, Bruno Lalande and Gautam Sewani<p>
+        Distributed under the Boost Software License, Version 1.0. (See accompanying
+        file LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_0.txt)
+      </p>
+</div></td>
+</tr></table>
+<hr>
+<div class="spirit-nav">
+<a accesskey="p" href="building.html"><img src="../../../../doc/html/images/prev.png" alt="Prev"></a><a accesskey="u" href="../main_overview.html"><img src="../../../../doc/html/images/up.png" alt="Up"></a><a accesskey="h" href="../../index.html"><img src="../../../../doc/html/images/home.png" alt="Home"></a><a accesskey="n" href="tr1.html"><img src="../../../../doc/html/images/next.png" alt="Next"></a>
+</div>
+</body>
+</html>

Added: sandbox/tools/auto_index/example/math/doc/sf_and_dist/html/math_toolkit/main_overview/intro.html
==============================================================================
--- (empty file)
+++ sandbox/tools/auto_index/example/math/doc/sf_and_dist/html/math_toolkit/main_overview/intro.html	2008-11-28 05:25:28 EST (Fri, 28 Nov 2008)
@@ -0,0 +1,134 @@
+<html>
+<head>
+<meta http-equiv="Content-Type" content="text/html; charset=ISO-8859-1">
+<title>About the Math Toolkit</title>
+<link rel="stylesheet" href="../../boostbook.css" type="text/css">
+<meta name="generator" content="DocBook XSL Stylesheets Vsnapshot_8125">
+<link rel="home" href="../../index.html" title="Math Toolkit">
+<link rel="up" href="../main_overview.html" title="Overview">
+<link rel="prev" href="../main_overview.html" title="Overview">
+<link rel="next" href="navigation.html" title="Navigation">
+</head>
+<body bgcolor="white" text="black" link="#0000FF" vlink="#840084" alink="#0000FF">
+<table cellpadding="2" width="100%"><tr>
+<td valign="top"><img alt="Boost C++ Libraries" width="277" height="86" src="../../../../boost.png"></td>
+<td align="center">Home</td>
+<td align="center">Libraries</td>
+<td align="center">People</td>
+<td align="center">FAQ</td>
+<td align="center">More</td>
+</tr></table>
+<hr>
+<div class="spirit-nav">
+<a accesskey="p" href="../main_overview.html"><img src="../../../../doc/html/images/prev.png" alt="Prev"></a><a accesskey="u" href="../main_overview.html"><img src="../../../../doc/html/images/up.png" alt="Up"></a><a accesskey="h" href="../../index.html"><img src="../../../../doc/html/images/home.png" alt="Home"></a><a accesskey="n" href="navigation.html"><img src="../../../../doc/html/images/next.png" alt="Next"></a>
+</div>
+<div class="section" lang="en">
+<div class="titlepage"><div><div><h3 class="title">
+<a name="math_toolkit.main_overview.intro"></a><a class="link" href="intro.html" title="About the Math Toolkit"> About the Math Toolkit</a>
+</h3></div></div></div>
+<p>
+        This library is divided into three interconnected parts:
+      </p>
+<a name="math_toolkit.main_overview.intro.statistical_distributions"></a><h5>
+<a name="id473335"></a>
+        <a class="link" href="intro.html#math_toolkit.main_overview.intro.statistical_distributions">Statistical
+        Distributions</a>
+      </h5>
+<p>
+        Provides a reasonably comprehensive set of <a class="link" href="../dist.html" title="Statistical Distributions and Functions">statistical
+        distributions</a>, upon which higher level statistical tests can be built.
+      </p>
+<p>
+        The initial focus is on the central <a href="http://en.wikipedia.org/wiki/Univariate" target="_top">univariate
+        </a> distributions.
+        Both continuous
+        (like <a class="link" href="../dist/dist_ref/dists/normal_dist.html" title="Normal (Gaussian) Distribution">normal</a>
+        &amp; <a class="link" href="../dist/dist_ref/dists/f_dist.html" title="F Distribution">Fisher</a>)
+        and discrete
+        (like <a class="link" href="../dist/dist_ref/dists/binomial_dist.html" title="Binomial Distribution">binomial</a>
+        &amp; <a class="link" href="../dist/dist_ref/dists/poisson_dist.html" title="Poisson Distribution">Poisson</a>)
+        distributions are provided.
+      </p>
+<p>
+        A <a class="link" href="../dist/stat_tut.html" title="Statistical Distributions Tutorial">comprehensive tutorial is provided</a>,
+        along with a series of <a class="link" href="../dist/stat_tut/weg.html" title="Worked Examples">worked
+        examples</a> illustrating how the library is used to conduct statistical
+        tests.
+      </p>
+<a name="math_toolkit.main_overview.intro.mathematical_special_functions"></a><h5>
+<a name="id473384"></a>
+        <a class="link" href="intro.html#math_toolkit.main_overview.intro.mathematical_special_functions">Mathematical
+        Special Functions</a>
+      </h5>
+<p>
+        Provides a small number of high quality <a class="link" href="../special.html" title="Special Functions">special
+        functions</a>, initially these were concentrated on functions used in
+        statistical applications along with those in the <a href="http://www.open-std.org/jtc1/sc22/wg21/docs/papers/2005/n1836.pdf" target="_top">Technical
+        Report on C++ Library Extensions</a>.
+      </p>
+<p>
+        The function families currently implemented are the gamma, beta &amp; erf
+        functions along with the incomplete gamma and beta functions (four variants
+        of each) and all the possible inverses of these, plus digamma, various factorial
+        functions, Bessel functions, elliptic integrals, sinus cardinals (along with
+        their hyperbolic variants), inverse hyperbolic functions, Legrendre/Laguerre/Hermite
+        polynomials and various special power and logarithmic functions.
+      </p>
+<p>
+        All the implementations are fully generic and support the use of arbitrary
+        "real-number" types, although they are optimised for use with types
+        with known-about <a href="http://en.wikipedia.org/wiki/Significand" target="_top">significand
+        (or mantissa)</a> sizes: typically <code class="computeroutput"><span class="keyword">float</span></code>,
+        <code class="computeroutput"><span class="keyword">double</span></code> or <code class="computeroutput"><span class="keyword">long</span>
+        <span class="keyword">double</span></code>.
+      </p>
+<a name="math_toolkit.main_overview.intro.implementation_toolkit"></a><h5>
+<a name="id473505"></a>
+        <a class="link" href="intro.html#math_toolkit.main_overview.intro.implementation_toolkit">Implementation
+        Toolkit</a>
+      </h5>
+<p>
+        Provides <a class="link" href="../toolkit.html" title="Internal Details and Tools (Experimental)">many of the tools</a> required
+        to implement mathematical special functions: hopefully the presence of these
+        will encourage other authors to contribute more special function implementations
+        in the future. These tools are currently considered experimental: they are
+        "exposed implementation details" whose interfaces and/or implementations
+        may change.
+      </p>
+<p>
+        There are helpers for the <a class="link" href="../toolkit/internals1/series_evaluation.html" title="Series Evaluation">evaluation
+        of infinite series</a>, <a class="link" href="../toolkit/internals1/cf.html" title="Continued Fraction Evaluation">continued
+        fractions</a> and <a class="link" href="../toolkit/internals1/rational.html" title="Polynomial and Rational Function Evaluation">rational
+        approximations</a>.
+      </p>
+<p>
+        There is a fairly comprehensive set of root finding and <a class="link" href="../toolkit/internals1/minima.html" title="Locating Function Minima">function
+        minimisation algorithms</a>: the root finding algorithms are both <a class="link" href="../toolkit/internals1/roots.html" title="Root Finding With Derivatives">with</a> and <a class="link" href="../toolkit/internals1/roots2.html" title="Root Finding Without Derivatives">without</a>
+        derivative support.
+      </p>
+<p>
+        A <a class="link" href="../toolkit/internals2/minimax.html" title="Minimax Approximations and the Remez Algorithm">Remez algorithm
+        implementation</a> allows for the locating of minimax rational approximations.
+      </p>
+<p>
+        There are also (experimental) classes for the <a class="link" href="../toolkit/internals2/polynomials.html" title="Polynomials">manipulation
+        of polynomials</a>, for <a class="link" href="../toolkit/internals2/error_test.html" title="Relative Error and Testing">testing
+        a special function against tabulated test data</a>, and for the <a class="link" href="../toolkit/internals2/test_data.html" title="Graphing, Profiling, and Generating Test Data for Special Functions">rapid generation of test
+        data</a> and/or data for output to an external graphing application.
+      </p>
+</div>
+<table xmlns:rev="http://www.cs.rpi.edu/~gregod/boost/tools/doc/revision" width="100%"><tr>
+<td align="left"></td>
+<td align="right"><div class="copyright-footer">Copyright © 2006 , 2007, 2008 John Maddock, Paul A. Bristow, Hubert
+      Holin, Xiaogang Zhang, Bruno Lalande and Gautam Sewani<p>
+        Distributed under the Boost Software License, Version 1.0. (See accompanying
+        file LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_0.txt)
+      </p>
+</div></td>
+</tr></table>
+<hr>
+<div class="spirit-nav">
+<a accesskey="p" href="../main_overview.html"><img src="../../../../doc/html/images/prev.png" alt="Prev"></a><a accesskey="u" href="../main_overview.html"><img src="../../../../doc/html/images/up.png" alt="Up"></a><a accesskey="h" href="../../index.html"><img src="../../../../doc/html/images/home.png" alt="Home"></a><a accesskey="n" href="navigation.html"><img src="../../../../doc/html/images/next.png" alt="Next"></a>
+</div>
+</body>
+</html>

Added: sandbox/tools/auto_index/example/math/doc/sf_and_dist/html/math_toolkit/main_overview/namespaces.html
==============================================================================
--- (empty file)
+++ sandbox/tools/auto_index/example/math/doc/sf_and_dist/html/math_toolkit/main_overview/namespaces.html	2008-11-28 05:25:28 EST (Fri, 28 Nov 2008)
@@ -0,0 +1,74 @@
+<html>
+<head>
+<meta http-equiv="Content-Type" content="text/html; charset=ISO-8859-1">
+<title>Namespaces</title>
+<link rel="stylesheet" href="../../boostbook.css" type="text/css">
+<meta name="generator" content="DocBook XSL Stylesheets Vsnapshot_8125">
+<link rel="home" href="../../index.html" title="Math Toolkit">
+<link rel="up" href="../main_overview.html" title="Overview">
+<link rel="prev" href="directories.html" title="Directory and File Structure">
+<link rel="next" href="result_type.html" title="Calculation of the Type of the Result">
+</head>
+<body bgcolor="white" text="black" link="#0000FF" vlink="#840084" alink="#0000FF">
+<table cellpadding="2" width="100%"><tr>
+<td valign="top"><img alt="Boost C++ Libraries" width="277" height="86" src="../../../../boost.png"></td>
+<td align="center">Home</td>
+<td align="center">Libraries</td>
+<td align="center">People</td>
+<td align="center">FAQ</td>
+<td align="center">More</td>
+</tr></table>
+<hr>
+<div class="spirit-nav">
+<a accesskey="p" href="directories.html"><img src="../../../../doc/html/images/prev.png" alt="Prev"></a><a accesskey="u" href="../main_overview.html"><img src="../../../../doc/html/images/up.png" alt="Up"></a><a accesskey="h" href="../../index.html"><img src="../../../../doc/html/images/home.png" alt="Home"></a><a accesskey="n" href="result_type.html"><img src="../../../../doc/html/images/next.png" alt="Next"></a>
+</div>
+<div class="section" lang="en">
+<div class="titlepage"><div><div><h3 class="title">
+<a name="math_toolkit.main_overview.namespaces"></a><a class="link" href="namespaces.html" title="Namespaces"> Namespaces</a>
+</h3></div></div></div>
+<p>
+        All math functions and distributions are in <code class="computeroutput"><span class="keyword">namespace</span>
+        <span class="identifier">boost</span><span class="special">::</span><span class="identifier">math</span></code>
+      </p>
+<p>
+        So, for example, the Students-t distribution template in <code class="computeroutput"><span class="keyword">namespace</span>
+        <span class="identifier">boost</span><span class="special">::</span><span class="identifier">math</span></code> is
+      </p>
+<pre class="programlisting"><span class="keyword">template</span> <span class="special">&lt;</span><span class="keyword">class</span> <span class="identifier">RealType</span><span class="special">&gt;</span> <span class="keyword">class</span> <span class="identifier">students_t_distribution</span>
+</pre>
+<p>
+        and can be instantiated with the help of the reserved name <code class="computeroutput"><span class="identifier">students_t</span></code>(for <code class="computeroutput"><span class="identifier">RealType</span>
+        <span class="keyword">double</span></code>)
+      </p>
+<pre class="programlisting"><span class="keyword">typedef</span> <span class="identifier">students_t_distribution</span><span class="special">&lt;</span><span class="keyword">double</span><span class="special">&gt;</span> <span class="identifier">students_t</span><span class="special">;</span>
+
+<span class="identifier">student_t</span> <span class="identifier">mydist</span><span class="special">(</span><span class="number">10</span><span class="special">);</span>
+</pre>
+<p>
+        Functions not intended for use by applications are in <code class="computeroutput"><span class="identifier">boost</span><span class="special">::</span><span class="identifier">math</span><span class="special">::</span><span class="identifier">detail</span></code>.
+      </p>
+<p>
+        Functions that may have more general use, like <code class="computeroutput"><span class="identifier">digits</span></code>
+        (significand), <code class="computeroutput"><span class="identifier">max_value</span></code>,
+        <code class="computeroutput"><span class="identifier">min_value</span></code> and <code class="computeroutput"><span class="identifier">epsilon</span></code> are in <code class="computeroutput"><span class="identifier">boost</span><span class="special">::</span><span class="identifier">math</span><span class="special">::</span><span class="identifier">tools</span></code>.
+      </p>
+<p>
+        <a class="link" href="../policy.html" title="Policies">Policy</a> and configuration information
+        is in namespace <code class="computeroutput"><span class="identifier">boost</span><span class="special">::</span><span class="identifier">math</span><span class="special">::</span><span class="identifier">policies</span></code>.
+      </p>
+</div>
+<table xmlns:rev="http://www.cs.rpi.edu/~gregod/boost/tools/doc/revision" width="100%"><tr>
+<td align="left"></td>
+<td align="right"><div class="copyright-footer">Copyright © 2006 , 2007, 2008 John Maddock, Paul A. Bristow, Hubert
+      Holin, Xiaogang Zhang, Bruno Lalande and Gautam Sewani<p>
+        Distributed under the Boost Software License, Version 1.0. (See accompanying
+        file LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_0.txt)
+      </p>
+</div></td>
+</tr></table>
+<hr>
+<div class="spirit-nav">
+<a accesskey="p" href="directories.html"><img src="../../../../doc/html/images/prev.png" alt="Prev"></a><a accesskey="u" href="../main_overview.html"><img src="../../../../doc/html/images/up.png" alt="Up"></a><a accesskey="h" href="../../index.html"><img src="../../../../doc/html/images/home.png" alt="Home"></a><a accesskey="n" href="result_type.html"><img src="../../../../doc/html/images/next.png" alt="Next"></a>
+</div>
+</body>
+</html>

Added: sandbox/tools/auto_index/example/math/doc/sf_and_dist/html/math_toolkit/main_overview/navigation.html
==============================================================================
--- (empty file)
+++ sandbox/tools/auto_index/example/math/doc/sf_and_dist/html/math_toolkit/main_overview/navigation.html	2008-11-28 05:25:28 EST (Fri, 28 Nov 2008)
@@ -0,0 +1,154 @@
+<html>
+<head>
+<meta http-equiv="Content-Type" content="text/html; charset=ISO-8859-1">
+<title>Navigation</title>
+<link rel="stylesheet" href="../../boostbook.css" type="text/css">
+<meta name="generator" content="DocBook XSL Stylesheets Vsnapshot_8125">
+<link rel="home" href="../../index.html" title="Math Toolkit">
+<link rel="up" href="../main_overview.html" title="Overview">
+<link rel="prev" href="intro.html" title="About the Math Toolkit">
+<link rel="next" href="directories.html" title="Directory and File Structure">
+</head>
+<body bgcolor="white" text="black" link="#0000FF" vlink="#840084" alink="#0000FF">
+<table cellpadding="2" width="100%"><tr>
+<td valign="top"><img alt="Boost C++ Libraries" width="277" height="86" src="../../../../boost.png"></td>
+<td align="center">Home</td>
+<td align="center">Libraries</td>
+<td align="center">People</td>
+<td align="center">FAQ</td>
+<td align="center">More</td>
+</tr></table>
+<hr>
+<div class="spirit-nav">
+<a accesskey="p" href="intro.html"><img src="../../../../doc/html/images/prev.png" alt="Prev"></a><a accesskey="u" href="../main_overview.html"><img src="../../../../doc/html/images/up.png" alt="Up"></a><a accesskey="h" href="../../index.html"><img src="../../../../doc/html/images/home.png" alt="Home"></a><a accesskey="n" href="directories.html"><img src="../../../../doc/html/images/next.png" alt="Next"></a>
+</div>
+<div class="section" lang="en">
+<div class="titlepage"><div><div><h3 class="title">
+<a name="math_toolkit.main_overview.navigation"></a><a class="link" href="navigation.html" title="Navigation"> Navigation</a>
+</h3></div></div></div>
+<p>
+        Used in combination with the configured browser key, the following keys act
+        as handy shortcuts for common navigation tasks.
+      </p>
+<a name="math_toolkit.main_overview.navigation.shortcuts"></a><h6>
+<a name="id473670"></a>
+        <a class="link" href="navigation.html#math_toolkit.main_overview.navigation.shortcuts">Shortcuts</a>
+      </h6>
+<div class="blockquote"><blockquote class="blockquote">
+<p>
+          </p>
+<p>
+            <code class="literal"><span class="bold"><strong>p</strong></span></code> - Previous page
+          </p>
+<p>
+          </p>
+<p>
+            <code class="literal"><span class="bold"><strong>n</strong></span></code> - Next page
+          </p>
+<p>
+          </p>
+<p>
+            <code class="literal"><span class="bold"><strong>h</strong></span></code> - home
+          </p>
+<p>
+          </p>
+<p>
+            <code class="literal"><span class="bold"><strong>u</strong></span></code> - Up
+          </p>
+<p>
+        </p>
+</blockquote></div>
+<p>
+        The following table shows how to access these from common browsers:
+      </p>
+<div class="informaltable"><table class="table">
+<colgroup>
+<col>
+<col>
+</colgroup>
+<thead><tr>
+<th>
+              <p>
+                Browser
+              </p>
+              </th>
+<th>
+              <p>
+                Access Method
+              </p>
+              </th>
+</tr></thead>
+<tbody>
+<tr>
+<td>
+              <p>
+                Internet Explorer
+              </p>
+              </td>
+<td>
+              <p>
+                Alt+Key highlights the link only, so for example to move to the next
+                topic you would need "Alt+n" followed by "Enter".
+              </p>
+              </td>
+</tr>
+<tr>
+<td>
+              <p>
+                Firefox 2.0 and later
+              </p>
+              </td>
+<td>
+              <p>
+                Alt+Shift+Key follows the link, so for example "Alt+Shift+n"
+                will take you to the next topic.
+              </p>
+              </td>
+</tr>
+<tr>
+<td>
+              <p>
+                Opera
+              </p>
+              </td>
+<td>
+              <p>
+                Press Shift+Esc followed by the access key.
+              </p>
+              </td>
+</tr>
+<tr>
+<td>
+              <p>
+                Konqueror
+              </p>
+              </td>
+<td>
+              <p>
+                Press and release the Ctrl key, followed by the access key
+              </p>
+              </td>
+</tr>
+</tbody>
+</table></div>
+<p>
+        Some browsers also make these links available in their site-navigation toolbars:
+        in Opera for example you can use Ctrl plus the left and right arrow keys
+        to move between "next" and "previous" topics.
+      </p>
+</div>
+<table xmlns:rev="http://www.cs.rpi.edu/~gregod/boost/tools/doc/revision" width="100%"><tr>
+<td align="left"></td>
+<td align="right"><div class="copyright-footer">Copyright © 2006 , 2007, 2008 John Maddock, Paul A. Bristow, Hubert
+      Holin, Xiaogang Zhang, Bruno Lalande and Gautam Sewani<p>
+        Distributed under the Boost Software License, Version 1.0. (See accompanying
+        file LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_0.txt)
+      </p>
+</div></td>
+</tr></table>
+<hr>
+<div class="spirit-nav">
+<a accesskey="p" href="intro.html"><img src="../../../../doc/html/images/prev.png" alt="Prev"></a><a accesskey="u" href="../main_overview.html"><img src="../../../../doc/html/images/up.png" alt="Up"></a><a accesskey="h" href="../../index.html"><img src="../../../../doc/html/images/home.png" alt="Home"></a><a accesskey="n" href="directories.html"><img src="../../../../doc/html/images/next.png" alt="Next"></a>
+</div>
+</body>
+</html>

Added: sandbox/tools/auto_index/example/math/doc/sf_and_dist/html/math_toolkit/main_overview/perf_over.html
==============================================================================
--- (empty file)
+++ sandbox/tools/auto_index/example/math/doc/sf_and_dist/html/math_toolkit/main_overview/perf_over.html	2008-11-28 05:25:28 EST (Fri, 28 Nov 2008)
@@ -0,0 +1,93 @@
+<html>
+<head>
+<meta http-equiv="Content-Type" content="text/html; charset=ISO-8859-1">
+<title>Performance</title>
+<link rel="stylesheet" href="../../boostbook.css" type="text/css">
+<meta name="generator" content="DocBook XSL Stylesheets Vsnapshot_8125">
+<link rel="home" href="../../index.html" title="Math Toolkit">
+<link rel="up" href="../main_overview.html" title="Overview">
+<link rel="prev" href="threads.html" title="Thread Safety">
+<link rel="next" href="building.html" title="If and How to Build the Library and its Examples and Tests">
+</head>
+<body bgcolor="white" text="black" link="#0000FF" vlink="#840084" alink="#0000FF">
+<table cellpadding="2" width="100%"><tr>
+<td valign="top"><img alt="Boost C++ Libraries" width="277" height="86" src="../../../../boost.png"></td>
+<td align="center">Home</td>
+<td align="center">Libraries</td>
+<td align="center">People</td>
+<td align="center">FAQ</td>
+<td align="center">More</td>
+</tr></table>
+<hr>
+<div class="spirit-nav">
+<a accesskey="p" href="threads.html"><img src="../../../../doc/html/images/prev.png" alt="Prev"></a><a accesskey="u" href="../main_overview.html"><img src="../../../../doc/html/images/up.png" alt="Up"></a><a accesskey="h" href="../../index.html"><img src="../../../../doc/html/images/home.png" alt="Home"></a><a accesskey="n" href="building.html"><img src="../../../../doc/html/images/next.png" alt="Next"></a>
+</div>
+<div class="section" lang="en">
+<div class="titlepage"><div><div><h3 class="title">
+<a name="math_toolkit.main_overview.perf_over"></a><a class="link" href="perf_over.html" title="Performance"> Performance</a>
+</h3></div></div></div>
+<p>
+        </p>
+<p>
+          By and large the performance of this library should be acceptable for most
+          needs. However, you should note that the library's primary emphasis is
+          on accuracy and numerical stability, and <span class="emphasis"><em>not</em></span> speed.
+        </p>
+<p>
+        </p>
+<p>
+          In terms of the algorithms used, this library aims to use the same "best
+          of breed" algorithms as many other libraries: the principle difference
+          is that this library is implemented in C++ - taking advantage of all the
+          abstraction mechanisms that C++ offers - where as most traditional numeric
+          libraries are implemented in C or FORTRAN. Traditionally languages such
+          as C or FORTRAN are perceived as easier to optimise than more complex languages
+          like C++, so in a sense this library provides a good test of current compiler
+          technology, and the "abstraction penalty" - if any - of C++ compared
+          to other languages.
+        </p>
+<p>
+        </p>
+<p>
+          The two most important things you can do to ensure the best performance
+          from this library are:
+        </p>
+<p>
+        </p>
+<div class="orderedlist"><ol type="1">
+<li>
+            Turn on your compilers optimisations: the difference between "release"
+            and "debug" builds can easily be a <a class="link" href="../perf/getting_best.html" title="Getting the Best Performance from this Library">factor
+            of 20</a>.
+          </li>
+<li>
+            Pick your compiler carefully: <a class="link" href="../perf/comp_compilers.html" title="Comparing Compilers">performance
+            differences of up to 8 fold</a> have been found between some windows
+            compilers for example.
+          </li>
+</ol></div>
+<p>
+        </p>
+<p>
+          The <a class="link" href="../perf.html" title="Performance">performance section</a> contains
+          more information on the performance of this library, what you can do to
+          fine tune it, and how this library compares to some other open source alternatives.
+        </p>
+<p>
+      </p>
+</div>
+<table xmlns:rev="http://www.cs.rpi.edu/~gregod/boost/tools/doc/revision" width="100%"><tr>
+<td align="left"></td>
+<td align="right"><div class="copyright-footer">Copyright © 2006 , 2007, 2008 John Maddock, Paul A. Bristow, Hubert
+      Holin, Xiaogang Zhang, Bruno Lalande and Gautam Sewani<p>
+        Distributed under the Boost Software License, Version 1.0. (See accompanying
+        file LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_0.txt)
+      </p>
+</div></td>
+</tr></table>
+<hr>
+<div class="spirit-nav">
+<a accesskey="p" href="threads.html"><img src="../../../../doc/html/images/prev.png" alt="Prev"></a><a accesskey="u" href="../main_overview.html"><img src="../../../../doc/html/images/up.png" alt="Up"></a><a accesskey="h" href="../../index.html"><img src="../../../../doc/html/images/home.png" alt="Home"></a><a accesskey="n" href="building.html"><img src="../../../../doc/html/images/next.png" alt="Next"></a>
+</div>
+</body>
+</html>

Added: sandbox/tools/auto_index/example/math/doc/sf_and_dist/html/math_toolkit/main_overview/pol_overview.html
==============================================================================
--- (empty file)
+++ sandbox/tools/auto_index/example/math/doc/sf_and_dist/html/math_toolkit/main_overview/pol_overview.html	2008-11-28 05:25:28 EST (Fri, 28 Nov 2008)
@@ -0,0 +1,136 @@
+<html>
+<head>
+<meta http-equiv="Content-Type" content="text/html; charset=ISO-8859-1">
+<title>Configuration and Policies</title>
+<link rel="stylesheet" href="../../boostbook.css" type="text/css">
+<meta name="generator" content="DocBook XSL Stylesheets Vsnapshot_8125">
+<link rel="home" href="../../index.html" title="Math Toolkit">
+<link rel="up" href="../main_overview.html" title="Overview">
+<link rel="prev" href="compilers_overview.html" title="Compilers">
+<link rel="next" href="threads.html" title="Thread Safety">
+</head>
+<body bgcolor="white" text="black" link="#0000FF" vlink="#840084" alink="#0000FF">
+<table cellpadding="2" width="100%"><tr>
+<td valign="top"><img alt="Boost C++ Libraries" width="277" height="86" src="../../../../boost.png"></td>
+<td align="center">Home</td>
+<td align="center">Libraries</td>
+<td align="center">People</td>
+<td align="center">FAQ</td>
+<td align="center">More</td>
+</tr></table>
+<hr>
+<div class="spirit-nav">
+<a accesskey="p" href="compilers_overview.html"><img src="../../../../doc/html/images/prev.png" alt="Prev"></a><a accesskey="u" href="../main_overview.html"><img src="../../../../doc/html/images/up.png" alt="Up"></a><a accesskey="h" href="../../index.html"><img src="../../../../doc/html/images/home.png" alt="Home"></a><a accesskey="n" href="threads.html"><img src="../../../../doc/html/images/next.png" alt="Next"></a>
+</div>
+<div class="section" lang="en">
+<div class="titlepage"><div><div><h3 class="title">
+<a name="math_toolkit.main_overview.pol_overview"></a><a class="link" href="pol_overview.html" title="Configuration and Policies"> Configuration
+      and Policies</a>
+</h3></div></div></div>
+<p>
+        </p>
+<p>
+          Policies are a powerful fine-grain mechanism that allow you to customise
+          the behaviour of this library according to your needs. There is more information
+          available in the <a class="link" href="../policy/pol_tutorial.html" title="Policy Tutorial">policy
+          tutorial</a> and the <a class="link" href="../policy/pol_ref.html" title="Policy Reference">policy
+          reference</a>.
+        </p>
+<p>
+        </p>
+<p>
+          Generally speaking unless you find that the <a class="link" href="../policy/pol_tutorial/policy_tut_defaults.html" title="Policies Have Sensible Defaults">default
+          policy behaviour</a> when encountering 'bad' argument values does not
+          meet your needs, you should not need to worry about policies.
+        </p>
+<p>
+        </p>
+<p>
+          Policies are a compile-time mechanism that allow you to change error-handling
+          or calculation precision either program wide, or at the call site.
+        </p>
+<p>
+        </p>
+<p>
+          Although the policy mechanism itself is rather complicated, in practice
+          it is easy to use, and very flexible.
+        </p>
+<p>
+        </p>
+<p>
+          Using policies you can control:
+        </p>
+<p>
+        </p>
+<div class="itemizedlist"><ul type="disc">
+<li>
+<a class="link" href="../policy/pol_ref/error_handling_policies.html" title="Error Handling Policies">How
+            results from 'bad' arguments are handled</a>, including those that
+            cannot be fully evaluated.
+          </li>
+<li>
+            How <a class="link" href="../policy/pol_ref/internal_promotion.html" title="Internal Promotion Policies">accuracy
+            is controlled by internal promotion</a> to use more precise types.
+          </li>
+<li>
+            What working <a class="link" href="../policy/pol_ref/precision_pol.html" title="Precision Policies">precision</a>
+            should be used to calculate results.
+          </li>
+<li>
+            What to do when a <a class="link" href="../policy/pol_ref/assert_undefined.html" title="Mathematically Undefined Function Policies">mathematically
+            undefined function</a> is used: Should this raise a run-time or compile-time
+            error?
+          </li>
+<li>
+            Whether <a class="link" href="../policy/pol_ref/discrete_quant_ref.html" title="Discrete Quantile Policies">discrete
+            functions</a>, like the binomial, should return real or only integral
+            values, and how they are rounded.
+          </li>
+<li>
+            How many iterations a special function is permitted to perform in a series
+            evaluation or root finding algorithm before it gives up and raises an
+            <a class="link" href="error_handling.html#evaluation_error">evaluation_error</a>.
+          </li>
+</ul></div>
+<p>
+        </p>
+<p>
+          You can control policies:
+        </p>
+<p>
+        </p>
+<div class="itemizedlist"><ul type="disc">
+<li>
+            Using <a class="link" href="../policy/pol_ref/policy_defaults.html" title="Using macros to Change the Policy Defaults">macros</a>
+            to change any default policy: the is the prefered method for installation
+            wide policies.
+          </li>
+<li>
+            At your chosen <a class="link" href="../policy/pol_ref/namespace_pol.html" title="Setting Polices at Namespace Scope">namespace
+            scope</a> for distributions and/or functions: this is the prefered
+            method for project, namespace, or translation unit scope policies.
+          </li>
+<li>
+            In an ad-hoc manner <a class="link" href="../policy/pol_tutorial/ad_hoc_sf_policies.html" title="Changing the Policy on an Ad Hoc Basis for the Special Functions">by
+            passing a specific policy to a special function</a>, or to a <a class="link" href="../policy/pol_tutorial/ad_hoc_dist_policies.html" title="Setting Policies for Distributions on an Ad Hoc Basis">statistical
+            distribution</a>.
+          </li>
+</ul></div>
+<p>
+      </p>
+</div>
+<table xmlns:rev="http://www.cs.rpi.edu/~gregod/boost/tools/doc/revision" width="100%"><tr>
+<td align="left"></td>
+<td align="right"><div class="copyright-footer">Copyright © 2006 , 2007, 2008 John Maddock, Paul A. Bristow, Hubert
+      Holin, Xiaogang Zhang, Bruno Lalande and Gautam Sewani<p>
+        Distributed under the Boost Software License, Version 1.0. (See accompanying
+        file LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_0.txt)
+      </p>
+</div></td>
+</tr></table>
+<hr>
+<div class="spirit-nav">
+<a accesskey="p" href="compilers_overview.html"><img src="../../../../doc/html/images/prev.png" alt="Prev"></a><a accesskey="u" href="../main_overview.html"><img src="../../../../doc/html/images/up.png" alt="Up"></a><a accesskey="h" href="../../index.html"><img src="../../../../doc/html/images/home.png" alt="Home"></a><a accesskey="n" href="threads.html"><img src="../../../../doc/html/images/next.png" alt="Next"></a>
+</div>
+</body>
+</html>

Added: sandbox/tools/auto_index/example/math/doc/sf_and_dist/html/math_toolkit/main_overview/result_type.html
==============================================================================
--- (empty file)
+++ sandbox/tools/auto_index/example/math/doc/sf_and_dist/html/math_toolkit/main_overview/result_type.html	2008-11-28 05:25:28 EST (Fri, 28 Nov 2008)
@@ -0,0 +1,148 @@
+<html>
+<head>
+<meta http-equiv="Content-Type" content="text/html; charset=ISO-8859-1">
+<title>Calculation of the Type of the Result</title>
+<link rel="stylesheet" href="../../boostbook.css" type="text/css">
+<meta name="generator" content="DocBook XSL Stylesheets Vsnapshot_8125">
+<link rel="home" href="../../index.html" title="Math Toolkit">
+<link rel="up" href="../main_overview.html" title="Overview">
+<link rel="prev" href="namespaces.html" title="Namespaces">
+<link rel="next" href="error_handling.html" title="Error Handling">
+</head>
+<body bgcolor="white" text="black" link="#0000FF" vlink="#840084" alink="#0000FF">
+<table cellpadding="2" width="100%"><tr>
+<td valign="top"><img alt="Boost C++ Libraries" width="277" height="86" src="../../../../boost.png"></td>
+<td align="center">Home</td>
+<td align="center">Libraries</td>
+<td align="center">People</td>
+<td align="center">FAQ</td>
+<td align="center">More</td>
+</tr></table>
+<hr>
+<div class="spirit-nav">
+<a accesskey="p" href="namespaces.html"><img src="../../../../doc/html/images/prev.png" alt="Prev"></a><a accesskey="u" href="../main_overview.html"><img src="../../../../doc/html/images/up.png" alt="Up"></a><a accesskey="h" href="../../index.html"><img src="../../../../doc/html/images/home.png" alt="Home"></a><a accesskey="n" href="error_handling.html"><img src="../../../../doc/html/images/next.png" alt="Next"></a>
+</div>
+<div class="section" lang="en">
+<div class="titlepage"><div><div><h3 class="title">
+<a name="math_toolkit.main_overview.result_type"></a><a class="link" href="result_type.html" title="Calculation of the Type of the Result"> Calculation
+      of the Type of the Result</a>
+</h3></div></div></div>
+<p>
+        The functions in this library are all overloaded to accept mixed floating
+        point (or mixed integer and floating point type) arguments. So for example:
+      </p>
+<pre class="programlisting"><span class="identifier">foo</span><span class="special">(</span><span class="number">1.0</span><span class="special">,</span> <span class="number">2.0</span><span class="special">);</span>
+<span class="identifier">foo</span><span class="special">(</span><span class="number">1.0f</span><span class="special">,</span> <span class="number">2</span><span class="special">);</span>
+<span class="identifier">foo</span><span class="special">(</span><span class="number">1.0</span><span class="special">,</span> <span class="number">2L</span><span class="special">);</span>
+</pre>
+<p>
+        etc, are all valid calls, as long as "foo" is a function taking
+        two floating-point arguments. But that leaves the question:
+      </p>
+<div class="sidebar">
+<p class="title"><b></b></p>
+<p>
+        <span class="emphasis"><em>"Given a special function with N arguments of types T1, T2,
+        T3 ... TN, then what type is the result?"</em></span>
+      </p>
+</div>
+<p>
+        <span class="bold"><strong>If all the arguments are of the same (floating point)
+        type then the result is the same type as the arguments.</strong></span>
+      </p>
+<p>
+        Otherwise, the type of the result is computed using the following logic:
+      </p>
+<div class="orderedlist"><ol type="1">
+<li>
+          Any arguments that are not template arguments are disregarded from further
+          analysis.
+        </li>
+<li>
+          For each type in the argument list, if that type is an integer type then
+          it is treated as if it were of type double for the purposes of further
+          analysis.
+        </li>
+<li>
+          If any of the arguments is a user-defined class type, then the result type
+          is the first such class type that is constructible from all of the other
+          argument types.
+        </li>
+<li>
+          If any of the arguments is of type <code class="computeroutput"><span class="keyword">long</span>
+          <span class="keyword">double</span></code>, then the result is of type
+          <code class="computeroutput"><span class="keyword">long</span> <span class="keyword">double</span></code>.
+        </li>
+<li>
+          If any of the arguments is of type <code class="computeroutput"><span class="keyword">double</span></code>,
+          then the result is of type <code class="computeroutput"><span class="keyword">double</span></code>.
+        </li>
+<li>
+          Otherwise the result is of type <code class="computeroutput"><span class="keyword">float</span></code>.
+        </li>
+</ol></div>
+<p>
+        For example:
+      </p>
+<pre class="programlisting"><span class="identifier">cyl_bessel</span><span class="special">(</span><span class="number">2</span><span class="special">,</span> <span class="number">3.0</span><span class="special">);</span>
+</pre>
+<p>
+        Returns a <code class="computeroutput"><span class="keyword">double</span></code> result, as
+        does:
+      </p>
+<pre class="programlisting"><span class="identifier">cyl_bessel</span><span class="special">(</span><span class="number">2</span><span class="special">,</span> <span class="number">3.0f</span><span class="special">);</span>
+</pre>
+<p>
+        as in this case the integer first argument is treated as a <code class="computeroutput"><span class="keyword">double</span></code> and takes precedence over the <code class="computeroutput"><span class="keyword">float</span></code> second argument. To get a <code class="computeroutput"><span class="keyword">float</span></code> result we would need all the arguments
+        to be of type float:
+      </p>
+<pre class="programlisting"><span class="identifier">cyl_bessel_j</span><span class="special">(</span><span class="number">2.0f</span><span class="special">,</span> <span class="number">3.0f</span><span class="special">);</span>
+</pre>
+<p>
+        When one or more of the arguments is not a template argument then it doesn't
+        effect the return type at all, for example:
+      </p>
+<pre class="programlisting"><span class="identifier">sph_bessel</span><span class="special">(</span><span class="number">2</span><span class="special">,</span> <span class="number">3.0f</span><span class="special">);</span>
+</pre>
+<p>
+        returns a <code class="computeroutput"><span class="keyword">float</span></code>, since the first
+        argument is not a template argument and so doesn't effect the result: without
+        this rule functions that take explicitly integer arguments could never return
+        <code class="computeroutput"><span class="keyword">float</span></code>.
+      </p>
+<p>
+        And for user defined types, all of the following return an NTL::RR result:
+      </p>
+<pre class="programlisting"><span class="identifier">cyl_bessel_j</span><span class="special">(</span><span class="number">0</span><span class="special">,</span> <span class="identifier">NTL</span><span class="special">::</span><span class="identifier">RR</span><span class="special">(</span><span class="number">2</span><span class="special">));</span>
+
+<span class="identifier">cyl_bessel_j</span><span class="special">(</span><span class="identifier">NTL</span><span class="special">::</span><span class="identifier">RR</span><span class="special">(</span><span class="number">2</span><span class="special">),</span> <span class="number">3</span><span class="special">);</span>
+
+<span class="identifier">cyl_bessel_j</span><span class="special">(</span><span class="identifier">NTL</span><span class="special">::</span><span class="identifier">quad_float</span><span class="special">(</span><span class="number">2</span><span class="special">),</span> <span class="identifier">NTL</span><span class="special">::</span><span class="identifier">RR</span><span class="special">(</span><span class="number">3</span><span class="special">));</span>
+</pre>
+<p>
+        In the last case, quad_float is convertible to RR, but not vice-versa, so
+        the result will be an NTL::RR. Note that this assumes that you are using
+        a <a class="link" href="../using_udt/use_ntl.html" title="Using With NTL - a High-Precision Floating-Point Library">patched NTL library</a>.
+      </p>
+<p>
+        These rules are chosen to be compatible with the behaviour of <span class="emphasis"><em>ISO/IEC
+        9899:1999 Programming languages - C</em></span> and with the <a href="http://www.open-std.org/jtc1/sc22/wg21/docs/papers/2005/n1836.pdf" target="_top">Draft
+        Technical Report on C++ Library Extensions, 2005-06-24, section 5.2.1, paragraph
+        5</a>.
+      </p>
+</div>
+<table xmlns:rev="http://www.cs.rpi.edu/~gregod/boost/tools/doc/revision" width="100%"><tr>
+<td align="left"></td>
+<td align="right"><div class="copyright-footer">Copyright © 2006 , 2007, 2008 John Maddock, Paul A. Bristow, Hubert
+      Holin, Xiaogang Zhang, Bruno Lalande and Gautam Sewani<p>
+        Distributed under the Boost Software License, Version 1.0. (See accompanying
+        file LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_0.txt)
+      </p>
+</div></td>
+</tr></table>
+<hr>
+<div class="spirit-nav">
+<a accesskey="p" href="namespaces.html"><img src="../../../../doc/html/images/prev.png" alt="Prev"></a><a accesskey="u" href="../main_overview.html"><img src="../../../../doc/html/images/up.png" alt="Up"></a><a accesskey="h" href="../../index.html"><img src="../../../../doc/html/images/home.png" alt="Home"></a><a accesskey="n" href="error_handling.html"><img src="../../../../doc/html/images/next.png" alt="Next"></a>
+</div>
+</body>
+</html>

Added: sandbox/tools/auto_index/example/math/doc/sf_and_dist/html/math_toolkit/main_overview/threads.html
==============================================================================
--- (empty file)
+++ sandbox/tools/auto_index/example/math/doc/sf_and_dist/html/math_toolkit/main_overview/threads.html	2008-11-28 05:25:28 EST (Fri, 28 Nov 2008)
@@ -0,0 +1,69 @@
+<html>
+<head>
+<meta http-equiv="Content-Type" content="text/html; charset=ISO-8859-1">
+<title>Thread Safety</title>
+<link rel="stylesheet" href="../../boostbook.css" type="text/css">
+<meta name="generator" content="DocBook XSL Stylesheets Vsnapshot_8125">
+<link rel="home" href="../../index.html" title="Math Toolkit">
+<link rel="up" href="../main_overview.html" title="Overview">
+<link rel="prev" href="pol_overview.html" title="Configuration and Policies">
+<link rel="next" href="perf_over.html" title="Performance">
+</head>
+<body bgcolor="white" text="black" link="#0000FF" vlink="#840084" alink="#0000FF">
+<table cellpadding="2" width="100%"><tr>
+<td valign="top"><img alt="Boost C++ Libraries" width="277" height="86" src="../../../../boost.png"></td>
+<td align="center">Home</td>
+<td align="center">Libraries</td>
+<td align="center">People</td>
+<td align="center">FAQ</td>
+<td align="center">More</td>
+</tr></table>
+<hr>
+<div class="spirit-nav">
+<a accesskey="p" href="pol_overview.html"><img src="../../../../doc/html/images/prev.png" alt="Prev"></a><a accesskey="u" href="../main_overview.html"><img src="../../../../doc/html/images/up.png" alt="Up"></a><a accesskey="h" href="../../index.html"><img src="../../../../doc/html/images/home.png" alt="Home"></a><a accesskey="n" href="perf_over.html"><img src="../../../../doc/html/images/next.png" alt="Next"></a>
+</div>
+<div class="section" lang="en">
+<div class="titlepage"><div><div><h3 class="title">
+<a name="math_toolkit.main_overview.threads"></a><a class="link" href="threads.html" title="Thread Safety"> Thread Safety</a>
+</h3></div></div></div>
+<p>
+        The library is fully thread safe and re-entrant provided the function and
+        class templates in the library are instantiated with built-in floating point
+        types: i.e. the types <code class="computeroutput"><span class="keyword">float</span></code>,
+        <code class="computeroutput"><span class="keyword">double</span></code> and <code class="computeroutput"><span class="keyword">long</span>
+        <span class="keyword">double</span></code>.
+      </p>
+<p>
+        However, the library <span class="bold"><strong>is not thread safe</strong></span>
+        when used with user-defined (i.e. class type) numeric types.
+      </p>
+<p>
+        The reason for the latter limitation is the need to initialise symbolic constants
+        using constructs such as:
+      </p>
+<pre class="programlisting"><span class="keyword">static</span> <span class="keyword">const</span> <span class="identifier">T</span> <span class="identifier">coefficient_array</span> <span class="special">=</span> <span class="special">{</span> <span class="special">...</span> <span class="identifier">list</span> <span class="identifier">of</span> <span class="identifier">values</span> <span class="special">...</span> <span class="special">};</span>
+</pre>
+<p>
+        Which is always thread safe when T is a built-in floating point type, but
+        not when T is a user defined type: as in this case there is a need for T's
+        constructors to be run, leading to potential race conditions.
+      </p>
+<p>
+        This limitation may be addressed in a future release.
+      </p>
+</div>
+<table xmlns:rev="http://www.cs.rpi.edu/~gregod/boost/tools/doc/revision" width="100%"><tr>
+<td align="left"></td>
+<td align="right"><div class="copyright-footer">Copyright © 2006 , 2007, 2008 John Maddock, Paul A. Bristow, Hubert
+      Holin, Xiaogang Zhang, Bruno Lalande and Gautam Sewani<p>
+        Distributed under the Boost Software License, Version 1.0. (See accompanying
+        file LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_0.txt)
+      </p>
+</div></td>
+</tr></table>
+<hr>
+<div class="spirit-nav">
+<a accesskey="p" href="pol_overview.html"><img src="../../../../doc/html/images/prev.png" alt="Prev"></a><a accesskey="u" href="../main_overview.html"><img src="../../../../doc/html/images/up.png" alt="Up"></a><a accesskey="h" href="../../index.html"><img src="../../../../doc/html/images/home.png" alt="Home"></a><a accesskey="n" href="perf_over.html"><img src="../../../../doc/html/images/next.png" alt="Next"></a>
+</div>
+</body>
+</html>

Added: sandbox/tools/auto_index/example/math/doc/sf_and_dist/html/math_toolkit/main_overview/tr1.html
==============================================================================
--- (empty file)
+++ sandbox/tools/auto_index/example/math/doc/sf_and_dist/html/math_toolkit/main_overview/tr1.html	2008-11-28 05:25:28 EST (Fri, 28 Nov 2008)
@@ -0,0 +1,688 @@
+<html>
+<head>
+<meta http-equiv="Content-Type" content="text/html; charset=ISO-8859-1">
+<title>C99 and TR1 C Functions</title>
+<link rel="stylesheet" href="../../boostbook.css" type="text/css">
+<meta name="generator" content="DocBook XSL Stylesheets Vsnapshot_8125">
+<link rel="home" href="../../index.html" title="Math Toolkit">
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+<table cellpadding="2" width="100%"><tr>
+<td valign="top"><img alt="Boost C++ Libraries" width="277" height="86" src="../../../../boost.png"></td>
+<td align="center">Home</td>
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+<hr>
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+<a accesskey="p" href="history1.html"><img src="../../../../doc/html/images/prev.png" alt="Prev"></a><a accesskey="u" href="../main_overview.html"><img src="../../../../doc/html/images/up.png" alt="Up"></a><a accesskey="h" href="../../index.html"><img src="../../../../doc/html/images/home.png" alt="Home"></a><a accesskey="n" href="contact.html"><img src="../../../../doc/html/images/next.png" alt="Next"></a>
+</div>
+<div class="section" lang="en">
+<div class="titlepage"><div><div><h3 class="title">
+<a name="math_toolkit.main_overview.tr1"></a><a class="link" href="tr1.html" title="C99 and TR1 C Functions"> C99 and TR1 C Functions</a>
+</h3></div></div></div>
+<p>
+        </p>
+<p>
+          Many of the special functions included in this library are also a part
+          of the either the C99 standard or the <a href="http://www.open-std.org/jtc1/sc22/wg21/docs/papers/2005/n1836.pdf" target="_top">Technical
+          Report on C++ Library Extensions</a>. Therefore this library includes
+          a thin wrapper header <code class="computeroutput"><span class="identifier">boost</span><span class="special">/</span><span class="identifier">math</span><span class="special">/</span><span class="identifier">tr1</span><span class="special">.</span><span class="identifier">hpp</span></code>
+          that provides compatibility with these two standards.
+        </p>
+<p>
+        </p>
+<p>
+          There are various pros and cons to using the library in this way:
+        </p>
+<p>
+        </p>
+<p>
+          Pros:
+        </p>
+<p>
+        </p>
+<div class="itemizedlist"><ul type="disc">
+<li>
+            The header to include is lightweight (i.e. fast to compile).
+          </li>
+<li>
+            The functions have extern "C" linkage, and so are usable from
+            other languages.
+          </li>
+<li>
+            Standard compatibility.
+          </li>
+</ul></div>
+<p>
+        </p>
+<p>
+          Cons:
+        </p>
+<p>
+        </p>
+<div class="itemizedlist"><ul type="disc">
+<li>
+            You will need to compile and link to the external Boost.Math libraries.
+          </li>
+<li>
+            Limited to support for the types, <code class="computeroutput"><span class="keyword">float</span></code>,
+            <code class="computeroutput"><span class="keyword">double</span></code> and <code class="computeroutput"><span class="keyword">long</span> <span class="keyword">double</span></code>.
+          </li>
+<li>
+            Error handling is handled via setting ::errno and returning NaN's and
+            infinities: this may be less flexible than an C++ exception based approach.
+          </li>
+</ul></div>
+<p>
+        </p>
+<div class="note"><table border="0" summary="Note">
+<tr>
+<td rowspan="2" align="center" valign="top" width="25"><img alt="[Note]" src="../../../../doc/html/images/note.png"></td>
+<th align="left">Note</th>
+</tr>
+<tr><td align="left" valign="top"><p>
+            The separate libraries are required <span class="bold"><strong>only</strong></span>
+            if you choose to use boost/math/tr1.hpp rather than some other Boost.Math
+            header, the rest of Boost.Math remains header-only.
+          </p></td></tr>
+</table></div>
+<p>
+        </p>
+<p>
+          The separate libraries required in order to use tr1.hpp can be compiled
+          using bjam from within the libs/math/build directory, or from the Boost
+          root directory using the usual Boost-wide install procedure. Alternatively
+          the source files are located in libs/math/src and each have the same name
+          as the function they implement. The various libraries are named as follows:
+        </p>
+<p>
+        </p>
+<div class="informaltable"><table class="table">
+<colgroup>
+<col>
+<col>
+<col>
+</colgroup>
+<thead><tr>
+<th>
+                <p>
+                  Name
+                </p>
+                </th>
+<th>
+                <p>
+                  Type
+                </p>
+                </th>
+<th>
+                <p>
+                  Functions
+                </p>
+                </th>
+</tr></thead>
+<tbody>
+<tr>
+<td>
+                <p>
+                  boost_math_c99f-&lt;suffix&gt;
+                </p>
+                </td>
+<td>
+                <p>
+                  float
+                </p>
+                </td>
+<td>
+                <p>
+                  C99 Functions
+                </p>
+                </td>
+</tr>
+<tr>
+<td>
+                <p>
+                  boost_math_c99-&lt;suffix&gt;
+                </p>
+                </td>
+<td>
+                <p>
+                  double
+                </p>
+                </td>
+<td>
+                <p>
+                  C99 Functions
+                </p>
+                </td>
+</tr>
+<tr>
+<td>
+                <p>
+                  boost_math_c99l-&lt;suffix&gt;
+                </p>
+                </td>
+<td>
+                <p>
+                  long double
+                </p>
+                </td>
+<td>
+                <p>
+                  C99 Functions
+                </p>
+                </td>
+</tr>
+<tr>
+<td>
+                <p>
+                  boost_math_tr1f-&lt;suffix&gt;
+                </p>
+                </td>
+<td>
+                <p>
+                  float
+                </p>
+                </td>
+<td>
+                <p>
+                  TR1 Functions
+                </p>
+                </td>
+</tr>
+<tr>
+<td>
+                <p>
+                  boost_math_tr1-&lt;suffix&gt;
+                </p>
+                </td>
+<td>
+                <p>
+                  double
+                </p>
+                </td>
+<td>
+                <p>
+                  TR1 Functions
+                </p>
+                </td>
+</tr>
+<tr>
+<td>
+                <p>
+                  boost_math_tr1l-&lt;suffix&gt;
+                </p>
+                </td>
+<td>
+                <p>
+                  long double
+                </p>
+                </td>
+<td>
+                <p>
+                  TR1 Functions
+                </p>
+                </td>
+</tr>
+</tbody>
+</table></div>
+<p>
+        </p>
+<p>
+          Where <code class="computeroutput"><span class="special">&lt;</span><span class="identifier">suffix</span><span class="special">&gt;</span></code> encodes the compiler and build options
+          used to build the libraries: for example "libboost_math_tr1-vc80-mt-gd.lib"
+          would be the statically linked TR1 library to use with Visual C++ 8.0,
+          in multithreading debug mode, with the DLL VC++ runtime, where as "boost_math_tr1-vc80-mt.lib"
+          would be import library for the TR1 DLL to be used with Visual C++ 8.0
+          with the release multithreaded DLL VC++ runtime. Refer to the getting started
+          guide for a <a href="http://www.boost.org/doc/libs/1_35_0/more/getting_started/windows.html#library-naming" target="_top">full
+          explanation of the <code class="computeroutput"><span class="special">&lt;</span><span class="identifier">suffix</span><span class="special">&gt;</span></code> meanings</a>.
+        </p>
+<p>
+        </p>
+<div class="note"><table border="0" summary="Note">
+<tr>
+<td rowspan="2" align="center" valign="top" width="25"><img alt="[Note]" src="../../../../doc/html/images/note.png"></td>
+<th align="left">Note</th>
+</tr>
+<tr><td align="left" valign="top">
+<p>
+            Visual C++ users will typically have the correct library variant to link
+            against selected for them by boost/math/tr1.hpp based on your compiler
+            settings.
+          </p>
+<p>
+            Users will need to define BOOST_MATH_TR1_DYN_LINK when building their
+            code if they want to link against the DLL versions of these libraries
+            rather than the static versions.
+          </p>
+<p>
+            Users can disable auto-linking by defining BOOST_MATH_TR1_NO_LIB when
+            building: this is typically only used when linking against a customised
+            build of the libraries.
+          </p>
+</td></tr>
+</table></div>
+<p>
+        </p>
+<div class="note"><table border="0" summary="Note">
+<tr>
+<td rowspan="2" align="center" valign="top" width="25"><img alt="[Note]" src="../../../../doc/html/images/note.png"></td>
+<th align="left">Note</th>
+</tr>
+<tr><td align="left" valign="top"><p>
+            Linux and Unix users will generally only have one variant of these libraries
+            installed, and can generally just link against -lboost_math_tr1 etc.
+          </p></td></tr>
+</table></div>
+<p>
+        <a name="math_toolkit.main_overview.tr1.usage_recomendations"></a>
+        </p>
+<h5>
+<a name="id550808"></a>
+          <a class="link" href="tr1.html#math_toolkit.main_overview.tr1.usage_recomendations">Usage
+          Recomendations</a>
+        </h5>
+<p>
+        </p>
+<p>
+          This library now presents the user with a choice:
+        </p>
+<p>
+        </p>
+<div class="itemizedlist"><ul type="disc">
+<li>
+            To include the header only versions of the functions and have an easier
+            time linking, but a longer compile time.
+          </li>
+<li>
+            To include the TR1 headers and link against an external library.
+          </li>
+</ul></div>
+<p>
+        </p>
+<p>
+          Which option you choose depends largely on how you prefer to work and how
+          your system is set up.
+        </p>
+<p>
+        </p>
+<p>
+          For example a casual user who just needs the acosh function, would probably
+          be better off including <code class="computeroutput"><span class="special">&lt;</span><span class="identifier">boost</span><span class="special">/</span><span class="identifier">math</span><span class="special">/</span><span class="identifier">special_functions</span><span class="special">/</span><span class="identifier">acosh</span><span class="special">.</span><span class="identifier">hpp</span><span class="special">&gt;</span></code>
+          and using <code class="computeroutput"><span class="identifier">boost</span><span class="special">::</span><span class="identifier">math</span><span class="special">::</span><span class="identifier">acosh</span><span class="special">(</span><span class="identifier">x</span><span class="special">)</span></code> in
+          their code.
+        </p>
+<p>
+        </p>
+<p>
+          However, for large scale software development where compile times are significant,
+          and where the Boost libraries are already built and installed on the system,
+          then including <code class="computeroutput"><span class="special">&lt;</span><span class="identifier">boost</span><span class="special">/</span><span class="identifier">math</span><span class="special">/</span><span class="identifier">tr1</span><span class="special">.</span><span class="identifier">hpp</span><span class="special">&gt;</span></code> and using <code class="computeroutput"><span class="identifier">boost</span><span class="special">::</span><span class="identifier">math</span><span class="special">::</span><span class="identifier">tr1</span><span class="special">::</span><span class="identifier">acosh</span><span class="special">(</span><span class="identifier">x</span><span class="special">)</span></code>
+          will speed up compile times, reduce object files sizes (since there are
+          no templates being instantiated any more), and also speed up debugging
+          runtimes - since the externally compiled libraries can be compiler optimised,
+          rather than built using full settings - the difference in performance between
+          <a class="link" href="../perf/getting_best.html" title="Getting the Best Performance from this Library">release and debug builds
+          can be as much as 20 times</a>, so for complex applications this can
+          be a big win.
+        </p>
+<p>
+        <a name="math_toolkit.main_overview.tr1.supported_c99_functions"></a>
+        </p>
+<h5>
+<a name="id551101"></a>
+          <a class="link" href="tr1.html#math_toolkit.main_overview.tr1.supported_c99_functions">Supported
+          C99 Functions</a>
+        </h5>
+<p>
+        </p>
+<p>
+          See also the <a class="link" href="../special/extern_c/c99.html" title="C99 C Functions">quick reference
+          guide for these functions</a>.
+        </p>
+<p>
+        
+</p>
+<pre class="programlisting"><span class="keyword">namespace</span> <span class="identifier">boost</span><span class="special">{</span> <span class="keyword">namespace</span> <span class="identifier">math</span><span class="special">{</span> <span class="keyword">namespace</span> <span class="identifier">tr1</span><span class="special">{</span> <span class="keyword">extern</span> <span class="string">"C"</span><span class="special">{</span>
+
+<span class="keyword">typedef</span> <span class="identifier">unspecified</span> <span class="identifier">float_t</span><span class="special">;</span>
+<span class="keyword">typedef</span> <span class="identifier">unspecified</span> <span class="identifier">double_t</span><span class="special">;</span>
+
+<span class="keyword">double</span> <span class="identifier">acosh</span><span class="special">(</span><span class="keyword">double</span> <span class="identifier">x</span><span class="special">);</span>
+<span class="keyword">float</span> <span class="identifier">acoshf</span><span class="special">(</span><span class="keyword">float</span> <span class="identifier">x</span><span class="special">);</span>
+<span class="keyword">long</span> <span class="keyword">double</span> <span class="identifier">acoshl</span><span class="special">(</span><span class="keyword">long</span> <span class="keyword">double</span> <span class="identifier">x</span><span class="special">);</span>
+
+<span class="keyword">double</span> <span class="identifier">asinh</span><span class="special">(</span><span class="keyword">double</span> <span class="identifier">x</span><span class="special">);</span>
+<span class="keyword">float</span> <span class="identifier">asinhf</span><span class="special">(</span><span class="keyword">float</span> <span class="identifier">x</span><span class="special">);</span>
+<span class="keyword">long</span> <span class="keyword">double</span> <span class="identifier">asinhl</span><span class="special">(</span><span class="keyword">long</span> <span class="keyword">double</span> <span class="identifier">x</span><span class="special">);</span>
+
+<span class="keyword">double</span> <span class="identifier">atanh</span><span class="special">(</span><span class="keyword">double</span> <span class="identifier">x</span><span class="special">);</span>
+<span class="keyword">float</span> <span class="identifier">atanhf</span><span class="special">(</span><span class="keyword">float</span> <span class="identifier">x</span><span class="special">);</span>
+<span class="keyword">long</span> <span class="keyword">double</span> <span class="identifier">atanhl</span><span class="special">(</span><span class="keyword">long</span> <span class="keyword">double</span> <span class="identifier">x</span><span class="special">);</span>
+
+<span class="keyword">double</span> <span class="identifier">cbrt</span><span class="special">(</span><span class="keyword">double</span> <span class="identifier">x</span><span class="special">);</span>
+<span class="keyword">float</span> <span class="identifier">cbrtf</span><span class="special">(</span><span class="keyword">float</span> <span class="identifier">x</span><span class="special">);</span>
+<span class="keyword">long</span> <span class="keyword">double</span> <span class="identifier">cbrtl</span><span class="special">(</span><span class="keyword">long</span> <span class="keyword">double</span> <span class="identifier">x</span><span class="special">);</span>
+
+<span class="keyword">double</span> <span class="identifier">copysign</span><span class="special">(</span><span class="keyword">double</span> <span class="identifier">x</span><span class="special">,</span> <span class="keyword">double</span> <span class="identifier">y</span><span class="special">);</span>
+<span class="keyword">float</span> <span class="identifier">copysignf</span><span class="special">(</span><span class="keyword">float</span> <span class="identifier">x</span><span class="special">,</span> <span class="keyword">float</span> <span class="identifier">y</span><span class="special">);</span>
+<span class="keyword">long</span> <span class="keyword">double</span> <span class="identifier">copysignl</span><span class="special">(</span><span class="keyword">long</span> <span class="keyword">double</span> <span class="identifier">x</span><span class="special">,</span> <span class="keyword">long</span> <span class="keyword">double</span> <span class="identifier">y</span><span class="special">);</span>
+
+<span class="keyword">double</span> <span class="identifier">erf</span><span class="special">(</span><span class="keyword">double</span> <span class="identifier">x</span><span class="special">);</span>
+<span class="keyword">float</span> <span class="identifier">erff</span><span class="special">(</span><span class="keyword">float</span> <span class="identifier">x</span><span class="special">);</span>
+<span class="keyword">long</span> <span class="keyword">double</span> <span class="identifier">erfl</span><span class="special">(</span><span class="keyword">long</span> <span class="keyword">double</span> <span class="identifier">x</span><span class="special">);</span>
+
+<span class="keyword">double</span> <span class="identifier">erfc</span><span class="special">(</span><span class="keyword">double</span> <span class="identifier">x</span><span class="special">);</span>
+<span class="keyword">float</span> <span class="identifier">erfcf</span><span class="special">(</span><span class="keyword">float</span> <span class="identifier">x</span><span class="special">);</span>
+<span class="keyword">long</span> <span class="keyword">double</span> <span class="identifier">erfcl</span><span class="special">(</span><span class="keyword">long</span> <span class="keyword">double</span> <span class="identifier">x</span><span class="special">);</span>
+
+<span class="keyword">double</span> <span class="identifier">expm1</span><span class="special">(</span><span class="keyword">double</span> <span class="identifier">x</span><span class="special">);</span>
+<span class="keyword">float</span> <span class="identifier">expm1f</span><span class="special">(</span><span class="keyword">float</span> <span class="identifier">x</span><span class="special">);</span>
+<span class="keyword">long</span> <span class="keyword">double</span> <span class="identifier">expm1l</span><span class="special">(</span><span class="keyword">long</span> <span class="keyword">double</span> <span class="identifier">x</span><span class="special">);</span>
+
+<span class="keyword">double</span> <span class="identifier">fmax</span><span class="special">(</span><span class="keyword">double</span> <span class="identifier">x</span><span class="special">,</span> <span class="keyword">double</span> <span class="identifier">y</span><span class="special">);</span>
+<span class="keyword">float</span> <span class="identifier">fmaxf</span><span class="special">(</span><span class="keyword">float</span> <span class="identifier">x</span><span class="special">,</span> <span class="keyword">float</span> <span class="identifier">y</span><span class="special">);</span>
+<span class="keyword">long</span> <span class="keyword">double</span> <span class="identifier">fmaxl</span><span class="special">(</span><span class="keyword">long</span> <span class="keyword">double</span> <span class="identifier">x</span><span class="special">,</span> <span class="keyword">long</span> <span class="keyword">double</span> <span class="identifier">y</span><span class="special">);</span>
+
+<span class="keyword">double</span> <span class="identifier">fmin</span><span class="special">(</span><span class="keyword">double</span> <span class="identifier">x</span><span class="special">,</span> <span class="keyword">double</span> <span class="identifier">y</span><span class="special">);</span>
+<span class="keyword">float</span> <span class="identifier">fminf</span><span class="special">(</span><span class="keyword">float</span> <span class="identifier">x</span><span class="special">,</span> <span class="keyword">float</span> <span class="identifier">y</span><span class="special">);</span>
+<span class="keyword">long</span> <span class="keyword">double</span> <span class="identifier">fminl</span><span class="special">(</span><span class="keyword">long</span> <span class="keyword">double</span> <span class="identifier">x</span><span class="special">,</span> <span class="keyword">long</span> <span class="keyword">double</span> <span class="identifier">y</span><span class="special">);</span>
+
+<span class="keyword">double</span> <span class="identifier">hypot</span><span class="special">(</span><span class="keyword">double</span> <span class="identifier">x</span><span class="special">,</span> <span class="keyword">double</span> <span class="identifier">y</span><span class="special">);</span>
+<span class="keyword">float</span> <span class="identifier">hypotf</span><span class="special">(</span><span class="keyword">float</span> <span class="identifier">x</span><span class="special">,</span> <span class="keyword">float</span> <span class="identifier">y</span><span class="special">);</span>
+<span class="keyword">long</span> <span class="keyword">double</span> <span class="identifier">hypotl</span><span class="special">(</span><span class="keyword">long</span> <span class="keyword">double</span> <span class="identifier">x</span><span class="special">,</span> <span class="keyword">long</span> <span class="keyword">double</span> <span class="identifier">y</span><span class="special">);</span>
+
+<span class="keyword">double</span> <span class="identifier">lgamma</span><span class="special">(</span><span class="keyword">double</span> <span class="identifier">x</span><span class="special">);</span>
+<span class="keyword">float</span> <span class="identifier">lgammaf</span><span class="special">(</span><span class="keyword">float</span> <span class="identifier">x</span><span class="special">);</span>
+<span class="keyword">long</span> <span class="keyword">double</span> <span class="identifier">lgammal</span><span class="special">(</span><span class="keyword">long</span> <span class="keyword">double</span> <span class="identifier">x</span><span class="special">);</span>
+
+<span class="keyword">long</span> <span class="keyword">long</span> <span class="identifier">llround</span><span class="special">(</span><span class="keyword">double</span> <span class="identifier">x</span><span class="special">);</span>
+<span class="keyword">long</span> <span class="keyword">long</span> <span class="identifier">llroundf</span><span class="special">(</span><span class="keyword">float</span> <span class="identifier">x</span><span class="special">);</span>
+<span class="keyword">long</span> <span class="keyword">long</span> <span class="identifier">llroundl</span><span class="special">(</span><span class="keyword">long</span> <span class="keyword">double</span> <span class="identifier">x</span><span class="special">);</span>
+
+<span class="keyword">double</span> <span class="identifier">log1p</span><span class="special">(</span><span class="keyword">double</span> <span class="identifier">x</span><span class="special">);</span>
+<span class="keyword">float</span> <span class="identifier">log1pf</span><span class="special">(</span><span class="keyword">float</span> <span class="identifier">x</span><span class="special">);</span>
+<span class="keyword">long</span> <span class="keyword">double</span> <span class="identifier">log1pl</span><span class="special">(</span><span class="keyword">long</span> <span class="keyword">double</span> <span class="identifier">x</span><span class="special">);</span>
+
+<span class="keyword">long</span> <span class="identifier">lround</span><span class="special">(</span><span class="keyword">double</span> <span class="identifier">x</span><span class="special">);</span>
+<span class="keyword">long</span> <span class="identifier">lroundf</span><span class="special">(</span><span class="keyword">float</span> <span class="identifier">x</span><span class="special">);</span>
+<span class="keyword">long</span> <span class="identifier">lroundl</span><span class="special">(</span><span class="keyword">long</span> <span class="keyword">double</span> <span class="identifier">x</span><span class="special">);</span>
+
+<span class="keyword">double</span> <span class="identifier">nextafter</span><span class="special">(</span><span class="keyword">double</span> <span class="identifier">x</span><span class="special">,</span> <span class="keyword">double</span> <span class="identifier">y</span><span class="special">);</span>
+<span class="keyword">float</span> <span class="identifier">nextafterf</span><span class="special">(</span><span class="keyword">float</span> <span class="identifier">x</span><span class="special">,</span> <span class="keyword">float</span> <span class="identifier">y</span><span class="special">);</span>
+<span class="keyword">long</span> <span class="keyword">double</span> <span class="identifier">nextafterl</span><span class="special">(</span><span class="keyword">long</span> <span class="keyword">double</span> <span class="identifier">x</span><span class="special">,</span> <span class="keyword">long</span> <span class="keyword">double</span> <span class="identifier">y</span><span class="special">);</span>
+
+<span class="keyword">double</span> <span class="identifier">nexttoward</span><span class="special">(</span><span class="keyword">double</span> <span class="identifier">x</span><span class="special">,</span> <span class="keyword">long</span> <span class="keyword">double</span> <span class="identifier">y</span><span class="special">);</span>
+<span class="keyword">float</span> <span class="identifier">nexttowardf</span><span class="special">(</span><span class="keyword">float</span> <span class="identifier">x</span><span class="special">,</span> <span class="keyword">long</span> <span class="keyword">double</span> <span class="identifier">y</span><span class="special">);</span>
+<span class="keyword">long</span> <span class="keyword">double</span> <span class="identifier">nexttowardl</span><span class="special">(</span><span class="keyword">long</span> <span class="keyword">double</span> <span class="identifier">x</span><span class="special">,</span> <span class="keyword">long</span> <span class="keyword">double</span> <span class="identifier">y</span><span class="special">);</span>
+
+<span class="keyword">double</span> <span class="identifier">round</span><span class="special">(</span><span class="keyword">double</span> <span class="identifier">x</span><span class="special">);</span>
+<span class="keyword">float</span> <span class="identifier">roundf</span><span class="special">(</span><span class="keyword">float</span> <span class="identifier">x</span><span class="special">);</span>
+<span class="keyword">long</span> <span class="keyword">double</span> <span class="identifier">roundl</span><span class="special">(</span><span class="keyword">long</span> <span class="keyword">double</span> <span class="identifier">x</span><span class="special">);</span>
+
+<span class="keyword">double</span> <span class="identifier">tgamma</span><span class="special">(</span><span class="keyword">double</span> <span class="identifier">x</span><span class="special">);</span>
+<span class="keyword">float</span> <span class="identifier">tgammaf</span><span class="special">(</span><span class="keyword">float</span> <span class="identifier">x</span><span class="special">);</span>
+<span class="keyword">long</span> <span class="keyword">double</span> <span class="identifier">tgammal</span><span class="special">(</span><span class="keyword">long</span> <span class="keyword">double</span> <span class="identifier">x</span><span class="special">);</span>
+
+<span class="keyword">double</span> <span class="identifier">trunc</span><span class="special">(</span><span class="keyword">double</span> <span class="identifier">x</span><span class="special">);</span>
+<span class="keyword">float</span> <span class="identifier">truncf</span><span class="special">(</span><span class="keyword">float</span> <span class="identifier">x</span><span class="special">);</span>
+<span class="keyword">long</span> <span class="keyword">double</span> <span class="identifier">truncl</span><span class="special">(</span><span class="keyword">long</span> <span class="keyword">double</span> <span class="identifier">x</span><span class="special">);</span>
+
+<span class="special">}}}}</span> <span class="comment">// namespaces
+</span></pre>
+<p>
+        <a name="math_toolkit.main_overview.tr1.supported_tr1_functions"></a>
+        </p>
+<h5>
+<a name="id553677"></a>
+          <a class="link" href="tr1.html#math_toolkit.main_overview.tr1.supported_tr1_functions">Supported
+          TR1 Functions</a>
+        </h5>
+<p>
+        </p>
+<p>
+          See also the <a class="link" href="../special/extern_c/tr1.html" title="C99 and TR1 C Functions Overview">quick reference
+          guide for these functions</a>.
+        </p>
+<p>
+        
+</p>
+<pre class="programlisting"><span class="keyword">namespace</span> <span class="identifier">boost</span><span class="special">{</span> <span class="keyword">namespace</span> <span class="identifier">math</span><span class="special">{</span> <span class="keyword">namespace</span> <span class="identifier">tr1</span><span class="special">{</span> <span class="keyword">extern</span> <span class="string">"C"</span><span class="special">{</span>
+   
+<span class="comment">// [5.2.1.1] associated Laguerre polynomials:
+</span><span class="keyword">double</span> <span class="identifier">assoc_laguerre</span><span class="special">(</span><span class="keyword">unsigned</span> <span class="identifier">n</span><span class="special">,</span> <span class="keyword">unsigned</span> <span class="identifier">m</span><span class="special">,</span> <span class="keyword">double</span> <span class="identifier">x</span><span class="special">);</span>
+<span class="keyword">float</span> <span class="identifier">assoc_laguerref</span><span class="special">(</span><span class="keyword">unsigned</span> <span class="identifier">n</span><span class="special">,</span> <span class="keyword">unsigned</span> <span class="identifier">m</span><span class="special">,</span> <span class="keyword">float</span> <span class="identifier">x</span><span class="special">);</span>
+<span class="keyword">long</span> <span class="keyword">double</span> <span class="identifier">assoc_laguerrel</span><span class="special">(</span><span class="keyword">unsigned</span> <span class="identifier">n</span><span class="special">,</span> <span class="keyword">unsigned</span> <span class="identifier">m</span><span class="special">,</span> <span class="keyword">long</span> <span class="keyword">double</span> <span class="identifier">x</span><span class="special">);</span>
+
+<span class="comment">// [5.2.1.2] associated Legendre functions:
+</span><span class="keyword">double</span> <span class="identifier">assoc_legendre</span><span class="special">(</span><span class="keyword">unsigned</span> <span class="identifier">l</span><span class="special">,</span> <span class="keyword">unsigned</span> <span class="identifier">m</span><span class="special">,</span> <span class="keyword">double</span> <span class="identifier">x</span><span class="special">);</span>
+<span class="keyword">float</span> <span class="identifier">assoc_legendref</span><span class="special">(</span><span class="keyword">unsigned</span> <span class="identifier">l</span><span class="special">,</span> <span class="keyword">unsigned</span> <span class="identifier">m</span><span class="special">,</span> <span class="keyword">float</span> <span class="identifier">x</span><span class="special">);</span>
+<span class="keyword">long</span> <span class="keyword">double</span> <span class="identifier">assoc_legendrel</span><span class="special">(</span><span class="keyword">unsigned</span> <span class="identifier">l</span><span class="special">,</span> <span class="keyword">unsigned</span> <span class="identifier">m</span><span class="special">,</span> <span class="keyword">long</span> <span class="keyword">double</span> <span class="identifier">x</span><span class="special">);</span>
+
+<span class="comment">// [5.2.1.3] beta function:
+</span><span class="keyword">double</span> <span class="identifier">beta</span><span class="special">(</span><span class="keyword">double</span> <span class="identifier">x</span><span class="special">,</span> <span class="keyword">double</span> <span class="identifier">y</span><span class="special">);</span>
+<span class="keyword">float</span> <span class="identifier">betaf</span><span class="special">(</span><span class="keyword">float</span> <span class="identifier">x</span><span class="special">,</span> <span class="keyword">float</span> <span class="identifier">y</span><span class="special">);</span>
+<span class="keyword">long</span> <span class="keyword">double</span> <span class="identifier">betal</span><span class="special">(</span><span class="keyword">long</span> <span class="keyword">double</span> <span class="identifier">x</span><span class="special">,</span> <span class="keyword">long</span> <span class="keyword">double</span> <span class="identifier">y</span><span class="special">);</span>
+
+<span class="comment">// [5.2.1.4] (complete) elliptic integral of the first kind:
+</span><span class="keyword">double</span> <span class="identifier">comp_ellint_1</span><span class="special">(</span><span class="keyword">double</span> <span class="identifier">k</span><span class="special">);</span>
+<span class="keyword">float</span> <span class="identifier">comp_ellint_1f</span><span class="special">(</span><span class="keyword">float</span> <span class="identifier">k</span><span class="special">);</span>
+<span class="keyword">long</span> <span class="keyword">double</span> <span class="identifier">comp_ellint_1l</span><span class="special">(</span><span class="keyword">long</span> <span class="keyword">double</span> <span class="identifier">k</span><span class="special">);</span>
+
+<span class="comment">// [5.2.1.5] (complete) elliptic integral of the second kind:
+</span><span class="keyword">double</span> <span class="identifier">comp_ellint_2</span><span class="special">(</span><span class="keyword">double</span> <span class="identifier">k</span><span class="special">);</span>
+<span class="keyword">float</span> <span class="identifier">comp_ellint_2f</span><span class="special">(</span><span class="keyword">float</span> <span class="identifier">k</span><span class="special">);</span>
+<span class="keyword">long</span> <span class="keyword">double</span> <span class="identifier">comp_ellint_2l</span><span class="special">(</span><span class="keyword">long</span> <span class="keyword">double</span> <span class="identifier">k</span><span class="special">);</span>
+
+<span class="comment">// [5.2.1.6] (complete) elliptic integral of the third kind:
+</span><span class="keyword">double</span> <span class="identifier">comp_ellint_3</span><span class="special">(</span><span class="keyword">double</span> <span class="identifier">k</span><span class="special">,</span> <span class="keyword">double</span> <span class="identifier">nu</span><span class="special">);</span>
+<span class="keyword">float</span> <span class="identifier">comp_ellint_3f</span><span class="special">(</span><span class="keyword">float</span> <span class="identifier">k</span><span class="special">,</span> <span class="keyword">float</span> <span class="identifier">nu</span><span class="special">);</span>
+<span class="keyword">long</span> <span class="keyword">double</span> <span class="identifier">comp_ellint_3l</span><span class="special">(</span><span class="keyword">long</span> <span class="keyword">double</span> <span class="identifier">k</span><span class="special">,</span> <span class="keyword">long</span> <span class="keyword">double</span> <span class="identifier">nu</span><span class="special">);</span>
+
+<span class="comment">// [5.2.1.8] regular modified cylindrical Bessel functions:
+</span><span class="keyword">double</span> <span class="identifier">cyl_bessel_i</span><span class="special">(</span><span class="keyword">double</span> <span class="identifier">nu</span><span class="special">,</span> <span class="keyword">double</span> <span class="identifier">x</span><span class="special">);</span>
+<span class="keyword">float</span> <span class="identifier">cyl_bessel_if</span><span class="special">(</span><span class="keyword">float</span> <span class="identifier">nu</span><span class="special">,</span> <span class="keyword">float</span> <span class="identifier">x</span><span class="special">);</span>
+<span class="keyword">long</span> <span class="keyword">double</span> <span class="identifier">cyl_bessel_il</span><span class="special">(</span><span class="keyword">long</span> <span class="keyword">double</span> <span class="identifier">nu</span><span class="special">,</span> <span class="keyword">long</span> <span class="keyword">double</span> <span class="identifier">x</span><span class="special">);</span>
+
+<span class="comment">// [5.2.1.9] cylindrical Bessel functions (of the first kind):
+</span><span class="keyword">double</span> <span class="identifier">cyl_bessel_j</span><span class="special">(</span><span class="keyword">double</span> <span class="identifier">nu</span><span class="special">,</span> <span class="keyword">double</span> <span class="identifier">x</span><span class="special">);</span>
+<span class="keyword">float</span> <span class="identifier">cyl_bessel_jf</span><span class="special">(</span><span class="keyword">float</span> <span class="identifier">nu</span><span class="special">,</span> <span class="keyword">float</span> <span class="identifier">x</span><span class="special">);</span>
+<span class="keyword">long</span> <span class="keyword">double</span> <span class="identifier">cyl_bessel_jl</span><span class="special">(</span><span class="keyword">long</span> <span class="keyword">double</span> <span class="identifier">nu</span><span class="special">,</span> <span class="keyword">long</span> <span class="keyword">double</span> <span class="identifier">x</span><span class="special">);</span>
+
+<span class="comment">// [5.2.1.10] irregular modified cylindrical Bessel functions:
+</span><span class="keyword">double</span> <span class="identifier">cyl_bessel_k</span><span class="special">(</span><span class="keyword">double</span> <span class="identifier">nu</span><span class="special">,</span> <span class="keyword">double</span> <span class="identifier">x</span><span class="special">);</span>
+<span class="keyword">float</span> <span class="identifier">cyl_bessel_kf</span><span class="special">(</span><span class="keyword">float</span> <span class="identifier">nu</span><span class="special">,</span> <span class="keyword">float</span> <span class="identifier">x</span><span class="special">);</span>
+<span class="keyword">long</span> <span class="keyword">double</span> <span class="identifier">cyl_bessel_kl</span><span class="special">(</span><span class="keyword">long</span> <span class="keyword">double</span> <span class="identifier">nu</span><span class="special">,</span> <span class="keyword">long</span> <span class="keyword">double</span> <span class="identifier">x</span><span class="special">);</span>
+
+<span class="comment">// [5.2.1.11] cylindrical Neumann functions;
+</span><span class="comment">// cylindrical Bessel functions (of the second kind):
+</span><span class="keyword">double</span> <span class="identifier">cyl_neumann</span><span class="special">(</span><span class="keyword">double</span> <span class="identifier">nu</span><span class="special">,</span> <span class="keyword">double</span> <span class="identifier">x</span><span class="special">);</span>
+<span class="keyword">float</span> <span class="identifier">cyl_neumannf</span><span class="special">(</span><span class="keyword">float</span> <span class="identifier">nu</span><span class="special">,</span> <span class="keyword">float</span> <span class="identifier">x</span><span class="special">);</span>
+<span class="keyword">long</span> <span class="keyword">double</span> <span class="identifier">cyl_neumannl</span><span class="special">(</span><span class="keyword">long</span> <span class="keyword">double</span> <span class="identifier">nu</span><span class="special">,</span> <span class="keyword">long</span> <span class="keyword">double</span> <span class="identifier">x</span><span class="special">);</span>
+
+<span class="comment">// [5.2.1.12] (incomplete) elliptic integral of the first kind:
+</span><span class="keyword">double</span> <span class="identifier">ellint_1</span><span class="special">(</span><span class="keyword">double</span> <span class="identifier">k</span><span class="special">,</span> <span class="keyword">double</span> <span class="identifier">phi</span><span class="special">);</span>
+<span class="keyword">float</span> <span class="identifier">ellint_1f</span><span class="special">(</span><span class="keyword">float</span> <span class="identifier">k</span><span class="special">,</span> <span class="keyword">float</span> <span class="identifier">phi</span><span class="special">);</span>
+<span class="keyword">long</span> <span class="keyword">double</span> <span class="identifier">ellint_1l</span><span class="special">(</span><span class="keyword">long</span> <span class="keyword">double</span> <span class="identifier">k</span><span class="special">,</span> <span class="keyword">long</span> <span class="keyword">double</span> <span class="identifier">phi</span><span class="special">);</span>
+
+<span class="comment">// [5.2.1.13] (incomplete) elliptic integral of the second kind:
+</span><span class="keyword">double</span> <span class="identifier">ellint_2</span><span class="special">(</span><span class="keyword">double</span> <span class="identifier">k</span><span class="special">,</span> <span class="keyword">double</span> <span class="identifier">phi</span><span class="special">);</span>
+<span class="keyword">float</span> <span class="identifier">ellint_2f</span><span class="special">(</span><span class="keyword">float</span> <span class="identifier">k</span><span class="special">,</span> <span class="keyword">float</span> <span class="identifier">phi</span><span class="special">);</span>
+<span class="keyword">long</span> <span class="keyword">double</span> <span class="identifier">ellint_2l</span><span class="special">(</span><span class="keyword">long</span> <span class="keyword">double</span> <span class="identifier">k</span><span class="special">,</span> <span class="keyword">long</span> <span class="keyword">double</span> <span class="identifier">phi</span><span class="special">);</span>
+
+<span class="comment">// [5.2.1.14] (incomplete) elliptic integral of the third kind:
+</span><span class="keyword">double</span> <span class="identifier">ellint_3</span><span class="special">(</span><span class="keyword">double</span> <span class="identifier">k</span><span class="special">,</span> <span class="keyword">double</span> <span class="identifier">nu</span><span class="special">,</span> <span class="keyword">double</span> <span class="identifier">phi</span><span class="special">);</span>
+<span class="keyword">float</span> <span class="identifier">ellint_3f</span><span class="special">(</span><span class="keyword">float</span> <span class="identifier">k</span><span class="special">,</span> <span class="keyword">float</span> <span class="identifier">nu</span><span class="special">,</span> <span class="keyword">float</span> <span class="identifier">phi</span><span class="special">);</span>
+<span class="keyword">long</span> <span class="keyword">double</span> <span class="identifier">ellint_3l</span><span class="special">(</span><span class="keyword">long</span> <span class="keyword">double</span> <span class="identifier">k</span><span class="special">,</span> <span class="keyword">long</span> <span class="keyword">double</span> <span class="identifier">nu</span><span class="special">,</span> <span class="keyword">long</span> <span class="keyword">double</span> <span class="identifier">phi</span><span class="special">);</span>
+
+<span class="comment">// [5.2.1.15] exponential integral:
+</span><span class="keyword">double</span> <span class="identifier">expint</span><span class="special">(</span><span class="keyword">double</span> <span class="identifier">x</span><span class="special">);</span>
+<span class="keyword">float</span> <span class="identifier">expintf</span><span class="special">(</span><span class="keyword">float</span> <span class="identifier">x</span><span class="special">);</span>
+<span class="keyword">long</span> <span class="keyword">double</span> <span class="identifier">expintl</span><span class="special">(</span><span class="keyword">long</span> <span class="keyword">double</span> <span class="identifier">x</span><span class="special">);</span>
+
+<span class="comment">// [5.2.1.16] Hermite polynomials:
+</span><span class="keyword">double</span> <span class="identifier">hermite</span><span class="special">(</span><span class="keyword">unsigned</span> <span class="identifier">n</span><span class="special">,</span> <span class="keyword">double</span> <span class="identifier">x</span><span class="special">);</span>
+<span class="keyword">float</span> <span class="identifier">hermitef</span><span class="special">(</span><span class="keyword">unsigned</span> <span class="identifier">n</span><span class="special">,</span> <span class="keyword">float</span> <span class="identifier">x</span><span class="special">);</span>
+<span class="keyword">long</span> <span class="keyword">double</span> <span class="identifier">hermitel</span><span class="special">(</span><span class="keyword">unsigned</span> <span class="identifier">n</span><span class="special">,</span> <span class="keyword">long</span> <span class="keyword">double</span> <span class="identifier">x</span><span class="special">);</span>
+
+<span class="comment">// [5.2.1.18] Laguerre polynomials:
+</span><span class="keyword">double</span> <span class="identifier">laguerre</span><span class="special">(</span><span class="keyword">unsigned</span> <span class="identifier">n</span><span class="special">,</span> <span class="keyword">double</span> <span class="identifier">x</span><span class="special">);</span>
+<span class="keyword">float</span> <span class="identifier">laguerref</span><span class="special">(</span><span class="keyword">unsigned</span> <span class="identifier">n</span><span class="special">,</span> <span class="keyword">float</span> <span class="identifier">x</span><span class="special">);</span>
+<span class="keyword">long</span> <span class="keyword">double</span> <span class="identifier">laguerrel</span><span class="special">(</span><span class="keyword">unsigned</span> <span class="identifier">n</span><span class="special">,</span> <span class="keyword">long</span> <span class="keyword">double</span> <span class="identifier">x</span><span class="special">);</span>
+
+<span class="comment">// [5.2.1.19] Legendre polynomials:
+</span><span class="keyword">double</span> <span class="identifier">legendre</span><span class="special">(</span><span class="keyword">unsigned</span> <span class="identifier">l</span><span class="special">,</span> <span class="keyword">double</span> <span class="identifier">x</span><span class="special">);</span>
+<span class="keyword">float</span> <span class="identifier">legendref</span><span class="special">(</span><span class="keyword">unsigned</span> <span class="identifier">l</span><span class="special">,</span> <span class="keyword">float</span> <span class="identifier">x</span><span class="special">);</span>
+<span class="keyword">long</span> <span class="keyword">double</span> <span class="identifier">legendrel</span><span class="special">(</span><span class="keyword">unsigned</span> <span class="identifier">l</span><span class="special">,</span> <span class="keyword">long</span> <span class="keyword">double</span> <span class="identifier">x</span><span class="special">);</span>
+
+<span class="comment">// [5.2.1.20] Riemann zeta function:
+</span><span class="keyword">double</span> <span class="identifier">riemann_zeta</span><span class="special">(</span><span class="keyword">double</span><span class="special">);</span>
+<span class="keyword">float</span> <span class="identifier">riemann_zetaf</span><span class="special">(</span><span class="keyword">float</span><span class="special">);</span>
+<span class="keyword">long</span> <span class="keyword">double</span> <span class="identifier">riemann_zetal</span><span class="special">(</span><span class="keyword">long</span> <span class="keyword">double</span><span class="special">);</span>
+
+<span class="comment">// [5.2.1.21] spherical Bessel functions (of the first kind):
+</span><span class="keyword">double</span> <span class="identifier">sph_bessel</span><span class="special">(</span><span class="keyword">unsigned</span> <span class="identifier">n</span><span class="special">,</span> <span class="keyword">double</span> <span class="identifier">x</span><span class="special">);</span>
+<span class="keyword">float</span> <span class="identifier">sph_besself</span><span class="special">(</span><span class="keyword">unsigned</span> <span class="identifier">n</span><span class="special">,</span> <span class="keyword">float</span> <span class="identifier">x</span><span class="special">);</span>
+<span class="keyword">long</span> <span class="keyword">double</span> <span class="identifier">sph_bessell</span><span class="special">(</span><span class="keyword">unsigned</span> <span class="identifier">n</span><span class="special">,</span> <span class="keyword">long</span> <span class="keyword">double</span> <span class="identifier">x</span><span class="special">);</span>
+
+<span class="comment">// [5.2.1.22] spherical associated Legendre functions:
+</span><span class="keyword">double</span> <span class="identifier">sph_legendre</span><span class="special">(</span><span class="keyword">unsigned</span> <span class="identifier">l</span><span class="special">,</span> <span class="keyword">unsigned</span> <span class="identifier">m</span><span class="special">,</span> <span class="keyword">double</span> <span class="identifier">theta</span><span class="special">);</span>
+<span class="keyword">float</span> <span class="identifier">sph_legendref</span><span class="special">(</span><span class="keyword">unsigned</span> <span class="identifier">l</span><span class="special">,</span> <span class="keyword">unsigned</span> <span class="identifier">m</span><span class="special">,</span> <span class="keyword">float</span> <span class="identifier">theta</span><span class="special">);</span>
+<span class="keyword">long</span> <span class="keyword">double</span> <span class="identifier">sph_legendrel</span><span class="special">(</span><span class="keyword">unsigned</span> <span class="identifier">l</span><span class="special">,</span> <span class="keyword">unsigned</span> <span class="identifier">m</span><span class="special">,</span> <span class="keyword">long</span> <span class="keyword">double</span> <span class="identifier">theta</span><span class="special">);</span>
+
+<span class="comment">// [5.2.1.23] spherical Neumann functions;
+</span><span class="comment">// spherical Bessel functions (of the second kind):
+</span><span class="keyword">double</span> <span class="identifier">sph_neumann</span><span class="special">(</span><span class="keyword">unsigned</span> <span class="identifier">n</span><span class="special">,</span> <span class="keyword">double</span> <span class="identifier">x</span><span class="special">);</span>
+<span class="keyword">float</span> <span class="identifier">sph_neumannf</span><span class="special">(</span><span class="keyword">unsigned</span> <span class="identifier">n</span><span class="special">,</span> <span class="keyword">float</span> <span class="identifier">x</span><span class="special">);</span>
+<span class="keyword">long</span> <span class="keyword">double</span> <span class="identifier">sph_neumannl</span><span class="special">(</span><span class="keyword">unsigned</span> <span class="identifier">n</span><span class="special">,</span> <span class="keyword">long</span> <span class="keyword">double</span> <span class="identifier">x</span><span class="special">);</span>
+
+<span class="special">}}}}</span> <span class="comment">// namespaces
+</span></pre>
+<p>
+        </p>
+<p>
+          In addition sufficient additional overloads of the <code class="computeroutput"><span class="keyword">double</span></code>
+          versions of the above functions are provided, so that calling the function
+          with any mixture of <code class="computeroutput"><span class="keyword">float</span></code>,
+          <code class="computeroutput"><span class="keyword">double</span></code>, <code class="computeroutput"><span class="keyword">long</span>
+          <span class="keyword">double</span></code>, or <span class="emphasis"><em>integer</em></span>
+          arguments is supported, with the return type determined by the <a class="link" href="result_type.html" title="Calculation of the Type of the Result"><span class="emphasis"><em>result
+          type calculation rules</em></span></a>.
+        </p>
+<p>
+        <a name="math_toolkit.main_overview.tr1.currently_unsupported_c99_functions"></a>
+        </p>
+<h5>
+<a name="id557243"></a>
+          <a class="link" href="tr1.html#math_toolkit.main_overview.tr1.currently_unsupported_c99_functions">Currently
+          Unsupported C99 Functions</a>
+        </h5>
+<p>
+        
+</p>
+<pre class="programlisting"><span class="keyword">double</span> <span class="identifier">exp2</span><span class="special">(</span><span class="keyword">double</span> <span class="identifier">x</span><span class="special">);</span>
+<span class="keyword">float</span> <span class="identifier">exp2f</span><span class="special">(</span><span class="keyword">float</span> <span class="identifier">x</span><span class="special">);</span>
+<span class="keyword">long</span> <span class="keyword">double</span> <span class="identifier">exp2l</span><span class="special">(</span><span class="keyword">long</span> <span class="keyword">double</span> <span class="identifier">x</span><span class="special">);</span>
+
+<span class="keyword">double</span> <span class="identifier">fdim</span><span class="special">(</span><span class="keyword">double</span> <span class="identifier">x</span><span class="special">,</span> <span class="keyword">double</span> <span class="identifier">y</span><span class="special">);</span>
+<span class="keyword">float</span> <span class="identifier">fdimf</span><span class="special">(</span><span class="keyword">float</span> <span class="identifier">x</span><span class="special">,</span> <span class="keyword">float</span> <span class="identifier">y</span><span class="special">);</span>
+<span class="keyword">long</span> <span class="keyword">double</span> <span class="identifier">fdiml</span><span class="special">(</span><span class="keyword">long</span> <span class="keyword">double</span> <span class="identifier">x</span><span class="special">,</span> <span class="keyword">long</span> <span class="keyword">double</span> <span class="identifier">y</span><span class="special">);</span>
+
+<span class="keyword">double</span> <span class="identifier">fma</span><span class="special">(</span><span class="keyword">double</span> <span class="identifier">x</span><span class="special">,</span> <span class="keyword">double</span> <span class="identifier">y</span><span class="special">,</span> <span class="keyword">double</span> <span class="identifier">z</span><span class="special">);</span>
+<span class="keyword">float</span> <span class="identifier">fmaf</span><span class="special">(</span><span class="keyword">float</span> <span class="identifier">x</span><span class="special">,</span> <span class="keyword">float</span> <span class="identifier">y</span><span class="special">,</span> <span class="keyword">float</span> <span class="identifier">z</span><span class="special">);</span>
+<span class="keyword">long</span> <span class="keyword">double</span> <span class="identifier">fmal</span><span class="special">(</span><span class="keyword">long</span> <span class="keyword">double</span> <span class="identifier">x</span><span class="special">,</span> <span class="keyword">long</span> <span class="keyword">double</span> <span class="identifier">y</span><span class="special">,</span> <span class="keyword">long</span> <span class="keyword">double</span> <span class="identifier">z</span><span class="special">);</span>
+
+<span class="keyword">int</span> <span class="identifier">ilogb</span><span class="special">(</span><span class="keyword">double</span> <span class="identifier">x</span><span class="special">);</span>
+<span class="keyword">int</span> <span class="identifier">ilogbf</span><span class="special">(</span><span class="keyword">float</span> <span class="identifier">x</span><span class="special">);</span>
+<span class="keyword">int</span> <span class="identifier">ilogbl</span><span class="special">(</span><span class="keyword">long</span> <span class="keyword">double</span> <span class="identifier">x</span><span class="special">);</span>
+
+<span class="keyword">long</span> <span class="keyword">long</span> <span class="identifier">llrint</span><span class="special">(</span><span class="keyword">double</span> <span class="identifier">x</span><span class="special">);</span>
+<span class="keyword">long</span> <span class="keyword">long</span> <span class="identifier">llrintf</span><span class="special">(</span><span class="keyword">float</span> <span class="identifier">x</span><span class="special">);</span>
+<span class="keyword">long</span> <span class="keyword">long</span> <span class="identifier">llrintl</span><span class="special">(</span><span class="keyword">long</span> <span class="keyword">double</span> <span class="identifier">x</span><span class="special">);</span>
+
+<span class="keyword">double</span> <span class="identifier">log2</span><span class="special">(</span><span class="keyword">double</span> <span class="identifier">x</span><span class="special">);</span>
+<span class="keyword">float</span> <span class="identifier">log2f</span><span class="special">(</span><span class="keyword">float</span> <span class="identifier">x</span><span class="special">);</span>
+<span class="keyword">long</span> <span class="keyword">double</span> <span class="identifier">log2l</span><span class="special">(</span><span class="keyword">long</span> <span class="keyword">double</span> <span class="identifier">x</span><span class="special">);</span>
+
+<span class="keyword">double</span> <span class="identifier">logb</span><span class="special">(</span><span class="keyword">double</span> <span class="identifier">x</span><span class="special">);</span>
+<span class="keyword">float</span> <span class="identifier">logbf</span><span class="special">(</span><span class="keyword">float</span> <span class="identifier">x</span><span class="special">);</span>
+<span class="keyword">long</span> <span class="keyword">double</span> <span class="identifier">logbl</span><span class="special">(</span><span class="keyword">long</span> <span class="keyword">double</span> <span class="identifier">x</span><span class="special">);</span>
+
+<span class="keyword">long</span> <span class="identifier">lrint</span><span class="special">(</span><span class="keyword">double</span> <span class="identifier">x</span><span class="special">);</span>
+<span class="keyword">long</span> <span class="identifier">lrintf</span><span class="special">(</span><span class="keyword">float</span> <span class="identifier">x</span><span class="special">);</span>
+<span class="keyword">long</span> <span class="identifier">lrintl</span><span class="special">(</span><span class="keyword">long</span> <span class="keyword">double</span> <span class="identifier">x</span><span class="special">);</span>
+
+<span class="keyword">double</span> <span class="identifier">nan</span><span class="special">(</span><span class="keyword">const</span> <span class="keyword">char</span> <span class="special">*</span><span class="identifier">str</span><span class="special">);</span>
+<span class="keyword">float</span> <span class="identifier">nanf</span><span class="special">(</span><span class="keyword">const</span> <span class="keyword">char</span> <span class="special">*</span><span class="identifier">str</span><span class="special">);</span>
+<span class="keyword">long</span> <span class="keyword">double</span> <span class="identifier">nanl</span><span class="special">(</span><span class="keyword">const</span> <span class="keyword">char</span> <span class="special">*</span><span class="identifier">str</span><span class="special">);</span>
+
+<span class="keyword">double</span> <span class="identifier">nearbyint</span><span class="special">(</span><span class="keyword">double</span> <span class="identifier">x</span><span class="special">);</span>
+<span class="keyword">float</span> <span class="identifier">nearbyintf</span><span class="special">(</span><span class="keyword">float</span> <span class="identifier">x</span><span class="special">);</span>
+<span class="keyword">long</span> <span class="keyword">double</span> <span class="identifier">nearbyintl</span><span class="special">(</span><span class="keyword">long</span> <span class="keyword">double</span> <span class="identifier">x</span><span class="special">);</span>
+
+<span class="keyword">double</span> <span class="identifier">remainder</span><span class="special">(</span><span class="keyword">double</span> <span class="identifier">x</span><span class="special">,</span> <span class="keyword">double</span> <span class="identifier">y</span><span class="special">);</span>
+<span class="keyword">float</span> <span class="identifier">remainderf</span><span class="special">(</span><span class="keyword">float</span> <span class="identifier">x</span><span class="special">,</span> <span class="keyword">float</span> <span class="identifier">y</span><span class="special">);</span>
+<span class="keyword">long</span> <span class="keyword">double</span> <span class="identifier">remainderl</span><span class="special">(</span><span class="keyword">long</span> <span class="keyword">double</span> <span class="identifier">x</span><span class="special">,</span> <span class="keyword">long</span> <span class="keyword">double</span> <span class="identifier">y</span><span class="special">);</span>
+
+<span class="keyword">double</span> <span class="identifier">remquo</span><span class="special">(</span><span class="keyword">double</span> <span class="identifier">x</span><span class="special">,</span> <span class="keyword">double</span> <span class="identifier">y</span><span class="special">,</span> <span class="keyword">int</span> <span class="special">*</span><span class="identifier">pquo</span><span class="special">);</span>
+<span class="keyword">float</span> <span class="identifier">remquof</span><span class="special">(</span><span class="keyword">float</span> <span class="identifier">x</span><span class="special">,</span> <span class="keyword">float</span> <span class="identifier">y</span><span class="special">,</span> <span class="keyword">int</span> <span class="special">*</span><span class="identifier">pquo</span><span class="special">);</span>
+<span class="keyword">long</span> <span class="keyword">double</span> <span class="identifier">remquol</span><span class="special">(</span><span class="keyword">long</span> <span class="keyword">double</span> <span class="identifier">x</span><span class="special">,</span> <span class="keyword">long</span> <span class="keyword">double</span> <span class="identifier">y</span><span class="special">,</span> <span class="keyword">int</span> <span class="special">*</span><span class="identifier">pquo</span><span class="special">);</span>
+
+<span class="keyword">double</span> <span class="identifier">rint</span><span class="special">(</span><span class="keyword">double</span> <span class="identifier">x</span><span class="special">);</span>
+<span class="keyword">float</span> <span class="identifier">rintf</span><span class="special">(</span><span class="keyword">float</span> <span class="identifier">x</span><span class="special">);</span>
+<span class="keyword">long</span> <span class="keyword">double</span> <span class="identifier">rintl</span><span class="special">(</span><span class="keyword">long</span> <span class="keyword">double</span> <span class="identifier">x</span><span class="special">);</span>
+
+<span class="keyword">double</span> <span class="identifier">scalbln</span><span class="special">(</span><span class="keyword">double</span> <span class="identifier">x</span><span class="special">,</span> <span class="keyword">long</span> <span class="identifier">ex</span><span class="special">);</span>
+<span class="keyword">float</span> <span class="identifier">scalblnf</span><span class="special">(</span><span class="keyword">float</span> <span class="identifier">x</span><span class="special">,</span> <span class="keyword">long</span> <span class="identifier">ex</span><span class="special">);</span>
+<span class="keyword">long</span> <span class="keyword">double</span> <span class="identifier">scalblnl</span><span class="special">(</span><span class="keyword">long</span> <span class="keyword">double</span> <span class="identifier">x</span><span class="special">,</span> <span class="keyword">long</span> <span class="identifier">ex</span><span class="special">);</span>
+
+<span class="keyword">double</span> <span class="identifier">scalbn</span><span class="special">(</span><span class="keyword">double</span> <span class="identifier">x</span><span class="special">,</span> <span class="keyword">int</span> <span class="identifier">ex</span><span class="special">);</span>
+<span class="keyword">float</span> <span class="identifier">scalbnf</span><span class="special">(</span><span class="keyword">float</span> <span class="identifier">x</span><span class="special">,</span> <span class="keyword">int</span> <span class="identifier">ex</span><span class="special">);</span>
+<span class="keyword">long</span> <span class="keyword">double</span> <span class="identifier">scalbnl</span><span class="special">(</span><span class="keyword">long</span> <span class="keyword">double</span> <span class="identifier">x</span><span class="special">,</span> <span class="keyword">int</span> <span class="identifier">ex</span><span class="special">);</span>
+</pre>
+<p>
+        <a name="math_toolkit.main_overview.tr1.currently_unsupported_tr1_functions"></a>
+        </p>
+<h5>
+<a name="id559283"></a>
+          <a class="link" href="tr1.html#math_toolkit.main_overview.tr1.currently_unsupported_tr1_functions">Currently
+          Unsupported TR1 Functions</a>
+        </h5>
+<p>
+        
+</p>
+<pre class="programlisting"><span class="comment">// [5.2.1.7] confluent hypergeometric functions:
+</span><span class="keyword">double</span> <span class="identifier">conf_hyperg</span><span class="special">(</span><span class="keyword">double</span> <span class="identifier">a</span><span class="special">,</span> <span class="keyword">double</span> <span class="identifier">c</span><span class="special">,</span> <span class="keyword">double</span> <span class="identifier">x</span><span class="special">);</span>
+<span class="keyword">float</span> <span class="identifier">conf_hypergf</span><span class="special">(</span><span class="keyword">float</span> <span class="identifier">a</span><span class="special">,</span> <span class="keyword">float</span> <span class="identifier">c</span><span class="special">,</span> <span class="keyword">float</span> <span class="identifier">x</span><span class="special">);</span>
+<span class="keyword">long</span> <span class="keyword">double</span> <span class="identifier">conf_hypergl</span><span class="special">(</span><span class="keyword">long</span> <span class="keyword">double</span> <span class="identifier">a</span><span class="special">,</span> <span class="keyword">long</span> <span class="keyword">double</span> <span class="identifier">c</span><span class="special">,</span> <span class="keyword">long</span> <span class="keyword">double</span> <span class="identifier">x</span><span class="special">);</span>
+
+<span class="comment">// [5.2.1.17] hypergeometric functions:
+</span><span class="keyword">double</span> <span class="identifier">hyperg</span><span class="special">(</span><span class="keyword">double</span> <span class="identifier">a</span><span class="special">,</span> <span class="keyword">double</span> <span class="identifier">b</span><span class="special">,</span> <span class="keyword">double</span> <span class="identifier">c</span><span class="special">,</span> <span class="keyword">double</span> <span class="identifier">x</span><span class="special">);</span>
+<span class="keyword">float</span> <span class="identifier">hypergf</span><span class="special">(</span><span class="keyword">float</span> <span class="identifier">a</span><span class="special">,</span> <span class="keyword">float</span> <span class="identifier">b</span><span class="special">,</span> <span class="keyword">float</span> <span class="identifier">c</span><span class="special">,</span> <span class="keyword">float</span> <span class="identifier">x</span><span class="special">);</span>
+<span class="keyword">long</span> <span class="keyword">double</span> <span class="identifier">hypergl</span><span class="special">(</span><span class="keyword">long</span> <span class="keyword">double</span> <span class="identifier">a</span><span class="special">,</span> <span class="keyword">long</span> <span class="keyword">double</span> <span class="identifier">b</span><span class="special">,</span> <span class="keyword">long</span> <span class="keyword">double</span> <span class="identifier">c</span><span class="special">,</span>
+<span class="keyword">long</span> <span class="keyword">double</span> <span class="identifier">x</span><span class="special">);</span>
+</pre>
+<p>
+      </p>
+</div>
+<table xmlns:rev="http://www.cs.rpi.edu/~gregod/boost/tools/doc/revision" width="100%"><tr>
+<td align="left"></td>
+<td align="right"><div class="copyright-footer">Copyright © 2006 , 2007, 2008 John Maddock, Paul A. Bristow, Hubert
+      Holin, Xiaogang Zhang, Bruno Lalande and Gautam Sewani<p>
+        Distributed under the Boost Software License, Version 1.0. (See accompanying
+        file LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_0.txt)
+      </p>
+</div></td>
+</tr></table>
+<hr>
+<div class="spirit-nav">
+<a accesskey="p" href="history1.html"><img src="../../../../doc/html/images/prev.png" alt="Prev"></a><a accesskey="u" href="../main_overview.html"><img src="../../../../doc/html/images/up.png" alt="Up"></a><a accesskey="h" href="../../index.html"><img src="../../../../doc/html/images/home.png" alt="Home"></a><a accesskey="n" href="contact.html"><img src="../../../../doc/html/images/next.png" alt="Next"></a>
+</div>
+</body>
+</html>

Added: sandbox/tools/auto_index/example/math/doc/sf_and_dist/html/math_toolkit/perf.html
==============================================================================
--- (empty file)
+++ sandbox/tools/auto_index/example/math/doc/sf_and_dist/html/math_toolkit/perf.html	2008-11-28 05:25:28 EST (Fri, 28 Nov 2008)
@@ -0,0 +1,56 @@
+<html>
+<head>
+<meta http-equiv="Content-Type" content="text/html; charset=ISO-8859-1">
+<title>Performance</title>
+<link rel="stylesheet" href="../boostbook.css" type="text/css">
+<meta name="generator" content="DocBook XSL Stylesheets Vsnapshot_8125">
+<link rel="home" href="../index.html" title="Math Toolkit">
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+<link rel="next" href="perf/perf_over.html" title="Performance Overview">
+</head>
+<body bgcolor="white" text="black" link="#0000FF" vlink="#840084" alink="#0000FF">
+<table cellpadding="2" width="100%"><tr>
+<td valign="top"><img alt="Boost C++ Libraries" width="277" height="86" src="../../../boost.png"></td>
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+<hr>
+<div class="spirit-nav">
+<a accesskey="p" href="policy/pol_ref/pol_ref_ref.html"><img src="../../../doc/html/images/prev.png" alt="Prev"></a><a accesskey="u" href="../index.html"><img src="../../../doc/html/images/up.png" alt="Up"></a><a accesskey="h" href="../index.html"><img src="../../../doc/html/images/home.png" alt="Home"></a><a accesskey="n" href="perf/perf_over.html"><img src="../../../doc/html/images/next.png" alt="Next"></a>
+</div>
+<div class="section" lang="en">
+<div class="titlepage"><div><div><h2 class="title" style="clear: both">
+<a name="math_toolkit.perf"></a><a class="link" href="perf.html" title="Performance"> Performance</a>
+</h2></div></div></div>
+<div class="toc"><dl>
+<dt><span class="section"> Performance Overview</span></dt>
+<dt><span class="section"> Interpreting these Results</span></dt>
+<dt><span class="section"><a href="perf/getting_best.html"> Getting the Best Performance
+      from this Library</a></span></dt>
+<dt><span class="section"> Comparing Compilers</span></dt>
+<dt><span class="section"> Performance Tuning Macros</span></dt>
+<dt><span class="section"><a href="perf/comparisons.html"> Comparisons to Other
+      Open Source Libraries</a></span></dt>
+<dt><span class="section"><a href="perf/perf_test_app.html"> The Performance Test
+      Application</a></span></dt>
+</dl></div>
+</div>
+<table xmlns:rev="http://www.cs.rpi.edu/~gregod/boost/tools/doc/revision" width="100%"><tr>
+<td align="left"></td>
+<td align="right"><div class="copyright-footer">Copyright © 2006 , 2007, 2008 John Maddock, Paul A. Bristow, Hubert
+      Holin, Xiaogang Zhang, Bruno Lalande and Gautam Sewani<p>
+        Distributed under the Boost Software License, Version 1.0. (See accompanying
+        file LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_0.txt)
+      </p>
+</div></td>
+</tr></table>
+<hr>
+<div class="spirit-nav">
+<a accesskey="p" href="policy/pol_ref/pol_ref_ref.html"><img src="../../../doc/html/images/prev.png" alt="Prev"></a><a accesskey="u" href="../index.html"><img src="../../../doc/html/images/up.png" alt="Up"></a><a accesskey="h" href="../index.html"><img src="../../../doc/html/images/home.png" alt="Home"></a><a accesskey="n" href="perf/perf_over.html"><img src="../../../doc/html/images/next.png" alt="Next"></a>
+</div>
+</body>
+</html>

Added: sandbox/tools/auto_index/example/math/doc/sf_and_dist/html/math_toolkit/perf/comp_compilers.html
==============================================================================
--- (empty file)
+++ sandbox/tools/auto_index/example/math/doc/sf_and_dist/html/math_toolkit/perf/comp_compilers.html	2008-11-28 05:25:28 EST (Fri, 28 Nov 2008)
@@ -0,0 +1,377 @@
+<html>
+<head>
+<meta http-equiv="Content-Type" content="text/html; charset=ISO-8859-1">
+<title>Comparing Compilers</title>
+<link rel="stylesheet" href="../../boostbook.css" type="text/css">
+<meta name="generator" content="DocBook XSL Stylesheets Vsnapshot_8125">
+<link rel="home" href="../../index.html" title="Math Toolkit">
+<link rel="up" href="../perf.html" title="Performance">
+<link rel="prev" href="getting_best.html" title="Getting the Best Performance from this Library">
+<link rel="next" href="tuning.html" title="Performance Tuning Macros">
+</head>
+<body bgcolor="white" text="black" link="#0000FF" vlink="#840084" alink="#0000FF">
+<table cellpadding="2" width="100%"><tr>
+<td valign="top"><img alt="Boost C++ Libraries" width="277" height="86" src="../../../../boost.png"></td>
+<td align="center">Home</td>
+<td align="center">Libraries</td>
+<td align="center">People</td>
+<td align="center">FAQ</td>
+<td align="center">More</td>
+</tr></table>
+<hr>
+<div class="spirit-nav">
+<a accesskey="p" href="getting_best.html"><img src="../../../../doc/html/images/prev.png" alt="Prev"></a><a accesskey="u" href="../perf.html"><img src="../../../../doc/html/images/up.png" alt="Up"></a><a accesskey="h" href="../../index.html"><img src="../../../../doc/html/images/home.png" alt="Home"></a><a accesskey="n" href="tuning.html"><img src="../../../../doc/html/images/next.png" alt="Next"></a>
+</div>
+<div class="section" lang="en">
+<div class="titlepage"><div><div><h3 class="title">
+<a name="math_toolkit.perf.comp_compilers"></a><a class="link" href="comp_compilers.html" title="Comparing Compilers"> Comparing Compilers</a>
+</h3></div></div></div>
+<p>
+        After a good choice of build settings the next most important thing you can
+        do, is choose your compiler - and the standard C library it sits on top of
+        - very carefully. GCC-3.x in particular has been found to be particularly
+        bad at inlining code, and performing the kinds of high level transformations
+        that good C++ performance demands (thankfully GCC-4.x is somewhat better
+        in this respect).
+      </p>
+<div class="table">
+<a name="id905806"></a><p class="title"><b>Table 48. Performance Comparison of Various Windows Compilers</b></p>
+<div class="table-contents"><table class="table" summary="Performance Comparison of Various Windows Compilers">
+<colgroup>
+<col>
+<col>
+<col>
+<col>
+</colgroup>
+<thead><tr>
+<th>
+            <p>
+              Function
+            </p>
+            </th>
+<th>
+            <p>
+              Intel C++ 10.0
+            </p>
+            <p>
+              ( /Ox /Qipo /QxN )
+            </p>
+            </th>
+<th>
+            <p>
+              Microsoft Visual C++ 8.0
+            </p>
+            <p>
+              ( /Ox /arch:SSE2 )
+            </p>
+            </th>
+<th>
+            <p>
+              Cygwin G++ 3.4
+            </p>
+            <p>
+              ( /O3 )
+            </p>
+            </th>
+</tr></thead>
+<tbody>
+<tr>
+<td>
+            <p>
+              <a class="link" href="../special/sf_erf/error_function.html" title="Error Functions">erf</a>
+            </p>
+            </td>
+<td>
+            <p>
+              </p>
+<p><span class="bold"><strong>1.00</strong></span></p>
+<p> </p>
+<p>(4.118e-008s)</p>
+<p>
+            </p>
+            </td>
+<td>
+            <p>
+              </p>
+<p>1.50</p>
+<p> </p>
+<p>(6.173e-008s)</p>
+<p>
+            </p>
+            </td>
+<td>
+            <p>
+              </p>
+<p>3.24</p>
+<p> </p>
+<p>(1.336e-007s)</p>
+<p>
+            </p>
+            </td>
+</tr>
+<tr>
+<td>
+            <p>
+              <a class="link" href="../special/sf_erf/error_inv.html" title="Error Function Inverses">erf_inv</a>
+            </p>
+            </td>
+<td>
+            <p>
+              </p>
+<p><span class="bold"><strong>1.00</strong></span></p>
+<p> </p>
+<p>(4.439e-008s)</p>
+<p>
+            </p>
+            </td>
+<td>
+            <p>
+              </p>
+<p>1.42</p>
+<p> </p>
+<p>(6.302e-008s)</p>
+<p>
+            </p>
+            </td>
+<td>
+            <p>
+              </p>
+<p>7.88</p>
+<p> </p>
+<p>(3.500e-007s)</p>
+<p>
+            </p>
+            </td>
+</tr>
+<tr>
+<td>
+            <p>
+              <a class="link" href="../special/sf_beta/ibeta_function.html" title="Incomplete Beta Functions">ibeta</a>
+              and <a class="link" href="../special/sf_beta/ibeta_function.html" title="Incomplete Beta Functions">ibetac</a>
+            </p>
+            </td>
+<td>
+            <p>
+              </p>
+<p><span class="bold"><strong>1.00</strong></span></p>
+<p> </p>
+<p>(1.631e-006s)</p>
+<p>
+            </p>
+            </td>
+<td>
+            <p>
+              </p>
+<p>1.14</p>
+<p> </p>
+<p>(1.852e-006s)</p>
+<p>
+            </p>
+            </td>
+<td>
+            <p>
+              </p>
+<p>3.05</p>
+<p> </p>
+<p>(4.975e-006s)</p>
+<p>
+            </p>
+            </td>
+</tr>
+<tr>
+<td>
+            <p>
+              <a class="link" href="../special/sf_beta/ibeta_inv_function.html" title="The Incomplete Beta Function Inverses">ibeta_inv</a>
+              and <a class="link" href="../special/sf_beta/ibeta_inv_function.html" title="The Incomplete Beta Function Inverses">ibetac_inv</a>
+            </p>
+            </td>
+<td>
+            <p>
+              </p>
+<p><span class="bold"><strong>1.00</strong></span></p>
+<p> </p>
+<p>(6.133e-006s)</p>
+<p>
+            </p>
+            </td>
+<td>
+            <p>
+              </p>
+<p>1.19</p>
+<p> </p>
+<p>(7.311e-006s)</p>
+<p>
+            </p>
+            </td>
+<td>
+            <p>
+              </p>
+<p>2.60</p>
+<p> </p>
+<p>(1.597e-005s)</p>
+<p>
+            </p>
+            </td>
+</tr>
+<tr>
+<td>
+            <p>
+              <a class="link" href="../special/sf_beta/ibeta_inv_function.html" title="The Incomplete Beta Function Inverses">ibeta_inva</a>,
+              <a class="link" href="../special/sf_beta/ibeta_inv_function.html" title="The Incomplete Beta Function Inverses">ibetac_inva</a>,
+              <a class="link" href="../special/sf_beta/ibeta_inv_function.html" title="The Incomplete Beta Function Inverses">ibeta_invb</a>
+              and <a class="link" href="../special/sf_beta/ibeta_inv_function.html" title="The Incomplete Beta Function Inverses">ibetac_invb</a>
+            </p>
+            </td>
+<td>
+            <p>
+              </p>
+<p><span class="bold"><strong>1.00</strong></span></p>
+<p> </p>
+<p>(2.453e-005s)</p>
+<p>
+            </p>
+            </td>
+<td>
+            <p>
+              </p>
+<p>1.16</p>
+<p> </p>
+<p>(2.847e-005s)</p>
+<p>
+            </p>
+            </td>
+<td>
+            <p>
+              </p>
+<p>2.83</p>
+<p> </p>
+<p>(6.947e-005s)</p>
+<p>
+            </p>
+            </td>
+</tr>
+<tr>
+<td>
+            <p>
+              <a class="link" href="../special/sf_gamma/igamma.html" title="Incomplete Gamma Functions">gamma_p</a>
+              and <a class="link" href="../special/sf_gamma/igamma.html" title="Incomplete Gamma Functions">gamma_q</a>
+            </p>
+            </td>
+<td>
+            <p>
+              </p>
+<p><span class="bold"><strong>1.00</strong></span></p>
+<p> </p>
+<p>(6.735e-007s)</p>
+<p>
+            </p>
+            </td>
+<td>
+            <p>
+              </p>
+<p>1.41</p>
+<p> </p>
+<p>(9.504e-007s)</p>
+<p>
+            </p>
+            </td>
+<td>
+            <p>
+              </p>
+<p>2.78</p>
+<p> </p>
+<p>(1.872e-006s)</p>
+<p>
+            </p>
+            </td>
+</tr>
+<tr>
+<td>
+            <p>
+              <a class="link" href="../special/sf_gamma/igamma_inv.html" title="Incomplete Gamma Function Inverses">gamma_p_inv</a>
+              and <a class="link" href="../special/sf_gamma/igamma_inv.html" title="Incomplete Gamma Function Inverses">gamma_q_inv</a>
+            </p>
+            </td>
+<td>
+            <p>
+              </p>
+<p><span class="bold"><strong>1.00</strong></span></p>
+<p> </p>
+<p>(2.637e-006s)</p>
+<p>
+            </p>
+            </td>
+<td>
+            <p>
+              </p>
+<p>1.38</p>
+<p> </p>
+<p>(3.631e-006s)</p>
+<p>
+            </p>
+            </td>
+<td>
+            <p>
+              </p>
+<p>3.31</p>
+<p> </p>
+<p>(8.736e-006s)</p>
+<p>
+            </p>
+            </td>
+</tr>
+<tr>
+<td>
+            <p>
+              <a class="link" href="../special/sf_gamma/igamma_inv.html" title="Incomplete Gamma Function Inverses">gamma_p_inva</a>
+              and <a class="link" href="../special/sf_gamma/igamma_inv.html" title="Incomplete Gamma Function Inverses">gamma_q_inva</a>
+            </p>
+            </td>
+<td>
+            <p>
+              </p>
+<p><span class="bold"><strong>1.00</strong></span></p>
+<p> </p>
+<p>(7.716e-006s)</p>
+<p>
+            </p>
+            </td>
+<td>
+            <p>
+              </p>
+<p>1.29</p>
+<p> </p>
+<p>(9.982e-006s)</p>
+<p>
+            </p>
+            </td>
+<td>
+            <p>
+              </p>
+<p>2.56</p>
+<p> </p>
+<p>(1.974e-005s)</p>
+<p>
+            </p>
+            </td>
+</tr>
+</tbody>
+</table></div>
+</div>
+<br class="table-break">
+</div>
+<table xmlns:rev="http://www.cs.rpi.edu/~gregod/boost/tools/doc/revision" width="100%"><tr>
+<td align="left"></td>
+<td align="right"><div class="copyright-footer">Copyright © 2006 , 2007, 2008 John Maddock, Paul A. Bristow, Hubert
+      Holin, Xiaogang Zhang, Bruno Lalande and Gautam Sewani<p>
+        Distributed under the Boost Software License, Version 1.0. (See accompanying
+        file LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_0.txt)
+      </p>
+</div></td>
+</tr></table>
+<hr>
+<div class="spirit-nav">
+<a accesskey="p" href="getting_best.html"><img src="../../../../doc/html/images/prev.png" alt="Prev"></a><a accesskey="u" href="../perf.html"><img src="../../../../doc/html/images/up.png" alt="Up"></a><a accesskey="h" href="../../index.html"><img src="../../../../doc/html/images/home.png" alt="Home"></a><a accesskey="n" href="tuning.html"><img src="../../../../doc/html/images/next.png" alt="Next"></a>
+</div>
+</body>
+</html>

Added: sandbox/tools/auto_index/example/math/doc/sf_and_dist/html/math_toolkit/perf/comparisons.html
==============================================================================
--- (empty file)
+++ sandbox/tools/auto_index/example/math/doc/sf_and_dist/html/math_toolkit/perf/comparisons.html	2008-11-28 05:25:28 EST (Fri, 28 Nov 2008)
@@ -0,0 +1,1772 @@
+<html>
+<head>
+<meta http-equiv="Content-Type" content="text/html; charset=ISO-8859-1">
+<title>Comparisons to Other Open Source Libraries</title>
+<link rel="stylesheet" href="../../boostbook.css" type="text/css">
+<meta name="generator" content="DocBook XSL Stylesheets Vsnapshot_8125">
+<link rel="home" href="../../index.html" title="Math Toolkit">
+<link rel="up" href="../perf.html" title="Performance">
+<link rel="prev" href="tuning.html" title="Performance Tuning Macros">
+<link rel="next" href="perf_test_app.html" title="The Performance Test Application">
+</head>
+<body bgcolor="white" text="black" link="#0000FF" vlink="#840084" alink="#0000FF">
+<table cellpadding="2" width="100%"><tr>
+<td valign="top"><img alt="Boost C++ Libraries" width="277" height="86" src="../../../../boost.png"></td>
+<td align="center">Home</td>
+<td align="center">Libraries</td>
+<td align="center">People</td>
+<td align="center">FAQ</td>
+<td align="center">More</td>
+</tr></table>
+<hr>
+<div class="spirit-nav">
+<a accesskey="p" href="tuning.html"><img src="../../../../doc/html/images/prev.png" alt="Prev"></a><a accesskey="u" href="../perf.html"><img src="../../../../doc/html/images/up.png" alt="Up"></a><a accesskey="h" href="../../index.html"><img src="../../../../doc/html/images/home.png" alt="Home"></a><a accesskey="n" href="perf_test_app.html"><img src="../../../../doc/html/images/next.png" alt="Next"></a>
+</div>
+<div class="section" lang="en">
+<div class="titlepage"><div><div><h3 class="title">
+<a name="math_toolkit.perf.comparisons"></a><a class="link" href="comparisons.html" title="Comparisons to Other Open Source Libraries"> Comparisons to Other
+      Open Source Libraries</a>
+</h3></div></div></div>
+<p>
+        We've run our performance tests both for our own code, and against other
+        open source implementations of the same functions. The results are presented
+        below to give you a rough idea of how they all compare.
+      </p>
+<div class="caution"><table border="0" summary="Caution">
+<tr>
+<td rowspan="2" align="center" valign="top" width="25"><img alt="[Caution]" src="../../../../doc/html/images/caution.png"></td>
+<th align="left">Caution</th>
+</tr>
+<tr><td align="left" valign="top"><p>
+          You should exercise extreme caution when interpreting these results, relative
+          performance may vary by platform, the tests use data that gives good code
+          coverage of <span class="emphasis"><em>our</em></span> code, but which may skew the results
+          towards the corner cases. Finally, remember that different libraries make
+          different choices with regard to performance verses numerical stability.
+        </p></td></tr>
+</table></div>
+<a name="math_toolkit.perf.comparisons.comparison_to_gsl_1_9_and_cephes"></a><h5>
+<a name="id908374"></a>
+        <a class="link" href="comparisons.html#math_toolkit.perf.comparisons.comparison_to_gsl_1_9_and_cephes">Comparison
+        to GSL-1.9 and Cephes</a>
+      </h5>
+<p>
+        All the results were measured on a 2.8GHz Intel Pentium 4, 2Gb RAM, Windows
+        XP machine, with all the libraries compiled with Microsoft Visual C++ 2005
+        using the <code class="computeroutput"><span class="special">/</span><span class="identifier">Ox</span>
+        <span class="special">/</span><span class="identifier">arch</span><span class="special">:</span><span class="identifier">SSE2</span></code> options.
+      </p>
+<div class="informaltable"><table class="table">
+<colgroup>
+<col>
+<col>
+<col>
+<col>
+</colgroup>
+<thead><tr>
+<th>
+              <p>
+                Function
+              </p>
+              </th>
+<th>
+              <p>
+                Boost
+              </p>
+              </th>
+<th>
+              <p>
+                GSL-1.9
+              </p>
+              </th>
+<th>
+              <p>
+                Cephes
+              </p>
+              </th>
+</tr></thead>
+<tbody>
+<tr>
+<td>
+              <p>
+                <a class="link" href="../special/sf_gamma/tgamma.html" title="Gamma">tgamma</a>
+              </p>
+              </td>
+<td>
+              <p>
+                </p>
+<p>1.50</p>
+<p> </p>
+<p>(2.566e-007s)</p>
+<p>
+              </p>
+              </td>
+<td>
+              <p>
+                </p>
+<p>1.54</p>
+<p> </p>
+<p>(2.627e-007s)</p>
+<p>
+              </p>
+              </td>
+<td>
+              <p>
+                </p>
+<p><span class="bold"><strong>1.00</strong></span></p>
+<p> </p>
+<p>(1.709e-007s)</p>
+<p>
+              </p>
+              </td>
+</tr>
+<tr>
+<td>
+              <p>
+                <a class="link" href="../special/sf_gamma/lgamma.html" title="Log Gamma">lgamma</a>
+              </p>
+              </td>
+<td>
+              <p>
+                </p>
+<p>1.73</p>
+<p> </p>
+<p>(2.688e-007s)</p>
+<p>
+              </p>
+              </td>
+<td>
+              <p>
+                </p>
+<p>3.61</p>
+<p> </p>
+<p>(5.621e-007s)</p>
+<p>
+              </p>
+              </td>
+<td>
+              <p>
+                </p>
+<p><span class="bold"><strong>1.00</strong></span></p>
+<p> </p>
+<p>(1.556e-007s)</p>
+<p>
+              </p>
+              </td>
+</tr>
+<tr>
+<td>
+              <p>
+                <a class="link" href="../special/sf_gamma/igamma.html" title="Incomplete Gamma Functions">gamma_p</a>
+                and <a class="link" href="../special/sf_gamma/igamma.html" title="Incomplete Gamma Functions">gamma_q</a>
+              </p>
+              </td>
+<td>
+              <p>
+                </p>
+<p><span class="bold"><strong>1.00</strong></span></p>
+<p> </p>
+<p>(9.504e-007s)</p>
+<p>
+              </p>
+              </td>
+<td>
+              <p>
+                </p>
+<p>2.15</p>
+<p> </p>
+<p>(2.042e-006s)</p>
+<p>
+              </p>
+              </td>
+<td>
+              <p>
+                </p>
+<p>2.57</p>
+<p> </p>
+<p>(2.439e-006s)</p>
+<p>
+              </p>
+              </td>
+</tr>
+<tr>
+<td>
+              <p>
+                <a class="link" href="../special/sf_gamma/igamma_inv.html" title="Incomplete Gamma Function Inverses">gamma_p_inv</a>
+                and <a class="link" href="../special/sf_gamma/igamma_inv.html" title="Incomplete Gamma Function Inverses">gamma_q_inv</a>
+              </p>
+              </td>
+<td>
+              <p>
+                </p>
+<p><span class="bold"><strong>1.00</strong></span></p>
+<p> </p>
+<p>(3.631e-006s)</p>
+<p>
+              </p>
+              </td>
+<td>
+              <p>
+                N/A
+              </p>
+              </td>
+<td>
+              <p>
+                +INF
+                <sup>[<a name="id908749" href="#ftn.id908749" class="footnote">1</a>]</sup>
+              </p>
+              </td>
+</tr>
+<tr>
+<td>
+              <p>
+                <a class="link" href="../special/sf_beta/ibeta_function.html" title="Incomplete Beta Functions">ibeta</a>
+                and <a class="link" href="../special/sf_beta/ibeta_function.html" title="Incomplete Beta Functions">ibetac</a>
+              </p>
+              </td>
+<td>
+              <p>
+                </p>
+<p><span class="bold"><strong>1.00</strong></span></p>
+<p> </p>
+<p>(1.852e-006s)</p>
+<p>
+              </p>
+              </td>
+<td>
+              <p>
+                </p>
+<p>1.07</p>
+<p> </p>
+<p>(1.974e-006s)</p>
+<p>
+              </p>
+              </td>
+<td>
+              <p>
+                </p>
+<p>1.07</p>
+<p> </p>
+<p>(1.974e-006s)</p>
+<p>
+              </p>
+              </td>
+</tr>
+<tr>
+<td>
+              <p>
+                <a class="link" href="../special/sf_beta/ibeta_inv_function.html" title="The Incomplete Beta Function Inverses">ibeta_inv</a>
+                and <a class="link" href="../special/sf_beta/ibeta_inv_function.html" title="The Incomplete Beta Function Inverses">ibetac_inv</a>
+              </p>
+              </td>
+<td>
+              <p>
+                </p>
+<p><span class="bold"><strong>1.00</strong></span></p>
+<p> </p>
+<p>(7.311e-006s)</p>
+<p>
+              </p>
+              </td>
+<td>
+              <p>
+                N/A
+              </p>
+              </td>
+<td>
+              <p>
+                </p>
+<p>2.24</p>
+<p> </p>
+<p>(1.637e-005s)</p>
+<p>
+              </p>
+              </td>
+</tr>
+</tbody>
+<tbody class="footnotes"><tr><td colspan="4"><div class="footnote"><p><sup>[<a name="ftn.id908749" href="#id908749" class="para">1</a>] </sup>
+                    Cephes gets stuck in an infinite loop while trying to execute
+                    our test cases.
+                  </p></div></td></tr></tbody>
+</table></div>
+<a name="math_toolkit.perf.comparisons.comparison_to_the_r_statistical_library_on_windows"></a><h5>
+<a name="id908919"></a>
+        <a class="link" href="comparisons.html#math_toolkit.perf.comparisons.comparison_to_the_r_statistical_library_on_windows">Comparison
+        to the R Statistical Library on Windows</a>
+      </h5>
+<p>
+        All the results were measured on a 2.8GHz Intel Pentium 4, 2Gb RAM, Windows
+        XP machine, with the test program compiled with Microsoft Visual C++ 2005,
+        and R-2.5.0 compiled in "standalone mode" with MinGW-3.4 (R-2.5.0
+        appears not to be buildable with Visual C++).
+      </p>
+<div class="table">
+<a name="id908947"></a><p class="title"><b>Table 51. A Comparison to the R Statistical Library on Windows
+      XP</b></p>
+<div class="table-contents"><table class="table" summary="A Comparison to the R Statistical Library on Windows
+      XP">
+<colgroup>
+<col>
+<col>
+<col>
+</colgroup>
+<thead><tr>
+<th>
+            <p>
+              Statistical Function
+            </p>
+            </th>
+<th>
+            <p>
+              Boost
+            </p>
+            </th>
+<th>
+            <p>
+              R
+            </p>
+            </th>
+</tr></thead>
+<tbody>
+<tr>
+<td>
+            <p>
+              <a class="link" href="../dist/dist_ref/dists/beta_dist.html" title="Beta Distribution">Beta Distribution</a>
+              CDF
+            </p>
+            </td>
+<td>
+            <p>
+              </p>
+<p>1.20</p>
+<p> </p>
+<p>(1.916e-006s)</p>
+<p>
+            </p>
+            </td>
+<td>
+            <p>
+              </p>
+<p><span class="bold"><strong>1.00</strong></span></p>
+<p> </p>
+<p>(1.597e-006s)</p>
+<p>
+            </p>
+            </td>
+</tr>
+<tr>
+<td>
+            <p>
+              <a class="link" href="../dist/dist_ref/dists/beta_dist.html" title="Beta Distribution">Beta Distribution</a>
+              Quantile
+            </p>
+            </td>
+<td>
+            <p>
+              </p>
+<p><span class="bold"><strong>1.00</strong></span></p>
+<p> </p>
+<p>(6.570e-006s)</p>
+<p>
+            </p>
+            </td>
+<td>
+            <p>
+              </p>
+<p>74.66
+              <sup>[<a name="id909092" href="#ftn.id909092" class="footnote">1</a>]</sup>
+              </p>
+<p> </p>
+<p>(4.905e-004s)</p>
+<p>
+            </p>
+            </td>
+</tr>
+<tr>
+<td>
+            <p>
+              <a class="link" href="../dist/dist_ref/dists/binomial_dist.html" title="Binomial Distribution">Binomial
+              Distribution</a> CDF
+            </p>
+            </td>
+<td>
+            <p>
+              </p>
+<p><span class="bold"><strong>1.00</strong></span></p>
+<p> </p>
+<p>(5.276e-007s)</p>
+<p>
+            </p>
+            </td>
+<td>
+            <p>
+              </p>
+<p>2.45</p>
+<p> </p>
+<p>(1.293e-006s)</p>
+<p>
+            </p>
+            </td>
+</tr>
+<tr>
+<td>
+            <p>
+              <a class="link" href="../dist/dist_ref/dists/binomial_dist.html" title="Binomial Distribution">Binomial
+              Distribution</a> Quantile
+            </p>
+            </td>
+<td>
+            <p>
+              </p>
+<p><span class="bold"><strong>1.00</strong></span></p>
+<p> </p>
+<p>(4.013e-006s)</p>
+<p>
+            </p>
+            </td>
+<td>
+            <p>
+              </p>
+<p>1.32</p>
+<p> </p>
+<p>(5.280e-006s)</p>
+<p>
+            </p>
+            </td>
+</tr>
+<tr>
+<td>
+            <p>
+              <a class="link" href="../dist/dist_ref/dists/cauchy_dist.html" title="Cauchy-Lorentz Distribution">Cauchy
+              Distribution</a> CDF
+            </p>
+            </td>
+<td>
+            <p>
+              </p>
+<p><span class="bold"><strong>1.00</strong></span></p>
+<p> </p>
+<p>(1.231e-007s)</p>
+<p>
+            </p>
+            </td>
+<td>
+            <p>
+              </p>
+<p>1.28</p>
+<p> </p>
+<p>(1.576e-007s)</p>
+<p>
+            </p>
+            </td>
+</tr>
+<tr>
+<td>
+            <p>
+              <a class="link" href="../dist/dist_ref/dists/cauchy_dist.html" title="Cauchy-Lorentz Distribution">Cauchy
+              Distribution</a> Quantile
+            </p>
+            </td>
+<td>
+            <p>
+              </p>
+<p><span class="bold"><strong>1.00</strong></span></p>
+<p> </p>
+<p>(1.498e-007s)</p>
+<p>
+            </p>
+            </td>
+<td>
+            <p>
+              </p>
+<p><span class="bold"><strong>1.00</strong></span></p>
+<p> </p>
+<p>(1.498e-007s)</p>
+<p>
+            </p>
+            </td>
+</tr>
+<tr>
+<td>
+            <p>
+              <a class="link" href="../dist/dist_ref/dists/chi_squared_dist.html" title="Chi Squared Distribution">Chi
+              Squared Distribution</a> CDF
+            </p>
+            </td>
+<td>
+            <p>
+              </p>
+<p><span class="bold"><strong>1.00</strong></span></p>
+<p> </p>
+<p>(7.889e-007s)</p>
+<p>
+            </p>
+            </td>
+<td>
+            <p>
+              </p>
+<p>2.48</p>
+<p> </p>
+<p>(1.955e-006s)</p>
+<p>
+            </p>
+            </td>
+</tr>
+<tr>
+<td>
+            <p>
+              <a class="link" href="../dist/dist_ref/dists/chi_squared_dist.html" title="Chi Squared Distribution">Chi
+              Squared Distribution</a> Quantile
+            </p>
+            </td>
+<td>
+            <p>
+              </p>
+<p><span class="bold"><strong>1.00</strong></span></p>
+<p> </p>
+<p>(4.303e-006s)</p>
+<p>
+            </p>
+            </td>
+<td>
+            <p>
+              </p>
+<p>1.61</p>
+<p> </p>
+<p>(6.925e-006s)</p>
+<p>
+            </p>
+            </td>
+</tr>
+<tr>
+<td>
+            <p>
+              <a class="link" href="../dist/dist_ref/dists/exp_dist.html" title="Exponential Distribution">Exponential
+              Distribution</a> CDF
+            </p>
+            </td>
+<td>
+            <p>
+              </p>
+<p><span class="bold"><strong>1.00</strong></span></p>
+<p> </p>
+<p>(1.955e-007s)</p>
+<p>
+            </p>
+            </td>
+<td>
+            <p>
+              </p>
+<p>1.97</p>
+<p> </p>
+<p>(3.844e-007s)</p>
+<p>
+            </p>
+            </td>
+</tr>
+<tr>
+<td>
+            <p>
+              <a class="link" href="../dist/dist_ref/dists/exp_dist.html" title="Exponential Distribution">Exponential
+              Distribution</a> Quantile
+            </p>
+            </td>
+<td>
+            <p>
+              </p>
+<p>1.07</p>
+<p> </p>
+<p>(1.206e-007s)</p>
+<p>
+            </p>
+            </td>
+<td>
+            <p>
+              </p>
+<p><span class="bold"><strong>1.00</strong></span></p>
+<p> </p>
+<p>(1.126e-007s)</p>
+<p>
+            </p>
+            </td>
+</tr>
+<tr>
+<td>
+            <p>
+              <a class="link" href="../dist/dist_ref/dists/f_dist.html" title="F Distribution">Fisher F Distribution</a>
+              CDF
+            </p>
+            </td>
+<td>
+            <p>
+              </p>
+<p><span class="bold"><strong>1.00</strong></span></p>
+<p> </p>
+<p>(1.309e-006s)</p>
+<p>
+            </p>
+            </td>
+<td>
+            <p>
+              </p>
+<p>2.12</p>
+<p> </p>
+<p>(2.780e-006s)</p>
+<p>
+            </p>
+            </td>
+</tr>
+<tr>
+<td>
+            <p>
+              <a class="link" href="../dist/dist_ref/dists/f_dist.html" title="F Distribution">Fisher F Distribution</a>
+              Quantile
+            </p>
+            </td>
+<td>
+            <p>
+              </p>
+<p><span class="bold"><strong>1.00</strong></span></p>
+<p> </p>
+<p>(7.204e-006s)</p>
+<p>
+            </p>
+            </td>
+<td>
+            <p>
+              </p>
+<p>1.78</p>
+<p> </p>
+<p>(1.280e-005s)</p>
+<p>
+            </p>
+            </td>
+</tr>
+<tr>
+<td>
+            <p>
+              <a class="link" href="../dist/dist_ref/dists/gamma_dist.html" title="Gamma (and Erlang) Distribution">Gamma Distribution</a>
+              CDF
+            </p>
+            </td>
+<td>
+            <p>
+              </p>
+<p><span class="bold"><strong>1.00</strong></span></p>
+<p> </p>
+<p>(1.076e-006s)</p>
+<p>
+            </p>
+            </td>
+<td>
+            <p>
+              </p>
+<p>2.07</p>
+<p> </p>
+<p>(2.227e-006s)</p>
+<p>
+            </p>
+            </td>
+</tr>
+<tr>
+<td>
+            <p>
+              <a class="link" href="../dist/dist_ref/dists/gamma_dist.html" title="Gamma (and Erlang) Distribution">Gamma Distribution</a>
+              Quantile
+            </p>
+            </td>
+<td>
+            <p>
+              </p>
+<p><span class="bold"><strong>1.00</strong></span></p>
+<p> </p>
+<p>(5.189e-006s)</p>
+<p>
+            </p>
+            </td>
+<td>
+            <p>
+              </p>
+<p>1.14</p>
+<p> </p>
+<p>(5.937e-006s)</p>
+<p>
+            </p>
+            </td>
+</tr>
+<tr>
+<td>
+            <p>
+              <a class="link" href="../dist/dist_ref/dists/lognormal_dist.html" title="Log Normal Distribution">Log-normal
+              Distribution</a> CDF
+            </p>
+            </td>
+<td>
+            <p>
+              </p>
+<p><span class="bold"><strong>1.00</strong></span></p>
+<p> </p>
+<p>(2.078e-007s)</p>
+<p>
+            </p>
+            </td>
+<td>
+            <p>
+              </p>
+<p>1.41</p>
+<p> </p>
+<p>(2.930e-007s)</p>
+<p>
+            </p>
+            </td>
+</tr>
+<tr>
+<td>
+            <p>
+              <a class="link" href="../dist/dist_ref/dists/lognormal_dist.html" title="Log Normal Distribution">Log-normal
+              Distribution</a> Quantile
+            </p>
+            </td>
+<td>
+            <p>
+              </p>
+<p><span class="bold"><strong>1.00</strong></span></p>
+<p> </p>
+<p>(6.692e-007s)</p>
+<p>
+            </p>
+            </td>
+<td>
+            <p>
+              </p>
+<p>1.63</p>
+<p> </p>
+<p>(1.090e-006s)</p>
+<p>
+            </p>
+            </td>
+</tr>
+<tr>
+<td>
+            <p>
+              <a class="link" href="../dist/dist_ref/dists/negative_binomial_dist.html" title="Negative Binomial Distribution">Negative
+              Binomial Distribution</a> CDF
+            </p>
+            </td>
+<td>
+            <p>
+              </p>
+<p><span class="bold"><strong>1.00</strong></span></p>
+<p> </p>
+<p>(9.005e-007s)</p>
+<p>
+            </p>
+            </td>
+<td>
+            <p>
+              </p>
+<p>2.42</p>
+<p> </p>
+<p>(2.178e-006s)</p>
+<p>
+            </p>
+            </td>
+</tr>
+<tr>
+<td>
+            <p>
+              <a class="link" href="../dist/dist_ref/dists/negative_binomial_dist.html" title="Negative Binomial Distribution">Negative
+              Binomial Distribution</a> Quantile
+            </p>
+            </td>
+<td>
+            <p>
+              </p>
+<p><span class="bold"><strong>1.00</strong></span></p>
+<p> </p>
+<p>(9.601e-006s)</p>
+<p>
+            </p>
+            </td>
+<td>
+            <p>
+              </p>
+<p>53.59
+              <sup>[<a name="id909957" href="#ftn.id909957" class="footnote">2</a>]</sup>
+              </p>
+<p> </p>
+<p>(5.145e-004s)</p>
+<p>
+            </p>
+            </td>
+</tr>
+<tr>
+<td>
+            <p>
+              <a class="link" href="../dist/dist_ref/dists/normal_dist.html" title="Normal (Gaussian) Distribution">Normal
+              Distribution</a> CDF
+            </p>
+            </td>
+<td>
+            <p>
+              </p>
+<p><span class="bold"><strong>1.00</strong></span></p>
+<p> </p>
+<p>(5.926e-008s)</p>
+<p>
+            </p>
+            </td>
+<td>
+            <p>
+              </p>
+<p>3.01</p>
+<p> </p>
+<p>(1.785e-007s)</p>
+<p>
+            </p>
+            </td>
+</tr>
+<tr>
+<td>
+            <p>
+              <a class="link" href="../dist/dist_ref/dists/normal_dist.html" title="Normal (Gaussian) Distribution">Normal
+              Distribution</a> Quantile
+            </p>
+            </td>
+<td>
+            <p>
+              </p>
+<p><span class="bold"><strong>1.00</strong></span></p>
+<p> </p>
+<p>(1.248e-007s)</p>
+<p>
+            </p>
+            </td>
+<td>
+            <p>
+              </p>
+<p>1.05</p>
+<p> </p>
+<p>(1.311e-007s)</p>
+<p>
+            </p>
+            </td>
+</tr>
+<tr>
+<td>
+            <p>
+              <a class="link" href="../dist/dist_ref/dists/poisson_dist.html" title="Poisson Distribution">Poisson
+              Distribution</a> CDF
+            </p>
+            </td>
+<td>
+            <p>
+              </p>
+<p><span class="bold"><strong>1.00</strong></span></p>
+<p> </p>
+<p>(8.999e-007s)</p>
+<p>
+            </p>
+            </td>
+<td>
+            <p>
+              </p>
+<p>2.42</p>
+<p> </p>
+<p>(2.175e-006s)</p>
+<p>
+            </p>
+            </td>
+</tr>
+<tr>
+<td>
+            <p>
+              <a class="link" href="../dist/dist_ref/dists/poisson_dist.html" title="Poisson Distribution">Poisson
+              Distribution</a>
+            </p>
+            </td>
+<td>
+            <p>
+              </p>
+<p><span class="bold"><strong>1.00</strong></span></p>
+<p> </p>
+<p>(1.853e-006s)</p>
+<p>
+            </p>
+            </td>
+<td>
+            <p>
+              </p>
+<p>2.17</p>
+<p> </p>
+<p>(4.014e-006s)</p>
+<p>
+            </p>
+            </td>
+</tr>
+<tr>
+<td>
+            <p>
+              <a class="link" href="../dist/dist_ref/dists/students_t_dist.html" title="Students t Distribution">Students
+              t Distribution</a> CDF
+            </p>
+            </td>
+<td>
+            <p>
+              </p>
+<p><span class="bold"><strong>1.00</strong></span></p>
+<p> </p>
+<p>(1.223e-006s)</p>
+<p>
+            </p>
+            </td>
+<td>
+            <p>
+              </p>
+<p>1.13</p>
+<p> </p>
+<p>(1.376e-006s)</p>
+<p>
+            </p>
+            </td>
+</tr>
+<tr>
+<td>
+            <p>
+              <a class="link" href="../dist/dist_ref/dists/students_t_dist.html" title="Students t Distribution">Students
+              t Distribution</a> Quantile
+            </p>
+            </td>
+<td>
+            <p>
+              </p>
+<p><span class="bold"><strong>1.00</strong></span></p>
+<p> </p>
+<p>(2.570e-006s)</p>
+<p>
+            </p>
+            </td>
+<td>
+            <p>
+              </p>
+<p>1.04</p>
+<p> </p>
+<p>(2.668e-006s)</p>
+<p>
+            </p>
+            </td>
+</tr>
+<tr>
+<td>
+            <p>
+              <a class="link" href="../dist/dist_ref/dists/weibull.html" title="Weibull Distribution">Weibull Distribution</a>
+              CDF
+            </p>
+            </td>
+<td>
+            <p>
+              </p>
+<p><span class="bold"><strong>1.00</strong></span></p>
+<p> </p>
+<p>(4.741e-007s)</p>
+<p>
+            </p>
+            </td>
+<td>
+            <p>
+              </p>
+<p>1.46</p>
+<p> </p>
+<p>(6.943e-007s)</p>
+<p>
+            </p>
+            </td>
+</tr>
+<tr>
+<td>
+            <p>
+              <a class="link" href="../dist/dist_ref/dists/weibull.html" title="Weibull Distribution">Weibull Distribution</a>
+              Quantile
+            </p>
+            </td>
+<td>
+            <p>
+              </p>
+<p><span class="bold"><strong>1.00</strong></span></p>
+<p> </p>
+<p>(7.926e-007s)</p>
+<p>
+            </p>
+            </td>
+<td>
+            <p>
+              </p>
+<p>1.08</p>
+<p> </p>
+<p>(8.542e-007s)</p>
+<p>
+            </p>
+            </td>
+</tr>
+</tbody>
+<tbody class="footnotes"><tr><td colspan="3">
+<div class="footnote"><p><sup>[<a name="ftn.id909092" href="#id909092" class="para">1</a>] </sup>
+                  There are a small number of our test cases where the R library
+                  fails to converge on a result: these tend to dominate the performance
+                  result.
+                </p></div>
+<div class="footnote"><p><sup>[<a name="ftn.id909957" href="#id909957" class="para">2</a>] </sup>
+                  The R library appears to use a linear-search strategy, that can
+                  perform very badly in a small number of pathological cases, but
+                  may or may not be more efficient in "typical" cases
+                </p></div>
+</td></tr></tbody>
+</table></div>
+</div>
+<br class="table-break"><a name="math_toolkit.perf.comparisons.comparison_to_the_r_statistical_library_on_linux"></a><h5>
+<a name="id910416"></a>
+        <a class="link" href="comparisons.html#math_toolkit.perf.comparisons.comparison_to_the_r_statistical_library_on_linux">Comparison
+        to the R Statistical Library on Linux</a>
+      </h5>
+<p>
+        All the results were measured on a 2.8GHz Intel Pentium 4, 2Gb RAM, Mandriva
+        Linux machine, with the test program and R-2.5.0 compiled with GNU G++ 4.2.0.
+      </p>
+<div class="table">
+<a name="id910444"></a><p class="title"><b>Table 52. A Comparison to the R Statistical Library on Linux</b></p>
+<div class="table-contents"><table class="table" summary="A Comparison to the R Statistical Library on Linux">
+<colgroup>
+<col>
+<col>
+<col>
+</colgroup>
+<thead><tr>
+<th>
+            <p>
+              Statistical Function
+            </p>
+            </th>
+<th>
+            <p>
+              Boost
+            </p>
+            </th>
+<th>
+            <p>
+              R
+            </p>
+            </th>
+</tr></thead>
+<tbody>
+<tr>
+<td>
+            <p>
+              <a class="link" href="../dist/dist_ref/dists/beta_dist.html" title="Beta Distribution">Beta Distribution</a>
+              CDF
+            </p>
+            </td>
+<td>
+            <p>
+              </p>
+<p>1.71</p>
+<p> </p>
+<p>(3.508e-006s)</p>
+<p>
+            </p>
+            </td>
+<td>
+            <p>
+              </p>
+<p><span class="bold"><strong>1.00</strong></span></p>
+<p> </p>
+<p>(2.050e-006s)</p>
+<p>
+            </p>
+            </td>
+</tr>
+<tr>
+<td>
+            <p>
+              <a class="link" href="../dist/dist_ref/dists/beta_dist.html" title="Beta Distribution">Beta Distribution</a>
+              Quantile
+            </p>
+            </td>
+<td>
+            <p>
+              </p>
+<p><span class="bold"><strong>1.00</strong></span></p>
+<p> </p>
+<p>(1.294e-005s)</p>
+<p>
+            </p>
+            </td>
+<td>
+            <p>
+              </p>
+<p>44.06
+              <sup>[<a name="id910587" href="#ftn.id910587" class="footnote">1</a>]</sup>
+              </p>
+<p> </p>
+<p>(5.701e-004s)</p>
+<p>
+            </p>
+            </td>
+</tr>
+<tr>
+<td>
+            <p>
+              <a class="link" href="../dist/dist_ref/dists/binomial_dist.html" title="Binomial Distribution">Binomial
+              Distribution</a> CDF
+            </p>
+            </td>
+<td>
+            <p>
+              </p>
+<p>1.22</p>
+<p> </p>
+<p>(1.342e-006s)</p>
+<p>
+            </p>
+            </td>
+<td>
+            <p>
+              </p>
+<p><span class="bold"><strong>1.00</strong></span></p>
+<p> </p>
+<p>(1.104e-006s)</p>
+<p>
+            </p>
+            </td>
+</tr>
+<tr>
+<td>
+            <p>
+              <a class="link" href="../dist/dist_ref/dists/binomial_dist.html" title="Binomial Distribution">Binomial
+              Distribution</a> Quantile
+            </p>
+            </td>
+<td>
+            <p>
+              </p>
+<p>1.36</p>
+<p> </p>
+<p>(7.083e-006s)</p>
+<p>
+            </p>
+            </td>
+<td>
+            <p>
+              </p>
+<p><span class="bold"><strong>1.00</strong></span></p>
+<p> </p>
+<p>(5.194e-006s)</p>
+<p>
+            </p>
+            </td>
+</tr>
+<tr>
+<td>
+            <p>
+              <a class="link" href="../dist/dist_ref/dists/cauchy_dist.html" title="Cauchy-Lorentz Distribution">Cauchy
+              Distribution</a> CDF
+            </p>
+            </td>
+<td>
+            <p>
+              </p>
+<p><span class="bold"><strong>1.00</strong></span></p>
+<p> </p>
+<p>(1.372e-007s)</p>
+<p>
+            </p>
+            </td>
+<td>
+            <p>
+              </p>
+<p>1.47</p>
+<p> </p>
+<p>(2.017e-007s)</p>
+<p>
+            </p>
+            </td>
+</tr>
+<tr>
+<td>
+            <p>
+              <a class="link" href="../dist/dist_ref/dists/cauchy_dist.html" title="Cauchy-Lorentz Distribution">Cauchy
+              Distribution</a> Quantile
+            </p>
+            </td>
+<td>
+            <p>
+              </p>
+<p><span class="bold"><strong>1.00</strong></span></p>
+<p> </p>
+<p>(1.542e-007s)</p>
+<p>
+            </p>
+            </td>
+<td>
+            <p>
+              </p>
+<p>1.14</p>
+<p> </p>
+<p>(1.752e-007s)</p>
+<p>
+            </p>
+            </td>
+</tr>
+<tr>
+<td>
+            <p>
+              <a class="link" href="../dist/dist_ref/dists/chi_squared_dist.html" title="Chi Squared Distribution">Chi
+              Squared Distribution</a> CDF
+            </p>
+            </td>
+<td>
+            <p>
+              </p>
+<p>1.04</p>
+<p> </p>
+<p>(1.820e-006s)</p>
+<p>
+            </p>
+            </td>
+<td>
+            <p>
+              </p>
+<p><span class="bold"><strong>1.00</strong></span></p>
+<p> </p>
+<p>(1.753e-006s)</p>
+<p>
+            </p>
+            </td>
+</tr>
+<tr>
+<td>
+            <p>
+              <a class="link" href="../dist/dist_ref/dists/chi_squared_dist.html" title="Chi Squared Distribution">Chi
+              Squared Distribution</a> Quantile
+            </p>
+            </td>
+<td>
+            <p>
+              </p>
+<p>1.39</p>
+<p> </p>
+<p>(9.345e-006s)</p>
+<p>
+            </p>
+            </td>
+<td>
+            <p>
+              </p>
+<p><span class="bold"><strong>1.00</strong></span></p>
+<p> </p>
+<p>(6.728e-006s)</p>
+<p>
+            </p>
+            </td>
+</tr>
+<tr>
+<td>
+            <p>
+              <a class="link" href="../dist/dist_ref/dists/exp_dist.html" title="Exponential Distribution">Exponential
+              Distribution</a> CDF
+            </p>
+            </td>
+<td>
+            <p>
+              </p>
+<p><span class="bold"><strong>1.00</strong></span></p>
+<p> </p>
+<p>(2.195e-007s)</p>
+<p>
+            </p>
+            </td>
+<td>
+            <p>
+              </p>
+<p>1.17</p>
+<p> </p>
+<p>(2.561e-007s)</p>
+<p>
+            </p>
+            </td>
+</tr>
+<tr>
+<td>
+            <p>
+              <a class="link" href="../dist/dist_ref/dists/exp_dist.html" title="Exponential Distribution">Exponential
+              Distribution</a> Quantile
+            </p>
+            </td>
+<td>
+            <p>
+              </p>
+<p><span class="bold"><strong>1.00</strong></span></p>
+<p> </p>
+<p>(1.123e-007s)</p>
+<p>
+            </p>
+            </td>
+<td>
+            <p>
+              </p>
+<p>1.03</p>
+<p> </p>
+<p>(1.155e-007s)</p>
+<p>
+            </p>
+            </td>
+</tr>
+<tr>
+<td>
+            <p>
+              <a class="link" href="../dist/dist_ref/dists/f_dist.html" title="F Distribution">Fisher F Distribution</a>
+              CDF
+            </p>
+            </td>
+<td>
+            <p>
+              </p>
+<p><span class="bold"><strong>1.00</strong></span></p>
+<p> </p>
+<p>(2.744e-006s)</p>
+<p>
+            </p>
+            </td>
+<td>
+            <p>
+              </p>
+<p>1.08</p>
+<p> </p>
+<p>(2.970e-006s)</p>
+<p>
+            </p>
+            </td>
+</tr>
+<tr>
+<td>
+            <p>
+              <a class="link" href="../dist/dist_ref/dists/f_dist.html" title="F Distribution">Fisher F Distribution</a>
+              Quantile
+            </p>
+            </td>
+<td>
+            <p>
+              </p>
+<p>1.14</p>
+<p> </p>
+<p>(1.550e-005s)</p>
+<p>
+            </p>
+            </td>
+<td>
+            <p>
+              </p>
+<p><span class="bold"><strong>1.00</strong></span></p>
+<p> </p>
+<p>(1.359e-005s)</p>
+<p>
+            </p>
+            </td>
+</tr>
+<tr>
+<td>
+            <p>
+              <a class="link" href="../dist/dist_ref/dists/gamma_dist.html" title="Gamma (and Erlang) Distribution">Gamma Distribution</a>
+              CDF
+            </p>
+            </td>
+<td>
+            <p>
+              </p>
+<p>1.29</p>
+<p> </p>
+<p>(2.578e-006s)</p>
+<p>
+            </p>
+            </td>
+<td>
+            <p>
+              </p>
+<p><span class="bold"><strong>1.00</strong></span></p>
+<p> </p>
+<p>(1.992e-006s)</p>
+<p>
+            </p>
+            </td>
+</tr>
+<tr>
+<td>
+            <p>
+              <a class="link" href="../dist/dist_ref/dists/gamma_dist.html" title="Gamma (and Erlang) Distribution">Gamma Distribution</a>
+              Quantile
+            </p>
+            </td>
+<td>
+            <p>
+              </p>
+<p>1.77</p>
+<p> </p>
+<p>(1.020e-005s)</p>
+<p>
+            </p>
+            </td>
+<td>
+            <p>
+              </p>
+<p><span class="bold"><strong>1.00</strong></span></p>
+<p> </p>
+<p>(5.757e-006s)</p>
+<p>
+            </p>
+            </td>
+</tr>
+<tr>
+<td>
+            <p>
+              <a class="link" href="../dist/dist_ref/dists/lognormal_dist.html" title="Log Normal Distribution">Log-normal
+              Distribution</a> CDF
+            </p>
+            </td>
+<td>
+            <p>
+              </p>
+<p><span class="bold"><strong>1.00</strong></span></p>
+<p> </p>
+<p>(1.782e-007s)</p>
+<p>
+            </p>
+            </td>
+<td>
+            <p>
+              </p>
+<p>2.00</p>
+<p> </p>
+<p>(3.564e-007s)</p>
+<p>
+            </p>
+            </td>
+</tr>
+<tr>
+<td>
+            <p>
+              <a class="link" href="../dist/dist_ref/dists/lognormal_dist.html" title="Log Normal Distribution">Log-normal
+              Distribution</a> Quantile
+            </p>
+            </td>
+<td>
+            <p>
+              </p>
+<p><span class="bold"><strong>1.00</strong></span></p>
+<p> </p>
+<p>(7.093e-007s)</p>
+<p>
+            </p>
+            </td>
+<td>
+            <p>
+              </p>
+<p>1.07</p>
+<p> </p>
+<p>(7.607e-007s)</p>
+<p>
+            </p>
+            </td>
+</tr>
+<tr>
+<td>
+            <p>
+              <a class="link" href="../dist/dist_ref/dists/negative_binomial_dist.html" title="Negative Binomial Distribution">Negative
+              Binomial Distribution</a> CDF
+            </p>
+            </td>
+<td>
+            <p>
+              </p>
+<p>1.03</p>
+<p> </p>
+<p>(2.209e-006s)</p>
+<p>
+            </p>
+            </td>
+<td>
+            <p>
+              </p>
+<p><span class="bold"><strong>1.00</strong></span></p>
+<p> </p>
+<p>(2.141e-006s)</p>
+<p>
+            </p>
+            </td>
+</tr>
+<tr>
+<td>
+            <p>
+              <a class="link" href="../dist/dist_ref/dists/negative_binomial_dist.html" title="Negative Binomial Distribution">Negative
+              Binomial Distribution</a> Quantile
+            </p>
+            </td>
+<td>
+            <p>
+              </p>
+<p><span class="bold"><strong>1.00</strong></span></p>
+<p> </p>
+<p>(1.826e-005s)</p>
+<p>
+            </p>
+            </td>
+<td>
+            <p>
+              </p>
+<p>30.07
+              <sup>[<a name="id911449" href="#ftn.id911449" class="footnote">2</a>]</sup>
+              </p>
+<p> </p>
+<p>(5.490e-004s)</p>
+<p>
+            </p>
+            </td>
+</tr>
+<tr>
+<td>
+            <p>
+              <a class="link" href="../dist/dist_ref/dists/normal_dist.html" title="Normal (Gaussian) Distribution">Normal
+              Distribution</a> CDF
+            </p>
+            </td>
+<td>
+            <p>
+              </p>
+<p><span class="bold"><strong>1.00</strong></span></p>
+<p> </p>
+<p>(8.542e-008s)</p>
+<p>
+            </p>
+            </td>
+<td>
+            <p>
+              </p>
+<p>2.09</p>
+<p> </p>
+<p>(1.782e-007s)</p>
+<p>
+            </p>
+            </td>
+</tr>
+<tr>
+<td>
+            <p>
+              <a class="link" href="../dist/dist_ref/dists/normal_dist.html" title="Normal (Gaussian) Distribution">Normal
+              Distribution</a> Quantile
+            </p>
+            </td>
+<td>
+            <p>
+              </p>
+<p><span class="bold"><strong>1.00</strong></span></p>
+<p> </p>
+<p>(1.362e-007s)</p>
+<p>
+            </p>
+            </td>
+<td>
+            <p>
+              </p>
+<p>1.26</p>
+<p> </p>
+<p>(1.722e-007s)</p>
+<p>
+            </p>
+            </td>
+</tr>
+<tr>
+<td>
+            <p>
+              <a class="link" href="../dist/dist_ref/dists/poisson_dist.html" title="Poisson Distribution">Poisson
+              Distribution</a> CDF
+            </p>
+            </td>
+<td>
+            <p>
+              </p>
+<p>1.10</p>
+<p> </p>
+<p>(1.953e-006s)</p>
+<p>
+            </p>
+            </td>
+<td>
+            <p>
+              </p>
+<p><span class="bold"><strong>1.00</strong></span></p>
+<p> </p>
+<p>(1.775e-006s)</p>
+<p>
+            </p>
+            </td>
+</tr>
+<tr>
+<td>
+            <p>
+              <a class="link" href="../dist/dist_ref/dists/poisson_dist.html" title="Poisson Distribution">Poisson
+              Distribution</a>
+            </p>
+            </td>
+<td>
+            <p>
+              </p>
+<p>1.12</p>
+<p> </p>
+<p>(4.214e-006s)</p>
+<p>
+            </p>
+            </td>
+<td>
+            <p>
+              </p>
+<p><span class="bold"><strong>1.00</strong></span></p>
+<p> </p>
+<p>(3.752e-006s)</p>
+<p>
+            </p>
+            </td>
+</tr>
+<tr>
+<td>
+            <p>
+              <a class="link" href="../dist/dist_ref/dists/students_t_dist.html" title="Students t Distribution">Students
+              t Distribution</a> CDF
+            </p>
+            </td>
+<td>
+            <p>
+              </p>
+<p>1.55</p>
+<p> </p>
+<p>(2.441e-006s)</p>
+<p>
+            </p>
+            </td>
+<td>
+            <p>
+              </p>
+<p><span class="bold"><strong>1.00</strong></span></p>
+<p> </p>
+<p>(1.576e-006s)</p>
+<p>
+            </p>
+            </td>
+</tr>
+<tr>
+<td>
+            <p>
+              <a class="link" href="../dist/dist_ref/dists/students_t_dist.html" title="Students t Distribution">Students
+              t Distribution</a> Quantile
+            </p>
+            </td>
+<td>
+            <p>
+              </p>
+<p>1.33</p>
+<p> </p>
+<p>(3.972e-006s)</p>
+<p>
+            </p>
+            </td>
+<td>
+            <p>
+              </p>
+<p><span class="bold"><strong>1.00</strong></span></p>
+<p> </p>
+<p>(2.990e-006s)</p>
+<p>
+            </p>
+            </td>
+</tr>
+<tr>
+<td>
+            <p>
+              <a class="link" href="../dist/dist_ref/dists/weibull.html" title="Weibull Distribution">Weibull Distribution</a>
+              CDF
+            </p>
+            </td>
+<td>
+            <p>
+              </p>
+<p><span class="bold"><strong>1.00</strong></span></p>
+<p> </p>
+<p>(6.640e-007s)</p>
+<p>
+            </p>
+            </td>
+<td>
+            <p>
+              </p>
+<p>1.06</p>
+<p> </p>
+<p>(7.031e-007s)</p>
+<p>
+            </p>
+            </td>
+</tr>
+<tr>
+<td>
+            <p>
+              <a class="link" href="../dist/dist_ref/dists/weibull.html" title="Weibull Distribution">Weibull Distribution</a>
+              Quantile
+            </p>
+            </td>
+<td>
+            <p>
+              </p>
+<p><span class="bold"><strong>1.00</strong></span></p>
+<p> </p>
+<p>(7.504e-007s)</p>
+<p>
+            </p>
+            </td>
+<td>
+            <p>
+              </p>
+<p>1.03</p>
+<p> </p>
+<p>(7.710e-007s)</p>
+<p>
+            </p>
+            </td>
+</tr>
+</tbody>
+<tbody class="footnotes"><tr><td colspan="3">
+<div class="footnote"><p><sup>[<a name="ftn.id910587" href="#id910587" class="para">1</a>] </sup>
+                  There are a small number of our test cases where the R library
+                  fails to converge on a result: these tend to dominate the performance
+                  result.
+                </p></div>
+<div class="footnote"><p><sup>[<a name="ftn.id911449" href="#id911449" class="para">2</a>] </sup>
+                  The R library appears to use a linear-search strategy, that can
+                  perform very badly in a small number of pathological cases, but
+                  may or may not be more efficient in "typical" cases
+                </p></div>
+</td></tr></tbody>
+</table></div>
+</div>
+<br class="table-break">
+</div>
+<table xmlns:rev="http://www.cs.rpi.edu/~gregod/boost/tools/doc/revision" width="100%"><tr>
+<td align="left"></td>
+<td align="right"><div class="copyright-footer">Copyright © 2006 , 2007, 2008 John Maddock, Paul A. Bristow, Hubert
+      Holin, Xiaogang Zhang, Bruno Lalande and Gautam Sewani<p>
+        Distributed under the Boost Software License, Version 1.0. (See accompanying
+        file LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_0.txt)
+      </p>
+</div></td>
+</tr></table>
+<hr>
+<div class="spirit-nav">
+<a accesskey="p" href="tuning.html"><img src="../../../../doc/html/images/prev.png" alt="Prev"></a><a accesskey="u" href="../perf.html"><img src="../../../../doc/html/images/up.png" alt="Up"></a><a accesskey="h" href="../../index.html"><img src="../../../../doc/html/images/home.png" alt="Home"></a><a accesskey="n" href="perf_test_app.html"><img src="../../../../doc/html/images/next.png" alt="Next"></a>
+</div>
+</body>
+</html>

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@@ -0,0 +1,294 @@
+<html>
+<head>
+<meta http-equiv="Content-Type" content="text/html; charset=ISO-8859-1">
+<title>Getting the Best Performance from this Library</title>
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+<link rel="home" href="../../index.html" title="Math Toolkit">
+<link rel="up" href="../perf.html" title="Performance">
+<link rel="prev" href="interp.html" title="Interpreting these Results">
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+<td align="center">Home</td>
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+<hr>
+<div class="spirit-nav">
+<a accesskey="p" href="interp.html"><img src="../../../../doc/html/images/prev.png" alt="Prev"></a><a accesskey="u" href="../perf.html"><img src="../../../../doc/html/images/up.png" alt="Up"></a><a accesskey="h" href="../../index.html"><img src="../../../../doc/html/images/home.png" alt="Home"></a><a accesskey="n" href="comp_compilers.html"><img src="../../../../doc/html/images/next.png" alt="Next"></a>
+</div>
+<div class="section" lang="en">
+<div class="titlepage"><div><div><h3 class="title">
+<a name="math_toolkit.perf.getting_best"></a><a class="link" href="getting_best.html" title="Getting the Best Performance from this Library"> Getting the Best Performance
+      from this Library</a>
+</h3></div></div></div>
+<p>
+        By far the most important thing you can do when using this library is turn
+        on your compiler's optimisation options. As the following table shows the
+        penalty for using the library in debug mode can be quite large.
+      </p>
+<div class="table">
+<a name="id905224"></a><p class="title"><b>Table 47. Performance Comparison of Release and Debug Settings</b></p>
+<div class="table-contents"><table class="table" summary="Performance Comparison of Release and Debug Settings">
+<colgroup>
+<col>
+<col>
+<col>
+</colgroup>
+<thead><tr>
+<th>
+            <p>
+              Function
+            </p>
+            </th>
+<th>
+            <p>
+              Microsoft Visual C++ 8.0
+            </p>
+            <p>
+              Debug Settings: /Od /ZI
+            </p>
+            </th>
+<th>
+            <p>
+              Microsoft Visual C++ 8.0
+            </p>
+            <p>
+              Release settings: /Ox /arch:SSE2
+            </p>
+            </th>
+</tr></thead>
+<tbody>
+<tr>
+<td>
+            <p>
+              <a class="link" href="../special/sf_erf/error_function.html" title="Error Functions">erf</a>
+            </p>
+            </td>
+<td>
+            <p>
+              </p>
+<p>16.65</p>
+<p> </p>
+<p>(1.028e-006s)</p>
+<p>
+            </p>
+            </td>
+<td>
+            <p>
+              </p>
+<p><span class="bold"><strong>1.00</strong></span></p>
+<p> </p>
+<p>(6.173e-008s)</p>
+<p>
+            </p>
+            </td>
+</tr>
+<tr>
+<td>
+            <p>
+              <a class="link" href="../special/sf_erf/error_inv.html" title="Error Function Inverses">erf_inv</a>
+            </p>
+            </td>
+<td>
+            <p>
+              </p>
+<p>19.28</p>
+<p> </p>
+<p>(1.215e-006s)</p>
+<p>
+            </p>
+            </td>
+<td>
+            <p>
+              </p>
+<p><span class="bold"><strong>1.00</strong></span></p>
+<p> </p>
+<p>(6.302e-008s)</p>
+<p>
+            </p>
+            </td>
+</tr>
+<tr>
+<td>
+            <p>
+              <a class="link" href="../special/sf_beta/ibeta_function.html" title="Incomplete Beta Functions">ibeta</a>
+              and <a class="link" href="../special/sf_beta/ibeta_function.html" title="Incomplete Beta Functions">ibetac</a>
+            </p>
+            </td>
+<td>
+            <p>
+              </p>
+<p>8.32</p>
+<p> </p>
+<p>(1.540e-005s)</p>
+<p>
+            </p>
+            </td>
+<td>
+            <p>
+              </p>
+<p><span class="bold"><strong>1.00</strong></span></p>
+<p> </p>
+<p>(1.852e-006s)</p>
+<p>
+            </p>
+            </td>
+</tr>
+<tr>
+<td>
+            <p>
+              <a class="link" href="../special/sf_beta/ibeta_inv_function.html" title="The Incomplete Beta Function Inverses">ibeta_inv</a>
+              and <a class="link" href="../special/sf_beta/ibeta_inv_function.html" title="The Incomplete Beta Function Inverses">ibetac_inv</a>
+            </p>
+            </td>
+<td>
+            <p>
+              </p>
+<p>10.25</p>
+<p> </p>
+<p>(7.492e-005s)</p>
+<p>
+            </p>
+            </td>
+<td>
+            <p>
+              </p>
+<p><span class="bold"><strong>1.00</strong></span></p>
+<p> </p>
+<p>(7.311e-006s)</p>
+<p>
+            </p>
+            </td>
+</tr>
+<tr>
+<td>
+            <p>
+              <a class="link" href="../special/sf_beta/ibeta_inv_function.html" title="The Incomplete Beta Function Inverses">ibeta_inva</a>,
+              <a class="link" href="../special/sf_beta/ibeta_inv_function.html" title="The Incomplete Beta Function Inverses">ibetac_inva</a>,
+              <a class="link" href="../special/sf_beta/ibeta_inv_function.html" title="The Incomplete Beta Function Inverses">ibeta_invb</a>
+              and <a class="link" href="../special/sf_beta/ibeta_inv_function.html" title="The Incomplete Beta Function Inverses">ibetac_invb</a>
+            </p>
+            </td>
+<td>
+            <p>
+              </p>
+<p>8.57</p>
+<p> </p>
+<p>(2.441e-004s)</p>
+<p>
+            </p>
+            </td>
+<td>
+            <p>
+              </p>
+<p><span class="bold"><strong>1.00</strong></span></p>
+<p> </p>
+<p>(2.847e-005s)</p>
+<p>
+            </p>
+            </td>
+</tr>
+<tr>
+<td>
+            <p>
+              <a class="link" href="../special/sf_gamma/igamma.html" title="Incomplete Gamma Functions">gamma_p</a>
+              and <a class="link" href="../special/sf_gamma/igamma.html" title="Incomplete Gamma Functions">gamma_q</a>
+            </p>
+            </td>
+<td>
+            <p>
+              </p>
+<p>10.98</p>
+<p> </p>
+<p>(1.044e-005s)</p>
+<p>
+            </p>
+            </td>
+<td>
+            <p>
+              </p>
+<p><span class="bold"><strong>1.00</strong></span></p>
+<p> </p>
+<p>(9.504e-007s)</p>
+<p>
+            </p>
+            </td>
+</tr>
+<tr>
+<td>
+            <p>
+              <a class="link" href="../special/sf_gamma/igamma_inv.html" title="Incomplete Gamma Function Inverses">gamma_p_inv</a>
+              and <a class="link" href="../special/sf_gamma/igamma_inv.html" title="Incomplete Gamma Function Inverses">gamma_q_inv</a>
+            </p>
+            </td>
+<td>
+            <p>
+              </p>
+<p>10.25</p>
+<p> </p>
+<p>(3.721e-005s)</p>
+<p>
+            </p>
+            </td>
+<td>
+            <p>
+              </p>
+<p><span class="bold"><strong>1.00</strong></span></p>
+<p> </p>
+<p>(3.631e-006s)</p>
+<p>
+            </p>
+            </td>
+</tr>
+<tr>
+<td>
+            <p>
+              <a class="link" href="../special/sf_gamma/igamma_inv.html" title="Incomplete Gamma Function Inverses">gamma_p_inva</a>
+              and <a class="link" href="../special/sf_gamma/igamma_inv.html" title="Incomplete Gamma Function Inverses">gamma_q_inva</a>
+            </p>
+            </td>
+<td>
+            <p>
+              </p>
+<p>11.26</p>
+<p> </p>
+<p>(1.124e-004s)</p>
+<p>
+            </p>
+            </td>
+<td>
+            <p>
+              </p>
+<p><span class="bold"><strong>1.00</strong></span></p>
+<p> </p>
+<p>(9.982e-006s)</p>
+<p>
+            </p>
+            </td>
+</tr>
+</tbody>
+</table></div>
+</div>
+<br class="table-break">
+</div>
+<table xmlns:rev="http://www.cs.rpi.edu/~gregod/boost/tools/doc/revision" width="100%"><tr>
+<td align="left"></td>
+<td align="right"><div class="copyright-footer">Copyright © 2006 , 2007, 2008 John Maddock, Paul A. Bristow, Hubert
+      Holin, Xiaogang Zhang, Bruno Lalande and Gautam Sewani<p>
+        Distributed under the Boost Software License, Version 1.0. (See accompanying
+        file LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_0.txt)
+      </p>
+</div></td>
+</tr></table>
+<hr>
+<div class="spirit-nav">
+<a accesskey="p" href="interp.html"><img src="../../../../doc/html/images/prev.png" alt="Prev"></a><a accesskey="u" href="../perf.html"><img src="../../../../doc/html/images/up.png" alt="Up"></a><a accesskey="h" href="../../index.html"><img src="../../../../doc/html/images/home.png" alt="Home"></a><a accesskey="n" href="comp_compilers.html"><img src="../../../../doc/html/images/next.png" alt="Next"></a>
+</div>
+</body>
+</html>

Added: sandbox/tools/auto_index/example/math/doc/sf_and_dist/html/math_toolkit/perf/interp.html
==============================================================================
--- (empty file)
+++ sandbox/tools/auto_index/example/math/doc/sf_and_dist/html/math_toolkit/perf/interp.html	2008-11-28 05:25:28 EST (Fri, 28 Nov 2008)
@@ -0,0 +1,70 @@
+<html>
+<head>
+<meta http-equiv="Content-Type" content="text/html; charset=ISO-8859-1">
+<title>Interpreting these Results</title>
+<link rel="stylesheet" href="../../boostbook.css" type="text/css">
+<meta name="generator" content="DocBook XSL Stylesheets Vsnapshot_8125">
+<link rel="home" href="../../index.html" title="Math Toolkit">
+<link rel="up" href="../perf.html" title="Performance">
+<link rel="prev" href="perf_over.html" title="Performance Overview">
+<link rel="next" href="getting_best.html" title="Getting the Best Performance from this Library">
+</head>
+<body bgcolor="white" text="black" link="#0000FF" vlink="#840084" alink="#0000FF">
+<table cellpadding="2" width="100%"><tr>
+<td valign="top"><img alt="Boost C++ Libraries" width="277" height="86" src="../../../../boost.png"></td>
+<td align="center">Home</td>
+<td align="center">Libraries</td>
+<td align="center">People</td>
+<td align="center">FAQ</td>
+<td align="center">More</td>
+</tr></table>
+<hr>
+<div class="spirit-nav">
+<a accesskey="p" href="perf_over.html"><img src="../../../../doc/html/images/prev.png" alt="Prev"></a><a accesskey="u" href="../perf.html"><img src="../../../../doc/html/images/up.png" alt="Up"></a><a accesskey="h" href="../../index.html"><img src="../../../../doc/html/images/home.png" alt="Home"></a><a accesskey="n" href="getting_best.html"><img src="../../../../doc/html/images/next.png" alt="Next"></a>
+</div>
+<div class="section" lang="en">
+<div class="titlepage"><div><div><h3 class="title">
+<a name="math_toolkit.perf.interp"></a><a class="link" href="interp.html" title="Interpreting these Results"> Interpreting these Results</a>
+</h3></div></div></div>
+<p>
+        In all of the following tables, the best performing result in each row, is
+        assigned a relative value of "1" and shown in bold, so a score
+        of "2" means <span class="emphasis"><em>"twice as slow as the best performing
+        result".</em></span> Actual timings in seconds per function call are
+        also shown in parenthesis.
+      </p>
+<p>
+        Result were obtained on a system with an Intel 2.8GHz Pentium 4 processor
+        with 2Gb of RAM and running either Windows XP or Mandriva Linux.
+      </p>
+<div class="caution"><table border="0" summary="Caution">
+<tr>
+<td rowspan="2" align="center" valign="top" width="25"><img alt="[Caution]" src="../../../../doc/html/images/caution.png"></td>
+<th align="left">Caution</th>
+</tr>
+<tr><td align="left" valign="top"><p>
+          As usual with performance results these should be taken with a large pinch
+          of salt: relative performance is known to shift quite a bit depending upon
+          the architecture of the particular test system used. Further more, our
+          performance results were obtained using our own test data: these test values
+          are designed to provide good coverage of our code and test all the appropriate
+          corner cases. They do not necessarily represent "typical" usage:
+          whatever that may be!
+        </p></td></tr>
+</table></div>
+</div>
+<table xmlns:rev="http://www.cs.rpi.edu/~gregod/boost/tools/doc/revision" width="100%"><tr>
+<td align="left"></td>
+<td align="right"><div class="copyright-footer">Copyright © 2006 , 2007, 2008 John Maddock, Paul A. Bristow, Hubert
+      Holin, Xiaogang Zhang, Bruno Lalande and Gautam Sewani<p>
+        Distributed under the Boost Software License, Version 1.0. (See accompanying
+        file LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_0.txt)
+      </p>
+</div></td>
+</tr></table>
+<hr>
+<div class="spirit-nav">
+<a accesskey="p" href="perf_over.html"><img src="../../../../doc/html/images/prev.png" alt="Prev"></a><a accesskey="u" href="../perf.html"><img src="../../../../doc/html/images/up.png" alt="Up"></a><a accesskey="h" href="../../index.html"><img src="../../../../doc/html/images/home.png" alt="Home"></a><a accesskey="n" href="getting_best.html"><img src="../../../../doc/html/images/next.png" alt="Next"></a>
+</div>
+</body>
+</html>

Added: sandbox/tools/auto_index/example/math/doc/sf_and_dist/html/math_toolkit/perf/perf_over.html
==============================================================================
--- (empty file)
+++ sandbox/tools/auto_index/example/math/doc/sf_and_dist/html/math_toolkit/perf/perf_over.html	2008-11-28 05:25:28 EST (Fri, 28 Nov 2008)
@@ -0,0 +1,93 @@
+<html>
+<head>
+<meta http-equiv="Content-Type" content="text/html; charset=ISO-8859-1">
+<title>Performance Overview</title>
+<link rel="stylesheet" href="../../boostbook.css" type="text/css">
+<meta name="generator" content="DocBook XSL Stylesheets Vsnapshot_8125">
+<link rel="home" href="../../index.html" title="Math Toolkit">
+<link rel="up" href="../perf.html" title="Performance">
+<link rel="prev" href="../perf.html" title="Performance">
+<link rel="next" href="interp.html" title="Interpreting these Results">
+</head>
+<body bgcolor="white" text="black" link="#0000FF" vlink="#840084" alink="#0000FF">
+<table cellpadding="2" width="100%"><tr>
+<td valign="top"><img alt="Boost C++ Libraries" width="277" height="86" src="../../../../boost.png"></td>
+<td align="center">Home</td>
+<td align="center">Libraries</td>
+<td align="center">People</td>
+<td align="center">FAQ</td>
+<td align="center">More</td>
+</tr></table>
+<hr>
+<div class="spirit-nav">
+<a accesskey="p" href="../perf.html"><img src="../../../../doc/html/images/prev.png" alt="Prev"></a><a accesskey="u" href="../perf.html"><img src="../../../../doc/html/images/up.png" alt="Up"></a><a accesskey="h" href="../../index.html"><img src="../../../../doc/html/images/home.png" alt="Home"></a><a accesskey="n" href="interp.html"><img src="../../../../doc/html/images/next.png" alt="Next"></a>
+</div>
+<div class="section" lang="en">
+<div class="titlepage"><div><div><h3 class="title">
+<a name="math_toolkit.perf.perf_over"></a><a class="link" href="perf_over.html" title="Performance Overview"> Performance Overview</a>
+</h3></div></div></div>
+<p>
+        </p>
+<p>
+          By and large the performance of this library should be acceptable for most
+          needs. However, you should note that the library's primary emphasis is
+          on accuracy and numerical stability, and <span class="emphasis"><em>not</em></span> speed.
+        </p>
+<p>
+        </p>
+<p>
+          In terms of the algorithms used, this library aims to use the same "best
+          of breed" algorithms as many other libraries: the principle difference
+          is that this library is implemented in C++ - taking advantage of all the
+          abstraction mechanisms that C++ offers - where as most traditional numeric
+          libraries are implemented in C or FORTRAN. Traditionally languages such
+          as C or FORTRAN are perceived as easier to optimise than more complex languages
+          like C++, so in a sense this library provides a good test of current compiler
+          technology, and the "abstraction penalty" - if any - of C++ compared
+          to other languages.
+        </p>
+<p>
+        </p>
+<p>
+          The two most important things you can do to ensure the best performance
+          from this library are:
+        </p>
+<p>
+        </p>
+<div class="orderedlist"><ol type="1">
+<li>
+            Turn on your compilers optimisations: the difference between "release"
+            and "debug" builds can easily be a <a class="link" href="getting_best.html" title="Getting the Best Performance from this Library">factor
+            of 20</a>.
+          </li>
+<li>
+            Pick your compiler carefully: <a class="link" href="comp_compilers.html" title="Comparing Compilers">performance
+            differences of up to 8 fold</a> have been found between some windows
+            compilers for example.
+          </li>
+</ol></div>
+<p>
+        </p>
+<p>
+          The <a class="link" href="../perf.html" title="Performance">performance section</a> contains
+          more information on the performance of this library, what you can do to
+          fine tune it, and how this library compares to some other open source alternatives.
+        </p>
+<p>
+      </p>
+</div>
+<table xmlns:rev="http://www.cs.rpi.edu/~gregod/boost/tools/doc/revision" width="100%"><tr>
+<td align="left"></td>
+<td align="right"><div class="copyright-footer">Copyright © 2006 , 2007, 2008 John Maddock, Paul A. Bristow, Hubert
+      Holin, Xiaogang Zhang, Bruno Lalande and Gautam Sewani<p>
+        Distributed under the Boost Software License, Version 1.0. (See accompanying
+        file LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_0.txt)
+      </p>
+</div></td>
+</tr></table>
+<hr>
+<div class="spirit-nav">
+<a accesskey="p" href="../perf.html"><img src="../../../../doc/html/images/prev.png" alt="Prev"></a><a accesskey="u" href="../perf.html"><img src="../../../../doc/html/images/up.png" alt="Up"></a><a accesskey="h" href="../../index.html"><img src="../../../../doc/html/images/home.png" alt="Home"></a><a accesskey="n" href="interp.html"><img src="../../../../doc/html/images/next.png" alt="Next"></a>
+</div>
+</body>
+</html>

Added: sandbox/tools/auto_index/example/math/doc/sf_and_dist/html/math_toolkit/perf/perf_test_app.html
==============================================================================
--- (empty file)
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@@ -0,0 +1,63 @@
+<html>
+<head>
+<meta http-equiv="Content-Type" content="text/html; charset=ISO-8859-1">
+<title>The Performance Test Application</title>
+<link rel="stylesheet" href="../../boostbook.css" type="text/css">
+<meta name="generator" content="DocBook XSL Stylesheets Vsnapshot_8125">
+<link rel="home" href="../../index.html" title="Math Toolkit">
+<link rel="up" href="../perf.html" title="Performance">
+<link rel="prev" href="comparisons.html" title="Comparisons to Other Open Source Libraries">
+<link rel="next" href="../backgrounders.html" title="Backgrounders">
+</head>
+<body bgcolor="white" text="black" link="#0000FF" vlink="#840084" alink="#0000FF">
+<table cellpadding="2" width="100%"><tr>
+<td valign="top"><img alt="Boost C++ Libraries" width="277" height="86" src="../../../../boost.png"></td>
+<td align="center">Home</td>
+<td align="center">Libraries</td>
+<td align="center">People</td>
+<td align="center">FAQ</td>
+<td align="center">More</td>
+</tr></table>
+<hr>
+<div class="spirit-nav">
+<a accesskey="p" href="comparisons.html"><img src="../../../../doc/html/images/prev.png" alt="Prev"></a><a accesskey="u" href="../perf.html"><img src="../../../../doc/html/images/up.png" alt="Up"></a><a accesskey="h" href="../../index.html"><img src="../../../../doc/html/images/home.png" alt="Home"></a><a accesskey="n" href="../backgrounders.html"><img src="../../../../doc/html/images/next.png" alt="Next"></a>
+</div>
+<div class="section" lang="en">
+<div class="titlepage"><div><div><h3 class="title">
+<a name="math_toolkit.perf.perf_test_app"></a><a class="link" href="perf_test_app.html" title="The Performance Test Application"> The Performance Test
+      Application</a>
+</h3></div></div></div>
+<p>
+        Under <span class="emphasis"><em>boost-path</em></span>/libs/math/performance you will find
+        a (fairly rudimentary) performance test application for this library.
+      </p>
+<p>
+        To run this application yourself, build the all the .cpp files in <span class="emphasis"><em>boost-path</em></span>/libs/math/performance
+        into an application using your usual release-build settings. Run the application
+        with --help to see a full list of options, or with --all to test everything
+        (which takes quite a while), or with --tune to test the <a class="link" href="tuning.html" title="Performance Tuning Macros">available
+        performance tuning options</a>.
+      </p>
+<p>
+        If you want to use this application to test the effect of changing any of
+        the <a class="link" href="../policy.html" title="Policies">Policies</a>, then you will need
+        to build and run it twice: once with the default <a class="link" href="../policy.html" title="Policies">Policies</a>,
+        and then a second time with the <a class="link" href="../policy.html" title="Policies">Policies</a>
+        you want to test set as the default.
+      </p>
+</div>
+<table xmlns:rev="http://www.cs.rpi.edu/~gregod/boost/tools/doc/revision" width="100%"><tr>
+<td align="left"></td>
+<td align="right"><div class="copyright-footer">Copyright © 2006 , 2007, 2008 John Maddock, Paul A. Bristow, Hubert
+      Holin, Xiaogang Zhang, Bruno Lalande and Gautam Sewani<p>
+        Distributed under the Boost Software License, Version 1.0. (See accompanying
+        file LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_0.txt)
+      </p>
+</div></td>
+</tr></table>
+<hr>
+<div class="spirit-nav">
+<a accesskey="p" href="comparisons.html"><img src="../../../../doc/html/images/prev.png" alt="Prev"></a><a accesskey="u" href="../perf.html"><img src="../../../../doc/html/images/up.png" alt="Up"></a><a accesskey="h" href="../../index.html"><img src="../../../../doc/html/images/home.png" alt="Home"></a><a accesskey="n" href="../backgrounders.html"><img src="../../../../doc/html/images/next.png" alt="Next"></a>
+</div>
+</body>
+</html>

Added: sandbox/tools/auto_index/example/math/doc/sf_and_dist/html/math_toolkit/perf/tuning.html
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@@ -0,0 +1,897 @@
+<html>
+<head>
+<meta http-equiv="Content-Type" content="text/html; charset=ISO-8859-1">
+<title>Performance Tuning Macros</title>
+<link rel="stylesheet" href="../../boostbook.css" type="text/css">
+<meta name="generator" content="DocBook XSL Stylesheets Vsnapshot_8125">
+<link rel="home" href="../../index.html" title="Math Toolkit">
+<link rel="up" href="../perf.html" title="Performance">
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+</div>
+<div class="section" lang="en">
+<div class="titlepage"><div><div><h3 class="title">
+<a name="math_toolkit.perf.tuning"></a><a class="link" href="tuning.html" title="Performance Tuning Macros"> Performance Tuning Macros</a>
+</h3></div></div></div>
+<p>
+        There are a small number of performance tuning options that are determined
+        by configuration macros. These should be set in boost/math/tools/user.hpp;
+        or else reported to the Boost-development mailing list so that the appropriate
+        option for a given compiler and OS platform can be set automatically in our
+        configuration setup.
+      </p>
+<div class="informaltable"><table class="table">
+<colgroup>
+<col>
+<col>
+</colgroup>
+<thead><tr>
+<th>
+              <p>
+                Macro
+              </p>
+              </th>
+<th>
+              <p>
+                Meaning
+              </p>
+              </th>
+</tr></thead>
+<tbody>
+<tr>
+<td>
+              <p>
+                BOOST_MATH_POLY_METHOD
+              </p>
+              </td>
+<td>
+              <p>
+                Determines how polynomials and most rational functions are evaluated.
+                Define to one of the values 0, 1, 2 or 3: see below for the meaning
+                of these values.
+              </p>
+              </td>
+</tr>
+<tr>
+<td>
+              <p>
+                BOOST_MATH_RATIONAL_METHOD
+              </p>
+              </td>
+<td>
+              <p>
+                Determines how symmetrical rational functions are evaluated: mostly
+                this only effects how the Lanczos approximation is evaluated, and
+                how the <code class="computeroutput"><span class="identifier">evaluate_rational</span></code>
+                function behaves. Define to one of the values 0, 1, 2 or 3: see below
+                for the meaning of these values.
+              </p>
+              </td>
+</tr>
+<tr>
+<td>
+              <p>
+                BOOST_MATH_MAX_POLY_ORDER
+              </p>
+              </td>
+<td>
+              <p>
+                The maximum order of polynomial or rational function that will be
+                evaluated by a method other than 0 (a simple "for" loop).
+              </p>
+              </td>
+</tr>
+<tr>
+<td>
+              <p>
+                BOOST_MATH_INT_TABLE_TYPE(RT, IT)
+              </p>
+              </td>
+<td>
+              <p>
+                Many of the coefficients to the polynomials and rational functions
+                used by this library are integers. Normally these are stored as tables
+                as integers, but if mixed integer / floating point arithmetic is
+                much slower than regular floating point arithmetic then they can
+                be stored as tables of floating point values instead. If mixed arithmetic
+                is slow then add:
+              </p>
+              <p>
+                #define BOOST_MATH_INT_TABLE_TYPE(RT, IT) RT
+              </p>
+              <p>
+                to boost/math/tools/user.hpp, otherwise the default of:
+              </p>
+              <p>
+                #define BOOST_MATH_INT_TABLE_TYPE(RT, IT) IT
+              </p>
+              <p>
+                Set in boost/math/config.hpp is fine, and may well result in smaller
+                code.
+              </p>
+              </td>
+</tr>
+</tbody>
+</table></div>
+<p>
+        The values to which <code class="computeroutput"><span class="identifier">BOOST_MATH_POLY_METHOD</span></code>
+        and <code class="computeroutput"><span class="identifier">BOOST_MATH_RATIONAL_METHOD</span></code>
+        may be set are as follows:
+      </p>
+<div class="informaltable"><table class="table">
+<colgroup>
+<col>
+<col>
+</colgroup>
+<thead><tr>
+<th>
+              <p>
+                Value
+              </p>
+              </th>
+<th>
+              <p>
+                Effect
+              </p>
+              </th>
+</tr></thead>
+<tbody>
+<tr>
+<td>
+              <p>
+                0
+              </p>
+              </td>
+<td>
+              <p>
+                The polynomial or rational function is evaluated using Horner's method,
+                and a simple for-loop.
+              </p>
+              <p>
+                Note that if the order of the polynomial or rational function is
+                a runtime parameter, or the order is greater than the value of <code class="computeroutput"><span class="identifier">BOOST_MATH_MAX_POLY_ORDER</span></code>, then
+                this method is always used, irrespective of the value of <code class="computeroutput"><span class="identifier">BOOST_MATH_POLY_METHOD</span></code> or <code class="computeroutput"><span class="identifier">BOOST_MATH_RATIONAL_METHOD</span></code>.
+              </p>
+              </td>
+</tr>
+<tr>
+<td>
+              <p>
+                1
+              </p>
+              </td>
+<td>
+              <p>
+                The polynomial or rational function is evaluated without the use
+                of a loop, and using Horner's method. This only occurs if the order
+                of the polynomial is known at compile time and is less than or equal
+                to <code class="computeroutput"><span class="identifier">BOOST_MATH_MAX_POLY_ORDER</span></code>.
+              </p>
+              </td>
+</tr>
+<tr>
+<td>
+              <p>
+                2
+              </p>
+              </td>
+<td>
+              <p>
+                The polynomial or rational function is evaluated without the use
+                of a loop, and using a second order Horner's method. In theory this
+                permits two operations to occur in parallel for polynomials, and
+                four in parallel for rational functions. This only occurs if the
+                order of the polynomial is known at compile time and is less than
+                or equal to <code class="computeroutput"><span class="identifier">BOOST_MATH_MAX_POLY_ORDER</span></code>.
+              </p>
+              </td>
+</tr>
+<tr>
+<td>
+              <p>
+                3
+              </p>
+              </td>
+<td>
+              <p>
+                The polynomial or rational function is evaluated without the use
+                of a loop, and using a second order Horner's method. In theory this
+                permits two operations to occur in parallel for polynomials, and
+                four in parallel for rational functions. This differs from method
+                "2" in that the code is carefully ordered to make the parallelisation
+                more obvious to the compiler: rather than relying on the compiler's
+                optimiser to spot the parallelisation opportunities. This only occurs
+                if the order of the polynomial is known at compile time and is less
+                than or equal to <code class="computeroutput"><span class="identifier">BOOST_MATH_MAX_POLY_ORDER</span></code>.
+              </p>
+              </td>
+</tr>
+</tbody>
+</table></div>
+<p>
+        To determine which of these options is best for your particular compiler/platform
+        build the performance test application with your usual release settings,
+        and run the program with the --tune command line option.
+      </p>
+<p>
+        In practice the difference between methods is rather small at present, as
+        the following table shows. However, parallelisation /vectorisation is likely
+        to become more important in the future: quite likely the methods currently
+        supported will need to be supplemented or replaced by ones more suited to
+        highly vectorisable processors in the future.
+      </p>
+<div class="table">
+<a name="id906988"></a><p class="title"><b>Table 49. A Comparison of Polynomial Evaluation Methods</b></p>
+<div class="table-contents"><table class="table" summary="A Comparison of Polynomial Evaluation Methods">
+<colgroup>
+<col>
+<col>
+<col>
+<col>
+<col>
+</colgroup>
+<thead><tr>
+<th>
+            <p>
+              Compiler/platform
+            </p>
+            </th>
+<th>
+            <p>
+              Method 0
+            </p>
+            </th>
+<th>
+            <p>
+              Method 1
+            </p>
+            </th>
+<th>
+            <p>
+              Method 2
+            </p>
+            </th>
+<th>
+            <p>
+              Method 3
+            </p>
+            </th>
+</tr></thead>
+<tbody>
+<tr>
+<td>
+            <p>
+              Microsoft C++ 8.0, Polynomial evaluation
+            </p>
+            </td>
+<td>
+            <p>
+              </p>
+<p>1.34</p>
+<p> </p>
+<p>(1.161e-007s)</p>
+<p>
+            </p>
+            </td>
+<td>
+            <p>
+              </p>
+<p>1.13</p>
+<p> </p>
+<p>(9.777e-008s)</p>
+<p>
+            </p>
+            </td>
+<td>
+            <p>
+              </p>
+<p>1.07</p>
+<p> </p>
+<p>(9.289e-008s)</p>
+<p>
+            </p>
+            </td>
+<td>
+            <p>
+              </p>
+<p><span class="bold"><strong>1.00</strong></span></p>
+<p> </p>
+<p>(8.678e-008s)</p>
+<p>
+            </p>
+            </td>
+</tr>
+<tr>
+<td>
+            <p>
+              Microsoft C++ 8.0, Rational evaluation
+            </p>
+            </td>
+<td>
+            <p>
+              </p>
+<p><span class="bold"><strong>1.00</strong></span></p>
+<p> </p>
+<p>(1.443e-007s)</p>
+<p>
+            </p>
+            </td>
+<td>
+            <p>
+              </p>
+<p>1.03</p>
+<p> </p>
+<p>(1.492e-007s)</p>
+<p>
+            </p>
+            </td>
+<td>
+            <p>
+              </p>
+<p>1.20</p>
+<p> </p>
+<p>(1.736e-007s)</p>
+<p>
+            </p>
+            </td>
+<td>
+            <p>
+              </p>
+<p>1.07</p>
+<p> </p>
+<p>(1.540e-007s)</p>
+<p>
+            </p>
+            </td>
+</tr>
+<tr>
+<td>
+            <p>
+              Intel C++ 10.0 (Windows), Polynomial evaluation
+            </p>
+            </td>
+<td>
+            <p>
+              </p>
+<p>1.03</p>
+<p> </p>
+<p>(7.702e-008s)</p>
+<p>
+            </p>
+            </td>
+<td>
+            <p>
+              </p>
+<p>1.03</p>
+<p> </p>
+<p>(7.702e-008s)</p>
+<p>
+            </p>
+            </td>
+<td>
+            <p>
+              </p>
+<p><span class="bold"><strong>1.00</strong></span></p>
+<p> </p>
+<p>(7.446e-008s)</p>
+<p>
+            </p>
+            </td>
+<td>
+            <p>
+              </p>
+<p>1.03</p>
+<p> </p>
+<p>(7.690e-008s)</p>
+<p>
+            </p>
+            </td>
+</tr>
+<tr>
+<td>
+            <p>
+              Intel C++ 10.0 (Windows), Rational evaluation
+            </p>
+            </td>
+<td>
+            <p>
+              </p>
+<p><span class="bold"><strong>1.00</strong></span></p>
+<p> </p>
+<p>(1.245e-007s)</p>
+<p>
+            </p>
+            </td>
+<td>
+            <p>
+              </p>
+<p><span class="bold"><strong>1.00</strong></span></p>
+<p> </p>
+<p>(1.245e-007s)</p>
+<p>
+            </p>
+            </td>
+<td>
+            <p>
+              </p>
+<p>1.18</p>
+<p> </p>
+<p>(1.465e-007s)</p>
+<p>
+            </p>
+            </td>
+<td>
+            <p>
+              </p>
+<p>1.06</p>
+<p> </p>
+<p>(1.318e-007s)</p>
+<p>
+            </p>
+            </td>
+</tr>
+<tr>
+<td>
+            <p>
+              GNU G++ 4.2 (Linux), Polynomial evaluation
+            </p>
+            </td>
+<td>
+            <p>
+              </p>
+<p>1.61</p>
+<p> </p>
+<p>(1.220e-007s)</p>
+<p>
+            </p>
+            </td>
+<td>
+            <p>
+              </p>
+<p>1.68</p>
+<p> </p>
+<p>(1.269e-007s)</p>
+<p>
+            </p>
+            </td>
+<td>
+            <p>
+              </p>
+<p>1.23</p>
+<p> </p>
+<p>(9.275e-008s)</p>
+<p>
+            </p>
+            </td>
+<td>
+            <p>
+              </p>
+<p><span class="bold"><strong>1.00</strong></span></p>
+<p> </p>
+<p>(7.566e-008s)</p>
+<p>
+            </p>
+            </td>
+</tr>
+<tr>
+<td>
+            <p>
+              GNU G++ 4.2 (Linux), Rational evaluation
+            </p>
+            </td>
+<td>
+            <p>
+              </p>
+<p>1.26</p>
+<p> </p>
+<p>(1.660e-007s)</p>
+<p>
+            </p>
+            </td>
+<td>
+            <p>
+              </p>
+<p>1.33</p>
+<p> </p>
+<p>(1.758e-007s)</p>
+<p>
+            </p>
+            </td>
+<td>
+            <p>
+              </p>
+<p><span class="bold"><strong>1.00</strong></span></p>
+<p> </p>
+<p>(1.318e-007s)</p>
+<p>
+            </p>
+            </td>
+<td>
+            <p>
+              </p>
+<p>1.15</p>
+<p> </p>
+<p>(1.513e-007s)</p>
+<p>
+            </p>
+            </td>
+</tr>
+<tr>
+<td>
+            <p>
+              Intel C++ 10.0 (Linux), Polynomial evaluation
+            </p>
+            </td>
+<td>
+            <p>
+              </p>
+<p>1.15</p>
+<p> </p>
+<p>(9.154e-008s)</p>
+<p>
+            </p>
+            </td>
+<td>
+            <p>
+              </p>
+<p>1.15</p>
+<p> </p>
+<p>(9.154e-008s)</p>
+<p>
+            </p>
+            </td>
+<td>
+            <p>
+              </p>
+<p><span class="bold"><strong>1.00</strong></span></p>
+<p> </p>
+<p>(7.934e-008s)</p>
+<p>
+            </p>
+            </td>
+<td>
+            <p>
+              </p>
+<p><span class="bold"><strong>1.00</strong></span></p>
+<p> </p>
+<p>(7.934e-008s)</p>
+<p>
+            </p>
+            </td>
+</tr>
+<tr>
+<td>
+            <p>
+              Intel C++ 10.0 (Linux), Rational evaluation
+            </p>
+            </td>
+<td>
+            <p>
+              </p>
+<p><span class="bold"><strong>1.00</strong></span></p>
+<p> </p>
+<p>(1.245e-007s)</p>
+<p>
+            </p>
+            </td>
+<td>
+            <p>
+              </p>
+<p><span class="bold"><strong>1.00</strong></span></p>
+<p> </p>
+<p>(1.245e-007s)</p>
+<p>
+            </p>
+            </td>
+<td>
+            <p>
+              </p>
+<p>1.35</p>
+<p> </p>
+<p>(1.684e-007s)</p>
+<p>
+            </p>
+            </td>
+<td>
+            <p>
+              </p>
+<p>1.04</p>
+<p> </p>
+<p>(1.294e-007s)</p>
+<p>
+            </p>
+            </td>
+</tr>
+</tbody>
+</table></div>
+</div>
+<br class="table-break"><p>
+        There is one final performance tuning option that is available as a compile
+        time <a class="link" href="../policy.html" title="Policies">policy</a>. Normally when evaluating
+        functions at <code class="computeroutput"><span class="keyword">double</span></code> precision,
+        these are actually evaluated at <code class="computeroutput"><span class="keyword">long</span>
+        <span class="keyword">double</span></code> precision internally: this
+        helps to ensure that as close to full <code class="computeroutput"><span class="keyword">double</span></code>
+        precision as possible is achieved, but may slow down execution in some environments.
+        The defaults for this policy can be changed by <a class="link" href="../policy/pol_ref/policy_defaults.html" title="Using macros to Change the Policy Defaults">defining
+        the macro <code class="computeroutput"><span class="identifier">BOOST_MATH_PROMOTE_DOUBLE_POLICY</span></code></a>
+        to <code class="computeroutput"><span class="keyword">false</span></code>, or <a class="link" href="../policy/pol_ref/internal_promotion.html" title="Internal Promotion Policies">by
+        specifying a specific policy</a> when calling the special functions or
+        distributions. See also the <a class="link" href="../policy/pol_tutorial.html" title="Policy Tutorial">policy
+        tutorial</a>.
+      </p>
+<div class="table">
+<a name="id907765"></a><p class="title"><b>Table 50. Performance Comparison with and Without Internal
+      Promotion to long double</b></p>
+<div class="table-contents"><table class="table" summary="Performance Comparison with and Without Internal
+      Promotion to long double">
+<colgroup>
+<col>
+<col>
+<col>
+</colgroup>
+<thead><tr>
+<th>
+            <p>
+              Function
+            </p>
+            </th>
+<th>
+            <p>
+              GCC 4.2 , Linux
+            </p>
+            <p>
+              (with internal promotion of double to long double).
+            </p>
+            </th>
+<th>
+            <p>
+              GCC 4.2, Linux
+            </p>
+            <p>
+              (without promotion of double).
+            </p>
+            </th>
+</tr></thead>
+<tbody>
+<tr>
+<td>
+            <p>
+              <a class="link" href="../special/sf_erf/error_function.html" title="Error Functions">erf</a>
+            </p>
+            </td>
+<td>
+            <p>
+              </p>
+<p>1.48</p>
+<p> </p>
+<p>(1.387e-007s)</p>
+<p>
+            </p>
+            </td>
+<td>
+            <p>
+              </p>
+<p><span class="bold"><strong>1.00</strong></span></p>
+<p> </p>
+<p>(9.377e-008s)</p>
+<p>
+            </p>
+            </td>
+</tr>
+<tr>
+<td>
+            <p>
+              <a class="link" href="../special/sf_erf/error_inv.html" title="Error Function Inverses">erf_inv</a>
+            </p>
+            </td>
+<td>
+            <p>
+              </p>
+<p>1.11</p>
+<p> </p>
+<p>(4.009e-007s)</p>
+<p>
+            </p>
+            </td>
+<td>
+            <p>
+              </p>
+<p><span class="bold"><strong>1.00</strong></span></p>
+<p> </p>
+<p>(3.598e-007s)</p>
+<p>
+            </p>
+            </td>
+</tr>
+<tr>
+<td>
+            <p>
+              <a class="link" href="../special/sf_beta/ibeta_function.html" title="Incomplete Beta Functions">ibeta</a>
+              and <a class="link" href="../special/sf_beta/ibeta_function.html" title="Incomplete Beta Functions">ibetac</a>
+            </p>
+            </td>
+<td>
+            <p>
+              </p>
+<p>1.29</p>
+<p> </p>
+<p>(5.354e-006s)</p>
+<p>
+            </p>
+            </td>
+<td>
+            <p>
+              </p>
+<p><span class="bold"><strong>1.00</strong></span></p>
+<p> </p>
+<p>(4.137e-006s)</p>
+<p>
+            </p>
+            </td>
+</tr>
+<tr>
+<td>
+            <p>
+              <a class="link" href="../special/sf_beta/ibeta_inv_function.html" title="The Incomplete Beta Function Inverses">ibeta_inv</a>
+              and <a class="link" href="../special/sf_beta/ibeta_inv_function.html" title="The Incomplete Beta Function Inverses">ibetac_inv</a>
+            </p>
+            </td>
+<td>
+            <p>
+              </p>
+<p>1.44</p>
+<p> </p>
+<p>(2.220e-005s)</p>
+<p>
+            </p>
+            </td>
+<td>
+            <p>
+              </p>
+<p><span class="bold"><strong>1.00</strong></span></p>
+<p> </p>
+<p>(1.538e-005s)</p>
+<p>
+            </p>
+            </td>
+</tr>
+<tr>
+<td>
+            <p>
+              <a class="link" href="../special/sf_beta/ibeta_inv_function.html" title="The Incomplete Beta Function Inverses">ibeta_inva</a>,
+              <a class="link" href="../special/sf_beta/ibeta_inv_function.html" title="The Incomplete Beta Function Inverses">ibetac_inva</a>,
+              <a class="link" href="../special/sf_beta/ibeta_inv_function.html" title="The Incomplete Beta Function Inverses">ibeta_invb</a>
+              and <a class="link" href="../special/sf_beta/ibeta_inv_function.html" title="The Incomplete Beta Function Inverses">ibetac_invb</a>
+            </p>
+            </td>
+<td>
+            <p>
+              </p>
+<p>1.25</p>
+<p> </p>
+<p>(7.009e-005s)</p>
+<p>
+            </p>
+            </td>
+<td>
+            <p>
+              </p>
+<p><span class="bold"><strong>1.00</strong></span></p>
+<p> </p>
+<p>(5.607e-005s)</p>
+<p>
+            </p>
+            </td>
+</tr>
+<tr>
+<td>
+            <p>
+              <a class="link" href="../special/sf_gamma/igamma.html" title="Incomplete Gamma Functions">gamma_p</a>
+              and <a class="link" href="../special/sf_gamma/igamma.html" title="Incomplete Gamma Functions">gamma_q</a>
+            </p>
+            </td>
+<td>
+            <p>
+              </p>
+<p>1.26</p>
+<p> </p>
+<p>(3.116e-006s)</p>
+<p>
+            </p>
+            </td>
+<td>
+            <p>
+              </p>
+<p><span class="bold"><strong>1.00</strong></span></p>
+<p> </p>
+<p>(2.464e-006s)</p>
+<p>
+            </p>
+            </td>
+</tr>
+<tr>
+<td>
+            <p>
+              <a class="link" href="../special/sf_gamma/igamma_inv.html" title="Incomplete Gamma Function Inverses">gamma_p_inv</a>
+              and <a class="link" href="../special/sf_gamma/igamma_inv.html" title="Incomplete Gamma Function Inverses">gamma_q_inv</a>
+            </p>
+            </td>
+<td>
+            <p>
+              </p>
+<p>1.27</p>
+<p> </p>
+<p>(1.178e-005s)</p>
+<p>
+            </p>
+            </td>
+<td>
+            <p>
+              </p>
+<p><span class="bold"><strong>1.00</strong></span></p>
+<p> </p>
+<p>(9.291e-006s)</p>
+<p>
+            </p>
+            </td>
+</tr>
+<tr>
+<td>
+            <p>
+              <a class="link" href="../special/sf_gamma/igamma_inv.html" title="Incomplete Gamma Function Inverses">gamma_p_inva</a>
+              and <a class="link" href="../special/sf_gamma/igamma_inv.html" title="Incomplete Gamma Function Inverses">gamma_q_inva</a>
+            </p>
+            </td>
+<td>
+            <p>
+              </p>
+<p>1.20</p>
+<p> </p>
+<p>(2.765e-005s)</p>
+<p>
+            </p>
+            </td>
+<td>
+            <p>
+              </p>
+<p><span class="bold"><strong>1.00</strong></span></p>
+<p> </p>
+<p>(2.311e-005s)</p>
+<p>
+            </p>
+            </td>
+</tr>
+</tbody>
+</table></div>
+</div>
+<br class="table-break">
+</div>
+<table xmlns:rev="http://www.cs.rpi.edu/~gregod/boost/tools/doc/revision" width="100%"><tr>
+<td align="left"></td>
+<td align="right"><div class="copyright-footer">Copyright © 2006 , 2007, 2008 John Maddock, Paul A. Bristow, Hubert
+      Holin, Xiaogang Zhang, Bruno Lalande and Gautam Sewani<p>
+        Distributed under the Boost Software License, Version 1.0. (See accompanying
+        file LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_0.txt)
+      </p>
+</div></td>
+</tr></table>
+<hr>
+<div class="spirit-nav">
+<a accesskey="p" href="comp_compilers.html"><img src="../../../../doc/html/images/prev.png" alt="Prev"></a><a accesskey="u" href="../perf.html"><img src="../../../../doc/html/images/up.png" alt="Up"></a><a accesskey="h" href="../../index.html"><img src="../../../../doc/html/images/home.png" alt="Home"></a><a accesskey="n" href="comparisons.html"><img src="../../../../doc/html/images/next.png" alt="Next"></a>
+</div>
+</body>
+</html>

Added: sandbox/tools/auto_index/example/math/doc/sf_and_dist/html/math_toolkit/policy.html
==============================================================================
--- (empty file)
+++ sandbox/tools/auto_index/example/math/doc/sf_and_dist/html/math_toolkit/policy.html	2008-11-28 05:25:28 EST (Fri, 28 Nov 2008)
@@ -0,0 +1,91 @@
+<html>
+<head>
+<meta http-equiv="Content-Type" content="text/html; charset=ISO-8859-1">
+<title>Policies</title>
+<link rel="stylesheet" href="../boostbook.css" type="text/css">
+<meta name="generator" content="DocBook XSL Stylesheets Vsnapshot_8125">
+<link rel="home" href="../index.html" title="Math Toolkit">
+<link rel="up" href="../index.html" title="Math Toolkit">
+<link rel="prev" href="using_udt/archetypes.html" title="Conceptual Archetypes and Testing">
+<link rel="next" href="policy/pol_overview.html" title="Policy Overview">
+</head>
+<body bgcolor="white" text="black" link="#0000FF" vlink="#840084" alink="#0000FF">
+<table cellpadding="2" width="100%"><tr>
+<td valign="top"><img alt="Boost C++ Libraries" width="277" height="86" src="../../../boost.png"></td>
+<td align="center">Home</td>
+<td align="center">Libraries</td>
+<td align="center">People</td>
+<td align="center">FAQ</td>
+<td align="center">More</td>
+</tr></table>
+<hr>
+<div class="spirit-nav">
+<a accesskey="p" href="using_udt/archetypes.html"><img src="../../../doc/html/images/prev.png" alt="Prev"></a><a accesskey="u" href="../index.html"><img src="../../../doc/html/images/up.png" alt="Up"></a><a accesskey="h" href="../index.html"><img src="../../../doc/html/images/home.png" alt="Home"></a><a accesskey="n" href="policy/pol_overview.html"><img src="../../../doc/html/images/next.png" alt="Next"></a>
+</div>
+<div class="section" lang="en">
+<div class="titlepage"><div><div><h2 class="title" style="clear: both">
+<a name="math_toolkit.policy"></a><a class="link" href="policy.html" title="Policies"> Policies</a>
+</h2></div></div></div>
+<div class="toc"><dl>
+<dt><span class="section"> Policy Overview</span></dt>
+<dt><span class="section"> Policy Tutorial</span></dt>
+<dd><dl>
+<dt><span class="section"><a href="policy/pol_tutorial/what_is_a_policy.html">
+        So Just What is a Policy Anyway?</a></span></dt>
+<dt><span class="section"><a href="policy/pol_tutorial/policy_tut_defaults.html">
+        Policies Have Sensible Defaults</a></span></dt>
+<dt><span class="section"><a href="policy/pol_tutorial/policy_usage.html"> So
+        How are Policies Used Anyway?</a></span></dt>
+<dt><span class="section"><a href="policy/pol_tutorial/changing_policy_defaults.html">
+        Changing the Policy Defaults</a></span></dt>
+<dt><span class="section"><a href="policy/pol_tutorial/ad_hoc_dist_policies.html">
+        Setting Policies for Distributions on an Ad Hoc Basis</a></span></dt>
+<dt><span class="section"><a href="policy/pol_tutorial/ad_hoc_sf_policies.html">
+        Changing the Policy on an Ad Hoc Basis for the Special Functions</a></span></dt>
+<dt><span class="section"><a href="policy/pol_tutorial/namespace_policies.html">
+        Setting Policies at Namespace or Translation Unit Scope</a></span></dt>
+<dt><span class="section"><a href="policy/pol_tutorial/user_def_err_pol.html">
+        Calling User Defined Error Handlers</a></span></dt>
+<dt><span class="section"><a href="policy/pol_tutorial/understand_dis_quant.html">
+        Understanding Quantiles of Discrete Distributions</a></span></dt>
+</dl></dd>
+<dt><span class="section"> Policy Reference</span></dt>
+<dd><dl>
+<dt><span class="section"><a href="policy/pol_ref/error_handling_policies.html">
+        Error Handling Policies</a></span></dt>
+<dt><span class="section"><a href="policy/pol_ref/internal_promotion.html"> Internal
+        Promotion Policies</a></span></dt>
+<dt><span class="section"><a href="policy/pol_ref/assert_undefined.html"> Mathematically
+        Undefined Function Policies</a></span></dt>
+<dt><span class="section"><a href="policy/pol_ref/discrete_quant_ref.html"> Discrete
+        Quantile Policies</a></span></dt>
+<dt><span class="section"><a href="policy/pol_ref/precision_pol.html"> Precision
+        Policies</a></span></dt>
+<dt><span class="section"><a href="policy/pol_ref/iteration_pol.html"> Iteration
+        Limits Policies</a></span></dt>
+<dt><span class="section"><a href="policy/pol_ref/policy_defaults.html"> Using
+        macros to Change the Policy Defaults</a></span></dt>
+<dt><span class="section"><a href="policy/pol_ref/namespace_pol.html"> Setting
+        Polices at Namespace Scope</a></span></dt>
+<dt><span class="section"><a href="policy/pol_ref/pol_ref_ref.html"> Policy Class
+        Reference</a></span></dt>
+</dl></dd>
+</dl></div>
+<p>
+    </p>
+</div>
+<table xmlns:rev="http://www.cs.rpi.edu/~gregod/boost/tools/doc/revision" width="100%"><tr>
+<td align="left"></td>
+<td align="right"><div class="copyright-footer">Copyright © 2006 , 2007, 2008 John Maddock, Paul A. Bristow, Hubert
+      Holin, Xiaogang Zhang, Bruno Lalande and Gautam Sewani<p>
+        Distributed under the Boost Software License, Version 1.0. (See accompanying
+        file LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_0.txt)
+      </p>
+</div></td>
+</tr></table>
+<hr>
+<div class="spirit-nav">
+<a accesskey="p" href="using_udt/archetypes.html"><img src="../../../doc/html/images/prev.png" alt="Prev"></a><a accesskey="u" href="../index.html"><img src="../../../doc/html/images/up.png" alt="Up"></a><a accesskey="h" href="../index.html"><img src="../../../doc/html/images/home.png" alt="Home"></a><a accesskey="n" href="policy/pol_overview.html"><img src="../../../doc/html/images/next.png" alt="Next"></a>
+</div>
+</body>
+</html>

Added: sandbox/tools/auto_index/example/math/doc/sf_and_dist/html/math_toolkit/policy/pol_overview.html
==============================================================================
--- (empty file)
+++ sandbox/tools/auto_index/example/math/doc/sf_and_dist/html/math_toolkit/policy/pol_overview.html	2008-11-28 05:25:28 EST (Fri, 28 Nov 2008)
@@ -0,0 +1,135 @@
+<html>
+<head>
+<meta http-equiv="Content-Type" content="text/html; charset=ISO-8859-1">
+<title>Policy Overview</title>
+<link rel="stylesheet" href="../../boostbook.css" type="text/css">
+<meta name="generator" content="DocBook XSL Stylesheets Vsnapshot_8125">
+<link rel="home" href="../../index.html" title="Math Toolkit">
+<link rel="up" href="../policy.html" title="Policies">
+<link rel="prev" href="../policy.html" title="Policies">
+<link rel="next" href="pol_tutorial.html" title="Policy Tutorial">
+</head>
+<body bgcolor="white" text="black" link="#0000FF" vlink="#840084" alink="#0000FF">
+<table cellpadding="2" width="100%"><tr>
+<td valign="top"><img alt="Boost C++ Libraries" width="277" height="86" src="../../../../boost.png"></td>
+<td align="center">Home</td>
+<td align="center">Libraries</td>
+<td align="center">People</td>
+<td align="center">FAQ</td>
+<td align="center">More</td>
+</tr></table>
+<hr>
+<div class="spirit-nav">
+<a accesskey="p" href="../policy.html"><img src="../../../../doc/html/images/prev.png" alt="Prev"></a><a accesskey="u" href="../policy.html"><img src="../../../../doc/html/images/up.png" alt="Up"></a><a accesskey="h" href="../../index.html"><img src="../../../../doc/html/images/home.png" alt="Home"></a><a accesskey="n" href="pol_tutorial.html"><img src="../../../../doc/html/images/next.png" alt="Next"></a>
+</div>
+<div class="section" lang="en">
+<div class="titlepage"><div><div><h3 class="title">
+<a name="math_toolkit.policy.pol_overview"></a><a class="link" href="pol_overview.html" title="Policy Overview"> Policy Overview</a>
+</h3></div></div></div>
+<p>
+        </p>
+<p>
+          Policies are a powerful fine-grain mechanism that allow you to customise
+          the behaviour of this library according to your needs. There is more information
+          available in the <a class="link" href="pol_tutorial.html" title="Policy Tutorial">policy
+          tutorial</a> and the <a class="link" href="pol_ref.html" title="Policy Reference">policy
+          reference</a>.
+        </p>
+<p>
+        </p>
+<p>
+          Generally speaking unless you find that the <a class="link" href="pol_tutorial/policy_tut_defaults.html" title="Policies Have Sensible Defaults">default
+          policy behaviour</a> when encountering 'bad' argument values does not
+          meet your needs, you should not need to worry about policies.
+        </p>
+<p>
+        </p>
+<p>
+          Policies are a compile-time mechanism that allow you to change error-handling
+          or calculation precision either program wide, or at the call site.
+        </p>
+<p>
+        </p>
+<p>
+          Although the policy mechanism itself is rather complicated, in practice
+          it is easy to use, and very flexible.
+        </p>
+<p>
+        </p>
+<p>
+          Using policies you can control:
+        </p>
+<p>
+        </p>
+<div class="itemizedlist"><ul type="disc">
+<li>
+<a class="link" href="pol_ref/error_handling_policies.html" title="Error Handling Policies">How
+            results from 'bad' arguments are handled</a>, including those that
+            cannot be fully evaluated.
+          </li>
+<li>
+            How <a class="link" href="pol_ref/internal_promotion.html" title="Internal Promotion Policies">accuracy
+            is controlled by internal promotion</a> to use more precise types.
+          </li>
+<li>
+            What working <a class="link" href="pol_ref/precision_pol.html" title="Precision Policies">precision</a>
+            should be used to calculate results.
+          </li>
+<li>
+            What to do when a <a class="link" href="pol_ref/assert_undefined.html" title="Mathematically Undefined Function Policies">mathematically
+            undefined function</a> is used: Should this raise a run-time or compile-time
+            error?
+          </li>
+<li>
+            Whether <a class="link" href="pol_ref/discrete_quant_ref.html" title="Discrete Quantile Policies">discrete
+            functions</a>, like the binomial, should return real or only integral
+            values, and how they are rounded.
+          </li>
+<li>
+            How many iterations a special function is permitted to perform in a series
+            evaluation or root finding algorithm before it gives up and raises an
+            <a class="link" href="../main_overview/error_handling.html#evaluation_error">evaluation_error</a>.
+          </li>
+</ul></div>
+<p>
+        </p>
+<p>
+          You can control policies:
+        </p>
+<p>
+        </p>
+<div class="itemizedlist"><ul type="disc">
+<li>
+            Using <a class="link" href="pol_ref/policy_defaults.html" title="Using macros to Change the Policy Defaults">macros</a>
+            to change any default policy: the is the prefered method for installation
+            wide policies.
+          </li>
+<li>
+            At your chosen <a class="link" href="pol_ref/namespace_pol.html" title="Setting Polices at Namespace Scope">namespace
+            scope</a> for distributions and/or functions: this is the prefered
+            method for project, namespace, or translation unit scope policies.
+          </li>
+<li>
+            In an ad-hoc manner <a class="link" href="pol_tutorial/ad_hoc_sf_policies.html" title="Changing the Policy on an Ad Hoc Basis for the Special Functions">by
+            passing a specific policy to a special function</a>, or to a <a class="link" href="pol_tutorial/ad_hoc_dist_policies.html" title="Setting Policies for Distributions on an Ad Hoc Basis">statistical
+            distribution</a>.
+          </li>
+</ul></div>
+<p>
+      </p>
+</div>
+<table xmlns:rev="http://www.cs.rpi.edu/~gregod/boost/tools/doc/revision" width="100%"><tr>
+<td align="left"></td>
+<td align="right"><div class="copyright-footer">Copyright © 2006 , 2007, 2008 John Maddock, Paul A. Bristow, Hubert
+      Holin, Xiaogang Zhang, Bruno Lalande and Gautam Sewani<p>
+        Distributed under the Boost Software License, Version 1.0. (See accompanying
+        file LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_0.txt)
+      </p>
+</div></td>
+</tr></table>
+<hr>
+<div class="spirit-nav">
+<a accesskey="p" href="../policy.html"><img src="../../../../doc/html/images/prev.png" alt="Prev"></a><a accesskey="u" href="../policy.html"><img src="../../../../doc/html/images/up.png" alt="Up"></a><a accesskey="h" href="../../index.html"><img src="../../../../doc/html/images/home.png" alt="Home"></a><a accesskey="n" href="pol_tutorial.html"><img src="../../../../doc/html/images/next.png" alt="Next"></a>
+</div>
+</body>
+</html>

Added: sandbox/tools/auto_index/example/math/doc/sf_and_dist/html/math_toolkit/policy/pol_ref.html
==============================================================================
--- (empty file)
+++ sandbox/tools/auto_index/example/math/doc/sf_and_dist/html/math_toolkit/policy/pol_ref.html	2008-11-28 05:25:28 EST (Fri, 28 Nov 2008)
@@ -0,0 +1,64 @@
+<html>
+<head>
+<meta http-equiv="Content-Type" content="text/html; charset=ISO-8859-1">
+<title>Policy Reference</title>
+<link rel="stylesheet" href="../../boostbook.css" type="text/css">
+<meta name="generator" content="DocBook XSL Stylesheets Vsnapshot_8125">
+<link rel="home" href="../../index.html" title="Math Toolkit">
+<link rel="up" href="../policy.html" title="Policies">
+<link rel="prev" href="pol_tutorial/understand_dis_quant.html" title="Understanding Quantiles of Discrete Distributions">
+<link rel="next" href="pol_ref/error_handling_policies.html" title="Error Handling Policies">
+</head>
+<body bgcolor="white" text="black" link="#0000FF" vlink="#840084" alink="#0000FF">
+<table cellpadding="2" width="100%"><tr>
+<td valign="top"><img alt="Boost C++ Libraries" width="277" height="86" src="../../../../boost.png"></td>
+<td align="center">Home</td>
+<td align="center">Libraries</td>
+<td align="center">People</td>
+<td align="center">FAQ</td>
+<td align="center">More</td>
+</tr></table>
+<hr>
+<div class="spirit-nav">
+<a accesskey="p" href="pol_tutorial/understand_dis_quant.html"><img src="../../../../doc/html/images/prev.png" alt="Prev"></a><a accesskey="u" href="../policy.html"><img src="../../../../doc/html/images/up.png" alt="Up"></a><a accesskey="h" href="../../index.html"><img src="../../../../doc/html/images/home.png" alt="Home"></a><a accesskey="n" href="pol_ref/error_handling_policies.html"><img src="../../../../doc/html/images/next.png" alt="Next"></a>
+</div>
+<div class="section" lang="en">
+<div class="titlepage"><div><div><h3 class="title">
+<a name="math_toolkit.policy.pol_ref"></a><a class="link" href="pol_ref.html" title="Policy Reference"> Policy Reference</a>
+</h3></div></div></div>
+<div class="toc"><dl>
+<dt><span class="section"><a href="pol_ref/error_handling_policies.html">
+        Error Handling Policies</a></span></dt>
+<dt><span class="section"><a href="pol_ref/internal_promotion.html"> Internal
+        Promotion Policies</a></span></dt>
+<dt><span class="section"><a href="pol_ref/assert_undefined.html"> Mathematically
+        Undefined Function Policies</a></span></dt>
+<dt><span class="section"><a href="pol_ref/discrete_quant_ref.html"> Discrete
+        Quantile Policies</a></span></dt>
+<dt><span class="section"><a href="pol_ref/precision_pol.html"> Precision
+        Policies</a></span></dt>
+<dt><span class="section"><a href="pol_ref/iteration_pol.html"> Iteration
+        Limits Policies</a></span></dt>
+<dt><span class="section"><a href="pol_ref/policy_defaults.html"> Using
+        macros to Change the Policy Defaults</a></span></dt>
+<dt><span class="section"><a href="pol_ref/namespace_pol.html"> Setting
+        Polices at Namespace Scope</a></span></dt>
+<dt><span class="section"><a href="pol_ref/pol_ref_ref.html"> Policy Class
+        Reference</a></span></dt>
+</dl></div>
+</div>
+<table xmlns:rev="http://www.cs.rpi.edu/~gregod/boost/tools/doc/revision" width="100%"><tr>
+<td align="left"></td>
+<td align="right"><div class="copyright-footer">Copyright © 2006 , 2007, 2008 John Maddock, Paul A. Bristow, Hubert
+      Holin, Xiaogang Zhang, Bruno Lalande and Gautam Sewani<p>
+        Distributed under the Boost Software License, Version 1.0. (See accompanying
+        file LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_0.txt)
+      </p>
+</div></td>
+</tr></table>
+<hr>
+<div class="spirit-nav">
+<a accesskey="p" href="pol_tutorial/understand_dis_quant.html"><img src="../../../../doc/html/images/prev.png" alt="Prev"></a><a accesskey="u" href="../policy.html"><img src="../../../../doc/html/images/up.png" alt="Up"></a><a accesskey="h" href="../../index.html"><img src="../../../../doc/html/images/home.png" alt="Home"></a><a accesskey="n" href="pol_ref/error_handling_policies.html"><img src="../../../../doc/html/images/next.png" alt="Next"></a>
+</div>
+</body>
+</html>

Added: sandbox/tools/auto_index/example/math/doc/sf_and_dist/html/math_toolkit/policy/pol_ref/assert_undefined.html
==============================================================================
--- (empty file)
+++ sandbox/tools/auto_index/example/math/doc/sf_and_dist/html/math_toolkit/policy/pol_ref/assert_undefined.html	2008-11-28 05:25:28 EST (Fri, 28 Nov 2008)
@@ -0,0 +1,89 @@
+<html>
+<head>
+<meta http-equiv="Content-Type" content="text/html; charset=ISO-8859-1">
+<title>Mathematically Undefined Function Policies</title>
+<link rel="stylesheet" href="../../../boostbook.css" type="text/css">
+<meta name="generator" content="DocBook XSL Stylesheets Vsnapshot_8125">
+<link rel="home" href="../../../index.html" title="Math Toolkit">
+<link rel="up" href="../pol_ref.html" title="Policy Reference">
+<link rel="prev" href="internal_promotion.html" title="Internal Promotion Policies">
+<link rel="next" href="discrete_quant_ref.html" title="Discrete Quantile Policies">
+</head>
+<body bgcolor="white" text="black" link="#0000FF" vlink="#840084" alink="#0000FF">
+<table cellpadding="2" width="100%"><tr>
+<td valign="top"><img alt="Boost C++ Libraries" width="277" height="86" src="../../../../../boost.png"></td>
+<td align="center">Home</td>
+<td align="center">Libraries</td>
+<td align="center">People</td>
+<td align="center">FAQ</td>
+<td align="center">More</td>
+</tr></table>
+<hr>
+<div class="spirit-nav">
+<a accesskey="p" href="internal_promotion.html"><img src="../../../../../doc/html/images/prev.png" alt="Prev"></a><a accesskey="u" href="../pol_ref.html"><img src="../../../../../doc/html/images/up.png" alt="Up"></a><a accesskey="h" href="../../../index.html"><img src="../../../../../doc/html/images/home.png" alt="Home"></a><a accesskey="n" href="discrete_quant_ref.html"><img src="../../../../../doc/html/images/next.png" alt="Next"></a>
+</div>
+<div class="section" lang="en">
+<div class="titlepage"><div><div><h4 class="title">
+<a name="math_toolkit.policy.pol_ref.assert_undefined"></a><a class="link" href="assert_undefined.html" title="Mathematically Undefined Function Policies"> Mathematically
+        Undefined Function Policies</a>
+</h4></div></div></div>
+<p>
+          There are some functions that are generic (they are present for all the
+          statistical distributions supported) but which may be mathematically undefined
+          for certain distributions, but defined for others.
+        </p>
+<p>
+          For example, the Cauchy distribution does not have a mean, so what should
+        </p>
+<pre class="programlisting"><span class="identifier">mean</span><span class="special">(</span><span class="identifier">cauchy</span><span class="special">&lt;&gt;());</span>
+</pre>
+<p>
+          return, and should such an expression even compile at all?
+        </p>
+<p>
+          The default behaviour is for all such functions to not compile at all -
+          in fact they will raise a <a href="http://www.boost.org/libs/static_assert/index.html" target="_top">static
+          assertion</a> - but by changing the policy we can have them return
+          the result of a domain error instead (which may well throw an exception,
+          depending on the error handling policy).
+        </p>
+<p>
+          This behaviour is controlled by the <code class="computeroutput"><span class="identifier">assert_undefined</span><span class="special">&lt;&gt;</span></code> policy:
+        </p>
+<pre class="programlisting"><span class="keyword">namespace</span> <span class="identifier">boost</span><span class="special">{</span> <span class="keyword">namespace</span> <span class="identifier">math</span><span class="special">{</span> <span class="keyword">namespace</span> <span class="identifier">policies</span> <span class="special">{</span>
+
+<span class="keyword">template</span> <span class="special">&lt;</span><span class="keyword">bool</span> <span class="identifier">b</span><span class="special">&gt;</span>
+<span class="keyword">class</span> <span class="identifier">assert_undefined</span><span class="special">;</span>
+
+<span class="special">}}}</span> <span class="comment">//namespaces
+</span></pre>
+<p>
+          For example:
+        </p>
+<pre class="programlisting"><span class="preprocessor">#include</span> <span class="special">&lt;</span><span class="identifier">boost</span><span class="special">/</span><span class="identifier">math</span><span class="special">/</span><span class="identifier">distributions</span><span class="special">/</span><span class="identifier">cauchy</span><span class="special">.</span><span class="identifier">hpp</span><span class="special">&gt;</span>
+
+<span class="keyword">using</span> <span class="keyword">namespace</span> <span class="identifier">boost</span><span class="special">::</span><span class="identifier">math</span><span class="special">::</span><span class="identifier">policies</span><span class="special">;</span>
+<span class="keyword">using</span> <span class="keyword">namespace</span> <span class="identifier">boost</span><span class="special">::</span><span class="identifier">math</span><span class="special">;</span>
+
+<span class="comment">// This will not compile, cauchy has no mean!
+</span><span class="keyword">double</span> <span class="identifier">m1</span> <span class="special">=</span> <span class="identifier">mean</span><span class="special">(</span><span class="identifier">cauchy</span><span class="special">());</span> 
+
+<span class="comment">// This will compile, but raises a domain error!
+</span><span class="keyword">double</span> <span class="identifier">m2</span> <span class="special">=</span> <span class="identifier">mean</span><span class="special">(</span><span class="identifier">cauchy_distribution</span><span class="special">&lt;</span><span class="keyword">double</span><span class="special">,</span> <span class="identifier">policy</span><span class="special">&lt;</span><span class="identifier">assert_undefined</span><span class="special">&lt;</span><span class="keyword">false</span><span class="special">&gt;</span> <span class="special">&gt;</span> <span class="special">&gt;());</span>
+</pre>
+</div>
+<table xmlns:rev="http://www.cs.rpi.edu/~gregod/boost/tools/doc/revision" width="100%"><tr>
+<td align="left"></td>
+<td align="right"><div class="copyright-footer">Copyright © 2006 , 2007, 2008 John Maddock, Paul A. Bristow, Hubert
+      Holin, Xiaogang Zhang, Bruno Lalande and Gautam Sewani<p>
+        Distributed under the Boost Software License, Version 1.0. (See accompanying
+        file LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_0.txt)
+      </p>
+</div></td>
+</tr></table>
+<hr>
+<div class="spirit-nav">
+<a accesskey="p" href="internal_promotion.html"><img src="../../../../../doc/html/images/prev.png" alt="Prev"></a><a accesskey="u" href="../pol_ref.html"><img src="../../../../../doc/html/images/up.png" alt="Up"></a><a accesskey="h" href="../../../index.html"><img src="../../../../../doc/html/images/home.png" alt="Home"></a><a accesskey="n" href="discrete_quant_ref.html"><img src="../../../../../doc/html/images/next.png" alt="Next"></a>
+</div>
+</body>
+</html>

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+++ sandbox/tools/auto_index/example/math/doc/sf_and_dist/html/math_toolkit/policy/pol_ref/discrete_quant_ref.html	2008-11-28 05:25:28 EST (Fri, 28 Nov 2008)
@@ -0,0 +1,290 @@
+<html>
+<head>
+<meta http-equiv="Content-Type" content="text/html; charset=ISO-8859-1">
+<title>Discrete Quantile Policies</title>
+<link rel="stylesheet" href="../../../boostbook.css" type="text/css">
+<meta name="generator" content="DocBook XSL Stylesheets Vsnapshot_8125">
+<link rel="home" href="../../../index.html" title="Math Toolkit">
+<link rel="up" href="../pol_ref.html" title="Policy Reference">
+<link rel="prev" href="assert_undefined.html" title="Mathematically Undefined Function Policies">
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+</div>
+<div class="section" lang="en">
+<div class="titlepage"><div><div><h4 class="title">
+<a name="math_toolkit.policy.pol_ref.discrete_quant_ref"></a><a class="link" href="discrete_quant_ref.html" title="Discrete Quantile Policies"> Discrete
+        Quantile Policies</a>
+</h4></div></div></div>
+<p>
+          If a statistical distribution is <span class="emphasis"><em>discrete</em></span> then the
+          random variable can only have integer values - this leaves us with a problem
+          when calculating quantiles - we can either ignore the discreteness of the
+          distribution and return a real value, or we can round to an integer. As
+          it happens, computing integer values can be substantially faster than calculating
+          a real value, so there are definite advantages to returning an integer,
+          but we do then need to decide how best to round the result. The <code class="computeroutput"><span class="identifier">discrete_quantile</span></code> policy defines how
+          discrete quantiles work, and how integer results are rounded:
+        </p>
+<pre class="programlisting"><span class="keyword">enum</span> <span class="identifier">discrete_quantile_policy_type</span>
+<span class="special">{</span>
+   <span class="identifier">real</span><span class="special">,</span>
+   <span class="identifier">integer_round_outwards</span><span class="special">,</span> <span class="comment">// default
+</span>   <span class="identifier">integer_round_inwards</span><span class="special">,</span>
+   <span class="identifier">integer_round_down</span><span class="special">,</span>
+   <span class="identifier">integer_round_up</span><span class="special">,</span>
+   <span class="identifier">integer_round_nearest</span>
+<span class="special">};</span>
+
+<span class="keyword">template</span> <span class="special">&lt;</span><span class="identifier">discrete_quantile_policy_type</span><span class="special">&gt;</span>
+<span class="keyword">struct</span> <span class="identifier">discrete_quantile</span><span class="special">;</span>
+</pre>
+<p>
+          The values that <code class="computeroutput"><span class="identifier">discrete_quantile</span></code>
+          can take have the following meanings:
+        </p>
+<a name="math_toolkit.policy.pol_ref.discrete_quant_ref.real"></a><h6>
+<a name="id894659"></a>
+          <a class="link" href="discrete_quant_ref.html#math_toolkit.policy.pol_ref.discrete_quant_ref.real">real</a>
+        </h6>
+<p>
+          Ignores the discreteness of the distribution, and returns a real-valued
+          result. For example:
+        </p>
+<p>
+          </p>
+<p>
+            
+</p>
+<pre class="programlisting"><span class="preprocessor">#include</span> <span class="special">&lt;</span><span class="identifier">boost</span><span class="special">/</span><span class="identifier">math</span><span class="special">/</span><span class="identifier">distributions</span><span class="special">/</span><span class="identifier">negative_binomial</span><span class="special">.</span><span class="identifier">hpp</span><span class="special">&gt;</span>
+
+<span class="keyword">using</span> <span class="keyword">namespace</span> <span class="identifier">boost</span><span class="special">::</span><span class="identifier">math</span><span class="special">;</span>
+<span class="keyword">using</span> <span class="keyword">namespace</span> <span class="identifier">boost</span><span class="special">::</span><span class="identifier">math</span><span class="special">::</span><span class="identifier">policies</span><span class="special">;</span>
+
+<span class="keyword">typedef</span> <span class="identifier">negative_binomial_distribution</span><span class="special">&lt;</span>
+      <span class="keyword">double</span><span class="special">,</span> 
+      <span class="identifier">policy</span><span class="special">&lt;</span><span class="identifier">discrete_quantile</span><span class="special">&lt;</span><span class="identifier">integer_round_inwards</span><span class="special">&gt;</span> <span class="special">&gt;</span> 
+   <span class="special">&gt;</span> <span class="identifier">dist_type</span><span class="special">;</span>
+   
+<span class="comment">// Lower quantile:
+</span><span class="keyword">double</span> <span class="identifier">x</span> <span class="special">=</span> <span class="identifier">quantile</span><span class="special">(</span><span class="identifier">dist_type</span><span class="special">(</span><span class="number">20</span><span class="special">,</span> <span class="number">0.3</span><span class="special">),</span> <span class="number">0.05</span><span class="special">);</span>
+<span class="comment">// Upper quantile:
+</span><span class="keyword">double</span> <span class="identifier">y</span> <span class="special">=</span> <span class="identifier">quantile</span><span class="special">(</span><span class="identifier">complement</span><span class="special">(</span><span class="identifier">dist_type</span><span class="special">(</span><span class="number">20</span><span class="special">,</span> <span class="number">0.3</span><span class="special">),</span> <span class="number">0.05</span><span class="special">));</span>
+
+</pre>
+<p>
+          </p>
+<p>
+        </p>
+<p>
+          Results in <code class="computeroutput"><span class="identifier">x</span> <span class="special">=</span>
+          <span class="number">27.3898</span></code> and <code class="computeroutput"><span class="identifier">y</span>
+          <span class="special">=</span> <span class="number">68.1584</span></code>.
+        </p>
+<a name="math_toolkit.policy.pol_ref.discrete_quant_ref.integer_round_outwards"></a><h6>
+<a name="id895150"></a>
+          <a class="link" href="discrete_quant_ref.html#math_toolkit.policy.pol_ref.discrete_quant_ref.integer_round_outwards">integer_round_outwards</a>
+        </h6>
+<p>
+          This is the default policy: an integer value is returned so that:
+        </p>
+<div class="itemizedlist"><ul type="disc">
+<li>
+            Lower quantiles (where the probability is less than 0.5) are rounded
+            down.
+          </li>
+<li>
+            Upper quantiles (where the probability is greater than 0.5) are rounded
+            up.
+          </li>
+</ul></div>
+<p>
+          This is normally the safest rounding policy, since it ensures that both
+          one and two sided intervals are guaranteed to have <span class="emphasis"><em>at least</em></span>
+          the requested coverage. For example:
+        </p>
+<p>
+          </p>
+<p>
+            
+</p>
+<pre class="programlisting"><span class="preprocessor">#include</span> <span class="special">&lt;</span><span class="identifier">boost</span><span class="special">/</span><span class="identifier">math</span><span class="special">/</span><span class="identifier">distributions</span><span class="special">/</span><span class="identifier">negative_binomial</span><span class="special">.</span><span class="identifier">hpp</span><span class="special">&gt;</span>
+
+<span class="keyword">using</span> <span class="keyword">namespace</span> <span class="identifier">boost</span><span class="special">::</span><span class="identifier">math</span><span class="special">;</span>
+
+<span class="comment">// Lower quantile rounded down:
+</span><span class="keyword">double</span> <span class="identifier">x</span> <span class="special">=</span> <span class="identifier">quantile</span><span class="special">(</span><span class="identifier">negative_binomial</span><span class="special">(</span><span class="number">20</span><span class="special">,</span> <span class="number">0.3</span><span class="special">),</span> <span class="number">0.05</span><span class="special">);</span>
+<span class="comment">// Upper quantile rounded up:
+</span><span class="keyword">double</span> <span class="identifier">y</span> <span class="special">=</span> <span class="identifier">quantile</span><span class="special">(</span><span class="identifier">complement</span><span class="special">(</span><span class="identifier">negative_binomial</span><span class="special">(</span><span class="number">20</span><span class="special">,</span> <span class="number">0.3</span><span class="special">),</span> <span class="number">0.05</span><span class="special">));</span>
+
+</pre>
+<p>
+          </p>
+<p>
+        </p>
+<p>
+          Results in <code class="computeroutput"><span class="identifier">x</span> <span class="special">=</span>
+          <span class="number">27</span></code> (rounded down from 27.3898) and
+          <code class="computeroutput"><span class="identifier">y</span> <span class="special">=</span>
+          <span class="number">69</span></code> (rounded up from 68.1584).
+        </p>
+<p>
+          The variables x and y are now defined so that:
+        </p>
+<pre class="programlisting"><span class="identifier">cdf</span><span class="special">(</span><span class="identifier">negative_binomial</span><span class="special">(</span><span class="number">20</span><span class="special">),</span> <span class="identifier">x</span><span class="special">)</span> <span class="special">&lt;=</span> <span class="number">0.05</span>
+<span class="identifier">cdf</span><span class="special">(</span><span class="identifier">negative_binomial</span><span class="special">(</span><span class="number">20</span><span class="special">),</span> <span class="identifier">y</span><span class="special">)</span> <span class="special">&gt;=</span> <span class="number">0.95</span>
+</pre>
+<p>
+          In other words we guarantee <span class="emphasis"><em>at least 90% coverage in the central
+          region overall</em></span>, and also <span class="emphasis"><em>no more than 5% coverage
+          in each tail</em></span>.
+        </p>
+<a name="math_toolkit.policy.pol_ref.discrete_quant_ref.integer_round_inwards"></a><h6>
+<a name="id895684"></a>
+          <a class="link" href="discrete_quant_ref.html#math_toolkit.policy.pol_ref.discrete_quant_ref.integer_round_inwards">integer_round_inwards</a>
+        </h6>
+<p>
+          This is the opposite of <span class="emphasis"><em>integer_round_outwards</em></span>: an
+          integer value is returned so that:
+        </p>
+<div class="itemizedlist"><ul type="disc">
+<li>
+            Lower quantiles (where the probability is less than 0.5) are rounded
+            <span class="emphasis"><em>up</em></span>.
+          </li>
+<li>
+            Upper quantiles (where the probability is greater than 0.5) are rounded
+            <span class="emphasis"><em>down</em></span>.
+          </li>
+</ul></div>
+<p>
+          For example:
+        </p>
+<p>
+          </p>
+<p>
+            
+</p>
+<pre class="programlisting"><span class="preprocessor">#include</span> <span class="special">&lt;</span><span class="identifier">boost</span><span class="special">/</span><span class="identifier">math</span><span class="special">/</span><span class="identifier">distributions</span><span class="special">/</span><span class="identifier">negative_binomial</span><span class="special">.</span><span class="identifier">hpp</span><span class="special">&gt;</span>
+
+<span class="keyword">using</span> <span class="keyword">namespace</span> <span class="identifier">boost</span><span class="special">::</span><span class="identifier">math</span><span class="special">;</span>
+<span class="keyword">using</span> <span class="keyword">namespace</span> <span class="identifier">boost</span><span class="special">::</span><span class="identifier">math</span><span class="special">::</span><span class="identifier">policies</span><span class="special">;</span>
+
+<span class="keyword">typedef</span> <span class="identifier">negative_binomial_distribution</span><span class="special">&lt;</span>
+      <span class="keyword">double</span><span class="special">,</span> 
+      <span class="identifier">policy</span><span class="special">&lt;</span><span class="identifier">discrete_quantile</span><span class="special">&lt;</span><span class="identifier">integer_round_inwards</span><span class="special">&gt;</span> <span class="special">&gt;</span> 
+   <span class="special">&gt;</span> <span class="identifier">dist_type</span><span class="special">;</span>
+   
+<span class="comment">// Lower quantile rounded up:
+</span><span class="keyword">double</span> <span class="identifier">x</span> <span class="special">=</span> <span class="identifier">quantile</span><span class="special">(</span><span class="identifier">dist_type</span><span class="special">(</span><span class="number">20</span><span class="special">,</span> <span class="number">0.3</span><span class="special">),</span> <span class="number">0.05</span><span class="special">);</span>
+<span class="comment">// Upper quantile rounded down:
+</span><span class="keyword">double</span> <span class="identifier">y</span> <span class="special">=</span> <span class="identifier">quantile</span><span class="special">(</span><span class="identifier">complement</span><span class="special">(</span><span class="identifier">dist_type</span><span class="special">(</span><span class="number">20</span><span class="special">,</span> <span class="number">0.3</span><span class="special">),</span> <span class="number">0.05</span><span class="special">));</span>
+
+</pre>
+<p>
+          </p>
+<p>
+        </p>
+<p>
+          Results in <code class="computeroutput"><span class="identifier">x</span> <span class="special">=</span>
+          <span class="number">28</span></code> (rounded up from 27.3898) and
+          <code class="computeroutput"><span class="identifier">y</span> <span class="special">=</span>
+          <span class="number">68</span></code> (rounded down from 68.1584).
+        </p>
+<p>
+          The variables x and y are now defined so that:
+        </p>
+<pre class="programlisting"><span class="identifier">cdf</span><span class="special">(</span><span class="identifier">negative_binomial</span><span class="special">(</span><span class="number">20</span><span class="special">),</span> <span class="identifier">x</span><span class="special">)</span> <span class="special">&gt;=</span> <span class="number">0.05</span>
+<span class="identifier">cdf</span><span class="special">(</span><span class="identifier">negative_binomial</span><span class="special">(</span><span class="number">20</span><span class="special">),</span> <span class="identifier">y</span><span class="special">)</span> <span class="special">&lt;=</span> <span class="number">0.95</span>
+</pre>
+<p>
+          In other words we guarantee <span class="emphasis"><em>at no more than 90% coverage in the
+          central region overall</em></span>, and also <span class="emphasis"><em>at least 5% coverage
+          in each tail</em></span>.
+        </p>
+<a name="math_toolkit.policy.pol_ref.discrete_quant_ref.integer_round_down"></a><h6>
+<a name="id896352"></a>
+          <a class="link" href="discrete_quant_ref.html#math_toolkit.policy.pol_ref.discrete_quant_ref.integer_round_down">integer_round_down</a>
+        </h6>
+<p>
+          Always rounds down to an integer value, no matter whether it's an upper
+          or a lower quantile.
+        </p>
+<a name="math_toolkit.policy.pol_ref.discrete_quant_ref.integer_round_up"></a><h6>
+<a name="id896385"></a>
+          <a class="link" href="discrete_quant_ref.html#math_toolkit.policy.pol_ref.discrete_quant_ref.integer_round_up">integer_round_up</a>
+        </h6>
+<p>
+          Always rounds up to an integer value, no matter whether it's an upper or
+          a lower quantile.
+        </p>
+<a name="math_toolkit.policy.pol_ref.discrete_quant_ref.integer_round_nearest"></a><h6>
+<a name="id896418"></a>
+          <a class="link" href="discrete_quant_ref.html#math_toolkit.policy.pol_ref.discrete_quant_ref.integer_round_nearest">integer_round_nearest</a>
+        </h6>
+<p>
+          Always rounds to the nearest integer value, no matter whether it's an upper
+          or a lower quantile. This will produce the requested coverage <span class="emphasis"><em>in
+          the average case</em></span>, but for any specific example may results in
+          either significantly more or less coverage than the requested amount. For
+          example:
+        </p>
+<p>
+          For example:
+        </p>
+<p>
+          </p>
+<p>
+            
+</p>
+<pre class="programlisting"><span class="preprocessor">#include</span> <span class="special">&lt;</span><span class="identifier">boost</span><span class="special">/</span><span class="identifier">math</span><span class="special">/</span><span class="identifier">distributions</span><span class="special">/</span><span class="identifier">negative_binomial</span><span class="special">.</span><span class="identifier">hpp</span><span class="special">&gt;</span>
+
+<span class="keyword">using</span> <span class="keyword">namespace</span> <span class="identifier">boost</span><span class="special">::</span><span class="identifier">math</span><span class="special">;</span>
+<span class="keyword">using</span> <span class="keyword">namespace</span> <span class="identifier">boost</span><span class="special">::</span><span class="identifier">math</span><span class="special">::</span><span class="identifier">policies</span><span class="special">;</span>
+
+<span class="keyword">typedef</span> <span class="identifier">negative_binomial_distribution</span><span class="special">&lt;</span>
+      <span class="keyword">double</span><span class="special">,</span> 
+      <span class="identifier">policy</span><span class="special">&lt;</span><span class="identifier">discrete_quantile</span><span class="special">&lt;</span><span class="identifier">integer_round_nearest</span><span class="special">&gt;</span> <span class="special">&gt;</span> 
+   <span class="special">&gt;</span> <span class="identifier">dist_type</span><span class="special">;</span>
+   
+<span class="comment">// Lower quantile rounded up:
+</span><span class="keyword">double</span> <span class="identifier">x</span> <span class="special">=</span> <span class="identifier">quantile</span><span class="special">(</span><span class="identifier">dist_type</span><span class="special">(</span><span class="number">20</span><span class="special">,</span> <span class="number">0.3</span><span class="special">),</span> <span class="number">0.05</span><span class="special">);</span>
+<span class="comment">// Upper quantile rounded down:
+</span><span class="keyword">double</span> <span class="identifier">y</span> <span class="special">=</span> <span class="identifier">quantile</span><span class="special">(</span><span class="identifier">complement</span><span class="special">(</span><span class="identifier">dist_type</span><span class="special">(</span><span class="number">20</span><span class="special">,</span> <span class="number">0.3</span><span class="special">),</span> <span class="number">0.05</span><span class="special">));</span>
+
+</pre>
+<p>
+          </p>
+<p>
+        </p>
+<p>
+          Results in <code class="computeroutput"><span class="identifier">x</span> <span class="special">=</span>
+          <span class="number">27</span></code> (rounded from 27.3898) and <code class="computeroutput"><span class="identifier">y</span> <span class="special">=</span> <span class="number">68</span></code> (rounded from 68.1584).
+        </p>
+</div>
+<table xmlns:rev="http://www.cs.rpi.edu/~gregod/boost/tools/doc/revision" width="100%"><tr>
+<td align="left"></td>
+<td align="right"><div class="copyright-footer">Copyright © 2006 , 2007, 2008 John Maddock, Paul A. Bristow, Hubert
+      Holin, Xiaogang Zhang, Bruno Lalande and Gautam Sewani<p>
+        Distributed under the Boost Software License, Version 1.0. (See accompanying
+        file LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_0.txt)
+      </p>
+</div></td>
+</tr></table>
+<hr>
+<div class="spirit-nav">
+<a accesskey="p" href="assert_undefined.html"><img src="../../../../../doc/html/images/prev.png" alt="Prev"></a><a accesskey="u" href="../pol_ref.html"><img src="../../../../../doc/html/images/up.png" alt="Up"></a><a accesskey="h" href="../../../index.html"><img src="../../../../../doc/html/images/home.png" alt="Home"></a><a accesskey="n" href="precision_pol.html"><img src="../../../../../doc/html/images/next.png" alt="Next"></a>
+</div>
+</body>
+</html>

Added: sandbox/tools/auto_index/example/math/doc/sf_and_dist/html/math_toolkit/policy/pol_ref/error_handling_policies.html
==============================================================================
--- (empty file)
+++ sandbox/tools/auto_index/example/math/doc/sf_and_dist/html/math_toolkit/policy/pol_ref/error_handling_policies.html	2008-11-28 05:25:28 EST (Fri, 28 Nov 2008)
@@ -0,0 +1,778 @@
+<html>
+<head>
+<meta http-equiv="Content-Type" content="text/html; charset=ISO-8859-1">
+<title>Error Handling Policies</title>
+<link rel="stylesheet" href="../../../boostbook.css" type="text/css">
+<meta name="generator" content="DocBook XSL Stylesheets Vsnapshot_8125">
+<link rel="home" href="../../../index.html" title="Math Toolkit">
+<link rel="up" href="../pol_ref.html" title="Policy Reference">
+<link rel="prev" href="../pol_ref.html" title="Policy Reference">
+<link rel="next" href="internal_promotion.html" title="Internal Promotion Policies">
+</head>
+<body bgcolor="white" text="black" link="#0000FF" vlink="#840084" alink="#0000FF">
+<table cellpadding="2" width="100%"><tr>
+<td valign="top"><img alt="Boost C++ Libraries" width="277" height="86" src="../../../../../boost.png"></td>
+<td align="center">Home</td>
+<td align="center">Libraries</td>
+<td align="center">People</td>
+<td align="center">FAQ</td>
+<td align="center">More</td>
+</tr></table>
+<hr>
+<div class="spirit-nav">
+<a accesskey="p" href="../pol_ref.html"><img src="../../../../../doc/html/images/prev.png" alt="Prev"></a><a accesskey="u" href="../pol_ref.html"><img src="../../../../../doc/html/images/up.png" alt="Up"></a><a accesskey="h" href="../../../index.html"><img src="../../../../../doc/html/images/home.png" alt="Home"></a><a accesskey="n" href="internal_promotion.html"><img src="../../../../../doc/html/images/next.png" alt="Next"></a>
+</div>
+<div class="section" lang="en">
+<div class="titlepage"><div><div><h4 class="title">
+<a name="math_toolkit.policy.pol_ref.error_handling_policies"></a><a class="link" href="error_handling_policies.html" title="Error Handling Policies">
+        Error Handling Policies</a>
+</h4></div></div></div>
+<p>
+          There are two orthogonal aspects to error handling:
+        </p>
+<div class="itemizedlist"><ul type="disc">
+<li>
+            What to do (if anything) with the error.
+          </li>
+<li>
+            What kind of error is being raised.
+          </li>
+</ul></div>
+<a name="math_toolkit.policy.pol_ref.error_handling_policies.available_actions_when_an_error_is_raised"></a><h5>
+<a name="id888479"></a>
+          <a class="link" href="error_handling_policies.html#math_toolkit.policy.pol_ref.error_handling_policies.available_actions_when_an_error_is_raised">Available
+          Actions When an Error is Raised</a>
+        </h5>
+<p>
+          What to do with the error is encapsulated by an enumerated type:
+        </p>
+<pre class="programlisting"><span class="keyword">namespace</span> <span class="identifier">boost</span> <span class="special">{</span> <span class="keyword">namespace</span> <span class="identifier">math</span> <span class="special">{</span> <span class="keyword">namespace</span> <span class="identifier">policies</span> <span class="special">{</span>
+
+<span class="keyword">enum</span> <span class="identifier">error_policy_type</span>
+<span class="special">{</span>
+   <span class="identifier">throw_on_error</span> <span class="special">=</span> <span class="number">0</span><span class="special">,</span> <span class="comment">// throw an exception.
+</span>   <span class="identifier">errno_on_error</span> <span class="special">=</span> <span class="number">1</span><span class="special">,</span> <span class="comment">// set ::errno &amp; return 0, NaN, infinity or best guess.
+</span>   <span class="identifier">ignore_error</span> <span class="special">=</span> <span class="number">2</span><span class="special">,</span> <span class="comment">// return 0, NaN, infinity or best guess.
+</span>   <span class="identifier">user_error</span> <span class="special">=</span> <span class="number">3</span>  <span class="comment">// call a user-defined error handler.
+</span><span class="special">};</span>
+
+<span class="special">}}}</span> <span class="comment">// namespaces
+</span></pre>
+<p>
+          The various enumerated values have the following meanings:
+        </p>
+<a name="math_toolkit.policy.pol_ref.error_handling_policies.throw_on_error"></a><h6>
+<a name="id888739"></a>
+          <a class="link" href="error_handling_policies.html#math_toolkit.policy.pol_ref.error_handling_policies.throw_on_error">throw_on_error</a>
+        </h6>
+<p>
+          Will throw one of the following exceptions, depending upon the type of
+          the error:
+        </p>
+<div class="informaltable"><table class="table">
+<colgroup>
+<col>
+<col>
+</colgroup>
+<thead><tr>
+<th>
+                <p>
+                  Error Type
+                </p>
+                </th>
+<th>
+                <p>
+                  Exception
+                </p>
+                </th>
+</tr></thead>
+<tbody>
+<tr>
+<td>
+                <p>
+                  Domain Error
+                </p>
+                </td>
+<td>
+                <p>
+                  std::domain_error
+                </p>
+                </td>
+</tr>
+<tr>
+<td>
+                <p>
+                  Pole Error
+                </p>
+                </td>
+<td>
+                <p>
+                  std::domain_error
+                </p>
+                </td>
+</tr>
+<tr>
+<td>
+                <p>
+                  Overflow Error
+                </p>
+                </td>
+<td>
+                <p>
+                  std::overflow_error
+                </p>
+                </td>
+</tr>
+<tr>
+<td>
+                <p>
+                  Underflow Error
+                </p>
+                </td>
+<td>
+                <p>
+                  std::underflow_error
+                </p>
+                </td>
+</tr>
+<tr>
+<td>
+                <p>
+                  Denorm Error
+                </p>
+                </td>
+<td>
+                <p>
+                  std::underflow_error
+                </p>
+                </td>
+</tr>
+<tr>
+<td>
+                <p>
+                  Evaluation Error
+                </p>
+                </td>
+<td>
+                <p>
+                  boost::math::evaluation_error
+                </p>
+                </td>
+</tr>
+<tr>
+<td>
+                <p>
+                  Indeterminate Result Error
+                </p>
+                </td>
+<td>
+                <p>
+                  std::domain_error
+                </p>
+                </td>
+</tr>
+</tbody>
+</table></div>
+<a name="math_toolkit.policy.pol_ref.error_handling_policies.errno_on_error"></a><h6>
+<a name="id888957"></a>
+          <a class="link" href="error_handling_policies.html#math_toolkit.policy.pol_ref.error_handling_policies.errno_on_error">errno_on_error</a>
+        </h6>
+<p>
+          Will set global <code class="computeroutput"><span class="special">::</span><span class="identifier">errno</span></code>
+          to one of the following values depending upon the error type, and then
+          return the same value as if the error had been ignored:
+        </p>
+<div class="informaltable"><table class="table">
+<colgroup>
+<col>
+<col>
+</colgroup>
+<thead><tr>
+<th>
+                <p>
+                  Error Type
+                </p>
+                </th>
+<th>
+                <p>
+                  errno value
+                </p>
+                </th>
+</tr></thead>
+<tbody>
+<tr>
+<td>
+                <p>
+                  Domain Error
+                </p>
+                </td>
+<td>
+                <p>
+                  EDOM
+                </p>
+                </td>
+</tr>
+<tr>
+<td>
+                <p>
+                  Pole Error
+                </p>
+                </td>
+<td>
+                <p>
+                  EDOM
+                </p>
+                </td>
+</tr>
+<tr>
+<td>
+                <p>
+                  Overflow Error
+                </p>
+                </td>
+<td>
+                <p>
+                  ERANGE
+                </p>
+                </td>
+</tr>
+<tr>
+<td>
+                <p>
+                  Underflow Error
+                </p>
+                </td>
+<td>
+                <p>
+                  ERANGE
+                </p>
+                </td>
+</tr>
+<tr>
+<td>
+                <p>
+                  Denorm Error
+                </p>
+                </td>
+<td>
+                <p>
+                  ERANGE
+                </p>
+                </td>
+</tr>
+<tr>
+<td>
+                <p>
+                  Evaluation Error
+                </p>
+                </td>
+<td>
+                <p>
+                  EDOM
+                </p>
+                </td>
+</tr>
+<tr>
+<td>
+                <p>
+                  Indeterminate Result Error
+                </p>
+                </td>
+<td>
+                <p>
+                  EDOM
+                </p>
+                </td>
+</tr>
+</tbody>
+</table></div>
+<a name="math_toolkit.policy.pol_ref.error_handling_policies.ignore_error"></a><h6>
+<a name="id889190"></a>
+          <a class="link" href="error_handling_policies.html#math_toolkit.policy.pol_ref.error_handling_policies.ignore_error">ignore_error</a>
+        </h6>
+<p>
+          Will return one of the values below depending on the error type (<code class="computeroutput"><span class="special">::</span><span class="identifier">errno</span></code>
+          is NOT changed)::
+        </p>
+<div class="informaltable"><table class="table">
+<colgroup>
+<col>
+<col>
+</colgroup>
+<thead><tr>
+<th>
+                <p>
+                  Error Type
+                </p>
+                </th>
+<th>
+                <p>
+                  Returned Value
+                </p>
+                </th>
+</tr></thead>
+<tbody>
+<tr>
+<td>
+                <p>
+                  Domain Error
+                </p>
+                </td>
+<td>
+                <p>
+                  std::numeric_limits&lt;T&gt;::quiet_NaN()
+                </p>
+                </td>
+</tr>
+<tr>
+<td>
+                <p>
+                  Pole Error
+                </p>
+                </td>
+<td>
+                <p>
+                  std::numeric_limits&lt;T&gt;::quiet_NaN()
+                </p>
+                </td>
+</tr>
+<tr>
+<td>
+                <p>
+                  Overflow Error
+                </p>
+                </td>
+<td>
+                <p>
+                  std::numeric_limits&lt;T&gt;::infinity()
+                </p>
+                </td>
+</tr>
+<tr>
+<td>
+                <p>
+                  Underflow Error
+                </p>
+                </td>
+<td>
+                <p>
+                  0
+                </p>
+                </td>
+</tr>
+<tr>
+<td>
+                <p>
+                  Denorm Error
+                </p>
+                </td>
+<td>
+                <p>
+                  The denormalised value.
+                </p>
+                </td>
+</tr>
+<tr>
+<td>
+                <p>
+                  Evaluation Error
+                </p>
+                </td>
+<td>
+                <p>
+                  The best guess as to the result: which may be significantly in
+                  error.
+                </p>
+                </td>
+</tr>
+<tr>
+<td>
+                <p>
+                  Indeterminate Result Error
+                </p>
+                </td>
+<td>
+                <p>
+                  Depends on the function where the error occurred
+                </p>
+                </td>
+</tr>
+</tbody>
+</table></div>
+<a name="math_toolkit.policy.pol_ref.error_handling_policies.user_error"></a><h6>
+<a name="id889424"></a>
+          <a class="link" href="error_handling_policies.html#math_toolkit.policy.pol_ref.error_handling_policies.user_error">user_error</a>
+        </h6>
+<p>
+          Will call a user defined error handler: these are forward declared in boost/math/policies/error_handling.hpp,
+          but the actual definitions must be provided by the user:
+        </p>
+<pre class="programlisting"><span class="keyword">namespace</span> <span class="identifier">boost</span><span class="special">{</span> <span class="keyword">namespace</span> <span class="identifier">math</span><span class="special">{</span> <span class="keyword">namespace</span> <span class="identifier">policies</span><span class="special">{</span>
+
+<span class="keyword">template</span> <span class="special">&lt;</span><span class="keyword">class</span> <span class="identifier">T</span><span class="special">&gt;</span>
+<span class="identifier">T</span> <span class="identifier">user_domain_error</span><span class="special">(</span><span class="keyword">const</span> <span class="keyword">char</span><span class="special">*</span> <span class="identifier">function</span><span class="special">,</span> <span class="keyword">const</span> <span class="keyword">char</span><span class="special">*</span> <span class="identifier">message</span><span class="special">,</span> <span class="keyword">const</span> <span class="identifier">T</span><span class="special">&amp;</span> <span class="identifier">val</span><span class="special">);</span>
+
+<span class="keyword">template</span> <span class="special">&lt;</span><span class="keyword">class</span> <span class="identifier">T</span><span class="special">&gt;</span>
+<span class="identifier">T</span> <span class="identifier">user_pole_error</span><span class="special">(</span><span class="keyword">const</span> <span class="keyword">char</span><span class="special">*</span> <span class="identifier">function</span><span class="special">,</span> <span class="keyword">const</span> <span class="keyword">char</span><span class="special">*</span> <span class="identifier">message</span><span class="special">,</span> <span class="keyword">const</span> <span class="identifier">T</span><span class="special">&amp;</span> <span class="identifier">val</span><span class="special">);</span>
+
+<span class="keyword">template</span> <span class="special">&lt;</span><span class="keyword">class</span> <span class="identifier">T</span><span class="special">&gt;</span>
+<span class="identifier">T</span> <span class="identifier">user_overflow_error</span><span class="special">(</span><span class="keyword">const</span> <span class="keyword">char</span><span class="special">*</span> <span class="identifier">function</span><span class="special">,</span> <span class="keyword">const</span> <span class="keyword">char</span><span class="special">*</span> <span class="identifier">message</span><span class="special">,</span> <span class="keyword">const</span> <span class="identifier">T</span><span class="special">&amp;</span> <span class="identifier">val</span><span class="special">);</span>
+
+<span class="keyword">template</span> <span class="special">&lt;</span><span class="keyword">class</span> <span class="identifier">T</span><span class="special">&gt;</span>
+<span class="identifier">T</span> <span class="identifier">user_underflow_error</span><span class="special">(</span><span class="keyword">const</span> <span class="keyword">char</span><span class="special">*</span> <span class="identifier">function</span><span class="special">,</span> <span class="keyword">const</span> <span class="keyword">char</span><span class="special">*</span> <span class="identifier">message</span><span class="special">,</span> <span class="keyword">const</span> <span class="identifier">T</span><span class="special">&amp;</span> <span class="identifier">val</span><span class="special">);</span>
+
+<span class="keyword">template</span> <span class="special">&lt;</span><span class="keyword">class</span> <span class="identifier">T</span><span class="special">&gt;</span>
+<span class="identifier">T</span> <span class="identifier">user_denorm_error</span><span class="special">(</span><span class="keyword">const</span> <span class="keyword">char</span><span class="special">*</span> <span class="identifier">function</span><span class="special">,</span> <span class="keyword">const</span> <span class="keyword">char</span><span class="special">*</span> <span class="identifier">message</span><span class="special">,</span> <span class="keyword">const</span> <span class="identifier">T</span><span class="special">&amp;</span> <span class="identifier">val</span><span class="special">);</span>
+
+<span class="keyword">template</span> <span class="special">&lt;</span><span class="keyword">class</span> <span class="identifier">T</span><span class="special">&gt;</span>
+<span class="identifier">T</span> <span class="identifier">user_rounding_error</span><span class="special">(</span><span class="keyword">const</span> <span class="keyword">char</span><span class="special">*</span> <span class="identifier">function</span><span class="special">,</span> <span class="keyword">const</span> <span class="keyword">char</span><span class="special">*</span> <span class="identifier">message</span><span class="special">,</span> <span class="keyword">const</span> <span class="identifier">T</span><span class="special">&amp;</span> <span class="identifier">val</span><span class="special">);</span>
+
+<span class="keyword">template</span> <span class="special">&lt;</span><span class="keyword">class</span> <span class="identifier">T</span><span class="special">&gt;</span>
+<span class="identifier">T</span> <span class="identifier">user_evaluation_error</span><span class="special">(</span><span class="keyword">const</span> <span class="keyword">char</span><span class="special">*</span> <span class="identifier">function</span><span class="special">,</span> <span class="keyword">const</span> <span class="keyword">char</span><span class="special">*</span> <span class="identifier">message</span><span class="special">,</span> <span class="keyword">const</span> <span class="identifier">T</span><span class="special">&amp;</span> <span class="identifier">val</span><span class="special">);</span>
+
+<span class="keyword">template</span> <span class="special">&lt;</span><span class="keyword">class</span> <span class="identifier">T</span><span class="special">&gt;</span>
+<span class="identifier">T</span> <span class="identifier">user_indeterminate_result_error</span><span class="special">(</span><span class="keyword">const</span> <span class="keyword">char</span><span class="special">*</span> <span class="identifier">function</span><span class="special">,</span> <span class="keyword">const</span> <span class="keyword">char</span><span class="special">*</span> <span class="identifier">message</span><span class="special">,</span> <span class="keyword">const</span> <span class="identifier">T</span><span class="special">&amp;</span> <span class="identifier">val</span><span class="special">);</span>
+
+<span class="special">}}}</span> <span class="comment">// namespaces
+</span></pre>
+<p>
+          Note that the strings <span class="emphasis"><em>function</em></span> and <span class="emphasis"><em>message</em></span>
+          may contain "%1%" format specifiers designed to be used in conjunction
+          with Boost.Format. If these strings are to be presented to the program's
+          end-user then the "%1%" format specifier should be replaced with
+          the name of type T in the <span class="emphasis"><em>function</em></span> string, and if
+          there is a %1% specifier in the <span class="emphasis"><em>message</em></span> string then
+          it should be replaced with the value of <span class="emphasis"><em>val</em></span>.
+        </p>
+<p>
+          There is more information on user-defined error handlers in the <a class="link" href="../pol_tutorial/user_def_err_pol.html" title="Calling User Defined Error Handlers">tutorial
+          here</a>.
+        </p>
+<a name="math_toolkit.policy.pol_ref.error_handling_policies.kinds_of_error_raised"></a><h5>
+<a name="id890627"></a>
+          <a class="link" href="error_handling_policies.html#math_toolkit.policy.pol_ref.error_handling_policies.kinds_of_error_raised">Kinds
+          of Error Raised</a>
+        </h5>
+<p>
+          There are six kinds of error reported by this library, which are summarised
+          in the following table:
+        </p>
+<div class="informaltable"><table class="table">
+<colgroup>
+<col>
+<col>
+<col>
+</colgroup>
+<thead><tr>
+<th>
+                <p>
+                  Error Type
+                </p>
+                </th>
+<th>
+                <p>
+                  Policy Class
+                </p>
+                </th>
+<th>
+                <p>
+                  Description
+                </p>
+                </th>
+</tr></thead>
+<tbody>
+<tr>
+<td>
+                <p>
+                  Domain Error
+                </p>
+                </td>
+<td>
+                <p>
+                  boost::math::policies::domain_error&lt;<span class="emphasis"><em>action</em></span>&gt;
+                </p>
+                </td>
+<td>
+                <p>
+                  Raised when more or more arguments are outside the defined range
+                  of the function.
+                </p>
+                <p>
+                  Defaults to <code class="computeroutput"><span class="identifier">boost</span><span class="special">::</span><span class="identifier">math</span><span class="special">::</span><span class="identifier">policies</span><span class="special">::</span><span class="identifier">domain_error</span><span class="special">&lt;</span><span class="identifier">throw_on_error</span><span class="special">&gt;</span></code>
+                </p>
+                <p>
+                  When the action is set to <span class="emphasis"><em>throw_on_error</em></span> then
+                  throws <code class="computeroutput"><span class="identifier">std</span><span class="special">::</span><span class="identifier">domain_error</span></code>
+                </p>
+                </td>
+</tr>
+<tr>
+<td>
+                <p>
+                  Pole Error
+                </p>
+                </td>
+<td>
+                <p>
+                  boost::math::policies::pole_error&lt;<span class="emphasis"><em>action</em></span>&gt;
+                </p>
+                </td>
+<td>
+                <p>
+                  Raised when more or more arguments would cause the function to
+                  be evaluated at a pole.
+                </p>
+                <p>
+                  Defaults to <code class="computeroutput"><span class="identifier">boost</span><span class="special">::</span><span class="identifier">math</span><span class="special">::</span><span class="identifier">policies</span><span class="special">::</span><span class="identifier">pole_error</span><span class="special">&lt;</span><span class="identifier">throw_on_error</span><span class="special">&gt;</span></code>
+                </p>
+                <p>
+                  When the action is <span class="emphasis"><em>throw_on_error</em></span> then throw
+                  a <code class="computeroutput"><span class="identifier">std</span><span class="special">::</span><span class="identifier">domain_error</span></code>
+                </p>
+                </td>
+</tr>
+<tr>
+<td>
+                <p>
+                  Overflow Error
+                </p>
+                </td>
+<td>
+                <p>
+                  boost::math::policies::overflow_error&lt;<span class="emphasis"><em>action</em></span>&gt;
+                </p>
+                </td>
+<td>
+                <p>
+                  Raised when the result of the function is outside the representable
+                  range of the floating point type used.
+                </p>
+                <p>
+                  Defaults to <code class="computeroutput"><span class="identifier">boost</span><span class="special">::</span><span class="identifier">math</span><span class="special">::</span><span class="identifier">policies</span><span class="special">::</span><span class="identifier">overflow_error</span><span class="special">&lt;</span><span class="identifier">throw_on_error</span><span class="special">&gt;</span></code>.
+                </p>
+                <p>
+                  When the action is <span class="emphasis"><em>throw_on_error</em></span> then throws
+                  a <code class="computeroutput"><span class="identifier">std</span><span class="special">::</span><span class="identifier">overflow_error</span></code>.
+                </p>
+                </td>
+</tr>
+<tr>
+<td>
+                <p>
+                  Underflow Error
+                </p>
+                </td>
+<td>
+                <p>
+                  boost::math::policies::underflow_error&lt;<span class="emphasis"><em>action</em></span>&gt;
+                </p>
+                </td>
+<td>
+                <p>
+                  Raised when the result of the function is too small to be represented
+                  in the floating point type used.
+                </p>
+                <p>
+                  Defaults to <code class="computeroutput"><span class="identifier">boost</span><span class="special">::</span><span class="identifier">math</span><span class="special">::</span><span class="identifier">policies</span><span class="special">::</span><span class="identifier">underflow_error</span><span class="special">&lt;</span><span class="identifier">ignore_error</span><span class="special">&gt;</span></code>
+                </p>
+                <p>
+                  When the specified action is <span class="emphasis"><em>throw_on_error</em></span>
+                  then throws a <code class="computeroutput"><span class="identifier">std</span><span class="special">::</span><span class="identifier">underflow_error</span></code>
+                </p>
+                </td>
+</tr>
+<tr>
+<td>
+                <p>
+                  Denorm Error
+                </p>
+                </td>
+<td>
+                <p>
+                  boost::math::policies::denorm_error&lt;<span class="emphasis"><em>action</em></span>&gt;
+                </p>
+                </td>
+<td>
+                <p>
+                  Raised when the result of the function is a denormalised value.
+                </p>
+                <p>
+                  Defaults to <code class="computeroutput"><span class="identifier">boost</span><span class="special">::</span><span class="identifier">math</span><span class="special">::</span><span class="identifier">policies</span><span class="special">::</span><span class="identifier">denorm_error</span><span class="special">&lt;</span><span class="identifier">ignore_error</span><span class="special">&gt;</span></code>
+                </p>
+                <p>
+                  When the action is <span class="emphasis"><em>throw_on_error</em></span> then throws
+                  a <code class="computeroutput"><span class="identifier">std</span><span class="special">::</span><span class="identifier">underflow_error</span></code>
+                </p>
+                </td>
+</tr>
+<tr>
+<td>
+                <p>
+                  Rounding Error
+                </p>
+                </td>
+<td>
+                <p>
+                  boost::math::policies::rounding_error&lt;<span class="emphasis"><em>action</em></span>&gt;
+                </p>
+                </td>
+<td>
+                <p>
+                  Raised When one of the rounding functions <a class="link" href="../../special/rounding/round.html" title="Rounding Functions">round</a>,
+                  <a class="link" href="../../special/rounding/trunc.html" title="Truncation Functions">trunc</a>
+                  or <a class="link" href="../../special/rounding/modf.html" title="Integer and Fractional Part Splitting (modf)">modf</a>
+                  is called with an argument that has no integer representation,
+                  or is too large to be represented in the result type
+                </p>
+                <p>
+                  Defaults to <code class="computeroutput"><span class="identifier">boost</span><span class="special">::</span><span class="identifier">math</span><span class="special">::</span><span class="identifier">policies</span><span class="special">::</span><span class="identifier">rounding_error</span><span class="special">&lt;</span><span class="identifier">throw_on_error</span><span class="special">&gt;</span></code>
+                </p>
+                <p>
+                  When the action is <span class="emphasis"><em>throw_on_error</em></span> then throws
+                  <code class="computeroutput"><span class="identifier">boost</span><span class="special">::</span><span class="identifier">math</span><span class="special">::</span><span class="identifier">rounding_error</span></code>
+                </p>
+                </td>
+</tr>
+<tr>
+<td>
+                <p>
+                  Evaluation Error
+                </p>
+                </td>
+<td>
+                <p>
+                  boost::math::policies::evaluation_error&lt;<span class="emphasis"><em>action</em></span>&gt;
+                </p>
+                </td>
+<td>
+                <p>
+                  Raised when the result of the function is well defined and finite,
+                  but we were unable to compute it. Typically this occurs when an
+                  iterative method fails to converge. Of course ideally this error
+                  should never be raised: feel free to report it as a bug if it is!
+                </p>
+                <p>
+                  Defaults to <code class="computeroutput"><span class="identifier">boost</span><span class="special">::</span><span class="identifier">math</span><span class="special">::</span><span class="identifier">policies</span><span class="special">::</span><span class="identifier">evaluation_error</span><span class="special">&lt;</span><span class="identifier">throw_on_error</span><span class="special">&gt;</span></code>
+                </p>
+                <p>
+                  When the action is <span class="emphasis"><em>throw_on_error</em></span> then throws
+                  <code class="computeroutput"><span class="identifier">boost</span><span class="special">::</span><span class="identifier">math</span><span class="special">::</span><span class="identifier">evaluation_error</span></code>
+                </p>
+                </td>
+</tr>
+<tr>
+<td>
+                <p>
+                  Indeterminate Result Error
+                </p>
+                </td>
+<td>
+                <p>
+                  boost::math::policies::indeterminate_result_error&lt;<span class="emphasis"><em>action</em></span>&gt;
+                </p>
+                </td>
+<td>
+                <p>
+                  Raised when the result of a function is not defined for the values
+                  that were passed to it.
+                </p>
+                <p>
+                  Defaults to <code class="computeroutput"><span class="identifier">boost</span><span class="special">::</span><span class="identifier">math</span><span class="special">::</span><span class="identifier">policies</span><span class="special">::</span><span class="identifier">indeterminate_result_error</span><span class="special">&lt;</span><span class="identifier">ignore_error</span><span class="special">&gt;</span></code>
+                </p>
+                <p>
+                  When the action is <span class="emphasis"><em>throw_on_error</em></span> then throws
+                  <code class="computeroutput"><span class="identifier">std</span><span class="special">::</span><span class="identifier">domain_error</span></code>
+                </p>
+                </td>
+</tr>
+</tbody>
+</table></div>
+<a name="math_toolkit.policy.pol_ref.error_handling_policies.examples"></a><h5>
+<a name="id891794"></a>
+          <a class="link" href="error_handling_policies.html#math_toolkit.policy.pol_ref.error_handling_policies.examples">Examples</a>
+        </h5>
+<p>
+          Suppose we want a call to <code class="computeroutput"><span class="identifier">tgamma</span></code>
+          to behave in a C-compatible way and set global <code class="computeroutput"><span class="special">::</span><span class="identifier">errno</span></code> rather than throw an exception,
+          we can achieve this at the call site using:
+        </p>
+<p>
+          </p>
+<p>
+            
+</p>
+<pre class="programlisting"><span class="preprocessor">#include</span> <span class="special">&lt;</span><span class="identifier">boost</span><span class="special">/</span><span class="identifier">math</span><span class="special">/</span><span class="identifier">special_functions</span><span class="special">/</span><span class="identifier">gamma</span><span class="special">.</span><span class="identifier">hpp</span><span class="special">&gt;</span>
+
+<span class="keyword">using</span> <span class="keyword">namespace</span> <span class="identifier">boost</span><span class="special">::</span><span class="identifier">math</span><span class="special">::</span><span class="identifier">policies</span><span class="special">;</span>
+<span class="keyword">using</span> <span class="keyword">namespace</span> <span class="identifier">boost</span><span class="special">::</span><span class="identifier">math</span><span class="special">;</span>
+
+<span class="comment">// Define a policy:
+</span><span class="keyword">typedef</span> <span class="identifier">policy</span><span class="special">&lt;</span>
+      <span class="identifier">domain_error</span><span class="special">&lt;</span><span class="identifier">errno_on_error</span><span class="special">&gt;,</span> 
+      <span class="identifier">pole_error</span><span class="special">&lt;</span><span class="identifier">errno_on_error</span><span class="special">&gt;,</span>
+      <span class="identifier">overflow_error</span><span class="special">&lt;</span><span class="identifier">errno_on_error</span><span class="special">&gt;,</span>
+      <span class="identifier">policies</span><span class="special">::</span><span class="identifier">evaluation_error</span><span class="special">&lt;</span><span class="identifier">errno_on_error</span><span class="special">&gt;</span> 
+      <span class="special">&gt;</span> <span class="identifier">my_policy</span><span class="special">;</span>
+      
+<span class="comment">// call the function:
+</span><span class="keyword">double</span> <span class="identifier">t1</span> <span class="special">=</span> <span class="identifier">tgamma</span><span class="special">(</span><span class="identifier">some_value</span><span class="special">,</span> <span class="identifier">my_policy</span><span class="special">());</span>
+
+<span class="comment">// Alternatively we could use make_policy and define everything at the call site:
+</span><span class="keyword">double</span> <span class="identifier">t2</span> <span class="special">=</span> <span class="identifier">tgamma</span><span class="special">(</span><span class="identifier">some_value</span><span class="special">,</span> <span class="identifier">make_policy</span><span class="special">(</span>
+         <span class="identifier">domain_error</span><span class="special">&lt;</span><span class="identifier">errno_on_error</span><span class="special">&gt;(),</span> 
+         <span class="identifier">pole_error</span><span class="special">&lt;</span><span class="identifier">errno_on_error</span><span class="special">&gt;(),</span>
+         <span class="identifier">overflow_error</span><span class="special">&lt;</span><span class="identifier">errno_on_error</span><span class="special">&gt;(),</span>
+         <span class="identifier">policies</span><span class="special">::</span><span class="identifier">evaluation_error</span><span class="special">&lt;</span><span class="identifier">errno_on_error</span><span class="special">&gt;()</span> 
+      <span class="special">));</span>
+
+</pre>
+<p>
+          </p>
+<p>
+        </p>
+<p>
+          Suppose we want a statistical distribution to return infinities, rather
+          than throw exceptions, then we can use:
+        </p>
+<p>
+          </p>
+<p>
+            
+</p>
+<pre class="programlisting"><span class="preprocessor">#include</span> <span class="special">&lt;</span><span class="identifier">boost</span><span class="special">/</span><span class="identifier">math</span><span class="special">/</span><span class="identifier">distributions</span><span class="special">/</span><span class="identifier">normal</span><span class="special">.</span><span class="identifier">hpp</span><span class="special">&gt;</span>
+
+<span class="keyword">using</span> <span class="keyword">namespace</span> <span class="identifier">boost</span><span class="special">::</span><span class="identifier">math</span><span class="special">::</span><span class="identifier">policies</span><span class="special">;</span>
+<span class="keyword">using</span> <span class="keyword">namespace</span> <span class="identifier">boost</span><span class="special">::</span><span class="identifier">math</span><span class="special">;</span>
+
+<span class="comment">// Define a policy:
+</span><span class="keyword">typedef</span> <span class="identifier">policy</span><span class="special">&lt;</span>
+      <span class="identifier">overflow_error</span><span class="special">&lt;</span><span class="identifier">ignore_error</span><span class="special">&gt;</span>
+      <span class="special">&gt;</span> <span class="identifier">my_policy</span><span class="special">;</span>
+      
+<span class="comment">// Define the distribution:
+</span><span class="keyword">typedef</span> <span class="identifier">normal_distribution</span><span class="special">&lt;</span><span class="keyword">double</span><span class="special">,</span> <span class="identifier">my_policy</span><span class="special">&gt;</span> <span class="identifier">my_norm</span><span class="special">;</span>
+
+<span class="comment">// Get a quantile:
+</span><span class="keyword">double</span> <span class="identifier">q</span> <span class="special">=</span> <span class="identifier">quantile</span><span class="special">(</span><span class="identifier">my_norm</span><span class="special">(),</span> <span class="number">0.05</span><span class="special">);</span>
+
+</pre>
+<p>
+          </p>
+<p>
+        </p>
+</div>
+<table xmlns:rev="http://www.cs.rpi.edu/~gregod/boost/tools/doc/revision" width="100%"><tr>
+<td align="left"></td>
+<td align="right"><div class="copyright-footer">Copyright © 2006 , 2007, 2008 John Maddock, Paul A. Bristow, Hubert
+      Holin, Xiaogang Zhang, Bruno Lalande and Gautam Sewani<p>
+        Distributed under the Boost Software License, Version 1.0. (See accompanying
+        file LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_0.txt)
+      </p>
+</div></td>
+</tr></table>
+<hr>
+<div class="spirit-nav">
+<a accesskey="p" href="../pol_ref.html"><img src="../../../../../doc/html/images/prev.png" alt="Prev"></a><a accesskey="u" href="../pol_ref.html"><img src="../../../../../doc/html/images/up.png" alt="Up"></a><a accesskey="h" href="../../../index.html"><img src="../../../../../doc/html/images/home.png" alt="Home"></a><a accesskey="n" href="internal_promotion.html"><img src="../../../../../doc/html/images/next.png" alt="Next"></a>
+</div>
+</body>
+</html>

Added: sandbox/tools/auto_index/example/math/doc/sf_and_dist/html/math_toolkit/policy/pol_ref/internal_promotion.html
==============================================================================
--- (empty file)
+++ sandbox/tools/auto_index/example/math/doc/sf_and_dist/html/math_toolkit/policy/pol_ref/internal_promotion.html	2008-11-28 05:25:28 EST (Fri, 28 Nov 2008)
@@ -0,0 +1,166 @@
+<html>
+<head>
+<meta http-equiv="Content-Type" content="text/html; charset=ISO-8859-1">
+<title>Internal Promotion Policies</title>
+<link rel="stylesheet" href="../../../boostbook.css" type="text/css">
+<meta name="generator" content="DocBook XSL Stylesheets Vsnapshot_8125">
+<link rel="home" href="../../../index.html" title="Math Toolkit">
+<link rel="up" href="../pol_ref.html" title="Policy Reference">
+<link rel="prev" href="error_handling_policies.html" title="Error Handling Policies">
+<link rel="next" href="assert_undefined.html" title="Mathematically Undefined Function Policies">
+</head>
+<body bgcolor="white" text="black" link="#0000FF" vlink="#840084" alink="#0000FF">
+<table cellpadding="2" width="100%"><tr>
+<td valign="top"><img alt="Boost C++ Libraries" width="277" height="86" src="../../../../../boost.png"></td>
+<td align="center">Home</td>
+<td align="center">Libraries</td>
+<td align="center">People</td>
+<td align="center">FAQ</td>
+<td align="center">More</td>
+</tr></table>
+<hr>
+<div class="spirit-nav">
+<a accesskey="p" href="error_handling_policies.html"><img src="../../../../../doc/html/images/prev.png" alt="Prev"></a><a accesskey="u" href="../pol_ref.html"><img src="../../../../../doc/html/images/up.png" alt="Up"></a><a accesskey="h" href="../../../index.html"><img src="../../../../../doc/html/images/home.png" alt="Home"></a><a accesskey="n" href="assert_undefined.html"><img src="../../../../../doc/html/images/next.png" alt="Next"></a>
+</div>
+<div class="section" lang="en">
+<div class="titlepage"><div><div><h4 class="title">
+<a name="math_toolkit.policy.pol_ref.internal_promotion"></a><a class="link" href="internal_promotion.html" title="Internal Promotion Policies"> Internal
+        Promotion Policies</a>
+</h4></div></div></div>
+<p>
+          Normally when evaluating a function at say <code class="computeroutput"><span class="keyword">float</span></code>
+          precision, maximal accuracy is assured by conducting the calculation at
+          <code class="computeroutput"><span class="keyword">double</span></code> precision internally,
+          and then rounding the result. There are two policies that effect whether
+          internal promotion takes place or not:
+        </p>
+<div class="informaltable"><table class="table">
+<colgroup>
+<col>
+<col>
+</colgroup>
+<thead><tr>
+<th>
+                <p>
+                  Policy
+                </p>
+                </th>
+<th>
+                <p>
+                  Meaning
+                </p>
+                </th>
+</tr></thead>
+<tbody>
+<tr>
+<td>
+                <p>
+                  <code class="computeroutput"><span class="identifier">boost</span><span class="special">::</span><span class="identifier">math</span><span class="special">::</span><span class="identifier">policies</span><span class="special">::</span><span class="identifier">promote_float</span><span class="special">&lt;</span><span class="identifier">B</span><span class="special">&gt;</span></code>
+                </p>
+                </td>
+<td>
+                <p>
+                  Indicates whether <code class="computeroutput"><span class="keyword">float</span></code>
+                  arguments should be promoted to <code class="computeroutput"><span class="keyword">double</span></code>
+                  precision internally: defaults to <code class="computeroutput"><span class="identifier">boost</span><span class="special">::</span><span class="identifier">math</span><span class="special">::</span><span class="identifier">policies</span><span class="special">::</span><span class="identifier">promote_float</span><span class="special">&lt;</span><span class="keyword">true</span><span class="special">&gt;</span></code>
+                </p>
+                </td>
+</tr>
+<tr>
+<td>
+                <p>
+                  <code class="computeroutput"><span class="identifier">boost</span><span class="special">::</span><span class="identifier">math</span><span class="special">::</span><span class="identifier">policies</span><span class="special">::</span><span class="identifier">promote_double</span><span class="special">&lt;</span><span class="identifier">B</span><span class="special">&gt;</span></code>
+                </p>
+                </td>
+<td>
+                <p>
+                  Indicates whether <code class="computeroutput"><span class="keyword">double</span></code>
+                  arguments should be promoted to <code class="computeroutput"><span class="keyword">long</span>
+                  <span class="keyword">double</span></code> precision internally:
+                  defaults to <code class="computeroutput"><span class="identifier">boost</span><span class="special">::</span><span class="identifier">math</span><span class="special">::</span><span class="identifier">policies</span><span class="special">::</span><span class="identifier">promote_double</span><span class="special">&lt;</span><span class="keyword">true</span><span class="special">&gt;</span></code>
+                </p>
+                </td>
+</tr>
+</tbody>
+</table></div>
+<a name="math_toolkit.policy.pol_ref.internal_promotion.examples"></a><h5>
+<a name="id893129"></a>
+          <a class="link" href="internal_promotion.html#math_toolkit.policy.pol_ref.internal_promotion.examples">Examples</a>
+        </h5>
+<p>
+          Suppose we want <code class="computeroutput"><span class="identifier">tgamma</span></code>
+          to be evaluated without internal promotion to <code class="computeroutput"><span class="keyword">long</span>
+          <span class="keyword">double</span></code>, then we could use:
+        </p>
+<p>
+          </p>
+<p>
+            
+</p>
+<pre class="programlisting"><span class="preprocessor">#include</span> <span class="special">&lt;</span><span class="identifier">boost</span><span class="special">/</span><span class="identifier">math</span><span class="special">/</span><span class="identifier">special_functions</span><span class="special">/</span><span class="identifier">gamma</span><span class="special">.</span><span class="identifier">hpp</span><span class="special">&gt;</span>
+
+<span class="keyword">using</span> <span class="keyword">namespace</span> <span class="identifier">boost</span><span class="special">::</span><span class="identifier">math</span><span class="special">::</span><span class="identifier">policies</span><span class="special">;</span>
+<span class="keyword">using</span> <span class="keyword">namespace</span> <span class="identifier">boost</span><span class="special">::</span><span class="identifier">math</span><span class="special">;</span>
+
+<span class="comment">// Define a policy:
+</span><span class="keyword">typedef</span> <span class="identifier">policy</span><span class="special">&lt;</span>
+      <span class="identifier">promote_double</span><span class="special">&lt;</span><span class="keyword">false</span><span class="special">&gt;</span> 
+      <span class="special">&gt;</span> <span class="identifier">my_policy</span><span class="special">;</span>
+      
+<span class="comment">// Call the function:
+</span><span class="keyword">double</span> <span class="identifier">t1</span> <span class="special">=</span> <span class="identifier">tgamma</span><span class="special">(</span><span class="identifier">some_value</span><span class="special">,</span> <span class="identifier">my_policy</span><span class="special">());</span>
+
+<span class="comment">// Alternatively we could use make_policy and define everything at the call site:
+</span><span class="keyword">double</span> <span class="identifier">t2</span> <span class="special">=</span> <span class="identifier">tgamma</span><span class="special">(</span><span class="identifier">some_value</span><span class="special">,</span> <span class="identifier">make_policy</span><span class="special">(</span><span class="identifier">promote_double</span><span class="special">&lt;</span><span class="keyword">false</span><span class="special">&gt;()));</span>
+
+</pre>
+<p>
+          </p>
+<p>
+        </p>
+<p>
+          Alternatively, suppose we want a distribution to perform calculations without
+          promoting <code class="computeroutput"><span class="keyword">float</span></code> to <code class="computeroutput"><span class="keyword">double</span></code>, then we could use:
+        </p>
+<p>
+          </p>
+<p>
+            
+</p>
+<pre class="programlisting"><span class="preprocessor">#include</span> <span class="special">&lt;</span><span class="identifier">boost</span><span class="special">/</span><span class="identifier">math</span><span class="special">/</span><span class="identifier">distributions</span><span class="special">/</span><span class="identifier">normal</span><span class="special">.</span><span class="identifier">hpp</span><span class="special">&gt;</span>
+
+<span class="keyword">using</span> <span class="keyword">namespace</span> <span class="identifier">boost</span><span class="special">::</span><span class="identifier">math</span><span class="special">::</span><span class="identifier">policies</span><span class="special">;</span>
+<span class="keyword">using</span> <span class="keyword">namespace</span> <span class="identifier">boost</span><span class="special">::</span><span class="identifier">math</span><span class="special">;</span>
+
+<span class="comment">// Define a policy:
+</span><span class="keyword">typedef</span> <span class="identifier">policy</span><span class="special">&lt;</span>
+      <span class="identifier">promote_float</span><span class="special">&lt;</span><span class="keyword">false</span><span class="special">&gt;</span>
+      <span class="special">&gt;</span> <span class="identifier">my_policy</span><span class="special">;</span>
+
+<span class="comment">// Define the distribution:
+</span><span class="keyword">typedef</span> <span class="identifier">normal_distribution</span><span class="special">&lt;</span><span class="keyword">float</span><span class="special">,</span> <span class="identifier">my_policy</span><span class="special">&gt;</span> <span class="identifier">my_norm</span><span class="special">;</span>
+
+<span class="comment">// Get a quantile:
+</span><span class="keyword">float</span> <span class="identifier">q</span> <span class="special">=</span> <span class="identifier">quantile</span><span class="special">(</span><span class="identifier">my_norm</span><span class="special">(),</span> <span class="number">0.05f</span><span class="special">);</span>
+
+</pre>
+<p>
+          </p>
+<p>
+        </p>
+</div>
+<table xmlns:rev="http://www.cs.rpi.edu/~gregod/boost/tools/doc/revision" width="100%"><tr>
+<td align="left"></td>
+<td align="right"><div class="copyright-footer">Copyright © 2006 , 2007, 2008 John Maddock, Paul A. Bristow, Hubert
+      Holin, Xiaogang Zhang, Bruno Lalande and Gautam Sewani<p>
+        Distributed under the Boost Software License, Version 1.0. (See accompanying
+        file LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_0.txt)
+      </p>
+</div></td>
+</tr></table>
+<hr>
+<div class="spirit-nav">
+<a accesskey="p" href="error_handling_policies.html"><img src="../../../../../doc/html/images/prev.png" alt="Prev"></a><a accesskey="u" href="../pol_ref.html"><img src="../../../../../doc/html/images/up.png" alt="Up"></a><a accesskey="h" href="../../../index.html"><img src="../../../../../doc/html/images/home.png" alt="Home"></a><a accesskey="n" href="assert_undefined.html"><img src="../../../../../doc/html/images/next.png" alt="Next"></a>
+</div>
+</body>
+</html>

Added: sandbox/tools/auto_index/example/math/doc/sf_and_dist/html/math_toolkit/policy/pol_ref/iteration_pol.html
==============================================================================
--- (empty file)
+++ sandbox/tools/auto_index/example/math/doc/sf_and_dist/html/math_toolkit/policy/pol_ref/iteration_pol.html	2008-11-28 05:25:28 EST (Fri, 28 Nov 2008)
@@ -0,0 +1,66 @@
+<html>
+<head>
+<meta http-equiv="Content-Type" content="text/html; charset=ISO-8859-1">
+<title>Iteration Limits Policies</title>
+<link rel="stylesheet" href="../../../boostbook.css" type="text/css">
+<meta name="generator" content="DocBook XSL Stylesheets Vsnapshot_8125">
+<link rel="home" href="../../../index.html" title="Math Toolkit">
+<link rel="up" href="../pol_ref.html" title="Policy Reference">
+<link rel="prev" href="precision_pol.html" title="Precision Policies">
+<link rel="next" href="policy_defaults.html" title="Using macros to Change the Policy Defaults">
+</head>
+<body bgcolor="white" text="black" link="#0000FF" vlink="#840084" alink="#0000FF">
+<table cellpadding="2" width="100%"><tr>
+<td valign="top"><img alt="Boost C++ Libraries" width="277" height="86" src="../../../../../boost.png"></td>
+<td align="center">Home</td>
+<td align="center">Libraries</td>
+<td align="center">People</td>
+<td align="center">FAQ</td>
+<td align="center">More</td>
+</tr></table>
+<hr>
+<div class="spirit-nav">
+<a accesskey="p" href="precision_pol.html"><img src="../../../../../doc/html/images/prev.png" alt="Prev"></a><a accesskey="u" href="../pol_ref.html"><img src="../../../../../doc/html/images/up.png" alt="Up"></a><a accesskey="h" href="../../../index.html"><img src="../../../../../doc/html/images/home.png" alt="Home"></a><a accesskey="n" href="policy_defaults.html"><img src="../../../../../doc/html/images/next.png" alt="Next"></a>
+</div>
+<div class="section" lang="en">
+<div class="titlepage"><div><div><h4 class="title">
+<a name="math_toolkit.policy.pol_ref.iteration_pol"></a><a class="link" href="iteration_pol.html" title="Iteration Limits Policies"> Iteration
+        Limits Policies</a>
+</h4></div></div></div>
+<p>
+          There are two policies that effect the iterative algorithms used to implement
+          the special functions in this library:
+        </p>
+<pre class="programlisting"><span class="keyword">template</span> <span class="special">&lt;</span><span class="keyword">unsigned</span> <span class="keyword">long</span> <span class="identifier">limit</span> <span class="special">=</span> <span class="identifier">BOOST_MATH_MAX_SERIES_ITERATION_POLICY</span><span class="special">&gt;</span>
+<span class="keyword">class</span> <span class="identifier">max_series_iterations</span><span class="special">;</span>
+
+<span class="keyword">template</span> <span class="special">&lt;</span><span class="keyword">unsigned</span> <span class="keyword">long</span> <span class="identifier">limit</span> <span class="special">=</span> <span class="identifier">BOOST_MATH_MAX_ROOT_ITERATION_POLICY</span><span class="special">&gt;</span>
+<span class="keyword">class</span> <span class="identifier">max_root_iterations</span><span class="special">;</span>
+</pre>
+<p>
+          The class <code class="computeroutput"><span class="identifier">max_series_iterations</span></code>
+          determines the maximum number of iterations permitted in a series evaluation,
+          before the special function gives up and returns the result of <a class="link" href="../../main_overview/error_handling.html#evaluation_error">evaluation_error</a>.
+        </p>
+<p>
+          The class <code class="computeroutput"><span class="identifier">max_root_iterations</span></code>
+          determines the maximum number of iterations permitted in a root-finding
+          algorithm before the special function gives up and returns the result of
+          <a class="link" href="../../main_overview/error_handling.html#evaluation_error">evaluation_error</a>.
+        </p>
+</div>
+<table xmlns:rev="http://www.cs.rpi.edu/~gregod/boost/tools/doc/revision" width="100%"><tr>
+<td align="left"></td>
+<td align="right"><div class="copyright-footer">Copyright © 2006 , 2007, 2008 John Maddock, Paul A. Bristow, Hubert
+      Holin, Xiaogang Zhang, Bruno Lalande and Gautam Sewani<p>
+        Distributed under the Boost Software License, Version 1.0. (See accompanying
+        file LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_0.txt)
+      </p>
+</div></td>
+</tr></table>
+<hr>
+<div class="spirit-nav">
+<a accesskey="p" href="precision_pol.html"><img src="../../../../../doc/html/images/prev.png" alt="Prev"></a><a accesskey="u" href="../pol_ref.html"><img src="../../../../../doc/html/images/up.png" alt="Up"></a><a accesskey="h" href="../../../index.html"><img src="../../../../../doc/html/images/home.png" alt="Home"></a><a accesskey="n" href="policy_defaults.html"><img src="../../../../../doc/html/images/next.png" alt="Next"></a>
+</div>
+</body>
+</html>

Added: sandbox/tools/auto_index/example/math/doc/sf_and_dist/html/math_toolkit/policy/pol_ref/namespace_pol.html
==============================================================================
--- (empty file)
+++ sandbox/tools/auto_index/example/math/doc/sf_and_dist/html/math_toolkit/policy/pol_ref/namespace_pol.html	2008-11-28 05:25:28 EST (Fri, 28 Nov 2008)
@@ -0,0 +1,166 @@
+<html>
+<head>
+<meta http-equiv="Content-Type" content="text/html; charset=ISO-8859-1">
+<title>Setting Polices at Namespace Scope</title>
+<link rel="stylesheet" href="../../../boostbook.css" type="text/css">
+<meta name="generator" content="DocBook XSL Stylesheets Vsnapshot_8125">
+<link rel="home" href="../../../index.html" title="Math Toolkit">
+<link rel="up" href="../pol_ref.html" title="Policy Reference">
+<link rel="prev" href="policy_defaults.html" title="Using macros to Change the Policy Defaults">
+<link rel="next" href="pol_ref_ref.html" title="Policy Class Reference">
+</head>
+<body bgcolor="white" text="black" link="#0000FF" vlink="#840084" alink="#0000FF">
+<table cellpadding="2" width="100%"><tr>
+<td valign="top"><img alt="Boost C++ Libraries" width="277" height="86" src="../../../../../boost.png"></td>
+<td align="center">Home</td>
+<td align="center">Libraries</td>
+<td align="center">People</td>
+<td align="center">FAQ</td>
+<td align="center">More</td>
+</tr></table>
+<hr>
+<div class="spirit-nav">
+<a accesskey="p" href="policy_defaults.html"><img src="../../../../../doc/html/images/prev.png" alt="Prev"></a><a accesskey="u" href="../pol_ref.html"><img src="../../../../../doc/html/images/up.png" alt="Up"></a><a accesskey="h" href="../../../index.html"><img src="../../../../../doc/html/images/home.png" alt="Home"></a><a accesskey="n" href="pol_ref_ref.html"><img src="../../../../../doc/html/images/next.png" alt="Next"></a>
+</div>
+<div class="section" lang="en">
+<div class="titlepage"><div><div><h4 class="title">
+<a name="math_toolkit.policy.pol_ref.namespace_pol"></a><a class="link" href="namespace_pol.html" title="Setting Polices at Namespace Scope"> Setting
+        Polices at Namespace Scope</a>
+</h4></div></div></div>
+<p>
+          Sometimes what you really want to do is bring all the special functions,
+          or all the distributions into a specific namespace-scope, along with a
+          specific policy to use with them. There are two macros defined to assist
+          with that:
+        </p>
+<pre class="programlisting"><span class="identifier">BOOST_MATH_DECLARE_SPECIAL_FUNCTIONS</span><span class="special">(</span><span class="identifier">Policy</span><span class="special">)</span>
+</pre>
+<p>
+          and:
+        </p>
+<pre class="programlisting"><span class="identifier">BOOST_MATH_DECLARE_DISTRIBUTIONS</span><span class="special">(</span><span class="identifier">Type</span><span class="special">,</span> <span class="identifier">Policy</span><span class="special">)</span>
+</pre>
+<p>
+          You can use either of these macros after including any special function
+          or distribution header. For example:
+        </p>
+<p>
+          </p>
+<p>
+            
+</p>
+<pre class="programlisting"><span class="preprocessor">#include</span> <span class="special">&lt;</span><span class="identifier">boost</span><span class="special">/</span><span class="identifier">math</span><span class="special">/</span><span class="identifier">special_functions</span><span class="special">/</span><span class="identifier">gamma</span><span class="special">.</span><span class="identifier">hpp</span><span class="special">&gt;</span>
+
+<span class="keyword">namespace</span> <span class="identifier">myspace</span><span class="special">{</span>
+
+<span class="keyword">using</span> <span class="keyword">namespace</span> <span class="identifier">boost</span><span class="special">::</span><span class="identifier">math</span><span class="special">::</span><span class="identifier">policies</span><span class="special">;</span>
+
+<span class="comment">// Define a policy that does not throw on overflow:
+</span><span class="keyword">typedef</span> <span class="identifier">policy</span><span class="special">&lt;</span><span class="identifier">overflow_error</span><span class="special">&lt;</span><span class="identifier">errno_on_error</span><span class="special">&gt;</span> <span class="special">&gt;</span> <span class="identifier">my_policy</span><span class="special">;</span>
+
+<span class="comment">// Define the special functions in this scope to use the policy:   
+</span><span class="identifier">BOOST_MATH_DECLARE_SPECIAL_FUNCTIONS</span><span class="special">(</span><span class="identifier">my_policy</span><span class="special">)</span>
+
+<span class="special">}</span>
+
+<span class="comment">//
+</span><span class="comment">// Now we can use myspace::tgamma etc.
+</span><span class="comment">// They will automatically use "my_policy":
+</span><span class="comment">//
+</span><span class="keyword">double</span> <span class="identifier">t</span> <span class="special">=</span> <span class="identifier">myspace</span><span class="special">::</span><span class="identifier">tgamma</span><span class="special">(</span><span class="number">30.0</span><span class="special">);</span> <span class="comment">// will not throw on overflow
+</span>
+</pre>
+<p>
+          </p>
+<p>
+        </p>
+<p>
+          In this example, using BOOST_MATH_DECLARE_SPECIAL_FUNCTIONS results in
+          a set of thin inline forwarding functions being defined:
+        </p>
+<pre class="programlisting"><span class="keyword">template</span> <span class="special">&lt;</span><span class="keyword">class</span> <span class="identifier">T</span><span class="special">&gt;</span>
+<span class="keyword">inline</span> <span class="identifier">T</span> <span class="identifier">tgamma</span><span class="special">(</span><span class="identifier">T</span> <span class="identifier">a</span><span class="special">){</span> <span class="keyword">return</span> <span class="special">::</span><span class="identifier">boost</span><span class="special">::</span><span class="identifier">math</span><span class="special">::</span><span class="identifier">tgamma</span><span class="special">(</span><span class="identifier">a</span><span class="special">,</span> <span class="identifier">mypolicy</span><span class="special">());</span> <span class="special">}</span>
+
+<span class="keyword">template</span> <span class="special">&lt;</span><span class="keyword">class</span> <span class="identifier">T</span><span class="special">&gt;</span>
+<span class="keyword">inline</span> <span class="identifier">T</span> <span class="identifier">lgamma</span><span class="special">(</span><span class="identifier">T</span> <span class="identifier">a</span><span class="special">)</span> <span class="special">(</span> <span class="keyword">return</span> <span class="special">::</span><span class="identifier">boost</span><span class="special">::</span><span class="identifier">math</span><span class="special">::</span><span class="identifier">lgamma</span><span class="special">(</span><span class="identifier">a</span><span class="special">,</span> <span class="identifier">mypolicy</span><span class="special">());</span> <span class="special">}</span>
+</pre>
+<p>
+          and so on. Note that while a forwarding function is defined for all the
+          special functions, however, unless you include the specific header for
+          the special function you use (or boost/math/special_functions.hpp to include
+          everything), you will get linker errors from functions that are forward
+          declared, but not defined.
+        </p>
+<p>
+          We can do the same thing with the distributions, but this time we need
+          to specify the floating-point type to use:
+        </p>
+<p>
+          </p>
+<p>
+            
+</p>
+<pre class="programlisting"><span class="preprocessor">#include</span> <span class="special">&lt;</span><span class="identifier">boost</span><span class="special">/</span><span class="identifier">math</span><span class="special">/</span><span class="identifier">distributions</span><span class="special">/</span><span class="identifier">cauchy</span><span class="special">.</span><span class="identifier">hpp</span><span class="special">&gt;</span>
+
+<span class="keyword">namespace</span> <span class="identifier">myspace</span><span class="special">{</span>
+
+<span class="keyword">using</span> <span class="keyword">namespace</span> <span class="identifier">boost</span><span class="special">::</span><span class="identifier">math</span><span class="special">::</span><span class="identifier">policies</span><span class="special">;</span>
+
+<span class="comment">// Define a policy to use, in this case we want all the distribution
+</span><span class="comment">// accessor functions to compile, even if they are mathematically
+</span><span class="comment">// undefined:
+</span><span class="keyword">typedef</span> <span class="identifier">policy</span><span class="special">&lt;</span><span class="identifier">assert_undefined</span><span class="special">&lt;</span><span class="keyword">false</span><span class="special">&gt;</span> <span class="special">&gt;</span> <span class="identifier">my_policy</span><span class="special">;</span>
+
+<span class="identifier">BOOST_MATH_DECLARE_DISTRIBUTIONS</span><span class="special">(</span><span class="keyword">double</span><span class="special">,</span> <span class="identifier">my_policy</span><span class="special">)</span>
+
+<span class="special">}</span>
+
+<span class="comment">// Now we can use myspace::cauchy etc, which will use policy
+</span><span class="comment">// myspace::mypolicy:
+</span><span class="comment">//
+</span><span class="comment">// This compiles but raises a domain error at runtime:
+</span><span class="comment">//
+</span><span class="keyword">void</span> <span class="identifier">test_cauchy</span><span class="special">()</span>
+<span class="special">{</span>
+   <span class="keyword">try</span>
+   <span class="special">{</span>
+      <span class="keyword">double</span> <span class="identifier">d</span> <span class="special">=</span> <span class="identifier">mean</span><span class="special">(</span><span class="identifier">myspace</span><span class="special">::</span><span class="identifier">cauchy</span><span class="special">());</span>
+   <span class="special">}</span>
+   <span class="keyword">catch</span><span class="special">(</span><span class="keyword">const</span> <span class="identifier">std</span><span class="special">::</span><span class="identifier">domain_error</span><span class="special">&amp;</span> <span class="identifier">e</span><span class="special">)</span>
+   <span class="special">{</span>
+      <span class="identifier">std</span><span class="special">::</span><span class="identifier">cout</span> <span class="special">&lt;&lt;</span> <span class="identifier">e</span><span class="special">.</span><span class="identifier">what</span><span class="special">()</span> <span class="special">&lt;&lt;</span> <span class="identifier">std</span><span class="special">::</span><span class="identifier">endl</span><span class="special">;</span>
+   <span class="special">}</span>
+<span class="special">}</span>
+
+</pre>
+<p>
+          </p>
+<p>
+        </p>
+<p>
+          In this example the result of BOOST_MATH_DECLARE_DISTRIBUTIONS is to declare
+          a typedef for each distribution like this:
+        </p>
+<pre class="programlisting"><span class="keyword">typedef</span> <span class="identifier">boost</span><span class="special">::</span><span class="identifier">math</span><span class="special">::</span><span class="identifier">cauchy_distribution</span><span class="special">&lt;</span><span class="keyword">double</span><span class="special">,</span> <span class="identifier">my_policy</span><span class="special">&gt;</span> <span class="identifier">cauchy</span><span class="special">;</span>
+<span class="identifier">tyepdef</span> <span class="identifier">boost</span><span class="special">::</span><span class="identifier">math</span><span class="special">::</span><span class="identifier">gamma_distribution</span><span class="special">&lt;</span><span class="keyword">double</span><span class="special">,</span> <span class="identifier">my_policy</span><span class="special">&gt;</span> <span class="identifier">gamma</span><span class="special">;</span>
+</pre>
+<p>
+          and so on. The name given to each typedef is the name of the distribution
+          with the "_distribution" suffix removed.
+        </p>
+</div>
+<table xmlns:rev="http://www.cs.rpi.edu/~gregod/boost/tools/doc/revision" width="100%"><tr>
+<td align="left"></td>
+<td align="right"><div class="copyright-footer">Copyright © 2006 , 2007, 2008 John Maddock, Paul A. Bristow, Hubert
+      Holin, Xiaogang Zhang, Bruno Lalande and Gautam Sewani<p>
+        Distributed under the Boost Software License, Version 1.0. (See accompanying
+        file LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_0.txt)
+      </p>
+</div></td>
+</tr></table>
+<hr>
+<div class="spirit-nav">
+<a accesskey="p" href="policy_defaults.html"><img src="../../../../../doc/html/images/prev.png" alt="Prev"></a><a accesskey="u" href="../pol_ref.html"><img src="../../../../../doc/html/images/up.png" alt="Up"></a><a accesskey="h" href="../../../index.html"><img src="../../../../../doc/html/images/home.png" alt="Home"></a><a accesskey="n" href="pol_ref_ref.html"><img src="../../../../../doc/html/images/next.png" alt="Next"></a>
+</div>
+</body>
+</html>

Added: sandbox/tools/auto_index/example/math/doc/sf_and_dist/html/math_toolkit/policy/pol_ref/pol_ref_ref.html
==============================================================================
--- (empty file)
+++ sandbox/tools/auto_index/example/math/doc/sf_and_dist/html/math_toolkit/policy/pol_ref/pol_ref_ref.html	2008-11-28 05:25:28 EST (Fri, 28 Nov 2008)
@@ -0,0 +1,260 @@
+<html>
+<head>
+<meta http-equiv="Content-Type" content="text/html; charset=ISO-8859-1">
+<title>Policy Class Reference</title>
+<link rel="stylesheet" href="../../../boostbook.css" type="text/css">
+<meta name="generator" content="DocBook XSL Stylesheets Vsnapshot_8125">
+<link rel="home" href="../../../index.html" title="Math Toolkit">
+<link rel="up" href="../pol_ref.html" title="Policy Reference">
+<link rel="prev" href="namespace_pol.html" title="Setting Polices at Namespace Scope">
+<link rel="next" href="../../perf.html" title="Performance">
+</head>
+<body bgcolor="white" text="black" link="#0000FF" vlink="#840084" alink="#0000FF">
+<table cellpadding="2" width="100%"><tr>
+<td valign="top"><img alt="Boost C++ Libraries" width="277" height="86" src="../../../../../boost.png"></td>
+<td align="center">Home</td>
+<td align="center">Libraries</td>
+<td align="center">People</td>
+<td align="center">FAQ</td>
+<td align="center">More</td>
+</tr></table>
+<hr>
+<div class="spirit-nav">
+<a accesskey="p" href="namespace_pol.html"><img src="../../../../../doc/html/images/prev.png" alt="Prev"></a><a accesskey="u" href="../pol_ref.html"><img src="../../../../../doc/html/images/up.png" alt="Up"></a><a accesskey="h" href="../../../index.html"><img src="../../../../../doc/html/images/home.png" alt="Home"></a><a accesskey="n" href="../../perf.html"><img src="../../../../../doc/html/images/next.png" alt="Next"></a>
+</div>
+<div class="section" lang="en">
+<div class="titlepage"><div><div><h4 class="title">
+<a name="math_toolkit.policy.pol_ref.pol_ref_ref"></a><a class="link" href="pol_ref_ref.html" title="Policy Class Reference"> Policy Class
+        Reference</a>
+</h4></div></div></div>
+<p>
+          There's very little to say here, the <code class="computeroutput"><span class="identifier">policy</span></code>
+          class is just a rag-bag compile-time container for a collection of policies:
+        </p>
+<p>
+          
+</p>
+<pre class="programlisting"><span class="preprocessor">#include</span> <span class="special">&lt;</span><span class="identifier">boost</span><span class="special">/</span><span class="identifier">math</span><span class="special">/</span><span class="identifier">policies</span><span class="special">/</span><span class="identifier">policy</span><span class="special">.</span><span class="identifier">hpp</span><span class="special">&gt;</span></pre>
+<p>
+        </p>
+<pre class="programlisting"><span class="keyword">namespace</span> <span class="identifier">boost</span><span class="special">{</span>
+<span class="keyword">namespace</span> <span class="identifier">math</span><span class="special">{</span>
+<span class="keyword">namespace</span> <span class="identifier">policies</span>
+
+<span class="keyword">template</span> <span class="special">&lt;</span><span class="keyword">class</span> <span class="identifier">A1</span> <span class="special">=</span> <span class="identifier">default_policy</span><span class="special">,</span> 
+          <span class="keyword">class</span> <span class="identifier">A2</span> <span class="special">=</span> <span class="identifier">default_policy</span><span class="special">,</span> 
+          <span class="keyword">class</span> <span class="identifier">A3</span> <span class="special">=</span> <span class="identifier">default_policy</span><span class="special">,</span>
+          <span class="keyword">class</span> <span class="identifier">A4</span> <span class="special">=</span> <span class="identifier">default_policy</span><span class="special">,</span>
+          <span class="keyword">class</span> <span class="identifier">A5</span> <span class="special">=</span> <span class="identifier">default_policy</span><span class="special">,</span>
+          <span class="keyword">class</span> <span class="identifier">A6</span> <span class="special">=</span> <span class="identifier">default_policy</span><span class="special">,</span>
+          <span class="keyword">class</span> <span class="identifier">A7</span> <span class="special">=</span> <span class="identifier">default_policy</span><span class="special">,</span>
+          <span class="keyword">class</span> <span class="identifier">A8</span> <span class="special">=</span> <span class="identifier">default_policy</span><span class="special">,</span>
+          <span class="keyword">class</span> <span class="identifier">A9</span> <span class="special">=</span> <span class="identifier">default_policy</span><span class="special">,</span>
+          <span class="keyword">class</span> <span class="identifier">A10</span> <span class="special">=</span> <span class="identifier">default_policy</span><span class="special">,</span>
+          <span class="keyword">class</span> <span class="identifier">A11</span> <span class="special">=</span> <span class="identifier">default_policy</span><span class="special">,</span>
+          <span class="keyword">class</span> <span class="identifier">A12</span> <span class="special">=</span> <span class="identifier">default_policy</span><span class="special">,</span>
+          <span class="keyword">class</span> <span class="identifier">A13</span> <span class="special">=</span> <span class="identifier">default_policy</span><span class="special">&gt;</span>
+<span class="keyword">struct</span> <span class="identifier">policy</span>
+<span class="special">{</span>
+<span class="keyword">public</span><span class="special">:</span>
+   <span class="keyword">typedef</span> <span class="emphasis"><em>computed-from-template-arguments</em></span> <span class="identifier">domain_error_type</span><span class="special">;</span>
+   <span class="keyword">typedef</span> <span class="emphasis"><em>computed-from-template-arguments</em></span> <span class="identifier">pole_error_type</span><span class="special">;</span>
+   <span class="keyword">typedef</span> <span class="emphasis"><em>computed-from-template-arguments</em></span> <span class="identifier">overflow_error_type</span><span class="special">;</span>
+   <span class="keyword">typedef</span> <span class="emphasis"><em>computed-from-template-arguments</em></span> <span class="identifier">underflow_error_type</span><span class="special">;</span>
+   <span class="keyword">typedef</span> <span class="emphasis"><em>computed-from-template-arguments</em></span> <span class="identifier">denorm_error_type</span><span class="special">;</span>
+   <span class="keyword">typedef</span> <span class="emphasis"><em>computed-from-template-arguments</em></span> <span class="identifier">rounding_error_type</span><span class="special">;</span>
+   <span class="keyword">typedef</span> <span class="emphasis"><em>computed-from-template-arguments</em></span> <span class="identifier">evaluation_error_type</span><span class="special">;</span>
+   <span class="keyword">typedef</span> <span class="emphasis"><em>computed-from-template-arguments</em></span> <span class="identifier">indeterminate_result_error_type</span><span class="special">;</span>
+   <span class="keyword">typedef</span> <span class="emphasis"><em>computed-from-template-arguments</em></span> <span class="identifier">precision_type</span><span class="special">;</span>
+   <span class="keyword">typedef</span> <span class="emphasis"><em>computed-from-template-arguments</em></span> <span class="identifier">promote_float_type</span><span class="special">;</span>
+   <span class="keyword">typedef</span> <span class="emphasis"><em>computed-from-template-arguments</em></span> <span class="identifier">promote_double_type</span><span class="special">;</span>
+   <span class="keyword">typedef</span> <span class="emphasis"><em>computed-from-template-arguments</em></span> <span class="identifier">discrete_quantile_type</span><span class="special">;</span>
+   <span class="keyword">typedef</span> <span class="emphasis"><em>computed-from-template-arguments</em></span> <span class="identifier">assert_undefined_type</span><span class="special">;</span>
+<span class="special">};</span>
+
+<span class="keyword">template</span> <span class="special">&lt;...</span><span class="identifier">argument</span> <span class="identifier">list</span><span class="special">...&gt;</span>
+<span class="keyword">typename</span> <span class="identifier">normalise</span><span class="special">&lt;</span><span class="identifier">policy</span><span class="special">&lt;&gt;,</span> <span class="identifier">A1</span><span class="special">&gt;::</span><span class="identifier">type</span> <span class="identifier">make_policy</span><span class="special">(...</span><span class="identifier">argument</span> <span class="identifier">list</span><span class="special">..);</span>
+
+<span class="keyword">template</span> <span class="special">&lt;</span><span class="keyword">class</span> <span class="identifier">Policy</span><span class="special">,</span> 
+          <span class="keyword">class</span> <span class="identifier">A1</span> <span class="special">=</span> <span class="identifier">default_policy</span><span class="special">,</span> 
+          <span class="keyword">class</span> <span class="identifier">A2</span> <span class="special">=</span> <span class="identifier">default_policy</span><span class="special">,</span> 
+          <span class="keyword">class</span> <span class="identifier">A3</span> <span class="special">=</span> <span class="identifier">default_policy</span><span class="special">,</span>
+          <span class="keyword">class</span> <span class="identifier">A4</span> <span class="special">=</span> <span class="identifier">default_policy</span><span class="special">,</span>
+          <span class="keyword">class</span> <span class="identifier">A5</span> <span class="special">=</span> <span class="identifier">default_policy</span><span class="special">,</span>
+          <span class="keyword">class</span> <span class="identifier">A6</span> <span class="special">=</span> <span class="identifier">default_policy</span><span class="special">,</span>
+          <span class="keyword">class</span> <span class="identifier">A7</span> <span class="special">=</span> <span class="identifier">default_policy</span><span class="special">,</span>
+          <span class="keyword">class</span> <span class="identifier">A8</span> <span class="special">=</span> <span class="identifier">default_policy</span><span class="special">,</span>
+          <span class="keyword">class</span> <span class="identifier">A9</span> <span class="special">=</span> <span class="identifier">default_policy</span><span class="special">,</span>
+          <span class="keyword">class</span> <span class="identifier">A10</span> <span class="special">=</span> <span class="identifier">default_policy</span><span class="special">,</span>
+          <span class="keyword">class</span> <span class="identifier">A11</span> <span class="special">=</span> <span class="identifier">default_policy</span><span class="special">,</span>
+          <span class="keyword">class</span> <span class="identifier">A12</span> <span class="special">=</span> <span class="identifier">default_policy</span><span class="special">,</span>
+          <span class="keyword">class</span> <span class="identifier">A13</span> <span class="special">=</span> <span class="identifier">default_policy</span><span class="special">&gt;</span>
+<span class="keyword">struct</span> <span class="identifier">normalise</span>
+<span class="special">{</span>
+   <span class="keyword">typedef</span> computed-from-template-arguments <span class="identifier">type</span><span class="special">;</span>
+<span class="special">};</span>
+</pre>
+<p>
+          The member typedefs of class <code class="computeroutput"><span class="identifier">policy</span></code>
+          are intended for internal use but are documented briefly here for the sake
+          of completeness.
+        </p>
+<pre class="programlisting"><span class="identifier">policy</span><span class="special">&lt;...&gt;::</span><span class="identifier">domain_error_type</span>
+</pre>
+<p>
+          Specifies how domain errors are handled, will be an instance of <code class="computeroutput"><span class="identifier">boost</span><span class="special">::</span><span class="identifier">math</span><span class="special">::</span><span class="identifier">policies</span><span class="special">::</span><span class="identifier">domain_error</span><span class="special">&lt;&gt;</span></code>
+          with the template argument to <code class="computeroutput"><span class="identifier">domain_error</span></code>
+          one of the <code class="computeroutput"><span class="identifier">error_policy_type</span></code>
+          enumerated values.
+        </p>
+<pre class="programlisting"><span class="identifier">policy</span><span class="special">&lt;...&gt;::</span><span class="identifier">pole_error_type</span>
+</pre>
+<p>
+          Specifies how pole-errors are handled, will be an instance of <code class="computeroutput"><span class="identifier">boost</span><span class="special">::</span><span class="identifier">math</span><span class="special">::</span><span class="identifier">policies</span><span class="special">::</span><span class="identifier">pole_error</span><span class="special">&lt;&gt;</span></code>
+          with the template argument to <code class="computeroutput"><span class="identifier">pole_error</span></code>
+          one of the <code class="computeroutput"><span class="identifier">error_policy_type</span></code>
+          enumerated values.
+        </p>
+<pre class="programlisting"><span class="identifier">policy</span><span class="special">&lt;...&gt;::</span><span class="identifier">overflow_error_type</span>
+</pre>
+<p>
+          Specifies how overflow errors are handled, will be an instance of <code class="computeroutput"><span class="identifier">boost</span><span class="special">::</span><span class="identifier">math</span><span class="special">::</span><span class="identifier">policies</span><span class="special">::</span><span class="identifier">overflow_error</span><span class="special">&lt;&gt;</span></code>
+          with the template argument to <code class="computeroutput"><span class="identifier">overflow_error</span></code>
+          one of the <code class="computeroutput"><span class="identifier">error_policy_type</span></code>
+          enumerated values.
+        </p>
+<pre class="programlisting"><span class="identifier">policy</span><span class="special">&lt;...&gt;::</span><span class="identifier">underflow_error_type</span>
+</pre>
+<p>
+          Specifies how underflow errors are handled, will be an instance of <code class="computeroutput"><span class="identifier">boost</span><span class="special">::</span><span class="identifier">math</span><span class="special">::</span><span class="identifier">policies</span><span class="special">::</span><span class="identifier">underflow_error</span><span class="special">&lt;&gt;</span></code>
+          with the template argument to <code class="computeroutput"><span class="identifier">underflow_error</span></code>
+          one of the <code class="computeroutput"><span class="identifier">error_policy_type</span></code>
+          enumerated values.
+        </p>
+<pre class="programlisting"><span class="identifier">policy</span><span class="special">&lt;...&gt;::</span><span class="identifier">denorm_error_type</span>
+</pre>
+<p>
+          Specifies how denorm errors are handled, will be an instance of <code class="computeroutput"><span class="identifier">boost</span><span class="special">::</span><span class="identifier">math</span><span class="special">::</span><span class="identifier">policies</span><span class="special">::</span><span class="identifier">denorm_error</span><span class="special">&lt;&gt;</span></code>
+          with the template argument to <code class="computeroutput"><span class="identifier">denorm_error</span></code>
+          one of the <code class="computeroutput"><span class="identifier">error_policy_type</span></code>
+          enumerated values.
+        </p>
+<pre class="programlisting"><span class="identifier">policy</span><span class="special">&lt;...&gt;::</span><span class="identifier">rounding_error_type</span>
+</pre>
+<p>
+          Specifies how rounding errors are handled, will be an instance of <code class="computeroutput"><span class="identifier">boost</span><span class="special">::</span><span class="identifier">math</span><span class="special">::</span><span class="identifier">policies</span><span class="special">::</span><span class="identifier">rounding_error</span><span class="special">&lt;&gt;</span></code>
+          with the template argument to <code class="computeroutput"><span class="identifier">rounding_error</span></code>
+          one of the <code class="computeroutput"><span class="identifier">error_policy_type</span></code>
+          enumerated values.
+        </p>
+<pre class="programlisting"><span class="identifier">policy</span><span class="special">&lt;...&gt;::</span><span class="identifier">evaluation_error_type</span>
+</pre>
+<p>
+          Specifies how evaluation errors are handled, will be an instance of <code class="computeroutput"><span class="identifier">boost</span><span class="special">::</span><span class="identifier">math</span><span class="special">::</span><span class="identifier">policies</span><span class="special">::</span><span class="identifier">evaluation_error</span><span class="special">&lt;&gt;</span></code>
+          with the template argument to <code class="computeroutput"><span class="identifier">evaluation_error</span></code>
+          one of the <code class="computeroutput"><span class="identifier">error_policy_type</span></code>
+          enumerated values.
+        </p>
+<pre class="programlisting"><span class="identifier">policy</span><span class="special">&lt;...&gt;::</span><span class="identifier">indeterminate_error_type</span>
+</pre>
+<p>
+          Specifies how indeterminate result errors are handled, will be an instance
+          of <code class="computeroutput"><span class="identifier">boost</span><span class="special">::</span><span class="identifier">math</span><span class="special">::</span><span class="identifier">policies</span><span class="special">::</span><span class="identifier">indeterminate_result_error</span><span class="special">&lt;&gt;</span></code>
+          with the template argument to <code class="computeroutput"><span class="identifier">indeterminate_result_error</span></code>
+          one of the <code class="computeroutput"><span class="identifier">error_policy_type</span></code>
+          enumerated values.
+        </p>
+<pre class="programlisting"><span class="identifier">policy</span><span class="special">&lt;...&gt;::</span><span class="identifier">precision_type</span>
+</pre>
+<p>
+          Specifies the internal precision to use in binary digits (uses zero to
+          represent whatever the default precision is). Will be an instance of <code class="computeroutput"><span class="identifier">boost</span><span class="special">::</span><span class="identifier">math</span><span class="special">::</span><span class="identifier">policies</span><span class="special">::</span><span class="identifier">digits2</span><span class="special">&lt;</span><span class="identifier">N</span><span class="special">&gt;</span></code>
+          which in turn inherits from <code class="computeroutput"><span class="identifier">boost</span><span class="special">::</span><span class="identifier">mpl</span><span class="special">::</span><span class="identifier">int_</span><span class="special">&lt;</span><span class="identifier">N</span><span class="special">&gt;</span></code>.
+        </p>
+<pre class="programlisting"><span class="identifier">policy</span><span class="special">&lt;...&gt;::</span><span class="identifier">promote_float_type</span>
+</pre>
+<p>
+          Specifies whether or not to promote <code class="computeroutput"><span class="keyword">float</span></code>
+          arguments to <code class="computeroutput"><span class="keyword">double</span></code> precision
+          internally. Will be an instance of <code class="computeroutput"><span class="identifier">boost</span><span class="special">::</span><span class="identifier">math</span><span class="special">::</span><span class="identifier">policies</span><span class="special">::</span><span class="identifier">promote_float</span><span class="special">&lt;</span><span class="identifier">B</span><span class="special">&gt;</span></code> which in turn inherits from <code class="computeroutput"><span class="identifier">boost</span><span class="special">::</span><span class="identifier">mpl</span><span class="special">::</span><span class="identifier">bool_</span><span class="special">&lt;</span><span class="identifier">B</span><span class="special">&gt;</span></code>.
+        </p>
+<pre class="programlisting"><span class="identifier">policy</span><span class="special">&lt;...&gt;::</span><span class="identifier">promote_double_type</span>
+</pre>
+<p>
+          Specifies whether or not to promote <code class="computeroutput"><span class="keyword">double</span></code>
+          arguments to <code class="computeroutput"><span class="keyword">long</span> <span class="keyword">double</span></code>
+          precision internally. Will be an instance of <code class="computeroutput"><span class="identifier">boost</span><span class="special">::</span><span class="identifier">math</span><span class="special">::</span><span class="identifier">policies</span><span class="special">::</span><span class="identifier">promote_float</span><span class="special">&lt;</span><span class="identifier">B</span><span class="special">&gt;</span></code> which in turn inherits from <code class="computeroutput"><span class="identifier">boost</span><span class="special">::</span><span class="identifier">mpl</span><span class="special">::</span><span class="identifier">bool_</span><span class="special">&lt;</span><span class="identifier">B</span><span class="special">&gt;</span></code>.
+        </p>
+<pre class="programlisting"><span class="identifier">policy</span><span class="special">&lt;...&gt;::</span><span class="identifier">discrete_quantile_type</span>
+</pre>
+<p>
+          Specifies how discrete quantiles are evaluated, will be an instance of
+          <code class="computeroutput"><span class="identifier">boost</span><span class="special">::</span><span class="identifier">math</span><span class="special">::</span><span class="identifier">policies</span><span class="special">::</span><span class="identifier">discrete_quantile</span><span class="special">&lt;&gt;</span></code>
+          instantiated with one of the <code class="computeroutput"><span class="identifier">discrete_quantile_policy_type</span></code>
+          enumerated type.
+        </p>
+<pre class="programlisting"><span class="identifier">policy</span><span class="special">&lt;...&gt;::</span><span class="identifier">assert_undefined_type</span>
+</pre>
+<p>
+          Specifies whether mathematically-undefined properties are asserted as compile-time
+          errors, or treated as runtime errors instead. Will be an instance of <code class="computeroutput"><span class="identifier">boost</span><span class="special">::</span><span class="identifier">math</span><span class="special">::</span><span class="identifier">policies</span><span class="special">::</span><span class="identifier">assert_undefined</span><span class="special">&lt;</span><span class="identifier">B</span><span class="special">&gt;</span></code>
+          which in turn inherits from <code class="computeroutput"><span class="identifier">boost</span><span class="special">::</span><span class="identifier">math</span><span class="special">::</span><span class="identifier">mpl</span><span class="special">::</span><span class="identifier">bool_</span><span class="special">&lt;</span><span class="identifier">B</span><span class="special">&gt;</span></code>.
+        </p>
+<pre class="programlisting"><span class="keyword">template</span> <span class="special">&lt;...</span><span class="identifier">argument</span> <span class="identifier">list</span><span class="special">...&gt;</span>
+<span class="keyword">typename</span> <span class="identifier">normalise</span><span class="special">&lt;</span><span class="identifier">policy</span><span class="special">&lt;&gt;,</span> <span class="identifier">A1</span><span class="special">&gt;::</span><span class="identifier">type</span> <span class="identifier">make_policy</span><span class="special">(...</span><span class="identifier">argument</span> <span class="identifier">list</span><span class="special">..);</span>
+</pre>
+<p>
+          <code class="computeroutput"><span class="identifier">make_policy</span></code> is a helper
+          function that converts a list of policies into a normalised <code class="computeroutput"><span class="identifier">policy</span></code> class.
+        </p>
+<pre class="programlisting"><span class="keyword">template</span> <span class="special">&lt;</span><span class="keyword">class</span> <span class="identifier">Policy</span><span class="special">,</span> 
+          <span class="keyword">class</span> <span class="identifier">A1</span> <span class="special">=</span> <span class="identifier">default_policy</span><span class="special">,</span> 
+          <span class="keyword">class</span> <span class="identifier">A2</span> <span class="special">=</span> <span class="identifier">default_policy</span><span class="special">,</span> 
+          <span class="keyword">class</span> <span class="identifier">A3</span> <span class="special">=</span> <span class="identifier">default_policy</span><span class="special">,</span>
+          <span class="keyword">class</span> <span class="identifier">A4</span> <span class="special">=</span> <span class="identifier">default_policy</span><span class="special">,</span>
+          <span class="keyword">class</span> <span class="identifier">A5</span> <span class="special">=</span> <span class="identifier">default_policy</span><span class="special">,</span>
+          <span class="keyword">class</span> <span class="identifier">A6</span> <span class="special">=</span> <span class="identifier">default_policy</span><span class="special">,</span>
+          <span class="keyword">class</span> <span class="identifier">A7</span> <span class="special">=</span> <span class="identifier">default_policy</span><span class="special">,</span>
+          <span class="keyword">class</span> <span class="identifier">A8</span> <span class="special">=</span> <span class="identifier">default_policy</span><span class="special">,</span>
+          <span class="keyword">class</span> <span class="identifier">A9</span> <span class="special">=</span> <span class="identifier">default_policy</span><span class="special">,</span>
+          <span class="keyword">class</span> <span class="identifier">A10</span> <span class="special">=</span> <span class="identifier">default_policy</span><span class="special">,</span>
+          <span class="keyword">class</span> <span class="identifier">A11</span> <span class="special">=</span> <span class="identifier">default_policy</span><span class="special">,</span>
+          <span class="keyword">class</span> <span class="identifier">A12</span> <span class="special">=</span> <span class="identifier">default_policy</span><span class="special">,</span>
+          <span class="keyword">class</span> <span class="identifier">A13</span> <span class="special">=</span> <span class="identifier">default_policy</span><span class="special">&gt;</span>
+<span class="keyword">struct</span> <span class="identifier">normalise</span>
+<span class="special">{</span>
+   <span class="keyword">typedef</span> computed-from-template-arguments <span class="identifier">type</span><span class="special">;</span>
+<span class="special">};</span>
+</pre>
+<p>
+          The <code class="computeroutput"><span class="identifier">normalise</span></code> class template
+          converts one instantiation of the <code class="computeroutput"><span class="identifier">policy</span></code>
+          class into a normalised form. This is used internally to reduce code bloat:
+          so that instantiating a special function on <code class="computeroutput"><span class="identifier">policy</span><span class="special">&lt;</span><span class="identifier">A</span><span class="special">,</span><span class="identifier">B</span><span class="special">&gt;</span></code>
+          or <code class="computeroutput"><span class="identifier">policy</span><span class="special">&lt;</span><span class="identifier">B</span><span class="special">,</span><span class="identifier">A</span><span class="special">&gt;</span></code> actually both generate the same code
+          internally.
+        </p>
+<p>
+          Further more, <code class="computeroutput"><span class="identifier">normalise</span></code>
+          can be used to combine a policy with one or more policies: for example
+          many of the special functions will use this to set policies which they
+          don't make use of to their default values, before forwarding to the actual
+          implementation. In this way code bloat is reduced, since the actual implementation
+          depends only on the policy types that they actually use.
+        </p>
+</div>
+<table xmlns:rev="http://www.cs.rpi.edu/~gregod/boost/tools/doc/revision" width="100%"><tr>
+<td align="left"></td>
+<td align="right"><div class="copyright-footer">Copyright © 2006 , 2007, 2008 John Maddock, Paul A. Bristow, Hubert
+      Holin, Xiaogang Zhang, Bruno Lalande and Gautam Sewani<p>
+        Distributed under the Boost Software License, Version 1.0. (See accompanying
+        file LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_0.txt)
+      </p>
+</div></td>
+</tr></table>
+<hr>
+<div class="spirit-nav">
+<a accesskey="p" href="namespace_pol.html"><img src="../../../../../doc/html/images/prev.png" alt="Prev"></a><a accesskey="u" href="../pol_ref.html"><img src="../../../../../doc/html/images/up.png" alt="Up"></a><a accesskey="h" href="../../../index.html"><img src="../../../../../doc/html/images/home.png" alt="Home"></a><a accesskey="n" href="../../perf.html"><img src="../../../../../doc/html/images/next.png" alt="Next"></a>
+</div>
+</body>
+</html>

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+++ sandbox/tools/auto_index/example/math/doc/sf_and_dist/html/math_toolkit/policy/pol_ref/policy_defaults.html	2008-11-28 05:25:28 EST (Fri, 28 Nov 2008)
@@ -0,0 +1,259 @@
+<html>
+<head>
+<meta http-equiv="Content-Type" content="text/html; charset=ISO-8859-1">
+<title>Using macros to Change the Policy Defaults</title>
+<link rel="stylesheet" href="../../../boostbook.css" type="text/css">
+<meta name="generator" content="DocBook XSL Stylesheets Vsnapshot_8125">
+<link rel="home" href="../../../index.html" title="Math Toolkit">
+<link rel="up" href="../pol_ref.html" title="Policy Reference">
+<link rel="prev" href="iteration_pol.html" title="Iteration Limits Policies">
+<link rel="next" href="namespace_pol.html" title="Setting Polices at Namespace Scope">
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+</div>
+<div class="section" lang="en">
+<div class="titlepage"><div><div><h4 class="title">
+<a name="math_toolkit.policy.pol_ref.policy_defaults"></a><a class="link" href="policy_defaults.html" title="Using macros to Change the Policy Defaults"> Using
+        macros to Change the Policy Defaults</a>
+</h4></div></div></div>
+<p>
+          You can use the various macros below to change any (or all) of the policies.
+        </p>
+<p>
+          You can make a local change by placing a macro definition <span class="bold"><strong>before</strong></span>
+          a function or distribution #include.
+        </p>
+<div class="caution"><table border="0" summary="Caution">
+<tr>
+<td rowspan="2" align="center" valign="top" width="25"><img alt="[Caution]" src="../../../../../doc/html/images/caution.png"></td>
+<th align="left">Caution</th>
+</tr>
+<tr><td align="left" valign="top"><p>
+            There is a danger of One-Definition-Rule violations if you add ad-hock
+            macros to more than one source files: these must be set the same in
+            <span class="bold"><strong>every translation unit</strong></span>.
+          </p></td></tr>
+</table></div>
+<div class="caution"><table border="0" summary="Caution">
+<tr>
+<td rowspan="2" align="center" valign="top" width="25"><img alt="[Caution]" src="../../../../../doc/html/images/caution.png"></td>
+<th align="left">Caution</th>
+</tr>
+<tr><td align="left" valign="top"><p>
+            If you place it after the #include it will have no effect, (and it will
+            affect only any other following #includes). This is probably not what
+            you intend!
+          </p></td></tr>
+</table></div>
+<p>
+          If you want to alter the defaults for any or all of the policies for <span class="bold"><strong>all</strong></span> functions and distributions, installation-wide,
+          then you can do so by defining various macros in boost/math/tools/user.hpp.
+        </p>
+<a name="math_toolkit.policy.pol_ref.policy_defaults.boost_math_domain_error_policy"></a><h6>
+<a name="id898263"></a>
+          <a class="link" href="policy_defaults.html#math_toolkit.policy.pol_ref.policy_defaults.boost_math_domain_error_policy">BOOST_MATH_DOMAIN_ERROR_POLICY</a>
+        </h6>
+<p>
+          Defines what happens when a domain error occurs, if not defined then defaults
+          to <code class="computeroutput"><span class="identifier">throw_on_error</span></code>, but
+          can be set to any of the enumerated actions for error handing: <code class="computeroutput"><span class="identifier">throw_on_error</span></code>, <code class="computeroutput"><span class="identifier">errno_on_error</span></code>,
+          <code class="computeroutput"><span class="identifier">ignore_error</span></code> or <code class="computeroutput"><span class="identifier">user_error</span></code>.
+        </p>
+<a name="math_toolkit.policy.pol_ref.policy_defaults.boost_math_pole_error_policy"></a><h6>
+<a name="id898359"></a>
+          <a class="link" href="policy_defaults.html#math_toolkit.policy.pol_ref.policy_defaults.boost_math_pole_error_policy">BOOST_MATH_POLE_ERROR_POLICY</a>
+        </h6>
+<p>
+          Defines what happens when a pole error occurs, if not defined then defaults
+          to <code class="computeroutput"><span class="identifier">throw_on_error</span></code>, but
+          can be set to any of the enumerated actions for error handing: <code class="computeroutput"><span class="identifier">throw_on_error</span></code>, <code class="computeroutput"><span class="identifier">errno_on_error</span></code>,
+          <code class="computeroutput"><span class="identifier">ignore_error</span></code> or <code class="computeroutput"><span class="identifier">user_error</span></code>.
+        </p>
+<a name="math_toolkit.policy.pol_ref.policy_defaults.boost_math_overflow_error_policy"></a><h6>
+<a name="id898455"></a>
+          <a class="link" href="policy_defaults.html#math_toolkit.policy.pol_ref.policy_defaults.boost_math_overflow_error_policy">BOOST_MATH_OVERFLOW_ERROR_POLICY</a>
+        </h6>
+<p>
+          Defines what happens when an overflow error occurs, if not defined then
+          defaults to <code class="computeroutput"><span class="identifier">throw_on_error</span></code>,
+          but can be set to any of the enumerated actions for error handing: <code class="computeroutput"><span class="identifier">throw_on_error</span></code>, <code class="computeroutput"><span class="identifier">errno_on_error</span></code>,
+          <code class="computeroutput"><span class="identifier">ignore_error</span></code> or <code class="computeroutput"><span class="identifier">user_error</span></code>.
+        </p>
+<a name="math_toolkit.policy.pol_ref.policy_defaults.boost_math_rounding_error_policy"></a><h6>
+<a name="id898551"></a>
+          <a class="link" href="policy_defaults.html#math_toolkit.policy.pol_ref.policy_defaults.boost_math_rounding_error_policy">BOOST_MATH_ROUNDING_ERROR_POLICY</a>
+        </h6>
+<p>
+          Defines what happens when a rounding error occurs, if not defined then
+          defaults to <code class="computeroutput"><span class="identifier">throw_on_error</span></code>,
+          but can be set to any of the enumerated actions for error handing: <code class="computeroutput"><span class="identifier">throw_on_error</span></code>, <code class="computeroutput"><span class="identifier">errno_on_error</span></code>,
+          <code class="computeroutput"><span class="identifier">ignore_error</span></code> or <code class="computeroutput"><span class="identifier">user_error</span></code>.
+        </p>
+<a name="math_toolkit.policy.pol_ref.policy_defaults.boost_math_evaluation_error_policy"></a><h6>
+<a name="id898647"></a>
+          <a class="link" href="policy_defaults.html#math_toolkit.policy.pol_ref.policy_defaults.boost_math_evaluation_error_policy">BOOST_MATH_EVALUATION_ERROR_POLICY</a>
+        </h6>
+<p>
+          Defines what happens when an internal evaluation error occurs, if not defined
+          then defaults to <code class="computeroutput"><span class="identifier">throw_on_error</span></code>,
+          but can be set to any of the enumerated actions for error handing: <code class="computeroutput"><span class="identifier">throw_on_error</span></code>, <code class="computeroutput"><span class="identifier">errno_on_error</span></code>,
+          <code class="computeroutput"><span class="identifier">ignore_error</span></code> or <code class="computeroutput"><span class="identifier">user_error</span></code>.
+        </p>
+<a name="math_toolkit.policy.pol_ref.policy_defaults.boost_math_underflow_error_policy"></a><h6>
+<a name="id898744"></a>
+          <a class="link" href="policy_defaults.html#math_toolkit.policy.pol_ref.policy_defaults.boost_math_underflow_error_policy">BOOST_MATH_UNDERFLOW_ERROR_POLICY</a>
+        </h6>
+<p>
+          Defines what happens when an overflow error occurs, if not defined then
+          defaults to <code class="computeroutput"><span class="identifier">ignore_error</span></code>,
+          but can be set to any of the enumerated actions for error handing: <code class="computeroutput"><span class="identifier">throw_on_error</span></code>, <code class="computeroutput"><span class="identifier">errno_on_error</span></code>,
+          <code class="computeroutput"><span class="identifier">ignore_error</span></code> or <code class="computeroutput"><span class="identifier">user_error</span></code>.
+        </p>
+<a name="math_toolkit.policy.pol_ref.policy_defaults.boost_math_denorm_error_policy"></a><h6>
+<a name="id898841"></a>
+          <a class="link" href="policy_defaults.html#math_toolkit.policy.pol_ref.policy_defaults.boost_math_denorm_error_policy">BOOST_MATH_DENORM_ERROR_POLICY</a>
+        </h6>
+<p>
+          Defines what happens when a denormalisation error occurs, if not defined
+          then defaults to <code class="computeroutput"><span class="identifier">ignore_error</span></code>,
+          but can be set to any of the enumerated actions for error handing: <code class="computeroutput"><span class="identifier">throw_on_error</span></code>, <code class="computeroutput"><span class="identifier">errno_on_error</span></code>,
+          <code class="computeroutput"><span class="identifier">ignore_error</span></code> or <code class="computeroutput"><span class="identifier">user_error</span></code>.
+        </p>
+<a name="math_toolkit.policy.pol_ref.policy_defaults.boost_math_indeterminate_result_error_policy"></a><h6>
+<a name="id898937"></a>
+          <a class="link" href="policy_defaults.html#math_toolkit.policy.pol_ref.policy_defaults.boost_math_indeterminate_result_error_policy">BOOST_MATH_INDETERMINATE_RESULT_ERROR_POLICY</a>
+        </h6>
+<p>
+          Defines what happens when the result is indeterminate, but where there
+          is none the less a convention for the result. If not defined then defaults
+          to <code class="computeroutput"><span class="identifier">ignore_error</span></code>, but can
+          be set to any of the enumerated actions for error handing: <code class="computeroutput"><span class="identifier">throw_on_error</span></code>, <code class="computeroutput"><span class="identifier">errno_on_error</span></code>,
+          <code class="computeroutput"><span class="identifier">ignore_error</span></code> or <code class="computeroutput"><span class="identifier">user_error</span></code>.
+        </p>
+<a name="math_toolkit.policy.pol_ref.policy_defaults.boost_math_digits10_policy"></a><h6>
+<a name="id899037"></a>
+          <a class="link" href="policy_defaults.html#math_toolkit.policy.pol_ref.policy_defaults.boost_math_digits10_policy">BOOST_MATH_DIGITS10_POLICY</a>
+        </h6>
+<p>
+          Defines how many decimal digits to use in internal computations: defaults
+          to <code class="computeroutput"><span class="number">0</span></code> - meaning use all available
+          digits - but can be set to some other decimal value. Since setting this
+          is likely to have a substantial impact on accuracy, it's not generally
+          recommended that you change this from the default.
+        </p>
+<a name="math_toolkit.policy.pol_ref.policy_defaults.boost_math_promote_float_policy"></a><h6>
+<a name="id899092"></a>
+          <a class="link" href="policy_defaults.html#math_toolkit.policy.pol_ref.policy_defaults.boost_math_promote_float_policy">BOOST_MATH_PROMOTE_FLOAT_POLICY</a>
+        </h6>
+<p>
+          Determines whether <code class="computeroutput"><span class="keyword">float</span></code> types
+          get promoted to <code class="computeroutput"><span class="keyword">double</span></code> internally
+          to ensure maximum precision in the result, defaults to <code class="computeroutput"><span class="keyword">true</span></code>,
+          but can be set to <code class="computeroutput"><span class="keyword">false</span></code> to
+          turn promotion of <code class="computeroutput"><span class="keyword">float</span></code>'s
+          off.
+        </p>
+<a name="math_toolkit.policy.pol_ref.policy_defaults.boost_math_promote_double_policy"></a><h6>
+<a name="id899187"></a>
+          <a class="link" href="policy_defaults.html#math_toolkit.policy.pol_ref.policy_defaults.boost_math_promote_double_policy">BOOST_MATH_PROMOTE_DOUBLE_POLICY</a>
+        </h6>
+<p>
+          Determines whether <code class="computeroutput"><span class="keyword">double</span></code>
+          types get promoted to <code class="computeroutput"><span class="keyword">long</span> <span class="keyword">double</span></code> internally to ensure maximum precision
+          in the result, defaults to <code class="computeroutput"><span class="keyword">true</span></code>,
+          but can be set to <code class="computeroutput"><span class="keyword">false</span></code> to
+          turn promotion of <code class="computeroutput"><span class="keyword">double</span></code>'s
+          off.
+        </p>
+<a name="math_toolkit.policy.pol_ref.policy_defaults.boost_math_discrete_quantile_policy"></a><h6>
+<a name="id899289"></a>
+          <a class="link" href="policy_defaults.html#math_toolkit.policy.pol_ref.policy_defaults.boost_math_discrete_quantile_policy">BOOST_MATH_DISCRETE_QUANTILE_POLICY</a>
+        </h6>
+<p>
+          Determines how discrete quantiles return their results: either as an integer,
+          or as a real value, can be set to one of the enumerated values: <code class="computeroutput"><span class="identifier">real</span></code>, <code class="computeroutput"><span class="identifier">integer_round_outwards</span></code>,
+          <code class="computeroutput"><span class="identifier">integer_round_inwards</span></code>,
+          <code class="computeroutput"><span class="identifier">integer_round_down</span></code>, <code class="computeroutput"><span class="identifier">integer_round_up</span></code>, <code class="computeroutput"><span class="identifier">integer_round_nearest</span></code>.
+          Defaults to <code class="computeroutput"><span class="identifier">integer_round_outwards</span></code>.
+        </p>
+<a name="math_toolkit.policy.pol_ref.policy_defaults.boost_math_assert_undefined_policy"></a><h6>
+<a name="id899409"></a>
+          <a class="link" href="policy_defaults.html#math_toolkit.policy.pol_ref.policy_defaults.boost_math_assert_undefined_policy">BOOST_MATH_ASSERT_UNDEFINED_POLICY</a>
+        </h6>
+<p>
+          Determines whether functions that are mathematically undefined for a specific
+          distribution compile or raise a static (i.e. compile-time) assertion. Defaults
+          to <code class="computeroutput"><span class="keyword">true</span></code>: meaning that any
+          mathematically undefined function will not compile. When set to <code class="computeroutput"><span class="keyword">false</span></code> then the function will compile but
+          return the result of a domain error: this can be useful for some generic
+          code, that needs to work with all distributions and determine at runtime
+          whether or not a particular property is well defined.
+        </p>
+<a name="math_toolkit.policy.pol_ref.policy_defaults.boost_math_max_series_iteration_policy"></a><h6>
+<a name="id899483"></a>
+          <a class="link" href="policy_defaults.html#math_toolkit.policy.pol_ref.policy_defaults.boost_math_max_series_iteration_policy">BOOST_MATH_MAX_SERIES_ITERATION_POLICY</a>
+        </h6>
+<p>
+          Determines how many series iterations a special function is permitted to
+          perform before it gives up and returns an <a class="link" href="../../main_overview/error_handling.html#evaluation_error">evaluation_error</a>:
+          Defaults to 1000000.
+        </p>
+<a name="math_toolkit.policy.pol_ref.policy_defaults.boost_math_max_root_iteration_policy"></a><h6>
+<a name="id899528"></a>
+          <a class="link" href="policy_defaults.html#math_toolkit.policy.pol_ref.policy_defaults.boost_math_max_root_iteration_policy">BOOST_MATH_MAX_ROOT_ITERATION_POLICY</a>
+        </h6>
+<p>
+          Determines how many root-finding iterations a special function is permitted
+          to perform before it gives up and returns an <a class="link" href="../../main_overview/error_handling.html#evaluation_error">evaluation_error</a>:
+          Defaults to 200.
+        </p>
+<a name="math_toolkit.policy.pol_ref.policy_defaults.example"></a><h6>
+<a name="id899571"></a>
+          <a class="link" href="policy_defaults.html#math_toolkit.policy.pol_ref.policy_defaults.example">Example</a>
+        </h6>
+<p>
+          Suppose we want overflow errors to set <code class="computeroutput"><span class="special">::</span><span class="identifier">errno</span></code> and return an infinity, discrete
+          quantiles to return a real-valued result (rather than round to integer),
+          and for mathematically undefined functions to compile, but return a domain
+          error. Then we could add the following to boost/math/tools/user.hpp:
+        </p>
+<pre class="programlisting"><span class="preprocessor">#define</span> <span class="identifier">BOOST_MATH_OVERFLOW_ERROR_POLICY</span> <span class="identifier">errno_on_error</span>
+<span class="preprocessor">#define</span> <span class="identifier">BOOST_MATH_DISCRETE_QUANTILE_POLICY</span> <span class="identifier">real</span>
+<span class="preprocessor">#define</span> <span class="identifier">BOOST_MATH_ASSERT_UNDEFINED_POLICY</span> <span class="keyword">false</span>
+</pre>
+<p>
+          or we could place these definitions <span class="bold"><strong>before</strong></span>
+        </p>
+<pre class="programlisting"><span class="preprocessor">#include</span> <span class="special">&lt;</span><span class="identifier">boost</span><span class="special">/</span><span class="identifier">math</span><span class="special">/</span><span class="identifier">distributions</span><span class="special">/</span><span class="identifier">normal</span><span class="special">.</span><span class="identifier">hpp</span><span class="special">&gt;</span>
+  <span class="keyword">using</span> <span class="identifier">boost</span><span class="special">::</span><span class="identifier">math</span><span class="special">::</span><span class="identifier">normal_distribution</span><span class="special">;</span>
+</pre>
+<p>
+          in a source .cpp file.
+        </p>
+</div>
+<table xmlns:rev="http://www.cs.rpi.edu/~gregod/boost/tools/doc/revision" width="100%"><tr>
+<td align="left"></td>
+<td align="right"><div class="copyright-footer">Copyright © 2006 , 2007, 2008 John Maddock, Paul A. Bristow, Hubert
+      Holin, Xiaogang Zhang, Bruno Lalande and Gautam Sewani<p>
+        Distributed under the Boost Software License, Version 1.0. (See accompanying
+        file LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_0.txt)
+      </p>
+</div></td>
+</tr></table>
+<hr>
+<div class="spirit-nav">
+<a accesskey="p" href="iteration_pol.html"><img src="../../../../../doc/html/images/prev.png" alt="Prev"></a><a accesskey="u" href="../pol_ref.html"><img src="../../../../../doc/html/images/up.png" alt="Up"></a><a accesskey="h" href="../../../index.html"><img src="../../../../../doc/html/images/home.png" alt="Home"></a><a accesskey="n" href="namespace_pol.html"><img src="../../../../../doc/html/images/next.png" alt="Next"></a>
+</div>
+</body>
+</html>

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==============================================================================
--- (empty file)
+++ sandbox/tools/auto_index/example/math/doc/sf_and_dist/html/math_toolkit/policy/pol_ref/precision_pol.html	2008-11-28 05:25:28 EST (Fri, 28 Nov 2008)
@@ -0,0 +1,137 @@
+<html>
+<head>
+<meta http-equiv="Content-Type" content="text/html; charset=ISO-8859-1">
+<title>Precision Policies</title>
+<link rel="stylesheet" href="../../../boostbook.css" type="text/css">
+<meta name="generator" content="DocBook XSL Stylesheets Vsnapshot_8125">
+<link rel="home" href="../../../index.html" title="Math Toolkit">
+<link rel="up" href="../pol_ref.html" title="Policy Reference">
+<link rel="prev" href="discrete_quant_ref.html" title="Discrete Quantile Policies">
+<link rel="next" href="iteration_pol.html" title="Iteration Limits Policies">
+</head>
+<body bgcolor="white" text="black" link="#0000FF" vlink="#840084" alink="#0000FF">
+<table cellpadding="2" width="100%"><tr>
+<td valign="top"><img alt="Boost C++ Libraries" width="277" height="86" src="../../../../../boost.png"></td>
+<td align="center">Home</td>
+<td align="center">Libraries</td>
+<td align="center">People</td>
+<td align="center">FAQ</td>
+<td align="center">More</td>
+</tr></table>
+<hr>
+<div class="spirit-nav">
+<a accesskey="p" href="discrete_quant_ref.html"><img src="../../../../../doc/html/images/prev.png" alt="Prev"></a><a accesskey="u" href="../pol_ref.html"><img src="../../../../../doc/html/images/up.png" alt="Up"></a><a accesskey="h" href="../../../index.html"><img src="../../../../../doc/html/images/home.png" alt="Home"></a><a accesskey="n" href="iteration_pol.html"><img src="../../../../../doc/html/images/next.png" alt="Next"></a>
+</div>
+<div class="section" lang="en">
+<div class="titlepage"><div><div><h4 class="title">
+<a name="math_toolkit.policy.pol_ref.precision_pol"></a><a class="link" href="precision_pol.html" title="Precision Policies"> Precision
+        Policies</a>
+</h4></div></div></div>
+<p>
+          There are two equivalent policies that effect the <span class="emphasis"><em>working precision</em></span>
+          used to calculate results, these policies both default to 0 - meaning calculate
+          to the maximum precision available in the type being used - but can be
+          set to other values to cause lower levels of precision to be used.
+        </p>
+<pre class="programlisting"><span class="keyword">namespace</span> <span class="identifier">boost</span><span class="special">{</span> <span class="keyword">namespace</span> <span class="identifier">math</span><span class="special">{</span> <span class="keyword">namespace</span> <span class="identifier">policies</span><span class="special">{</span>
+
+<span class="keyword">template</span> <span class="special">&lt;</span><span class="keyword">int</span> <span class="identifier">N</span><span class="special">&gt;</span>
+<span class="identifier">digits10</span><span class="special">;</span>
+
+<span class="keyword">template</span> <span class="special">&lt;</span><span class="keyword">int</span> <span class="identifier">N</span><span class="special">&gt;</span>
+<span class="identifier">digits2</span><span class="special">;</span>
+
+<span class="special">}}}</span> <span class="comment">// namespaces
+</span></pre>
+<p>
+          As you would expect, <span class="emphasis"><em>digits10</em></span> specifies the number
+          of decimal digits to use, and <span class="emphasis"><em>digits2</em></span> the number of
+          binary digits. Internally, whichever is used, the precision is always converted
+          to <span class="emphasis"><em>binary digits</em></span>.
+        </p>
+<p>
+          These policies are specified at compile-time, because many of the special
+          functions use compile-time-dispatch to select which approximation to use
+          based on the precision requested and the numeric type being used.
+        </p>
+<p>
+          For example we could calculate <code class="computeroutput"><span class="identifier">tgamma</span></code>
+          to approximately 5 decimal digits using:
+        </p>
+<p>
+          </p>
+<p>
+            
+</p>
+<pre class="programlisting"><span class="preprocessor">#include</span> <span class="special">&lt;</span><span class="identifier">boost</span><span class="special">/</span><span class="identifier">math</span><span class="special">/</span><span class="identifier">special_functions</span><span class="special">/</span><span class="identifier">gamma</span><span class="special">.</span><span class="identifier">hpp</span><span class="special">&gt;</span>
+
+<span class="keyword">using</span> <span class="keyword">namespace</span> <span class="identifier">boost</span><span class="special">::</span><span class="identifier">math</span><span class="special">;</span>
+<span class="keyword">using</span> <span class="keyword">namespace</span> <span class="identifier">boost</span><span class="special">::</span><span class="identifier">math</span><span class="special">::</span><span class="identifier">policies</span><span class="special">;</span>
+
+<span class="keyword">typedef</span> <span class="identifier">policy</span><span class="special">&lt;</span><span class="identifier">digits10</span><span class="special">&lt;</span><span class="number">5</span><span class="special">&gt;</span> <span class="special">&gt;</span> <span class="identifier">pol</span><span class="special">;</span>
+
+<span class="keyword">double</span> <span class="identifier">t</span> <span class="special">=</span> <span class="identifier">tgamma</span><span class="special">(</span><span class="number">12</span><span class="special">,</span> <span class="identifier">pol</span><span class="special">());</span>
+
+</pre>
+<p>
+          </p>
+<p>
+        </p>
+<p>
+          Or again using <span class="emphasis"><em>make_policy</em></span>:
+        </p>
+<p>
+          </p>
+<p>
+            
+</p>
+<pre class="programlisting"><span class="preprocessor">#include</span> <span class="special">&lt;</span><span class="identifier">boost</span><span class="special">/</span><span class="identifier">math</span><span class="special">/</span><span class="identifier">special_functions</span><span class="special">/</span><span class="identifier">gamma</span><span class="special">.</span><span class="identifier">hpp</span><span class="special">&gt;</span>
+
+<span class="keyword">using</span> <span class="keyword">namespace</span> <span class="identifier">boost</span><span class="special">::</span><span class="identifier">math</span><span class="special">;</span>
+<span class="keyword">using</span> <span class="keyword">namespace</span> <span class="identifier">boost</span><span class="special">::</span><span class="identifier">math</span><span class="special">::</span><span class="identifier">policies</span><span class="special">;</span>
+
+<span class="keyword">double</span> <span class="identifier">t</span> <span class="special">=</span> <span class="identifier">tgamma</span><span class="special">(</span><span class="number">12</span><span class="special">,</span> <span class="identifier">policy</span><span class="special">&lt;</span><span class="identifier">digits10</span><span class="special">&lt;</span><span class="number">5</span><span class="special">&gt;</span> <span class="special">&gt;());</span>
+
+</pre>
+<p>
+          </p>
+<p>
+        </p>
+<p>
+          And for a quantile of a distribution to approximately 25-bit precision:
+        </p>
+<p>
+          </p>
+<p>
+            
+</p>
+<pre class="programlisting"><span class="preprocessor">#include</span> <span class="special">&lt;</span><span class="identifier">boost</span><span class="special">/</span><span class="identifier">math</span><span class="special">/</span><span class="identifier">distributions</span><span class="special">/</span><span class="identifier">normal</span><span class="special">.</span><span class="identifier">hpp</span><span class="special">&gt;</span>
+
+<span class="keyword">using</span> <span class="keyword">namespace</span> <span class="identifier">boost</span><span class="special">::</span><span class="identifier">math</span><span class="special">;</span>
+<span class="keyword">using</span> <span class="keyword">namespace</span> <span class="identifier">boost</span><span class="special">::</span><span class="identifier">math</span><span class="special">::</span><span class="identifier">policies</span><span class="special">;</span>
+
+<span class="keyword">double</span> <span class="identifier">q</span> <span class="special">=</span> <span class="identifier">quantile</span><span class="special">(</span>
+      <span class="identifier">normal_distribution</span><span class="special">&lt;</span><span class="keyword">double</span><span class="special">,</span> <span class="identifier">policy</span><span class="special">&lt;</span><span class="identifier">digits2</span><span class="special">&lt;</span><span class="number">25</span><span class="special">&gt;</span> <span class="special">&gt;</span> <span class="special">&gt;(),</span> 
+      <span class="number">0.05</span><span class="special">);</span>
+
+</pre>
+<p>
+          </p>
+<p>
+        </p>
+</div>
+<table xmlns:rev="http://www.cs.rpi.edu/~gregod/boost/tools/doc/revision" width="100%"><tr>
+<td align="left"></td>
+<td align="right"><div class="copyright-footer">Copyright © 2006 , 2007, 2008 John Maddock, Paul A. Bristow, Hubert
+      Holin, Xiaogang Zhang, Bruno Lalande and Gautam Sewani<p>
+        Distributed under the Boost Software License, Version 1.0. (See accompanying
+        file LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_0.txt)
+      </p>
+</div></td>
+</tr></table>
+<hr>
+<div class="spirit-nav">
+<a accesskey="p" href="discrete_quant_ref.html"><img src="../../../../../doc/html/images/prev.png" alt="Prev"></a><a accesskey="u" href="../pol_ref.html"><img src="../../../../../doc/html/images/up.png" alt="Up"></a><a accesskey="h" href="../../../index.html"><img src="../../../../../doc/html/images/home.png" alt="Home"></a><a accesskey="n" href="iteration_pol.html"><img src="../../../../../doc/html/images/next.png" alt="Next"></a>
+</div>
+</body>
+</html>

Added: sandbox/tools/auto_index/example/math/doc/sf_and_dist/html/math_toolkit/policy/pol_tutorial.html
==============================================================================
--- (empty file)
+++ sandbox/tools/auto_index/example/math/doc/sf_and_dist/html/math_toolkit/policy/pol_tutorial.html	2008-11-28 05:25:28 EST (Fri, 28 Nov 2008)
@@ -0,0 +1,64 @@
+<html>
+<head>
+<meta http-equiv="Content-Type" content="text/html; charset=ISO-8859-1">
+<title>Policy Tutorial</title>
+<link rel="stylesheet" href="../../boostbook.css" type="text/css">
+<meta name="generator" content="DocBook XSL Stylesheets Vsnapshot_8125">
+<link rel="home" href="../../index.html" title="Math Toolkit">
+<link rel="up" href="../policy.html" title="Policies">
+<link rel="prev" href="pol_overview.html" title="Policy Overview">
+<link rel="next" href="pol_tutorial/what_is_a_policy.html" title="So Just What is a Policy Anyway?">
+</head>
+<body bgcolor="white" text="black" link="#0000FF" vlink="#840084" alink="#0000FF">
+<table cellpadding="2" width="100%"><tr>
+<td valign="top"><img alt="Boost C++ Libraries" width="277" height="86" src="../../../../boost.png"></td>
+<td align="center">Home</td>
+<td align="center">Libraries</td>
+<td align="center">People</td>
+<td align="center">FAQ</td>
+<td align="center">More</td>
+</tr></table>
+<hr>
+<div class="spirit-nav">
+<a accesskey="p" href="pol_overview.html"><img src="../../../../doc/html/images/prev.png" alt="Prev"></a><a accesskey="u" href="../policy.html"><img src="../../../../doc/html/images/up.png" alt="Up"></a><a accesskey="h" href="../../index.html"><img src="../../../../doc/html/images/home.png" alt="Home"></a><a accesskey="n" href="pol_tutorial/what_is_a_policy.html"><img src="../../../../doc/html/images/next.png" alt="Next"></a>
+</div>
+<div class="section" lang="en">
+<div class="titlepage"><div><div><h3 class="title">
+<a name="math_toolkit.policy.pol_tutorial"></a><a class="link" href="pol_tutorial.html" title="Policy Tutorial"> Policy Tutorial</a>
+</h3></div></div></div>
+<div class="toc"><dl>
+<dt><span class="section"><a href="pol_tutorial/what_is_a_policy.html">
+        So Just What is a Policy Anyway?</a></span></dt>
+<dt><span class="section"><a href="pol_tutorial/policy_tut_defaults.html">
+        Policies Have Sensible Defaults</a></span></dt>
+<dt><span class="section"><a href="pol_tutorial/policy_usage.html"> So
+        How are Policies Used Anyway?</a></span></dt>
+<dt><span class="section"><a href="pol_tutorial/changing_policy_defaults.html">
+        Changing the Policy Defaults</a></span></dt>
+<dt><span class="section"><a href="pol_tutorial/ad_hoc_dist_policies.html">
+        Setting Policies for Distributions on an Ad Hoc Basis</a></span></dt>
+<dt><span class="section"><a href="pol_tutorial/ad_hoc_sf_policies.html">
+        Changing the Policy on an Ad Hoc Basis for the Special Functions</a></span></dt>
+<dt><span class="section"><a href="pol_tutorial/namespace_policies.html">
+        Setting Policies at Namespace or Translation Unit Scope</a></span></dt>
+<dt><span class="section"><a href="pol_tutorial/user_def_err_pol.html">
+        Calling User Defined Error Handlers</a></span></dt>
+<dt><span class="section"><a href="pol_tutorial/understand_dis_quant.html">
+        Understanding Quantiles of Discrete Distributions</a></span></dt>
+</dl></div>
+</div>
+<table xmlns:rev="http://www.cs.rpi.edu/~gregod/boost/tools/doc/revision" width="100%"><tr>
+<td align="left"></td>
+<td align="right"><div class="copyright-footer">Copyright © 2006 , 2007, 2008 John Maddock, Paul A. Bristow, Hubert
+      Holin, Xiaogang Zhang, Bruno Lalande and Gautam Sewani<p>
+        Distributed under the Boost Software License, Version 1.0. (See accompanying
+        file LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_0.txt)
+      </p>
+</div></td>
+</tr></table>
+<hr>
+<div class="spirit-nav">
+<a accesskey="p" href="pol_overview.html"><img src="../../../../doc/html/images/prev.png" alt="Prev"></a><a accesskey="u" href="../policy.html"><img src="../../../../doc/html/images/up.png" alt="Up"></a><a accesskey="h" href="../../index.html"><img src="../../../../doc/html/images/home.png" alt="Home"></a><a accesskey="n" href="pol_tutorial/what_is_a_policy.html"><img src="../../../../doc/html/images/next.png" alt="Next"></a>
+</div>
+</body>
+</html>

Added: sandbox/tools/auto_index/example/math/doc/sf_and_dist/html/math_toolkit/policy/pol_tutorial/ad_hoc_dist_policies.html
==============================================================================
--- (empty file)
+++ sandbox/tools/auto_index/example/math/doc/sf_and_dist/html/math_toolkit/policy/pol_tutorial/ad_hoc_dist_policies.html	2008-11-28 05:25:28 EST (Fri, 28 Nov 2008)
@@ -0,0 +1,108 @@
+<html>
+<head>
+<meta http-equiv="Content-Type" content="text/html; charset=ISO-8859-1">
+<title>Setting Policies for Distributions on an Ad Hoc Basis</title>
+<link rel="stylesheet" href="../../../boostbook.css" type="text/css">
+<meta name="generator" content="DocBook XSL Stylesheets Vsnapshot_8125">
+<link rel="home" href="../../../index.html" title="Math Toolkit">
+<link rel="up" href="../pol_tutorial.html" title="Policy Tutorial">
+<link rel="prev" href="changing_policy_defaults.html" title="Changing the Policy Defaults">
+<link rel="next" href="ad_hoc_sf_policies.html" title="Changing the Policy on an Ad Hoc Basis for the Special Functions">
+</head>
+<body bgcolor="white" text="black" link="#0000FF" vlink="#840084" alink="#0000FF">
+<table cellpadding="2" width="100%"><tr>
+<td valign="top"><img alt="Boost C++ Libraries" width="277" height="86" src="../../../../../boost.png"></td>
+<td align="center">Home</td>
+<td align="center">Libraries</td>
+<td align="center">People</td>
+<td align="center">FAQ</td>
+<td align="center">More</td>
+</tr></table>
+<hr>
+<div class="spirit-nav">
+<a accesskey="p" href="changing_policy_defaults.html"><img src="../../../../../doc/html/images/prev.png" alt="Prev"></a><a accesskey="u" href="../pol_tutorial.html"><img src="../../../../../doc/html/images/up.png" alt="Up"></a><a accesskey="h" href="../../../index.html"><img src="../../../../../doc/html/images/home.png" alt="Home"></a><a accesskey="n" href="ad_hoc_sf_policies.html"><img src="../../../../../doc/html/images/next.png" alt="Next"></a>
+</div>
+<div class="section" lang="en">
+<div class="titlepage"><div><div><h4 class="title">
+<a name="math_toolkit.policy.pol_tutorial.ad_hoc_dist_policies"></a><a class="link" href="ad_hoc_dist_policies.html" title="Setting Policies for Distributions on an Ad Hoc Basis">
+        Setting Policies for Distributions on an Ad Hoc Basis</a>
+</h4></div></div></div>
+<p>
+          All of the statistical distributions in this library are class templates
+          that accept two template parameters, both with sensible defaults, for example:
+        </p>
+<pre class="programlisting"><span class="keyword">namespace</span> <span class="identifier">boost</span><span class="special">{</span> <span class="keyword">namespace</span> <span class="identifier">math</span><span class="special">{</span>
+
+<span class="keyword">template</span> <span class="special">&lt;</span><span class="keyword">class</span> <span class="identifier">RealType</span> <span class="special">=</span> <span class="keyword">double</span><span class="special">,</span> <span class="keyword">class</span> <span class="identifier">Policy</span> <span class="special">=</span> <span class="identifier">policies</span><span class="special">::</span><span class="identifier">policy</span><span class="special">&lt;&gt;</span> <span class="special">&gt;</span>
+<span class="keyword">class</span> <span class="identifier">fisher_f_distribution</span><span class="special">;</span>
+
+<span class="keyword">typedef</span> <span class="identifier">fisher_f_distribution</span><span class="special">&lt;&gt;</span> <span class="identifier">fisher_f</span><span class="special">;</span>
+
+<span class="special">}}</span>
+</pre>
+<p>
+          This policy gets used by all the accessor functions that accept a distribution
+          as an argument, and forwarded to all the functions called by these. So
+          if you use the shorthand-typedef for the distribution, then you get <code class="computeroutput"><span class="keyword">double</span></code> precision arithmetic and all the
+          default policies.
+        </p>
+<p>
+          However, say for example we wanted to evaluate the quantile of the binomial
+          distribution at float precision, without internal promotion to double,
+          and with the result rounded to the <span class="emphasis"><em>nearest</em></span> integer,
+          then here's how it can be done:
+        </p>
+<p>
+          </p>
+<p>
+            
+</p>
+<pre class="programlisting"><span class="preprocessor">#include</span> <span class="special">&lt;</span><span class="identifier">boost</span><span class="special">/</span><span class="identifier">math</span><span class="special">/</span><span class="identifier">distributions</span><span class="special">/</span><span class="identifier">binomial</span><span class="special">.</span><span class="identifier">hpp</span><span class="special">&gt;</span>
+
+<span class="comment">//
+</span><span class="comment">// Begin by defining a policy type, that gives the
+</span><span class="comment">// behaviour we want:
+</span><span class="comment">//
+</span><span class="keyword">using</span> <span class="keyword">namespace</span> <span class="identifier">boost</span><span class="special">::</span><span class="identifier">math</span><span class="special">::</span><span class="identifier">policies</span><span class="special">;</span>
+<span class="keyword">typedef</span> <span class="identifier">policy</span><span class="special">&lt;</span>
+   <span class="identifier">promote_float</span><span class="special">&lt;</span><span class="keyword">false</span><span class="special">&gt;,</span>
+   <span class="identifier">discrete_quantile</span><span class="special">&lt;</span><span class="identifier">integer_round_nearest</span><span class="special">&gt;</span>
+<span class="special">&gt;</span> <span class="identifier">mypolicy</span><span class="special">;</span>
+<span class="comment">//
+</span><span class="comment">// Then define a distribution that uses it:
+</span><span class="comment">//
+</span><span class="keyword">typedef</span> <span class="identifier">boost</span><span class="special">::</span><span class="identifier">math</span><span class="special">::</span><span class="identifier">binomial_distribution</span><span class="special">&lt;</span><span class="keyword">float</span><span class="special">,</span> <span class="identifier">mypolicy</span><span class="special">&gt;</span> <span class="identifier">mybinom</span><span class="special">;</span>
+<span class="comment">//
+</span><span class="comment">//  And now use it to get the quantile:
+</span><span class="comment">//
+</span><span class="keyword">int</span> <span class="identifier">main</span><span class="special">()</span>
+<span class="special">{</span>
+   <span class="identifier">std</span><span class="special">::</span><span class="identifier">cout</span> <span class="special">&lt;&lt;</span> <span class="string">"quantile is: "</span> <span class="special">&lt;&lt;</span>
+      <span class="identifier">quantile</span><span class="special">(</span><span class="identifier">mybinom</span><span class="special">(</span><span class="number">200</span><span class="special">,</span> <span class="number">0.25</span><span class="special">),</span> <span class="number">0.05</span><span class="special">)</span> <span class="special">&lt;&lt;</span> <span class="identifier">std</span><span class="special">::</span><span class="identifier">endl</span><span class="special">;</span>
+<span class="special">}</span>
+
+</pre>
+<p>
+          </p>
+<p>
+        </p>
+<p>
+          Which outputs:
+        </p>
+<pre class="programlisting">quantile is: 40</pre>
+</div>
+<table xmlns:rev="http://www.cs.rpi.edu/~gregod/boost/tools/doc/revision" width="100%"><tr>
+<td align="left"></td>
+<td align="right"><div class="copyright-footer">Copyright © 2006 , 2007, 2008 John Maddock, Paul A. Bristow, Hubert
+      Holin, Xiaogang Zhang, Bruno Lalande and Gautam Sewani<p>
+        Distributed under the Boost Software License, Version 1.0. (See accompanying
+        file LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_0.txt)
+      </p>
+</div></td>
+</tr></table>
+<hr>
+<div class="spirit-nav">
+<a accesskey="p" href="changing_policy_defaults.html"><img src="../../../../../doc/html/images/prev.png" alt="Prev"></a><a accesskey="u" href="../pol_tutorial.html"><img src="../../../../../doc/html/images/up.png" alt="Up"></a><a accesskey="h" href="../../../index.html"><img src="../../../../../doc/html/images/home.png" alt="Home"></a><a accesskey="n" href="ad_hoc_sf_policies.html"><img src="../../../../../doc/html/images/next.png" alt="Next"></a>
+</div>
+</body>
+</html>

Added: sandbox/tools/auto_index/example/math/doc/sf_and_dist/html/math_toolkit/policy/pol_tutorial/ad_hoc_sf_policies.html
==============================================================================
--- (empty file)
+++ sandbox/tools/auto_index/example/math/doc/sf_and_dist/html/math_toolkit/policy/pol_tutorial/ad_hoc_sf_policies.html	2008-11-28 05:25:28 EST (Fri, 28 Nov 2008)
@@ -0,0 +1,167 @@
+<html>
+<head>
+<meta http-equiv="Content-Type" content="text/html; charset=ISO-8859-1">
+<title>Changing the Policy on an Ad Hoc Basis for the Special Functions</title>
+<link rel="stylesheet" href="../../../boostbook.css" type="text/css">
+<meta name="generator" content="DocBook XSL Stylesheets Vsnapshot_8125">
+<link rel="home" href="../../../index.html" title="Math Toolkit">
+<link rel="up" href="../pol_tutorial.html" title="Policy Tutorial">
+<link rel="prev" href="ad_hoc_dist_policies.html" title="Setting Policies for Distributions on an Ad Hoc Basis">
+<link rel="next" href="namespace_policies.html" title="Setting Policies at Namespace or Translation Unit Scope">
+</head>
+<body bgcolor="white" text="black" link="#0000FF" vlink="#840084" alink="#0000FF">
+<table cellpadding="2" width="100%"><tr>
+<td valign="top"><img alt="Boost C++ Libraries" width="277" height="86" src="../../../../../boost.png"></td>
+<td align="center">Home</td>
+<td align="center">Libraries</td>
+<td align="center">People</td>
+<td align="center">FAQ</td>
+<td align="center">More</td>
+</tr></table>
+<hr>
+<div class="spirit-nav">
+<a accesskey="p" href="ad_hoc_dist_policies.html"><img src="../../../../../doc/html/images/prev.png" alt="Prev"></a><a accesskey="u" href="../pol_tutorial.html"><img src="../../../../../doc/html/images/up.png" alt="Up"></a><a accesskey="h" href="../../../index.html"><img src="../../../../../doc/html/images/home.png" alt="Home"></a><a accesskey="n" href="namespace_policies.html"><img src="../../../../../doc/html/images/next.png" alt="Next"></a>
+</div>
+<div class="section" lang="en">
+<div class="titlepage"><div><div><h4 class="title">
+<a name="math_toolkit.policy.pol_tutorial.ad_hoc_sf_policies"></a><a class="link" href="ad_hoc_sf_policies.html" title="Changing the Policy on an Ad Hoc Basis for the Special Functions">
+        Changing the Policy on an Ad Hoc Basis for the Special Functions</a>
+</h4></div></div></div>
+<p>
+          All of the special functions in this library come in two overloaded forms,
+          one with a final "policy" parameter, and one without. For example:
+        </p>
+<pre class="programlisting"><span class="keyword">namespace</span> <span class="identifier">boost</span><span class="special">{</span> <span class="keyword">namespace</span> <span class="identifier">math</span><span class="special">{</span>
+
+<span class="keyword">template</span> <span class="special">&lt;</span><span class="keyword">class</span> <span class="identifier">RealType</span><span class="special">,</span> <span class="keyword">class</span> <span class="identifier">Policy</span><span class="special">&gt;</span>
+<span class="identifier">RealType</span> <span class="identifier">tgamma</span><span class="special">(</span><span class="identifier">RealType</span><span class="special">,</span> <span class="keyword">const</span> <span class="identifier">Policy</span><span class="special">&amp;);</span>
+
+<span class="keyword">template</span> <span class="special">&lt;</span><span class="keyword">class</span> <span class="identifier">RealType</span><span class="special">&gt;</span>
+<span class="identifier">RealType</span> <span class="identifier">tgamma</span><span class="special">(</span><span class="identifier">RealType</span><span class="special">);</span>
+
+<span class="special">}}</span> <span class="comment">// namespaces
+</span></pre>
+<p>
+          Normally, the second version is just a forwarding wrapper to the first
+          like this:
+        </p>
+<pre class="programlisting"><span class="keyword">template</span> <span class="special">&lt;</span><span class="keyword">class</span> <span class="identifier">RealType</span><span class="special">&gt;</span>
+<span class="keyword">inline</span> <span class="identifier">RealType</span> <span class="identifier">tgamma</span><span class="special">(</span><span class="identifier">RealType</span> <span class="identifier">x</span><span class="special">)</span>
+<span class="special">{</span>
+   <span class="keyword">return</span> <span class="identifier">tgamma</span><span class="special">(</span><span class="identifier">x</span><span class="special">,</span> <span class="identifier">policies</span><span class="special">::</span><span class="identifier">policy</span><span class="special">&lt;&gt;());</span>
+<span class="special">}</span>
+</pre>
+<p>
+          So calling a special function with a specific policy is just a matter of
+          defining the policy type to use and passing it as the final parameter.
+          For example, suppose we want <code class="computeroutput"><span class="identifier">tgamma</span></code>
+          to behave in a C-compatible fashion and set <code class="computeroutput"><span class="special">::</span><span class="identifier">errno</span></code> when an error occurs, and never
+          throw an exception:
+        </p>
+<p>
+          </p>
+<p>
+            
+</p>
+<pre class="programlisting"><span class="preprocessor">#include</span> <span class="special">&lt;</span><span class="identifier">boost</span><span class="special">/</span><span class="identifier">math</span><span class="special">/</span><span class="identifier">special_functions</span><span class="special">/</span><span class="identifier">gamma</span><span class="special">.</span><span class="identifier">hpp</span><span class="special">&gt;</span>
+<span class="comment">//
+</span><span class="comment">// Define the policy to use:
+</span><span class="comment">//
+</span><span class="keyword">using</span> <span class="keyword">namespace</span> <span class="identifier">boost</span><span class="special">::</span><span class="identifier">math</span><span class="special">::</span><span class="identifier">policies</span><span class="special">;</span>
+<span class="keyword">typedef</span> <span class="identifier">policy</span><span class="special">&lt;</span>
+   <span class="identifier">domain_error</span><span class="special">&lt;</span><span class="identifier">errno_on_error</span><span class="special">&gt;,</span>
+   <span class="identifier">pole_error</span><span class="special">&lt;</span><span class="identifier">errno_on_error</span><span class="special">&gt;,</span>
+   <span class="identifier">overflow_error</span><span class="special">&lt;</span><span class="identifier">errno_on_error</span><span class="special">&gt;,</span>
+   <span class="identifier">evaluation_error</span><span class="special">&lt;</span><span class="identifier">errno_on_error</span><span class="special">&gt;</span> 
+<span class="special">&gt;</span> <span class="identifier">c_policy</span><span class="special">;</span>
+<span class="comment">//
+</span><span class="comment">// Now use the policy when calling tgamma:
+</span><span class="comment">//
+</span><span class="keyword">int</span> <span class="identifier">main</span><span class="special">()</span>
+<span class="special">{</span>
+   <span class="identifier">errno</span> <span class="special">=</span> <span class="number">0</span><span class="special">;</span>
+   <span class="identifier">std</span><span class="special">::</span><span class="identifier">cout</span> <span class="special">&lt;&lt;</span> <span class="string">"Result of tgamma(30000) is: "</span> 
+      <span class="special">&lt;&lt;</span> <span class="identifier">boost</span><span class="special">::</span><span class="identifier">math</span><span class="special">::</span><span class="identifier">tgamma</span><span class="special">(</span><span class="number">30000</span><span class="special">,</span> <span class="identifier">c_policy</span><span class="special">())</span> <span class="special">&lt;&lt;</span> <span class="identifier">std</span><span class="special">::</span><span class="identifier">endl</span><span class="special">;</span>
+   <span class="identifier">std</span><span class="special">::</span><span class="identifier">cout</span> <span class="special">&lt;&lt;</span> <span class="string">"errno = "</span> <span class="special">&lt;&lt;</span> <span class="identifier">errno</span> <span class="special">&lt;&lt;</span> <span class="identifier">std</span><span class="special">::</span><span class="identifier">endl</span><span class="special">;</span>
+   <span class="identifier">std</span><span class="special">::</span><span class="identifier">cout</span> <span class="special">&lt;&lt;</span> <span class="string">"Result of tgamma(-10) is: "</span> 
+      <span class="special">&lt;&lt;</span> <span class="identifier">boost</span><span class="special">::</span><span class="identifier">math</span><span class="special">::</span><span class="identifier">tgamma</span><span class="special">(-</span><span class="number">10</span><span class="special">,</span> <span class="identifier">c_policy</span><span class="special">())</span> <span class="special">&lt;&lt;</span> <span class="identifier">std</span><span class="special">::</span><span class="identifier">endl</span><span class="special">;</span>
+   <span class="identifier">std</span><span class="special">::</span><span class="identifier">cout</span> <span class="special">&lt;&lt;</span> <span class="string">"errno = "</span> <span class="special">&lt;&lt;</span> <span class="identifier">errno</span> <span class="special">&lt;&lt;</span> <span class="identifier">std</span><span class="special">::</span><span class="identifier">endl</span><span class="special">;</span>
+<span class="special">}</span>
+
+</pre>
+<p>
+          </p>
+<p>
+        </p>
+<p>
+          which outputs:
+        </p>
+<pre class="programlisting">Result of tgamma(30000) is: 1.#INF
+errno = 34
+Result of tgamma(-10) is: 1.#QNAN
+errno = 33
+</pre>
+<p>
+          Alternatively, for ad hoc use, we can use the <code class="computeroutput"><span class="identifier">make_policy</span></code>
+          helper function to create a policy for us: this usage is more verbose,
+          so is probably only preferred when a policy is going to be used once only:
+        </p>
+<p>
+          </p>
+<p>
+            
+</p>
+<pre class="programlisting"><span class="preprocessor">#include</span> <span class="special">&lt;</span><span class="identifier">boost</span><span class="special">/</span><span class="identifier">math</span><span class="special">/</span><span class="identifier">special_functions</span><span class="special">/</span><span class="identifier">gamma</span><span class="special">.</span><span class="identifier">hpp</span><span class="special">&gt;</span>
+
+<span class="keyword">int</span> <span class="identifier">main</span><span class="special">()</span>
+<span class="special">{</span>
+   <span class="keyword">using</span> <span class="keyword">namespace</span> <span class="identifier">boost</span><span class="special">::</span><span class="identifier">math</span><span class="special">::</span><span class="identifier">policies</span><span class="special">;</span>
+   <span class="identifier">errno</span> <span class="special">=</span> <span class="number">0</span><span class="special">;</span>
+   <span class="identifier">std</span><span class="special">::</span><span class="identifier">cout</span> <span class="special">&lt;&lt;</span> <span class="string">"Result of tgamma(30000) is: "</span> 
+      <span class="special">&lt;&lt;</span> <span class="identifier">boost</span><span class="special">::</span><span class="identifier">math</span><span class="special">::</span><span class="identifier">tgamma</span><span class="special">(</span>
+         <span class="number">30000</span><span class="special">,</span> 
+         <span class="identifier">make_policy</span><span class="special">(</span>
+            <span class="identifier">domain_error</span><span class="special">&lt;</span><span class="identifier">errno_on_error</span><span class="special">&gt;(),</span>
+            <span class="identifier">pole_error</span><span class="special">&lt;</span><span class="identifier">errno_on_error</span><span class="special">&gt;(),</span>
+            <span class="identifier">overflow_error</span><span class="special">&lt;</span><span class="identifier">errno_on_error</span><span class="special">&gt;(),</span>
+            <span class="identifier">evaluation_error</span><span class="special">&lt;</span><span class="identifier">errno_on_error</span><span class="special">&gt;()</span> 
+         <span class="special">)</span>
+      <span class="special">)</span> <span class="special">&lt;&lt;</span> <span class="identifier">std</span><span class="special">::</span><span class="identifier">endl</span><span class="special">;</span>
+   <span class="comment">// Check errno was set:
+</span>   <span class="identifier">std</span><span class="special">::</span><span class="identifier">cout</span> <span class="special">&lt;&lt;</span> <span class="string">"errno = "</span> <span class="special">&lt;&lt;</span> <span class="identifier">errno</span> <span class="special">&lt;&lt;</span> <span class="identifier">std</span><span class="special">::</span><span class="identifier">endl</span><span class="special">;</span>
+   <span class="comment">// and again with evaluation at a pole:
+</span>   <span class="identifier">std</span><span class="special">::</span><span class="identifier">cout</span> <span class="special">&lt;&lt;</span> <span class="string">"Result of tgamma(-10) is: "</span> 
+      <span class="special">&lt;&lt;</span> <span class="identifier">boost</span><span class="special">::</span><span class="identifier">math</span><span class="special">::</span><span class="identifier">tgamma</span><span class="special">(</span>
+         <span class="special">-</span><span class="number">10</span><span class="special">,</span> 
+         <span class="identifier">make_policy</span><span class="special">(</span>
+            <span class="identifier">domain_error</span><span class="special">&lt;</span><span class="identifier">errno_on_error</span><span class="special">&gt;(),</span>
+            <span class="identifier">pole_error</span><span class="special">&lt;</span><span class="identifier">errno_on_error</span><span class="special">&gt;(),</span>
+            <span class="identifier">overflow_error</span><span class="special">&lt;</span><span class="identifier">errno_on_error</span><span class="special">&gt;(),</span>
+            <span class="identifier">evaluation_error</span><span class="special">&lt;</span><span class="identifier">errno_on_error</span><span class="special">&gt;()</span> 
+         <span class="special">)</span>
+      <span class="special">)</span> <span class="special">&lt;&lt;</span> <span class="identifier">std</span><span class="special">::</span><span class="identifier">endl</span><span class="special">;</span>
+   <span class="comment">// Check errno was set:
+</span>   <span class="identifier">std</span><span class="special">::</span><span class="identifier">cout</span> <span class="special">&lt;&lt;</span> <span class="string">"errno = "</span> <span class="special">&lt;&lt;</span> <span class="identifier">errno</span> <span class="special">&lt;&lt;</span> <span class="identifier">std</span><span class="special">::</span><span class="identifier">endl</span><span class="special">;</span>
+<span class="special">}</span>
+
+</pre>
+<p>
+          </p>
+<p>
+        </p>
+</div>
+<table xmlns:rev="http://www.cs.rpi.edu/~gregod/boost/tools/doc/revision" width="100%"><tr>
+<td align="left"></td>
+<td align="right"><div class="copyright-footer">Copyright © 2006 , 2007, 2008 John Maddock, Paul A. Bristow, Hubert
+      Holin, Xiaogang Zhang, Bruno Lalande and Gautam Sewani<p>
+        Distributed under the Boost Software License, Version 1.0. (See accompanying
+        file LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_0.txt)
+      </p>
+</div></td>
+</tr></table>
+<hr>
+<div class="spirit-nav">
+<a accesskey="p" href="ad_hoc_dist_policies.html"><img src="../../../../../doc/html/images/prev.png" alt="Prev"></a><a accesskey="u" href="../pol_tutorial.html"><img src="../../../../../doc/html/images/up.png" alt="Up"></a><a accesskey="h" href="../../../index.html"><img src="../../../../../doc/html/images/home.png" alt="Home"></a><a accesskey="n" href="namespace_policies.html"><img src="../../../../../doc/html/images/next.png" alt="Next"></a>
+</div>
+</body>
+</html>

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--- (empty file)
+++ sandbox/tools/auto_index/example/math/doc/sf_and_dist/html/math_toolkit/policy/pol_tutorial/changing_policy_defaults.html	2008-11-28 05:25:28 EST (Fri, 28 Nov 2008)
@@ -0,0 +1,331 @@
+<html>
+<head>
+<meta http-equiv="Content-Type" content="text/html; charset=ISO-8859-1">
+<title>Changing the Policy Defaults</title>
+<link rel="stylesheet" href="../../../boostbook.css" type="text/css">
+<meta name="generator" content="DocBook XSL Stylesheets Vsnapshot_8125">
+<link rel="home" href="../../../index.html" title="Math Toolkit">
+<link rel="up" href="../pol_tutorial.html" title="Policy Tutorial">
+<link rel="prev" href="policy_usage.html" title="So How are Policies Used Anyway?">
+<link rel="next" href="ad_hoc_dist_policies.html" title="Setting Policies for Distributions on an Ad Hoc Basis">
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+<table cellpadding="2" width="100%"><tr>
+<td valign="top"><img alt="Boost C++ Libraries" width="277" height="86" src="../../../../../boost.png"></td>
+<td align="center">Home</td>
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+<td align="center">People</td>
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+<a accesskey="p" href="policy_usage.html"><img src="../../../../../doc/html/images/prev.png" alt="Prev"></a><a accesskey="u" href="../pol_tutorial.html"><img src="../../../../../doc/html/images/up.png" alt="Up"></a><a accesskey="h" href="../../../index.html"><img src="../../../../../doc/html/images/home.png" alt="Home"></a><a accesskey="n" href="ad_hoc_dist_policies.html"><img src="../../../../../doc/html/images/next.png" alt="Next"></a>
+</div>
+<div class="section" lang="en">
+<div class="titlepage"><div><div><h4 class="title">
+<a name="math_toolkit.policy.pol_tutorial.changing_policy_defaults"></a><a class="link" href="changing_policy_defaults.html" title="Changing the Policy Defaults">
+        Changing the Policy Defaults</a>
+</h4></div></div></div>
+<p>
+          The default policies used by the library are changed by the usual configuration
+          macro method.
+        </p>
+<p>
+          For example, passing <code class="computeroutput"><span class="special">-</span><span class="identifier">DBOOST_MATH_DOMAIN_ERROR_POLICY</span><span class="special">=</span><span class="identifier">errno_on_error</span></code>
+          to your compiler will cause domain errors to set <code class="computeroutput"><span class="special">::</span><span class="identifier">errno</span></code> and return a NaN rather than the
+          usual default behaviour of throwing a <code class="computeroutput"><span class="identifier">std</span><span class="special">::</span><span class="identifier">domain_error</span></code>
+          exception.
+        </p>
+<div class="tip"><table border="0" summary="Tip">
+<tr>
+<td rowspan="2" align="center" valign="top" width="25"><img alt="[Tip]" src="../../../../../doc/html/images/tip.png"></td>
+<th align="left">Tip</th>
+</tr>
+<tr><td align="left" valign="top">
+<p>
+            For Microsoft Visual Studio,you can add to the Project Property Page,
+            C/C++, Preprocessor, Preprocessor definitions like:
+          </p>
+<p>
+            
+</p>
+<pre class="programlisting"><span class="identifier">BOOST_MATH_ASSERT_UNDEFINED_POLICY</span><span class="special">=</span><span class="number">0</span>
+<span class="identifier">BOOST_MATH_OVERFLOW_ERROR_POLICY</span><span class="special">=</span><span class="identifier">errno_on_error</span></pre>
+<p>
+          </p>
+<p>
+            This may be helpful to avoid complications with pre-compiled headers
+            that may mean that the equivalent definitions in source code:
+          </p>
+<p>
+            
+</p>
+<pre class="programlisting"><span class="preprocessor">#define</span> <span class="identifier">BOOST_MATH_ASSERT_UNDEFINED_POLICY</span> <span class="keyword">false</span>
+<span class="preprocessor">#define</span> <span class="identifier">BOOST_MATH_OVERFLOW_ERROR_POLICY</span> <span class="identifier">errno_on_error</span></pre>
+<p>
+          </p>
+<p>
+            may be ignored.
+          </p>
+<p>
+            The compiler command line shows:
+          </p>
+<p>
+            
+</p>
+<pre class="programlisting"><span class="special">/</span><span class="identifier">D</span> <span class="string">"BOOST_MATH_ASSERT_UNDEFINED_POLICY=0"</span>
+<span class="special">/</span><span class="identifier">D</span> <span class="string">"BOOST_MATH_OVERFLOW_ERROR_POLICY=errno_on_error"</span></pre>
+<p>
+          </p>
+</td></tr>
+</table></div>
+<p>
+          There is however a very important caveat to this:
+        </p>
+<div class="important"><table border="0" summary="Important">
+<tr>
+<td rowspan="2" align="center" valign="top" width="25"><img alt="[Important]" src="../../../../../doc/html/images/important.png"></td>
+<th align="left">Important</th>
+</tr>
+<tr><td align="left" valign="top">
+<p>
+            <span class="bold"><strong><span class="emphasis"><em>Default policies changed by setting configuration
+            macros must be changed uniformly in every translation unit in the program.</em></span></strong></span>
+          </p>
+<p>
+            Failure to follow this rule may result in violations of the "One
+            Definition Rule (ODR)" and result in unpredictable program behaviour.
+          </p>
+</td></tr>
+</table></div>
+<p>
+          That means there are only two safe ways to use these macros:
+        </p>
+<div class="itemizedlist"><ul type="disc">
+<li>
+            Edit them in boost/math/tools/user.hpp,
+            so that the defaults are set on an installation-wide basis. Unfortunately
+            this may not be convenient if you are using a pre-installed Boost distribution
+            (on Linux for example).
+          </li>
+<li>
+            Set the defines in your project's Makefile or build environment, so that
+            they are set uniformly across all translation units.
+          </li>
+</ul></div>
+<p>
+          What you should <span class="bold"><strong>not</strong></span> do is:
+        </p>
+<div class="itemizedlist"><ul type="disc"><li>
+            Set the defines in the source file using <code class="computeroutput"><span class="preprocessor">#define</span></code>
+            as doing so almost certainly will break your program, unless you're absolutely
+            certain that the program is restricted to a single translation unit.
+          </li></ul></div>
+<p>
+          And, yes, you will find examples in our test programs where we break this
+          rule: but only because we know there will always be a single translation
+          unit only: <span class="emphasis"><em>don't say that you weren't warned!</em></span>
+        </p>
+<p>
+          </p>
+<p>
+            The following example demonstrates the effect of setting the macro BOOST_MATH_DOMAIN_ERROR_POLICY
+            when an invalid argument is encountered. For the purposes of this example,
+            we'll pass a negative degrees of freedom parameter to the student's t
+            distribution.
+          </p>
+<p>
+          </p>
+<p>
+            Since we know that this is a single file program we could just add:
+          </p>
+<p>
+          
+</p>
+<pre class="programlisting"><span class="preprocessor">#define</span> <span class="identifier">BOOST_MATH_DOMAIN_ERROR_POLICY</span> <span class="identifier">ignore_error</span>
+</pre>
+<p>
+          </p>
+<p>
+            to the top of the source file to change the default policy to one that
+            simply returns a NaN when a domain error occurs. Alternatively we could
+            use:
+          </p>
+<p>
+          
+</p>
+<pre class="programlisting"><span class="preprocessor">#define</span> <span class="identifier">BOOST_MATH_DOMAIN_ERROR_POLICY</span> <span class="identifier">errno_on_error</span>
+</pre>
+<p>
+          </p>
+<p>
+            To ensure the <code class="computeroutput"><span class="special">::</span><span class="identifier">errno</span></code>
+            is set when a domain error occurs as well as returning a NaN.
+          </p>
+<p>
+          </p>
+<p>
+            This is safe provided the program consists of a single translation unit
+            <span class="emphasis"><em>and</em></span> we place the define <span class="emphasis"><em>before</em></span>
+            any #includes. Note that should we add the define after the includes
+            then it will have no effect! A warning such as:
+          </p>
+<p>
+          
+</p>
+<pre class="programlisting">warning C4005: 'BOOST_MATH_OVERFLOW_ERROR_POLICY' : macro redefinition</pre>
+<p>
+          </p>
+<p>
+            is a certain sign that it will <span class="emphasis"><em>not</em></span> have the desired
+            effect.
+          </p>
+<p>
+          </p>
+<p>
+            We'll begin our sample program with the needed includes:
+          </p>
+<p>
+          </p>
+<p>
+            
+</p>
+<pre class="programlisting"><span class="comment">// Boost
+</span><span class="preprocessor">#include</span> <span class="special">&lt;</span><span class="identifier">boost</span><span class="special">/</span><span class="identifier">math</span><span class="special">/</span><span class="identifier">distributions</span><span class="special">/</span><span class="identifier">students_t</span><span class="special">.</span><span class="identifier">hpp</span><span class="special">&gt;</span>
+   <span class="keyword">using</span> <span class="identifier">boost</span><span class="special">::</span><span class="identifier">math</span><span class="special">::</span><span class="identifier">students_t</span><span class="special">;</span>  <span class="comment">// Probability of students_t(df, t).
+</span>
+<span class="comment">// std
+</span><span class="preprocessor">#include</span> <span class="special">&lt;</span><span class="identifier">iostream</span><span class="special">&gt;</span>
+   <span class="keyword">using</span> <span class="identifier">std</span><span class="special">::</span><span class="identifier">cout</span><span class="special">;</span>
+   <span class="keyword">using</span> <span class="identifier">std</span><span class="special">::</span><span class="identifier">endl</span><span class="special">;</span>
+
+<span class="preprocessor">#include</span> <span class="special">&lt;</span><span class="identifier">stdexcept</span><span class="special">&gt;</span>
+   <span class="keyword">using</span> <span class="identifier">std</span><span class="special">::</span><span class="identifier">exception</span><span class="special">;</span></pre>
+<p>
+          </p>
+<p>
+          </p>
+<p>
+            Next we'll define the program's main() to call the student's t distribution
+            with an invalid degrees of freedom parameter, the program is set up to
+            handle either an exception or a NaN:
+          </p>
+<p>
+          </p>
+<p>
+            
+</p>
+<pre class="programlisting"><span class="keyword">int</span> <span class="identifier">main</span><span class="special">()</span>
+<span class="special">{</span>
+   <span class="identifier">cout</span> <span class="special">&lt;&lt;</span> <span class="string">"Example error handling using Student's t function. "</span> <span class="special">&lt;&lt;</span> <span class="identifier">endl</span><span class="special">;</span>
+   <span class="identifier">cout</span> <span class="special">&lt;&lt;</span> <span class="string">"BOOST_MATH_DOMAIN_ERROR_POLICY is set to: "</span>
+      <span class="special">&lt;&lt;</span> <span class="identifier">BOOST_STRINGIZE</span><span class="special">(</span><span class="identifier">BOOST_MATH_DOMAIN_ERROR_POLICY</span><span class="special">)</span> <span class="special">&lt;&lt;</span> <span class="identifier">endl</span><span class="special">;</span>
+
+   <span class="keyword">double</span> <span class="identifier">degrees_of_freedom</span> <span class="special">=</span> <span class="special">-</span><span class="number">1</span><span class="special">;</span> <span class="comment">// A bad argument!
+</span>   <span class="keyword">double</span> <span class="identifier">t</span> <span class="special">=</span> <span class="number">10</span><span class="special">;</span>
+
+   <span class="keyword">try</span>
+   <span class="special">{</span>
+      <span class="identifier">errno</span> <span class="special">=</span> <span class="number">0</span><span class="special">;</span>
+      <span class="identifier">students_t</span> <span class="identifier">dist</span><span class="special">(</span><span class="identifier">degrees_of_freedom</span><span class="special">);</span> <span class="comment">// exception is thrown here if enabled
+</span>      <span class="keyword">double</span> <span class="identifier">p</span> <span class="special">=</span> <span class="identifier">cdf</span><span class="special">(</span><span class="identifier">dist</span><span class="special">,</span> <span class="identifier">t</span><span class="special">);</span>
+      <span class="comment">// test for error reported by other means:
+</span>      <span class="keyword">if</span><span class="special">((</span><span class="identifier">boost</span><span class="special">::</span><span class="identifier">math</span><span class="special">::</span><span class="identifier">isnan</span><span class="special">)(</span><span class="identifier">p</span><span class="special">))</span>
+      <span class="special">{</span>
+         <span class="identifier">cout</span> <span class="special">&lt;&lt;</span> <span class="string">"cdf returned a NaN!"</span> <span class="special">&lt;&lt;</span> <span class="identifier">endl</span><span class="special">;</span>
+         <span class="identifier">cout</span> <span class="special">&lt;&lt;</span> <span class="string">"errno is set to: "</span> <span class="special">&lt;&lt;</span> <span class="identifier">errno</span> <span class="special">&lt;&lt;</span> <span class="identifier">endl</span><span class="special">;</span>
+      <span class="special">}</span>
+      <span class="keyword">else</span>
+         <span class="identifier">cout</span> <span class="special">&lt;&lt;</span> <span class="string">"Probability of Student's t is "</span> <span class="special">&lt;&lt;</span> <span class="identifier">p</span> <span class="special">&lt;&lt;</span> <span class="identifier">endl</span><span class="special">;</span>
+   <span class="special">}</span>
+   <span class="keyword">catch</span><span class="special">(</span><span class="keyword">const</span> <span class="identifier">std</span><span class="special">::</span><span class="identifier">exception</span><span class="special">&amp;</span> <span class="identifier">e</span><span class="special">)</span>
+   <span class="special">{</span>
+      <span class="identifier">std</span><span class="special">::</span><span class="identifier">cout</span> <span class="special">&lt;&lt;</span>
+         <span class="string">"\n"</span><span class="string">"Message from thrown exception was:\n   "</span> <span class="special">&lt;&lt;</span> <span class="identifier">e</span><span class="special">.</span><span class="identifier">what</span><span class="special">()</span> <span class="special">&lt;&lt;</span> <span class="identifier">std</span><span class="special">::</span><span class="identifier">endl</span><span class="special">;</span>
+   <span class="special">}</span>
+
+   <span class="keyword">return</span> <span class="number">0</span><span class="special">;</span>
+<span class="special">}</span> <span class="comment">// int main()</span></pre>
+<p>
+          </p>
+<p>
+          </p>
+<p>
+            Here's what the program output looks like with a default build (one that
+            does throw exceptions):
+          </p>
+<p>
+          
+</p>
+<pre class="programlisting">Example error handling using Student's t function.
+BOOST_MATH_DOMAIN_ERROR_POLICY is set to: throw_on_error
+
+Message from thrown exception was:
+   Error in function boost::math::students_t_distribution&lt;double&gt;::students_t_distribution:
+   Degrees of freedom argument is -1, but must be &gt; 0 !
+</pre>
+<p>
+          </p>
+<p>
+            Alternatively let's build with:
+          </p>
+<p>
+          
+</p>
+<pre class="programlisting"><span class="preprocessor">#define</span> <span class="identifier">BOOST_MATH_DOMAIN_ERROR_POLICY</span> <span class="identifier">ignore_error</span>
+</pre>
+<p>
+          </p>
+<p>
+            Now the program output is:
+          </p>
+<p>
+          
+</p>
+<pre class="programlisting">Example error handling using Student's t function.
+BOOST_MATH_DOMAIN_ERROR_POLICY is set to: ignore_error
+cdf returned a NaN!
+errno is set to: 0
+</pre>
+<p>
+          </p>
+<p>
+            And finally let's build with:
+          </p>
+<p>
+          
+</p>
+<pre class="programlisting"><span class="preprocessor">#define</span> <span class="identifier">BOOST_MATH_DOMAIN_ERROR_POLICY</span> <span class="identifier">errno_on_error</span>
+</pre>
+<p>
+          </p>
+<p>
+            Which gives the output:
+          </p>
+<p>
+          
+</p>
+<pre class="programlisting">Example error handling using Student's t function.
+BOOST_MATH_DOMAIN_ERROR_POLICY is set to: errno_on_error
+cdf returned a NaN!
+errno is set to: 33
+</pre>
+<p>
+        </p>
+</div>
+<table xmlns:rev="http://www.cs.rpi.edu/~gregod/boost/tools/doc/revision" width="100%"><tr>
+<td align="left"></td>
+<td align="right"><div class="copyright-footer">Copyright © 2006 , 2007, 2008 John Maddock, Paul A. Bristow, Hubert
+      Holin, Xiaogang Zhang, Bruno Lalande and Gautam Sewani<p>
+        Distributed under the Boost Software License, Version 1.0. (See accompanying
+        file LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_0.txt)
+      </p>
+</div></td>
+</tr></table>
+<hr>
+<div class="spirit-nav">
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@@ -0,0 +1,463 @@
+<html>
+<head>
+<meta http-equiv="Content-Type" content="text/html; charset=ISO-8859-1">
+<title>Setting Policies at Namespace or Translation Unit Scope</title>
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+</div>
+<div class="section" lang="en">
+<div class="titlepage"><div><div><h4 class="title">
+<a name="math_toolkit.policy.pol_tutorial.namespace_policies"></a><a class="link" href="namespace_policies.html" title="Setting Policies at Namespace or Translation Unit Scope">
+        Setting Policies at Namespace or Translation Unit Scope</a>
+</h4></div></div></div>
+<p>
+          Sometimes what you want to do is just change a set of policies within the
+          current scope: the one thing you should not do in this situation is use
+          the configuration macros, as this can lead to "One Definition Rule"
+          violations. Instead this library provides a pair of macros especially for
+          this purpose.
+        </p>
+<p>
+          Let's consider the special functions first: we can declare a set of forwarding
+          functions that all use a specific policy using the macro BOOST_MATH_DECLARE_SPECIAL_FUNCTIONS(<span class="emphasis"><em>Policy</em></span>).
+          This macro should be used either inside a unique namespace set aside for
+          the purpose, or an unnamed namespace if you just want the functions visible
+          in global scope for the current file only.
+        </p>
+<p>
+          </p>
+<p>
+            Suppose we want <code class="computeroutput"><span class="identifier">C</span><span class="special">::</span><span class="identifier">foo</span><span class="special">()</span></code>
+            to behave in a C-compatible way and set <code class="computeroutput"><span class="special">::</span><span class="identifier">errno</span></code> on error rather than throwing
+            any exceptions.
+          </p>
+<p>
+          </p>
+<p>
+            We'll begin by including the needed header:
+          </p>
+<p>
+          </p>
+<p>
+            
+</p>
+<pre class="programlisting"><span class="preprocessor">#include</span> <span class="special">&lt;</span><span class="identifier">boost</span><span class="special">/</span><span class="identifier">math</span><span class="special">/</span><span class="identifier">special_functions</span><span class="special">.</span><span class="identifier">hpp</span><span class="special">&gt;</span></pre>
+<p>
+          </p>
+<p>
+          </p>
+<p>
+            Open up the "C" namespace that we'll use for our functions,
+            and define the policy type we want: in this case one that sets ::errno
+            rather than throwing exceptions. Any policies we don't specify here will
+            inherit the defaults:
+          </p>
+<p>
+          </p>
+<p>
+            
+</p>
+<pre class="programlisting"><span class="keyword">namespace</span> <span class="identifier">C</span><span class="special">{</span>
+
+<span class="keyword">using</span> <span class="keyword">namespace</span> <span class="identifier">boost</span><span class="special">::</span><span class="identifier">math</span><span class="special">::</span><span class="identifier">policies</span><span class="special">;</span>
+
+<span class="keyword">typedef</span> <span class="identifier">policy</span><span class="special">&lt;</span>
+   <span class="identifier">domain_error</span><span class="special">&lt;</span><span class="identifier">errno_on_error</span><span class="special">&gt;,</span>
+   <span class="identifier">pole_error</span><span class="special">&lt;</span><span class="identifier">errno_on_error</span><span class="special">&gt;,</span>
+   <span class="identifier">overflow_error</span><span class="special">&lt;</span><span class="identifier">errno_on_error</span><span class="special">&gt;,</span>
+   <span class="identifier">evaluation_error</span><span class="special">&lt;</span><span class="identifier">errno_on_error</span><span class="special">&gt;</span>
+<span class="special">&gt;</span> <span class="identifier">c_policy</span><span class="special">;</span></pre>
+<p>
+          </p>
+<p>
+          </p>
+<p>
+            All we need do now is invoke the BOOST_MATH_DECLARE_SPECIAL_FUNCTIONS
+            macro passing our policy type as the single argument:
+          </p>
+<p>
+          </p>
+<p>
+            
+</p>
+<pre class="programlisting"><span class="identifier">BOOST_MATH_DECLARE_SPECIAL_FUNCTIONS</span><span class="special">(</span><span class="identifier">c_policy</span><span class="special">)</span>
+
+<span class="special">}</span> <span class="comment">// close namespace C</span></pre>
+<p>
+          </p>
+<p>
+          </p>
+<p>
+            We now have a set of forwarding functions defined in namespace C that
+            all look something like this:
+          </p>
+<p>
+          </p>
+<p>
+            
+</p>
+<pre class="programlisting"><span class="keyword">template</span> <span class="special">&lt;</span><span class="keyword">class</span> <span class="identifier">RealType</span><span class="special">&gt;</span>
+<span class="keyword">inline</span> <span class="keyword">typename</span> <span class="identifier">boost</span><span class="special">::</span><span class="identifier">math</span><span class="special">::</span><span class="identifier">tools</span><span class="special">::</span><span class="identifier">promote_args</span><span class="special">&lt;</span><span class="identifier">RT</span><span class="special">&gt;::</span><span class="identifier">type</span>
+   <span class="identifier">tgamma</span><span class="special">(</span><span class="identifier">RT</span> <span class="identifier">z</span><span class="special">)</span>
+<span class="special">{</span>
+   <span class="keyword">return</span> <span class="identifier">boost</span><span class="special">::</span><span class="identifier">math</span><span class="special">::</span><span class="identifier">tgamma</span><span class="special">(</span><span class="identifier">z</span><span class="special">,</span> <span class="identifier">c_policy</span><span class="special">());</span>
+<span class="special">}</span>
+</pre>
+<p>
+          </p>
+<p>
+          </p>
+<p>
+            So that when we call <code class="computeroutput"><span class="identifier">C</span><span class="special">::</span><span class="identifier">tgamma</span><span class="special">(</span><span class="identifier">z</span><span class="special">)</span></code> we really end up calling <code class="computeroutput"><span class="identifier">boost</span><span class="special">::</span><span class="identifier">math</span><span class="special">::</span><span class="identifier">tgamma</span><span class="special">(</span><span class="identifier">z</span><span class="special">,</span> <span class="identifier">C</span><span class="special">::</span><span class="identifier">c_policy</span><span class="special">())</span></code>:
+          </p>
+<p>
+          </p>
+<p>
+            
+</p>
+<pre class="programlisting"><span class="keyword">int</span> <span class="identifier">main</span><span class="special">()</span>
+<span class="special">{</span>
+   <span class="identifier">errno</span> <span class="special">=</span> <span class="number">0</span><span class="special">;</span>
+   <span class="identifier">std</span><span class="special">::</span><span class="identifier">cout</span> <span class="special">&lt;&lt;</span> <span class="string">"Result of tgamma(30000) is: "</span>
+      <span class="special">&lt;&lt;</span> <span class="identifier">C</span><span class="special">::</span><span class="identifier">tgamma</span><span class="special">(</span><span class="number">30000</span><span class="special">)</span> <span class="special">&lt;&lt;</span> <span class="identifier">std</span><span class="special">::</span><span class="identifier">endl</span><span class="special">;</span>
+   <span class="identifier">std</span><span class="special">::</span><span class="identifier">cout</span> <span class="special">&lt;&lt;</span> <span class="string">"errno = "</span> <span class="special">&lt;&lt;</span> <span class="identifier">errno</span> <span class="special">&lt;&lt;</span> <span class="identifier">std</span><span class="special">::</span><span class="identifier">endl</span><span class="special">;</span>
+   <span class="identifier">std</span><span class="special">::</span><span class="identifier">cout</span> <span class="special">&lt;&lt;</span> <span class="string">"Result of tgamma(-10) is: "</span>
+      <span class="special">&lt;&lt;</span> <span class="identifier">C</span><span class="special">::</span><span class="identifier">tgamma</span><span class="special">(-</span><span class="number">10</span><span class="special">)</span> <span class="special">&lt;&lt;</span> <span class="identifier">std</span><span class="special">::</span><span class="identifier">endl</span><span class="special">;</span>
+   <span class="identifier">std</span><span class="special">::</span><span class="identifier">cout</span> <span class="special">&lt;&lt;</span> <span class="string">"errno = "</span> <span class="special">&lt;&lt;</span> <span class="identifier">errno</span> <span class="special">&lt;&lt;</span> <span class="identifier">std</span><span class="special">::</span><span class="identifier">endl</span><span class="special">;</span>
+<span class="special">}</span></pre>
+<p>
+          </p>
+<p>
+          </p>
+<p>
+            Which outputs:
+          </p>
+<p>
+          
+</p>
+<pre class="programlisting">Result of C::tgamma(30000) is: 1.#INF
+errno = 34
+Result of C::tgamma(-10) is: 1.#QNAN
+errno = 33
+</pre>
+<p>
+          </p>
+<p>
+            This mechanism is particularly useful when we want to define a project-wide
+            policy, and don't want to modify the Boost source or set - possibly fragile
+            and easy to forget - project wide build macros.
+          </p>
+<p>
+        </p>
+<p>
+          The same mechanism works well at file scope as well, by using an unnamed
+          namespace, we can ensure that these declarations don't conflict with any
+          alternate policies present in other translation units:
+        </p>
+<p>
+          </p>
+<p>
+            
+</p>
+<pre class="programlisting"><span class="preprocessor">#include</span> <span class="special">&lt;</span><span class="identifier">boost</span><span class="special">/</span><span class="identifier">math</span><span class="special">/</span><span class="identifier">special_functions</span><span class="special">.</span><span class="identifier">hpp</span><span class="special">&gt;</span>
+
+<span class="keyword">namespace</span> <span class="special">{</span>
+
+<span class="keyword">using</span> <span class="keyword">namespace</span> <span class="identifier">boost</span><span class="special">::</span><span class="identifier">math</span><span class="special">::</span><span class="identifier">policies</span><span class="special">;</span>
+
+<span class="keyword">typedef</span> <span class="identifier">policy</span><span class="special">&lt;</span>
+   <span class="identifier">domain_error</span><span class="special">&lt;</span><span class="identifier">errno_on_error</span><span class="special">&gt;,</span>
+   <span class="identifier">pole_error</span><span class="special">&lt;</span><span class="identifier">errno_on_error</span><span class="special">&gt;,</span>
+   <span class="identifier">overflow_error</span><span class="special">&lt;</span><span class="identifier">errno_on_error</span><span class="special">&gt;,</span>
+   <span class="identifier">evaluation_error</span><span class="special">&lt;</span><span class="identifier">errno_on_error</span><span class="special">&gt;</span> 
+<span class="special">&gt;</span> <span class="identifier">c_policy</span><span class="special">;</span>
+
+<span class="identifier">BOOST_MATH_DECLARE_SPECIAL_FUNCTIONS</span><span class="special">(</span><span class="identifier">c_policy</span><span class="special">)</span>
+
+<span class="special">}</span> <span class="comment">// close unnamed namespace
+</span>
+<span class="keyword">int</span> <span class="identifier">main</span><span class="special">()</span>
+<span class="special">{</span>
+   <span class="identifier">errno</span> <span class="special">=</span> <span class="number">0</span><span class="special">;</span>
+   <span class="identifier">std</span><span class="special">::</span><span class="identifier">cout</span> <span class="special">&lt;&lt;</span> <span class="string">"Result of tgamma(30000) is: "</span> 
+      <span class="special">&lt;&lt;</span> <span class="identifier">tgamma</span><span class="special">(</span><span class="number">30000</span><span class="special">)</span> <span class="special">&lt;&lt;</span> <span class="identifier">std</span><span class="special">::</span><span class="identifier">endl</span><span class="special">;</span>
+   <span class="identifier">std</span><span class="special">::</span><span class="identifier">cout</span> <span class="special">&lt;&lt;</span> <span class="string">"errno = "</span> <span class="special">&lt;&lt;</span> <span class="identifier">errno</span> <span class="special">&lt;&lt;</span> <span class="identifier">std</span><span class="special">::</span><span class="identifier">endl</span><span class="special">;</span>
+   <span class="identifier">std</span><span class="special">::</span><span class="identifier">cout</span> <span class="special">&lt;&lt;</span> <span class="string">"Result of tgamma(-10) is: "</span> 
+      <span class="special">&lt;&lt;</span> <span class="identifier">tgamma</span><span class="special">(-</span><span class="number">10</span><span class="special">)</span> <span class="special">&lt;&lt;</span> <span class="identifier">std</span><span class="special">::</span><span class="identifier">endl</span><span class="special">;</span>
+   <span class="identifier">std</span><span class="special">::</span><span class="identifier">cout</span> <span class="special">&lt;&lt;</span> <span class="string">"errno = "</span> <span class="special">&lt;&lt;</span> <span class="identifier">errno</span> <span class="special">&lt;&lt;</span> <span class="identifier">std</span><span class="special">::</span><span class="identifier">endl</span><span class="special">;</span>
+<span class="special">}</span>
+
+</pre>
+<p>
+          </p>
+<p>
+        </p>
+<p>
+          Handling the statistical distributions is very similar except that now
+          the macro BOOST_MATH_DECLARE_DISTRIBUTIONS accepts two parameters: the
+          floating point type to use, and the policy type to apply. For example:
+        </p>
+<pre class="programlisting"><span class="identifier">BOOST_MATH_DECLARE_DISTRIBUTIONS</span><span class="special">(</span><span class="keyword">double</span><span class="special">,</span> <span class="identifier">mypolicy</span><span class="special">)</span>
+</pre>
+<p>
+          Results a set of typedefs being defined like this:
+        </p>
+<pre class="programlisting"><span class="keyword">typedef</span> <span class="identifier">boost</span><span class="special">::</span><span class="identifier">math</span><span class="special">::</span><span class="identifier">normal_distribution</span><span class="special">&lt;</span><span class="keyword">double</span><span class="special">,</span> <span class="identifier">mypolicy</span><span class="special">&gt;</span> <span class="identifier">normal</span><span class="special">;</span>
+</pre>
+<p>
+          The name of each typedef is the same as the name of the distribution class
+          template, but without the "_distribution" suffix.
+        </p>
+<p>
+          </p>
+<p>
+            Suppose we want a set of distributions to behave as follows:
+          </p>
+<p>
+          </p>
+<div class="itemizedlist"><ul type="disc">
+<li>
+              Return infinity on overflow, rather than throwing an exception.
+            </li>
+<li>
+              Don't perform any promotion from double to long double internally.
+            </li>
+<li>
+              Return the closest integer result from the quantiles of discrete distributions.
+            </li>
+</ul></div>
+<p>
+          </p>
+<p>
+            We'll begin by including the needed header:
+          </p>
+<p>
+          </p>
+<p>
+            
+</p>
+<pre class="programlisting"><span class="preprocessor">#include</span> <span class="special">&lt;</span><span class="identifier">boost</span><span class="special">/</span><span class="identifier">math</span><span class="special">/</span><span class="identifier">distributions</span><span class="special">.</span><span class="identifier">hpp</span><span class="special">&gt;</span></pre>
+<p>
+          </p>
+<p>
+          </p>
+<p>
+            Open up an appropriate namespace for our distributions, and define the
+            policy type we want. Any policies we don't specify here will inherit
+            the defaults:
+          </p>
+<p>
+          </p>
+<p>
+            
+</p>
+<pre class="programlisting"><span class="keyword">namespace</span> <span class="identifier">my_distributions</span><span class="special">{</span>
+
+<span class="keyword">using</span> <span class="keyword">namespace</span> <span class="identifier">boost</span><span class="special">::</span><span class="identifier">math</span><span class="special">::</span><span class="identifier">policies</span><span class="special">;</span>
+
+<span class="keyword">typedef</span> <span class="identifier">policy</span><span class="special">&lt;</span>
+   <span class="comment">// return infinity and set errno rather than throw:
+</span>   <span class="identifier">overflow_error</span><span class="special">&lt;</span><span class="identifier">errno_on_error</span><span class="special">&gt;,</span>
+   <span class="comment">// Don't promote double -&gt; long double internally:
+</span>   <span class="identifier">promote_double</span><span class="special">&lt;</span><span class="keyword">false</span><span class="special">&gt;,</span>
+   <span class="comment">// Return the closest integer result for discrete quantiles:
+</span>   <span class="identifier">discrete_quantile</span><span class="special">&lt;</span><span class="identifier">integer_round_nearest</span><span class="special">&gt;</span>
+<span class="special">&gt;</span> <span class="identifier">my_policy</span><span class="special">;</span></pre>
+<p>
+          </p>
+<p>
+          </p>
+<p>
+            All we need do now is invoke the BOOST_MATH_DECLARE_DISTRIBUTIONS macro
+            passing the floating point and policy types as arguments:
+          </p>
+<p>
+          </p>
+<p>
+            
+</p>
+<pre class="programlisting"><span class="identifier">BOOST_MATH_DECLARE_DISTRIBUTIONS</span><span class="special">(</span><span class="keyword">double</span><span class="special">,</span> <span class="identifier">my_policy</span><span class="special">)</span>
+
+<span class="special">}</span> <span class="comment">// close namespace my_namespace</span></pre>
+<p>
+          </p>
+<p>
+          </p>
+<p>
+            We now have a set of typedefs defined in namespace my_namespace that
+            all look something like this:
+          </p>
+<p>
+          </p>
+<p>
+            
+</p>
+<pre class="programlisting"><span class="keyword">typedef</span> <span class="identifier">boost</span><span class="special">::</span><span class="identifier">math</span><span class="special">::</span><span class="identifier">normal_distribution</span><span class="special">&lt;</span><span class="keyword">double</span><span class="special">,</span> <span class="identifier">my_policy</span><span class="special">&gt;</span> <span class="identifier">normal</span><span class="special">;</span>
+<span class="keyword">typedef</span> <span class="identifier">boost</span><span class="special">::</span><span class="identifier">math</span><span class="special">::</span><span class="identifier">cauchy_distribution</span><span class="special">&lt;</span><span class="keyword">double</span><span class="special">,</span> <span class="identifier">my_policy</span><span class="special">&gt;</span> <span class="identifier">cauchy</span><span class="special">;</span>
+<span class="keyword">typedef</span> <span class="identifier">boost</span><span class="special">::</span><span class="identifier">math</span><span class="special">::</span><span class="identifier">gamma_distribution</span><span class="special">&lt;</span><span class="keyword">double</span><span class="special">,</span> <span class="identifier">my_policy</span><span class="special">&gt;</span> <span class="identifier">gamma</span><span class="special">;</span>
+<span class="comment">// etc
+</span></pre>
+<p>
+          </p>
+<p>
+          </p>
+<p>
+            So that when we use my_namespace::normal we really end up using <code class="computeroutput"><span class="identifier">boost</span><span class="special">::</span><span class="identifier">math</span><span class="special">::</span><span class="identifier">normal_distribution</span><span class="special">&lt;</span><span class="keyword">double</span><span class="special">,</span> <span class="identifier">my_policy</span><span class="special">&gt;</span></code>:
+          </p>
+<p>
+          </p>
+<p>
+            
+</p>
+<pre class="programlisting"><span class="keyword">int</span> <span class="identifier">main</span><span class="special">()</span>
+<span class="special">{</span>
+   <span class="comment">//
+</span>   <span class="comment">// Start with something we know will overflow:
+</span>   <span class="comment">//
+</span>   <span class="identifier">my_distributions</span><span class="special">::</span><span class="identifier">normal</span> <span class="identifier">norm</span><span class="special">(</span><span class="number">10</span><span class="special">,</span> <span class="number">2</span><span class="special">);</span>
+   <span class="identifier">errno</span> <span class="special">=</span> <span class="number">0</span><span class="special">;</span>
+   <span class="identifier">std</span><span class="special">::</span><span class="identifier">cout</span> <span class="special">&lt;&lt;</span> <span class="string">"Result of quantile(norm, 0) is: "</span> 
+      <span class="special">&lt;&lt;</span> <span class="identifier">quantile</span><span class="special">(</span><span class="identifier">norm</span><span class="special">,</span> <span class="number">0</span><span class="special">)</span> <span class="special">&lt;&lt;</span> <span class="identifier">std</span><span class="special">::</span><span class="identifier">endl</span><span class="special">;</span>
+   <span class="identifier">std</span><span class="special">::</span><span class="identifier">cout</span> <span class="special">&lt;&lt;</span> <span class="string">"errno = "</span> <span class="special">&lt;&lt;</span> <span class="identifier">errno</span> <span class="special">&lt;&lt;</span> <span class="identifier">std</span><span class="special">::</span><span class="identifier">endl</span><span class="special">;</span>
+   <span class="identifier">errno</span> <span class="special">=</span> <span class="number">0</span><span class="special">;</span>
+   <span class="identifier">std</span><span class="special">::</span><span class="identifier">cout</span> <span class="special">&lt;&lt;</span> <span class="string">"Result of quantile(norm, 1) is: "</span> 
+      <span class="special">&lt;&lt;</span> <span class="identifier">quantile</span><span class="special">(</span><span class="identifier">norm</span><span class="special">,</span> <span class="number">1</span><span class="special">)</span> <span class="special">&lt;&lt;</span> <span class="identifier">std</span><span class="special">::</span><span class="identifier">endl</span><span class="special">;</span>
+   <span class="identifier">std</span><span class="special">::</span><span class="identifier">cout</span> <span class="special">&lt;&lt;</span> <span class="string">"errno = "</span> <span class="special">&lt;&lt;</span> <span class="identifier">errno</span> <span class="special">&lt;&lt;</span> <span class="identifier">std</span><span class="special">::</span><span class="identifier">endl</span><span class="special">;</span>
+   <span class="comment">//
+</span>   <span class="comment">// Now try a discrete distribution:
+</span>   <span class="comment">//
+</span>   <span class="identifier">my_distributions</span><span class="special">::</span><span class="identifier">binomial</span> <span class="identifier">binom</span><span class="special">(</span><span class="number">20</span><span class="special">,</span> <span class="number">0.25</span><span class="special">);</span>
+   <span class="identifier">std</span><span class="special">::</span><span class="identifier">cout</span> <span class="special">&lt;&lt;</span> <span class="string">"Result of quantile(binom, 0.05) is: "</span> 
+      <span class="special">&lt;&lt;</span> <span class="identifier">quantile</span><span class="special">(</span><span class="identifier">binom</span><span class="special">,</span> <span class="number">0.05</span><span class="special">)</span> <span class="special">&lt;&lt;</span> <span class="identifier">std</span><span class="special">::</span><span class="identifier">endl</span><span class="special">;</span>
+   <span class="identifier">std</span><span class="special">::</span><span class="identifier">cout</span> <span class="special">&lt;&lt;</span> <span class="string">"Result of quantile(complement(binom, 0.05)) is: "</span> 
+      <span class="special">&lt;&lt;</span> <span class="identifier">quantile</span><span class="special">(</span><span class="identifier">complement</span><span class="special">(</span><span class="identifier">binom</span><span class="special">,</span> <span class="number">0.05</span><span class="special">))</span> <span class="special">&lt;&lt;</span> <span class="identifier">std</span><span class="special">::</span><span class="identifier">endl</span><span class="special">;</span>
+<span class="special">}</span></pre>
+<p>
+          </p>
+<p>
+          </p>
+<p>
+            Which outputs:
+          </p>
+<p>
+          
+</p>
+<pre class="programlisting">Result of quantile(norm, 0) is: -1.#INF
+errno = 34
+Result of quantile(norm, 1) is: 1.#INF
+errno = 34
+Result of quantile(binom, 0.05) is: 1
+Result of quantile(complement(binom, 0.05)) is: 8
+</pre>
+<p>
+          </p>
+<p>
+            This mechanism is particularly useful when we want to define a project-wide
+            policy, and don't want to modify the Boost source or set - possibly fragile
+            and easy to forget - project wide build macros.
+          </p>
+<p>
+        </p>
+<div class="note"><table border="0" summary="Note">
+<tr>
+<td rowspan="2" align="center" valign="top" width="25"><img alt="[Note]" src="../../../../../doc/html/images/note.png"></td>
+<th align="left">Note</th>
+</tr>
+<tr><td align="left" valign="top"><p>
+            There is an important limitation to note: you can not use the macros
+            BOOST_MATH_DECLARE_DISTRIBUTIONS and BOOST_MATH_DECLARE_SPECIAL_FUNCTIONS
+            <span class="emphasis"><em>in the same namespace</em></span>, as doing so creates ambiguities
+            between functions and distributions of the same name.
+          </p></td></tr>
+</table></div>
+<p>
+          As before, the same mechanism works well at file scope as well: by using
+          an unnamed namespace, we can ensure that these declarations don't conflict
+          with any alternate policies present in other translation units:
+        </p>
+<p>
+          </p>
+<p>
+            
+</p>
+<pre class="programlisting"><span class="preprocessor">#include</span> <span class="special">&lt;</span><span class="identifier">boost</span><span class="special">/</span><span class="identifier">math</span><span class="special">/</span><span class="identifier">distributions</span><span class="special">.</span><span class="identifier">hpp</span><span class="special">&gt;</span>
+
+<span class="keyword">namespace</span> <span class="special">{</span>
+
+<span class="keyword">using</span> <span class="keyword">namespace</span> <span class="identifier">boost</span><span class="special">::</span><span class="identifier">math</span><span class="special">::</span><span class="identifier">policies</span><span class="special">;</span>
+
+<span class="keyword">typedef</span> <span class="identifier">policy</span><span class="special">&lt;</span>
+   <span class="comment">// return infinity and set errno rather than throw:
+</span>   <span class="identifier">overflow_error</span><span class="special">&lt;</span><span class="identifier">errno_on_error</span><span class="special">&gt;,</span>
+   <span class="comment">// Don't promote double -&gt; long double internally:
+</span>   <span class="identifier">promote_double</span><span class="special">&lt;</span><span class="keyword">false</span><span class="special">&gt;,</span>
+   <span class="comment">// Return the closest integer result for discrete quantiles:
+</span>   <span class="identifier">discrete_quantile</span><span class="special">&lt;</span><span class="identifier">integer_round_nearest</span><span class="special">&gt;</span>
+<span class="special">&gt;</span> <span class="identifier">my_policy</span><span class="special">;</span>
+
+<span class="identifier">BOOST_MATH_DECLARE_DISTRIBUTIONS</span><span class="special">(</span><span class="keyword">double</span><span class="special">,</span> <span class="identifier">my_policy</span><span class="special">)</span>
+
+<span class="special">}</span> <span class="comment">// close namespace my_namespace
+</span>
+<span class="keyword">int</span> <span class="identifier">main</span><span class="special">()</span>
+<span class="special">{</span>
+   <span class="comment">//
+</span>   <span class="comment">// Start with something we know will overflow:
+</span>   <span class="comment">//
+</span>   <span class="identifier">normal</span> <span class="identifier">norm</span><span class="special">(</span><span class="number">10</span><span class="special">,</span> <span class="number">2</span><span class="special">);</span>
+   <span class="identifier">errno</span> <span class="special">=</span> <span class="number">0</span><span class="special">;</span>
+   <span class="identifier">std</span><span class="special">::</span><span class="identifier">cout</span> <span class="special">&lt;&lt;</span> <span class="string">"Result of quantile(norm, 0) is: "</span> 
+      <span class="special">&lt;&lt;</span> <span class="identifier">quantile</span><span class="special">(</span><span class="identifier">norm</span><span class="special">,</span> <span class="number">0</span><span class="special">)</span> <span class="special">&lt;&lt;</span> <span class="identifier">std</span><span class="special">::</span><span class="identifier">endl</span><span class="special">;</span>
+   <span class="identifier">std</span><span class="special">::</span><span class="identifier">cout</span> <span class="special">&lt;&lt;</span> <span class="string">"errno = "</span> <span class="special">&lt;&lt;</span> <span class="identifier">errno</span> <span class="special">&lt;&lt;</span> <span class="identifier">std</span><span class="special">::</span><span class="identifier">endl</span><span class="special">;</span>
+   <span class="identifier">errno</span> <span class="special">=</span> <span class="number">0</span><span class="special">;</span>
+   <span class="identifier">std</span><span class="special">::</span><span class="identifier">cout</span> <span class="special">&lt;&lt;</span> <span class="string">"Result of quantile(norm, 1) is: "</span> 
+      <span class="special">&lt;&lt;</span> <span class="identifier">quantile</span><span class="special">(</span><span class="identifier">norm</span><span class="special">,</span> <span class="number">1</span><span class="special">)</span> <span class="special">&lt;&lt;</span> <span class="identifier">std</span><span class="special">::</span><span class="identifier">endl</span><span class="special">;</span>
+   <span class="identifier">std</span><span class="special">::</span><span class="identifier">cout</span> <span class="special">&lt;&lt;</span> <span class="string">"errno = "</span> <span class="special">&lt;&lt;</span> <span class="identifier">errno</span> <span class="special">&lt;&lt;</span> <span class="identifier">std</span><span class="special">::</span><span class="identifier">endl</span><span class="special">;</span>
+   <span class="comment">//
+</span>   <span class="comment">// Now try a discrete distribution:
+</span>   <span class="comment">//
+</span>   <span class="identifier">binomial</span> <span class="identifier">binom</span><span class="special">(</span><span class="number">20</span><span class="special">,</span> <span class="number">0.25</span><span class="special">);</span>
+   <span class="identifier">std</span><span class="special">::</span><span class="identifier">cout</span> <span class="special">&lt;&lt;</span> <span class="string">"Result of quantile(binom, 0.05) is: "</span> 
+      <span class="special">&lt;&lt;</span> <span class="identifier">quantile</span><span class="special">(</span><span class="identifier">binom</span><span class="special">,</span> <span class="number">0.05</span><span class="special">)</span> <span class="special">&lt;&lt;</span> <span class="identifier">std</span><span class="special">::</span><span class="identifier">endl</span><span class="special">;</span>
+   <span class="identifier">std</span><span class="special">::</span><span class="identifier">cout</span> <span class="special">&lt;&lt;</span> <span class="string">"Result of quantile(complement(binom, 0.05)) is: "</span> 
+      <span class="special">&lt;&lt;</span> <span class="identifier">quantile</span><span class="special">(</span><span class="identifier">complement</span><span class="special">(</span><span class="identifier">binom</span><span class="special">,</span> <span class="number">0.05</span><span class="special">))</span> <span class="special">&lt;&lt;</span> <span class="identifier">std</span><span class="special">::</span><span class="identifier">endl</span><span class="special">;</span>
+<span class="special">}</span>
+
+</pre>
+<p>
+          </p>
+<p>
+        </p>
+</div>
+<table xmlns:rev="http://www.cs.rpi.edu/~gregod/boost/tools/doc/revision" width="100%"><tr>
+<td align="left"></td>
+<td align="right"><div class="copyright-footer">Copyright © 2006 , 2007, 2008 John Maddock, Paul A. Bristow, Hubert
+      Holin, Xiaogang Zhang, Bruno Lalande and Gautam Sewani<p>
+        Distributed under the Boost Software License, Version 1.0. (See accompanying
+        file LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_0.txt)
+      </p>
+</div></td>
+</tr></table>
+<hr>
+<div class="spirit-nav">
+<a accesskey="p" href="ad_hoc_sf_policies.html"><img src="../../../../../doc/html/images/prev.png" alt="Prev"></a><a accesskey="u" href="../pol_tutorial.html"><img src="../../../../../doc/html/images/up.png" alt="Up"></a><a accesskey="h" href="../../../index.html"><img src="../../../../../doc/html/images/home.png" alt="Home"></a><a accesskey="n" href="user_def_err_pol.html"><img src="../../../../../doc/html/images/next.png" alt="Next"></a>
+</div>
+</body>
+</html>

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+++ sandbox/tools/auto_index/example/math/doc/sf_and_dist/html/math_toolkit/policy/pol_tutorial/policy_tut_defaults.html	2008-11-28 05:25:28 EST (Fri, 28 Nov 2008)
@@ -0,0 +1,137 @@
+<html>
+<head>
+<meta http-equiv="Content-Type" content="text/html; charset=ISO-8859-1">
+<title>Policies Have Sensible Defaults</title>
+<link rel="stylesheet" href="../../../boostbook.css" type="text/css">
+<meta name="generator" content="DocBook XSL Stylesheets Vsnapshot_8125">
+<link rel="home" href="../../../index.html" title="Math Toolkit">
+<link rel="up" href="../pol_tutorial.html" title="Policy Tutorial">
+<link rel="prev" href="what_is_a_policy.html" title="So Just What is a Policy Anyway?">
+<link rel="next" href="policy_usage.html" title="So How are Policies Used Anyway?">
+</head>
+<body bgcolor="white" text="black" link="#0000FF" vlink="#840084" alink="#0000FF">
+<table cellpadding="2" width="100%"><tr>
+<td valign="top"><img alt="Boost C++ Libraries" width="277" height="86" src="../../../../../boost.png"></td>
+<td align="center">Home</td>
+<td align="center">Libraries</td>
+<td align="center">People</td>
+<td align="center">FAQ</td>
+<td align="center">More</td>
+</tr></table>
+<hr>
+<div class="spirit-nav">
+<a accesskey="p" href="what_is_a_policy.html"><img src="../../../../../doc/html/images/prev.png" alt="Prev"></a><a accesskey="u" href="../pol_tutorial.html"><img src="../../../../../doc/html/images/up.png" alt="Up"></a><a accesskey="h" href="../../../index.html"><img src="../../../../../doc/html/images/home.png" alt="Home"></a><a accesskey="n" href="policy_usage.html"><img src="../../../../../doc/html/images/next.png" alt="Next"></a>
+</div>
+<div class="section" lang="en">
+<div class="titlepage"><div><div><h4 class="title">
+<a name="math_toolkit.policy.pol_tutorial.policy_tut_defaults"></a><a class="link" href="policy_tut_defaults.html" title="Policies Have Sensible Defaults">
+        Policies Have Sensible Defaults</a>
+</h4></div></div></div>
+<p>
+          Most of the time you can just ignore the policy framework, the defaults
+          for the various policies are as follows, if these work OK for you then
+          you can stop reading now!
+        </p>
+<div class="variablelist">
+<p class="title"><b></b></p>
+<dl>
+<dt><span class="term">Domain Error</span></dt>
+<dd><p>
+              Throws a <code class="computeroutput"><span class="identifier">std</span><span class="special">::</span><span class="identifier">domain_error</span></code> exception.
+            </p></dd>
+<dt><span class="term">Pole Error</span></dt>
+<dd><p>
+              Occurs when a function is evaluated at a pole: throws a <code class="computeroutput"><span class="identifier">std</span><span class="special">::</span><span class="identifier">domain_error</span></code> exception.
+            </p></dd>
+<dt><span class="term">Overflow Error</span></dt>
+<dd><p>
+              Throws a <code class="computeroutput"><span class="identifier">std</span><span class="special">::</span><span class="identifier">overflow_error</span></code> exception.
+            </p></dd>
+<dt><span class="term">Underflow</span></dt>
+<dd><p>
+              Ignores the underflow, and returns zero.
+            </p></dd>
+<dt><span class="term">Denormalised Result</span></dt>
+<dd><p>
+              Ignores the fact that the result is denormalised, and returns it.
+            </p></dd>
+<dt><span class="term">Rounding Error</span></dt>
+<dd><p>
+              Throws a <code class="computeroutput"><span class="identifier">boost</span><span class="special">::</span><span class="identifier">math</span><span class="special">::</span><span class="identifier">rounding_error</span></code> exception.
+            </p></dd>
+<dt><span class="term">Internal Evaluation Error</span></dt>
+<dd><p>
+              Throws a <code class="computeroutput"><span class="identifier">boost</span><span class="special">::</span><span class="identifier">math</span><span class="special">::</span><span class="identifier">evaluation_error</span></code> exception.
+            </p></dd>
+<dt><span class="term">Indeterminate Result Error</span></dt>
+<dd><p>
+              Returns a result that depends on the function where the error occurred.
+            </p></dd>
+<dt><span class="term">Promotion of float to double</span></dt>
+<dd><p>
+              Does occur by default - gives full float precision results.
+            </p></dd>
+<dt><span class="term">Promotion of double to long double</span></dt>
+<dd><p>
+              Does occur by default if long double offers more precision than double.
+            </p></dd>
+<dt><span class="term">Precision of Approximation Used</span></dt>
+<dd><p>
+              By default uses an approximation that will result in the lowest level
+              of error for the type of the result.
+            </p></dd>
+<dt><span class="term">Behaviour of Discrete Quantiles</span></dt>
+<dd>
+<p>
+              The quantile function will by default return an integer result that
+              has been <span class="emphasis"><em>rounded outwards</em></span>. That is to say lower
+              quantiles (where the probability is less than 0.5) are rounded downward,
+              and upper quantiles (where the probability is greater than 0.5) are
+              rounded upwards. This behaviour ensures that if an X% quantile is requested,
+              then <span class="emphasis"><em>at least</em></span> the requested coverage will be present
+              in the central region, and <span class="emphasis"><em>no more than</em></span> the requested
+              coverage will be present in the tails.
+            </p>
+<p>
+              This behaviour can be changed so that the quantile functions are rounded
+              differently, or even return a real-valued result using <a class="link" href="../pol_overview.html" title="Policy Overview">Policies</a>.
+              It is strongly recommended that you read the tutorial <a class="link" href="understand_dis_quant.html" title="Understanding Quantiles of Discrete Distributions">Understanding
+              Quantiles of Discrete Distributions</a> before using the quantile
+              function on a discrete distribution. The <a class="link" href="../pol_ref/discrete_quant_ref.html" title="Discrete Quantile Policies">reference
+              docs</a> describe how to change the rounding policy for these distributions.
+            </p>
+</dd>
+</dl>
+</div>
+<p>
+          What's more, if you define your own policy type, then it automatically
+          inherits the defaults for any policies not explicitly set, so given:
+        </p>
+<pre class="programlisting"><span class="keyword">using</span> <span class="keyword">namespace</span> <span class="identifier">boost</span><span class="special">::</span><span class="identifier">math</span><span class="special">::</span><span class="identifier">policies</span><span class="special">;</span>
+<span class="comment">//
+</span><span class="comment">// Define a policy that sets ::errno on overflow, and does
+</span><span class="comment">// not promote double to long double internally:
+</span><span class="comment">//
+</span><span class="keyword">typedef</span> <span class="identifier">policy</span><span class="special">&lt;</span><span class="identifier">domain_error</span><span class="special">&lt;</span><span class="identifier">errno_on_error</span><span class="special">&gt;,</span> <span class="identifier">promote_double</span><span class="special">&lt;</span><span class="keyword">false</span><span class="special">&gt;</span> <span class="special">&gt;</span> <span class="identifier">mypolicy</span><span class="special">;</span>
+</pre>
+<p>
+          then <code class="computeroutput"><span class="identifier">mypolicy</span></code> defines a
+          policy where only the overflow error handling and <code class="computeroutput"><span class="keyword">double</span></code>-promotion
+          policies differ from the defaults.
+        </p>
+</div>
+<table xmlns:rev="http://www.cs.rpi.edu/~gregod/boost/tools/doc/revision" width="100%"><tr>
+<td align="left"></td>
+<td align="right"><div class="copyright-footer">Copyright © 2006 , 2007, 2008 John Maddock, Paul A. Bristow, Hubert
+      Holin, Xiaogang Zhang, Bruno Lalande and Gautam Sewani<p>
+        Distributed under the Boost Software License, Version 1.0. (See accompanying
+        file LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_0.txt)
+      </p>
+</div></td>
+</tr></table>
+<hr>
+<div class="spirit-nav">
+<a accesskey="p" href="what_is_a_policy.html"><img src="../../../../../doc/html/images/prev.png" alt="Prev"></a><a accesskey="u" href="../pol_tutorial.html"><img src="../../../../../doc/html/images/up.png" alt="Up"></a><a accesskey="h" href="../../../index.html"><img src="../../../../../doc/html/images/home.png" alt="Home"></a><a accesskey="n" href="policy_usage.html"><img src="../../../../../doc/html/images/next.png" alt="Next"></a>
+</div>
+</body>
+</html>

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+++ sandbox/tools/auto_index/example/math/doc/sf_and_dist/html/math_toolkit/policy/pol_tutorial/policy_usage.html	2008-11-28 05:25:28 EST (Fri, 28 Nov 2008)
@@ -0,0 +1,71 @@
+<html>
+<head>
+<meta http-equiv="Content-Type" content="text/html; charset=ISO-8859-1">
+<title>So How are Policies Used Anyway?</title>
+<link rel="stylesheet" href="../../../boostbook.css" type="text/css">
+<meta name="generator" content="DocBook XSL Stylesheets Vsnapshot_8125">
+<link rel="home" href="../../../index.html" title="Math Toolkit">
+<link rel="up" href="../pol_tutorial.html" title="Policy Tutorial">
+<link rel="prev" href="policy_tut_defaults.html" title="Policies Have Sensible Defaults">
+<link rel="next" href="changing_policy_defaults.html" title="Changing the Policy Defaults">
+</head>
+<body bgcolor="white" text="black" link="#0000FF" vlink="#840084" alink="#0000FF">
+<table cellpadding="2" width="100%"><tr>
+<td valign="top"><img alt="Boost C++ Libraries" width="277" height="86" src="../../../../../boost.png"></td>
+<td align="center">Home</td>
+<td align="center">Libraries</td>
+<td align="center">People</td>
+<td align="center">FAQ</td>
+<td align="center">More</td>
+</tr></table>
+<hr>
+<div class="spirit-nav">
+<a accesskey="p" href="policy_tut_defaults.html"><img src="../../../../../doc/html/images/prev.png" alt="Prev"></a><a accesskey="u" href="../pol_tutorial.html"><img src="../../../../../doc/html/images/up.png" alt="Up"></a><a accesskey="h" href="../../../index.html"><img src="../../../../../doc/html/images/home.png" alt="Home"></a><a accesskey="n" href="changing_policy_defaults.html"><img src="../../../../../doc/html/images/next.png" alt="Next"></a>
+</div>
+<div class="section" lang="en">
+<div class="titlepage"><div><div><h4 class="title">
+<a name="math_toolkit.policy.pol_tutorial.policy_usage"></a><a class="link" href="policy_usage.html" title="So How are Policies Used Anyway?"> So
+        How are Policies Used Anyway?</a>
+</h4></div></div></div>
+<p>
+          The details follow later, but basically policies can be set by either:
+        </p>
+<div class="itemizedlist"><ul type="disc">
+<li>
+            Defining some macros that change the default behaviour: <span class="bold"><strong>this
+            is the recommended method for setting installation-wide policies</strong></span>.
+          </li>
+<li>
+            By instantiating a distribution object with an explicit policy: this
+            is mainly reserved for ad hoc policy changes.
+          </li>
+<li>
+            By passing a policy to a special function as an optional final argument:
+            this is mainly reserved for ad hoc policy changes.
+          </li>
+<li>
+            By using some helper macros to define a set of functions or distributions
+            in the current namespace that use a specific policy: <span class="bold"><strong>this
+            is the recommended method for setting policies on a project- or translation-unit-wide
+            basis</strong></span>.
+          </li>
+</ul></div>
+<p>
+          The following sections introduce these methods in more detail.
+        </p>
+</div>
+<table xmlns:rev="http://www.cs.rpi.edu/~gregod/boost/tools/doc/revision" width="100%"><tr>
+<td align="left"></td>
+<td align="right"><div class="copyright-footer">Copyright © 2006 , 2007, 2008 John Maddock, Paul A. Bristow, Hubert
+      Holin, Xiaogang Zhang, Bruno Lalande and Gautam Sewani<p>
+        Distributed under the Boost Software License, Version 1.0. (See accompanying
+        file LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_0.txt)
+      </p>
+</div></td>
+</tr></table>
+<hr>
+<div class="spirit-nav">
+<a accesskey="p" href="policy_tut_defaults.html"><img src="../../../../../doc/html/images/prev.png" alt="Prev"></a><a accesskey="u" href="../pol_tutorial.html"><img src="../../../../../doc/html/images/up.png" alt="Up"></a><a accesskey="h" href="../../../index.html"><img src="../../../../../doc/html/images/home.png" alt="Home"></a><a accesskey="n" href="changing_policy_defaults.html"><img src="../../../../../doc/html/images/next.png" alt="Next"></a>
+</div>
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+<title>Understanding Quantiles of Discrete Distributions</title>
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+<div class="section" lang="en">
+<div class="titlepage"><div><div><h4 class="title">
+<a name="math_toolkit.policy.pol_tutorial.understand_dis_quant"></a><a class="link" href="understand_dis_quant.html" title="Understanding Quantiles of Discrete Distributions">
+        Understanding Quantiles of Discrete Distributions</a>
+</h4></div></div></div>
+<p>
+          Discrete distributions present us with a problem when calculating the quantile:
+          we are starting from a continuous real-valued variable - the probability
+          - but the result (the value of the random variable) should really be discrete.
+        </p>
+<p>
+          Consider for example a Binomial distribution, with a sample size of 50,
+          and a success fraction of 0.5. There are a variety of ways we can plot
+          a discrete distribution, but if we plot the PDF as a step-function then
+          it looks something like this:
+        </p>
+<p>
+          <span class="inlinemediaobject"><img src="../../../../graphs/binomial_pdf.png" alt="binomial_pdf"></span>
+        </p>
+<p>
+          Now lets suppose that the user asks for a the quantile that corresponds
+          to a probability of 0.05, if we zoom in on the CDF for that region here's
+          what we see:
+        </p>
+<p>
+          <span class="inlinemediaobject"><img src="../../../../graphs/binomial_quantile_1.png" alt="binomial_quantile_1"></span>
+        </p>
+<p>
+          As can be seen there is no random variable that corresponds to a probability
+          of exactly 0.05, so we're left with two choices as shown in the figure:
+        </p>
+<div class="itemizedlist"><ul type="disc">
+<li>
+            We could round the result down to 18.
+          </li>
+<li>
+            We could round the result up to 19.
+          </li>
+</ul></div>
+<p>
+          In fact there's actually a third choice as well: we could "pretend"
+          that the distribution was continuous and return a real valued result: in
+          this case we would calculate a result of approximately 18.701 (this accurately
+          reflects the fact that the result is nearer to 19 than 18).
+        </p>
+<p>
+          By using policies we can offer any of the above as options, but that still
+          leaves the question: <span class="emphasis"><em>What is actually the right thing to do?</em></span>
+        </p>
+<p>
+          And in particular: <span class="emphasis"><em>What policy should we use by default?</em></span>
+        </p>
+<p>
+          In coming to an answer we should realise that:
+        </p>
+<div class="itemizedlist"><ul type="disc">
+<li>
+            Calculating an integer result is often much faster than calculating a
+            real-valued result: in fact in our tests it was up to 20 times faster.
+          </li>
+<li>
+            Normally people calculate quantiles so that they can perform a test of
+            some kind: <span class="emphasis"><em>"If the random variable is less than N then
+            we can reject our null-hypothesis with 90% confidence."</em></span>
+</li>
+</ul></div>
+<p>
+          So there is a genuine benefit to calculating an integer result as well
+          as it being "the right thing to do" from a philosophical point
+          of view. What's more if someone asks for a quantile at 0.05, then we can
+          normally assume that they are asking for <span class="emphasis"><em><span class="bold"><strong>at
+          least</strong></span> 95% of the probability to the right of the value chosen,
+          and <span class="bold"><strong>no more than</strong></span> 5% of the probability
+          to the left of the value chosen.</em></span>
+        </p>
+<p>
+          In the above binomial example we would therefore round the result down
+          to 18.
+        </p>
+<p>
+          The converse applies to upper-quantiles: If the probability is greater
+          than 0.5 we would want to round the quantile up, <span class="emphasis"><em>so that <span class="bold"><strong>at least</strong></span> the requested probability is to the left
+          of the value returned, and <span class="bold"><strong>no more than</strong></span>
+          1 - the requested probability is to the right of the value returned.</em></span>
+        </p>
+<p>
+          Likewise for two-sided intervals, we would round lower quantiles down,
+          and upper quantiles up. This ensures that we have <span class="emphasis"><em>at least the
+          requested probability in the central region</em></span> and <span class="emphasis"><em>no
+          more than 1 minus the requested probability in the tail areas.</em></span>
+        </p>
+<p>
+          For example, taking our 50 sample binomial distribution with a success
+          fraction of 0.5, if we wanted a two sided 90% confidence interval, then
+          we would ask for the 0.05 and 0.95 quantiles with the results <span class="emphasis"><em>rounded
+          outwards</em></span> so that <span class="emphasis"><em>at least 90% of the probability</em></span>
+          is in the central area:
+        </p>
+<p>
+          <span class="inlinemediaobject"><img src="../../../../graphs/binomial_pdf_3.png" alt="binomial_pdf_3"></span>
+        </p>
+<p>
+          So far so good, but there is in fact a trap waiting for the unwary here:
+        </p>
+<pre class="programlisting"><span class="identifier">quantile</span><span class="special">(</span><span class="identifier">binomial</span><span class="special">(</span><span class="number">50</span><span class="special">,</span> <span class="number">0.5</span><span class="special">),</span> <span class="number">0.05</span><span class="special">);</span>
+</pre>
+<p>
+          returns 18 as the result, which is what we would expect from the graph
+          above, and indeed there is no x greater than 18 for which:
+        </p>
+<pre class="programlisting"><span class="identifier">cdf</span><span class="special">(</span><span class="identifier">binomial</span><span class="special">(</span><span class="number">50</span><span class="special">,</span> <span class="number">0.5</span><span class="special">),</span> <span class="identifier">x</span><span class="special">)</span> <span class="special">&lt;=</span> <span class="number">0.05</span><span class="special">;</span>
+</pre>
+<p>
+          However:
+        </p>
+<pre class="programlisting"><span class="identifier">quantile</span><span class="special">(</span><span class="identifier">binomial</span><span class="special">(</span><span class="number">50</span><span class="special">,</span> <span class="number">0.5</span><span class="special">),</span> <span class="number">0.95</span><span class="special">);</span>
+</pre>
+<p>
+          returns 31, and indeed while there is no x less than 31 for which:
+        </p>
+<pre class="programlisting"><span class="identifier">cdf</span><span class="special">(</span><span class="identifier">binomial</span><span class="special">(</span><span class="number">50</span><span class="special">,</span> <span class="number">0.5</span><span class="special">),</span> <span class="identifier">x</span><span class="special">)</span> <span class="special">&gt;=</span> <span class="number">0.95</span><span class="special">;</span>
+</pre>
+<p>
+          We might naively expect that for this symmetrical distribution the result
+          would be 32 (since 32 = 50 - 18), but we need to remember that the cdf
+          of the binomial is <span class="emphasis"><em>inclusive</em></span> of the random variable.
+          So while the left tail area <span class="emphasis"><em>includes</em></span> the quantile
+          returned, the right tail area always excludes an upper quantile value:
+          since that "belongs" to the central area.
+        </p>
+<p>
+          Look at the graph above to see what's going on here: the lower quantile
+          of 18 belongs to the left tail, so any value &lt;= 18 is in the left tail.
+          The upper quantile of 31 on the other hand belongs to the central area,
+          so the tail area actually starts at 32, so any value &gt; 31 is in the
+          right tail.
+        </p>
+<p>
+          Therefore if U and L are the upper and lower quantiles respectively, then
+          a random variable X is in the tail area - where we would reject the null
+          hypothesis if:
+        </p>
+<pre class="programlisting"><span class="identifier">X</span> <span class="special">&lt;=</span> <span class="identifier">L</span> <span class="special">||</span> <span class="identifier">X</span> <span class="special">&gt;</span> <span class="identifier">U</span>
+</pre>
+<p>
+          And the a variable X is inside the central region if:
+        </p>
+<pre class="programlisting"><span class="identifier">L</span> <span class="special">&lt;</span> <span class="identifier">X</span> <span class="special">&lt;=</span> <span class="identifier">U</span>
+</pre>
+<p>
+          The moral here is to <span class="emphasis"><em>always be very careful with your comparisons
+          when dealing with a discrete distribution</em></span>, and if in doubt,
+          <span class="emphasis"><em>base your comparisons on CDF's instead</em></span>.
+        </p>
+<a name="math_toolkit.policy.pol_tutorial.understand_dis_quant.other_rounding_policies_are_available"></a><h6>
+<a name="id884946"></a>
+          <a class="link" href="understand_dis_quant.html#math_toolkit.policy.pol_tutorial.understand_dis_quant.other_rounding_policies_are_available">Other
+          Rounding Policies are Available</a>
+        </h6>
+<p>
+          As you would expect from a section on policies, you won't be surprised
+          to know that other rounding options are available:
+        </p>
+<div class="variablelist">
+<p class="title"><b></b></p>
+<dl>
+<dt><span class="term">integer_round_outwards</span></dt>
+<dd>
+<p>
+              This is the default policy as described above: lower quantiles are
+              rounded down (probability &lt; 0.5), and upper quantiles (probability
+              &gt; 0.5) are rounded up.
+            </p>
+<p>
+              This gives <span class="emphasis"><em>no more than</em></span> the requested probability
+              in the tails, and <span class="emphasis"><em>at least</em></span> the requested probability
+              in the central area.
+            </p>
+</dd>
+<dt><span class="term">integer_round_inwards</span></dt>
+<dd>
+<p>
+              This is the exact opposite of the default policy: lower quantiles are
+              rounded up (probability &lt; 0.5), and upper quantiles (probability
+              &gt; 0.5) are rounded down.
+            </p>
+<p>
+              This gives <span class="emphasis"><em>at least</em></span> the requested probability
+              in the tails, and <span class="emphasis"><em>no more than</em></span> the requested probability
+              in the central area.
+            </p>
+</dd>
+<dt><span class="term">integer_round_down</span></dt>
+<dd><p>
+              This policy will always round the result down no matter whether it
+              is an upper or lower quantile
+            </p></dd>
+<dt><span class="term">integer_round_up</span></dt>
+<dd><p>
+              This policy will always round the result up no matter whether it is
+              an upper or lower quantile
+            </p></dd>
+<dt><span class="term">integer_round_nearest</span></dt>
+<dd><p>
+              This policy will always round the result to the nearest integer no
+              matter whether it is an upper or lower quantile
+            </p></dd>
+<dt><span class="term">real</span></dt>
+<dd><p>
+              This policy will return a real valued result for the quantile of a
+              discrete distribution: this is generally much slower than finding an
+              integer result but does allow for more sophisticated rounding policies.
+            </p></dd>
+</dl>
+</div>
+<p>
+          </p>
+<p>
+            To understand how the rounding policies for the discrete distributions
+            can be used, we'll use the 50-sample binomial distribution with a success
+            fraction of 0.5 once again, and calculate all the possible quantiles
+            at 0.05 and 0.95.
+          </p>
+<p>
+          </p>
+<p>
+            Begin by including the needed headers:
+          </p>
+<p>
+          </p>
+<p>
+            
+</p>
+<pre class="programlisting"><span class="preprocessor">#include</span> <span class="special">&lt;</span><span class="identifier">iostream</span><span class="special">&gt;</span>
+<span class="preprocessor">#include</span> <span class="special">&lt;</span><span class="identifier">boost</span><span class="special">/</span><span class="identifier">math</span><span class="special">/</span><span class="identifier">distributions</span><span class="special">/</span><span class="identifier">binomial</span><span class="special">.</span><span class="identifier">hpp</span><span class="special">&gt;</span></pre>
+<p>
+          </p>
+<p>
+          </p>
+<p>
+            Next we'll bring the needed declarations into scope, and define distribution
+            types for all the available rounding policies:
+          </p>
+<p>
+          </p>
+<p>
+            
+</p>
+<pre class="programlisting"><span class="keyword">using</span> <span class="keyword">namespace</span> <span class="identifier">boost</span><span class="special">::</span><span class="identifier">math</span><span class="special">::</span><span class="identifier">policies</span><span class="special">;</span>
+<span class="keyword">using</span> <span class="keyword">namespace</span> <span class="identifier">boost</span><span class="special">::</span><span class="identifier">math</span><span class="special">;</span>
+
+<span class="keyword">typedef</span> <span class="identifier">binomial_distribution</span><span class="special">&lt;</span>
+            <span class="keyword">double</span><span class="special">,</span> 
+            <span class="identifier">policy</span><span class="special">&lt;</span><span class="identifier">discrete_quantile</span><span class="special">&lt;</span><span class="identifier">integer_round_outwards</span><span class="special">&gt;</span> <span class="special">&gt;</span> <span class="special">&gt;</span> 
+        <span class="identifier">binom_round_outwards</span><span class="special">;</span>
+
+<span class="keyword">typedef</span> <span class="identifier">binomial_distribution</span><span class="special">&lt;</span>
+            <span class="keyword">double</span><span class="special">,</span> 
+            <span class="identifier">policy</span><span class="special">&lt;</span><span class="identifier">discrete_quantile</span><span class="special">&lt;</span><span class="identifier">integer_round_inwards</span><span class="special">&gt;</span> <span class="special">&gt;</span> <span class="special">&gt;</span> 
+        <span class="identifier">binom_round_inwards</span><span class="special">;</span>
+
+<span class="keyword">typedef</span> <span class="identifier">binomial_distribution</span><span class="special">&lt;</span>
+            <span class="keyword">double</span><span class="special">,</span> 
+            <span class="identifier">policy</span><span class="special">&lt;</span><span class="identifier">discrete_quantile</span><span class="special">&lt;</span><span class="identifier">integer_round_down</span><span class="special">&gt;</span> <span class="special">&gt;</span> <span class="special">&gt;</span> 
+        <span class="identifier">binom_round_down</span><span class="special">;</span>
+
+<span class="keyword">typedef</span> <span class="identifier">binomial_distribution</span><span class="special">&lt;</span>
+            <span class="keyword">double</span><span class="special">,</span> 
+            <span class="identifier">policy</span><span class="special">&lt;</span><span class="identifier">discrete_quantile</span><span class="special">&lt;</span><span class="identifier">integer_round_up</span><span class="special">&gt;</span> <span class="special">&gt;</span> <span class="special">&gt;</span> 
+        <span class="identifier">binom_round_up</span><span class="special">;</span>
+
+<span class="keyword">typedef</span> <span class="identifier">binomial_distribution</span><span class="special">&lt;</span>
+            <span class="keyword">double</span><span class="special">,</span> 
+            <span class="identifier">policy</span><span class="special">&lt;</span><span class="identifier">discrete_quantile</span><span class="special">&lt;</span><span class="identifier">integer_round_nearest</span><span class="special">&gt;</span> <span class="special">&gt;</span> <span class="special">&gt;</span> 
+        <span class="identifier">binom_round_nearest</span><span class="special">;</span>
+
+<span class="keyword">typedef</span> <span class="identifier">binomial_distribution</span><span class="special">&lt;</span>
+            <span class="keyword">double</span><span class="special">,</span> 
+            <span class="identifier">policy</span><span class="special">&lt;</span><span class="identifier">discrete_quantile</span><span class="special">&lt;</span><span class="identifier">real</span><span class="special">&gt;</span> <span class="special">&gt;</span> <span class="special">&gt;</span> 
+        <span class="identifier">binom_real_quantile</span><span class="special">;</span></pre>
+<p>
+          </p>
+<p>
+          </p>
+<p>
+            Now let's set to work calling those quantiles:
+          </p>
+<p>
+          </p>
+<p>
+            
+</p>
+<pre class="programlisting"><span class="keyword">int</span> <span class="identifier">main</span><span class="special">()</span>
+<span class="special">{</span>
+   <span class="identifier">std</span><span class="special">::</span><span class="identifier">cout</span> <span class="special">&lt;&lt;</span> 
+      <span class="string">"Testing rounding policies for a 50 sample binomial distribution,\n"</span>
+      <span class="string">"with a success fraction of 0.5.\n\n"</span>
+      <span class="string">"Lower quantiles are calculated at p = 0.05\n\n"</span>
+      <span class="string">"Upper quantiles at p = 0.95.\n\n"</span><span class="special">;</span>
+
+   <span class="identifier">std</span><span class="special">::</span><span class="identifier">cout</span> <span class="special">&lt;&lt;</span> <span class="identifier">std</span><span class="special">::</span><span class="identifier">setw</span><span class="special">(</span><span class="number">25</span><span class="special">)</span> <span class="special">&lt;&lt;</span> <span class="identifier">std</span><span class="special">::</span><span class="identifier">right</span>
+      <span class="special">&lt;&lt;</span> <span class="string">"Policy"</span><span class="special">&lt;&lt;</span> <span class="identifier">std</span><span class="special">::</span><span class="identifier">setw</span><span class="special">(</span><span class="number">18</span><span class="special">)</span> <span class="special">&lt;&lt;</span> <span class="identifier">std</span><span class="special">::</span><span class="identifier">right</span> 
+      <span class="special">&lt;&lt;</span> <span class="string">"Lower Quantile"</span> <span class="special">&lt;&lt;</span> <span class="identifier">std</span><span class="special">::</span><span class="identifier">setw</span><span class="special">(</span><span class="number">18</span><span class="special">)</span> <span class="special">&lt;&lt;</span> <span class="identifier">std</span><span class="special">::</span><span class="identifier">right</span> 
+      <span class="special">&lt;&lt;</span> <span class="string">"Upper Quantile"</span> <span class="special">&lt;&lt;</span> <span class="identifier">std</span><span class="special">::</span><span class="identifier">endl</span><span class="special">;</span>
+   
+   <span class="comment">// Test integer_round_outwards:
+</span>   <span class="identifier">std</span><span class="special">::</span><span class="identifier">cout</span> <span class="special">&lt;&lt;</span> <span class="identifier">std</span><span class="special">::</span><span class="identifier">setw</span><span class="special">(</span><span class="number">25</span><span class="special">)</span> <span class="special">&lt;&lt;</span> <span class="identifier">std</span><span class="special">::</span><span class="identifier">right</span>
+      <span class="special">&lt;&lt;</span> <span class="string">"integer_round_outwards"</span>
+      <span class="special">&lt;&lt;</span> <span class="identifier">std</span><span class="special">::</span><span class="identifier">setw</span><span class="special">(</span><span class="number">18</span><span class="special">)</span> <span class="special">&lt;&lt;</span> <span class="identifier">std</span><span class="special">::</span><span class="identifier">right</span>
+      <span class="special">&lt;&lt;</span> <span class="identifier">quantile</span><span class="special">(</span><span class="identifier">binom_round_outwards</span><span class="special">(</span><span class="number">50</span><span class="special">,</span> <span class="number">0.5</span><span class="special">),</span> <span class="number">0.05</span><span class="special">)</span>
+      <span class="special">&lt;&lt;</span> <span class="identifier">std</span><span class="special">::</span><span class="identifier">setw</span><span class="special">(</span><span class="number">18</span><span class="special">)</span> <span class="special">&lt;&lt;</span> <span class="identifier">std</span><span class="special">::</span><span class="identifier">right</span>
+      <span class="special">&lt;&lt;</span> <span class="identifier">quantile</span><span class="special">(</span><span class="identifier">binom_round_outwards</span><span class="special">(</span><span class="number">50</span><span class="special">,</span> <span class="number">0.5</span><span class="special">),</span> <span class="number">0.95</span><span class="special">)</span> 
+      <span class="special">&lt;&lt;</span> <span class="identifier">std</span><span class="special">::</span><span class="identifier">endl</span><span class="special">;</span>
+   
+   <span class="comment">// Test integer_round_inwards:
+</span>   <span class="identifier">std</span><span class="special">::</span><span class="identifier">cout</span> <span class="special">&lt;&lt;</span> <span class="identifier">std</span><span class="special">::</span><span class="identifier">setw</span><span class="special">(</span><span class="number">25</span><span class="special">)</span> <span class="special">&lt;&lt;</span> <span class="identifier">std</span><span class="special">::</span><span class="identifier">right</span>
+      <span class="special">&lt;&lt;</span> <span class="string">"integer_round_inwards"</span>
+      <span class="special">&lt;&lt;</span> <span class="identifier">std</span><span class="special">::</span><span class="identifier">setw</span><span class="special">(</span><span class="number">18</span><span class="special">)</span> <span class="special">&lt;&lt;</span> <span class="identifier">std</span><span class="special">::</span><span class="identifier">right</span>
+      <span class="special">&lt;&lt;</span> <span class="identifier">quantile</span><span class="special">(</span><span class="identifier">binom_round_inwards</span><span class="special">(</span><span class="number">50</span><span class="special">,</span> <span class="number">0.5</span><span class="special">),</span> <span class="number">0.05</span><span class="special">)</span>
+      <span class="special">&lt;&lt;</span> <span class="identifier">std</span><span class="special">::</span><span class="identifier">setw</span><span class="special">(</span><span class="number">18</span><span class="special">)</span> <span class="special">&lt;&lt;</span> <span class="identifier">std</span><span class="special">::</span><span class="identifier">right</span>
+      <span class="special">&lt;&lt;</span> <span class="identifier">quantile</span><span class="special">(</span><span class="identifier">binom_round_inwards</span><span class="special">(</span><span class="number">50</span><span class="special">,</span> <span class="number">0.5</span><span class="special">),</span> <span class="number">0.95</span><span class="special">)</span> 
+      <span class="special">&lt;&lt;</span> <span class="identifier">std</span><span class="special">::</span><span class="identifier">endl</span><span class="special">;</span>
+   
+   <span class="comment">// Test integer_round_down:
+</span>   <span class="identifier">std</span><span class="special">::</span><span class="identifier">cout</span> <span class="special">&lt;&lt;</span> <span class="identifier">std</span><span class="special">::</span><span class="identifier">setw</span><span class="special">(</span><span class="number">25</span><span class="special">)</span> <span class="special">&lt;&lt;</span> <span class="identifier">std</span><span class="special">::</span><span class="identifier">right</span>
+      <span class="special">&lt;&lt;</span> <span class="string">"integer_round_down"</span>
+      <span class="special">&lt;&lt;</span> <span class="identifier">std</span><span class="special">::</span><span class="identifier">setw</span><span class="special">(</span><span class="number">18</span><span class="special">)</span> <span class="special">&lt;&lt;</span> <span class="identifier">std</span><span class="special">::</span><span class="identifier">right</span>
+      <span class="special">&lt;&lt;</span> <span class="identifier">quantile</span><span class="special">(</span><span class="identifier">binom_round_down</span><span class="special">(</span><span class="number">50</span><span class="special">,</span> <span class="number">0.5</span><span class="special">),</span> <span class="number">0.05</span><span class="special">)</span>
+      <span class="special">&lt;&lt;</span> <span class="identifier">std</span><span class="special">::</span><span class="identifier">setw</span><span class="special">(</span><span class="number">18</span><span class="special">)</span> <span class="special">&lt;&lt;</span> <span class="identifier">std</span><span class="special">::</span><span class="identifier">right</span>
+      <span class="special">&lt;&lt;</span> <span class="identifier">quantile</span><span class="special">(</span><span class="identifier">binom_round_down</span><span class="special">(</span><span class="number">50</span><span class="special">,</span> <span class="number">0.5</span><span class="special">),</span> <span class="number">0.95</span><span class="special">)</span> 
+      <span class="special">&lt;&lt;</span> <span class="identifier">std</span><span class="special">::</span><span class="identifier">endl</span><span class="special">;</span>
+   
+   <span class="comment">// Test integer_round_up:
+</span>   <span class="identifier">std</span><span class="special">::</span><span class="identifier">cout</span> <span class="special">&lt;&lt;</span> <span class="identifier">std</span><span class="special">::</span><span class="identifier">setw</span><span class="special">(</span><span class="number">25</span><span class="special">)</span> <span class="special">&lt;&lt;</span> <span class="identifier">std</span><span class="special">::</span><span class="identifier">right</span>
+      <span class="special">&lt;&lt;</span> <span class="string">"integer_round_up"</span>
+      <span class="special">&lt;&lt;</span> <span class="identifier">std</span><span class="special">::</span><span class="identifier">setw</span><span class="special">(</span><span class="number">18</span><span class="special">)</span> <span class="special">&lt;&lt;</span> <span class="identifier">std</span><span class="special">::</span><span class="identifier">right</span>
+      <span class="special">&lt;&lt;</span> <span class="identifier">quantile</span><span class="special">(</span><span class="identifier">binom_round_up</span><span class="special">(</span><span class="number">50</span><span class="special">,</span> <span class="number">0.5</span><span class="special">),</span> <span class="number">0.05</span><span class="special">)</span>
+      <span class="special">&lt;&lt;</span> <span class="identifier">std</span><span class="special">::</span><span class="identifier">setw</span><span class="special">(</span><span class="number">18</span><span class="special">)</span> <span class="special">&lt;&lt;</span> <span class="identifier">std</span><span class="special">::</span><span class="identifier">right</span>
+      <span class="special">&lt;&lt;</span> <span class="identifier">quantile</span><span class="special">(</span><span class="identifier">binom_round_up</span><span class="special">(</span><span class="number">50</span><span class="special">,</span> <span class="number">0.5</span><span class="special">),</span> <span class="number">0.95</span><span class="special">)</span> 
+      <span class="special">&lt;&lt;</span> <span class="identifier">std</span><span class="special">::</span><span class="identifier">endl</span><span class="special">;</span>
+   
+   <span class="comment">// Test integer_round_nearest:
+</span>   <span class="identifier">std</span><span class="special">::</span><span class="identifier">cout</span> <span class="special">&lt;&lt;</span> <span class="identifier">std</span><span class="special">::</span><span class="identifier">setw</span><span class="special">(</span><span class="number">25</span><span class="special">)</span> <span class="special">&lt;&lt;</span> <span class="identifier">std</span><span class="special">::</span><span class="identifier">right</span>
+      <span class="special">&lt;&lt;</span> <span class="string">"integer_round_nearest"</span>
+      <span class="special">&lt;&lt;</span> <span class="identifier">std</span><span class="special">::</span><span class="identifier">setw</span><span class="special">(</span><span class="number">18</span><span class="special">)</span> <span class="special">&lt;&lt;</span> <span class="identifier">std</span><span class="special">::</span><span class="identifier">right</span>
+      <span class="special">&lt;&lt;</span> <span class="identifier">quantile</span><span class="special">(</span><span class="identifier">binom_round_nearest</span><span class="special">(</span><span class="number">50</span><span class="special">,</span> <span class="number">0.5</span><span class="special">),</span> <span class="number">0.05</span><span class="special">)</span>
+      <span class="special">&lt;&lt;</span> <span class="identifier">std</span><span class="special">::</span><span class="identifier">setw</span><span class="special">(</span><span class="number">18</span><span class="special">)</span> <span class="special">&lt;&lt;</span> <span class="identifier">std</span><span class="special">::</span><span class="identifier">right</span>
+      <span class="special">&lt;&lt;</span> <span class="identifier">quantile</span><span class="special">(</span><span class="identifier">binom_round_nearest</span><span class="special">(</span><span class="number">50</span><span class="special">,</span> <span class="number">0.5</span><span class="special">),</span> <span class="number">0.95</span><span class="special">)</span> 
+      <span class="special">&lt;&lt;</span> <span class="identifier">std</span><span class="special">::</span><span class="identifier">endl</span><span class="special">;</span>
+   
+   <span class="comment">// Test real:
+</span>   <span class="identifier">std</span><span class="special">::</span><span class="identifier">cout</span> <span class="special">&lt;&lt;</span> <span class="identifier">std</span><span class="special">::</span><span class="identifier">setw</span><span class="special">(</span><span class="number">25</span><span class="special">)</span> <span class="special">&lt;&lt;</span> <span class="identifier">std</span><span class="special">::</span><span class="identifier">right</span>
+      <span class="special">&lt;&lt;</span> <span class="string">"real"</span>
+      <span class="special">&lt;&lt;</span> <span class="identifier">std</span><span class="special">::</span><span class="identifier">setw</span><span class="special">(</span><span class="number">18</span><span class="special">)</span> <span class="special">&lt;&lt;</span> <span class="identifier">std</span><span class="special">::</span><span class="identifier">right</span>
+      <span class="special">&lt;&lt;</span> <span class="identifier">quantile</span><span class="special">(</span><span class="identifier">binom_real_quantile</span><span class="special">(</span><span class="number">50</span><span class="special">,</span> <span class="number">0.5</span><span class="special">),</span> <span class="number">0.05</span><span class="special">)</span>
+      <span class="special">&lt;&lt;</span> <span class="identifier">std</span><span class="special">::</span><span class="identifier">setw</span><span class="special">(</span><span class="number">18</span><span class="special">)</span> <span class="special">&lt;&lt;</span> <span class="identifier">std</span><span class="special">::</span><span class="identifier">right</span>
+      <span class="special">&lt;&lt;</span> <span class="identifier">quantile</span><span class="special">(</span><span class="identifier">binom_real_quantile</span><span class="special">(</span><span class="number">50</span><span class="special">,</span> <span class="number">0.5</span><span class="special">),</span> <span class="number">0.95</span><span class="special">)</span> 
+      <span class="special">&lt;&lt;</span> <span class="identifier">std</span><span class="special">::</span><span class="identifier">endl</span><span class="special">;</span>
+<span class="special">}</span></pre>
+<p>
+          </p>
+<p>
+          </p>
+<p>
+            Which produces the program output:
+          </p>
+<p>
+          
+</p>
+<pre class="programlisting">Testing rounding policies for a 50 sample binomial distribution,
+with a success fraction of 0.5.
+
+Lower quantiles are calculated at p = 0.05
+
+Upper quantiles at p = 0.95.
+
+Testing rounding policies for a 50 sample binomial distribution,
+with a success fraction of 0.5.
+
+Lower quantiles are calculated at p = 0.05
+
+Upper quantiles at p = 0.95.
+
+                   Policy    Lower Quantile    Upper Quantile
+   integer_round_outwards                18                31
+    integer_round_inwards                19                30
+       integer_round_down                18                30
+         integer_round_up                19                31
+    integer_round_nearest                19                30
+                     real            18.701            30.299
+</pre>
+<p>
+        </p>
+</div>
+<table xmlns:rev="http://www.cs.rpi.edu/~gregod/boost/tools/doc/revision" width="100%"><tr>
+<td align="left"></td>
+<td align="right"><div class="copyright-footer">Copyright © 2006 , 2007, 2008 John Maddock, Paul A. Bristow, Hubert
+      Holin, Xiaogang Zhang, Bruno Lalande and Gautam Sewani<p>
+        Distributed under the Boost Software License, Version 1.0. (See accompanying
+        file LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_0.txt)
+      </p>
+</div></td>
+</tr></table>
+<hr>
+<div class="spirit-nav">
+<a accesskey="p" href="user_def_err_pol.html"><img src="../../../../../doc/html/images/prev.png" alt="Prev"></a><a accesskey="u" href="../pol_tutorial.html"><img src="../../../../../doc/html/images/up.png" alt="Up"></a><a accesskey="h" href="../../../index.html"><img src="../../../../../doc/html/images/home.png" alt="Home"></a><a accesskey="n" href="../pol_ref.html"><img src="../../../../../doc/html/images/next.png" alt="Next"></a>
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@@ -0,0 +1,628 @@
+<html>
+<head>
+<meta http-equiv="Content-Type" content="text/html; charset=ISO-8859-1">
+<title>Calling User Defined Error Handlers</title>
+<link rel="stylesheet" href="../../../boostbook.css" type="text/css">
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+</div>
+<div class="section" lang="en">
+<div class="titlepage"><div><div><h4 class="title">
+<a name="math_toolkit.policy.pol_tutorial.user_def_err_pol"></a><a class="link" href="user_def_err_pol.html" title="Calling User Defined Error Handlers">
+        Calling User Defined Error Handlers</a>
+</h4></div></div></div>
+<p>
+          </p>
+<p>
+            Suppose we want our own user-defined error handlers rather than the any
+            of the default ones supplied by the library to be used. If we set the
+            policy for a specific type of error to <code class="computeroutput"><span class="identifier">user_error</span></code>
+            then the library will call a user-supplied error handler. These are forward
+            declared, but not defined in boost/math/policies/error_handling.hpp like
+            this:
+          </p>
+<p>
+          
+</p>
+<pre class="programlisting"><span class="keyword">namespace</span> <span class="identifier">boost</span><span class="special">{</span> <span class="keyword">namespace</span> <span class="identifier">math</span><span class="special">{</span> <span class="keyword">namespace</span> <span class="identifier">policies</span><span class="special">{</span>
+
+<span class="keyword">template</span> <span class="special">&lt;</span><span class="keyword">class</span> <span class="identifier">T</span><span class="special">&gt;</span>
+<span class="identifier">T</span> <span class="identifier">user_domain_error</span><span class="special">(</span><span class="keyword">const</span> <span class="keyword">char</span><span class="special">*</span> <span class="identifier">function</span><span class="special">,</span> <span class="keyword">const</span> <span class="keyword">char</span><span class="special">*</span> <span class="identifier">message</span><span class="special">,</span> <span class="keyword">const</span> <span class="identifier">T</span><span class="special">&amp;</span> <span class="identifier">val</span><span class="special">);</span>
+<span class="keyword">template</span> <span class="special">&lt;</span><span class="keyword">class</span> <span class="identifier">T</span><span class="special">&gt;</span>
+<span class="identifier">T</span> <span class="identifier">user_pole_error</span><span class="special">(</span><span class="keyword">const</span> <span class="keyword">char</span><span class="special">*</span> <span class="identifier">function</span><span class="special">,</span> <span class="keyword">const</span> <span class="keyword">char</span><span class="special">*</span> <span class="identifier">message</span><span class="special">,</span> <span class="keyword">const</span> <span class="identifier">T</span><span class="special">&amp;</span> <span class="identifier">val</span><span class="special">);</span>
+<span class="keyword">template</span> <span class="special">&lt;</span><span class="keyword">class</span> <span class="identifier">T</span><span class="special">&gt;</span>
+<span class="identifier">T</span> <span class="identifier">user_overflow_error</span><span class="special">(</span><span class="keyword">const</span> <span class="keyword">char</span><span class="special">*</span> <span class="identifier">function</span><span class="special">,</span> <span class="keyword">const</span> <span class="keyword">char</span><span class="special">*</span> <span class="identifier">message</span><span class="special">,</span> <span class="keyword">const</span> <span class="identifier">T</span><span class="special">&amp;</span> <span class="identifier">val</span><span class="special">);</span>
+<span class="keyword">template</span> <span class="special">&lt;</span><span class="keyword">class</span> <span class="identifier">T</span><span class="special">&gt;</span>
+<span class="identifier">T</span> <span class="identifier">user_underflow_error</span><span class="special">(</span><span class="keyword">const</span> <span class="keyword">char</span><span class="special">*</span> <span class="identifier">function</span><span class="special">,</span> <span class="keyword">const</span> <span class="keyword">char</span><span class="special">*</span> <span class="identifier">message</span><span class="special">,</span> <span class="keyword">const</span> <span class="identifier">T</span><span class="special">&amp;</span> <span class="identifier">val</span><span class="special">);</span>
+<span class="keyword">template</span> <span class="special">&lt;</span><span class="keyword">class</span> <span class="identifier">T</span><span class="special">&gt;</span>
+<span class="identifier">T</span> <span class="identifier">user_denorm_error</span><span class="special">(</span><span class="keyword">const</span> <span class="keyword">char</span><span class="special">*</span> <span class="identifier">function</span><span class="special">,</span> <span class="keyword">const</span> <span class="keyword">char</span><span class="special">*</span> <span class="identifier">message</span><span class="special">,</span> <span class="keyword">const</span> <span class="identifier">T</span><span class="special">&amp;</span> <span class="identifier">val</span><span class="special">);</span>
+<span class="keyword">template</span> <span class="special">&lt;</span><span class="keyword">class</span> <span class="identifier">T</span><span class="special">&gt;</span>
+<span class="identifier">T</span> <span class="identifier">user_evaluation_error</span><span class="special">(</span><span class="keyword">const</span> <span class="keyword">char</span><span class="special">*</span> <span class="identifier">function</span><span class="special">,</span> <span class="keyword">const</span> <span class="keyword">char</span><span class="special">*</span> <span class="identifier">message</span><span class="special">,</span> <span class="keyword">const</span> <span class="identifier">T</span><span class="special">&amp;</span> <span class="identifier">val</span><span class="special">);</span>
+<span class="keyword">template</span> <span class="special">&lt;</span><span class="keyword">class</span> <span class="identifier">T</span><span class="special">&gt;</span>
+<span class="identifier">T</span> <span class="identifier">user_indeterminate_result_error</span><span class="special">(</span><span class="keyword">const</span> <span class="keyword">char</span><span class="special">*</span> <span class="identifier">function</span><span class="special">,</span> <span class="keyword">const</span> <span class="keyword">char</span><span class="special">*</span> <span class="identifier">message</span><span class="special">,</span> <span class="keyword">const</span> <span class="identifier">T</span><span class="special">&amp;</span> <span class="identifier">val</span><span class="special">);</span>
+
+<span class="special">}}}</span> <span class="comment">// namespaces
+</span></pre>
+<p>
+          </p>
+<p>
+            So out first job is to include the header we want to use, and then provide
+            definitions for the user-defined error handlers we want to use:
+          </p>
+<p>
+          </p>
+<p>
+            
+</p>
+<pre class="programlisting"><span class="preprocessor">#include</span> <span class="special">&lt;</span><span class="identifier">iostream</span><span class="special">&gt;</span>
+<span class="preprocessor">#include</span> <span class="special">&lt;</span><span class="identifier">boost</span><span class="special">/</span><span class="identifier">math</span><span class="special">/</span><span class="identifier">special_functions</span><span class="special">.</span><span class="identifier">hpp</span><span class="special">&gt;</span>
+
+<span class="keyword">namespace</span> <span class="identifier">boost</span><span class="special">{</span> <span class="keyword">namespace</span> <span class="identifier">math</span><span class="special">{</span> <span class="keyword">namespace</span> <span class="identifier">policies</span><span class="special">{</span>
+
+<span class="keyword">template</span> <span class="special">&lt;</span><span class="keyword">class</span> <span class="identifier">T</span><span class="special">&gt;</span>
+<span class="identifier">T</span> <span class="identifier">user_domain_error</span><span class="special">(</span><span class="keyword">const</span> <span class="keyword">char</span><span class="special">*</span> <span class="identifier">function</span><span class="special">,</span> <span class="keyword">const</span> <span class="keyword">char</span><span class="special">*</span> <span class="identifier">message</span><span class="special">,</span> <span class="keyword">const</span> <span class="identifier">T</span><span class="special">&amp;</span> <span class="identifier">val</span><span class="special">)</span>
+<span class="special">{</span>
+   <span class="identifier">std</span><span class="special">::</span><span class="identifier">cerr</span> <span class="special">&lt;&lt;</span> <span class="string">"Domain Error."</span> <span class="special">&lt;&lt;</span> <span class="identifier">std</span><span class="special">::</span><span class="identifier">endl</span><span class="special">;</span>
+   <span class="keyword">return</span> <span class="identifier">std</span><span class="special">::</span><span class="identifier">numeric_limits</span><span class="special">&lt;</span><span class="identifier">T</span><span class="special">&gt;::</span><span class="identifier">quiet_NaN</span><span class="special">();</span>
+<span class="special">}</span>
+
+<span class="keyword">template</span> <span class="special">&lt;</span><span class="keyword">class</span> <span class="identifier">T</span><span class="special">&gt;</span>
+<span class="identifier">T</span> <span class="identifier">user_pole_error</span><span class="special">(</span><span class="keyword">const</span> <span class="keyword">char</span><span class="special">*</span> <span class="identifier">function</span><span class="special">,</span> <span class="keyword">const</span> <span class="keyword">char</span><span class="special">*</span> <span class="identifier">message</span><span class="special">,</span> <span class="keyword">const</span> <span class="identifier">T</span><span class="special">&amp;</span> <span class="identifier">val</span><span class="special">)</span>
+<span class="special">{</span>
+   <span class="identifier">std</span><span class="special">::</span><span class="identifier">cerr</span> <span class="special">&lt;&lt;</span> <span class="string">"Pole Error."</span> <span class="special">&lt;&lt;</span> <span class="identifier">std</span><span class="special">::</span><span class="identifier">endl</span><span class="special">;</span>
+   <span class="keyword">return</span> <span class="identifier">std</span><span class="special">::</span><span class="identifier">numeric_limits</span><span class="special">&lt;</span><span class="identifier">T</span><span class="special">&gt;::</span><span class="identifier">quiet_NaN</span><span class="special">();</span>
+<span class="special">}</span>
+
+
+<span class="special">}}}</span> <span class="comment">// namespaces</span></pre>
+<p>
+          </p>
+<p>
+          </p>
+<p>
+            Now we'll need to define a suitable policy that will call these handlers,
+            and define some forwarding functions that make use of the policy:
+          </p>
+<p>
+          </p>
+<p>
+            
+</p>
+<pre class="programlisting"><span class="keyword">namespace</span><span class="special">{</span>
+
+<span class="keyword">using</span> <span class="keyword">namespace</span> <span class="identifier">boost</span><span class="special">::</span><span class="identifier">math</span><span class="special">::</span><span class="identifier">policies</span><span class="special">;</span>
+
+<span class="keyword">typedef</span> <span class="identifier">policy</span><span class="special">&lt;</span>
+   <span class="identifier">domain_error</span><span class="special">&lt;</span><span class="identifier">user_error</span><span class="special">&gt;,</span>
+   <span class="identifier">pole_error</span><span class="special">&lt;</span><span class="identifier">user_error</span><span class="special">&gt;</span>
+<span class="special">&gt;</span> <span class="identifier">user_error_policy</span><span class="special">;</span>
+
+<span class="identifier">BOOST_MATH_DECLARE_SPECIAL_FUNCTIONS</span><span class="special">(</span><span class="identifier">user_error_policy</span><span class="special">)</span>
+
+<span class="special">}</span> <span class="comment">// close unnamed namespace</span></pre>
+<p>
+          </p>
+<p>
+          </p>
+<p>
+            We now have a set of forwarding functions defined in an unnamed namespace
+            that all look something like this:
+          </p>
+<p>
+          </p>
+<p>
+            
+</p>
+<pre class="programlisting"><span class="keyword">template</span> <span class="special">&lt;</span><span class="keyword">class</span> <span class="identifier">RealType</span><span class="special">&gt;</span>
+<span class="keyword">inline</span> <span class="keyword">typename</span> <span class="identifier">boost</span><span class="special">::</span><span class="identifier">math</span><span class="special">::</span><span class="identifier">tools</span><span class="special">::</span><span class="identifier">promote_args</span><span class="special">&lt;</span><span class="identifier">RT</span><span class="special">&gt;::</span><span class="identifier">type</span>
+   <span class="identifier">tgamma</span><span class="special">(</span><span class="identifier">RT</span> <span class="identifier">z</span><span class="special">)</span>
+<span class="special">{</span>
+   <span class="keyword">return</span> <span class="identifier">boost</span><span class="special">::</span><span class="identifier">math</span><span class="special">::</span><span class="identifier">tgamma</span><span class="special">(</span><span class="identifier">z</span><span class="special">,</span> <span class="identifier">user_error_policy</span><span class="special">());</span>
+<span class="special">}</span>
+</pre>
+<p>
+          </p>
+<p>
+          </p>
+<p>
+            So that when we call <code class="computeroutput"><span class="identifier">tgamma</span><span class="special">(</span><span class="identifier">z</span><span class="special">)</span></code> we really end up calling <code class="computeroutput"><span class="identifier">boost</span><span class="special">::</span><span class="identifier">math</span><span class="special">::</span><span class="identifier">tgamma</span><span class="special">(</span><span class="identifier">z</span><span class="special">,</span> <span class="identifier">user_error_policy</span><span class="special">())</span></code>,
+            and any errors will get directed to our own error handlers:
+          </p>
+<p>
+          </p>
+<p>
+            
+</p>
+<pre class="programlisting"><span class="keyword">int</span> <span class="identifier">main</span><span class="special">()</span>
+<span class="special">{</span>
+   <span class="identifier">std</span><span class="special">::</span><span class="identifier">cout</span> <span class="special">&lt;&lt;</span> <span class="string">"Result of erf_inv(-10) is: "</span>
+      <span class="special">&lt;&lt;</span> <span class="identifier">erf_inv</span><span class="special">(-</span><span class="number">10</span><span class="special">)</span> <span class="special">&lt;&lt;</span> <span class="identifier">std</span><span class="special">::</span><span class="identifier">endl</span><span class="special">;</span>
+   <span class="identifier">std</span><span class="special">::</span><span class="identifier">cout</span> <span class="special">&lt;&lt;</span> <span class="string">"Result of tgamma(-10) is: "</span>
+      <span class="special">&lt;&lt;</span> <span class="identifier">tgamma</span><span class="special">(-</span><span class="number">10</span><span class="special">)</span> <span class="special">&lt;&lt;</span> <span class="identifier">std</span><span class="special">::</span><span class="identifier">endl</span><span class="special">;</span>
+<span class="special">}</span></pre>
+<p>
+          </p>
+<p>
+          </p>
+<p>
+            Which outputs:
+          </p>
+<p>
+          
+</p>
+<pre class="programlisting">Domain Error.
+Result of erf_inv(-10) is: 1.#QNAN
+Pole Error.
+Result of tgamma(-10) is: 1.#QNAN
+</pre>
+<p>
+        </p>
+<p>
+          </p>
+<p>
+            The previous example was all well and good, but the custom error handlers
+            didn't really do much of any use. In this example we'll implement all
+            the custom handlers and show how the information provided to them can
+            be used to generate nice formatted error messages.
+          </p>
+<p>
+          </p>
+<p>
+            Each error handler has the general form:
+          </p>
+<p>
+          
+</p>
+<pre class="programlisting"><span class="keyword">template</span> <span class="special">&lt;</span><span class="keyword">class</span> <span class="identifier">T</span><span class="special">&gt;</span>
+<span class="identifier">T</span> <span class="identifier">user_</span><span class="emphasis"><em>error_type</em></span><span class="special">(</span>
+   <span class="keyword">const</span> <span class="keyword">char</span><span class="special">*</span> <span class="identifier">function</span><span class="special">,</span> 
+   <span class="keyword">const</span> <span class="keyword">char</span><span class="special">*</span> <span class="identifier">message</span><span class="special">,</span> 
+   <span class="keyword">const</span> <span class="identifier">T</span><span class="special">&amp;</span> <span class="identifier">val</span><span class="special">);</span>
+</pre>
+<p>
+          </p>
+<p>
+            and accepts three arguments:
+          </p>
+<p>
+          </p>
+<div class="variablelist">
+<p class="title"><b></b></p>
+<dl>
+<dt><span class="term">const char* function</span></dt>
+<dd><p>
+                The name of the function that raised the error, this string contains
+                one or more %1% format specifiers that should be replaced by the
+                name of type T.
+              </p></dd>
+<dt><span class="term">const char* message</span></dt>
+<dd><p>
+                A message associated with the error, normally this contains a %1%
+                format specifier that should be replaced with the value of <span class="emphasis"><em>value</em></span>:
+                however note that overflow and underflow messages do not contain
+                this %1% specifier (since the value of <span class="emphasis"><em>value</em></span>
+                is immaterial in these cases).
+              </p></dd>
+<dt><span class="term">const T&amp; value</span></dt>
+<dd><p>
+                The value that caused the error: either an argument to the function
+                if this is a domain or pole error, the tentative result if this is
+                a denorm or evaluation error, or zero or infinity for underflow or
+                overflow errors.
+              </p></dd>
+</dl>
+</div>
+<p>
+          </p>
+<p>
+            As before we'll include the headers we need first:
+          </p>
+<p>
+          </p>
+<p>
+            
+</p>
+<pre class="programlisting"><span class="preprocessor">#include</span> <span class="special">&lt;</span><span class="identifier">iostream</span><span class="special">&gt;</span>
+<span class="preprocessor">#include</span> <span class="special">&lt;</span><span class="identifier">boost</span><span class="special">/</span><span class="identifier">math</span><span class="special">/</span><span class="identifier">special_functions</span><span class="special">.</span><span class="identifier">hpp</span><span class="special">&gt;</span></pre>
+<p>
+          </p>
+<p>
+          </p>
+<p>
+            Next we'll implement the error handlers for each type of error, starting
+            with domain errors:
+          </p>
+<p>
+          </p>
+<p>
+            
+</p>
+<pre class="programlisting"><span class="keyword">namespace</span> <span class="identifier">boost</span><span class="special">{</span> <span class="keyword">namespace</span> <span class="identifier">math</span><span class="special">{</span> <span class="keyword">namespace</span> <span class="identifier">policies</span><span class="special">{</span>
+
+<span class="keyword">template</span> <span class="special">&lt;</span><span class="keyword">class</span> <span class="identifier">T</span><span class="special">&gt;</span>
+<span class="identifier">T</span> <span class="identifier">user_domain_error</span><span class="special">(</span><span class="keyword">const</span> <span class="keyword">char</span><span class="special">*</span> <span class="identifier">function</span><span class="special">,</span> <span class="keyword">const</span> <span class="keyword">char</span><span class="special">*</span> <span class="identifier">message</span><span class="special">,</span> <span class="keyword">const</span> <span class="identifier">T</span><span class="special">&amp;</span> <span class="identifier">val</span><span class="special">)</span>
+<span class="special">{</span></pre>
+<p>
+          </p>
+<p>
+          </p>
+<p>
+            We'll begin with a bit of defensive programming:
+          </p>
+<p>
+          </p>
+<p>
+            
+</p>
+<pre class="programlisting"><span class="keyword">if</span><span class="special">(</span><span class="identifier">function</span> <span class="special">==</span> <span class="number">0</span><span class="special">)</span>
+    <span class="identifier">function</span> <span class="special">=</span> <span class="string">"Unknown function with arguments of type %1%"</span><span class="special">;</span>
+<span class="keyword">if</span><span class="special">(</span><span class="identifier">message</span> <span class="special">==</span> <span class="number">0</span><span class="special">)</span>
+    <span class="identifier">message</span> <span class="special">=</span> <span class="string">"Cause unknown with bad argument %1%"</span><span class="special">;</span></pre>
+<p>
+          </p>
+<p>
+          </p>
+<p>
+            Next we'll format the name of the function with the name of type T:
+          </p>
+<p>
+          </p>
+<p>
+            
+</p>
+<pre class="programlisting"><span class="identifier">std</span><span class="special">::</span><span class="identifier">string</span> <span class="identifier">msg</span><span class="special">(</span><span class="string">"Error in function "</span><span class="special">);</span>
+<span class="identifier">msg</span> <span class="special">+=</span> <span class="special">(</span><span class="identifier">boost</span><span class="special">::</span><span class="identifier">format</span><span class="special">(</span><span class="identifier">function</span><span class="special">)</span> <span class="special">%</span> <span class="keyword">typeid</span><span class="special">(</span><span class="identifier">T</span><span class="special">).</span><span class="identifier">name</span><span class="special">()).</span><span class="identifier">str</span><span class="special">();</span></pre>
+<p>
+          </p>
+<p>
+          </p>
+<p>
+            Then likewise format the error message with the value of parameter <span class="emphasis"><em>val</em></span>,
+            making sure we output all the digits of <span class="emphasis"><em>val</em></span>:
+          </p>
+<p>
+          </p>
+<p>
+            
+</p>
+<pre class="programlisting"><span class="identifier">msg</span> <span class="special">+=</span> <span class="string">": \n"</span><span class="special">;</span>
+<span class="keyword">int</span> <span class="identifier">prec</span> <span class="special">=</span> <span class="number">2</span> <span class="special">+</span> <span class="special">(</span><span class="identifier">std</span><span class="special">::</span><span class="identifier">numeric_limits</span><span class="special">&lt;</span><span class="identifier">T</span><span class="special">&gt;::</span><span class="identifier">digits</span> <span class="special">*</span> <span class="number">30103UL</span><span class="special">)</span> <span class="special">/</span> <span class="number">100000UL</span><span class="special">;</span>
+<span class="identifier">msg</span> <span class="special">+=</span> <span class="special">(</span><span class="identifier">boost</span><span class="special">::</span><span class="identifier">format</span><span class="special">(</span><span class="identifier">message</span><span class="special">)</span> <span class="special">%</span> <span class="identifier">boost</span><span class="special">::</span><span class="identifier">io</span><span class="special">::</span><span class="identifier">group</span><span class="special">(</span><span class="identifier">std</span><span class="special">::</span><span class="identifier">setprecision</span><span class="special">(</span><span class="identifier">prec</span><span class="special">),</span> <span class="identifier">val</span><span class="special">)).</span><span class="identifier">str</span><span class="special">();</span></pre>
+<p>
+          </p>
+<p>
+          </p>
+<p>
+            Now we just have to do something with the message, we could throw an
+            exception, but for the purposes of this example we'll just dump the message
+            to std::cerr:
+          </p>
+<p>
+          </p>
+<p>
+            
+</p>
+<pre class="programlisting"><span class="identifier">std</span><span class="special">::</span><span class="identifier">cerr</span> <span class="special">&lt;&lt;</span> <span class="identifier">msg</span> <span class="special">&lt;&lt;</span> <span class="identifier">std</span><span class="special">::</span><span class="identifier">endl</span><span class="special">;</span></pre>
+<p>
+          </p>
+<p>
+          </p>
+<p>
+            Finally the only sensible value we can return from a domain error is
+            a NaN:
+          </p>
+<p>
+          </p>
+<p>
+            
+</p>
+<pre class="programlisting">   <span class="keyword">return</span> <span class="identifier">std</span><span class="special">::</span><span class="identifier">numeric_limits</span><span class="special">&lt;</span><span class="identifier">T</span><span class="special">&gt;::</span><span class="identifier">quiet_NaN</span><span class="special">();</span>
+<span class="special">}</span></pre>
+<p>
+          </p>
+<p>
+          </p>
+<p>
+            Pole errors are essentially a special case of domain errors, so in this
+            example we'll just return the result of a domain error:
+          </p>
+<p>
+          </p>
+<p>
+            
+</p>
+<pre class="programlisting"><span class="keyword">template</span> <span class="special">&lt;</span><span class="keyword">class</span> <span class="identifier">T</span><span class="special">&gt;</span>
+<span class="identifier">T</span> <span class="identifier">user_pole_error</span><span class="special">(</span><span class="keyword">const</span> <span class="keyword">char</span><span class="special">*</span> <span class="identifier">function</span><span class="special">,</span> <span class="keyword">const</span> <span class="keyword">char</span><span class="special">*</span> <span class="identifier">message</span><span class="special">,</span> <span class="keyword">const</span> <span class="identifier">T</span><span class="special">&amp;</span> <span class="identifier">val</span><span class="special">)</span>
+<span class="special">{</span>
+   <span class="keyword">return</span> <span class="identifier">user_domain_error</span><span class="special">(</span><span class="identifier">function</span><span class="special">,</span> <span class="identifier">message</span><span class="special">,</span> <span class="identifier">val</span><span class="special">);</span>
+<span class="special">}</span></pre>
+<p>
+          </p>
+<p>
+          </p>
+<p>
+            Overflow errors are very similar to domain errors, except that there's
+            no %1% format specifier in the <span class="emphasis"><em>message</em></span> parameter:
+          </p>
+<p>
+          </p>
+<p>
+            
+</p>
+<pre class="programlisting"><span class="keyword">template</span> <span class="special">&lt;</span><span class="keyword">class</span> <span class="identifier">T</span><span class="special">&gt;</span>
+<span class="identifier">T</span> <span class="identifier">user_overflow_error</span><span class="special">(</span><span class="keyword">const</span> <span class="keyword">char</span><span class="special">*</span> <span class="identifier">function</span><span class="special">,</span> <span class="keyword">const</span> <span class="keyword">char</span><span class="special">*</span> <span class="identifier">message</span><span class="special">,</span> <span class="keyword">const</span> <span class="identifier">T</span><span class="special">&amp;</span> <span class="identifier">val</span><span class="special">)</span>
+<span class="special">{</span>
+   <span class="keyword">if</span><span class="special">(</span><span class="identifier">function</span> <span class="special">==</span> <span class="number">0</span><span class="special">)</span>
+       <span class="identifier">function</span> <span class="special">=</span> <span class="string">"Unknown function with arguments of type %1%"</span><span class="special">;</span>
+   <span class="keyword">if</span><span class="special">(</span><span class="identifier">message</span> <span class="special">==</span> <span class="number">0</span><span class="special">)</span>
+       <span class="identifier">message</span> <span class="special">=</span> <span class="string">"Result of function is too large to represent"</span><span class="special">;</span>
+
+   <span class="identifier">std</span><span class="special">::</span><span class="identifier">string</span> <span class="identifier">msg</span><span class="special">(</span><span class="string">"Error in function "</span><span class="special">);</span>
+   <span class="identifier">msg</span> <span class="special">+=</span> <span class="special">(</span><span class="identifier">boost</span><span class="special">::</span><span class="identifier">format</span><span class="special">(</span><span class="identifier">function</span><span class="special">)</span> <span class="special">%</span> <span class="keyword">typeid</span><span class="special">(</span><span class="identifier">T</span><span class="special">).</span><span class="identifier">name</span><span class="special">()).</span><span class="identifier">str</span><span class="special">();</span>
+
+   <span class="identifier">msg</span> <span class="special">+=</span> <span class="string">": \n"</span><span class="special">;</span>
+   <span class="identifier">msg</span> <span class="special">+=</span> <span class="identifier">message</span><span class="special">;</span>
+
+   <span class="identifier">std</span><span class="special">::</span><span class="identifier">cerr</span> <span class="special">&lt;&lt;</span> <span class="identifier">msg</span> <span class="special">&lt;&lt;</span> <span class="identifier">std</span><span class="special">::</span><span class="identifier">endl</span><span class="special">;</span>
+   
+   <span class="comment">// Value passed to the function is an infinity, just return it:
+</span>   <span class="keyword">return</span> <span class="identifier">val</span><span class="special">;</span> 
+<span class="special">}</span></pre>
+<p>
+          </p>
+<p>
+          </p>
+<p>
+            Underflow errors are much the same as overflow:
+          </p>
+<p>
+          </p>
+<p>
+            
+</p>
+<pre class="programlisting"><span class="keyword">template</span> <span class="special">&lt;</span><span class="keyword">class</span> <span class="identifier">T</span><span class="special">&gt;</span>
+<span class="identifier">T</span> <span class="identifier">user_underflow_error</span><span class="special">(</span><span class="keyword">const</span> <span class="keyword">char</span><span class="special">*</span> <span class="identifier">function</span><span class="special">,</span> <span class="keyword">const</span> <span class="keyword">char</span><span class="special">*</span> <span class="identifier">message</span><span class="special">,</span> <span class="keyword">const</span> <span class="identifier">T</span><span class="special">&amp;</span> <span class="identifier">val</span><span class="special">)</span>
+<span class="special">{</span>
+   <span class="keyword">if</span><span class="special">(</span><span class="identifier">function</span> <span class="special">==</span> <span class="number">0</span><span class="special">)</span>
+       <span class="identifier">function</span> <span class="special">=</span> <span class="string">"Unknown function with arguments of type %1%"</span><span class="special">;</span>
+   <span class="keyword">if</span><span class="special">(</span><span class="identifier">message</span> <span class="special">==</span> <span class="number">0</span><span class="special">)</span>
+       <span class="identifier">message</span> <span class="special">=</span> <span class="string">"Result of function is too small to represent"</span><span class="special">;</span>
+
+   <span class="identifier">std</span><span class="special">::</span><span class="identifier">string</span> <span class="identifier">msg</span><span class="special">(</span><span class="string">"Error in function "</span><span class="special">);</span>
+   <span class="identifier">msg</span> <span class="special">+=</span> <span class="special">(</span><span class="identifier">boost</span><span class="special">::</span><span class="identifier">format</span><span class="special">(</span><span class="identifier">function</span><span class="special">)</span> <span class="special">%</span> <span class="keyword">typeid</span><span class="special">(</span><span class="identifier">T</span><span class="special">).</span><span class="identifier">name</span><span class="special">()).</span><span class="identifier">str</span><span class="special">();</span>
+
+   <span class="identifier">msg</span> <span class="special">+=</span> <span class="string">": \n"</span><span class="special">;</span>
+   <span class="identifier">msg</span> <span class="special">+=</span> <span class="identifier">message</span><span class="special">;</span>
+
+   <span class="identifier">std</span><span class="special">::</span><span class="identifier">cerr</span> <span class="special">&lt;&lt;</span> <span class="identifier">msg</span> <span class="special">&lt;&lt;</span> <span class="identifier">std</span><span class="special">::</span><span class="identifier">endl</span><span class="special">;</span>
+   
+   <span class="comment">// Value passed to the function is zero, just return it:
+</span>   <span class="keyword">return</span> <span class="identifier">val</span><span class="special">;</span> 
+<span class="special">}</span></pre>
+<p>
+          </p>
+<p>
+          </p>
+<p>
+            Denormalised results are much the same as underflow:
+          </p>
+<p>
+          </p>
+<p>
+            
+</p>
+<pre class="programlisting"><span class="keyword">template</span> <span class="special">&lt;</span><span class="keyword">class</span> <span class="identifier">T</span><span class="special">&gt;</span>
+<span class="identifier">T</span> <span class="identifier">user_denorm_error</span><span class="special">(</span><span class="keyword">const</span> <span class="keyword">char</span><span class="special">*</span> <span class="identifier">function</span><span class="special">,</span> <span class="keyword">const</span> <span class="keyword">char</span><span class="special">*</span> <span class="identifier">message</span><span class="special">,</span> <span class="keyword">const</span> <span class="identifier">T</span><span class="special">&amp;</span> <span class="identifier">val</span><span class="special">)</span>
+<span class="special">{</span>
+   <span class="keyword">if</span><span class="special">(</span><span class="identifier">function</span> <span class="special">==</span> <span class="number">0</span><span class="special">)</span>
+       <span class="identifier">function</span> <span class="special">=</span> <span class="string">"Unknown function with arguments of type %1%"</span><span class="special">;</span>
+   <span class="keyword">if</span><span class="special">(</span><span class="identifier">message</span> <span class="special">==</span> <span class="number">0</span><span class="special">)</span>
+       <span class="identifier">message</span> <span class="special">=</span> <span class="string">"Result of function is denormalised"</span><span class="special">;</span>
+
+   <span class="identifier">std</span><span class="special">::</span><span class="identifier">string</span> <span class="identifier">msg</span><span class="special">(</span><span class="string">"Error in function "</span><span class="special">);</span>
+   <span class="identifier">msg</span> <span class="special">+=</span> <span class="special">(</span><span class="identifier">boost</span><span class="special">::</span><span class="identifier">format</span><span class="special">(</span><span class="identifier">function</span><span class="special">)</span> <span class="special">%</span> <span class="keyword">typeid</span><span class="special">(</span><span class="identifier">T</span><span class="special">).</span><span class="identifier">name</span><span class="special">()).</span><span class="identifier">str</span><span class="special">();</span>
+
+   <span class="identifier">msg</span> <span class="special">+=</span> <span class="string">": \n"</span><span class="special">;</span>
+   <span class="identifier">msg</span> <span class="special">+=</span> <span class="identifier">message</span><span class="special">;</span>
+
+   <span class="identifier">std</span><span class="special">::</span><span class="identifier">cerr</span> <span class="special">&lt;&lt;</span> <span class="identifier">msg</span> <span class="special">&lt;&lt;</span> <span class="identifier">std</span><span class="special">::</span><span class="identifier">endl</span><span class="special">;</span>
+   
+   <span class="comment">// Value passed to the function is denormalised, just return it:
+</span>   <span class="keyword">return</span> <span class="identifier">val</span><span class="special">;</span> 
+<span class="special">}</span></pre>
+<p>
+          </p>
+<p>
+          </p>
+<p>
+            Which leaves us with evaluation errors, these occur when an internal
+            error occurs that prevents the function being fully evaluated. The parameter
+            <span class="emphasis"><em>val</em></span> contains the closest approximation to the result
+            found so far:
+          </p>
+<p>
+          </p>
+<p>
+            
+</p>
+<pre class="programlisting"><span class="keyword">template</span> <span class="special">&lt;</span><span class="keyword">class</span> <span class="identifier">T</span><span class="special">&gt;</span>
+<span class="identifier">T</span> <span class="identifier">user_evaluation_error</span><span class="special">(</span><span class="keyword">const</span> <span class="keyword">char</span><span class="special">*</span> <span class="identifier">function</span><span class="special">,</span> <span class="keyword">const</span> <span class="keyword">char</span><span class="special">*</span> <span class="identifier">message</span><span class="special">,</span> <span class="keyword">const</span> <span class="identifier">T</span><span class="special">&amp;</span> <span class="identifier">val</span><span class="special">)</span>
+<span class="special">{</span>
+   <span class="keyword">if</span><span class="special">(</span><span class="identifier">function</span> <span class="special">==</span> <span class="number">0</span><span class="special">)</span>
+       <span class="identifier">function</span> <span class="special">=</span> <span class="string">"Unknown function with arguments of type %1%"</span><span class="special">;</span>
+   <span class="keyword">if</span><span class="special">(</span><span class="identifier">message</span> <span class="special">==</span> <span class="number">0</span><span class="special">)</span>
+       <span class="identifier">message</span> <span class="special">=</span> <span class="string">"An internal evaluation error occured with "</span>
+                  <span class="string">"the best value calculated so far of %1%"</span><span class="special">;</span>
+
+   <span class="identifier">std</span><span class="special">::</span><span class="identifier">string</span> <span class="identifier">msg</span><span class="special">(</span><span class="string">"Error in function "</span><span class="special">);</span>
+   <span class="identifier">msg</span> <span class="special">+=</span> <span class="special">(</span><span class="identifier">boost</span><span class="special">::</span><span class="identifier">format</span><span class="special">(</span><span class="identifier">function</span><span class="special">)</span> <span class="special">%</span> <span class="keyword">typeid</span><span class="special">(</span><span class="identifier">T</span><span class="special">).</span><span class="identifier">name</span><span class="special">()).</span><span class="identifier">str</span><span class="special">();</span>
+
+   <span class="identifier">msg</span> <span class="special">+=</span> <span class="string">": \n"</span><span class="special">;</span>
+   <span class="keyword">int</span> <span class="identifier">prec</span> <span class="special">=</span> <span class="number">2</span> <span class="special">+</span> <span class="special">(</span><span class="identifier">std</span><span class="special">::</span><span class="identifier">numeric_limits</span><span class="special">&lt;</span><span class="identifier">T</span><span class="special">&gt;::</span><span class="identifier">digits</span> <span class="special">*</span> <span class="number">30103UL</span><span class="special">)</span> <span class="special">/</span> <span class="number">100000UL</span><span class="special">;</span>
+   <span class="identifier">msg</span> <span class="special">+=</span> <span class="special">(</span><span class="identifier">boost</span><span class="special">::</span><span class="identifier">format</span><span class="special">(</span><span class="identifier">message</span><span class="special">)</span> <span class="special">%</span> <span class="identifier">boost</span><span class="special">::</span><span class="identifier">io</span><span class="special">::</span><span class="identifier">group</span><span class="special">(</span><span class="identifier">std</span><span class="special">::</span><span class="identifier">setprecision</span><span class="special">(</span><span class="identifier">prec</span><span class="special">),</span> <span class="identifier">val</span><span class="special">)).</span><span class="identifier">str</span><span class="special">();</span>
+
+   <span class="identifier">std</span><span class="special">::</span><span class="identifier">cerr</span> <span class="special">&lt;&lt;</span> <span class="identifier">msg</span> <span class="special">&lt;&lt;</span> <span class="identifier">std</span><span class="special">::</span><span class="identifier">endl</span><span class="special">;</span>
+
+   <span class="comment">// What do we return here?  This is generally a fatal error,
+</span>   <span class="comment">// that should never occur, just return a NaN for the purposes
+</span>   <span class="comment">// of the example:
+</span>   <span class="keyword">return</span> <span class="identifier">std</span><span class="special">::</span><span class="identifier">numeric_limits</span><span class="special">&lt;</span><span class="identifier">T</span><span class="special">&gt;::</span><span class="identifier">quiet_NaN</span><span class="special">();</span>
+<span class="special">}</span>
+
+<span class="special">}}}</span> <span class="comment">// namespaces</span></pre>
+<p>
+          </p>
+<p>
+          </p>
+<p>
+            Now we'll need to define a suitable policy that will call these handlers,
+            and define some forwarding functions that make use of the policy:
+          </p>
+<p>
+          </p>
+<p>
+            
+</p>
+<pre class="programlisting"><span class="keyword">namespace</span><span class="special">{</span>
+
+<span class="keyword">using</span> <span class="keyword">namespace</span> <span class="identifier">boost</span><span class="special">::</span><span class="identifier">math</span><span class="special">::</span><span class="identifier">policies</span><span class="special">;</span>
+
+<span class="keyword">typedef</span> <span class="identifier">policy</span><span class="special">&lt;</span>
+   <span class="identifier">domain_error</span><span class="special">&lt;</span><span class="identifier">user_error</span><span class="special">&gt;,</span>
+   <span class="identifier">pole_error</span><span class="special">&lt;</span><span class="identifier">user_error</span><span class="special">&gt;,</span>
+   <span class="identifier">overflow_error</span><span class="special">&lt;</span><span class="identifier">user_error</span><span class="special">&gt;,</span>
+   <span class="identifier">underflow_error</span><span class="special">&lt;</span><span class="identifier">user_error</span><span class="special">&gt;,</span>
+   <span class="identifier">denorm_error</span><span class="special">&lt;</span><span class="identifier">user_error</span><span class="special">&gt;,</span>
+   <span class="identifier">evaluation_error</span><span class="special">&lt;</span><span class="identifier">user_error</span><span class="special">&gt;</span>
+<span class="special">&gt;</span> <span class="identifier">user_error_policy</span><span class="special">;</span>
+
+<span class="identifier">BOOST_MATH_DECLARE_SPECIAL_FUNCTIONS</span><span class="special">(</span><span class="identifier">user_error_policy</span><span class="special">)</span>
+
+<span class="special">}</span> <span class="comment">// close unnamed namespace</span></pre>
+<p>
+          </p>
+<p>
+          </p>
+<p>
+            We now have a set of forwarding functions defined in an unnamed namespace
+            that all look something like this:
+          </p>
+<p>
+          </p>
+<p>
+            
+</p>
+<pre class="programlisting"><span class="keyword">template</span> <span class="special">&lt;</span><span class="keyword">class</span> <span class="identifier">RealType</span><span class="special">&gt;</span>
+<span class="keyword">inline</span> <span class="keyword">typename</span> <span class="identifier">boost</span><span class="special">::</span><span class="identifier">math</span><span class="special">::</span><span class="identifier">tools</span><span class="special">::</span><span class="identifier">promote_args</span><span class="special">&lt;</span><span class="identifier">RT</span><span class="special">&gt;::</span><span class="identifier">type</span>
+   <span class="identifier">tgamma</span><span class="special">(</span><span class="identifier">RT</span> <span class="identifier">z</span><span class="special">)</span>
+<span class="special">{</span>
+   <span class="keyword">return</span> <span class="identifier">boost</span><span class="special">::</span><span class="identifier">math</span><span class="special">::</span><span class="identifier">tgamma</span><span class="special">(</span><span class="identifier">z</span><span class="special">,</span> <span class="identifier">user_error_policy</span><span class="special">());</span>
+<span class="special">}</span>
+</pre>
+<p>
+          </p>
+<p>
+          </p>
+<p>
+            So that when we call <code class="computeroutput"><span class="identifier">tgamma</span><span class="special">(</span><span class="identifier">z</span><span class="special">)</span></code> we really end up calling <code class="computeroutput"><span class="identifier">boost</span><span class="special">::</span><span class="identifier">math</span><span class="special">::</span><span class="identifier">tgamma</span><span class="special">(</span><span class="identifier">z</span><span class="special">,</span> <span class="identifier">user_error_policy</span><span class="special">())</span></code>,
+            and any errors will get directed to our own error handlers:
+          </p>
+<p>
+          </p>
+<p>
+            
+</p>
+<pre class="programlisting"><span class="keyword">int</span> <span class="identifier">main</span><span class="special">()</span>
+<span class="special">{</span>
+   <span class="comment">// Raise a domain error:
+</span>   <span class="identifier">std</span><span class="special">::</span><span class="identifier">cout</span> <span class="special">&lt;&lt;</span> <span class="string">"Result of erf_inv(-10) is: "</span>
+      <span class="special">&lt;&lt;</span> <span class="identifier">erf_inv</span><span class="special">(-</span><span class="number">10</span><span class="special">)</span> <span class="special">&lt;&lt;</span> <span class="identifier">std</span><span class="special">::</span><span class="identifier">endl</span> <span class="special">&lt;&lt;</span> <span class="identifier">std</span><span class="special">::</span><span class="identifier">endl</span><span class="special">;</span>
+   <span class="comment">// Raise a pole error:
+</span>   <span class="identifier">std</span><span class="special">::</span><span class="identifier">cout</span> <span class="special">&lt;&lt;</span> <span class="string">"Result of tgamma(-10) is: "</span>
+      <span class="special">&lt;&lt;</span> <span class="identifier">tgamma</span><span class="special">(-</span><span class="number">10</span><span class="special">)</span> <span class="special">&lt;&lt;</span> <span class="identifier">std</span><span class="special">::</span><span class="identifier">endl</span> <span class="special">&lt;&lt;</span> <span class="identifier">std</span><span class="special">::</span><span class="identifier">endl</span><span class="special">;</span>
+   <span class="comment">// Raise an overflow error:
+</span>   <span class="identifier">std</span><span class="special">::</span><span class="identifier">cout</span> <span class="special">&lt;&lt;</span> <span class="string">"Result of tgamma(3000) is: "</span>
+      <span class="special">&lt;&lt;</span> <span class="identifier">tgamma</span><span class="special">(</span><span class="number">3000</span><span class="special">)</span> <span class="special">&lt;&lt;</span> <span class="identifier">std</span><span class="special">::</span><span class="identifier">endl</span> <span class="special">&lt;&lt;</span> <span class="identifier">std</span><span class="special">::</span><span class="identifier">endl</span><span class="special">;</span>
+   <span class="comment">// Raise an underflow error:
+</span>   <span class="identifier">std</span><span class="special">::</span><span class="identifier">cout</span> <span class="special">&lt;&lt;</span> <span class="string">"Result of tgamma(-190.5) is: "</span>
+      <span class="special">&lt;&lt;</span> <span class="identifier">tgamma</span><span class="special">(-</span><span class="number">190.5</span><span class="special">)</span> <span class="special">&lt;&lt;</span> <span class="identifier">std</span><span class="special">::</span><span class="identifier">endl</span> <span class="special">&lt;&lt;</span> <span class="identifier">std</span><span class="special">::</span><span class="identifier">endl</span><span class="special">;</span>
+   <span class="comment">// Unfortunately we can't predicably raise a denormalised
+</span>   <span class="comment">// result, nor can we raise an evaluation error in this example
+</span>   <span class="comment">// since these should never really occur!
+</span><span class="special">}</span></pre>
+<p>
+          </p>
+<p>
+          </p>
+<p>
+            Which outputs:
+          </p>
+<p>
+          
+</p>
+<pre class="programlisting">Error in function boost::math::erf_inv&lt;double&gt;(double, double):
+Argument outside range [-1, 1] in inverse erf function (got p=-10).
+Result of erf_inv(-10) is: 1.#QNAN
+
+Error in function boost::math::tgamma&lt;long double&gt;(long double):
+Evaluation of tgamma at a negative integer -10.
+Result of tgamma(-10) is: 1.#QNAN
+
+Error in function boost::math::tgamma&lt;long double&gt;(long double):
+Result of tgamma is too large to represent.
+Error in function boost::math::tgamma&lt;double&gt;(double):
+Result of function is too large to represent
+Result of tgamma(3000) is: 1.#INF
+
+Error in function boost::math::tgamma&lt;long double&gt;(long double):
+Result of tgamma is too large to represent.
+Error in function boost::math::tgamma&lt;long double&gt;(long double):
+Result of tgamma is too small to represent.
+Result of tgamma(-190.5) is: 0
+</pre>
+<p>
+          </p>
+<p>
+            Notice how some of the calls result in an error handler being called
+            more than once, or for more than one handler to be called: this is an
+            artefact of the fact that many functions are implemented in terms of
+            one or more sub-routines each of which may have it's own error handling.
+            For example <code class="computeroutput"><span class="identifier">tgamma</span><span class="special">(-</span><span class="number">190.5</span><span class="special">)</span></code>
+            is implemented in terms of <code class="computeroutput"><span class="identifier">tgamma</span><span class="special">(</span><span class="number">190.5</span><span class="special">)</span></code> - which overflows - the reflection formula
+            for <code class="computeroutput"><span class="identifier">tgamma</span></code> then notices
+            that it's dividing by infinity and underflows.
+          </p>
+<p>
+        </p>
+</div>
+<table xmlns:rev="http://www.cs.rpi.edu/~gregod/boost/tools/doc/revision" width="100%"><tr>
+<td align="left"></td>
+<td align="right"><div class="copyright-footer">Copyright © 2006 , 2007, 2008 John Maddock, Paul A. Bristow, Hubert
+      Holin, Xiaogang Zhang, Bruno Lalande and Gautam Sewani<p>
+        Distributed under the Boost Software License, Version 1.0. (See accompanying
+        file LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_0.txt)
+      </p>
+</div></td>
+</tr></table>
+<hr>
+<div class="spirit-nav">
+<a accesskey="p" href="namespace_policies.html"><img src="../../../../../doc/html/images/prev.png" alt="Prev"></a><a accesskey="u" href="../pol_tutorial.html"><img src="../../../../../doc/html/images/up.png" alt="Up"></a><a accesskey="h" href="../../../index.html"><img src="../../../../../doc/html/images/home.png" alt="Home"></a><a accesskey="n" href="understand_dis_quant.html"><img src="../../../../../doc/html/images/next.png" alt="Next"></a>
+</div>
+</body>
+</html>

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+++ sandbox/tools/auto_index/example/math/doc/sf_and_dist/html/math_toolkit/policy/pol_tutorial/what_is_a_policy.html	2008-11-28 05:25:28 EST (Fri, 28 Nov 2008)
@@ -0,0 +1,87 @@
+<html>
+<head>
+<meta http-equiv="Content-Type" content="text/html; charset=ISO-8859-1">
+<title>So Just What is a Policy Anyway?</title>
+<link rel="stylesheet" href="../../../boostbook.css" type="text/css">
+<meta name="generator" content="DocBook XSL Stylesheets Vsnapshot_8125">
+<link rel="home" href="../../../index.html" title="Math Toolkit">
+<link rel="up" href="../pol_tutorial.html" title="Policy Tutorial">
+<link rel="prev" href="../pol_tutorial.html" title="Policy Tutorial">
+<link rel="next" href="policy_tut_defaults.html" title="Policies Have Sensible Defaults">
+</head>
+<body bgcolor="white" text="black" link="#0000FF" vlink="#840084" alink="#0000FF">
+<table cellpadding="2" width="100%"><tr>
+<td valign="top"><img alt="Boost C++ Libraries" width="277" height="86" src="../../../../../boost.png"></td>
+<td align="center">Home</td>
+<td align="center">Libraries</td>
+<td align="center">People</td>
+<td align="center">FAQ</td>
+<td align="center">More</td>
+</tr></table>
+<hr>
+<div class="spirit-nav">
+<a accesskey="p" href="../pol_tutorial.html"><img src="../../../../../doc/html/images/prev.png" alt="Prev"></a><a accesskey="u" href="../pol_tutorial.html"><img src="../../../../../doc/html/images/up.png" alt="Up"></a><a accesskey="h" href="../../../index.html"><img src="../../../../../doc/html/images/home.png" alt="Home"></a><a accesskey="n" href="policy_tut_defaults.html"><img src="../../../../../doc/html/images/next.png" alt="Next"></a>
+</div>
+<div class="section" lang="en">
+<div class="titlepage"><div><div><h4 class="title">
+<a name="math_toolkit.policy.pol_tutorial.what_is_a_policy"></a><a class="link" href="what_is_a_policy.html" title="So Just What is a Policy Anyway?">
+        So Just What is a Policy Anyway?</a>
+</h4></div></div></div>
+<p>
+          A policy is a compile-time mechanism for customising the behaviour of a
+          special function, or a statistical distribution. With Policies you can
+          control:
+        </p>
+<div class="itemizedlist"><ul type="disc">
+<li>
+            What action to take when an error occurs.
+          </li>
+<li>
+            What happens when you call a function that is mathematically undefined
+            (for example if you ask for the mean of a Cauchy distribution).
+          </li>
+<li>
+            What happens when you ask for a quantile of a discrete distribution.
+          </li>
+<li>
+            Whether the library is allowed to internally promote <code class="computeroutput"><span class="keyword">float</span></code>
+            to <code class="computeroutput"><span class="keyword">double</span></code> and <code class="computeroutput"><span class="keyword">double</span></code> to <code class="computeroutput"><span class="keyword">long</span>
+            <span class="keyword">double</span></code> in order to improve precision.
+          </li>
+<li>
+            What precision to use when calculating the result.
+          </li>
+</ul></div>
+<p>
+          Some of these policies could arguably be runtime variables, but then we
+          couldn't use compile-time dispatch internally to select the best evaluation
+          method for the given policies.
+        </p>
+<p>
+          For this reason a Policy is a <span class="emphasis"><em>type</em></span>: in fact it's an
+          instance of the class template <code class="computeroutput"><span class="identifier">boost</span><span class="special">::</span><span class="identifier">math</span><span class="special">::</span><span class="identifier">policies</span><span class="special">::</span><span class="identifier">policy</span><span class="special">&lt;&gt;</span></code>. This class is just a compile-time-container
+          of user-selected policies (sometimes called a type-list):
+        </p>
+<pre class="programlisting"><span class="keyword">using</span> <span class="keyword">namespace</span> <span class="identifier">boost</span><span class="special">::</span><span class="identifier">math</span><span class="special">::</span><span class="identifier">policies</span><span class="special">;</span>
+<span class="comment">//
+</span><span class="comment">// Define a policy that sets ::errno on overflow, and does
+</span><span class="comment">// not promote double to long double internally:
+</span><span class="comment">//
+</span><span class="keyword">typedef</span> <span class="identifier">policy</span><span class="special">&lt;</span><span class="identifier">domain_error</span><span class="special">&lt;</span><span class="identifier">errno_on_error</span><span class="special">&gt;,</span> <span class="identifier">promote_double</span><span class="special">&lt;</span><span class="keyword">false</span><span class="special">&gt;</span> <span class="special">&gt;</span> <span class="identifier">mypolicy</span><span class="special">;</span>
+</pre>
+</div>
+<table xmlns:rev="http://www.cs.rpi.edu/~gregod/boost/tools/doc/revision" width="100%"><tr>
+<td align="left"></td>
+<td align="right"><div class="copyright-footer">Copyright © 2006 , 2007, 2008 John Maddock, Paul A. Bristow, Hubert
+      Holin, Xiaogang Zhang, Bruno Lalande and Gautam Sewani<p>
+        Distributed under the Boost Software License, Version 1.0. (See accompanying
+        file LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_0.txt)
+      </p>
+</div></td>
+</tr></table>
+<hr>
+<div class="spirit-nav">
+<a accesskey="p" href="../pol_tutorial.html"><img src="../../../../../doc/html/images/prev.png" alt="Prev"></a><a accesskey="u" href="../pol_tutorial.html"><img src="../../../../../doc/html/images/up.png" alt="Up"></a><a accesskey="h" href="../../../index.html"><img src="../../../../../doc/html/images/home.png" alt="Home"></a><a accesskey="n" href="policy_tut_defaults.html"><img src="../../../../../doc/html/images/next.png" alt="Next"></a>
+</div>
+</body>
+</html>

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+++ sandbox/tools/auto_index/example/math/doc/sf_and_dist/html/math_toolkit/special.html	2008-11-28 05:25:28 EST (Fri, 28 Nov 2008)
@@ -0,0 +1,195 @@
+<html>
+<head>
+<meta http-equiv="Content-Type" content="text/html; charset=ISO-8859-1">
+<title>Special Functions</title>
+<link rel="stylesheet" href="../boostbook.css" type="text/css">
+<meta name="generator" content="DocBook XSL Stylesheets Vsnapshot_8125">
+<link rel="home" href="../index.html" title="Math Toolkit">
+<link rel="up" href="../index.html" title="Math Toolkit">
+<link rel="prev" href="dist/future.html" title="Extras/Future Directions">
+<link rel="next" href="special/sf_gamma.html" title="Gamma Functions">
+</head>
+<body bgcolor="white" text="black" link="#0000FF" vlink="#840084" alink="#0000FF">
+<table cellpadding="2" width="100%"><tr>
+<td valign="top"><img alt="Boost C++ Libraries" width="277" height="86" src="../../../boost.png"></td>
+<td align="center">Home</td>
+<td align="center">Libraries</td>
+<td align="center">People</td>
+<td align="center">FAQ</td>
+<td align="center">More</td>
+</tr></table>
+<hr>
+<div class="spirit-nav">
+<a accesskey="p" href="dist/future.html"><img src="../../../doc/html/images/prev.png" alt="Prev"></a><a accesskey="u" href="../index.html"><img src="../../../doc/html/images/up.png" alt="Up"></a><a accesskey="h" href="../index.html"><img src="../../../doc/html/images/home.png" alt="Home"></a><a accesskey="n" href="special/sf_gamma.html"><img src="../../../doc/html/images/next.png" alt="Next"></a>
+</div>
+<div class="section" lang="en">
+<div class="titlepage"><div><div><h2 class="title" style="clear: both">
+<a name="math_toolkit.special"></a><a class="link" href="special.html" title="Special Functions"> Special Functions</a>
+</h2></div></div></div>
+<div class="toc"><dl>
+<dt><span class="section"> Gamma Functions</span></dt>
+<dd><dl>
+<dt><span class="section"> Gamma</span></dt>
+<dt><span class="section"> Log Gamma</span></dt>
+<dt><span class="section"> Digamma</span></dt>
+<dt><span class="section"><a href="special/sf_gamma/gamma_ratios.html"> Ratios
+        of Gamma Functions</a></span></dt>
+<dt><span class="section"><a href="special/sf_gamma/igamma.html"> Incomplete Gamma
+        Functions</a></span></dt>
+<dt><span class="section"><a href="special/sf_gamma/igamma_inv.html"> Incomplete
+        Gamma Function Inverses</a></span></dt>
+<dt><span class="section"><a href="special/sf_gamma/gamma_derivatives.html"> Derivative
+        of the Incomplete Gamma Function</a></span></dt>
+</dl></dd>
+<dt><span class="section"><a href="special/factorials.html"> Factorials and Binomial
+      Coefficients</a></span></dt>
+<dd><dl>
+<dt><span class="section"> Factorial</span></dt>
+<dt><span class="section"><a href="special/factorials/sf_double_factorial.html">
+        Double Factorial</a></span></dt>
+<dt><span class="section"><a href="special/factorials/sf_rising_factorial.html">
+        Rising Factorial</a></span></dt>
+<dt><span class="section"><a href="special/factorials/sf_falling_factorial.html">
+        Falling Factorial</a></span></dt>
+<dt><span class="section"><a href="special/factorials/sf_binomial.html"> Binomial
+        Coefficients</a></span></dt>
+</dl></dd>
+<dt><span class="section"> Beta Functions</span></dt>
+<dd><dl>
+<dt><span class="section"> Beta</span></dt>
+<dt><span class="section"><a href="special/sf_beta/ibeta_function.html"> Incomplete
+        Beta Functions</a></span></dt>
+<dt><span class="section"><a href="special/sf_beta/ibeta_inv_function.html"> The
+        Incomplete Beta Function Inverses</a></span></dt>
+<dt><span class="section"><a href="special/sf_beta/beta_derivative.html"> Derivative
+        of the Incomplete Beta Function</a></span></dt>
+</dl></dd>
+<dt><span class="section"> Error Functions</span></dt>
+<dd><dl>
+<dt><span class="section"><a href="special/sf_erf/error_function.html"> Error
+        Functions</a></span></dt>
+<dt><span class="section"><a href="special/sf_erf/error_inv.html"> Error Function
+        Inverses</a></span></dt>
+</dl></dd>
+<dt><span class="section"> Polynomials</span></dt>
+<dd><dl>
+<dt><span class="section"><a href="special/sf_poly/legendre.html"> Legendre (and
+        Associated) Polynomials</a></span></dt>
+<dt><span class="section"><a href="special/sf_poly/laguerre.html"> Laguerre (and
+        Associated) Polynomials</a></span></dt>
+<dt><span class="section"> Hermite Polynomials</span></dt>
+<dt><span class="section"> Spherical Harmonics</span></dt>
+</dl></dd>
+<dt><span class="section"> Bessel Functions</span></dt>
+<dd><dl>
+<dt><span class="section"><a href="special/bessel/bessel_over.html"> Bessel Function
+        Overview</a></span></dt>
+<dt><span class="section"><a href="special/bessel/bessel.html"> Bessel Functions
+        of the First and Second Kinds</a></span></dt>
+<dt><span class="section"><a href="special/bessel/mbessel.html"> Modified Bessel
+        Functions of the First and Second Kinds</a></span></dt>
+<dt><span class="section"><a href="special/bessel/sph_bessel.html"> Spherical
+        Bessel Functions of the First and Second Kinds</a></span></dt>
+</dl></dd>
+<dt><span class="section"> Elliptic Integrals</span></dt>
+<dd><dl>
+<dt><span class="section"><a href="special/ellint/ellint_intro.html"> Elliptic
+        Integral Overview</a></span></dt>
+<dt><span class="section"><a href="special/ellint/ellint_carlson.html"> Elliptic
+        Integrals - Carlson Form</a></span></dt>
+<dt><span class="section"><a href="special/ellint/ellint_1.html"> Elliptic Integrals
+        of the First Kind - Legendre Form</a></span></dt>
+<dt><span class="section"><a href="special/ellint/ellint_2.html"> Elliptic Integrals
+        of the Second Kind - Legendre Form</a></span></dt>
+<dt><span class="section"><a href="special/ellint/ellint_3.html"> Elliptic Integrals
+        of the Third Kind - Legendre Form</a></span></dt>
+</dl></dd>
+<dt><span class="section"> Zeta Functions</span></dt>
+<dd><dl><dt><span class="section"> Riemann Zeta Function</span></dt></dl></dd>
+<dt><span class="section"> Exponential Integrals</span></dt>
+<dd><dl>
+<dt><span class="section"><a href="special/expint/expint_n.html"> Exponential
+        Integral En</a></span></dt>
+<dt><span class="section"><a href="special/expint/expint_i.html"> Exponential
+        Integral Ei</a></span></dt>
+</dl></dd>
+<dt><span class="section"><a href="special/powers.html"> Logs, Powers, Roots and
+      Exponentials</a></span></dt>
+<dd><dl>
+<dt><span class="section"> log1p</span></dt>
+<dt><span class="section"> expm1</span></dt>
+<dt><span class="section"> cbrt</span></dt>
+<dt><span class="section"> sqrt1pm1</span></dt>
+<dt><span class="section"> powm1</span></dt>
+<dt><span class="section"> hypot</span></dt>
+<dt><span class="section"><a href="special/powers/ct_pow.html"> Compile Time Power
+        of a Runtime Base</a></span></dt>
+</dl></dd>
+<dt><span class="section"><a href="special/sinc.html"> Sinus Cardinal and Hyperbolic
+      Sinus Cardinal Functions</a></span></dt>
+<dd><dl>
+<dt><span class="section"><a href="special/sinc/sinc_overview.html"> Sinus Cardinal
+        and Hyperbolic Sinus Cardinal Functions Overview</a></span></dt>
+<dt><span class="section">sinc_pi</span></dt>
+<dt><span class="section">sinhc_pi</span></dt>
+</dl></dd>
+<dt><span class="section"> Inverse Hyperbolic Functions</span></dt>
+<dd><dl>
+<dt><span class="section"><a href="special/inv_hyper/inv_hyper_over.html"> Inverse
+        Hyperbolic Functions Overview</a></span></dt>
+<dt><span class="section"> acosh</span></dt>
+<dt><span class="section"> asinh</span></dt>
+<dt><span class="section"> atanh</span></dt>
+</dl></dd>
+<dt><span class="section"><a href="special/rounding.html"> Rounding Truncation and
+      Integer Conversion</a></span></dt>
+<dd><dl>
+<dt><span class="section"> Rounding Functions</span></dt>
+<dt><span class="section"> Truncation Functions</span></dt>
+<dt><span class="section"><a href="special/rounding/modf.html"> Integer and Fractional
+        Part Splitting (modf)</a></span></dt>
+</dl></dd>
+<dt><span class="section"><a href="special/fpclass.html"> Floating-Point Classification:
+      Infinities and NaN's</a></span></dt>
+<dt><span class="section"><a href="special/next_float.html"> Floating-Point Representation
+      Distance (ULP), and Finding Adjacent Floating-Point Values</a></span></dt>
+<dd><dl>
+<dt><span class="section"><a href="special/next_float/nextafter.html"> Finding
+        the Next Representable Value in a Specific Direction (nextafter)</a></span></dt>
+<dt><span class="section"><a href="special/next_float/float_next.html"> Finding
+        the Next Greater Representable Value (float_next)</a></span></dt>
+<dt><span class="section"><a href="special/next_float/float_prior.html"> Finding
+        the Next Smaller Representable Value (float_prior)</a></span></dt>
+<dt><span class="section"><a href="special/next_float/float_distance.html"> Calculating
+        the Representation Distance Between Two Floating Point Values (ULP) float_distance</a></span></dt>
+<dt><span class="section"><a href="special/next_float/float_advance.html"> Advancing
+        a Floating Point Value by a Specific Representation Distance (ULP) float_advance</a></span></dt>
+</dl></dd>
+<dt><span class="section"><a href="special/extern_c.html"> TR1 and C99 external
+      "C" Functions</a></span></dt>
+<dd><dl>
+<dt><span class="section"><a href="special/extern_c/tr1.html"> C99 and TR1 C Functions
+        Overview</a></span></dt>
+<dt><span class="section"> C99 C Functions</span></dt>
+<dt><span class="section"><a href="special/extern_c/tr1_ref.html"> TR1 C Functions
+        Quick Reference</a></span></dt>
+</dl></dd>
+</dl></div>
+<p>
+    </p>
+</div>
+<table xmlns:rev="http://www.cs.rpi.edu/~gregod/boost/tools/doc/revision" width="100%"><tr>
+<td align="left"></td>
+<td align="right"><div class="copyright-footer">Copyright © 2006 , 2007, 2008 John Maddock, Paul A. Bristow, Hubert
+      Holin, Xiaogang Zhang, Bruno Lalande and Gautam Sewani<p>
+        Distributed under the Boost Software License, Version 1.0. (See accompanying
+        file LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_0.txt)
+      </p>
+</div></td>
+</tr></table>
+<hr>
+<div class="spirit-nav">
+<a accesskey="p" href="dist/future.html"><img src="../../../doc/html/images/prev.png" alt="Prev"></a><a accesskey="u" href="../index.html"><img src="../../../doc/html/images/up.png" alt="Up"></a><a accesskey="h" href="../index.html"><img src="../../../doc/html/images/home.png" alt="Home"></a><a accesskey="n" href="special/sf_gamma.html"><img src="../../../doc/html/images/next.png" alt="Next"></a>
+</div>
+</body>
+</html>

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+++ sandbox/tools/auto_index/example/math/doc/sf_and_dist/html/math_toolkit/special/bessel.html	2008-11-28 05:25:28 EST (Fri, 28 Nov 2008)
@@ -0,0 +1,62 @@
+<html>
+<head>
+<meta http-equiv="Content-Type" content="text/html; charset=ISO-8859-1">
+<title>Bessel Functions</title>
+<link rel="stylesheet" href="../../boostbook.css" type="text/css">
+<meta name="generator" content="DocBook XSL Stylesheets Vsnapshot_8125">
+<link rel="home" href="../../index.html" title="Math Toolkit">
+<link rel="up" href="../special.html" title="Special Functions">
+<link rel="prev" href="sf_poly/sph_harm.html" title="Spherical Harmonics">
+<link rel="next" href="bessel/bessel_over.html" title="Bessel Function Overview">
+</head>
+<body bgcolor="white" text="black" link="#0000FF" vlink="#840084" alink="#0000FF">
+<table cellpadding="2" width="100%"><tr>
+<td valign="top"><img alt="Boost C++ Libraries" width="277" height="86" src="../../../../boost.png"></td>
+<td align="center">Home</td>
+<td align="center">Libraries</td>
+<td align="center">People</td>
+<td align="center">FAQ</td>
+<td align="center">More</td>
+</tr></table>
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+<a accesskey="p" href="sf_poly/sph_harm.html"><img src="../../../../doc/html/images/prev.png" alt="Prev"></a><a accesskey="u" href="../special.html"><img src="../../../../doc/html/images/up.png" alt="Up"></a><a accesskey="h" href="../../index.html"><img src="../../../../doc/html/images/home.png" alt="Home"></a><a accesskey="n" href="bessel/bessel_over.html"><img src="../../../../doc/html/images/next.png" alt="Next"></a>
+</div>
+<div class="section" lang="en">
+<div class="titlepage"><div><div><h3 class="title">
+<a name="math_toolkit.special.bessel"></a><a class="link" href="bessel.html" title="Bessel Functions"> Bessel Functions</a>
+</h3></div></div></div>
+<div class="toc"><dl>
+<dt><span class="section"><a href="bessel/bessel_over.html"> Bessel Function
+        Overview</a></span></dt>
+<dt><span class="section"><a href="bessel/bessel.html"> Bessel Functions
+        of the First and Second Kinds</a></span></dt>
+<dt><span class="section"><a href="bessel/mbessel.html"> Modified Bessel
+        Functions of the First and Second Kinds</a></span></dt>
+<dt><span class="section"><a href="bessel/sph_bessel.html"> Spherical
+        Bessel Functions of the First and Second Kinds</a></span></dt>
+</dl></div>
+<p>
+      </p>
+<p>
+      </p>
+<p>
+      </p>
+<p>
+      </p>
+</div>
+<table xmlns:rev="http://www.cs.rpi.edu/~gregod/boost/tools/doc/revision" width="100%"><tr>
+<td align="left"></td>
+<td align="right"><div class="copyright-footer">Copyright © 2006 , 2007, 2008 John Maddock, Paul A. Bristow, Hubert
+      Holin, Xiaogang Zhang, Bruno Lalande and Gautam Sewani<p>
+        Distributed under the Boost Software License, Version 1.0. (See accompanying
+        file LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_0.txt)
+      </p>
+</div></td>
+</tr></table>
+<hr>
+<div class="spirit-nav">
+<a accesskey="p" href="sf_poly/sph_harm.html"><img src="../../../../doc/html/images/prev.png" alt="Prev"></a><a accesskey="u" href="../special.html"><img src="../../../../doc/html/images/up.png" alt="Up"></a><a accesskey="h" href="../../index.html"><img src="../../../../doc/html/images/home.png" alt="Home"></a><a accesskey="n" href="bessel/bessel_over.html"><img src="../../../../doc/html/images/next.png" alt="Next"></a>
+</div>
+</body>
+</html>

Added: sandbox/tools/auto_index/example/math/doc/sf_and_dist/html/math_toolkit/special/bessel/bessel.html
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--- (empty file)
+++ sandbox/tools/auto_index/example/math/doc/sf_and_dist/html/math_toolkit/special/bessel/bessel.html	2008-11-28 05:25:28 EST (Fri, 28 Nov 2008)
@@ -0,0 +1,672 @@
+<html>
+<head>
+<meta http-equiv="Content-Type" content="text/html; charset=ISO-8859-1">
+<title>Bessel Functions of the First and Second Kinds</title>
+<link rel="stylesheet" href="../../../boostbook.css" type="text/css">
+<meta name="generator" content="DocBook XSL Stylesheets Vsnapshot_8125">
+<link rel="home" href="../../../index.html" title="Math Toolkit">
+<link rel="up" href="../bessel.html" title="Bessel Functions">
+<link rel="prev" href="bessel_over.html" title="Bessel Function Overview">
+<link rel="next" href="mbessel.html" title="Modified Bessel Functions of the First and Second Kinds">
+</head>
+<body bgcolor="white" text="black" link="#0000FF" vlink="#840084" alink="#0000FF">
+<table cellpadding="2" width="100%"><tr>
+<td valign="top"><img alt="Boost C++ Libraries" width="277" height="86" src="../../../../../boost.png"></td>
+<td align="center">Home</td>
+<td align="center">Libraries</td>
+<td align="center">People</td>
+<td align="center">FAQ</td>
+<td align="center">More</td>
+</tr></table>
+<hr>
+<div class="spirit-nav">
+<a accesskey="p" href="bessel_over.html"><img src="../../../../../doc/html/images/prev.png" alt="Prev"></a><a accesskey="u" href="../bessel.html"><img src="../../../../../doc/html/images/up.png" alt="Up"></a><a accesskey="h" href="../../../index.html"><img src="../../../../../doc/html/images/home.png" alt="Home"></a><a accesskey="n" href="mbessel.html"><img src="../../../../../doc/html/images/next.png" alt="Next"></a>
+</div>
+<div class="section" lang="en">
+<div class="titlepage"><div><div><h4 class="title">
+<a name="math_toolkit.special.bessel.bessel"></a><a class="link" href="bessel.html" title="Bessel Functions of the First and Second Kinds"> Bessel Functions
+        of the First and Second Kinds</a>
+</h4></div></div></div>
+<a name="math_toolkit.special.bessel.bessel.synopsis"></a><h5>
+<a name="id755868"></a>
+          <a class="link" href="bessel.html#math_toolkit.special.bessel.bessel.synopsis">Synopsis</a>
+        </h5>
+<pre class="programlisting"><span class="keyword">template</span> <span class="special">&lt;</span><span class="keyword">class</span> <span class="identifier">T1</span><span class="special">,</span> <span class="keyword">class</span> <span class="identifier">T2</span><span class="special">&gt;</span>
+<a class="link" href="../../main_overview/result_type.html" title="Calculation of the Type of the Result"><span class="emphasis"><em>calculated-result-type</em></span></a> <span class="identifier">cyl_bessel_j</span><span class="special">(</span><span class="identifier">T1</span> <span class="identifier">v</span><span class="special">,</span> <span class="identifier">T2</span> <span class="identifier">x</span><span class="special">);</span>
+
+<span class="keyword">template</span> <span class="special">&lt;</span><span class="keyword">class</span> <span class="identifier">T1</span><span class="special">,</span> <span class="keyword">class</span> <span class="identifier">T2</span><span class="special">,</span> <span class="keyword">class</span> <a class="link" href="../../policy.html" title="Policies">Policy</a><span class="special">&gt;</span>
+<a class="link" href="../../main_overview/result_type.html" title="Calculation of the Type of the Result"><span class="emphasis"><em>calculated-result-type</em></span></a> <span class="identifier">cyl_bessel_j</span><span class="special">(</span><span class="identifier">T1</span> <span class="identifier">v</span><span class="special">,</span> <span class="identifier">T2</span> <span class="identifier">x</span><span class="special">,</span> <span class="keyword">const</span> <a class="link" href="../../policy.html" title="Policies">Policy</a><span class="special">&amp;);</span>
+
+<span class="keyword">template</span> <span class="special">&lt;</span><span class="keyword">class</span> <span class="identifier">T1</span><span class="special">,</span> <span class="keyword">class</span> <span class="identifier">T2</span><span class="special">&gt;</span>
+<a class="link" href="../../main_overview/result_type.html" title="Calculation of the Type of the Result"><span class="emphasis"><em>calculated-result-type</em></span></a> <span class="identifier">cyl_neumann</span><span class="special">(</span><span class="identifier">T1</span> <span class="identifier">v</span><span class="special">,</span> <span class="identifier">T2</span> <span class="identifier">x</span><span class="special">);</span>
+
+<span class="keyword">template</span> <span class="special">&lt;</span><span class="keyword">class</span> <span class="identifier">T1</span><span class="special">,</span> <span class="keyword">class</span> <span class="identifier">T2</span><span class="special">,</span> <span class="keyword">class</span> <a class="link" href="../../policy.html" title="Policies">Policy</a><span class="special">&gt;</span>
+<a class="link" href="../../main_overview/result_type.html" title="Calculation of the Type of the Result"><span class="emphasis"><em>calculated-result-type</em></span></a> <span class="identifier">cyl_neumann</span><span class="special">(</span><span class="identifier">T1</span> <span class="identifier">v</span><span class="special">,</span> <span class="identifier">T2</span> <span class="identifier">x</span><span class="special">,</span> <span class="keyword">const</span> <a class="link" href="../../policy.html" title="Policies">Policy</a><span class="special">&amp;);</span>
+</pre>
+<a name="math_toolkit.special.bessel.bessel.description"></a><h5>
+<a name="id756378"></a>
+          <a class="link" href="bessel.html#math_toolkit.special.bessel.bessel.description">Description</a>
+        </h5>
+<p>
+          The functions <a class="link" href="bessel.html" title="Bessel Functions of the First and Second Kinds">cyl_bessel_j</a>
+          and <a class="link" href="bessel.html" title="Bessel Functions of the First and Second Kinds">cyl_neumann</a>
+          return the result of the Bessel functions of the first and second kinds
+          respectively:
+        </p>
+<p>
+          cyl_bessel_j(v, x) = J<sub>v</sub>(x)
+        </p>
+<p>
+          cyl_neumann(v, x) = Y<sub>v</sub>(x) = N<sub>v</sub>(x)
+        </p>
+<p>
+          where:
+        </p>
+<p>
+          <span class="inlinemediaobject"><img src="../../../../equations/bessel2.png"></span>
+        </p>
+<p>
+          <span class="inlinemediaobject"><img src="../../../../equations/bessel3.png"></span>
+        </p>
+<p>
+          The return type of these functions is computed using the <a class="link" href="../../main_overview/result_type.html" title="Calculation of the Type of the Result"><span class="emphasis"><em>result
+          type calculation rules</em></span></a> when T1 and T2 are different types.
+          The functions are also optimised for the relatively common case that T1
+          is an integer.
+        </p>
+<p>
+          </p>
+<p>
+            The final <a class="link" href="../../policy.html" title="Policies">Policy</a> argument
+            is optional and can be used to control the behaviour of the function:
+            how it handles errors, what level of precision to use etc. Refer to the
+            <a class="link" href="../../policy.html" title="Policies">policy documentation for more details</a>.
+          </p>
+<p>
+        </p>
+<p>
+          The functions return the result of <a class="link" href="../../main_overview/error_handling.html#domain_error">domain_error</a>
+          whenever the result is undefined or complex. For <a class="link" href="bessel.html" title="Bessel Functions of the First and Second Kinds">cyl_bessel_j</a>
+          this occurs when <code class="computeroutput"><span class="identifier">x</span> <span class="special">&lt;</span>
+          <span class="number">0</span></code> and v is not an integer, or when
+          <code class="computeroutput"><span class="identifier">x</span> <span class="special">==</span>
+          <span class="number">0</span></code> and <code class="computeroutput"><span class="identifier">v</span>
+          <span class="special">!=</span> <span class="number">0</span></code>.
+          For <a class="link" href="bessel.html" title="Bessel Functions of the First and Second Kinds">cyl_neumann</a>
+          this occurs when <code class="computeroutput"><span class="identifier">x</span> <span class="special">&lt;=</span>
+          <span class="number">0</span></code>.
+        </p>
+<p>
+          The following graph illustrates the cyclic nature of J<sub>v</sub>:
+        </p>
+<p>
+          <span class="inlinemediaobject"><img src="../../../../graphs/cyl_bessel_j.png" align="middle"></span>
+        </p>
+<p>
+          The following graph shows the behaviour of Y<sub>v</sub>: this is also cyclic for
+          large <span class="emphasis"><em>x</em></span>, but tends to -&#8734; for small <span class="emphasis"><em>x</em></span>:
+        </p>
+<p>
+          <span class="inlinemediaobject"><img src="../../../../graphs/cyl_neumann.png" align="middle"></span>
+        </p>
+<a name="math_toolkit.special.bessel.bessel.testing"></a><h5>
+<a name="id756790"></a>
+          <a class="link" href="bessel.html#math_toolkit.special.bessel.bessel.testing">Testing</a>
+        </h5>
+<p>
+          There are two sets of test values: spot values calculated using functions.wolfram.com, and a
+          much larger set of tests computed using a simplified version of this implementation
+          (with all the special case handling removed).
+        </p>
+<a name="math_toolkit.special.bessel.bessel.accuracy"></a><h5>
+<a name="id756829"></a>
+          <a class="link" href="bessel.html#math_toolkit.special.bessel.bessel.accuracy">Accuracy</a>
+        </h5>
+<p>
+          The following tables show how the accuracy of these functions varies on
+          various platforms, along with comparisons to the GSL-1.9
+          and Cephes libraries.
+          Note that the cyclic nature of these functions means that they have an
+          infinite number of irrational roots: in general these functions have arbitrarily
+          large <span class="emphasis"><em>relative</em></span> errors when the arguments are sufficiently
+          close to a root. Of course the absolute error in such cases is always small.
+          Note that only results for the widest floating-point type on the system
+          are given as narrower types have <a class="link" href="../../backgrounders/relative_error.html#zero_error">effectively
+          zero error</a>. All values are relative errors in units of epsilon.
+        </p>
+<div class="table">
+<a name="id756893"></a><p class="title"><b>Table 36. Errors Rates in cyl_bessel_j</b></p>
+<div class="table-contents"><table class="table" summary="Errors Rates in cyl_bessel_j">
+<colgroup>
+<col>
+<col>
+<col>
+<col>
+<col>
+</colgroup>
+<thead><tr>
+<th>
+              <p>
+                Significand Size
+              </p>
+              </th>
+<th>
+              <p>
+                Platform and Compiler
+              </p>
+              </th>
+<th>
+              <p>
+                J<sub>0</sub> and J<sub>1</sub>
+              </p>
+              </th>
+<th>
+              <p>
+                J<sub>v</sub>
+              </p>
+              </th>
+<th>
+              <p>
+                J<sub>v</sub> (large values of x &gt; 1000)
+              </p>
+              </th>
+</tr></thead>
+<tbody>
+<tr>
+<td>
+              <p>
+                53
+              </p>
+              </td>
+<td>
+              <p>
+                Win32 / Visual C++ 8.0
+              </p>
+              </td>
+<td>
+              <p>
+                Peak=2.5 Mean=1.1
+              </p>
+              <p>
+                GSL Peak=6.6
+              </p>
+              <p>
+                Cephes Peak=2.5
+                Mean=1.1
+              </p>
+              </td>
+<td>
+              <p>
+                Peak=11 Mean=2.2
+              </p>
+              <p>
+                GSL Peak=11
+              </p>
+              <p>
+                Cephes Peak=17
+                Mean=2.5
+              </p>
+              </td>
+<td>
+              <p>
+                Peak=413 Mean=110
+              </p>
+              <p>
+                GSL Peak=6x10<sup>11</sup>
+              </p>
+              <p>
+                Cephes Peak=2x10<sup>5</sup>
+              </p>
+              </td>
+</tr>
+<tr>
+<td>
+              <p>
+                64
+              </p>
+              </td>
+<td>
+              <p>
+                Red Hat Linux IA64 / G++ 3.4
+              </p>
+              </td>
+<td>
+              <p>
+                Peak=7 Mean=3
+              </p>
+              </td>
+<td>
+              <p>
+                Peak=117 Mean=10
+              </p>
+              </td>
+<td>
+              <p>
+                Peak=2x10<sup>4</sup> Mean=6x10<sup>3</sup>
+              </p>
+              </td>
+</tr>
+<tr>
+<td>
+              <p>
+                64
+              </p>
+              </td>
+<td>
+              <p>
+                SUSE Linux AMD64 / G++ 4.1
+              </p>
+              </td>
+<td>
+              <p>
+                Peak=7 Mean=3
+              </p>
+              </td>
+<td>
+              <p>
+                Peak=400 Mean=40
+              </p>
+              </td>
+<td>
+              <p>
+                Peak=2x10<sup>4</sup> Mean=1x10<sup>4</sup>
+              </p>
+              </td>
+</tr>
+<tr>
+<td>
+              <p>
+                113
+              </p>
+              </td>
+<td>
+              <p>
+                HP-UX / HP aCC 6
+              </p>
+              </td>
+<td>
+              <p>
+                Peak=14 Mean=6
+              </p>
+              </td>
+<td>
+              <p>
+                Peak=29 Mean=3
+              </p>
+              </td>
+<td>
+              <p>
+                Peak=2700 Mean=450
+              </p>
+              </td>
+</tr>
+</tbody>
+</table></div>
+</div>
+<br class="table-break"><div class="table">
+<a name="id757215"></a><p class="title"><b>Table 37. Errors Rates in cyl_neumann</b></p>
+<div class="table-contents"><table class="table" summary="Errors Rates in cyl_neumann">
+<colgroup>
+<col>
+<col>
+<col>
+<col>
+<col>
+</colgroup>
+<thead><tr>
+<th>
+              <p>
+                Significand Size
+              </p>
+              </th>
+<th>
+              <p>
+                Platform and Compiler
+              </p>
+              </th>
+<th>
+              <p>
+                J<sub>0</sub> and J<sub>1</sub>
+              </p>
+              </th>
+<th>
+              <p>
+                J<sub>n</sub> (integer orders)
+              </p>
+              </th>
+<th>
+              <p>
+                J<sub>v</sub> (fractional orders)
+              </p>
+              </th>
+</tr></thead>
+<tbody>
+<tr>
+<td>
+              <p>
+                53
+              </p>
+              </td>
+<td>
+              <p>
+                Win32 / Visual C++ 8.0
+              </p>
+              </td>
+<td>
+              <p>
+                Peak=330 Mean=54
+              </p>
+              <p>
+                GSL Peak=34 Mean=9
+              </p>
+              <p>
+                Cephes Peak=330
+                Mean=54
+              </p>
+              </td>
+<td>
+              <p>
+                Peak=923 Mean=83
+              </p>
+              <p>
+                GSL Peak=500 Mean=54
+              </p>
+              <p>
+                Cephes Peak=923
+                Mean=83
+              </p>
+              </td>
+<td>
+              <p>
+                Peak=561 Mean=36
+              </p>
+              <p>
+                GSL Peak=1.4x10<sup>6</sup> Mean=7x10<sup>4</sup>
+              </p>
+              <p>
+                Cephes Peak=+INF
+              </p>
+              </td>
+</tr>
+<tr>
+<td>
+              <p>
+                64
+              </p>
+              </td>
+<td>
+              <p>
+                Red Hat Linux IA64 / G++ 3.4
+              </p>
+              </td>
+<td>
+              <p>
+                Peak=470 Mean=56
+              </p>
+              </td>
+<td>
+              <p>
+                Peak=843 Mean=51
+              </p>
+              </td>
+<td>
+              <p>
+                Peak=741 Mean=51
+              </p>
+              </td>
+</tr>
+<tr>
+<td>
+              <p>
+                64
+              </p>
+              </td>
+<td>
+              <p>
+                SUSE Linux AMD64 / G++ 4.1
+              </p>
+              </td>
+<td>
+              <p>
+                Peak=1300 Mean=424
+              </p>
+              </td>
+<td>
+              <p>
+                Peak=2x10<sup>4</sup> Mean=8x10<sup>3</sup>
+              </p>
+              </td>
+<td>
+              <p>
+                Peak=1x10<sup>5</sup> Mean=6x10<sup>3</sup>
+              </p>
+              </td>
+</tr>
+<tr>
+<td>
+              <p>
+                113
+              </p>
+              </td>
+<td>
+              <p>
+                HP-UX / HP aCC 6
+              </p>
+              </td>
+<td>
+              <p>
+                Peak=180 Mean=63
+              </p>
+              </td>
+<td>
+              <p>
+                Peak=340 Mean=150
+              </p>
+              </td>
+<td>
+              <p>
+                Peak=2x10<sup>4</sup> Mean=1200
+              </p>
+              </td>
+</tr>
+</tbody>
+</table></div>
+</div>
+<br class="table-break"><p>
+          Note that for large <span class="emphasis"><em>x</em></span> these functions are largely
+          dependent on the accuracy of the <code class="computeroutput"><span class="identifier">std</span><span class="special">::</span><span class="identifier">sin</span></code>
+          and <code class="computeroutput"><span class="identifier">std</span><span class="special">::</span><span class="identifier">cos</span></code> functions.
+        </p>
+<p>
+          Comparison to GSL and Cephes
+          is interesting: both Cephes
+          and this library optimise the integer order case - leading to identical
+          results - simply using the general case is for the most part slightly more
+          accurate though, as noted by the better accuracy of GSL in the integer
+          argument cases. This implementation tends to perform much better when the
+          arguments become large, Cephes
+          in particular produces some remarkably inaccurate results with some of
+          the test data (no significant figures correct), and even GSL performs badly
+          with some inputs to J<sub>v</sub>. Note that by way of double-checking these results,
+          the worst performing Cephes
+          and GSL cases were recomputed using functions.wolfram.com,
+          and the result checked against our test data: no errors in the test data
+          were found.
+        </p>
+<a name="math_toolkit.special.bessel.bessel.implementation"></a><h5>
+<a name="id757681"></a>
+          <a class="link" href="bessel.html#math_toolkit.special.bessel.bessel.implementation">Implementation</a>
+        </h5>
+<p>
+          The implementation is mostly about filtering off various special cases:
+        </p>
+<p>
+          When <span class="emphasis"><em>x</em></span> is negative, then the order <span class="emphasis"><em>v</em></span>
+          must be an integer or the result is a domain error. If the order is an
+          integer then the function is odd for odd orders and even for even orders,
+          so we reflect to <span class="emphasis"><em>x &gt; 0</em></span>.
+        </p>
+<p>
+          When the order <span class="emphasis"><em>v</em></span> is negative then the reflection formulae
+          can be used to move to <span class="emphasis"><em>v &gt; 0</em></span>:
+        </p>
+<p>
+          <span class="inlinemediaobject"><img src="../../../../equations/bessel9.png"></span>
+        </p>
+<p>
+          <span class="inlinemediaobject"><img src="../../../../equations/bessel10.png"></span>
+        </p>
+<p>
+          Note that if the order is an integer, then these formulae reduce to:
+        </p>
+<p>
+          J<sub>-n</sub> = (-1)<sup>n</sup>J<sub>n</sub>
+        </p>
+<p>
+          Y<sub>-n</sub> = (-1)<sup>n</sup>Y<sub>n</sub>
+        </p>
+<p>
+          However, in general, a negative order implies that we will need to compute
+          both J and Y.
+        </p>
+<p>
+          When <span class="emphasis"><em>x</em></span> is large compared to the order <span class="emphasis"><em>v</em></span>
+          then the asymptotic expansions for large <span class="emphasis"><em>x</em></span> in M. Abramowitz
+          and I.A. Stegun, <span class="emphasis"><em>Handbook of Mathematical Functions</em></span>
+          9.2.19 are used (these were found to be more reliable than those in A&amp;S
+          9.2.5).
+        </p>
+<p>
+          When the order <span class="emphasis"><em>v</em></span> is an integer the method first relates
+          the result to J<sub>0</sub>, J<sub>1</sub>, Y<sub>0</sub> and Y<sub>1</sub> using either forwards or backwards recurrence
+          (Miller's algorithm) depending upon which is stable. The values for J<sub>0</sub>,
+          J<sub>1</sub>, Y<sub>0</sub> and Y<sub>1</sub> are calculated using the rational minimax approximations on
+          root-bracketing intervals for small <span class="emphasis"><em>|x|</em></span> and Hankel
+          asymptotic expansion for large <span class="emphasis"><em>|x|</em></span>. The coefficients
+          are from:
+        </p>
+<p>
+          W.J. Cody, <span class="emphasis"><em>ALGORITHM 715: SPECFUN - A Portable FORTRAN Package
+          of Special Function Routines and Test Drivers</em></span>, ACM Transactions
+          on Mathematical Software, vol 19, 22 (1993).
+        </p>
+<p>
+          and
+        </p>
+<p>
+          J.F. Hart et al, <span class="emphasis"><em>Computer Approximations</em></span>, John Wiley
+          &amp; Sons, New York, 1968.
+        </p>
+<p>
+          These approximations are accurate to around 19 decimal digits: therefore
+          these methods are not used when type T has more than 64 binary digits.
+        </p>
+<p>
+          When <span class="emphasis"><em>x</em></span> is small, J<sub>x</sub> is best computed directly from
+          the series:
+        </p>
+<p>
+          <span class="inlinemediaobject"><img src="../../../../equations/bessel2.png"></span>
+        </p>
+<p>
+          In the general case we compute J<sub>v</sub> and Y<sub>v</sub> simultaneously.
+        </p>
+<p>
+          To get the initial values, let &#956; = &#957; - floor(&#957; + 1/2), then &#956; is the fractional
+          part of &#957; such that |&#956;| &lt;= 1/2 (we need this for convergence later). The
+          idea is to calculate J<sub>&#956;</sub>(x), J<sub>&#956;+1</sub>(x), Y<sub>&#956;</sub>(x), Y<sub>&#956;+1</sub>(x) and use them to obtain
+          J<sub>&#957;</sub>(x), Y<sub>&#957;</sub>(x).
+        </p>
+<p>
+          The algorithm is called Steed's method, which needs two continued fractions
+          as well as the Wronskian:
+        </p>
+<p>
+          <span class="inlinemediaobject"><img src="../../../../equations/bessel8.png"></span>
+        </p>
+<p>
+          <span class="inlinemediaobject"><img src="../../../../equations/bessel11.png"></span>
+        </p>
+<p>
+          <span class="inlinemediaobject"><img src="../../../../equations/bessel12.png"></span>
+        </p>
+<p>
+          See: F.S. Acton, <span class="emphasis"><em>Numerical Methods that Work</em></span>, The
+          Mathematical Association of America, Washington, 1997.
+        </p>
+<p>
+          The continued fractions are computed using the modified Lentz's method
+          (W.J. Lentz, <span class="emphasis"><em>Generating Bessel functions in Mie scattering calculations
+          using continued fractions</em></span>, Applied Optics, vol 15, 668 (1976)).
+          Their convergence rates depend on <span class="emphasis"><em>x</em></span>, therefore we
+          need different strategies for large <span class="emphasis"><em>x</em></span> and small <span class="emphasis"><em>x</em></span>.
+        </p>
+<p>
+          <span class="emphasis"><em>x &gt; v</em></span>, CF1 needs O(<span class="emphasis"><em>x</em></span>) iterations
+          to converge, CF2 converges rapidly
+        </p>
+<p>
+          <span class="emphasis"><em>x &lt;= v</em></span>, CF1 converges rapidly, CF2 fails to converge
+          when <span class="emphasis"><em>x</em></span> <code class="literal">-&gt;</code> 0
+        </p>
+<p>
+          When <span class="emphasis"><em>x</em></span> is large (<span class="emphasis"><em>x</em></span> &gt; 2), both
+          continued fractions converge (CF1 may be slow for really large <span class="emphasis"><em>x</em></span>).
+          J<sub>&#956;</sub>, J<sub>&#956;+1</sub>, Y<sub>&#956;</sub>, Y<sub>&#956;+1</sub> can be calculated by
+        </p>
+<p>
+          <span class="inlinemediaobject"><img src="../../../../equations/bessel13.png"></span>
+        </p>
+<p>
+          where
+        </p>
+<p>
+          <span class="inlinemediaobject"><img src="../../../../equations/bessel14.png"></span>
+        </p>
+<p>
+          J<sub>&#957;</sub> and Y<sub>&#956;</sub> are then calculated using backward (Miller's algorithm) and forward
+          recurrence respectively.
+        </p>
+<p>
+          When <span class="emphasis"><em>x</em></span> is small (<span class="emphasis"><em>x</em></span> &lt;= 2),
+          CF2 convergence may fail (but CF1 works very well). The solution here is
+          Temme's series:
+        </p>
+<p>
+          <span class="inlinemediaobject"><img src="../../../../equations/bessel15.png"></span>
+        </p>
+<p>
+          where
+        </p>
+<p>
+          <span class="inlinemediaobject"><img src="../../../../equations/bessel16.png"></span>
+        </p>
+<p>
+          g<sub>k</sub> and h<sub>k</sub>
+are also computed by recursions (involving gamma functions), but
+          the formulas are a little complicated, readers are refered to N.M. Temme,
+          <span class="emphasis"><em>On the numerical evaluation of the ordinary Bessel function of
+          the second kind</em></span>, Journal of Computational Physics, vol 21, 343
+          (1976). Note Temme's series converge only for |&#956;| &lt;= 1/2.
+        </p>
+<p>
+          As the previous case, Y<sub>&#957;</sub> is calculated from the forward recurrence, so is
+          Y<sub>&#957;+1</sub>. With these two values and f<sub>&#957;</sub>, the Wronskian yields J<sub>&#957;</sub>(x) directly without
+          backward recurrence.
+        </p>
+</div>
+<table xmlns:rev="http://www.cs.rpi.edu/~gregod/boost/tools/doc/revision" width="100%"><tr>
+<td align="left"></td>
+<td align="right"><div class="copyright-footer">Copyright © 2006 , 2007, 2008 John Maddock, Paul A. Bristow, Hubert
+      Holin, Xiaogang Zhang, Bruno Lalande and Gautam Sewani<p>
+        Distributed under the Boost Software License, Version 1.0. (See accompanying
+        file LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_0.txt)
+      </p>
+</div></td>
+</tr></table>
+<hr>
+<div class="spirit-nav">
+<a accesskey="p" href="bessel_over.html"><img src="../../../../../doc/html/images/prev.png" alt="Prev"></a><a accesskey="u" href="../bessel.html"><img src="../../../../../doc/html/images/up.png" alt="Up"></a><a accesskey="h" href="../../../index.html"><img src="../../../../../doc/html/images/home.png" alt="Home"></a><a accesskey="n" href="mbessel.html"><img src="../../../../../doc/html/images/next.png" alt="Next"></a>
+</div>
+</body>
+</html>

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+++ sandbox/tools/auto_index/example/math/doc/sf_and_dist/html/math_toolkit/special/bessel/bessel_over.html	2008-11-28 05:25:28 EST (Fri, 28 Nov 2008)
@@ -0,0 +1,213 @@
+<html>
+<head>
+<meta http-equiv="Content-Type" content="text/html; charset=ISO-8859-1">
+<title>Bessel Function Overview</title>
+<link rel="stylesheet" href="../../../boostbook.css" type="text/css">
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+<table cellpadding="2" width="100%"><tr>
+<td valign="top"><img alt="Boost C++ Libraries" width="277" height="86" src="../../../../../boost.png"></td>
+<td align="center">Home</td>
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+</div>
+<div class="section" lang="en">
+<div class="titlepage"><div><div><h4 class="title">
+<a name="math_toolkit.special.bessel.bessel_over"></a><a class="link" href="bessel_over.html" title="Bessel Function Overview"> Bessel Function
+        Overview</a>
+</h4></div></div></div>
+<a name="math_toolkit.special.bessel.bessel_over.ordinary_bessel_functions"></a><h5>
+<a name="id754850"></a>
+          <a class="link" href="bessel_over.html#math_toolkit.special.bessel.bessel_over.ordinary_bessel_functions">Ordinary
+          Bessel Functions</a>
+        </h5>
+<p>
+          Bessel Functions are solutions to Bessel's ordinary differential equation:
+        </p>
+<p>
+          <span class="inlinemediaobject"><img src="../../../../equations/bessel1.png"></span>
+        </p>
+<p>
+          where &#957; is the <span class="emphasis"><em>order</em></span> of the equation, and may be an
+          arbitrary real or complex number, although integer orders are the most
+          common occurrence.
+        </p>
+<p>
+          This library supports either integer or real orders.
+        </p>
+<p>
+          Since this is a second order differential equation, there must be two linearly
+          independent solutions, the first of these is denoted J<sub>v</sub>
+and known as a Bessel
+          function of the first kind:
+        </p>
+<p>
+          <span class="inlinemediaobject"><img src="../../../../equations/bessel2.png"></span>
+        </p>
+<p>
+          This function is implemented in this library as <a class="link" href="bessel.html" title="Bessel Functions of the First and Second Kinds">cyl_bessel_j</a>.
+        </p>
+<p>
+          The second solution is denoted either Y<sub>v</sub> or N<sub>v</sub>
+and is known as either a Bessel
+          Function of the second kind, or as a Neumann function:
+        </p>
+<p>
+          <span class="inlinemediaobject"><img src="../../../../equations/bessel3.png"></span>
+        </p>
+<p>
+          This function is implemented in this library as <a class="link" href="bessel.html" title="Bessel Functions of the First and Second Kinds">cyl_neumann</a>.
+        </p>
+<p>
+          The Bessel functions satisfy the recurrence relations:
+        </p>
+<p>
+          <span class="inlinemediaobject"><img src="../../../../equations/bessel4.png"></span>
+        </p>
+<p>
+          <span class="inlinemediaobject"><img src="../../../../equations/bessel5.png"></span>
+        </p>
+<p>
+          Have the derivatives:
+        </p>
+<p>
+          <span class="inlinemediaobject"><img src="../../../../equations/bessel6.png"></span>
+        </p>
+<p>
+          <span class="inlinemediaobject"><img src="../../../../equations/bessel7.png"></span>
+        </p>
+<p>
+          Have the Wronskian relation:
+        </p>
+<p>
+          <span class="inlinemediaobject"><img src="../../../../equations/bessel8.png"></span>
+        </p>
+<p>
+          and the reflection formulae:
+        </p>
+<p>
+          <span class="inlinemediaobject"><img src="../../../../equations/bessel9.png"></span>
+        </p>
+<p>
+          <span class="inlinemediaobject"><img src="../../../../equations/bessel10.png"></span>
+        </p>
+<a name="math_toolkit.special.bessel.bessel_over.modified_bessel_functions"></a><h5>
+<a name="id755278"></a>
+          <a class="link" href="bessel_over.html#math_toolkit.special.bessel.bessel_over.modified_bessel_functions">Modified
+          Bessel Functions</a>
+        </h5>
+<p>
+          The Bessel functions are valid for complex argument <span class="emphasis"><em>x</em></span>,
+          and an important special case is the situation where <span class="emphasis"><em>x</em></span>
+          is purely imaginary: giving a real valued result. In this case the functions
+          are the two linearly independent solutions to the modified Bessel equation:
+        </p>
+<p>
+          <span class="inlinemediaobject"><img src="../../../../equations/mbessel1.png"></span>
+        </p>
+<p>
+          The solutions are known as the modified Bessel functions of the first and
+          second kind (or occasionally as the hyperbolic Bessel functions of the
+          first and second kind). They are denoted I<sub>v</sub> and K<sub>v</sub>
+respectively:
+        </p>
+<p>
+          <span class="inlinemediaobject"><img src="../../../../equations/mbessel2.png"></span>
+        </p>
+<p>
+          <span class="inlinemediaobject"><img src="../../../../equations/mbessel3.png"></span>
+        </p>
+<p>
+          These functions are implemented in this library as <a class="link" href="mbessel.html" title="Modified Bessel Functions of the First and Second Kinds">cyl_bessel_i</a>
+          and <a class="link" href="mbessel.html" title="Modified Bessel Functions of the First and Second Kinds">cyl_bessel_k</a>
+          respectively.
+        </p>
+<p>
+          The modified Bessel functions satisfy the recurrence relations:
+        </p>
+<p>
+          <span class="inlinemediaobject"><img src="../../../../equations/mbessel4.png"></span>
+        </p>
+<p>
+          <span class="inlinemediaobject"><img src="../../../../equations/mbessel5.png"></span>
+        </p>
+<p>
+          Have the derivatives:
+        </p>
+<p>
+          <span class="inlinemediaobject"><img src="../../../../equations/mbessel6.png"></span>
+        </p>
+<p>
+          <span class="inlinemediaobject"><img src="../../../../equations/mbessel7.png"></span>
+        </p>
+<p>
+          Have the Wronskian relation:
+        </p>
+<p>
+          <span class="inlinemediaobject"><img src="../../../../equations/mbessel8.png"></span>
+        </p>
+<p>
+          and the reflection formulae:
+        </p>
+<p>
+          <span class="inlinemediaobject"><img src="../../../../equations/mbessel9.png"></span>
+        </p>
+<p>
+          <span class="inlinemediaobject"><img src="../../../../equations/mbessel10.png"></span>
+        </p>
+<a name="math_toolkit.special.bessel.bessel_over.spherical_bessel_functions"></a><h5>
+<a name="id755685"></a>
+          <a class="link" href="bessel_over.html#math_toolkit.special.bessel.bessel_over.spherical_bessel_functions">Spherical
+          Bessel Functions</a>
+        </h5>
+<p>
+          When solving the Helmholtz equation in spherical coordinates by separation
+          of variables, the radial equation has the form:
+        </p>
+<p>
+          <span class="inlinemediaobject"><img src="../../../../equations/sbessel1.png"></span>
+        </p>
+<p>
+          The two linearly independent solutions to this equation are called the
+          spherical Bessel functions j<sub>n</sub> and y<sub>n</sub>, and are related to the ordinary Bessel
+          functions J<sub>n</sub> and Y<sub>n</sub> by:
+        </p>
+<p>
+          <span class="inlinemediaobject"><img src="../../../../equations/sbessel2.png"></span>
+        </p>
+<p>
+          The spherical Bessel function of the second kind y<sub>n</sub>
+is also known as the
+          spherical Neumann function n<sub>n</sub>.
+        </p>
+<p>
+          These functions are implemented in this library as <a class="link" href="sph_bessel.html" title="Spherical Bessel Functions of the First and Second Kinds">sph_bessel</a>
+          and <a class="link" href="sph_bessel.html" title="Spherical Bessel Functions of the First and Second Kinds">sph_neumann</a>.
+        </p>
+</div>
+<table xmlns:rev="http://www.cs.rpi.edu/~gregod/boost/tools/doc/revision" width="100%"><tr>
+<td align="left"></td>
+<td align="right"><div class="copyright-footer">Copyright © 2006 , 2007, 2008 John Maddock, Paul A. Bristow, Hubert
+      Holin, Xiaogang Zhang, Bruno Lalande and Gautam Sewani<p>
+        Distributed under the Boost Software License, Version 1.0. (See accompanying
+        file LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_0.txt)
+      </p>
+</div></td>
+</tr></table>
+<hr>
+<div class="spirit-nav">
+<a accesskey="p" href="../bessel.html"><img src="../../../../../doc/html/images/prev.png" alt="Prev"></a><a accesskey="u" href="../bessel.html"><img src="../../../../../doc/html/images/up.png" alt="Up"></a><a accesskey="h" href="../../../index.html"><img src="../../../../../doc/html/images/home.png" alt="Home"></a><a accesskey="n" href="bessel.html"><img src="../../../../../doc/html/images/next.png" alt="Next"></a>
+</div>
+</body>
+</html>

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@@ -0,0 +1,484 @@
+<html>
+<head>
+<meta http-equiv="Content-Type" content="text/html; charset=ISO-8859-1">
+<title>Modified Bessel Functions of the First and Second Kinds</title>
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+</div>
+<div class="section" lang="en">
+<div class="titlepage"><div><div><h4 class="title">
+<a name="math_toolkit.special.bessel.mbessel"></a><a class="link" href="mbessel.html" title="Modified Bessel Functions of the First and Second Kinds"> Modified Bessel
+        Functions of the First and Second Kinds</a>
+</h4></div></div></div>
+<a name="math_toolkit.special.bessel.mbessel.synopsis"></a><h5>
+<a name="id758508"></a>
+          <a class="link" href="mbessel.html#math_toolkit.special.bessel.mbessel.synopsis">Synopsis</a>
+        </h5>
+<pre class="programlisting"><span class="keyword">template</span> <span class="special">&lt;</span><span class="keyword">class</span> <span class="identifier">T1</span><span class="special">,</span> <span class="keyword">class</span> <span class="identifier">T2</span><span class="special">&gt;</span>
+<a class="link" href="../../main_overview/result_type.html" title="Calculation of the Type of the Result"><span class="emphasis"><em>calculated-result-type</em></span></a> <span class="identifier">cyl_bessel_i</span><span class="special">(</span><span class="identifier">T1</span> <span class="identifier">v</span><span class="special">,</span> <span class="identifier">T2</span> <span class="identifier">x</span><span class="special">);</span>
+
+<span class="keyword">template</span> <span class="special">&lt;</span><span class="keyword">class</span> <span class="identifier">T1</span><span class="special">,</span> <span class="keyword">class</span> <span class="identifier">T2</span><span class="special">,</span> <span class="keyword">class</span> <a class="link" href="../../policy.html" title="Policies">Policy</a><span class="special">&gt;</span>
+<a class="link" href="../../main_overview/result_type.html" title="Calculation of the Type of the Result"><span class="emphasis"><em>calculated-result-type</em></span></a> <span class="identifier">cyl_bessel_i</span><span class="special">(</span><span class="identifier">T1</span> <span class="identifier">v</span><span class="special">,</span> <span class="identifier">T2</span> <span class="identifier">x</span><span class="special">,</span> <span class="keyword">const</span> <a class="link" href="../../policy.html" title="Policies">Policy</a><span class="special">&amp;);</span>
+
+<span class="keyword">template</span> <span class="special">&lt;</span><span class="keyword">class</span> <span class="identifier">T1</span><span class="special">,</span> <span class="keyword">class</span> <span class="identifier">T2</span><span class="special">&gt;</span>
+<a class="link" href="../../main_overview/result_type.html" title="Calculation of the Type of the Result"><span class="emphasis"><em>calculated-result-type</em></span></a> <span class="identifier">cyl_bessel_k</span><span class="special">(</span><span class="identifier">T1</span> <span class="identifier">v</span><span class="special">,</span> <span class="identifier">T2</span> <span class="identifier">x</span><span class="special">);</span>
+
+<span class="keyword">template</span> <span class="special">&lt;</span><span class="keyword">class</span> <span class="identifier">T1</span><span class="special">,</span> <span class="keyword">class</span> <span class="identifier">T2</span><span class="special">,</span> <span class="keyword">class</span> <a class="link" href="../../policy.html" title="Policies">Policy</a><span class="special">&gt;</span>
+<a class="link" href="../../main_overview/result_type.html" title="Calculation of the Type of the Result"><span class="emphasis"><em>calculated-result-type</em></span></a> <span class="identifier">cyl_bessel_k</span><span class="special">(</span><span class="identifier">T1</span> <span class="identifier">v</span><span class="special">,</span> <span class="identifier">T2</span> <span class="identifier">x</span><span class="special">,</span> <span class="keyword">const</span> <a class="link" href="../../policy.html" title="Policies">Policy</a><span class="special">&amp;);</span>
+</pre>
+<a name="math_toolkit.special.bessel.mbessel.description"></a><h5>
+<a name="id759019"></a>
+          <a class="link" href="mbessel.html#math_toolkit.special.bessel.mbessel.description">Description</a>
+        </h5>
+<p>
+          The functions <a class="link" href="mbessel.html" title="Modified Bessel Functions of the First and Second Kinds">cyl_bessel_i</a>
+          and <a class="link" href="mbessel.html" title="Modified Bessel Functions of the First and Second Kinds">cyl_bessel_k</a>
+          return the result of the modified Bessel functions of the first and second
+          kind respectively:
+        </p>
+<p>
+          cyl_bessel_i(v, x) = I<sub>v</sub>(x)
+        </p>
+<p>
+          cyl_bessel_k(v, x) = K<sub>v</sub>(x)
+        </p>
+<p>
+          where:
+        </p>
+<p>
+          <span class="inlinemediaobject"><img src="../../../../equations/mbessel2.png"></span>
+        </p>
+<p>
+          <span class="inlinemediaobject"><img src="../../../../equations/mbessel3.png"></span>
+        </p>
+<p>
+          The return type of these functions is computed using the <a class="link" href="../../main_overview/result_type.html" title="Calculation of the Type of the Result"><span class="emphasis"><em>result
+          type calculation rules</em></span></a> when T1 and T2 are different types.
+          The functions are also optimised for the relatively common case that T1
+          is an integer.
+        </p>
+<p>
+          </p>
+<p>
+            The final <a class="link" href="../../policy.html" title="Policies">Policy</a> argument
+            is optional and can be used to control the behaviour of the function:
+            how it handles errors, what level of precision to use etc. Refer to the
+            <a class="link" href="../../policy.html" title="Policies">policy documentation for more details</a>.
+          </p>
+<p>
+        </p>
+<p>
+          The functions return the result of <a class="link" href="../../main_overview/error_handling.html#domain_error">domain_error</a>
+          whenever the result is undefined or complex. For <a class="link" href="bessel.html" title="Bessel Functions of the First and Second Kinds">cyl_bessel_j</a>
+          this occurs when <code class="computeroutput"><span class="identifier">x</span> <span class="special">&lt;</span>
+          <span class="number">0</span></code> and v is not an integer, or when
+          <code class="computeroutput"><span class="identifier">x</span> <span class="special">==</span>
+          <span class="number">0</span></code> and <code class="computeroutput"><span class="identifier">v</span>
+          <span class="special">!=</span> <span class="number">0</span></code>.
+          For <a class="link" href="bessel.html" title="Bessel Functions of the First and Second Kinds">cyl_neumann</a>
+          this occurs when <code class="computeroutput"><span class="identifier">x</span> <span class="special">&lt;=</span>
+          <span class="number">0</span></code>.
+        </p>
+<p>
+          The following graph illustrates the exponential behaviour of I<sub>v</sub>.
+        </p>
+<p>
+          <span class="inlinemediaobject"><img src="../../../../graphs/cyl_bessel_i.png" align="middle"></span>
+        </p>
+<p>
+          The following graph illustrates the exponential decay of K<sub>v</sub>.
+        </p>
+<p>
+          <span class="inlinemediaobject"><img src="../../../../graphs/cyl_bessel_k.png" align="middle"></span>
+        </p>
+<a name="math_toolkit.special.bessel.mbessel.testing"></a><h5>
+<a name="id759418"></a>
+          <a class="link" href="mbessel.html#math_toolkit.special.bessel.mbessel.testing">Testing</a>
+        </h5>
+<p>
+          There are two sets of test values: spot values calculated using functions.wolfram.com, and a
+          much larger set of tests computed using a simplified version of this implementation
+          (with all the special case handling removed).
+        </p>
+<a name="math_toolkit.special.bessel.mbessel.accuracy"></a><h5>
+<a name="id759457"></a>
+          <a class="link" href="mbessel.html#math_toolkit.special.bessel.mbessel.accuracy">Accuracy</a>
+        </h5>
+<p>
+          The following tables show how the accuracy of these functions varies on
+          various platforms, along with a comparison to the GSL-1.9
+          library. Note that only results for the widest floating-point type on the
+          system are given, as narrower types have <a class="link" href="../../backgrounders/relative_error.html#zero_error">effectively
+          zero error</a>. All values are relative errors in units of epsilon.
+        </p>
+<div class="table">
+<a name="id759504"></a><p class="title"><b>Table 38. Errors Rates in cyl_bessel_i</b></p>
+<div class="table-contents"><table class="table" summary="Errors Rates in cyl_bessel_i">
+<colgroup>
+<col>
+<col>
+<col>
+</colgroup>
+<thead><tr>
+<th>
+              <p>
+                Significand Size
+              </p>
+              </th>
+<th>
+              <p>
+                Platform and Compiler
+              </p>
+              </th>
+<th>
+              <p>
+                I<sub>v</sub>
+              </p>
+              </th>
+</tr></thead>
+<tbody>
+<tr>
+<td>
+              <p>
+                53
+              </p>
+              </td>
+<td>
+              <p>
+                Win32 / Visual C++ 8.0
+              </p>
+              </td>
+<td>
+              <p>
+                Peak=10 Mean=3.4 GSL Peak=6000
+              </p>
+              </td>
+</tr>
+<tr>
+<td>
+              <p>
+                64
+              </p>
+              </td>
+<td>
+              <p>
+                Red Hat Linux IA64 / G++ 3.4
+              </p>
+              </td>
+<td>
+              <p>
+                Peak=11 Mean=3
+              </p>
+              </td>
+</tr>
+<tr>
+<td>
+              <p>
+                64
+              </p>
+              </td>
+<td>
+              <p>
+                SUSE Linux AMD64 / G++ 4.1
+              </p>
+              </td>
+<td>
+              <p>
+                Peak=11 Mean=4
+              </p>
+              </td>
+</tr>
+<tr>
+<td>
+              <p>
+                113
+              </p>
+              </td>
+<td>
+              <p>
+                HP-UX / HP aCC 6
+              </p>
+              </td>
+<td>
+              <p>
+                Peak=15 Mean=4
+              </p>
+              </td>
+</tr>
+</tbody>
+</table></div>
+</div>
+<br class="table-break"><div class="table">
+<a name="id759670"></a><p class="title"><b>Table 39. Errors Rates in cyl_bessel_k</b></p>
+<div class="table-contents"><table class="table" summary="Errors Rates in cyl_bessel_k">
+<colgroup>
+<col>
+<col>
+<col>
+</colgroup>
+<thead><tr>
+<th>
+              <p>
+                Significand Size
+              </p>
+              </th>
+<th>
+              <p>
+                Platform and Compiler
+              </p>
+              </th>
+<th>
+              <p>
+                K<sub>v</sub>
+              </p>
+              </th>
+</tr></thead>
+<tbody>
+<tr>
+<td>
+              <p>
+                53
+              </p>
+              </td>
+<td>
+              <p>
+                Win32 / Visual C++ 8.0
+              </p>
+              </td>
+<td>
+              <p>
+                Peak=9 Mean=2
+              </p>
+              <p>
+                GSL Peak=9
+              </p>
+              </td>
+</tr>
+<tr>
+<td>
+              <p>
+                64
+              </p>
+              </td>
+<td>
+              <p>
+                Red Hat Linux IA64 / G++ 3.4
+              </p>
+              </td>
+<td>
+              <p>
+                Peak=10 Mean=2
+              </p>
+              </td>
+</tr>
+<tr>
+<td>
+              <p>
+                64
+              </p>
+              </td>
+<td>
+              <p>
+                SUSE Linux AMD64 / G++ 4.1
+              </p>
+              </td>
+<td>
+              <p>
+                Peak=10 Mean=2
+              </p>
+              </td>
+</tr>
+<tr>
+<td>
+              <p>
+                113
+              </p>
+              </td>
+<td>
+              <p>
+                HP-UX / HP aCC 6
+              </p>
+              </td>
+<td>
+              <p>
+                Peak=12 Mean=5
+              </p>
+              </td>
+</tr>
+</tbody>
+</table></div>
+</div>
+<br class="table-break"><a name="math_toolkit.special.bessel.mbessel.implementation"></a><h5>
+<a name="id759849"></a>
+          <a class="link" href="mbessel.html#math_toolkit.special.bessel.mbessel.implementation">Implementation</a>
+        </h5>
+<p>
+          The following are handled as special cases first:
+        </p>
+<p>
+          When computing I<sub>v</sub> for <span class="emphasis"><em>x &lt; 0</em></span>, then &#957; must be an integer
+          or a domain error occurs. If &#957; is an integer, then the function is odd if
+          &#957; is odd and even if &#957; is even, and we can reflect to <span class="emphasis"><em>x &gt; 0</em></span>.
+        </p>
+<p>
+          For I<sub>v</sub> with v equal to 0, 1 or 0.5 are handled as special cases.
+        </p>
+<p>
+          The 0 and 1 cases use minimax rational approximations on finite and infinite
+          intervals. The coefficients are from:
+        </p>
+<div class="itemizedlist"><ul type="disc">
+<li>
+            J.M. Blair and C.A. Edwards, <span class="emphasis"><em>Stable rational minimax approximations
+            to the modified Bessel functions I_0(x) and I_1(x)</em></span>, Atomic
+            Energy of Canada Limited Report 4928, Chalk River, 1974.
+          </li>
+<li>
+            S. Moshier, <span class="emphasis"><em>Methods and Programs for Mathematical Functions</em></span>,
+            Ellis Horwood Ltd, Chichester, 1989.
+          </li>
+</ul></div>
+<p>
+          While the 0.5 case is a simple trigonometric function:
+        </p>
+<p>
+          I<sub>0.5</sub>(x) = sqrt(2 / &#960;x) * sinh(x)
+        </p>
+<p>
+          For K<sub>v</sub> with <span class="emphasis"><em>v</em></span> an integer, the result is calculated
+          using the recurrence relation:
+        </p>
+<p>
+          <span class="inlinemediaobject"><img src="../../../../equations/mbessel5.png"></span>
+        </p>
+<p>
+          starting from K<sub>0</sub> and K<sub>1</sub> which are calculated using rational the approximations
+          above. These rational approximations are accurate to around 19 digits,
+          and are therefore only used when T has no more than 64 binary digits of
+          precision.
+        </p>
+<p>
+          In the general case, we first normalize &#957; to [<code class="literal">0, [inf</code>])
+          with the help of the reflection formulae:
+        </p>
+<p>
+          <span class="inlinemediaobject"><img src="../../../../equations/mbessel9.png"></span>
+        </p>
+<p>
+          <span class="inlinemediaobject"><img src="../../../../equations/mbessel10.png"></span>
+        </p>
+<p>
+          Let &#956; = &#957; - floor(&#957; + 1/2), then &#956; is the fractional part of &#957; such that |&#956;| &lt;=
+          1/2 (we need this for convergence later). The idea is to calculate K<sub>&#956;</sub>(x)
+          and K<sub>&#956;+1</sub>(x), and use them to obtain I<sub>&#957;</sub>(x) and K<sub>&#957;</sub>(x).
+        </p>
+<p>
+          The algorithm is proposed by Temme in N.M. Temme, <span class="emphasis"><em>On the numerical
+          evaluation of the modified bessel function of the third kind</em></span>,
+          Journal of Computational Physics, vol 19, 324 (1975), which needs two continued
+          fractions as well as the Wronskian:
+        </p>
+<p>
+          <span class="inlinemediaobject"><img src="../../../../equations/mbessel11.png"></span>
+        </p>
+<p>
+          <span class="inlinemediaobject"><img src="../../../../equations/mbessel12.png"></span>
+        </p>
+<p>
+          <span class="inlinemediaobject"><img src="../../../../equations/mbessel8.png"></span>
+        </p>
+<p>
+          The continued fractions are computed using the modified Lentz's method
+          (W.J. Lentz, <span class="emphasis"><em>Generating Bessel functions in Mie scattering calculations
+          using continued fractions</em></span>, Applied Optics, vol 15, 668 (1976)).
+          Their convergence rates depend on <span class="emphasis"><em>x</em></span>, therefore we
+          need different strategies for large <span class="emphasis"><em>x</em></span> and small <span class="emphasis"><em>x</em></span>.
+        </p>
+<p>
+          <span class="emphasis"><em>x &gt; v</em></span>, CF1 needs O(<span class="emphasis"><em>x</em></span>) iterations
+          to converge, CF2 converges rapidly.
+        </p>
+<p>
+          <span class="emphasis"><em>x &lt;= v</em></span>, CF1 converges rapidly, CF2 fails to converge
+          when <span class="emphasis"><em>x</em></span> <code class="literal">-&gt;</code> 0.
+        </p>
+<p>
+          When <span class="emphasis"><em>x</em></span> is large (<span class="emphasis"><em>x</em></span> &gt; 2), both
+          continued fractions converge (CF1 may be slow for really large <span class="emphasis"><em>x</em></span>).
+          K<sub>&#956;</sub> and K<sub>&#956;+1</sub>
+can be calculated by
+        </p>
+<p>
+          <span class="inlinemediaobject"><img src="../../../../equations/mbessel13.png"></span>
+        </p>
+<p>
+          where
+        </p>
+<p>
+          <span class="inlinemediaobject"><img src="../../../../equations/mbessel14.png"></span>
+        </p>
+<p>
+          <span class="emphasis"><em>S</em></span> is also a series that is summed along with CF2,
+          see I.J. Thompson and A.R. Barnett, <span class="emphasis"><em>Modified Bessel functions
+          I_v and K_v of real order and complex argument to selected accuracy</em></span>,
+          Computer Physics Communications, vol 47, 245 (1987).
+        </p>
+<p>
+          When <span class="emphasis"><em>x</em></span> is small (<span class="emphasis"><em>x</em></span> &lt;= 2),
+          CF2 convergence may fail (but CF1 works very well). The solution here is
+          Temme's series:
+        </p>
+<p>
+          <span class="inlinemediaobject"><img src="../../../../equations/mbessel15.png"></span>
+        </p>
+<p>
+          where
+        </p>
+<p>
+          <span class="inlinemediaobject"><img src="../../../../equations/mbessel16.png"></span>
+        </p>
+<p>
+          f<sub>k</sub> and h<sub>k</sub>
+are also computed by recursions (involving gamma functions), but
+          the formulas are a little complicated, readers are referred to N.M. Temme,
+          <span class="emphasis"><em>On the numerical evaluation of the modified Bessel function of
+          the third kind</em></span>, Journal of Computational Physics, vol 19, 324
+          (1975). Note: Temme's series converge only for |&#956;| &lt;= 1/2.
+        </p>
+<p>
+          K<sub>&#957;</sub>(x) is then calculated from the forward recurrence, as is K<sub>&#957;+1</sub>(x). With
+          these two values and f<sub>&#957;</sub>, the Wronskian yields I<sub>&#957;</sub>(x) directly.
+        </p>
+</div>
+<table xmlns:rev="http://www.cs.rpi.edu/~gregod/boost/tools/doc/revision" width="100%"><tr>
+<td align="left"></td>
+<td align="right"><div class="copyright-footer">Copyright © 2006 , 2007, 2008 John Maddock, Paul A. Bristow, Hubert
+      Holin, Xiaogang Zhang, Bruno Lalande and Gautam Sewani<p>
+        Distributed under the Boost Software License, Version 1.0. (See accompanying
+        file LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_0.txt)
+      </p>
+</div></td>
+</tr></table>
+<hr>
+<div class="spirit-nav">
+<a accesskey="p" href="bessel.html"><img src="../../../../../doc/html/images/prev.png" alt="Prev"></a><a accesskey="u" href="../bessel.html"><img src="../../../../../doc/html/images/up.png" alt="Up"></a><a accesskey="h" href="../../../index.html"><img src="../../../../../doc/html/images/home.png" alt="Home"></a><a accesskey="n" href="sph_bessel.html"><img src="../../../../../doc/html/images/next.png" alt="Next"></a>
+</div>
+</body>
+</html>

Added: sandbox/tools/auto_index/example/math/doc/sf_and_dist/html/math_toolkit/special/bessel/sph_bessel.html
==============================================================================
--- (empty file)
+++ sandbox/tools/auto_index/example/math/doc/sf_and_dist/html/math_toolkit/special/bessel/sph_bessel.html	2008-11-28 05:25:28 EST (Fri, 28 Nov 2008)
@@ -0,0 +1,161 @@
+<html>
+<head>
+<meta http-equiv="Content-Type" content="text/html; charset=ISO-8859-1">
+<title>Spherical Bessel Functions of the First and Second Kinds</title>
+<link rel="stylesheet" href="../../../boostbook.css" type="text/css">
+<meta name="generator" content="DocBook XSL Stylesheets Vsnapshot_8125">
+<link rel="home" href="../../../index.html" title="Math Toolkit">
+<link rel="up" href="../bessel.html" title="Bessel Functions">
+<link rel="prev" href="mbessel.html" title="Modified Bessel Functions of the First and Second Kinds">
+<link rel="next" href="../ellint.html" title="Elliptic Integrals">
+</head>
+<body bgcolor="white" text="black" link="#0000FF" vlink="#840084" alink="#0000FF">
+<table cellpadding="2" width="100%"><tr>
+<td valign="top"><img alt="Boost C++ Libraries" width="277" height="86" src="../../../../../boost.png"></td>
+<td align="center">Home</td>
+<td align="center">Libraries</td>
+<td align="center">People</td>
+<td align="center">FAQ</td>
+<td align="center">More</td>
+</tr></table>
+<hr>
+<div class="spirit-nav">
+<a accesskey="p" href="mbessel.html"><img src="../../../../../doc/html/images/prev.png" alt="Prev"></a><a accesskey="u" href="../bessel.html"><img src="../../../../../doc/html/images/up.png" alt="Up"></a><a accesskey="h" href="../../../index.html"><img src="../../../../../doc/html/images/home.png" alt="Home"></a><a accesskey="n" href="../ellint.html"><img src="../../../../../doc/html/images/next.png" alt="Next"></a>
+</div>
+<div class="section" lang="en">
+<div class="titlepage"><div><div><h4 class="title">
+<a name="math_toolkit.special.bessel.sph_bessel"></a><a class="link" href="sph_bessel.html" title="Spherical Bessel Functions of the First and Second Kinds"> Spherical
+        Bessel Functions of the First and Second Kinds</a>
+</h4></div></div></div>
+<a name="math_toolkit.special.bessel.sph_bessel.synopsis"></a><h5>
+<a name="id760562"></a>
+          <a class="link" href="sph_bessel.html#math_toolkit.special.bessel.sph_bessel.synopsis">Synopsis</a>
+        </h5>
+<pre class="programlisting"><span class="keyword">template</span> <span class="special">&lt;</span><span class="keyword">class</span> <span class="identifier">T1</span><span class="special">,</span> <span class="keyword">class</span> <span class="identifier">T2</span><span class="special">&gt;</span>
+<a class="link" href="../../main_overview/result_type.html" title="Calculation of the Type of the Result"><span class="emphasis"><em>calculated-result-type</em></span></a> <span class="identifier">sph_bessel</span><span class="special">(</span><span class="keyword">unsigned</span> <span class="identifier">v</span><span class="special">,</span> <span class="identifier">T2</span> <span class="identifier">x</span><span class="special">);</span>
+
+<span class="keyword">template</span> <span class="special">&lt;</span><span class="keyword">class</span> <span class="identifier">T1</span><span class="special">,</span> <span class="keyword">class</span> <span class="identifier">T2</span><span class="special">,</span> <span class="keyword">class</span> <a class="link" href="../../policy.html" title="Policies">Policy</a><span class="special">&gt;</span>
+<a class="link" href="../../main_overview/result_type.html" title="Calculation of the Type of the Result"><span class="emphasis"><em>calculated-result-type</em></span></a> <span class="identifier">sph_bessel</span><span class="special">(</span><span class="keyword">unsigned</span> <span class="identifier">v</span><span class="special">,</span> <span class="identifier">T2</span> <span class="identifier">x</span><span class="special">,</span> <span class="keyword">const</span> <a class="link" href="../../policy.html" title="Policies">Policy</a><span class="special">&amp;);</span>
+
+<span class="keyword">template</span> <span class="special">&lt;</span><span class="keyword">class</span> <span class="identifier">T1</span><span class="special">,</span> <span class="keyword">class</span> <span class="identifier">T2</span><span class="special">&gt;</span>
+<a class="link" href="../../main_overview/result_type.html" title="Calculation of the Type of the Result"><span class="emphasis"><em>calculated-result-type</em></span></a> <span class="identifier">sph_neumann</span><span class="special">(</span><span class="keyword">unsigned</span> <span class="identifier">v</span><span class="special">,</span> <span class="identifier">T2</span> <span class="identifier">x</span><span class="special">);</span>
+
+<span class="keyword">template</span> <span class="special">&lt;</span><span class="keyword">class</span> <span class="identifier">T1</span><span class="special">,</span> <span class="keyword">class</span> <span class="identifier">T2</span><span class="special">,</span> <span class="keyword">class</span> <a class="link" href="../../policy.html" title="Policies">Policy</a><span class="special">&gt;</span>
+<a class="link" href="../../main_overview/result_type.html" title="Calculation of the Type of the Result"><span class="emphasis"><em>calculated-result-type</em></span></a> <span class="identifier">sph_neumann</span><span class="special">(</span><span class="keyword">unsigned</span> <span class="identifier">v</span><span class="special">,</span> <span class="identifier">T2</span> <span class="identifier">x</span><span class="special">,</span> <span class="keyword">const</span> <a class="link" href="../../policy.html" title="Policies">Policy</a><span class="special">&amp;);</span>
+</pre>
+<a name="math_toolkit.special.bessel.sph_bessel.description"></a><h5>
+<a name="id761072"></a>
+          <a class="link" href="sph_bessel.html#math_toolkit.special.bessel.sph_bessel.description">Description</a>
+        </h5>
+<p>
+          The functions <a class="link" href="sph_bessel.html" title="Spherical Bessel Functions of the First and Second Kinds">sph_bessel</a>
+          and <a class="link" href="sph_bessel.html" title="Spherical Bessel Functions of the First and Second Kinds">sph_neumann</a>
+          return the result of the Spherical Bessel functions of the first and second
+          kinds respectively:
+        </p>
+<p>
+          sph_bessel(v, x) = j<sub>v</sub>(x)
+        </p>
+<p>
+          sph_neumann(v, x) = y<sub>v</sub>(x) = n<sub>v</sub>(x)
+        </p>
+<p>
+          where:
+        </p>
+<p>
+          <span class="inlinemediaobject"><img src="../../../../equations/sbessel2.png"></span>
+        </p>
+<p>
+          The return type of these functions is computed using the <a class="link" href="../../main_overview/result_type.html" title="Calculation of the Type of the Result"><span class="emphasis"><em>result
+          type calculation rules</em></span></a> for the single argument type T.
+        </p>
+<p>
+          </p>
+<p>
+            The final <a class="link" href="../../policy.html" title="Policies">Policy</a> argument
+            is optional and can be used to control the behaviour of the function:
+            how it handles errors, what level of precision to use etc. Refer to the
+            <a class="link" href="../../policy.html" title="Policies">policy documentation for more details</a>.
+          </p>
+<p>
+        </p>
+<p>
+          The functions return the result of <a class="link" href="../../main_overview/error_handling.html#domain_error">domain_error</a>
+          whenever the result is undefined or complex: this occurs when <code class="computeroutput"><span class="identifier">x</span> <span class="special">&lt;</span> <span class="number">0</span></code>.
+        </p>
+<p>
+          The j<sub>v</sub> function is cyclic like J<sub>v</sub> but differs in its behaviour at the origin:
+        </p>
+<p>
+          <span class="inlinemediaobject"><img src="../../../../graphs/sph_bessel.png" align="middle"></span>
+        </p>
+<p>
+          Likewise y<sub>v</sub> is also cyclic for large x, but tends to -&#8734;
+for small <span class="emphasis"><em>x</em></span>:
+        </p>
+<p>
+          <span class="inlinemediaobject"><img src="../../../../graphs/sph_neumann.png" align="middle"></span>
+        </p>
+<a name="math_toolkit.special.bessel.sph_bessel.testing"></a><h5>
+<a name="id761359"></a>
+          <a class="link" href="sph_bessel.html#math_toolkit.special.bessel.sph_bessel.testing">Testing</a>
+        </h5>
+<p>
+          There are two sets of test values: spot values calculated using functions.wolfram.com, and
+          a much larger set of tests computed using a simplified version of this
+          implementation (with all the special case handling removed).
+        </p>
+<a name="math_toolkit.special.bessel.sph_bessel.accuracy"></a><h5>
+<a name="id761398"></a>
+          <a class="link" href="sph_bessel.html#math_toolkit.special.bessel.sph_bessel.accuracy">Accuracy</a>
+        </h5>
+<p>
+          Other than for some special cases, these functions are computed in terms
+          of <a class="link" href="bessel.html" title="Bessel Functions of the First and Second Kinds">cyl_bessel_j</a>
+          and <a class="link" href="bessel.html" title="Bessel Functions of the First and Second Kinds">cyl_neumann</a>:
+          refer to these functions for accuracy data.
+        </p>
+<a name="math_toolkit.special.bessel.sph_bessel.implementation"></a><h5>
+<a name="id761449"></a>
+          <a class="link" href="sph_bessel.html#math_toolkit.special.bessel.sph_bessel.implementation">Implementation</a>
+        </h5>
+<p>
+          Other than error handling and a couple of special cases these functions
+          are implemented directly in terms of their definitions:
+        </p>
+<p>
+          <span class="inlinemediaobject"><img src="../../../../equations/sbessel2.png"></span>
+        </p>
+<p>
+          The special cases occur for:
+        </p>
+<p>
+          j<sub>0</sub>= <a class="link" href="../sinc/sinc_pi.html" title="sinc_pi">sinc_pi</a>(x)
+          = sin(x) / x
+        </p>
+<p>
+          and for small <span class="emphasis"><em>x &lt; 1</em></span>, we can use the series:
+        </p>
+<p>
+          <span class="inlinemediaobject"><img src="../../../../equations/sbessel5.png"></span>
+        </p>
+<p>
+          which neatly avoids the problem of calculating 0/0 that can occur with
+          the main definition as x &#8594; 0.
+        </p>
+</div>
+<table xmlns:rev="http://www.cs.rpi.edu/~gregod/boost/tools/doc/revision" width="100%"><tr>
+<td align="left"></td>
+<td align="right"><div class="copyright-footer">Copyright © 2006 , 2007, 2008 John Maddock, Paul A. Bristow, Hubert
+      Holin, Xiaogang Zhang, Bruno Lalande and Gautam Sewani<p>
+        Distributed under the Boost Software License, Version 1.0. (See accompanying
+        file LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_0.txt)
+      </p>
+</div></td>
+</tr></table>
+<hr>
+<div class="spirit-nav">
+<a accesskey="p" href="mbessel.html"><img src="../../../../../doc/html/images/prev.png" alt="Prev"></a><a accesskey="u" href="../bessel.html"><img src="../../../../../doc/html/images/up.png" alt="Up"></a><a accesskey="h" href="../../../index.html"><img src="../../../../../doc/html/images/home.png" alt="Home"></a><a accesskey="n" href="../ellint.html"><img src="../../../../../doc/html/images/next.png" alt="Next"></a>
+</div>
+</body>
+</html>

Added: sandbox/tools/auto_index/example/math/doc/sf_and_dist/html/math_toolkit/special/ellint.html
==============================================================================
--- (empty file)
+++ sandbox/tools/auto_index/example/math/doc/sf_and_dist/html/math_toolkit/special/ellint.html	2008-11-28 05:25:28 EST (Fri, 28 Nov 2008)
@@ -0,0 +1,56 @@
+<html>
+<head>
+<meta http-equiv="Content-Type" content="text/html; charset=ISO-8859-1">
+<title>Elliptic Integrals</title>
+<link rel="stylesheet" href="../../boostbook.css" type="text/css">
+<meta name="generator" content="DocBook XSL Stylesheets Vsnapshot_8125">
+<link rel="home" href="../../index.html" title="Math Toolkit">
+<link rel="up" href="../special.html" title="Special Functions">
+<link rel="prev" href="bessel/sph_bessel.html" title="Spherical Bessel Functions of the First and Second Kinds">
+<link rel="next" href="ellint/ellint_intro.html" title="Elliptic Integral Overview">
+</head>
+<body bgcolor="white" text="black" link="#0000FF" vlink="#840084" alink="#0000FF">
+<table cellpadding="2" width="100%"><tr>
+<td valign="top"><img alt="Boost C++ Libraries" width="277" height="86" src="../../../../boost.png"></td>
+<td align="center">Home</td>
+<td align="center">Libraries</td>
+<td align="center">People</td>
+<td align="center">FAQ</td>
+<td align="center">More</td>
+</tr></table>
+<hr>
+<div class="spirit-nav">
+<a accesskey="p" href="bessel/sph_bessel.html"><img src="../../../../doc/html/images/prev.png" alt="Prev"></a><a accesskey="u" href="../special.html"><img src="../../../../doc/html/images/up.png" alt="Up"></a><a accesskey="h" href="../../index.html"><img src="../../../../doc/html/images/home.png" alt="Home"></a><a accesskey="n" href="ellint/ellint_intro.html"><img src="../../../../doc/html/images/next.png" alt="Next"></a>
+</div>
+<div class="section" lang="en">
+<div class="titlepage"><div><div><h3 class="title">
+<a name="math_toolkit.special.ellint"></a><a class="link" href="ellint.html" title="Elliptic Integrals"> Elliptic Integrals</a>
+</h3></div></div></div>
+<div class="toc"><dl>
+<dt><span class="section"><a href="ellint/ellint_intro.html"> Elliptic
+        Integral Overview</a></span></dt>
+<dt><span class="section"><a href="ellint/ellint_carlson.html"> Elliptic
+        Integrals - Carlson Form</a></span></dt>
+<dt><span class="section"><a href="ellint/ellint_1.html"> Elliptic Integrals
+        of the First Kind - Legendre Form</a></span></dt>
+<dt><span class="section"><a href="ellint/ellint_2.html"> Elliptic Integrals
+        of the Second Kind - Legendre Form</a></span></dt>
+<dt><span class="section"><a href="ellint/ellint_3.html"> Elliptic Integrals
+        of the Third Kind - Legendre Form</a></span></dt>
+</dl></div>
+</div>
+<table xmlns:rev="http://www.cs.rpi.edu/~gregod/boost/tools/doc/revision" width="100%"><tr>
+<td align="left"></td>
+<td align="right"><div class="copyright-footer">Copyright © 2006 , 2007, 2008 John Maddock, Paul A. Bristow, Hubert
+      Holin, Xiaogang Zhang, Bruno Lalande and Gautam Sewani<p>
+        Distributed under the Boost Software License, Version 1.0. (See accompanying
+        file LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_0.txt)
+      </p>
+</div></td>
+</tr></table>
+<hr>
+<div class="spirit-nav">
+<a accesskey="p" href="bessel/sph_bessel.html"><img src="../../../../doc/html/images/prev.png" alt="Prev"></a><a accesskey="u" href="../special.html"><img src="../../../../doc/html/images/up.png" alt="Up"></a><a accesskey="h" href="../../index.html"><img src="../../../../doc/html/images/home.png" alt="Home"></a><a accesskey="n" href="ellint/ellint_intro.html"><img src="../../../../doc/html/images/next.png" alt="Next"></a>
+</div>
+</body>
+</html>

Added: sandbox/tools/auto_index/example/math/doc/sf_and_dist/html/math_toolkit/special/ellint/ellint_1.html
==============================================================================
--- (empty file)
+++ sandbox/tools/auto_index/example/math/doc/sf_and_dist/html/math_toolkit/special/ellint/ellint_1.html	2008-11-28 05:25:28 EST (Fri, 28 Nov 2008)
@@ -0,0 +1,281 @@
+<html>
+<head>
+<meta http-equiv="Content-Type" content="text/html; charset=ISO-8859-1">
+<title>Elliptic Integrals of the First Kind - Legendre Form</title>
+<link rel="stylesheet" href="../../../boostbook.css" type="text/css">
+<meta name="generator" content="DocBook XSL Stylesheets Vsnapshot_8125">
+<link rel="home" href="../../../index.html" title="Math Toolkit">
+<link rel="up" href="../ellint.html" title="Elliptic Integrals">
+<link rel="prev" href="ellint_carlson.html" title="Elliptic Integrals - Carlson Form">
+<link rel="next" href="ellint_2.html" title="Elliptic Integrals of the Second Kind - Legendre Form">
+</head>
+<body bgcolor="white" text="black" link="#0000FF" vlink="#840084" alink="#0000FF">
+<table cellpadding="2" width="100%"><tr>
+<td valign="top"><img alt="Boost C++ Libraries" width="277" height="86" src="../../../../../boost.png"></td>
+<td align="center">Home</td>
+<td align="center">Libraries</td>
+<td align="center">People</td>
+<td align="center">FAQ</td>
+<td align="center">More</td>
+</tr></table>
+<hr>
+<div class="spirit-nav">
+<a accesskey="p" href="ellint_carlson.html"><img src="../../../../../doc/html/images/prev.png" alt="Prev"></a><a accesskey="u" href="../ellint.html"><img src="../../../../../doc/html/images/up.png" alt="Up"></a><a accesskey="h" href="../../../index.html"><img src="../../../../../doc/html/images/home.png" alt="Home"></a><a accesskey="n" href="ellint_2.html"><img src="../../../../../doc/html/images/next.png" alt="Next"></a>
+</div>
+<div class="section" lang="en">
+<div class="titlepage"><div><div><h4 class="title">
+<a name="math_toolkit.special.ellint.ellint_1"></a><a class="link" href="ellint_1.html" title="Elliptic Integrals of the First Kind - Legendre Form"> Elliptic Integrals
+        of the First Kind - Legendre Form</a>
+</h4></div></div></div>
+<a name="math_toolkit.special.ellint.ellint_1.synopsis"></a><h6>
+<a name="id767302"></a>
+          <a class="link" href="ellint_1.html#math_toolkit.special.ellint.ellint_1.synopsis">Synopsis</a>
+        </h6>
+<p>
+          
+</p>
+<pre class="programlisting"><span class="preprocessor">#include</span> <span class="special">&lt;</span><span class="identifier">boost</span><span class="special">/</span><span class="identifier">math</span><span class="special">/</span><span class="identifier">special_functions</span><span class="special">/</span><span class="identifier">ellint_1</span><span class="special">.</span><span class="identifier">hpp</span><span class="special">&gt;</span>
+</pre>
+<p>
+        </p>
+<pre class="programlisting"><span class="keyword">namespace</span> <span class="identifier">boost</span> <span class="special">{</span> <span class="keyword">namespace</span> <span class="identifier">math</span> <span class="special">{</span>
+
+<span class="keyword">template</span> <span class="special">&lt;</span><span class="keyword">class</span> <span class="identifier">T1</span><span class="special">,</span> <span class="keyword">class</span> <span class="identifier">T2</span><span class="special">&gt;</span>
+<a class="link" href="../../main_overview/result_type.html" title="Calculation of the Type of the Result"><span class="emphasis"><em>calculated-result-type</em></span></a> <span class="identifier">ellint_1</span><span class="special">(</span><span class="identifier">T1</span> <span class="identifier">k</span><span class="special">,</span> <span class="identifier">T2</span> <span class="identifier">phi</span><span class="special">);</span>
+
+<span class="keyword">template</span> <span class="special">&lt;</span><span class="keyword">class</span> <span class="identifier">T1</span><span class="special">,</span> <span class="keyword">class</span> <span class="identifier">T2</span><span class="special">,</span> <span class="keyword">class</span> <a class="link" href="../../policy.html" title="Policies">Policy</a><span class="special">&gt;</span>
+<a class="link" href="../../main_overview/result_type.html" title="Calculation of the Type of the Result"><span class="emphasis"><em>calculated-result-type</em></span></a> <span class="identifier">ellint_1</span><span class="special">(</span><span class="identifier">T1</span> <span class="identifier">k</span><span class="special">,</span> <span class="identifier">T2</span> <span class="identifier">phi</span><span class="special">,</span> <span class="keyword">const</span> <a class="link" href="../../policy.html" title="Policies">Policy</a><span class="special">&amp;);</span>
+
+<span class="keyword">template</span> <span class="special">&lt;</span><span class="keyword">class</span> <span class="identifier">T</span><span class="special">&gt;</span>
+<a class="link" href="../../main_overview/result_type.html" title="Calculation of the Type of the Result"><span class="emphasis"><em>calculated-result-type</em></span></a> <span class="identifier">ellint_1</span><span class="special">(</span><span class="identifier">T</span> <span class="identifier">k</span><span class="special">);</span>
+
+<span class="keyword">template</span> <span class="special">&lt;</span><span class="keyword">class</span> <span class="identifier">T</span><span class="special">,</span> <span class="keyword">class</span> <a class="link" href="../../policy.html" title="Policies">Policy</a><span class="special">&gt;</span>
+<a class="link" href="../../main_overview/result_type.html" title="Calculation of the Type of the Result"><span class="emphasis"><em>calculated-result-type</em></span></a> <span class="identifier">ellint_1</span><span class="special">(</span><span class="identifier">T</span> <span class="identifier">k</span><span class="special">,</span> <span class="keyword">const</span> <a class="link" href="../../policy.html" title="Policies">Policy</a><span class="special">&amp;);</span>
+
+<span class="special">}}</span> <span class="comment">// namespaces
+</span></pre>
+<a name="math_toolkit.special.ellint.ellint_1.description"></a><h6>
+<a name="id767868"></a>
+          <a class="link" href="ellint_1.html#math_toolkit.special.ellint.ellint_1.description">Description</a>
+        </h6>
+<p>
+          These two functions evaluate the incomplete elliptic integral of the first
+          kind <span class="emphasis"><em>F(&#966;, k)</em></span> and its complete counterpart <span class="emphasis"><em>K(k)
+          = F(&#960;/2, k)</em></span>.
+        </p>
+<p>
+          <span class="inlinemediaobject"><img src="../../../../graphs/ellint_1.png" align="middle"></span>
+        </p>
+<p>
+          The return type of these functions is computed using the <a class="link" href="../../main_overview/result_type.html" title="Calculation of the Type of the Result"><span class="emphasis"><em>result
+          type calculation rules</em></span></a> when T1 and T2 are different types:
+          when they are the same type then the result is the same type as the arguments.
+        </p>
+<pre class="programlisting"><span class="keyword">template</span> <span class="special">&lt;</span><span class="keyword">class</span> <span class="identifier">T1</span><span class="special">,</span> <span class="keyword">class</span> <span class="identifier">T2</span><span class="special">&gt;</span>
+<a class="link" href="../../main_overview/result_type.html" title="Calculation of the Type of the Result"><span class="emphasis"><em>calculated-result-type</em></span></a> <span class="identifier">ellint_1</span><span class="special">(</span><span class="identifier">T1</span> <span class="identifier">k</span><span class="special">,</span> <span class="identifier">T2</span> <span class="identifier">phi</span><span class="special">);</span>
+
+<span class="keyword">template</span> <span class="special">&lt;</span><span class="keyword">class</span> <span class="identifier">T1</span><span class="special">,</span> <span class="keyword">class</span> <span class="identifier">T2</span><span class="special">,</span> <span class="keyword">class</span> <a class="link" href="../../policy.html" title="Policies">Policy</a><span class="special">&gt;</span>
+<a class="link" href="../../main_overview/result_type.html" title="Calculation of the Type of the Result"><span class="emphasis"><em>calculated-result-type</em></span></a> <span class="identifier">ellint_1</span><span class="special">(</span><span class="identifier">T1</span> <span class="identifier">k</span><span class="special">,</span> <span class="identifier">T2</span> <span class="identifier">phi</span><span class="special">,</span> <span class="keyword">const</span> <a class="link" href="../../policy.html" title="Policies">Policy</a><span class="special">&amp;);</span>
+</pre>
+<p>
+          Returns the incomplete elliptic integral of the first kind <span class="emphasis"><em>F(&#966;,
+          k)</em></span>:
+        </p>
+<p>
+          <span class="inlinemediaobject"><img src="../../../../equations/ellint2.png"></span>
+        </p>
+<p>
+          Requires -1 &lt;= k &lt;= 1, otherwise returns the result of <a class="link" href="../../main_overview/error_handling.html#domain_error">domain_error</a>.
+        </p>
+<p>
+          </p>
+<p>
+            The final <a class="link" href="../../policy.html" title="Policies">Policy</a> argument
+            is optional and can be used to control the behaviour of the function:
+            how it handles errors, what level of precision to use etc. Refer to the
+            <a class="link" href="../../policy.html" title="Policies">policy documentation for more details</a>.
+          </p>
+<p>
+        </p>
+<pre class="programlisting"><span class="keyword">template</span> <span class="special">&lt;</span><span class="keyword">class</span> <span class="identifier">T</span><span class="special">&gt;</span>
+<a class="link" href="../../main_overview/result_type.html" title="Calculation of the Type of the Result"><span class="emphasis"><em>calculated-result-type</em></span></a> <span class="identifier">ellint_1</span><span class="special">(</span><span class="identifier">T</span> <span class="identifier">k</span><span class="special">);</span>
+
+<span class="keyword">template</span> <span class="special">&lt;</span><span class="keyword">class</span> <span class="identifier">T</span><span class="special">&gt;</span>
+<a class="link" href="../../main_overview/result_type.html" title="Calculation of the Type of the Result"><span class="emphasis"><em>calculated-result-type</em></span></a> <span class="identifier">ellint_1</span><span class="special">(</span><span class="identifier">T</span> <span class="identifier">k</span><span class="special">,</span> <span class="keyword">const</span> <a class="link" href="../../policy.html" title="Policies">Policy</a><span class="special">&amp;);</span>
+</pre>
+<p>
+          Returns the complete elliptic integral of the first kind <span class="emphasis"><em>K(k)</em></span>:
+        </p>
+<p>
+          <span class="inlinemediaobject"><img src="../../../../equations/ellint6.png"></span>
+        </p>
+<p>
+          Requires -1 &lt;= k &lt;= 1, otherwise returns the result of <a class="link" href="../../main_overview/error_handling.html#domain_error">domain_error</a>.
+        </p>
+<p>
+          </p>
+<p>
+            The final <a class="link" href="../../policy.html" title="Policies">Policy</a> argument
+            is optional and can be used to control the behaviour of the function:
+            how it handles errors, what level of precision to use etc. Refer to the
+            <a class="link" href="../../policy.html" title="Policies">policy documentation for more details</a>.
+          </p>
+<p>
+        </p>
+<a name="math_toolkit.special.ellint.ellint_1.accuracy"></a><h6>
+<a name="id768541"></a>
+          <a class="link" href="ellint_1.html#math_toolkit.special.ellint.ellint_1.accuracy">Accuracy</a>
+        </h6>
+<p>
+          These functions are computed using only basic arithmetic operations, so
+          there isn't much variation in accuracy over differing platforms. Note that
+          only results for the widest floating point type on the system are given
+          as narrower types have <a class="link" href="../../backgrounders/relative_error.html#zero_error">effectively zero error</a>.
+          All values are relative errors in units of epsilon.
+        </p>
+<div class="table">
+<a name="id768576"></a><p class="title"><b>Table 41. Errors Rates in the Elliptic Integrals of the
+        First Kind</b></p>
+<div class="table-contents"><table class="table" summary="Errors Rates in the Elliptic Integrals of the
+        First Kind">
+<colgroup>
+<col>
+<col>
+<col>
+<col>
+</colgroup>
+<thead><tr>
+<th>
+              <p>
+                Significand Size
+              </p>
+              </th>
+<th>
+              <p>
+                Platform and Compiler
+              </p>
+              </th>
+<th>
+              <p>
+                F(&#966;, k)
+              </p>
+              </th>
+<th>
+              <p>
+                K(k)
+              </p>
+              </th>
+</tr></thead>
+<tbody>
+<tr>
+<td>
+              <p>
+                53
+              </p>
+              </td>
+<td>
+              <p>
+                Win32 / Visual C++ 8.0
+              </p>
+              </td>
+<td>
+              <p>
+                Peak=3 Mean=0.8
+              </p>
+              </td>
+<td>
+              <p>
+                Peak=1.8 Mean=0.7
+              </p>
+              </td>
+</tr>
+<tr>
+<td>
+              <p>
+                64
+              </p>
+              </td>
+<td>
+              <p>
+                Red Hat Linux / G++ 3.4
+              </p>
+              </td>
+<td>
+              <p>
+                Peak=2.6 Mean=1.7
+              </p>
+              </td>
+<td>
+              <p>
+                Peak=2.2 Mean=1.8
+              </p>
+              </td>
+</tr>
+<tr>
+<td>
+              <p>
+                113
+              </p>
+              </td>
+<td>
+              <p>
+                HP-UX / HP aCC 6
+              </p>
+              </td>
+<td>
+              <p>
+                Peak=4.6 Mean=1.5
+              </p>
+              </td>
+<td>
+              <p>
+                Peak=3.7 Mean=1.5
+              </p>
+              </td>
+</tr>
+</tbody>
+</table></div>
+</div>
+<br class="table-break"><a name="math_toolkit.special.ellint.ellint_1.testing"></a><h6>
+<a name="id768753"></a>
+          <a class="link" href="ellint_1.html#math_toolkit.special.ellint.ellint_1.testing">Testing</a>
+        </h6>
+<p>
+          The tests use a mixture of spot test values calculated using the online
+          calculator at functions.wolfram.com,
+          and random test data generated using NTL::RR at 1000-bit precision and
+          this implementation.
+        </p>
+<a name="math_toolkit.special.ellint.ellint_1.implementation"></a><h6>
+<a name="id768793"></a>
+          <a class="link" href="ellint_1.html#math_toolkit.special.ellint.ellint_1.implementation">Implementation</a>
+        </h6>
+<p>
+          These functions are implemented in terms of Carlson's integrals using the
+          relations:
+        </p>
+<p>
+          <span class="inlinemediaobject"><img src="../../../../equations/ellint19.png"></span>
+        </p>
+<p>
+          and
+        </p>
+<p>
+          <span class="inlinemediaobject"><img src="../../../../equations/ellint20.png"></span>
+        </p>
+</div>
+<table xmlns:rev="http://www.cs.rpi.edu/~gregod/boost/tools/doc/revision" width="100%"><tr>
+<td align="left"></td>
+<td align="right"><div class="copyright-footer">Copyright © 2006 , 2007, 2008 John Maddock, Paul A. Bristow, Hubert
+      Holin, Xiaogang Zhang, Bruno Lalande and Gautam Sewani<p>
+        Distributed under the Boost Software License, Version 1.0. (See accompanying
+        file LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_0.txt)
+      </p>
+</div></td>
+</tr></table>
+<hr>
+<div class="spirit-nav">
+<a accesskey="p" href="ellint_carlson.html"><img src="../../../../../doc/html/images/prev.png" alt="Prev"></a><a accesskey="u" href="../ellint.html"><img src="../../../../../doc/html/images/up.png" alt="Up"></a><a accesskey="h" href="../../../index.html"><img src="../../../../../doc/html/images/home.png" alt="Home"></a><a accesskey="n" href="ellint_2.html"><img src="../../../../../doc/html/images/next.png" alt="Next"></a>
+</div>
+</body>
+</html>

Added: sandbox/tools/auto_index/example/math/doc/sf_and_dist/html/math_toolkit/special/ellint/ellint_2.html
==============================================================================
--- (empty file)
+++ sandbox/tools/auto_index/example/math/doc/sf_and_dist/html/math_toolkit/special/ellint/ellint_2.html	2008-11-28 05:25:28 EST (Fri, 28 Nov 2008)
@@ -0,0 +1,281 @@
+<html>
+<head>
+<meta http-equiv="Content-Type" content="text/html; charset=ISO-8859-1">
+<title>Elliptic Integrals of the Second Kind - Legendre Form</title>
+<link rel="stylesheet" href="../../../boostbook.css" type="text/css">
+<meta name="generator" content="DocBook XSL Stylesheets Vsnapshot_8125">
+<link rel="home" href="../../../index.html" title="Math Toolkit">
+<link rel="up" href="../ellint.html" title="Elliptic Integrals">
+<link rel="prev" href="ellint_1.html" title="Elliptic Integrals of the First Kind - Legendre Form">
+<link rel="next" href="ellint_3.html" title="Elliptic Integrals of the Third Kind - Legendre Form">
+</head>
+<body bgcolor="white" text="black" link="#0000FF" vlink="#840084" alink="#0000FF">
+<table cellpadding="2" width="100%"><tr>
+<td valign="top"><img alt="Boost C++ Libraries" width="277" height="86" src="../../../../../boost.png"></td>
+<td align="center">Home</td>
+<td align="center">Libraries</td>
+<td align="center">People</td>
+<td align="center">FAQ</td>
+<td align="center">More</td>
+</tr></table>
+<hr>
+<div class="spirit-nav">
+<a accesskey="p" href="ellint_1.html"><img src="../../../../../doc/html/images/prev.png" alt="Prev"></a><a accesskey="u" href="../ellint.html"><img src="../../../../../doc/html/images/up.png" alt="Up"></a><a accesskey="h" href="../../../index.html"><img src="../../../../../doc/html/images/home.png" alt="Home"></a><a accesskey="n" href="ellint_3.html"><img src="../../../../../doc/html/images/next.png" alt="Next"></a>
+</div>
+<div class="section" lang="en">
+<div class="titlepage"><div><div><h4 class="title">
+<a name="math_toolkit.special.ellint.ellint_2"></a><a class="link" href="ellint_2.html" title="Elliptic Integrals of the Second Kind - Legendre Form"> Elliptic Integrals
+        of the Second Kind - Legendre Form</a>
+</h4></div></div></div>
+<a name="math_toolkit.special.ellint.ellint_2.synopsis"></a><h6>
+<a name="id768912"></a>
+          <a class="link" href="ellint_2.html#math_toolkit.special.ellint.ellint_2.synopsis">Synopsis</a>
+        </h6>
+<p>
+          
+</p>
+<pre class="programlisting"><span class="preprocessor">#include</span> <span class="special">&lt;</span><span class="identifier">boost</span><span class="special">/</span><span class="identifier">math</span><span class="special">/</span><span class="identifier">special_functions</span><span class="special">/</span><span class="identifier">ellint_2</span><span class="special">.</span><span class="identifier">hpp</span><span class="special">&gt;</span>
+</pre>
+<p>
+        </p>
+<pre class="programlisting"><span class="keyword">namespace</span> <span class="identifier">boost</span> <span class="special">{</span> <span class="keyword">namespace</span> <span class="identifier">math</span> <span class="special">{</span>
+
+<span class="keyword">template</span> <span class="special">&lt;</span><span class="keyword">class</span> <span class="identifier">T1</span><span class="special">,</span> <span class="keyword">class</span> <span class="identifier">T2</span><span class="special">&gt;</span>
+<a class="link" href="../../main_overview/result_type.html" title="Calculation of the Type of the Result"><span class="emphasis"><em>calculated-result-type</em></span></a> <span class="identifier">ellint_2</span><span class="special">(</span><span class="identifier">T1</span> <span class="identifier">k</span><span class="special">,</span> <span class="identifier">T2</span> <span class="identifier">phi</span><span class="special">);</span>
+
+<span class="keyword">template</span> <span class="special">&lt;</span><span class="keyword">class</span> <span class="identifier">T1</span><span class="special">,</span> <span class="keyword">class</span> <span class="identifier">T2</span><span class="special">,</span> <span class="keyword">class</span> <a class="link" href="../../policy.html" title="Policies">Policy</a><span class="special">&gt;</span>
+<a class="link" href="../../main_overview/result_type.html" title="Calculation of the Type of the Result"><span class="emphasis"><em>calculated-result-type</em></span></a> <span class="identifier">ellint_2</span><span class="special">(</span><span class="identifier">T1</span> <span class="identifier">k</span><span class="special">,</span> <span class="identifier">T2</span> <span class="identifier">phi</span><span class="special">,</span> <span class="keyword">const</span> <a class="link" href="../../policy.html" title="Policies">Policy</a><span class="special">&amp;);</span>
+
+<span class="keyword">template</span> <span class="special">&lt;</span><span class="keyword">class</span> <span class="identifier">T</span><span class="special">&gt;</span>
+<a class="link" href="../../main_overview/result_type.html" title="Calculation of the Type of the Result"><span class="emphasis"><em>calculated-result-type</em></span></a> <span class="identifier">ellint_2</span><span class="special">(</span><span class="identifier">T</span> <span class="identifier">k</span><span class="special">);</span>
+
+<span class="keyword">template</span> <span class="special">&lt;</span><span class="keyword">class</span> <span class="identifier">T</span><span class="special">,</span> <span class="keyword">class</span> <a class="link" href="../../policy.html" title="Policies">Policy</a><span class="special">&gt;</span>
+<a class="link" href="../../main_overview/result_type.html" title="Calculation of the Type of the Result"><span class="emphasis"><em>calculated-result-type</em></span></a> <span class="identifier">ellint_2</span><span class="special">(</span><span class="identifier">T</span> <span class="identifier">k</span><span class="special">,</span> <span class="keyword">const</span> <a class="link" href="../../policy.html" title="Policies">Policy</a><span class="special">&amp;);</span>
+
+<span class="special">}}</span> <span class="comment">// namespaces
+</span></pre>
+<a name="math_toolkit.special.ellint.ellint_2.description"></a><h6>
+<a name="id769476"></a>
+          <a class="link" href="ellint_2.html#math_toolkit.special.ellint.ellint_2.description">Description</a>
+        </h6>
+<p>
+          These two functions evaluate the incomplete elliptic integral of the second
+          kind <span class="emphasis"><em>E(&#966;, k)</em></span> and its complete counterpart <span class="emphasis"><em>E(k)
+          = E(&#960;/2, k)</em></span>.
+        </p>
+<p>
+          <span class="inlinemediaobject"><img src="../../../../graphs/ellint_2.png" align="middle"></span>
+        </p>
+<p>
+          The return type of these functions is computed using the <a class="link" href="../../main_overview/result_type.html" title="Calculation of the Type of the Result"><span class="emphasis"><em>result
+          type calculation rules</em></span></a> when T1 and T2 are different types:
+          when they are the same type then the result is the same type as the arguments.
+        </p>
+<pre class="programlisting"><span class="keyword">template</span> <span class="special">&lt;</span><span class="keyword">class</span> <span class="identifier">T1</span><span class="special">,</span> <span class="keyword">class</span> <span class="identifier">T2</span><span class="special">&gt;</span>
+<a class="link" href="../../main_overview/result_type.html" title="Calculation of the Type of the Result"><span class="emphasis"><em>calculated-result-type</em></span></a> <span class="identifier">ellint_2</span><span class="special">(</span><span class="identifier">T1</span> <span class="identifier">k</span><span class="special">,</span> <span class="identifier">T2</span> <span class="identifier">phi</span><span class="special">);</span>
+
+<span class="keyword">template</span> <span class="special">&lt;</span><span class="keyword">class</span> <span class="identifier">T1</span><span class="special">,</span> <span class="keyword">class</span> <span class="identifier">T2</span><span class="special">,</span> <span class="keyword">class</span> <a class="link" href="../../policy.html" title="Policies">Policy</a><span class="special">&gt;</span>
+<a class="link" href="../../main_overview/result_type.html" title="Calculation of the Type of the Result"><span class="emphasis"><em>calculated-result-type</em></span></a> <span class="identifier">ellint_2</span><span class="special">(</span><span class="identifier">T1</span> <span class="identifier">k</span><span class="special">,</span> <span class="identifier">T2</span> <span class="identifier">phi</span><span class="special">,</span> <span class="keyword">const</span> <a class="link" href="../../policy.html" title="Policies">Policy</a><span class="special">&amp;);</span>
+</pre>
+<p>
+          Returns the incomplete elliptic integral of the second kind <span class="emphasis"><em>E(&#966;,
+          k)</em></span>:
+        </p>
+<p>
+          <span class="inlinemediaobject"><img src="../../../../equations/ellint3.png"></span>
+        </p>
+<p>
+          Requires -1 &lt;= k &lt;= 1, otherwise returns the result of <a class="link" href="../../main_overview/error_handling.html#domain_error">domain_error</a>.
+        </p>
+<p>
+          </p>
+<p>
+            The final <a class="link" href="../../policy.html" title="Policies">Policy</a> argument
+            is optional and can be used to control the behaviour of the function:
+            how it handles errors, what level of precision to use etc. Refer to the
+            <a class="link" href="../../policy.html" title="Policies">policy documentation for more details</a>.
+          </p>
+<p>
+        </p>
+<pre class="programlisting"><span class="keyword">template</span> <span class="special">&lt;</span><span class="keyword">class</span> <span class="identifier">T</span><span class="special">&gt;</span>
+<a class="link" href="../../main_overview/result_type.html" title="Calculation of the Type of the Result"><span class="emphasis"><em>calculated-result-type</em></span></a> <span class="identifier">ellint_2</span><span class="special">(</span><span class="identifier">T</span> <span class="identifier">k</span><span class="special">);</span>
+
+<span class="keyword">template</span> <span class="special">&lt;</span><span class="keyword">class</span> <span class="identifier">T</span><span class="special">&gt;</span>
+<a class="link" href="../../main_overview/result_type.html" title="Calculation of the Type of the Result"><span class="emphasis"><em>calculated-result-type</em></span></a> <span class="identifier">ellint_2</span><span class="special">(</span><span class="identifier">T</span> <span class="identifier">k</span><span class="special">,</span> <span class="keyword">const</span> <a class="link" href="../../policy.html" title="Policies">Policy</a><span class="special">&amp;);</span>
+</pre>
+<p>
+          Returns the complete elliptic integral of the second kind <span class="emphasis"><em>E(k)</em></span>:
+        </p>
+<p>
+          <span class="inlinemediaobject"><img src="../../../../equations/ellint7.png"></span>
+        </p>
+<p>
+          Requires -1 &lt;= k &lt;= 1, otherwise returns the result of <a class="link" href="../../main_overview/error_handling.html#domain_error">domain_error</a>.
+        </p>
+<p>
+          </p>
+<p>
+            The final <a class="link" href="../../policy.html" title="Policies">Policy</a> argument
+            is optional and can be used to control the behaviour of the function:
+            how it handles errors, what level of precision to use etc. Refer to the
+            <a class="link" href="../../policy.html" title="Policies">policy documentation for more details</a>.
+          </p>
+<p>
+        </p>
+<a name="math_toolkit.special.ellint.ellint_2.accuracy"></a><h6>
+<a name="id770149"></a>
+          <a class="link" href="ellint_2.html#math_toolkit.special.ellint.ellint_2.accuracy">Accuracy</a>
+        </h6>
+<p>
+          These functions are computed using only basic arithmetic operations, so
+          there isn't much variation in accuracy over differing platforms. Note that
+          only results for the widest floating point type on the system are given
+          as narrower types have <a class="link" href="../../backgrounders/relative_error.html#zero_error">effectively zero error</a>.
+          All values are relative errors in units of epsilon.
+        </p>
+<div class="table">
+<a name="id770185"></a><p class="title"><b>Table 42. Errors Rates in the Elliptic Integrals of the
+        Second Kind</b></p>
+<div class="table-contents"><table class="table" summary="Errors Rates in the Elliptic Integrals of the
+        Second Kind">
+<colgroup>
+<col>
+<col>
+<col>
+<col>
+</colgroup>
+<thead><tr>
+<th>
+              <p>
+                Significand Size
+              </p>
+              </th>
+<th>
+              <p>
+                Platform and Compiler
+              </p>
+              </th>
+<th>
+              <p>
+                F(&#966;, k)
+              </p>
+              </th>
+<th>
+              <p>
+                K(k)
+              </p>
+              </th>
+</tr></thead>
+<tbody>
+<tr>
+<td>
+              <p>
+                53
+              </p>
+              </td>
+<td>
+              <p>
+                Win32 / Visual C++ 8.0
+              </p>
+              </td>
+<td>
+              <p>
+                Peak=4.6 Mean=1.2
+              </p>
+              </td>
+<td>
+              <p>
+                Peak=3.5 Mean=1.0
+              </p>
+              </td>
+</tr>
+<tr>
+<td>
+              <p>
+                64
+              </p>
+              </td>
+<td>
+              <p>
+                Red Hat Linux / G++ 3.4
+              </p>
+              </td>
+<td>
+              <p>
+                Peak=4.3 Mean=1.1
+              </p>
+              </td>
+<td>
+              <p>
+                Peak=4.6 Mean=1.2
+              </p>
+              </td>
+</tr>
+<tr>
+<td>
+              <p>
+                113
+              </p>
+              </td>
+<td>
+              <p>
+                HP-UX / HP aCC 6
+              </p>
+              </td>
+<td>
+              <p>
+                Peak=5.8 Mean=2.2
+              </p>
+              </td>
+<td>
+              <p>
+                Peak=10.8 Mean=2.3
+              </p>
+              </td>
+</tr>
+</tbody>
+</table></div>
+</div>
+<br class="table-break"><a name="math_toolkit.special.ellint.ellint_2.testing"></a><h6>
+<a name="id770361"></a>
+          <a class="link" href="ellint_2.html#math_toolkit.special.ellint.ellint_2.testing">Testing</a>
+        </h6>
+<p>
+          The tests use a mixture of spot test values calculated using the online
+          calculator at functions.wolfram.com,
+          and random test data generated using NTL::RR at 1000-bit precision and
+          this implementation.
+        </p>
+<a name="math_toolkit.special.ellint.ellint_2.implementation"></a><h6>
+<a name="id770402"></a>
+          <a class="link" href="ellint_2.html#math_toolkit.special.ellint.ellint_2.implementation">Implementation</a>
+        </h6>
+<p>
+          These functions are implemented in terms of Carlson's integrals using the
+          relations:
+        </p>
+<p>
+          <span class="inlinemediaobject"><img src="../../../../equations/ellint21.png"></span>
+        </p>
+<p>
+          and
+        </p>
+<p>
+          <span class="inlinemediaobject"><img src="../../../../equations/ellint22.png"></span>
+        </p>
+</div>
+<table xmlns:rev="http://www.cs.rpi.edu/~gregod/boost/tools/doc/revision" width="100%"><tr>
+<td align="left"></td>
+<td align="right"><div class="copyright-footer">Copyright © 2006 , 2007, 2008 John Maddock, Paul A. Bristow, Hubert
+      Holin, Xiaogang Zhang, Bruno Lalande and Gautam Sewani<p>
+        Distributed under the Boost Software License, Version 1.0. (See accompanying
+        file LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_0.txt)
+      </p>
+</div></td>
+</tr></table>
+<hr>
+<div class="spirit-nav">
+<a accesskey="p" href="ellint_1.html"><img src="../../../../../doc/html/images/prev.png" alt="Prev"></a><a accesskey="u" href="../ellint.html"><img src="../../../../../doc/html/images/up.png" alt="Up"></a><a accesskey="h" href="../../../index.html"><img src="../../../../../doc/html/images/home.png" alt="Home"></a><a accesskey="n" href="ellint_3.html"><img src="../../../../../doc/html/images/next.png" alt="Next"></a>
+</div>
+</body>
+</html>

Added: sandbox/tools/auto_index/example/math/doc/sf_and_dist/html/math_toolkit/special/ellint/ellint_3.html
==============================================================================
--- (empty file)
+++ sandbox/tools/auto_index/example/math/doc/sf_and_dist/html/math_toolkit/special/ellint/ellint_3.html	2008-11-28 05:25:28 EST (Fri, 28 Nov 2008)
@@ -0,0 +1,336 @@
+<html>
+<head>
+<meta http-equiv="Content-Type" content="text/html; charset=ISO-8859-1">
+<title>Elliptic Integrals of the Third Kind - Legendre Form</title>
+<link rel="stylesheet" href="../../../boostbook.css" type="text/css">
+<meta name="generator" content="DocBook XSL Stylesheets Vsnapshot_8125">
+<link rel="home" href="../../../index.html" title="Math Toolkit">
+<link rel="up" href="../ellint.html" title="Elliptic Integrals">
+<link rel="prev" href="ellint_2.html" title="Elliptic Integrals of the Second Kind - Legendre Form">
+<link rel="next" href="../zetas.html" title="Zeta Functions">
+</head>
+<body bgcolor="white" text="black" link="#0000FF" vlink="#840084" alink="#0000FF">
+<table cellpadding="2" width="100%"><tr>
+<td valign="top"><img alt="Boost C++ Libraries" width="277" height="86" src="../../../../../boost.png"></td>
+<td align="center">Home</td>
+<td align="center">Libraries</td>
+<td align="center">People</td>
+<td align="center">FAQ</td>
+<td align="center">More</td>
+</tr></table>
+<hr>
+<div class="spirit-nav">
+<a accesskey="p" href="ellint_2.html"><img src="../../../../../doc/html/images/prev.png" alt="Prev"></a><a accesskey="u" href="../ellint.html"><img src="../../../../../doc/html/images/up.png" alt="Up"></a><a accesskey="h" href="../../../index.html"><img src="../../../../../doc/html/images/home.png" alt="Home"></a><a accesskey="n" href="../zetas.html"><img src="../../../../../doc/html/images/next.png" alt="Next"></a>
+</div>
+<div class="section" lang="en">
+<div class="titlepage"><div><div><h4 class="title">
+<a name="math_toolkit.special.ellint.ellint_3"></a><a class="link" href="ellint_3.html" title="Elliptic Integrals of the Third Kind - Legendre Form"> Elliptic Integrals
+        of the Third Kind - Legendre Form</a>
+</h4></div></div></div>
+<a name="math_toolkit.special.ellint.ellint_3.synopsis"></a><h6>
+<a name="id770521"></a>
+          <a class="link" href="ellint_3.html#math_toolkit.special.ellint.ellint_3.synopsis">Synopsis</a>
+        </h6>
+<p>
+          
+</p>
+<pre class="programlisting"><span class="preprocessor">#include</span> <span class="special">&lt;</span><span class="identifier">boost</span><span class="special">/</span><span class="identifier">math</span><span class="special">/</span><span class="identifier">special_functions</span><span class="special">/</span><span class="identifier">ellint_3</span><span class="special">.</span><span class="identifier">hpp</span><span class="special">&gt;</span>
+</pre>
+<p>
+        </p>
+<pre class="programlisting"><span class="keyword">namespace</span> <span class="identifier">boost</span> <span class="special">{</span> <span class="keyword">namespace</span> <span class="identifier">math</span> <span class="special">{</span>
+
+<span class="keyword">template</span> <span class="special">&lt;</span><span class="keyword">class</span> <span class="identifier">T1</span><span class="special">,</span> <span class="keyword">class</span> <span class="identifier">T2</span><span class="special">,</span> <span class="keyword">class</span> <span class="identifier">T3</span><span class="special">&gt;</span>
+<a class="link" href="../../main_overview/result_type.html" title="Calculation of the Type of the Result"><span class="emphasis"><em>calculated-result-type</em></span></a> <span class="identifier">ellint_3</span><span class="special">(</span><span class="identifier">T1</span> <span class="identifier">k</span><span class="special">,</span> <span class="identifier">T2</span> <span class="identifier">n</span><span class="special">,</span> <span class="identifier">T3</span> <span class="identifier">phi</span><span class="special">);</span>
+
+<span class="keyword">template</span> <span class="special">&lt;</span><span class="keyword">class</span> <span class="identifier">T1</span><span class="special">,</span> <span class="keyword">class</span> <span class="identifier">T2</span><span class="special">,</span> <span class="keyword">class</span> <span class="identifier">T3</span><span class="special">,</span> <span class="keyword">class</span> <a class="link" href="../../policy.html" title="Policies">Policy</a><span class="special">&gt;</span>
+<a class="link" href="../../main_overview/result_type.html" title="Calculation of the Type of the Result"><span class="emphasis"><em>calculated-result-type</em></span></a> <span class="identifier">ellint_3</span><span class="special">(</span><span class="identifier">T1</span> <span class="identifier">k</span><span class="special">,</span> <span class="identifier">T2</span> <span class="identifier">n</span><span class="special">,</span> <span class="identifier">T3</span> <span class="identifier">phi</span><span class="special">,</span> <span class="keyword">const</span> <a class="link" href="../../policy.html" title="Policies">Policy</a><span class="special">&amp;);</span>
+
+<span class="keyword">template</span> <span class="special">&lt;</span><span class="keyword">class</span> <span class="identifier">T1</span><span class="special">,</span> <span class="keyword">class</span> <span class="identifier">T2</span><span class="special">&gt;</span>
+<a class="link" href="../../main_overview/result_type.html" title="Calculation of the Type of the Result"><span class="emphasis"><em>calculated-result-type</em></span></a> <span class="identifier">ellint_3</span><span class="special">(</span><span class="identifier">T1</span> <span class="identifier">k</span><span class="special">,</span> <span class="identifier">T2</span> <span class="identifier">n</span><span class="special">);</span>
+
+<span class="keyword">template</span> <span class="special">&lt;</span><span class="keyword">class</span> <span class="identifier">T1</span><span class="special">,</span> <span class="keyword">class</span> <span class="identifier">T2</span><span class="special">,</span> <span class="keyword">class</span> <a class="link" href="../../policy.html" title="Policies">Policy</a><span class="special">&gt;</span>
+<a class="link" href="../../main_overview/result_type.html" title="Calculation of the Type of the Result"><span class="emphasis"><em>calculated-result-type</em></span></a> <span class="identifier">ellint_3</span><span class="special">(</span><span class="identifier">T1</span> <span class="identifier">k</span><span class="special">,</span> <span class="identifier">T2</span> <span class="identifier">n</span><span class="special">,</span> <span class="keyword">const</span> <a class="link" href="../../policy.html" title="Policies">Policy</a><span class="special">&amp;);</span>
+
+<span class="special">}}</span> <span class="comment">// namespaces
+</span></pre>
+<a name="math_toolkit.special.ellint.ellint_3.description"></a><h6>
+<a name="id771222"></a>
+          <a class="link" href="ellint_3.html#math_toolkit.special.ellint.ellint_3.description">Description</a>
+        </h6>
+<p>
+          These two functions evaluate the incomplete elliptic integral of the third
+          kind <span class="emphasis"><em>&#928;(n, &#966;, k)</em></span> and its complete counterpart <span class="emphasis"><em>&#928;(n,
+          k) = E(n, &#960;/2, k)</em></span>.
+        </p>
+<p>
+          <span class="inlinemediaobject"><img src="../../../../graphs/ellint_3.png" align="middle"></span>
+        </p>
+<p>
+          The return type of these functions is computed using the <a class="link" href="../../main_overview/result_type.html" title="Calculation of the Type of the Result"><span class="emphasis"><em>result
+          type calculation rules</em></span></a> when the arguments are of different
+          types: when they are the same type then the result is the same type as
+          the arguments.
+        </p>
+<pre class="programlisting"><span class="keyword">template</span> <span class="special">&lt;</span><span class="keyword">class</span> <span class="identifier">T1</span><span class="special">,</span> <span class="keyword">class</span> <span class="identifier">T2</span><span class="special">,</span> <span class="keyword">class</span> <span class="identifier">T3</span><span class="special">&gt;</span>
+<a class="link" href="../../main_overview/result_type.html" title="Calculation of the Type of the Result"><span class="emphasis"><em>calculated-result-type</em></span></a> <span class="identifier">ellint_3</span><span class="special">(</span><span class="identifier">T1</span> <span class="identifier">k</span><span class="special">,</span> <span class="identifier">T2</span> <span class="identifier">n</span><span class="special">,</span> <span class="identifier">T3</span> <span class="identifier">phi</span><span class="special">);</span>
+
+<span class="keyword">template</span> <span class="special">&lt;</span><span class="keyword">class</span> <span class="identifier">T1</span><span class="special">,</span> <span class="keyword">class</span> <span class="identifier">T2</span><span class="special">,</span> <span class="keyword">class</span> <span class="identifier">T3</span><span class="special">,</span> <span class="keyword">class</span> <a class="link" href="../../policy.html" title="Policies">Policy</a><span class="special">&gt;</span>
+<a class="link" href="../../main_overview/result_type.html" title="Calculation of the Type of the Result"><span class="emphasis"><em>calculated-result-type</em></span></a> <span class="identifier">ellint_3</span><span class="special">(</span><span class="identifier">T1</span> <span class="identifier">k</span><span class="special">,</span> <span class="identifier">T2</span> <span class="identifier">n</span><span class="special">,</span> <span class="identifier">T3</span> <span class="identifier">phi</span><span class="special">,</span> <span class="keyword">const</span> <a class="link" href="../../policy.html" title="Policies">Policy</a><span class="special">&amp;);</span>
+</pre>
+<p>
+          Returns the incomplete elliptic integral of the third kind <span class="emphasis"><em>&#928;(n,
+          &#966;, k)</em></span>:
+        </p>
+<p>
+          <span class="inlinemediaobject"><img src="../../../../equations/ellint4.png"></span>
+        </p>
+<p>
+          Requires <span class="emphasis"><em>-1 &lt;= k &lt;= 1</em></span> and <span class="emphasis"><em>n &lt; 1/sin<sup>2</sup>(&#966;)</em></span>,
+          otherwise returns the result of <a class="link" href="../../main_overview/error_handling.html#domain_error">domain_error</a>
+          (outside this range the result would be complex).
+        </p>
+<p>
+          </p>
+<p>
+            The final <a class="link" href="../../policy.html" title="Policies">Policy</a> argument
+            is optional and can be used to control the behaviour of the function:
+            how it handles errors, what level of precision to use etc. Refer to the
+            <a class="link" href="../../policy.html" title="Policies">policy documentation for more details</a>.
+          </p>
+<p>
+        </p>
+<pre class="programlisting"><span class="keyword">template</span> <span class="special">&lt;</span><span class="keyword">class</span> <span class="identifier">T1</span><span class="special">,</span> <span class="keyword">class</span> <span class="identifier">T2</span><span class="special">&gt;</span>
+<a class="link" href="../../main_overview/result_type.html" title="Calculation of the Type of the Result"><span class="emphasis"><em>calculated-result-type</em></span></a> <span class="identifier">ellint_3</span><span class="special">(</span><span class="identifier">T1</span> <span class="identifier">k</span><span class="special">,</span> <span class="identifier">T2</span> <span class="identifier">n</span><span class="special">);</span>
+
+<span class="keyword">template</span> <span class="special">&lt;</span><span class="keyword">class</span> <span class="identifier">T1</span><span class="special">,</span> <span class="keyword">class</span> <span class="identifier">T2</span><span class="special">,</span> <span class="keyword">class</span> <a class="link" href="../../policy.html" title="Policies">Policy</a><span class="special">&gt;</span>
+<a class="link" href="../../main_overview/result_type.html" title="Calculation of the Type of the Result"><span class="emphasis"><em>calculated-result-type</em></span></a> <span class="identifier">ellint_3</span><span class="special">(</span><span class="identifier">T1</span> <span class="identifier">k</span><span class="special">,</span> <span class="identifier">T2</span> <span class="identifier">n</span><span class="special">,</span> <span class="keyword">const</span> <a class="link" href="../../policy.html" title="Policies">Policy</a><span class="special">&amp;);</span>
+</pre>
+<p>
+          Returns the complete elliptic integral of the first kind <span class="emphasis"><em>&#928;(n,
+          k)</em></span>:
+        </p>
+<p>
+          <span class="inlinemediaobject"><img src="../../../../equations/ellint8.png"></span>
+        </p>
+<p>
+          Requires <span class="emphasis"><em>-1 &lt;= k &lt;= 1</em></span> and <span class="emphasis"><em>n &lt; 1</em></span>,
+          otherwise returns the result of <a class="link" href="../../main_overview/error_handling.html#domain_error">domain_error</a>
+          (outside this range the result would be complex).
+        </p>
+<p>
+          </p>
+<p>
+            The final <a class="link" href="../../policy.html" title="Policies">Policy</a> argument
+            is optional and can be used to control the behaviour of the function:
+            how it handles errors, what level of precision to use etc. Refer to the
+            <a class="link" href="../../policy.html" title="Policies">policy documentation for more details</a>.
+          </p>
+<p>
+        </p>
+<a name="math_toolkit.special.ellint.ellint_3.accuracy"></a><h6>
+<a name="id772075"></a>
+          <a class="link" href="ellint_3.html#math_toolkit.special.ellint.ellint_3.accuracy">Accuracy</a>
+        </h6>
+<p>
+          These functions are computed using only basic arithmetic operations, so
+          there isn't much variation in accuracy over differing platforms. Note that
+          only results for the widest floating point type on the system are given
+          as narrower types have <a class="link" href="../../backgrounders/relative_error.html#zero_error">effectively zero error</a>.
+          All values are relative errors in units of epsilon.
+        </p>
+<div class="table">
+<a name="id772112"></a><p class="title"><b>Table 43. Errors Rates in the Elliptic Integrals of the
+        Third Kind</b></p>
+<div class="table-contents"><table class="table" summary="Errors Rates in the Elliptic Integrals of the
+        Third Kind">
+<colgroup>
+<col>
+<col>
+<col>
+<col>
+</colgroup>
+<thead><tr>
+<th>
+              <p>
+                Significand Size
+              </p>
+              </th>
+<th>
+              <p>
+                Platform and Compiler
+              </p>
+              </th>
+<th>
+              <p>
+                &#928;(n, &#966;, k)
+              </p>
+              </th>
+<th>
+              <p>
+                &#928;(n, k)
+              </p>
+              </th>
+</tr></thead>
+<tbody>
+<tr>
+<td>
+              <p>
+                53
+              </p>
+              </td>
+<td>
+              <p>
+                Win32 / Visual C++ 8.0
+              </p>
+              </td>
+<td>
+              <p>
+                Peak=29 Mean=2.2
+              </p>
+              </td>
+<td>
+              <p>
+                Peak=3 Mean=0.8
+              </p>
+              </td>
+</tr>
+<tr>
+<td>
+              <p>
+                64
+              </p>
+              </td>
+<td>
+              <p>
+                Red Hat Linux / G++ 3.4
+              </p>
+              </td>
+<td>
+              <p>
+                Peak=14 Mean=1.3
+              </p>
+              </td>
+<td>
+              <p>
+                Peak=2.3 Mean=0.8
+              </p>
+              </td>
+</tr>
+<tr>
+<td>
+              <p>
+                113
+              </p>
+              </td>
+<td>
+              <p>
+                HP-UX / HP aCC 6
+              </p>
+              </td>
+<td>
+              <p>
+                Peak=10 Mean=1.4
+              </p>
+              </td>
+<td>
+              <p>
+                Peak=4.2 Mean=1.1
+              </p>
+              </td>
+</tr>
+</tbody>
+</table></div>
+</div>
+<br class="table-break"><a name="math_toolkit.special.ellint.ellint_3.testing"></a><h6>
+<a name="id772288"></a>
+          <a class="link" href="ellint_3.html#math_toolkit.special.ellint.ellint_3.testing">Testing</a>
+        </h6>
+<p>
+          The tests use a mixture of spot test values calculated using the online
+          calculator at functions.wolfram.com,
+          and random test data generated using NTL::RR at 1000-bit precision and
+          this implementation.
+        </p>
+<a name="math_toolkit.special.ellint.ellint_3.implementation"></a><h6>
+<a name="id772328"></a>
+          <a class="link" href="ellint_3.html#math_toolkit.special.ellint.ellint_3.implementation">Implementation</a>
+        </h6>
+<p>
+          The implementation for &#928;(n, &#966;, k) first siphons off the special cases:
+        </p>
+<p>
+          <span class="emphasis"><em>&#928;(0, &#966;, k) = F(&#966;, k)</em></span>
+        </p>
+<p>
+          <span class="emphasis"><em>&#928;(n, &#960;/2, k) = &#928;(n, k)</em></span>
+        </p>
+<p>
+          and
+        </p>
+<p>
+          <span class="inlinemediaobject"><img src="../../../../equations/ellint23.png"></span>
+        </p>
+<p>
+          Then if n &lt; 0 the relations (A&amp;S 17.7.15/16):
+        </p>
+<p>
+          <span class="inlinemediaobject"><img src="../../../../equations/ellint24.png"></span>
+        </p>
+<p>
+          are used to shift <span class="emphasis"><em>n</em></span> to the range [0, 1].
+        </p>
+<p>
+          Then the relations:
+        </p>
+<p>
+          <span class="emphasis"><em>&#928;(n, -&#966;, k) = -&#928;(n, &#966;, k)</em></span>
+        </p>
+<p>
+          <span class="emphasis"><em>&#928;(n, &#966;+m&#960;, k) = &#928;(n, &#966;, k) + 2m&#928;(n, k) ; n &lt;= 1</em></span>
+        </p>
+<p>
+          <span class="emphasis"><em>&#928;(n, &#966;+m&#960;, k) = &#928;(n, &#966;, k) ; n &gt; 1</em></span>
+          <sup>[<a name="id772475" href="#ftn.id772475" class="footnote">1</a>]</sup>
+        </p>
+<p>
+          are used to move &#966; to the range [0, &#960;/2].
+        </p>
+<p>
+          The functions are then implemented in terms of Carlson's integrals using
+          the relations:
+        </p>
+<p>
+          <span class="inlinemediaobject"><img src="../../../../equations/ellint25.png"></span>
+        </p>
+<p>
+          and
+        </p>
+<p>
+          <span class="inlinemediaobject"><img src="../../../../equations/ellint26.png"></span>
+        </p>
+<div class="footnotes">
+<br><hr width="100" align="left">
+<div class="footnote"><p><sup>[<a name="ftn.id772475" href="#id772475" class="para">1</a>] </sup>
+              I haven't been able to find a literature reference for this relation,
+              but it appears to be the convention used by Mathematica. Intuitively
+              the first <span class="emphasis"><em>2 * m * &#928;(n, k)</em></span> terms cancel out as the
+              derivative alternates between +&#8734; and -&#8734;.
+            </p></div>
+</div>
+</div>
+<table xmlns:rev="http://www.cs.rpi.edu/~gregod/boost/tools/doc/revision" width="100%"><tr>
+<td align="left"></td>
+<td align="right"><div class="copyright-footer">Copyright © 2006 , 2007, 2008 John Maddock, Paul A. Bristow, Hubert
+      Holin, Xiaogang Zhang, Bruno Lalande and Gautam Sewani<p>
+        Distributed under the Boost Software License, Version 1.0. (See accompanying
+        file LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_0.txt)
+      </p>
+</div></td>
+</tr></table>
+<hr>
+<div class="spirit-nav">
+<a accesskey="p" href="ellint_2.html"><img src="../../../../../doc/html/images/prev.png" alt="Prev"></a><a accesskey="u" href="../ellint.html"><img src="../../../../../doc/html/images/up.png" alt="Up"></a><a accesskey="h" href="../../../index.html"><img src="../../../../../doc/html/images/home.png" alt="Home"></a><a accesskey="n" href="../zetas.html"><img src="../../../../../doc/html/images/next.png" alt="Next"></a>
+</div>
+</body>
+</html>

Added: sandbox/tools/auto_index/example/math/doc/sf_and_dist/html/math_toolkit/special/ellint/ellint_carlson.html
==============================================================================
--- (empty file)
+++ sandbox/tools/auto_index/example/math/doc/sf_and_dist/html/math_toolkit/special/ellint/ellint_carlson.html	2008-11-28 05:25:28 EST (Fri, 28 Nov 2008)
@@ -0,0 +1,472 @@
+<html>
+<head>
+<meta http-equiv="Content-Type" content="text/html; charset=ISO-8859-1">
+<title>Elliptic Integrals - Carlson Form</title>
+<link rel="stylesheet" href="../../../boostbook.css" type="text/css">
+<meta name="generator" content="DocBook XSL Stylesheets Vsnapshot_8125">
+<link rel="home" href="../../../index.html" title="Math Toolkit">
+<link rel="up" href="../ellint.html" title="Elliptic Integrals">
+<link rel="prev" href="ellint_intro.html" title="Elliptic Integral Overview">
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+<body bgcolor="white" text="black" link="#0000FF" vlink="#840084" alink="#0000FF">
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+<a accesskey="p" href="ellint_intro.html"><img src="../../../../../doc/html/images/prev.png" alt="Prev"></a><a accesskey="u" href="../ellint.html"><img src="../../../../../doc/html/images/up.png" alt="Up"></a><a accesskey="h" href="../../../index.html"><img src="../../../../../doc/html/images/home.png" alt="Home"></a><a accesskey="n" href="ellint_1.html"><img src="../../../../../doc/html/images/next.png" alt="Next"></a>
+</div>
+<div class="section" lang="en">
+<div class="titlepage"><div><div><h4 class="title">
+<a name="math_toolkit.special.ellint.ellint_carlson"></a><a class="link" href="ellint_carlson.html" title="Elliptic Integrals - Carlson Form"> Elliptic
+        Integrals - Carlson Form</a>
+</h4></div></div></div>
+<a name="math_toolkit.special.ellint.ellint_carlson.synopsis"></a><h6>
+<a name="id763109"></a>
+          <a class="link" href="ellint_carlson.html#math_toolkit.special.ellint.ellint_carlson.synopsis">Synopsis</a>
+        </h6>
+<p>
+          
+</p>
+<pre class="programlisting"><span class="preprocessor">#include</span> <span class="special">&lt;</span><span class="identifier">boost</span><span class="special">/</span><span class="identifier">math</span><span class="special">/</span><span class="identifier">special_functions</span><span class="special">/</span><span class="identifier">ellint_rf</span><span class="special">.</span><span class="identifier">hpp</span><span class="special">&gt;</span>
+</pre>
+<p>
+        </p>
+<pre class="programlisting"><span class="keyword">namespace</span> <span class="identifier">boost</span> <span class="special">{</span> <span class="keyword">namespace</span> <span class="identifier">math</span> <span class="special">{</span>
+
+<span class="keyword">template</span> <span class="special">&lt;</span><span class="keyword">class</span> <span class="identifier">T1</span><span class="special">,</span> <span class="keyword">class</span> <span class="identifier">T2</span><span class="special">,</span> <span class="keyword">class</span> <span class="identifier">T3</span><span class="special">&gt;</span>
+<a class="link" href="../../main_overview/result_type.html" title="Calculation of the Type of the Result"><span class="emphasis"><em>calculated-result-type</em></span></a> <span class="identifier">ellint_rf</span><span class="special">(</span><span class="identifier">T1</span> <span class="identifier">x</span><span class="special">,</span> <span class="identifier">T2</span> <span class="identifier">y</span><span class="special">,</span> <span class="identifier">T3</span> <span class="identifier">z</span><span class="special">)</span>
+
+<span class="keyword">template</span> <span class="special">&lt;</span><span class="keyword">class</span> <span class="identifier">T1</span><span class="special">,</span> <span class="keyword">class</span> <span class="identifier">T2</span><span class="special">,</span> <span class="keyword">class</span> <span class="identifier">T3</span><span class="special">,</span> <span class="keyword">class</span> <a class="link" href="../../policy.html" title="Policies">Policy</a><span class="special">&gt;</span>
+<a class="link" href="../../main_overview/result_type.html" title="Calculation of the Type of the Result"><span class="emphasis"><em>calculated-result-type</em></span></a> <span class="identifier">ellint_rf</span><span class="special">(</span><span class="identifier">T1</span> <span class="identifier">x</span><span class="special">,</span> <span class="identifier">T2</span> <span class="identifier">y</span><span class="special">,</span> <span class="identifier">T3</span> <span class="identifier">z</span><span class="special">,</span> <span class="keyword">const</span> <a class="link" href="../../policy.html" title="Policies">Policy</a><span class="special">&amp;)</span>
+
+<span class="special">}}</span> <span class="comment">// namespaces
+</span></pre>
+<p>
+          
+</p>
+<pre class="programlisting"><span class="preprocessor">#include</span> <span class="special">&lt;</span><span class="identifier">boost</span><span class="special">/</span><span class="identifier">math</span><span class="special">/</span><span class="identifier">special_functions</span><span class="special">/</span><span class="identifier">ellint_rd</span><span class="special">.</span><span class="identifier">hpp</span><span class="special">&gt;</span>
+</pre>
+<p>
+        </p>
+<pre class="programlisting"><span class="keyword">namespace</span> <span class="identifier">boost</span> <span class="special">{</span> <span class="keyword">namespace</span> <span class="identifier">math</span> <span class="special">{</span>
+
+<span class="keyword">template</span> <span class="special">&lt;</span><span class="keyword">class</span> <span class="identifier">T1</span><span class="special">,</span> <span class="keyword">class</span> <span class="identifier">T2</span><span class="special">,</span> <span class="keyword">class</span> <span class="identifier">T3</span><span class="special">&gt;</span>
+<a class="link" href="../../main_overview/result_type.html" title="Calculation of the Type of the Result"><span class="emphasis"><em>calculated-result-type</em></span></a> <span class="identifier">ellint_rd</span><span class="special">(</span><span class="identifier">T1</span> <span class="identifier">x</span><span class="special">,</span> <span class="identifier">T2</span> <span class="identifier">y</span><span class="special">,</span> <span class="identifier">T3</span> <span class="identifier">z</span><span class="special">)</span>
+
+<span class="keyword">template</span> <span class="special">&lt;</span><span class="keyword">class</span> <span class="identifier">T1</span><span class="special">,</span> <span class="keyword">class</span> <span class="identifier">T2</span><span class="special">,</span> <span class="keyword">class</span> <span class="identifier">T3</span><span class="special">,</span> <span class="keyword">class</span> <a class="link" href="../../policy.html" title="Policies">Policy</a><span class="special">&gt;</span>
+<a class="link" href="../../main_overview/result_type.html" title="Calculation of the Type of the Result"><span class="emphasis"><em>calculated-result-type</em></span></a> <span class="identifier">ellint_rd</span><span class="special">(</span><span class="identifier">T1</span> <span class="identifier">x</span><span class="special">,</span> <span class="identifier">T2</span> <span class="identifier">y</span><span class="special">,</span> <span class="identifier">T3</span> <span class="identifier">z</span><span class="special">,</span> <span class="keyword">const</span> <a class="link" href="../../policy.html" title="Policies">Policy</a><span class="special">&amp;)</span>
+
+<span class="special">}}</span> <span class="comment">// namespaces
+</span></pre>
+<p>
+          
+</p>
+<pre class="programlisting"><span class="preprocessor">#include</span> <span class="special">&lt;</span><span class="identifier">boost</span><span class="special">/</span><span class="identifier">math</span><span class="special">/</span><span class="identifier">special_functions</span><span class="special">/</span><span class="identifier">ellint_rj</span><span class="special">.</span><span class="identifier">hpp</span><span class="special">&gt;</span>
+</pre>
+<p>
+        </p>
+<pre class="programlisting"><span class="keyword">namespace</span> <span class="identifier">boost</span> <span class="special">{</span> <span class="keyword">namespace</span> <span class="identifier">math</span> <span class="special">{</span>
+
+<span class="keyword">template</span> <span class="special">&lt;</span><span class="keyword">class</span> <span class="identifier">T1</span><span class="special">,</span> <span class="keyword">class</span> <span class="identifier">T2</span><span class="special">,</span> <span class="keyword">class</span> <span class="identifier">T3</span><span class="special">,</span> <span class="keyword">class</span> <span class="identifier">T4</span><span class="special">&gt;</span>
+<a class="link" href="../../main_overview/result_type.html" title="Calculation of the Type of the Result"><span class="emphasis"><em>calculated-result-type</em></span></a> <span class="identifier">ellint_rj</span><span class="special">(</span><span class="identifier">T1</span> <span class="identifier">x</span><span class="special">,</span> <span class="identifier">T2</span> <span class="identifier">y</span><span class="special">,</span> <span class="identifier">T3</span> <span class="identifier">z</span><span class="special">,</span> <span class="identifier">T4</span> <span class="identifier">p</span><span class="special">)</span>
+
+<span class="keyword">template</span> <span class="special">&lt;</span><span class="keyword">class</span> <span class="identifier">T1</span><span class="special">,</span> <span class="keyword">class</span> <span class="identifier">T2</span><span class="special">,</span> <span class="keyword">class</span> <span class="identifier">T3</span><span class="special">,</span> <span class="keyword">class</span> <span class="identifier">T4</span><span class="special">,</span> <span class="keyword">class</span> <a class="link" href="../../policy.html" title="Policies">Policy</a><span class="special">&gt;</span>
+<a class="link" href="../../main_overview/result_type.html" title="Calculation of the Type of the Result"><span class="emphasis"><em>calculated-result-type</em></span></a> <span class="identifier">ellint_rj</span><span class="special">(</span><span class="identifier">T1</span> <span class="identifier">x</span><span class="special">,</span> <span class="identifier">T2</span> <span class="identifier">y</span><span class="special">,</span> <span class="identifier">T3</span> <span class="identifier">z</span><span class="special">,</span> <span class="identifier">T4</span> <span class="identifier">p</span><span class="special">,</span> <span class="keyword">const</span> <a class="link" href="../../policy.html" title="Policies">Policy</a><span class="special">&amp;)</span>
+
+<span class="special">}}</span> <span class="comment">// namespaces
+</span></pre>
+<p>
+          
+</p>
+<pre class="programlisting"><span class="preprocessor">#include</span> <span class="special">&lt;</span><span class="identifier">boost</span><span class="special">/</span><span class="identifier">math</span><span class="special">/</span><span class="identifier">special_functions</span><span class="special">/</span><span class="identifier">ellint_rc</span><span class="special">.</span><span class="identifier">hpp</span><span class="special">&gt;</span>
+</pre>
+<p>
+        </p>
+<pre class="programlisting"><span class="keyword">namespace</span> <span class="identifier">boost</span> <span class="special">{</span> <span class="keyword">namespace</span> <span class="identifier">math</span> <span class="special">{</span>
+
+<span class="keyword">template</span> <span class="special">&lt;</span><span class="keyword">class</span> <span class="identifier">T1</span><span class="special">,</span> <span class="keyword">class</span> <span class="identifier">T2</span><span class="special">&gt;</span>
+<a class="link" href="../../main_overview/result_type.html" title="Calculation of the Type of the Result"><span class="emphasis"><em>calculated-result-type</em></span></a> <span class="identifier">ellint_rc</span><span class="special">(</span><span class="identifier">T1</span> <span class="identifier">x</span><span class="special">,</span> <span class="identifier">T2</span> <span class="identifier">y</span><span class="special">)</span>
+
+<span class="keyword">template</span> <span class="special">&lt;</span><span class="keyword">class</span> <span class="identifier">T1</span><span class="special">,</span> <span class="keyword">class</span> <span class="identifier">T2</span><span class="special">,</span> <span class="keyword">class</span> <a class="link" href="../../policy.html" title="Policies">Policy</a><span class="special">&gt;</span>
+<a class="link" href="../../main_overview/result_type.html" title="Calculation of the Type of the Result"><span class="emphasis"><em>calculated-result-type</em></span></a> <span class="identifier">ellint_rc</span><span class="special">(</span><span class="identifier">T1</span> <span class="identifier">x</span><span class="special">,</span> <span class="identifier">T2</span> <span class="identifier">y</span><span class="special">,</span> <span class="keyword">const</span> <a class="link" href="../../policy.html" title="Policies">Policy</a><span class="special">&amp;)</span>
+
+<span class="special">}}</span> <span class="comment">// namespaces
+</span></pre>
+<a name="math_toolkit.special.ellint.ellint_carlson.description"></a><h6>
+<a name="id764889"></a>
+          <a class="link" href="ellint_carlson.html#math_toolkit.special.ellint.ellint_carlson.description">Description</a>
+        </h6>
+<p>
+          These functions return Carlson's symmetrical elliptic integrals, the functions
+          have complicated behavior over all their possible domains, but the following
+          graph gives an idea of their behavior:
+        </p>
+<p>
+          <span class="inlinemediaobject"><img src="../../../../graphs/ellint_carlson.png" align="middle"></span>
+        </p>
+<p>
+          The return type of these functions is computed using the <a class="link" href="../../main_overview/result_type.html" title="Calculation of the Type of the Result"><span class="emphasis"><em>result
+          type calculation rules</em></span></a> when the arguments are of different
+          types: otherwise the return is the same type as the arguments.
+        </p>
+<pre class="programlisting"><span class="keyword">template</span> <span class="special">&lt;</span><span class="keyword">class</span> <span class="identifier">T1</span><span class="special">,</span> <span class="keyword">class</span> <span class="identifier">T2</span><span class="special">,</span> <span class="keyword">class</span> <span class="identifier">T3</span><span class="special">&gt;</span>
+<a class="link" href="../../main_overview/result_type.html" title="Calculation of the Type of the Result"><span class="emphasis"><em>calculated-result-type</em></span></a> <span class="identifier">ellint_rf</span><span class="special">(</span><span class="identifier">T1</span> <span class="identifier">x</span><span class="special">,</span> <span class="identifier">T2</span> <span class="identifier">y</span><span class="special">,</span> <span class="identifier">T3</span> <span class="identifier">z</span><span class="special">)</span>
+
+<span class="keyword">template</span> <span class="special">&lt;</span><span class="keyword">class</span> <span class="identifier">T1</span><span class="special">,</span> <span class="keyword">class</span> <span class="identifier">T2</span><span class="special">,</span> <span class="keyword">class</span> <span class="identifier">T3</span><span class="special">,</span> <span class="keyword">class</span> <a class="link" href="../../policy.html" title="Policies">Policy</a><span class="special">&gt;</span>
+<a class="link" href="../../main_overview/result_type.html" title="Calculation of the Type of the Result"><span class="emphasis"><em>calculated-result-type</em></span></a> <span class="identifier">ellint_rf</span><span class="special">(</span><span class="identifier">T1</span> <span class="identifier">x</span><span class="special">,</span> <span class="identifier">T2</span> <span class="identifier">y</span><span class="special">,</span> <span class="identifier">T3</span> <span class="identifier">z</span><span class="special">,</span> <span class="keyword">const</span> <a class="link" href="../../policy.html" title="Policies">Policy</a><span class="special">&amp;)</span>
+</pre>
+<p>
+          Returns Carlson's Elliptic Integral R<sub>F</sub>:
+        </p>
+<p>
+          <span class="inlinemediaobject"><img src="../../../../equations/ellint9.png"></span>
+        </p>
+<p>
+          Requires that all of the arguments are non-negative, and at most one may
+          be zero. Otherwise returns the result of <a class="link" href="../../main_overview/error_handling.html#domain_error">domain_error</a>.
+        </p>
+<p>
+          </p>
+<p>
+            The final <a class="link" href="../../policy.html" title="Policies">Policy</a> argument
+            is optional and can be used to control the behaviour of the function:
+            how it handles errors, what level of precision to use etc. Refer to the
+            <a class="link" href="../../policy.html" title="Policies">policy documentation for more details</a>.
+          </p>
+<p>
+        </p>
+<pre class="programlisting"><span class="keyword">template</span> <span class="special">&lt;</span><span class="keyword">class</span> <span class="identifier">T1</span><span class="special">,</span> <span class="keyword">class</span> <span class="identifier">T2</span><span class="special">,</span> <span class="keyword">class</span> <span class="identifier">T3</span><span class="special">&gt;</span>
+<a class="link" href="../../main_overview/result_type.html" title="Calculation of the Type of the Result"><span class="emphasis"><em>calculated-result-type</em></span></a> <span class="identifier">ellint_rd</span><span class="special">(</span><span class="identifier">T1</span> <span class="identifier">x</span><span class="special">,</span> <span class="identifier">T2</span> <span class="identifier">y</span><span class="special">,</span> <span class="identifier">T3</span> <span class="identifier">z</span><span class="special">)</span>
+
+<span class="keyword">template</span> <span class="special">&lt;</span><span class="keyword">class</span> <span class="identifier">T1</span><span class="special">,</span> <span class="keyword">class</span> <span class="identifier">T2</span><span class="special">,</span> <span class="keyword">class</span> <span class="identifier">T3</span><span class="special">,</span> <span class="keyword">class</span> <a class="link" href="../../policy.html" title="Policies">Policy</a><span class="special">&gt;</span>
+<a class="link" href="../../main_overview/result_type.html" title="Calculation of the Type of the Result"><span class="emphasis"><em>calculated-result-type</em></span></a> <span class="identifier">ellint_rd</span><span class="special">(</span><span class="identifier">T1</span> <span class="identifier">x</span><span class="special">,</span> <span class="identifier">T2</span> <span class="identifier">y</span><span class="special">,</span> <span class="identifier">T3</span> <span class="identifier">z</span><span class="special">,</span> <span class="keyword">const</span> <a class="link" href="../../policy.html" title="Policies">Policy</a><span class="special">&amp;)</span>
+</pre>
+<p>
+          Returns Carlson's elliptic integral R<sub>D</sub>:
+        </p>
+<p>
+          <span class="inlinemediaobject"><img src="../../../../equations/ellint10.png"></span>
+        </p>
+<p>
+          Requires that x and y are non-negative, with at most one of them zero,
+          and that z &gt;= 0. Otherwise returns the result of <a class="link" href="../../main_overview/error_handling.html#domain_error">domain_error</a>.
+        </p>
+<p>
+          </p>
+<p>
+            The final <a class="link" href="../../policy.html" title="Policies">Policy</a> argument
+            is optional and can be used to control the behaviour of the function:
+            how it handles errors, what level of precision to use etc. Refer to the
+            <a class="link" href="../../policy.html" title="Policies">policy documentation for more details</a>.
+          </p>
+<p>
+        </p>
+<pre class="programlisting"><span class="keyword">template</span> <span class="special">&lt;</span><span class="keyword">class</span> <span class="identifier">T1</span><span class="special">,</span> <span class="keyword">class</span> <span class="identifier">T2</span><span class="special">,</span> <span class="keyword">class</span> <span class="identifier">T3</span><span class="special">,</span> <span class="keyword">class</span> <span class="identifier">T4</span><span class="special">&gt;</span>
+<a class="link" href="../../main_overview/result_type.html" title="Calculation of the Type of the Result"><span class="emphasis"><em>calculated-result-type</em></span></a> <span class="identifier">ellint_rj</span><span class="special">(</span><span class="identifier">T1</span> <span class="identifier">x</span><span class="special">,</span> <span class="identifier">T2</span> <span class="identifier">y</span><span class="special">,</span> <span class="identifier">T3</span> <span class="identifier">z</span><span class="special">,</span> <span class="identifier">T4</span> <span class="identifier">p</span><span class="special">)</span>
+
+<span class="keyword">template</span> <span class="special">&lt;</span><span class="keyword">class</span> <span class="identifier">T1</span><span class="special">,</span> <span class="keyword">class</span> <span class="identifier">T2</span><span class="special">,</span> <span class="keyword">class</span> <span class="identifier">T3</span><span class="special">,</span> <span class="keyword">class</span> <span class="identifier">T4</span><span class="special">,</span> <span class="keyword">class</span> <a class="link" href="../../policy.html" title="Policies">Policy</a><span class="special">&gt;</span>
+<a class="link" href="../../main_overview/result_type.html" title="Calculation of the Type of the Result"><span class="emphasis"><em>calculated-result-type</em></span></a> <span class="identifier">ellint_rj</span><span class="special">(</span><span class="identifier">T1</span> <span class="identifier">x</span><span class="special">,</span> <span class="identifier">T2</span> <span class="identifier">y</span><span class="special">,</span> <span class="identifier">T3</span> <span class="identifier">z</span><span class="special">,</span> <span class="identifier">T4</span> <span class="identifier">p</span><span class="special">,</span> <span class="keyword">const</span> <a class="link" href="../../policy.html" title="Policies">Policy</a><span class="special">&amp;)</span>
+</pre>
+<p>
+          Returns Carlson's elliptic integral R<sub>J</sub>:
+        </p>
+<p>
+          <span class="inlinemediaobject"><img src="../../../../equations/ellint11.png"></span>
+        </p>
+<p>
+          Requires that x, y and z are non-negative, with at most one of them zero,
+          and that <span class="emphasis"><em>p != 0</em></span>. Otherwise returns the result of
+          <a class="link" href="../../main_overview/error_handling.html#domain_error">domain_error</a>.
+        </p>
+<p>
+          </p>
+<p>
+            The final <a class="link" href="../../policy.html" title="Policies">Policy</a> argument
+            is optional and can be used to control the behaviour of the function:
+            how it handles errors, what level of precision to use etc. Refer to the
+            <a class="link" href="../../policy.html" title="Policies">policy documentation for more details</a>.
+          </p>
+<p>
+        </p>
+<p>
+          When <span class="emphasis"><em>p &lt; 0</em></span> the function returns the <a href="http://en.wikipedia.org/wiki/Cauchy_principal_value" target="_top">Cauchy
+          principal value</a> using the relation:
+        </p>
+<p>
+          <span class="inlinemediaobject"><img src="../../../../equations/ellint17.png"></span>
+        </p>
+<pre class="programlisting"><span class="keyword">template</span> <span class="special">&lt;</span><span class="keyword">class</span> <span class="identifier">T1</span><span class="special">,</span> <span class="keyword">class</span> <span class="identifier">T2</span><span class="special">&gt;</span>
+<a class="link" href="../../main_overview/result_type.html" title="Calculation of the Type of the Result"><span class="emphasis"><em>calculated-result-type</em></span></a> <span class="identifier">ellint_rc</span><span class="special">(</span><span class="identifier">T1</span> <span class="identifier">x</span><span class="special">,</span> <span class="identifier">T2</span> <span class="identifier">y</span><span class="special">)</span>
+
+<span class="keyword">template</span> <span class="special">&lt;</span><span class="keyword">class</span> <span class="identifier">T1</span><span class="special">,</span> <span class="keyword">class</span> <span class="identifier">T2</span><span class="special">,</span> <span class="keyword">class</span> <a class="link" href="../../policy.html" title="Policies">Policy</a><span class="special">&gt;</span>
+<a class="link" href="../../main_overview/result_type.html" title="Calculation of the Type of the Result"><span class="emphasis"><em>calculated-result-type</em></span></a> <span class="identifier">ellint_rc</span><span class="special">(</span><span class="identifier">T1</span> <span class="identifier">x</span><span class="special">,</span> <span class="identifier">T2</span> <span class="identifier">y</span><span class="special">,</span> <span class="keyword">const</span> <a class="link" href="../../policy.html" title="Policies">Policy</a><span class="special">&amp;)</span>
+</pre>
+<p>
+          Returns Carlson's elliptic integral R<sub>C</sub>:
+        </p>
+<p>
+          <span class="inlinemediaobject"><img src="../../../../equations/ellint12.png"></span>
+        </p>
+<p>
+          Requires that <span class="emphasis"><em>x &gt; 0</em></span> and that <span class="emphasis"><em>y != 0</em></span>.
+          Otherwise returns the result of <a class="link" href="../../main_overview/error_handling.html#domain_error">domain_error</a>.
+        </p>
+<p>
+          </p>
+<p>
+            The final <a class="link" href="../../policy.html" title="Policies">Policy</a> argument
+            is optional and can be used to control the behaviour of the function:
+            how it handles errors, what level of precision to use etc. Refer to the
+            <a class="link" href="../../policy.html" title="Policies">policy documentation for more details</a>.
+          </p>
+<p>
+        </p>
+<p>
+          When <span class="emphasis"><em>y &lt; 0</em></span> the function returns the <a href="http://mathworld.wolfram.com/CauchyPrincipalValue.html" target="_top">Cauchy
+          principal value</a> using the relation:
+        </p>
+<p>
+          <span class="inlinemediaobject"><img src="../../../../equations/ellint18.png"></span>
+        </p>
+<a name="math_toolkit.special.ellint.ellint_carlson.testing"></a><h6>
+<a name="id766688"></a>
+          <a class="link" href="ellint_carlson.html#math_toolkit.special.ellint.ellint_carlson.testing">Testing</a>
+        </h6>
+<p>
+          There are two sets of tests.
+        </p>
+<p>
+          Spot tests compare selected values with test data given in:
+        </p>
+<div class="blockquote"><blockquote class="blockquote">
+<p>
+            </p>
+<p>
+              B. C. Carlson, <span class="emphasis"><em><a href="http://arxiv.org/abs/math.CA/9409227" target="_top">Numerical
+              computation of real or complex elliptic integrals</a></em></span>.
+              Numerical Algorithms, Volume 10, Number 1 / March, 1995, pp 13-26.
+            </p>
+<p>
+          </p>
+</blockquote></div>
+<p>
+          Random test data generated using NTL::RR at 1000-bit precision and our
+          implementation checks for rounding-errors and/or regressions.
+        </p>
+<p>
+          There are also sanity checks that use the inter-relations between the integrals
+          to verify their correctness: see the above Carlson paper for details.
+        </p>
+<a name="math_toolkit.special.ellint.ellint_carlson.accuracy"></a><h6>
+<a name="id766768"></a>
+          <a class="link" href="ellint_carlson.html#math_toolkit.special.ellint.ellint_carlson.accuracy">Accuracy</a>
+        </h6>
+<p>
+          These functions are computed using only basic arithmetic operations, so
+          there isn't much variation in accuracy over differing platforms. Note that
+          only results for the widest floating-point type on the system are given
+          as narrower types have <a class="link" href="../../backgrounders/relative_error.html#zero_error">effectively zero error</a>.
+          All values are relative errors in units of epsilon.
+        </p>
+<div class="table">
+<a name="id766805"></a><p class="title"><b>Table 40. Errors Rates in the Carlson Elliptic Integrals</b></p>
+<div class="table-contents"><table class="table" summary="Errors Rates in the Carlson Elliptic Integrals">
+<colgroup>
+<col>
+<col>
+<col>
+<col>
+<col>
+<col>
+</colgroup>
+<thead><tr>
+<th>
+              <p>
+                Significand Size
+              </p>
+              </th>
+<th>
+              <p>
+                Platform and Compiler
+              </p>
+              </th>
+<th>
+              <p>
+                R<sub>F</sub>
+              </p>
+              </th>
+<th>
+              <p>
+                R<sub>D</sub>
+              </p>
+              </th>
+<th>
+              <p>
+                R<sub>J</sub>
+              </p>
+              </th>
+<th>
+              <p>
+                R<sub>C</sub>
+              </p>
+              </th>
+</tr></thead>
+<tbody>
+<tr>
+<td>
+              <p>
+                53
+              </p>
+              </td>
+<td>
+              <p>
+                Win32 / Visual C++ 8.0
+              </p>
+              </td>
+<td>
+              <p>
+                Peak=2.9 Mean=0.75
+              </p>
+              </td>
+<td>
+              <p>
+                Peak=2.6 Mean=0.9
+              </p>
+              </td>
+<td>
+              <p>
+                Peak=108 Mean=6.9
+              </p>
+              </td>
+<td>
+              <p>
+                Peak=2.4 Mean=0.6
+              </p>
+              </td>
+</tr>
+<tr>
+<td>
+              <p>
+                64
+              </p>
+              </td>
+<td>
+              <p>
+                Red Hat Linux / G++ 3.4
+              </p>
+              </td>
+<td>
+              <p>
+                Peak=2.5 Mean=0.75
+              </p>
+              </td>
+<td>
+              <p>
+                Peak=2.7 Mean=0.9
+              </p>
+              </td>
+<td>
+              <p>
+                Peak=105 Mean=8
+              </p>
+              </td>
+<td>
+              <p>
+                Peak=1.9 Mean=0.7
+              </p>
+              </td>
+</tr>
+<tr>
+<td>
+              <p>
+                113
+              </p>
+              </td>
+<td>
+              <p>
+                HP-UX / HP aCC 6
+              </p>
+              </td>
+<td>
+              <p>
+                Peak=5.3 Mean=1.6
+              </p>
+              </td>
+<td>
+              <p>
+                Peak=2.9 Mean=0.99
+              </p>
+              </td>
+<td>
+              <p>
+                Peak=180 Mean=12
+              </p>
+              </td>
+<td>
+              <p>
+                Peak=1.8 Mean=0.7
+              </p>
+              </td>
+</tr>
+</tbody>
+</table></div>
+</div>
+<br class="table-break"><a name="math_toolkit.special.ellint.ellint_carlson.implementation"></a><h6>
+<a name="id767052"></a>
+          <a class="link" href="ellint_carlson.html#math_toolkit.special.ellint.ellint_carlson.implementation">Implementation</a>
+        </h6>
+<p>
+          The key of Carlson's algorithm [<a class="link" href="ellint_intro.html#ellint_ref_carlson79">Carlson79</a>]
+          is the duplication theorem:
+        </p>
+<p>
+          <span class="inlinemediaobject"><img src="../../../../equations/ellint13.png"></span>
+        </p>
+<p>
+          By applying it repeatedly, <span class="emphasis"><em>x</em></span>, <span class="emphasis"><em>y</em></span>,
+          <span class="emphasis"><em>z</em></span> get closer and closer. When they are nearly equal,
+          the special case equation
+        </p>
+<p>
+          <span class="inlinemediaobject"><img src="../../../../equations/ellint16.png"></span>
+        </p>
+<p>
+          is used. More specifically, <span class="emphasis"><em>[R F</em></span>] is evaluated from
+          a Taylor series expansion to the fifth order. The calculations of the other
+          three integrals are analogous.
+        </p>
+<p>
+          For <span class="emphasis"><em>p &lt; 0</em></span> in <span class="emphasis"><em>R<sub>J</sub>(x, y, z, p)</em></span>
+          and <span class="emphasis"><em>y &lt; 0</em></span> in <span class="emphasis"><em>R<sub>C</sub>(x, y)</em></span>, the
+          integrals are singular and their <a href="http://mathworld.wolfram.com/CauchyPrincipalValue.html" target="_top">Cauchy
+          principal values</a> are returned via the relations:
+        </p>
+<p>
+          <span class="inlinemediaobject"><img src="../../../../equations/ellint17.png"></span>
+        </p>
+<p>
+          <span class="inlinemediaobject"><img src="../../../../equations/ellint18.png"></span>
+        </p>
+</div>
+<table xmlns:rev="http://www.cs.rpi.edu/~gregod/boost/tools/doc/revision" width="100%"><tr>
+<td align="left"></td>
+<td align="right"><div class="copyright-footer">Copyright © 2006 , 2007, 2008 John Maddock, Paul A. Bristow, Hubert
+      Holin, Xiaogang Zhang, Bruno Lalande and Gautam Sewani<p>
+        Distributed under the Boost Software License, Version 1.0. (See accompanying
+        file LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_0.txt)
+      </p>
+</div></td>
+</tr></table>
+<hr>
+<div class="spirit-nav">
+<a accesskey="p" href="ellint_intro.html"><img src="../../../../../doc/html/images/prev.png" alt="Prev"></a><a accesskey="u" href="../ellint.html"><img src="../../../../../doc/html/images/up.png" alt="Up"></a><a accesskey="h" href="../../../index.html"><img src="../../../../../doc/html/images/home.png" alt="Home"></a><a accesskey="n" href="ellint_1.html"><img src="../../../../../doc/html/images/next.png" alt="Next"></a>
+</div>
+</body>
+</html>

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@@ -0,0 +1,423 @@
+<html>
+<head>
+<meta http-equiv="Content-Type" content="text/html; charset=ISO-8859-1">
+<title>Elliptic Integral Overview</title>
+<link rel="stylesheet" href="../../../boostbook.css" type="text/css">
+<meta name="generator" content="DocBook XSL Stylesheets Vsnapshot_8125">
+<link rel="home" href="../../../index.html" title="Math Toolkit">
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+</head>
+<body bgcolor="white" text="black" link="#0000FF" vlink="#840084" alink="#0000FF">
+<table cellpadding="2" width="100%"><tr>
+<td valign="top"><img alt="Boost C++ Libraries" width="277" height="86" src="../../../../../boost.png"></td>
+<td align="center">Home</td>
+<td align="center">Libraries</td>
+<td align="center">People</td>
+<td align="center">FAQ</td>
+<td align="center">More</td>
+</tr></table>
+<hr>
+<div class="spirit-nav">
+<a accesskey="p" href="../ellint.html"><img src="../../../../../doc/html/images/prev.png" alt="Prev"></a><a accesskey="u" href="../ellint.html"><img src="../../../../../doc/html/images/up.png" alt="Up"></a><a accesskey="h" href="../../../index.html"><img src="../../../../../doc/html/images/home.png" alt="Home"></a><a accesskey="n" href="ellint_carlson.html"><img src="../../../../../doc/html/images/next.png" alt="Next"></a>
+</div>
+<div class="section" lang="en">
+<div class="titlepage"><div><div><h4 class="title">
+<a name="math_toolkit.special.ellint.ellint_intro"></a><a class="link" href="ellint_intro.html" title="Elliptic Integral Overview"> Elliptic
+        Integral Overview</a>
+</h4></div></div></div>
+<p>
+          The main reference for the elliptic integrals is:
+        </p>
+<div class="blockquote"><blockquote class="blockquote">
+<p>
+            </p>
+<p>
+              M. Abramowitz and I. A. Stegun (Eds.) (1964) Handbook of Mathematical
+              Functions with Formulas, Graphs, and Mathematical Tables, National
+              Bureau of Standards Applied Mathematics Series, U.S. Government Printing
+              Office, Washington, D.C.
+            </p>
+<p>
+          </p>
+</blockquote></div>
+<p>
+          Mathworld also contain a lot of useful background information:
+        </p>
+<div class="blockquote"><blockquote class="blockquote">
+<p>
+            </p>
+<p>
+              <a href="http://mathworld.wolfram.com/EllipticIntegral.html" target="_top">Weisstein,
+              Eric W. "Elliptic Integral." From MathWorld--A Wolfram Web
+              Resource.</a>
+            </p>
+<p>
+          </p>
+</blockquote></div>
+<p>
+          As does <a href="http://en.wikipedia.org/wiki/Elliptic_integral" target="_top">Wikipedia
+          Elliptic integral</a>.
+        </p>
+<a name="math_toolkit.special.ellint.ellint_intro.notation"></a><h5>
+<a name="id761687"></a>
+          <a class="link" href="ellint_intro.html#math_toolkit.special.ellint.ellint_intro.notation">Notation</a>
+        </h5>
+<p>
+          All variables are real numbers unless otherwise noted.
+        </p>
+<a name="ellint_def"></a><a name="math_toolkit.special.ellint.ellint_intro.definition"></a><h5>
+<a name="id761725"></a>
+          <a class="link" href="ellint_intro.html#math_toolkit.special.ellint.ellint_intro.definition">Definition</a>
+        </h5>
+<p>
+          <span class="inlinemediaobject"><img src="../../../../equations/ellint1.png"></span>
+        </p>
+<p>
+          is called elliptic integral if <span class="emphasis"><em>R(t, s)</em></span> is a rational
+          function of <span class="emphasis"><em>t</em></span> and <span class="emphasis"><em>s</em></span>, and <span class="emphasis"><em>s<sup>2</sup></em></span>
+          is a cubic or quartic polynomial in <span class="emphasis"><em>t</em></span>.
+        </p>
+<p>
+          Elliptic integrals generally can not be expressed in terms of elementary
+          functions. However, Legendre showed that all elliptic integrals can be
+          reduced to the following three canonical forms:
+        </p>
+<p>
+          Elliptic Integral of the First Kind (Legendre form)
+        </p>
+<p>
+          <span class="inlinemediaobject"><img src="../../../../equations/ellint2.png"></span>
+        </p>
+<p>
+          Elliptic Integral of the Second Kind (Legendre form)
+        </p>
+<p>
+          <span class="inlinemediaobject"><img src="../../../../equations/ellint3.png"></span>
+        </p>
+<p>
+          Elliptic Integral of the Third Kind (Legendre form)
+        </p>
+<p>
+          <span class="inlinemediaobject"><img src="../../../../equations/ellint4.png"></span>
+        </p>
+<p>
+          where
+        </p>
+<p>
+          <span class="inlinemediaobject"><img src="../../../../equations/ellint5.png"></span>
+        </p>
+<div class="note"><table border="0" summary="Note">
+<tr>
+<td rowspan="2" align="center" valign="top" width="25"><img alt="[Note]" src="../../../../../doc/html/images/note.png"></td>
+<th align="left">Note</th>
+</tr>
+<tr><td align="left" valign="top">
+<p>
+            <span class="emphasis"><em>&#966;</em></span> is called the amplitude.
+          </p>
+<p>
+            <span class="emphasis"><em>k</em></span> is called the modulus.
+          </p>
+<p>
+            <span class="emphasis"><em>&#945;</em></span> is called the modular angle.
+          </p>
+<p>
+            <span class="emphasis"><em>n</em></span> is called the characteristic.
+          </p>
+</td></tr>
+</table></div>
+<div class="caution"><table border="0" summary="Caution">
+<tr>
+<td rowspan="2" align="center" valign="top" width="25"><img alt="[Caution]" src="../../../../../doc/html/images/caution.png"></td>
+<th align="left">Caution</th>
+</tr>
+<tr><td align="left" valign="top">
+<p>
+            Perhaps more than any other special functions the elliptic integrals
+            are expressed in a variety of different ways. In particular, the final
+            parameter <span class="emphasis"><em>k</em></span> (the modulus) may be expressed using
+            a modular angle &#945;, or a parameter <span class="emphasis"><em>m</em></span>. These are related
+            by:
+          </p>
+<p>
+            k = sin&#945;
+          </p>
+<p>
+            m = k<sup>2</sup> = sin<sup>2</sup>&#945;
+          </p>
+<p>
+            So that the integral of the third kind (for example) may be expressed
+            as either:
+          </p>
+<p>
+            &#928;(n, &#966;, k)
+          </p>
+<p>
+            &#928;(n, &#966; \ &#945;)
+          </p>
+<p>
+            &#928;(n, &#966;| m)
+          </p>
+<p>
+            To further complicate matters, some texts refer to the <span class="emphasis"><em>complement
+            of the parameter m</em></span>, or 1 - m, where:
+          </p>
+<p>
+            1 - m = 1 - k<sup>2</sup> = cos<sup>2</sup>&#945;
+          </p>
+<p>
+            This implementation uses <span class="emphasis"><em>k</em></span> throughout: this matches
+            the requirements of the <a href="http://www.open-std.org/jtc1/sc22/wg21/docs/papers/2005/n1836.pdf" target="_top">Technical
+            Report on C++ Library Extensions</a>. However, you should be extra
+            careful when using these functions!
+          </p>
+</td></tr>
+</table></div>
+<p>
+          When <span class="emphasis"><em>&#966;</em></span> = <span class="emphasis"><em>&#960;</em></span> / 2, the elliptic integrals
+          are called <span class="emphasis"><em>complete</em></span>.
+        </p>
+<p>
+          Complete Elliptic Integral of the First Kind (Legendre form)
+        </p>
+<p>
+          <span class="inlinemediaobject"><img src="../../../../equations/ellint6.png"></span>
+        </p>
+<p>
+          Complete Elliptic Integral of the Second Kind (Legendre form)
+        </p>
+<p>
+          <span class="inlinemediaobject"><img src="../../../../equations/ellint7.png"></span>
+        </p>
+<p>
+          Complete Elliptic Integral of the Third Kind (Legendre form)
+        </p>
+<p>
+          <span class="inlinemediaobject"><img src="../../../../equations/ellint8.png"></span>
+        </p>
+<p>
+          Carlson [<a class="link" href="ellint_intro.html#ellint_ref_carlson77">Carlson77</a>] [<a class="link" href="ellint_intro.html#ellint_ref_carlson78">Carlson78</a>] gives an alternative definition
+          of elliptic integral's canonical forms:
+        </p>
+<p>
+          Carlson's Elliptic Integral of the First Kind
+        </p>
+<p>
+          <span class="inlinemediaobject"><img src="../../../../equations/ellint9.png"></span>
+        </p>
+<p>
+          where <span class="emphasis"><em>x</em></span>, <span class="emphasis"><em>y</em></span>, <span class="emphasis"><em>z</em></span>
+          are nonnegative and at most one of them may be zero.
+        </p>
+<p>
+          Carlson's Elliptic Integral of the Second Kind
+        </p>
+<p>
+          <span class="inlinemediaobject"><img src="../../../../equations/ellint10.png"></span>
+        </p>
+<p>
+          where <span class="emphasis"><em>x</em></span>, <span class="emphasis"><em>y</em></span> are nonnegative, at
+          most one of them may be zero, and <span class="emphasis"><em>z</em></span> must be positive.
+        </p>
+<p>
+          Carlson's Elliptic Integral of the Third Kind
+        </p>
+<p>
+          <span class="inlinemediaobject"><img src="../../../../equations/ellint11.png"></span>
+        </p>
+<p>
+          where <span class="emphasis"><em>x</em></span>, <span class="emphasis"><em>y</em></span>, <span class="emphasis"><em>z</em></span>
+          are nonnegative, at most one of them may be zero, and <span class="emphasis"><em>p</em></span>
+          must be nonzero.
+        </p>
+<p>
+          Carlson's Degenerate Elliptic Integral
+        </p>
+<p>
+          <span class="inlinemediaobject"><img src="../../../../equations/ellint12.png"></span>
+        </p>
+<p>
+          where <span class="emphasis"><em>x</em></span> is nonnegative and <span class="emphasis"><em>y</em></span>
+          is nonzero.
+        </p>
+<div class="note"><table border="0" summary="Note">
+<tr>
+<td rowspan="2" align="center" valign="top" width="25"><img alt="[Note]" src="../../../../../doc/html/images/note.png"></td>
+<th align="left">Note</th>
+</tr>
+<tr><td align="left" valign="top">
+<p>
+            <span class="emphasis"><em>R<sub>C</sub>(x, y) = R<sub>F</sub>(x, y, y)</em></span>
+          </p>
+<p>
+            <span class="emphasis"><em>R<sub>D</sub>(x, y, z) = R<sub>J</sub>(x, y, z, z)</em></span>
+          </p>
+</td></tr>
+</table></div>
+<a name="ellint_theorem"></a><a name="math_toolkit.special.ellint.ellint_intro.duplication_theorem"></a><h5>
+<a name="id762512"></a>
+          <a class="link" href="ellint_intro.html#math_toolkit.special.ellint.ellint_intro.duplication_theorem">Duplication
+          Theorem</a>
+        </h5>
+<p>
+          Carlson proved in [<a class="link" href="ellint_intro.html#ellint_ref_carlson78">Carlson78</a>]
+          that
+        </p>
+<p>
+          <span class="inlinemediaobject"><img src="../../../../equations/ellint13.png"></span>
+        </p>
+<a name="ellint_formula"></a><a name="math_toolkit.special.ellint.ellint_intro.carlson_s_formulas"></a><h5>
+<a name="id762588"></a>
+          <a class="link" href="ellint_intro.html#math_toolkit.special.ellint.ellint_intro.carlson_s_formulas">Carlson's
+          Formulas</a>
+        </h5>
+<p>
+          The Legendre form and Carlson form of elliptic integrals are related by
+          equations:
+        </p>
+<p>
+          <span class="inlinemediaobject"><img src="../../../../equations/ellint14.png"></span>
+        </p>
+<p>
+          In particular,
+        </p>
+<p>
+          <span class="inlinemediaobject"><img src="../../../../equations/ellint15.png"></span>
+        </p>
+<a name="math_toolkit.special.ellint.ellint_intro.numerical_algorithms"></a><h5>
+<a name="id762685"></a>
+          <a class="link" href="ellint_intro.html#math_toolkit.special.ellint.ellint_intro.numerical_algorithms">Numerical
+          Algorithms</a>
+        </h5>
+<p>
+          The conventional methods for computing elliptic integrals are Gauss and
+          Landen transformations, which converge quadratically and work well for
+          elliptic integrals of the first and second kinds. Unfortunately they suffer
+          from loss of significant digits for the third kind. Carlson's algorithm
+          [<a class="link" href="ellint_intro.html#ellint_ref_carlson79">Carlson79</a>] [<a class="link" href="ellint_intro.html#ellint_ref_carlson78">Carlson78</a>],
+          by contrast, provides a unified method for all three kinds of elliptic
+          integrals with satisfactory precisions.
+        </p>
+<a name="ellint_refs"></a><a name="math_toolkit.special.ellint.ellint_intro.references"></a><h5>
+<a name="id762755"></a>
+          <a class="link" href="ellint_intro.html#math_toolkit.special.ellint.ellint_intro.references">References</a>
+        </h5>
+<p>
+          Special mention goes to:
+        </p>
+<div class="blockquote"><blockquote class="blockquote">
+<p>
+            </p>
+<p>
+              A. M. Legendre, <span class="emphasis"><em>Traitd des Fonctions Elliptiques et des Integrales
+              Euleriennes</em></span>, Vol. 1. Paris (1825).
+            </p>
+<p>
+          </p>
+</blockquote></div>
+<p>
+          However the main references are:
+        </p>
+<a name="ellint_ref_AS"></a><a name="ellint_ref_carlson79"></a><a name="ellint_ref_carlson77"></a><a name="ellint_ref_carlson78"></a><a name="ellint_ref_carlson81"></a><div class="orderedlist"><ol type="1">
+<li>
+            M. Abramowitz and I. A. Stegun (Eds.) (1964) Handbook of Mathematical
+            Functions with Formulas, Graphs, and Mathematical Tables, National Bureau
+            of Standards Applied Mathematics Series, U.S. Government Printing Office,
+            Washington, D.C.
+          </li>
+<li>
+            B.C. Carlson, <span class="emphasis"><em>Computing elliptic integrals by duplication</em></span>,
+            Numerische Mathematik, vol 33, 1 (1979).
+          </li>
+<li>
+            B.C. Carlson, <span class="emphasis"><em>Elliptic Integrals of the First Kind</em></span>,
+            SIAM Journal on Mathematical Analysis, vol 8, 231 (1977).
+          </li>
+<li>
+            B.C. Carlson, <span class="emphasis"><em>Short Proofs of Three Theorems on Elliptic Integrals</em></span>,
+            SIAM Journal on Mathematical Analysis, vol 9, 524 (1978).
+          </li>
+<li>
+            B.C. Carlson and E.M. Notis, <span class="emphasis"><em>ALGORITHM 577: Algorithms for
+            Incomplete Elliptic Integrals</em></span>, ACM Transactions on Mathematmal
+            Software, vol 7, 398 (1981).
+          </li>
+<li>
+            B. C. Carlson, <span class="emphasis"><em>On computing elliptic integrals and functions</em></span>.
+            J. Math. and Phys., 44 (1965), pp. 36-51.
+          </li>
+<li>
+            B. C. Carlson, <span class="emphasis"><em>A table of elliptic integrals of the second
+            kind</em></span>. Math. Comp., 49 (1987), pp. 595-606. (Supplement, ibid.,
+            pp. S13-S17.)
+          </li>
+<li>
+            B. C. Carlson, <span class="emphasis"><em>A table of elliptic integrals of the third kind</em></span>.
+            Math. Comp., 51 (1988), pp. 267-280. (Supplement, ibid., pp. S1-S5.)
+          </li>
+<li>
+            B. C. Carlson, <span class="emphasis"><em>A table of elliptic integrals: cubic cases</em></span>.
+            Math. Comp., 53 (1989), pp. 327-333.
+          </li>
+<li>
+            B. C. Carlson, <span class="emphasis"><em>A table of elliptic integrals: one quadratic
+            factor</em></span>. Math. Comp., 56 (1991), pp. 267-280.
+          </li>
+<li>
+            B. C. Carlson, <span class="emphasis"><em>A table of elliptic integrals: two quadratic
+            factors</em></span>. Math. Comp., 59 (1992), pp. 165-180.
+          </li>
+<li>
+            B. C. Carlson, <span class="emphasis"><em><a href="http://arxiv.org/abs/math.CA/9409227" target="_top">Numerical
+            computation of real or complex elliptic integrals</a></em></span>.
+            Numerical Algorithms, Volume 10, Number 1 / March, 1995, p13-26.
+          </li>
+<li>
+            B. C. Carlson and John L. Gustafson, <span class="emphasis"><em><a href="http://arxiv.org/abs/math.CA/9310223" target="_top">Asymptotic
+            Approximations for Symmetric Elliptic Integrals</a></em></span>, SIAM
+            Journal on Mathematical Analysis, Volume 25, Issue 2 (March 1994), 288-303.
+          </li>
+</ol></div>
+<p>
+          The following references, while not directly relevent to our implementation,
+          may also be of interest:
+        </p>
+<div class="orderedlist"><ol type="1">
+<li>
+            R. Burlisch, <span class="emphasis"><em>Numerical Compuation of Elliptic Integrals and
+            Elliptic Functions.</em></span> Numerical Mathematik 7, 78-90.
+          </li>
+<li>
+            R. Burlisch, <span class="emphasis"><em>An extension of the Bartky Transformation to Incomplete
+            Elliptic Integrals of the Third Kind</em></span>. Numerical Mathematik
+            13, 266-284.
+          </li>
+<li>
+            R. Burlisch, <span class="emphasis"><em>Numerical Compuation of Elliptic Integrals and
+            Elliptic Functions. III</em></span>. Numerical Mathematik 13, 305-315.
+          </li>
+<li>
+            T. Fukushima and H. Ishizaki, <span class="emphasis"><em><a href="http://adsabs.harvard.edu/abs/1994CeMDA..59..237F" target="_top">Numerical
+            Computation of Incomplete Elliptic Integrals of a General Form.</a></em></span>
+            Celestial Mechanics and Dynamical Astronomy, Volume 59, Number 3 / July,
+            1994, 237-251.
+          </li>
+</ol></div>
+</div>
+<table xmlns:rev="http://www.cs.rpi.edu/~gregod/boost/tools/doc/revision" width="100%"><tr>
+<td align="left"></td>
+<td align="right"><div class="copyright-footer">Copyright © 2006 , 2007, 2008 John Maddock, Paul A. Bristow, Hubert
+      Holin, Xiaogang Zhang, Bruno Lalande and Gautam Sewani<p>
+        Distributed under the Boost Software License, Version 1.0. (See accompanying
+        file LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_0.txt)
+      </p>
+</div></td>
+</tr></table>
+<hr>
+<div class="spirit-nav">
+<a accesskey="p" href="../ellint.html"><img src="../../../../../doc/html/images/prev.png" alt="Prev"></a><a accesskey="u" href="../ellint.html"><img src="../../../../../doc/html/images/up.png" alt="Up"></a><a accesskey="h" href="../../../index.html"><img src="../../../../../doc/html/images/home.png" alt="Home"></a><a accesskey="n" href="ellint_carlson.html"><img src="../../../../../doc/html/images/next.png" alt="Next"></a>
+</div>
+</body>
+</html>

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@@ -0,0 +1,50 @@
+<html>
+<head>
+<meta http-equiv="Content-Type" content="text/html; charset=ISO-8859-1">
+<title>Exponential Integrals</title>
+<link rel="stylesheet" href="../../boostbook.css" type="text/css">
+<meta name="generator" content="DocBook XSL Stylesheets Vsnapshot_8125">
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+<body bgcolor="white" text="black" link="#0000FF" vlink="#840084" alink="#0000FF">
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+</div>
+<div class="section" lang="en">
+<div class="titlepage"><div><div><h3 class="title">
+<a name="math_toolkit.special.expint"></a><a class="link" href="expint.html" title="Exponential Integrals"> Exponential Integrals</a>
+</h3></div></div></div>
+<div class="toc"><dl>
+<dt><span class="section"><a href="expint/expint_n.html"> Exponential
+        Integral En</a></span></dt>
+<dt><span class="section"><a href="expint/expint_i.html"> Exponential
+        Integral Ei</a></span></dt>
+</dl></div>
+</div>
+<table xmlns:rev="http://www.cs.rpi.edu/~gregod/boost/tools/doc/revision" width="100%"><tr>
+<td align="left"></td>
+<td align="right"><div class="copyright-footer">Copyright © 2006 , 2007, 2008 John Maddock, Paul A. Bristow, Hubert
+      Holin, Xiaogang Zhang, Bruno Lalande and Gautam Sewani<p>
+        Distributed under the Boost Software License, Version 1.0. (See accompanying
+        file LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_0.txt)
+      </p>
+</div></td>
+</tr></table>
+<hr>
+<div class="spirit-nav">
+<a accesskey="p" href="zetas/zeta.html"><img src="../../../../doc/html/images/prev.png" alt="Prev"></a><a accesskey="u" href="../special.html"><img src="../../../../doc/html/images/up.png" alt="Up"></a><a accesskey="h" href="../../index.html"><img src="../../../../doc/html/images/home.png" alt="Home"></a><a accesskey="n" href="expint/expint_n.html"><img src="../../../../doc/html/images/next.png" alt="Next"></a>
+</div>
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+</html>

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@@ -0,0 +1,309 @@
+<html>
+<head>
+<meta http-equiv="Content-Type" content="text/html; charset=ISO-8859-1">
+<title>Exponential Integral Ei</title>
+<link rel="stylesheet" href="../../../boostbook.css" type="text/css">
+<meta name="generator" content="DocBook XSL Stylesheets Vsnapshot_8125">
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+<link rel="prev" href="expint_n.html" title="Exponential Integral En">
+<link rel="next" href="../powers.html" title="Logs, Powers, Roots and Exponentials">
+</head>
+<body bgcolor="white" text="black" link="#0000FF" vlink="#840084" alink="#0000FF">
+<table cellpadding="2" width="100%"><tr>
+<td valign="top"><img alt="Boost C++ Libraries" width="277" height="86" src="../../../../../boost.png"></td>
+<td align="center">Home</td>
+<td align="center">Libraries</td>
+<td align="center">People</td>
+<td align="center">FAQ</td>
+<td align="center">More</td>
+</tr></table>
+<hr>
+<div class="spirit-nav">
+<a accesskey="p" href="expint_n.html"><img src="../../../../../doc/html/images/prev.png" alt="Prev"></a><a accesskey="u" href="../expint.html"><img src="../../../../../doc/html/images/up.png" alt="Up"></a><a accesskey="h" href="../../../index.html"><img src="../../../../../doc/html/images/home.png" alt="Home"></a><a accesskey="n" href="../powers.html"><img src="../../../../../doc/html/images/next.png" alt="Next"></a>
+</div>
+<div class="section" lang="en">
+<div class="titlepage"><div><div><h4 class="title">
+<a name="math_toolkit.special.expint.expint_i"></a><a class="link" href="expint_i.html" title="Exponential Integral Ei"> Exponential
+        Integral Ei</a>
+</h4></div></div></div>
+<a name="math_toolkit.special.expint.expint_i.synopsis"></a><h5>
+<a name="id775363"></a>
+          <a class="link" href="expint_i.html#math_toolkit.special.expint.expint_i.synopsis">Synopsis</a>
+        </h5>
+<p>
+          
+</p>
+<pre class="programlisting"><span class="preprocessor">#include</span> <span class="special">&lt;</span><span class="identifier">boost</span><span class="special">/</span><span class="identifier">math</span><span class="special">/</span><span class="identifier">special_functions</span><span class="special">/</span><span class="identifier">expint</span><span class="special">.</span><span class="identifier">hpp</span><span class="special">&gt;</span>
+</pre>
+<p>
+        </p>
+<pre class="programlisting"><span class="keyword">namespace</span> <span class="identifier">boost</span><span class="special">{</span> <span class="keyword">namespace</span> <span class="identifier">math</span><span class="special">{</span>
+
+<span class="keyword">template</span> <span class="special">&lt;</span><span class="keyword">class</span> <span class="identifier">T</span><span class="special">&gt;</span>
+<a class="link" href="../../main_overview/result_type.html" title="Calculation of the Type of the Result"><span class="emphasis"><em>calculated-result-type</em></span></a> <span class="identifier">expint</span><span class="special">(</span><span class="identifier">T</span> <span class="identifier">z</span><span class="special">);</span>
+
+<span class="keyword">template</span> <span class="special">&lt;</span><span class="keyword">class</span> <span class="identifier">T</span><span class="special">,</span> <span class="keyword">class</span> <a class="link" href="../../policy.html" title="Policies">Policy</a><span class="special">&gt;</span>
+<a class="link" href="../../main_overview/result_type.html" title="Calculation of the Type of the Result"><span class="emphasis"><em>calculated-result-type</em></span></a> <span class="identifier">expint</span><span class="special">(</span><span class="identifier">T</span> <span class="identifier">z</span><span class="special">,</span> <span class="keyword">const</span> <a class="link" href="../../policy.html" title="Policies">Policy</a><span class="special">&amp;);</span>
+
+<span class="special">}}</span> <span class="comment">// namespaces
+</span></pre>
+<p>
+          The return type of these functions is computed using the <a class="link" href="../../main_overview/result_type.html" title="Calculation of the Type of the Result"><span class="emphasis"><em>result
+          type calculation rules</em></span></a>: the return type is <code class="computeroutput"><span class="keyword">double</span></code> if T is an integer type, and T otherwise.
+        </p>
+<p>
+          </p>
+<p>
+            The final <a class="link" href="../../policy.html" title="Policies">Policy</a> argument
+            is optional and can be used to control the behaviour of the function:
+            how it handles errors, what level of precision to use etc. Refer to the
+            <a class="link" href="../../policy.html" title="Policies">policy documentation for more details</a>.
+          </p>
+<p>
+        </p>
+<a name="math_toolkit.special.expint.expint_i.description"></a><h5>
+<a name="id775744"></a>
+          <a class="link" href="expint_i.html#math_toolkit.special.expint.expint_i.description">Description</a>
+        </h5>
+<pre class="programlisting"><span class="keyword">template</span> <span class="special">&lt;</span><span class="keyword">class</span> <span class="identifier">T</span><span class="special">&gt;</span>
+<a class="link" href="../../main_overview/result_type.html" title="Calculation of the Type of the Result"><span class="emphasis"><em>calculated-result-type</em></span></a> <span class="identifier">expint</span><span class="special">(</span><span class="identifier">T</span> <span class="identifier">z</span><span class="special">);</span>
+
+<span class="keyword">template</span> <span class="special">&lt;</span><span class="keyword">class</span> <span class="identifier">T</span><span class="special">,</span> <span class="keyword">class</span> <a class="link" href="../../policy.html" title="Policies">Policy</a><span class="special">&gt;</span>
+<a class="link" href="../../main_overview/result_type.html" title="Calculation of the Type of the Result"><span class="emphasis"><em>calculated-result-type</em></span></a> <span class="identifier">expint</span><span class="special">(</span><span class="identifier">T</span> <span class="identifier">z</span><span class="special">,</span> <span class="keyword">const</span> <a class="link" href="../../policy.html" title="Policies">Policy</a><span class="special">&amp;);</span>
+</pre>
+<p>
+          Returns the <a href="http://mathworld.wolfram.com/ExponentialIntegral.html" target="_top">exponential
+          integral</a> of z:
+        </p>
+<p>
+          <span class="inlinemediaobject"><img src="../../../../equations/expint_i_1.png"></span>
+        </p>
+<p>
+          <span class="inlinemediaobject"><img src="../../../../graphs/expint_i.png" align="middle"></span>
+        </p>
+<a name="math_toolkit.special.expint.expint_i.accuracy"></a><h5>
+<a name="id776024"></a>
+          <a class="link" href="expint_i.html#math_toolkit.special.expint.expint_i.accuracy">Accuracy</a>
+        </h5>
+<p>
+          The following table shows the peak errors (in units of epsilon) found on
+          various platforms with various floating point types, along with comparisons
+          to Cody's SPECFUN implementation and the GSL-1.9
+          library. Unless otherwise specified any floating point type that is narrower
+          than the one shown will have <a class="link" href="../../backgrounders/relative_error.html#zero_error">effectively zero
+          error</a>.
+        </p>
+<div class="table">
+<a name="id776069"></a><p class="title"><b>Table 46. Errors In the Function expint(z)</b></p>
+<div class="table-contents"><table class="table" summary="Errors In the Function expint(z)">
+<colgroup>
+<col>
+<col>
+<col>
+</colgroup>
+<thead><tr>
+<th>
+              <p>
+                Significand Size
+              </p>
+              </th>
+<th>
+              <p>
+                Platform and Compiler
+              </p>
+              </th>
+<th>
+              <p>
+                Error
+              </p>
+              </th>
+</tr></thead>
+<tbody>
+<tr>
+<td>
+              <p>
+                53
+              </p>
+              </td>
+<td>
+              <p>
+                Win32, Visual C++ 8
+              </p>
+              </td>
+<td>
+              <p>
+                Peak=2.4 Mean=0.6
+              </p>
+              <p>
+                GSL Peak=8.9 Mean=0.7
+              </p>
+              <p>
+                SPECFUN (Cody) Peak=2.5 Mean=0.6
+              </p>
+              </td>
+</tr>
+<tr>
+<td>
+              <p>
+                64
+              </p>
+              </td>
+<td>
+              <p>
+                RedHat Linux IA_EM64, gcc-4.1
+              </p>
+              </td>
+<td>
+              <p>
+                Peak=5.1 Mean=0.8
+              </p>
+              </td>
+</tr>
+<tr>
+<td>
+              <p>
+                64
+              </p>
+              </td>
+<td>
+              <p>
+                Redhat Linux IA64, gcc-4.1
+              </p>
+              </td>
+<td>
+              <p>
+                Peak=5.0 Mean=0.8
+              </p>
+              </td>
+</tr>
+<tr>
+<td>
+              <p>
+                113
+              </p>
+              </td>
+<td>
+              <p>
+                HPUX IA64, aCC A.06.06
+              </p>
+              </td>
+<td>
+              <p>
+                Peak=1.9 Mean=0.63
+              </p>
+              </td>
+</tr>
+</tbody>
+</table></div>
+</div>
+<br class="table-break"><p>
+          It should be noted that all three libraries tested above offer sub-epsilon
+          precision over most of their range.
+        </p>
+<p>
+          GSL has the greatest difficulty near the positive root of En, while Cody's
+          SPECFUN along with this implementation increase their error rates very
+          slightly over the range [4,6].
+        </p>
+<a name="math_toolkit.special.expint.expint_i.testing"></a><h5>
+<a name="id776271"></a>
+          <a class="link" href="expint_i.html#math_toolkit.special.expint.expint_i.testing">Testing</a>
+        </h5>
+<p>
+          The tests for these functions come in two parts: basic sanity checks use
+          spot values calculated using <a href="http://functions.wolfram.com/webMathematica/FunctionEvaluation.jsp?name=ExpIntegralEi" target="_top">Mathworld's
+          online evaluator</a>, while accuracy checks use high-precision test
+          values calculated at 1000-bit precision with NTL::RR
+          and this implementation. Note that the generic and type-specific versions
+          of these functions use differing implementations internally, so this gives
+          us reasonably independent test data. Using our test data to test other
+          "known good" implementations also provides an additional sanity
+          check.
+        </p>
+<a name="math_toolkit.special.expint.expint_i.implementation"></a><h5>
+<a name="id776333"></a>
+          <a class="link" href="expint_i.html#math_toolkit.special.expint.expint_i.implementation">Implementation</a>
+        </h5>
+<p>
+          For x &lt; 0 this function just calls <a class="link" href="expint_n.html" title="Exponential Integral En">zeta</a>(1,
+          -x): which in turn is implemented in terms of rational approximations when
+          the type of x has 113 or fewer bits of precision.
+        </p>
+<p>
+          For x &gt; 0 the generic version is implemented using the infinte series:
+        </p>
+<p>
+          <span class="inlinemediaobject"><img src="../../../../equations/expint_i_2.png"></span>
+        </p>
+<p>
+          However, when the precision of the argument type is known at compile time
+          and is 113 bits or less, then rational approximations <a class="link" href="../../backgrounders/implementation.html#math_toolkit.backgrounders.implementation.rational_approximations_used">devised
+          by JM</a> are used.
+        </p>
+<p>
+          For 0 &lt; z &lt; 6 a root-preserving approximation of the form:
+        </p>
+<p>
+          <span class="inlinemediaobject"><img src="../../../../equations/expint_i_3.png"></span>
+        </p>
+<p>
+          is used, where z<sub>0</sub> is the positive root of the function, and R(z/3 - 1) is
+          a minimax rational approximation rescaled so that it is evaluated over
+          [-1,1]. Note that while the rational approximation over [0,6] converges
+          rapidly to the minimax solution it is rather ill-conditioned in practice.
+          Cody and Thacher
+          <sup>[<a name="id776481" href="#ftn.id776481" class="footnote">2</a>]</sup>
+          experienced the same issue and converted the polynomials into Chebeshev
+          form to ensure stable computation. By experiment we found that the polynomials
+          are just as stable in polynomial as Chebyshev form, <span class="emphasis"><em>provided</em></span>
+          they are computed over the interval [-1,1].
+        </p>
+<p>
+          Over the a series of intervals [a,b] and [b,INF] the rational approximation
+          takes the form:
+        </p>
+<p>
+          <span class="inlinemediaobject"><img src="../../../../equations/expint_i_4.png"></span>
+        </p>
+<p>
+          where <span class="emphasis"><em>c</em></span> is a constant, and R(t) is a minimax solution
+          optimised for low absolute error compared to <span class="emphasis"><em>c</em></span>. Variable
+          <span class="emphasis"><em>t</em></span> is <code class="computeroutput"><span class="number">1</span><span class="special">/</span><span class="identifier">z</span></code> when
+          the range in infinite and <code class="computeroutput"><span class="number">2</span><span class="identifier">z</span><span class="special">/(</span><span class="identifier">b</span><span class="special">-</span><span class="identifier">a</span><span class="special">)</span>
+          <span class="special">-</span> <span class="special">(</span><span class="number">2</span><span class="identifier">a</span><span class="special">/(</span><span class="identifier">b</span><span class="special">-</span><span class="identifier">a</span><span class="special">)</span> <span class="special">+</span> <span class="number">1</span><span class="special">)</span></code> otherwise: this has the effect of scaling
+          z to the interval [-1,1]. As before rational approximations over arbitrary
+          intervals were found to be ill-conditioned: Cody and Thacher solved this
+          issue by converting the polynomials to their J-Fraction equivalent. However,
+          as long as the interval of evaluation was [-1,1] and the number of terms
+          carefully chosen, it was found that the polynomials <span class="emphasis"><em>could</em></span>
+          be evaluated to suitable precision: error rates are typically 2 to 3 epsilon
+          which is comparible to the error rate that Cody and Thacher achieved using
+          J-Fractions, but marginally more efficient given that fewer divisions are
+          involved.
+        </p>
+<div class="footnotes">
+<br><hr width="100" align="left">
+<div class="footnote"><p><sup>[<a name="ftn.id776481" href="#id776481" class="para">2</a>] </sup>
+              W. J. Cody and H. C. Thacher, Jr., Rational Chebyshev approximations
+              for the exponential integral E<sub>1</sub>(x), Math. Comp. 22 (1968), 641-649,
+              and W. J. Cody and H. C. Thacher, Jr., Chebyshev approximations for
+              the exponential integral Ei(x), Math. Comp. 23 (1969), 289-303.
+            </p></div>
+</div>
+</div>
+<table xmlns:rev="http://www.cs.rpi.edu/~gregod/boost/tools/doc/revision" width="100%"><tr>
+<td align="left"></td>
+<td align="right"><div class="copyright-footer">Copyright © 2006 , 2007, 2008 John Maddock, Paul A. Bristow, Hubert
+      Holin, Xiaogang Zhang, Bruno Lalande and Gautam Sewani<p>
+        Distributed under the Boost Software License, Version 1.0. (See accompanying
+        file LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_0.txt)
+      </p>
+</div></td>
+</tr></table>
+<hr>
+<div class="spirit-nav">
+<a accesskey="p" href="expint_n.html"><img src="../../../../../doc/html/images/prev.png" alt="Prev"></a><a accesskey="u" href="../expint.html"><img src="../../../../../doc/html/images/up.png" alt="Up"></a><a accesskey="h" href="../../../index.html"><img src="../../../../../doc/html/images/home.png" alt="Home"></a><a accesskey="n" href="../powers.html"><img src="../../../../../doc/html/images/next.png" alt="Next"></a>
+</div>
+</body>
+</html>

Added: sandbox/tools/auto_index/example/math/doc/sf_and_dist/html/math_toolkit/special/expint/expint_n.html
==============================================================================
--- (empty file)
+++ sandbox/tools/auto_index/example/math/doc/sf_and_dist/html/math_toolkit/special/expint/expint_n.html	2008-11-28 05:25:28 EST (Fri, 28 Nov 2008)
@@ -0,0 +1,302 @@
+<html>
+<head>
+<meta http-equiv="Content-Type" content="text/html; charset=ISO-8859-1">
+<title>Exponential Integral En</title>
+<link rel="stylesheet" href="../../../boostbook.css" type="text/css">
+<meta name="generator" content="DocBook XSL Stylesheets Vsnapshot_8125">
+<link rel="home" href="../../../index.html" title="Math Toolkit">
+<link rel="up" href="../expint.html" title="Exponential Integrals">
+<link rel="prev" href="../expint.html" title="Exponential Integrals">
+<link rel="next" href="expint_i.html" title="Exponential Integral Ei">
+</head>
+<body bgcolor="white" text="black" link="#0000FF" vlink="#840084" alink="#0000FF">
+<table cellpadding="2" width="100%"><tr>
+<td valign="top"><img alt="Boost C++ Libraries" width="277" height="86" src="../../../../../boost.png"></td>
+<td align="center">Home</td>
+<td align="center">Libraries</td>
+<td align="center">People</td>
+<td align="center">FAQ</td>
+<td align="center">More</td>
+</tr></table>
+<hr>
+<div class="spirit-nav">
+<a accesskey="p" href="../expint.html"><img src="../../../../../doc/html/images/prev.png" alt="Prev"></a><a accesskey="u" href="../expint.html"><img src="../../../../../doc/html/images/up.png" alt="Up"></a><a accesskey="h" href="../../../index.html"><img src="../../../../../doc/html/images/home.png" alt="Home"></a><a accesskey="n" href="expint_i.html"><img src="../../../../../doc/html/images/next.png" alt="Next"></a>
+</div>
+<div class="section" lang="en">
+<div class="titlepage"><div><div><h4 class="title">
+<a name="math_toolkit.special.expint.expint_n"></a><a class="link" href="expint_n.html" title="Exponential Integral En"> Exponential
+        Integral En</a>
+</h4></div></div></div>
+<a name="math_toolkit.special.expint.expint_n.synopsis"></a><h5>
+<a name="id773992"></a>
+          <a class="link" href="expint_n.html#math_toolkit.special.expint.expint_n.synopsis">Synopsis</a>
+        </h5>
+<p>
+          
+</p>
+<pre class="programlisting"><span class="preprocessor">#include</span> <span class="special">&lt;</span><span class="identifier">boost</span><span class="special">/</span><span class="identifier">math</span><span class="special">/</span><span class="identifier">special_functions</span><span class="special">/</span><span class="identifier">expint</span><span class="special">.</span><span class="identifier">hpp</span><span class="special">&gt;</span>
+</pre>
+<p>
+        </p>
+<pre class="programlisting"><span class="keyword">namespace</span> <span class="identifier">boost</span><span class="special">{</span> <span class="keyword">namespace</span> <span class="identifier">math</span><span class="special">{</span>
+
+<span class="keyword">template</span> <span class="special">&lt;</span><span class="keyword">class</span> <span class="identifier">T</span><span class="special">&gt;</span>
+<a class="link" href="../../main_overview/result_type.html" title="Calculation of the Type of the Result"><span class="emphasis"><em>calculated-result-type</em></span></a> <span class="identifier">expint</span><span class="special">(</span><span class="keyword">unsigned</span> <span class="identifier">n</span><span class="special">,</span> <span class="identifier">T</span> <span class="identifier">z</span><span class="special">);</span>
+
+<span class="keyword">template</span> <span class="special">&lt;</span><span class="keyword">class</span> <span class="identifier">T</span><span class="special">,</span> <span class="keyword">class</span> <a class="link" href="../../policy.html" title="Policies">Policy</a><span class="special">&gt;</span>
+<a class="link" href="../../main_overview/result_type.html" title="Calculation of the Type of the Result"><span class="emphasis"><em>calculated-result-type</em></span></a> <span class="identifier">expint</span><span class="special">(</span><span class="keyword">unsigned</span> <span class="identifier">n</span><span class="special">,</span> <span class="identifier">T</span> <span class="identifier">z</span><span class="special">,</span> <span class="keyword">const</span> <a class="link" href="../../policy.html" title="Policies">Policy</a><span class="special">&amp;);</span>
+
+<span class="special">}}</span> <span class="comment">// namespaces
+</span></pre>
+<p>
+          The return type of these functions is computed using the <a class="link" href="../../main_overview/result_type.html" title="Calculation of the Type of the Result"><span class="emphasis"><em>result
+          type calculation rules</em></span></a>: the return type is <code class="computeroutput"><span class="keyword">double</span></code> if T is an integer type, and T otherwise.
+        </p>
+<p>
+          </p>
+<p>
+            The final <a class="link" href="../../policy.html" title="Policies">Policy</a> argument
+            is optional and can be used to control the behaviour of the function:
+            how it handles errors, what level of precision to use etc. Refer to the
+            <a class="link" href="../../policy.html" title="Policies">policy documentation for more details</a>.
+          </p>
+<p>
+        </p>
+<a name="math_toolkit.special.expint.expint_n.description"></a><h5>
+<a name="id774409"></a>
+          <a class="link" href="expint_n.html#math_toolkit.special.expint.expint_n.description">Description</a>
+        </h5>
+<pre class="programlisting"><span class="keyword">template</span> <span class="special">&lt;</span><span class="keyword">class</span> <span class="identifier">T</span><span class="special">&gt;</span>
+<a class="link" href="../../main_overview/result_type.html" title="Calculation of the Type of the Result"><span class="emphasis"><em>calculated-result-type</em></span></a> <span class="identifier">expint</span><span class="special">(</span><span class="keyword">unsigned</span> <span class="identifier">n</span><span class="special">,</span> <span class="identifier">T</span> <span class="identifier">z</span><span class="special">);</span>
+
+<span class="keyword">template</span> <span class="special">&lt;</span><span class="keyword">class</span> <span class="identifier">T</span><span class="special">,</span> <span class="keyword">class</span> <a class="link" href="../../policy.html" title="Policies">Policy</a><span class="special">&gt;</span>
+<a class="link" href="../../main_overview/result_type.html" title="Calculation of the Type of the Result"><span class="emphasis"><em>calculated-result-type</em></span></a> <span class="identifier">expint</span><span class="special">(</span><span class="keyword">unsigned</span> <span class="identifier">n</span><span class="special">,</span> <span class="identifier">T</span> <span class="identifier">z</span><span class="special">,</span> <span class="keyword">const</span> <a class="link" href="../../policy.html" title="Policies">Policy</a><span class="special">&amp;);</span>
+</pre>
+<p>
+          Returns the <a href="http://mathworld.wolfram.com/En-Function.html" target="_top">exponential
+          integral En</a> of z:
+        </p>
+<p>
+          <span class="inlinemediaobject"><img src="../../../../equations/expint_n_1.png"></span>
+        </p>
+<p>
+          <span class="inlinemediaobject"><img src="../../../../graphs/expint2.png" align="middle"></span>
+        </p>
+<a name="math_toolkit.special.expint.expint_n.accuracy"></a><h5>
+<a name="id774724"></a>
+          <a class="link" href="expint_n.html#math_toolkit.special.expint.expint_n.accuracy">Accuracy</a>
+        </h5>
+<p>
+          The following table shows the peak errors (in units of epsilon) found on
+          various platforms with various floating point types, along with comparisons
+          to the Cephes library.
+          Unless otherwise specified any floating point type that is narrower than
+          the one shown will have <a class="link" href="../../backgrounders/relative_error.html#zero_error">effectively zero error</a>.
+        </p>
+<div class="table">
+<a name="id774767"></a><p class="title"><b>Table 45. Errors In the Function expint(n, z)</b></p>
+<div class="table-contents"><table class="table" summary="Errors In the Function expint(n, z)">
+<colgroup>
+<col>
+<col>
+<col>
+<col>
+</colgroup>
+<thead><tr>
+<th>
+              <p>
+                Significand Size
+              </p>
+              </th>
+<th>
+              <p>
+                Platform and Compiler
+              </p>
+              </th>
+<th>
+              <p>
+                En
+              </p>
+              </th>
+<th>
+              <p>
+                E1
+              </p>
+              </th>
+</tr></thead>
+<tbody>
+<tr>
+<td>
+              <p>
+                53
+              </p>
+              </td>
+<td>
+              <p>
+                Win32, Visual C++ 8
+              </p>
+              </td>
+<td>
+              <p>
+                Peak=7.1 Mean=1.8
+              </p>
+              <p>
+                Cephes Peak=5.1
+                Mean=1.3
+              </p>
+              </td>
+<td>
+              <p>
+                Peak=0.99 Mean=0.5
+              </p>
+              <p>
+                Cephes Peak=3.1
+                Mean=1.1
+              </p>
+              </td>
+</tr>
+<tr>
+<td>
+              <p>
+                64
+              </p>
+              </td>
+<td>
+              <p>
+                RedHat Linux IA_EM64, gcc-4.1
+              </p>
+              </td>
+<td>
+              <p>
+                Peak=9.9 Mean=2.1
+              </p>
+              </td>
+<td>
+              <p>
+                Peak=0.97 Mean=0.4
+              </p>
+              </td>
+</tr>
+<tr>
+<td>
+              <p>
+                64
+              </p>
+              </td>
+<td>
+              <p>
+                Redhat Linux IA64, gcc-4.1
+              </p>
+              </td>
+<td>
+              <p>
+                Peak=9.9 Mean=2.1
+              </p>
+              </td>
+<td>
+              <p>
+                Peak=0.97 Mean=0.4
+              </p>
+              </td>
+</tr>
+<tr>
+<td>
+              <p>
+                113
+              </p>
+              </td>
+<td>
+              <p>
+                HPUX IA64, aCC A.06.06
+              </p>
+              </td>
+<td>
+              <p>
+                Peak=23.3 Mean=3.7
+              </p>
+              </td>
+<td>
+              <p>
+                Peak=1.6 Mean=0.5
+              </p>
+              </td>
+</tr>
+</tbody>
+</table></div>
+</div>
+<br class="table-break"><a name="math_toolkit.special.expint.expint_n.testing"></a><h5>
+<a name="id775000"></a>
+          <a class="link" href="expint_n.html#math_toolkit.special.expint.expint_n.testing">Testing</a>
+        </h5>
+<p>
+          The tests for these functions come in two parts: basic sanity checks use
+          spot values calculated using <a href="http://functions.wolfram.com/webMathematica/FunctionEvaluation.jsp?name=ExpIntegralE" target="_top">Mathworld's
+          online evaluator</a>, while accuracy checks use high-precision test
+          values calculated at 1000-bit precision with NTL::RR
+          and this implementation. Note that the generic and type-specific versions
+          of these functions use differing implementations internally, so this gives
+          us reasonably independent test data. Using our test data to test other
+          "known good" implementations also provides an additional sanity
+          check.
+        </p>
+<a name="math_toolkit.special.expint.expint_n.implementation"></a><h5>
+<a name="id775061"></a>
+          <a class="link" href="expint_n.html#math_toolkit.special.expint.expint_n.implementation">Implementation</a>
+        </h5>
+<p>
+          The generic version of this function uses the continued fraction:
+        </p>
+<p>
+          <span class="inlinemediaobject"><img src="../../../../equations/expint_n_3.png"></span>
+        </p>
+<p>
+          for large <span class="emphasis"><em>x</em></span> and the infinite series:
+        </p>
+<p>
+          <span class="inlinemediaobject"><img src="../../../../equations/expint_n_2.png"></span>
+        </p>
+<p>
+          for small <span class="emphasis"><em>x</em></span>.
+        </p>
+<p>
+          Where the precision of <span class="emphasis"><em>x</em></span> is known at compile time
+          and is 113 bits or fewer in precision, then rational approximations <a class="link" href="../../backgrounders/implementation.html#math_toolkit.backgrounders.implementation.rational_approximations_used">devised
+          by JM</a> are used for the <code class="computeroutput"><span class="identifier">n</span>
+          <span class="special">==</span> <span class="number">1</span></code>
+          case.
+        </p>
+<p>
+          For <code class="computeroutput"><span class="identifier">x</span> <span class="special">&lt;</span>
+          <span class="number">1</span></code> the approximating form is a minimax
+          approximation:
+        </p>
+<p>
+          <span class="inlinemediaobject"><img src="../../../../equations/expint_n_4.png"></span>
+        </p>
+<p>
+          and for <code class="computeroutput"><span class="identifier">x</span> <span class="special">&gt;</span>
+          <span class="number">1</span></code> a Chebyshev interpolated approximation
+          of the form:
+        </p>
+<p>
+          <span class="inlinemediaobject"><img src="../../../../equations/expint_n_5.png"></span>
+        </p>
+<p>
+          is used.
+        </p>
+</div>
+<table xmlns:rev="http://www.cs.rpi.edu/~gregod/boost/tools/doc/revision" width="100%"><tr>
+<td align="left"></td>
+<td align="right"><div class="copyright-footer">Copyright © 2006 , 2007, 2008 John Maddock, Paul A. Bristow, Hubert
+      Holin, Xiaogang Zhang, Bruno Lalande and Gautam Sewani<p>
+        Distributed under the Boost Software License, Version 1.0. (See accompanying
+        file LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_0.txt)
+      </p>
+</div></td>
+</tr></table>
+<hr>
+<div class="spirit-nav">
+<a accesskey="p" href="../expint.html"><img src="../../../../../doc/html/images/prev.png" alt="Prev"></a><a accesskey="u" href="../expint.html"><img src="../../../../../doc/html/images/up.png" alt="Up"></a><a accesskey="h" href="../../../index.html"><img src="../../../../../doc/html/images/home.png" alt="Home"></a><a accesskey="n" href="expint_i.html"><img src="../../../../../doc/html/images/next.png" alt="Next"></a>
+</div>
+</body>
+</html>

Added: sandbox/tools/auto_index/example/math/doc/sf_and_dist/html/math_toolkit/special/extern_c.html
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--- (empty file)
+++ sandbox/tools/auto_index/example/math/doc/sf_and_dist/html/math_toolkit/special/extern_c.html	2008-11-28 05:25:28 EST (Fri, 28 Nov 2008)
@@ -0,0 +1,52 @@
+<html>
+<head>
+<meta http-equiv="Content-Type" content="text/html; charset=ISO-8859-1">
+<title>TR1 and C99 external "C" Functions</title>
+<link rel="stylesheet" href="../../boostbook.css" type="text/css">
+<meta name="generator" content="DocBook XSL Stylesheets Vsnapshot_8125">
+<link rel="home" href="../../index.html" title="Math Toolkit">
+<link rel="up" href="../special.html" title="Special Functions">
+<link rel="prev" href="next_float/float_advance.html" title="Advancing a Floating Point Value by a Specific Representation Distance (ULP) float_advance">
+<link rel="next" href="extern_c/tr1.html" title="C99 and TR1 C Functions Overview">
+</head>
+<body bgcolor="white" text="black" link="#0000FF" vlink="#840084" alink="#0000FF">
+<table cellpadding="2" width="100%"><tr>
+<td valign="top"><img alt="Boost C++ Libraries" width="277" height="86" src="../../../../boost.png"></td>
+<td align="center">Home</td>
+<td align="center">Libraries</td>
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+</tr></table>
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+<a accesskey="p" href="next_float/float_advance.html"><img src="../../../../doc/html/images/prev.png" alt="Prev"></a><a accesskey="u" href="../special.html"><img src="../../../../doc/html/images/up.png" alt="Up"></a><a accesskey="h" href="../../index.html"><img src="../../../../doc/html/images/home.png" alt="Home"></a><a accesskey="n" href="extern_c/tr1.html"><img src="../../../../doc/html/images/next.png" alt="Next"></a>
+</div>
+<div class="section" lang="en">
+<div class="titlepage"><div><div><h3 class="title">
+<a name="math_toolkit.special.extern_c"></a><a class="link" href="extern_c.html" title='TR1 and C99 external "C" Functions'> TR1 and C99 external
+      "C" Functions</a>
+</h3></div></div></div>
+<div class="toc"><dl>
+<dt><span class="section"><a href="extern_c/tr1.html"> C99 and TR1 C Functions
+        Overview</a></span></dt>
+<dt><span class="section"> C99 C Functions</span></dt>
+<dt><span class="section"><a href="extern_c/tr1_ref.html"> TR1 C Functions
+        Quick Reference</a></span></dt>
+</dl></div>
+</div>
+<table xmlns:rev="http://www.cs.rpi.edu/~gregod/boost/tools/doc/revision" width="100%"><tr>
+<td align="left"></td>
+<td align="right"><div class="copyright-footer">Copyright © 2006 , 2007, 2008 John Maddock, Paul A. Bristow, Hubert
+      Holin, Xiaogang Zhang, Bruno Lalande and Gautam Sewani<p>
+        Distributed under the Boost Software License, Version 1.0. (See accompanying
+        file LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_0.txt)
+      </p>
+</div></td>
+</tr></table>
+<hr>
+<div class="spirit-nav">
+<a accesskey="p" href="next_float/float_advance.html"><img src="../../../../doc/html/images/prev.png" alt="Prev"></a><a accesskey="u" href="../special.html"><img src="../../../../doc/html/images/up.png" alt="Up"></a><a accesskey="h" href="../../index.html"><img src="../../../../doc/html/images/home.png" alt="Home"></a><a accesskey="n" href="extern_c/tr1.html"><img src="../../../../doc/html/images/next.png" alt="Next"></a>
+</div>
+</body>
+</html>

Added: sandbox/tools/auto_index/example/math/doc/sf_and_dist/html/math_toolkit/special/extern_c/c99.html
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--- (empty file)
+++ sandbox/tools/auto_index/example/math/doc/sf_and_dist/html/math_toolkit/special/extern_c/c99.html	2008-11-28 05:25:28 EST (Fri, 28 Nov 2008)
@@ -0,0 +1,476 @@
+<html>
+<head>
+<meta http-equiv="Content-Type" content="text/html; charset=ISO-8859-1">
+<title>C99 C Functions</title>
+<link rel="stylesheet" href="../../../boostbook.css" type="text/css">
+<meta name="generator" content="DocBook XSL Stylesheets Vsnapshot_8125">
+<link rel="home" href="../../../index.html" title="Math Toolkit">
+<link rel="up" href="../extern_c.html" title='TR1 and C99 external "C" Functions'>
+<link rel="prev" href="tr1.html" title="C99 and TR1 C Functions Overview">
+<link rel="next" href="tr1_ref.html" title="TR1 C Functions Quick Reference">
+</head>
+<body bgcolor="white" text="black" link="#0000FF" vlink="#840084" alink="#0000FF">
+<table cellpadding="2" width="100%"><tr>
+<td valign="top"><img alt="Boost C++ Libraries" width="277" height="86" src="../../../../../boost.png"></td>
+<td align="center">Home</td>
+<td align="center">Libraries</td>
+<td align="center">People</td>
+<td align="center">FAQ</td>
+<td align="center">More</td>
+</tr></table>
+<hr>
+<div class="spirit-nav">
+<a accesskey="p" href="tr1.html"><img src="../../../../../doc/html/images/prev.png" alt="Prev"></a><a accesskey="u" href="../extern_c.html"><img src="../../../../../doc/html/images/up.png" alt="Up"></a><a accesskey="h" href="../../../index.html"><img src="../../../../../doc/html/images/home.png" alt="Home"></a><a accesskey="n" href="tr1_ref.html"><img src="../../../../../doc/html/images/next.png" alt="Next"></a>
+</div>
+<div class="section" lang="en">
+<div class="titlepage"><div><div><h4 class="title">
+<a name="math_toolkit.special.extern_c.c99"></a><a class="link" href="c99.html" title="C99 C Functions"> C99 C Functions</a>
+</h4></div></div></div>
+<a name="math_toolkit.special.extern_c.c99.supported_c99_functions"></a><h5>
+<a name="id804642"></a>
+          <a class="link" href="c99.html#math_toolkit.special.extern_c.c99.supported_c99_functions">Supported
+          C99 Functions</a>
+        </h5>
+<pre class="programlisting"><span class="keyword">namespace</span> <span class="identifier">boost</span><span class="special">{</span> <span class="keyword">namespace</span> <span class="identifier">math</span><span class="special">{</span> <span class="keyword">namespace</span> <span class="identifier">tr1</span><span class="special">{</span> <span class="keyword">extern</span> <span class="string">"C"</span><span class="special">{</span>
+
+<span class="keyword">typedef</span> <span class="identifier">unspecified</span> <span class="identifier">float_t</span><span class="special">;</span>
+<span class="keyword">typedef</span> <span class="identifier">unspecified</span> <span class="identifier">double_t</span><span class="special">;</span>
+
+<span class="keyword">double</span> <span class="identifier">acosh</span><span class="special">(</span><span class="keyword">double</span> <span class="identifier">x</span><span class="special">);</span>
+<span class="keyword">float</span> <span class="identifier">acoshf</span><span class="special">(</span><span class="keyword">float</span> <span class="identifier">x</span><span class="special">);</span>
+<span class="keyword">long</span> <span class="keyword">double</span> <span class="identifier">acoshl</span><span class="special">(</span><span class="keyword">long</span> <span class="keyword">double</span> <span class="identifier">x</span><span class="special">);</span>
+
+<span class="keyword">double</span> <span class="identifier">asinh</span><span class="special">(</span><span class="keyword">double</span> <span class="identifier">x</span><span class="special">);</span>
+<span class="keyword">float</span> <span class="identifier">asinhf</span><span class="special">(</span><span class="keyword">float</span> <span class="identifier">x</span><span class="special">);</span>
+<span class="keyword">long</span> <span class="keyword">double</span> <span class="identifier">asinhl</span><span class="special">(</span><span class="keyword">long</span> <span class="keyword">double</span> <span class="identifier">x</span><span class="special">);</span>
+
+<span class="keyword">double</span> <span class="identifier">atanh</span><span class="special">(</span><span class="keyword">double</span> <span class="identifier">x</span><span class="special">);</span>
+<span class="keyword">float</span> <span class="identifier">atanhf</span><span class="special">(</span><span class="keyword">float</span> <span class="identifier">x</span><span class="special">);</span>
+<span class="keyword">long</span> <span class="keyword">double</span> <span class="identifier">atanhl</span><span class="special">(</span><span class="keyword">long</span> <span class="keyword">double</span> <span class="identifier">x</span><span class="special">);</span>
+
+<span class="keyword">double</span> <span class="identifier">cbrt</span><span class="special">(</span><span class="keyword">double</span> <span class="identifier">x</span><span class="special">);</span>
+<span class="keyword">float</span> <span class="identifier">cbrtf</span><span class="special">(</span><span class="keyword">float</span> <span class="identifier">x</span><span class="special">);</span>
+<span class="keyword">long</span> <span class="keyword">double</span> <span class="identifier">cbrtl</span><span class="special">(</span><span class="keyword">long</span> <span class="keyword">double</span> <span class="identifier">x</span><span class="special">);</span>
+
+<span class="keyword">double</span> <span class="identifier">copysign</span><span class="special">(</span><span class="keyword">double</span> <span class="identifier">x</span><span class="special">,</span> <span class="keyword">double</span> <span class="identifier">y</span><span class="special">);</span>
+<span class="keyword">float</span> <span class="identifier">copysignf</span><span class="special">(</span><span class="keyword">float</span> <span class="identifier">x</span><span class="special">,</span> <span class="keyword">float</span> <span class="identifier">y</span><span class="special">);</span>
+<span class="keyword">long</span> <span class="keyword">double</span> <span class="identifier">copysignl</span><span class="special">(</span><span class="keyword">long</span> <span class="keyword">double</span> <span class="identifier">x</span><span class="special">,</span> <span class="keyword">long</span> <span class="keyword">double</span> <span class="identifier">y</span><span class="special">);</span>
+
+<span class="keyword">double</span> <span class="identifier">erf</span><span class="special">(</span><span class="keyword">double</span> <span class="identifier">x</span><span class="special">);</span>
+<span class="keyword">float</span> <span class="identifier">erff</span><span class="special">(</span><span class="keyword">float</span> <span class="identifier">x</span><span class="special">);</span>
+<span class="keyword">long</span> <span class="keyword">double</span> <span class="identifier">erfl</span><span class="special">(</span><span class="keyword">long</span> <span class="keyword">double</span> <span class="identifier">x</span><span class="special">);</span>
+
+<span class="keyword">double</span> <span class="identifier">erfc</span><span class="special">(</span><span class="keyword">double</span> <span class="identifier">x</span><span class="special">);</span>
+<span class="keyword">float</span> <span class="identifier">erfcf</span><span class="special">(</span><span class="keyword">float</span> <span class="identifier">x</span><span class="special">);</span>
+<span class="keyword">long</span> <span class="keyword">double</span> <span class="identifier">erfcl</span><span class="special">(</span><span class="keyword">long</span> <span class="keyword">double</span> <span class="identifier">x</span><span class="special">);</span>
+
+<span class="keyword">double</span> <span class="identifier">expm1</span><span class="special">(</span><span class="keyword">double</span> <span class="identifier">x</span><span class="special">);</span>
+<span class="keyword">float</span> <span class="identifier">expm1f</span><span class="special">(</span><span class="keyword">float</span> <span class="identifier">x</span><span class="special">);</span>
+<span class="keyword">long</span> <span class="keyword">double</span> <span class="identifier">expm1l</span><span class="special">(</span><span class="keyword">long</span> <span class="keyword">double</span> <span class="identifier">x</span><span class="special">);</span>
+
+<span class="keyword">double</span> <span class="identifier">fmax</span><span class="special">(</span><span class="keyword">double</span> <span class="identifier">x</span><span class="special">,</span> <span class="keyword">double</span> <span class="identifier">y</span><span class="special">);</span>
+<span class="keyword">float</span> <span class="identifier">fmaxf</span><span class="special">(</span><span class="keyword">float</span> <span class="identifier">x</span><span class="special">,</span> <span class="keyword">float</span> <span class="identifier">y</span><span class="special">);</span>
+<span class="keyword">long</span> <span class="keyword">double</span> <span class="identifier">fmaxl</span><span class="special">(</span><span class="keyword">long</span> <span class="keyword">double</span> <span class="identifier">x</span><span class="special">,</span> <span class="keyword">long</span> <span class="keyword">double</span> <span class="identifier">y</span><span class="special">);</span>
+
+<span class="keyword">double</span> <span class="identifier">fmin</span><span class="special">(</span><span class="keyword">double</span> <span class="identifier">x</span><span class="special">,</span> <span class="keyword">double</span> <span class="identifier">y</span><span class="special">);</span>
+<span class="keyword">float</span> <span class="identifier">fminf</span><span class="special">(</span><span class="keyword">float</span> <span class="identifier">x</span><span class="special">,</span> <span class="keyword">float</span> <span class="identifier">y</span><span class="special">);</span>
+<span class="keyword">long</span> <span class="keyword">double</span> <span class="identifier">fminl</span><span class="special">(</span><span class="keyword">long</span> <span class="keyword">double</span> <span class="identifier">x</span><span class="special">,</span> <span class="keyword">long</span> <span class="keyword">double</span> <span class="identifier">y</span><span class="special">);</span>
+
+<span class="keyword">double</span> <span class="identifier">hypot</span><span class="special">(</span><span class="keyword">double</span> <span class="identifier">x</span><span class="special">,</span> <span class="keyword">double</span> <span class="identifier">y</span><span class="special">);</span>
+<span class="keyword">float</span> <span class="identifier">hypotf</span><span class="special">(</span><span class="keyword">float</span> <span class="identifier">x</span><span class="special">,</span> <span class="keyword">float</span> <span class="identifier">y</span><span class="special">);</span>
+<span class="keyword">long</span> <span class="keyword">double</span> <span class="identifier">hypotl</span><span class="special">(</span><span class="keyword">long</span> <span class="keyword">double</span> <span class="identifier">x</span><span class="special">,</span> <span class="keyword">long</span> <span class="keyword">double</span> <span class="identifier">y</span><span class="special">);</span>
+
+<span class="keyword">double</span> <span class="identifier">lgamma</span><span class="special">(</span><span class="keyword">double</span> <span class="identifier">x</span><span class="special">);</span>
+<span class="keyword">float</span> <span class="identifier">lgammaf</span><span class="special">(</span><span class="keyword">float</span> <span class="identifier">x</span><span class="special">);</span>
+<span class="keyword">long</span> <span class="keyword">double</span> <span class="identifier">lgammal</span><span class="special">(</span><span class="keyword">long</span> <span class="keyword">double</span> <span class="identifier">x</span><span class="special">);</span>
+
+<span class="keyword">long</span> <span class="keyword">long</span> <span class="identifier">llround</span><span class="special">(</span><span class="keyword">double</span> <span class="identifier">x</span><span class="special">);</span>
+<span class="keyword">long</span> <span class="keyword">long</span> <span class="identifier">llroundf</span><span class="special">(</span><span class="keyword">float</span> <span class="identifier">x</span><span class="special">);</span>
+<span class="keyword">long</span> <span class="keyword">long</span> <span class="identifier">llroundl</span><span class="special">(</span><span class="keyword">long</span> <span class="keyword">double</span> <span class="identifier">x</span><span class="special">);</span>
+
+<span class="keyword">double</span> <span class="identifier">log1p</span><span class="special">(</span><span class="keyword">double</span> <span class="identifier">x</span><span class="special">);</span>
+<span class="keyword">float</span> <span class="identifier">log1pf</span><span class="special">(</span><span class="keyword">float</span> <span class="identifier">x</span><span class="special">);</span>
+<span class="keyword">long</span> <span class="keyword">double</span> <span class="identifier">log1pl</span><span class="special">(</span><span class="keyword">long</span> <span class="keyword">double</span> <span class="identifier">x</span><span class="special">);</span>
+
+<span class="keyword">long</span> <span class="identifier">lround</span><span class="special">(</span><span class="keyword">double</span> <span class="identifier">x</span><span class="special">);</span>
+<span class="keyword">long</span> <span class="identifier">lroundf</span><span class="special">(</span><span class="keyword">float</span> <span class="identifier">x</span><span class="special">);</span>
+<span class="keyword">long</span> <span class="identifier">lroundl</span><span class="special">(</span><span class="keyword">long</span> <span class="keyword">double</span> <span class="identifier">x</span><span class="special">);</span>
+
+<span class="keyword">double</span> <span class="identifier">nextafter</span><span class="special">(</span><span class="keyword">double</span> <span class="identifier">x</span><span class="special">,</span> <span class="keyword">double</span> <span class="identifier">y</span><span class="special">);</span>
+<span class="keyword">float</span> <span class="identifier">nextafterf</span><span class="special">(</span><span class="keyword">float</span> <span class="identifier">x</span><span class="special">,</span> <span class="keyword">float</span> <span class="identifier">y</span><span class="special">);</span>
+<span class="keyword">long</span> <span class="keyword">double</span> <span class="identifier">nextafterl</span><span class="special">(</span><span class="keyword">long</span> <span class="keyword">double</span> <span class="identifier">x</span><span class="special">,</span> <span class="keyword">long</span> <span class="keyword">double</span> <span class="identifier">y</span><span class="special">);</span>
+
+<span class="keyword">double</span> <span class="identifier">nexttoward</span><span class="special">(</span><span class="keyword">double</span> <span class="identifier">x</span><span class="special">,</span> <span class="keyword">long</span> <span class="keyword">double</span> <span class="identifier">y</span><span class="special">);</span>
+<span class="keyword">float</span> <span class="identifier">nexttowardf</span><span class="special">(</span><span class="keyword">float</span> <span class="identifier">x</span><span class="special">,</span> <span class="keyword">long</span> <span class="keyword">double</span> <span class="identifier">y</span><span class="special">);</span>
+<span class="keyword">long</span> <span class="keyword">double</span> <span class="identifier">nexttowardl</span><span class="special">(</span><span class="keyword">long</span> <span class="keyword">double</span> <span class="identifier">x</span><span class="special">,</span> <span class="keyword">long</span> <span class="keyword">double</span> <span class="identifier">y</span><span class="special">);</span>
+
+<span class="keyword">double</span> <span class="identifier">round</span><span class="special">(</span><span class="keyword">double</span> <span class="identifier">x</span><span class="special">);</span>
+<span class="keyword">float</span> <span class="identifier">roundf</span><span class="special">(</span><span class="keyword">float</span> <span class="identifier">x</span><span class="special">);</span>
+<span class="keyword">long</span> <span class="keyword">double</span> <span class="identifier">roundl</span><span class="special">(</span><span class="keyword">long</span> <span class="keyword">double</span> <span class="identifier">x</span><span class="special">);</span>
+
+<span class="keyword">double</span> <span class="identifier">tgamma</span><span class="special">(</span><span class="keyword">double</span> <span class="identifier">x</span><span class="special">);</span>
+<span class="keyword">float</span> <span class="identifier">tgammaf</span><span class="special">(</span><span class="keyword">float</span> <span class="identifier">x</span><span class="special">);</span>
+<span class="keyword">long</span> <span class="keyword">double</span> <span class="identifier">tgammal</span><span class="special">(</span><span class="keyword">long</span> <span class="keyword">double</span> <span class="identifier">x</span><span class="special">);</span>
+
+<span class="keyword">double</span> <span class="identifier">trunc</span><span class="special">(</span><span class="keyword">double</span> <span class="identifier">x</span><span class="special">);</span>
+<span class="keyword">float</span> <span class="identifier">truncf</span><span class="special">(</span><span class="keyword">float</span> <span class="identifier">x</span><span class="special">);</span>
+<span class="keyword">long</span> <span class="keyword">double</span> <span class="identifier">truncl</span><span class="special">(</span><span class="keyword">long</span> <span class="keyword">double</span> <span class="identifier">x</span><span class="special">);</span>
+
+<span class="special">}}}}</span> <span class="comment">// namespaces
+</span></pre>
+<p>
+          In addition sufficient additional overloads of the <code class="computeroutput"><span class="keyword">double</span></code>
+          versions of the above functions are provided, so that calling the function
+          with any mixture of <code class="computeroutput"><span class="keyword">float</span></code>,
+          <code class="computeroutput"><span class="keyword">double</span></code>, <code class="computeroutput"><span class="keyword">long</span>
+          <span class="keyword">double</span></code>, or <span class="emphasis"><em>integer</em></span>
+          arguments is supported, with the return type determined by the <a class="link" href="../../main_overview/result_type.html" title="Calculation of the Type of the Result"><span class="emphasis"><em>result
+          type calculation rules</em></span></a>.
+        </p>
+<p>
+          For example:
+        </p>
+<pre class="programlisting"><span class="identifier">acoshf</span><span class="special">(</span><span class="number">2.0f</span><span class="special">);</span>  <span class="comment">// float version, returns float.
+</span><span class="identifier">acosh</span><span class="special">(</span><span class="number">2.0f</span><span class="special">);</span>   <span class="comment">// also calls the float version and returns float.
+</span><span class="identifier">acosh</span><span class="special">(</span><span class="number">2.0</span><span class="special">);</span>    <span class="comment">// double version, returns double.
+</span><span class="identifier">acoshl</span><span class="special">(</span><span class="number">2.0L</span><span class="special">);</span>  <span class="comment">// long double version, returns a long double.
+</span><span class="identifier">acosh</span><span class="special">(</span><span class="number">2.0L</span><span class="special">);</span>   <span class="comment">// also calls the long double version.
+</span><span class="identifier">acosh</span><span class="special">(</span><span class="number">2</span><span class="special">);</span>      <span class="comment">// integer argument is treated as a double, returns double.
+</span></pre>
+<a name="math_toolkit.special.extern_c.c99.quick_reference"></a><h5>
+<a name="id807689"></a>
+          <a class="link" href="c99.html#math_toolkit.special.extern_c.c99.quick_reference">Quick
+          Reference</a>
+        </h5>
+<p>
+          More detailed descriptions of these functions are available in the C99
+          standard.
+        </p>
+<pre class="programlisting"><span class="keyword">typedef</span> <span class="identifier">unspecified</span> <span class="identifier">float_t</span><span class="special">;</span>
+<span class="keyword">typedef</span> <span class="identifier">unspecified</span> <span class="identifier">double_t</span><span class="special">;</span>
+</pre>
+<p>
+          In this implementation <code class="computeroutput"><span class="identifier">float_t</span></code>
+          is the same as type <code class="computeroutput"><span class="keyword">float</span></code>,
+          and <code class="computeroutput"><span class="identifier">double_t</span></code> the same as
+          type <code class="computeroutput"><span class="keyword">double</span></code> unless the preprocessor
+          symbol FLT_EVAL_METHOD is defined, in which case these are set as follows:
+        </p>
+<div class="informaltable"><table class="table">
+<colgroup>
+<col>
+<col>
+<col>
+</colgroup>
+<thead><tr>
+<th>
+                <p>
+                  FLT_EVAL_METHOD
+                </p>
+                </th>
+<th>
+                <p>
+                  float_t
+                </p>
+                </th>
+<th>
+                <p>
+                  double_t
+                </p>
+                </th>
+</tr></thead>
+<tbody>
+<tr>
+<td>
+                <p>
+                  0
+                </p>
+                </td>
+<td>
+                <p>
+                  float
+                </p>
+                </td>
+<td>
+                <p>
+                  double
+                </p>
+                </td>
+</tr>
+<tr>
+<td>
+                <p>
+                  1
+                </p>
+                </td>
+<td>
+                <p>
+                  double
+                </p>
+                </td>
+<td>
+                <p>
+                  double
+                </p>
+                </td>
+</tr>
+<tr>
+<td>
+                <p>
+                  2
+                </p>
+                </td>
+<td>
+                <p>
+                  long double
+                </p>
+                </td>
+<td>
+                <p>
+                  long double
+                </p>
+                </td>
+</tr>
+</tbody>
+</table></div>
+<pre class="programlisting"><span class="keyword">double</span> <span class="identifier">acosh</span><span class="special">(</span><span class="keyword">double</span> <span class="identifier">x</span><span class="special">);</span>
+<span class="keyword">float</span> <span class="identifier">acoshf</span><span class="special">(</span><span class="keyword">float</span> <span class="identifier">x</span><span class="special">);</span>
+<span class="keyword">long</span> <span class="keyword">double</span> <span class="identifier">acoshl</span><span class="special">(</span><span class="keyword">long</span> <span class="keyword">double</span> <span class="identifier">x</span><span class="special">);</span>
+</pre>
+<p>
+          Returns the inverse hyperbolic cosine of <span class="emphasis"><em>x</em></span>.
+        </p>
+<p>
+          See also <a class="link" href="../inv_hyper/acosh.html" title="acosh">acosh</a>
+          for the full template (header only) version of this function.
+        </p>
+<pre class="programlisting"><span class="keyword">double</span> <span class="identifier">asinh</span><span class="special">(</span><span class="keyword">double</span> <span class="identifier">x</span><span class="special">);</span>
+<span class="keyword">float</span> <span class="identifier">asinhf</span><span class="special">(</span><span class="keyword">float</span> <span class="identifier">x</span><span class="special">);</span>
+<span class="keyword">long</span> <span class="keyword">double</span> <span class="identifier">asinhl</span><span class="special">(</span><span class="keyword">long</span> <span class="keyword">double</span> <span class="identifier">x</span><span class="special">);</span>
+</pre>
+<p>
+          Returns the inverse hyperbolic sine of <span class="emphasis"><em>x</em></span>.
+        </p>
+<p>
+          See also <a class="link" href="../inv_hyper/asinh.html" title="asinh">asinh</a>
+          for the full template (header only) version of this function.
+        </p>
+<pre class="programlisting"><span class="keyword">double</span> <span class="identifier">atanh</span><span class="special">(</span><span class="keyword">double</span> <span class="identifier">x</span><span class="special">);</span>
+<span class="keyword">float</span> <span class="identifier">atanhf</span><span class="special">(</span><span class="keyword">float</span> <span class="identifier">x</span><span class="special">);</span>
+<span class="keyword">long</span> <span class="keyword">double</span> <span class="identifier">atanhl</span><span class="special">(</span><span class="keyword">long</span> <span class="keyword">double</span> <span class="identifier">x</span><span class="special">);</span>
+</pre>
+<p>
+          Returns the inverse hyperbolic tangent of <span class="emphasis"><em>x</em></span>.
+        </p>
+<p>
+          See also <a class="link" href="../inv_hyper/atanh.html" title="atanh">atanh</a>
+          for the full template (header only) version of this function.
+        </p>
+<pre class="programlisting"><span class="keyword">double</span> <span class="identifier">cbrt</span><span class="special">(</span><span class="keyword">double</span> <span class="identifier">x</span><span class="special">);</span>
+<span class="keyword">float</span> <span class="identifier">cbrtf</span><span class="special">(</span><span class="keyword">float</span> <span class="identifier">x</span><span class="special">);</span>
+<span class="keyword">long</span> <span class="keyword">double</span> <span class="identifier">cbrtl</span><span class="special">(</span><span class="keyword">long</span> <span class="keyword">double</span> <span class="identifier">x</span><span class="special">);</span>
+</pre>
+<p>
+          Returns the cubed root of <span class="emphasis"><em>x</em></span>.
+        </p>
+<p>
+          See also <a class="link" href="../powers/cbrt.html" title="cbrt">cbrt</a> for
+          the full template (header only) version of this function.
+        </p>
+<pre class="programlisting"><span class="keyword">double</span> <span class="identifier">copysign</span><span class="special">(</span><span class="keyword">double</span> <span class="identifier">x</span><span class="special">,</span> <span class="keyword">double</span> <span class="identifier">y</span><span class="special">);</span>
+<span class="keyword">float</span> <span class="identifier">copysignf</span><span class="special">(</span><span class="keyword">float</span> <span class="identifier">x</span><span class="special">,</span> <span class="keyword">float</span> <span class="identifier">y</span><span class="special">);</span>
+<span class="keyword">long</span> <span class="keyword">double</span> <span class="identifier">copysignl</span><span class="special">(</span><span class="keyword">long</span> <span class="keyword">double</span> <span class="identifier">x</span><span class="special">,</span> <span class="keyword">long</span> <span class="keyword">double</span> <span class="identifier">y</span><span class="special">);</span>
+</pre>
+<p>
+          Returns a value with the magnitude of <span class="emphasis"><em>x</em></span> and the sign
+          of <span class="emphasis"><em>y</em></span>.
+        </p>
+<pre class="programlisting"><span class="keyword">double</span> <span class="identifier">erf</span><span class="special">(</span><span class="keyword">double</span> <span class="identifier">x</span><span class="special">);</span>
+<span class="keyword">float</span> <span class="identifier">erff</span><span class="special">(</span><span class="keyword">float</span> <span class="identifier">x</span><span class="special">);</span>
+<span class="keyword">long</span> <span class="keyword">double</span> <span class="identifier">erfl</span><span class="special">(</span><span class="keyword">long</span> <span class="keyword">double</span> <span class="identifier">x</span><span class="special">);</span>
+</pre>
+<p>
+          Returns the error function of <span class="emphasis"><em>x</em></span>:
+        </p>
+<p>
+          <span class="inlinemediaobject"><img src="../../../../equations/erf1.png"></span>
+        </p>
+<p>
+          See also <a class="link" href="../sf_erf/error_function.html" title="Error Functions">erf</a>
+          for the full template (header only) version of this function.
+        </p>
+<pre class="programlisting"><span class="keyword">double</span> <span class="identifier">erfc</span><span class="special">(</span><span class="keyword">double</span> <span class="identifier">x</span><span class="special">);</span>
+<span class="keyword">float</span> <span class="identifier">erfcf</span><span class="special">(</span><span class="keyword">float</span> <span class="identifier">x</span><span class="special">);</span>
+<span class="keyword">long</span> <span class="keyword">double</span> <span class="identifier">erfcl</span><span class="special">(</span><span class="keyword">long</span> <span class="keyword">double</span> <span class="identifier">x</span><span class="special">);</span>
+</pre>
+<p>
+          Returns the complementary error function of <span class="emphasis"><em>x</em></span> <code class="computeroutput"><span class="number">1</span><span class="special">-</span><span class="identifier">erf</span><span class="special">(</span><span class="identifier">x</span><span class="special">)</span></code>
+          without the loss of precision implied by the subtraction.
+        </p>
+<p>
+          See also <a class="link" href="../sf_erf/error_function.html" title="Error Functions">erfc</a>
+          for the full template (header only) version of this function.
+        </p>
+<pre class="programlisting"><span class="keyword">double</span> <span class="identifier">expm1</span><span class="special">(</span><span class="keyword">double</span> <span class="identifier">x</span><span class="special">);</span>
+<span class="keyword">float</span> <span class="identifier">expm1f</span><span class="special">(</span><span class="keyword">float</span> <span class="identifier">x</span><span class="special">);</span>
+<span class="keyword">long</span> <span class="keyword">double</span> <span class="identifier">expm1l</span><span class="special">(</span><span class="keyword">long</span> <span class="keyword">double</span> <span class="identifier">x</span><span class="special">);</span>
+</pre>
+<p>
+          Returns <code class="computeroutput"><span class="identifier">exp</span><span class="special">(</span><span class="identifier">x</span><span class="special">)-</span><span class="number">1</span></code>
+          without the loss of precision implied by the subtraction.
+        </p>
+<p>
+          See also <a class="link" href="../powers/expm1.html" title="expm1">expm1</a>
+          for the full template (header only) version of this function.
+        </p>
+<pre class="programlisting"><span class="keyword">double</span> <span class="identifier">fmax</span><span class="special">(</span><span class="keyword">double</span> <span class="identifier">x</span><span class="special">,</span> <span class="keyword">double</span> <span class="identifier">y</span><span class="special">);</span>
+<span class="keyword">float</span> <span class="identifier">fmaxf</span><span class="special">(</span><span class="keyword">float</span> <span class="identifier">x</span><span class="special">,</span> <span class="keyword">float</span> <span class="identifier">y</span><span class="special">);</span>
+<span class="keyword">long</span> <span class="keyword">double</span> <span class="identifier">fmaxl</span><span class="special">(</span><span class="keyword">long</span> <span class="keyword">double</span> <span class="identifier">x</span><span class="special">,</span> <span class="keyword">long</span> <span class="keyword">double</span> <span class="identifier">y</span><span class="special">);</span>
+</pre>
+<p>
+          Returns the larger (most positive) of <span class="emphasis"><em>x</em></span> and <span class="emphasis"><em>y</em></span>.
+        </p>
+<pre class="programlisting"><span class="keyword">double</span> <span class="identifier">fmin</span><span class="special">(</span><span class="keyword">double</span> <span class="identifier">x</span><span class="special">,</span> <span class="keyword">double</span> <span class="identifier">y</span><span class="special">);</span>
+<span class="keyword">float</span> <span class="identifier">fminf</span><span class="special">(</span><span class="keyword">float</span> <span class="identifier">x</span><span class="special">,</span> <span class="keyword">float</span> <span class="identifier">y</span><span class="special">);</span>
+<span class="keyword">long</span> <span class="keyword">double</span> <span class="identifier">fminl</span><span class="special">(</span><span class="keyword">long</span> <span class="keyword">double</span> <span class="identifier">x</span><span class="special">,</span> <span class="keyword">long</span> <span class="keyword">double</span> <span class="identifier">y</span><span class="special">);</span>
+</pre>
+<p>
+          Returns the smaller (most negative) of <span class="emphasis"><em>x</em></span> and <span class="emphasis"><em>y</em></span>.
+        </p>
+<pre class="programlisting"><span class="keyword">double</span> <span class="identifier">hypot</span><span class="special">(</span><span class="keyword">double</span> <span class="identifier">x</span><span class="special">,</span> <span class="keyword">double</span> <span class="identifier">y</span><span class="special">);</span>
+<span class="keyword">float</span> <span class="identifier">hypotf</span><span class="special">(</span><span class="keyword">float</span> <span class="identifier">x</span><span class="special">,</span> <span class="keyword">float</span> <span class="identifier">y</span><span class="special">);</span>
+<span class="keyword">long</span> <span class="keyword">double</span> <span class="identifier">hypotl</span><span class="special">(</span><span class="keyword">long</span> <span class="keyword">double</span> <span class="identifier">x</span><span class="special">,</span> <span class="keyword">long</span> <span class="keyword">double</span> <span class="identifier">y</span><span class="special">);</span>
+</pre>
+<p>
+          Returns <code class="computeroutput"><span class="identifier">sqrt</span><span class="special">(</span><span class="identifier">x</span><span class="special">*</span><span class="identifier">x</span>
+          <span class="special">+</span> <span class="identifier">y</span><span class="special">*</span><span class="identifier">y</span><span class="special">)</span></code>
+          without the danger of numeric overflow implied by that formulation.
+        </p>
+<p>
+          See also <a class="link" href="../powers/hypot.html" title="hypot">hypot</a>
+          for the full template (header only) version of this function.
+        </p>
+<pre class="programlisting"><span class="keyword">double</span> <span class="identifier">lgamma</span><span class="special">(</span><span class="keyword">double</span> <span class="identifier">x</span><span class="special">);</span>
+<span class="keyword">float</span> <span class="identifier">lgammaf</span><span class="special">(</span><span class="keyword">float</span> <span class="identifier">x</span><span class="special">);</span>
+<span class="keyword">long</span> <span class="keyword">double</span> <span class="identifier">lgammal</span><span class="special">(</span><span class="keyword">long</span> <span class="keyword">double</span> <span class="identifier">x</span><span class="special">);</span>
+</pre>
+<p>
+          Returns the log of the gamma function of <span class="emphasis"><em>x</em></span>.
+        </p>
+<p>
+          <span class="inlinemediaobject"><img src="../../../../equations/lgamm1.png"></span>
+        </p>
+<p>
+          See also <a class="link" href="../sf_gamma/lgamma.html" title="Log Gamma">lgamma</a>
+          for the full template (header only) version of this function.
+        </p>
+<pre class="programlisting"><span class="keyword">long</span> <span class="keyword">long</span> <span class="identifier">llround</span><span class="special">(</span><span class="keyword">double</span> <span class="identifier">x</span><span class="special">);</span>
+<span class="keyword">long</span> <span class="keyword">long</span> <span class="identifier">llroundf</span><span class="special">(</span><span class="keyword">float</span> <span class="identifier">x</span><span class="special">);</span>
+<span class="keyword">long</span> <span class="keyword">long</span> <span class="identifier">llroundl</span><span class="special">(</span><span class="keyword">long</span> <span class="keyword">double</span> <span class="identifier">x</span><span class="special">);</span>
+</pre>
+<p>
+          Returns the value <span class="emphasis"><em>x</em></span> rounded to the nearest integer
+          as a <code class="computeroutput"><span class="keyword">long</span> <span class="keyword">long</span></code>:
+          equivalent to <code class="computeroutput"><span class="identifier">floor</span><span class="special">(</span><span class="identifier">x</span> <span class="special">+</span> <span class="number">0.5</span><span class="special">)</span></code>
+        </p>
+<p>
+          See also <a class="link" href="../rounding/round.html" title="Rounding Functions">round</a>
+          for the full template (header only) version of this function.
+        </p>
+<pre class="programlisting"><span class="keyword">double</span> <span class="identifier">log1p</span><span class="special">(</span><span class="keyword">double</span> <span class="identifier">x</span><span class="special">);</span>
+<span class="keyword">float</span> <span class="identifier">log1pf</span><span class="special">(</span><span class="keyword">float</span> <span class="identifier">x</span><span class="special">);</span>
+<span class="keyword">long</span> <span class="keyword">double</span> <span class="identifier">log1pl</span><span class="special">(</span><span class="keyword">long</span> <span class="keyword">double</span> <span class="identifier">x</span><span class="special">);</span>
+</pre>
+<p>
+          Returns the <code class="computeroutput"><span class="identifier">log</span><span class="special">(</span><span class="identifier">x</span><span class="special">+</span><span class="number">1</span><span class="special">)</span></code> without the loss of precision implied
+          by that formulation.
+        </p>
+<p>
+          See also <a class="link" href="../powers/log1p.html" title="log1p">log1p</a>
+          for the full template (header only) version of this function.
+        </p>
+<pre class="programlisting"><span class="keyword">long</span> <span class="identifier">lround</span><span class="special">(</span><span class="keyword">double</span> <span class="identifier">x</span><span class="special">);</span>
+<span class="keyword">long</span> <span class="identifier">lroundf</span><span class="special">(</span><span class="keyword">float</span> <span class="identifier">x</span><span class="special">);</span>
+<span class="keyword">long</span> <span class="identifier">lroundl</span><span class="special">(</span><span class="keyword">long</span> <span class="keyword">double</span> <span class="identifier">x</span><span class="special">);</span>
+</pre>
+<p>
+          Returns the value <span class="emphasis"><em>x</em></span> rounded to the nearest integer
+          as a <code class="computeroutput"><span class="keyword">long</span></code>: equivalent to
+          <code class="computeroutput"><span class="identifier">floor</span><span class="special">(</span><span class="identifier">x</span> <span class="special">+</span> <span class="number">0.5</span><span class="special">)</span></code>
+        </p>
+<p>
+          See also <a class="link" href="../rounding/round.html" title="Rounding Functions">round</a>
+          for the full template (header only) version of this function.
+        </p>
+<pre class="programlisting"><span class="keyword">double</span> <span class="identifier">nextafter</span><span class="special">(</span><span class="keyword">double</span> <span class="identifier">x</span><span class="special">,</span> <span class="keyword">double</span> <span class="identifier">y</span><span class="special">);</span>
+<span class="keyword">float</span> <span class="identifier">nextafterf</span><span class="special">(</span><span class="keyword">float</span> <span class="identifier">x</span><span class="special">,</span> <span class="keyword">float</span> <span class="identifier">y</span><span class="special">);</span>
+<span class="keyword">long</span> <span class="keyword">double</span> <span class="identifier">nextafterl</span><span class="special">(</span><span class="keyword">long</span> <span class="keyword">double</span> <span class="identifier">x</span><span class="special">,</span> <span class="keyword">long</span> <span class="keyword">double</span> <span class="identifier">y</span><span class="special">);</span>
+</pre>
+<p>
+          Returns the next representable floating point number after <span class="emphasis"><em>x</em></span>
+          in the direction of <span class="emphasis"><em>y</em></span>, or <span class="emphasis"><em>x</em></span> if
+          <code class="computeroutput"><span class="identifier">x</span> <span class="special">==</span>
+          <span class="identifier">y</span></code>.
+        </p>
+<pre class="programlisting"><span class="keyword">double</span> <span class="identifier">nexttoward</span><span class="special">(</span><span class="keyword">double</span> <span class="identifier">x</span><span class="special">,</span> <span class="keyword">long</span> <span class="keyword">double</span> <span class="identifier">y</span><span class="special">);</span>
+<span class="keyword">float</span> <span class="identifier">nexttowardf</span><span class="special">(</span><span class="keyword">float</span> <span class="identifier">x</span><span class="special">,</span> <span class="keyword">long</span> <span class="keyword">double</span> <span class="identifier">y</span><span class="special">);</span>
+<span class="keyword">long</span> <span class="keyword">double</span> <span class="identifier">nexttowardl</span><span class="special">(</span><span class="keyword">long</span> <span class="keyword">double</span> <span class="identifier">x</span><span class="special">,</span> <span class="keyword">long</span> <span class="keyword">double</span> <span class="identifier">y</span><span class="special">);</span>
+</pre>
+<p>
+          As <code class="computeroutput"><span class="identifier">nextafter</span></code>, but with
+          <span class="emphasis"><em>y</em></span> always expressed as a <code class="computeroutput"><span class="keyword">long</span>
+          <span class="keyword">double</span></code>.
+        </p>
+<pre class="programlisting"><span class="keyword">double</span> <span class="identifier">round</span><span class="special">(</span><span class="keyword">double</span> <span class="identifier">x</span><span class="special">);</span>
+<span class="keyword">float</span> <span class="identifier">roundf</span><span class="special">(</span><span class="keyword">float</span> <span class="identifier">x</span><span class="special">);</span>
+<span class="keyword">long</span> <span class="keyword">double</span> <span class="identifier">roundl</span><span class="special">(</span><span class="keyword">long</span> <span class="keyword">double</span> <span class="identifier">x</span><span class="special">);</span>
+</pre>
+<p>
+          Returns the value <span class="emphasis"><em>x</em></span> rounded to the nearest integer:
+          equivalent to <code class="computeroutput"><span class="identifier">floor</span><span class="special">(</span><span class="identifier">x</span> <span class="special">+</span> <span class="number">0.5</span><span class="special">)</span></code>
+        </p>
+<p>
+          See also <a class="link" href="../rounding/round.html" title="Rounding Functions">round</a>
+          for the full template (header only) version of this function.
+        </p>
+<pre class="programlisting"><span class="keyword">double</span> <span class="identifier">tgamma</span><span class="special">(</span><span class="keyword">double</span> <span class="identifier">x</span><span class="special">);</span>
+<span class="keyword">float</span> <span class="identifier">tgammaf</span><span class="special">(</span><span class="keyword">float</span> <span class="identifier">x</span><span class="special">);</span>
+<span class="keyword">long</span> <span class="keyword">double</span> <span class="identifier">tgammal</span><span class="special">(</span><span class="keyword">long</span> <span class="keyword">double</span> <span class="identifier">x</span><span class="special">);</span>
+</pre>
+<p>
+          Returns the gamma function of <span class="emphasis"><em>x</em></span>:
+        </p>
+<p>
+          <span class="inlinemediaobject"><img src="../../../../equations/gamm1.png"></span>
+        </p>
+<p>
+          See also <a class="link" href="../sf_gamma/tgamma.html" title="Gamma">tgamma</a>
+          for the full template (header only) version of this function.
+        </p>
+<pre class="programlisting"><span class="keyword">double</span> <span class="identifier">trunc</span><span class="special">(</span><span class="keyword">double</span> <span class="identifier">x</span><span class="special">);</span>
+<span class="keyword">float</span> <span class="identifier">truncf</span><span class="special">(</span><span class="keyword">float</span> <span class="identifier">x</span><span class="special">);</span>
+<span class="keyword">long</span> <span class="keyword">double</span> <span class="identifier">truncl</span><span class="special">(</span><span class="keyword">long</span> <span class="keyword">double</span> <span class="identifier">x</span><span class="special">);</span>
+</pre>
+<p>
+          Returns <span class="emphasis"><em>x</em></span> truncated to the nearest integer.
+        </p>
+<p>
+          See also <a class="link" href="../rounding/trunc.html" title="Truncation Functions">trunc</a>
+          for the full template (header only) version of this function.
+        </p>
+</div>
+<table xmlns:rev="http://www.cs.rpi.edu/~gregod/boost/tools/doc/revision" width="100%"><tr>
+<td align="left"></td>
+<td align="right"><div class="copyright-footer">Copyright © 2006 , 2007, 2008 John Maddock, Paul A. Bristow, Hubert
+      Holin, Xiaogang Zhang, Bruno Lalande and Gautam Sewani<p>
+        Distributed under the Boost Software License, Version 1.0. (See accompanying
+        file LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_0.txt)
+      </p>
+</div></td>
+</tr></table>
+<hr>
+<div class="spirit-nav">
+<a accesskey="p" href="tr1.html"><img src="../../../../../doc/html/images/prev.png" alt="Prev"></a><a accesskey="u" href="../extern_c.html"><img src="../../../../../doc/html/images/up.png" alt="Up"></a><a accesskey="h" href="../../../index.html"><img src="../../../../../doc/html/images/home.png" alt="Home"></a><a accesskey="n" href="tr1_ref.html"><img src="../../../../../doc/html/images/next.png" alt="Next"></a>
+</div>
+</body>
+</html>

Added: sandbox/tools/auto_index/example/math/doc/sf_and_dist/html/math_toolkit/special/extern_c/tr1.html
==============================================================================
--- (empty file)
+++ sandbox/tools/auto_index/example/math/doc/sf_and_dist/html/math_toolkit/special/extern_c/tr1.html	2008-11-28 05:25:28 EST (Fri, 28 Nov 2008)
@@ -0,0 +1,693 @@
+<html>
+<head>
+<meta http-equiv="Content-Type" content="text/html; charset=ISO-8859-1">
+<title>C99 and TR1 C Functions Overview</title>
+<link rel="stylesheet" href="../../../boostbook.css" type="text/css">
+<meta name="generator" content="DocBook XSL Stylesheets Vsnapshot_8125">
+<link rel="home" href="../../../index.html" title="Math Toolkit">
+<link rel="up" href="../extern_c.html" title='TR1 and C99 external "C" Functions'>
+<link rel="prev" href="../extern_c.html" title='TR1 and C99 external "C" Functions'>
+<link rel="next" href="c99.html" title="C99 C Functions">
+</head>
+<body bgcolor="white" text="black" link="#0000FF" vlink="#840084" alink="#0000FF">
+<table cellpadding="2" width="100%"><tr>
+<td valign="top"><img alt="Boost C++ Libraries" width="277" height="86" src="../../../../../boost.png"></td>
+<td align="center">Home</td>
+<td align="center">Libraries</td>
+<td align="center">People</td>
+<td align="center">FAQ</td>
+<td align="center">More</td>
+</tr></table>
+<hr>
+<div class="spirit-nav">
+<a accesskey="p" href="../extern_c.html"><img src="../../../../../doc/html/images/prev.png" alt="Prev"></a><a accesskey="u" href="../extern_c.html"><img src="../../../../../doc/html/images/up.png" alt="Up"></a><a accesskey="h" href="../../../index.html"><img src="../../../../../doc/html/images/home.png" alt="Home"></a><a accesskey="n" href="c99.html"><img src="../../../../../doc/html/images/next.png" alt="Next"></a>
+</div>
+<div class="section" lang="en">
+<div class="titlepage"><div><div><h4 class="title">
+<a name="math_toolkit.special.extern_c.tr1"></a><a class="link" href="tr1.html" title="C99 and TR1 C Functions Overview"> C99 and TR1 C Functions
+        Overview</a>
+</h4></div></div></div>
+<p>
+          </p>
+<p>
+            Many of the special functions included in this library are also a part
+            of the either the C99 standard or the <a href="http://www.open-std.org/jtc1/sc22/wg21/docs/papers/2005/n1836.pdf" target="_top">Technical
+            Report on C++ Library Extensions</a>. Therefore this library includes
+            a thin wrapper header <code class="computeroutput"><span class="identifier">boost</span><span class="special">/</span><span class="identifier">math</span><span class="special">/</span><span class="identifier">tr1</span><span class="special">.</span><span class="identifier">hpp</span></code>
+            that provides compatibility with these two standards.
+          </p>
+<p>
+          </p>
+<p>
+            There are various pros and cons to using the library in this way:
+          </p>
+<p>
+          </p>
+<p>
+            Pros:
+          </p>
+<p>
+          </p>
+<div class="itemizedlist"><ul type="disc">
+<li>
+              The header to include is lightweight (i.e. fast to compile).
+            </li>
+<li>
+              The functions have extern "C" linkage, and so are usable
+              from other languages.
+            </li>
+<li>
+              Standard compatibility.
+            </li>
+</ul></div>
+<p>
+          </p>
+<p>
+            Cons:
+          </p>
+<p>
+          </p>
+<div class="itemizedlist"><ul type="disc">
+<li>
+              You will need to compile and link to the external Boost.Math libraries.
+            </li>
+<li>
+              Limited to support for the types, <code class="computeroutput"><span class="keyword">float</span></code>,
+              <code class="computeroutput"><span class="keyword">double</span></code> and <code class="computeroutput"><span class="keyword">long</span> <span class="keyword">double</span></code>.
+            </li>
+<li>
+              Error handling is handled via setting ::errno and returning NaN's and
+              infinities: this may be less flexible than an C++ exception based approach.
+            </li>
+</ul></div>
+<p>
+          </p>
+<div class="note"><table border="0" summary="Note">
+<tr>
+<td rowspan="2" align="center" valign="top" width="25"><img alt="[Note]" src="../../../../../doc/html/images/note.png"></td>
+<th align="left">Note</th>
+</tr>
+<tr><td align="left" valign="top"><p>
+              The separate libraries are required <span class="bold"><strong>only</strong></span>
+              if you choose to use boost/math/tr1.hpp rather than some other Boost.Math
+              header, the rest of Boost.Math remains header-only.
+            </p></td></tr>
+</table></div>
+<p>
+          </p>
+<p>
+            The separate libraries required in order to use tr1.hpp can be compiled
+            using bjam from within the libs/math/build directory, or from the Boost
+            root directory using the usual Boost-wide install procedure. Alternatively
+            the source files are located in libs/math/src and each have the same
+            name as the function they implement. The various libraries are named
+            as follows:
+          </p>
+<p>
+          </p>
+<div class="informaltable"><table class="table">
+<colgroup>
+<col>
+<col>
+<col>
+</colgroup>
+<thead><tr>
+<th>
+                  <p>
+                    Name
+                  </p>
+                  </th>
+<th>
+                  <p>
+                    Type
+                  </p>
+                  </th>
+<th>
+                  <p>
+                    Functions
+                  </p>
+                  </th>
+</tr></thead>
+<tbody>
+<tr>
+<td>
+                  <p>
+                    boost_math_c99f-&lt;suffix&gt;
+                  </p>
+                  </td>
+<td>
+                  <p>
+                    float
+                  </p>
+                  </td>
+<td>
+                  <p>
+                    C99 Functions
+                  </p>
+                  </td>
+</tr>
+<tr>
+<td>
+                  <p>
+                    boost_math_c99-&lt;suffix&gt;
+                  </p>
+                  </td>
+<td>
+                  <p>
+                    double
+                  </p>
+                  </td>
+<td>
+                  <p>
+                    C99 Functions
+                  </p>
+                  </td>
+</tr>
+<tr>
+<td>
+                  <p>
+                    boost_math_c99l-&lt;suffix&gt;
+                  </p>
+                  </td>
+<td>
+                  <p>
+                    long double
+                  </p>
+                  </td>
+<td>
+                  <p>
+                    C99 Functions
+                  </p>
+                  </td>
+</tr>
+<tr>
+<td>
+                  <p>
+                    boost_math_tr1f-&lt;suffix&gt;
+                  </p>
+                  </td>
+<td>
+                  <p>
+                    float
+                  </p>
+                  </td>
+<td>
+                  <p>
+                    TR1 Functions
+                  </p>
+                  </td>
+</tr>
+<tr>
+<td>
+                  <p>
+                    boost_math_tr1-&lt;suffix&gt;
+                  </p>
+                  </td>
+<td>
+                  <p>
+                    double
+                  </p>
+                  </td>
+<td>
+                  <p>
+                    TR1 Functions
+                  </p>
+                  </td>
+</tr>
+<tr>
+<td>
+                  <p>
+                    boost_math_tr1l-&lt;suffix&gt;
+                  </p>
+                  </td>
+<td>
+                  <p>
+                    long double
+                  </p>
+                  </td>
+<td>
+                  <p>
+                    TR1 Functions
+                  </p>
+                  </td>
+</tr>
+</tbody>
+</table></div>
+<p>
+          </p>
+<p>
+            Where <code class="computeroutput"><span class="special">&lt;</span><span class="identifier">suffix</span><span class="special">&gt;</span></code> encodes the compiler and build options
+            used to build the libraries: for example "libboost_math_tr1-vc80-mt-gd.lib"
+            would be the statically linked TR1 library to use with Visual C++ 8.0,
+            in multithreading debug mode, with the DLL VC++ runtime, where as "boost_math_tr1-vc80-mt.lib"
+            would be import library for the TR1 DLL to be used with Visual C++ 8.0
+            with the release multithreaded DLL VC++ runtime. Refer to the getting
+            started guide for a <a href="http://www.boost.org/doc/libs/1_35_0/more/getting_started/windows.html#library-naming" target="_top">full
+            explanation of the <code class="computeroutput"><span class="special">&lt;</span><span class="identifier">suffix</span><span class="special">&gt;</span></code>
+            meanings</a>.
+          </p>
+<p>
+          </p>
+<div class="note"><table border="0" summary="Note">
+<tr>
+<td rowspan="2" align="center" valign="top" width="25"><img alt="[Note]" src="../../../../../doc/html/images/note.png"></td>
+<th align="left">Note</th>
+</tr>
+<tr><td align="left" valign="top">
+<p>
+              Visual C++ users will typically have the correct library variant to
+              link against selected for them by boost/math/tr1.hpp based on your
+              compiler settings.
+            </p>
+<p>
+              Users will need to define BOOST_MATH_TR1_DYN_LINK when building their
+              code if they want to link against the DLL versions of these libraries
+              rather than the static versions.
+            </p>
+<p>
+              Users can disable auto-linking by defining BOOST_MATH_TR1_NO_LIB when
+              building: this is typically only used when linking against a customised
+              build of the libraries.
+            </p>
+</td></tr>
+</table></div>
+<p>
+          </p>
+<div class="note"><table border="0" summary="Note">
+<tr>
+<td rowspan="2" align="center" valign="top" width="25"><img alt="[Note]" src="../../../../../doc/html/images/note.png"></td>
+<th align="left">Note</th>
+</tr>
+<tr><td align="left" valign="top"><p>
+              Linux and Unix users will generally only have one variant of these
+              libraries installed, and can generally just link against -lboost_math_tr1
+              etc.
+            </p></td></tr>
+</table></div>
+<p>
+          <a name="math_toolkit.special.extern_c.tr1.usage_recomendations"></a>
+          </p>
+<h5>
+<a name="id794833"></a>
+            <a class="link" href="tr1.html#math_toolkit.special.extern_c.tr1.usage_recomendations">Usage
+            Recomendations</a>
+          </h5>
+<p>
+          </p>
+<p>
+            This library now presents the user with a choice:
+          </p>
+<p>
+          </p>
+<div class="itemizedlist"><ul type="disc">
+<li>
+              To include the header only versions of the functions and have an easier
+              time linking, but a longer compile time.
+            </li>
+<li>
+              To include the TR1 headers and link against an external library.
+            </li>
+</ul></div>
+<p>
+          </p>
+<p>
+            Which option you choose depends largely on how you prefer to work and
+            how your system is set up.
+          </p>
+<p>
+          </p>
+<p>
+            For example a casual user who just needs the acosh function, would probably
+            be better off including <code class="computeroutput"><span class="special">&lt;</span><span class="identifier">boost</span><span class="special">/</span><span class="identifier">math</span><span class="special">/</span><span class="identifier">special_functions</span><span class="special">/</span><span class="identifier">acosh</span><span class="special">.</span><span class="identifier">hpp</span><span class="special">&gt;</span></code>
+            and using <code class="computeroutput"><span class="identifier">boost</span><span class="special">::</span><span class="identifier">math</span><span class="special">::</span><span class="identifier">acosh</span><span class="special">(</span><span class="identifier">x</span><span class="special">)</span></code>
+            in their code.
+          </p>
+<p>
+          </p>
+<p>
+            However, for large scale software development where compile times are
+            significant, and where the Boost libraries are already built and installed
+            on the system, then including <code class="computeroutput"><span class="special">&lt;</span><span class="identifier">boost</span><span class="special">/</span><span class="identifier">math</span><span class="special">/</span><span class="identifier">tr1</span><span class="special">.</span><span class="identifier">hpp</span><span class="special">&gt;</span></code>
+            and using <code class="computeroutput"><span class="identifier">boost</span><span class="special">::</span><span class="identifier">math</span><span class="special">::</span><span class="identifier">tr1</span><span class="special">::</span><span class="identifier">acosh</span><span class="special">(</span><span class="identifier">x</span><span class="special">)</span></code>
+            will speed up compile times, reduce object files sizes (since there are
+            no templates being instantiated any more), and also speed up debugging
+            runtimes - since the externally compiled libraries can be compiler optimised,
+            rather than built using full settings - the difference in performance
+            between <a class="link" href="../../perf/getting_best.html" title="Getting the Best Performance from this Library">release and debug
+            builds can be as much as 20 times</a>, so for complex applications
+            this can be a big win.
+          </p>
+<p>
+          <a name="math_toolkit.special.extern_c.tr1.supported_c99_functions"></a>
+          </p>
+<h5>
+<a name="id795154"></a>
+            <a class="link" href="tr1.html#math_toolkit.special.extern_c.tr1.supported_c99_functions">Supported
+            C99 Functions</a>
+          </h5>
+<p>
+          </p>
+<p>
+            See also the <a class="link" href="c99.html" title="C99 C Functions">quick
+            reference guide for these functions</a>.
+          </p>
+<p>
+          
+</p>
+<pre class="programlisting"><span class="keyword">namespace</span> <span class="identifier">boost</span><span class="special">{</span> <span class="keyword">namespace</span> <span class="identifier">math</span><span class="special">{</span> <span class="keyword">namespace</span> <span class="identifier">tr1</span><span class="special">{</span> <span class="keyword">extern</span> <span class="string">"C"</span><span class="special">{</span>
+
+<span class="keyword">typedef</span> <span class="identifier">unspecified</span> <span class="identifier">float_t</span><span class="special">;</span>
+<span class="keyword">typedef</span> <span class="identifier">unspecified</span> <span class="identifier">double_t</span><span class="special">;</span>
+
+<span class="keyword">double</span> <span class="identifier">acosh</span><span class="special">(</span><span class="keyword">double</span> <span class="identifier">x</span><span class="special">);</span>
+<span class="keyword">float</span> <span class="identifier">acoshf</span><span class="special">(</span><span class="keyword">float</span> <span class="identifier">x</span><span class="special">);</span>
+<span class="keyword">long</span> <span class="keyword">double</span> <span class="identifier">acoshl</span><span class="special">(</span><span class="keyword">long</span> <span class="keyword">double</span> <span class="identifier">x</span><span class="special">);</span>
+
+<span class="keyword">double</span> <span class="identifier">asinh</span><span class="special">(</span><span class="keyword">double</span> <span class="identifier">x</span><span class="special">);</span>
+<span class="keyword">float</span> <span class="identifier">asinhf</span><span class="special">(</span><span class="keyword">float</span> <span class="identifier">x</span><span class="special">);</span>
+<span class="keyword">long</span> <span class="keyword">double</span> <span class="identifier">asinhl</span><span class="special">(</span><span class="keyword">long</span> <span class="keyword">double</span> <span class="identifier">x</span><span class="special">);</span>
+
+<span class="keyword">double</span> <span class="identifier">atanh</span><span class="special">(</span><span class="keyword">double</span> <span class="identifier">x</span><span class="special">);</span>
+<span class="keyword">float</span> <span class="identifier">atanhf</span><span class="special">(</span><span class="keyword">float</span> <span class="identifier">x</span><span class="special">);</span>
+<span class="keyword">long</span> <span class="keyword">double</span> <span class="identifier">atanhl</span><span class="special">(</span><span class="keyword">long</span> <span class="keyword">double</span> <span class="identifier">x</span><span class="special">);</span>
+
+<span class="keyword">double</span> <span class="identifier">cbrt</span><span class="special">(</span><span class="keyword">double</span> <span class="identifier">x</span><span class="special">);</span>
+<span class="keyword">float</span> <span class="identifier">cbrtf</span><span class="special">(</span><span class="keyword">float</span> <span class="identifier">x</span><span class="special">);</span>
+<span class="keyword">long</span> <span class="keyword">double</span> <span class="identifier">cbrtl</span><span class="special">(</span><span class="keyword">long</span> <span class="keyword">double</span> <span class="identifier">x</span><span class="special">);</span>
+
+<span class="keyword">double</span> <span class="identifier">copysign</span><span class="special">(</span><span class="keyword">double</span> <span class="identifier">x</span><span class="special">,</span> <span class="keyword">double</span> <span class="identifier">y</span><span class="special">);</span>
+<span class="keyword">float</span> <span class="identifier">copysignf</span><span class="special">(</span><span class="keyword">float</span> <span class="identifier">x</span><span class="special">,</span> <span class="keyword">float</span> <span class="identifier">y</span><span class="special">);</span>
+<span class="keyword">long</span> <span class="keyword">double</span> <span class="identifier">copysignl</span><span class="special">(</span><span class="keyword">long</span> <span class="keyword">double</span> <span class="identifier">x</span><span class="special">,</span> <span class="keyword">long</span> <span class="keyword">double</span> <span class="identifier">y</span><span class="special">);</span>
+
+<span class="keyword">double</span> <span class="identifier">erf</span><span class="special">(</span><span class="keyword">double</span> <span class="identifier">x</span><span class="special">);</span>
+<span class="keyword">float</span> <span class="identifier">erff</span><span class="special">(</span><span class="keyword">float</span> <span class="identifier">x</span><span class="special">);</span>
+<span class="keyword">long</span> <span class="keyword">double</span> <span class="identifier">erfl</span><span class="special">(</span><span class="keyword">long</span> <span class="keyword">double</span> <span class="identifier">x</span><span class="special">);</span>
+
+<span class="keyword">double</span> <span class="identifier">erfc</span><span class="special">(</span><span class="keyword">double</span> <span class="identifier">x</span><span class="special">);</span>
+<span class="keyword">float</span> <span class="identifier">erfcf</span><span class="special">(</span><span class="keyword">float</span> <span class="identifier">x</span><span class="special">);</span>
+<span class="keyword">long</span> <span class="keyword">double</span> <span class="identifier">erfcl</span><span class="special">(</span><span class="keyword">long</span> <span class="keyword">double</span> <span class="identifier">x</span><span class="special">);</span>
+
+<span class="keyword">double</span> <span class="identifier">expm1</span><span class="special">(</span><span class="keyword">double</span> <span class="identifier">x</span><span class="special">);</span>
+<span class="keyword">float</span> <span class="identifier">expm1f</span><span class="special">(</span><span class="keyword">float</span> <span class="identifier">x</span><span class="special">);</span>
+<span class="keyword">long</span> <span class="keyword">double</span> <span class="identifier">expm1l</span><span class="special">(</span><span class="keyword">long</span> <span class="keyword">double</span> <span class="identifier">x</span><span class="special">);</span>
+
+<span class="keyword">double</span> <span class="identifier">fmax</span><span class="special">(</span><span class="keyword">double</span> <span class="identifier">x</span><span class="special">,</span> <span class="keyword">double</span> <span class="identifier">y</span><span class="special">);</span>
+<span class="keyword">float</span> <span class="identifier">fmaxf</span><span class="special">(</span><span class="keyword">float</span> <span class="identifier">x</span><span class="special">,</span> <span class="keyword">float</span> <span class="identifier">y</span><span class="special">);</span>
+<span class="keyword">long</span> <span class="keyword">double</span> <span class="identifier">fmaxl</span><span class="special">(</span><span class="keyword">long</span> <span class="keyword">double</span> <span class="identifier">x</span><span class="special">,</span> <span class="keyword">long</span> <span class="keyword">double</span> <span class="identifier">y</span><span class="special">);</span>
+
+<span class="keyword">double</span> <span class="identifier">fmin</span><span class="special">(</span><span class="keyword">double</span> <span class="identifier">x</span><span class="special">,</span> <span class="keyword">double</span> <span class="identifier">y</span><span class="special">);</span>
+<span class="keyword">float</span> <span class="identifier">fminf</span><span class="special">(</span><span class="keyword">float</span> <span class="identifier">x</span><span class="special">,</span> <span class="keyword">float</span> <span class="identifier">y</span><span class="special">);</span>
+<span class="keyword">long</span> <span class="keyword">double</span> <span class="identifier">fminl</span><span class="special">(</span><span class="keyword">long</span> <span class="keyword">double</span> <span class="identifier">x</span><span class="special">,</span> <span class="keyword">long</span> <span class="keyword">double</span> <span class="identifier">y</span><span class="special">);</span>
+
+<span class="keyword">double</span> <span class="identifier">hypot</span><span class="special">(</span><span class="keyword">double</span> <span class="identifier">x</span><span class="special">,</span> <span class="keyword">double</span> <span class="identifier">y</span><span class="special">);</span>
+<span class="keyword">float</span> <span class="identifier">hypotf</span><span class="special">(</span><span class="keyword">float</span> <span class="identifier">x</span><span class="special">,</span> <span class="keyword">float</span> <span class="identifier">y</span><span class="special">);</span>
+<span class="keyword">long</span> <span class="keyword">double</span> <span class="identifier">hypotl</span><span class="special">(</span><span class="keyword">long</span> <span class="keyword">double</span> <span class="identifier">x</span><span class="special">,</span> <span class="keyword">long</span> <span class="keyword">double</span> <span class="identifier">y</span><span class="special">);</span>
+
+<span class="keyword">double</span> <span class="identifier">lgamma</span><span class="special">(</span><span class="keyword">double</span> <span class="identifier">x</span><span class="special">);</span>
+<span class="keyword">float</span> <span class="identifier">lgammaf</span><span class="special">(</span><span class="keyword">float</span> <span class="identifier">x</span><span class="special">);</span>
+<span class="keyword">long</span> <span class="keyword">double</span> <span class="identifier">lgammal</span><span class="special">(</span><span class="keyword">long</span> <span class="keyword">double</span> <span class="identifier">x</span><span class="special">);</span>
+
+<span class="keyword">long</span> <span class="keyword">long</span> <span class="identifier">llround</span><span class="special">(</span><span class="keyword">double</span> <span class="identifier">x</span><span class="special">);</span>
+<span class="keyword">long</span> <span class="keyword">long</span> <span class="identifier">llroundf</span><span class="special">(</span><span class="keyword">float</span> <span class="identifier">x</span><span class="special">);</span>
+<span class="keyword">long</span> <span class="keyword">long</span> <span class="identifier">llroundl</span><span class="special">(</span><span class="keyword">long</span> <span class="keyword">double</span> <span class="identifier">x</span><span class="special">);</span>
+
+<span class="keyword">double</span> <span class="identifier">log1p</span><span class="special">(</span><span class="keyword">double</span> <span class="identifier">x</span><span class="special">);</span>
+<span class="keyword">float</span> <span class="identifier">log1pf</span><span class="special">(</span><span class="keyword">float</span> <span class="identifier">x</span><span class="special">);</span>
+<span class="keyword">long</span> <span class="keyword">double</span> <span class="identifier">log1pl</span><span class="special">(</span><span class="keyword">long</span> <span class="keyword">double</span> <span class="identifier">x</span><span class="special">);</span>
+
+<span class="keyword">long</span> <span class="identifier">lround</span><span class="special">(</span><span class="keyword">double</span> <span class="identifier">x</span><span class="special">);</span>
+<span class="keyword">long</span> <span class="identifier">lroundf</span><span class="special">(</span><span class="keyword">float</span> <span class="identifier">x</span><span class="special">);</span>
+<span class="keyword">long</span> <span class="identifier">lroundl</span><span class="special">(</span><span class="keyword">long</span> <span class="keyword">double</span> <span class="identifier">x</span><span class="special">);</span>
+
+<span class="keyword">double</span> <span class="identifier">nextafter</span><span class="special">(</span><span class="keyword">double</span> <span class="identifier">x</span><span class="special">,</span> <span class="keyword">double</span> <span class="identifier">y</span><span class="special">);</span>
+<span class="keyword">float</span> <span class="identifier">nextafterf</span><span class="special">(</span><span class="keyword">float</span> <span class="identifier">x</span><span class="special">,</span> <span class="keyword">float</span> <span class="identifier">y</span><span class="special">);</span>
+<span class="keyword">long</span> <span class="keyword">double</span> <span class="identifier">nextafterl</span><span class="special">(</span><span class="keyword">long</span> <span class="keyword">double</span> <span class="identifier">x</span><span class="special">,</span> <span class="keyword">long</span> <span class="keyword">double</span> <span class="identifier">y</span><span class="special">);</span>
+
+<span class="keyword">double</span> <span class="identifier">nexttoward</span><span class="special">(</span><span class="keyword">double</span> <span class="identifier">x</span><span class="special">,</span> <span class="keyword">long</span> <span class="keyword">double</span> <span class="identifier">y</span><span class="special">);</span>
+<span class="keyword">float</span> <span class="identifier">nexttowardf</span><span class="special">(</span><span class="keyword">float</span> <span class="identifier">x</span><span class="special">,</span> <span class="keyword">long</span> <span class="keyword">double</span> <span class="identifier">y</span><span class="special">);</span>
+<span class="keyword">long</span> <span class="keyword">double</span> <span class="identifier">nexttowardl</span><span class="special">(</span><span class="keyword">long</span> <span class="keyword">double</span> <span class="identifier">x</span><span class="special">,</span> <span class="keyword">long</span> <span class="keyword">double</span> <span class="identifier">y</span><span class="special">);</span>
+
+<span class="keyword">double</span> <span class="identifier">round</span><span class="special">(</span><span class="keyword">double</span> <span class="identifier">x</span><span class="special">);</span>
+<span class="keyword">float</span> <span class="identifier">roundf</span><span class="special">(</span><span class="keyword">float</span> <span class="identifier">x</span><span class="special">);</span>
+<span class="keyword">long</span> <span class="keyword">double</span> <span class="identifier">roundl</span><span class="special">(</span><span class="keyword">long</span> <span class="keyword">double</span> <span class="identifier">x</span><span class="special">);</span>
+
+<span class="keyword">double</span> <span class="identifier">tgamma</span><span class="special">(</span><span class="keyword">double</span> <span class="identifier">x</span><span class="special">);</span>
+<span class="keyword">float</span> <span class="identifier">tgammaf</span><span class="special">(</span><span class="keyword">float</span> <span class="identifier">x</span><span class="special">);</span>
+<span class="keyword">long</span> <span class="keyword">double</span> <span class="identifier">tgammal</span><span class="special">(</span><span class="keyword">long</span> <span class="keyword">double</span> <span class="identifier">x</span><span class="special">);</span>
+
+<span class="keyword">double</span> <span class="identifier">trunc</span><span class="special">(</span><span class="keyword">double</span> <span class="identifier">x</span><span class="special">);</span>
+<span class="keyword">float</span> <span class="identifier">truncf</span><span class="special">(</span><span class="keyword">float</span> <span class="identifier">x</span><span class="special">);</span>
+<span class="keyword">long</span> <span class="keyword">double</span> <span class="identifier">truncl</span><span class="special">(</span><span class="keyword">long</span> <span class="keyword">double</span> <span class="identifier">x</span><span class="special">);</span>
+
+<span class="special">}}}}</span> <span class="comment">// namespaces
+</span></pre>
+<p>
+          <a name="math_toolkit.special.extern_c.tr1.supported_tr1_functions"></a>
+          </p>
+<h5>
+<a name="id797963"></a>
+            <a class="link" href="tr1.html#math_toolkit.special.extern_c.tr1.supported_tr1_functions">Supported
+            TR1 Functions</a>
+          </h5>
+<p>
+          </p>
+<p>
+            See also the <a class="link" href="tr1.html" title="C99 and TR1 C Functions Overview">quick
+            reference guide for these functions</a>.
+          </p>
+<p>
+          
+</p>
+<pre class="programlisting"><span class="keyword">namespace</span> <span class="identifier">boost</span><span class="special">{</span> <span class="keyword">namespace</span> <span class="identifier">math</span><span class="special">{</span> <span class="keyword">namespace</span> <span class="identifier">tr1</span><span class="special">{</span> <span class="keyword">extern</span> <span class="string">"C"</span><span class="special">{</span>
+   
+<span class="comment">// [5.2.1.1] associated Laguerre polynomials:
+</span><span class="keyword">double</span> <span class="identifier">assoc_laguerre</span><span class="special">(</span><span class="keyword">unsigned</span> <span class="identifier">n</span><span class="special">,</span> <span class="keyword">unsigned</span> <span class="identifier">m</span><span class="special">,</span> <span class="keyword">double</span> <span class="identifier">x</span><span class="special">);</span>
+<span class="keyword">float</span> <span class="identifier">assoc_laguerref</span><span class="special">(</span><span class="keyword">unsigned</span> <span class="identifier">n</span><span class="special">,</span> <span class="keyword">unsigned</span> <span class="identifier">m</span><span class="special">,</span> <span class="keyword">float</span> <span class="identifier">x</span><span class="special">);</span>
+<span class="keyword">long</span> <span class="keyword">double</span> <span class="identifier">assoc_laguerrel</span><span class="special">(</span><span class="keyword">unsigned</span> <span class="identifier">n</span><span class="special">,</span> <span class="keyword">unsigned</span> <span class="identifier">m</span><span class="special">,</span> <span class="keyword">long</span> <span class="keyword">double</span> <span class="identifier">x</span><span class="special">);</span>
+
+<span class="comment">// [5.2.1.2] associated Legendre functions:
+</span><span class="keyword">double</span> <span class="identifier">assoc_legendre</span><span class="special">(</span><span class="keyword">unsigned</span> <span class="identifier">l</span><span class="special">,</span> <span class="keyword">unsigned</span> <span class="identifier">m</span><span class="special">,</span> <span class="keyword">double</span> <span class="identifier">x</span><span class="special">);</span>
+<span class="keyword">float</span> <span class="identifier">assoc_legendref</span><span class="special">(</span><span class="keyword">unsigned</span> <span class="identifier">l</span><span class="special">,</span> <span class="keyword">unsigned</span> <span class="identifier">m</span><span class="special">,</span> <span class="keyword">float</span> <span class="identifier">x</span><span class="special">);</span>
+<span class="keyword">long</span> <span class="keyword">double</span> <span class="identifier">assoc_legendrel</span><span class="special">(</span><span class="keyword">unsigned</span> <span class="identifier">l</span><span class="special">,</span> <span class="keyword">unsigned</span> <span class="identifier">m</span><span class="special">,</span> <span class="keyword">long</span> <span class="keyword">double</span> <span class="identifier">x</span><span class="special">);</span>
+
+<span class="comment">// [5.2.1.3] beta function:
+</span><span class="keyword">double</span> <span class="identifier">beta</span><span class="special">(</span><span class="keyword">double</span> <span class="identifier">x</span><span class="special">,</span> <span class="keyword">double</span> <span class="identifier">y</span><span class="special">);</span>
+<span class="keyword">float</span> <span class="identifier">betaf</span><span class="special">(</span><span class="keyword">float</span> <span class="identifier">x</span><span class="special">,</span> <span class="keyword">float</span> <span class="identifier">y</span><span class="special">);</span>
+<span class="keyword">long</span> <span class="keyword">double</span> <span class="identifier">betal</span><span class="special">(</span><span class="keyword">long</span> <span class="keyword">double</span> <span class="identifier">x</span><span class="special">,</span> <span class="keyword">long</span> <span class="keyword">double</span> <span class="identifier">y</span><span class="special">);</span>
+
+<span class="comment">// [5.2.1.4] (complete) elliptic integral of the first kind:
+</span><span class="keyword">double</span> <span class="identifier">comp_ellint_1</span><span class="special">(</span><span class="keyword">double</span> <span class="identifier">k</span><span class="special">);</span>
+<span class="keyword">float</span> <span class="identifier">comp_ellint_1f</span><span class="special">(</span><span class="keyword">float</span> <span class="identifier">k</span><span class="special">);</span>
+<span class="keyword">long</span> <span class="keyword">double</span> <span class="identifier">comp_ellint_1l</span><span class="special">(</span><span class="keyword">long</span> <span class="keyword">double</span> <span class="identifier">k</span><span class="special">);</span>
+
+<span class="comment">// [5.2.1.5] (complete) elliptic integral of the second kind:
+</span><span class="keyword">double</span> <span class="identifier">comp_ellint_2</span><span class="special">(</span><span class="keyword">double</span> <span class="identifier">k</span><span class="special">);</span>
+<span class="keyword">float</span> <span class="identifier">comp_ellint_2f</span><span class="special">(</span><span class="keyword">float</span> <span class="identifier">k</span><span class="special">);</span>
+<span class="keyword">long</span> <span class="keyword">double</span> <span class="identifier">comp_ellint_2l</span><span class="special">(</span><span class="keyword">long</span> <span class="keyword">double</span> <span class="identifier">k</span><span class="special">);</span>
+
+<span class="comment">// [5.2.1.6] (complete) elliptic integral of the third kind:
+</span><span class="keyword">double</span> <span class="identifier">comp_ellint_3</span><span class="special">(</span><span class="keyword">double</span> <span class="identifier">k</span><span class="special">,</span> <span class="keyword">double</span> <span class="identifier">nu</span><span class="special">);</span>
+<span class="keyword">float</span> <span class="identifier">comp_ellint_3f</span><span class="special">(</span><span class="keyword">float</span> <span class="identifier">k</span><span class="special">,</span> <span class="keyword">float</span> <span class="identifier">nu</span><span class="special">);</span>
+<span class="keyword">long</span> <span class="keyword">double</span> <span class="identifier">comp_ellint_3l</span><span class="special">(</span><span class="keyword">long</span> <span class="keyword">double</span> <span class="identifier">k</span><span class="special">,</span> <span class="keyword">long</span> <span class="keyword">double</span> <span class="identifier">nu</span><span class="special">);</span>
+
+<span class="comment">// [5.2.1.8] regular modified cylindrical Bessel functions:
+</span><span class="keyword">double</span> <span class="identifier">cyl_bessel_i</span><span class="special">(</span><span class="keyword">double</span> <span class="identifier">nu</span><span class="special">,</span> <span class="keyword">double</span> <span class="identifier">x</span><span class="special">);</span>
+<span class="keyword">float</span> <span class="identifier">cyl_bessel_if</span><span class="special">(</span><span class="keyword">float</span> <span class="identifier">nu</span><span class="special">,</span> <span class="keyword">float</span> <span class="identifier">x</span><span class="special">);</span>
+<span class="keyword">long</span> <span class="keyword">double</span> <span class="identifier">cyl_bessel_il</span><span class="special">(</span><span class="keyword">long</span> <span class="keyword">double</span> <span class="identifier">nu</span><span class="special">,</span> <span class="keyword">long</span> <span class="keyword">double</span> <span class="identifier">x</span><span class="special">);</span>
+
+<span class="comment">// [5.2.1.9] cylindrical Bessel functions (of the first kind):
+</span><span class="keyword">double</span> <span class="identifier">cyl_bessel_j</span><span class="special">(</span><span class="keyword">double</span> <span class="identifier">nu</span><span class="special">,</span> <span class="keyword">double</span> <span class="identifier">x</span><span class="special">);</span>
+<span class="keyword">float</span> <span class="identifier">cyl_bessel_jf</span><span class="special">(</span><span class="keyword">float</span> <span class="identifier">nu</span><span class="special">,</span> <span class="keyword">float</span> <span class="identifier">x</span><span class="special">);</span>
+<span class="keyword">long</span> <span class="keyword">double</span> <span class="identifier">cyl_bessel_jl</span><span class="special">(</span><span class="keyword">long</span> <span class="keyword">double</span> <span class="identifier">nu</span><span class="special">,</span> <span class="keyword">long</span> <span class="keyword">double</span> <span class="identifier">x</span><span class="special">);</span>
+
+<span class="comment">// [5.2.1.10] irregular modified cylindrical Bessel functions:
+</span><span class="keyword">double</span> <span class="identifier">cyl_bessel_k</span><span class="special">(</span><span class="keyword">double</span> <span class="identifier">nu</span><span class="special">,</span> <span class="keyword">double</span> <span class="identifier">x</span><span class="special">);</span>
+<span class="keyword">float</span> <span class="identifier">cyl_bessel_kf</span><span class="special">(</span><span class="keyword">float</span> <span class="identifier">nu</span><span class="special">,</span> <span class="keyword">float</span> <span class="identifier">x</span><span class="special">);</span>
+<span class="keyword">long</span> <span class="keyword">double</span> <span class="identifier">cyl_bessel_kl</span><span class="special">(</span><span class="keyword">long</span> <span class="keyword">double</span> <span class="identifier">nu</span><span class="special">,</span> <span class="keyword">long</span> <span class="keyword">double</span> <span class="identifier">x</span><span class="special">);</span>
+
+<span class="comment">// [5.2.1.11] cylindrical Neumann functions;
+</span><span class="comment">// cylindrical Bessel functions (of the second kind):
+</span><span class="keyword">double</span> <span class="identifier">cyl_neumann</span><span class="special">(</span><span class="keyword">double</span> <span class="identifier">nu</span><span class="special">,</span> <span class="keyword">double</span> <span class="identifier">x</span><span class="special">);</span>
+<span class="keyword">float</span> <span class="identifier">cyl_neumannf</span><span class="special">(</span><span class="keyword">float</span> <span class="identifier">nu</span><span class="special">,</span> <span class="keyword">float</span> <span class="identifier">x</span><span class="special">);</span>
+<span class="keyword">long</span> <span class="keyword">double</span> <span class="identifier">cyl_neumannl</span><span class="special">(</span><span class="keyword">long</span> <span class="keyword">double</span> <span class="identifier">nu</span><span class="special">,</span> <span class="keyword">long</span> <span class="keyword">double</span> <span class="identifier">x</span><span class="special">);</span>
+
+<span class="comment">// [5.2.1.12] (incomplete) elliptic integral of the first kind:
+</span><span class="keyword">double</span> <span class="identifier">ellint_1</span><span class="special">(</span><span class="keyword">double</span> <span class="identifier">k</span><span class="special">,</span> <span class="keyword">double</span> <span class="identifier">phi</span><span class="special">);</span>
+<span class="keyword">float</span> <span class="identifier">ellint_1f</span><span class="special">(</span><span class="keyword">float</span> <span class="identifier">k</span><span class="special">,</span> <span class="keyword">float</span> <span class="identifier">phi</span><span class="special">);</span>
+<span class="keyword">long</span> <span class="keyword">double</span> <span class="identifier">ellint_1l</span><span class="special">(</span><span class="keyword">long</span> <span class="keyword">double</span> <span class="identifier">k</span><span class="special">,</span> <span class="keyword">long</span> <span class="keyword">double</span> <span class="identifier">phi</span><span class="special">);</span>
+
+<span class="comment">// [5.2.1.13] (incomplete) elliptic integral of the second kind:
+</span><span class="keyword">double</span> <span class="identifier">ellint_2</span><span class="special">(</span><span class="keyword">double</span> <span class="identifier">k</span><span class="special">,</span> <span class="keyword">double</span> <span class="identifier">phi</span><span class="special">);</span>
+<span class="keyword">float</span> <span class="identifier">ellint_2f</span><span class="special">(</span><span class="keyword">float</span> <span class="identifier">k</span><span class="special">,</span> <span class="keyword">float</span> <span class="identifier">phi</span><span class="special">);</span>
+<span class="keyword">long</span> <span class="keyword">double</span> <span class="identifier">ellint_2l</span><span class="special">(</span><span class="keyword">long</span> <span class="keyword">double</span> <span class="identifier">k</span><span class="special">,</span> <span class="keyword">long</span> <span class="keyword">double</span> <span class="identifier">phi</span><span class="special">);</span>
+
+<span class="comment">// [5.2.1.14] (incomplete) elliptic integral of the third kind:
+</span><span class="keyword">double</span> <span class="identifier">ellint_3</span><span class="special">(</span><span class="keyword">double</span> <span class="identifier">k</span><span class="special">,</span> <span class="keyword">double</span> <span class="identifier">nu</span><span class="special">,</span> <span class="keyword">double</span> <span class="identifier">phi</span><span class="special">);</span>
+<span class="keyword">float</span> <span class="identifier">ellint_3f</span><span class="special">(</span><span class="keyword">float</span> <span class="identifier">k</span><span class="special">,</span> <span class="keyword">float</span> <span class="identifier">nu</span><span class="special">,</span> <span class="keyword">float</span> <span class="identifier">phi</span><span class="special">);</span>
+<span class="keyword">long</span> <span class="keyword">double</span> <span class="identifier">ellint_3l</span><span class="special">(</span><span class="keyword">long</span> <span class="keyword">double</span> <span class="identifier">k</span><span class="special">,</span> <span class="keyword">long</span> <span class="keyword">double</span> <span class="identifier">nu</span><span class="special">,</span> <span class="keyword">long</span> <span class="keyword">double</span> <span class="identifier">phi</span><span class="special">);</span>
+
+<span class="comment">// [5.2.1.15] exponential integral:
+</span><span class="keyword">double</span> <span class="identifier">expint</span><span class="special">(</span><span class="keyword">double</span> <span class="identifier">x</span><span class="special">);</span>
+<span class="keyword">float</span> <span class="identifier">expintf</span><span class="special">(</span><span class="keyword">float</span> <span class="identifier">x</span><span class="special">);</span>
+<span class="keyword">long</span> <span class="keyword">double</span> <span class="identifier">expintl</span><span class="special">(</span><span class="keyword">long</span> <span class="keyword">double</span> <span class="identifier">x</span><span class="special">);</span>
+
+<span class="comment">// [5.2.1.16] Hermite polynomials:
+</span><span class="keyword">double</span> <span class="identifier">hermite</span><span class="special">(</span><span class="keyword">unsigned</span> <span class="identifier">n</span><span class="special">,</span> <span class="keyword">double</span> <span class="identifier">x</span><span class="special">);</span>
+<span class="keyword">float</span> <span class="identifier">hermitef</span><span class="special">(</span><span class="keyword">unsigned</span> <span class="identifier">n</span><span class="special">,</span> <span class="keyword">float</span> <span class="identifier">x</span><span class="special">);</span>
+<span class="keyword">long</span> <span class="keyword">double</span> <span class="identifier">hermitel</span><span class="special">(</span><span class="keyword">unsigned</span> <span class="identifier">n</span><span class="special">,</span> <span class="keyword">long</span> <span class="keyword">double</span> <span class="identifier">x</span><span class="special">);</span>
+
+<span class="comment">// [5.2.1.18] Laguerre polynomials:
+</span><span class="keyword">double</span> <span class="identifier">laguerre</span><span class="special">(</span><span class="keyword">unsigned</span> <span class="identifier">n</span><span class="special">,</span> <span class="keyword">double</span> <span class="identifier">x</span><span class="special">);</span>
+<span class="keyword">float</span> <span class="identifier">laguerref</span><span class="special">(</span><span class="keyword">unsigned</span> <span class="identifier">n</span><span class="special">,</span> <span class="keyword">float</span> <span class="identifier">x</span><span class="special">);</span>
+<span class="keyword">long</span> <span class="keyword">double</span> <span class="identifier">laguerrel</span><span class="special">(</span><span class="keyword">unsigned</span> <span class="identifier">n</span><span class="special">,</span> <span class="keyword">long</span> <span class="keyword">double</span> <span class="identifier">x</span><span class="special">);</span>
+
+<span class="comment">// [5.2.1.19] Legendre polynomials:
+</span><span class="keyword">double</span> <span class="identifier">legendre</span><span class="special">(</span><span class="keyword">unsigned</span> <span class="identifier">l</span><span class="special">,</span> <span class="keyword">double</span> <span class="identifier">x</span><span class="special">);</span>
+<span class="keyword">float</span> <span class="identifier">legendref</span><span class="special">(</span><span class="keyword">unsigned</span> <span class="identifier">l</span><span class="special">,</span> <span class="keyword">float</span> <span class="identifier">x</span><span class="special">);</span>
+<span class="keyword">long</span> <span class="keyword">double</span> <span class="identifier">legendrel</span><span class="special">(</span><span class="keyword">unsigned</span> <span class="identifier">l</span><span class="special">,</span> <span class="keyword">long</span> <span class="keyword">double</span> <span class="identifier">x</span><span class="special">);</span>
+
+<span class="comment">// [5.2.1.20] Riemann zeta function:
+</span><span class="keyword">double</span> <span class="identifier">riemann_zeta</span><span class="special">(</span><span class="keyword">double</span><span class="special">);</span>
+<span class="keyword">float</span> <span class="identifier">riemann_zetaf</span><span class="special">(</span><span class="keyword">float</span><span class="special">);</span>
+<span class="keyword">long</span> <span class="keyword">double</span> <span class="identifier">riemann_zetal</span><span class="special">(</span><span class="keyword">long</span> <span class="keyword">double</span><span class="special">);</span>
+
+<span class="comment">// [5.2.1.21] spherical Bessel functions (of the first kind):
+</span><span class="keyword">double</span> <span class="identifier">sph_bessel</span><span class="special">(</span><span class="keyword">unsigned</span> <span class="identifier">n</span><span class="special">,</span> <span class="keyword">double</span> <span class="identifier">x</span><span class="special">);</span>
+<span class="keyword">float</span> <span class="identifier">sph_besself</span><span class="special">(</span><span class="keyword">unsigned</span> <span class="identifier">n</span><span class="special">,</span> <span class="keyword">float</span> <span class="identifier">x</span><span class="special">);</span>
+<span class="keyword">long</span> <span class="keyword">double</span> <span class="identifier">sph_bessell</span><span class="special">(</span><span class="keyword">unsigned</span> <span class="identifier">n</span><span class="special">,</span> <span class="keyword">long</span> <span class="keyword">double</span> <span class="identifier">x</span><span class="special">);</span>
+
+<span class="comment">// [5.2.1.22] spherical associated Legendre functions:
+</span><span class="keyword">double</span> <span class="identifier">sph_legendre</span><span class="special">(</span><span class="keyword">unsigned</span> <span class="identifier">l</span><span class="special">,</span> <span class="keyword">unsigned</span> <span class="identifier">m</span><span class="special">,</span> <span class="keyword">double</span> <span class="identifier">theta</span><span class="special">);</span>
+<span class="keyword">float</span> <span class="identifier">sph_legendref</span><span class="special">(</span><span class="keyword">unsigned</span> <span class="identifier">l</span><span class="special">,</span> <span class="keyword">unsigned</span> <span class="identifier">m</span><span class="special">,</span> <span class="keyword">float</span> <span class="identifier">theta</span><span class="special">);</span>
+<span class="keyword">long</span> <span class="keyword">double</span> <span class="identifier">sph_legendrel</span><span class="special">(</span><span class="keyword">unsigned</span> <span class="identifier">l</span><span class="special">,</span> <span class="keyword">unsigned</span> <span class="identifier">m</span><span class="special">,</span> <span class="keyword">long</span> <span class="keyword">double</span> <span class="identifier">theta</span><span class="special">);</span>
+
+<span class="comment">// [5.2.1.23] spherical Neumann functions;
+</span><span class="comment">// spherical Bessel functions (of the second kind):
+</span><span class="keyword">double</span> <span class="identifier">sph_neumann</span><span class="special">(</span><span class="keyword">unsigned</span> <span class="identifier">n</span><span class="special">,</span> <span class="keyword">double</span> <span class="identifier">x</span><span class="special">);</span>
+<span class="keyword">float</span> <span class="identifier">sph_neumannf</span><span class="special">(</span><span class="keyword">unsigned</span> <span class="identifier">n</span><span class="special">,</span> <span class="keyword">float</span> <span class="identifier">x</span><span class="special">);</span>
+<span class="keyword">long</span> <span class="keyword">double</span> <span class="identifier">sph_neumannl</span><span class="special">(</span><span class="keyword">unsigned</span> <span class="identifier">n</span><span class="special">,</span> <span class="keyword">long</span> <span class="keyword">double</span> <span class="identifier">x</span><span class="special">);</span>
+
+<span class="special">}}}}</span> <span class="comment">// namespaces
+</span></pre>
+<p>
+          </p>
+<p>
+            In addition sufficient additional overloads of the <code class="computeroutput"><span class="keyword">double</span></code>
+            versions of the above functions are provided, so that calling the function
+            with any mixture of <code class="computeroutput"><span class="keyword">float</span></code>,
+            <code class="computeroutput"><span class="keyword">double</span></code>, <code class="computeroutput"><span class="keyword">long</span>
+            <span class="keyword">double</span></code>, or <span class="emphasis"><em>integer</em></span>
+            arguments is supported, with the return type determined by the <a class="link" href="../../main_overview/result_type.html" title="Calculation of the Type of the Result"><span class="emphasis"><em>result type
+            calculation rules</em></span></a>.
+          </p>
+<p>
+          <a name="math_toolkit.special.extern_c.tr1.currently_unsupported_c99_functions"></a>
+          </p>
+<h5>
+<a name="id801846"></a>
+            <a class="link" href="tr1.html#math_toolkit.special.extern_c.tr1.currently_unsupported_c99_functions">Currently
+            Unsupported C99 Functions</a>
+          </h5>
+<p>
+          
+</p>
+<pre class="programlisting"><span class="keyword">double</span> <span class="identifier">exp2</span><span class="special">(</span><span class="keyword">double</span> <span class="identifier">x</span><span class="special">);</span>
+<span class="keyword">float</span> <span class="identifier">exp2f</span><span class="special">(</span><span class="keyword">float</span> <span class="identifier">x</span><span class="special">);</span>
+<span class="keyword">long</span> <span class="keyword">double</span> <span class="identifier">exp2l</span><span class="special">(</span><span class="keyword">long</span> <span class="keyword">double</span> <span class="identifier">x</span><span class="special">);</span>
+
+<span class="keyword">double</span> <span class="identifier">fdim</span><span class="special">(</span><span class="keyword">double</span> <span class="identifier">x</span><span class="special">,</span> <span class="keyword">double</span> <span class="identifier">y</span><span class="special">);</span>
+<span class="keyword">float</span> <span class="identifier">fdimf</span><span class="special">(</span><span class="keyword">float</span> <span class="identifier">x</span><span class="special">,</span> <span class="keyword">float</span> <span class="identifier">y</span><span class="special">);</span>
+<span class="keyword">long</span> <span class="keyword">double</span> <span class="identifier">fdiml</span><span class="special">(</span><span class="keyword">long</span> <span class="keyword">double</span> <span class="identifier">x</span><span class="special">,</span> <span class="keyword">long</span> <span class="keyword">double</span> <span class="identifier">y</span><span class="special">);</span>
+
+<span class="keyword">double</span> <span class="identifier">fma</span><span class="special">(</span><span class="keyword">double</span> <span class="identifier">x</span><span class="special">,</span> <span class="keyword">double</span> <span class="identifier">y</span><span class="special">,</span> <span class="keyword">double</span> <span class="identifier">z</span><span class="special">);</span>
+<span class="keyword">float</span> <span class="identifier">fmaf</span><span class="special">(</span><span class="keyword">float</span> <span class="identifier">x</span><span class="special">,</span> <span class="keyword">float</span> <span class="identifier">y</span><span class="special">,</span> <span class="keyword">float</span> <span class="identifier">z</span><span class="special">);</span>
+<span class="keyword">long</span> <span class="keyword">double</span> <span class="identifier">fmal</span><span class="special">(</span><span class="keyword">long</span> <span class="keyword">double</span> <span class="identifier">x</span><span class="special">,</span> <span class="keyword">long</span> <span class="keyword">double</span> <span class="identifier">y</span><span class="special">,</span> <span class="keyword">long</span> <span class="keyword">double</span> <span class="identifier">z</span><span class="special">);</span>
+
+<span class="keyword">int</span> <span class="identifier">ilogb</span><span class="special">(</span><span class="keyword">double</span> <span class="identifier">x</span><span class="special">);</span>
+<span class="keyword">int</span> <span class="identifier">ilogbf</span><span class="special">(</span><span class="keyword">float</span> <span class="identifier">x</span><span class="special">);</span>
+<span class="keyword">int</span> <span class="identifier">ilogbl</span><span class="special">(</span><span class="keyword">long</span> <span class="keyword">double</span> <span class="identifier">x</span><span class="special">);</span>
+
+<span class="keyword">long</span> <span class="keyword">long</span> <span class="identifier">llrint</span><span class="special">(</span><span class="keyword">double</span> <span class="identifier">x</span><span class="special">);</span>
+<span class="keyword">long</span> <span class="keyword">long</span> <span class="identifier">llrintf</span><span class="special">(</span><span class="keyword">float</span> <span class="identifier">x</span><span class="special">);</span>
+<span class="keyword">long</span> <span class="keyword">long</span> <span class="identifier">llrintl</span><span class="special">(</span><span class="keyword">long</span> <span class="keyword">double</span> <span class="identifier">x</span><span class="special">);</span>
+
+<span class="keyword">double</span> <span class="identifier">log2</span><span class="special">(</span><span class="keyword">double</span> <span class="identifier">x</span><span class="special">);</span>
+<span class="keyword">float</span> <span class="identifier">log2f</span><span class="special">(</span><span class="keyword">float</span> <span class="identifier">x</span><span class="special">);</span>
+<span class="keyword">long</span> <span class="keyword">double</span> <span class="identifier">log2l</span><span class="special">(</span><span class="keyword">long</span> <span class="keyword">double</span> <span class="identifier">x</span><span class="special">);</span>
+
+<span class="keyword">double</span> <span class="identifier">logb</span><span class="special">(</span><span class="keyword">double</span> <span class="identifier">x</span><span class="special">);</span>
+<span class="keyword">float</span> <span class="identifier">logbf</span><span class="special">(</span><span class="keyword">float</span> <span class="identifier">x</span><span class="special">);</span>
+<span class="keyword">long</span> <span class="keyword">double</span> <span class="identifier">logbl</span><span class="special">(</span><span class="keyword">long</span> <span class="keyword">double</span> <span class="identifier">x</span><span class="special">);</span>
+
+<span class="keyword">long</span> <span class="identifier">lrint</span><span class="special">(</span><span class="keyword">double</span> <span class="identifier">x</span><span class="special">);</span>
+<span class="keyword">long</span> <span class="identifier">lrintf</span><span class="special">(</span><span class="keyword">float</span> <span class="identifier">x</span><span class="special">);</span>
+<span class="keyword">long</span> <span class="identifier">lrintl</span><span class="special">(</span><span class="keyword">long</span> <span class="keyword">double</span> <span class="identifier">x</span><span class="special">);</span>
+
+<span class="keyword">double</span> <span class="identifier">nan</span><span class="special">(</span><span class="keyword">const</span> <span class="keyword">char</span> <span class="special">*</span><span class="identifier">str</span><span class="special">);</span>
+<span class="keyword">float</span> <span class="identifier">nanf</span><span class="special">(</span><span class="keyword">const</span> <span class="keyword">char</span> <span class="special">*</span><span class="identifier">str</span><span class="special">);</span>
+<span class="keyword">long</span> <span class="keyword">double</span> <span class="identifier">nanl</span><span class="special">(</span><span class="keyword">const</span> <span class="keyword">char</span> <span class="special">*</span><span class="identifier">str</span><span class="special">);</span>
+
+<span class="keyword">double</span> <span class="identifier">nearbyint</span><span class="special">(</span><span class="keyword">double</span> <span class="identifier">x</span><span class="special">);</span>
+<span class="keyword">float</span> <span class="identifier">nearbyintf</span><span class="special">(</span><span class="keyword">float</span> <span class="identifier">x</span><span class="special">);</span>
+<span class="keyword">long</span> <span class="keyword">double</span> <span class="identifier">nearbyintl</span><span class="special">(</span><span class="keyword">long</span> <span class="keyword">double</span> <span class="identifier">x</span><span class="special">);</span>
+
+<span class="keyword">double</span> <span class="identifier">remainder</span><span class="special">(</span><span class="keyword">double</span> <span class="identifier">x</span><span class="special">,</span> <span class="keyword">double</span> <span class="identifier">y</span><span class="special">);</span>
+<span class="keyword">float</span> <span class="identifier">remainderf</span><span class="special">(</span><span class="keyword">float</span> <span class="identifier">x</span><span class="special">,</span> <span class="keyword">float</span> <span class="identifier">y</span><span class="special">);</span>
+<span class="keyword">long</span> <span class="keyword">double</span> <span class="identifier">remainderl</span><span class="special">(</span><span class="keyword">long</span> <span class="keyword">double</span> <span class="identifier">x</span><span class="special">,</span> <span class="keyword">long</span> <span class="keyword">double</span> <span class="identifier">y</span><span class="special">);</span>
+
+<span class="keyword">double</span> <span class="identifier">remquo</span><span class="special">(</span><span class="keyword">double</span> <span class="identifier">x</span><span class="special">,</span> <span class="keyword">double</span> <span class="identifier">y</span><span class="special">,</span> <span class="keyword">int</span> <span class="special">*</span><span class="identifier">pquo</span><span class="special">);</span>
+<span class="keyword">float</span> <span class="identifier">remquof</span><span class="special">(</span><span class="keyword">float</span> <span class="identifier">x</span><span class="special">,</span> <span class="keyword">float</span> <span class="identifier">y</span><span class="special">,</span> <span class="keyword">int</span> <span class="special">*</span><span class="identifier">pquo</span><span class="special">);</span>
+<span class="keyword">long</span> <span class="keyword">double</span> <span class="identifier">remquol</span><span class="special">(</span><span class="keyword">long</span> <span class="keyword">double</span> <span class="identifier">x</span><span class="special">,</span> <span class="keyword">long</span> <span class="keyword">double</span> <span class="identifier">y</span><span class="special">,</span> <span class="keyword">int</span> <span class="special">*</span><span class="identifier">pquo</span><span class="special">);</span>
+
+<span class="keyword">double</span> <span class="identifier">rint</span><span class="special">(</span><span class="keyword">double</span> <span class="identifier">x</span><span class="special">);</span>
+<span class="keyword">float</span> <span class="identifier">rintf</span><span class="special">(</span><span class="keyword">float</span> <span class="identifier">x</span><span class="special">);</span>
+<span class="keyword">long</span> <span class="keyword">double</span> <span class="identifier">rintl</span><span class="special">(</span><span class="keyword">long</span> <span class="keyword">double</span> <span class="identifier">x</span><span class="special">);</span>
+
+<span class="keyword">double</span> <span class="identifier">scalbln</span><span class="special">(</span><span class="keyword">double</span> <span class="identifier">x</span><span class="special">,</span> <span class="keyword">long</span> <span class="identifier">ex</span><span class="special">);</span>
+<span class="keyword">float</span> <span class="identifier">scalblnf</span><span class="special">(</span><span class="keyword">float</span> <span class="identifier">x</span><span class="special">,</span> <span class="keyword">long</span> <span class="identifier">ex</span><span class="special">);</span>
+<span class="keyword">long</span> <span class="keyword">double</span> <span class="identifier">scalblnl</span><span class="special">(</span><span class="keyword">long</span> <span class="keyword">double</span> <span class="identifier">x</span><span class="special">,</span> <span class="keyword">long</span> <span class="identifier">ex</span><span class="special">);</span>
+
+<span class="keyword">double</span> <span class="identifier">scalbn</span><span class="special">(</span><span class="keyword">double</span> <span class="identifier">x</span><span class="special">,</span> <span class="keyword">int</span> <span class="identifier">ex</span><span class="special">);</span>
+<span class="keyword">float</span> <span class="identifier">scalbnf</span><span class="special">(</span><span class="keyword">float</span> <span class="identifier">x</span><span class="special">,</span> <span class="keyword">int</span> <span class="identifier">ex</span><span class="special">);</span>
+<span class="keyword">long</span> <span class="keyword">double</span> <span class="identifier">scalbnl</span><span class="special">(</span><span class="keyword">long</span> <span class="keyword">double</span> <span class="identifier">x</span><span class="special">,</span> <span class="keyword">int</span> <span class="identifier">ex</span><span class="special">);</span>
+</pre>
+<p>
+          <a name="math_toolkit.special.extern_c.tr1.currently_unsupported_tr1_functions"></a>
+          </p>
+<h5>
+<a name="id804060"></a>
+            <a class="link" href="tr1.html#math_toolkit.special.extern_c.tr1.currently_unsupported_tr1_functions">Currently
+            Unsupported TR1 Functions</a>
+          </h5>
+<p>
+          
+</p>
+<pre class="programlisting"><span class="comment">// [5.2.1.7] confluent hypergeometric functions:
+</span><span class="keyword">double</span> <span class="identifier">conf_hyperg</span><span class="special">(</span><span class="keyword">double</span> <span class="identifier">a</span><span class="special">,</span> <span class="keyword">double</span> <span class="identifier">c</span><span class="special">,</span> <span class="keyword">double</span> <span class="identifier">x</span><span class="special">);</span>
+<span class="keyword">float</span> <span class="identifier">conf_hypergf</span><span class="special">(</span><span class="keyword">float</span> <span class="identifier">a</span><span class="special">,</span> <span class="keyword">float</span> <span class="identifier">c</span><span class="special">,</span> <span class="keyword">float</span> <span class="identifier">x</span><span class="special">);</span>
+<span class="keyword">long</span> <span class="keyword">double</span> <span class="identifier">conf_hypergl</span><span class="special">(</span><span class="keyword">long</span> <span class="keyword">double</span> <span class="identifier">a</span><span class="special">,</span> <span class="keyword">long</span> <span class="keyword">double</span> <span class="identifier">c</span><span class="special">,</span> <span class="keyword">long</span> <span class="keyword">double</span> <span class="identifier">x</span><span class="special">);</span>
+
+<span class="comment">// [5.2.1.17] hypergeometric functions:
+</span><span class="keyword">double</span> <span class="identifier">hyperg</span><span class="special">(</span><span class="keyword">double</span> <span class="identifier">a</span><span class="special">,</span> <span class="keyword">double</span> <span class="identifier">b</span><span class="special">,</span> <span class="keyword">double</span> <span class="identifier">c</span><span class="special">,</span> <span class="keyword">double</span> <span class="identifier">x</span><span class="special">);</span>
+<span class="keyword">float</span> <span class="identifier">hypergf</span><span class="special">(</span><span class="keyword">float</span> <span class="identifier">a</span><span class="special">,</span> <span class="keyword">float</span> <span class="identifier">b</span><span class="special">,</span> <span class="keyword">float</span> <span class="identifier">c</span><span class="special">,</span> <span class="keyword">float</span> <span class="identifier">x</span><span class="special">);</span>
+<span class="keyword">long</span> <span class="keyword">double</span> <span class="identifier">hypergl</span><span class="special">(</span><span class="keyword">long</span> <span class="keyword">double</span> <span class="identifier">a</span><span class="special">,</span> <span class="keyword">long</span> <span class="keyword">double</span> <span class="identifier">b</span><span class="special">,</span> <span class="keyword">long</span> <span class="keyword">double</span> <span class="identifier">c</span><span class="special">,</span>
+<span class="keyword">long</span> <span class="keyword">double</span> <span class="identifier">x</span><span class="special">);</span>
+</pre>
+<p>
+        </p>
+</div>
+<table xmlns:rev="http://www.cs.rpi.edu/~gregod/boost/tools/doc/revision" width="100%"><tr>
+<td align="left"></td>
+<td align="right"><div class="copyright-footer">Copyright © 2006 , 2007, 2008 John Maddock, Paul A. Bristow, Hubert
+      Holin, Xiaogang Zhang, Bruno Lalande and Gautam Sewani<p>
+        Distributed under the Boost Software License, Version 1.0. (See accompanying
+        file LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_0.txt)
+      </p>
+</div></td>
+</tr></table>
+<hr>
+<div class="spirit-nav">
+<a accesskey="p" href="../extern_c.html"><img src="../../../../../doc/html/images/prev.png" alt="Prev"></a><a accesskey="u" href="../extern_c.html"><img src="../../../../../doc/html/images/up.png" alt="Up"></a><a accesskey="h" href="../../../index.html"><img src="../../../../../doc/html/images/home.png" alt="Home"></a><a accesskey="n" href="c99.html"><img src="../../../../../doc/html/images/next.png" alt="Next"></a>
+</div>
+</body>
+</html>

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+++ sandbox/tools/auto_index/example/math/doc/sf_and_dist/html/math_toolkit/special/extern_c/tr1_ref.html	2008-11-28 05:25:28 EST (Fri, 28 Nov 2008)
@@ -0,0 +1,538 @@
+<html>
+<head>
+<meta http-equiv="Content-Type" content="text/html; charset=ISO-8859-1">
+<title>TR1 C Functions Quick Reference</title>
+<link rel="stylesheet" href="../../../boostbook.css" type="text/css">
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+<link rel="home" href="../../../index.html" title="Math Toolkit">
+<link rel="up" href="../extern_c.html" title='TR1 and C99 external "C" Functions'>
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+<link rel="next" href="../../toolkit.html" title="Internal Details and Tools (Experimental)">
+</head>
+<body bgcolor="white" text="black" link="#0000FF" vlink="#840084" alink="#0000FF">
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+<td valign="top"><img alt="Boost C++ Libraries" width="277" height="86" src="../../../../../boost.png"></td>
+<td align="center">Home</td>
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+</div>
+<div class="section" lang="en">
+<div class="titlepage"><div><div><h4 class="title">
+<a name="math_toolkit.special.extern_c.tr1_ref"></a><a class="link" href="tr1_ref.html" title="TR1 C Functions Quick Reference"> TR1 C Functions
+        Quick Reference</a>
+</h4></div></div></div>
+<a name="math_toolkit.special.extern_c.tr1_ref.supported_tr1_functions"></a><h5>
+<a name="id811624"></a>
+          <a class="link" href="tr1_ref.html#math_toolkit.special.extern_c.tr1_ref.supported_tr1_functions">Supported
+          TR1 Functions</a>
+        </h5>
+<pre class="programlisting"><span class="keyword">namespace</span> <span class="identifier">boost</span><span class="special">{</span> <span class="keyword">namespace</span> <span class="identifier">math</span><span class="special">{</span> <span class="keyword">namespace</span> <span class="identifier">tr1</span><span class="special">{</span> <span class="keyword">extern</span> <span class="string">"C"</span><span class="special">{</span>
+   
+<span class="comment">// [5.2.1.1] associated Laguerre polynomials:
+</span><span class="keyword">double</span> <span class="identifier">assoc_laguerre</span><span class="special">(</span><span class="keyword">unsigned</span> <span class="identifier">n</span><span class="special">,</span> <span class="keyword">unsigned</span> <span class="identifier">m</span><span class="special">,</span> <span class="keyword">double</span> <span class="identifier">x</span><span class="special">);</span>
+<span class="keyword">float</span> <span class="identifier">assoc_laguerref</span><span class="special">(</span><span class="keyword">unsigned</span> <span class="identifier">n</span><span class="special">,</span> <span class="keyword">unsigned</span> <span class="identifier">m</span><span class="special">,</span> <span class="keyword">float</span> <span class="identifier">x</span><span class="special">);</span>
+<span class="keyword">long</span> <span class="keyword">double</span> <span class="identifier">assoc_laguerrel</span><span class="special">(</span><span class="keyword">unsigned</span> <span class="identifier">n</span><span class="special">,</span> <span class="keyword">unsigned</span> <span class="identifier">m</span><span class="special">,</span> <span class="keyword">long</span> <span class="keyword">double</span> <span class="identifier">x</span><span class="special">);</span>
+
+<span class="comment">// [5.2.1.2] associated Legendre functions:
+</span><span class="keyword">double</span> <span class="identifier">assoc_legendre</span><span class="special">(</span><span class="keyword">unsigned</span> <span class="identifier">l</span><span class="special">,</span> <span class="keyword">unsigned</span> <span class="identifier">m</span><span class="special">,</span> <span class="keyword">double</span> <span class="identifier">x</span><span class="special">);</span>
+<span class="keyword">float</span> <span class="identifier">assoc_legendref</span><span class="special">(</span><span class="keyword">unsigned</span> <span class="identifier">l</span><span class="special">,</span> <span class="keyword">unsigned</span> <span class="identifier">m</span><span class="special">,</span> <span class="keyword">float</span> <span class="identifier">x</span><span class="special">);</span>
+<span class="keyword">long</span> <span class="keyword">double</span> <span class="identifier">assoc_legendrel</span><span class="special">(</span><span class="keyword">unsigned</span> <span class="identifier">l</span><span class="special">,</span> <span class="keyword">unsigned</span> <span class="identifier">m</span><span class="special">,</span> <span class="keyword">long</span> <span class="keyword">double</span> <span class="identifier">x</span><span class="special">);</span>
+
+<span class="comment">// [5.2.1.3] beta function:
+</span><span class="keyword">double</span> <span class="identifier">beta</span><span class="special">(</span><span class="keyword">double</span> <span class="identifier">x</span><span class="special">,</span> <span class="keyword">double</span> <span class="identifier">y</span><span class="special">);</span>
+<span class="keyword">float</span> <span class="identifier">betaf</span><span class="special">(</span><span class="keyword">float</span> <span class="identifier">x</span><span class="special">,</span> <span class="keyword">float</span> <span class="identifier">y</span><span class="special">);</span>
+<span class="keyword">long</span> <span class="keyword">double</span> <span class="identifier">betal</span><span class="special">(</span><span class="keyword">long</span> <span class="keyword">double</span> <span class="identifier">x</span><span class="special">,</span> <span class="keyword">long</span> <span class="keyword">double</span> <span class="identifier">y</span><span class="special">);</span>
+
+<span class="comment">// [5.2.1.4] (complete) elliptic integral of the first kind:
+</span><span class="keyword">double</span> <span class="identifier">comp_ellint_1</span><span class="special">(</span><span class="keyword">double</span> <span class="identifier">k</span><span class="special">);</span>
+<span class="keyword">float</span> <span class="identifier">comp_ellint_1f</span><span class="special">(</span><span class="keyword">float</span> <span class="identifier">k</span><span class="special">);</span>
+<span class="keyword">long</span> <span class="keyword">double</span> <span class="identifier">comp_ellint_1l</span><span class="special">(</span><span class="keyword">long</span> <span class="keyword">double</span> <span class="identifier">k</span><span class="special">);</span>
+
+<span class="comment">// [5.2.1.5] (complete) elliptic integral of the second kind:
+</span><span class="keyword">double</span> <span class="identifier">comp_ellint_2</span><span class="special">(</span><span class="keyword">double</span> <span class="identifier">k</span><span class="special">);</span>
+<span class="keyword">float</span> <span class="identifier">comp_ellint_2f</span><span class="special">(</span><span class="keyword">float</span> <span class="identifier">k</span><span class="special">);</span>
+<span class="keyword">long</span> <span class="keyword">double</span> <span class="identifier">comp_ellint_2l</span><span class="special">(</span><span class="keyword">long</span> <span class="keyword">double</span> <span class="identifier">k</span><span class="special">);</span>
+
+<span class="comment">// [5.2.1.6] (complete) elliptic integral of the third kind:
+</span><span class="keyword">double</span> <span class="identifier">comp_ellint_3</span><span class="special">(</span><span class="keyword">double</span> <span class="identifier">k</span><span class="special">,</span> <span class="keyword">double</span> <span class="identifier">nu</span><span class="special">);</span>
+<span class="keyword">float</span> <span class="identifier">comp_ellint_3f</span><span class="special">(</span><span class="keyword">float</span> <span class="identifier">k</span><span class="special">,</span> <span class="keyword">float</span> <span class="identifier">nu</span><span class="special">);</span>
+<span class="keyword">long</span> <span class="keyword">double</span> <span class="identifier">comp_ellint_3l</span><span class="special">(</span><span class="keyword">long</span> <span class="keyword">double</span> <span class="identifier">k</span><span class="special">,</span> <span class="keyword">long</span> <span class="keyword">double</span> <span class="identifier">nu</span><span class="special">);</span>
+
+<span class="comment">// [5.2.1.8] regular modified cylindrical Bessel functions:
+</span><span class="keyword">double</span> <span class="identifier">cyl_bessel_i</span><span class="special">(</span><span class="keyword">double</span> <span class="identifier">nu</span><span class="special">,</span> <span class="keyword">double</span> <span class="identifier">x</span><span class="special">);</span>
+<span class="keyword">float</span> <span class="identifier">cyl_bessel_if</span><span class="special">(</span><span class="keyword">float</span> <span class="identifier">nu</span><span class="special">,</span> <span class="keyword">float</span> <span class="identifier">x</span><span class="special">);</span>
+<span class="keyword">long</span> <span class="keyword">double</span> <span class="identifier">cyl_bessel_il</span><span class="special">(</span><span class="keyword">long</span> <span class="keyword">double</span> <span class="identifier">nu</span><span class="special">,</span> <span class="keyword">long</span> <span class="keyword">double</span> <span class="identifier">x</span><span class="special">);</span>
+
+<span class="comment">// [5.2.1.9] cylindrical Bessel functions (of the first kind):
+</span><span class="keyword">double</span> <span class="identifier">cyl_bessel_j</span><span class="special">(</span><span class="keyword">double</span> <span class="identifier">nu</span><span class="special">,</span> <span class="keyword">double</span> <span class="identifier">x</span><span class="special">);</span>
+<span class="keyword">float</span> <span class="identifier">cyl_bessel_jf</span><span class="special">(</span><span class="keyword">float</span> <span class="identifier">nu</span><span class="special">,</span> <span class="keyword">float</span> <span class="identifier">x</span><span class="special">);</span>
+<span class="keyword">long</span> <span class="keyword">double</span> <span class="identifier">cyl_bessel_jl</span><span class="special">(</span><span class="keyword">long</span> <span class="keyword">double</span> <span class="identifier">nu</span><span class="special">,</span> <span class="keyword">long</span> <span class="keyword">double</span> <span class="identifier">x</span><span class="special">);</span>
+
+<span class="comment">// [5.2.1.10] irregular modified cylindrical Bessel functions:
+</span><span class="keyword">double</span> <span class="identifier">cyl_bessel_k</span><span class="special">(</span><span class="keyword">double</span> <span class="identifier">nu</span><span class="special">,</span> <span class="keyword">double</span> <span class="identifier">x</span><span class="special">);</span>
+<span class="keyword">float</span> <span class="identifier">cyl_bessel_kf</span><span class="special">(</span><span class="keyword">float</span> <span class="identifier">nu</span><span class="special">,</span> <span class="keyword">float</span> <span class="identifier">x</span><span class="special">);</span>
+<span class="keyword">long</span> <span class="keyword">double</span> <span class="identifier">cyl_bessel_kl</span><span class="special">(</span><span class="keyword">long</span> <span class="keyword">double</span> <span class="identifier">nu</span><span class="special">,</span> <span class="keyword">long</span> <span class="keyword">double</span> <span class="identifier">x</span><span class="special">);</span>
+
+<span class="comment">// [5.2.1.11] cylindrical Neumann functions;
+</span><span class="comment">// cylindrical Bessel functions (of the second kind):
+</span><span class="keyword">double</span> <span class="identifier">cyl_neumann</span><span class="special">(</span><span class="keyword">double</span> <span class="identifier">nu</span><span class="special">,</span> <span class="keyword">double</span> <span class="identifier">x</span><span class="special">);</span>
+<span class="keyword">float</span> <span class="identifier">cyl_neumannf</span><span class="special">(</span><span class="keyword">float</span> <span class="identifier">nu</span><span class="special">,</span> <span class="keyword">float</span> <span class="identifier">x</span><span class="special">);</span>
+<span class="keyword">long</span> <span class="keyword">double</span> <span class="identifier">cyl_neumannl</span><span class="special">(</span><span class="keyword">long</span> <span class="keyword">double</span> <span class="identifier">nu</span><span class="special">,</span> <span class="keyword">long</span> <span class="keyword">double</span> <span class="identifier">x</span><span class="special">);</span>
+
+<span class="comment">// [5.2.1.12] (incomplete) elliptic integral of the first kind:
+</span><span class="keyword">double</span> <span class="identifier">ellint_1</span><span class="special">(</span><span class="keyword">double</span> <span class="identifier">k</span><span class="special">,</span> <span class="keyword">double</span> <span class="identifier">phi</span><span class="special">);</span>
+<span class="keyword">float</span> <span class="identifier">ellint_1f</span><span class="special">(</span><span class="keyword">float</span> <span class="identifier">k</span><span class="special">,</span> <span class="keyword">float</span> <span class="identifier">phi</span><span class="special">);</span>
+<span class="keyword">long</span> <span class="keyword">double</span> <span class="identifier">ellint_1l</span><span class="special">(</span><span class="keyword">long</span> <span class="keyword">double</span> <span class="identifier">k</span><span class="special">,</span> <span class="keyword">long</span> <span class="keyword">double</span> <span class="identifier">phi</span><span class="special">);</span>
+
+<span class="comment">// [5.2.1.13] (incomplete) elliptic integral of the second kind:
+</span><span class="keyword">double</span> <span class="identifier">ellint_2</span><span class="special">(</span><span class="keyword">double</span> <span class="identifier">k</span><span class="special">,</span> <span class="keyword">double</span> <span class="identifier">phi</span><span class="special">);</span>
+<span class="keyword">float</span> <span class="identifier">ellint_2f</span><span class="special">(</span><span class="keyword">float</span> <span class="identifier">k</span><span class="special">,</span> <span class="keyword">float</span> <span class="identifier">phi</span><span class="special">);</span>
+<span class="keyword">long</span> <span class="keyword">double</span> <span class="identifier">ellint_2l</span><span class="special">(</span><span class="keyword">long</span> <span class="keyword">double</span> <span class="identifier">k</span><span class="special">,</span> <span class="keyword">long</span> <span class="keyword">double</span> <span class="identifier">phi</span><span class="special">);</span>
+
+<span class="comment">// [5.2.1.14] (incomplete) elliptic integral of the third kind:
+</span><span class="keyword">double</span> <span class="identifier">ellint_3</span><span class="special">(</span><span class="keyword">double</span> <span class="identifier">k</span><span class="special">,</span> <span class="keyword">double</span> <span class="identifier">nu</span><span class="special">,</span> <span class="keyword">double</span> <span class="identifier">phi</span><span class="special">);</span>
+<span class="keyword">float</span> <span class="identifier">ellint_3f</span><span class="special">(</span><span class="keyword">float</span> <span class="identifier">k</span><span class="special">,</span> <span class="keyword">float</span> <span class="identifier">nu</span><span class="special">,</span> <span class="keyword">float</span> <span class="identifier">phi</span><span class="special">);</span>
+<span class="keyword">long</span> <span class="keyword">double</span> <span class="identifier">ellint_3l</span><span class="special">(</span><span class="keyword">long</span> <span class="keyword">double</span> <span class="identifier">k</span><span class="special">,</span> <span class="keyword">long</span> <span class="keyword">double</span> <span class="identifier">nu</span><span class="special">,</span> <span class="keyword">long</span> <span class="keyword">double</span> <span class="identifier">phi</span><span class="special">);</span>
+
+<span class="comment">// [5.2.1.15] exponential integral:
+</span><span class="keyword">double</span> <span class="identifier">expint</span><span class="special">(</span><span class="keyword">double</span> <span class="identifier">x</span><span class="special">);</span>
+<span class="keyword">float</span> <span class="identifier">expintf</span><span class="special">(</span><span class="keyword">float</span> <span class="identifier">x</span><span class="special">);</span>
+<span class="keyword">long</span> <span class="keyword">double</span> <span class="identifier">expintl</span><span class="special">(</span><span class="keyword">long</span> <span class="keyword">double</span> <span class="identifier">x</span><span class="special">);</span>
+
+<span class="comment">// [5.2.1.16] Hermite polynomials:
+</span><span class="keyword">double</span> <span class="identifier">hermite</span><span class="special">(</span><span class="keyword">unsigned</span> <span class="identifier">n</span><span class="special">,</span> <span class="keyword">double</span> <span class="identifier">x</span><span class="special">);</span>
+<span class="keyword">float</span> <span class="identifier">hermitef</span><span class="special">(</span><span class="keyword">unsigned</span> <span class="identifier">n</span><span class="special">,</span> <span class="keyword">float</span> <span class="identifier">x</span><span class="special">);</span>
+<span class="keyword">long</span> <span class="keyword">double</span> <span class="identifier">hermitel</span><span class="special">(</span><span class="keyword">unsigned</span> <span class="identifier">n</span><span class="special">,</span> <span class="keyword">long</span> <span class="keyword">double</span> <span class="identifier">x</span><span class="special">);</span>
+
+<span class="comment">// [5.2.1.18] Laguerre polynomials:
+</span><span class="keyword">double</span> <span class="identifier">laguerre</span><span class="special">(</span><span class="keyword">unsigned</span> <span class="identifier">n</span><span class="special">,</span> <span class="keyword">double</span> <span class="identifier">x</span><span class="special">);</span>
+<span class="keyword">float</span> <span class="identifier">laguerref</span><span class="special">(</span><span class="keyword">unsigned</span> <span class="identifier">n</span><span class="special">,</span> <span class="keyword">float</span> <span class="identifier">x</span><span class="special">);</span>
+<span class="keyword">long</span> <span class="keyword">double</span> <span class="identifier">laguerrel</span><span class="special">(</span><span class="keyword">unsigned</span> <span class="identifier">n</span><span class="special">,</span> <span class="keyword">long</span> <span class="keyword">double</span> <span class="identifier">x</span><span class="special">);</span>
+
+<span class="comment">// [5.2.1.19] Legendre polynomials:
+</span><span class="keyword">double</span> <span class="identifier">legendre</span><span class="special">(</span><span class="keyword">unsigned</span> <span class="identifier">l</span><span class="special">,</span> <span class="keyword">double</span> <span class="identifier">x</span><span class="special">);</span>
+<span class="keyword">float</span> <span class="identifier">legendref</span><span class="special">(</span><span class="keyword">unsigned</span> <span class="identifier">l</span><span class="special">,</span> <span class="keyword">float</span> <span class="identifier">x</span><span class="special">);</span>
+<span class="keyword">long</span> <span class="keyword">double</span> <span class="identifier">legendrel</span><span class="special">(</span><span class="keyword">unsigned</span> <span class="identifier">l</span><span class="special">,</span> <span class="keyword">long</span> <span class="keyword">double</span> <span class="identifier">x</span><span class="special">);</span>
+
+<span class="comment">// [5.2.1.20] Riemann zeta function:
+</span><span class="keyword">double</span> <span class="identifier">riemann_zeta</span><span class="special">(</span><span class="keyword">double</span><span class="special">);</span>
+<span class="keyword">float</span> <span class="identifier">riemann_zetaf</span><span class="special">(</span><span class="keyword">float</span><span class="special">);</span>
+<span class="keyword">long</span> <span class="keyword">double</span> <span class="identifier">riemann_zetal</span><span class="special">(</span><span class="keyword">long</span> <span class="keyword">double</span><span class="special">);</span>
+
+<span class="comment">// [5.2.1.21] spherical Bessel functions (of the first kind):
+</span><span class="keyword">double</span> <span class="identifier">sph_bessel</span><span class="special">(</span><span class="keyword">unsigned</span> <span class="identifier">n</span><span class="special">,</span> <span class="keyword">double</span> <span class="identifier">x</span><span class="special">);</span>
+<span class="keyword">float</span> <span class="identifier">sph_besself</span><span class="special">(</span><span class="keyword">unsigned</span> <span class="identifier">n</span><span class="special">,</span> <span class="keyword">float</span> <span class="identifier">x</span><span class="special">);</span>
+<span class="keyword">long</span> <span class="keyword">double</span> <span class="identifier">sph_bessell</span><span class="special">(</span><span class="keyword">unsigned</span> <span class="identifier">n</span><span class="special">,</span> <span class="keyword">long</span> <span class="keyword">double</span> <span class="identifier">x</span><span class="special">);</span>
+
+<span class="comment">// [5.2.1.22] spherical associated Legendre functions:
+</span><span class="keyword">double</span> <span class="identifier">sph_legendre</span><span class="special">(</span><span class="keyword">unsigned</span> <span class="identifier">l</span><span class="special">,</span> <span class="keyword">unsigned</span> <span class="identifier">m</span><span class="special">,</span> <span class="keyword">double</span> <span class="identifier">theta</span><span class="special">);</span>
+<span class="keyword">float</span> <span class="identifier">sph_legendref</span><span class="special">(</span><span class="keyword">unsigned</span> <span class="identifier">l</span><span class="special">,</span> <span class="keyword">unsigned</span> <span class="identifier">m</span><span class="special">,</span> <span class="keyword">float</span> <span class="identifier">theta</span><span class="special">);</span>
+<span class="keyword">long</span> <span class="keyword">double</span> <span class="identifier">sph_legendrel</span><span class="special">(</span><span class="keyword">unsigned</span> <span class="identifier">l</span><span class="special">,</span> <span class="keyword">unsigned</span> <span class="identifier">m</span><span class="special">,</span> <span class="keyword">long</span> <span class="keyword">double</span> <span class="identifier">theta</span><span class="special">);</span>
+
+<span class="comment">// [5.2.1.23] spherical Neumann functions;
+</span><span class="comment">// spherical Bessel functions (of the second kind):
+</span><span class="keyword">double</span> <span class="identifier">sph_neumann</span><span class="special">(</span><span class="keyword">unsigned</span> <span class="identifier">n</span><span class="special">,</span> <span class="keyword">double</span> <span class="identifier">x</span><span class="special">);</span>
+<span class="keyword">float</span> <span class="identifier">sph_neumannf</span><span class="special">(</span><span class="keyword">unsigned</span> <span class="identifier">n</span><span class="special">,</span> <span class="keyword">float</span> <span class="identifier">x</span><span class="special">);</span>
+<span class="keyword">long</span> <span class="keyword">double</span> <span class="identifier">sph_neumannl</span><span class="special">(</span><span class="keyword">unsigned</span> <span class="identifier">n</span><span class="special">,</span> <span class="keyword">long</span> <span class="keyword">double</span> <span class="identifier">x</span><span class="special">);</span>
+
+<span class="special">}}}}</span> <span class="comment">// namespaces
+</span></pre>
+<p>
+          In addition sufficient additional overloads of the <code class="computeroutput"><span class="keyword">double</span></code>
+          versions of the above functions are provided, so that calling the function
+          with any mixture of <code class="computeroutput"><span class="keyword">float</span></code>,
+          <code class="computeroutput"><span class="keyword">double</span></code>, <code class="computeroutput"><span class="keyword">long</span>
+          <span class="keyword">double</span></code>, or <span class="emphasis"><em>integer</em></span>
+          arguments is supported, with the return type determined by the <a class="link" href="../../main_overview/result_type.html" title="Calculation of the Type of the Result"><span class="emphasis"><em>result
+          type calculation rules</em></span></a>.
+        </p>
+<p>
+          For example:
+        </p>
+<pre class="programlisting"><span class="identifier">expintf</span><span class="special">(</span><span class="number">2.0f</span><span class="special">);</span>  <span class="comment">// float version, returns float.
+</span><span class="identifier">expint</span><span class="special">(</span><span class="number">2.0f</span><span class="special">);</span>   <span class="comment">// also calls the float version and returns float.
+</span><span class="identifier">expint</span><span class="special">(</span><span class="number">2.0</span><span class="special">);</span>    <span class="comment">// double version, returns double.
+</span><span class="identifier">expintl</span><span class="special">(</span><span class="number">2.0L</span><span class="special">);</span>  <span class="comment">// long double version, returns a long double.
+</span><span class="identifier">expint</span><span class="special">(</span><span class="number">2.0L</span><span class="special">);</span>   <span class="comment">// also calls the long double version.
+</span><span class="identifier">expint</span><span class="special">(</span><span class="number">2</span><span class="special">);</span>      <span class="comment">// integer argument is treated as a double, returns double.
+</span></pre>
+<a name="math_toolkit.special.extern_c.tr1_ref.quick_reference"></a><h5>
+<a name="id815667"></a>
+          <a class="link" href="tr1_ref.html#math_toolkit.special.extern_c.tr1_ref.quick_reference">Quick
+          Reference</a>
+        </h5>
+<pre class="programlisting"><span class="comment">// [5.2.1.1] associated Laguerre polynomials:
+</span><span class="keyword">double</span> <span class="identifier">assoc_laguerre</span><span class="special">(</span><span class="keyword">unsigned</span> <span class="identifier">n</span><span class="special">,</span> <span class="keyword">unsigned</span> <span class="identifier">m</span><span class="special">,</span> <span class="keyword">double</span> <span class="identifier">x</span><span class="special">);</span>
+<span class="keyword">float</span> <span class="identifier">assoc_laguerref</span><span class="special">(</span><span class="keyword">unsigned</span> <span class="identifier">n</span><span class="special">,</span> <span class="keyword">unsigned</span> <span class="identifier">m</span><span class="special">,</span> <span class="keyword">float</span> <span class="identifier">x</span><span class="special">);</span>
+<span class="keyword">long</span> <span class="keyword">double</span> <span class="identifier">assoc_laguerrel</span><span class="special">(</span><span class="keyword">unsigned</span> <span class="identifier">n</span><span class="special">,</span> <span class="keyword">unsigned</span> <span class="identifier">m</span><span class="special">,</span> <span class="keyword">long</span> <span class="keyword">double</span> <span class="identifier">x</span><span class="special">);</span>
+</pre>
+<p>
+          The assoc_laguerre functions return:
+        </p>
+<p>
+          <span class="inlinemediaobject"><img src="../../../../equations/laguerre_1.png"></span>
+        </p>
+<p>
+          See also <a class="link" href="../sf_poly/laguerre.html" title="Laguerre (and Associated) Polynomials">laguerre</a>
+          for the full template (header only) version of this function.
+        </p>
+<pre class="programlisting"><span class="comment">// [5.2.1.2] associated Legendre functions:
+</span><span class="keyword">double</span> <span class="identifier">assoc_legendre</span><span class="special">(</span><span class="keyword">unsigned</span> <span class="identifier">l</span><span class="special">,</span> <span class="keyword">unsigned</span> <span class="identifier">m</span><span class="special">,</span> <span class="keyword">double</span> <span class="identifier">x</span><span class="special">);</span>
+<span class="keyword">float</span> <span class="identifier">assoc_legendref</span><span class="special">(</span><span class="keyword">unsigned</span> <span class="identifier">l</span><span class="special">,</span> <span class="keyword">unsigned</span> <span class="identifier">m</span><span class="special">,</span> <span class="keyword">float</span> <span class="identifier">x</span><span class="special">);</span>
+<span class="keyword">long</span> <span class="keyword">double</span> <span class="identifier">assoc_legendrel</span><span class="special">(</span><span class="keyword">unsigned</span> <span class="identifier">l</span><span class="special">,</span> <span class="keyword">unsigned</span> <span class="identifier">m</span><span class="special">,</span> <span class="keyword">long</span> <span class="keyword">double</span> <span class="identifier">x</span><span class="special">);</span>
+</pre>
+<p>
+          The assoc_legendre functions return:
+        </p>
+<p>
+          <span class="inlinemediaobject"><img src="../../../../equations/legendre_1b.png"></span>
+        </p>
+<p>
+          See also <a class="link" href="../sf_poly/legendre.html" title="Legendre (and Associated) Polynomials">legendre_p</a>
+          for the full template (header only) version of this function.
+        </p>
+<pre class="programlisting"><span class="comment">// [5.2.1.3] beta function:
+</span><span class="keyword">double</span> <span class="identifier">beta</span><span class="special">(</span><span class="keyword">double</span> <span class="identifier">x</span><span class="special">,</span> <span class="keyword">double</span> <span class="identifier">y</span><span class="special">);</span>
+<span class="keyword">float</span> <span class="identifier">betaf</span><span class="special">(</span><span class="keyword">float</span> <span class="identifier">x</span><span class="special">,</span> <span class="keyword">float</span> <span class="identifier">y</span><span class="special">);</span>
+<span class="keyword">long</span> <span class="keyword">double</span> <span class="identifier">betal</span><span class="special">(</span><span class="keyword">long</span> <span class="keyword">double</span> <span class="identifier">x</span><span class="special">,</span> <span class="keyword">long</span> <span class="keyword">double</span> <span class="identifier">y</span><span class="special">);</span>
+</pre>
+<p>
+          Returns the beta function of <span class="emphasis"><em>x</em></span> and <span class="emphasis"><em>y</em></span>:
+        </p>
+<p>
+          <span class="inlinemediaobject"><img src="../../../../equations/beta1.png"></span>
+        </p>
+<p>
+          See also <a class="link" href="../sf_beta/beta_function.html" title="Beta">beta</a>
+          for the full template (header only) version of this function.
+        </p>
+<pre class="programlisting"><span class="comment">// [5.2.1.4] (complete) elliptic integral of the first kind:
+</span><span class="keyword">double</span> <span class="identifier">comp_ellint_1</span><span class="special">(</span><span class="keyword">double</span> <span class="identifier">k</span><span class="special">);</span>
+<span class="keyword">float</span> <span class="identifier">comp_ellint_1f</span><span class="special">(</span><span class="keyword">float</span> <span class="identifier">k</span><span class="special">);</span>
+<span class="keyword">long</span> <span class="keyword">double</span> <span class="identifier">comp_ellint_1l</span><span class="special">(</span><span class="keyword">long</span> <span class="keyword">double</span> <span class="identifier">k</span><span class="special">);</span>
+</pre>
+<p>
+          Returns the complete elliptic integral of the first kind of <span class="emphasis"><em>k</em></span>:
+        </p>
+<p>
+          <span class="inlinemediaobject"><img src="../../../../equations/ellint6.png"></span>
+        </p>
+<p>
+          See also <a class="link" href="../ellint/ellint_1.html" title="Elliptic Integrals of the First Kind - Legendre Form">ellint_1</a>
+          for the full template (header only) version of this function.
+        </p>
+<pre class="programlisting"><span class="comment">// [5.2.1.5] (complete) elliptic integral of the second kind:
+</span><span class="keyword">double</span> <span class="identifier">comp_ellint_2</span><span class="special">(</span><span class="keyword">double</span> <span class="identifier">k</span><span class="special">);</span>
+<span class="keyword">float</span> <span class="identifier">comp_ellint_2f</span><span class="special">(</span><span class="keyword">float</span> <span class="identifier">k</span><span class="special">);</span>
+<span class="keyword">long</span> <span class="keyword">double</span> <span class="identifier">comp_ellint_2l</span><span class="special">(</span><span class="keyword">long</span> <span class="keyword">double</span> <span class="identifier">k</span><span class="special">);</span>
+</pre>
+<p>
+          Returns the complete elliptic integral of the second kind of <span class="emphasis"><em>k</em></span>:
+        </p>
+<p>
+          <span class="inlinemediaobject"><img src="../../../../equations/ellint7.png"></span>
+        </p>
+<p>
+          See also <a class="link" href="../ellint/ellint_2.html" title="Elliptic Integrals of the Second Kind - Legendre Form">ellint_2</a>
+          for the full template (header only) version of this function.
+        </p>
+<pre class="programlisting"><span class="comment">// [5.2.1.6] (complete) elliptic integral of the third kind:
+</span><span class="keyword">double</span> <span class="identifier">comp_ellint_3</span><span class="special">(</span><span class="keyword">double</span> <span class="identifier">k</span><span class="special">,</span> <span class="keyword">double</span> <span class="identifier">nu</span><span class="special">);</span>
+<span class="keyword">float</span> <span class="identifier">comp_ellint_3f</span><span class="special">(</span><span class="keyword">float</span> <span class="identifier">k</span><span class="special">,</span> <span class="keyword">float</span> <span class="identifier">nu</span><span class="special">);</span>
+<span class="keyword">long</span> <span class="keyword">double</span> <span class="identifier">comp_ellint_3l</span><span class="special">(</span><span class="keyword">long</span> <span class="keyword">double</span> <span class="identifier">k</span><span class="special">,</span> <span class="keyword">long</span> <span class="keyword">double</span> <span class="identifier">nu</span><span class="special">);</span>
+</pre>
+<p>
+          Returns the complete elliptic integral of the third kind of <span class="emphasis"><em>k</em></span>
+          and <span class="emphasis"><em>nu</em></span>:
+        </p>
+<p>
+          <span class="inlinemediaobject"><img src="../../../../equations/ellint8.png"></span>
+        </p>
+<p>
+          See also <a class="link" href="../ellint/ellint_3.html" title="Elliptic Integrals of the Third Kind - Legendre Form">ellint_3</a>
+          for the full template (header only) version of this function.
+        </p>
+<pre class="programlisting"><span class="comment">// [5.2.1.8] regular modified cylindrical Bessel functions:
+</span><span class="keyword">double</span> <span class="identifier">cyl_bessel_i</span><span class="special">(</span><span class="keyword">double</span> <span class="identifier">nu</span><span class="special">,</span> <span class="keyword">double</span> <span class="identifier">x</span><span class="special">);</span>
+<span class="keyword">float</span> <span class="identifier">cyl_bessel_if</span><span class="special">(</span><span class="keyword">float</span> <span class="identifier">nu</span><span class="special">,</span> <span class="keyword">float</span> <span class="identifier">x</span><span class="special">);</span>
+<span class="keyword">long</span> <span class="keyword">double</span> <span class="identifier">cyl_bessel_il</span><span class="special">(</span><span class="keyword">long</span> <span class="keyword">double</span> <span class="identifier">nu</span><span class="special">,</span> <span class="keyword">long</span> <span class="keyword">double</span> <span class="identifier">x</span><span class="special">);</span>
+</pre>
+<p>
+          Returns the modified bessel function of the first kind of <span class="emphasis"><em>nu</em></span>
+          and <span class="emphasis"><em>x</em></span>:
+        </p>
+<p>
+          <span class="inlinemediaobject"><img src="../../../../equations/mbessel2.png"></span>
+        </p>
+<p>
+          See also <a class="link" href="../bessel/mbessel.html" title="Modified Bessel Functions of the First and Second Kinds">cyl_bessel_i</a>
+          for the full template (header only) version of this function.
+        </p>
+<pre class="programlisting"><span class="comment">// [5.2.1.9] cylindrical Bessel functions (of the first kind):
+</span><span class="keyword">double</span> <span class="identifier">cyl_bessel_j</span><span class="special">(</span><span class="keyword">double</span> <span class="identifier">nu</span><span class="special">,</span> <span class="keyword">double</span> <span class="identifier">x</span><span class="special">);</span>
+<span class="keyword">float</span> <span class="identifier">cyl_bessel_jf</span><span class="special">(</span><span class="keyword">float</span> <span class="identifier">nu</span><span class="special">,</span> <span class="keyword">float</span> <span class="identifier">x</span><span class="special">);</span>
+<span class="keyword">long</span> <span class="keyword">double</span> <span class="identifier">cyl_bessel_jl</span><span class="special">(</span><span class="keyword">long</span> <span class="keyword">double</span> <span class="identifier">nu</span><span class="special">,</span> <span class="keyword">long</span> <span class="keyword">double</span> <span class="identifier">x</span><span class="special">);</span>
+</pre>
+<p>
+          Returns the bessel function of the first kind of <span class="emphasis"><em>nu</em></span>
+          and <span class="emphasis"><em>x</em></span>:
+        </p>
+<p>
+          <span class="inlinemediaobject"><img src="../../../../equations/bessel2.png"></span>
+        </p>
+<p>
+          See also <a class="link" href="../bessel/bessel.html" title="Bessel Functions of the First and Second Kinds">cyl_bessel_j</a>
+          for the full template (header only) version of this function.
+        </p>
+<pre class="programlisting"><span class="comment">// [5.2.1.10] irregular modified cylindrical Bessel functions:
+</span><span class="keyword">double</span> <span class="identifier">cyl_bessel_k</span><span class="special">(</span><span class="keyword">double</span> <span class="identifier">nu</span><span class="special">,</span> <span class="keyword">double</span> <span class="identifier">x</span><span class="special">);</span>
+<span class="keyword">float</span> <span class="identifier">cyl_bessel_kf</span><span class="special">(</span><span class="keyword">float</span> <span class="identifier">nu</span><span class="special">,</span> <span class="keyword">float</span> <span class="identifier">x</span><span class="special">);</span>
+<span class="keyword">long</span> <span class="keyword">double</span> <span class="identifier">cyl_bessel_kl</span><span class="special">(</span><span class="keyword">long</span> <span class="keyword">double</span> <span class="identifier">nu</span><span class="special">,</span> <span class="keyword">long</span> <span class="keyword">double</span> <span class="identifier">x</span><span class="special">);</span>
+</pre>
+<p>
+          Returns the modified bessel function of the second kind of <span class="emphasis"><em>nu</em></span>
+          and <span class="emphasis"><em>x</em></span>:
+        </p>
+<p>
+          <span class="inlinemediaobject"><img src="../../../../equations/mbessel3.png"></span>
+        </p>
+<p>
+          See also <a class="link" href="../bessel/mbessel.html" title="Modified Bessel Functions of the First and Second Kinds">cyl_bessel_k</a>
+          for the full template (header only) version of this function.
+        </p>
+<pre class="programlisting"><span class="comment">// [5.2.1.11] cylindrical Neumann functions;
+</span><span class="comment">// cylindrical Bessel functions (of the second kind):
+</span><span class="keyword">double</span> <span class="identifier">cyl_neumann</span><span class="special">(</span><span class="keyword">double</span> <span class="identifier">nu</span><span class="special">,</span> <span class="keyword">double</span> <span class="identifier">x</span><span class="special">);</span>
+<span class="keyword">float</span> <span class="identifier">cyl_neumannf</span><span class="special">(</span><span class="keyword">float</span> <span class="identifier">nu</span><span class="special">,</span> <span class="keyword">float</span> <span class="identifier">x</span><span class="special">);</span>
+<span class="keyword">long</span> <span class="keyword">double</span> <span class="identifier">cyl_neumannl</span><span class="special">(</span><span class="keyword">long</span> <span class="keyword">double</span> <span class="identifier">nu</span><span class="special">,</span> <span class="keyword">long</span> <span class="keyword">double</span> <span class="identifier">x</span><span class="special">);</span>
+</pre>
+<p>
+          Returns the bessel function of the second kind (Neumann function) of <span class="emphasis"><em>nu</em></span>
+          and <span class="emphasis"><em>x</em></span>:
+        </p>
+<p>
+          <span class="inlinemediaobject"><img src="../../../../equations/bessel3.png"></span>
+        </p>
+<p>
+          See also <a class="link" href="../bessel/bessel.html" title="Bessel Functions of the First and Second Kinds">cyl_neumann</a>
+          for the full template (header only) version of this function.
+        </p>
+<pre class="programlisting"><span class="comment">// [5.2.1.12] (incomplete) elliptic integral of the first kind:
+</span><span class="keyword">double</span> <span class="identifier">ellint_1</span><span class="special">(</span><span class="keyword">double</span> <span class="identifier">k</span><span class="special">,</span> <span class="keyword">double</span> <span class="identifier">phi</span><span class="special">);</span>
+<span class="keyword">float</span> <span class="identifier">ellint_1f</span><span class="special">(</span><span class="keyword">float</span> <span class="identifier">k</span><span class="special">,</span> <span class="keyword">float</span> <span class="identifier">phi</span><span class="special">);</span>
+<span class="keyword">long</span> <span class="keyword">double</span> <span class="identifier">ellint_1l</span><span class="special">(</span><span class="keyword">long</span> <span class="keyword">double</span> <span class="identifier">k</span><span class="special">,</span> <span class="keyword">long</span> <span class="keyword">double</span> <span class="identifier">phi</span><span class="special">);</span>
+</pre>
+<p>
+          Returns the incomplete elliptic integral of the first kind of <span class="emphasis"><em>k</em></span>
+          and <span class="emphasis"><em>phi</em></span>:
+        </p>
+<p>
+          <span class="inlinemediaobject"><img src="../../../../equations/ellint2.png"></span>
+        </p>
+<p>
+          See also <a class="link" href="../ellint/ellint_1.html" title="Elliptic Integrals of the First Kind - Legendre Form">ellint_1</a>
+          for the full template (header only) version of this function.
+        </p>
+<pre class="programlisting"><span class="comment">// [5.2.1.13] (incomplete) elliptic integral of the second kind:
+</span><span class="keyword">double</span> <span class="identifier">ellint_2</span><span class="special">(</span><span class="keyword">double</span> <span class="identifier">k</span><span class="special">,</span> <span class="keyword">double</span> <span class="identifier">phi</span><span class="special">);</span>
+<span class="keyword">float</span> <span class="identifier">ellint_2f</span><span class="special">(</span><span class="keyword">float</span> <span class="identifier">k</span><span class="special">,</span> <span class="keyword">float</span> <span class="identifier">phi</span><span class="special">);</span>
+<span class="keyword">long</span> <span class="keyword">double</span> <span class="identifier">ellint_2l</span><span class="special">(</span><span class="keyword">long</span> <span class="keyword">double</span> <span class="identifier">k</span><span class="special">,</span> <span class="keyword">long</span> <span class="keyword">double</span> <span class="identifier">phi</span><span class="special">);</span>
+</pre>
+<p>
+          Returns the incomplete elliptic integral of the second kind of <span class="emphasis"><em>k</em></span>
+          and <span class="emphasis"><em>phi</em></span>:
+        </p>
+<p>
+          <span class="inlinemediaobject"><img src="../../../../equations/ellint3.png"></span>
+        </p>
+<p>
+          See also <a class="link" href="../ellint/ellint_2.html" title="Elliptic Integrals of the Second Kind - Legendre Form">ellint_2</a>
+          for the full template (header only) version of this function.
+        </p>
+<pre class="programlisting"><span class="comment">// [5.2.1.14] (incomplete) elliptic integral of the third kind:
+</span><span class="keyword">double</span> <span class="identifier">ellint_3</span><span class="special">(</span><span class="keyword">double</span> <span class="identifier">k</span><span class="special">,</span> <span class="keyword">double</span> <span class="identifier">nu</span><span class="special">,</span> <span class="keyword">double</span> <span class="identifier">phi</span><span class="special">);</span>
+<span class="keyword">float</span> <span class="identifier">ellint_3f</span><span class="special">(</span><span class="keyword">float</span> <span class="identifier">k</span><span class="special">,</span> <span class="keyword">float</span> <span class="identifier">nu</span><span class="special">,</span> <span class="keyword">float</span> <span class="identifier">phi</span><span class="special">);</span>
+<span class="keyword">long</span> <span class="keyword">double</span> <span class="identifier">ellint_3l</span><span class="special">(</span><span class="keyword">long</span> <span class="keyword">double</span> <span class="identifier">k</span><span class="special">,</span> <span class="keyword">long</span> <span class="keyword">double</span> <span class="identifier">nu</span><span class="special">,</span> <span class="keyword">long</span> <span class="keyword">double</span> <span class="identifier">phi</span><span class="special">);</span>
+</pre>
+<p>
+          Returns the incomplete elliptic integral of the third kind of <span class="emphasis"><em>k</em></span>,
+          <span class="emphasis"><em>nu</em></span> and <span class="emphasis"><em>phi</em></span>:
+        </p>
+<p>
+          <span class="inlinemediaobject"><img src="../../../../equations/ellint4.png"></span>
+        </p>
+<p>
+          See also <a class="link" href="../ellint/ellint_3.html" title="Elliptic Integrals of the Third Kind - Legendre Form">ellint_3</a>
+          for the full template (header only) version of this function.
+        </p>
+<pre class="programlisting"><span class="comment">// [5.2.1.15] exponential integral:
+</span><span class="keyword">double</span> <span class="identifier">expint</span><span class="special">(</span><span class="keyword">double</span> <span class="identifier">x</span><span class="special">);</span>
+<span class="keyword">float</span> <span class="identifier">expintf</span><span class="special">(</span><span class="keyword">float</span> <span class="identifier">x</span><span class="special">);</span>
+<span class="keyword">long</span> <span class="keyword">double</span> <span class="identifier">expintl</span><span class="special">(</span><span class="keyword">long</span> <span class="keyword">double</span> <span class="identifier">x</span><span class="special">);</span>
+</pre>
+<p>
+          Returns the exponential integral Ei of <span class="emphasis"><em>x</em></span>:
+        </p>
+<p>
+          <span class="inlinemediaobject"><img src="../../../../equations/expint_i_1.png"></span>
+        </p>
+<p>
+          See also <a class="link" href="../expint/expint_i.html" title="Exponential Integral Ei">expint</a>
+          for the full template (header only) version of this function.
+        </p>
+<pre class="programlisting"><span class="comment">// [5.2.1.16] Hermite polynomials:
+</span><span class="keyword">double</span> <span class="identifier">hermite</span><span class="special">(</span><span class="keyword">unsigned</span> <span class="identifier">n</span><span class="special">,</span> <span class="keyword">double</span> <span class="identifier">x</span><span class="special">);</span>
+<span class="keyword">float</span> <span class="identifier">hermitef</span><span class="special">(</span><span class="keyword">unsigned</span> <span class="identifier">n</span><span class="special">,</span> <span class="keyword">float</span> <span class="identifier">x</span><span class="special">);</span>
+<span class="keyword">long</span> <span class="keyword">double</span> <span class="identifier">hermitel</span><span class="special">(</span><span class="keyword">unsigned</span> <span class="identifier">n</span><span class="special">,</span> <span class="keyword">long</span> <span class="keyword">double</span> <span class="identifier">x</span><span class="special">);</span>
+</pre>
+<p>
+          Returns the n'th Hermite polynomial of <span class="emphasis"><em>x</em></span>:
+        </p>
+<p>
+          <span class="inlinemediaobject"><img src="../../../../equations/hermite_0.png"></span>
+        </p>
+<p>
+          See also <a class="link" href="../sf_poly/hermite.html" title="Hermite Polynomials">hermite</a>
+          for the full template (header only) version of this function.
+        </p>
+<pre class="programlisting"><span class="comment">// [5.2.1.18] Laguerre polynomials:
+</span><span class="keyword">double</span> <span class="identifier">laguerre</span><span class="special">(</span><span class="keyword">unsigned</span> <span class="identifier">n</span><span class="special">,</span> <span class="keyword">double</span> <span class="identifier">x</span><span class="special">);</span>
+<span class="keyword">float</span> <span class="identifier">laguerref</span><span class="special">(</span><span class="keyword">unsigned</span> <span class="identifier">n</span><span class="special">,</span> <span class="keyword">float</span> <span class="identifier">x</span><span class="special">);</span>
+<span class="keyword">long</span> <span class="keyword">double</span> <span class="identifier">laguerrel</span><span class="special">(</span><span class="keyword">unsigned</span> <span class="identifier">n</span><span class="special">,</span> <span class="keyword">long</span> <span class="keyword">double</span> <span class="identifier">x</span><span class="special">);</span>
+</pre>
+<p>
+          Returns the n'th Laguerre polynomial of <span class="emphasis"><em>x</em></span>:
+        </p>
+<p>
+          <span class="inlinemediaobject"><img src="../../../../equations/laguerre_0.png"></span>
+        </p>
+<p>
+          See also <a class="link" href="../sf_poly/laguerre.html" title="Laguerre (and Associated) Polynomials">laguerre</a>
+          for the full template (header only) version of this function.
+        </p>
+<pre class="programlisting"><span class="comment">// [5.2.1.19] Legendre polynomials:
+</span><span class="keyword">double</span> <span class="identifier">legendre</span><span class="special">(</span><span class="keyword">unsigned</span> <span class="identifier">l</span><span class="special">,</span> <span class="keyword">double</span> <span class="identifier">x</span><span class="special">);</span>
+<span class="keyword">float</span> <span class="identifier">legendref</span><span class="special">(</span><span class="keyword">unsigned</span> <span class="identifier">l</span><span class="special">,</span> <span class="keyword">float</span> <span class="identifier">x</span><span class="special">);</span>
+<span class="keyword">long</span> <span class="keyword">double</span> <span class="identifier">legendrel</span><span class="special">(</span><span class="keyword">unsigned</span> <span class="identifier">l</span><span class="special">,</span> <span class="keyword">long</span> <span class="keyword">double</span> <span class="identifier">x</span><span class="special">);</span>
+</pre>
+<p>
+          Returns the l'th Legendre polynomial of <span class="emphasis"><em>x</em></span>:
+        </p>
+<p>
+          <span class="inlinemediaobject"><img src="../../../../equations/legendre_0.png"></span>
+        </p>
+<p>
+          See also <a class="link" href="../sf_poly/legendre.html" title="Legendre (and Associated) Polynomials">legendre_p</a>
+          for the full template (header only) version of this function.
+        </p>
+<pre class="programlisting"><span class="comment">// [5.2.1.20] Riemann zeta function:
+</span><span class="keyword">double</span> <span class="identifier">riemann_zeta</span><span class="special">(</span><span class="keyword">double</span><span class="special">);</span>
+<span class="keyword">float</span> <span class="identifier">riemann_zetaf</span><span class="special">(</span><span class="keyword">float</span><span class="special">);</span>
+<span class="keyword">long</span> <span class="keyword">double</span> <span class="identifier">riemann_zetal</span><span class="special">(</span><span class="keyword">long</span> <span class="keyword">double</span><span class="special">);</span>
+</pre>
+<p>
+          Returns the Riemann Zeta function of <span class="emphasis"><em>x</em></span>:
+        </p>
+<p>
+          <span class="inlinemediaobject"><img src="../../../../equations/zeta1.png"></span>
+        </p>
+<p>
+          See also <a class="link" href="../zetas/zeta.html" title="Riemann Zeta Function">zeta</a> for
+          the full template (header only) version of this function.
+        </p>
+<pre class="programlisting"><span class="comment">// [5.2.1.21] spherical Bessel functions (of the first kind):
+</span><span class="keyword">double</span> <span class="identifier">sph_bessel</span><span class="special">(</span><span class="keyword">unsigned</span> <span class="identifier">n</span><span class="special">,</span> <span class="keyword">double</span> <span class="identifier">x</span><span class="special">);</span>
+<span class="keyword">float</span> <span class="identifier">sph_besself</span><span class="special">(</span><span class="keyword">unsigned</span> <span class="identifier">n</span><span class="special">,</span> <span class="keyword">float</span> <span class="identifier">x</span><span class="special">);</span>
+<span class="keyword">long</span> <span class="keyword">double</span> <span class="identifier">sph_bessell</span><span class="special">(</span><span class="keyword">unsigned</span> <span class="identifier">n</span><span class="special">,</span> <span class="keyword">long</span> <span class="keyword">double</span> <span class="identifier">x</span><span class="special">);</span>
+</pre>
+<p>
+          Returns the spherical Bessel function of the first kind of <span class="emphasis"><em>x</em></span>
+          j<sub>n</sub>(x):
+        </p>
+<p>
+          <span class="inlinemediaobject"><img src="../../../../equations/sbessel2.png"></span>
+        </p>
+<p>
+          See also <a class="link" href="../bessel/sph_bessel.html" title="Spherical Bessel Functions of the First and Second Kinds">sph_bessel</a>
+          for the full template (header only) version of this function.
+        </p>
+<pre class="programlisting"><span class="comment">// [5.2.1.22] spherical associated Legendre functions:
+</span><span class="keyword">double</span> <span class="identifier">sph_legendre</span><span class="special">(</span><span class="keyword">unsigned</span> <span class="identifier">l</span><span class="special">,</span> <span class="keyword">unsigned</span> <span class="identifier">m</span><span class="special">,</span> <span class="keyword">double</span> <span class="identifier">theta</span><span class="special">);</span>
+<span class="keyword">float</span> <span class="identifier">sph_legendref</span><span class="special">(</span><span class="keyword">unsigned</span> <span class="identifier">l</span><span class="special">,</span> <span class="keyword">unsigned</span> <span class="identifier">m</span><span class="special">,</span> <span class="keyword">float</span> <span class="identifier">theta</span><span class="special">);</span>
+<span class="keyword">long</span> <span class="keyword">double</span> <span class="identifier">sph_legendrel</span><span class="special">(</span><span class="keyword">unsigned</span> <span class="identifier">l</span><span class="special">,</span> <span class="keyword">unsigned</span> <span class="identifier">m</span><span class="special">,</span> <span class="keyword">long</span> <span class="keyword">double</span> <span class="identifier">theta</span><span class="special">);</span>
+</pre>
+<p>
+          Returns the spherical associated Legendre function of <span class="emphasis"><em>l</em></span>,
+          <span class="emphasis"><em>m</em></span> and <span class="emphasis"><em>theta</em></span>:
+        </p>
+<p>
+          <span class="inlinemediaobject"><img src="../../../../equations/spherical_3.png"></span>
+        </p>
+<p>
+          See also <a class="link" href="../sf_poly/sph_harm.html" title="Spherical Harmonics">spherical_harmonic</a>
+          for the full template (header only) version of this function.
+        </p>
+<pre class="programlisting"><span class="comment">// [5.2.1.23] spherical Neumann functions;
+</span><span class="comment">// spherical Bessel functions (of the second kind):
+</span><span class="keyword">double</span> <span class="identifier">sph_neumann</span><span class="special">(</span><span class="keyword">unsigned</span> <span class="identifier">n</span><span class="special">,</span> <span class="keyword">double</span> <span class="identifier">x</span><span class="special">);</span>
+<span class="keyword">float</span> <span class="identifier">sph_neumannf</span><span class="special">(</span><span class="keyword">unsigned</span> <span class="identifier">n</span><span class="special">,</span> <span class="keyword">float</span> <span class="identifier">x</span><span class="special">);</span>
+<span class="keyword">long</span> <span class="keyword">double</span> <span class="identifier">sph_neumannl</span><span class="special">(</span><span class="keyword">unsigned</span> <span class="identifier">n</span><span class="special">,</span> <span class="keyword">long</span> <span class="keyword">double</span> <span class="identifier">x</span><span class="special">);</span>
+</pre>
+<p>
+          Returns the spherical Neumann function of <span class="emphasis"><em>x</em></span> y<sub>n</sub>(x):
+        </p>
+<p>
+          <span class="inlinemediaobject"><img src="../../../../equations/sbessel2.png"></span>
+        </p>
+<p>
+          See also <a class="link" href="../bessel/sph_bessel.html" title="Spherical Bessel Functions of the First and Second Kinds">sph_bessel</a>
+          for the full template (header only) version of this function.
+        </p>
+<a name="math_toolkit.special.extern_c.tr1_ref.currently_unsupported_tr1_functions"></a><h5>
+<a name="id820697"></a>
+          <a class="link" href="tr1_ref.html#math_toolkit.special.extern_c.tr1_ref.currently_unsupported_tr1_functions">Currently
+          Unsupported TR1 Functions</a>
+        </h5>
+<pre class="programlisting"><span class="comment">// [5.2.1.7] confluent hypergeometric functions:
+</span><span class="keyword">double</span> <span class="identifier">conf_hyperg</span><span class="special">(</span><span class="keyword">double</span> <span class="identifier">a</span><span class="special">,</span> <span class="keyword">double</span> <span class="identifier">c</span><span class="special">,</span> <span class="keyword">double</span> <span class="identifier">x</span><span class="special">);</span>
+<span class="keyword">float</span> <span class="identifier">conf_hypergf</span><span class="special">(</span><span class="keyword">float</span> <span class="identifier">a</span><span class="special">,</span> <span class="keyword">float</span> <span class="identifier">c</span><span class="special">,</span> <span class="keyword">float</span> <span class="identifier">x</span><span class="special">);</span>
+<span class="keyword">long</span> <span class="keyword">double</span> <span class="identifier">conf_hypergl</span><span class="special">(</span><span class="keyword">long</span> <span class="keyword">double</span> <span class="identifier">a</span><span class="special">,</span> <span class="keyword">long</span> <span class="keyword">double</span> <span class="identifier">c</span><span class="special">,</span> <span class="keyword">long</span> <span class="keyword">double</span> <span class="identifier">x</span><span class="special">);</span>
+
+<span class="comment">// [5.2.1.17] hypergeometric functions:
+</span><span class="keyword">double</span> <span class="identifier">hyperg</span><span class="special">(</span><span class="keyword">double</span> <span class="identifier">a</span><span class="special">,</span> <span class="keyword">double</span> <span class="identifier">b</span><span class="special">,</span> <span class="keyword">double</span> <span class="identifier">c</span><span class="special">,</span> <span class="keyword">double</span> <span class="identifier">x</span><span class="special">);</span>
+<span class="keyword">float</span> <span class="identifier">hypergf</span><span class="special">(</span><span class="keyword">float</span> <span class="identifier">a</span><span class="special">,</span> <span class="keyword">float</span> <span class="identifier">b</span><span class="special">,</span> <span class="keyword">float</span> <span class="identifier">c</span><span class="special">,</span> <span class="keyword">float</span> <span class="identifier">x</span><span class="special">);</span>
+<span class="keyword">long</span> <span class="keyword">double</span> <span class="identifier">hypergl</span><span class="special">(</span><span class="keyword">long</span> <span class="keyword">double</span> <span class="identifier">a</span><span class="special">,</span> <span class="keyword">long</span> <span class="keyword">double</span> <span class="identifier">b</span><span class="special">,</span> <span class="keyword">long</span> <span class="keyword">double</span> <span class="identifier">c</span><span class="special">,</span>
+<span class="keyword">long</span> <span class="keyword">double</span> <span class="identifier">x</span><span class="special">);</span>
+</pre>
+<div class="note"><table border="0" summary="Note">
+<tr>
+<td rowspan="2" align="center" valign="top" width="25"><img alt="[Note]" src="../../../../../doc/html/images/note.png"></td>
+<th align="left">Note</th>
+</tr>
+<tr><td align="left" valign="top"><p>
+            Thes two functions are not implemented as they are not believed to be
+            numerically stable.
+          </p></td></tr>
+</table></div>
+</div>
+<table xmlns:rev="http://www.cs.rpi.edu/~gregod/boost/tools/doc/revision" width="100%"><tr>
+<td align="left"></td>
+<td align="right"><div class="copyright-footer">Copyright © 2006 , 2007, 2008 John Maddock, Paul A. Bristow, Hubert
+      Holin, Xiaogang Zhang, Bruno Lalande and Gautam Sewani<p>
+        Distributed under the Boost Software License, Version 1.0. (See accompanying
+        file LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_0.txt)
+      </p>
+</div></td>
+</tr></table>
+<hr>
+<div class="spirit-nav">
+<a accesskey="p" href="c99.html"><img src="../../../../../doc/html/images/prev.png" alt="Prev"></a><a accesskey="u" href="../extern_c.html"><img src="../../../../../doc/html/images/up.png" alt="Up"></a><a accesskey="h" href="../../../index.html"><img src="../../../../../doc/html/images/home.png" alt="Home"></a><a accesskey="n" href="../../toolkit.html"><img src="../../../../../doc/html/images/next.png" alt="Next"></a>
+</div>
+</body>
+</html>

Added: sandbox/tools/auto_index/example/math/doc/sf_and_dist/html/math_toolkit/special/factorials.html
==============================================================================
--- (empty file)
+++ sandbox/tools/auto_index/example/math/doc/sf_and_dist/html/math_toolkit/special/factorials.html	2008-11-28 05:25:28 EST (Fri, 28 Nov 2008)
@@ -0,0 +1,56 @@
+<html>
+<head>
+<meta http-equiv="Content-Type" content="text/html; charset=ISO-8859-1">
+<title>Factorials and Binomial Coefficients</title>
+<link rel="stylesheet" href="../../boostbook.css" type="text/css">
+<meta name="generator" content="DocBook XSL Stylesheets Vsnapshot_8125">
+<link rel="home" href="../../index.html" title="Math Toolkit">
+<link rel="up" href="../special.html" title="Special Functions">
+<link rel="prev" href="sf_gamma/gamma_derivatives.html" title="Derivative of the Incomplete Gamma Function">
+<link rel="next" href="factorials/sf_factorial.html" title="Factorial">
+</head>
+<body bgcolor="white" text="black" link="#0000FF" vlink="#840084" alink="#0000FF">
+<table cellpadding="2" width="100%"><tr>
+<td valign="top"><img alt="Boost C++ Libraries" width="277" height="86" src="../../../../boost.png"></td>
+<td align="center">Home</td>
+<td align="center">Libraries</td>
+<td align="center">People</td>
+<td align="center">FAQ</td>
+<td align="center">More</td>
+</tr></table>
+<hr>
+<div class="spirit-nav">
+<a accesskey="p" href="sf_gamma/gamma_derivatives.html"><img src="../../../../doc/html/images/prev.png" alt="Prev"></a><a accesskey="u" href="../special.html"><img src="../../../../doc/html/images/up.png" alt="Up"></a><a accesskey="h" href="../../index.html"><img src="../../../../doc/html/images/home.png" alt="Home"></a><a accesskey="n" href="factorials/sf_factorial.html"><img src="../../../../doc/html/images/next.png" alt="Next"></a>
+</div>
+<div class="section" lang="en">
+<div class="titlepage"><div><div><h3 class="title">
+<a name="math_toolkit.special.factorials"></a><a class="link" href="factorials.html" title="Factorials and Binomial Coefficients"> Factorials and Binomial
+      Coefficients</a>
+</h3></div></div></div>
+<div class="toc"><dl>
+<dt><span class="section"> Factorial</span></dt>
+<dt><span class="section"><a href="factorials/sf_double_factorial.html">
+        Double Factorial</a></span></dt>
+<dt><span class="section"><a href="factorials/sf_rising_factorial.html">
+        Rising Factorial</a></span></dt>
+<dt><span class="section"><a href="factorials/sf_falling_factorial.html">
+        Falling Factorial</a></span></dt>
+<dt><span class="section"><a href="factorials/sf_binomial.html"> Binomial
+        Coefficients</a></span></dt>
+</dl></div>
+</div>
+<table xmlns:rev="http://www.cs.rpi.edu/~gregod/boost/tools/doc/revision" width="100%"><tr>
+<td align="left"></td>
+<td align="right"><div class="copyright-footer">Copyright © 2006 , 2007, 2008 John Maddock, Paul A. Bristow, Hubert
+      Holin, Xiaogang Zhang, Bruno Lalande and Gautam Sewani<p>
+        Distributed under the Boost Software License, Version 1.0. (See accompanying
+        file LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_0.txt)
+      </p>
+</div></td>
+</tr></table>
+<hr>
+<div class="spirit-nav">
+<a accesskey="p" href="sf_gamma/gamma_derivatives.html"><img src="../../../../doc/html/images/prev.png" alt="Prev"></a><a accesskey="u" href="../special.html"><img src="../../../../doc/html/images/up.png" alt="Up"></a><a accesskey="h" href="../../index.html"><img src="../../../../doc/html/images/home.png" alt="Home"></a><a accesskey="n" href="factorials/sf_factorial.html"><img src="../../../../doc/html/images/next.png" alt="Next"></a>
+</div>
+</body>
+</html>

Added: sandbox/tools/auto_index/example/math/doc/sf_and_dist/html/math_toolkit/special/factorials/sf_binomial.html
==============================================================================
--- (empty file)
+++ sandbox/tools/auto_index/example/math/doc/sf_and_dist/html/math_toolkit/special/factorials/sf_binomial.html	2008-11-28 05:25:28 EST (Fri, 28 Nov 2008)
@@ -0,0 +1,123 @@
+<html>
+<head>
+<meta http-equiv="Content-Type" content="text/html; charset=ISO-8859-1">
+<title>Binomial Coefficients</title>
+<link rel="stylesheet" href="../../../boostbook.css" type="text/css">
+<meta name="generator" content="DocBook XSL Stylesheets Vsnapshot_8125">
+<link rel="home" href="../../../index.html" title="Math Toolkit">
+<link rel="up" href="../factorials.html" title="Factorials and Binomial Coefficients">
+<link rel="prev" href="sf_falling_factorial.html" title="Falling Factorial">
+<link rel="next" href="../sf_beta.html" title="Beta Functions">
+</head>
+<body bgcolor="white" text="black" link="#0000FF" vlink="#840084" alink="#0000FF">
+<table cellpadding="2" width="100%"><tr>
+<td valign="top"><img alt="Boost C++ Libraries" width="277" height="86" src="../../../../../boost.png"></td>
+<td align="center">Home</td>
+<td align="center">Libraries</td>
+<td align="center">People</td>
+<td align="center">FAQ</td>
+<td align="center">More</td>
+</tr></table>
+<hr>
+<div class="spirit-nav">
+<a accesskey="p" href="sf_falling_factorial.html"><img src="../../../../../doc/html/images/prev.png" alt="Prev"></a><a accesskey="u" href="../factorials.html"><img src="../../../../../doc/html/images/up.png" alt="Up"></a><a accesskey="h" href="../../../index.html"><img src="../../../../../doc/html/images/home.png" alt="Home"></a><a accesskey="n" href="../sf_beta.html"><img src="../../../../../doc/html/images/next.png" alt="Next"></a>
+</div>
+<div class="section" lang="en">
+<div class="titlepage"><div><div><h4 class="title">
+<a name="math_toolkit.special.factorials.sf_binomial"></a><a class="link" href="sf_binomial.html" title="Binomial Coefficients"> Binomial
+        Coefficients</a>
+</h4></div></div></div>
+<p>
+          
+</p>
+<pre class="programlisting"><span class="preprocessor">#include</span> <span class="special">&lt;</span><span class="identifier">boost</span><span class="special">/</span><span class="identifier">math</span><span class="special">/</span><span class="identifier">special_functions</span><span class="special">/</span><span class="identifier">binomial</span><span class="special">.</span><span class="identifier">hpp</span><span class="special">&gt;</span>
+</pre>
+<p>
+        </p>
+<pre class="programlisting"><span class="keyword">namespace</span> <span class="identifier">boost</span><span class="special">{</span> <span class="keyword">namespace</span> <span class="identifier">math</span><span class="special">{</span>
+
+<span class="keyword">template</span> <span class="special">&lt;</span><span class="keyword">class</span> <span class="identifier">T</span><span class="special">&gt;</span>
+<span class="identifier">T</span> <span class="identifier">binomial_coefficient</span><span class="special">(</span><span class="keyword">unsigned</span> <span class="identifier">n</span><span class="special">,</span> <span class="keyword">unsigned</span> <span class="identifier">k</span><span class="special">);</span>
+
+<span class="keyword">template</span> <span class="special">&lt;</span><span class="keyword">class</span> <span class="identifier">T</span><span class="special">,</span> <span class="keyword">class</span> <a class="link" href="../../policy.html" title="Policies">Policy</a><span class="special">&gt;</span>
+<span class="identifier">T</span> <span class="identifier">binomial_coefficient</span><span class="special">(</span><span class="keyword">unsigned</span> <span class="identifier">n</span><span class="special">,</span> <span class="keyword">unsigned</span> <span class="identifier">k</span><span class="special">,</span> <span class="keyword">const</span> <a class="link" href="../../policy.html" title="Policies">Policy</a><span class="special">&amp;);</span>
+
+<span class="special">}}</span> <span class="comment">// namespaces
+</span></pre>
+<p>
+          Returns the binomial coefficient: <sub>n</sub>C<sub>k</sub>.
+        </p>
+<p>
+          Requires k &lt;= n.
+        </p>
+<p>
+          </p>
+<p>
+            The final <a class="link" href="../../policy.html" title="Policies">Policy</a> argument
+            is optional and can be used to control the behaviour of the function:
+            how it handles errors, what level of precision to use etc. Refer to the
+            <a class="link" href="../../policy.html" title="Policies">policy documentation for more details</a>.
+          </p>
+<p>
+        </p>
+<p>
+          May return the result of <a class="link" href="../../main_overview/error_handling.html#overflow_error">overflow_error</a>
+          if the result is too large to represent in type T.
+        </p>
+<a name="math_toolkit.special.factorials.sf_binomial.accuracy"></a><h5>
+<a name="id718358"></a>
+          <a class="link" href="sf_binomial.html#math_toolkit.special.factorials.sf_binomial.accuracy">Accuracy</a>
+        </h5>
+<p>
+          The accuracy will be the same as for the factorials for small arguments
+          (i.e. no more than one or two epsilon), and the <a class="link" href="../sf_beta/beta_function.html" title="Beta">beta</a>
+          function for larger arguments.
+        </p>
+<a name="math_toolkit.special.factorials.sf_binomial.testing"></a><h5>
+<a name="id718401"></a>
+          <a class="link" href="sf_binomial.html#math_toolkit.special.factorials.sf_binomial.testing">Testing</a>
+        </h5>
+<p>
+          The spot tests for the binomial coefficients use data generated by functions.wolfram.com.
+        </p>
+<a name="math_toolkit.special.factorials.sf_binomial.implementation"></a><h5>
+<a name="id718432"></a>
+          <a class="link" href="sf_binomial.html#math_toolkit.special.factorials.sf_binomial.implementation">Implementation</a>
+        </h5>
+<p>
+          Binomial coefficients are calculated using table lookup of factorials where
+          possible using:
+        </p>
+<p>
+          <sub>n</sub>C<sub>k</sub> = n! / (k!(n-k)!)
+        </p>
+<p>
+          Otherwise it is implemented in terms of the beta function using the relations:
+        </p>
+<p>
+          <sub>n</sub>C<sub>k</sub> = 1 / (k * <a class="link" href="../sf_beta/beta_function.html" title="Beta">beta</a>(k,
+          n-k+1))
+        </p>
+<p>
+          and
+        </p>
+<p>
+          <sub>n</sub>C<sub>k</sub> = 1 / ((n-k) * <a class="link" href="../sf_beta/beta_function.html" title="Beta">beta</a>(k+1,
+          n-k))
+        </p>
+</div>
+<table xmlns:rev="http://www.cs.rpi.edu/~gregod/boost/tools/doc/revision" width="100%"><tr>
+<td align="left"></td>
+<td align="right"><div class="copyright-footer">Copyright © 2006 , 2007, 2008 John Maddock, Paul A. Bristow, Hubert
+      Holin, Xiaogang Zhang, Bruno Lalande and Gautam Sewani<p>
+        Distributed under the Boost Software License, Version 1.0. (See accompanying
+        file LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_0.txt)
+      </p>
+</div></td>
+</tr></table>
+<hr>
+<div class="spirit-nav">
+<a accesskey="p" href="sf_falling_factorial.html"><img src="../../../../../doc/html/images/prev.png" alt="Prev"></a><a accesskey="u" href="../factorials.html"><img src="../../../../../doc/html/images/up.png" alt="Up"></a><a accesskey="h" href="../../../index.html"><img src="../../../../../doc/html/images/home.png" alt="Home"></a><a accesskey="n" href="../sf_beta.html"><img src="../../../../../doc/html/images/next.png" alt="Next"></a>
+</div>
+</body>
+</html>

Added: sandbox/tools/auto_index/example/math/doc/sf_and_dist/html/math_toolkit/special/factorials/sf_double_factorial.html
==============================================================================
--- (empty file)
+++ sandbox/tools/auto_index/example/math/doc/sf_and_dist/html/math_toolkit/special/factorials/sf_double_factorial.html	2008-11-28 05:25:28 EST (Fri, 28 Nov 2008)
@@ -0,0 +1,116 @@
+<html>
+<head>
+<meta http-equiv="Content-Type" content="text/html; charset=ISO-8859-1">
+<title>Double Factorial</title>
+<link rel="stylesheet" href="../../../boostbook.css" type="text/css">
+<meta name="generator" content="DocBook XSL Stylesheets Vsnapshot_8125">
+<link rel="home" href="../../../index.html" title="Math Toolkit">
+<link rel="up" href="../factorials.html" title="Factorials and Binomial Coefficients">
+<link rel="prev" href="sf_factorial.html" title="Factorial">
+<link rel="next" href="sf_rising_factorial.html" title="Rising Factorial">
+</head>
+<body bgcolor="white" text="black" link="#0000FF" vlink="#840084" alink="#0000FF">
+<table cellpadding="2" width="100%"><tr>
+<td valign="top"><img alt="Boost C++ Libraries" width="277" height="86" src="../../../../../boost.png"></td>
+<td align="center">Home</td>
+<td align="center">Libraries</td>
+<td align="center">People</td>
+<td align="center">FAQ</td>
+<td align="center">More</td>
+</tr></table>
+<hr>
+<div class="spirit-nav">
+<a accesskey="p" href="sf_factorial.html"><img src="../../../../../doc/html/images/prev.png" alt="Prev"></a><a accesskey="u" href="../factorials.html"><img src="../../../../../doc/html/images/up.png" alt="Up"></a><a accesskey="h" href="../../../index.html"><img src="../../../../../doc/html/images/home.png" alt="Home"></a><a accesskey="n" href="sf_rising_factorial.html"><img src="../../../../../doc/html/images/next.png" alt="Next"></a>
+</div>
+<div class="section" lang="en">
+<div class="titlepage"><div><div><h4 class="title">
+<a name="math_toolkit.special.factorials.sf_double_factorial"></a><a class="link" href="sf_double_factorial.html" title="Double Factorial">
+        Double Factorial</a>
+</h4></div></div></div>
+<p>
+          
+</p>
+<pre class="programlisting"><span class="preprocessor">#include</span> <span class="special">&lt;</span><span class="identifier">boost</span><span class="special">/</span><span class="identifier">math</span><span class="special">/</span><span class="identifier">special_functions</span><span class="special">/</span><span class="identifier">factorials</span><span class="special">.</span><span class="identifier">hpp</span><span class="special">&gt;</span>
+</pre>
+<p>
+        </p>
+<pre class="programlisting"><span class="keyword">namespace</span> <span class="identifier">boost</span><span class="special">{</span> <span class="keyword">namespace</span> <span class="identifier">math</span><span class="special">{</span>
+
+<span class="keyword">template</span> <span class="special">&lt;</span><span class="keyword">class</span> <span class="identifier">T</span><span class="special">&gt;</span>
+<span class="identifier">T</span> <span class="identifier">double_factorial</span><span class="special">(</span><span class="keyword">unsigned</span> <span class="identifier">i</span><span class="special">);</span>
+
+<span class="keyword">template</span> <span class="special">&lt;</span><span class="keyword">class</span> <span class="identifier">T</span><span class="special">,</span> <span class="keyword">class</span> <a class="link" href="../../policy.html" title="Policies">Policy</a><span class="special">&gt;</span>
+<span class="identifier">T</span> <span class="identifier">double_factorial</span><span class="special">(</span><span class="keyword">unsigned</span> <span class="identifier">i</span><span class="special">,</span> <span class="keyword">const</span> <a class="link" href="../../policy.html" title="Policies">Policy</a><span class="special">&amp;);</span>
+
+<span class="special">}}</span> <span class="comment">// namespaces
+</span></pre>
+<p>
+          Returns <code class="literal">i!!</code>.
+        </p>
+<p>
+          </p>
+<p>
+            The final <a class="link" href="../../policy.html" title="Policies">Policy</a> argument
+            is optional and can be used to control the behaviour of the function:
+            how it handles errors, what level of precision to use etc. Refer to the
+            <a class="link" href="../../policy.html" title="Policies">policy documentation for more details</a>.
+          </p>
+<p>
+        </p>
+<p>
+          May return the result of <a class="link" href="../../main_overview/error_handling.html#overflow_error">overflow_error</a>
+          if the result is too large to represent in type T. The implementation is
+          designed to be optimised for small <span class="emphasis"><em>i</em></span> where table lookup
+          of i! is possible.
+        </p>
+<a name="math_toolkit.special.factorials.sf_double_factorial.accuracy"></a><h5>
+<a name="id716631"></a>
+          <a class="link" href="sf_double_factorial.html#math_toolkit.special.factorials.sf_double_factorial.accuracy">Accuracy</a>
+        </h5>
+<p>
+          The implementation uses a trivial adaptation of the factorial function,
+          so error rates should be no more than a couple of epsilon higher.
+        </p>
+<a name="math_toolkit.special.factorials.sf_double_factorial.testing"></a><h5>
+<a name="id716665"></a>
+          <a class="link" href="sf_double_factorial.html#math_toolkit.special.factorials.sf_double_factorial.testing">Testing</a>
+        </h5>
+<p>
+          The spot tests for the double factorial use data generated by functions.wolfram.com.
+        </p>
+<a name="math_toolkit.special.factorials.sf_double_factorial.implementation"></a><h5>
+<a name="id716698"></a>
+          <a class="link" href="sf_double_factorial.html#math_toolkit.special.factorials.sf_double_factorial.implementation">Implementation</a>
+        </h5>
+<p>
+          The double factorial is implemented in terms of the factorial and gamma
+          functions using the relations:
+        </p>
+<p>
+          (2n)!! = 2<sup>n </sup> * n!
+        </p>
+<p>
+          (2n+1)!! = (2n+1)! / (2<sup>n </sup> n!)
+        </p>
+<p>
+          and
+        </p>
+<p>
+          (2n-1)!! = &#915;((2n+1)/2) * 2<sup>n </sup> / sqrt(pi)
+        </p>
+</div>
+<table xmlns:rev="http://www.cs.rpi.edu/~gregod/boost/tools/doc/revision" width="100%"><tr>
+<td align="left"></td>
+<td align="right"><div class="copyright-footer">Copyright © 2006 , 2007, 2008 John Maddock, Paul A. Bristow, Hubert
+      Holin, Xiaogang Zhang, Bruno Lalande and Gautam Sewani<p>
+        Distributed under the Boost Software License, Version 1.0. (See accompanying
+        file LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_0.txt)
+      </p>
+</div></td>
+</tr></table>
+<hr>
+<div class="spirit-nav">
+<a accesskey="p" href="sf_factorial.html"><img src="../../../../../doc/html/images/prev.png" alt="Prev"></a><a accesskey="u" href="../factorials.html"><img src="../../../../../doc/html/images/up.png" alt="Up"></a><a accesskey="h" href="../../../index.html"><img src="../../../../../doc/html/images/home.png" alt="Home"></a><a accesskey="n" href="sf_rising_factorial.html"><img src="../../../../../doc/html/images/next.png" alt="Next"></a>
+</div>
+</body>
+</html>

Added: sandbox/tools/auto_index/example/math/doc/sf_and_dist/html/math_toolkit/special/factorials/sf_factorial.html
==============================================================================
--- (empty file)
+++ sandbox/tools/auto_index/example/math/doc/sf_and_dist/html/math_toolkit/special/factorials/sf_factorial.html	2008-11-28 05:25:28 EST (Fri, 28 Nov 2008)
@@ -0,0 +1,156 @@
+<html>
+<head>
+<meta http-equiv="Content-Type" content="text/html; charset=ISO-8859-1">
+<title>Factorial</title>
+<link rel="stylesheet" href="../../../boostbook.css" type="text/css">
+<meta name="generator" content="DocBook XSL Stylesheets Vsnapshot_8125">
+<link rel="home" href="../../../index.html" title="Math Toolkit">
+<link rel="up" href="../factorials.html" title="Factorials and Binomial Coefficients">
+<link rel="prev" href="../factorials.html" title="Factorials and Binomial Coefficients">
+<link rel="next" href="sf_double_factorial.html" title="Double Factorial">
+</head>
+<body bgcolor="white" text="black" link="#0000FF" vlink="#840084" alink="#0000FF">
+<table cellpadding="2" width="100%"><tr>
+<td valign="top"><img alt="Boost C++ Libraries" width="277" height="86" src="../../../../../boost.png"></td>
+<td align="center">Home</td>
+<td align="center">Libraries</td>
+<td align="center">People</td>
+<td align="center">FAQ</td>
+<td align="center">More</td>
+</tr></table>
+<hr>
+<div class="spirit-nav">
+<a accesskey="p" href="../factorials.html"><img src="../../../../../doc/html/images/prev.png" alt="Prev"></a><a accesskey="u" href="../factorials.html"><img src="../../../../../doc/html/images/up.png" alt="Up"></a><a accesskey="h" href="../../../index.html"><img src="../../../../../doc/html/images/home.png" alt="Home"></a><a accesskey="n" href="sf_double_factorial.html"><img src="../../../../../doc/html/images/next.png" alt="Next"></a>
+</div>
+<div class="section" lang="en">
+<div class="titlepage"><div><div><h4 class="title">
+<a name="math_toolkit.special.factorials.sf_factorial"></a><a class="link" href="sf_factorial.html" title="Factorial"> Factorial</a>
+</h4></div></div></div>
+<a name="math_toolkit.special.factorials.sf_factorial.synopsis"></a><h5>
+<a name="id715140"></a>
+          <a class="link" href="sf_factorial.html#math_toolkit.special.factorials.sf_factorial.synopsis">Synopsis</a>
+        </h5>
+<p>
+          
+</p>
+<pre class="programlisting"><span class="preprocessor">#include</span> <span class="special">&lt;</span><span class="identifier">boost</span><span class="special">/</span><span class="identifier">math</span><span class="special">/</span><span class="identifier">special_functions</span><span class="special">/</span><span class="identifier">factorials</span><span class="special">.</span><span class="identifier">hpp</span><span class="special">&gt;</span>
+</pre>
+<p>
+        </p>
+<pre class="programlisting"><span class="keyword">namespace</span> <span class="identifier">boost</span><span class="special">{</span> <span class="keyword">namespace</span> <span class="identifier">math</span><span class="special">{</span>
+
+<span class="keyword">template</span> <span class="special">&lt;</span><span class="keyword">class</span> <span class="identifier">T</span><span class="special">&gt;</span>
+<span class="identifier">T</span> <span class="identifier">factorial</span><span class="special">(</span><span class="keyword">unsigned</span> <span class="identifier">i</span><span class="special">);</span>
+
+<span class="keyword">template</span> <span class="special">&lt;</span><span class="keyword">class</span> <span class="identifier">T</span><span class="special">,</span> <span class="keyword">class</span> <a class="link" href="../../policy.html" title="Policies">Policy</a><span class="special">&gt;</span>
+<span class="identifier">T</span> <span class="identifier">factorial</span><span class="special">(</span><span class="keyword">unsigned</span> <span class="identifier">i</span><span class="special">,</span> <span class="keyword">const</span> <a class="link" href="../../policy.html" title="Policies">Policy</a><span class="special">&amp;);</span>
+
+<span class="keyword">template</span> <span class="special">&lt;</span><span class="keyword">class</span> <span class="identifier">T</span><span class="special">&gt;</span>
+<span class="identifier">T</span> <span class="identifier">unchecked_factorial</span><span class="special">(</span><span class="keyword">unsigned</span> <span class="identifier">i</span><span class="special">);</span>
+
+<span class="keyword">template</span> <span class="special">&lt;</span><span class="keyword">class</span> <span class="identifier">T</span><span class="special">&gt;</span>
+<span class="keyword">struct</span> <span class="identifier">max_factorial</span><span class="special">;</span>
+
+<span class="special">}}</span> <span class="comment">// namespaces
+</span></pre>
+<a name="math_toolkit.special.factorials.sf_factorial.description"></a><h5>
+<a name="id715566"></a>
+          <a class="link" href="sf_factorial.html#math_toolkit.special.factorials.sf_factorial.description">Description</a>
+        </h5>
+<pre class="programlisting"><span class="keyword">template</span> <span class="special">&lt;</span><span class="keyword">class</span> <span class="identifier">T</span><span class="special">&gt;</span>
+<span class="identifier">T</span> <span class="identifier">factorial</span><span class="special">(</span><span class="keyword">unsigned</span> <span class="identifier">i</span><span class="special">);</span>
+
+<span class="keyword">template</span> <span class="special">&lt;</span><span class="keyword">class</span> <span class="identifier">T</span><span class="special">,</span> <span class="keyword">class</span> <a class="link" href="../../policy.html" title="Policies">Policy</a><span class="special">&gt;</span>
+<span class="identifier">T</span> <span class="identifier">factorial</span><span class="special">(</span><span class="keyword">unsigned</span> <span class="identifier">i</span><span class="special">,</span> <span class="keyword">const</span> <a class="link" href="../../policy.html" title="Policies">Policy</a><span class="special">&amp;);</span>
+</pre>
+<p>
+          Returns <code class="literal">i!</code>.
+        </p>
+<p>
+          </p>
+<p>
+            The final <a class="link" href="../../policy.html" title="Policies">Policy</a> argument
+            is optional and can be used to control the behaviour of the function:
+            how it handles errors, what level of precision to use etc. Refer to the
+            <a class="link" href="../../policy.html" title="Policies">policy documentation for more details</a>.
+          </p>
+<p>
+        </p>
+<p>
+          For <code class="literal">i &lt;= max_factorial&lt;T&gt;::value</code> this is implemented
+          by table lookup, for larger values of <code class="literal">i</code>, this function
+          is implemented in terms of <a class="link" href="../sf_gamma/tgamma.html" title="Gamma">tgamma</a>.
+        </p>
+<p>
+          If <code class="literal">i</code> is so large that the result can not be represented
+          in type T, then calls <a class="link" href="../../main_overview/error_handling.html#overflow_error">overflow_error</a>.
+        </p>
+<pre class="programlisting"><span class="keyword">template</span> <span class="special">&lt;</span><span class="keyword">class</span> <span class="identifier">T</span><span class="special">&gt;</span>
+<span class="identifier">T</span> <span class="identifier">unchecked_factorial</span><span class="special">(</span><span class="keyword">unsigned</span> <span class="identifier">i</span><span class="special">);</span>
+</pre>
+<p>
+          Returns <code class="literal">i!</code>.
+        </p>
+<p>
+          Internally this function performs table lookup of the result. Further it
+          performs no range checking on the value of i: it is up to the caller to
+          ensure that <code class="literal">i &lt;= max_factorial&lt;T&gt;::value</code>. This
+          function is intended to be used inside inner loops that require fast table
+          lookup of factorials, but requires care to ensure that argument <code class="literal">i</code>
+          never grows too large.
+        </p>
+<pre class="programlisting"><span class="keyword">template</span> <span class="special">&lt;</span><span class="keyword">class</span> <span class="identifier">T</span><span class="special">&gt;</span>
+<span class="keyword">struct</span> <span class="identifier">max_factorial</span>
+<span class="special">{</span>
+   <span class="keyword">static</span> <span class="keyword">const</span> <span class="keyword">unsigned</span> <span class="identifier">value</span> <span class="special">=</span> <span class="identifier">X</span><span class="special">;</span>
+<span class="special">};</span>
+</pre>
+<p>
+          This traits class defines the largest value that can be passed to <code class="literal">unchecked_factorial</code>.
+          The member <code class="computeroutput"><span class="identifier">value</span></code> can be
+          used where integral constant expressions are required: for example to define
+          the size of further tables that depend on the factorials.
+        </p>
+<a name="math_toolkit.special.factorials.sf_factorial.accuracy"></a><h5>
+<a name="id716094"></a>
+          <a class="link" href="sf_factorial.html#math_toolkit.special.factorials.sf_factorial.accuracy">Accuracy</a>
+        </h5>
+<p>
+          For arguments smaller than <code class="computeroutput"><span class="identifier">max_factorial</span><span class="special">&lt;</span><span class="identifier">T</span><span class="special">&gt;::</span><span class="identifier">value</span></code>
+          the result should be correctly rounded. For larger arguments the accuracy
+          will be the same as for <a class="link" href="../sf_gamma/tgamma.html" title="Gamma">tgamma</a>.
+        </p>
+<a name="math_toolkit.special.factorials.sf_factorial.testing"></a><h5>
+<a name="id716168"></a>
+          <a class="link" href="sf_factorial.html#math_toolkit.special.factorials.sf_factorial.testing">Testing</a>
+        </h5>
+<p>
+          Basic sanity checks and spot values to verify the data tables: the main
+          tests for the <a class="link" href="../sf_gamma/tgamma.html" title="Gamma">tgamma</a>
+          function handle those cases already.
+        </p>
+<a name="math_toolkit.special.factorials.sf_factorial.implementation"></a><h5>
+<a name="id716211"></a>
+          <a class="link" href="sf_factorial.html#math_toolkit.special.factorials.sf_factorial.implementation">Implementation</a>
+        </h5>
+<p>
+          The factorial function is table driven for small arguments, and is implemented
+          in terms of <a class="link" href="../sf_gamma/tgamma.html" title="Gamma">tgamma</a>
+          for larger arguments.
+        </p>
+</div>
+<table xmlns:rev="http://www.cs.rpi.edu/~gregod/boost/tools/doc/revision" width="100%"><tr>
+<td align="left"></td>
+<td align="right"><div class="copyright-footer">Copyright © 2006 , 2007, 2008 John Maddock, Paul A. Bristow, Hubert
+      Holin, Xiaogang Zhang, Bruno Lalande and Gautam Sewani<p>
+        Distributed under the Boost Software License, Version 1.0. (See accompanying
+        file LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_0.txt)
+      </p>
+</div></td>
+</tr></table>
+<hr>
+<div class="spirit-nav">
+<a accesskey="p" href="../factorials.html"><img src="../../../../../doc/html/images/prev.png" alt="Prev"></a><a accesskey="u" href="../factorials.html"><img src="../../../../../doc/html/images/up.png" alt="Up"></a><a accesskey="h" href="../../../index.html"><img src="../../../../../doc/html/images/home.png" alt="Home"></a><a accesskey="n" href="sf_double_factorial.html"><img src="../../../../../doc/html/images/next.png" alt="Next"></a>
+</div>
+</body>
+</html>

Added: sandbox/tools/auto_index/example/math/doc/sf_and_dist/html/math_toolkit/special/factorials/sf_falling_factorial.html
==============================================================================
--- (empty file)
+++ sandbox/tools/auto_index/example/math/doc/sf_and_dist/html/math_toolkit/special/factorials/sf_falling_factorial.html	2008-11-28 05:25:28 EST (Fri, 28 Nov 2008)
@@ -0,0 +1,118 @@
+<html>
+<head>
+<meta http-equiv="Content-Type" content="text/html; charset=ISO-8859-1">
+<title>Falling Factorial</title>
+<link rel="stylesheet" href="../../../boostbook.css" type="text/css">
+<meta name="generator" content="DocBook XSL Stylesheets Vsnapshot_8125">
+<link rel="home" href="../../../index.html" title="Math Toolkit">
+<link rel="up" href="../factorials.html" title="Factorials and Binomial Coefficients">
+<link rel="prev" href="sf_rising_factorial.html" title="Rising Factorial">
+<link rel="next" href="sf_binomial.html" title="Binomial Coefficients">
+</head>
+<body bgcolor="white" text="black" link="#0000FF" vlink="#840084" alink="#0000FF">
+<table cellpadding="2" width="100%"><tr>
+<td valign="top"><img alt="Boost C++ Libraries" width="277" height="86" src="../../../../../boost.png"></td>
+<td align="center">Home</td>
+<td align="center">Libraries</td>
+<td align="center">People</td>
+<td align="center">FAQ</td>
+<td align="center">More</td>
+</tr></table>
+<hr>
+<div class="spirit-nav">
+<a accesskey="p" href="sf_rising_factorial.html"><img src="../../../../../doc/html/images/prev.png" alt="Prev"></a><a accesskey="u" href="../factorials.html"><img src="../../../../../doc/html/images/up.png" alt="Up"></a><a accesskey="h" href="../../../index.html"><img src="../../../../../doc/html/images/home.png" alt="Home"></a><a accesskey="n" href="sf_binomial.html"><img src="../../../../../doc/html/images/next.png" alt="Next"></a>
+</div>
+<div class="section" lang="en">
+<div class="titlepage"><div><div><h4 class="title">
+<a name="math_toolkit.special.factorials.sf_falling_factorial"></a><a class="link" href="sf_falling_factorial.html" title="Falling Factorial">
+        Falling Factorial</a>
+</h4></div></div></div>
+<p>
+          
+</p>
+<pre class="programlisting"><span class="preprocessor">#include</span> <span class="special">&lt;</span><span class="identifier">boost</span><span class="special">/</span><span class="identifier">math</span><span class="special">/</span><span class="identifier">special_functions</span><span class="special">/</span><span class="identifier">factorials</span><span class="special">.</span><span class="identifier">hpp</span><span class="special">&gt;</span>
+</pre>
+<p>
+        </p>
+<pre class="programlisting"><span class="keyword">namespace</span> <span class="identifier">boost</span><span class="special">{</span> <span class="keyword">namespace</span> <span class="identifier">math</span><span class="special">{</span>
+
+<span class="keyword">template</span> <span class="special">&lt;</span><span class="keyword">class</span> <span class="identifier">T</span><span class="special">&gt;</span>
+<a class="link" href="../../main_overview/result_type.html" title="Calculation of the Type of the Result"><span class="emphasis"><em>calculated-result-type</em></span></a> <span class="identifier">falling_factorial</span><span class="special">(</span><span class="identifier">T</span> <span class="identifier">x</span><span class="special">,</span> <span class="keyword">unsigned</span> <span class="identifier">i</span><span class="special">);</span>
+
+<span class="keyword">template</span> <span class="special">&lt;</span><span class="keyword">class</span> <span class="identifier">T</span><span class="special">,</span> <span class="keyword">class</span> <a class="link" href="../../policy.html" title="Policies">Policy</a><span class="special">&gt;</span>
+<a class="link" href="../../main_overview/result_type.html" title="Calculation of the Type of the Result"><span class="emphasis"><em>calculated-result-type</em></span></a> <span class="identifier">falling_factorial</span><span class="special">(</span><span class="identifier">T</span> <span class="identifier">x</span><span class="special">,</span> <span class="keyword">unsigned</span> <span class="identifier">i</span><span class="special">,</span> <span class="keyword">const</span> <a class="link" href="../../policy.html" title="Policies">Policy</a><span class="special">&amp;);</span>
+
+<span class="special">}}</span> <span class="comment">// namespaces
+</span></pre>
+<p>
+          Returns the falling factorial of <span class="emphasis"><em>x</em></span> and <span class="emphasis"><em>i</em></span>:
+        </p>
+<p>
+          falling_factorial(x, i) = x(x-1)(x-2)(x-3)...(x-i+1)
+        </p>
+<p>
+          Note that this function is only defined for positive <span class="emphasis"><em>i</em></span>,
+          hence the <code class="computeroutput"><span class="keyword">unsigned</span></code> second
+          argument. Argument <span class="emphasis"><em>x</em></span> can be either positive or negative
+          however.
+        </p>
+<p>
+          </p>
+<p>
+            The final <a class="link" href="../../policy.html" title="Policies">Policy</a> argument
+            is optional and can be used to control the behaviour of the function:
+            how it handles errors, what level of precision to use etc. Refer to the
+            <a class="link" href="../../policy.html" title="Policies">policy documentation for more details</a>.
+          </p>
+<p>
+        </p>
+<p>
+          May return the result of <a class="link" href="../../main_overview/error_handling.html#overflow_error">overflow_error</a>
+          if the result is too large to represent in type T.
+        </p>
+<p>
+          The return type of these functions is computed using the <a class="link" href="../../main_overview/result_type.html" title="Calculation of the Type of the Result"><span class="emphasis"><em>result
+          type calculation rules</em></span></a>: the type of the result is <code class="computeroutput"><span class="keyword">double</span></code> if T is an integer type, otherwise
+          the type of the result is T.
+        </p>
+<a name="math_toolkit.special.factorials.sf_falling_factorial.accuracy"></a><h5>
+<a name="id717831"></a>
+          <a class="link" href="sf_falling_factorial.html#math_toolkit.special.factorials.sf_falling_factorial.accuracy">Accuracy</a>
+        </h5>
+<p>
+          The accuracy will be the same as the <a class="link" href="../sf_gamma/gamma_ratios.html" title="Ratios of Gamma Functions">tgamma_delta_ratio</a>
+          function.
+        </p>
+<a name="math_toolkit.special.factorials.sf_falling_factorial.testing"></a><h5>
+<a name="id717869"></a>
+          <a class="link" href="sf_falling_factorial.html#math_toolkit.special.factorials.sf_falling_factorial.testing">Testing</a>
+        </h5>
+<p>
+          The spot tests for the falling factorials use data generated by functions.wolfram.com.
+        </p>
+<a name="math_toolkit.special.factorials.sf_falling_factorial.implementation"></a><h5>
+<a name="id717903"></a>
+          <a class="link" href="sf_falling_factorial.html#math_toolkit.special.factorials.sf_falling_factorial.implementation">Implementation</a>
+        </h5>
+<p>
+          Rising and falling factorials are implemented as ratios of gamma functions
+          using <a class="link" href="../sf_gamma/gamma_ratios.html" title="Ratios of Gamma Functions">tgamma_delta_ratio</a>.
+          Optimisations for small integer arguments are handled internally by that
+          function.
+        </p>
+</div>
+<table xmlns:rev="http://www.cs.rpi.edu/~gregod/boost/tools/doc/revision" width="100%"><tr>
+<td align="left"></td>
+<td align="right"><div class="copyright-footer">Copyright © 2006 , 2007, 2008 John Maddock, Paul A. Bristow, Hubert
+      Holin, Xiaogang Zhang, Bruno Lalande and Gautam Sewani<p>
+        Distributed under the Boost Software License, Version 1.0. (See accompanying
+        file LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_0.txt)
+      </p>
+</div></td>
+</tr></table>
+<hr>
+<div class="spirit-nav">
+<a accesskey="p" href="sf_rising_factorial.html"><img src="../../../../../doc/html/images/prev.png" alt="Prev"></a><a accesskey="u" href="../factorials.html"><img src="../../../../../doc/html/images/up.png" alt="Up"></a><a accesskey="h" href="../../../index.html"><img src="../../../../../doc/html/images/home.png" alt="Home"></a><a accesskey="n" href="sf_binomial.html"><img src="../../../../../doc/html/images/next.png" alt="Next"></a>
+</div>
+</body>
+</html>

Added: sandbox/tools/auto_index/example/math/doc/sf_and_dist/html/math_toolkit/special/factorials/sf_rising_factorial.html
==============================================================================
--- (empty file)
+++ sandbox/tools/auto_index/example/math/doc/sf_and_dist/html/math_toolkit/special/factorials/sf_rising_factorial.html	2008-11-28 05:25:28 EST (Fri, 28 Nov 2008)
@@ -0,0 +1,122 @@
+<html>
+<head>
+<meta http-equiv="Content-Type" content="text/html; charset=ISO-8859-1">
+<title>Rising Factorial</title>
+<link rel="stylesheet" href="../../../boostbook.css" type="text/css">
+<meta name="generator" content="DocBook XSL Stylesheets Vsnapshot_8125">
+<link rel="home" href="../../../index.html" title="Math Toolkit">
+<link rel="up" href="../factorials.html" title="Factorials and Binomial Coefficients">
+<link rel="prev" href="sf_double_factorial.html" title="Double Factorial">
+<link rel="next" href="sf_falling_factorial.html" title="Falling Factorial">
+</head>
+<body bgcolor="white" text="black" link="#0000FF" vlink="#840084" alink="#0000FF">
+<table cellpadding="2" width="100%"><tr>
+<td valign="top"><img alt="Boost C++ Libraries" width="277" height="86" src="../../../../../boost.png"></td>
+<td align="center">Home</td>
+<td align="center">Libraries</td>
+<td align="center">People</td>
+<td align="center">FAQ</td>
+<td align="center">More</td>
+</tr></table>
+<hr>
+<div class="spirit-nav">
+<a accesskey="p" href="sf_double_factorial.html"><img src="../../../../../doc/html/images/prev.png" alt="Prev"></a><a accesskey="u" href="../factorials.html"><img src="../../../../../doc/html/images/up.png" alt="Up"></a><a accesskey="h" href="../../../index.html"><img src="../../../../../doc/html/images/home.png" alt="Home"></a><a accesskey="n" href="sf_falling_factorial.html"><img src="../../../../../doc/html/images/next.png" alt="Next"></a>
+</div>
+<div class="section" lang="en">
+<div class="titlepage"><div><div><h4 class="title">
+<a name="math_toolkit.special.factorials.sf_rising_factorial"></a><a class="link" href="sf_rising_factorial.html" title="Rising Factorial">
+        Rising Factorial</a>
+</h4></div></div></div>
+<p>
+          
+</p>
+<pre class="programlisting"><span class="preprocessor">#include</span> <span class="special">&lt;</span><span class="identifier">boost</span><span class="special">/</span><span class="identifier">math</span><span class="special">/</span><span class="identifier">special_functions</span><span class="special">/</span><span class="identifier">factorials</span><span class="special">.</span><span class="identifier">hpp</span><span class="special">&gt;</span>
+</pre>
+<p>
+        </p>
+<pre class="programlisting"><span class="keyword">namespace</span> <span class="identifier">boost</span><span class="special">{</span> <span class="keyword">namespace</span> <span class="identifier">math</span><span class="special">{</span>
+
+<span class="keyword">template</span> <span class="special">&lt;</span><span class="keyword">class</span> <span class="identifier">T</span><span class="special">&gt;</span>
+<a class="link" href="../../main_overview/result_type.html" title="Calculation of the Type of the Result"><span class="emphasis"><em>calculated-result-type</em></span></a> <span class="identifier">rising_factorial</span><span class="special">(</span><span class="identifier">T</span> <span class="identifier">x</span><span class="special">,</span> <span class="keyword">int</span> <span class="identifier">i</span><span class="special">);</span>
+
+<span class="keyword">template</span> <span class="special">&lt;</span><span class="keyword">class</span> <span class="identifier">T</span><span class="special">,</span> <span class="keyword">class</span> <a class="link" href="../../policy.html" title="Policies">Policy</a><span class="special">&gt;</span>
+<a class="link" href="../../main_overview/result_type.html" title="Calculation of the Type of the Result"><span class="emphasis"><em>calculated-result-type</em></span></a> <span class="identifier">rising_factorial</span><span class="special">(</span><span class="identifier">T</span> <span class="identifier">x</span><span class="special">,</span> <span class="keyword">int</span> <span class="identifier">i</span><span class="special">,</span> <span class="keyword">const</span> <a class="link" href="../../policy.html" title="Policies">Policy</a><span class="special">&amp;);</span>
+
+<span class="special">}}</span> <span class="comment">// namespaces
+</span></pre>
+<p>
+          Returns the rising factorial of <span class="emphasis"><em>x</em></span> and <span class="emphasis"><em>i</em></span>:
+        </p>
+<p>
+          rising_factorial(x, i) = &#915;(x + i) / &#915;(x);
+        </p>
+<p>
+          or
+        </p>
+<p>
+          rising_factorial(x, i) = x(x+1)(x+2)(x+3)...(x+i)
+        </p>
+<p>
+          Note that both <span class="emphasis"><em>x</em></span> and <span class="emphasis"><em>i</em></span> can be
+          negative as well as positive.
+        </p>
+<p>
+          </p>
+<p>
+            The final <a class="link" href="../../policy.html" title="Policies">Policy</a> argument
+            is optional and can be used to control the behaviour of the function:
+            how it handles errors, what level of precision to use etc. Refer to the
+            <a class="link" href="../../policy.html" title="Policies">policy documentation for more details</a>.
+          </p>
+<p>
+        </p>
+<p>
+          May return the result of <a class="link" href="../../main_overview/error_handling.html#overflow_error">overflow_error</a>
+          if the result is too large to represent in type T.
+        </p>
+<p>
+          The return type of these functions is computed using the <a class="link" href="../../main_overview/result_type.html" title="Calculation of the Type of the Result"><span class="emphasis"><em>result
+          type calculation rules</em></span></a>: the type of the result is <code class="computeroutput"><span class="keyword">double</span></code> if T is an integer type, otherwise
+          the type of the result is T.
+        </p>
+<a name="math_toolkit.special.factorials.sf_rising_factorial.accuracy"></a><h5>
+<a name="id717236"></a>
+          <a class="link" href="sf_rising_factorial.html#math_toolkit.special.factorials.sf_rising_factorial.accuracy">Accuracy</a>
+        </h5>
+<p>
+          The accuracy will be the same as the <a class="link" href="../sf_gamma/gamma_ratios.html" title="Ratios of Gamma Functions">tgamma_delta_ratio</a>
+          function.
+        </p>
+<a name="math_toolkit.special.factorials.sf_rising_factorial.testing"></a><h5>
+<a name="id717275"></a>
+          <a class="link" href="sf_rising_factorial.html#math_toolkit.special.factorials.sf_rising_factorial.testing">Testing</a>
+        </h5>
+<p>
+          The spot tests for the rising factorials use data generated by functions.wolfram.com.
+        </p>
+<a name="math_toolkit.special.factorials.sf_rising_factorial.implementation"></a><h5>
+<a name="id717308"></a>
+          <a class="link" href="sf_rising_factorial.html#math_toolkit.special.factorials.sf_rising_factorial.implementation">Implementation</a>
+        </h5>
+<p>
+          Rising and falling factorials are implemented as ratios of gamma functions
+          using <a class="link" href="../sf_gamma/gamma_ratios.html" title="Ratios of Gamma Functions">tgamma_delta_ratio</a>.
+          Optimisations for small integer arguments are handled internally by that
+          function.
+        </p>
+</div>
+<table xmlns:rev="http://www.cs.rpi.edu/~gregod/boost/tools/doc/revision" width="100%"><tr>
+<td align="left"></td>
+<td align="right"><div class="copyright-footer">Copyright © 2006 , 2007, 2008 John Maddock, Paul A. Bristow, Hubert
+      Holin, Xiaogang Zhang, Bruno Lalande and Gautam Sewani<p>
+        Distributed under the Boost Software License, Version 1.0. (See accompanying
+        file LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_0.txt)
+      </p>
+</div></td>
+</tr></table>
+<hr>
+<div class="spirit-nav">
+<a accesskey="p" href="sf_double_factorial.html"><img src="../../../../../doc/html/images/prev.png" alt="Prev"></a><a accesskey="u" href="../factorials.html"><img src="../../../../../doc/html/images/up.png" alt="Up"></a><a accesskey="h" href="../../../index.html"><img src="../../../../../doc/html/images/home.png" alt="Home"></a><a accesskey="n" href="sf_falling_factorial.html"><img src="../../../../../doc/html/images/next.png" alt="Next"></a>
+</div>
+</body>
+</html>

Added: sandbox/tools/auto_index/example/math/doc/sf_and_dist/html/math_toolkit/special/fpclass.html
==============================================================================
--- (empty file)
+++ sandbox/tools/auto_index/example/math/doc/sf_and_dist/html/math_toolkit/special/fpclass.html	2008-11-28 05:25:28 EST (Fri, 28 Nov 2008)
@@ -0,0 +1,234 @@
+<html>
+<head>
+<meta http-equiv="Content-Type" content="text/html; charset=ISO-8859-1">
+<title>Floating-Point Classification: Infinities and NaN's</title>
+<link rel="stylesheet" href="../../boostbook.css" type="text/css">
+<meta name="generator" content="DocBook XSL Stylesheets Vsnapshot_8125">
+<link rel="home" href="../../index.html" title="Math Toolkit">
+<link rel="up" href="../special.html" title="Special Functions">
+<link rel="prev" href="rounding/modf.html" title="Integer and Fractional Part Splitting (modf)">
+<link rel="next" href="next_float.html" title="Floating-Point Representation Distance (ULP), and Finding Adjacent Floating-Point Values">
+</head>
+<body bgcolor="white" text="black" link="#0000FF" vlink="#840084" alink="#0000FF">
+<table cellpadding="2" width="100%"><tr>
+<td valign="top"><img alt="Boost C++ Libraries" width="277" height="86" src="../../../../boost.png"></td>
+<td align="center">Home</td>
+<td align="center">Libraries</td>
+<td align="center">People</td>
+<td align="center">FAQ</td>
+<td align="center">More</td>
+</tr></table>
+<hr>
+<div class="spirit-nav">
+<a accesskey="p" href="rounding/modf.html"><img src="../../../../doc/html/images/prev.png" alt="Prev"></a><a accesskey="u" href="../special.html"><img src="../../../../doc/html/images/up.png" alt="Up"></a><a accesskey="h" href="../../index.html"><img src="../../../../doc/html/images/home.png" alt="Home"></a><a accesskey="n" href="next_float.html"><img src="../../../../doc/html/images/next.png" alt="Next"></a>
+</div>
+<div class="section" lang="en">
+<div class="titlepage"><div><div><h3 class="title">
+<a name="math_toolkit.special.fpclass"></a><a class="link" href="fpclass.html" title="Floating-Point Classification: Infinities and NaN's"> Floating-Point Classification:
+      Infinities and NaN's</a>
+</h3></div></div></div>
+<a name="math_toolkit.special.fpclass.synopsis"></a><h5>
+<a name="id790220"></a>
+        <a class="link" href="fpclass.html#math_toolkit.special.fpclass.synopsis">Synopsis</a>
+      </h5>
+<pre class="programlisting"><span class="preprocessor">#define</span> <span class="identifier">FP_ZERO</span>        <span class="comment">/* implementation specific value */</span>
+<span class="preprocessor">#define</span> <span class="identifier">FP_NORMAL</span>      <span class="comment">/* implementation specific value */</span>
+<span class="preprocessor">#define</span> <span class="identifier">FP_INFINITE</span>    <span class="comment">/* implementation specific value */</span>
+<span class="preprocessor">#define</span> <span class="identifier">FP_NAN</span>         <span class="comment">/* implementation specific value */</span>
+<span class="preprocessor">#define</span> <span class="identifier">FP_SUBNORMAL</span>   <span class="comment">/* implementation specific value */</span>
+
+<span class="keyword">template</span> <span class="special">&lt;</span><span class="keyword">class</span> <span class="identifier">T</span><span class="special">&gt;</span>
+<span class="keyword">int</span> <span class="identifier">fpclassify</span><span class="special">(</span><span class="identifier">T</span> <span class="identifier">t</span><span class="special">);</span>
+
+<span class="keyword">template</span> <span class="special">&lt;</span><span class="keyword">class</span> <span class="identifier">T</span><span class="special">&gt;</span>
+<span class="keyword">bool</span> <span class="identifier">isfinite</span><span class="special">(</span><span class="identifier">T</span> <span class="identifier">z</span><span class="special">);</span> <span class="comment">// Neither infinity nor NaN.
+</span>
+<span class="keyword">template</span> <span class="special">&lt;</span><span class="keyword">class</span> <span class="identifier">T</span><span class="special">&gt;</span>
+<span class="keyword">bool</span> <span class="identifier">isinf</span><span class="special">(</span><span class="identifier">T</span> <span class="identifier">t</span><span class="special">);</span> <span class="comment">// Infinity (+ or -).
+</span>
+<span class="keyword">template</span> <span class="special">&lt;</span><span class="keyword">class</span> <span class="identifier">T</span><span class="special">&gt;</span>
+<span class="keyword">bool</span> <span class="identifier">isnan</span><span class="special">(</span><span class="identifier">T</span> <span class="identifier">t</span><span class="special">);</span> <span class="comment">// NaN.
+</span>
+<span class="keyword">template</span> <span class="special">&lt;</span><span class="keyword">class</span> <span class="identifier">T</span><span class="special">&gt;</span>
+<span class="keyword">bool</span> <span class="identifier">isnormal</span><span class="special">(</span><span class="identifier">T</span> <span class="identifier">t</span><span class="special">);</span> <span class="comment">// isfinite and not denormalised.
+</span>
+<span class="preprocessor">#include</span> <span class="special">&lt;</span><span class="identifier">boost</span><span class="special">\</span><span class="identifier">math</span><span class="special">\</span><span class="identifier">special_functions</span><span class="special">\</span><span class="identifier">fpclassify</span><span class="special">.</span><span class="identifier">hpp</span><span class="special">&gt;</span>
+</pre>
+<p>
+        to use these functions.
+      </p>
+<a name="math_toolkit.special.fpclass.description"></a><h5>
+<a name="id790757"></a>
+        <a class="link" href="fpclass.html#math_toolkit.special.fpclass.description">Description</a>
+      </h5>
+<p>
+        These functions provide the same functionality as the macros with the same
+        name in C99, indeed if the C99 macros are available, then these functions
+        are implemented in terms of them, otherwise they rely on std::numeric_limits&lt;&gt;
+        to function.
+      </p>
+<p>
+        Note that the definition of these functions <span class="emphasis"><em>does not suppress the
+        definition of these names as macros by math.h</em></span> on those platforms
+        that already provide these as macros. That mean that the following have differing
+        meanings:
+      </p>
+<pre class="programlisting"><span class="keyword">using</span> <span class="keyword">namespace</span> <span class="identifier">boost</span><span class="special">::</span><span class="identifier">math</span><span class="special">;</span>
+
+<span class="comment">// This might call a global macro if defined,
+</span><span class="comment">// but might not work if the type of z is unsupported 
+</span><span class="comment">// by the std lib macro:
+</span><span class="identifier">isnan</span><span class="special">(</span><span class="identifier">z</span><span class="special">);</span>
+<span class="comment">//
+</span><span class="comment">// This calls the Boost version
+</span><span class="comment">// (found via the "using namespace boost::math" declaration)
+</span><span class="comment">// it works for any type that has numeric_limits support for type z:
+</span><span class="special">(</span><span class="identifier">isnan</span><span class="special">)(</span><span class="identifier">z</span><span class="special">);</span> 
+<span class="comment">//
+</span><span class="comment">// As above but with namespace qualification.
+</span><span class="special">(</span><span class="identifier">boost</span><span class="special">::</span><span class="identifier">math</span><span class="special">::</span><span class="identifier">isnan</span><span class="special">)(</span><span class="identifier">z</span><span class="special">);</span> 
+<span class="comment">//
+</span><span class="comment">// This will cause a compiler error if isnan is a native macro:
+</span><span class="identifier">boost</span><span class="special">::</span><span class="identifier">math</span><span class="special">::</span><span class="identifier">isnan</span><span class="special">(</span><span class="identifier">z</span><span class="special">);</span>
+<span class="comment">// So always use instead:
+</span><span class="special">(</span><span class="identifier">boost</span><span class="special">::</span><span class="identifier">math</span><span class="special">::</span><span class="identifier">isnan</span><span class="special">)(</span><span class="identifier">z</span><span class="special">);</span>
+<span class="comment">//
+</span><span class="comment">// You can also add a using statment,
+</span><span class="comment">// globally to a .cpp file, or to a local function in a .hpp file.
+</span><span class="keyword">using</span> <span class="identifier">boost</span><span class="special">::</span><span class="identifier">math</span><span class="special">::</span><span class="identifier">isnan</span><span class="special">;</span>
+<span class="comment">// so you can write the shorter and less cluttered
+</span><span class="special">(</span><span class="identifier">isnan</span><span class="special">)(</span><span class="identifier">z</span><span class="special">)</span>
+<span class="comment">// But, as above, if isnan is a native macro, this causes a compiler error,
+</span><span class="comment">// because the macro always 'gets' the name first, unless enclosed in () brackets.
+</span></pre>
+<p>
+        Detailed descriptions for each of these functions follows:
+      </p>
+<pre class="programlisting"><span class="keyword">template</span> <span class="special">&lt;</span><span class="keyword">class</span> <span class="identifier">T</span><span class="special">&gt;</span>
+<span class="keyword">int</span> <span class="identifier">fpclassify</span><span class="special">(</span><span class="identifier">T</span> <span class="identifier">t</span><span class="special">);</span>
+</pre>
+<p>
+        Returns an integer value that classifies the value <span class="emphasis"><em>t</em></span>:
+      </p>
+<div class="informaltable"><table class="table">
+<colgroup>
+<col>
+<col>
+</colgroup>
+<thead><tr>
+<th>
+              <p>
+                fpclassify value
+              </p>
+              </th>
+<th>
+              <p>
+                class of t.
+              </p>
+              </th>
+</tr></thead>
+<tbody>
+<tr>
+<td>
+              <p>
+                FP_ZERO
+              </p>
+              </td>
+<td>
+              <p>
+                If <span class="emphasis"><em>t</em></span> is zero.
+              </p>
+              </td>
+</tr>
+<tr>
+<td>
+              <p>
+                FP_NORMAL
+              </p>
+              </td>
+<td>
+              <p>
+                If <span class="emphasis"><em>t</em></span> is a non-zero, non-denormalised finite
+                value.
+              </p>
+              </td>
+</tr>
+<tr>
+<td>
+              <p>
+                FP_INFINITE
+              </p>
+              </td>
+<td>
+              <p>
+                If <span class="emphasis"><em>t</em></span> is plus or minus infinity.
+              </p>
+              </td>
+</tr>
+<tr>
+<td>
+              <p>
+                FP_NAN
+              </p>
+              </td>
+<td>
+              <p>
+                If <span class="emphasis"><em>t</em></span> is a NaN.
+              </p>
+              </td>
+</tr>
+<tr>
+<td>
+              <p>
+                FP_SUBNORMAL
+              </p>
+              </td>
+<td>
+              <p>
+                If <span class="emphasis"><em>t</em></span> is a denormalised number.
+              </p>
+              </td>
+</tr>
+</tbody>
+</table></div>
+<pre class="programlisting"><span class="keyword">template</span> <span class="special">&lt;</span><span class="keyword">class</span> <span class="identifier">T</span><span class="special">&gt;</span>
+<span class="keyword">bool</span> <span class="identifier">isfinite</span><span class="special">(</span><span class="identifier">T</span> <span class="identifier">z</span><span class="special">);</span>
+</pre>
+<p>
+        Returns true only if <span class="emphasis"><em>z</em></span> is not an infinity or a NaN.
+      </p>
+<pre class="programlisting"><span class="keyword">template</span> <span class="special">&lt;</span><span class="keyword">class</span> <span class="identifier">T</span><span class="special">&gt;</span>
+<span class="keyword">bool</span> <span class="identifier">isinf</span><span class="special">(</span><span class="identifier">T</span> <span class="identifier">t</span><span class="special">);</span>
+</pre>
+<p>
+        Returns true only if <span class="emphasis"><em>z</em></span> is plus or minus infinity.
+      </p>
+<pre class="programlisting"><span class="keyword">template</span> <span class="special">&lt;</span><span class="keyword">class</span> <span class="identifier">T</span><span class="special">&gt;</span>
+<span class="keyword">bool</span> <span class="identifier">isnan</span><span class="special">(</span><span class="identifier">T</span> <span class="identifier">t</span><span class="special">);</span>
+</pre>
+<p>
+        Returns true only if <span class="emphasis"><em>z</em></span> is a NaN.
+      </p>
+<pre class="programlisting"><span class="keyword">template</span> <span class="special">&lt;</span><span class="keyword">class</span> <span class="identifier">T</span><span class="special">&gt;</span>
+<span class="keyword">bool</span> <span class="identifier">isnormal</span><span class="special">(</span><span class="identifier">T</span> <span class="identifier">t</span><span class="special">);</span>
+</pre>
+<p>
+        Returns true only if <span class="emphasis"><em>z</em></span> is a normal number (not zero,
+        infinite, NaN, or denormalised).
+      </p>
+</div>
+<table xmlns:rev="http://www.cs.rpi.edu/~gregod/boost/tools/doc/revision" width="100%"><tr>
+<td align="left"></td>
+<td align="right"><div class="copyright-footer">Copyright © 2006 , 2007, 2008 John Maddock, Paul A. Bristow, Hubert
+      Holin, Xiaogang Zhang, Bruno Lalande and Gautam Sewani<p>
+        Distributed under the Boost Software License, Version 1.0. (See accompanying
+        file LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_0.txt)
+      </p>
+</div></td>
+</tr></table>
+<hr>
+<div class="spirit-nav">
+<a accesskey="p" href="rounding/modf.html"><img src="../../../../doc/html/images/prev.png" alt="Prev"></a><a accesskey="u" href="../special.html"><img src="../../../../doc/html/images/up.png" alt="Up"></a><a accesskey="h" href="../../index.html"><img src="../../../../doc/html/images/home.png" alt="Home"></a><a accesskey="n" href="next_float.html"><img src="../../../../doc/html/images/next.png" alt="Next"></a>
+</div>
+</body>
+</html>

Added: sandbox/tools/auto_index/example/math/doc/sf_and_dist/html/math_toolkit/special/inv_hyper.html
==============================================================================
--- (empty file)
+++ sandbox/tools/auto_index/example/math/doc/sf_and_dist/html/math_toolkit/special/inv_hyper.html	2008-11-28 05:25:28 EST (Fri, 28 Nov 2008)
@@ -0,0 +1,51 @@
+<html>
+<head>
+<meta http-equiv="Content-Type" content="text/html; charset=ISO-8859-1">
+<title>Inverse Hyperbolic Functions</title>
+<link rel="stylesheet" href="../../boostbook.css" type="text/css">
+<meta name="generator" content="DocBook XSL Stylesheets Vsnapshot_8125">
+<link rel="home" href="../../index.html" title="Math Toolkit">
+<link rel="up" href="../special.html" title="Special Functions">
+<link rel="prev" href="sinc/sinhc_pi.html" title="sinhc_pi">
+<link rel="next" href="inv_hyper/inv_hyper_over.html" title="Inverse Hyperbolic Functions Overview">
+</head>
+<body bgcolor="white" text="black" link="#0000FF" vlink="#840084" alink="#0000FF">
+<table cellpadding="2" width="100%"><tr>
+<td valign="top"><img alt="Boost C++ Libraries" width="277" height="86" src="../../../../boost.png"></td>
+<td align="center">Home</td>
+<td align="center">Libraries</td>
+<td align="center">People</td>
+<td align="center">FAQ</td>
+<td align="center">More</td>
+</tr></table>
+<hr>
+<div class="spirit-nav">
+<a accesskey="p" href="sinc/sinhc_pi.html"><img src="../../../../doc/html/images/prev.png" alt="Prev"></a><a accesskey="u" href="../special.html"><img src="../../../../doc/html/images/up.png" alt="Up"></a><a accesskey="h" href="../../index.html"><img src="../../../../doc/html/images/home.png" alt="Home"></a><a accesskey="n" href="inv_hyper/inv_hyper_over.html"><img src="../../../../doc/html/images/next.png" alt="Next"></a>
+</div>
+<div class="section" lang="en">
+<div class="titlepage"><div><div><h3 class="title">
+<a name="math_toolkit.special.inv_hyper"></a><a class="link" href="inv_hyper.html" title="Inverse Hyperbolic Functions"> Inverse Hyperbolic Functions</a>
+</h3></div></div></div>
+<div class="toc"><dl>
+<dt><span class="section"><a href="inv_hyper/inv_hyper_over.html"> Inverse
+        Hyperbolic Functions Overview</a></span></dt>
+<dt><span class="section"> acosh</span></dt>
+<dt><span class="section"> asinh</span></dt>
+<dt><span class="section"> atanh</span></dt>
+</dl></div>
+</div>
+<table xmlns:rev="http://www.cs.rpi.edu/~gregod/boost/tools/doc/revision" width="100%"><tr>
+<td align="left"></td>
+<td align="right"><div class="copyright-footer">Copyright © 2006 , 2007, 2008 John Maddock, Paul A. Bristow, Hubert
+      Holin, Xiaogang Zhang, Bruno Lalande and Gautam Sewani<p>
+        Distributed under the Boost Software License, Version 1.0. (See accompanying
+        file LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_0.txt)
+      </p>
+</div></td>
+</tr></table>
+<hr>
+<div class="spirit-nav">
+<a accesskey="p" href="sinc/sinhc_pi.html"><img src="../../../../doc/html/images/prev.png" alt="Prev"></a><a accesskey="u" href="../special.html"><img src="../../../../doc/html/images/up.png" alt="Up"></a><a accesskey="h" href="../../index.html"><img src="../../../../doc/html/images/home.png" alt="Home"></a><a accesskey="n" href="inv_hyper/inv_hyper_over.html"><img src="../../../../doc/html/images/next.png" alt="Next"></a>
+</div>
+</body>
+</html>

Added: sandbox/tools/auto_index/example/math/doc/sf_and_dist/html/math_toolkit/special/inv_hyper/acosh.html
==============================================================================
--- (empty file)
+++ sandbox/tools/auto_index/example/math/doc/sf_and_dist/html/math_toolkit/special/inv_hyper/acosh.html	2008-11-28 05:25:28 EST (Fri, 28 Nov 2008)
@@ -0,0 +1,137 @@
+<html>
+<head>
+<meta http-equiv="Content-Type" content="text/html; charset=ISO-8859-1">
+<title>acosh</title>
+<link rel="stylesheet" href="../../../boostbook.css" type="text/css">
+<meta name="generator" content="DocBook XSL Stylesheets Vsnapshot_8125">
+<link rel="home" href="../../../index.html" title="Math Toolkit">
+<link rel="up" href="../inv_hyper.html" title="Inverse Hyperbolic Functions">
+<link rel="prev" href="inv_hyper_over.html" title="Inverse Hyperbolic Functions Overview">
+<link rel="next" href="asinh.html" title="asinh">
+</head>
+<body bgcolor="white" text="black" link="#0000FF" vlink="#840084" alink="#0000FF">
+<table cellpadding="2" width="100%"><tr>
+<td valign="top"><img alt="Boost C++ Libraries" width="277" height="86" src="../../../../../boost.png"></td>
+<td align="center">Home</td>
+<td align="center">Libraries</td>
+<td align="center">People</td>
+<td align="center">FAQ</td>
+<td align="center">More</td>
+</tr></table>
+<hr>
+<div class="spirit-nav">
+<a accesskey="p" href="inv_hyper_over.html"><img src="../../../../../doc/html/images/prev.png" alt="Prev"></a><a accesskey="u" href="../inv_hyper.html"><img src="../../../../../doc/html/images/up.png" alt="Up"></a><a accesskey="h" href="../../../index.html"><img src="../../../../../doc/html/images/home.png" alt="Home"></a><a accesskey="n" href="asinh.html"><img src="../../../../../doc/html/images/next.png" alt="Next"></a>
+</div>
+<div class="section" lang="en">
+<div class="titlepage"><div><div><h4 class="title">
+<a name="math_toolkit.special.inv_hyper.acosh"></a><a class="link" href="acosh.html" title="acosh"> acosh</a>
+</h4></div></div></div>
+<p>
+          
+</p>
+<pre class="programlisting"><span class="preprocessor">#include</span> <span class="special">&lt;</span><span class="identifier">boost</span><span class="special">/</span><span class="identifier">math</span><span class="special">/</span><span class="identifier">special_functions</span><span class="special">/</span><span class="identifier">acosh</span><span class="special">.</span><span class="identifier">hpp</span><span class="special">&gt;</span>
+</pre>
+<p>
+        </p>
+<pre class="programlisting"><span class="keyword">template</span><span class="special">&lt;</span><span class="keyword">class</span> <span class="identifier">T</span><span class="special">&gt;</span> 
+<a class="link" href="../../main_overview/result_type.html" title="Calculation of the Type of the Result"><span class="emphasis"><em>calculated-result-type</em></span></a> <span class="identifier">acosh</span><span class="special">(</span><span class="keyword">const</span> <span class="identifier">T</span> <span class="identifier">x</span><span class="special">);</span>
+
+<span class="keyword">template</span><span class="special">&lt;</span><span class="keyword">class</span> <span class="identifier">T</span><span class="special">,</span> <span class="keyword">class</span> <a class="link" href="../../policy.html" title="Policies">Policy</a><span class="special">&gt;</span> 
+<a class="link" href="../../main_overview/result_type.html" title="Calculation of the Type of the Result"><span class="emphasis"><em>calculated-result-type</em></span></a> <span class="identifier">acosh</span><span class="special">(</span><span class="keyword">const</span> <span class="identifier">T</span> <span class="identifier">x</span><span class="special">,</span> <span class="keyword">const</span> <a class="link" href="../../policy.html" title="Policies">Policy</a><span class="special">&amp;);</span>
+</pre>
+<p>
+          Computes the reciprocal of (the restriction to the range of <code class="literal">[0;+&#8734;[</code>)
+          <a class="link" href="inv_hyper_over.html" title="Inverse Hyperbolic Functions Overview">the hyperbolic
+          cosine function</a>, at x. Values returned are positive.
+        </p>
+<p>
+          If x is in the range <code class="literal">]-&#8734;;+1[</code> then returns the result
+          of <a class="link" href="../../main_overview/error_handling.html#domain_error">domain_error</a>.
+        </p>
+<p>
+          The return type of this function is computed using the <a class="link" href="../../main_overview/result_type.html" title="Calculation of the Type of the Result"><span class="emphasis"><em>result
+          type calculation rules</em></span></a>: the return type is <code class="computeroutput"><span class="keyword">double</span></code> when T is an integer type, and T
+          otherwise.
+        </p>
+<p>
+          </p>
+<p>
+            The final <a class="link" href="../../policy.html" title="Policies">Policy</a> argument
+            is optional and can be used to control the behaviour of the function:
+            how it handles errors, what level of precision to use etc. Refer to the
+            <a class="link" href="../../policy.html" title="Policies">policy documentation for more details</a>.
+          </p>
+<p>
+        </p>
+<p>
+          <span class="inlinemediaobject"><img src="../../../../graphs/acosh.png" align="middle"></span>
+        </p>
+<a name="math_toolkit.special.inv_hyper.acosh.accuracy"></a><h5>
+<a name="id785560"></a>
+          <a class="link" href="acosh.html#math_toolkit.special.inv_hyper.acosh.accuracy">Accuracy</a>
+        </h5>
+<p>
+          Generally accuracy is to within 1 or 2 epsilon across all supported platforms.
+        </p>
+<a name="math_toolkit.special.inv_hyper.acosh.testing"></a><h5>
+<a name="id785591"></a>
+          <a class="link" href="acosh.html#math_toolkit.special.inv_hyper.acosh.testing">Testing</a>
+        </h5>
+<p>
+          This function is tested using a combination of random test values designed
+          to give full function coverage computed at high precision using the "naive"
+          formula:
+        </p>
+<p>
+          <span class="inlinemediaobject"><img src="../../../../equations/acosh1.png"></span>
+        </p>
+<p>
+          along with a selection of sanity check values computed using functions.wolfram.com
+          to at least 50 decimal digits.
+        </p>
+<a name="math_toolkit.special.inv_hyper.acosh.implementation"></a><h5>
+<a name="id785662"></a>
+          <a class="link" href="acosh.html#math_toolkit.special.inv_hyper.acosh.implementation">Implementation</a>
+        </h5>
+<p>
+          For sufficiently large x, we can use the approximation:
+        </p>
+<p>
+          <span class="inlinemediaobject"><img src="../../../../equations/acosh2.png"></span>
+        </p>
+<p>
+          For x sufficiently close to 1 we can use the approximation:
+        </p>
+<p>
+          <span class="inlinemediaobject"><img src="../../../../equations/acosh4.png"></span>
+        </p>
+<p>
+          Otherwise for x close to 1 we can use the following rearrangement of the
+          primary definition to preserve accuracy:
+        </p>
+<p>
+          <span class="inlinemediaobject"><img src="../../../../equations/acosh3.png"></span>
+        </p>
+<p>
+          Otherwise the <a href="http://functions.wolfram.com/ElementaryFunctions/ArcCosh/02/" target="_top">primary
+          definition</a> is used:
+        </p>
+<p>
+          <span class="inlinemediaobject"><img src="../../../../equations/acosh1.png"></span>
+        </p>
+</div>
+<table xmlns:rev="http://www.cs.rpi.edu/~gregod/boost/tools/doc/revision" width="100%"><tr>
+<td align="left"></td>
+<td align="right"><div class="copyright-footer">Copyright © 2006 , 2007, 2008 John Maddock, Paul A. Bristow, Hubert
+      Holin, Xiaogang Zhang, Bruno Lalande and Gautam Sewani<p>
+        Distributed under the Boost Software License, Version 1.0. (See accompanying
+        file LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_0.txt)
+      </p>
+</div></td>
+</tr></table>
+<hr>
+<div class="spirit-nav">
+<a accesskey="p" href="inv_hyper_over.html"><img src="../../../../../doc/html/images/prev.png" alt="Prev"></a><a accesskey="u" href="../inv_hyper.html"><img src="../../../../../doc/html/images/up.png" alt="Up"></a><a accesskey="h" href="../../../index.html"><img src="../../../../../doc/html/images/home.png" alt="Home"></a><a accesskey="n" href="asinh.html"><img src="../../../../../doc/html/images/next.png" alt="Next"></a>
+</div>
+</body>
+</html>

Added: sandbox/tools/auto_index/example/math/doc/sf_and_dist/html/math_toolkit/special/inv_hyper/asinh.html
==============================================================================
--- (empty file)
+++ sandbox/tools/auto_index/example/math/doc/sf_and_dist/html/math_toolkit/special/inv_hyper/asinh.html	2008-11-28 05:25:28 EST (Fri, 28 Nov 2008)
@@ -0,0 +1,132 @@
+<html>
+<head>
+<meta http-equiv="Content-Type" content="text/html; charset=ISO-8859-1">
+<title>asinh</title>
+<link rel="stylesheet" href="../../../boostbook.css" type="text/css">
+<meta name="generator" content="DocBook XSL Stylesheets Vsnapshot_8125">
+<link rel="home" href="../../../index.html" title="Math Toolkit">
+<link rel="up" href="../inv_hyper.html" title="Inverse Hyperbolic Functions">
+<link rel="prev" href="acosh.html" title="acosh">
+<link rel="next" href="atanh.html" title="atanh">
+</head>
+<body bgcolor="white" text="black" link="#0000FF" vlink="#840084" alink="#0000FF">
+<table cellpadding="2" width="100%"><tr>
+<td valign="top"><img alt="Boost C++ Libraries" width="277" height="86" src="../../../../../boost.png"></td>
+<td align="center">Home</td>
+<td align="center">Libraries</td>
+<td align="center">People</td>
+<td align="center">FAQ</td>
+<td align="center">More</td>
+</tr></table>
+<hr>
+<div class="spirit-nav">
+<a accesskey="p" href="acosh.html"><img src="../../../../../doc/html/images/prev.png" alt="Prev"></a><a accesskey="u" href="../inv_hyper.html"><img src="../../../../../doc/html/images/up.png" alt="Up"></a><a accesskey="h" href="../../../index.html"><img src="../../../../../doc/html/images/home.png" alt="Home"></a><a accesskey="n" href="atanh.html"><img src="../../../../../doc/html/images/next.png" alt="Next"></a>
+</div>
+<div class="section" lang="en">
+<div class="titlepage"><div><div><h4 class="title">
+<a name="math_toolkit.special.inv_hyper.asinh"></a><a class="link" href="asinh.html" title="asinh"> asinh</a>
+</h4></div></div></div>
+<p>
+          
+</p>
+<pre class="programlisting"><span class="preprocessor">#include</span> <span class="special">&lt;</span><span class="identifier">boost</span><span class="special">/</span><span class="identifier">math</span><span class="special">/</span><span class="identifier">special_functions</span><span class="special">/</span><span class="identifier">asinh</span><span class="special">.</span><span class="identifier">hpp</span><span class="special">&gt;</span>
+</pre>
+<p>
+        </p>
+<pre class="programlisting"><span class="keyword">template</span><span class="special">&lt;</span><span class="keyword">class</span> <span class="identifier">T</span><span class="special">&gt;</span> 
+<a class="link" href="../../main_overview/result_type.html" title="Calculation of the Type of the Result"><span class="emphasis"><em>calculated-result-type</em></span></a> <span class="identifier">asinh</span><span class="special">(</span><span class="keyword">const</span> <span class="identifier">T</span> <span class="identifier">x</span><span class="special">);</span>
+
+<span class="keyword">template</span><span class="special">&lt;</span><span class="keyword">class</span> <span class="identifier">T</span><span class="special">,</span> <span class="keyword">class</span> <a class="link" href="../../policy.html" title="Policies">Policy</a><span class="special">&gt;</span> 
+<a class="link" href="../../main_overview/result_type.html" title="Calculation of the Type of the Result"><span class="emphasis"><em>calculated-result-type</em></span></a> <span class="identifier">asinh</span><span class="special">(</span><span class="keyword">const</span> <span class="identifier">T</span> <span class="identifier">x</span><span class="special">,</span> <span class="keyword">const</span> <a class="link" href="../../policy.html" title="Policies">Policy</a><span class="special">&amp;);</span>
+</pre>
+<p>
+          Computes the reciprocal of <a class="link" href="inv_hyper_over.html" title="Inverse Hyperbolic Functions Overview">the
+          hyperbolic sine function</a>.
+        </p>
+<p>
+          The return type of this function is computed using the <a class="link" href="../../main_overview/result_type.html" title="Calculation of the Type of the Result"><span class="emphasis"><em>result
+          type calculation rules</em></span></a>: the return type is <code class="computeroutput"><span class="keyword">double</span></code> when T is an integer type, and T
+          otherwise.
+        </p>
+<p>
+          <span class="inlinemediaobject"><img src="../../../../graphs/asinh.png" align="middle"></span>
+        </p>
+<p>
+          </p>
+<p>
+            The final <a class="link" href="../../policy.html" title="Policies">Policy</a> argument
+            is optional and can be used to control the behaviour of the function:
+            how it handles errors, what level of precision to use etc. Refer to the
+            <a class="link" href="../../policy.html" title="Policies">policy documentation for more details</a>.
+          </p>
+<p>
+        </p>
+<a name="math_toolkit.special.inv_hyper.asinh.accuracy"></a><h5>
+<a name="id786243"></a>
+          <a class="link" href="asinh.html#math_toolkit.special.inv_hyper.asinh.accuracy">Accuracy</a>
+        </h5>
+<p>
+          Generally accuracy is to within 1 or 2 epsilon across all supported platforms.
+        </p>
+<a name="math_toolkit.special.inv_hyper.asinh.testing"></a><h5>
+<a name="id786274"></a>
+          <a class="link" href="asinh.html#math_toolkit.special.inv_hyper.asinh.testing">Testing</a>
+        </h5>
+<p>
+          This function is tested using a combination of random test values designed
+          to give full function coverage computed at high precision using the "naive"
+          formula:
+        </p>
+<p>
+          <span class="inlinemediaobject"><img src="../../../../equations/asinh1.png"></span>
+        </p>
+<p>
+          along with a selection of sanity check values computed using functions.wolfram.com
+          to at least 50 decimal digits.
+        </p>
+<a name="math_toolkit.special.inv_hyper.asinh.implementation"></a><h5>
+<a name="id786345"></a>
+          <a class="link" href="asinh.html#math_toolkit.special.inv_hyper.asinh.implementation">Implementation</a>
+        </h5>
+<p>
+          For sufficiently large x we can use the approximation:
+        </p>
+<p>
+          <span class="inlinemediaobject"><img src="../../../../equations/asinh2.png"></span>
+        </p>
+<p>
+          While for very small x we can use the approximation:
+        </p>
+<p>
+          <span class="inlinemediaobject"><img src="../../../../equations/asinh3.png"></span>
+        </p>
+<p>
+          For 0.5 &gt; x &gt; &#949; the following rearrangement of the primary definition
+          is used:
+        </p>
+<p>
+          <span class="inlinemediaobject"><img src="../../../../equations/asinh4.png"></span>
+        </p>
+<p>
+          Otherwise evalution is via the <a href="http://functions.wolfram.com/ElementaryFunctions/ArcSinh/02/" target="_top">primary
+          definition</a>:
+        </p>
+<p>
+          <span class="inlinemediaobject"><img src="../../../../equations/asinh4.png"></span>
+        </p>
+</div>
+<table xmlns:rev="http://www.cs.rpi.edu/~gregod/boost/tools/doc/revision" width="100%"><tr>
+<td align="left"></td>
+<td align="right"><div class="copyright-footer">Copyright © 2006 , 2007, 2008 John Maddock, Paul A. Bristow, Hubert
+      Holin, Xiaogang Zhang, Bruno Lalande and Gautam Sewani<p>
+        Distributed under the Boost Software License, Version 1.0. (See accompanying
+        file LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_0.txt)
+      </p>
+</div></td>
+</tr></table>
+<hr>
+<div class="spirit-nav">
+<a accesskey="p" href="acosh.html"><img src="../../../../../doc/html/images/prev.png" alt="Prev"></a><a accesskey="u" href="../inv_hyper.html"><img src="../../../../../doc/html/images/up.png" alt="Up"></a><a accesskey="h" href="../../../index.html"><img src="../../../../../doc/html/images/home.png" alt="Home"></a><a accesskey="n" href="atanh.html"><img src="../../../../../doc/html/images/next.png" alt="Next"></a>
+</div>
+</body>
+</html>

Added: sandbox/tools/auto_index/example/math/doc/sf_and_dist/html/math_toolkit/special/inv_hyper/atanh.html
==============================================================================
--- (empty file)
+++ sandbox/tools/auto_index/example/math/doc/sf_and_dist/html/math_toolkit/special/inv_hyper/atanh.html	2008-11-28 05:25:28 EST (Fri, 28 Nov 2008)
@@ -0,0 +1,142 @@
+<html>
+<head>
+<meta http-equiv="Content-Type" content="text/html; charset=ISO-8859-1">
+<title>atanh</title>
+<link rel="stylesheet" href="../../../boostbook.css" type="text/css">
+<meta name="generator" content="DocBook XSL Stylesheets Vsnapshot_8125">
+<link rel="home" href="../../../index.html" title="Math Toolkit">
+<link rel="up" href="../inv_hyper.html" title="Inverse Hyperbolic Functions">
+<link rel="prev" href="asinh.html" title="asinh">
+<link rel="next" href="../rounding.html" title="Rounding Truncation and Integer Conversion">
+</head>
+<body bgcolor="white" text="black" link="#0000FF" vlink="#840084" alink="#0000FF">
+<table cellpadding="2" width="100%"><tr>
+<td valign="top"><img alt="Boost C++ Libraries" width="277" height="86" src="../../../../../boost.png"></td>
+<td align="center">Home</td>
+<td align="center">Libraries</td>
+<td align="center">People</td>
+<td align="center">FAQ</td>
+<td align="center">More</td>
+</tr></table>
+<hr>
+<div class="spirit-nav">
+<a accesskey="p" href="asinh.html"><img src="../../../../../doc/html/images/prev.png" alt="Prev"></a><a accesskey="u" href="../inv_hyper.html"><img src="../../../../../doc/html/images/up.png" alt="Up"></a><a accesskey="h" href="../../../index.html"><img src="../../../../../doc/html/images/home.png" alt="Home"></a><a accesskey="n" href="../rounding.html"><img src="../../../../../doc/html/images/next.png" alt="Next"></a>
+</div>
+<div class="section" lang="en">
+<div class="titlepage"><div><div><h4 class="title">
+<a name="math_toolkit.special.inv_hyper.atanh"></a><a class="link" href="atanh.html" title="atanh"> atanh</a>
+</h4></div></div></div>
+<p>
+          
+</p>
+<pre class="programlisting"><span class="preprocessor">#include</span> <span class="special">&lt;</span><span class="identifier">boost</span><span class="special">/</span><span class="identifier">math</span><span class="special">/</span><span class="identifier">special_functions</span><span class="special">/</span><span class="identifier">atanh</span><span class="special">.</span><span class="identifier">hpp</span><span class="special">&gt;</span>
+</pre>
+<p>
+        </p>
+<pre class="programlisting"><span class="keyword">template</span><span class="special">&lt;</span><span class="keyword">class</span> <span class="identifier">T</span><span class="special">&gt;</span> 
+<a class="link" href="../../main_overview/result_type.html" title="Calculation of the Type of the Result"><span class="emphasis"><em>calculated-result-type</em></span></a> <span class="identifier">atanh</span><span class="special">(</span><span class="keyword">const</span> <span class="identifier">T</span> <span class="identifier">x</span><span class="special">);</span>
+
+<span class="keyword">template</span><span class="special">&lt;</span><span class="keyword">class</span> <span class="identifier">T</span><span class="special">,</span> <span class="keyword">class</span> <a class="link" href="../../policy.html" title="Policies">Policy</a><span class="special">&gt;</span> 
+<a class="link" href="../../main_overview/result_type.html" title="Calculation of the Type of the Result"><span class="emphasis"><em>calculated-result-type</em></span></a> <span class="identifier">atanh</span><span class="special">(</span><span class="keyword">const</span> <span class="identifier">T</span> <span class="identifier">x</span><span class="special">,</span> <span class="keyword">const</span> <a class="link" href="../../policy.html" title="Policies">Policy</a><span class="special">&amp;);</span>
+</pre>
+<p>
+          Computes the reciprocal of <a class="link" href="inv_hyper_over.html" title="Inverse Hyperbolic Functions Overview">the
+          hyperbolic tangent function</a>, at x.
+        </p>
+<p>
+          </p>
+<p>
+            The final <a class="link" href="../../policy.html" title="Policies">Policy</a> argument
+            is optional and can be used to control the behaviour of the function:
+            how it handles errors, what level of precision to use etc. Refer to the
+            <a class="link" href="../../policy.html" title="Policies">policy documentation for more details</a>.
+          </p>
+<p>
+        </p>
+<p>
+          If x is in the range <code class="literal">]-&#8734;;-1[</code> or in the range <code class="literal">]+1;+&#8734;[</code>
+          then returns the result of <a class="link" href="../../main_overview/error_handling.html#domain_error">domain_error</a>.
+        </p>
+<p>
+          If x is in the range <code class="literal">[-1;-1+&#949;[</code>, then the result of -<a class="link" href="../../main_overview/error_handling.html#overflow_error">overflow_error</a> is returned, with &#949;
+denoting
+          numeric_limits&lt;T&gt;::epsilon().
+        </p>
+<p>
+          If x is in the range <code class="literal">]+1-&#949;;+1]</code>, then the result of <a class="link" href="../../main_overview/error_handling.html#overflow_error">overflow_error</a> is returned, with &#949;
+denoting
+          numeric_limits&lt;T&gt;::epsilon().
+        </p>
+<p>
+          The return type of this function is computed using the <a class="link" href="../../main_overview/result_type.html" title="Calculation of the Type of the Result"><span class="emphasis"><em>result
+          type calculation rules</em></span></a>: the return type is <code class="computeroutput"><span class="keyword">double</span></code> when T is an integer type, and T
+          otherwise.
+        </p>
+<p>
+          <span class="inlinemediaobject"><img src="../../../../graphs/atanh.png" align="middle"></span>
+        </p>
+<a name="math_toolkit.special.inv_hyper.atanh.accuracy"></a><h5>
+<a name="id787000"></a>
+          <a class="link" href="atanh.html#math_toolkit.special.inv_hyper.atanh.accuracy">Accuracy</a>
+        </h5>
+<p>
+          Generally accuracy is to within 1 or 2 epsilon across all supported platforms.
+        </p>
+<a name="math_toolkit.special.inv_hyper.atanh.testing"></a><h5>
+<a name="id787031"></a>
+          <a class="link" href="atanh.html#math_toolkit.special.inv_hyper.atanh.testing">Testing</a>
+        </h5>
+<p>
+          This function is tested using a combination of random test values designed
+          to give full function coverage computed at high precision using the "naive"
+          formula:
+        </p>
+<p>
+          <span class="inlinemediaobject"><img src="../../../../equations/atanh1.png"></span>
+        </p>
+<p>
+          along with a selection of sanity check values computed using functions.wolfram.com
+          to at least 50 decimal digits.
+        </p>
+<a name="math_toolkit.special.inv_hyper.atanh.implementation"></a><h5>
+<a name="id787102"></a>
+          <a class="link" href="atanh.html#math_toolkit.special.inv_hyper.atanh.implementation">Implementation</a>
+        </h5>
+<p>
+          For sufficiently small x we can use the approximation:
+        </p>
+<p>
+          <span class="inlinemediaobject"><img src="../../../../equations/atanh2.png"></span>
+        </p>
+<p>
+          Otherwise the <a href="http://functions.wolfram.com/ElementaryFunctions/ArcTanh/02/" target="_top">primary
+          definition</a>:
+        </p>
+<p>
+          <span class="inlinemediaobject"><img src="../../../../equations/atanh1.png"></span>
+        </p>
+<p>
+          or it's equivalent form:
+        </p>
+<p>
+          <span class="inlinemediaobject"><img src="../../../../equations/atanh3.png"></span>
+        </p>
+<p>
+          is used.
+        </p>
+</div>
+<table xmlns:rev="http://www.cs.rpi.edu/~gregod/boost/tools/doc/revision" width="100%"><tr>
+<td align="left"></td>
+<td align="right"><div class="copyright-footer">Copyright © 2006 , 2007, 2008 John Maddock, Paul A. Bristow, Hubert
+      Holin, Xiaogang Zhang, Bruno Lalande and Gautam Sewani<p>
+        Distributed under the Boost Software License, Version 1.0. (See accompanying
+        file LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_0.txt)
+      </p>
+</div></td>
+</tr></table>
+<hr>
+<div class="spirit-nav">
+<a accesskey="p" href="asinh.html"><img src="../../../../../doc/html/images/prev.png" alt="Prev"></a><a accesskey="u" href="../inv_hyper.html"><img src="../../../../../doc/html/images/up.png" alt="Up"></a><a accesskey="h" href="../../../index.html"><img src="../../../../../doc/html/images/home.png" alt="Home"></a><a accesskey="n" href="../rounding.html"><img src="../../../../../doc/html/images/next.png" alt="Next"></a>
+</div>
+</body>
+</html>

Added: sandbox/tools/auto_index/example/math/doc/sf_and_dist/html/math_toolkit/special/inv_hyper/inv_hyper_over.html
==============================================================================
--- (empty file)
+++ sandbox/tools/auto_index/example/math/doc/sf_and_dist/html/math_toolkit/special/inv_hyper/inv_hyper_over.html	2008-11-28 05:25:28 EST (Fri, 28 Nov 2008)
@@ -0,0 +1,163 @@
+<html>
+<head>
+<meta http-equiv="Content-Type" content="text/html; charset=ISO-8859-1">
+<title>Inverse Hyperbolic Functions Overview</title>
+<link rel="stylesheet" href="../../../boostbook.css" type="text/css">
+<meta name="generator" content="DocBook XSL Stylesheets Vsnapshot_8125">
+<link rel="home" href="../../../index.html" title="Math Toolkit">
+<link rel="up" href="../inv_hyper.html" title="Inverse Hyperbolic Functions">
+<link rel="prev" href="../inv_hyper.html" title="Inverse Hyperbolic Functions">
+<link rel="next" href="acosh.html" title="acosh">
+</head>
+<body bgcolor="white" text="black" link="#0000FF" vlink="#840084" alink="#0000FF">
+<table cellpadding="2" width="100%"><tr>
+<td valign="top"><img alt="Boost C++ Libraries" width="277" height="86" src="../../../../../boost.png"></td>
+<td align="center">Home</td>
+<td align="center">Libraries</td>
+<td align="center">People</td>
+<td align="center">FAQ</td>
+<td align="center">More</td>
+</tr></table>
+<hr>
+<div class="spirit-nav">
+<a accesskey="p" href="../inv_hyper.html"><img src="../../../../../doc/html/images/prev.png" alt="Prev"></a><a accesskey="u" href="../inv_hyper.html"><img src="../../../../../doc/html/images/up.png" alt="Up"></a><a accesskey="h" href="../../../index.html"><img src="../../../../../doc/html/images/home.png" alt="Home"></a><a accesskey="n" href="acosh.html"><img src="../../../../../doc/html/images/next.png" alt="Next"></a>
+</div>
+<div class="section" lang="en">
+<div class="titlepage"><div><div><h4 class="title">
+<a name="math_toolkit.special.inv_hyper.inv_hyper_over"></a><a class="link" href="inv_hyper_over.html" title="Inverse Hyperbolic Functions Overview"> Inverse
+        Hyperbolic Functions Overview</a>
+</h4></div></div></div>
+<p>
+          The exponential funtion is defined, for all objects for which this makes
+          sense, as the power series <span class="inlinemediaobject"><img src="../../../../equations/special_functions_blurb1.png"></span>,
+          with <span class="emphasis"><em><code class="literal">n! = 1x2x3x4x5...xn</code></em></span> (and
+          <span class="emphasis"><em><code class="literal">0! = 1</code></em></span> by definition) being the
+          factorial of <span class="emphasis"><em><code class="literal">n</code></em></span>. In particular,
+          the exponential function is well defined for real numbers, complex number,
+          quaternions, octonions, and matrices of complex numbers, among others.
+        </p>
+<div class="blockquote"><blockquote class="blockquote">
+<p>
+            </p>
+<p>
+              <span class="emphasis"><em><span class="bold"><strong>Graph of exp on R</strong></span></em></span>
+            </p>
+<p>
+          </p>
+</blockquote></div>
+<div class="blockquote"><blockquote class="blockquote">
+<p>
+            </p>
+<p>
+              <span class="inlinemediaobject"><img src="../../../../graphs/exp_on_r.png" alt="exp_on_r"></span>
+            </p>
+<p>
+          </p>
+</blockquote></div>
+<div class="blockquote"><blockquote class="blockquote">
+<p>
+            </p>
+<p>
+              <span class="emphasis"><em><span class="bold"><strong>Real and Imaginary parts of exp on
+              C</strong></span></em></span>
+            </p>
+<p>
+          </p>
+</blockquote></div>
+<div class="blockquote"><blockquote class="blockquote">
+<p>
+            </p>
+<p>
+              <span class="inlinemediaobject"><img src="../../../../graphs/im_exp_on_c.png" alt="im_exp_on_c"></span>
+            </p>
+<p>
+          </p>
+</blockquote></div>
+<p>
+          The hyperbolic functions are defined as power series which can be computed
+          (for reals, complex, quaternions and octonions) as:
+        </p>
+<p>
+          Hyperbolic cosine: <span class="inlinemediaobject"><img src="../../../../equations/special_functions_blurb5.png"></span>
+        </p>
+<p>
+          Hyperbolic sine: <span class="inlinemediaobject"><img src="../../../../equations/special_functions_blurb6.png"></span>
+        </p>
+<p>
+          Hyperbolic tangent: <span class="inlinemediaobject"><img src="../../../../equations/special_functions_blurb7.png"></span>
+        </p>
+<div class="blockquote"><blockquote class="blockquote">
+<p>
+            </p>
+<p>
+              <span class="emphasis"><em><span class="bold"><strong>Trigonometric functions on R (cos:
+              purple; sin: red; tan: blue)</strong></span></em></span>
+            </p>
+<p>
+          </p>
+</blockquote></div>
+<div class="blockquote"><blockquote class="blockquote">
+<p>
+            </p>
+<p>
+              <span class="inlinemediaobject"><img src="../../../../graphs/trigonometric.png" alt="trigonometric"></span>
+            </p>
+<p>
+          </p>
+</blockquote></div>
+<div class="blockquote"><blockquote class="blockquote">
+<p>
+            </p>
+<p>
+              <span class="emphasis"><em><span class="bold"><strong>Hyperbolic functions on r (cosh: purple;
+              sinh: red; tanh: blue)</strong></span></em></span>
+            </p>
+<p>
+          </p>
+</blockquote></div>
+<div class="blockquote"><blockquote class="blockquote">
+<p>
+            </p>
+<p>
+              <span class="inlinemediaobject"><img src="../../../../graphs/hyperbolic.png" alt="hyperbolic"></span>
+            </p>
+<p>
+          </p>
+</blockquote></div>
+<p>
+          The hyperbolic sine is one to one on the set of real numbers, with range
+          the full set of reals, while the hyperbolic tangent is also one to one
+          on the set of real numbers but with range <code class="literal">[0;+&#8734;[</code>, and
+          therefore both have inverses. The hyperbolic cosine is one to one from
+          <code class="literal">]-&#8734;;+1[</code> onto <code class="literal">]-&#8734;;-1[</code> (and from <code class="literal">]+1;+&#8734;[</code>
+          onto <code class="literal">]-&#8734;;-1[</code>); the inverse function we use here is defined
+          on <code class="literal">]-&#8734;;-1[</code> with range <code class="literal">]-&#8734;;+1[</code>.
+        </p>
+<p>
+          The inverse of the hyperbolic tangent is called the Argument hyperbolic
+          tangent, and can be computed as <span class="inlinemediaobject"><img src="../../../../equations/special_functions_blurb15.png"></span>.
+        </p>
+<p>
+          The inverse of the hyperbolic sine is called the Argument hyperbolic sine,
+          and can be computed (for <code class="literal">[-1;-1+&#949;[</code>) as <span class="inlinemediaobject"><img src="../../../../equations/special_functions_blurb17.png"></span>.
+        </p>
+<p>
+          The inverse of the hyperbolic cosine is called the Argument hyperbolic
+          cosine, and can be computed as <span class="inlinemediaobject"><img src="../../../../equations/special_functions_blurb18.png"></span>.
+        </p>
+</div>
+<table xmlns:rev="http://www.cs.rpi.edu/~gregod/boost/tools/doc/revision" width="100%"><tr>
+<td align="left"></td>
+<td align="right"><div class="copyright-footer">Copyright © 2006 , 2007, 2008 John Maddock, Paul A. Bristow, Hubert
+      Holin, Xiaogang Zhang, Bruno Lalande and Gautam Sewani<p>
+        Distributed under the Boost Software License, Version 1.0. (See accompanying
+        file LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_0.txt)
+      </p>
+</div></td>
+</tr></table>
+<hr>
+<div class="spirit-nav">
+<a accesskey="p" href="../inv_hyper.html"><img src="../../../../../doc/html/images/prev.png" alt="Prev"></a><a accesskey="u" href="../inv_hyper.html"><img src="../../../../../doc/html/images/up.png" alt="Up"></a><a accesskey="h" href="../../../index.html"><img src="../../../../../doc/html/images/home.png" alt="Home"></a><a accesskey="n" href="acosh.html"><img src="../../../../../doc/html/images/next.png" alt="Next"></a>
+</div>
+</body>
+</html>

Added: sandbox/tools/auto_index/example/math/doc/sf_and_dist/html/math_toolkit/special/next_float.html
==============================================================================
--- (empty file)
+++ sandbox/tools/auto_index/example/math/doc/sf_and_dist/html/math_toolkit/special/next_float.html	2008-11-28 05:25:28 EST (Fri, 28 Nov 2008)
@@ -0,0 +1,81 @@
+<html>
+<head>
+<meta http-equiv="Content-Type" content="text/html; charset=ISO-8859-1">
+<title>Floating-Point Representation Distance (ULP), and Finding Adjacent Floating-Point Values</title>
+<link rel="stylesheet" href="../../boostbook.css" type="text/css">
+<meta name="generator" content="DocBook XSL Stylesheets Vsnapshot_8125">
+<link rel="home" href="../../index.html" title="Math Toolkit">
+<link rel="up" href="../special.html" title="Special Functions">
+<link rel="prev" href="fpclass.html" title="Floating-Point Classification: Infinities and NaN's">
+<link rel="next" href="next_float/nextafter.html" title="Finding the Next Representable Value in a Specific Direction (nextafter)">
+</head>
+<body bgcolor="white" text="black" link="#0000FF" vlink="#840084" alink="#0000FF">
+<table cellpadding="2" width="100%"><tr>
+<td valign="top"><img alt="Boost C++ Libraries" width="277" height="86" src="../../../../boost.png"></td>
+<td align="center">Home</td>
+<td align="center">Libraries</td>
+<td align="center">People</td>
+<td align="center">FAQ</td>
+<td align="center">More</td>
+</tr></table>
+<hr>
+<div class="spirit-nav">
+<a accesskey="p" href="fpclass.html"><img src="../../../../doc/html/images/prev.png" alt="Prev"></a><a accesskey="u" href="../special.html"><img src="../../../../doc/html/images/up.png" alt="Up"></a><a accesskey="h" href="../../index.html"><img src="../../../../doc/html/images/home.png" alt="Home"></a><a accesskey="n" href="next_float/nextafter.html"><img src="../../../../doc/html/images/next.png" alt="Next"></a>
+</div>
+<div class="section" lang="en">
+<div class="titlepage"><div><div><h3 class="title">
+<a name="math_toolkit.special.next_float"></a><a class="link" href="next_float.html" title="Floating-Point Representation Distance (ULP), and Finding Adjacent Floating-Point Values"> Floating-Point Representation
+      Distance (ULP), and Finding Adjacent Floating-Point Values</a>
+</h3></div></div></div>
+<div class="toc"><dl>
+<dt><span class="section"><a href="next_float/nextafter.html"> Finding
+        the Next Representable Value in a Specific Direction (nextafter)</a></span></dt>
+<dt><span class="section"><a href="next_float/float_next.html"> Finding
+        the Next Greater Representable Value (float_next)</a></span></dt>
+<dt><span class="section"><a href="next_float/float_prior.html"> Finding
+        the Next Smaller Representable Value (float_prior)</a></span></dt>
+<dt><span class="section"><a href="next_float/float_distance.html"> Calculating
+        the Representation Distance Between Two Floating Point Values (ULP) float_distance</a></span></dt>
+<dt><span class="section"><a href="next_float/float_advance.html"> Advancing
+        a Floating Point Value by a Specific Representation Distance (ULP) float_advance</a></span></dt>
+</dl></div>
+<p>
+        <a href="http://en.wikipedia.org/wiki/Unit_in_the_last_place" target="_top">Unit of
+        Least Precision or Unit in the Last Place</a> is the gap between two
+        different, but as close as possible, floating-point numbers.
+      </p>
+<p>
+        Most decimal values, for example 0.1, cannot be exactly represented as floating-point
+        values, but will be stored as the closest representable floating-point.
+      </p>
+<p>
+        Functions are provided for finding adjacent greater and lesser floating-point
+        values, and estimating the number of gaps between any two floating-point
+        values.
+      </p>
+<p>
+        The floating-point type FPT must have has a fixed number of bits in the representation.
+        The number of bits may set at runtime, but must be the same for all numbers.
+        For example, NTL::quad_float
+        type (fixed 128-bit representation) or NTL::RR
+        type (arbitrary but fixed decimal digits, default 150) but <span class="bold"><strong>not</strong></span>
+        a type that extends the representation to provide an exact representation
+        for any number, for example <a href="http://keithbriggs.info/xrc.html" target="_top">XRC
+        eXact Real in C</a>.
+      </p>
+</div>
+<table xmlns:rev="http://www.cs.rpi.edu/~gregod/boost/tools/doc/revision" width="100%"><tr>
+<td align="left"></td>
+<td align="right"><div class="copyright-footer">Copyright © 2006 , 2007, 2008 John Maddock, Paul A. Bristow, Hubert
+      Holin, Xiaogang Zhang, Bruno Lalande and Gautam Sewani<p>
+        Distributed under the Boost Software License, Version 1.0. (See accompanying
+        file LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_0.txt)
+      </p>
+</div></td>
+</tr></table>
+<hr>
+<div class="spirit-nav">
+<a accesskey="p" href="fpclass.html"><img src="../../../../doc/html/images/prev.png" alt="Prev"></a><a accesskey="u" href="../special.html"><img src="../../../../doc/html/images/up.png" alt="Up"></a><a accesskey="h" href="../../index.html"><img src="../../../../doc/html/images/home.png" alt="Home"></a><a accesskey="n" href="next_float/nextafter.html"><img src="../../../../doc/html/images/next.png" alt="Next"></a>
+</div>
+</body>
+</html>

Added: sandbox/tools/auto_index/example/math/doc/sf_and_dist/html/math_toolkit/special/next_float/float_advance.html
==============================================================================
--- (empty file)
+++ sandbox/tools/auto_index/example/math/doc/sf_and_dist/html/math_toolkit/special/next_float/float_advance.html	2008-11-28 05:25:28 EST (Fri, 28 Nov 2008)
@@ -0,0 +1,76 @@
+<html>
+<head>
+<meta http-equiv="Content-Type" content="text/html; charset=ISO-8859-1">
+<title>Advancing a Floating Point Value by a Specific Representation Distance (ULP) float_advance</title>
+<link rel="stylesheet" href="../../../boostbook.css" type="text/css">
+<meta name="generator" content="DocBook XSL Stylesheets Vsnapshot_8125">
+<link rel="home" href="../../../index.html" title="Math Toolkit">
+<link rel="up" href="../next_float.html" title="Floating-Point Representation Distance (ULP), and Finding Adjacent Floating-Point Values">
+<link rel="prev" href="float_distance.html" title="Calculating the Representation Distance Between Two Floating Point Values (ULP) float_distance">
+<link rel="next" href="../extern_c.html" title='TR1 and C99 external "C" Functions'>
+</head>
+<body bgcolor="white" text="black" link="#0000FF" vlink="#840084" alink="#0000FF">
+<table cellpadding="2" width="100%"><tr>
+<td valign="top"><img alt="Boost C++ Libraries" width="277" height="86" src="../../../../../boost.png"></td>
+<td align="center">Home</td>
+<td align="center">Libraries</td>
+<td align="center">People</td>
+<td align="center">FAQ</td>
+<td align="center">More</td>
+</tr></table>
+<hr>
+<div class="spirit-nav">
+<a accesskey="p" href="float_distance.html"><img src="../../../../../doc/html/images/prev.png" alt="Prev"></a><a accesskey="u" href="../next_float.html"><img src="../../../../../doc/html/images/up.png" alt="Up"></a><a accesskey="h" href="../../../index.html"><img src="../../../../../doc/html/images/home.png" alt="Home"></a><a accesskey="n" href="../extern_c.html"><img src="../../../../../doc/html/images/next.png" alt="Next"></a>
+</div>
+<div class="section" lang="en">
+<div class="titlepage"><div><div><h4 class="title">
+<a name="math_toolkit.special.next_float.float_advance"></a><a class="link" href="float_advance.html" title="Advancing a Floating Point Value by a Specific Representation Distance (ULP) float_advance"> Advancing
+        a Floating Point Value by a Specific Representation Distance (ULP) float_advance</a>
+</h4></div></div></div>
+<p>
+          Function float_advance advances a floating point number by a specified
+          number of ULP.
+        </p>
+<a name="math_toolkit.special.next_float.float_advance.synopsis"></a><h5>
+<a name="id793945"></a>
+          <a class="link" href="float_advance.html#math_toolkit.special.next_float.float_advance.synopsis">Synopsis</a>
+        </h5>
+<p>
+          
+</p>
+<pre class="programlisting"><span class="preprocessor">#include</span> <span class="special">&lt;</span><span class="identifier">boost</span><span class="special">/</span><span class="identifier">math</span><span class="special">/</span><span class="identifier">special_functions</span><span class="special">/</span><span class="identifier">next</span><span class="special">.</span><span class="identifier">hpp</span><span class="special">&gt;</span>
+</pre>
+<p>
+        </p>
+<pre class="programlisting"><span class="keyword">namespace</span> <span class="identifier">boost</span><span class="special">{</span> <span class="keyword">namespace</span> <span class="identifier">math</span><span class="special">{</span>
+
+<span class="keyword">template</span> <span class="special">&lt;</span><span class="keyword">class</span> <span class="identifier">FPT</span><span class="special">&gt;</span>
+<span class="identifier">FPT</span> <span class="identifier">float_advance</span><span class="special">(</span><span class="identifier">FPT</span> <span class="identifier">val</span><span class="special">,</span> <span class="keyword">int</span> <span class="identifier">distance</span><span class="special">);</span>
+
+<span class="special">}}</span> <span class="comment">// namespaces
+</span></pre>
+<a name="math_toolkit.special.next_float.float_advance.description___float_advance"></a><h5>
+<a name="id794178"></a>
+          <a class="link" href="float_advance.html#math_toolkit.special.next_float.float_advance.description___float_advance">Description
+          - float_advance</a>
+        </h5>
+<p>
+          Returns a floating point number <span class="emphasis"><em>r</em></span> such that <code class="computeroutput"><span class="identifier">float_distance</span><span class="special">(</span><span class="identifier">val</span><span class="special">,</span> <span class="identifier">r</span><span class="special">)</span> <span class="special">==</span>
+          <span class="identifier">distance</span></code>.
+        </p>
+</div>
+<table xmlns:rev="http://www.cs.rpi.edu/~gregod/boost/tools/doc/revision" width="100%"><tr>
+<td align="left"></td>
+<td align="right"><div class="copyright-footer">Copyright © 2006 , 2007, 2008 John Maddock, Paul A. Bristow, Hubert
+      Holin, Xiaogang Zhang, Bruno Lalande and Gautam Sewani<p>
+        Distributed under the Boost Software License, Version 1.0. (See accompanying
+        file LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_0.txt)
+      </p>
+</div></td>
+</tr></table>
+<hr>
+<div class="spirit-nav">
+<a accesskey="p" href="float_distance.html"><img src="../../../../../doc/html/images/prev.png" alt="Prev"></a><a accesskey="u" href="../next_float.html"><img src="../../../../../doc/html/images/up.png" alt="Up"></a><a accesskey="h" href="../../../index.html"><img src="../../../../../doc/html/images/home.png" alt="Home"></a><a accesskey="n" href="../extern_c.html"><img src="../../../../../doc/html/images/next.png" alt="Next"></a>
+</div>
+</body>
+</html>

Added: sandbox/tools/auto_index/example/math/doc/sf_and_dist/html/math_toolkit/special/next_float/float_distance.html
==============================================================================
--- (empty file)
+++ sandbox/tools/auto_index/example/math/doc/sf_and_dist/html/math_toolkit/special/next_float/float_distance.html	2008-11-28 05:25:28 EST (Fri, 28 Nov 2008)
@@ -0,0 +1,110 @@
+<html>
+<head>
+<meta http-equiv="Content-Type" content="text/html; charset=ISO-8859-1">
+<title>Calculating the Representation Distance Between Two Floating Point Values (ULP) float_distance</title>
+<link rel="stylesheet" href="../../../boostbook.css" type="text/css">
+<meta name="generator" content="DocBook XSL Stylesheets Vsnapshot_8125">
+<link rel="home" href="../../../index.html" title="Math Toolkit">
+<link rel="up" href="../next_float.html" title="Floating-Point Representation Distance (ULP), and Finding Adjacent Floating-Point Values">
+<link rel="prev" href="float_prior.html" title="Finding the Next Smaller Representable Value (float_prior)">
+<link rel="next" href="float_advance.html" title="Advancing a Floating Point Value by a Specific Representation Distance (ULP) float_advance">
+</head>
+<body bgcolor="white" text="black" link="#0000FF" vlink="#840084" alink="#0000FF">
+<table cellpadding="2" width="100%"><tr>
+<td valign="top"><img alt="Boost C++ Libraries" width="277" height="86" src="../../../../../boost.png"></td>
+<td align="center">Home</td>
+<td align="center">Libraries</td>
+<td align="center">People</td>
+<td align="center">FAQ</td>
+<td align="center">More</td>
+</tr></table>
+<hr>
+<div class="spirit-nav">
+<a accesskey="p" href="float_prior.html"><img src="../../../../../doc/html/images/prev.png" alt="Prev"></a><a accesskey="u" href="../next_float.html"><img src="../../../../../doc/html/images/up.png" alt="Up"></a><a accesskey="h" href="../../../index.html"><img src="../../../../../doc/html/images/home.png" alt="Home"></a><a accesskey="n" href="float_advance.html"><img src="../../../../../doc/html/images/next.png" alt="Next"></a>
+</div>
+<div class="section" lang="en">
+<div class="titlepage"><div><div><h4 class="title">
+<a name="math_toolkit.special.next_float.float_distance"></a><a class="link" href="float_distance.html" title="Calculating the Representation Distance Between Two Floating Point Values (ULP) float_distance"> Calculating
+        the Representation Distance Between Two Floating Point Values (ULP) float_distance</a>
+</h4></div></div></div>
+<p>
+          Function float_distance finds the number of gaps/bits/ULP between any two
+          floating-point values. If the significands of floating-point numbers are
+          viewed as integers, then their difference is the number of ULP/gaps/bits
+          different.
+        </p>
+<a name="math_toolkit.special.next_float.float_distance.synopsis"></a><h5>
+<a name="id793412"></a>
+          <a class="link" href="float_distance.html#math_toolkit.special.next_float.float_distance.synopsis">Synopsis</a>
+        </h5>
+<p>
+          
+</p>
+<pre class="programlisting"><span class="preprocessor">#include</span> <span class="special">&lt;</span><span class="identifier">boost</span><span class="special">/</span><span class="identifier">math</span><span class="special">/</span><span class="identifier">special_functions</span><span class="special">/</span><span class="identifier">next</span><span class="special">.</span><span class="identifier">hpp</span><span class="special">&gt;</span>
+</pre>
+<p>
+        </p>
+<pre class="programlisting"><span class="keyword">namespace</span> <span class="identifier">boost</span><span class="special">{</span> <span class="keyword">namespace</span> <span class="identifier">math</span><span class="special">{</span>
+
+<span class="keyword">template</span> <span class="special">&lt;</span><span class="keyword">class</span> <span class="identifier">FPT</span><span class="special">&gt;</span>
+<span class="identifier">FPT</span> <span class="identifier">float_distance</span><span class="special">(</span><span class="identifier">FPT</span> <span class="identifier">a</span><span class="special">,</span> <span class="identifier">FPT</span> <span class="identifier">b</span><span class="special">);</span>
+
+<span class="special">}}</span> <span class="comment">// namespaces
+</span></pre>
+<a name="math_toolkit.special.next_float.float_distance.description___float_distance"></a><h5>
+<a name="id793646"></a>
+          <a class="link" href="float_distance.html#math_toolkit.special.next_float.float_distance.description___float_distance">Description
+          - float_distance</a>
+        </h5>
+<p>
+          Returns the distance between <span class="emphasis"><em>a</em></span> and <span class="emphasis"><em>b</em></span>:
+          the result is always a signed integer value (stored in floating-point type
+          FPT) representing the number of distinct representations between <span class="emphasis"><em>a</em></span>
+          and <span class="emphasis"><em>b</em></span>.
+        </p>
+<p>
+          Note that
+        </p>
+<div class="itemizedlist"><ul type="disc">
+<li>
+<code class="computeroutput"><span class="identifier">float_distance</span><span class="special">(</span><span class="identifier">a</span><span class="special">,</span> <span class="identifier">a</span><span class="special">)</span></code>
+            always returns 0.
+          </li>
+<li>
+<code class="computeroutput"><span class="identifier">float_distance</span><span class="special">(</span><span class="identifier">float_next</span><span class="special">(</span><span class="identifier">a</span><span class="special">),</span> <span class="identifier">a</span><span class="special">)</span></code>
+            always returns 1.
+          </li>
+<li>
+<code class="computeroutput"><span class="identifier">float_distance</span><span class="special">(</span><span class="identifier">float_prior</span><span class="special">(</span><span class="identifier">a</span><span class="special">),</span> <span class="identifier">a</span><span class="special">)</span></code>
+            always returns -1.
+          </li>
+</ul></div>
+<p>
+          The function <code class="computeroutput"><span class="identifier">float_distance</span></code>
+          is equivalent to calculating the number of ULP (Units in the Last Place)
+          between <span class="emphasis"><em>a</em></span> and <span class="emphasis"><em>b</em></span> except that it
+          returns a signed value indicating whether <code class="computeroutput"><span class="identifier">a</span>
+          <span class="special">&gt;</span> <span class="identifier">b</span></code>
+          or not.
+        </p>
+<p>
+          If the distance is too great then it may not be able to be represented
+          as an exact integer by type FPT, but in practice this is unlikely to be
+          a issue.
+        </p>
+</div>
+<table xmlns:rev="http://www.cs.rpi.edu/~gregod/boost/tools/doc/revision" width="100%"><tr>
+<td align="left"></td>
+<td align="right"><div class="copyright-footer">Copyright © 2006 , 2007, 2008 John Maddock, Paul A. Bristow, Hubert
+      Holin, Xiaogang Zhang, Bruno Lalande and Gautam Sewani<p>
+        Distributed under the Boost Software License, Version 1.0. (See accompanying
+        file LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_0.txt)
+      </p>
+</div></td>
+</tr></table>
+<hr>
+<div class="spirit-nav">
+<a accesskey="p" href="float_prior.html"><img src="../../../../../doc/html/images/prev.png" alt="Prev"></a><a accesskey="u" href="../next_float.html"><img src="../../../../../doc/html/images/up.png" alt="Up"></a><a accesskey="h" href="../../../index.html"><img src="../../../../../doc/html/images/home.png" alt="Home"></a><a accesskey="n" href="float_advance.html"><img src="../../../../../doc/html/images/next.png" alt="Next"></a>
+</div>
+</body>
+</html>

Added: sandbox/tools/auto_index/example/math/doc/sf_and_dist/html/math_toolkit/special/next_float/float_next.html
==============================================================================
--- (empty file)
+++ sandbox/tools/auto_index/example/math/doc/sf_and_dist/html/math_toolkit/special/next_float/float_next.html	2008-11-28 05:25:28 EST (Fri, 28 Nov 2008)
@@ -0,0 +1,78 @@
+<html>
+<head>
+<meta http-equiv="Content-Type" content="text/html; charset=ISO-8859-1">
+<title>Finding the Next Greater Representable Value (float_next)</title>
+<link rel="stylesheet" href="../../../boostbook.css" type="text/css">
+<meta name="generator" content="DocBook XSL Stylesheets Vsnapshot_8125">
+<link rel="home" href="../../../index.html" title="Math Toolkit">
+<link rel="up" href="../next_float.html" title="Floating-Point Representation Distance (ULP), and Finding Adjacent Floating-Point Values">
+<link rel="prev" href="nextafter.html" title="Finding the Next Representable Value in a Specific Direction (nextafter)">
+<link rel="next" href="float_prior.html" title="Finding the Next Smaller Representable Value (float_prior)">
+</head>
+<body bgcolor="white" text="black" link="#0000FF" vlink="#840084" alink="#0000FF">
+<table cellpadding="2" width="100%"><tr>
+<td valign="top"><img alt="Boost C++ Libraries" width="277" height="86" src="../../../../../boost.png"></td>
+<td align="center">Home</td>
+<td align="center">Libraries</td>
+<td align="center">People</td>
+<td align="center">FAQ</td>
+<td align="center">More</td>
+</tr></table>
+<hr>
+<div class="spirit-nav">
+<a accesskey="p" href="nextafter.html"><img src="../../../../../doc/html/images/prev.png" alt="Prev"></a><a accesskey="u" href="../next_float.html"><img src="../../../../../doc/html/images/up.png" alt="Up"></a><a accesskey="h" href="../../../index.html"><img src="../../../../../doc/html/images/home.png" alt="Home"></a><a accesskey="n" href="float_prior.html"><img src="../../../../../doc/html/images/next.png" alt="Next"></a>
+</div>
+<div class="section" lang="en">
+<div class="titlepage"><div><div><h4 class="title">
+<a name="math_toolkit.special.next_float.float_next"></a><a class="link" href="float_next.html" title="Finding the Next Greater Representable Value (float_next)"> Finding
+        the Next Greater Representable Value (float_next)</a>
+</h4></div></div></div>
+<a name="math_toolkit.special.next_float.float_next.synopsis"></a><h5>
+<a name="id792643"></a>
+          <a class="link" href="float_next.html#math_toolkit.special.next_float.float_next.synopsis">Synopsis</a>
+        </h5>
+<p>
+          
+</p>
+<pre class="programlisting"><span class="preprocessor">#include</span> <span class="special">&lt;</span><span class="identifier">boost</span><span class="special">/</span><span class="identifier">math</span><span class="special">/</span><span class="identifier">special_functions</span><span class="special">/</span><span class="identifier">next</span><span class="special">.</span><span class="identifier">hpp</span><span class="special">&gt;</span>
+</pre>
+<p>
+        </p>
+<pre class="programlisting"><span class="keyword">namespace</span> <span class="identifier">boost</span><span class="special">{</span> <span class="keyword">namespace</span> <span class="identifier">math</span><span class="special">{</span>
+
+<span class="keyword">template</span> <span class="special">&lt;</span><span class="keyword">class</span> <span class="identifier">FPT</span><span class="special">&gt;</span>
+<span class="identifier">FPT</span> <span class="identifier">float_next</span><span class="special">(</span><span class="identifier">FPT</span> <span class="identifier">val</span><span class="special">);</span>
+
+<span class="special">}}</span> <span class="comment">// namespaces
+</span></pre>
+<a name="math_toolkit.special.next_float.float_next.description___float_next"></a><h5>
+<a name="id792858"></a>
+          <a class="link" href="float_next.html#math_toolkit.special.next_float.float_next.description___float_next">Description
+          - float_next</a>
+        </h5>
+<p>
+          Returns the next representable value which is greater than <span class="emphasis"><em>x</em></span>.
+          If <span class="emphasis"><em>x</em></span> is non-finite then returns the result of a <a class="link" href="../../main_overview/error_handling.html#domain_error">domain_error</a>. If there is no such value greater
+          than <span class="emphasis"><em>x</em></span> then returns an <a class="link" href="../../main_overview/error_handling.html#overflow_error">overflow_error</a>.
+        </p>
+<p>
+          Has the same effect as
+        </p>
+<pre class="programlisting"><span class="identifier">nextafter</span><span class="special">(</span><span class="identifier">val</span><span class="special">,</span> <span class="identifier">std</span><span class="special">::</span><span class="identifier">numeric_limits</span><span class="special">&lt;</span><span class="identifier">FPT</span><span class="special">&gt;::</span><span class="identifier">max</span><span class="special">());</span>
+</pre>
+</div>
+<table xmlns:rev="http://www.cs.rpi.edu/~gregod/boost/tools/doc/revision" width="100%"><tr>
+<td align="left"></td>
+<td align="right"><div class="copyright-footer">Copyright © 2006 , 2007, 2008 John Maddock, Paul A. Bristow, Hubert
+      Holin, Xiaogang Zhang, Bruno Lalande and Gautam Sewani<p>
+        Distributed under the Boost Software License, Version 1.0. (See accompanying
+        file LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_0.txt)
+      </p>
+</div></td>
+</tr></table>
+<hr>
+<div class="spirit-nav">
+<a accesskey="p" href="nextafter.html"><img src="../../../../../doc/html/images/prev.png" alt="Prev"></a><a accesskey="u" href="../next_float.html"><img src="../../../../../doc/html/images/up.png" alt="Up"></a><a accesskey="h" href="../../../index.html"><img src="../../../../../doc/html/images/home.png" alt="Home"></a><a accesskey="n" href="float_prior.html"><img src="../../../../../doc/html/images/next.png" alt="Next"></a>
+</div>
+</body>
+</html>

Added: sandbox/tools/auto_index/example/math/doc/sf_and_dist/html/math_toolkit/special/next_float/float_prior.html
==============================================================================
--- (empty file)
+++ sandbox/tools/auto_index/example/math/doc/sf_and_dist/html/math_toolkit/special/next_float/float_prior.html	2008-11-28 05:25:28 EST (Fri, 28 Nov 2008)
@@ -0,0 +1,78 @@
+<html>
+<head>
+<meta http-equiv="Content-Type" content="text/html; charset=ISO-8859-1">
+<title>Finding the Next Smaller Representable Value (float_prior)</title>
+<link rel="stylesheet" href="../../../boostbook.css" type="text/css">
+<meta name="generator" content="DocBook XSL Stylesheets Vsnapshot_8125">
+<link rel="home" href="../../../index.html" title="Math Toolkit">
+<link rel="up" href="../next_float.html" title="Floating-Point Representation Distance (ULP), and Finding Adjacent Floating-Point Values">
+<link rel="prev" href="float_next.html" title="Finding the Next Greater Representable Value (float_next)">
+<link rel="next" href="float_distance.html" title="Calculating the Representation Distance Between Two Floating Point Values (ULP) float_distance">
+</head>
+<body bgcolor="white" text="black" link="#0000FF" vlink="#840084" alink="#0000FF">
+<table cellpadding="2" width="100%"><tr>
+<td valign="top"><img alt="Boost C++ Libraries" width="277" height="86" src="../../../../../boost.png"></td>
+<td align="center">Home</td>
+<td align="center">Libraries</td>
+<td align="center">People</td>
+<td align="center">FAQ</td>
+<td align="center">More</td>
+</tr></table>
+<hr>
+<div class="spirit-nav">
+<a accesskey="p" href="float_next.html"><img src="../../../../../doc/html/images/prev.png" alt="Prev"></a><a accesskey="u" href="../next_float.html"><img src="../../../../../doc/html/images/up.png" alt="Up"></a><a accesskey="h" href="../../../index.html"><img src="../../../../../doc/html/images/home.png" alt="Home"></a><a accesskey="n" href="float_distance.html"><img src="../../../../../doc/html/images/next.png" alt="Next"></a>
+</div>
+<div class="section" lang="en">
+<div class="titlepage"><div><div><h4 class="title">
+<a name="math_toolkit.special.next_float.float_prior"></a><a class="link" href="float_prior.html" title="Finding the Next Smaller Representable Value (float_prior)"> Finding
+        the Next Smaller Representable Value (float_prior)</a>
+</h4></div></div></div>
+<a name="math_toolkit.special.next_float.float_prior.synopsis"></a><h5>
+<a name="id793015"></a>
+          <a class="link" href="float_prior.html#math_toolkit.special.next_float.float_prior.synopsis">Synopsis</a>
+        </h5>
+<p>
+          
+</p>
+<pre class="programlisting"><span class="preprocessor">#include</span> <span class="special">&lt;</span><span class="identifier">boost</span><span class="special">/</span><span class="identifier">math</span><span class="special">/</span><span class="identifier">special_functions</span><span class="special">/</span><span class="identifier">next</span><span class="special">.</span><span class="identifier">hpp</span><span class="special">&gt;</span>
+</pre>
+<p>
+        </p>
+<pre class="programlisting"><span class="keyword">namespace</span> <span class="identifier">boost</span><span class="special">{</span> <span class="keyword">namespace</span> <span class="identifier">math</span><span class="special">{</span>
+
+<span class="keyword">template</span> <span class="special">&lt;</span><span class="keyword">class</span> <span class="identifier">FPT</span><span class="special">&gt;</span>
+<span class="identifier">FPT</span> <span class="identifier">float_prior</span><span class="special">(</span><span class="identifier">FPT</span> <span class="identifier">val</span><span class="special">);</span>
+
+<span class="special">}}</span> <span class="comment">// namespaces
+</span></pre>
+<a name="math_toolkit.special.next_float.float_prior.description___float_prior"></a><h5>
+<a name="id793232"></a>
+          <a class="link" href="float_prior.html#math_toolkit.special.next_float.float_prior.description___float_prior">Description
+          - float_prior</a>
+        </h5>
+<p>
+          Returns the next representable value which is less than <span class="emphasis"><em>x</em></span>.
+          If <span class="emphasis"><em>x</em></span> is non-finite then returns the result of a <a class="link" href="../../main_overview/error_handling.html#domain_error">domain_error</a>. If there is no such value less
+          than <span class="emphasis"><em>x</em></span> then returns an <a class="link" href="../../main_overview/error_handling.html#overflow_error">overflow_error</a>.
+        </p>
+<p>
+          Has the same effect as
+        </p>
+<pre class="programlisting"><span class="identifier">nextafter</span><span class="special">(</span><span class="identifier">val</span><span class="special">,</span> <span class="special">-</span><span class="identifier">std</span><span class="special">::</span><span class="identifier">numeric_limits</span><span class="special">&lt;</span><span class="identifier">FPT</span><span class="special">&gt;::</span><span class="identifier">max</span><span class="special">());</span>  <span class="comment">// Note most negative value -max.
+</span></pre>
+</div>
+<table xmlns:rev="http://www.cs.rpi.edu/~gregod/boost/tools/doc/revision" width="100%"><tr>
+<td align="left"></td>
+<td align="right"><div class="copyright-footer">Copyright © 2006 , 2007, 2008 John Maddock, Paul A. Bristow, Hubert
+      Holin, Xiaogang Zhang, Bruno Lalande and Gautam Sewani<p>
+        Distributed under the Boost Software License, Version 1.0. (See accompanying
+        file LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_0.txt)
+      </p>
+</div></td>
+</tr></table>
+<hr>
+<div class="spirit-nav">
+<a accesskey="p" href="float_next.html"><img src="../../../../../doc/html/images/prev.png" alt="Prev"></a><a accesskey="u" href="../next_float.html"><img src="../../../../../doc/html/images/up.png" alt="Up"></a><a accesskey="h" href="../../../index.html"><img src="../../../../../doc/html/images/home.png" alt="Home"></a><a accesskey="n" href="float_distance.html"><img src="../../../../../doc/html/images/next.png" alt="Next"></a>
+</div>
+</body>
+</html>

Added: sandbox/tools/auto_index/example/math/doc/sf_and_dist/html/math_toolkit/special/next_float/nextafter.html
==============================================================================
--- (empty file)
+++ sandbox/tools/auto_index/example/math/doc/sf_and_dist/html/math_toolkit/special/next_float/nextafter.html	2008-11-28 05:25:28 EST (Fri, 28 Nov 2008)
@@ -0,0 +1,112 @@
+<html>
+<head>
+<meta http-equiv="Content-Type" content="text/html; charset=ISO-8859-1">
+<title>Finding the Next Representable Value in a Specific Direction (nextafter)</title>
+<link rel="stylesheet" href="../../../boostbook.css" type="text/css">
+<meta name="generator" content="DocBook XSL Stylesheets Vsnapshot_8125">
+<link rel="home" href="../../../index.html" title="Math Toolkit">
+<link rel="up" href="../next_float.html" title="Floating-Point Representation Distance (ULP), and Finding Adjacent Floating-Point Values">
+<link rel="prev" href="../next_float.html" title="Floating-Point Representation Distance (ULP), and Finding Adjacent Floating-Point Values">
+<link rel="next" href="float_next.html" title="Finding the Next Greater Representable Value (float_next)">
+</head>
+<body bgcolor="white" text="black" link="#0000FF" vlink="#840084" alink="#0000FF">
+<table cellpadding="2" width="100%"><tr>
+<td valign="top"><img alt="Boost C++ Libraries" width="277" height="86" src="../../../../../boost.png"></td>
+<td align="center">Home</td>
+<td align="center">Libraries</td>
+<td align="center">People</td>
+<td align="center">FAQ</td>
+<td align="center">More</td>
+</tr></table>
+<hr>
+<div class="spirit-nav">
+<a accesskey="p" href="../next_float.html"><img src="../../../../../doc/html/images/prev.png" alt="Prev"></a><a accesskey="u" href="../next_float.html"><img src="../../../../../doc/html/images/up.png" alt="Up"></a><a accesskey="h" href="../../../index.html"><img src="../../../../../doc/html/images/home.png" alt="Home"></a><a accesskey="n" href="float_next.html"><img src="../../../../../doc/html/images/next.png" alt="Next"></a>
+</div>
+<div class="section" lang="en">
+<div class="titlepage"><div><div><h4 class="title">
+<a name="math_toolkit.special.next_float.nextafter"></a><a class="link" href="nextafter.html" title="Finding the Next Representable Value in a Specific Direction (nextafter)"> Finding
+        the Next Representable Value in a Specific Direction (nextafter)</a>
+</h4></div></div></div>
+<a name="math_toolkit.special.next_float.nextafter.synopsis"></a><h5>
+<a name="id791895"></a>
+          <a class="link" href="nextafter.html#math_toolkit.special.next_float.nextafter.synopsis">Synopsis</a>
+        </h5>
+<p>
+          
+</p>
+<pre class="programlisting"><span class="preprocessor">#include</span> <span class="special">&lt;</span><span class="identifier">boost</span><span class="special">/</span><span class="identifier">math</span><span class="special">/</span><span class="identifier">special_functions</span><span class="special">/</span><span class="identifier">next</span><span class="special">.</span><span class="identifier">hpp</span><span class="special">&gt;</span>
+</pre>
+<p>
+        </p>
+<pre class="programlisting"><span class="keyword">namespace</span> <span class="identifier">boost</span><span class="special">{</span> <span class="keyword">namespace</span> <span class="identifier">math</span><span class="special">{</span>
+ 
+<span class="keyword">template</span> <span class="special">&lt;</span><span class="keyword">class</span> <span class="identifier">FPT</span><span class="special">&gt;</span>
+<span class="identifier">FPT</span> <span class="identifier">nextafter</span><span class="special">(</span><span class="identifier">FPT</span> <span class="identifier">val</span><span class="special">,</span> <span class="identifier">FPT</span> <span class="identifier">direction</span><span class="special">);</span>
+ 
+<span class="special">}}</span> <span class="comment">// namespaces
+</span></pre>
+<a name="math_toolkit.special.next_float.nextafter.description___nextafter"></a><h5>
+<a name="id792129"></a>
+          <a class="link" href="nextafter.html#math_toolkit.special.next_float.nextafter.description___nextafter">Description
+          - nextafter</a>
+        </h5>
+<p>
+          This is an implementation of the <code class="computeroutput"><span class="identifier">nextafter</span></code>
+          function included in the C99 standard. (It is also effectively an implementation
+          of the C99 'nexttoward' legacy function which differs only having a long
+          double direction, and can generally serve in its place if required).
+        </p>
+<div class="note"><table border="0" summary="Note">
+<tr>
+<td rowspan="2" align="center" valign="top" width="25"><img alt="[Note]" src="../../../../../doc/html/images/note.png"></td>
+<th align="left">Note</th>
+</tr>
+<tr><td align="left" valign="top"><p>
+            The C99 functions must use suffixes f and l to distinguish float and
+            long double versions. C++ uses the template mechanism instead.
+          </p></td></tr>
+</table></div>
+<p>
+          Returns the next representable value after <span class="emphasis"><em>x</em></span> in the
+          direction of <span class="emphasis"><em>y</em></span>. If <code class="computeroutput"><span class="identifier">x</span>
+          <span class="special">==</span> <span class="identifier">y</span></code>
+          then returns <span class="emphasis"><em>x</em></span>. If <span class="emphasis"><em>x</em></span> is non-finite
+          then returns the result of a <a class="link" href="../../main_overview/error_handling.html#domain_error">domain_error</a>.
+          If there is no such value in the direction of <span class="emphasis"><em>y</em></span> then
+          returns an <a class="link" href="../../main_overview/error_handling.html#overflow_error">overflow_error</a>.
+        </p>
+<a name="math_toolkit.special.next_float.nextafter.examples___nextafter"></a><h5>
+<a name="id792261"></a>
+          <a class="link" href="nextafter.html#math_toolkit.special.next_float.nextafter.examples___nextafter">Examples
+          - nextafter</a>
+        </h5>
+<p>
+          The two representations using a 32-bit float either side of unity are:
+          
+</p>
+<pre class="programlisting"><span class="identifier">The</span> <span class="identifier">nearest</span> <span class="special">(</span><span class="identifier">exact</span><span class="special">)</span> <span class="identifier">representation</span> <span class="identifier">of</span> <span class="number">1.F</span> <span class="identifier">is</span>      <span class="number">1.00000000</span>
+<span class="identifier">nextafter</span><span class="special">(</span><span class="number">1.F</span><span class="special">,</span> <span class="number">999</span><span class="special">)</span> <span class="identifier">is</span>                            <span class="number">1.00000012</span>
+<span class="identifier">nextafter</span><span class="special">(</span><span class="number">1</span><span class="special">/</span><span class="identifier">f</span><span class="special">,</span> <span class="special">-</span><span class="number">999</span><span class="special">)</span> <span class="identifier">is</span>                           <span class="number">0.99999994</span>
+
+<span class="identifier">The</span> <span class="identifier">nearest</span> <span class="special">(</span><span class="keyword">not</span> <span class="identifier">exact</span><span class="special">)</span> <span class="identifier">representation</span> <span class="identifier">of</span> <span class="number">0.1F</span> <span class="identifier">is</span> <span class="number">0.100000001</span>
+<span class="identifier">nextafter</span><span class="special">(</span><span class="number">0.1F</span><span class="special">,</span> <span class="number">10</span><span class="special">)</span> <span class="identifier">is</span>                            <span class="number">0.100000009</span>
+<span class="identifier">nextafter</span><span class="special">(</span><span class="number">0.1F</span><span class="special">,</span> <span class="number">10</span><span class="special">)</span> <span class="identifier">is</span>                            <span class="number">0.099999994</span>
+</pre>
+<p>
+        </p>
+</div>
+<table xmlns:rev="http://www.cs.rpi.edu/~gregod/boost/tools/doc/revision" width="100%"><tr>
+<td align="left"></td>
+<td align="right"><div class="copyright-footer">Copyright © 2006 , 2007, 2008 John Maddock, Paul A. Bristow, Hubert
+      Holin, Xiaogang Zhang, Bruno Lalande and Gautam Sewani<p>
+        Distributed under the Boost Software License, Version 1.0. (See accompanying
+        file LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_0.txt)
+      </p>
+</div></td>
+</tr></table>
+<hr>
+<div class="spirit-nav">
+<a accesskey="p" href="../next_float.html"><img src="../../../../../doc/html/images/prev.png" alt="Prev"></a><a accesskey="u" href="../next_float.html"><img src="../../../../../doc/html/images/up.png" alt="Up"></a><a accesskey="h" href="../../../index.html"><img src="../../../../../doc/html/images/home.png" alt="Home"></a><a accesskey="n" href="float_next.html"><img src="../../../../../doc/html/images/next.png" alt="Next"></a>
+</div>
+</body>
+</html>

Added: sandbox/tools/auto_index/example/math/doc/sf_and_dist/html/math_toolkit/special/powers.html
==============================================================================
--- (empty file)
+++ sandbox/tools/auto_index/example/math/doc/sf_and_dist/html/math_toolkit/special/powers.html	2008-11-28 05:25:28 EST (Fri, 28 Nov 2008)
@@ -0,0 +1,55 @@
+<html>
+<head>
+<meta http-equiv="Content-Type" content="text/html; charset=ISO-8859-1">
+<title>Logs, Powers, Roots and Exponentials</title>
+<link rel="stylesheet" href="../../boostbook.css" type="text/css">
+<meta name="generator" content="DocBook XSL Stylesheets Vsnapshot_8125">
+<link rel="home" href="../../index.html" title="Math Toolkit">
+<link rel="up" href="../special.html" title="Special Functions">
+<link rel="prev" href="expint/expint_i.html" title="Exponential Integral Ei">
+<link rel="next" href="powers/log1p.html" title="log1p">
+</head>
+<body bgcolor="white" text="black" link="#0000FF" vlink="#840084" alink="#0000FF">
+<table cellpadding="2" width="100%"><tr>
+<td valign="top"><img alt="Boost C++ Libraries" width="277" height="86" src="../../../../boost.png"></td>
+<td align="center">Home</td>
+<td align="center">Libraries</td>
+<td align="center">People</td>
+<td align="center">FAQ</td>
+<td align="center">More</td>
+</tr></table>
+<hr>
+<div class="spirit-nav">
+<a accesskey="p" href="expint/expint_i.html"><img src="../../../../doc/html/images/prev.png" alt="Prev"></a><a accesskey="u" href="../special.html"><img src="../../../../doc/html/images/up.png" alt="Up"></a><a accesskey="h" href="../../index.html"><img src="../../../../doc/html/images/home.png" alt="Home"></a><a accesskey="n" href="powers/log1p.html"><img src="../../../../doc/html/images/next.png" alt="Next"></a>
+</div>
+<div class="section" lang="en">
+<div class="titlepage"><div><div><h3 class="title">
+<a name="math_toolkit.special.powers"></a><a class="link" href="powers.html" title="Logs, Powers, Roots and Exponentials"> Logs, Powers, Roots and
+      Exponentials</a>
+</h3></div></div></div>
+<div class="toc"><dl>
+<dt><span class="section"> log1p</span></dt>
+<dt><span class="section"> expm1</span></dt>
+<dt><span class="section"> cbrt</span></dt>
+<dt><span class="section"> sqrt1pm1</span></dt>
+<dt><span class="section"> powm1</span></dt>
+<dt><span class="section"> hypot</span></dt>
+<dt><span class="section"><a href="powers/ct_pow.html"> Compile Time Power
+        of a Runtime Base</a></span></dt>
+</dl></div>
+</div>
+<table xmlns:rev="http://www.cs.rpi.edu/~gregod/boost/tools/doc/revision" width="100%"><tr>
+<td align="left"></td>
+<td align="right"><div class="copyright-footer">Copyright © 2006 , 2007, 2008 John Maddock, Paul A. Bristow, Hubert
+      Holin, Xiaogang Zhang, Bruno Lalande and Gautam Sewani<p>
+        Distributed under the Boost Software License, Version 1.0. (See accompanying
+        file LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_0.txt)
+      </p>
+</div></td>
+</tr></table>
+<hr>
+<div class="spirit-nav">
+<a accesskey="p" href="expint/expint_i.html"><img src="../../../../doc/html/images/prev.png" alt="Prev"></a><a accesskey="u" href="../special.html"><img src="../../../../doc/html/images/up.png" alt="Up"></a><a accesskey="h" href="../../index.html"><img src="../../../../doc/html/images/home.png" alt="Home"></a><a accesskey="n" href="powers/log1p.html"><img src="../../../../doc/html/images/next.png" alt="Next"></a>
+</div>
+</body>
+</html>

Added: sandbox/tools/auto_index/example/math/doc/sf_and_dist/html/math_toolkit/special/powers/cbrt.html
==============================================================================
--- (empty file)
+++ sandbox/tools/auto_index/example/math/doc/sf_and_dist/html/math_toolkit/special/powers/cbrt.html	2008-11-28 05:25:28 EST (Fri, 28 Nov 2008)
@@ -0,0 +1,104 @@
+<html>
+<head>
+<meta http-equiv="Content-Type" content="text/html; charset=ISO-8859-1">
+<title>cbrt</title>
+<link rel="stylesheet" href="../../../boostbook.css" type="text/css">
+<meta name="generator" content="DocBook XSL Stylesheets Vsnapshot_8125">
+<link rel="home" href="../../../index.html" title="Math Toolkit">
+<link rel="up" href="../powers.html" title="Logs, Powers, Roots and Exponentials">
+<link rel="prev" href="expm1.html" title="expm1">
+<link rel="next" href="sqrt1pm1.html" title="sqrt1pm1">
+</head>
+<body bgcolor="white" text="black" link="#0000FF" vlink="#840084" alink="#0000FF">
+<table cellpadding="2" width="100%"><tr>
+<td valign="top"><img alt="Boost C++ Libraries" width="277" height="86" src="../../../../../boost.png"></td>
+<td align="center">Home</td>
+<td align="center">Libraries</td>
+<td align="center">People</td>
+<td align="center">FAQ</td>
+<td align="center">More</td>
+</tr></table>
+<hr>
+<div class="spirit-nav">
+<a accesskey="p" href="expm1.html"><img src="../../../../../doc/html/images/prev.png" alt="Prev"></a><a accesskey="u" href="../powers.html"><img src="../../../../../doc/html/images/up.png" alt="Up"></a><a accesskey="h" href="../../../index.html"><img src="../../../../../doc/html/images/home.png" alt="Home"></a><a accesskey="n" href="sqrt1pm1.html"><img src="../../../../../doc/html/images/next.png" alt="Next"></a>
+</div>
+<div class="section" lang="en">
+<div class="titlepage"><div><div><h4 class="title">
+<a name="math_toolkit.special.powers.cbrt"></a><a class="link" href="cbrt.html" title="cbrt"> cbrt</a>
+</h4></div></div></div>
+<p>
+          
+</p>
+<pre class="programlisting"><span class="preprocessor">#include</span> <span class="special">&lt;</span><span class="identifier">boost</span><span class="special">/</span><span class="identifier">math</span><span class="special">/</span><span class="identifier">special_functions</span><span class="special">/</span><span class="identifier">cbrt</span><span class="special">.</span><span class="identifier">hpp</span><span class="special">&gt;</span>
+</pre>
+<p>
+        </p>
+<pre class="programlisting"><span class="keyword">namespace</span> <span class="identifier">boost</span><span class="special">{</span> <span class="keyword">namespace</span> <span class="identifier">math</span><span class="special">{</span>
+
+<span class="keyword">template</span> <span class="special">&lt;</span><span class="keyword">class</span> <span class="identifier">T</span><span class="special">&gt;</span>
+<a class="link" href="../../main_overview/result_type.html" title="Calculation of the Type of the Result"><span class="emphasis"><em>calculated-result-type</em></span></a> <span class="identifier">cbrt</span><span class="special">(</span><span class="identifier">T</span> <span class="identifier">x</span><span class="special">);</span>
+
+<span class="keyword">template</span> <span class="special">&lt;</span><span class="keyword">class</span> <span class="identifier">T</span><span class="special">,</span> <span class="keyword">class</span> <a class="link" href="../../policy.html" title="Policies">Policy</a><span class="special">&gt;</span>
+<a class="link" href="../../main_overview/result_type.html" title="Calculation of the Type of the Result"><span class="emphasis"><em>calculated-result-type</em></span></a> <span class="identifier">cbrt</span><span class="special">(</span><span class="identifier">T</span> <span class="identifier">x</span><span class="special">,</span> <span class="keyword">const</span> <a class="link" href="../../policy.html" title="Policies">Policy</a><span class="special">&amp;);</span>
+
+<span class="special">}}</span> <span class="comment">// namespaces
+</span></pre>
+<p>
+          Returns the cubed root of x: x<sup>1/3</sup>.
+        </p>
+<p>
+          The return type of this function is computed using the <a class="link" href="../../main_overview/result_type.html" title="Calculation of the Type of the Result"><span class="emphasis"><em>result
+          type calculation rules</em></span></a>: the return is <code class="computeroutput"><span class="keyword">double</span></code>
+          when <span class="emphasis"><em>x</em></span> is an integer type and T otherwise.
+        </p>
+<p>
+          </p>
+<p>
+            The final <a class="link" href="../../policy.html" title="Policies">Policy</a> argument
+            is optional and can be used to control the behaviour of the function:
+            how it handles errors, what level of precision to use etc. Refer to the
+            <a class="link" href="../../policy.html" title="Policies">policy documentation for more details</a>.
+          </p>
+<p>
+        </p>
+<p>
+          Implemented using Halley iteration.
+        </p>
+<p>
+          The following graph illustrates the behaviour of cbrt:
+        </p>
+<p>
+          <span class="inlinemediaobject"><img src="../../../../graphs/cbrt.png" align="middle"></span>
+        </p>
+<a name="math_toolkit.special.powers.cbrt.accuracy"></a><h5>
+<a name="id778788"></a>
+          <a class="link" href="cbrt.html#math_toolkit.special.powers.cbrt.accuracy">Accuracy</a>
+        </h5>
+<p>
+          For built in floating-point types <code class="computeroutput"><span class="identifier">cbrt</span></code>
+          should have approximately 2 epsilon accuracy.
+        </p>
+<a name="math_toolkit.special.powers.cbrt.testing"></a><h5>
+<a name="id778830"></a>
+          <a class="link" href="cbrt.html#math_toolkit.special.powers.cbrt.testing">Testing</a>
+        </h5>
+<p>
+          A mixture of spot test sanity checks, and random high precision test values
+          calculated using NTL::RR at 1000-bit precision.
+        </p>
+</div>
+<table xmlns:rev="http://www.cs.rpi.edu/~gregod/boost/tools/doc/revision" width="100%"><tr>
+<td align="left"></td>
+<td align="right"><div class="copyright-footer">Copyright © 2006 , 2007, 2008 John Maddock, Paul A. Bristow, Hubert
+      Holin, Xiaogang Zhang, Bruno Lalande and Gautam Sewani<p>
+        Distributed under the Boost Software License, Version 1.0. (See accompanying
+        file LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_0.txt)
+      </p>
+</div></td>
+</tr></table>
+<hr>
+<div class="spirit-nav">
+<a accesskey="p" href="expm1.html"><img src="../../../../../doc/html/images/prev.png" alt="Prev"></a><a accesskey="u" href="../powers.html"><img src="../../../../../doc/html/images/up.png" alt="Up"></a><a accesskey="h" href="../../../index.html"><img src="../../../../../doc/html/images/home.png" alt="Home"></a><a accesskey="n" href="sqrt1pm1.html"><img src="../../../../../doc/html/images/next.png" alt="Next"></a>
+</div>
+</body>
+</html>

Added: sandbox/tools/auto_index/example/math/doc/sf_and_dist/html/math_toolkit/special/powers/ct_pow.html
==============================================================================
--- (empty file)
+++ sandbox/tools/auto_index/example/math/doc/sf_and_dist/html/math_toolkit/special/powers/ct_pow.html	2008-11-28 05:25:28 EST (Fri, 28 Nov 2008)
@@ -0,0 +1,267 @@
+<html>
+<head>
+<meta http-equiv="Content-Type" content="text/html; charset=ISO-8859-1">
+<title>Compile Time Power of a Runtime Base</title>
+<link rel="stylesheet" href="../../../boostbook.css" type="text/css">
+<meta name="generator" content="DocBook XSL Stylesheets Vsnapshot_8125">
+<link rel="home" href="../../../index.html" title="Math Toolkit">
+<link rel="up" href="../powers.html" title="Logs, Powers, Roots and Exponentials">
+<link rel="prev" href="hypot.html" title="hypot">
+<link rel="next" href="../sinc.html" title="Sinus Cardinal and Hyperbolic Sinus Cardinal Functions">
+</head>
+<body bgcolor="white" text="black" link="#0000FF" vlink="#840084" alink="#0000FF">
+<table cellpadding="2" width="100%"><tr>
+<td valign="top"><img alt="Boost C++ Libraries" width="277" height="86" src="../../../../../boost.png"></td>
+<td align="center">Home</td>
+<td align="center">Libraries</td>
+<td align="center">People</td>
+<td align="center">FAQ</td>
+<td align="center">More</td>
+</tr></table>
+<hr>
+<div class="spirit-nav">
+<a accesskey="p" href="hypot.html"><img src="../../../../../doc/html/images/prev.png" alt="Prev"></a><a accesskey="u" href="../powers.html"><img src="../../../../../doc/html/images/up.png" alt="Up"></a><a accesskey="h" href="../../../index.html"><img src="../../../../../doc/html/images/home.png" alt="Home"></a><a accesskey="n" href="../sinc.html"><img src="../../../../../doc/html/images/next.png" alt="Next"></a>
+</div>
+<div class="section" lang="en">
+<div class="titlepage"><div><div><h4 class="title">
+<a name="math_toolkit.special.powers.ct_pow"></a><a class="link" href="ct_pow.html" title="Compile Time Power of a Runtime Base"> Compile Time Power
+        of a Runtime Base</a>
+</h4></div></div></div>
+<p>
+          The <code class="computeroutput"><span class="identifier">pow</span></code> function effectively
+          computes the compile-time integral power of a run-time base.
+        </p>
+<a name="math_toolkit.special.powers.ct_pow.synopsis"></a><h5>
+<a name="id780538"></a>
+          <a class="link" href="ct_pow.html#math_toolkit.special.powers.ct_pow.synopsis">Synopsis</a>
+        </h5>
+<p>
+          #include <boost/math/special_functions/pow.hpp>
+        </p>
+<pre class="programlisting"><span class="keyword">namespace</span> <span class="identifier">boost</span> <span class="special">{</span> <span class="keyword">namespace</span> <span class="identifier">math</span> <span class="special">{</span>
+
+<span class="keyword">template</span> <span class="special">&lt;</span><span class="keyword">int</span> <span class="identifier">N</span><span class="special">,</span> <span class="keyword">typename</span> <span class="identifier">T</span><span class="special">&gt;</span>
+<a class="link" href="../../main_overview/result_type.html" title="Calculation of the Type of the Result"><span class="emphasis"><em>calculated-result-type</em></span></a> <span class="identifier">pow</span><span class="special">(</span><span class="identifier">T</span> <span class="identifier">base</span><span class="special">);</span>
+
+<span class="keyword">template</span> <span class="special">&lt;</span><span class="keyword">int</span> <span class="identifier">N</span><span class="special">,</span> <span class="keyword">typename</span> <span class="identifier">T</span><span class="special">,</span> <span class="keyword">class</span> <span class="identifier">Policy</span><span class="special">&gt;</span>
+<a class="link" href="../../main_overview/result_type.html" title="Calculation of the Type of the Result"><span class="emphasis"><em>calculated-result-type</em></span></a> <span class="identifier">pow</span><span class="special">(</span><span class="identifier">T</span> <span class="identifier">base</span><span class="special">,</span> <span class="keyword">const</span> <span class="identifier">Policy</span><span class="special">&amp;</span> <span class="identifier">policy</span><span class="special">);</span>
+
+<span class="special">}}</span>
+</pre>
+<a name="math_toolkit.special.powers.ct_pow.rationale_and_usage"></a><h5>
+<a name="id780902"></a>
+          <a class="link" href="ct_pow.html#math_toolkit.special.powers.ct_pow.rationale_and_usage">Rationale
+          and Usage</a>
+        </h5>
+<p>
+          Computing the power of a number with an exponent that is known at compile
+          time is a common need for programmers. In such cases, the usual method
+          is to avoid the overhead implied by the <code class="computeroutput"><span class="identifier">pow</span></code>,
+          <code class="computeroutput"><span class="identifier">powf</span></code> and <code class="computeroutput"><span class="identifier">powl</span></code> C functions by hardcoding an expression
+          such as:
+        </p>
+<pre class="programlisting"><span class="comment">// Hand-written 8th power of a 'base' variable
+</span><span class="keyword">double</span> <span class="identifier">result</span> <span class="special">=</span> <span class="identifier">base</span><span class="special">*</span><span class="identifier">base</span><span class="special">*</span><span class="identifier">base</span><span class="special">*</span><span class="identifier">base</span><span class="special">*</span><span class="identifier">base</span><span class="special">*</span><span class="identifier">base</span><span class="special">*</span><span class="identifier">base</span><span class="special">*</span><span class="identifier">base</span><span class="special">;</span>
+</pre>
+<p>
+          However, this kind of expression is not really readable (knowing the value
+          of the exponent involves counting the number of occurrences of <span class="emphasis"><em>base</em></span>),
+          error-prone (it's easy to forget an occurrence), syntactically bulky, and
+          non-optimal in terms of performance.
+        </p>
+<p>
+          The pow function of Boost.Math helps writing this kind expression along
+          with solving all the problems listed above:
+        </p>
+<pre class="programlisting"><span class="comment">// 8th power of a 'base' variable using math::pow
+</span><span class="keyword">double</span> <span class="identifier">result</span> <span class="special">=</span> <span class="identifier">pow</span><span class="special">&lt;</span><span class="number">8</span><span class="special">&gt;(</span><span class="identifier">base</span><span class="special">);</span>
+</pre>
+<p>
+          The expression is now shorter, easier to read, safer, and even faster.
+          Indeed, <code class="computeroutput"><span class="identifier">pow</span></code> will compute
+          the expression such that only log2(N) products are made for a power of
+          N. For instance in the example above, the resulting expression will be
+          the same as if we had written this, with only one computation of each identical
+          subexpression:
+        </p>
+<pre class="programlisting"><span class="comment">// Internal effect of pow&lt;8&gt;(base)
+</span><span class="keyword">double</span> <span class="identifier">result</span> <span class="special">=</span> <span class="special">((</span><span class="identifier">base</span><span class="special">*</span><span class="identifier">base</span><span class="special">)*(</span><span class="identifier">base</span><span class="special">*</span><span class="identifier">base</span><span class="special">))*((</span><span class="identifier">base</span><span class="special">*</span><span class="identifier">base</span><span class="special">)*(</span><span class="identifier">base</span><span class="special">*</span><span class="identifier">base</span><span class="special">));</span>
+</pre>
+<p>
+          Only 3 different products were actually computed.
+        </p>
+<a name="math_toolkit.special.powers.ct_pow.return_type"></a><h5>
+<a name="id781328"></a>
+          <a class="link" href="ct_pow.html#math_toolkit.special.powers.ct_pow.return_type">Return Type</a>
+        </h5>
+<p>
+          The return type of these functions is computed using the <a class="link" href="../../main_overview/result_type.html" title="Calculation of the Type of the Result"><span class="emphasis"><em>result
+          type calculation rules</em></span></a>. For example:
+        </p>
+<div class="itemizedlist"><ul type="disc">
+<li>
+            If T is a <code class="computeroutput"><span class="keyword">float</span></code>, the return
+            type is a <code class="computeroutput"><span class="keyword">float</span></code>.
+          </li>
+<li>
+            If T is a <code class="computeroutput"><span class="keyword">long</span> <span class="keyword">double</span></code>,
+            the return type is a <code class="computeroutput"><span class="keyword">long</span> <span class="keyword">double</span></code>.
+          </li>
+<li>
+            Otherwise, the return type is a <code class="computeroutput"><span class="keyword">double</span></code>.
+          </li>
+</ul></div>
+<a name="math_toolkit.special.powers.ct_pow.policies"></a><h5>
+<a name="id781459"></a>
+          <a class="link" href="ct_pow.html#math_toolkit.special.powers.ct_pow.policies">Policies</a>
+        </h5>
+<p>
+          </p>
+<p>
+            The final <a class="link" href="../../policy.html" title="Policies">Policy</a> argument
+            is optional and can be used to control the behaviour of the function:
+            how it handles errors, what level of precision to use etc. Refer to the
+            <a class="link" href="../../policy.html" title="Policies">policy documentation for more details</a>.
+          </p>
+<p>
+        </p>
+<a name="math_toolkit.special.powers.ct_pow.error_handling"></a><h5>
+<a name="id781513"></a>
+          <a class="link" href="ct_pow.html#math_toolkit.special.powers.ct_pow.error_handling">Error
+          Handling</a>
+        </h5>
+<p>
+          Two cases of errors can occur when using <code class="computeroutput"><span class="identifier">pow</span></code>:
+        </p>
+<div class="itemizedlist"><ul type="disc">
+<li>
+            In case of null base and negative exponent, an <a class="link" href="../../main_overview/error_handling.html#overflow_error">overflow_error</a>
+            occurs since this operation is a division by 0 (it equals to 1/0).
+          </li>
+<li>
+            In case of null exponent, an <a class="link" href="../../main_overview/error_handling.html#indeterminate_result_error">indeterminate_result_error</a>
+            occurs since the result of a null power is indeterminate. Those errors
+            follow the <a class="link" href="../../main_overview/error_handling.html" title="Error Handling">general
+            policies of error handling in Boost.Math</a>.
+          </li>
+</ul></div>
+<p>
+          The default overflow error policy is <code class="computeroutput"><span class="identifier">throw_on_error</span></code>.
+          A call like <code class="computeroutput"><span class="identifier">pow</span><span class="special">&lt;-</span><span class="number">2</span><span class="special">&gt;(</span><span class="number">0</span><span class="special">)</span></code> will thus throw a <code class="computeroutput"><span class="identifier">std</span><span class="special">::</span><span class="identifier">overflow_error</span></code>
+          exception. As shown in the link given above, other error handling policies
+          can be used:
+        </p>
+<div class="itemizedlist"><ul type="disc">
+<li>
+<code class="computeroutput"><span class="identifier">errno_on_error</span></code>: Sets
+            <code class="computeroutput"><span class="special">::</span><span class="identifier">errno</span></code>
+            to <code class="computeroutput"><span class="identifier">ERANGE</span></code> and returns
+            <code class="computeroutput"><span class="identifier">std</span><span class="special">::</span><span class="identifier">numeric_limits</span><span class="special">&lt;</span><span class="identifier">T</span><span class="special">&gt;::</span><span class="identifier">infinity</span><span class="special">()</span></code>.
+          </li>
+<li>
+<code class="computeroutput"><span class="identifier">ignore_error</span></code>: Returns
+            <code class="computeroutput"><span class="identifier">std</span><span class="special">::</span><span class="identifier">numeric_limits</span><span class="special">&lt;</span><span class="identifier">T</span><span class="special">&gt;::</span><span class="identifier">infinity</span><span class="special">()</span></code>.
+          </li>
+<li>
+<code class="computeroutput"><span class="identifier">user_error</span></code>: Returns the
+            result of <code class="computeroutput"><span class="identifier">boost</span><span class="special">::</span><span class="identifier">math</span><span class="special">::</span><span class="identifier">policies</span><span class="special">::</span><span class="identifier">user_overflow_error</span></code>: this function
+            must be defined by the user.
+          </li>
+</ul></div>
+<p>
+          The default indeterminate result error policy is <code class="computeroutput"><span class="identifier">ignore_error</span></code>,
+          which for this function returns 1 since it's the most commonly chosen result
+          for a power of 0. Here again, other error handling policies can be used:
+        </p>
+<div class="itemizedlist"><ul type="disc">
+<li>
+<code class="computeroutput"><span class="identifier">throw_on_error</span></code>: Throws
+            <code class="computeroutput"><span class="identifier">std</span><span class="special">::</span><span class="identifier">domain_error</span></code>
+</li>
+<li>
+<code class="computeroutput"><span class="identifier">errno_on_error</span></code>: Sets
+            <code class="computeroutput"><span class="special">::</span><span class="identifier">errno</span></code>
+            to <code class="computeroutput"><span class="identifier">EDOM</span></code> and returns 1.
+          </li>
+<li>
+<code class="computeroutput"><span class="identifier">user_error</span></code>: Returns the
+            result of <code class="computeroutput"><span class="identifier">boost</span><span class="special">::</span><span class="identifier">math</span><span class="special">::</span><span class="identifier">policies</span><span class="special">::</span><span class="identifier">user_indeterminate_result_error</span></code>: this
+            function must be defined by the user.
+          </li>
+</ul></div>
+<p>
+          Here is an example of error handling customization where we want to specify
+          the result that has to be returned in case of error. We will thus use the
+          <code class="computeroutput"><span class="identifier">user_error</span></code> policy, by passing
+          as second argument an instance of an overflow_error policy templated with
+          <code class="computeroutput"><span class="identifier">user_error</span></code>:
+        </p>
+<pre class="programlisting"><span class="comment">// First we open the boost::math::policies namespace and define the `user_overflow_error`
+</span><span class="comment">// by making it return the value we want in case of error (-1 here)
+</span>
+<span class="keyword">namespace</span> <span class="identifier">boost</span> <span class="special">{</span> <span class="keyword">namespace</span> <span class="identifier">math</span> <span class="special">{</span> <span class="keyword">namespace</span> <span class="identifier">policies</span> <span class="special">{</span>
+<span class="keyword">template</span> <span class="special">&lt;</span><span class="keyword">class</span> <span class="identifier">T</span><span class="special">&gt;</span>
+<span class="identifier">T</span> <span class="identifier">user_overflow_error</span><span class="special">(</span><span class="keyword">const</span> <span class="keyword">char</span><span class="special">*,</span> <span class="keyword">const</span> <span class="keyword">char</span><span class="special">*,</span> <span class="keyword">const</span> <span class="identifier">T</span><span class="special">&amp;)</span>
+<span class="special">{</span> <span class="keyword">return</span> <span class="special">-</span><span class="number">1</span><span class="special">;</span> <span class="special">}</span>
+<span class="special">}}}</span>
+
+
+<span class="comment">// Then we invoke pow and indicate that we want to use the user_error policy
+</span><span class="keyword">using</span> <span class="identifier">boost</span><span class="special">::</span><span class="identifier">math</span><span class="special">::</span><span class="identifier">policies</span><span class="special">;</span>
+<span class="keyword">double</span> <span class="identifier">result</span> <span class="special">=</span> <span class="identifier">pow</span><span class="special">&lt;-</span><span class="number">5</span><span class="special">&gt;(</span><span class="identifier">base</span><span class="special">,</span> <span class="identifier">policy</span><span class="special">&lt;</span><span class="identifier">overflow_error</span><span class="special">&lt;</span><span class="identifier">user_error</span><span class="special">&gt;</span> <span class="special">&gt;());</span>
+
+<span class="comment">// We can now test the returned value and treat the special case if needed:
+</span><span class="keyword">if</span> <span class="special">(</span><span class="identifier">result</span> <span class="special">==</span> <span class="special">-</span><span class="number">1</span><span class="special">)</span>
+<span class="special">{</span>
+    <span class="comment">// there was an error, do something...
+</span><span class="special">}</span>
+</pre>
+<p>
+          Another way is to redefine the default <code class="computeroutput"><span class="identifier">overflow_error</span></code>
+          policy by using the BOOST_MATH_OVERFLOW_ERROR_POLICY macro. Once the <code class="computeroutput"><span class="identifier">user_overflow_error</span></code> function is defined
+          as above, we can achieve the same result like this:
+        </p>
+<pre class="programlisting"><span class="comment">// Redefine the default error_overflow policy
+</span><span class="preprocessor">#define</span> <span class="identifier">BOOST_MATH_OVERFLOW_ERROR_POLICY</span> <span class="identifier">user_error</span>
+<span class="preprocessor">#include</span> <span class="special">&lt;</span><span class="identifier">boost</span><span class="special">/</span><span class="identifier">math</span><span class="special">/</span><span class="identifier">special_functions</span><span class="special">/</span><span class="identifier">pow</span><span class="special">.</span><span class="identifier">hpp</span><span class="special">&gt;</span>
+
+<span class="comment">// From this point, passing a policy in argument is no longer needed, a call like this one
+</span><span class="comment">// will return -1 in case of error:
+</span>
+<span class="keyword">double</span> <span class="identifier">result</span> <span class="special">=</span> <span class="identifier">pow</span><span class="special">&lt;-</span><span class="number">5</span><span class="special">&gt;(</span><span class="identifier">base</span><span class="special">);</span>
+</pre>
+<a name="math_toolkit.special.powers.ct_pow.acknowledgements"></a><h5>
+<a name="id782721"></a>
+          <a class="link" href="ct_pow.html#math_toolkit.special.powers.ct_pow.acknowledgements">Acknowledgements</a>
+        </h5>
+<p>
+          Bruno Lalande submitted this addition to Boost.Math.
+        </p>
+<p>
+          Thanks to Joaquín López Muñoz and Scott McMurray for their help in
+improving the implementation.
+        </p>
+<a name="math_toolkit.special.powers.ct_pow.references"></a><h5>
+<a name="id782760"></a>
+          <a class="link" href="ct_pow.html#math_toolkit.special.powers.ct_pow.references">References</a>
+        </h5>
+<p>
+          D.E. Knuth, <span class="emphasis"><em>The Art of Computer Programming, Vol. 2: Seminumerical
+          Algorithms</em></span>, 2nd ed., Addison-Wesley, Reading, MA, 1981
+        </p>
+</div>
+<table xmlns:rev="http://www.cs.rpi.edu/~gregod/boost/tools/doc/revision" width="100%"><tr>
+<td align="left"></td>
+<td align="right"><div class="copyright-footer">Copyright © 2006 , 2007, 2008 John Maddock, Paul A. Bristow, Hubert
+      Holin, Xiaogang Zhang, Bruno Lalande and Gautam Sewani<p>
+        Distributed under the Boost Software License, Version 1.0. (See accompanying
+        file LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_0.txt)
+      </p>
+</div></td>
+</tr></table>
+<hr>
+<div class="spirit-nav">
+<a accesskey="p" href="hypot.html"><img src="../../../../../doc/html/images/prev.png" alt="Prev"></a><a accesskey="u" href="../powers.html"><img src="../../../../../doc/html/images/up.png" alt="Up"></a><a accesskey="h" href="../../../index.html"><img src="../../../../../doc/html/images/home.png" alt="Home"></a><a accesskey="n" href="../sinc.html"><img src="../../../../../doc/html/images/next.png" alt="Next"></a>
+</div>
+</body>
+</html>

Added: sandbox/tools/auto_index/example/math/doc/sf_and_dist/html/math_toolkit/special/powers/expm1.html
==============================================================================
--- (empty file)
+++ sandbox/tools/auto_index/example/math/doc/sf_and_dist/html/math_toolkit/special/powers/expm1.html	2008-11-28 05:25:28 EST (Fri, 28 Nov 2008)
@@ -0,0 +1,113 @@
+<html>
+<head>
+<meta http-equiv="Content-Type" content="text/html; charset=ISO-8859-1">
+<title>expm1</title>
+<link rel="stylesheet" href="../../../boostbook.css" type="text/css">
+<meta name="generator" content="DocBook XSL Stylesheets Vsnapshot_8125">
+<link rel="home" href="../../../index.html" title="Math Toolkit">
+<link rel="up" href="../powers.html" title="Logs, Powers, Roots and Exponentials">
+<link rel="prev" href="log1p.html" title="log1p">
+<link rel="next" href="cbrt.html" title="cbrt">
+</head>
+<body bgcolor="white" text="black" link="#0000FF" vlink="#840084" alink="#0000FF">
+<table cellpadding="2" width="100%"><tr>
+<td valign="top"><img alt="Boost C++ Libraries" width="277" height="86" src="../../../../../boost.png"></td>
+<td align="center">Home</td>
+<td align="center">Libraries</td>
+<td align="center">People</td>
+<td align="center">FAQ</td>
+<td align="center">More</td>
+</tr></table>
+<hr>
+<div class="spirit-nav">
+<a accesskey="p" href="log1p.html"><img src="../../../../../doc/html/images/prev.png" alt="Prev"></a><a accesskey="u" href="../powers.html"><img src="../../../../../doc/html/images/up.png" alt="Up"></a><a accesskey="h" href="../../../index.html"><img src="../../../../../doc/html/images/home.png" alt="Home"></a><a accesskey="n" href="cbrt.html"><img src="../../../../../doc/html/images/next.png" alt="Next"></a>
+</div>
+<div class="section" lang="en">
+<div class="titlepage"><div><div><h4 class="title">
+<a name="math_toolkit.special.powers.expm1"></a><a class="link" href="expm1.html" title="expm1"> expm1</a>
+</h4></div></div></div>
+<p>
+          
+</p>
+<pre class="programlisting"><span class="preprocessor">#include</span> <span class="special">&lt;</span><span class="identifier">boost</span><span class="special">/</span><span class="identifier">math</span><span class="special">/</span><span class="identifier">special_functions</span><span class="special">/</span><span class="identifier">expm1</span><span class="special">.</span><span class="identifier">hpp</span><span class="special">&gt;</span>
+</pre>
+<p>
+        </p>
+<pre class="programlisting"><span class="keyword">namespace</span> <span class="identifier">boost</span><span class="special">{</span> <span class="keyword">namespace</span> <span class="identifier">math</span><span class="special">{</span>
+
+<span class="keyword">template</span> <span class="special">&lt;</span><span class="keyword">class</span> <span class="identifier">T</span><span class="special">&gt;</span>
+<a class="link" href="../../main_overview/result_type.html" title="Calculation of the Type of the Result"><span class="emphasis"><em>calculated-result-type</em></span></a> <span class="identifier">expm1</span><span class="special">(</span><span class="identifier">T</span> <span class="identifier">x</span><span class="special">);</span>
+
+<span class="keyword">template</span> <span class="special">&lt;</span><span class="keyword">class</span> <span class="identifier">T</span><span class="special">,</span> <span class="keyword">class</span> <a class="link" href="../../policy.html" title="Policies">Policy</a><span class="special">&gt;</span>
+<a class="link" href="../../main_overview/result_type.html" title="Calculation of the Type of the Result"><span class="emphasis"><em>calculated-result-type</em></span></a> <span class="identifier">expm1</span><span class="special">(</span><span class="identifier">T</span> <span class="identifier">x</span><span class="special">,</span> <span class="keyword">const</span> <a class="link" href="../../policy.html" title="Policies">Policy</a><span class="special">&amp;);</span>
+
+<span class="special">}}</span> <span class="comment">// namespaces
+</span></pre>
+<p>
+          Returns e<sup>x</sup> - 1.
+        </p>
+<p>
+          The return type of this function is computed using the <a class="link" href="../../main_overview/result_type.html" title="Calculation of the Type of the Result"><span class="emphasis"><em>result
+          type calculation rules</em></span></a>: the return is <code class="computeroutput"><span class="keyword">double</span></code>
+          when <span class="emphasis"><em>x</em></span> is an integer type and T otherwise.
+        </p>
+<p>
+          </p>
+<p>
+            The final <a class="link" href="../../policy.html" title="Policies">Policy</a> argument
+            is optional and can be used to control the behaviour of the function:
+            how it handles errors, what level of precision to use etc. Refer to the
+            <a class="link" href="../../policy.html" title="Policies">policy documentation for more details</a>.
+          </p>
+<p>
+        </p>
+<p>
+          For small x, then <code class="computeroutput">e<sup>x</sup></code> is very close to 1, as a result calculating <code class="computeroutput">e<sup>x</sup> - 1</code> results in
+          catastrophic cancellation errors when x is small. <code class="computeroutput"><span class="identifier">expm1</span></code>
+          calculates <code class="computeroutput">e<sup>x</sup> - 1</code> using rational approximations (for up to 128-bit long doubles),
+          otherwise via a series expansion when x is small (giving an accuracy of
+          less than 2&#603;).
+        </p>
+<p>
+          Finally when BOOST_HAS_EXPM1 is defined then the <code class="computeroutput"><span class="keyword">float</span><span class="special">/</span><span class="keyword">double</span><span class="special">/</span><span class="keyword">long</span> <span class="keyword">double</span></code>
+          specializations of this template simply forward to the platform's native
+          (POSIX) implementation of this function.
+        </p>
+<p>
+          The following graph illustrates the behaviour of expm1:
+        </p>
+<p>
+          <span class="inlinemediaobject"><img src="../../../../graphs/expm1.png" align="middle"></span>
+        </p>
+<a name="math_toolkit.special.powers.expm1.accuracy"></a><h5>
+<a name="id778274"></a>
+          <a class="link" href="expm1.html#math_toolkit.special.powers.expm1.accuracy">Accuracy</a>
+        </h5>
+<p>
+          For built in floating point types <code class="computeroutput"><span class="identifier">expm1</span></code>
+          should have approximately 1 epsilon accuracy.
+        </p>
+<a name="math_toolkit.special.powers.expm1.testing"></a><h5>
+<a name="id778317"></a>
+          <a class="link" href="expm1.html#math_toolkit.special.powers.expm1.testing">Testing</a>
+        </h5>
+<p>
+          A mixture of spot test sanity checks, and random high precision test values
+          calculated using NTL::RR at 1000-bit precision.
+        </p>
+</div>
+<table xmlns:rev="http://www.cs.rpi.edu/~gregod/boost/tools/doc/revision" width="100%"><tr>
+<td align="left"></td>
+<td align="right"><div class="copyright-footer">Copyright © 2006 , 2007, 2008 John Maddock, Paul A. Bristow, Hubert
+      Holin, Xiaogang Zhang, Bruno Lalande and Gautam Sewani<p>
+        Distributed under the Boost Software License, Version 1.0. (See accompanying
+        file LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_0.txt)
+      </p>
+</div></td>
+</tr></table>
+<hr>
+<div class="spirit-nav">
+<a accesskey="p" href="log1p.html"><img src="../../../../../doc/html/images/prev.png" alt="Prev"></a><a accesskey="u" href="../powers.html"><img src="../../../../../doc/html/images/up.png" alt="Up"></a><a accesskey="h" href="../../../index.html"><img src="../../../../../doc/html/images/home.png" alt="Home"></a><a accesskey="n" href="cbrt.html"><img src="../../../../../doc/html/images/next.png" alt="Next"></a>
+</div>
+</body>
+</html>

Added: sandbox/tools/auto_index/example/math/doc/sf_and_dist/html/math_toolkit/special/powers/hypot.html
==============================================================================
--- (empty file)
+++ sandbox/tools/auto_index/example/math/doc/sf_and_dist/html/math_toolkit/special/powers/hypot.html	2008-11-28 05:25:28 EST (Fri, 28 Nov 2008)
@@ -0,0 +1,93 @@
+<html>
+<head>
+<meta http-equiv="Content-Type" content="text/html; charset=ISO-8859-1">
+<title>hypot</title>
+<link rel="stylesheet" href="../../../boostbook.css" type="text/css">
+<meta name="generator" content="DocBook XSL Stylesheets Vsnapshot_8125">
+<link rel="home" href="../../../index.html" title="Math Toolkit">
+<link rel="up" href="../powers.html" title="Logs, Powers, Roots and Exponentials">
+<link rel="prev" href="powm1.html" title="powm1">
+<link rel="next" href="ct_pow.html" title="Compile Time Power of a Runtime Base">
+</head>
+<body bgcolor="white" text="black" link="#0000FF" vlink="#840084" alink="#0000FF">
+<table cellpadding="2" width="100%"><tr>
+<td valign="top"><img alt="Boost C++ Libraries" width="277" height="86" src="../../../../../boost.png"></td>
+<td align="center">Home</td>
+<td align="center">Libraries</td>
+<td align="center">People</td>
+<td align="center">FAQ</td>
+<td align="center">More</td>
+</tr></table>
+<hr>
+<div class="spirit-nav">
+<a accesskey="p" href="powm1.html"><img src="../../../../../doc/html/images/prev.png" alt="Prev"></a><a accesskey="u" href="../powers.html"><img src="../../../../../doc/html/images/up.png" alt="Up"></a><a accesskey="h" href="../../../index.html"><img src="../../../../../doc/html/images/home.png" alt="Home"></a><a accesskey="n" href="ct_pow.html"><img src="../../../../../doc/html/images/next.png" alt="Next"></a>
+</div>
+<div class="section" lang="en">
+<div class="titlepage"><div><div><h4 class="title">
+<a name="math_toolkit.special.powers.hypot"></a><a class="link" href="hypot.html" title="hypot"> hypot</a>
+</h4></div></div></div>
+<pre class="programlisting"><span class="keyword">template</span> <span class="special">&lt;</span><span class="keyword">class</span> <span class="identifier">T1</span><span class="special">,</span> <span class="keyword">class</span> <span class="identifier">T2</span><span class="special">&gt;</span>
+<a class="link" href="../../main_overview/result_type.html" title="Calculation of the Type of the Result"><span class="emphasis"><em>calculated-result-type</em></span></a> <span class="identifier">hypot</span><span class="special">(</span><span class="identifier">T1</span> <span class="identifier">x</span><span class="special">,</span> <span class="identifier">T2</span> <span class="identifier">y</span><span class="special">);</span>
+
+<span class="keyword">template</span> <span class="special">&lt;</span><span class="keyword">class</span> <span class="identifier">T1</span><span class="special">,</span> <span class="keyword">class</span> <span class="identifier">T2</span><span class="special">,</span> <span class="keyword">class</span> <a class="link" href="../../policy.html" title="Policies">Policy</a><span class="special">&gt;</span>
+<a class="link" href="../../main_overview/result_type.html" title="Calculation of the Type of the Result"><span class="emphasis"><em>calculated-result-type</em></span></a> <span class="identifier">hypot</span><span class="special">(</span><span class="identifier">T1</span> <span class="identifier">x</span><span class="special">,</span> <span class="identifier">T2</span> <span class="identifier">y</span><span class="special">,</span> <span class="keyword">const</span> <a class="link" href="../../policy.html" title="Policies">Policy</a><span class="special">&amp;);</span>
+</pre>
+<p>
+          <span class="bold"><strong>Effects: </strong></span> computes <span class="inlinemediaobject"><img src="../../../../equations/hypot.png"></span>
+in such a
+          way as to avoid undue underflow and overflow.
+        </p>
+<p>
+          The return type of this function is computed using the <a class="link" href="../../main_overview/result_type.html" title="Calculation of the Type of the Result"><span class="emphasis"><em>result
+          type calculation rules</em></span></a> when T1 and T2 are of different
+          types.
+        </p>
+<p>
+          </p>
+<p>
+            The final <a class="link" href="../../policy.html" title="Policies">Policy</a> argument
+            is optional and can be used to control the behaviour of the function:
+            how it handles errors, what level of precision to use etc. Refer to the
+            <a class="link" href="../../policy.html" title="Policies">policy documentation for more details</a>.
+          </p>
+<p>
+        </p>
+<p>
+          When calculating <span class="inlinemediaobject"><img src="../../../../equations/hypot.png"></span> it's quite easy for the intermediate terms to
+          either overflow or underflow, even though the result is in fact perfectly
+          representable.
+        </p>
+<a name="math_toolkit.special.powers.hypot.implementation"></a><h5>
+<a name="id780408"></a>
+          <a class="link" href="hypot.html#math_toolkit.special.powers.hypot.implementation">Implementation</a>
+        </h5>
+<p>
+          The function is even and symmetric in x and y, so first take assume <span class="emphasis"><em>x,y
+          &gt; 0</em></span> and <span class="emphasis"><em>x &gt; y</em></span> (we can permute the
+          arguments if this is not the case).
+        </p>
+<p>
+          Then if <span class="emphasis"><em>x * &#949; &gt;= y</em></span> we can simply return <span class="emphasis"><em>x</em></span>.
+        </p>
+<p>
+          Otherwise the result is given by:
+        </p>
+<p>
+          <span class="inlinemediaobject"><img src="../../../../equations/hypot2.png"></span>
+        </p>
+</div>
+<table xmlns:rev="http://www.cs.rpi.edu/~gregod/boost/tools/doc/revision" width="100%"><tr>
+<td align="left"></td>
+<td align="right"><div class="copyright-footer">Copyright © 2006 , 2007, 2008 John Maddock, Paul A. Bristow, Hubert
+      Holin, Xiaogang Zhang, Bruno Lalande and Gautam Sewani<p>
+        Distributed under the Boost Software License, Version 1.0. (See accompanying
+        file LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_0.txt)
+      </p>
+</div></td>
+</tr></table>
+<hr>
+<div class="spirit-nav">
+<a accesskey="p" href="powm1.html"><img src="../../../../../doc/html/images/prev.png" alt="Prev"></a><a accesskey="u" href="../powers.html"><img src="../../../../../doc/html/images/up.png" alt="Up"></a><a accesskey="h" href="../../../index.html"><img src="../../../../../doc/html/images/home.png" alt="Home"></a><a accesskey="n" href="ct_pow.html"><img src="../../../../../doc/html/images/next.png" alt="Next"></a>
+</div>
+</body>
+</html>

Added: sandbox/tools/auto_index/example/math/doc/sf_and_dist/html/math_toolkit/special/powers/log1p.html
==============================================================================
--- (empty file)
+++ sandbox/tools/auto_index/example/math/doc/sf_and_dist/html/math_toolkit/special/powers/log1p.html	2008-11-28 05:25:28 EST (Fri, 28 Nov 2008)
@@ -0,0 +1,126 @@
+<html>
+<head>
+<meta http-equiv="Content-Type" content="text/html; charset=ISO-8859-1">
+<title>log1p</title>
+<link rel="stylesheet" href="../../../boostbook.css" type="text/css">
+<meta name="generator" content="DocBook XSL Stylesheets Vsnapshot_8125">
+<link rel="home" href="../../../index.html" title="Math Toolkit">
+<link rel="up" href="../powers.html" title="Logs, Powers, Roots and Exponentials">
+<link rel="prev" href="../powers.html" title="Logs, Powers, Roots and Exponentials">
+<link rel="next" href="expm1.html" title="expm1">
+</head>
+<body bgcolor="white" text="black" link="#0000FF" vlink="#840084" alink="#0000FF">
+<table cellpadding="2" width="100%"><tr>
+<td valign="top"><img alt="Boost C++ Libraries" width="277" height="86" src="../../../../../boost.png"></td>
+<td align="center">Home</td>
+<td align="center">Libraries</td>
+<td align="center">People</td>
+<td align="center">FAQ</td>
+<td align="center">More</td>
+</tr></table>
+<hr>
+<div class="spirit-nav">
+<a accesskey="p" href="../powers.html"><img src="../../../../../doc/html/images/prev.png" alt="Prev"></a><a accesskey="u" href="../powers.html"><img src="../../../../../doc/html/images/up.png" alt="Up"></a><a accesskey="h" href="../../../index.html"><img src="../../../../../doc/html/images/home.png" alt="Home"></a><a accesskey="n" href="expm1.html"><img src="../../../../../doc/html/images/next.png" alt="Next"></a>
+</div>
+<div class="section" lang="en">
+<div class="titlepage"><div><div><h4 class="title">
+<a name="math_toolkit.special.powers.log1p"></a><a class="link" href="log1p.html" title="log1p"> log1p</a>
+</h4></div></div></div>
+<p>
+          
+</p>
+<pre class="programlisting"><span class="preprocessor">#include</span> <span class="special">&lt;</span><span class="identifier">boost</span><span class="special">/</span><span class="identifier">math</span><span class="special">/</span><span class="identifier">special_functions</span><span class="special">/</span><span class="identifier">log1p</span><span class="special">.</span><span class="identifier">hpp</span><span class="special">&gt;</span>
+</pre>
+<p>
+        </p>
+<pre class="programlisting"><span class="keyword">namespace</span> <span class="identifier">boost</span><span class="special">{</span> <span class="keyword">namespace</span> <span class="identifier">math</span><span class="special">{</span>
+
+<span class="keyword">template</span> <span class="special">&lt;</span><span class="keyword">class</span> <span class="identifier">T</span><span class="special">&gt;</span>
+<a class="link" href="../../main_overview/result_type.html" title="Calculation of the Type of the Result"><span class="emphasis"><em>calculated-result-type</em></span></a> <span class="identifier">log1p</span><span class="special">(</span><span class="identifier">T</span> <span class="identifier">x</span><span class="special">);</span>
+
+<span class="keyword">template</span> <span class="special">&lt;</span><span class="keyword">class</span> <span class="identifier">T</span><span class="special">,</span> <span class="keyword">class</span> <a class="link" href="../../policy.html" title="Policies">Policy</a><span class="special">&gt;</span>
+<a class="link" href="../../main_overview/result_type.html" title="Calculation of the Type of the Result"><span class="emphasis"><em>calculated-result-type</em></span></a> <span class="identifier">log1p</span><span class="special">(</span><span class="identifier">T</span> <span class="identifier">x</span><span class="special">,</span> <span class="keyword">const</span> <a class="link" href="../../policy.html" title="Policies">Policy</a><span class="special">&amp;);</span>
+
+<span class="special">}}</span> <span class="comment">// namespaces
+</span></pre>
+<p>
+          Returns the natural logarithm of <code class="computeroutput"><span class="identifier">x</span><span class="special">+</span><span class="number">1</span></code>.
+        </p>
+<p>
+          The return type of this function is computed using the <a class="link" href="../../main_overview/result_type.html" title="Calculation of the Type of the Result"><span class="emphasis"><em>result
+          type calculation rules</em></span></a>: the return is <code class="computeroutput"><span class="keyword">double</span></code>
+          when <span class="emphasis"><em>x</em></span> is an integer type and T otherwise.
+        </p>
+<p>
+          </p>
+<p>
+            The final <a class="link" href="../../policy.html" title="Policies">Policy</a> argument
+            is optional and can be used to control the behaviour of the function:
+            how it handles errors, what level of precision to use etc. Refer to the
+            <a class="link" href="../../policy.html" title="Policies">policy documentation for more details</a>.
+          </p>
+<p>
+        </p>
+<p>
+          There are many situations where it is desirable to compute <code class="computeroutput"><span class="identifier">log</span><span class="special">(</span><span class="identifier">x</span><span class="special">+</span><span class="number">1</span><span class="special">)</span></code>. However, for small <code class="computeroutput"><span class="identifier">x</span></code>
+          then <code class="computeroutput"><span class="identifier">x</span><span class="special">+</span><span class="number">1</span></code> suffers from catastrophic cancellation
+          errors so that <code class="computeroutput"><span class="identifier">x</span><span class="special">+</span><span class="number">1</span> <span class="special">==</span> <span class="number">1</span></code>
+          and <code class="computeroutput"><span class="identifier">log</span><span class="special">(</span><span class="identifier">x</span><span class="special">+</span><span class="number">1</span><span class="special">)</span> <span class="special">==</span> <span class="number">0</span></code>,
+          when in fact for very small x, the best approximation to <code class="computeroutput"><span class="identifier">log</span><span class="special">(</span><span class="identifier">x</span><span class="special">+</span><span class="number">1</span><span class="special">)</span></code> would be <code class="computeroutput"><span class="identifier">x</span></code>.
+          <code class="computeroutput"><span class="identifier">log1p</span></code> calculates the best
+          approximation to <code class="computeroutput"><span class="identifier">log</span><span class="special">(</span><span class="number">1</span><span class="special">+</span><span class="identifier">x</span><span class="special">)</span></code> using a Taylor series expansion for accuracy
+          (less than 2&#603;). Alternatively note that there are faster methods available,
+          for example using the equivalence:
+        </p>
+<pre class="programlisting"><span class="identifier">log</span><span class="special">(</span><span class="number">1</span><span class="special">+</span><span class="identifier">x</span><span class="special">)</span> <span class="special">==</span> <span class="special">(</span><span class="identifier">log</span><span class="special">(</span><span class="number">1</span><span class="special">+</span><span class="identifier">x</span><span class="special">)</span> <span class="special">*</span> <span class="identifier">x</span><span class="special">)</span> <span class="special">/</span> <span class="special">((</span><span class="number">1</span><span class="special">-</span><span class="identifier">x</span><span class="special">)</span> <span class="special">-</span> <span class="number">1</span><span class="special">)</span>
+</pre>
+<p>
+          However, experience has shown that these methods tend to fail quite spectacularly
+          once the compiler's optimizations are turned on, consequently they are
+          used only when known not to break with a particular compiler. In contrast,
+          the series expansion method seems to be reasonably immune to optimizer-induced
+          errors.
+        </p>
+<p>
+          Finally when BOOST_HAS_LOG1P is defined then the <code class="computeroutput"><span class="keyword">float</span><span class="special">/</span><span class="keyword">double</span><span class="special">/</span><span class="keyword">long</span> <span class="keyword">double</span></code>
+          specializations of this template simply forward to the platform's native
+          (POSIX) implementation of this function.
+        </p>
+<p>
+          The following graph illustrates the behaviour of log1p:
+        </p>
+<p>
+          <span class="inlinemediaobject"><img src="../../../../graphs/log1p.png" align="middle"></span>
+        </p>
+<a name="math_toolkit.special.powers.log1p.accuracy"></a><h5>
+<a name="id777666"></a>
+          <a class="link" href="log1p.html#math_toolkit.special.powers.log1p.accuracy">Accuracy</a>
+        </h5>
+<p>
+          For built in floating point types <code class="computeroutput"><span class="identifier">log1p</span></code>
+          should have approximately 1 epsilon accuracy.
+        </p>
+<a name="math_toolkit.special.powers.log1p.testing"></a><h5>
+<a name="id777708"></a>
+          <a class="link" href="log1p.html#math_toolkit.special.powers.log1p.testing">Testing</a>
+        </h5>
+<p>
+          A mixture of spot test sanity checks, and random high precision test values
+          calculated using NTL::RR at 1000-bit precision.
+        </p>
+</div>
+<table xmlns:rev="http://www.cs.rpi.edu/~gregod/boost/tools/doc/revision" width="100%"><tr>
+<td align="left"></td>
+<td align="right"><div class="copyright-footer">Copyright © 2006 , 2007, 2008 John Maddock, Paul A. Bristow, Hubert
+      Holin, Xiaogang Zhang, Bruno Lalande and Gautam Sewani<p>
+        Distributed under the Boost Software License, Version 1.0. (See accompanying
+        file LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_0.txt)
+      </p>
+</div></td>
+</tr></table>
+<hr>
+<div class="spirit-nav">
+<a accesskey="p" href="../powers.html"><img src="../../../../../doc/html/images/prev.png" alt="Prev"></a><a accesskey="u" href="../powers.html"><img src="../../../../../doc/html/images/up.png" alt="Up"></a><a accesskey="h" href="../../../index.html"><img src="../../../../../doc/html/images/home.png" alt="Home"></a><a accesskey="n" href="expm1.html"><img src="../../../../../doc/html/images/next.png" alt="Next"></a>
+</div>
+</body>
+</html>

Added: sandbox/tools/auto_index/example/math/doc/sf_and_dist/html/math_toolkit/special/powers/powm1.html
==============================================================================
--- (empty file)
+++ sandbox/tools/auto_index/example/math/doc/sf_and_dist/html/math_toolkit/special/powers/powm1.html	2008-11-28 05:25:28 EST (Fri, 28 Nov 2008)
@@ -0,0 +1,106 @@
+<html>
+<head>
+<meta http-equiv="Content-Type" content="text/html; charset=ISO-8859-1">
+<title>powm1</title>
+<link rel="stylesheet" href="../../../boostbook.css" type="text/css">
+<meta name="generator" content="DocBook XSL Stylesheets Vsnapshot_8125">
+<link rel="home" href="../../../index.html" title="Math Toolkit">
+<link rel="up" href="../powers.html" title="Logs, Powers, Roots and Exponentials">
+<link rel="prev" href="sqrt1pm1.html" title="sqrt1pm1">
+<link rel="next" href="hypot.html" title="hypot">
+</head>
+<body bgcolor="white" text="black" link="#0000FF" vlink="#840084" alink="#0000FF">
+<table cellpadding="2" width="100%"><tr>
+<td valign="top"><img alt="Boost C++ Libraries" width="277" height="86" src="../../../../../boost.png"></td>
+<td align="center">Home</td>
+<td align="center">Libraries</td>
+<td align="center">People</td>
+<td align="center">FAQ</td>
+<td align="center">More</td>
+</tr></table>
+<hr>
+<div class="spirit-nav">
+<a accesskey="p" href="sqrt1pm1.html"><img src="../../../../../doc/html/images/prev.png" alt="Prev"></a><a accesskey="u" href="../powers.html"><img src="../../../../../doc/html/images/up.png" alt="Up"></a><a accesskey="h" href="../../../index.html"><img src="../../../../../doc/html/images/home.png" alt="Home"></a><a accesskey="n" href="hypot.html"><img src="../../../../../doc/html/images/next.png" alt="Next"></a>
+</div>
+<div class="section" lang="en">
+<div class="titlepage"><div><div><h4 class="title">
+<a name="math_toolkit.special.powers.powm1"></a><a class="link" href="powm1.html" title="powm1"> powm1</a>
+</h4></div></div></div>
+<p>
+          
+</p>
+<pre class="programlisting"><span class="preprocessor">#include</span> <span class="special">&lt;</span><span class="identifier">boost</span><span class="special">/</span><span class="identifier">math</span><span class="special">/</span><span class="identifier">special_functions</span><span class="special">/</span><span class="identifier">powm1</span><span class="special">.</span><span class="identifier">hpp</span><span class="special">&gt;</span>
+</pre>
+<p>
+        </p>
+<pre class="programlisting"><span class="keyword">namespace</span> <span class="identifier">boost</span><span class="special">{</span> <span class="keyword">namespace</span> <span class="identifier">math</span><span class="special">{</span>
+
+<span class="keyword">template</span> <span class="special">&lt;</span><span class="keyword">class</span> <span class="identifier">T1</span><span class="special">,</span> <span class="keyword">class</span> <span class="identifier">T2</span><span class="special">&gt;</span>
+<a class="link" href="../../main_overview/result_type.html" title="Calculation of the Type of the Result"><span class="emphasis"><em>calculated-result-type</em></span></a> <span class="identifier">powm1</span><span class="special">(</span><span class="identifier">T1</span> <span class="identifier">x</span><span class="special">,</span> <span class="identifier">T2</span> <span class="identifier">y</span><span class="special">);</span>
+
+<span class="keyword">template</span> <span class="special">&lt;</span><span class="keyword">class</span> <span class="identifier">T1</span><span class="special">,</span> <span class="keyword">class</span> <span class="identifier">T2</span><span class="special">,</span> <span class="keyword">class</span> <a class="link" href="../../policy.html" title="Policies">Policy</a><span class="special">&gt;</span>
+<a class="link" href="../../main_overview/result_type.html" title="Calculation of the Type of the Result"><span class="emphasis"><em>calculated-result-type</em></span></a> <span class="identifier">powm1</span><span class="special">(</span><span class="identifier">T1</span> <span class="identifier">x</span><span class="special">,</span> <span class="identifier">T2</span> <span class="identifier">y</span><span class="special">,</span> <span class="keyword">const</span> <a class="link" href="../../policy.html" title="Policies">Policy</a><span class="special">&amp;);</span>
+
+<span class="special">}}</span> <span class="comment">// namespaces
+</span></pre>
+<p>
+          Returns x<sup>y </sup> - 1.
+        </p>
+<p>
+          The return type of this function is computed using the <a class="link" href="../../main_overview/result_type.html" title="Calculation of the Type of the Result"><span class="emphasis"><em>result
+          type calculation rules</em></span></a> when T1 and T2 are dufferent types.
+        </p>
+<p>
+          </p>
+<p>
+            The final <a class="link" href="../../policy.html" title="Policies">Policy</a> argument
+            is optional and can be used to control the behaviour of the function:
+            how it handles errors, what level of precision to use etc. Refer to the
+            <a class="link" href="../../policy.html" title="Policies">policy documentation for more details</a>.
+          </p>
+<p>
+        </p>
+<p>
+          There are two domains where this is useful: when y is very small, or when
+          x is close to 1.
+        </p>
+<p>
+          Implemented in terms of <code class="computeroutput"><span class="identifier">expm1</span></code>.
+        </p>
+<p>
+          The following graph illustrates the behaviour of powm1:
+        </p>
+<p>
+          <span class="inlinemediaobject"><img src="../../../../graphs/powm1.png" align="middle"></span>
+        </p>
+<a name="math_toolkit.special.powers.powm1.accuracy"></a><h5>
+<a name="id779959"></a>
+          <a class="link" href="powm1.html#math_toolkit.special.powers.powm1.accuracy">Accuracy</a>
+        </h5>
+<p>
+          Should have approximately 2-3 epsilon accuracy.
+        </p>
+<a name="math_toolkit.special.powers.powm1.testing"></a><h5>
+<a name="id779989"></a>
+          <a class="link" href="powm1.html#math_toolkit.special.powers.powm1.testing">Testing</a>
+        </h5>
+<p>
+          A selection of random high precision test values calculated using NTL::RR
+          at 1000-bit precision.
+        </p>
+</div>
+<table xmlns:rev="http://www.cs.rpi.edu/~gregod/boost/tools/doc/revision" width="100%"><tr>
+<td align="left"></td>
+<td align="right"><div class="copyright-footer">Copyright © 2006 , 2007, 2008 John Maddock, Paul A. Bristow, Hubert
+      Holin, Xiaogang Zhang, Bruno Lalande and Gautam Sewani<p>
+        Distributed under the Boost Software License, Version 1.0. (See accompanying
+        file LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_0.txt)
+      </p>
+</div></td>
+</tr></table>
+<hr>
+<div class="spirit-nav">
+<a accesskey="p" href="sqrt1pm1.html"><img src="../../../../../doc/html/images/prev.png" alt="Prev"></a><a accesskey="u" href="../powers.html"><img src="../../../../../doc/html/images/up.png" alt="Up"></a><a accesskey="h" href="../../../index.html"><img src="../../../../../doc/html/images/home.png" alt="Home"></a><a accesskey="n" href="hypot.html"><img src="../../../../../doc/html/images/next.png" alt="Next"></a>
+</div>
+</body>
+</html>

Added: sandbox/tools/auto_index/example/math/doc/sf_and_dist/html/math_toolkit/special/powers/sqrt1pm1.html
==============================================================================
--- (empty file)
+++ sandbox/tools/auto_index/example/math/doc/sf_and_dist/html/math_toolkit/special/powers/sqrt1pm1.html	2008-11-28 05:25:28 EST (Fri, 28 Nov 2008)
@@ -0,0 +1,109 @@
+<html>
+<head>
+<meta http-equiv="Content-Type" content="text/html; charset=ISO-8859-1">
+<title>sqrt1pm1</title>
+<link rel="stylesheet" href="../../../boostbook.css" type="text/css">
+<meta name="generator" content="DocBook XSL Stylesheets Vsnapshot_8125">
+<link rel="home" href="../../../index.html" title="Math Toolkit">
+<link rel="up" href="../powers.html" title="Logs, Powers, Roots and Exponentials">
+<link rel="prev" href="cbrt.html" title="cbrt">
+<link rel="next" href="powm1.html" title="powm1">
+</head>
+<body bgcolor="white" text="black" link="#0000FF" vlink="#840084" alink="#0000FF">
+<table cellpadding="2" width="100%"><tr>
+<td valign="top"><img alt="Boost C++ Libraries" width="277" height="86" src="../../../../../boost.png"></td>
+<td align="center">Home</td>
+<td align="center">Libraries</td>
+<td align="center">People</td>
+<td align="center">FAQ</td>
+<td align="center">More</td>
+</tr></table>
+<hr>
+<div class="spirit-nav">
+<a accesskey="p" href="cbrt.html"><img src="../../../../../doc/html/images/prev.png" alt="Prev"></a><a accesskey="u" href="../powers.html"><img src="../../../../../doc/html/images/up.png" alt="Up"></a><a accesskey="h" href="../../../index.html"><img src="../../../../../doc/html/images/home.png" alt="Home"></a><a accesskey="n" href="powm1.html"><img src="../../../../../doc/html/images/next.png" alt="Next"></a>
+</div>
+<div class="section" lang="en">
+<div class="titlepage"><div><div><h4 class="title">
+<a name="math_toolkit.special.powers.sqrt1pm1"></a><a class="link" href="sqrt1pm1.html" title="sqrt1pm1"> sqrt1pm1</a>
+</h4></div></div></div>
+<p>
+          
+</p>
+<pre class="programlisting"><span class="preprocessor">#include</span> <span class="special">&lt;</span><span class="identifier">boost</span><span class="special">/</span><span class="identifier">math</span><span class="special">/</span><span class="identifier">special_functions</span><span class="special">/</span><span class="identifier">sqrt1pm1</span><span class="special">.</span><span class="identifier">hpp</span><span class="special">&gt;</span>
+</pre>
+<p>
+        </p>
+<pre class="programlisting"><span class="keyword">namespace</span> <span class="identifier">boost</span><span class="special">{</span> <span class="keyword">namespace</span> <span class="identifier">math</span><span class="special">{</span>
+
+<span class="keyword">template</span> <span class="special">&lt;</span><span class="keyword">class</span> <span class="identifier">T</span><span class="special">&gt;</span>
+<a class="link" href="../../main_overview/result_type.html" title="Calculation of the Type of the Result"><span class="emphasis"><em>calculated-result-type</em></span></a> <span class="identifier">sqrt1pm1</span><span class="special">(</span><span class="identifier">T</span> <span class="identifier">x</span><span class="special">);</span>
+
+<span class="keyword">template</span> <span class="special">&lt;</span><span class="keyword">class</span> <span class="identifier">T</span><span class="special">,</span> <span class="keyword">class</span> <a class="link" href="../../policy.html" title="Policies">Policy</a><span class="special">&gt;</span>
+<a class="link" href="../../main_overview/result_type.html" title="Calculation of the Type of the Result"><span class="emphasis"><em>calculated-result-type</em></span></a> <span class="identifier">sqrt1pm1</span><span class="special">(</span><span class="identifier">T</span> <span class="identifier">x</span><span class="special">,</span> <span class="keyword">const</span> <a class="link" href="../../policy.html" title="Policies">Policy</a><span class="special">&amp;);</span>
+
+<span class="special">}}</span> <span class="comment">// namespaces
+</span></pre>
+<p>
+          Returns <code class="computeroutput"><span class="identifier">sqrt</span><span class="special">(</span><span class="number">1</span><span class="special">+</span><span class="identifier">x</span><span class="special">)</span> <span class="special">-</span> <span class="number">1</span></code>.
+        </p>
+<p>
+          The return type of this function is computed using the <a class="link" href="../../main_overview/result_type.html" title="Calculation of the Type of the Result"><span class="emphasis"><em>result
+          type calculation rules</em></span></a>: the return is <code class="computeroutput"><span class="keyword">double</span></code>
+          when <span class="emphasis"><em>x</em></span> is an integer type and T otherwise.
+        </p>
+<p>
+          </p>
+<p>
+            The final <a class="link" href="../../policy.html" title="Policies">Policy</a> argument
+            is optional and can be used to control the behaviour of the function:
+            how it handles errors, what level of precision to use etc. Refer to the
+            <a class="link" href="../../policy.html" title="Policies">policy documentation for more details</a>.
+          </p>
+<p>
+        </p>
+<p>
+          This function is useful when you need the difference between sqrt(x) and
+          1, when x is itself close to 1.
+        </p>
+<p>
+          Implemented in terms of <code class="computeroutput"><span class="identifier">log1p</span></code>
+          and <code class="computeroutput"><span class="identifier">expm1</span></code>.
+        </p>
+<p>
+          The following graph illustrates the behaviour of sqrt1pm1:
+        </p>
+<p>
+          <span class="inlinemediaobject"><img src="../../../../graphs/sqrt1pm1.png" align="middle"></span>
+        </p>
+<a name="math_toolkit.special.powers.sqrt1pm1.accuracy"></a><h5>
+<a name="id779378"></a>
+          <a class="link" href="sqrt1pm1.html#math_toolkit.special.powers.sqrt1pm1.accuracy">Accuracy</a>
+        </h5>
+<p>
+          For built in floating-point types <code class="computeroutput"><span class="identifier">sqrt1pm1</span></code>
+          should have approximately 3 epsilon accuracy.
+        </p>
+<a name="math_toolkit.special.powers.sqrt1pm1.testing"></a><h5>
+<a name="id779421"></a>
+          <a class="link" href="sqrt1pm1.html#math_toolkit.special.powers.sqrt1pm1.testing">Testing</a>
+        </h5>
+<p>
+          A selection of random high precision test values calculated using NTL::RR
+          at 1000-bit precision.
+        </p>
+</div>
+<table xmlns:rev="http://www.cs.rpi.edu/~gregod/boost/tools/doc/revision" width="100%"><tr>
+<td align="left"></td>
+<td align="right"><div class="copyright-footer">Copyright © 2006 , 2007, 2008 John Maddock, Paul A. Bristow, Hubert
+      Holin, Xiaogang Zhang, Bruno Lalande and Gautam Sewani<p>
+        Distributed under the Boost Software License, Version 1.0. (See accompanying
+        file LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_0.txt)
+      </p>
+</div></td>
+</tr></table>
+<hr>
+<div class="spirit-nav">
+<a accesskey="p" href="cbrt.html"><img src="../../../../../doc/html/images/prev.png" alt="Prev"></a><a accesskey="u" href="../powers.html"><img src="../../../../../doc/html/images/up.png" alt="Up"></a><a accesskey="h" href="../../../index.html"><img src="../../../../../doc/html/images/home.png" alt="Home"></a><a accesskey="n" href="powm1.html"><img src="../../../../../doc/html/images/next.png" alt="Next"></a>
+</div>
+</body>
+</html>

Added: sandbox/tools/auto_index/example/math/doc/sf_and_dist/html/math_toolkit/special/rounding.html
==============================================================================
--- (empty file)
+++ sandbox/tools/auto_index/example/math/doc/sf_and_dist/html/math_toolkit/special/rounding.html	2008-11-28 05:25:28 EST (Fri, 28 Nov 2008)
@@ -0,0 +1,51 @@
+<html>
+<head>
+<meta http-equiv="Content-Type" content="text/html; charset=ISO-8859-1">
+<title>Rounding Truncation and Integer Conversion</title>
+<link rel="stylesheet" href="../../boostbook.css" type="text/css">
+<meta name="generator" content="DocBook XSL Stylesheets Vsnapshot_8125">
+<link rel="home" href="../../index.html" title="Math Toolkit">
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+</div>
+<div class="section" lang="en">
+<div class="titlepage"><div><div><h3 class="title">
+<a name="math_toolkit.special.rounding"></a><a class="link" href="rounding.html" title="Rounding Truncation and Integer Conversion"> Rounding Truncation and
+      Integer Conversion</a>
+</h3></div></div></div>
+<div class="toc"><dl>
+<dt><span class="section"> Rounding Functions</span></dt>
+<dt><span class="section"> Truncation Functions</span></dt>
+<dt><span class="section"><a href="rounding/modf.html"> Integer and Fractional
+        Part Splitting (modf)</a></span></dt>
+</dl></div>
+</div>
+<table xmlns:rev="http://www.cs.rpi.edu/~gregod/boost/tools/doc/revision" width="100%"><tr>
+<td align="left"></td>
+<td align="right"><div class="copyright-footer">Copyright © 2006 , 2007, 2008 John Maddock, Paul A. Bristow, Hubert
+      Holin, Xiaogang Zhang, Bruno Lalande and Gautam Sewani<p>
+        Distributed under the Boost Software License, Version 1.0. (See accompanying
+        file LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_0.txt)
+      </p>
+</div></td>
+</tr></table>
+<hr>
+<div class="spirit-nav">
+<a accesskey="p" href="inv_hyper/atanh.html"><img src="../../../../doc/html/images/prev.png" alt="Prev"></a><a accesskey="u" href="../special.html"><img src="../../../../doc/html/images/up.png" alt="Up"></a><a accesskey="h" href="../../index.html"><img src="../../../../doc/html/images/home.png" alt="Home"></a><a accesskey="n" href="rounding/round.html"><img src="../../../../doc/html/images/next.png" alt="Next"></a>
+</div>
+</body>
+</html>

Added: sandbox/tools/auto_index/example/math/doc/sf_and_dist/html/math_toolkit/special/rounding/modf.html
==============================================================================
--- (empty file)
+++ sandbox/tools/auto_index/example/math/doc/sf_and_dist/html/math_toolkit/special/rounding/modf.html	2008-11-28 05:25:28 EST (Fri, 28 Nov 2008)
@@ -0,0 +1,85 @@
+<html>
+<head>
+<meta http-equiv="Content-Type" content="text/html; charset=ISO-8859-1">
+<title>Integer and Fractional Part Splitting (modf)</title>
+<link rel="stylesheet" href="../../../boostbook.css" type="text/css">
+<meta name="generator" content="DocBook XSL Stylesheets Vsnapshot_8125">
+<link rel="home" href="../../../index.html" title="Math Toolkit">
+<link rel="up" href="../rounding.html" title="Rounding Truncation and Integer Conversion">
+<link rel="prev" href="trunc.html" title="Truncation Functions">
+<link rel="next" href="../fpclass.html" title="Floating-Point Classification: Infinities and NaN's">
+</head>
+<body bgcolor="white" text="black" link="#0000FF" vlink="#840084" alink="#0000FF">
+<table cellpadding="2" width="100%"><tr>
+<td valign="top"><img alt="Boost C++ Libraries" width="277" height="86" src="../../../../../boost.png"></td>
+<td align="center">Home</td>
+<td align="center">Libraries</td>
+<td align="center">People</td>
+<td align="center">FAQ</td>
+<td align="center">More</td>
+</tr></table>
+<hr>
+<div class="spirit-nav">
+<a accesskey="p" href="trunc.html"><img src="../../../../../doc/html/images/prev.png" alt="Prev"></a><a accesskey="u" href="../rounding.html"><img src="../../../../../doc/html/images/up.png" alt="Up"></a><a accesskey="h" href="../../../index.html"><img src="../../../../../doc/html/images/home.png" alt="Home"></a><a accesskey="n" href="../fpclass.html"><img src="../../../../../doc/html/images/next.png" alt="Next"></a>
+</div>
+<div class="section" lang="en">
+<div class="titlepage"><div><div><h4 class="title">
+<a name="math_toolkit.special.rounding.modf"></a><a class="link" href="modf.html" title="Integer and Fractional Part Splitting (modf)"> Integer and Fractional
+        Part Splitting (modf)</a>
+</h4></div></div></div>
+<p>
+          
+</p>
+<pre class="programlisting"><span class="preprocessor">#include</span> <span class="special">&lt;</span><span class="identifier">boost</span><span class="special">/</span><span class="identifier">math</span><span class="special">/</span><span class="identifier">special_functions</span><span class="special">/</span><span class="identifier">modf</span><span class="special">.</span><span class="identifier">hpp</span><span class="special">&gt;</span></pre>
+<p>
+        </p>
+<pre class="programlisting"><span class="keyword">template</span> <span class="special">&lt;</span><span class="keyword">class</span> <span class="identifier">T</span><span class="special">&gt;</span>
+<span class="identifier">T</span> <span class="identifier">modf</span><span class="special">(</span><span class="keyword">const</span> <span class="identifier">T</span><span class="special">&amp;</span> <span class="identifier">v</span><span class="special">,</span> <span class="identifier">T</span><span class="special">*</span> <span class="identifier">ipart</span><span class="special">);</span>
+
+<span class="keyword">template</span> <span class="special">&lt;</span><span class="keyword">class</span> <span class="identifier">T</span><span class="special">,</span> <span class="keyword">class</span> <span class="identifier">Policy</span><span class="special">&gt;</span>
+<span class="identifier">T</span> <span class="identifier">modf</span><span class="special">(</span><span class="keyword">const</span> <span class="identifier">T</span><span class="special">&amp;</span> <span class="identifier">v</span><span class="special">,</span> <span class="identifier">T</span><span class="special">*</span> <span class="identifier">ipart</span><span class="special">,</span> <span class="keyword">const</span> <span class="identifier">Policy</span><span class="special">&amp;);</span>
+
+<span class="keyword">template</span> <span class="special">&lt;</span><span class="keyword">class</span> <span class="identifier">T</span><span class="special">&gt;</span>
+<span class="identifier">T</span> <span class="identifier">modf</span><span class="special">(</span><span class="keyword">const</span> <span class="identifier">T</span><span class="special">&amp;</span> <span class="identifier">v</span><span class="special">,</span> <span class="keyword">int</span><span class="special">*</span> <span class="identifier">ipart</span><span class="special">);</span>
+
+<span class="keyword">template</span> <span class="special">&lt;</span><span class="keyword">class</span> <span class="identifier">T</span><span class="special">,</span> <span class="keyword">class</span> <span class="identifier">Policy</span><span class="special">&gt;</span>
+<span class="identifier">T</span> <span class="identifier">modf</span><span class="special">(</span><span class="keyword">const</span> <span class="identifier">T</span><span class="special">&amp;</span> <span class="identifier">v</span><span class="special">,</span> <span class="keyword">int</span><span class="special">*</span> <span class="identifier">ipart</span><span class="special">,</span> <span class="keyword">const</span> <span class="identifier">Policy</span><span class="special">&amp;);</span>
+
+<span class="keyword">template</span> <span class="special">&lt;</span><span class="keyword">class</span> <span class="identifier">T</span><span class="special">&gt;</span>
+<span class="identifier">T</span> <span class="identifier">modf</span><span class="special">(</span><span class="keyword">const</span> <span class="identifier">T</span><span class="special">&amp;</span> <span class="identifier">v</span><span class="special">,</span> <span class="keyword">long</span><span class="special">*</span> <span class="identifier">ipart</span><span class="special">);</span>
+
+<span class="keyword">template</span> <span class="special">&lt;</span><span class="keyword">class</span> <span class="identifier">T</span><span class="special">,</span> <span class="keyword">class</span> <span class="identifier">Policy</span><span class="special">&gt;</span>
+<span class="identifier">T</span> <span class="identifier">modf</span><span class="special">(</span><span class="keyword">const</span> <span class="identifier">T</span><span class="special">&amp;</span> <span class="identifier">v</span><span class="special">,</span> <span class="keyword">long</span><span class="special">*</span> <span class="identifier">ipart</span><span class="special">,</span> <span class="keyword">const</span> <span class="identifier">Policy</span><span class="special">&amp;);</span>
+
+<span class="keyword">template</span> <span class="special">&lt;</span><span class="keyword">class</span> <span class="identifier">T</span><span class="special">&gt;</span>
+<span class="identifier">T</span> <span class="identifier">modf</span><span class="special">(</span><span class="keyword">const</span> <span class="identifier">T</span><span class="special">&amp;</span> <span class="identifier">v</span><span class="special">,</span> <span class="keyword">long</span> <span class="keyword">long</span><span class="special">*</span> <span class="identifier">ipart</span><span class="special">);</span>
+
+<span class="keyword">template</span> <span class="special">&lt;</span><span class="keyword">class</span> <span class="identifier">T</span><span class="special">,</span> <span class="keyword">class</span> <span class="identifier">Policy</span><span class="special">&gt;</span>
+<span class="identifier">T</span> <span class="identifier">modf</span><span class="special">(</span><span class="keyword">const</span> <span class="identifier">T</span><span class="special">&amp;</span> <span class="identifier">v</span><span class="special">,</span> <span class="keyword">long</span> <span class="keyword">long</span><span class="special">*</span> <span class="identifier">ipart</span><span class="special">,</span> <span class="keyword">const</span> <span class="identifier">Policy</span><span class="special">&amp;);</span>
+</pre>
+<p>
+          The <code class="computeroutput"><span class="identifier">modf</span></code> functions store
+          the integer part of <span class="emphasis"><em>v</em></span> in <code class="computeroutput"><span class="special">*</span><span class="identifier">ipart</span></code> and return the fractional part
+          of <span class="emphasis"><em>v</em></span>.
+        </p>
+<p>
+          If the argument <span class="emphasis"><em>v</em></span> is either non-finite or else outside
+          the range of the result type, then returns the result of <a class="link" href="../../main_overview/error_handling.html#rounding_error">rounding_error</a>:
+          by default this throws an instance of boost::math::rounding_error.
+        </p>
+</div>
+<table xmlns:rev="http://www.cs.rpi.edu/~gregod/boost/tools/doc/revision" width="100%"><tr>
+<td align="left"></td>
+<td align="right"><div class="copyright-footer">Copyright © 2006 , 2007, 2008 John Maddock, Paul A. Bristow, Hubert
+      Holin, Xiaogang Zhang, Bruno Lalande and Gautam Sewani<p>
+        Distributed under the Boost Software License, Version 1.0. (See accompanying
+        file LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_0.txt)
+      </p>
+</div></td>
+</tr></table>
+<hr>
+<div class="spirit-nav">
+<a accesskey="p" href="trunc.html"><img src="../../../../../doc/html/images/prev.png" alt="Prev"></a><a accesskey="u" href="../rounding.html"><img src="../../../../../doc/html/images/up.png" alt="Up"></a><a accesskey="h" href="../../../index.html"><img src="../../../../../doc/html/images/home.png" alt="Home"></a><a accesskey="n" href="../fpclass.html"><img src="../../../../../doc/html/images/next.png" alt="Next"></a>
+</div>
+</body>
+</html>

Added: sandbox/tools/auto_index/example/math/doc/sf_and_dist/html/math_toolkit/special/rounding/round.html
==============================================================================
--- (empty file)
+++ sandbox/tools/auto_index/example/math/doc/sf_and_dist/html/math_toolkit/special/rounding/round.html	2008-11-28 05:25:28 EST (Fri, 28 Nov 2008)
@@ -0,0 +1,86 @@
+<html>
+<head>
+<meta http-equiv="Content-Type" content="text/html; charset=ISO-8859-1">
+<title>Rounding Functions</title>
+<link rel="stylesheet" href="../../../boostbook.css" type="text/css">
+<meta name="generator" content="DocBook XSL Stylesheets Vsnapshot_8125">
+<link rel="home" href="../../../index.html" title="Math Toolkit">
+<link rel="up" href="../rounding.html" title="Rounding Truncation and Integer Conversion">
+<link rel="prev" href="../rounding.html" title="Rounding Truncation and Integer Conversion">
+<link rel="next" href="trunc.html" title="Truncation Functions">
+</head>
+<body bgcolor="white" text="black" link="#0000FF" vlink="#840084" alink="#0000FF">
+<table cellpadding="2" width="100%"><tr>
+<td valign="top"><img alt="Boost C++ Libraries" width="277" height="86" src="../../../../../boost.png"></td>
+<td align="center">Home</td>
+<td align="center">Libraries</td>
+<td align="center">People</td>
+<td align="center">FAQ</td>
+<td align="center">More</td>
+</tr></table>
+<hr>
+<div class="spirit-nav">
+<a accesskey="p" href="../rounding.html"><img src="../../../../../doc/html/images/prev.png" alt="Prev"></a><a accesskey="u" href="../rounding.html"><img src="../../../../../doc/html/images/up.png" alt="Up"></a><a accesskey="h" href="../../../index.html"><img src="../../../../../doc/html/images/home.png" alt="Home"></a><a accesskey="n" href="trunc.html"><img src="../../../../../doc/html/images/next.png" alt="Next"></a>
+</div>
+<div class="section" lang="en">
+<div class="titlepage"><div><div><h4 class="title">
+<a name="math_toolkit.special.rounding.round"></a><a class="link" href="round.html" title="Rounding Functions"> Rounding Functions</a>
+</h4></div></div></div>
+<p>
+          
+</p>
+<pre class="programlisting"><span class="preprocessor">#include</span> <span class="special">&lt;</span><span class="identifier">boost</span><span class="special">/</span><span class="identifier">math</span><span class="special">/</span><span class="identifier">special_functions</span><span class="special">/</span><span class="identifier">round</span><span class="special">.</span><span class="identifier">hpp</span><span class="special">&gt;</span></pre>
+<p>
+        </p>
+<pre class="programlisting"><span class="keyword">template</span> <span class="special">&lt;</span><span class="keyword">class</span> <span class="identifier">T</span><span class="special">&gt;</span>
+<span class="identifier">T</span> <span class="identifier">round</span><span class="special">(</span><span class="keyword">const</span> <span class="identifier">T</span><span class="special">&amp;</span> <span class="identifier">v</span><span class="special">);</span>
+
+<span class="keyword">template</span> <span class="special">&lt;</span><span class="keyword">class</span> <span class="identifier">T</span><span class="special">,</span> <span class="keyword">class</span> <span class="identifier">Policy</span><span class="special">&gt;</span>
+<span class="identifier">T</span> <span class="identifier">round</span><span class="special">(</span><span class="keyword">const</span> <span class="identifier">T</span><span class="special">&amp;</span> <span class="identifier">v</span><span class="special">,</span> <span class="keyword">const</span> <span class="identifier">Policy</span><span class="special">&amp;);</span>
+
+<span class="keyword">template</span> <span class="special">&lt;</span><span class="keyword">class</span> <span class="identifier">T</span><span class="special">&gt;</span>
+<span class="keyword">int</span> <span class="identifier">iround</span><span class="special">(</span><span class="keyword">const</span> <span class="identifier">T</span><span class="special">&amp;</span> <span class="identifier">v</span><span class="special">);</span>
+
+<span class="keyword">template</span> <span class="special">&lt;</span><span class="keyword">class</span> <span class="identifier">T</span><span class="special">,</span> <span class="keyword">class</span> <span class="identifier">Policy</span><span class="special">&gt;</span>
+<span class="keyword">int</span> <span class="identifier">iround</span><span class="special">(</span><span class="keyword">const</span> <span class="identifier">T</span><span class="special">&amp;</span> <span class="identifier">v</span><span class="special">,</span> <span class="keyword">const</span> <span class="identifier">Policy</span><span class="special">&amp;);</span>
+
+<span class="keyword">template</span> <span class="special">&lt;</span><span class="keyword">class</span> <span class="identifier">T</span><span class="special">&gt;</span>
+<span class="keyword">long</span> <span class="identifier">lround</span><span class="special">(</span><span class="keyword">const</span> <span class="identifier">T</span><span class="special">&amp;</span> <span class="identifier">v</span><span class="special">);</span>
+
+<span class="keyword">template</span> <span class="special">&lt;</span><span class="keyword">class</span> <span class="identifier">T</span><span class="special">,</span> <span class="keyword">class</span> <span class="identifier">Policy</span><span class="special">&gt;</span>
+<span class="keyword">long</span> <span class="identifier">lround</span><span class="special">(</span><span class="keyword">const</span> <span class="identifier">T</span><span class="special">&amp;</span> <span class="identifier">v</span><span class="special">,</span> <span class="keyword">const</span> <span class="identifier">Policy</span><span class="special">&amp;);</span>
+
+<span class="keyword">template</span> <span class="special">&lt;</span><span class="keyword">class</span> <span class="identifier">T</span><span class="special">&gt;</span>
+<span class="keyword">long</span> <span class="keyword">long</span> <span class="identifier">llround</span><span class="special">(</span><span class="keyword">const</span> <span class="identifier">T</span><span class="special">&amp;</span> <span class="identifier">v</span><span class="special">);</span>
+
+<span class="keyword">template</span> <span class="special">&lt;</span><span class="keyword">class</span> <span class="identifier">T</span><span class="special">,</span> <span class="keyword">class</span> <span class="identifier">Policy</span><span class="special">&gt;</span>
+<span class="keyword">long</span> <span class="keyword">long</span> <span class="identifier">llround</span><span class="special">(</span><span class="keyword">const</span> <span class="identifier">T</span><span class="special">&amp;</span> <span class="identifier">v</span><span class="special">,</span> <span class="keyword">const</span> <span class="identifier">Policy</span><span class="special">&amp;);</span>
+</pre>
+<p>
+          These functions return the closest integer to the argument <span class="emphasis"><em>v</em></span>.
+        </p>
+<p>
+          Halfway cases are rounded away from zero, regardless of the current rounding
+          direction.
+        </p>
+<p>
+          If the argument <span class="emphasis"><em>v</em></span> is either non-finite or else outside
+          the range of the result type, then returns the result of <a class="link" href="../../main_overview/error_handling.html#rounding_error">rounding_error</a>:
+          by default this throws an instance of boost::math::rounding_error.
+        </p>
+</div>
+<table xmlns:rev="http://www.cs.rpi.edu/~gregod/boost/tools/doc/revision" width="100%"><tr>
+<td align="left"></td>
+<td align="right"><div class="copyright-footer">Copyright © 2006 , 2007, 2008 John Maddock, Paul A. Bristow, Hubert
+      Holin, Xiaogang Zhang, Bruno Lalande and Gautam Sewani<p>
+        Distributed under the Boost Software License, Version 1.0. (See accompanying
+        file LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_0.txt)
+      </p>
+</div></td>
+</tr></table>
+<hr>
+<div class="spirit-nav">
+<a accesskey="p" href="../rounding.html"><img src="../../../../../doc/html/images/prev.png" alt="Prev"></a><a accesskey="u" href="../rounding.html"><img src="../../../../../doc/html/images/up.png" alt="Up"></a><a accesskey="h" href="../../../index.html"><img src="../../../../../doc/html/images/home.png" alt="Home"></a><a accesskey="n" href="trunc.html"><img src="../../../../../doc/html/images/next.png" alt="Next"></a>
+</div>
+</body>
+</html>

Added: sandbox/tools/auto_index/example/math/doc/sf_and_dist/html/math_toolkit/special/rounding/trunc.html
==============================================================================
--- (empty file)
+++ sandbox/tools/auto_index/example/math/doc/sf_and_dist/html/math_toolkit/special/rounding/trunc.html	2008-11-28 05:25:28 EST (Fri, 28 Nov 2008)
@@ -0,0 +1,88 @@
+<html>
+<head>
+<meta http-equiv="Content-Type" content="text/html; charset=ISO-8859-1">
+<title>Truncation Functions</title>
+<link rel="stylesheet" href="../../../boostbook.css" type="text/css">
+<meta name="generator" content="DocBook XSL Stylesheets Vsnapshot_8125">
+<link rel="home" href="../../../index.html" title="Math Toolkit">
+<link rel="up" href="../rounding.html" title="Rounding Truncation and Integer Conversion">
+<link rel="prev" href="round.html" title="Rounding Functions">
+<link rel="next" href="modf.html" title="Integer and Fractional Part Splitting (modf)">
+</head>
+<body bgcolor="white" text="black" link="#0000FF" vlink="#840084" alink="#0000FF">
+<table cellpadding="2" width="100%"><tr>
+<td valign="top"><img alt="Boost C++ Libraries" width="277" height="86" src="../../../../../boost.png"></td>
+<td align="center">Home</td>
+<td align="center">Libraries</td>
+<td align="center">People</td>
+<td align="center">FAQ</td>
+<td align="center">More</td>
+</tr></table>
+<hr>
+<div class="spirit-nav">
+<a accesskey="p" href="round.html"><img src="../../../../../doc/html/images/prev.png" alt="Prev"></a><a accesskey="u" href="../rounding.html"><img src="../../../../../doc/html/images/up.png" alt="Up"></a><a accesskey="h" href="../../../index.html"><img src="../../../../../doc/html/images/home.png" alt="Home"></a><a accesskey="n" href="modf.html"><img src="../../../../../doc/html/images/next.png" alt="Next"></a>
+</div>
+<div class="section" lang="en">
+<div class="titlepage"><div><div><h4 class="title">
+<a name="math_toolkit.special.rounding.trunc"></a><a class="link" href="trunc.html" title="Truncation Functions"> Truncation Functions</a>
+</h4></div></div></div>
+<p>
+          
+</p>
+<pre class="programlisting"><span class="preprocessor">#include</span> <span class="special">&lt;</span><span class="identifier">boost</span><span class="special">/</span><span class="identifier">math</span><span class="special">/</span><span class="identifier">special_functions</span><span class="special">/</span><span class="identifier">trunc</span><span class="special">.</span><span class="identifier">hpp</span><span class="special">&gt;</span></pre>
+<p>
+        </p>
+<pre class="programlisting"><span class="keyword">template</span> <span class="special">&lt;</span><span class="keyword">class</span> <span class="identifier">T</span><span class="special">&gt;</span>
+<span class="identifier">T</span> <span class="identifier">trunc</span><span class="special">(</span><span class="keyword">const</span> <span class="identifier">T</span><span class="special">&amp;</span> <span class="identifier">v</span><span class="special">);</span>
+
+<span class="keyword">template</span> <span class="special">&lt;</span><span class="keyword">class</span> <span class="identifier">T</span><span class="special">,</span> <span class="keyword">class</span> <span class="identifier">Policy</span><span class="special">&gt;</span>
+<span class="identifier">T</span> <span class="identifier">trunc</span><span class="special">(</span><span class="keyword">const</span> <span class="identifier">T</span><span class="special">&amp;</span> <span class="identifier">v</span><span class="special">,</span> <span class="keyword">const</span> <span class="identifier">Policy</span><span class="special">&amp;);</span>
+
+<span class="keyword">template</span> <span class="special">&lt;</span><span class="keyword">class</span> <span class="identifier">T</span><span class="special">&gt;</span>
+<span class="keyword">int</span> <span class="identifier">itrunc</span><span class="special">(</span><span class="keyword">const</span> <span class="identifier">T</span><span class="special">&amp;</span> <span class="identifier">v</span><span class="special">);</span>
+
+<span class="keyword">template</span> <span class="special">&lt;</span><span class="keyword">class</span> <span class="identifier">T</span><span class="special">,</span> <span class="keyword">class</span> <span class="identifier">Policy</span><span class="special">&gt;</span>
+<span class="keyword">int</span> <span class="identifier">itrunc</span><span class="special">(</span><span class="keyword">const</span> <span class="identifier">T</span><span class="special">&amp;</span> <span class="identifier">v</span><span class="special">,</span> <span class="keyword">const</span> <span class="identifier">Policy</span><span class="special">&amp;);</span>
+
+<span class="keyword">template</span> <span class="special">&lt;</span><span class="keyword">class</span> <span class="identifier">T</span><span class="special">&gt;</span>
+<span class="keyword">long</span> <span class="identifier">ltrunc</span><span class="special">(</span><span class="keyword">const</span> <span class="identifier">T</span><span class="special">&amp;</span> <span class="identifier">v</span><span class="special">);</span>
+
+<span class="keyword">template</span> <span class="special">&lt;</span><span class="keyword">class</span> <span class="identifier">T</span><span class="special">,</span> <span class="keyword">class</span> <span class="identifier">Policy</span><span class="special">&gt;</span>
+<span class="keyword">long</span> <span class="identifier">ltrunc</span><span class="special">(</span><span class="keyword">const</span> <span class="identifier">T</span><span class="special">&amp;</span> <span class="identifier">v</span><span class="special">,</span> <span class="keyword">const</span> <span class="identifier">Policy</span><span class="special">&amp;);</span>
+
+<span class="keyword">template</span> <span class="special">&lt;</span><span class="keyword">class</span> <span class="identifier">T</span><span class="special">&gt;</span>
+<span class="keyword">long</span> <span class="keyword">long</span> <span class="identifier">lltrunc</span><span class="special">(</span><span class="keyword">const</span> <span class="identifier">T</span><span class="special">&amp;</span> <span class="identifier">v</span><span class="special">);</span>
+
+<span class="keyword">template</span> <span class="special">&lt;</span><span class="keyword">class</span> <span class="identifier">T</span><span class="special">,</span> <span class="keyword">class</span> <span class="identifier">Policy</span><span class="special">&gt;</span>
+<span class="keyword">long</span> <span class="keyword">long</span> <span class="identifier">lltrunc</span><span class="special">(</span><span class="keyword">const</span> <span class="identifier">T</span><span class="special">&amp;</span> <span class="identifier">v</span><span class="special">,</span> <span class="keyword">const</span> <span class="identifier">Policy</span><span class="special">&amp;);</span>
+</pre>
+<p>
+          The trunc functions round their argument to the integer value, nearest
+          to but no larger in magnitude than the argument.
+        </p>
+<p>
+          For example <code class="computeroutput"><span class="identifier">itrunc</span><span class="special">(</span><span class="number">3.7</span><span class="special">)</span></code> would
+          return <code class="computeroutput"><span class="number">3</span></code> and <code class="computeroutput"><span class="identifier">ltrunc</span><span class="special">(-</span><span class="number">4.6</span><span class="special">)</span></code> would
+          return <code class="computeroutput"><span class="special">-</span><span class="number">4</span></code>.
+        </p>
+<p>
+          If the argument <span class="emphasis"><em>v</em></span> is either non-finite or else outside
+          the range of the result type, then returns the result of <a class="link" href="../../main_overview/error_handling.html#rounding_error">rounding_error</a>:
+          by default this throws an instance of boost::math::rounding_error.
+        </p>
+</div>
+<table xmlns:rev="http://www.cs.rpi.edu/~gregod/boost/tools/doc/revision" width="100%"><tr>
+<td align="left"></td>
+<td align="right"><div class="copyright-footer">Copyright © 2006 , 2007, 2008 John Maddock, Paul A. Bristow, Hubert
+      Holin, Xiaogang Zhang, Bruno Lalande and Gautam Sewani<p>
+        Distributed under the Boost Software License, Version 1.0. (See accompanying
+        file LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_0.txt)
+      </p>
+</div></td>
+</tr></table>
+<hr>
+<div class="spirit-nav">
+<a accesskey="p" href="round.html"><img src="../../../../../doc/html/images/prev.png" alt="Prev"></a><a accesskey="u" href="../rounding.html"><img src="../../../../../doc/html/images/up.png" alt="Up"></a><a accesskey="h" href="../../../index.html"><img src="../../../../../doc/html/images/home.png" alt="Home"></a><a accesskey="n" href="modf.html"><img src="../../../../../doc/html/images/next.png" alt="Next"></a>
+</div>
+</body>
+</html>

Added: sandbox/tools/auto_index/example/math/doc/sf_and_dist/html/math_toolkit/special/sf_beta.html
==============================================================================
--- (empty file)
+++ sandbox/tools/auto_index/example/math/doc/sf_and_dist/html/math_toolkit/special/sf_beta.html	2008-11-28 05:25:28 EST (Fri, 28 Nov 2008)
@@ -0,0 +1,53 @@
+<html>
+<head>
+<meta http-equiv="Content-Type" content="text/html; charset=ISO-8859-1">
+<title>Beta Functions</title>
+<link rel="stylesheet" href="../../boostbook.css" type="text/css">
+<meta name="generator" content="DocBook XSL Stylesheets Vsnapshot_8125">
+<link rel="home" href="../../index.html" title="Math Toolkit">
+<link rel="up" href="../special.html" title="Special Functions">
+<link rel="prev" href="factorials/sf_binomial.html" title="Binomial Coefficients">
+<link rel="next" href="sf_beta/beta_function.html" title="Beta">
+</head>
+<body bgcolor="white" text="black" link="#0000FF" vlink="#840084" alink="#0000FF">
+<table cellpadding="2" width="100%"><tr>
+<td valign="top"><img alt="Boost C++ Libraries" width="277" height="86" src="../../../../boost.png"></td>
+<td align="center">Home</td>
+<td align="center">Libraries</td>
+<td align="center">People</td>
+<td align="center">FAQ</td>
+<td align="center">More</td>
+</tr></table>
+<hr>
+<div class="spirit-nav">
+<a accesskey="p" href="factorials/sf_binomial.html"><img src="../../../../doc/html/images/prev.png" alt="Prev"></a><a accesskey="u" href="../special.html"><img src="../../../../doc/html/images/up.png" alt="Up"></a><a accesskey="h" href="../../index.html"><img src="../../../../doc/html/images/home.png" alt="Home"></a><a accesskey="n" href="sf_beta/beta_function.html"><img src="../../../../doc/html/images/next.png" alt="Next"></a>
+</div>
+<div class="section" lang="en">
+<div class="titlepage"><div><div><h3 class="title">
+<a name="math_toolkit.special.sf_beta"></a><a class="link" href="sf_beta.html" title="Beta Functions"> Beta Functions</a>
+</h3></div></div></div>
+<div class="toc"><dl>
+<dt><span class="section"> Beta</span></dt>
+<dt><span class="section"><a href="sf_beta/ibeta_function.html"> Incomplete
+        Beta Functions</a></span></dt>
+<dt><span class="section"><a href="sf_beta/ibeta_inv_function.html"> The
+        Incomplete Beta Function Inverses</a></span></dt>
+<dt><span class="section"><a href="sf_beta/beta_derivative.html"> Derivative
+        of the Incomplete Beta Function</a></span></dt>
+</dl></div>
+</div>
+<table xmlns:rev="http://www.cs.rpi.edu/~gregod/boost/tools/doc/revision" width="100%"><tr>
+<td align="left"></td>
+<td align="right"><div class="copyright-footer">Copyright © 2006 , 2007, 2008 John Maddock, Paul A. Bristow, Hubert
+      Holin, Xiaogang Zhang, Bruno Lalande and Gautam Sewani<p>
+        Distributed under the Boost Software License, Version 1.0. (See accompanying
+        file LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_0.txt)
+      </p>
+</div></td>
+</tr></table>
+<hr>
+<div class="spirit-nav">
+<a accesskey="p" href="factorials/sf_binomial.html"><img src="../../../../doc/html/images/prev.png" alt="Prev"></a><a accesskey="u" href="../special.html"><img src="../../../../doc/html/images/up.png" alt="Up"></a><a accesskey="h" href="../../index.html"><img src="../../../../doc/html/images/home.png" alt="Home"></a><a accesskey="n" href="sf_beta/beta_function.html"><img src="../../../../doc/html/images/next.png" alt="Next"></a>
+</div>
+</body>
+</html>

Added: sandbox/tools/auto_index/example/math/doc/sf_and_dist/html/math_toolkit/special/sf_beta/beta_derivative.html
==============================================================================
--- (empty file)
+++ sandbox/tools/auto_index/example/math/doc/sf_and_dist/html/math_toolkit/special/sf_beta/beta_derivative.html	2008-11-28 05:25:28 EST (Fri, 28 Nov 2008)
@@ -0,0 +1,109 @@
+<html>
+<head>
+<meta http-equiv="Content-Type" content="text/html; charset=ISO-8859-1">
+<title>Derivative of the Incomplete Beta Function</title>
+<link rel="stylesheet" href="../../../boostbook.css" type="text/css">
+<meta name="generator" content="DocBook XSL Stylesheets Vsnapshot_8125">
+<link rel="home" href="../../../index.html" title="Math Toolkit">
+<link rel="up" href="../sf_beta.html" title="Beta Functions">
+<link rel="prev" href="ibeta_inv_function.html" title="The Incomplete Beta Function Inverses">
+<link rel="next" href="../sf_erf.html" title="Error Functions">
+</head>
+<body bgcolor="white" text="black" link="#0000FF" vlink="#840084" alink="#0000FF">
+<table cellpadding="2" width="100%"><tr>
+<td valign="top"><img alt="Boost C++ Libraries" width="277" height="86" src="../../../../../boost.png"></td>
+<td align="center">Home</td>
+<td align="center">Libraries</td>
+<td align="center">People</td>
+<td align="center">FAQ</td>
+<td align="center">More</td>
+</tr></table>
+<hr>
+<div class="spirit-nav">
+<a accesskey="p" href="ibeta_inv_function.html"><img src="../../../../../doc/html/images/prev.png" alt="Prev"></a><a accesskey="u" href="../sf_beta.html"><img src="../../../../../doc/html/images/up.png" alt="Up"></a><a accesskey="h" href="../../../index.html"><img src="../../../../../doc/html/images/home.png" alt="Home"></a><a accesskey="n" href="../sf_erf.html"><img src="../../../../../doc/html/images/next.png" alt="Next"></a>
+</div>
+<div class="section" lang="en">
+<div class="titlepage"><div><div><h4 class="title">
+<a name="math_toolkit.special.sf_beta.beta_derivative"></a><a class="link" href="beta_derivative.html" title="Derivative of the Incomplete Beta Function"> Derivative
+        of the Incomplete Beta Function</a>
+</h4></div></div></div>
+<a name="math_toolkit.special.sf_beta.beta_derivative.synopsis"></a><h5>
+<a name="id736677"></a>
+          <a class="link" href="beta_derivative.html#math_toolkit.special.sf_beta.beta_derivative.synopsis">Synopsis</a>
+        </h5>
+<p>
+          
+</p>
+<pre class="programlisting"><span class="preprocessor">#include</span> <span class="special">&lt;</span><span class="identifier">boost</span><span class="special">/</span><span class="identifier">math</span><span class="special">/</span><span class="identifier">special_functions</span><span class="special">/</span><span class="identifier">beta</span><span class="special">.</span><span class="identifier">hpp</span><span class="special">&gt;</span>
+</pre>
+<p>
+        </p>
+<pre class="programlisting"><span class="keyword">namespace</span> <span class="identifier">boost</span><span class="special">{</span> <span class="keyword">namespace</span> <span class="identifier">math</span><span class="special">{</span> 
+
+<span class="keyword">template</span> <span class="special">&lt;</span><span class="keyword">class</span> <span class="identifier">T1</span><span class="special">,</span> <span class="keyword">class</span> <span class="identifier">T2</span><span class="special">,</span> <span class="keyword">class</span> <span class="identifier">T3</span><span class="special">&gt;</span>
+<a class="link" href="../../main_overview/result_type.html" title="Calculation of the Type of the Result"><span class="emphasis"><em>calculated-result-type</em></span></a> <span class="identifier">ibeta_derivative</span><span class="special">(</span><span class="identifier">T1</span> <span class="identifier">a</span><span class="special">,</span> <span class="identifier">T2</span> <span class="identifier">b</span><span class="special">,</span> <span class="identifier">T3</span> <span class="identifier">x</span><span class="special">);</span>
+
+<span class="keyword">template</span> <span class="special">&lt;</span><span class="keyword">class</span> <span class="identifier">T1</span><span class="special">,</span> <span class="keyword">class</span> <span class="identifier">T2</span><span class="special">,</span> <span class="keyword">class</span> <span class="identifier">T3</span><span class="special">,</span> <span class="keyword">class</span> <a class="link" href="../../policy.html" title="Policies">Policy</a><span class="special">&gt;</span>
+<a class="link" href="../../main_overview/result_type.html" title="Calculation of the Type of the Result"><span class="emphasis"><em>calculated-result-type</em></span></a> <span class="identifier">ibeta_derivative</span><span class="special">(</span><span class="identifier">T1</span> <span class="identifier">a</span><span class="special">,</span> <span class="identifier">T2</span> <span class="identifier">b</span><span class="special">,</span> <span class="identifier">T3</span> <span class="identifier">x</span><span class="special">,</span> <span class="keyword">const</span> <a class="link" href="../../policy.html" title="Policies">Policy</a><span class="special">&amp;);</span>
+
+<span class="special">}}</span> <span class="comment">// namespaces
+</span></pre>
+<a name="math_toolkit.special.sf_beta.beta_derivative.description"></a><h5>
+<a name="id737139"></a>
+          <a class="link" href="beta_derivative.html#math_toolkit.special.sf_beta.beta_derivative.description">Description</a>
+        </h5>
+<p>
+          This function finds some uses in statistical distributions: it computes
+          the partial derivative with respect to <span class="emphasis"><em>x</em></span> of the incomplete
+          beta function <a class="link" href="ibeta_function.html" title="Incomplete Beta Functions">ibeta</a>.
+        </p>
+<p>
+          <span class="inlinemediaobject"><img src="../../../../equations/derivative2.png"></span>
+        </p>
+<p>
+          The return type of this function is computed using the <a class="link" href="../../main_overview/result_type.html" title="Calculation of the Type of the Result"><span class="emphasis"><em>result
+          type calculation rules</em></span></a> when T1, T2 and T3 are different
+          types.
+        </p>
+<p>
+          </p>
+<p>
+            The final <a class="link" href="../../policy.html" title="Policies">Policy</a> argument
+            is optional and can be used to control the behaviour of the function:
+            how it handles errors, what level of precision to use etc. Refer to the
+            <a class="link" href="../../policy.html" title="Policies">policy documentation for more details</a>.
+          </p>
+<p>
+        </p>
+<a name="math_toolkit.special.sf_beta.beta_derivative.accuracy"></a><h5>
+<a name="id737262"></a>
+          <a class="link" href="beta_derivative.html#math_toolkit.special.sf_beta.beta_derivative.accuracy">Accuracy</a>
+        </h5>
+<p>
+          Almost identical to the incomplete beta function <a class="link" href="ibeta_function.html" title="Incomplete Beta Functions">ibeta</a>.
+        </p>
+<a name="math_toolkit.special.sf_beta.beta_derivative.implementation"></a><h5>
+<a name="id737300"></a>
+          <a class="link" href="beta_derivative.html#math_toolkit.special.sf_beta.beta_derivative.implementation">Implementation</a>
+        </h5>
+<p>
+          This function just expose some of the internals of the incomplete beta
+          function <a class="link" href="ibeta_function.html" title="Incomplete Beta Functions">ibeta</a>:
+          refer to the documentation for that function for more information.
+        </p>
+</div>
+<table xmlns:rev="http://www.cs.rpi.edu/~gregod/boost/tools/doc/revision" width="100%"><tr>
+<td align="left"></td>
+<td align="right"><div class="copyright-footer">Copyright © 2006 , 2007, 2008 John Maddock, Paul A. Bristow, Hubert
+      Holin, Xiaogang Zhang, Bruno Lalande and Gautam Sewani<p>
+        Distributed under the Boost Software License, Version 1.0. (See accompanying
+        file LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_0.txt)
+      </p>
+</div></td>
+</tr></table>
+<hr>
+<div class="spirit-nav">
+<a accesskey="p" href="ibeta_inv_function.html"><img src="../../../../../doc/html/images/prev.png" alt="Prev"></a><a accesskey="u" href="../sf_beta.html"><img src="../../../../../doc/html/images/up.png" alt="Up"></a><a accesskey="h" href="../../../index.html"><img src="../../../../../doc/html/images/home.png" alt="Home"></a><a accesskey="n" href="../sf_erf.html"><img src="../../../../../doc/html/images/next.png" alt="Next"></a>
+</div>
+</body>
+</html>

Added: sandbox/tools/auto_index/example/math/doc/sf_and_dist/html/math_toolkit/special/sf_beta/beta_function.html
==============================================================================
--- (empty file)
+++ sandbox/tools/auto_index/example/math/doc/sf_and_dist/html/math_toolkit/special/sf_beta/beta_function.html	2008-11-28 05:25:28 EST (Fri, 28 Nov 2008)
@@ -0,0 +1,334 @@
+<html>
+<head>
+<meta http-equiv="Content-Type" content="text/html; charset=ISO-8859-1">
+<title>Beta</title>
+<link rel="stylesheet" href="../../../boostbook.css" type="text/css">
+<meta name="generator" content="DocBook XSL Stylesheets Vsnapshot_8125">
+<link rel="home" href="../../../index.html" title="Math Toolkit">
+<link rel="up" href="../sf_beta.html" title="Beta Functions">
+<link rel="prev" href="../sf_beta.html" title="Beta Functions">
+<link rel="next" href="ibeta_function.html" title="Incomplete Beta Functions">
+</head>
+<body bgcolor="white" text="black" link="#0000FF" vlink="#840084" alink="#0000FF">
+<table cellpadding="2" width="100%"><tr>
+<td valign="top"><img alt="Boost C++ Libraries" width="277" height="86" src="../../../../../boost.png"></td>
+<td align="center">Home</td>
+<td align="center">Libraries</td>
+<td align="center">People</td>
+<td align="center">FAQ</td>
+<td align="center">More</td>
+</tr></table>
+<hr>
+<div class="spirit-nav">
+<a accesskey="p" href="../sf_beta.html"><img src="../../../../../doc/html/images/prev.png" alt="Prev"></a><a accesskey="u" href="../sf_beta.html"><img src="../../../../../doc/html/images/up.png" alt="Up"></a><a accesskey="h" href="../../../index.html"><img src="../../../../../doc/html/images/home.png" alt="Home"></a><a accesskey="n" href="ibeta_function.html"><img src="../../../../../doc/html/images/next.png" alt="Next"></a>
+</div>
+<div class="section" lang="en">
+<div class="titlepage"><div><div><h4 class="title">
+<a name="math_toolkit.special.sf_beta.beta_function"></a><a class="link" href="beta_function.html" title="Beta"> Beta</a>
+</h4></div></div></div>
+<a name="math_toolkit.special.sf_beta.beta_function.synopsis"></a><h5>
+<a name="id718569"></a>
+          <a class="link" href="beta_function.html#math_toolkit.special.sf_beta.beta_function.synopsis">Synopsis</a>
+        </h5>
+<p>
+          
+</p>
+<pre class="programlisting"><span class="preprocessor">#include</span> <span class="special">&lt;</span><span class="identifier">boost</span><span class="special">/</span><span class="identifier">math</span><span class="special">/</span><span class="identifier">special_functions</span><span class="special">/</span><span class="identifier">beta</span><span class="special">.</span><span class="identifier">hpp</span><span class="special">&gt;</span>
+</pre>
+<p>
+        </p>
+<pre class="programlisting"><span class="keyword">namespace</span> <span class="identifier">boost</span><span class="special">{</span> <span class="keyword">namespace</span> <span class="identifier">math</span><span class="special">{</span>
+
+<span class="keyword">template</span> <span class="special">&lt;</span><span class="keyword">class</span> <span class="identifier">T1</span><span class="special">,</span> <span class="keyword">class</span> <span class="identifier">T2</span><span class="special">&gt;</span>
+<a class="link" href="../../main_overview/result_type.html" title="Calculation of the Type of the Result"><span class="emphasis"><em>calculated-result-type</em></span></a> <span class="identifier">beta</span><span class="special">(</span><span class="identifier">T1</span> <span class="identifier">a</span><span class="special">,</span> <span class="identifier">T2</span> <span class="identifier">b</span><span class="special">);</span>
+
+<span class="keyword">template</span> <span class="special">&lt;</span><span class="keyword">class</span> <span class="identifier">T1</span><span class="special">,</span> <span class="keyword">class</span> <span class="identifier">T2</span><span class="special">,</span> <span class="keyword">class</span> <a class="link" href="../../policy.html" title="Policies">Policy</a><span class="special">&gt;</span>
+<a class="link" href="../../main_overview/result_type.html" title="Calculation of the Type of the Result"><span class="emphasis"><em>calculated-result-type</em></span></a> <span class="identifier">beta</span><span class="special">(</span><span class="identifier">T1</span> <span class="identifier">a</span><span class="special">,</span> <span class="identifier">T2</span> <span class="identifier">b</span><span class="special">,</span> <span class="keyword">const</span> <a class="link" href="../../policy.html" title="Policies">Policy</a><span class="special">&amp;);</span>
+
+<span class="special">}}</span> <span class="comment">// namespaces
+</span></pre>
+<a name="math_toolkit.special.sf_beta.beta_function.description"></a><h5>
+<a name="id718961"></a>
+          <a class="link" href="beta_function.html#math_toolkit.special.sf_beta.beta_function.description">Description</a>
+        </h5>
+<p>
+          The beta function is defined by:
+        </p>
+<p>
+          <span class="inlinemediaobject"><img src="../../../../equations/beta1.png"></span>
+        </p>
+<p>
+          <span class="inlinemediaobject"><img src="../../../../graphs/beta.png" align="middle"></span>
+        </p>
+<p>
+          </p>
+<p>
+            The final <a class="link" href="../../policy.html" title="Policies">Policy</a> argument
+            is optional and can be used to control the behaviour of the function:
+            how it handles errors, what level of precision to use etc. Refer to the
+            <a class="link" href="../../policy.html" title="Policies">policy documentation for more details</a>.
+          </p>
+<p>
+        </p>
+<p>
+          There are effectively two versions of this function internally: a fully
+          generic version that is slow, but reasonably accurate, and a much more
+          efficient approximation that is used where the number of digits in the
+          significand of T correspond to a certain <a class="link" href="../../backgrounders/lanczos.html" title="The Lanczos Approximation">Lanczos
+          approximation</a>. In practice any built-in floating-point type you
+          will encounter has an appropriate <a class="link" href="../../backgrounders/lanczos.html" title="The Lanczos Approximation">Lanczos
+          approximation</a> defined for it. It is also possible, given enough
+          machine time, to generate further <a class="link" href="../../backgrounders/lanczos.html" title="The Lanczos Approximation">Lanczos
+          approximation</a>'s using the program libs/math/tools/lanczos_generator.cpp.
+        </p>
+<p>
+          The return type of these functions is computed using the <a class="link" href="../../main_overview/result_type.html" title="Calculation of the Type of the Result"><span class="emphasis"><em>result
+          type calculation rules</em></span></a> when T1 and T2 are different types.
+        </p>
+<a name="math_toolkit.special.sf_beta.beta_function.accuracy"></a><h5>
+<a name="id719150"></a>
+          <a class="link" href="beta_function.html#math_toolkit.special.sf_beta.beta_function.accuracy">Accuracy</a>
+        </h5>
+<p>
+          The following table shows peak errors for various domains of input arguments,
+          along with comparisons to the GSL-1.9
+          and Cephes libraries.
+          Note that only results for the widest floating point type on the system
+          are given as narrower types have <a class="link" href="../../backgrounders/relative_error.html#zero_error">effectively
+          zero error</a>.
+        </p>
+<div class="table">
+<a name="id719200"></a><p class="title"><b>Table 22. Peak Errors In the Beta Function</b></p>
+<div class="table-contents"><table class="table" summary="Peak Errors In the Beta Function">
+<colgroup>
+<col>
+<col>
+<col>
+<col>
+</colgroup>
+<thead><tr>
+<th>
+              <p>
+                Significand Size
+              </p>
+              </th>
+<th>
+              <p>
+                Platform and Compiler
+              </p>
+              </th>
+<th>
+              <p>
+                Errors in range
+              </p>
+              <p>
+                0.4 &lt; a,b &lt; 100
+              </p>
+              </th>
+<th>
+              <p>
+                Errors in range
+              </p>
+              <p>
+                1e-6 &lt; a,b &lt; 36
+              </p>
+              </th>
+</tr></thead>
+<tbody>
+<tr>
+<td>
+              <p>
+                53
+              </p>
+              </td>
+<td>
+              <p>
+                Win32, Visual C++ 8
+              </p>
+              </td>
+<td>
+              <p>
+                Peak=99 Mean=22
+              </p>
+              <p>
+                (GSL Peak=1178 Mean=238)
+              </p>
+              <p>
+                (Cephes=1612)
+              </p>
+              </td>
+<td>
+              <p>
+                Peak=10.7 Mean=2.6
+              </p>
+              <p>
+                (GSL Peak=12 Mean=2.0)
+              </p>
+              <p>
+                (Cephes=174)
+              </p>
+              </td>
+</tr>
+<tr>
+<td>
+              <p>
+                64
+              </p>
+              </td>
+<td>
+              <p>
+                Red Hat Linux IA32, g++ 3.4.4
+              </p>
+              </td>
+<td>
+              <p>
+                Peak=112.1 Mean=26.9
+              </p>
+              </td>
+<td>
+              <p>
+                Peak=15.8 Mean=3.6
+              </p>
+              </td>
+</tr>
+<tr>
+<td>
+              <p>
+                64
+              </p>
+              </td>
+<td>
+              <p>
+                Red Hat Linux IA64, g++ 3.4.4
+              </p>
+              </td>
+<td>
+              <p>
+                Peak=61.4 Mean=19.5
+              </p>
+              </td>
+<td>
+              <p>
+                Peak=12.2 Mean=3.6
+              </p>
+              </td>
+</tr>
+<tr>
+<td>
+              <p>
+                113
+              </p>
+              </td>
+<td>
+              <p>
+                HPUX IA64, aCC A.06.06
+              </p>
+              </td>
+<td>
+              <p>
+                Peak=42.03 Mean=13.94
+              </p>
+              </td>
+<td>
+              <p>
+                Peak=9.8 Mean=3.1
+              </p>
+              </td>
+</tr>
+</tbody>
+</table></div>
+</div>
+<br class="table-break"><p>
+          Note that the worst errors occur when a or b are large, and that when this
+          is the case the result is very close to zero, so absolute errors will be
+          very small.
+        </p>
+<a name="math_toolkit.special.sf_beta.beta_function.testing"></a><h5>
+<a name="id719466"></a>
+          <a class="link" href="beta_function.html#math_toolkit.special.sf_beta.beta_function.testing">Testing</a>
+        </h5>
+<p>
+          A mixture of spot tests of exact values, and randomly generated test data
+          are used: the test data was computed using NTL::RR
+          at 1000-bit precision.
+        </p>
+<a name="math_toolkit.special.sf_beta.beta_function.implementation"></a><h5>
+<a name="id719507"></a>
+          <a class="link" href="beta_function.html#math_toolkit.special.sf_beta.beta_function.implementation">Implementation</a>
+        </h5>
+<p>
+          Traditional methods of evaluating the beta function either involve evaluating
+          the gamma functions directly, or taking logarithms and then exponentiating
+          the result. However, the former is prone to overflows for even very modest
+          arguments, while the latter is prone to cancellation errors. As an alternative,
+          if we regard the gamma function as a white-box containing the <a class="link" href="../../backgrounders/lanczos.html" title="The Lanczos Approximation">Lanczos
+          approximation</a>, then we can combine the power terms:
+        </p>
+<p>
+          <span class="inlinemediaobject"><img src="../../../../equations/beta2.png"></span>
+        </p>
+<p>
+          which is almost the ideal solution, however almost all of the error occurs
+          in evaluating the power terms when <span class="emphasis"><em>a</em></span> or <span class="emphasis"><em>b</em></span>
+          are large. If we assume that <span class="emphasis"><em>a &gt; b</em></span> then the larger
+          of the two power terms can be reduced by a factor of <span class="emphasis"><em>b</em></span>,
+          which immediately cuts the maximum error in half:
+        </p>
+<p>
+          <span class="inlinemediaobject"><img src="../../../../equations/beta3.png"></span>
+        </p>
+<p>
+          This may not be the final solution, but it is very competitive compared
+          to other implementation methods.
+        </p>
+<p>
+          The generic implementation - where no <a class="link" href="../../backgrounders/lanczos.html" title="The Lanczos Approximation">Lanczos
+          approximation</a> approximation is available - is implemented in a very
+          similar way to the generic version of the gamma function. Again in order
+          to avoid numerical overflow the power terms that prefix the series and
+          continued fraction parts are collected together into:
+        </p>
+<p>
+          <span class="inlinemediaobject"><img src="../../../../equations/beta8.png"></span>
+        </p>
+<p>
+          where la, lb and lc are the integration limits used for a, b, and a+b.
+        </p>
+<p>
+          There are a few special cases worth mentioning:
+        </p>
+<p>
+          When <span class="emphasis"><em>a</em></span> or <span class="emphasis"><em>b</em></span> are less than one,
+          we can use the recurrence relations:
+        </p>
+<p>
+          <span class="inlinemediaobject"><img src="../../../../equations/beta4.png"></span>
+        </p>
+<p>
+          <span class="inlinemediaobject"><img src="../../../../equations/beta5.png"></span>
+        </p>
+<p>
+          to move to a more favorable region where they are both greater than 1.
+        </p>
+<p>
+          In addition:
+        </p>
+<p>
+          <span class="inlinemediaobject"><img src="../../../../equations/beta7.png"></span>
+        </p>
+</div>
+<table xmlns:rev="http://www.cs.rpi.edu/~gregod/boost/tools/doc/revision" width="100%"><tr>
+<td align="left"></td>
+<td align="right"><div class="copyright-footer">Copyright © 2006 , 2007, 2008 John Maddock, Paul A. Bristow, Hubert
+      Holin, Xiaogang Zhang, Bruno Lalande and Gautam Sewani<p>
+        Distributed under the Boost Software License, Version 1.0. (See accompanying
+        file LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_0.txt)
+      </p>
+</div></td>
+</tr></table>
+<hr>
+<div class="spirit-nav">
+<a accesskey="p" href="../sf_beta.html"><img src="../../../../../doc/html/images/prev.png" alt="Prev"></a><a accesskey="u" href="../sf_beta.html"><img src="../../../../../doc/html/images/up.png" alt="Up"></a><a accesskey="h" href="../../../index.html"><img src="../../../../../doc/html/images/home.png" alt="Home"></a><a accesskey="n" href="ibeta_function.html"><img src="../../../../../doc/html/images/next.png" alt="Next"></a>
+</div>
+</body>
+</html>

Added: sandbox/tools/auto_index/example/math/doc/sf_and_dist/html/math_toolkit/special/sf_beta/ibeta_function.html
==============================================================================
--- (empty file)
+++ sandbox/tools/auto_index/example/math/doc/sf_and_dist/html/math_toolkit/special/sf_beta/ibeta_function.html	2008-11-28 05:25:28 EST (Fri, 28 Nov 2008)
@@ -0,0 +1,976 @@
+<html>
+<head>
+<meta http-equiv="Content-Type" content="text/html; charset=ISO-8859-1">
+<title>Incomplete Beta Functions</title>
+<link rel="stylesheet" href="../../../boostbook.css" type="text/css">
+<meta name="generator" content="DocBook XSL Stylesheets Vsnapshot_8125">
+<link rel="home" href="../../../index.html" title="Math Toolkit">
+<link rel="up" href="../sf_beta.html" title="Beta Functions">
+<link rel="prev" href="beta_function.html" title="Beta">
+<link rel="next" href="ibeta_inv_function.html" title="The Incomplete Beta Function Inverses">
+</head>
+<body bgcolor="white" text="black" link="#0000FF" vlink="#840084" alink="#0000FF">
+<table cellpadding="2" width="100%"><tr>
+<td valign="top"><img alt="Boost C++ Libraries" width="277" height="86" src="../../../../../boost.png"></td>
+<td align="center">Home</td>
+<td align="center">Libraries</td>
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+<td align="center">FAQ</td>
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+<hr>
+<div class="spirit-nav">
+<a accesskey="p" href="beta_function.html"><img src="../../../../../doc/html/images/prev.png" alt="Prev"></a><a accesskey="u" href="../sf_beta.html"><img src="../../../../../doc/html/images/up.png" alt="Up"></a><a accesskey="h" href="../../../index.html"><img src="../../../../../doc/html/images/home.png" alt="Home"></a><a accesskey="n" href="ibeta_inv_function.html"><img src="../../../../../doc/html/images/next.png" alt="Next"></a>
+</div>
+<div class="section" lang="en">
+<div class="titlepage"><div><div><h4 class="title">
+<a name="math_toolkit.special.sf_beta.ibeta_function"></a><a class="link" href="ibeta_function.html" title="Incomplete Beta Functions"> Incomplete
+        Beta Functions</a>
+</h4></div></div></div>
+<a name="math_toolkit.special.sf_beta.ibeta_function.synopsis"></a><h5>
+<a name="id724126"></a>
+          <a class="link" href="ibeta_function.html#math_toolkit.special.sf_beta.ibeta_function.synopsis">Synopsis</a>
+        </h5>
+<p>
+          
+</p>
+<pre class="programlisting"><span class="preprocessor">#include</span> <span class="special">&lt;</span><span class="identifier">boost</span><span class="special">/</span><span class="identifier">math</span><span class="special">/</span><span class="identifier">special_functions</span><span class="special">/</span><span class="identifier">gamma</span><span class="special">.</span><span class="identifier">hpp</span><span class="special">&gt;</span>
+</pre>
+<p>
+        </p>
+<pre class="programlisting"><span class="keyword">namespace</span> <span class="identifier">boost</span><span class="special">{</span> <span class="keyword">namespace</span> <span class="identifier">math</span><span class="special">{</span>
+
+<span class="keyword">template</span> <span class="special">&lt;</span><span class="keyword">class</span> <span class="identifier">T1</span><span class="special">,</span> <span class="keyword">class</span> <span class="identifier">T2</span><span class="special">,</span> <span class="keyword">class</span> <span class="identifier">T3</span><span class="special">&gt;</span>
+<a class="link" href="../../main_overview/result_type.html" title="Calculation of the Type of the Result"><span class="emphasis"><em>calculated-result-type</em></span></a> <span class="identifier">ibeta</span><span class="special">(</span><span class="identifier">T1</span> <span class="identifier">a</span><span class="special">,</span> <span class="identifier">T2</span> <span class="identifier">b</span><span class="special">,</span> <span class="identifier">T3</span> <span class="identifier">x</span><span class="special">);</span>
+
+<span class="keyword">template</span> <span class="special">&lt;</span><span class="keyword">class</span> <span class="identifier">T1</span><span class="special">,</span> <span class="keyword">class</span> <span class="identifier">T2</span><span class="special">,</span> <span class="keyword">class</span> <span class="identifier">T3</span><span class="special">,</span> <span class="keyword">class</span> <a class="link" href="../../policy.html" title="Policies">Policy</a><span class="special">&gt;</span>
+<a class="link" href="../../main_overview/result_type.html" title="Calculation of the Type of the Result"><span class="emphasis"><em>calculated-result-type</em></span></a> <span class="identifier">ibeta</span><span class="special">(</span><span class="identifier">T1</span> <span class="identifier">a</span><span class="special">,</span> <span class="identifier">T2</span> <span class="identifier">b</span><span class="special">,</span> <span class="identifier">T3</span> <span class="identifier">x</span><span class="special">,</span> <span class="keyword">const</span> <a class="link" href="../../policy.html" title="Policies">Policy</a><span class="special">&amp;);</span>
+
+<span class="keyword">template</span> <span class="special">&lt;</span><span class="keyword">class</span> <span class="identifier">T1</span><span class="special">,</span> <span class="keyword">class</span> <span class="identifier">T2</span><span class="special">,</span> <span class="keyword">class</span> <span class="identifier">T3</span><span class="special">&gt;</span>
+<a class="link" href="../../main_overview/result_type.html" title="Calculation of the Type of the Result"><span class="emphasis"><em>calculated-result-type</em></span></a> <span class="identifier">ibetac</span><span class="special">(</span><span class="identifier">T1</span> <span class="identifier">a</span><span class="special">,</span> <span class="identifier">T2</span> <span class="identifier">b</span><span class="special">,</span> <span class="identifier">T3</span> <span class="identifier">x</span><span class="special">);</span>
+
+<span class="keyword">template</span> <span class="special">&lt;</span><span class="keyword">class</span> <span class="identifier">T1</span><span class="special">,</span> <span class="keyword">class</span> <span class="identifier">T2</span><span class="special">,</span> <span class="keyword">class</span> <span class="identifier">T3</span><span class="special">,</span> <span class="keyword">class</span> <a class="link" href="../../policy.html" title="Policies">Policy</a><span class="special">&gt;</span>
+<a class="link" href="../../main_overview/result_type.html" title="Calculation of the Type of the Result"><span class="emphasis"><em>calculated-result-type</em></span></a> <span class="identifier">ibetac</span><span class="special">(</span><span class="identifier">T1</span> <span class="identifier">a</span><span class="special">,</span> <span class="identifier">T2</span> <span class="identifier">b</span><span class="special">,</span> <span class="identifier">T3</span> <span class="identifier">x</span><span class="special">,</span> <span class="keyword">const</span> <a class="link" href="../../policy.html" title="Policies">Policy</a><span class="special">&amp;);</span>
+
+<span class="keyword">template</span> <span class="special">&lt;</span><span class="keyword">class</span> <span class="identifier">T1</span><span class="special">,</span> <span class="keyword">class</span> <span class="identifier">T2</span><span class="special">,</span> <span class="keyword">class</span> <span class="identifier">T3</span><span class="special">&gt;</span>
+<a class="link" href="../../main_overview/result_type.html" title="Calculation of the Type of the Result"><span class="emphasis"><em>calculated-result-type</em></span></a> <span class="identifier">beta</span><span class="special">(</span><span class="identifier">T1</span> <span class="identifier">a</span><span class="special">,</span> <span class="identifier">T2</span> <span class="identifier">b</span><span class="special">,</span> <span class="identifier">T3</span> <span class="identifier">x</span><span class="special">);</span>
+
+<span class="keyword">template</span> <span class="special">&lt;</span><span class="keyword">class</span> <span class="identifier">T1</span><span class="special">,</span> <span class="keyword">class</span> <span class="identifier">T2</span><span class="special">,</span> <span class="keyword">class</span> <span class="identifier">T3</span><span class="special">,</span> <span class="keyword">class</span> <a class="link" href="../../policy.html" title="Policies">Policy</a><span class="special">&gt;</span>
+<a class="link" href="../../main_overview/result_type.html" title="Calculation of the Type of the Result"><span class="emphasis"><em>calculated-result-type</em></span></a> <span class="identifier">beta</span><span class="special">(</span><span class="identifier">T1</span> <span class="identifier">a</span><span class="special">,</span> <span class="identifier">T2</span> <span class="identifier">b</span><span class="special">,</span> <span class="identifier">T3</span> <span class="identifier">x</span><span class="special">,</span> <span class="keyword">const</span> <a class="link" href="../../policy.html" title="Policies">Policy</a><span class="special">&amp;);</span>
+
+<span class="keyword">template</span> <span class="special">&lt;</span><span class="keyword">class</span> <span class="identifier">T1</span><span class="special">,</span> <span class="keyword">class</span> <span class="identifier">T2</span><span class="special">,</span> <span class="keyword">class</span> <span class="identifier">T3</span><span class="special">&gt;</span>
+<a class="link" href="../../main_overview/result_type.html" title="Calculation of the Type of the Result"><span class="emphasis"><em>calculated-result-type</em></span></a> <span class="identifier">betac</span><span class="special">(</span><span class="identifier">T1</span> <span class="identifier">a</span><span class="special">,</span> <span class="identifier">T2</span> <span class="identifier">b</span><span class="special">,</span> <span class="identifier">T3</span> <span class="identifier">x</span><span class="special">);</span>
+
+<span class="keyword">template</span> <span class="special">&lt;</span><span class="keyword">class</span> <span class="identifier">T1</span><span class="special">,</span> <span class="keyword">class</span> <span class="identifier">T2</span><span class="special">,</span> <span class="keyword">class</span> <span class="identifier">T3</span><span class="special">,</span> <span class="keyword">class</span> <a class="link" href="../../policy.html" title="Policies">Policy</a><span class="special">&gt;</span>
+<a class="link" href="../../main_overview/result_type.html" title="Calculation of the Type of the Result"><span class="emphasis"><em>calculated-result-type</em></span></a> <span class="identifier">betac</span><span class="special">(</span><span class="identifier">T1</span> <span class="identifier">a</span><span class="special">,</span> <span class="identifier">T2</span> <span class="identifier">b</span><span class="special">,</span> <span class="identifier">T3</span> <span class="identifier">x</span><span class="special">,</span> <span class="keyword">const</span> <a class="link" href="../../policy.html" title="Policies">Policy</a><span class="special">&amp;);</span>
+
+<span class="special">}}</span> <span class="comment">// namespaces
+</span></pre>
+<a name="math_toolkit.special.sf_beta.ibeta_function.description"></a><h5>
+<a name="id725512"></a>
+          <a class="link" href="ibeta_function.html#math_toolkit.special.sf_beta.ibeta_function.description">Description</a>
+        </h5>
+<p>
+          There are four <a href="http://en.wikipedia.org/wiki/Incomplete_beta_function" target="_top">incomplete
+          beta functions</a> : two are normalised versions (also known as <span class="emphasis"><em>regularized</em></span>
+          beta functions) that return values in the range [0, 1], and two are non-normalised
+          and return values in the range [0, <a class="link" href="beta_function.html" title="Beta">beta</a>(a,
+          b)]. Users interested in statistical applications should use the normalised
+          (or regularized
+          ) versions (ibeta and ibetac).
+        </p>
+<p>
+          All of these functions require <span class="emphasis"><em>a &gt; 0</em></span>, <span class="emphasis"><em>b
+          &gt; 0</em></span> and <span class="emphasis"><em>0 &lt;= x &lt;= 1</em></span>.
+        </p>
+<p>
+          The return type of these functions is computed using the <a class="link" href="../../main_overview/result_type.html" title="Calculation of the Type of the Result"><span class="emphasis"><em>result
+          type calculation rules</em></span></a> when T1, T2 and T3 are different
+          types.
+        </p>
+<p>
+          </p>
+<p>
+            The final <a class="link" href="../../policy.html" title="Policies">Policy</a> argument
+            is optional and can be used to control the behaviour of the function:
+            how it handles errors, what level of precision to use etc. Refer to the
+            <a class="link" href="../../policy.html" title="Policies">policy documentation for more details</a>.
+          </p>
+<p>
+        </p>
+<pre class="programlisting"><span class="keyword">template</span> <span class="special">&lt;</span><span class="keyword">class</span> <span class="identifier">T1</span><span class="special">,</span> <span class="keyword">class</span> <span class="identifier">T2</span><span class="special">,</span> <span class="keyword">class</span> <span class="identifier">T3</span><span class="special">&gt;</span>
+<a class="link" href="../../main_overview/result_type.html" title="Calculation of the Type of the Result"><span class="emphasis"><em>calculated-result-type</em></span></a> <span class="identifier">ibeta</span><span class="special">(</span><span class="identifier">T1</span> <span class="identifier">a</span><span class="special">,</span> <span class="identifier">T2</span> <span class="identifier">b</span><span class="special">,</span> <span class="identifier">T3</span> <span class="identifier">x</span><span class="special">);</span>
+
+<span class="keyword">template</span> <span class="special">&lt;</span><span class="keyword">class</span> <span class="identifier">T1</span><span class="special">,</span> <span class="keyword">class</span> <span class="identifier">T2</span><span class="special">,</span> <span class="keyword">class</span> <span class="identifier">T3</span><span class="special">,</span> <span class="keyword">class</span> <a class="link" href="../../policy.html" title="Policies">Policy</a><span class="special">&gt;</span>
+<a class="link" href="../../main_overview/result_type.html" title="Calculation of the Type of the Result"><span class="emphasis"><em>calculated-result-type</em></span></a> <span class="identifier">ibeta</span><span class="special">(</span><span class="identifier">T1</span> <span class="identifier">a</span><span class="special">,</span> <span class="identifier">T2</span> <span class="identifier">b</span><span class="special">,</span> <span class="identifier">T3</span> <span class="identifier">x</span><span class="special">,</span> <span class="keyword">const</span> <a class="link" href="../../policy.html" title="Policies">Policy</a><span class="special">&amp;);</span>
+</pre>
+<p>
+          Returns the normalised incomplete beta function of a, b and x:
+        </p>
+<p>
+          <span class="inlinemediaobject"><img src="../../../../equations/ibeta3.png"></span>
+        </p>
+<p>
+          <span class="inlinemediaobject"><img src="../../../../graphs/ibeta.png" align="middle"></span>
+        </p>
+<pre class="programlisting"><span class="keyword">template</span> <span class="special">&lt;</span><span class="keyword">class</span> <span class="identifier">T1</span><span class="special">,</span> <span class="keyword">class</span> <span class="identifier">T2</span><span class="special">,</span> <span class="keyword">class</span> <span class="identifier">T3</span><span class="special">&gt;</span>
+<a class="link" href="../../main_overview/result_type.html" title="Calculation of the Type of the Result"><span class="emphasis"><em>calculated-result-type</em></span></a> <span class="identifier">ibetac</span><span class="special">(</span><span class="identifier">T1</span> <span class="identifier">a</span><span class="special">,</span> <span class="identifier">T2</span> <span class="identifier">b</span><span class="special">,</span> <span class="identifier">T3</span> <span class="identifier">x</span><span class="special">);</span>
+
+<span class="keyword">template</span> <span class="special">&lt;</span><span class="keyword">class</span> <span class="identifier">T1</span><span class="special">,</span> <span class="keyword">class</span> <span class="identifier">T2</span><span class="special">,</span> <span class="keyword">class</span> <span class="identifier">T3</span><span class="special">,</span> <span class="keyword">class</span> <a class="link" href="../../policy.html" title="Policies">Policy</a><span class="special">&gt;</span>
+<a class="link" href="../../main_overview/result_type.html" title="Calculation of the Type of the Result"><span class="emphasis"><em>calculated-result-type</em></span></a> <span class="identifier">ibetac</span><span class="special">(</span><span class="identifier">T1</span> <span class="identifier">a</span><span class="special">,</span> <span class="identifier">T2</span> <span class="identifier">b</span><span class="special">,</span> <span class="identifier">T3</span> <span class="identifier">x</span><span class="special">,</span> <span class="keyword">const</span> <a class="link" href="../../policy.html" title="Policies">Policy</a><span class="special">&amp;);</span>
+</pre>
+<p>
+          Returns the normalised complement of the incomplete beta function of a,
+          b and x:
+        </p>
+<p>
+          <span class="inlinemediaobject"><img src="../../../../equations/ibeta4.png"></span>
+        </p>
+<pre class="programlisting"><span class="keyword">template</span> <span class="special">&lt;</span><span class="keyword">class</span> <span class="identifier">T1</span><span class="special">,</span> <span class="keyword">class</span> <span class="identifier">T2</span><span class="special">,</span> <span class="keyword">class</span> <span class="identifier">T3</span><span class="special">&gt;</span>
+<a class="link" href="../../main_overview/result_type.html" title="Calculation of the Type of the Result"><span class="emphasis"><em>calculated-result-type</em></span></a> <span class="identifier">beta</span><span class="special">(</span><span class="identifier">T1</span> <span class="identifier">a</span><span class="special">,</span> <span class="identifier">T2</span> <span class="identifier">b</span><span class="special">,</span> <span class="identifier">T3</span> <span class="identifier">x</span><span class="special">);</span>
+
+<span class="keyword">template</span> <span class="special">&lt;</span><span class="keyword">class</span> <span class="identifier">T1</span><span class="special">,</span> <span class="keyword">class</span> <span class="identifier">T2</span><span class="special">,</span> <span class="keyword">class</span> <span class="identifier">T3</span><span class="special">,</span> <span class="keyword">class</span> <a class="link" href="../../policy.html" title="Policies">Policy</a><span class="special">&gt;</span>
+<a class="link" href="../../main_overview/result_type.html" title="Calculation of the Type of the Result"><span class="emphasis"><em>calculated-result-type</em></span></a> <span class="identifier">beta</span><span class="special">(</span><span class="identifier">T1</span> <span class="identifier">a</span><span class="special">,</span> <span class="identifier">T2</span> <span class="identifier">b</span><span class="special">,</span> <span class="identifier">T3</span> <span class="identifier">x</span><span class="special">,</span> <span class="keyword">const</span> <a class="link" href="../../policy.html" title="Policies">Policy</a><span class="special">&amp;);</span>
+</pre>
+<p>
+          Returns the full (non-normalised) incomplete beta function of a, b and
+          x:
+        </p>
+<p>
+          <span class="inlinemediaobject"><img src="../../../../equations/ibeta1.png"></span>
+        </p>
+<pre class="programlisting"><span class="keyword">template</span> <span class="special">&lt;</span><span class="keyword">class</span> <span class="identifier">T1</span><span class="special">,</span> <span class="keyword">class</span> <span class="identifier">T2</span><span class="special">,</span> <span class="keyword">class</span> <span class="identifier">T3</span><span class="special">&gt;</span>
+<a class="link" href="../../main_overview/result_type.html" title="Calculation of the Type of the Result"><span class="emphasis"><em>calculated-result-type</em></span></a> <span class="identifier">betac</span><span class="special">(</span><span class="identifier">T1</span> <span class="identifier">a</span><span class="special">,</span> <span class="identifier">T2</span> <span class="identifier">b</span><span class="special">,</span> <span class="identifier">T3</span> <span class="identifier">x</span><span class="special">);</span>
+
+<span class="keyword">template</span> <span class="special">&lt;</span><span class="keyword">class</span> <span class="identifier">T1</span><span class="special">,</span> <span class="keyword">class</span> <span class="identifier">T2</span><span class="special">,</span> <span class="keyword">class</span> <span class="identifier">T3</span><span class="special">,</span> <span class="keyword">class</span> <a class="link" href="../../policy.html" title="Policies">Policy</a><span class="special">&gt;</span>
+<a class="link" href="../../main_overview/result_type.html" title="Calculation of the Type of the Result"><span class="emphasis"><em>calculated-result-type</em></span></a> <span class="identifier">betac</span><span class="special">(</span><span class="identifier">T1</span> <span class="identifier">a</span><span class="special">,</span> <span class="identifier">T2</span> <span class="identifier">b</span><span class="special">,</span> <span class="identifier">T3</span> <span class="identifier">x</span><span class="special">,</span> <span class="keyword">const</span> <a class="link" href="../../policy.html" title="Policies">Policy</a><span class="special">&amp;);</span>
+</pre>
+<p>
+          Returns the full (non-normalised) complement of the incomplete beta function
+          of a, b and x:
+        </p>
+<p>
+          <span class="inlinemediaobject"><img src="../../../../equations/ibeta2.png"></span>
+        </p>
+<a name="math_toolkit.special.sf_beta.ibeta_function.accuracy"></a><h5>
+<a name="id727086"></a>
+          <a class="link" href="ibeta_function.html#math_toolkit.special.sf_beta.ibeta_function.accuracy">Accuracy</a>
+        </h5>
+<p>
+          The following tables give peak and mean relative errors in over various
+          domains of a, b and x, along with comparisons to the GSL-1.9
+          and Cephes libraries.
+          Note that only results for the widest floating-point type on the system
+          are given as narrower types have <a class="link" href="../../backgrounders/relative_error.html#zero_error">effectively
+          zero error</a>.
+        </p>
+<p>
+          Note that the results for 80 and 128-bit long doubles are noticeably higher
+          than for doubles: this is because the wider exponent range of these types
+          allow more extreme test cases to be tested. For example expected results
+          that are zero at double precision, may be finite but exceptionally small
+          with the wider exponent range of the long double types.
+        </p>
+<div class="table">
+<a name="id727156"></a><p class="title"><b>Table 23. Errors In the Function ibeta(a,b,x)</b></p>
+<div class="table-contents"><table class="table" summary="Errors In the Function ibeta(a,b,x)">
+<colgroup>
+<col>
+<col>
+<col>
+<col>
+<col>
+</colgroup>
+<thead><tr>
+<th>
+              <p>
+                Significand Size
+              </p>
+              </th>
+<th>
+              <p>
+                Platform and Compiler
+              </p>
+              </th>
+<th>
+              <p>
+                0 &lt; a,b &lt; 10
+              </p>
+              <p>
+                and
+              </p>
+              <p>
+                0 &lt; x &lt; 1
+              </p>
+              </th>
+<th>
+              <p>
+                0 &lt; a,b &lt; 100
+              </p>
+              <p>
+                and
+              </p>
+              <p>
+                0 &lt; x &lt; 1
+              </p>
+              </th>
+<th>
+              <p>
+                1x10<sup>-5</sup> &lt; a,b &lt; 1x10<sup>5</sup>
+              </p>
+              <p>
+                and
+              </p>
+              <p>
+                0 &lt; x &lt; 1
+              </p>
+              </th>
+</tr></thead>
+<tbody>
+<tr>
+<td>
+              <p>
+                53
+              </p>
+              </td>
+<td>
+              <p>
+                Win32, Visual C++ 8
+              </p>
+              </td>
+<td>
+              <p>
+                Peak=42.3 Mean=2.9
+              </p>
+              <p>
+                (GSL Peak=682 Mean=32.5)
+              </p>
+              <p>
+                (Cephes Peak=42.7
+                Mean=7.0)
+              </p>
+              </td>
+<td>
+              <p>
+                Peak=108 Mean=16.6
+              </p>
+              <p>
+                (GSL Peak=690 Mean=151)
+              </p>
+              <p>
+                (Cephes Peak=1545
+                Mean=218)
+              </p>
+              </td>
+<td>
+              <p>
+                Peak=4x10<sup>3</sup> Mean=203
+              </p>
+              <p>
+                (GSL Peak~3x10<sup>5</sup> Mean~2x10<sup>4</sup>)
+              </p>
+              <p>
+                (Cephes Peak~5x10<sup>5</sup> Mean~2x10<sup>4</sup>)
+              </p>
+              </td>
+</tr>
+<tr>
+<td>
+              <p>
+                64
+              </p>
+              </td>
+<td>
+              <p>
+                Redhat Linux IA32, gcc-3.4.4
+              </p>
+              </td>
+<td>
+              <p>
+                Peak=21.9 Mean=3.1
+              </p>
+              </td>
+<td>
+              <p>
+                Peak=270.7 Mean=26.8
+              </p>
+              </td>
+<td>
+              <p>
+                Peak~5x10<sup>4</sup> Mean=3x10<sup>3</sup>
+              </p>
+              </td>
+</tr>
+<tr>
+<td>
+              <p>
+                64
+              </p>
+              </td>
+<td>
+              <p>
+                Redhat Linux IA64, gcc-3.4.4
+              </p>
+              </td>
+<td>
+              <p>
+                Peak=15.4 Mean=3.0
+              </p>
+              </td>
+<td>
+              <p>
+                Peak=112.9 Mean=14.3
+              </p>
+              </td>
+<td>
+              <p>
+                Peak~5x10<sup>4</sup> Mean=3x10<sup>3</sup>
+              </p>
+              </td>
+</tr>
+<tr>
+<td>
+              <p>
+                113
+              </p>
+              </td>
+<td>
+              <p>
+                HPUX IA64, aCC A.06.06
+              </p>
+              </td>
+<td>
+              <p>
+                Peak=20.9 Mean=2.6
+              </p>
+              </td>
+<td>
+              <p>
+                Peak=88.1 Mean=14.3
+              </p>
+              </td>
+<td>
+              <p>
+                Peak~2x10<sup>4</sup> Mean=1x10<sup>3</sup>
+              </p>
+              </td>
+</tr>
+</tbody>
+</table></div>
+</div>
+<br class="table-break"><div class="table">
+<a name="id727524"></a><p class="title"><b>Table 24. Errors In the Function ibetac(a,b,x)</b></p>
+<div class="table-contents"><table class="table" summary="Errors In the Function ibetac(a,b,x)">
+<colgroup>
+<col>
+<col>
+<col>
+<col>
+<col>
+</colgroup>
+<thead><tr>
+<th>
+              <p>
+                Significand Size
+              </p>
+              </th>
+<th>
+              <p>
+                Platform and Compiler
+              </p>
+              </th>
+<th>
+              <p>
+                0 &lt; a,b &lt; 10
+              </p>
+              <p>
+                and
+              </p>
+              <p>
+                0 &lt; x &lt; 1
+              </p>
+              </th>
+<th>
+              <p>
+                0 &lt; a,b &lt; 100
+              </p>
+              <p>
+                and
+              </p>
+              <p>
+                0 &lt; x &lt; 1
+              </p>
+              </th>
+<th>
+              <p>
+                1x10<sup>-5</sup> &lt; a,b &lt; 1x10<sup>5</sup>
+              </p>
+              <p>
+                and
+              </p>
+              <p>
+                0 &lt; x &lt; 1
+              </p>
+              </th>
+</tr></thead>
+<tbody>
+<tr>
+<td>
+              <p>
+                53
+              </p>
+              </td>
+<td>
+              <p>
+                Win32, Visual C++ 8
+              </p>
+              </td>
+<td>
+              <p>
+                Peak=13.9 Mean=2.0
+              </p>
+              </td>
+<td>
+              <p>
+                Peak=56.2 Mean=14
+              </p>
+              </td>
+<td>
+              <p>
+                Peak=3x10<sup>3</sup> Mean=159
+              </p>
+              </td>
+</tr>
+<tr>
+<td>
+              <p>
+                64
+              </p>
+              </td>
+<td>
+              <p>
+                Redhat Linux IA32, gcc-3.4.4
+              </p>
+              </td>
+<td>
+              <p>
+                Peak=21.1 Mean=3.6
+              </p>
+              </td>
+<td>
+              <p>
+                Peak=221.7 Mean=25.8
+              </p>
+              </td>
+<td>
+              <p>
+                Peak~9x10<sup>4</sup> Mean=3x10<sup>3</sup>
+              </p>
+              </td>
+</tr>
+<tr>
+<td>
+              <p>
+                64
+              </p>
+              </td>
+<td>
+              <p>
+                Redhat Linux IA64, gcc-3.4.4
+              </p>
+              </td>
+<td>
+              <p>
+                Peak=10.6 Mean=2.2
+              </p>
+              </td>
+<td>
+              <p>
+                Peak=73.9 Mean=11.9
+              </p>
+              </td>
+<td>
+              <p>
+                Peak~9x10<sup>4</sup> Mean=3x10<sup>3</sup>
+              </p>
+              </td>
+</tr>
+<tr>
+<td>
+              <p>
+                113
+              </p>
+              </td>
+<td>
+              <p>
+                HPUX IA64, aCC A.06.06
+              </p>
+              </td>
+<td>
+              <p>
+                Peak=9.9 Mean=2.6
+              </p>
+              </td>
+<td>
+              <p>
+                Peak=117.7 Mean=15.1
+              </p>
+              </td>
+<td>
+              <p>
+                Peak~3x10<sup>4</sup> Mean=1x10<sup>3</sup>
+              </p>
+              </td>
+</tr>
+</tbody>
+</table></div>
+</div>
+<br class="table-break"><div class="table">
+<a name="id727826"></a><p class="title"><b>Table 25. Errors In the Function beta(a, b, x)</b></p>
+<div class="table-contents"><table class="table" summary="Errors In the Function beta(a, b, x)">
+<colgroup>
+<col>
+<col>
+<col>
+<col>
+<col>
+</colgroup>
+<thead><tr>
+<th>
+              <p>
+                Significand Size
+              </p>
+              </th>
+<th>
+              <p>
+                Platform and Compiler
+              </p>
+              </th>
+<th>
+              <p>
+                0 &lt; a,b &lt; 10
+              </p>
+              <p>
+                and
+              </p>
+              <p>
+                0 &lt; x &lt; 1
+              </p>
+              </th>
+<th>
+              <p>
+                0 &lt; a,b &lt; 100
+              </p>
+              <p>
+                and
+              </p>
+              <p>
+                0 &lt; x &lt; 1
+              </p>
+              </th>
+<th>
+              <p>
+                1x10<sup>-5</sup> &lt; a,b &lt; 1x10<sup>5</sup>
+              </p>
+              <p>
+                and
+              </p>
+              <p>
+                0 &lt; x &lt; 1
+              </p>
+              </th>
+</tr></thead>
+<tbody>
+<tr>
+<td>
+              <p>
+                53
+              </p>
+              </td>
+<td>
+              <p>
+                Win32, Visual C++ 8
+              </p>
+              </td>
+<td>
+              <p>
+                Peak=39 Mean=2.9
+              </p>
+              </td>
+<td>
+              <p>
+                Peak=91 Mean=12.7
+              </p>
+              </td>
+<td>
+              <p>
+                Peak=635 Mean=25
+              </p>
+              </td>
+</tr>
+<tr>
+<td>
+              <p>
+                64
+              </p>
+              </td>
+<td>
+              <p>
+                Redhat Linux IA32, gcc-3.4.4
+              </p>
+              </td>
+<td>
+              <p>
+                Peak=26 Mean=3.6
+              </p>
+              </td>
+<td>
+              <p>
+                Peak=180.7 Mean=30.1
+              </p>
+              </td>
+<td>
+              <p>
+                Peak~7x10<sup>4</sup> Mean=3x10<sup>3</sup>
+              </p>
+              </td>
+</tr>
+<tr>
+<td>
+              <p>
+                64
+              </p>
+              </td>
+<td>
+              <p>
+                Redhat Linux IA64, gcc-3.4.4
+              </p>
+              </td>
+<td>
+              <p>
+                Peak=13 Mean=2.4
+              </p>
+              </td>
+<td>
+              <p>
+                Peak=67.1 Mean=13.4
+              </p>
+              </td>
+<td>
+              <p>
+                Peak~7x10<sup>4</sup> Mean=3x10<sup>3</sup>
+              </p>
+              </td>
+</tr>
+<tr>
+<td>
+              <p>
+                113
+              </p>
+              </td>
+<td>
+              <p>
+                HPUX IA64, aCC A.06.06
+              </p>
+              </td>
+<td>
+              <p>
+                Peak=27.3 Mean=3.6
+              </p>
+              </td>
+<td>
+              <p>
+                Peak=49.8 Mean=9.1
+              </p>
+              </td>
+<td>
+              <p>
+                Peak~6x10<sup>4</sup> Mean=3x10<sup>3</sup>
+              </p>
+              </td>
+</tr>
+</tbody>
+</table></div>
+</div>
+<br class="table-break"><div class="table">
+<a name="id728122"></a><p class="title"><b>Table 26. Errors In the Function betac(a,b,x)</b></p>
+<div class="table-contents"><table class="table" summary="Errors In the Function betac(a,b,x)">
+<colgroup>
+<col>
+<col>
+<col>
+<col>
+<col>
+</colgroup>
+<thead><tr>
+<th>
+              <p>
+                Significand Size
+              </p>
+              </th>
+<th>
+              <p>
+                Platform and Compiler
+              </p>
+              </th>
+<th>
+              <p>
+                0 &lt; a,b &lt; 10
+              </p>
+              <p>
+                and
+              </p>
+              <p>
+                0 &lt; x &lt; 1
+              </p>
+              </th>
+<th>
+              <p>
+                0 &lt; a,b &lt; 100
+              </p>
+              <p>
+                and
+              </p>
+              <p>
+                0 &lt; x &lt; 1
+              </p>
+              </th>
+<th>
+              <p>
+                1x10<sup>-5</sup> &lt; a,b &lt; 1x10<sup>5</sup>
+              </p>
+              <p>
+                and
+              </p>
+              <p>
+                0 &lt; x &lt; 1
+              </p>
+              </th>
+</tr></thead>
+<tbody>
+<tr>
+<td>
+              <p>
+                53
+              </p>
+              </td>
+<td>
+              <p>
+                Win32, Visual C++ 8
+              </p>
+              </td>
+<td>
+              <p>
+                Peak=12.0 Mean=2.4
+              </p>
+              </td>
+<td>
+              <p>
+                Peak=91 Mean=15
+              </p>
+              </td>
+<td>
+              <p>
+                Peak=4x10<sup>3</sup> Mean=113
+              </p>
+              </td>
+</tr>
+<tr>
+<td>
+              <p>
+                64
+              </p>
+              </td>
+<td>
+              <p>
+                Redhat Linux IA32, gcc-3.4.4
+              </p>
+              </td>
+<td>
+              <p>
+                Peak=19.8 Mean=3.8
+              </p>
+              </td>
+<td>
+              <p>
+                Peak=295.1 Mean=33.9
+              </p>
+              </td>
+<td>
+              <p>
+                Peak~1x10<sup>5</sup> Mean=5x10<sup>3</sup>
+              </p>
+              </td>
+</tr>
+<tr>
+<td>
+              <p>
+                64
+              </p>
+              </td>
+<td>
+              <p>
+                Redhat Linux IA64, gcc-3.4.4
+              </p>
+              </td>
+<td>
+              <p>
+                Peak=11.2 Mean=2.4
+              </p>
+              </td>
+<td>
+              <p>
+                Peak=63.5 Mean=13.6
+              </p>
+              </td>
+<td>
+              <p>
+                Peak~1x10<sup>5</sup> Mean=5x10<sup>3</sup>
+              </p>
+              </td>
+</tr>
+<tr>
+<td>
+              <p>
+                113
+              </p>
+              </td>
+<td>
+              <p>
+                HPUX IA64, aCC A.06.06
+              </p>
+              </td>
+<td>
+              <p>
+                Peak=15.6 Mean=3.5
+              </p>
+              </td>
+<td>
+              <p>
+                Peak=39.8 Mean=8.9
+              </p>
+              </td>
+<td>
+              <p>
+                Peak~9x10<sup>4</sup> Mean=5x10<sup>3</sup>
+              </p>
+              </td>
+</tr>
+</tbody>
+</table></div>
+</div>
+<br class="table-break"><a name="math_toolkit.special.sf_beta.ibeta_function.testing"></a><h5>
+<a name="id728432"></a>
+          <a class="link" href="ibeta_function.html#math_toolkit.special.sf_beta.ibeta_function.testing">Testing</a>
+        </h5>
+<p>
+          There are two sets of tests: spot tests compare values taken from <a href="http://functions.wolfram.com/webMathematica/FunctionEvaluation.jsp?name=BetaRegularized" target="_top">Mathworld's
+          online function evaluator</a> with this implementation: they provide
+          a basic "sanity check" for the implementation, with one spot-test
+          in each implementation-domain (see implementation notes below).
+        </p>
+<p>
+          Accuracy tests use data generated at very high precision (with <a href="http://shoup.net/ntl/doc/RR.txt" target="_top">NTL
+          RR class</a> set at 1000-bit precision), using the "textbook"
+          continued fraction representation (refer to the first continued fraction
+          in the implementation discussion below). Note that this continued fraction
+          is <span class="emphasis"><em>not</em></span> used in the implementation, and therefore we
+          have test data that is fully independent of the code.
+        </p>
+<a name="math_toolkit.special.sf_beta.ibeta_function.implementation"></a><h5>
+<a name="id728497"></a>
+          <a class="link" href="ibeta_function.html#math_toolkit.special.sf_beta.ibeta_function.implementation">Implementation</a>
+        </h5>
+<p>
+          This implementation is closely based upon <a href="http://portal.acm.org/citation.cfm?doid=131766.131776" target="_top">"Algorithm
+          708; Significant digit computation of the incomplete beta function ratios",
+          DiDonato and Morris, ACM, 1992.</a>
+        </p>
+<p>
+          All four of these functions share a common implementation: this is passed
+          both x and y, and can return either p or q where these are related by:
+        </p>
+<p>
+          <span class="inlinemediaobject"><img src="../../../../equations/ibeta_inv5.png"></span>
+        </p>
+<p>
+          so at any point we can swap a for b, x for y and p for q if this results
+          in a more favourable position. Generally such swaps are performed so that
+          we always compute a value less than 0.9: when required this can then be
+          subtracted from 1 without undue cancellation error.
+        </p>
+<p>
+          The following continued fraction representation is found in many textbooks
+          but is not used in this implementation - it's both slower and less accurate
+          than the alternatives - however it is used to generate test data:
+        </p>
+<p>
+          <span class="inlinemediaobject"><img src="../../../../equations/ibeta5.png"></span>
+        </p>
+<p>
+          The following continued fraction is due to <a href="http://portal.acm.org/citation.cfm?doid=131766.131776" target="_top">Didonato
+          and Morris</a>, and is used in this implementation when a and b are
+          both greater than 1:
+        </p>
+<p>
+          <span class="inlinemediaobject"><img src="../../../../equations/ibeta6.png"></span>
+        </p>
+<p>
+          For smallish b and x then a series representation can be used:
+        </p>
+<p>
+          <span class="inlinemediaobject"><img src="../../../../equations/ibeta7.png"></span>
+        </p>
+<p>
+          When b &lt;&lt; a then the transition from 0 to 1 occurs very close to
+          x = 1 and some care has to be taken over the method of computation, in
+          that case the following series representation is used:
+        </p>
+<p>
+          <span class="inlinemediaobject"><img src="../../../../equations/ibeta8.png"></span>
+        </p>
+<p>
+          Where Q(a,x) is an <a href="http://functions.wolfram.com/GammaBetaErf/Gamma2/" target="_top">incomplete
+          gamma function</a>. Note that this method relies on keeping a table
+          of all the p<sub>n </sub> previously computed, which does limit the precision of the
+          method, depending upon the size of the table used.
+        </p>
+<p>
+          When <span class="emphasis"><em>a</em></span> and <span class="emphasis"><em>b</em></span> are both small integers,
+          then we can relate the incomplete beta to the binomial distribution and
+          use the following finite sum:
+        </p>
+<p>
+          <span class="inlinemediaobject"><img src="../../../../equations/ibeta12.png"></span>
+        </p>
+<p>
+          Finally we can sidestep difficult areas, or move to an area with a more
+          efficient means of computation, by using the duplication formulae:
+        </p>
+<p>
+          <span class="inlinemediaobject"><img src="../../../../equations/ibeta10.png"></span>
+        </p>
+<p>
+          <span class="inlinemediaobject"><img src="../../../../equations/ibeta11.png"></span>
+        </p>
+<p>
+          The domains of a, b and x for which the various methods are used are identical
+          to those described in the <a href="http://portal.acm.org/citation.cfm?doid=131766.131776" target="_top">Didonato
+          and Morris TOMS 708 paper</a>.
+        </p>
+</div>
+<table xmlns:rev="http://www.cs.rpi.edu/~gregod/boost/tools/doc/revision" width="100%"><tr>
+<td align="left"></td>
+<td align="right"><div class="copyright-footer">Copyright © 2006 , 2007, 2008 John Maddock, Paul A. Bristow, Hubert
+      Holin, Xiaogang Zhang, Bruno Lalande and Gautam Sewani<p>
+        Distributed under the Boost Software License, Version 1.0. (See accompanying
+        file LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_0.txt)
+      </p>
+</div></td>
+</tr></table>
+<hr>
+<div class="spirit-nav">
+<a accesskey="p" href="beta_function.html"><img src="../../../../../doc/html/images/prev.png" alt="Prev"></a><a accesskey="u" href="../sf_beta.html"><img src="../../../../../doc/html/images/up.png" alt="Up"></a><a accesskey="h" href="../../../index.html"><img src="../../../../../doc/html/images/home.png" alt="Home"></a><a accesskey="n" href="ibeta_inv_function.html"><img src="../../../../../doc/html/images/next.png" alt="Next"></a>
+</div>
+</body>
+</html>

Added: sandbox/tools/auto_index/example/math/doc/sf_and_dist/html/math_toolkit/special/sf_beta/ibeta_inv_function.html
==============================================================================
--- (empty file)
+++ sandbox/tools/auto_index/example/math/doc/sf_and_dist/html/math_toolkit/special/sf_beta/ibeta_inv_function.html	2008-11-28 05:25:28 EST (Fri, 28 Nov 2008)
@@ -0,0 +1,569 @@
+<html>
+<head>
+<meta http-equiv="Content-Type" content="text/html; charset=ISO-8859-1">
+<title>The Incomplete Beta Function Inverses</title>
+<link rel="stylesheet" href="../../../boostbook.css" type="text/css">
+<meta name="generator" content="DocBook XSL Stylesheets Vsnapshot_8125">
+<link rel="home" href="../../../index.html" title="Math Toolkit">
+<link rel="up" href="../sf_beta.html" title="Beta Functions">
+<link rel="prev" href="ibeta_function.html" title="Incomplete Beta Functions">
+<link rel="next" href="beta_derivative.html" title="Derivative of the Incomplete Beta Function">
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+<body bgcolor="white" text="black" link="#0000FF" vlink="#840084" alink="#0000FF">
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+<a accesskey="p" href="ibeta_function.html"><img src="../../../../../doc/html/images/prev.png" alt="Prev"></a><a accesskey="u" href="../sf_beta.html"><img src="../../../../../doc/html/images/up.png" alt="Up"></a><a accesskey="h" href="../../../index.html"><img src="../../../../../doc/html/images/home.png" alt="Home"></a><a accesskey="n" href="beta_derivative.html"><img src="../../../../../doc/html/images/next.png" alt="Next"></a>
+</div>
+<div class="section" lang="en">
+<div class="titlepage"><div><div><h4 class="title">
+<a name="math_toolkit.special.sf_beta.ibeta_inv_function"></a><a class="link" href="ibeta_inv_function.html" title="The Incomplete Beta Function Inverses"> The
+        Incomplete Beta Function Inverses</a>
+</h4></div></div></div>
+<p>
+          
+</p>
+<pre class="programlisting"><span class="preprocessor">#include</span> <span class="special">&lt;</span><span class="identifier">boost</span><span class="special">/</span><span class="identifier">math</span><span class="special">/</span><span class="identifier">special_functions</span><span class="special">/</span><span class="identifier">beta</span><span class="special">.</span><span class="identifier">hpp</span><span class="special">&gt;</span>
+</pre>
+<p>
+        </p>
+<pre class="programlisting"><span class="keyword">namespace</span> <span class="identifier">boost</span><span class="special">{</span> <span class="keyword">namespace</span> <span class="identifier">math</span><span class="special">{</span>
+
+<span class="keyword">template</span> <span class="special">&lt;</span><span class="keyword">class</span> <span class="identifier">T1</span><span class="special">,</span> <span class="keyword">class</span> <span class="identifier">T2</span><span class="special">,</span> <span class="keyword">class</span> <span class="identifier">T3</span><span class="special">&gt;</span>
+<a class="link" href="../../main_overview/result_type.html" title="Calculation of the Type of the Result"><span class="emphasis"><em>calculated-result-type</em></span></a> <span class="identifier">ibeta_inv</span><span class="special">(</span><span class="identifier">T1</span> <span class="identifier">a</span><span class="special">,</span> <span class="identifier">T2</span> <span class="identifier">b</span><span class="special">,</span> <span class="identifier">T3</span> <span class="identifier">p</span><span class="special">);</span>
+
+<span class="keyword">template</span> <span class="special">&lt;</span><span class="keyword">class</span> <span class="identifier">T1</span><span class="special">,</span> <span class="keyword">class</span> <span class="identifier">T2</span><span class="special">,</span> <span class="keyword">class</span> <span class="identifier">T3</span><span class="special">,</span> <span class="keyword">class</span> <a class="link" href="../../policy.html" title="Policies">Policy</a><span class="special">&gt;</span>
+<a class="link" href="../../main_overview/result_type.html" title="Calculation of the Type of the Result"><span class="emphasis"><em>calculated-result-type</em></span></a> <span class="identifier">ibeta_inv</span><span class="special">(</span><span class="identifier">T1</span> <span class="identifier">a</span><span class="special">,</span> <span class="identifier">T2</span> <span class="identifier">b</span><span class="special">,</span> <span class="identifier">T3</span> <span class="identifier">p</span><span class="special">,</span> <span class="keyword">const</span> <a class="link" href="../../policy.html" title="Policies">Policy</a><span class="special">&amp;);</span>
+
+<span class="keyword">template</span> <span class="special">&lt;</span><span class="keyword">class</span> <span class="identifier">T1</span><span class="special">,</span> <span class="keyword">class</span> <span class="identifier">T2</span><span class="special">,</span> <span class="keyword">class</span> <span class="identifier">T3</span><span class="special">,</span> <span class="keyword">class</span> <span class="identifier">T4</span><span class="special">&gt;</span>
+<a class="link" href="../../main_overview/result_type.html" title="Calculation of the Type of the Result"><span class="emphasis"><em>calculated-result-type</em></span></a> <span class="identifier">ibeta_inv</span><span class="special">(</span><span class="identifier">T1</span> <span class="identifier">a</span><span class="special">,</span> <span class="identifier">T2</span> <span class="identifier">b</span><span class="special">,</span> <span class="identifier">T3</span> <span class="identifier">p</span><span class="special">,</span> <span class="identifier">T4</span><span class="special">*</span> <span class="identifier">py</span><span class="special">);</span>
+
+<span class="keyword">template</span> <span class="special">&lt;</span><span class="keyword">class</span> <span class="identifier">T1</span><span class="special">,</span> <span class="keyword">class</span> <span class="identifier">T2</span><span class="special">,</span> <span class="keyword">class</span> <span class="identifier">T3</span><span class="special">,</span> <span class="keyword">class</span> <span class="identifier">T4</span><span class="special">,</span> <span class="keyword">class</span> <a class="link" href="../../policy.html" title="Policies">Policy</a><span class="special">&gt;</span>
+<a class="link" href="../../main_overview/result_type.html" title="Calculation of the Type of the Result"><span class="emphasis"><em>calculated-result-type</em></span></a> <span class="identifier">ibeta_inv</span><span class="special">(</span><span class="identifier">T1</span> <span class="identifier">a</span><span class="special">,</span> <span class="identifier">T2</span> <span class="identifier">b</span><span class="special">,</span> <span class="identifier">T3</span> <span class="identifier">p</span><span class="special">,</span> <span class="identifier">T4</span><span class="special">*</span> <span class="identifier">py</span><span class="special">,</span> <span class="keyword">const</span> <a class="link" href="../../policy.html" title="Policies">Policy</a><span class="special">&amp;);</span>
+
+<span class="keyword">template</span> <span class="special">&lt;</span><span class="keyword">class</span> <span class="identifier">T1</span><span class="special">,</span> <span class="keyword">class</span> <span class="identifier">T2</span><span class="special">,</span> <span class="keyword">class</span> <span class="identifier">T3</span><span class="special">&gt;</span>
+<a class="link" href="../../main_overview/result_type.html" title="Calculation of the Type of the Result"><span class="emphasis"><em>calculated-result-type</em></span></a> <span class="identifier">ibetac_inv</span><span class="special">(</span><span class="identifier">T1</span> <span class="identifier">a</span><span class="special">,</span> <span class="identifier">T2</span> <span class="identifier">b</span><span class="special">,</span> <span class="identifier">T3</span> <span class="identifier">q</span><span class="special">);</span>
+
+<span class="keyword">template</span> <span class="special">&lt;</span><span class="keyword">class</span> <span class="identifier">T1</span><span class="special">,</span> <span class="keyword">class</span> <span class="identifier">T2</span><span class="special">,</span> <span class="keyword">class</span> <span class="identifier">T3</span><span class="special">,</span> <span class="keyword">class</span> <a class="link" href="../../policy.html" title="Policies">Policy</a><span class="special">&gt;</span>
+<a class="link" href="../../main_overview/result_type.html" title="Calculation of the Type of the Result"><span class="emphasis"><em>calculated-result-type</em></span></a> <span class="identifier">ibetac_inv</span><span class="special">(</span><span class="identifier">T1</span> <span class="identifier">a</span><span class="special">,</span> <span class="identifier">T2</span> <span class="identifier">b</span><span class="special">,</span> <span class="identifier">T3</span> <span class="identifier">q</span><span class="special">,</span> <span class="keyword">const</span> <a class="link" href="../../policy.html" title="Policies">Policy</a><span class="special">&amp;);</span>
+
+<span class="keyword">template</span> <span class="special">&lt;</span><span class="keyword">class</span> <span class="identifier">T1</span><span class="special">,</span> <span class="keyword">class</span> <span class="identifier">T2</span><span class="special">,</span> <span class="keyword">class</span> <span class="identifier">T3</span><span class="special">,</span> <span class="keyword">class</span> <span class="identifier">T4</span><span class="special">&gt;</span>
+<a class="link" href="../../main_overview/result_type.html" title="Calculation of the Type of the Result"><span class="emphasis"><em>calculated-result-type</em></span></a> <span class="identifier">ibetac_inv</span><span class="special">(</span><span class="identifier">T1</span> <span class="identifier">a</span><span class="special">,</span> <span class="identifier">T2</span> <span class="identifier">b</span><span class="special">,</span> <span class="identifier">T3</span> <span class="identifier">q</span><span class="special">,</span> <span class="identifier">T4</span><span class="special">*</span> <span class="identifier">py</span><span class="special">);</span>
+
+<span class="keyword">template</span> <span class="special">&lt;</span><span class="keyword">class</span> <span class="identifier">T1</span><span class="special">,</span> <span class="keyword">class</span> <span class="identifier">T2</span><span class="special">,</span> <span class="keyword">class</span> <span class="identifier">T3</span><span class="special">,</span> <span class="keyword">class</span> <span class="identifier">T4</span><span class="special">,</span> <span class="keyword">class</span> <a class="link" href="../../policy.html" title="Policies">Policy</a><span class="special">&gt;</span>
+<a class="link" href="../../main_overview/result_type.html" title="Calculation of the Type of the Result"><span class="emphasis"><em>calculated-result-type</em></span></a> <span class="identifier">ibetac_inv</span><span class="special">(</span><span class="identifier">T1</span> <span class="identifier">a</span><span class="special">,</span> <span class="identifier">T2</span> <span class="identifier">b</span><span class="special">,</span> <span class="identifier">T3</span> <span class="identifier">q</span><span class="special">,</span> <span class="identifier">T4</span><span class="special">*</span> <span class="identifier">py</span><span class="special">,</span> <span class="keyword">const</span> <a class="link" href="../../policy.html" title="Policies">Policy</a><span class="special">&amp;);</span>
+
+<span class="keyword">template</span> <span class="special">&lt;</span><span class="keyword">class</span> <span class="identifier">T1</span><span class="special">,</span> <span class="keyword">class</span> <span class="identifier">T2</span><span class="special">,</span> <span class="keyword">class</span> <span class="identifier">T3</span><span class="special">&gt;</span>
+<a class="link" href="../../main_overview/result_type.html" title="Calculation of the Type of the Result"><span class="emphasis"><em>calculated-result-type</em></span></a> <span class="identifier">ibeta_inva</span><span class="special">(</span><span class="identifier">T1</span> <span class="identifier">b</span><span class="special">,</span> <span class="identifier">T2</span> <span class="identifier">x</span><span class="special">,</span> <span class="identifier">T3</span> <span class="identifier">p</span><span class="special">);</span>
+
+<span class="keyword">template</span> <span class="special">&lt;</span><span class="keyword">class</span> <span class="identifier">T1</span><span class="special">,</span> <span class="keyword">class</span> <span class="identifier">T2</span><span class="special">,</span> <span class="keyword">class</span> <span class="identifier">T3</span><span class="special">,</span> <span class="keyword">class</span> <a class="link" href="../../policy.html" title="Policies">Policy</a><span class="special">&gt;</span>
+<a class="link" href="../../main_overview/result_type.html" title="Calculation of the Type of the Result"><span class="emphasis"><em>calculated-result-type</em></span></a> <span class="identifier">ibeta_inva</span><span class="special">(</span><span class="identifier">T1</span> <span class="identifier">b</span><span class="special">,</span> <span class="identifier">T2</span> <span class="identifier">x</span><span class="special">,</span> <span class="identifier">T3</span> <span class="identifier">p</span><span class="special">,</span> <span class="keyword">const</span> <a class="link" href="../../policy.html" title="Policies">Policy</a><span class="special">&amp;);</span>
+
+<span class="keyword">template</span> <span class="special">&lt;</span><span class="keyword">class</span> <span class="identifier">T1</span><span class="special">,</span> <span class="keyword">class</span> <span class="identifier">T2</span><span class="special">,</span> <span class="keyword">class</span> <span class="identifier">T3</span><span class="special">&gt;</span>
+<a class="link" href="../../main_overview/result_type.html" title="Calculation of the Type of the Result"><span class="emphasis"><em>calculated-result-type</em></span></a> <span class="identifier">ibetac_inva</span><span class="special">(</span><span class="identifier">T1</span> <span class="identifier">b</span><span class="special">,</span> <span class="identifier">T2</span> <span class="identifier">x</span><span class="special">,</span> <span class="identifier">T3</span> <span class="identifier">q</span><span class="special">);</span>
+
+<span class="keyword">template</span> <span class="special">&lt;</span><span class="keyword">class</span> <span class="identifier">T1</span><span class="special">,</span> <span class="keyword">class</span> <span class="identifier">T2</span><span class="special">,</span> <span class="keyword">class</span> <span class="identifier">T3</span><span class="special">,</span> <span class="keyword">class</span> <a class="link" href="../../policy.html" title="Policies">Policy</a><span class="special">&gt;</span>
+<a class="link" href="../../main_overview/result_type.html" title="Calculation of the Type of the Result"><span class="emphasis"><em>calculated-result-type</em></span></a> <span class="identifier">ibetac_inva</span><span class="special">(</span><span class="identifier">T1</span> <span class="identifier">b</span><span class="special">,</span> <span class="identifier">T2</span> <span class="identifier">x</span><span class="special">,</span> <span class="identifier">T3</span> <span class="identifier">q</span><span class="special">,</span> <span class="keyword">const</span> <a class="link" href="../../policy.html" title="Policies">Policy</a><span class="special">&amp;);</span>
+
+<span class="keyword">template</span> <span class="special">&lt;</span><span class="keyword">class</span> <span class="identifier">T1</span><span class="special">,</span> <span class="keyword">class</span> <span class="identifier">T2</span><span class="special">,</span> <span class="keyword">class</span> <span class="identifier">T3</span><span class="special">&gt;</span>
+<a class="link" href="../../main_overview/result_type.html" title="Calculation of the Type of the Result"><span class="emphasis"><em>calculated-result-type</em></span></a> <span class="identifier">ibeta_invb</span><span class="special">(</span><span class="identifier">T1</span> <span class="identifier">a</span><span class="special">,</span> <span class="identifier">T2</span> <span class="identifier">x</span><span class="special">,</span> <span class="identifier">T3</span> <span class="identifier">p</span><span class="special">);</span>
+
+<span class="keyword">template</span> <span class="special">&lt;</span><span class="keyword">class</span> <span class="identifier">T1</span><span class="special">,</span> <span class="keyword">class</span> <span class="identifier">T2</span><span class="special">,</span> <span class="keyword">class</span> <span class="identifier">T3</span><span class="special">,</span> <span class="keyword">class</span> <a class="link" href="../../policy.html" title="Policies">Policy</a><span class="special">&gt;</span>
+<a class="link" href="../../main_overview/result_type.html" title="Calculation of the Type of the Result"><span class="emphasis"><em>calculated-result-type</em></span></a> <span class="identifier">ibeta_invb</span><span class="special">(</span><span class="identifier">T1</span> <span class="identifier">a</span><span class="special">,</span> <span class="identifier">T2</span> <span class="identifier">x</span><span class="special">,</span> <span class="identifier">T3</span> <span class="identifier">p</span><span class="special">,</span> <span class="keyword">const</span> <a class="link" href="../../policy.html" title="Policies">Policy</a><span class="special">&amp;);</span>
+
+<span class="keyword">template</span> <span class="special">&lt;</span><span class="keyword">class</span> <span class="identifier">T1</span><span class="special">,</span> <span class="keyword">class</span> <span class="identifier">T2</span><span class="special">,</span> <span class="keyword">class</span> <span class="identifier">T3</span><span class="special">&gt;</span>
+<a class="link" href="../../main_overview/result_type.html" title="Calculation of the Type of the Result"><span class="emphasis"><em>calculated-result-type</em></span></a> <span class="identifier">ibetac_invb</span><span class="special">(</span><span class="identifier">T1</span> <span class="identifier">a</span><span class="special">,</span> <span class="identifier">T2</span> <span class="identifier">x</span><span class="special">,</span> <span class="identifier">T3</span> <span class="identifier">q</span><span class="special">);</span>
+
+<span class="keyword">template</span> <span class="special">&lt;</span><span class="keyword">class</span> <span class="identifier">T1</span><span class="special">,</span> <span class="keyword">class</span> <span class="identifier">T2</span><span class="special">,</span> <span class="keyword">class</span> <span class="identifier">T3</span><span class="special">,</span> <span class="keyword">class</span> <a class="link" href="../../policy.html" title="Policies">Policy</a><span class="special">&gt;</span>
+<a class="link" href="../../main_overview/result_type.html" title="Calculation of the Type of the Result"><span class="emphasis"><em>calculated-result-type</em></span></a> <span class="identifier">ibetac_invb</span><span class="special">(</span><span class="identifier">T1</span> <span class="identifier">a</span><span class="special">,</span> <span class="identifier">T2</span> <span class="identifier">x</span><span class="special">,</span> <span class="identifier">T3</span> <span class="identifier">q</span><span class="special">,</span> <span class="keyword">const</span> <a class="link" href="../../policy.html" title="Policies">Policy</a><span class="special">&amp;);</span>
+
+<span class="special">}}</span> <span class="comment">// namespaces
+</span></pre>
+<a name="math_toolkit.special.sf_beta.ibeta_inv_function.description"></a><h5>
+<a name="id731670"></a>
+          <a class="link" href="ibeta_inv_function.html#math_toolkit.special.sf_beta.ibeta_inv_function.description">Description</a>
+        </h5>
+<p>
+          There are six <a href="http://functions.wolfram.com/GammaBetaErf/" target="_top">incomplete
+          beta function inverses</a> which allow you solve for any of the three
+          parameters to the incomplete beta, starting from either the result of the
+          incomplete beta (p) or its complement (q).
+        </p>
+<p>
+          </p>
+<p>
+            The final <a class="link" href="../../policy.html" title="Policies">Policy</a> argument
+            is optional and can be used to control the behaviour of the function:
+            how it handles errors, what level of precision to use etc. Refer to the
+            <a class="link" href="../../policy.html" title="Policies">policy documentation for more details</a>.
+          </p>
+<p>
+        </p>
+<div class="tip"><table border="0" summary="Tip">
+<tr>
+<td rowspan="2" align="center" valign="top" width="25"><img alt="[Tip]" src="../../../../../doc/html/images/tip.png"></td>
+<th align="left">Tip</th>
+</tr>
+<tr><td align="left" valign="top">
+<p>
+            When people normally talk about the inverse of the incomplete beta function,
+            they are talking about inverting on parameter <span class="emphasis"><em>x</em></span>.
+            These are implemented here as ibeta_inv and ibeta_inv, and are by far
+            the most efficient of the inverses presented here.
+          </p>
+<p>
+            The inverses on the <span class="emphasis"><em>a</em></span> and <span class="emphasis"><em>b</em></span>
+            parameters find use in some statistical applications, but have to be
+            computed by rather brute force numerical techniques and are consequently
+            several times slower. These are implemented here as ibeta_inva and ibeta_invb,
+            and complement versions ibetac_inva and ibetac_invb.
+          </p>
+</td></tr>
+</table></div>
+<p>
+          The return type of these functions is computed using the <a class="link" href="../../main_overview/result_type.html" title="Calculation of the Type of the Result"><span class="emphasis"><em>result
+          type calculation rules</em></span></a> when called with arguments T1...TN
+          of different types.
+        </p>
+<pre class="programlisting"><span class="keyword">template</span> <span class="special">&lt;</span><span class="keyword">class</span> <span class="identifier">T1</span><span class="special">,</span> <span class="keyword">class</span> <span class="identifier">T2</span><span class="special">,</span> <span class="keyword">class</span> <span class="identifier">T3</span><span class="special">&gt;</span>
+<a class="link" href="../../main_overview/result_type.html" title="Calculation of the Type of the Result"><span class="emphasis"><em>calculated-result-type</em></span></a> <span class="identifier">ibeta_inv</span><span class="special">(</span><span class="identifier">T1</span> <span class="identifier">a</span><span class="special">,</span> <span class="identifier">T2</span> <span class="identifier">b</span><span class="special">,</span> <span class="identifier">T3</span> <span class="identifier">p</span><span class="special">);</span>
+
+<span class="keyword">template</span> <span class="special">&lt;</span><span class="keyword">class</span> <span class="identifier">T1</span><span class="special">,</span> <span class="keyword">class</span> <span class="identifier">T2</span><span class="special">,</span> <span class="keyword">class</span> <span class="identifier">T3</span><span class="special">,</span> <span class="keyword">class</span> <a class="link" href="../../policy.html" title="Policies">Policy</a><span class="special">&gt;</span>
+<a class="link" href="../../main_overview/result_type.html" title="Calculation of the Type of the Result"><span class="emphasis"><em>calculated-result-type</em></span></a> <span class="identifier">ibeta_inv</span><span class="special">(</span><span class="identifier">T1</span> <span class="identifier">a</span><span class="special">,</span> <span class="identifier">T2</span> <span class="identifier">b</span><span class="special">,</span> <span class="identifier">T3</span> <span class="identifier">p</span><span class="special">,</span> <span class="keyword">const</span> <a class="link" href="../../policy.html" title="Policies">Policy</a><span class="special">&amp;);</span>
+
+<span class="keyword">template</span> <span class="special">&lt;</span><span class="keyword">class</span> <span class="identifier">T1</span><span class="special">,</span> <span class="keyword">class</span> <span class="identifier">T2</span><span class="special">,</span> <span class="keyword">class</span> <span class="identifier">T3</span><span class="special">,</span> <span class="keyword">class</span> <span class="identifier">T4</span><span class="special">&gt;</span>
+<a class="link" href="../../main_overview/result_type.html" title="Calculation of the Type of the Result"><span class="emphasis"><em>calculated-result-type</em></span></a> <span class="identifier">ibeta_inv</span><span class="special">(</span><span class="identifier">T1</span> <span class="identifier">a</span><span class="special">,</span> <span class="identifier">T2</span> <span class="identifier">b</span><span class="special">,</span> <span class="identifier">T3</span> <span class="identifier">p</span><span class="special">,</span> <span class="identifier">T4</span><span class="special">*</span> <span class="identifier">py</span><span class="special">);</span>
+
+<span class="keyword">template</span> <span class="special">&lt;</span><span class="keyword">class</span> <span class="identifier">T1</span><span class="special">,</span> <span class="keyword">class</span> <span class="identifier">T2</span><span class="special">,</span> <span class="keyword">class</span> <span class="identifier">T3</span><span class="special">,</span> <span class="keyword">class</span> <span class="identifier">T4</span><span class="special">,</span> <span class="keyword">class</span> <a class="link" href="../../policy.html" title="Policies">Policy</a><span class="special">&gt;</span>
+<a class="link" href="../../main_overview/result_type.html" title="Calculation of the Type of the Result"><span class="emphasis"><em>calculated-result-type</em></span></a> <span class="identifier">ibeta_inv</span><span class="special">(</span><span class="identifier">T1</span> <span class="identifier">a</span><span class="special">,</span> <span class="identifier">T2</span> <span class="identifier">b</span><span class="special">,</span> <span class="identifier">T3</span> <span class="identifier">p</span><span class="special">,</span> <span class="identifier">T4</span><span class="special">*</span> <span class="identifier">py</span><span class="special">,</span> <span class="keyword">const</span> <a class="link" href="../../policy.html" title="Policies">Policy</a><span class="special">&amp;);</span>
+</pre>
+<p>
+          Returns a value <span class="emphasis"><em>x</em></span> such that: <code class="computeroutput"><span class="identifier">p</span>
+          <span class="special">=</span> <span class="identifier">ibeta</span><span class="special">(</span><span class="identifier">a</span><span class="special">,</span>
+          <span class="identifier">b</span><span class="special">,</span>
+          <span class="identifier">x</span><span class="special">);</span></code>
+          and sets <code class="computeroutput"><span class="special">*</span><span class="identifier">py</span>
+          <span class="special">=</span> <span class="number">1</span> <span class="special">-</span> <span class="identifier">x</span></code> when
+          the <code class="computeroutput"><span class="identifier">py</span></code> parameter is provided
+          and is non-null. Note that internally this function computes whichever
+          is the smaller of <code class="computeroutput"><span class="identifier">x</span></code> and
+          <code class="computeroutput"><span class="number">1</span><span class="special">-</span><span class="identifier">x</span></code>, and therefore the value assigned to
+          <code class="computeroutput"><span class="special">*</span><span class="identifier">py</span></code>
+          is free from cancellation errors. That means that even if the function
+          returns <code class="computeroutput"><span class="number">1</span></code>, the value stored
+          in <code class="computeroutput"><span class="special">*</span><span class="identifier">py</span></code>
+          may be non-zero, albeit very small.
+        </p>
+<p>
+          Requires: <span class="emphasis"><em>a,b &gt; 0</em></span> and <span class="emphasis"><em>0 &lt;= p &lt;=
+          1</em></span>.
+        </p>
+<p>
+          </p>
+<p>
+            The final <a class="link" href="../../policy.html" title="Policies">Policy</a> argument
+            is optional and can be used to control the behaviour of the function:
+            how it handles errors, what level of precision to use etc. Refer to the
+            <a class="link" href="../../policy.html" title="Policies">policy documentation for more details</a>.
+          </p>
+<p>
+        </p>
+<pre class="programlisting"><span class="keyword">template</span> <span class="special">&lt;</span><span class="keyword">class</span> <span class="identifier">T1</span><span class="special">,</span> <span class="keyword">class</span> <span class="identifier">T2</span><span class="special">,</span> <span class="keyword">class</span> <span class="identifier">T3</span><span class="special">&gt;</span>
+<a class="link" href="../../main_overview/result_type.html" title="Calculation of the Type of the Result"><span class="emphasis"><em>calculated-result-type</em></span></a> <span class="identifier">ibetac_inv</span><span class="special">(</span><span class="identifier">T1</span> <span class="identifier">a</span><span class="special">,</span> <span class="identifier">T2</span> <span class="identifier">b</span><span class="special">,</span> <span class="identifier">T3</span> <span class="identifier">q</span><span class="special">);</span>
+
+<span class="keyword">template</span> <span class="special">&lt;</span><span class="keyword">class</span> <span class="identifier">T1</span><span class="special">,</span> <span class="keyword">class</span> <span class="identifier">T2</span><span class="special">,</span> <span class="keyword">class</span> <span class="identifier">T3</span><span class="special">,</span> <span class="keyword">class</span> <a class="link" href="../../policy.html" title="Policies">Policy</a><span class="special">&gt;</span>
+<a class="link" href="../../main_overview/result_type.html" title="Calculation of the Type of the Result"><span class="emphasis"><em>calculated-result-type</em></span></a> <span class="identifier">ibetac_inv</span><span class="special">(</span><span class="identifier">T1</span> <span class="identifier">a</span><span class="special">,</span> <span class="identifier">T2</span> <span class="identifier">b</span><span class="special">,</span> <span class="identifier">T3</span> <span class="identifier">q</span><span class="special">,</span> <span class="keyword">const</span> <a class="link" href="../../policy.html" title="Policies">Policy</a><span class="special">&amp;);</span>
+
+<span class="keyword">template</span> <span class="special">&lt;</span><span class="keyword">class</span> <span class="identifier">T1</span><span class="special">,</span> <span class="keyword">class</span> <span class="identifier">T2</span><span class="special">,</span> <span class="keyword">class</span> <span class="identifier">T3</span><span class="special">,</span> <span class="keyword">class</span> <span class="identifier">T4</span><span class="special">&gt;</span>
+<a class="link" href="../../main_overview/result_type.html" title="Calculation of the Type of the Result"><span class="emphasis"><em>calculated-result-type</em></span></a> <span class="identifier">ibetac_inv</span><span class="special">(</span><span class="identifier">T1</span> <span class="identifier">a</span><span class="special">,</span> <span class="identifier">T2</span> <span class="identifier">b</span><span class="special">,</span> <span class="identifier">T3</span> <span class="identifier">q</span><span class="special">,</span> <span class="identifier">T4</span><span class="special">*</span> <span class="identifier">py</span><span class="special">);</span>
+
+<span class="keyword">template</span> <span class="special">&lt;</span><span class="keyword">class</span> <span class="identifier">T1</span><span class="special">,</span> <span class="keyword">class</span> <span class="identifier">T2</span><span class="special">,</span> <span class="keyword">class</span> <span class="identifier">T3</span><span class="special">,</span> <span class="keyword">class</span> <span class="identifier">T4</span><span class="special">,</span> <span class="keyword">class</span> <a class="link" href="../../policy.html" title="Policies">Policy</a><span class="special">&gt;</span>
+<a class="link" href="../../main_overview/result_type.html" title="Calculation of the Type of the Result"><span class="emphasis"><em>calculated-result-type</em></span></a> <span class="identifier">ibetac_inv</span><span class="special">(</span><span class="identifier">T1</span> <span class="identifier">a</span><span class="special">,</span> <span class="identifier">T2</span> <span class="identifier">b</span><span class="special">,</span> <span class="identifier">T3</span> <span class="identifier">q</span><span class="special">,</span> <span class="identifier">T4</span><span class="special">*</span> <span class="identifier">py</span><span class="special">,</span> <span class="keyword">const</span> <a class="link" href="../../policy.html" title="Policies">Policy</a><span class="special">&amp;);</span>
+</pre>
+<p>
+          Returns a value <span class="emphasis"><em>x</em></span> such that: <code class="computeroutput"><span class="identifier">q</span>
+          <span class="special">=</span> <span class="identifier">ibetac</span><span class="special">(</span><span class="identifier">a</span><span class="special">,</span>
+          <span class="identifier">b</span><span class="special">,</span>
+          <span class="identifier">x</span><span class="special">);</span></code>
+          and sets <code class="computeroutput"><span class="special">*</span><span class="identifier">py</span>
+          <span class="special">=</span> <span class="number">1</span> <span class="special">-</span> <span class="identifier">x</span></code> when
+          the <code class="computeroutput"><span class="identifier">py</span></code> parameter is provided
+          and is non-null. Note that internally this function computes whichever
+          is the smaller of <code class="computeroutput"><span class="identifier">x</span></code> and
+          <code class="computeroutput"><span class="number">1</span><span class="special">-</span><span class="identifier">x</span></code>, and therefore the value assigned to
+          <code class="computeroutput"><span class="special">*</span><span class="identifier">py</span></code>
+          is free from cancellation errors. That means that even if the function
+          returns <code class="computeroutput"><span class="number">1</span></code>, the value stored
+          in <code class="computeroutput"><span class="special">*</span><span class="identifier">py</span></code>
+          may be non-zero, albeit very small.
+        </p>
+<p>
+          Requires: <span class="emphasis"><em>a,b &gt; 0</em></span> and <span class="emphasis"><em>0 &lt;= q &lt;=
+          1</em></span>.
+        </p>
+<p>
+          </p>
+<p>
+            The final <a class="link" href="../../policy.html" title="Policies">Policy</a> argument
+            is optional and can be used to control the behaviour of the function:
+            how it handles errors, what level of precision to use etc. Refer to the
+            <a class="link" href="../../policy.html" title="Policies">policy documentation for more details</a>.
+          </p>
+<p>
+        </p>
+<pre class="programlisting"><span class="keyword">template</span> <span class="special">&lt;</span><span class="keyword">class</span> <span class="identifier">T1</span><span class="special">,</span> <span class="keyword">class</span> <span class="identifier">T2</span><span class="special">,</span> <span class="keyword">class</span> <span class="identifier">T3</span><span class="special">&gt;</span>
+<a class="link" href="../../main_overview/result_type.html" title="Calculation of the Type of the Result"><span class="emphasis"><em>calculated-result-type</em></span></a> <span class="identifier">ibeta_inva</span><span class="special">(</span><span class="identifier">T1</span> <span class="identifier">b</span><span class="special">,</span> <span class="identifier">T2</span> <span class="identifier">x</span><span class="special">,</span> <span class="identifier">T3</span> <span class="identifier">p</span><span class="special">);</span>
+
+<span class="keyword">template</span> <span class="special">&lt;</span><span class="keyword">class</span> <span class="identifier">T1</span><span class="special">,</span> <span class="keyword">class</span> <span class="identifier">T2</span><span class="special">,</span> <span class="keyword">class</span> <span class="identifier">T3</span><span class="special">,</span> <span class="keyword">class</span> <a class="link" href="../../policy.html" title="Policies">Policy</a><span class="special">&gt;</span>
+<a class="link" href="../../main_overview/result_type.html" title="Calculation of the Type of the Result"><span class="emphasis"><em>calculated-result-type</em></span></a> <span class="identifier">ibeta_inva</span><span class="special">(</span><span class="identifier">T1</span> <span class="identifier">b</span><span class="special">,</span> <span class="identifier">T2</span> <span class="identifier">x</span><span class="special">,</span> <span class="identifier">T3</span> <span class="identifier">p</span><span class="special">,</span> <span class="keyword">const</span> <a class="link" href="../../policy.html" title="Policies">Policy</a><span class="special">&amp;);</span>
+</pre>
+<p>
+          Returns a value <span class="emphasis"><em>a</em></span> such that: <code class="computeroutput"><span class="identifier">p</span>
+          <span class="special">=</span> <span class="identifier">ibeta</span><span class="special">(</span><span class="identifier">a</span><span class="special">,</span>
+          <span class="identifier">b</span><span class="special">,</span>
+          <span class="identifier">x</span><span class="special">);</span></code>
+        </p>
+<p>
+          Requires: <span class="emphasis"><em>b &gt; 0</em></span>, <span class="emphasis"><em>0 &lt; x &lt; 1</em></span>
+          and <span class="emphasis"><em>0 &lt;= p &lt;= 1</em></span>.
+        </p>
+<p>
+          </p>
+<p>
+            The final <a class="link" href="../../policy.html" title="Policies">Policy</a> argument
+            is optional and can be used to control the behaviour of the function:
+            how it handles errors, what level of precision to use etc. Refer to the
+            <a class="link" href="../../policy.html" title="Policies">policy documentation for more details</a>.
+          </p>
+<p>
+        </p>
+<pre class="programlisting"><span class="keyword">template</span> <span class="special">&lt;</span><span class="keyword">class</span> <span class="identifier">T1</span><span class="special">,</span> <span class="keyword">class</span> <span class="identifier">T2</span><span class="special">,</span> <span class="keyword">class</span> <span class="identifier">T3</span><span class="special">&gt;</span>
+<a class="link" href="../../main_overview/result_type.html" title="Calculation of the Type of the Result"><span class="emphasis"><em>calculated-result-type</em></span></a> <span class="identifier">ibetac_inva</span><span class="special">(</span><span class="identifier">T1</span> <span class="identifier">b</span><span class="special">,</span> <span class="identifier">T2</span> <span class="identifier">x</span><span class="special">,</span> <span class="identifier">T3</span> <span class="identifier">p</span><span class="special">);</span>
+
+<span class="keyword">template</span> <span class="special">&lt;</span><span class="keyword">class</span> <span class="identifier">T1</span><span class="special">,</span> <span class="keyword">class</span> <span class="identifier">T2</span><span class="special">,</span> <span class="keyword">class</span> <span class="identifier">T3</span><span class="special">,</span> <span class="keyword">class</span> <a class="link" href="../../policy.html" title="Policies">Policy</a><span class="special">&gt;</span>
+<a class="link" href="../../main_overview/result_type.html" title="Calculation of the Type of the Result"><span class="emphasis"><em>calculated-result-type</em></span></a> <span class="identifier">ibetac_inva</span><span class="special">(</span><span class="identifier">T1</span> <span class="identifier">b</span><span class="special">,</span> <span class="identifier">T2</span> <span class="identifier">x</span><span class="special">,</span> <span class="identifier">T3</span> <span class="identifier">p</span><span class="special">,</span> <span class="keyword">const</span> <a class="link" href="../../policy.html" title="Policies">Policy</a><span class="special">&amp;);</span>
+</pre>
+<p>
+          Returns a value <span class="emphasis"><em>a</em></span> such that: <code class="computeroutput"><span class="identifier">q</span>
+          <span class="special">=</span> <span class="identifier">ibetac</span><span class="special">(</span><span class="identifier">a</span><span class="special">,</span>
+          <span class="identifier">b</span><span class="special">,</span>
+          <span class="identifier">x</span><span class="special">);</span></code>
+        </p>
+<p>
+          Requires: <span class="emphasis"><em>b &gt; 0</em></span>, <span class="emphasis"><em>0 &lt; x &lt; 1</em></span>
+          and <span class="emphasis"><em>0 &lt;= q &lt;= 1</em></span>.
+        </p>
+<p>
+          </p>
+<p>
+            The final <a class="link" href="../../policy.html" title="Policies">Policy</a> argument
+            is optional and can be used to control the behaviour of the function:
+            how it handles errors, what level of precision to use etc. Refer to the
+            <a class="link" href="../../policy.html" title="Policies">policy documentation for more details</a>.
+          </p>
+<p>
+        </p>
+<pre class="programlisting"><span class="keyword">template</span> <span class="special">&lt;</span><span class="keyword">class</span> <span class="identifier">T1</span><span class="special">,</span> <span class="keyword">class</span> <span class="identifier">T2</span><span class="special">,</span> <span class="keyword">class</span> <span class="identifier">T3</span><span class="special">&gt;</span>
+<a class="link" href="../../main_overview/result_type.html" title="Calculation of the Type of the Result"><span class="emphasis"><em>calculated-result-type</em></span></a> <span class="identifier">ibeta_invb</span><span class="special">(</span><span class="identifier">T1</span> <span class="identifier">b</span><span class="special">,</span> <span class="identifier">T2</span> <span class="identifier">x</span><span class="special">,</span> <span class="identifier">T3</span> <span class="identifier">p</span><span class="special">);</span>
+
+<span class="keyword">template</span> <span class="special">&lt;</span><span class="keyword">class</span> <span class="identifier">T1</span><span class="special">,</span> <span class="keyword">class</span> <span class="identifier">T2</span><span class="special">,</span> <span class="keyword">class</span> <span class="identifier">T3</span><span class="special">,</span> <span class="keyword">class</span> <a class="link" href="../../policy.html" title="Policies">Policy</a><span class="special">&gt;</span>
+<a class="link" href="../../main_overview/result_type.html" title="Calculation of the Type of the Result"><span class="emphasis"><em>calculated-result-type</em></span></a> <span class="identifier">ibeta_invb</span><span class="special">(</span><span class="identifier">T1</span> <span class="identifier">b</span><span class="special">,</span> <span class="identifier">T2</span> <span class="identifier">x</span><span class="special">,</span> <span class="identifier">T3</span> <span class="identifier">p</span><span class="special">,</span> <span class="keyword">const</span> <a class="link" href="../../policy.html" title="Policies">Policy</a><span class="special">&amp;);</span>
+</pre>
+<p>
+          Returns a value <span class="emphasis"><em>b</em></span> such that: <code class="computeroutput"><span class="identifier">p</span>
+          <span class="special">=</span> <span class="identifier">ibeta</span><span class="special">(</span><span class="identifier">a</span><span class="special">,</span>
+          <span class="identifier">b</span><span class="special">,</span>
+          <span class="identifier">x</span><span class="special">);</span></code>
+        </p>
+<p>
+          Requires: <span class="emphasis"><em>a &gt; 0</em></span>, <span class="emphasis"><em>0 &lt; x &lt; 1</em></span>
+          and <span class="emphasis"><em>0 &lt;= p &lt;= 1</em></span>.
+        </p>
+<p>
+          </p>
+<p>
+            The final <a class="link" href="../../policy.html" title="Policies">Policy</a> argument
+            is optional and can be used to control the behaviour of the function:
+            how it handles errors, what level of precision to use etc. Refer to the
+            <a class="link" href="../../policy.html" title="Policies">policy documentation for more details</a>.
+          </p>
+<p>
+        </p>
+<pre class="programlisting"><span class="keyword">template</span> <span class="special">&lt;</span><span class="keyword">class</span> <span class="identifier">T1</span><span class="special">,</span> <span class="keyword">class</span> <span class="identifier">T2</span><span class="special">,</span> <span class="keyword">class</span> <span class="identifier">T3</span><span class="special">&gt;</span>
+<a class="link" href="../../main_overview/result_type.html" title="Calculation of the Type of the Result"><span class="emphasis"><em>calculated-result-type</em></span></a> <span class="identifier">ibetac_invb</span><span class="special">(</span><span class="identifier">T1</span> <span class="identifier">b</span><span class="special">,</span> <span class="identifier">T2</span> <span class="identifier">x</span><span class="special">,</span> <span class="identifier">T3</span> <span class="identifier">p</span><span class="special">);</span>
+
+<span class="keyword">template</span> <span class="special">&lt;</span><span class="keyword">class</span> <span class="identifier">T1</span><span class="special">,</span> <span class="keyword">class</span> <span class="identifier">T2</span><span class="special">,</span> <span class="keyword">class</span> <span class="identifier">T3</span><span class="special">,</span> <span class="keyword">class</span> <a class="link" href="../../policy.html" title="Policies">Policy</a><span class="special">&gt;</span>
+<a class="link" href="../../main_overview/result_type.html" title="Calculation of the Type of the Result"><span class="emphasis"><em>calculated-result-type</em></span></a> <span class="identifier">ibetac_invb</span><span class="special">(</span><span class="identifier">T1</span> <span class="identifier">b</span><span class="special">,</span> <span class="identifier">T2</span> <span class="identifier">x</span><span class="special">,</span> <span class="identifier">T3</span> <span class="identifier">p</span><span class="special">,</span> <span class="keyword">const</span> <a class="link" href="../../policy.html" title="Policies">Policy</a><span class="special">&amp;);</span>
+</pre>
+<p>
+          Returns a value <span class="emphasis"><em>b</em></span> such that: <code class="computeroutput"><span class="identifier">q</span>
+          <span class="special">=</span> <span class="identifier">ibetac</span><span class="special">(</span><span class="identifier">a</span><span class="special">,</span>
+          <span class="identifier">b</span><span class="special">,</span>
+          <span class="identifier">x</span><span class="special">);</span></code>
+        </p>
+<p>
+          Requires: <span class="emphasis"><em>a &gt; 0</em></span>, <span class="emphasis"><em>0 &lt; x &lt; 1</em></span>
+          and <span class="emphasis"><em>0 &lt;= q &lt;= 1</em></span>.
+        </p>
+<p>
+          </p>
+<p>
+            The final <a class="link" href="../../policy.html" title="Policies">Policy</a> argument
+            is optional and can be used to control the behaviour of the function:
+            how it handles errors, what level of precision to use etc. Refer to the
+            <a class="link" href="../../policy.html" title="Policies">policy documentation for more details</a>.
+          </p>
+<p>
+        </p>
+<a name="math_toolkit.special.sf_beta.ibeta_inv_function.accuracy"></a><h5>
+<a name="id735439"></a>
+          <a class="link" href="ibeta_inv_function.html#math_toolkit.special.sf_beta.ibeta_inv_function.accuracy">Accuracy</a>
+        </h5>
+<p>
+          The accuracy of these functions should closely follow that of the regular
+          forward incomplete beta functions. However, note that in some parts of
+          their domain, these functions can be extremely sensitive to changes in
+          input, particularly when the argument <span class="emphasis"><em>p</em></span> (or it's complement
+          <span class="emphasis"><em>q</em></span>) is very close to <code class="computeroutput"><span class="number">0</span></code>
+          or <code class="computeroutput"><span class="number">1</span></code>.
+        </p>
+<a name="math_toolkit.special.sf_beta.ibeta_inv_function.testing"></a><h5>
+<a name="id735507"></a>
+          <a class="link" href="ibeta_inv_function.html#math_toolkit.special.sf_beta.ibeta_inv_function.testing">Testing</a>
+        </h5>
+<p>
+          There are two sets of tests:
+        </p>
+<div class="itemizedlist"><ul type="disc">
+<li>
+            Basic sanity checks attempt to "round-trip" from <span class="emphasis"><em>a,
+            b</em></span> and <span class="emphasis"><em>x</em></span> to <span class="emphasis"><em>p</em></span> or
+            <span class="emphasis"><em>q</em></span> and back again. These tests have quite generous
+            tolerances: in general both the incomplete beta and its inverses change
+            so rapidly, that round tripping to more than a couple of significant
+            digits isn't possible. This is especially true when <span class="emphasis"><em>p</em></span>
+            or <span class="emphasis"><em>q</em></span> is very near one: in this case there isn't
+            enough "information content" in the input to the inverse function
+            to get back where you started.
+          </li>
+<li>
+            Accuracy checks using high precision test values. These measure the accuracy
+            of the result, given exact input values.
+          </li>
+</ul></div>
+<a name="math_toolkit.special.sf_beta.ibeta_inv_function.implementation_of_ibeta_inv_and_ibetac_inv"></a><h5>
+<a name="id735596"></a>
+          <a class="link" href="ibeta_inv_function.html#math_toolkit.special.sf_beta.ibeta_inv_function.implementation_of_ibeta_inv_and_ibetac_inv">Implementation
+          of ibeta_inv and ibetac_inv</a>
+        </h5>
+<p>
+          These two functions share a common implementation.
+        </p>
+<p>
+          First an initial approximation to x is computed then the last few bits
+          are cleaned up using <a href="http://en.wikipedia.org/wiki/Simple_rational_approximation" target="_top">Halley
+          iteration</a>. The iteration limit is set to 1<span class="emphasis"><em>2 of the number
+          of bits in T, which by experiment is sufficient to ensure that the inverses
+          are at least as accurate as the normal incomplete beta functions. Up to
+          5 iterations may be required in extreme cases, although normally only one
+          or two are required. Further, the number of iterations required decreases
+          with increasing /a</em></span> and <span class="emphasis"><em>b</em></span> (which generally
+          form the more important use cases).
+        </p>
+<p>
+          The initial guesses used for iteration are obtained as follows:
+        </p>
+<p>
+          Firstly recall that:
+        </p>
+<p>
+          <span class="inlinemediaobject"><img src="../../../../equations/ibeta_inv5.png"></span>
+        </p>
+<p>
+          We may wish to start from either p or q, and to calculate either x or y.
+          In addition at any stage we can exchange a for b, p for q, and x for y
+          if it results in a more manageable problem.
+        </p>
+<p>
+          For <code class="computeroutput"><span class="identifier">a</span><span class="special">+</span><span class="identifier">b</span> <span class="special">&gt;=</span> <span class="number">5</span></code> the initial guess is computed using the
+          methods described in:
+        </p>
+<p>
+          Asymptotic Inversion of the Incomplete Beta Function, by N. M. Temme.
+          Journal of Computational and Applied Mathematics 41 (1992) 145-157.
+        </p>
+<p>
+          The nearly symmetrical case (section 2 of the paper) is used for
+        </p>
+<p>
+          <span class="inlinemediaobject"><img src="../../../../equations/ibeta_inv2.png"></span>
+        </p>
+<p>
+          and involves solving the inverse error function first. The method is accurate
+          to at least 2 decimal digits when <code class="literal">a = 5</code> rising to at
+          least 8 digits when <code class="literal">a = 10<sup>5</sup></code>.
+        </p>
+<p>
+          The general error function case (section 3 of the paper) is used for
+        </p>
+<p>
+          <span class="inlinemediaobject"><img src="../../../../equations/ibeta_inv3.png"></span>
+        </p>
+<p>
+          and again expresses the inverse incomplete beta in terms of the inverse
+          of the error function. The method is accurate to at least 2 decimal digits
+          when <code class="literal">a+b = 5</code> rising to 11 digits when <code class="literal">a+b =
+          10<sup>5</sup></code>. However, when the result is expected to be very small, and
+          when a+b is also small, then its accuracy tails off, in this case when
+          p<sup>1/a</sup> &lt; 0.0025 then it is better to use the following as an initial estimate:
+        </p>
+<p>
+          <span class="inlinemediaobject"><img src="../../../../equations/ibeta_inv4.png"></span>
+        </p>
+<p>
+          Finally the for all other cases where <code class="computeroutput"><span class="identifier">a</span><span class="special">+</span><span class="identifier">b</span> <span class="special">&gt;</span>
+          <span class="number">5</span></code> the method of section 4 of the
+          paper is used. This expresses the inverse incomplete beta in terms of the
+          inverse of the incomplete gamma function, and is therefore significantly
+          more expensive to compute than the other cases. However the method is accurate
+          to at least 3 decimal digits when <code class="literal">a = 5</code> rising to at
+          least 10 digits when <code class="literal">a = 10<sup>5</sup></code>. This method is limited
+          to a &gt; b, and therefore we need to perform an exchange a for b, p for
+          q and x for y when this is not the case. In addition when p is close to
+          1 the method is inaccurate should we actually want y rather than x as output.
+          Therefore when q is small (<code class="literal">q<sup>1/p</sup> &lt; 10<sup>-3</sup></code>) we use:
+        </p>
+<p>
+          <span class="inlinemediaobject"><img src="../../../../equations/ibeta_inv6.png"></span>
+        </p>
+<p>
+          which is both cheaper to compute than the full method, and a more accurate
+          estimate on q.
+        </p>
+<p>
+          When a and b are both small there is a distinct lack of information in
+          the literature on how to proceed. I am extremely grateful to Prof Nico
+          Temme who provided the following information with a great deal of patience
+          and explanation on his part. Any errors that follow are entirely my own,
+          and not Prof Temme's.
+        </p>
+<p>
+          When a and b are both less than 1, then there is a point of inflection
+          in the incomplete beta at point <code class="computeroutput"><span class="identifier">xs</span>
+          <span class="special">=</span> <span class="special">(</span><span class="number">1</span> <span class="special">-</span> <span class="identifier">a</span><span class="special">)</span> <span class="special">/</span> <span class="special">(</span><span class="number">2</span> <span class="special">-</span> <span class="identifier">a</span>
+          <span class="special">-</span> <span class="identifier">b</span><span class="special">)</span></code>. Therefore if <code class="literal">p &gt; I<sub>x</sub>(a,b)</code>
+          we swap a for b, p for q and x for y, so that now we always look for a
+          point x below the point of inflection <code class="computeroutput"><span class="identifier">xs</span></code>,
+          and on a convex curve. An initial estimate for x is made with:
+        </p>
+<p>
+          <span class="inlinemediaobject"><img src="../../../../equations/ibeta_inv7.png"></span>
+        </p>
+<p>
+          which is provably below the true value for x: <a href="http://en.wikipedia.org/wiki/Newton%27s_method" target="_top">Newton
+          iteration</a> will therefore smoothly converge on x without problems
+          caused by overshooting etc.
+        </p>
+<p>
+          When a and b are both greater than 1, but a+b is too small to use the other
+          methods mentioned above, we proceed as follows. Observe that there is a
+          point of inflection in the incomplete beta at <code class="computeroutput"><span class="identifier">xs</span>
+          <span class="special">=</span> <span class="special">(</span><span class="number">1</span> <span class="special">-</span> <span class="identifier">a</span><span class="special">)</span> <span class="special">/</span> <span class="special">(</span><span class="number">2</span> <span class="special">-</span> <span class="identifier">a</span>
+          <span class="special">-</span> <span class="identifier">b</span><span class="special">)</span></code>. Therefore if <code class="literal">p &gt; I<sub>x</sub>(a,b)</code>
+          we swap a for b, p for q and x for y, so that now we always look for a
+          point x below the point of inflection <code class="computeroutput"><span class="identifier">xs</span></code>,
+          and on a concave curve. An initial estimate for x is made with:
+        </p>
+<p>
+          <span class="inlinemediaobject"><img src="../../../../equations/ibeta_inv4.png"></span>
+        </p>
+<p>
+          which can be improved somewhat to:
+        </p>
+<p>
+          <span class="inlinemediaobject"><img src="../../../../equations/ibeta_inv1.png"></span>
+        </p>
+<p>
+          when b and x are both small (I've used b &lt; a and x &lt; 0.2). This actually
+          under-estimates x, which drops us on the wrong side of x for Newton iteration
+          to converge monotonically. However, use of higher derivatives and Halley
+          iteration keeps everything under control.
+        </p>
+<p>
+          The final case to be considered if when one of a and b is less than or
+          equal to 1, and the other greater that 1. Here, if b &lt; a we swap a for
+          b, p for q and x for y. Now the curve of the incomplete beta is convex
+          with no points of inflection in [0,1]. For small p, x can be estimated
+          using
+        </p>
+<p>
+          <span class="inlinemediaobject"><img src="../../../../equations/ibeta_inv4.png"></span>
+        </p>
+<p>
+          which under-estimates x, and drops us on the right side of the true value
+          for Newton iteration to converge monotonically. However, when p is large
+          this can quite badly underestimate x. This is especially an issue when
+          we really want to find y, in which case this method can be an arbitrary
+          number of order of magnitudes out, leading to very poor convergence during
+          iteration.
+        </p>
+<p>
+          Things can be improved by considering the incomplete beta as a distorted
+          quarter circle, and estimating y from:
+        </p>
+<p>
+          <span class="inlinemediaobject"><img src="../../../../equations/ibeta_inv8.png"></span>
+        </p>
+<p>
+          This doesn't guarantee that we will drop in on the right side of x for
+          monotonic convergence, but it does get us close enough that Halley iteration
+          rapidly converges on the true value.
+        </p>
+<a name="math_toolkit.special.sf_beta.ibeta_inv_function.implementation_of_inverses_on_the_a_and_b_parameters"></a><h5>
+<a name="id736566"></a>
+          <a class="link" href="ibeta_inv_function.html#math_toolkit.special.sf_beta.ibeta_inv_function.implementation_of_inverses_on_the_a_and_b_parameters">Implementation
+          of inverses on the a and b parameters</a>
+        </h5>
+<p>
+          These four functions share a common implementation.
+        </p>
+<p>
+          First an initial approximation is computed for <span class="emphasis"><em>a</em></span> or
+          <span class="emphasis"><em>b</em></span>: where possible this uses a Cornish-Fisher expansion
+          for the negative binomial distribution to get within around 1 of the result.
+          However, when <span class="emphasis"><em>a</em></span> or <span class="emphasis"><em>b</em></span> are very
+          small the Cornish Fisher expansion is not usable, in this case the initial
+          approximation is chosen so that I<sub>x</sub>(a, b) is near the middle of the range
+          [0,1].
+        </p>
+<p>
+          This initial guess is then used as a starting value for a generic root
+          finding algorithm. The algorithm converges rapidly on the root once it
+          has been bracketed, but bracketing the root may take several iterations.
+          A better initial approximation for <span class="emphasis"><em>a</em></span> or <span class="emphasis"><em>b</em></span>
+          would improve these functions quite substantially: currently 10-20 incomplete
+          beta function invocations are required to find the root.
+        </p>
+</div>
+<table xmlns:rev="http://www.cs.rpi.edu/~gregod/boost/tools/doc/revision" width="100%"><tr>
+<td align="left"></td>
+<td align="right"><div class="copyright-footer">Copyright © 2006 , 2007, 2008 John Maddock, Paul A. Bristow, Hubert
+      Holin, Xiaogang Zhang, Bruno Lalande and Gautam Sewani<p>
+        Distributed under the Boost Software License, Version 1.0. (See accompanying
+        file LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_0.txt)
+      </p>
+</div></td>
+</tr></table>
+<hr>
+<div class="spirit-nav">
+<a accesskey="p" href="ibeta_function.html"><img src="../../../../../doc/html/images/prev.png" alt="Prev"></a><a accesskey="u" href="../sf_beta.html"><img src="../../../../../doc/html/images/up.png" alt="Up"></a><a accesskey="h" href="../../../index.html"><img src="../../../../../doc/html/images/home.png" alt="Home"></a><a accesskey="n" href="beta_derivative.html"><img src="../../../../../doc/html/images/next.png" alt="Next"></a>
+</div>
+</body>
+</html>

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+<div class="titlepage"><div><div><h3 class="title">
+<a name="math_toolkit.special.sf_erf"></a><a class="link" href="sf_erf.html" title="Error Functions"> Error Functions</a>
+</h3></div></div></div>
+<div class="toc"><dl>
+<dt><span class="section"><a href="sf_erf/error_function.html"> Error
+        Functions</a></span></dt>
+<dt><span class="section"><a href="sf_erf/error_inv.html"> Error Function
+        Inverses</a></span></dt>
+</dl></div>
+</div>
+<table xmlns:rev="http://www.cs.rpi.edu/~gregod/boost/tools/doc/revision" width="100%"><tr>
+<td align="left"></td>
+<td align="right"><div class="copyright-footer">Copyright © 2006 , 2007, 2008 John Maddock, Paul A. Bristow, Hubert
+      Holin, Xiaogang Zhang, Bruno Lalande and Gautam Sewani<p>
+        Distributed under the Boost Software License, Version 1.0. (See accompanying
+        file LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_0.txt)
+      </p>
+</div></td>
+</tr></table>
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+</div>
+<div class="section" lang="en">
+<div class="titlepage"><div><div><h4 class="title">
+<a name="math_toolkit.special.sf_erf.error_function"></a><a class="link" href="error_function.html" title="Error Functions"> Error
+        Functions</a>
+</h4></div></div></div>
+<a name="math_toolkit.special.sf_erf.error_function.synopsis"></a><h5>
+<a name="id737382"></a>
+          <a class="link" href="error_function.html#math_toolkit.special.sf_erf.error_function.synopsis">Synopsis</a>
+        </h5>
+<p>
+          
+</p>
+<pre class="programlisting"><span class="preprocessor">#include</span> <span class="special">&lt;</span><span class="identifier">boost</span><span class="special">/</span><span class="identifier">math</span><span class="special">/</span><span class="identifier">special_functions</span><span class="special">/</span><span class="identifier">erf</span><span class="special">.</span><span class="identifier">hpp</span><span class="special">&gt;</span>
+</pre>
+<p>
+        </p>
+<pre class="programlisting"><span class="keyword">namespace</span> <span class="identifier">boost</span><span class="special">{</span> <span class="keyword">namespace</span> <span class="identifier">math</span><span class="special">{</span>
+
+<span class="keyword">template</span> <span class="special">&lt;</span><span class="keyword">class</span> <span class="identifier">T</span><span class="special">&gt;</span>
+<a class="link" href="../../main_overview/result_type.html" title="Calculation of the Type of the Result"><span class="emphasis"><em>calculated-result-type</em></span></a> <span class="identifier">erf</span><span class="special">(</span><span class="identifier">T</span> <span class="identifier">z</span><span class="special">);</span>
+
+<span class="keyword">template</span> <span class="special">&lt;</span><span class="keyword">class</span> <span class="identifier">T</span><span class="special">,</span> <span class="keyword">class</span> <a class="link" href="../../policy.html" title="Policies">Policy</a><span class="special">&gt;</span>
+<a class="link" href="../../main_overview/result_type.html" title="Calculation of the Type of the Result"><span class="emphasis"><em>calculated-result-type</em></span></a> <span class="identifier">erf</span><span class="special">(</span><span class="identifier">T</span> <span class="identifier">z</span><span class="special">,</span> <span class="keyword">const</span> <a class="link" href="../../policy.html" title="Policies">Policy</a><span class="special">&amp;);</span>
+
+<span class="keyword">template</span> <span class="special">&lt;</span><span class="keyword">class</span> <span class="identifier">T</span><span class="special">&gt;</span>
+<a class="link" href="../../main_overview/result_type.html" title="Calculation of the Type of the Result"><span class="emphasis"><em>calculated-result-type</em></span></a> <span class="identifier">erfc</span><span class="special">(</span><span class="identifier">T</span> <span class="identifier">z</span><span class="special">);</span>
+
+<span class="keyword">template</span> <span class="special">&lt;</span><span class="keyword">class</span> <span class="identifier">T</span><span class="special">,</span> <span class="keyword">class</span> <a class="link" href="../../policy.html" title="Policies">Policy</a><span class="special">&gt;</span>
+<a class="link" href="../../main_overview/result_type.html" title="Calculation of the Type of the Result"><span class="emphasis"><em>calculated-result-type</em></span></a> <span class="identifier">erfc</span><span class="special">(</span><span class="identifier">T</span> <span class="identifier">z</span><span class="special">,</span> <span class="keyword">const</span> <a class="link" href="../../policy.html" title="Policies">Policy</a><span class="special">&amp;);</span>
+
+<span class="special">}}</span> <span class="comment">// namespaces
+</span></pre>
+<p>
+          The return type of these functions is computed using the <a class="link" href="../../main_overview/result_type.html" title="Calculation of the Type of the Result"><span class="emphasis"><em>result
+          type calculation rules</em></span></a>: the return type is <code class="computeroutput"><span class="keyword">double</span></code> if T is an integer type, and T otherwise.
+        </p>
+<p>
+          </p>
+<p>
+            The final <a class="link" href="../../policy.html" title="Policies">Policy</a> argument
+            is optional and can be used to control the behaviour of the function:
+            how it handles errors, what level of precision to use etc. Refer to the
+            <a class="link" href="../../policy.html" title="Policies">policy documentation for more details</a>.
+          </p>
+<p>
+        </p>
+<a name="math_toolkit.special.sf_erf.error_function.description"></a><h5>
+<a name="id737936"></a>
+          <a class="link" href="error_function.html#math_toolkit.special.sf_erf.error_function.description">Description</a>
+        </h5>
+<pre class="programlisting"><span class="keyword">template</span> <span class="special">&lt;</span><span class="keyword">class</span> <span class="identifier">T</span><span class="special">&gt;</span>
+<a class="link" href="../../main_overview/result_type.html" title="Calculation of the Type of the Result"><span class="emphasis"><em>calculated-result-type</em></span></a> <span class="identifier">erf</span><span class="special">(</span><span class="identifier">T</span> <span class="identifier">z</span><span class="special">);</span>
+
+<span class="keyword">template</span> <span class="special">&lt;</span><span class="keyword">class</span> <span class="identifier">T</span><span class="special">,</span> <span class="keyword">class</span> <a class="link" href="../../policy.html" title="Policies">Policy</a><span class="special">&gt;</span>
+<a class="link" href="../../main_overview/result_type.html" title="Calculation of the Type of the Result"><span class="emphasis"><em>calculated-result-type</em></span></a> <span class="identifier">erf</span><span class="special">(</span><span class="identifier">T</span> <span class="identifier">z</span><span class="special">,</span> <span class="keyword">const</span> <a class="link" href="../../policy.html" title="Policies">Policy</a><span class="special">&amp;);</span>
+</pre>
+<p>
+          Returns the <a href="http://en.wikipedia.org/wiki/Error_function" target="_top">error
+          function</a> erf
+          of z:
+        </p>
+<p>
+          <span class="inlinemediaobject"><img src="../../../../equations/erf1.png"></span>
+        </p>
+<p>
+          <span class="inlinemediaobject"><img src="../../../../graphs/erf.png" align="middle"></span>
+        </p>
+<pre class="programlisting"><span class="keyword">template</span> <span class="special">&lt;</span><span class="keyword">class</span> <span class="identifier">T</span><span class="special">&gt;</span>
+<a class="link" href="../../main_overview/result_type.html" title="Calculation of the Type of the Result"><span class="emphasis"><em>calculated-result-type</em></span></a> <span class="identifier">erfc</span><span class="special">(</span><span class="identifier">T</span> <span class="identifier">z</span><span class="special">);</span>
+
+<span class="keyword">template</span> <span class="special">&lt;</span><span class="keyword">class</span> <span class="identifier">T</span><span class="special">,</span> <span class="keyword">class</span> <a class="link" href="../../policy.html" title="Policies">Policy</a><span class="special">&gt;</span>
+<a class="link" href="../../main_overview/result_type.html" title="Calculation of the Type of the Result"><span class="emphasis"><em>calculated-result-type</em></span></a> <span class="identifier">erfc</span><span class="special">(</span><span class="identifier">T</span> <span class="identifier">z</span><span class="special">,</span> <span class="keyword">const</span> <a class="link" href="../../policy.html" title="Policies">Policy</a><span class="special">&amp;);</span>
+</pre>
+<p>
+          Returns the complement of the <a href="http://functions.wolfram.com/GammaBetaErf/Erfc/" target="_top">error
+          function</a> of z:
+        </p>
+<p>
+          <span class="inlinemediaobject"><img src="../../../../equations/erf2.png"></span>
+        </p>
+<p>
+          <span class="inlinemediaobject"><img src="../../../../graphs/erfc.png" align="middle"></span>
+        </p>
+<a name="math_toolkit.special.sf_erf.error_function.accuracy"></a><h5>
+<a name="id738476"></a>
+          <a class="link" href="error_function.html#math_toolkit.special.sf_erf.error_function.accuracy">Accuracy</a>
+        </h5>
+<p>
+          The following table shows the peak errors (in units of epsilon) found on
+          various platforms with various floating point types, along with comparisons
+          to the GSL-1.9,
+          GNU C Lib, HP-UX C Library
+          and Cephes libraries.
+          Unless otherwise specified any floating point type that is narrower than
+          the one shown will have <a class="link" href="../../backgrounders/relative_error.html#zero_error">effectively zero error</a>.
+        </p>
+<div class="table">
+<a name="id738542"></a><p class="title"><b>Table 27. Errors In the Function erf(z)</b></p>
+<div class="table-contents"><table class="table" summary="Errors In the Function erf(z)">
+<colgroup>
+<col>
+<col>
+<col>
+<col>
+<col>
+</colgroup>
+<thead><tr>
+<th>
+              <p>
+                Significand Size
+              </p>
+              </th>
+<th>
+              <p>
+                Platform and Compiler
+              </p>
+              </th>
+<th>
+              <p>
+                z &lt; 0.5
+              </p>
+              </th>
+<th>
+              <p>
+                0.5 &lt; z &lt; 8
+              </p>
+              </th>
+<th>
+              <p>
+                z &gt; 8
+              </p>
+              </th>
+</tr></thead>
+<tbody>
+<tr>
+<td>
+              <p>
+                53
+              </p>
+              </td>
+<td>
+              <p>
+                Win32, Visual C++ 8
+              </p>
+              </td>
+<td>
+              <p>
+                Peak=0 Mean=0
+              </p>
+              <p>
+                GSL Peak=2.0 Mean=0.3
+              </p>
+              <p>
+                Cephes Peak=1.1
+                Mean=0.7
+              </p>
+              </td>
+<td>
+              <p>
+                Peak=0.9 Mean=0.09
+              </p>
+              <p>
+                GSL Peak=2.3 Mean=0.3
+              </p>
+              <p>
+                Cephes Peak=1.3
+                Mean=0.2
+              </p>
+              </td>
+<td>
+              <p>
+                Peak=0 Mean=0
+              </p>
+              <p>
+                GSL Peak=0 Mean=0
+              </p>
+              <p>
+                Cephes Peak=0
+                Mean=0
+              </p>
+              </td>
+</tr>
+<tr>
+<td>
+              <p>
+                64
+              </p>
+              </td>
+<td>
+              <p>
+                RedHat Linux IA32, gcc-3.3
+              </p>
+              </td>
+<td>
+              <p>
+                Peak=0.7 Mean=0.07
+              </p>
+              <p>
+                GNU C Lib
+                Peak=0.9 Mean=0.2
+              </p>
+              </td>
+<td>
+              <p>
+                Peak=0.9 Mean=0.2
+              </p>
+              <p>
+                GNU C Lib
+                Peak=0.9 Mean=0.07
+              </p>
+              </td>
+<td>
+              <p>
+                Peak=0 Mean=0
+              </p>
+              <p>
+                GNU C Lib
+                Peak=0 Mean=0
+              </p>
+              </td>
+</tr>
+<tr>
+<td>
+              <p>
+                64
+              </p>
+              </td>
+<td>
+              <p>
+                Redhat Linux IA64, gcc-3.4.4
+              </p>
+              </td>
+<td>
+              <p>
+                Peak=0.7 Mean=0.07
+              </p>
+              <p>
+                GNU C Lib
+                Peak=0 Mean=0
+              </p>
+              </td>
+<td>
+              <p>
+                Peak=0.9 Mean=0.1
+              </p>
+              <p>
+                GNU C Lib
+                Peak=0.5 Mean=0.03
+              </p>
+              </td>
+<td>
+              <p>
+                Peak=0 Mean=0
+              </p>
+              <p>
+                GNU C Lib
+                Peak=0 Mean=0
+              </p>
+              </td>
+</tr>
+<tr>
+<td>
+              <p>
+                113
+              </p>
+              </td>
+<td>
+              <p>
+                HPUX IA64, aCC A.06.06
+              </p>
+              </td>
+<td>
+              <p>
+                Peak=0.8 Mean=0.1
+              </p>
+              <p>
+                <a href="http://docs.hp.com/en/B9106-90010/index.html" target="_top">HP-UX C
+                Library</a> Lib Peak=0.9 Mean=0.2
+              </p>
+              </td>
+<td>
+              <p>
+                Peak=0.9 Mean=0.1
+              </p>
+              <p>
+                <a href="http://docs.hp.com/en/B9106-90010/index.html" target="_top">HP-UX C
+                Library</a> Lib Peak=0.5 Mean=0.02
+              </p>
+              </td>
+<td>
+              <p>
+                Peak=0 Mean=0
+              </p>
+              <p>
+                <a href="http://docs.hp.com/en/B9106-90010/index.html" target="_top">HP-UX C
+                Library</a> Lib Peak=0 Mean=0
+              </p>
+              </td>
+</tr>
+</tbody>
+</table></div>
+</div>
+<br class="table-break"><div class="table">
+<a name="id738945"></a><p class="title"><b>Table 28. Errors In the Function erfc(z)</b></p>
+<div class="table-contents"><table class="table" summary="Errors In the Function erfc(z)">
+<colgroup>
+<col>
+<col>
+<col>
+<col>
+<col>
+</colgroup>
+<thead><tr>
+<th>
+              <p>
+                Significand Size
+              </p>
+              </th>
+<th>
+              <p>
+                Platform and Compiler
+              </p>
+              </th>
+<th>
+              <p>
+                z &lt; 0.5
+              </p>
+              </th>
+<th>
+              <p>
+                0.5 &lt; z &lt; 8
+              </p>
+              </th>
+<th>
+              <p>
+                z &gt; 8
+              </p>
+              </th>
+</tr></thead>
+<tbody>
+<tr>
+<td>
+              <p>
+                53
+              </p>
+              </td>
+<td>
+              <p>
+                Win32, Visual C++ 8
+              </p>
+              </td>
+<td>
+              <p>
+                Peak=0.7 Mean=0.06
+              </p>
+              <p>
+                GSL Peak=1.0 Mean=0.4
+              </p>
+              <p>
+                Cephes Peak=0.7
+                Mean=0.06
+              </p>
+              </td>
+<td>
+              <p>
+                Peak=0.99 Mean=0.3
+              </p>
+              <p>
+                GSL Peak=2.6 Mean=0.6
+              </p>
+              <p>
+                Cephes Peak=3.6
+                Mean=0.7
+              </p>
+              </td>
+<td>
+              <p>
+                Peak=1.0 Mean=0.2
+              </p>
+              <p>
+                GSL Peak=3.9 Mean=0.4
+              </p>
+              <p>
+                Cephes Peak=2.7
+                Mean=0.4
+              </p>
+              </td>
+</tr>
+<tr>
+<td>
+              <p>
+                64
+              </p>
+              </td>
+<td>
+              <p>
+                RedHat Linux IA32, gcc-3.3
+              </p>
+              </td>
+<td>
+              <p>
+                Peak=0 Mean=0
+              </p>
+              <p>
+                GNU C Lib
+                Peak=0 Mean=0
+              </p>
+              </td>
+<td>
+              <p>
+                Peak=1.4 Mean=0.3
+              </p>
+              <p>
+                GNU C Lib
+                Peak=1.3 Mean=0.3
+              </p>
+              </td>
+<td>
+              <p>
+                Peak=1.6 Mean=0.4
+              </p>
+              <p>
+                GNU C Lib
+                Peak=1.3 Mean=0.4
+              </p>
+              </td>
+</tr>
+<tr>
+<td>
+              <p>
+                64
+              </p>
+              </td>
+<td>
+              <p>
+                Redhat Linux IA64, gcc-3.4.4
+              </p>
+              </td>
+<td>
+              <p>
+                Peak=0 Mean=0
+              </p>
+              <p>
+                GNU C Lib
+                Peak=0 Mean=0
+              </p>
+              </td>
+<td>
+              <p>
+                Peak=1.4 Mean=0.3
+              </p>
+              <p>
+                GNU C Lib
+                Peak=0 Mean=0
+              </p>
+              </td>
+<td>
+              <p>
+                Peak=1.5 Mean=0.4
+              </p>
+              <p>
+                GNU C Lib
+                Peak=0 Mean=0
+              </p>
+              </td>
+</tr>
+<tr>
+<td>
+              <p>
+                113
+              </p>
+              </td>
+<td>
+              <p>
+                HPUX IA64, aCC A.06.06
+              </p>
+              </td>
+<td>
+              <p>
+                Peak=0 Mean=0
+              </p>
+              <p>
+                <a href="http://docs.hp.com/en/B9106-90010/index.html" target="_top">HP-UX C
+                Library</a> Peak=0 Mean=0
+              </p>
+              </td>
+<td>
+              <p>
+                Peak=1.5 Mean=0.3
+              </p>
+              <p>
+                <a href="http://docs.hp.com/en/B9106-90010/index.html" target="_top">HP-UX C
+                Library</a> Peak=0.9 Mean=0.08
+              </p>
+              </td>
+<td>
+              <p>
+                Peak=1.6 Mean=0.4
+              </p>
+              <p>
+                <a href="http://docs.hp.com/en/B9106-90010/index.html" target="_top">HP-UX C
+                Library</a> Peak=0.9 Mean=0.1
+              </p>
+              </td>
+</tr>
+</tbody>
+</table></div>
+</div>
+<br class="table-break"><a name="math_toolkit.special.sf_erf.error_function.testing"></a><h5>
+<a name="id739355"></a>
+          <a class="link" href="error_function.html#math_toolkit.special.sf_erf.error_function.testing">Testing</a>
+        </h5>
+<p>
+          The tests for these functions come in two parts: basic sanity checks use
+          spot values calculated using <a href="http://functions.wolfram.com/webMathematica/FunctionEvaluation.jsp?name=Erf" target="_top">Mathworld's
+          online evaluator</a>, while accuracy checks use high-precision test
+          values calculated at 1000-bit precision with NTL::RR
+          and this implementation. Note that the generic and type-specific versions
+          of these functions use differing implementations internally, so this gives
+          us reasonably independent test data. Using our test data to test other
+          "known good" implementations also provides an additional sanity
+          check.
+        </p>
+<a name="math_toolkit.special.sf_erf.error_function.implementation"></a><h5>
+<a name="id739418"></a>
+          <a class="link" href="error_function.html#math_toolkit.special.sf_erf.error_function.implementation">Implementation</a>
+        </h5>
+<p>
+          All versions of these functions first use the usual reflection formulas
+          to make their arguments positive:
+        </p>
+<pre class="programlisting"><span class="identifier">erf</span><span class="special">(-</span><span class="identifier">z</span><span class="special">)</span> <span class="special">=</span> <span class="number">1</span> <span class="special">-</span> <span class="identifier">erf</span><span class="special">(</span><span class="identifier">z</span><span class="special">);</span>
+
+<span class="identifier">erfc</span><span class="special">(-</span><span class="identifier">z</span><span class="special">)</span> <span class="special">=</span> <span class="number">2</span> <span class="special">-</span> <span class="identifier">erfc</span><span class="special">(</span><span class="identifier">z</span><span class="special">);</span>  <span class="comment">// preferred when -z &lt; -0.5
+</span>
+<span class="identifier">erfc</span><span class="special">(-</span><span class="identifier">z</span><span class="special">)</span> <span class="special">=</span> <span class="number">1</span> <span class="special">+</span> <span class="identifier">erf</span><span class="special">(</span><span class="identifier">z</span><span class="special">);</span>   <span class="comment">// preferred when -0.5 &lt;= -z &lt; 0
+</span></pre>
+<p>
+          The generic versions of these functions are implemented in terms of the
+          incomplete gamma function.
+        </p>
+<p>
+          When the significand (mantissa) size is recognised (currently for 53, 64
+          and 113-bit reals, plus single-precision 24-bit handled via promotion to
+          double) then a series of rational approximations <a class="link" href="../../backgrounders/implementation.html#math_toolkit.backgrounders.implementation.rational_approximations_used">devised
+          by JM</a> are used.
+        </p>
+<p>
+          For <code class="computeroutput"><span class="identifier">z</span> <span class="special">&lt;=</span>
+          <span class="number">0.5</span></code> then a rational approximation
+          to erf is used, based on the observation that erf is an odd function and
+          therefore erf is calculated using:
+        </p>
+<pre class="programlisting"><span class="identifier">erf</span><span class="special">(</span><span class="identifier">z</span><span class="special">)</span> <span class="special">=</span> <span class="identifier">z</span> <span class="special">*</span> <span class="special">(</span><span class="identifier">C</span> <span class="special">+</span> <span class="identifier">R</span><span class="special">(</span><span class="identifier">z</span><span class="special">*</span><span class="identifier">z</span><span class="special">));</span>
+</pre>
+<p>
+          where the rational approximation R(z*z) is optimised for absolute error:
+          as long as its absolute error is small enough compared to the constant
+          C, then any round-off error incurred during the computation of R(z*z) will
+          effectively disappear from the result. As a result the error for erf and
+          erfc in this region is very low: the last bit is incorrect in only a very
+          small number of cases.
+        </p>
+<p>
+          For <code class="computeroutput"><span class="identifier">z</span> <span class="special">&gt;</span>
+          <span class="number">0.5</span></code> we observe that over a small
+          interval [a, b) then:
+        </p>
+<pre class="programlisting"><span class="identifier">erfc</span><span class="special">(</span><span class="identifier">z</span><span class="special">)</span> <span class="special">*</span> <span class="identifier">exp</span><span class="special">(</span><span class="identifier">z</span><span class="special">*</span><span class="identifier">z</span><span class="special">)</span> <span class="special">*</span> <span class="identifier">z</span> <span class="special">~</span> <span class="identifier">c</span>
+</pre>
+<p>
+          for some constant c.
+        </p>
+<p>
+          Therefore for <code class="computeroutput"><span class="identifier">z</span> <span class="special">&gt;</span>
+          <span class="number">0.5</span></code> we calculate erfc using:
+        </p>
+<pre class="programlisting"><span class="identifier">erfc</span><span class="special">(</span><span class="identifier">z</span><span class="special">)</span> <span class="special">=</span> <span class="identifier">exp</span><span class="special">(-</span><span class="identifier">z</span><span class="special">*</span><span class="identifier">z</span><span class="special">)</span> <span class="special">*</span> <span class="special">(</span><span class="identifier">C</span> <span class="special">+</span> <span class="identifier">R</span><span class="special">(</span><span class="identifier">z</span> <span class="special">-</span> <span class="identifier">B</span><span class="special">))</span> <span class="special">/</span> <span class="identifier">z</span><span class="special">;</span>
+</pre>
+<p>
+          Again R(z - B) is optimised for absolute error, and the constant <code class="computeroutput"><span class="identifier">C</span></code> is the average of <code class="computeroutput"><span class="identifier">erfc</span><span class="special">(</span><span class="identifier">z</span><span class="special">)</span>
+          <span class="special">*</span> <span class="identifier">exp</span><span class="special">(</span><span class="identifier">z</span><span class="special">*</span><span class="identifier">z</span><span class="special">)</span> <span class="special">*</span>
+          <span class="identifier">z</span></code> taken at the endpoints of the
+          range. Once again, as long as the absolute error in R(z - B) is small compared
+          to <code class="computeroutput"><span class="identifier">c</span></code> then <code class="computeroutput"><span class="identifier">c</span> <span class="special">+</span> <span class="identifier">R</span><span class="special">(</span><span class="identifier">z</span>
+          <span class="special">-</span> <span class="identifier">B</span><span class="special">)</span></code> will be correctly rounded, and the error
+          in the result will depend only on the accuracy of the exp function. In
+          practice, in all but a very small number of cases, the error is confined
+          to the last bit of the result. The constant <code class="computeroutput"><span class="identifier">B</span></code>
+          is chosen so that the left hand end of the range of the rational approximation
+          is 0.
+        </p>
+<p>
+          For large <code class="computeroutput"><span class="identifier">z</span></code> over a range
+          [a, +&#8734;] the above approximation is modified to:
+        </p>
+<pre class="programlisting"><span class="identifier">erfc</span><span class="special">(</span><span class="identifier">z</span><span class="special">)</span> <span class="special">=</span> <span class="identifier">exp</span><span class="special">(-</span><span class="identifier">z</span><span class="special">*</span><span class="identifier">z</span><span class="special">)</span> <span class="special">*</span> <span class="special">(</span><span class="identifier">C</span> <span class="special">+</span> <span class="identifier">R</span><span class="special">(</span><span class="number">1</span> <span class="special">/</span> <span class="identifier">z</span><span class="special">))</span> <span class="special">/</span> <span class="identifier">z</span><span class="special">;</span>
+</pre>
+</div>
+<table xmlns:rev="http://www.cs.rpi.edu/~gregod/boost/tools/doc/revision" width="100%"><tr>
+<td align="left"></td>
+<td align="right"><div class="copyright-footer">Copyright © 2006 , 2007, 2008 John Maddock, Paul A. Bristow, Hubert
+      Holin, Xiaogang Zhang, Bruno Lalande and Gautam Sewani<p>
+        Distributed under the Boost Software License, Version 1.0. (See accompanying
+        file LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_0.txt)
+      </p>
+</div></td>
+</tr></table>
+<hr>
+<div class="spirit-nav">
+<a accesskey="p" href="../sf_erf.html"><img src="../../../../../doc/html/images/prev.png" alt="Prev"></a><a accesskey="u" href="../sf_erf.html"><img src="../../../../../doc/html/images/up.png" alt="Up"></a><a accesskey="h" href="../../../index.html"><img src="../../../../../doc/html/images/home.png" alt="Home"></a><a accesskey="n" href="error_inv.html"><img src="../../../../../doc/html/images/next.png" alt="Next"></a>
+</div>
+</body>
+</html>

Added: sandbox/tools/auto_index/example/math/doc/sf_and_dist/html/math_toolkit/special/sf_erf/error_inv.html
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+++ sandbox/tools/auto_index/example/math/doc/sf_and_dist/html/math_toolkit/special/sf_erf/error_inv.html	2008-11-28 05:25:28 EST (Fri, 28 Nov 2008)
@@ -0,0 +1,210 @@
+<html>
+<head>
+<meta http-equiv="Content-Type" content="text/html; charset=ISO-8859-1">
+<title>Error Function Inverses</title>
+<link rel="stylesheet" href="../../../boostbook.css" type="text/css">
+<meta name="generator" content="DocBook XSL Stylesheets Vsnapshot_8125">
+<link rel="home" href="../../../index.html" title="Math Toolkit">
+<link rel="up" href="../sf_erf.html" title="Error Functions">
+<link rel="prev" href="error_function.html" title="Error Functions">
+<link rel="next" href="../sf_poly.html" title="Polynomials">
+</head>
+<body bgcolor="white" text="black" link="#0000FF" vlink="#840084" alink="#0000FF">
+<table cellpadding="2" width="100%"><tr>
+<td valign="top"><img alt="Boost C++ Libraries" width="277" height="86" src="../../../../../boost.png"></td>
+<td align="center">Home</td>
+<td align="center">Libraries</td>
+<td align="center">People</td>
+<td align="center">FAQ</td>
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+<hr>
+<div class="spirit-nav">
+<a accesskey="p" href="error_function.html"><img src="../../../../../doc/html/images/prev.png" alt="Prev"></a><a accesskey="u" href="../sf_erf.html"><img src="../../../../../doc/html/images/up.png" alt="Up"></a><a accesskey="h" href="../../../index.html"><img src="../../../../../doc/html/images/home.png" alt="Home"></a><a accesskey="n" href="../sf_poly.html"><img src="../../../../../doc/html/images/next.png" alt="Next"></a>
+</div>
+<div class="section" lang="en">
+<div class="titlepage"><div><div><h4 class="title">
+<a name="math_toolkit.special.sf_erf.error_inv"></a><a class="link" href="error_inv.html" title="Error Function Inverses"> Error Function
+        Inverses</a>
+</h4></div></div></div>
+<a name="math_toolkit.special.sf_erf.error_inv.synopsis"></a><h5>
+<a name="id740477"></a>
+          <a class="link" href="error_inv.html#math_toolkit.special.sf_erf.error_inv.synopsis">Synopsis</a>
+        </h5>
+<p>
+          
+</p>
+<pre class="programlisting"><span class="preprocessor">#include</span> <span class="special">&lt;</span><span class="identifier">boost</span><span class="special">/</span><span class="identifier">math</span><span class="special">/</span><span class="identifier">special_functions</span><span class="special">/</span><span class="identifier">erf</span><span class="special">.</span><span class="identifier">hpp</span><span class="special">&gt;</span>
+</pre>
+<p>
+        </p>
+<pre class="programlisting"><span class="keyword">namespace</span> <span class="identifier">boost</span><span class="special">{</span> <span class="keyword">namespace</span> <span class="identifier">math</span><span class="special">{</span>
+
+<span class="keyword">template</span> <span class="special">&lt;</span><span class="keyword">class</span> <span class="identifier">T</span><span class="special">&gt;</span>
+<a class="link" href="../../main_overview/result_type.html" title="Calculation of the Type of the Result"><span class="emphasis"><em>calculated-result-type</em></span></a> <span class="identifier">erf_inv</span><span class="special">(</span><span class="identifier">T</span> <span class="identifier">p</span><span class="special">);</span>
+
+<span class="keyword">template</span> <span class="special">&lt;</span><span class="keyword">class</span> <span class="identifier">T</span><span class="special">,</span> <span class="keyword">class</span> <a class="link" href="../../policy.html" title="Policies">Policy</a><span class="special">&gt;</span>
+<a class="link" href="../../main_overview/result_type.html" title="Calculation of the Type of the Result"><span class="emphasis"><em>calculated-result-type</em></span></a> <span class="identifier">erf_inv</span><span class="special">(</span><span class="identifier">T</span> <span class="identifier">p</span><span class="special">,</span> <span class="keyword">const</span> <a class="link" href="../../policy.html" title="Policies">Policy</a><span class="special">&amp;);</span>
+
+<span class="keyword">template</span> <span class="special">&lt;</span><span class="keyword">class</span> <span class="identifier">T</span><span class="special">&gt;</span>
+<a class="link" href="../../main_overview/result_type.html" title="Calculation of the Type of the Result"><span class="emphasis"><em>calculated-result-type</em></span></a> <span class="identifier">erfc_inv</span><span class="special">(</span><span class="identifier">T</span> <span class="identifier">p</span><span class="special">);</span>
+
+<span class="keyword">template</span> <span class="special">&lt;</span><span class="keyword">class</span> <span class="identifier">T</span><span class="special">,</span> <span class="keyword">class</span> <a class="link" href="../../policy.html" title="Policies">Policy</a><span class="special">&gt;</span>
+<a class="link" href="../../main_overview/result_type.html" title="Calculation of the Type of the Result"><span class="emphasis"><em>calculated-result-type</em></span></a> <span class="identifier">erfc_inv</span><span class="special">(</span><span class="identifier">T</span> <span class="identifier">p</span><span class="special">,</span> <span class="keyword">const</span> <a class="link" href="../../policy.html" title="Policies">Policy</a><span class="special">&amp;);</span>
+
+<span class="special">}}</span> <span class="comment">// namespaces
+</span></pre>
+<p>
+          The return type of these functions is computed using the <a class="link" href="../../main_overview/result_type.html" title="Calculation of the Type of the Result"><span class="emphasis"><em>result
+          type calculation rules</em></span></a>: the return type is <code class="computeroutput"><span class="keyword">double</span></code> if T is an integer type, and T otherwise.
+        </p>
+<p>
+          </p>
+<p>
+            The final <a class="link" href="../../policy.html" title="Policies">Policy</a> argument
+            is optional and can be used to control the behaviour of the function:
+            how it handles errors, what level of precision to use etc. Refer to the
+            <a class="link" href="../../policy.html" title="Policies">policy documentation for more details</a>.
+          </p>
+<p>
+        </p>
+<a name="math_toolkit.special.sf_erf.error_inv.description"></a><h5>
+<a name="id741029"></a>
+          <a class="link" href="error_inv.html#math_toolkit.special.sf_erf.error_inv.description">Description</a>
+        </h5>
+<pre class="programlisting"><span class="keyword">template</span> <span class="special">&lt;</span><span class="keyword">class</span> <span class="identifier">T</span><span class="special">&gt;</span>
+<a class="link" href="../../main_overview/result_type.html" title="Calculation of the Type of the Result"><span class="emphasis"><em>calculated-result-type</em></span></a> <span class="identifier">erf_inv</span><span class="special">(</span><span class="identifier">T</span> <span class="identifier">z</span><span class="special">);</span>
+
+<span class="keyword">template</span> <span class="special">&lt;</span><span class="keyword">class</span> <span class="identifier">T</span><span class="special">,</span> <span class="keyword">class</span> <a class="link" href="../../policy.html" title="Policies">Policy</a><span class="special">&gt;</span>
+<a class="link" href="../../main_overview/result_type.html" title="Calculation of the Type of the Result"><span class="emphasis"><em>calculated-result-type</em></span></a> <span class="identifier">erf_inv</span><span class="special">(</span><span class="identifier">T</span> <span class="identifier">z</span><span class="special">,</span> <span class="keyword">const</span> <a class="link" href="../../policy.html" title="Policies">Policy</a><span class="special">&amp;);</span>
+</pre>
+<p>
+          Returns the <a href="http://functions.wolfram.com/GammaBetaErf/InverseErf/" target="_top">inverse
+          error function</a> of z, that is a value x such that:
+        </p>
+<pre class="programlisting"><span class="identifier">p</span> <span class="special">=</span> <span class="identifier">erf</span><span class="special">(</span><span class="identifier">x</span><span class="special">);</span>
+</pre>
+<p>
+          <span class="inlinemediaobject"><img src="../../../../graphs/erf_inv.png" align="middle"></span>
+        </p>
+<pre class="programlisting"><span class="keyword">template</span> <span class="special">&lt;</span><span class="keyword">class</span> <span class="identifier">T</span><span class="special">&gt;</span>
+<a class="link" href="../../main_overview/result_type.html" title="Calculation of the Type of the Result"><span class="emphasis"><em>calculated-result-type</em></span></a> <span class="identifier">erfc_inv</span><span class="special">(</span><span class="identifier">T</span> <span class="identifier">z</span><span class="special">);</span>
+
+<span class="keyword">template</span> <span class="special">&lt;</span><span class="keyword">class</span> <span class="identifier">T</span><span class="special">,</span> <span class="keyword">class</span> <a class="link" href="../../policy.html" title="Policies">Policy</a><span class="special">&gt;</span>
+<a class="link" href="../../main_overview/result_type.html" title="Calculation of the Type of the Result"><span class="emphasis"><em>calculated-result-type</em></span></a> <span class="identifier">erfc_inv</span><span class="special">(</span><span class="identifier">T</span> <span class="identifier">z</span><span class="special">,</span> <span class="keyword">const</span> <a class="link" href="../../policy.html" title="Policies">Policy</a><span class="special">&amp;);</span>
+</pre>
+<p>
+          Returns the inverse of the complement of the error function of z, that
+          is a value x such that:
+        </p>
+<pre class="programlisting"><span class="identifier">p</span> <span class="special">=</span> <span class="identifier">erfc</span><span class="special">(</span><span class="identifier">x</span><span class="special">);</span>
+</pre>
+<p>
+          <span class="inlinemediaobject"><img src="../../../../graphs/erfc_inv.png" align="middle"></span>
+        </p>
+<a name="math_toolkit.special.sf_erf.error_inv.accuracy"></a><h5>
+<a name="id741579"></a>
+          <a class="link" href="error_inv.html#math_toolkit.special.sf_erf.error_inv.accuracy">Accuracy</a>
+        </h5>
+<p>
+          For types up to and including 80-bit long doubles the approximations used
+          are accurate to less than ~ 2 epsilon. For higher precision types these
+          functions have the same accuracy as the <a class="link" href="error_function.html" title="Error Functions">forward
+          error functions</a>.
+        </p>
+<a name="math_toolkit.special.sf_erf.error_inv.testing"></a><h5>
+<a name="id741617"></a>
+          <a class="link" href="error_inv.html#math_toolkit.special.sf_erf.error_inv.testing">Testing</a>
+        </h5>
+<p>
+          There are two sets of tests:
+        </p>
+<div class="itemizedlist"><ul type="disc">
+<li>
+            Basic sanity checks attempt to "round-trip" from <span class="emphasis"><em>x</em></span>
+            to <span class="emphasis"><em>p</em></span> and back again. These tests have quite generous
+            tolerances: in general both the error functions and their inverses change
+            so rapidly in some places that round tripping to more than a couple of
+            significant digits isn't possible. This is especially true when <span class="emphasis"><em>p</em></span>
+            is very near one: in this case there isn't enough "information content"
+            in the input to the inverse function to get back where you started.
+          </li>
+<li>
+            Accuracy checks using high-precision test values. These measure the accuracy
+            of the result, given <span class="emphasis"><em>exact</em></span> input values.
+          </li>
+</ul></div>
+<a name="math_toolkit.special.sf_erf.error_inv.implementation"></a><h5>
+<a name="id741697"></a>
+          <a class="link" href="error_inv.html#math_toolkit.special.sf_erf.error_inv.implementation">Implementation</a>
+        </h5>
+<p>
+          These functions use a rational approximation <a class="link" href="../../backgrounders/implementation.html#math_toolkit.backgrounders.implementation.rational_approximations_used">devised
+          by JM</a> to calculate an initial approximation to the result that is
+          accurate to ~10<sup>-19</sup>, then only if that has insufficient accuracy compared
+          to the epsilon for T, do we clean up the result using <a href="http://en.wikipedia.org/wiki/Simple_rational_approximation" target="_top">Halley
+          iteration</a>.
+        </p>
+<p>
+          Constructing rational approximations to the erf/erfc functions is actually
+          surprisingly hard, especially at high precision. For this reason no attempt
+          has been made to achieve 10<sup>-34 </sup> accuracy suitable for use with 128-bit reals.
+        </p>
+<p>
+          In the following discussion, <span class="emphasis"><em>p</em></span> is the value passed
+          to erf_inv, and <span class="emphasis"><em>q</em></span> is the value passed to erfc_inv,
+          so that <span class="emphasis"><em>p = 1 - q</em></span> and <span class="emphasis"><em>q = 1 - p</em></span>
+          and in both cases we want to solve for the same result <span class="emphasis"><em>x</em></span>.
+        </p>
+<p>
+          For <span class="emphasis"><em>p &lt; 0.5</em></span> the inverse erf function is reasonably
+          smooth and the approximation:
+        </p>
+<pre class="programlisting"><span class="identifier">x</span> <span class="special">=</span> <span class="identifier">p</span><span class="special">(</span><span class="identifier">p</span> <span class="special">+</span> <span class="number">10</span><span class="special">)(</span><span class="identifier">Y</span> <span class="special">+</span> <span class="identifier">R</span><span class="special">(</span><span class="identifier">p</span><span class="special">))</span>
+</pre>
+<p>
+          Gives a good result for a constant Y, and R(p) optimised for low absolute
+          error compared to |Y|.
+        </p>
+<p>
+          For q &lt; 0.5 things get trickier, over the interval <span class="emphasis"><em>0.5 &gt;
+          q &gt; 0.25</em></span> the following approximation works well:
+        </p>
+<pre class="programlisting"><span class="identifier">x</span> <span class="special">=</span> <span class="identifier">sqrt</span><span class="special">(-</span><span class="number">2l</span><span class="identifier">og</span><span class="special">(</span><span class="identifier">q</span><span class="special">))</span> <span class="special">/</span> <span class="special">(</span><span class="identifier">Y</span> <span class="special">+</span> <span class="identifier">R</span><span class="special">(</span><span class="identifier">q</span><span class="special">))</span>
+</pre>
+<p>
+          While for q &lt; 0.25, let
+        </p>
+<pre class="programlisting"><span class="identifier">z</span> <span class="special">=</span> <span class="identifier">sqrt</span><span class="special">(-</span><span class="identifier">log</span><span class="special">(</span><span class="identifier">q</span><span class="special">))</span>
+</pre>
+<p>
+          Then the result is given by:
+        </p>
+<pre class="programlisting"><span class="identifier">x</span> <span class="special">=</span> <span class="identifier">z</span><span class="special">(</span><span class="identifier">Y</span> <span class="special">+</span> <span class="identifier">R</span><span class="special">(</span><span class="identifier">z</span> <span class="special">-</span> <span class="identifier">B</span><span class="special">))</span>
+</pre>
+<p>
+          As before Y is a constant and the rational function R is optimised for
+          low absolute error compared to |Y|. B is also a constant: it is the smallest
+          value of <span class="emphasis"><em>z</em></span> for which each approximation is valid.
+          There are several approximations of this form each of which reaches a little
+          further into the tail of the erfc function (at <code class="computeroutput"><span class="keyword">long</span>
+          <span class="keyword">double</span></code> precision the extended exponent
+          range compared to <code class="computeroutput"><span class="keyword">double</span></code> means
+          that the tail goes on for a very long way indeed).
+        </p>
+</div>
+<table xmlns:rev="http://www.cs.rpi.edu/~gregod/boost/tools/doc/revision" width="100%"><tr>
+<td align="left"></td>
+<td align="right"><div class="copyright-footer">Copyright © 2006 , 2007, 2008 John Maddock, Paul A. Bristow, Hubert
+      Holin, Xiaogang Zhang, Bruno Lalande and Gautam Sewani<p>
+        Distributed under the Boost Software License, Version 1.0. (See accompanying
+        file LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_0.txt)
+      </p>
+</div></td>
+</tr></table>
+<hr>
+<div class="spirit-nav">
+<a accesskey="p" href="error_function.html"><img src="../../../../../doc/html/images/prev.png" alt="Prev"></a><a accesskey="u" href="../sf_erf.html"><img src="../../../../../doc/html/images/up.png" alt="Up"></a><a accesskey="h" href="../../../index.html"><img src="../../../../../doc/html/images/home.png" alt="Home"></a><a accesskey="n" href="../sf_poly.html"><img src="../../../../../doc/html/images/next.png" alt="Next"></a>
+</div>
+</body>
+</html>

Added: sandbox/tools/auto_index/example/math/doc/sf_and_dist/html/math_toolkit/special/sf_gamma.html
==============================================================================
--- (empty file)
+++ sandbox/tools/auto_index/example/math/doc/sf_and_dist/html/math_toolkit/special/sf_gamma.html	2008-11-28 05:25:28 EST (Fri, 28 Nov 2008)
@@ -0,0 +1,57 @@
+<html>
+<head>
+<meta http-equiv="Content-Type" content="text/html; charset=ISO-8859-1">
+<title>Gamma Functions</title>
+<link rel="stylesheet" href="../../boostbook.css" type="text/css">
+<meta name="generator" content="DocBook XSL Stylesheets Vsnapshot_8125">
+<link rel="home" href="../../index.html" title="Math Toolkit">
+<link rel="up" href="../special.html" title="Special Functions">
+<link rel="prev" href="../special.html" title="Special Functions">
+<link rel="next" href="sf_gamma/tgamma.html" title="Gamma">
+</head>
+<body bgcolor="white" text="black" link="#0000FF" vlink="#840084" alink="#0000FF">
+<table cellpadding="2" width="100%"><tr>
+<td valign="top"><img alt="Boost C++ Libraries" width="277" height="86" src="../../../../boost.png"></td>
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+</div>
+<div class="section" lang="en">
+<div class="titlepage"><div><div><h3 class="title">
+<a name="math_toolkit.special.sf_gamma"></a><a class="link" href="sf_gamma.html" title="Gamma Functions"> Gamma Functions</a>
+</h3></div></div></div>
+<div class="toc"><dl>
+<dt><span class="section"> Gamma</span></dt>
+<dt><span class="section"> Log Gamma</span></dt>
+<dt><span class="section"> Digamma</span></dt>
+<dt><span class="section"><a href="sf_gamma/gamma_ratios.html"> Ratios
+        of Gamma Functions</a></span></dt>
+<dt><span class="section"><a href="sf_gamma/igamma.html"> Incomplete Gamma
+        Functions</a></span></dt>
+<dt><span class="section"><a href="sf_gamma/igamma_inv.html"> Incomplete
+        Gamma Function Inverses</a></span></dt>
+<dt><span class="section"><a href="sf_gamma/gamma_derivatives.html"> Derivative
+        of the Incomplete Gamma Function</a></span></dt>
+</dl></div>
+</div>
+<table xmlns:rev="http://www.cs.rpi.edu/~gregod/boost/tools/doc/revision" width="100%"><tr>
+<td align="left"></td>
+<td align="right"><div class="copyright-footer">Copyright © 2006 , 2007, 2008 John Maddock, Paul A. Bristow, Hubert
+      Holin, Xiaogang Zhang, Bruno Lalande and Gautam Sewani<p>
+        Distributed under the Boost Software License, Version 1.0. (See accompanying
+        file LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_0.txt)
+      </p>
+</div></td>
+</tr></table>
+<hr>
+<div class="spirit-nav">
+<a accesskey="p" href="../special.html"><img src="../../../../doc/html/images/prev.png" alt="Prev"></a><a accesskey="u" href="../special.html"><img src="../../../../doc/html/images/up.png" alt="Up"></a><a accesskey="h" href="../../index.html"><img src="../../../../doc/html/images/home.png" alt="Home"></a><a accesskey="n" href="sf_gamma/tgamma.html"><img src="../../../../doc/html/images/next.png" alt="Next"></a>
+</div>
+</body>
+</html>

Added: sandbox/tools/auto_index/example/math/doc/sf_and_dist/html/math_toolkit/special/sf_gamma/digamma.html
==============================================================================
--- (empty file)
+++ sandbox/tools/auto_index/example/math/doc/sf_and_dist/html/math_toolkit/special/sf_gamma/digamma.html	2008-11-28 05:25:28 EST (Fri, 28 Nov 2008)
@@ -0,0 +1,394 @@
+<html>
+<head>
+<meta http-equiv="Content-Type" content="text/html; charset=ISO-8859-1">
+<title>Digamma</title>
+<link rel="stylesheet" href="../../../boostbook.css" type="text/css">
+<meta name="generator" content="DocBook XSL Stylesheets Vsnapshot_8125">
+<link rel="home" href="../../../index.html" title="Math Toolkit">
+<link rel="up" href="../sf_gamma.html" title="Gamma Functions">
+<link rel="prev" href="lgamma.html" title="Log Gamma">
+<link rel="next" href="gamma_ratios.html" title="Ratios of Gamma Functions">
+</head>
+<body bgcolor="white" text="black" link="#0000FF" vlink="#840084" alink="#0000FF">
+<table cellpadding="2" width="100%"><tr>
+<td valign="top"><img alt="Boost C++ Libraries" width="277" height="86" src="../../../../../boost.png"></td>
+<td align="center">Home</td>
+<td align="center">Libraries</td>
+<td align="center">People</td>
+<td align="center">FAQ</td>
+<td align="center">More</td>
+</tr></table>
+<hr>
+<div class="spirit-nav">
+<a accesskey="p" href="lgamma.html"><img src="../../../../../doc/html/images/prev.png" alt="Prev"></a><a accesskey="u" href="../sf_gamma.html"><img src="../../../../../doc/html/images/up.png" alt="Up"></a><a accesskey="h" href="../../../index.html"><img src="../../../../../doc/html/images/home.png" alt="Home"></a><a accesskey="n" href="gamma_ratios.html"><img src="../../../../../doc/html/images/next.png" alt="Next"></a>
+</div>
+<div class="section" lang="en">
+<div class="titlepage"><div><div><h4 class="title">
+<a name="math_toolkit.special.sf_gamma.digamma"></a><a class="link" href="digamma.html" title="Digamma"> Digamma</a>
+</h4></div></div></div>
+<a name="math_toolkit.special.sf_gamma.digamma.synopsis"></a><h5>
+<a name="id703216"></a>
+          <a class="link" href="digamma.html#math_toolkit.special.sf_gamma.digamma.synopsis">Synopsis</a>
+        </h5>
+<p>
+          
+</p>
+<pre class="programlisting"><span class="preprocessor">#include</span> <span class="special">&lt;</span><span class="identifier">boost</span><span class="special">/</span><span class="identifier">math</span><span class="special">/</span><span class="identifier">special_functions</span><span class="special">/</span><span class="identifier">digamma</span><span class="special">.</span><span class="identifier">hpp</span><span class="special">&gt;</span>
+</pre>
+<p>
+        </p>
+<pre class="programlisting"><span class="keyword">namespace</span> <span class="identifier">boost</span><span class="special">{</span> <span class="keyword">namespace</span> <span class="identifier">math</span><span class="special">{</span>
+
+<span class="keyword">template</span> <span class="special">&lt;</span><span class="keyword">class</span> <span class="identifier">T</span><span class="special">&gt;</span>
+<a class="link" href="../../main_overview/result_type.html" title="Calculation of the Type of the Result"><span class="emphasis"><em>calculated-result-type</em></span></a> <span class="identifier">digamma</span><span class="special">(</span><span class="identifier">T</span> <span class="identifier">z</span><span class="special">);</span>
+
+<span class="keyword">template</span> <span class="special">&lt;</span><span class="keyword">class</span> <span class="identifier">T</span><span class="special">,</span> <span class="keyword">class</span> <a class="link" href="../../policy.html" title="Policies">Policy</a><span class="special">&gt;</span>
+<a class="link" href="../../main_overview/result_type.html" title="Calculation of the Type of the Result"><span class="emphasis"><em>calculated-result-type</em></span></a> <span class="identifier">digamma</span><span class="special">(</span><span class="identifier">T</span> <span class="identifier">z</span><span class="special">,</span> <span class="keyword">const</span> <a class="link" href="../../policy.html" title="Policies">Policy</a><span class="special">&amp;);</span>
+
+<span class="special">}}</span> <span class="comment">// namespaces
+</span></pre>
+<a name="math_toolkit.special.sf_gamma.digamma.description"></a><h5>
+<a name="id703540"></a>
+          <a class="link" href="digamma.html#math_toolkit.special.sf_gamma.digamma.description">Description</a>
+        </h5>
+<p>
+          Returns the digamma or psi function of <span class="emphasis"><em>x</em></span>. Digamma
+          is defined as the logarithmic derivative of the gamma function:
+        </p>
+<p>
+          <span class="inlinemediaobject"><img src="../../../../equations/digamma1.png"></span>
+        </p>
+<p>
+          <span class="inlinemediaobject"><img src="../../../../graphs/digamma.png" align="middle"></span>
+        </p>
+<p>
+          </p>
+<p>
+            The final <a class="link" href="../../policy.html" title="Policies">Policy</a> argument
+            is optional and can be used to control the behaviour of the function:
+            how it handles errors, what level of precision to use etc. Refer to the
+            <a class="link" href="../../policy.html" title="Policies">policy documentation for more details</a>.
+          </p>
+<p>
+        </p>
+<p>
+          There is no fully generic version of this function: all the implementations
+          are tuned to specific accuracy levels, the most precise of which delivers
+          34-digits of precision.
+        </p>
+<p>
+          The return type of this function is computed using the <a class="link" href="../../main_overview/result_type.html" title="Calculation of the Type of the Result"><span class="emphasis"><em>result
+          type calculation rules</em></span></a>: the result is of type <code class="computeroutput"><span class="keyword">double</span></code> when T is an integer type, and type
+          T otherwise.
+        </p>
+<a name="math_toolkit.special.sf_gamma.digamma.accuracy"></a><h5>
+<a name="id703709"></a>
+          <a class="link" href="digamma.html#math_toolkit.special.sf_gamma.digamma.accuracy">Accuracy</a>
+        </h5>
+<p>
+          The following table shows the peak errors (in units of epsilon) found on
+          various platforms with various floating point types. Unless otherwise specified
+          any floating point type that is narrower than the one shown will have
+          <a class="link" href="../../backgrounders/relative_error.html#zero_error">effectively zero error</a>.
+        </p>
+<div class="informaltable"><table class="table">
+<colgroup>
+<col>
+<col>
+<col>
+<col>
+<col>
+<col>
+</colgroup>
+<thead><tr>
+<th>
+                <p>
+                  Significand Size
+                </p>
+                </th>
+<th>
+                <p>
+                  Platform and Compiler
+                </p>
+                </th>
+<th>
+                <p>
+                  Random Positive Values
+                </p>
+                </th>
+<th>
+                <p>
+                  Values Near The Positive Root
+                </p>
+                </th>
+<th>
+                <p>
+                  Values Near Zero
+                </p>
+                </th>
+<th>
+                <p>
+                  Negative Values
+                </p>
+                </th>
+</tr></thead>
+<tbody>
+<tr>
+<td>
+                <p>
+                  53
+                </p>
+                </td>
+<td>
+                <p>
+                  Win32 Visual C++ 8
+                </p>
+                </td>
+<td>
+                <p>
+                  Peak=0.98 Mean=0.36
+                </p>
+                </td>
+<td>
+                <p>
+                  Peak=0.99 Mean=0.5
+                </p>
+                </td>
+<td>
+                <p>
+                  Peak=0.95 Mean=0.5
+                </p>
+                </td>
+<td>
+                <p>
+                  Peak=214 Mean=16
+                </p>
+                </td>
+</tr>
+<tr>
+<td>
+                <p>
+                  64
+                </p>
+                </td>
+<td>
+                <p>
+                  Linux IA32 / GCC
+                </p>
+                </td>
+<td>
+                <p>
+                  Peak=1.4 Mean=0.4
+                </p>
+                </td>
+<td>
+                <p>
+                  Peak=1.3 Mean=0.45
+                </p>
+                </td>
+<td>
+                <p>
+                  Peak=0.98 Mean=0.35
+                </p>
+                </td>
+<td>
+                <p>
+                  Peak=180 Mean=13
+                </p>
+                </td>
+</tr>
+<tr>
+<td>
+                <p>
+                  64
+                </p>
+                </td>
+<td>
+                <p>
+                  Linux IA64 / GCC
+                </p>
+                </td>
+<td>
+                <p>
+                  Peak=0.92 Mean=0.4
+                </p>
+                </td>
+<td>
+                <p>
+                  Peak=1.3 Mean=0.45
+                </p>
+                </td>
+<td>
+                <p>
+                  Peak=0.98 Mean=0.4
+                </p>
+                </td>
+<td>
+                <p>
+                  Peak=180 Mean=13
+                </p>
+                </td>
+</tr>
+<tr>
+<td>
+                <p>
+                  113
+                </p>
+                </td>
+<td>
+                <p>
+                  HPUX IA64, aCC A.06.06
+                </p>
+                </td>
+<td>
+                <p>
+                  Peak=0.9 Mean=0.4
+                </p>
+                </td>
+<td>
+                <p>
+                  Peak=1.1 Mean=0.5
+                </p>
+                </td>
+<td>
+                <p>
+                  Peak=0.99 Mean=0.4
+                </p>
+                </td>
+<td>
+                <p>
+                  Peak=64 Mean=6
+                </p>
+                </td>
+</tr>
+</tbody>
+</table></div>
+<p>
+          As shown above, error rates for positive arguments are generally very low.
+          For negative arguments there are an infinite number of irrational roots:
+          relative errors very close to these can be arbitrarily large, although
+          absolute error will remain very low.
+        </p>
+<a name="math_toolkit.special.sf_gamma.digamma.testing"></a><h5>
+<a name="id704041"></a>
+          <a class="link" href="digamma.html#math_toolkit.special.sf_gamma.digamma.testing">Testing</a>
+        </h5>
+<p>
+          There are two sets of tests: spot values are computed using the online
+          calculator at functions.wolfram.com, while random test values are generated
+          using the high-precision reference implementation (a differentiated <a class="link" href="../../backgrounders/lanczos.html" title="The Lanczos Approximation">Lanczos approximation</a>
+          see below).
+        </p>
+<a name="math_toolkit.special.sf_gamma.digamma.implementation"></a><h5>
+<a name="id704085"></a>
+          <a class="link" href="digamma.html#math_toolkit.special.sf_gamma.digamma.implementation">Implementation</a>
+        </h5>
+<p>
+          The implementation is divided up into the following domains:
+        </p>
+<p>
+          For Negative arguments the reflection formula:
+        </p>
+<pre class="programlisting"><span class="identifier">digamma</span><span class="special">(</span><span class="number">1</span><span class="special">-</span><span class="identifier">x</span><span class="special">)</span> <span class="special">=</span> <span class="identifier">digamma</span><span class="special">(</span><span class="identifier">x</span><span class="special">)</span> <span class="special">+</span> <span class="identifier">pi</span><span class="special">/</span><span class="identifier">tan</span><span class="special">(</span><span class="identifier">pi</span><span class="special">*</span><span class="identifier">x</span><span class="special">);</span>
+</pre>
+<p>
+          is used to make <span class="emphasis"><em>x</em></span> positive.
+        </p>
+<p>
+          For arguments in the range [0,1] the recurrence relation:
+        </p>
+<pre class="programlisting"><span class="identifier">digamma</span><span class="special">(</span><span class="identifier">x</span><span class="special">)</span> <span class="special">=</span> <span class="identifier">digamma</span><span class="special">(</span><span class="identifier">x</span><span class="special">+</span><span class="number">1</span><span class="special">)</span> <span class="special">-</span> <span class="number">1</span><span class="special">/</span><span class="identifier">x</span>
+</pre>
+<p>
+          is used to shift the evaluation to [1,2].
+        </p>
+<p>
+          For arguments in the range [1,2] a rational approximation <a class="link" href="../../backgrounders/implementation.html#math_toolkit.backgrounders.implementation.rational_approximations_used">devised
+          by JM</a> is used (see below).
+        </p>
+<p>
+          For arguments in the range [2,BIG] the recurrence relation:
+        </p>
+<pre class="programlisting"><span class="identifier">digamma</span><span class="special">(</span><span class="identifier">x</span><span class="special">+</span><span class="number">1</span><span class="special">)</span> <span class="special">=</span> <span class="identifier">digamma</span><span class="special">(</span><span class="identifier">x</span><span class="special">)</span> <span class="special">+</span> <span class="number">1</span><span class="special">/</span><span class="identifier">x</span><span class="special">;</span>
+</pre>
+<p>
+          is used to shift the evaluation to the range [1,2].
+        </p>
+<p>
+          For arguments &gt; BIG the asymptotic expansion:
+        </p>
+<p>
+          <span class="inlinemediaobject"><img src="../../../../equations/digamma2.png"></span>
+        </p>
+<p>
+          can be used. However, this expansion is divergent after a few terms: exactly
+          how many terms depends on the size of <span class="emphasis"><em>x</em></span>. Therefore
+          the value of <span class="emphasis"><em>BIG</em></span> must be chosen so that the series
+          can be truncated at a term that is too small to have any effect on the
+          result when evaluated at <span class="emphasis"><em>BIG</em></span>. Choosing BIG=10 for
+          up to 80-bit reals, and BIG=20 for 128-bit reals allows the series to truncated
+          after a suitably small number of terms and evaluated as a polynomial in
+          <code class="computeroutput"><span class="number">1</span><span class="special">/(</span><span class="identifier">x</span><span class="special">*</span><span class="identifier">x</span><span class="special">)</span></code>.
+        </p>
+<p>
+          The rational approximation <a class="link" href="../../backgrounders/implementation.html#math_toolkit.backgrounders.implementation.rational_approximations_used">devised
+          by JM</a> in the range [1,2] is derived as follows.
+        </p>
+<p>
+          First a high precision approximation to digamma was constructed using a
+          60-term differentiated <a class="link" href="../../backgrounders/lanczos.html" title="The Lanczos Approximation">Lanczos
+          approximation</a>, the form used is:
+        </p>
+<p>
+          <span class="inlinemediaobject"><img src="../../../../equations/digamma3.png"></span>
+        </p>
+<p>
+          Where P(x) and Q(x) are the polynomials from the rational form of the Lanczos
+          sum, and P'(x) and Q'(x) are their first derivatives. The Lanzos part of
+          this approximation has a theoretical precision of ~100 decimal digits.
+          However, cancellation in the above sum will reduce that to around <code class="computeroutput"><span class="number">99</span><span class="special">-(</span><span class="number">1</span><span class="special">/</span><span class="identifier">y</span><span class="special">)</span></code>
+          digits if <span class="emphasis"><em>y</em></span> is the result. This approximation was
+          used to calculate the positive root of digamma, and was found to agree
+          with the value used by Cody to 25 digits (See Math. Comp. 27, 123-127 (1973)
+          by Cody, Strecok and Thacher) and with the value used by Morris to 35 digits
+          (See TOMS Algorithm 708).
+        </p>
+<p>
+          Likewise a few spot tests agreed with values calculated using functions.wolfram.com
+          to &gt;40 digits. That's sufficiently precise to insure that the approximation
+          below is accurate to double precision. Achieving 128-bit long double precision
+          requires that the location of the root is known to ~70 digits, and it's
+          not clear whether the value calculated by this method meets that requirement:
+          the difficulty lies in independently verifying the value obtained.
+        </p>
+<p>
+          The rational approximation <a class="link" href="../../backgrounders/implementation.html#math_toolkit.backgrounders.implementation.rational_approximations_used">devised
+          by JM</a> was optimised for absolute error using the form:
+        </p>
+<pre class="programlisting"><span class="identifier">digamma</span><span class="special">(</span><span class="identifier">x</span><span class="special">)</span> <span class="special">=</span> <span class="special">(</span><span class="identifier">x</span> <span class="special">-</span> <span class="identifier">X0</span><span class="special">)(</span><span class="identifier">Y</span> <span class="special">+</span> <span class="identifier">R</span><span class="special">(</span><span class="identifier">x</span> <span class="special">-</span> <span class="number">1</span><span class="special">));</span>
+</pre>
+<p>
+          Where X0 is the positive root of digamma, Y is a constant, and R(x - 1)
+          is the rational approximation. Note that since X0 is irrational, we need
+          twice as many digits in X0 as in x in order to avoid cancellation error
+          during the subtraction (this assumes that <span class="emphasis"><em>x</em></span> is an
+          exact value, if it's not then all bets are off). That means that even when
+          x is the value of the root rounded to the nearest representable value,
+          the result of digamma(x) <span class="emphasis"><em><span class="bold"><strong>will not be zero</strong></span></em></span>.
+        </p>
+</div>
+<table xmlns:rev="http://www.cs.rpi.edu/~gregod/boost/tools/doc/revision" width="100%"><tr>
+<td align="left"></td>
+<td align="right"><div class="copyright-footer">Copyright © 2006 , 2007, 2008 John Maddock, Paul A. Bristow, Hubert
+      Holin, Xiaogang Zhang, Bruno Lalande and Gautam Sewani<p>
+        Distributed under the Boost Software License, Version 1.0. (See accompanying
+        file LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_0.txt)
+      </p>
+</div></td>
+</tr></table>
+<hr>
+<div class="spirit-nav">
+<a accesskey="p" href="lgamma.html"><img src="../../../../../doc/html/images/prev.png" alt="Prev"></a><a accesskey="u" href="../sf_gamma.html"><img src="../../../../../doc/html/images/up.png" alt="Up"></a><a accesskey="h" href="../../../index.html"><img src="../../../../../doc/html/images/home.png" alt="Home"></a><a accesskey="n" href="gamma_ratios.html"><img src="../../../../../doc/html/images/next.png" alt="Next"></a>
+</div>
+</body>
+</html>

Added: sandbox/tools/auto_index/example/math/doc/sf_and_dist/html/math_toolkit/special/sf_gamma/gamma_derivatives.html
==============================================================================
--- (empty file)
+++ sandbox/tools/auto_index/example/math/doc/sf_and_dist/html/math_toolkit/special/sf_gamma/gamma_derivatives.html	2008-11-28 05:25:28 EST (Fri, 28 Nov 2008)
@@ -0,0 +1,114 @@
+<html>
+<head>
+<meta http-equiv="Content-Type" content="text/html; charset=ISO-8859-1">
+<title>Derivative of the Incomplete Gamma Function</title>
+<link rel="stylesheet" href="../../../boostbook.css" type="text/css">
+<meta name="generator" content="DocBook XSL Stylesheets Vsnapshot_8125">
+<link rel="home" href="../../../index.html" title="Math Toolkit">
+<link rel="up" href="../sf_gamma.html" title="Gamma Functions">
+<link rel="prev" href="igamma_inv.html" title="Incomplete Gamma Function Inverses">
+<link rel="next" href="../factorials.html" title="Factorials and Binomial Coefficients">
+</head>
+<body bgcolor="white" text="black" link="#0000FF" vlink="#840084" alink="#0000FF">
+<table cellpadding="2" width="100%"><tr>
+<td valign="top"><img alt="Boost C++ Libraries" width="277" height="86" src="../../../../../boost.png"></td>
+<td align="center">Home</td>
+<td align="center">Libraries</td>
+<td align="center">People</td>
+<td align="center">FAQ</td>
+<td align="center">More</td>
+</tr></table>
+<hr>
+<div class="spirit-nav">
+<a accesskey="p" href="igamma_inv.html"><img src="../../../../../doc/html/images/prev.png" alt="Prev"></a><a accesskey="u" href="../sf_gamma.html"><img src="../../../../../doc/html/images/up.png" alt="Up"></a><a accesskey="h" href="../../../index.html"><img src="../../../../../doc/html/images/home.png" alt="Home"></a><a accesskey="n" href="../factorials.html"><img src="../../../../../doc/html/images/next.png" alt="Next"></a>
+</div>
+<div class="section" lang="en">
+<div class="titlepage"><div><div><h4 class="title">
+<a name="math_toolkit.special.sf_gamma.gamma_derivatives"></a><a class="link" href="gamma_derivatives.html" title="Derivative of the Incomplete Gamma Function"> Derivative
+        of the Incomplete Gamma Function</a>
+</h4></div></div></div>
+<a name="math_toolkit.special.sf_gamma.gamma_derivatives.synopsis"></a><h5>
+<a name="id714491"></a>
+          <a class="link" href="gamma_derivatives.html#math_toolkit.special.sf_gamma.gamma_derivatives.synopsis">Synopsis</a>
+        </h5>
+<p>
+          
+</p>
+<pre class="programlisting"><span class="preprocessor">#include</span> <span class="special">&lt;</span><span class="identifier">boost</span><span class="special">/</span><span class="identifier">math</span><span class="special">/</span><span class="identifier">special_functions</span><span class="special">/</span><span class="identifier">gamma</span><span class="special">.</span><span class="identifier">hpp</span><span class="special">&gt;</span>
+</pre>
+<p>
+        </p>
+<pre class="programlisting"><span class="keyword">namespace</span> <span class="identifier">boost</span><span class="special">{</span> <span class="keyword">namespace</span> <span class="identifier">math</span><span class="special">{</span> 
+
+<span class="keyword">template</span> <span class="special">&lt;</span><span class="keyword">class</span> <span class="identifier">T1</span><span class="special">,</span> <span class="keyword">class</span> <span class="identifier">T2</span><span class="special">&gt;</span>
+<a class="link" href="../../main_overview/result_type.html" title="Calculation of the Type of the Result"><span class="emphasis"><em>calculated-result-type</em></span></a> <span class="identifier">gamma_p_derivative</span><span class="special">(</span><span class="identifier">T1</span> <span class="identifier">a</span><span class="special">,</span> <span class="identifier">T2</span> <span class="identifier">x</span><span class="special">);</span>
+
+<span class="keyword">template</span> <span class="special">&lt;</span><span class="keyword">class</span> <span class="identifier">T1</span><span class="special">,</span> <span class="keyword">class</span> <span class="identifier">T2</span><span class="special">,</span> <span class="keyword">class</span> <a class="link" href="../../policy.html" title="Policies">Policy</a><span class="special">&gt;</span>
+<a class="link" href="../../main_overview/result_type.html" title="Calculation of the Type of the Result"><span class="emphasis"><em>calculated-result-type</em></span></a> <span class="identifier">gamma_p_derivative</span><span class="special">(</span><span class="identifier">T1</span> <span class="identifier">a</span><span class="special">,</span> <span class="identifier">T2</span> <span class="identifier">x</span><span class="special">,</span> <span class="keyword">const</span> <a class="link" href="../../policy.html" title="Policies">Policy</a><span class="special">&amp;);</span>
+
+<span class="special">}}</span> <span class="comment">// namespaces
+</span></pre>
+<a name="math_toolkit.special.sf_gamma.gamma_derivatives.description"></a><h5>
+<a name="id714884"></a>
+          <a class="link" href="gamma_derivatives.html#math_toolkit.special.sf_gamma.gamma_derivatives.description">Description</a>
+        </h5>
+<p>
+          This function find some uses in statistical distributions: it implements
+          the partial derivative with respect to <span class="emphasis"><em>x</em></span> of the incomplete
+          gamma function.
+        </p>
+<p>
+          <span class="inlinemediaobject"><img src="../../../../equations/derivative1.png"></span>
+        </p>
+<p>
+          </p>
+<p>
+            The final <a class="link" href="../../policy.html" title="Policies">Policy</a> argument
+            is optional and can be used to control the behaviour of the function:
+            how it handles errors, what level of precision to use etc. Refer to the
+            <a class="link" href="../../policy.html" title="Policies">policy documentation for more details</a>.
+          </p>
+<p>
+        </p>
+<p>
+          Note that the derivative of the function <a class="link" href="igamma.html" title="Incomplete Gamma Functions">gamma_q</a>
+          can be obtained by negating the result of this function.
+        </p>
+<p>
+          The return type of this function is computed using the <a class="link" href="../../main_overview/result_type.html" title="Calculation of the Type of the Result"><span class="emphasis"><em>result
+          type calculation rules</em></span></a> when T1 and T2 are different types,
+          otherwise the return type is simply T1.
+        </p>
+<a name="math_toolkit.special.sf_gamma.gamma_derivatives.accuracy"></a><h5>
+<a name="id715018"></a>
+          <a class="link" href="gamma_derivatives.html#math_toolkit.special.sf_gamma.gamma_derivatives.accuracy">Accuracy</a>
+        </h5>
+<p>
+          Almost identical to the incomplete gamma function <a class="link" href="igamma.html" title="Incomplete Gamma Functions">gamma_p</a>:
+          refer to the documentation for that function for more information.
+        </p>
+<a name="math_toolkit.special.sf_gamma.gamma_derivatives.implementation"></a><h5>
+<a name="id715059"></a>
+          <a class="link" href="gamma_derivatives.html#math_toolkit.special.sf_gamma.gamma_derivatives.implementation">Implementation</a>
+        </h5>
+<p>
+          This function just expose some of the internals of the incomplete gamma
+          function <a class="link" href="igamma.html" title="Incomplete Gamma Functions">gamma_p</a>:
+          refer to the documentation for that function for more information.
+        </p>
+</div>
+<table xmlns:rev="http://www.cs.rpi.edu/~gregod/boost/tools/doc/revision" width="100%"><tr>
+<td align="left"></td>
+<td align="right"><div class="copyright-footer">Copyright © 2006 , 2007, 2008 John Maddock, Paul A. Bristow, Hubert
+      Holin, Xiaogang Zhang, Bruno Lalande and Gautam Sewani<p>
+        Distributed under the Boost Software License, Version 1.0. (See accompanying
+        file LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_0.txt)
+      </p>
+</div></td>
+</tr></table>
+<hr>
+<div class="spirit-nav">
+<a accesskey="p" href="igamma_inv.html"><img src="../../../../../doc/html/images/prev.png" alt="Prev"></a><a accesskey="u" href="../sf_gamma.html"><img src="../../../../../doc/html/images/up.png" alt="Up"></a><a accesskey="h" href="../../../index.html"><img src="../../../../../doc/html/images/home.png" alt="Home"></a><a accesskey="n" href="../factorials.html"><img src="../../../../../doc/html/images/next.png" alt="Next"></a>
+</div>
+</body>
+</html>

Added: sandbox/tools/auto_index/example/math/doc/sf_and_dist/html/math_toolkit/special/sf_gamma/gamma_ratios.html
==============================================================================
--- (empty file)
+++ sandbox/tools/auto_index/example/math/doc/sf_and_dist/html/math_toolkit/special/sf_gamma/gamma_ratios.html	2008-11-28 05:25:28 EST (Fri, 28 Nov 2008)
@@ -0,0 +1,370 @@
+<html>
+<head>
+<meta http-equiv="Content-Type" content="text/html; charset=ISO-8859-1">
+<title>Ratios of Gamma Functions</title>
+<link rel="stylesheet" href="../../../boostbook.css" type="text/css">
+<meta name="generator" content="DocBook XSL Stylesheets Vsnapshot_8125">
+<link rel="home" href="../../../index.html" title="Math Toolkit">
+<link rel="up" href="../sf_gamma.html" title="Gamma Functions">
+<link rel="prev" href="digamma.html" title="Digamma">
+<link rel="next" href="igamma.html" title="Incomplete Gamma Functions">
+</head>
+<body bgcolor="white" text="black" link="#0000FF" vlink="#840084" alink="#0000FF">
+<table cellpadding="2" width="100%"><tr>
+<td valign="top"><img alt="Boost C++ Libraries" width="277" height="86" src="../../../../../boost.png"></td>
+<td align="center">Home</td>
+<td align="center">Libraries</td>
+<td align="center">People</td>
+<td align="center">FAQ</td>
+<td align="center">More</td>
+</tr></table>
+<hr>
+<div class="spirit-nav">
+<a accesskey="p" href="digamma.html"><img src="../../../../../doc/html/images/prev.png" alt="Prev"></a><a accesskey="u" href="../sf_gamma.html"><img src="../../../../../doc/html/images/up.png" alt="Up"></a><a accesskey="h" href="../../../index.html"><img src="../../../../../doc/html/images/home.png" alt="Home"></a><a accesskey="n" href="igamma.html"><img src="../../../../../doc/html/images/next.png" alt="Next"></a>
+</div>
+<div class="section" lang="en">
+<div class="titlepage"><div><div><h4 class="title">
+<a name="math_toolkit.special.sf_gamma.gamma_ratios"></a><a class="link" href="gamma_ratios.html" title="Ratios of Gamma Functions"> Ratios
+        of Gamma Functions</a>
+</h4></div></div></div>
+<p>
+          
+</p>
+<pre class="programlisting"><span class="preprocessor">#include</span> <span class="special">&lt;</span><span class="identifier">boost</span><span class="special">/</span><span class="identifier">math</span><span class="special">/</span><span class="identifier">special_functions</span><span class="special">/</span><span class="identifier">gamma</span><span class="special">.</span><span class="identifier">hpp</span><span class="special">&gt;</span>
+</pre>
+<p>
+        </p>
+<pre class="programlisting"><span class="keyword">namespace</span> <span class="identifier">boost</span><span class="special">{</span> <span class="keyword">namespace</span> <span class="identifier">math</span><span class="special">{</span>
+
+<span class="keyword">template</span> <span class="special">&lt;</span><span class="keyword">class</span> <span class="identifier">T1</span><span class="special">,</span> <span class="keyword">class</span> <span class="identifier">T2</span><span class="special">&gt;</span>
+<a class="link" href="../../main_overview/result_type.html" title="Calculation of the Type of the Result"><span class="emphasis"><em>calculated-result-type</em></span></a> <span class="identifier">tgamma_ratio</span><span class="special">(</span><span class="identifier">T1</span> <span class="identifier">a</span><span class="special">,</span> <span class="identifier">T2</span> <span class="identifier">b</span><span class="special">);</span>
+
+<span class="keyword">template</span> <span class="special">&lt;</span><span class="keyword">class</span> <span class="identifier">T1</span><span class="special">,</span> <span class="keyword">class</span> <span class="identifier">T2</span><span class="special">,</span> <span class="keyword">class</span> <a class="link" href="../../policy.html" title="Policies">Policy</a><span class="special">&gt;</span>
+<a class="link" href="../../main_overview/result_type.html" title="Calculation of the Type of the Result"><span class="emphasis"><em>calculated-result-type</em></span></a> <span class="identifier">tgamma_ratio</span><span class="special">(</span><span class="identifier">T1</span> <span class="identifier">a</span><span class="special">,</span> <span class="identifier">T2</span> <span class="identifier">b</span><span class="special">,</span> <span class="keyword">const</span> <a class="link" href="../../policy.html" title="Policies">Policy</a><span class="special">&amp;);</span>
+
+<span class="keyword">template</span> <span class="special">&lt;</span><span class="keyword">class</span> <span class="identifier">T1</span><span class="special">,</span> <span class="keyword">class</span> <span class="identifier">T2</span><span class="special">&gt;</span>
+<a class="link" href="../../main_overview/result_type.html" title="Calculation of the Type of the Result"><span class="emphasis"><em>calculated-result-type</em></span></a> <span class="identifier">tgamma_delta_ratio</span><span class="special">(</span><span class="identifier">T1</span> <span class="identifier">a</span><span class="special">,</span> <span class="identifier">T2</span> <span class="identifier">delta</span><span class="special">);</span>
+
+<span class="keyword">template</span> <span class="special">&lt;</span><span class="keyword">class</span> <span class="identifier">T1</span><span class="special">,</span> <span class="keyword">class</span> <span class="identifier">T2</span><span class="special">,</span> <span class="keyword">class</span> <span class="identifier">Policy</span><span class="special">&gt;</span>
+<a class="link" href="../../main_overview/result_type.html" title="Calculation of the Type of the Result"><span class="emphasis"><em>calculated-result-type</em></span></a> <span class="identifier">tgamma_delta_ratio</span><span class="special">(</span><span class="identifier">T1</span> <span class="identifier">a</span><span class="special">,</span> <span class="identifier">T2</span> <span class="identifier">delta</span><span class="special">,</span> <span class="keyword">const</span> <a class="link" href="../../policy.html" title="Policies">Policy</a><span class="special">&amp;);</span>
+
+<span class="special">}}</span> <span class="comment">// namespaces
+</span></pre>
+<a name="math_toolkit.special.sf_gamma.gamma_ratios.description"></a><h5>
+<a name="id705479"></a>
+          <a class="link" href="gamma_ratios.html#math_toolkit.special.sf_gamma.gamma_ratios.description">Description</a>
+        </h5>
+<pre class="programlisting"><span class="keyword">template</span> <span class="special">&lt;</span><span class="keyword">class</span> <span class="identifier">T1</span><span class="special">,</span> <span class="keyword">class</span> <span class="identifier">T2</span><span class="special">&gt;</span> 
+<a class="link" href="../../main_overview/result_type.html" title="Calculation of the Type of the Result"><span class="emphasis"><em>calculated-result-type</em></span></a> <span class="identifier">tgamma_ratio</span><span class="special">(</span><span class="identifier">T1</span> <span class="identifier">a</span><span class="special">,</span> <span class="identifier">T2</span> <span class="identifier">b</span><span class="special">);</span>
+
+<span class="keyword">template</span> <span class="special">&lt;</span><span class="keyword">class</span> <span class="identifier">T1</span><span class="special">,</span> <span class="keyword">class</span> <span class="identifier">T2</span><span class="special">,</span> <span class="keyword">class</span> <a class="link" href="../../policy.html" title="Policies">Policy</a><span class="special">&gt;</span> 
+<a class="link" href="../../main_overview/result_type.html" title="Calculation of the Type of the Result"><span class="emphasis"><em>calculated-result-type</em></span></a> <span class="identifier">tgamma_ratio</span><span class="special">(</span><span class="identifier">T1</span> <span class="identifier">a</span><span class="special">,</span> <span class="identifier">T2</span> <span class="identifier">b</span><span class="special">,</span> <span class="keyword">const</span> <a class="link" href="../../policy.html" title="Policies">Policy</a><span class="special">&amp;);</span>
+</pre>
+<p>
+          Returns the ratio of gamma functions:
+        </p>
+<p>
+          <span class="inlinemediaobject"><img src="../../../../equations/gamma_ratio0.png"></span>
+        </p>
+<p>
+          </p>
+<p>
+            The final <a class="link" href="../../policy.html" title="Policies">Policy</a> argument
+            is optional and can be used to control the behaviour of the function:
+            how it handles errors, what level of precision to use etc. Refer to the
+            <a class="link" href="../../policy.html" title="Policies">policy documentation for more details</a>.
+          </p>
+<p>
+        </p>
+<p>
+          Internally this just calls <code class="computeroutput"><span class="identifier">tgamma_delta_ratio</span><span class="special">(</span><span class="identifier">a</span><span class="special">,</span>
+          <span class="identifier">b</span><span class="special">-</span><span class="identifier">a</span><span class="special">)</span></code>.
+        </p>
+<pre class="programlisting"><span class="keyword">template</span> <span class="special">&lt;</span><span class="keyword">class</span> <span class="identifier">T1</span><span class="special">,</span> <span class="keyword">class</span> <span class="identifier">T2</span><span class="special">&gt;</span>
+<a class="link" href="../../main_overview/result_type.html" title="Calculation of the Type of the Result"><span class="emphasis"><em>calculated-result-type</em></span></a> <span class="identifier">tgamma_delta_ratio</span><span class="special">(</span><span class="identifier">T1</span> <span class="identifier">a</span><span class="special">,</span> <span class="identifier">T2</span> <span class="identifier">delta</span><span class="special">);</span>
+
+<span class="keyword">template</span> <span class="special">&lt;</span><span class="keyword">class</span> <span class="identifier">T1</span><span class="special">,</span> <span class="keyword">class</span> <span class="identifier">T2</span><span class="special">,</span> <span class="keyword">class</span> <a class="link" href="../../policy.html" title="Policies">Policy</a><span class="special">&gt;</span>
+<a class="link" href="../../main_overview/result_type.html" title="Calculation of the Type of the Result"><span class="emphasis"><em>calculated-result-type</em></span></a> <span class="identifier">tgamma_delta_ratio</span><span class="special">(</span><span class="identifier">T1</span> <span class="identifier">a</span><span class="special">,</span> <span class="identifier">T2</span> <span class="identifier">delta</span><span class="special">,</span> <span class="keyword">const</span> <a class="link" href="../../policy.html" title="Policies">Policy</a><span class="special">&amp;);</span>
+</pre>
+<p>
+          Returns the ratio of gamma functions:
+        </p>
+<p>
+          <span class="inlinemediaobject"><img src="../../../../equations/gamma_ratio1.png"></span>
+        </p>
+<p>
+          </p>
+<p>
+            The final <a class="link" href="../../policy.html" title="Policies">Policy</a> argument
+            is optional and can be used to control the behaviour of the function:
+            how it handles errors, what level of precision to use etc. Refer to the
+            <a class="link" href="../../policy.html" title="Policies">policy documentation for more details</a>.
+          </p>
+<p>
+        </p>
+<p>
+          Note that the result is calculated accurately even when <span class="emphasis"><em>delta</em></span>
+          is small compared to <span class="emphasis"><em>a</em></span>: indeed even if <span class="emphasis"><em>a+delta
+          ~ a</em></span>. The function is typically used when <span class="emphasis"><em>a</em></span>
+          is large and <span class="emphasis"><em>delta</em></span> is very small.
+        </p>
+<p>
+          The return type of these functions is computed using the <a class="link" href="../../main_overview/result_type.html" title="Calculation of the Type of the Result"><span class="emphasis"><em>result
+          type calculation rules</em></span></a> when T1 and T2 are different types,
+          otherwise the result type is simple T1.
+        </p>
+<p>
+          <span class="inlinemediaobject"><img src="../../../../graphs/tgamma_delta_ratio.png" align="middle"></span>
+        </p>
+<a name="math_toolkit.special.sf_gamma.gamma_ratios.accuracy"></a><h5>
+<a name="id706264"></a>
+          <a class="link" href="gamma_ratios.html#math_toolkit.special.sf_gamma.gamma_ratios.accuracy">Accuracy</a>
+        </h5>
+<p>
+          The following table shows the peak errors (in units of epsilon) found on
+          various platforms with various floating point types. Unless otherwise specified
+          any floating point type that is narrower than the one shown will have
+          <a class="link" href="../../backgrounders/relative_error.html#zero_error">effectively zero error</a>.
+        </p>
+<div class="table">
+<a name="id706300"></a><p class="title"><b>Table 16. Errors In the Function tgamma_delta_ratio(a, delta)</b></p>
+<div class="table-contents"><table class="table" summary="Errors In the Function tgamma_delta_ratio(a, delta)">
+<colgroup>
+<col>
+<col>
+<col>
+</colgroup>
+<thead><tr>
+<th>
+              <p>
+                Significand Size
+              </p>
+              </th>
+<th>
+              <p>
+                Platform and Compiler
+              </p>
+              </th>
+<th>
+              <p>
+                20 &lt; a &lt; 80
+              </p>
+              <p>
+                and
+              </p>
+              <p>
+                delta &lt; 1
+              </p>
+              </th>
+</tr></thead>
+<tbody>
+<tr>
+<td>
+              <p>
+                53
+              </p>
+              </td>
+<td>
+              <p>
+                Win32, Visual C++ 8
+              </p>
+              </td>
+<td>
+              <p>
+                Peak=16.9 Mean=1.7
+              </p>
+              </td>
+</tr>
+<tr>
+<td>
+              <p>
+                64
+              </p>
+              </td>
+<td>
+              <p>
+                Redhat Linux IA32, gcc-3.4.4
+              </p>
+              </td>
+<td>
+              <p>
+                Peak=24 Mean=2.7
+              </p>
+              </td>
+</tr>
+<tr>
+<td>
+              <p>
+                64
+              </p>
+              </td>
+<td>
+              <p>
+                Redhat Linux IA64, gcc-3.4.4
+              </p>
+              </td>
+<td>
+              <p>
+                Peak=12.8 Mean=1.8
+              </p>
+              </td>
+</tr>
+<tr>
+<td>
+              <p>
+                113
+              </p>
+              </td>
+<td>
+              <p>
+                HPUX IA64, aCC A.06.06
+              </p>
+              </td>
+<td>
+              <p>
+                Peak=21.4 Mean=2.3
+              </p>
+              </td>
+</tr>
+</tbody>
+</table></div>
+</div>
+<br class="table-break"><div class="table">
+<a name="id706472"></a><p class="title"><b>Table 17. Errors In the Function tgamma_ratio(a,
+        b)</b></p>
+<div class="table-contents"><table class="table" summary="Errors In the Function tgamma_ratio(a,
+        b)">
+<colgroup>
+<col>
+<col>
+<col>
+</colgroup>
+<thead><tr>
+<th>
+              <p>
+                Significand Size
+              </p>
+              </th>
+<th>
+              <p>
+                Platform and Compiler
+              </p>
+              </th>
+<th>
+              <p>
+                6 &lt; a,b &lt; 50
+              </p>
+              </th>
+</tr></thead>
+<tbody>
+<tr>
+<td>
+              <p>
+                53
+              </p>
+              </td>
+<td>
+              <p>
+                Win32, Visual C++ 8
+              </p>
+              </td>
+<td>
+              <p>
+                Peak=34 Mean=9
+              </p>
+              </td>
+</tr>
+<tr>
+<td>
+              <p>
+                64
+              </p>
+              </td>
+<td>
+              <p>
+                Redhat Linux IA32, gcc-3.4.4
+              </p>
+              </td>
+<td>
+              <p>
+                Peak=91 Mean=23
+              </p>
+              </td>
+</tr>
+<tr>
+<td>
+              <p>
+                64
+              </p>
+              </td>
+<td>
+              <p>
+                Redhat Linux IA64, gcc-3.4.4
+              </p>
+              </td>
+<td>
+              <p>
+                Peak=35.6 Mean=9.3
+              </p>
+              </td>
+</tr>
+<tr>
+<td>
+              <p>
+                113
+              </p>
+              </td>
+<td>
+              <p>
+                HPUX IA64, aCC A.06.06
+              </p>
+              </td>
+<td>
+              <p>
+                Peak=43.9 Mean=13.2
+              </p>
+              </td>
+</tr>
+</tbody>
+</table></div>
+</div>
+<br class="table-break"><a name="math_toolkit.special.sf_gamma.gamma_ratios.testing"></a><h5>
+<a name="id706646"></a>
+          <a class="link" href="gamma_ratios.html#math_toolkit.special.sf_gamma.gamma_ratios.testing">Testing</a>
+        </h5>
+<p>
+          Accuracy tests use data generated at very high precision (with <a href="http://shoup.net/ntl/doc/RR.txt" target="_top">NTL
+          RR class</a> set at 1000-bit precision: about 300 decimal digits) and
+          a deliberately naive calculation of &#915;(x)/&#915;(y).
+        </p>
+<a name="math_toolkit.special.sf_gamma.gamma_ratios.implementation"></a><h5>
+<a name="id706685"></a>
+          <a class="link" href="gamma_ratios.html#math_toolkit.special.sf_gamma.gamma_ratios.implementation">Implementation</a>
+        </h5>
+<p>
+          The implementation of these functions is very similar to that of <a class="link" href="../sf_beta/beta_function.html" title="Beta">beta</a>, and is
+          based on combining similar power terms to improve accuracy and avoid spurious
+          overflow/underflow.
+        </p>
+<p>
+          In addition there are optimisations for the situation where <span class="emphasis"><em>delta</em></span>
+          is a small integer: in which case this function is basically the reciprocal
+          of a rising factorial, or where both arguments are smallish integers: in
+          which case table lookup of factorials can be used to calculate the ratio.
+        </p>
+</div>
+<table xmlns:rev="http://www.cs.rpi.edu/~gregod/boost/tools/doc/revision" width="100%"><tr>
+<td align="left"></td>
+<td align="right"><div class="copyright-footer">Copyright © 2006 , 2007, 2008 John Maddock, Paul A. Bristow, Hubert
+      Holin, Xiaogang Zhang, Bruno Lalande and Gautam Sewani<p>
+        Distributed under the Boost Software License, Version 1.0. (See accompanying
+        file LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_0.txt)
+      </p>
+</div></td>
+</tr></table>
+<hr>
+<div class="spirit-nav">
+<a accesskey="p" href="digamma.html"><img src="../../../../../doc/html/images/prev.png" alt="Prev"></a><a accesskey="u" href="../sf_gamma.html"><img src="../../../../../doc/html/images/up.png" alt="Up"></a><a accesskey="h" href="../../../index.html"><img src="../../../../../doc/html/images/home.png" alt="Home"></a><a accesskey="n" href="igamma.html"><img src="../../../../../doc/html/images/next.png" alt="Next"></a>
+</div>
+</body>
+</html>

Added: sandbox/tools/auto_index/example/math/doc/sf_and_dist/html/math_toolkit/special/sf_gamma/igamma.html
==============================================================================
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+++ sandbox/tools/auto_index/example/math/doc/sf_and_dist/html/math_toolkit/special/sf_gamma/igamma.html	2008-11-28 05:25:28 EST (Fri, 28 Nov 2008)
@@ -0,0 +1,1054 @@
+<html>
+<head>
+<meta http-equiv="Content-Type" content="text/html; charset=ISO-8859-1">
+<title>Incomplete Gamma Functions</title>
+<link rel="stylesheet" href="../../../boostbook.css" type="text/css">
+<meta name="generator" content="DocBook XSL Stylesheets Vsnapshot_8125">
+<link rel="home" href="../../../index.html" title="Math Toolkit">
+<link rel="up" href="../sf_gamma.html" title="Gamma Functions">
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+<body bgcolor="white" text="black" link="#0000FF" vlink="#840084" alink="#0000FF">
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+<td valign="top"><img alt="Boost C++ Libraries" width="277" height="86" src="../../../../../boost.png"></td>
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+<a accesskey="p" href="gamma_ratios.html"><img src="../../../../../doc/html/images/prev.png" alt="Prev"></a><a accesskey="u" href="../sf_gamma.html"><img src="../../../../../doc/html/images/up.png" alt="Up"></a><a accesskey="h" href="../../../index.html"><img src="../../../../../doc/html/images/home.png" alt="Home"></a><a accesskey="n" href="igamma_inv.html"><img src="../../../../../doc/html/images/next.png" alt="Next"></a>
+</div>
+<div class="section" lang="en">
+<div class="titlepage"><div><div><h4 class="title">
+<a name="math_toolkit.special.sf_gamma.igamma"></a><a class="link" href="igamma.html" title="Incomplete Gamma Functions"> Incomplete Gamma
+        Functions</a>
+</h4></div></div></div>
+<a name="math_toolkit.special.sf_gamma.igamma.synopsis"></a><h5>
+<a name="id706762"></a>
+          <a class="link" href="igamma.html#math_toolkit.special.sf_gamma.igamma.synopsis">Synopsis</a>
+        </h5>
+<p>
+          
+</p>
+<pre class="programlisting"><span class="preprocessor">#include</span> <span class="special">&lt;</span><span class="identifier">boost</span><span class="special">/</span><span class="identifier">math</span><span class="special">/</span><span class="identifier">special_functions</span><span class="special">/</span><span class="identifier">gamma</span><span class="special">.</span><span class="identifier">hpp</span><span class="special">&gt;</span>
+</pre>
+<p>
+        </p>
+<pre class="programlisting"><span class="keyword">namespace</span> <span class="identifier">boost</span><span class="special">{</span> <span class="keyword">namespace</span> <span class="identifier">math</span><span class="special">{</span>
+
+<span class="keyword">template</span> <span class="special">&lt;</span><span class="keyword">class</span> <span class="identifier">T1</span><span class="special">,</span> <span class="keyword">class</span> <span class="identifier">T2</span><span class="special">&gt;</span>
+<a class="link" href="../../main_overview/result_type.html" title="Calculation of the Type of the Result"><span class="emphasis"><em>calculated-result-type</em></span></a> <span class="identifier">gamma_p</span><span class="special">(</span><span class="identifier">T1</span> <span class="identifier">a</span><span class="special">,</span> <span class="identifier">T2</span> <span class="identifier">z</span><span class="special">);</span>
+
+<span class="keyword">template</span> <span class="special">&lt;</span><span class="keyword">class</span> <span class="identifier">T1</span><span class="special">,</span> <span class="keyword">class</span> <span class="identifier">T2</span><span class="special">,</span> <span class="keyword">class</span> <a class="link" href="../../policy.html" title="Policies">Policy</a><span class="special">&gt;</span>
+<a class="link" href="../../main_overview/result_type.html" title="Calculation of the Type of the Result"><span class="emphasis"><em>calculated-result-type</em></span></a> <span class="identifier">gamma_p</span><span class="special">(</span><span class="identifier">T1</span> <span class="identifier">a</span><span class="special">,</span> <span class="identifier">T2</span> <span class="identifier">z</span><span class="special">,</span> <span class="keyword">const</span> <a class="link" href="../../policy.html" title="Policies">Policy</a><span class="special">&amp;);</span>
+
+<span class="keyword">template</span> <span class="special">&lt;</span><span class="keyword">class</span> <span class="identifier">T1</span><span class="special">,</span> <span class="keyword">class</span> <span class="identifier">T2</span><span class="special">&gt;</span>
+<a class="link" href="../../main_overview/result_type.html" title="Calculation of the Type of the Result"><span class="emphasis"><em>calculated-result-type</em></span></a> <span class="identifier">gamma_q</span><span class="special">(</span><span class="identifier">T1</span> <span class="identifier">a</span><span class="special">,</span> <span class="identifier">T2</span> <span class="identifier">z</span><span class="special">);</span>
+
+<span class="keyword">template</span> <span class="special">&lt;</span><span class="keyword">class</span> <span class="identifier">T1</span><span class="special">,</span> <span class="keyword">class</span> <span class="identifier">T2</span><span class="special">,</span> <span class="keyword">class</span> <a class="link" href="../../policy.html" title="Policies">Policy</a><span class="special">&gt;</span>
+<a class="link" href="../../main_overview/result_type.html" title="Calculation of the Type of the Result"><span class="emphasis"><em>calculated-result-type</em></span></a> <span class="identifier">gamma_q</span><span class="special">(</span><span class="identifier">T1</span> <span class="identifier">a</span><span class="special">,</span> <span class="identifier">T2</span> <span class="identifier">z</span><span class="special">,</span> <span class="keyword">const</span> <a class="link" href="../../policy.html" title="Policies">Policy</a><span class="special">&amp;);</span>
+
+<span class="keyword">template</span> <span class="special">&lt;</span><span class="keyword">class</span> <span class="identifier">T1</span><span class="special">,</span> <span class="keyword">class</span> <span class="identifier">T2</span><span class="special">&gt;</span>
+<a class="link" href="../../main_overview/result_type.html" title="Calculation of the Type of the Result"><span class="emphasis"><em>calculated-result-type</em></span></a> <span class="identifier">tgamma_lower</span><span class="special">(</span><span class="identifier">T1</span> <span class="identifier">a</span><span class="special">,</span> <span class="identifier">T2</span> <span class="identifier">z</span><span class="special">);</span>
+
+<span class="keyword">template</span> <span class="special">&lt;</span><span class="keyword">class</span> <span class="identifier">T1</span><span class="special">,</span> <span class="keyword">class</span> <span class="identifier">T2</span><span class="special">,</span> <span class="keyword">class</span> <a class="link" href="../../policy.html" title="Policies">Policy</a><span class="special">&gt;</span>
+<a class="link" href="../../main_overview/result_type.html" title="Calculation of the Type of the Result"><span class="emphasis"><em>calculated-result-type</em></span></a> <span class="identifier">tgamma_lower</span><span class="special">(</span><span class="identifier">T1</span> <span class="identifier">a</span><span class="special">,</span> <span class="identifier">T2</span> <span class="identifier">z</span><span class="special">,</span> <span class="keyword">const</span> <a class="link" href="../../policy.html" title="Policies">Policy</a><span class="special">&amp;);</span>
+
+<span class="keyword">template</span> <span class="special">&lt;</span><span class="keyword">class</span> <span class="identifier">T1</span><span class="special">,</span> <span class="keyword">class</span> <span class="identifier">T2</span><span class="special">&gt;</span>
+<a class="link" href="../../main_overview/result_type.html" title="Calculation of the Type of the Result"><span class="emphasis"><em>calculated-result-type</em></span></a> <span class="identifier">tgamma</span><span class="special">(</span><span class="identifier">T1</span> <span class="identifier">a</span><span class="special">,</span> <span class="identifier">T2</span> <span class="identifier">z</span><span class="special">);</span>
+
+<span class="keyword">template</span> <span class="special">&lt;</span><span class="keyword">class</span> <span class="identifier">T1</span><span class="special">,</span> <span class="keyword">class</span> <span class="identifier">T2</span><span class="special">,</span> <span class="keyword">class</span> <a class="link" href="../../policy.html" title="Policies">Policy</a><span class="special">&gt;</span>
+<a class="link" href="../../main_overview/result_type.html" title="Calculation of the Type of the Result"><span class="emphasis"><em>calculated-result-type</em></span></a> <span class="identifier">tgamma</span><span class="special">(</span><span class="identifier">T1</span> <span class="identifier">a</span><span class="special">,</span> <span class="identifier">T2</span> <span class="identifier">z</span><span class="special">,</span> <span class="keyword">const</span> <a class="link" href="../../policy.html" title="Policies">Policy</a><span class="special">&amp;);</span>
+
+<span class="special">}}</span> <span class="comment">// namespaces
+</span></pre>
+<a name="math_toolkit.special.sf_gamma.igamma.description"></a><h5>
+<a name="id707872"></a>
+          <a class="link" href="igamma.html#math_toolkit.special.sf_gamma.igamma.description">Description</a>
+        </h5>
+<p>
+          There are four <a href="http://mathworld.wolfram.com/IncompleteGammaFunction.html" target="_top">incomplete
+          gamma functions</a>: two are normalised versions (also known as <span class="emphasis"><em>regularized</em></span>
+          incomplete gamma functions) that return values in the range [0, 1], and
+          two are non-normalised and return values in the range [0, &#915;(a)]. Users interested
+          in statistical applications should use the <a href="http://mathworld.wolfram.com/RegularizedGammaFunction.html" target="_top">normalised
+          versions (gamma_p and gamma_q)</a>.
+        </p>
+<p>
+          All of these functions require <span class="emphasis"><em>a &gt; 0</em></span> and <span class="emphasis"><em>z
+          &gt;= 0</em></span>, otherwise they return the result of <a class="link" href="../../main_overview/error_handling.html#domain_error">domain_error</a>.
+        </p>
+<p>
+          </p>
+<p>
+            The final <a class="link" href="../../policy.html" title="Policies">Policy</a> argument
+            is optional and can be used to control the behaviour of the function:
+            how it handles errors, what level of precision to use etc. Refer to the
+            <a class="link" href="../../policy.html" title="Policies">policy documentation for more details</a>.
+          </p>
+<p>
+        </p>
+<p>
+          The return type of these functions is computed using the <a class="link" href="../../main_overview/result_type.html" title="Calculation of the Type of the Result"><span class="emphasis"><em>result
+          type calculation rules</em></span></a> when T1 and T2 are different types,
+          otherwise the return type is simply T1.
+        </p>
+<pre class="programlisting"><span class="keyword">template</span> <span class="special">&lt;</span><span class="keyword">class</span> <span class="identifier">T1</span><span class="special">,</span> <span class="keyword">class</span> <span class="identifier">T2</span><span class="special">&gt;</span>
+<a class="link" href="../../main_overview/result_type.html" title="Calculation of the Type of the Result"><span class="emphasis"><em>calculated-result-type</em></span></a> <span class="identifier">gamma_p</span><span class="special">(</span><span class="identifier">T1</span> <span class="identifier">a</span><span class="special">,</span> <span class="identifier">T2</span> <span class="identifier">z</span><span class="special">);</span>
+
+<span class="keyword">template</span> <span class="special">&lt;</span><span class="keyword">class</span> <span class="identifier">T1</span><span class="special">,</span> <span class="keyword">class</span> <span class="identifier">T2</span><span class="special">,</span> <span class="keyword">class</span> <span class="identifier">Policy</span><span class="special">&gt;</span>
+<a class="link" href="../../main_overview/result_type.html" title="Calculation of the Type of the Result"><span class="emphasis"><em>calculated-result-type</em></span></a> <span class="identifier">gamma_p</span><span class="special">(</span><span class="identifier">T1</span> <span class="identifier">a</span><span class="special">,</span> <span class="identifier">T2</span> <span class="identifier">z</span><span class="special">,</span> <span class="keyword">const</span> <a class="link" href="../../policy.html" title="Policies">Policy</a><span class="special">&amp;);</span>
+</pre>
+<p>
+          Returns the normalised lower incomplete gamma function of a and z:
+        </p>
+<p>
+          <span class="inlinemediaobject"><img src="../../../../equations/igamma4.png"></span>
+        </p>
+<p>
+          This function changes rapidly from 0 to 1 around the point z == a:
+        </p>
+<p>
+          <span class="inlinemediaobject"><img src="../../../../graphs/gamma_p.png" align="middle"></span>
+        </p>
+<pre class="programlisting"><span class="keyword">template</span> <span class="special">&lt;</span><span class="keyword">class</span> <span class="identifier">T1</span><span class="special">,</span> <span class="keyword">class</span> <span class="identifier">T2</span><span class="special">&gt;</span>
+<a class="link" href="../../main_overview/result_type.html" title="Calculation of the Type of the Result"><span class="emphasis"><em>calculated-result-type</em></span></a> <span class="identifier">gamma_q</span><span class="special">(</span><span class="identifier">T1</span> <span class="identifier">a</span><span class="special">,</span> <span class="identifier">T2</span> <span class="identifier">z</span><span class="special">);</span>
+
+<span class="keyword">template</span> <span class="special">&lt;</span><span class="keyword">class</span> <span class="identifier">T1</span><span class="special">,</span> <span class="keyword">class</span> <span class="identifier">T2</span><span class="special">,</span> <span class="keyword">class</span> <a class="link" href="../../policy.html" title="Policies">Policy</a><span class="special">&gt;</span>
+<a class="link" href="../../main_overview/result_type.html" title="Calculation of the Type of the Result"><span class="emphasis"><em>calculated-result-type</em></span></a> <span class="identifier">gamma_q</span><span class="special">(</span><span class="identifier">T1</span> <span class="identifier">a</span><span class="special">,</span> <span class="identifier">T2</span> <span class="identifier">z</span><span class="special">,</span> <span class="keyword">const</span> <a class="link" href="../../policy.html" title="Policies">Policy</a><span class="special">&amp;);</span>
+</pre>
+<p>
+          Returns the normalised upper incomplete gamma function of a and z:
+        </p>
+<p>
+          <span class="inlinemediaobject"><img src="../../../../equations/igamma3.png"></span>
+        </p>
+<p>
+          This function changes rapidly from 1 to 0 around the point z == a:
+        </p>
+<p>
+          <span class="inlinemediaobject"><img src="../../../../graphs/gamma_q.png" align="middle"></span>
+        </p>
+<pre class="programlisting"><span class="keyword">template</span> <span class="special">&lt;</span><span class="keyword">class</span> <span class="identifier">T1</span><span class="special">,</span> <span class="keyword">class</span> <span class="identifier">T2</span><span class="special">&gt;</span>
+<a class="link" href="../../main_overview/result_type.html" title="Calculation of the Type of the Result"><span class="emphasis"><em>calculated-result-type</em></span></a> <span class="identifier">tgamma_lower</span><span class="special">(</span><span class="identifier">T1</span> <span class="identifier">a</span><span class="special">,</span> <span class="identifier">T2</span> <span class="identifier">z</span><span class="special">);</span>
+
+<span class="keyword">template</span> <span class="special">&lt;</span><span class="keyword">class</span> <span class="identifier">T1</span><span class="special">,</span> <span class="keyword">class</span> <span class="identifier">T2</span><span class="special">,</span> <span class="keyword">class</span> <a class="link" href="../../policy.html" title="Policies">Policy</a><span class="special">&gt;</span>
+<a class="link" href="../../main_overview/result_type.html" title="Calculation of the Type of the Result"><span class="emphasis"><em>calculated-result-type</em></span></a> <span class="identifier">tgamma_lower</span><span class="special">(</span><span class="identifier">T1</span> <span class="identifier">a</span><span class="special">,</span> <span class="identifier">T2</span> <span class="identifier">z</span><span class="special">,</span> <span class="keyword">const</span> <a class="link" href="../../policy.html" title="Policies">Policy</a><span class="special">&amp;);</span>
+</pre>
+<p>
+          Returns the full (non-normalised) lower incomplete gamma function of a
+          and z:
+        </p>
+<p>
+          <span class="inlinemediaobject"><img src="../../../../equations/igamma2.png"></span>
+        </p>
+<pre class="programlisting"><span class="keyword">template</span> <span class="special">&lt;</span><span class="keyword">class</span> <span class="identifier">T1</span><span class="special">,</span> <span class="keyword">class</span> <span class="identifier">T2</span><span class="special">&gt;</span>
+<a class="link" href="../../main_overview/result_type.html" title="Calculation of the Type of the Result"><span class="emphasis"><em>calculated-result-type</em></span></a> <span class="identifier">tgamma</span><span class="special">(</span><span class="identifier">T1</span> <span class="identifier">a</span><span class="special">,</span> <span class="identifier">T2</span> <span class="identifier">z</span><span class="special">);</span>
+
+<span class="keyword">template</span> <span class="special">&lt;</span><span class="keyword">class</span> <span class="identifier">T1</span><span class="special">,</span> <span class="keyword">class</span> <span class="identifier">T2</span><span class="special">,</span> <span class="keyword">class</span> <a class="link" href="../../policy.html" title="Policies">Policy</a><span class="special">&gt;</span>
+<a class="link" href="../../main_overview/result_type.html" title="Calculation of the Type of the Result"><span class="emphasis"><em>calculated-result-type</em></span></a> <span class="identifier">tgamma</span><span class="special">(</span><span class="identifier">T1</span> <span class="identifier">a</span><span class="special">,</span> <span class="identifier">T2</span> <span class="identifier">z</span><span class="special">,</span> <span class="keyword">const</span> <a class="link" href="../../policy.html" title="Policies">Policy</a><span class="special">&amp;);</span>
+</pre>
+<p>
+          Returns the full (non-normalised) upper incomplete gamma function of a
+          and z:
+        </p>
+<p>
+          <span class="inlinemediaobject"><img src="../../../../equations/igamma1.png"></span>
+        </p>
+<a name="math_toolkit.special.sf_gamma.igamma.accuracy"></a><h5>
+<a name="id709213"></a>
+          <a class="link" href="igamma.html#math_toolkit.special.sf_gamma.igamma.accuracy">Accuracy</a>
+        </h5>
+<p>
+          The following tables give peak and mean relative errors in over various
+          domains of a and z, along with comparisons to the GSL-1.9
+          and Cephes libraries.
+          Note that only results for the widest floating point type on the system
+          are given as narrower types have <a class="link" href="../../backgrounders/relative_error.html#zero_error">effectively
+          zero error</a>.
+        </p>
+<p>
+          Note that errors grow as <span class="emphasis"><em>a</em></span> grows larger.
+        </p>
+<p>
+          Note also that the higher error rates for the 80 and 128 bit long double
+          results are somewhat misleading: expected results that are zero at 64-bit
+          double precision may be non-zero - but exceptionally small - with the larger
+          exponent range of a long double. These results therefore reflect the more
+          extreme nature of the tests conducted for these types.
+        </p>
+<p>
+          All values are in units of epsilon.
+        </p>
+<div class="table">
+<a name="id709296"></a><p class="title"><b>Table 18. Errors In the Function gamma_p(a,z)</b></p>
+<div class="table-contents"><table class="table" summary="Errors In the Function gamma_p(a,z)">
+<colgroup>
+<col>
+<col>
+<col>
+<col>
+<col>
+</colgroup>
+<thead><tr>
+<th>
+              <p>
+                Significand Size
+              </p>
+              </th>
+<th>
+              <p>
+                Platform and Compiler
+              </p>
+              </th>
+<th>
+              <p>
+                0.5 &lt; a &lt; 100
+              </p>
+              <p>
+                and
+              </p>
+              <p>
+                0.01*a &lt; z &lt; 100*a
+              </p>
+              </th>
+<th>
+              <p>
+                1x10<sup>-12</sup> &lt; a &lt; 5x10<sup>-2</sup>
+              </p>
+              <p>
+                and
+              </p>
+              <p>
+                0.01*a &lt; z &lt; 100*a
+              </p>
+              </th>
+<th>
+              <p>
+                1e-6 &lt; a &lt; 1.7x10<sup>6</sup>
+              </p>
+              <p>
+                and
+              </p>
+              <p>
+                1 &lt; z &lt; 100*a
+              </p>
+              </th>
+</tr></thead>
+<tbody>
+<tr>
+<td>
+              <p>
+                53
+              </p>
+              </td>
+<td>
+              <p>
+                Win32, Visual C++ 8
+              </p>
+              </td>
+<td>
+              <p>
+                Peak=36 Mean=9.1
+              </p>
+              <p>
+                (GSL Peak=342 Mean=46)
+              </p>
+              <p>
+                (Cephes Peak=491
+                Mean=102)
+              </p>
+              </td>
+<td>
+              <p>
+                Peak=4.5 Mean=1.4
+              </p>
+              <p>
+                (GSL Peak=4.8 Mean=0.76)
+              </p>
+              <p>
+                (Cephes Peak=21
+                Mean=5.6)
+              </p>
+              </td>
+<td>
+              <p>
+                Peak=244 Mean=21
+              </p>
+              <p>
+                (GSL Peak=1022 Mean=1054)
+              </p>
+              <p>
+                (Cephes Peak~8x10<sup>6</sup> Mean~7x10<sup>4</sup>)
+              </p>
+              </td>
+</tr>
+<tr>
+<td>
+              <p>
+                64
+              </p>
+              </td>
+<td>
+              <p>
+                RedHat Linux IA32, gcc-3.3
+              </p>
+              </td>
+<td>
+              <p>
+                Peak=241 Mean=36
+              </p>
+              </td>
+<td>
+              <p>
+                Peak=4.7 Mean=1.5
+              </p>
+              </td>
+<td>
+              <p>
+                Peak~30,220 Mean=1929
+              </p>
+              </td>
+</tr>
+<tr>
+<td>
+              <p>
+                64
+              </p>
+              </td>
+<td>
+              <p>
+                Redhat Linux IA64, gcc-3.4
+              </p>
+              </td>
+<td>
+              <p>
+                Peak=41 Mean=10
+              </p>
+              </td>
+<td>
+              <p>
+                Peak=4.7 Mean=1.4
+              </p>
+              </td>
+<td>
+              <p>
+                Peak~30,790 Mean=1864
+              </p>
+              </td>
+</tr>
+<tr>
+<td>
+              <p>
+                113
+              </p>
+              </td>
+<td>
+              <p>
+                HPUX IA64, aCC A.06.06
+              </p>
+              </td>
+<td>
+              <p>
+                Peak=40.2 Mean=10.2
+              </p>
+              </td>
+<td>
+              <p>
+                Peak=5 Mean=1.6
+              </p>
+              </td>
+<td>
+              <p>
+                Peak=5,476 Mean=440
+              </p>
+              </td>
+</tr>
+</tbody>
+</table></div>
+</div>
+<br class="table-break"><div class="table">
+<a name="id709638"></a><p class="title"><b>Table 19. Errors In the Function gamma_q(a,z)</b></p>
+<div class="table-contents"><table class="table" summary="Errors In the Function gamma_q(a,z)">
+<colgroup>
+<col>
+<col>
+<col>
+<col>
+<col>
+</colgroup>
+<thead><tr>
+<th>
+              <p>
+                Significand Size
+              </p>
+              </th>
+<th>
+              <p>
+                Platform and Compiler
+              </p>
+              </th>
+<th>
+              <p>
+                0.5 &lt; a &lt; 100
+              </p>
+              <p>
+                and
+              </p>
+              <p>
+                0.01*a &lt; z &lt; 100*a
+              </p>
+              </th>
+<th>
+              <p>
+                1x10<sup>-12</sup> &lt; a &lt; 5x10<sup>-2</sup>
+              </p>
+              <p>
+                and
+              </p>
+              <p>
+                0.01*a &lt; z &lt; 100*a
+              </p>
+              </th>
+<th>
+              <p>
+                1x10<sup>-6</sup> &lt; a &lt; 1.7x10<sup>6</sup>
+              </p>
+              <p>
+                and
+              </p>
+              <p>
+                1 &lt; z &lt; 100*a
+              </p>
+              </th>
+</tr></thead>
+<tbody>
+<tr>
+<td>
+              <p>
+                53
+              </p>
+              </td>
+<td>
+              <p>
+                Win32, Visual C++ 8
+              </p>
+              </td>
+<td>
+              <p>
+                Peak=28.3 Mean=7.2
+              </p>
+              <p>
+                (GSL Peak=201 Mean=13)
+              </p>
+              <p>
+                (Cephes Peak=556
+                Mean=97)
+              </p>
+              </td>
+<td>
+              <p>
+                Peak=4.8 Mean=1.6
+              </p>
+              <p>
+                (GSL Peak~1.3x10<sup>10</sup> Mean=1x10<sup>+9</sup>)
+              </p>
+              <p>
+                (Cephes Peak~3x10<sup>11</sup> Mean=4x10<sup>10</sup>)
+              </p>
+              </td>
+<td>
+              <p>
+                Peak=469 Mean=33
+              </p>
+              <p>
+                (GSL Peak=27,050 Mean=2159)
+              </p>
+              <p>
+                (Cephes Peak~8x10<sup>6</sup> Mean~7x10<sup>5</sup>)
+              </p>
+              </td>
+</tr>
+<tr>
+<td>
+              <p>
+                64
+              </p>
+              </td>
+<td>
+              <p>
+                RedHat Linux IA32, gcc-3.3
+              </p>
+              </td>
+<td>
+              <p>
+                Peak=280 Mean=33
+              </p>
+              </td>
+<td>
+              <p>
+                Peak=4.1 Mean=1.6
+              </p>
+              </td>
+<td>
+              <p>
+                Peak=11,490 Mean=732
+              </p>
+              </td>
+</tr>
+<tr>
+<td>
+              <p>
+                64
+              </p>
+              </td>
+<td>
+              <p>
+                Redhat Linux IA64, gcc-3.4
+              </p>
+              </td>
+<td>
+              <p>
+                Peak=32 Mean=9.4
+              </p>
+              </td>
+<td>
+              <p>
+                Peak=4.7 Mean=1.5
+              </p>
+              </td>
+<td>
+              <p>
+                Peak=6815 Mean=414
+              </p>
+              </td>
+</tr>
+<tr>
+<td>
+              <p>
+                113
+              </p>
+              </td>
+<td>
+              <p>
+                HPUX IA64, aCC A.06.06
+              </p>
+              </td>
+<td>
+              <p>
+                Peak=37 Mean=10
+              </p>
+              </td>
+<td>
+              <p>
+                Peak=11.2 Mean=2.0
+              </p>
+              </td>
+<td>
+              <p>
+                Peak=4,999 Mean=298
+              </p>
+              </td>
+</tr>
+</tbody>
+</table></div>
+</div>
+<br class="table-break"><div class="table">
+<a name="id709997"></a><p class="title"><b>Table 20. Errors In the Function tgamma_lower(a,z)</b></p>
+<div class="table-contents"><table class="table" summary="Errors In the Function tgamma_lower(a,z)">
+<colgroup>
+<col>
+<col>
+<col>
+<col>
+</colgroup>
+<thead><tr>
+<th>
+              <p>
+                Significand Size
+              </p>
+              </th>
+<th>
+              <p>
+                Platform and Compiler
+              </p>
+              </th>
+<th>
+              <p>
+                0.5 &lt; a &lt; 100
+              </p>
+              <p>
+                and
+              </p>
+              <p>
+                0.01*a &lt; z &lt; 100*a
+              </p>
+              </th>
+<th>
+              <p>
+                1x10<sup>-12</sup> &lt; a &lt; 5x10<sup>-2</sup>
+              </p>
+              <p>
+                and
+              </p>
+              <p>
+                0.01*a &lt; z &lt; 100*a
+              </p>
+              </th>
+</tr></thead>
+<tbody>
+<tr>
+<td>
+              <p>
+                53
+              </p>
+              </td>
+<td>
+              <p>
+                Win32, Visual C++ 8
+              </p>
+              </td>
+<td>
+              <p>
+                Peak=5.5 Mean=1.4
+              </p>
+              </td>
+<td>
+              <p>
+                Peak=3.6 Mean=0.78
+              </p>
+              </td>
+</tr>
+<tr>
+<td>
+              <p>
+                64
+              </p>
+              </td>
+<td>
+              <p>
+                RedHat Linux IA32, gcc-3.3
+              </p>
+              </td>
+<td>
+              <p>
+                Peak=402 Mean=79
+              </p>
+              </td>
+<td>
+              <p>
+                Peak=3.4 Mean=0.8
+              </p>
+              </td>
+</tr>
+<tr>
+<td>
+              <p>
+                64
+              </p>
+              </td>
+<td>
+              <p>
+                Redhat Linux IA64, gcc-3.4
+              </p>
+              </td>
+<td>
+              <p>
+                Peak=6.8 Mean=1.4
+              </p>
+              </td>
+<td>
+              <p>
+                Peak=3.4 Mean=0.78
+              </p>
+              </td>
+</tr>
+<tr>
+<td>
+              <p>
+                113
+              </p>
+              </td>
+<td>
+              <p>
+                HPUX IA64, aCC A.06.06
+              </p>
+              </td>
+<td>
+              <p>
+                Peak=6.1 Mean=1.8
+              </p>
+              </td>
+<td>
+              <p>
+                Peak=3.7 Mean=0.89
+              </p>
+              </td>
+</tr>
+</tbody>
+</table></div>
+</div>
+<br class="table-break"><div class="table">
+<a name="id710225"></a><p class="title"><b>Table 21. Errors In the Function tgamma(a,z)</b></p>
+<div class="table-contents"><table class="table" summary="Errors In the Function tgamma(a,z)">
+<colgroup>
+<col>
+<col>
+<col>
+<col>
+</colgroup>
+<thead><tr>
+<th>
+              <p>
+                Significand Size
+              </p>
+              </th>
+<th>
+              <p>
+                Platform and Compiler
+              </p>
+              </th>
+<th>
+              <p>
+                0.5 &lt; a &lt; 100
+              </p>
+              <p>
+                and
+              </p>
+              <p>
+                0.01*a &lt; z &lt; 100*a
+              </p>
+              </th>
+<th>
+              <p>
+                1x10<sup>-12</sup> &lt; a &lt; 5x10<sup>-2</sup>
+              </p>
+              <p>
+                and
+              </p>
+              <p>
+                0.01*a &lt; z &lt; 100*a
+              </p>
+              </th>
+</tr></thead>
+<tbody>
+<tr>
+<td>
+              <p>
+                53
+              </p>
+              </td>
+<td>
+              <p>
+                Win32, Visual C++ 8
+              </p>
+              </td>
+<td>
+              <p>
+                Peak=5.9 Mean=1.5
+              </p>
+              </td>
+<td>
+              <p>
+                Peak=1.8 Mean=0.6
+              </p>
+              </td>
+</tr>
+<tr>
+<td>
+              <p>
+                64
+              </p>
+              </td>
+<td>
+              <p>
+                RedHat Linux IA32, gcc-3.3
+              </p>
+              </td>
+<td>
+              <p>
+                Peak=596 Mean=116
+              </p>
+              </td>
+<td>
+              <p>
+                Peak=3.2 Mean=0.84
+              </p>
+              </td>
+</tr>
+<tr>
+<td>
+              <p>
+                64
+              </p>
+              </td>
+<td>
+              <p>
+                Redhat Linux IA64, gcc-3.4.4
+              </p>
+              </td>
+<td>
+              <p>
+                Peak=40.2 Mean=2.5
+              </p>
+              </td>
+<td>
+              <p>
+                Peak=3.2 Mean=0.8
+              </p>
+              </td>
+</tr>
+<tr>
+<td>
+              <p>
+                113
+              </p>
+              </td>
+<td>
+              <p>
+                HPUX IA64, aCC A.06.06
+              </p>
+              </td>
+<td>
+              <p>
+                Peak=364 Mean=17.6
+              </p>
+              </td>
+<td>
+              <p>
+                Peak=12.7 Mean=1.8
+              </p>
+              </td>
+</tr>
+</tbody>
+</table></div>
+</div>
+<br class="table-break"><a name="math_toolkit.special.sf_gamma.igamma.testing"></a><h5>
+<a name="id710461"></a>
+          <a class="link" href="igamma.html#math_toolkit.special.sf_gamma.igamma.testing">Testing</a>
+        </h5>
+<p>
+          There are two sets of tests: spot tests compare values taken from Mathworld's online evaluator
+          with this implementation to perform a basic "sanity check". Accuracy
+          tests use data generated at very high precision (using NTL's RR class set
+          at 1000-bit precision) using this implementation with a very high precision
+          60-term <a class="link" href="../../backgrounders/lanczos.html" title="The Lanczos Approximation">Lanczos approximation</a>,
+          and some but not all of the special case handling disabled. This is less
+          than satisfactory: an independent method should really be used, but apparently
+          a complete lack of such methods are available. We can't even use a deliberately
+          naive implementation without special case handling since Legendre's continued
+          fraction (see below) is unstable for small a and z.
+        </p>
+<a name="math_toolkit.special.sf_gamma.igamma.implementation"></a><h5>
+<a name="id710520"></a>
+          <a class="link" href="igamma.html#math_toolkit.special.sf_gamma.igamma.implementation">Implementation</a>
+        </h5>
+<p>
+          These four functions share a common implementation since they are all related
+          via:
+        </p>
+<p>
+          1) <span class="inlinemediaobject"><img src="../../../../equations/igamma5.png"></span>
+        </p>
+<p>
+          2) <span class="inlinemediaobject"><img src="../../../../equations/igamma6.png"></span>
+        </p>
+<p>
+          3) <span class="inlinemediaobject"><img src="../../../../equations/igamma7.png"></span>
+        </p>
+<p>
+          The lower incomplete gamma is computed from its series representation:
+        </p>
+<p>
+          4) <span class="inlinemediaobject"><img src="../../../../equations/igamma8.png"></span>
+        </p>
+<p>
+          Or by subtraction of the upper integral from either &#915;(a) or 1 when <span class="emphasis"><em>x
+          &gt; a and x &gt; 1.1</em></span>.
+        </p>
+<p>
+          The upper integral is computed from Legendre's continued fraction representation:
+        </p>
+<p>
+          5) <span class="inlinemediaobject"><img src="../../../../equations/igamma9.png"></span>
+        </p>
+<p>
+          When <span class="emphasis"><em>x &gt; 1.1</em></span> or by subtraction of the lower integral
+          from either &#915;(a) or 1 when <span class="emphasis"><em>x &lt; a</em></span>.
+        </p>
+<p>
+          For <span class="emphasis"><em>x &lt; 1.1</em></span> computation of the upper integral is
+          more complex as the continued fraction representation is unstable in this
+          area. However there is another series representation for the lower integral:
+        </p>
+<p>
+          6) <span class="inlinemediaobject"><img src="../../../../equations/igamma10.png"></span>
+        </p>
+<p>
+          That lends itself to calculation of the upper integral via rearrangement
+          to:
+        </p>
+<p>
+          7) <span class="inlinemediaobject"><img src="../../../../equations/igamma11.png"></span>
+        </p>
+<p>
+          Refer to the documentation for <a class="link" href="../powers/powm1.html" title="powm1">powm1</a>
+          and <a class="link" href="tgamma.html" title="Gamma">tgamma1pm1</a>
+          for details of their implementation. Note however that the precision of
+          <a class="link" href="tgamma.html" title="Gamma">tgamma1pm1</a>
+          is capped to either around 35 digits, or to that of the <a class="link" href="../../backgrounders/lanczos.html" title="The Lanczos Approximation">Lanczos
+          approximation</a> associated with type T - if there is one - whichever
+          of the two is the greater. That therefore imposes a similar limit on the
+          precision of this function in this region.
+        </p>
+<p>
+          For <span class="emphasis"><em>x &lt; 1.1</em></span> the crossover point where the result
+          is ~0.5 no longer occurs for <span class="emphasis"><em>x ~ y</em></span>. Using <span class="emphasis"><em>x
+          * 1.1 &lt; a</em></span> as the crossover criterion for <span class="emphasis"><em>0.5 &lt;
+          x &lt;= 1.1</em></span> keeps the maximum value computed (whether it's the
+          upper or lower interval) to around 0.6. Likewise for <span class="emphasis"><em>x &lt;=
+          0.5</em></span> then using <span class="emphasis"><em>-0.4 / log(x) &lt; a</em></span> as
+          the crossover criterion keeps the maximum value computed to around 0.7
+          (whether it's the upper or lower interval).
+        </p>
+<p>
+          There are two special cases used when a is an integer or half integer,
+          and the crossover conditions listed above indicate that we should compute
+          the upper integral Q. If a is an integer in the range <span class="emphasis"><em>1 &lt;=
+          a &lt; 30</em></span> then the following finite sum is used:
+        </p>
+<p>
+          9) <span class="inlinemediaobject"><img src="../../../../equations/igamma1f.png"></span>
+        </p>
+<p>
+          While for half integers in the range <span class="emphasis"><em>0.5 &lt;= a &lt; 30</em></span>
+          then the following finite sum is used:
+        </p>
+<p>
+          10) <span class="inlinemediaobject"><img src="../../../../equations/igamma2f.png"></span>
+        </p>
+<p>
+          These are both more stable and more efficient than the continued fraction
+          alternative.
+        </p>
+<p>
+          When the argument <span class="emphasis"><em>a</em></span> is large, and <span class="emphasis"><em>x ~ a</em></span>
+          then the series (4) and continued fraction (5) above are very slow to converge.
+          In this area an expansion due to Temme is used:
+        </p>
+<p>
+          11) <span class="inlinemediaobject"><img src="../../../../equations/igamma16.png"></span>
+        </p>
+<p>
+          12) <span class="inlinemediaobject"><img src="../../../../equations/igamma17.png"></span>
+        </p>
+<p>
+          13) <span class="inlinemediaobject"><img src="../../../../equations/igamma18.png"></span>
+        </p>
+<p>
+          14) <span class="inlinemediaobject"><img src="../../../../equations/igamma19.png"></span>
+        </p>
+<p>
+          The double sum is truncated to a fixed number of terms - to give a specific
+          target precision - and evaluated as a polynomial-of-polynomials. There
+          are versions for up to 128-bit long double precision: types requiring greater
+          precision than that do not use these expansions. The coefficients C<sub>k</sub><sup>n</sup> are
+          computed in advance using the recurrence relations given by Temme. The
+          zone where these expansions are used is
+        </p>
+<pre class="programlisting"><span class="special">(</span><span class="identifier">a</span> <span class="special">&gt;</span> <span class="number">20</span><span class="special">)</span> <span class="special">&amp;&amp;</span> <span class="special">(</span><span class="identifier">a</span> <span class="special">&lt;</span> <span class="number">200</span><span class="special">)</span> <span class="special">&amp;&amp;</span> <span class="identifier">fabs</span><span class="special">(</span><span class="identifier">x</span><span class="special">-</span><span class="identifier">a</span><span class="special">)/</span><span class="identifier">a</span> <span class="special">&lt;</span> <span class="number">0.4</span>
+</pre>
+<p>
+          And:
+        </p>
+<pre class="programlisting"><span class="special">(</span><span class="identifier">a</span> <span class="special">&gt;</span> <span class="number">200</span><span class="special">)</span> <span class="special">&amp;&amp;</span> <span class="special">(</span><span class="identifier">fabs</span><span class="special">(</span><span class="identifier">x</span><span class="special">-</span><span class="identifier">a</span><span class="special">)/</span><span class="identifier">a</span> <span class="special">&lt;</span> <span class="number">4.5</span><span class="special">/</span><span class="identifier">sqrt</span><span class="special">(</span><span class="identifier">a</span><span class="special">))</span>
+</pre>
+<p>
+          The latter range is valid for all types up to 128-bit long doubles, and
+          is designed to ensure that the result is larger than 10<sup>-6</sup>, the first range
+          is used only for types up to 80-bit long doubles. These domains are narrower
+          than the ones recommended by either Temme or Didonato and Morris. However,
+          using a wider range results in large and inexact (i.e. computed) values
+          being passed to the <code class="computeroutput"><span class="identifier">exp</span></code>
+          and <code class="computeroutput"><span class="identifier">erfc</span></code> functions resulting
+          in significantly larger error rates. In other words there is a fine trade
+          off here between efficiency and error. The current limits should keep the
+          number of terms required by (4) and (5) to no more than ~20 at double precision.
+        </p>
+<p>
+          For the normalised incomplete gamma functions, calculation of the leading
+          power terms is central to the accuracy of the function. For smallish a
+          and x combining the power terms with the <a class="link" href="../../backgrounders/lanczos.html" title="The Lanczos Approximation">Lanczos
+          approximation</a> gives the greatest accuracy:
+        </p>
+<p>
+          15) <span class="inlinemediaobject"><img src="../../../../equations/igamma12.png"></span>
+        </p>
+<p>
+          In the event that this causes underflow<span class="emphasis"><em>overflow then the exponent
+          can be reduced by a factor of /a</em></span> and brought inside the power
+          term.
+        </p>
+<p>
+          When a and x are large, we end up with a very large exponent with a base
+          near one: this will not be computed accurately via the pow function, and
+          taking logs simply leads to cancellation errors. The worst of the errors
+          can be avoided by using:
+        </p>
+<p>
+          16) <span class="inlinemediaobject"><img src="../../../../equations/igamma13.png"></span>
+        </p>
+<p>
+          when <span class="emphasis"><em>a-x</em></span> is small and a and x are large. There is
+          still a subtraction and therefore some cancellation errors - but the terms
+          are small so the absolute error will be small - and it is absolute rather
+          than relative error that counts in the argument to the <span class="emphasis"><em>exp</em></span>
+          function. Note that for sufficiently large a and x the errors will still
+          get you eventually, although this does delay the inevitable much longer
+          than other methods. Use of <span class="emphasis"><em>log(1+x)-x</em></span> here is inspired
+          by Temme (see references below).
+        </p>
+<a name="math_toolkit.special.sf_gamma.igamma.references"></a><h5>
+<a name="id711601"></a>
+          <a class="link" href="igamma.html#math_toolkit.special.sf_gamma.igamma.references">References</a>
+        </h5>
+<div class="itemizedlist"><ul type="disc">
+<li>
+            N. M. Temme, A Set of Algorithms for the Incomplete Gamma Functions,
+            Probability in the Engineering and Informational Sciences, 8, 1994.
+          </li>
+<li>
+            N. M. Temme, The Asymptotic Expansion of the Incomplete Gamma Functions,
+            Siam J. Math Anal. Vol 10 No 4, July 1979, p757.
+          </li>
+<li>
+            A. R. Didonato and A. H. Morris, Computation of the Incomplete Gamma
+            Function Ratios and their Inverse. ACM TOMS, Vol 12, No 4, Dec 1986,
+            p377.
+          </li>
+<li>
+            W. Gautschi, The Incomplete Gamma Functions Since Tricomi, In Tricomi's
+            Ideas and Contemporary Applied Mathematics, Atti dei Convegni Lincei,
+            n. 147, Accademia Nazionale dei Lincei, Roma, 1998, pp. 203--237. http://citeseer.ist.psu.edu/gautschi98incomplete.html
+</li>
+</ul></div>
+</div>
+<table xmlns:rev="http://www.cs.rpi.edu/~gregod/boost/tools/doc/revision" width="100%"><tr>
+<td align="left"></td>
+<td align="right"><div class="copyright-footer">Copyright © 2006 , 2007, 2008 John Maddock, Paul A. Bristow, Hubert
+      Holin, Xiaogang Zhang, Bruno Lalande and Gautam Sewani<p>
+        Distributed under the Boost Software License, Version 1.0. (See accompanying
+        file LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_0.txt)
+      </p>
+</div></td>
+</tr></table>
+<hr>
+<div class="spirit-nav">
+<a accesskey="p" href="gamma_ratios.html"><img src="../../../../../doc/html/images/prev.png" alt="Prev"></a><a accesskey="u" href="../sf_gamma.html"><img src="../../../../../doc/html/images/up.png" alt="Up"></a><a accesskey="h" href="../../../index.html"><img src="../../../../../doc/html/images/home.png" alt="Home"></a><a accesskey="n" href="igamma_inv.html"><img src="../../../../../doc/html/images/next.png" alt="Next"></a>
+</div>
+</body>
+</html>

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+++ sandbox/tools/auto_index/example/math/doc/sf_and_dist/html/math_toolkit/special/sf_gamma/igamma_inv.html	2008-11-28 05:25:28 EST (Fri, 28 Nov 2008)
@@ -0,0 +1,264 @@
+<html>
+<head>
+<meta http-equiv="Content-Type" content="text/html; charset=ISO-8859-1">
+<title>Incomplete Gamma Function Inverses</title>
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+</div>
+<div class="section" lang="en">
+<div class="titlepage"><div><div><h4 class="title">
+<a name="math_toolkit.special.sf_gamma.igamma_inv"></a><a class="link" href="igamma_inv.html" title="Incomplete Gamma Function Inverses"> Incomplete
+        Gamma Function Inverses</a>
+</h4></div></div></div>
+<a name="math_toolkit.special.sf_gamma.igamma_inv.synopsis"></a><h5>
+<a name="id711693"></a>
+          <a class="link" href="igamma_inv.html#math_toolkit.special.sf_gamma.igamma_inv.synopsis">Synopsis</a>
+        </h5>
+<p>
+          
+</p>
+<pre class="programlisting"><span class="preprocessor">#include</span> <span class="special">&lt;</span><span class="identifier">boost</span><span class="special">/</span><span class="identifier">math</span><span class="special">/</span><span class="identifier">special_functions</span><span class="special">/</span><span class="identifier">gamma</span><span class="special">.</span><span class="identifier">hpp</span><span class="special">&gt;</span>
+</pre>
+<p>
+        </p>
+<pre class="programlisting"><span class="keyword">namespace</span> <span class="identifier">boost</span><span class="special">{</span> <span class="keyword">namespace</span> <span class="identifier">math</span><span class="special">{</span>
+
+<span class="keyword">template</span> <span class="special">&lt;</span><span class="keyword">class</span> <span class="identifier">T1</span><span class="special">,</span> <span class="keyword">class</span> <span class="identifier">T2</span><span class="special">&gt;</span>
+<a class="link" href="../../main_overview/result_type.html" title="Calculation of the Type of the Result"><span class="emphasis"><em>calculated-result-type</em></span></a> <span class="identifier">gamma_q_inv</span><span class="special">(</span><span class="identifier">T1</span> <span class="identifier">a</span><span class="special">,</span> <span class="identifier">T2</span> <span class="identifier">q</span><span class="special">);</span>
+
+<span class="keyword">template</span> <span class="special">&lt;</span><span class="keyword">class</span> <span class="identifier">T1</span><span class="special">,</span> <span class="keyword">class</span> <span class="identifier">T2</span><span class="special">,</span> <span class="keyword">class</span> <a class="link" href="../../policy.html" title="Policies">Policy</a><span class="special">&gt;</span>
+<a class="link" href="../../main_overview/result_type.html" title="Calculation of the Type of the Result"><span class="emphasis"><em>calculated-result-type</em></span></a> <span class="identifier">gamma_q_inv</span><span class="special">(</span><span class="identifier">T1</span> <span class="identifier">a</span><span class="special">,</span> <span class="identifier">T2</span> <span class="identifier">q</span><span class="special">,</span> <span class="keyword">const</span> <a class="link" href="../../policy.html" title="Policies">Policy</a><span class="special">&amp;);</span>
+
+<span class="keyword">template</span> <span class="special">&lt;</span><span class="keyword">class</span> <span class="identifier">T1</span><span class="special">,</span> <span class="keyword">class</span> <span class="identifier">T2</span><span class="special">&gt;</span>
+<a class="link" href="../../main_overview/result_type.html" title="Calculation of the Type of the Result"><span class="emphasis"><em>calculated-result-type</em></span></a> <span class="identifier">gamma_p_inv</span><span class="special">(</span><span class="identifier">T1</span> <span class="identifier">a</span><span class="special">,</span> <span class="identifier">T2</span> <span class="identifier">p</span><span class="special">);</span>
+
+<span class="keyword">template</span> <span class="special">&lt;</span><span class="keyword">class</span> <span class="identifier">T1</span><span class="special">,</span> <span class="keyword">class</span> <span class="identifier">T2</span><span class="special">,</span> <span class="keyword">class</span> <a class="link" href="../../policy.html" title="Policies">Policy</a><span class="special">&gt;</span>
+<a class="link" href="../../main_overview/result_type.html" title="Calculation of the Type of the Result"><span class="emphasis"><em>calculated-result-type</em></span></a> <span class="identifier">gamma_p_inv</span><span class="special">(</span><span class="identifier">T1</span> <span class="identifier">a</span><span class="special">,</span> <span class="identifier">T2</span> <span class="identifier">p</span><span class="special">,</span> <span class="keyword">const</span> <a class="link" href="../../policy.html" title="Policies">Policy</a><span class="special">&amp;);</span>
+
+<span class="keyword">template</span> <span class="special">&lt;</span><span class="keyword">class</span> <span class="identifier">T1</span><span class="special">,</span> <span class="keyword">class</span> <span class="identifier">T2</span><span class="special">&gt;</span>
+<a class="link" href="../../main_overview/result_type.html" title="Calculation of the Type of the Result"><span class="emphasis"><em>calculated-result-type</em></span></a> <span class="identifier">gamma_q_inva</span><span class="special">(</span><span class="identifier">T1</span> <span class="identifier">x</span><span class="special">,</span> <span class="identifier">T2</span> <span class="identifier">q</span><span class="special">);</span>
+
+<span class="keyword">template</span> <span class="special">&lt;</span><span class="keyword">class</span> <span class="identifier">T1</span><span class="special">,</span> <span class="keyword">class</span> <span class="identifier">T2</span><span class="special">,</span> <span class="keyword">class</span> <a class="link" href="../../policy.html" title="Policies">Policy</a><span class="special">&gt;</span>
+<a class="link" href="../../main_overview/result_type.html" title="Calculation of the Type of the Result"><span class="emphasis"><em>calculated-result-type</em></span></a> <span class="identifier">gamma_q_inva</span><span class="special">(</span><span class="identifier">T1</span> <span class="identifier">x</span><span class="special">,</span> <span class="identifier">T2</span> <span class="identifier">q</span><span class="special">,</span> <span class="keyword">const</span> <a class="link" href="../../policy.html" title="Policies">Policy</a><span class="special">&amp;);</span>
+
+<span class="keyword">template</span> <span class="special">&lt;</span><span class="keyword">class</span> <span class="identifier">T1</span><span class="special">,</span> <span class="keyword">class</span> <span class="identifier">T2</span><span class="special">&gt;</span>
+<a class="link" href="../../main_overview/result_type.html" title="Calculation of the Type of the Result"><span class="emphasis"><em>calculated-result-type</em></span></a> <span class="identifier">gamma_p_inva</span><span class="special">(</span><span class="identifier">T1</span> <span class="identifier">x</span><span class="special">,</span> <span class="identifier">T2</span> <span class="identifier">p</span><span class="special">);</span>
+
+<span class="keyword">template</span> <span class="special">&lt;</span><span class="keyword">class</span> <span class="identifier">T1</span><span class="special">,</span> <span class="keyword">class</span> <span class="identifier">T2</span><span class="special">,</span> <span class="keyword">class</span> <a class="link" href="../../policy.html" title="Policies">Policy</a><span class="special">&gt;</span>
+<a class="link" href="../../main_overview/result_type.html" title="Calculation of the Type of the Result"><span class="emphasis"><em>calculated-result-type</em></span></a> <span class="identifier">gamma_p_inva</span><span class="special">(</span><span class="identifier">T1</span> <span class="identifier">x</span><span class="special">,</span> <span class="identifier">T2</span> <span class="identifier">p</span><span class="special">,</span> <span class="keyword">const</span> <a class="link" href="../../policy.html" title="Policies">Policy</a><span class="special">&amp;);</span>
+
+<span class="special">}}</span> <span class="comment">// namespaces
+</span></pre>
+<a name="math_toolkit.special.sf_gamma.igamma_inv.description"></a><h5>
+<a name="id712804"></a>
+          <a class="link" href="igamma_inv.html#math_toolkit.special.sf_gamma.igamma_inv.description">Description</a>
+        </h5>
+<p>
+          There are four <a href="http://mathworld.wolfram.com/IncompleteGammaFunction.html" target="_top">incomplete
+          gamma function</a> inverses which either compute <span class="emphasis"><em>x</em></span>
+          given <span class="emphasis"><em>a</em></span> and <span class="emphasis"><em>p</em></span> or <span class="emphasis"><em>q</em></span>,
+          or else compute <span class="emphasis"><em>a</em></span> given <span class="emphasis"><em>x</em></span> and
+          either <span class="emphasis"><em>p</em></span> or <span class="emphasis"><em>q</em></span>.
+        </p>
+<p>
+          The return type of these functions is computed using the <a class="link" href="../../main_overview/result_type.html" title="Calculation of the Type of the Result"><span class="emphasis"><em>result
+          type calculation rules</em></span></a> when T1 and T2 are different types,
+          otherwise the return type is simply T1.
+        </p>
+<p>
+          </p>
+<p>
+            The final <a class="link" href="../../policy.html" title="Policies">Policy</a> argument
+            is optional and can be used to control the behaviour of the function:
+            how it handles errors, what level of precision to use etc. Refer to the
+            <a class="link" href="../../policy.html" title="Policies">policy documentation for more details</a>.
+          </p>
+<p>
+        </p>
+<div class="tip"><table border="0" summary="Tip">
+<tr>
+<td rowspan="2" align="center" valign="top" width="25"><img alt="[Tip]" src="../../../../../doc/html/images/tip.png"></td>
+<th align="left">Tip</th>
+</tr>
+<tr><td align="left" valign="top">
+<p>
+            When people normally talk about the inverse of the incomplete gamma function,
+            they are talking about inverting on parameter <span class="emphasis"><em>x</em></span>.
+            These are implemented here as gamma_p_inv and gamma_q_inv, and are by
+            far the most efficient of the inverses presented here.
+          </p>
+<p>
+            The inverse on the <span class="emphasis"><em>a</em></span> parameter finds use in some
+            statistical applications but has to be computed by rather brute force
+            numerical techniques and is consequently several times slower. These
+            are implemented here as gamma_p_inva and gamma_q_inva.
+          </p>
+</td></tr>
+</table></div>
+<pre class="programlisting"><span class="keyword">template</span> <span class="special">&lt;</span><span class="keyword">class</span> <span class="identifier">T1</span><span class="special">,</span> <span class="keyword">class</span> <span class="identifier">T2</span><span class="special">&gt;</span>
+<a class="link" href="../../main_overview/result_type.html" title="Calculation of the Type of the Result"><span class="emphasis"><em>calculated-result-type</em></span></a> <span class="identifier">gamma_q_inv</span><span class="special">(</span><span class="identifier">T1</span> <span class="identifier">a</span><span class="special">,</span> <span class="identifier">T2</span> <span class="identifier">q</span><span class="special">);</span>
+
+<span class="keyword">template</span> <span class="special">&lt;</span><span class="keyword">class</span> <span class="identifier">T1</span><span class="special">,</span> <span class="keyword">class</span> <span class="identifier">T2</span><span class="special">,</span> <span class="keyword">class</span> <a class="link" href="../../policy.html" title="Policies">Policy</a><span class="special">&gt;</span>
+<a class="link" href="../../main_overview/result_type.html" title="Calculation of the Type of the Result"><span class="emphasis"><em>calculated-result-type</em></span></a> <span class="identifier">gamma_q_inv</span><span class="special">(</span><span class="identifier">T1</span> <span class="identifier">a</span><span class="special">,</span> <span class="identifier">T2</span> <span class="identifier">q</span><span class="special">,</span> <span class="keyword">const</span> <a class="link" href="../../policy.html" title="Policies">Policy</a><span class="special">&amp;);</span>
+</pre>
+<p>
+          Returns a value x such that: <code class="computeroutput"><span class="identifier">q</span>
+          <span class="special">=</span> <span class="identifier">gamma_q</span><span class="special">(</span><span class="identifier">a</span><span class="special">,</span>
+          <span class="identifier">x</span><span class="special">);</span></code>
+        </p>
+<p>
+          Requires: <span class="emphasis"><em>a &gt; 0</em></span> and <span class="emphasis"><em>1 &gt;= p,q &gt;=
+          0</em></span>.
+        </p>
+<pre class="programlisting"><span class="keyword">template</span> <span class="special">&lt;</span><span class="keyword">class</span> <span class="identifier">T1</span><span class="special">,</span> <span class="keyword">class</span> <span class="identifier">T2</span><span class="special">&gt;</span>
+<a class="link" href="../../main_overview/result_type.html" title="Calculation of the Type of the Result"><span class="emphasis"><em>calculated-result-type</em></span></a> <span class="identifier">gamma_p_inv</span><span class="special">(</span><span class="identifier">T1</span> <span class="identifier">a</span><span class="special">,</span> <span class="identifier">T2</span> <span class="identifier">p</span><span class="special">);</span>
+
+<span class="keyword">template</span> <span class="special">&lt;</span><span class="keyword">class</span> <span class="identifier">T1</span><span class="special">,</span> <span class="keyword">class</span> <span class="identifier">T2</span><span class="special">,</span> <span class="keyword">class</span> <a class="link" href="../../policy.html" title="Policies">Policy</a><span class="special">&gt;</span>
+<a class="link" href="../../main_overview/result_type.html" title="Calculation of the Type of the Result"><span class="emphasis"><em>calculated-result-type</em></span></a> <span class="identifier">gamma_p_inv</span><span class="special">(</span><span class="identifier">T1</span> <span class="identifier">a</span><span class="special">,</span> <span class="identifier">T2</span> <span class="identifier">p</span><span class="special">,</span> <span class="keyword">const</span> <a class="link" href="../../policy.html" title="Policies">Policy</a><span class="special">&amp;);</span>
+</pre>
+<p>
+          Returns a value x such that: <code class="computeroutput"><span class="identifier">p</span>
+          <span class="special">=</span> <span class="identifier">gamma_p</span><span class="special">(</span><span class="identifier">a</span><span class="special">,</span>
+          <span class="identifier">x</span><span class="special">);</span></code>
+        </p>
+<p>
+          Requires: <span class="emphasis"><em>a &gt; 0</em></span> and <span class="emphasis"><em>1 &gt;= p,q &gt;=
+          0</em></span>.
+        </p>
+<pre class="programlisting"><span class="keyword">template</span> <span class="special">&lt;</span><span class="keyword">class</span> <span class="identifier">T1</span><span class="special">,</span> <span class="keyword">class</span> <span class="identifier">T2</span><span class="special">&gt;</span>
+<a class="link" href="../../main_overview/result_type.html" title="Calculation of the Type of the Result"><span class="emphasis"><em>calculated-result-type</em></span></a> <span class="identifier">gamma_q_inva</span><span class="special">(</span><span class="identifier">T1</span> <span class="identifier">x</span><span class="special">,</span> <span class="identifier">T2</span> <span class="identifier">q</span><span class="special">);</span>
+
+<span class="keyword">template</span> <span class="special">&lt;</span><span class="keyword">class</span> <span class="identifier">T1</span><span class="special">,</span> <span class="keyword">class</span> <span class="identifier">T2</span><span class="special">,</span> <span class="keyword">class</span> <a class="link" href="../../policy.html" title="Policies">Policy</a><span class="special">&gt;</span>
+<a class="link" href="../../main_overview/result_type.html" title="Calculation of the Type of the Result"><span class="emphasis"><em>calculated-result-type</em></span></a> <span class="identifier">gamma_q_inva</span><span class="special">(</span><span class="identifier">T1</span> <span class="identifier">x</span><span class="special">,</span> <span class="identifier">T2</span> <span class="identifier">q</span><span class="special">,</span> <span class="keyword">const</span> <a class="link" href="../../policy.html" title="Policies">Policy</a><span class="special">&amp;);</span>
+</pre>
+<p>
+          Returns a value a such that: <code class="computeroutput"><span class="identifier">q</span>
+          <span class="special">=</span> <span class="identifier">gamma_q</span><span class="special">(</span><span class="identifier">a</span><span class="special">,</span>
+          <span class="identifier">x</span><span class="special">);</span></code>
+        </p>
+<p>
+          Requires: <span class="emphasis"><em>x &gt; 0</em></span> and <span class="emphasis"><em>1 &gt;= p,q &gt;=
+          0</em></span>.
+        </p>
+<pre class="programlisting"><span class="keyword">template</span> <span class="special">&lt;</span><span class="keyword">class</span> <span class="identifier">T1</span><span class="special">,</span> <span class="keyword">class</span> <span class="identifier">T2</span><span class="special">&gt;</span>
+<a class="link" href="../../main_overview/result_type.html" title="Calculation of the Type of the Result"><span class="emphasis"><em>calculated-result-type</em></span></a> <span class="identifier">gamma_p_inva</span><span class="special">(</span><span class="identifier">T1</span> <span class="identifier">x</span><span class="special">,</span> <span class="identifier">T2</span> <span class="identifier">p</span><span class="special">);</span>
+
+<span class="keyword">template</span> <span class="special">&lt;</span><span class="keyword">class</span> <span class="identifier">T1</span><span class="special">,</span> <span class="keyword">class</span> <span class="identifier">T2</span><span class="special">,</span> <span class="keyword">class</span> <a class="link" href="../../policy.html" title="Policies">Policy</a><span class="special">&gt;</span>
+<a class="link" href="../../main_overview/result_type.html" title="Calculation of the Type of the Result"><span class="emphasis"><em>calculated-result-type</em></span></a> <span class="identifier">gamma_p_inva</span><span class="special">(</span><span class="identifier">T1</span> <span class="identifier">x</span><span class="special">,</span> <span class="identifier">T2</span> <span class="identifier">p</span><span class="special">,</span> <span class="keyword">const</span> <a class="link" href="../../policy.html" title="Policies">Policy</a><span class="special">&amp;);</span>
+</pre>
+<p>
+          Returns a value a such that: <code class="computeroutput"><span class="identifier">p</span>
+          <span class="special">=</span> <span class="identifier">gamma_p</span><span class="special">(</span><span class="identifier">a</span><span class="special">,</span>
+          <span class="identifier">x</span><span class="special">);</span></code>
+        </p>
+<p>
+          Requires: <span class="emphasis"><em>x &gt; 0</em></span> and <span class="emphasis"><em>1 &gt;= p,q &gt;=
+          0</em></span>.
+        </p>
+<a name="math_toolkit.special.sf_gamma.igamma_inv.accuracy"></a><h5>
+<a name="id714215"></a>
+          <a class="link" href="igamma_inv.html#math_toolkit.special.sf_gamma.igamma_inv.accuracy">Accuracy</a>
+        </h5>
+<p>
+          The accuracy of these functions doesn't vary much by platform or by the
+          type T. Given that these functions are computed by iterative methods, they
+          are deliberately "detuned" so as not to be too accurate: it is
+          in any case impossible for these function to be more accurate than the
+          regular forward incomplete gamma functions. In practice, the accuracy of
+          these functions is very similar to that of <a class="link" href="igamma.html" title="Incomplete Gamma Functions">gamma_p</a>
+          and <a class="link" href="igamma.html" title="Incomplete Gamma Functions">gamma_q</a>
+          functions.
+        </p>
+<a name="math_toolkit.special.sf_gamma.igamma_inv.testing"></a><h5>
+<a name="id714276"></a>
+          <a class="link" href="igamma_inv.html#math_toolkit.special.sf_gamma.igamma_inv.testing">Testing</a>
+        </h5>
+<p>
+          There are two sets of tests:
+        </p>
+<div class="itemizedlist"><ul type="disc">
+<li>
+            Basic sanity checks attempt to "round-trip" from <span class="emphasis"><em>a</em></span>
+            and <span class="emphasis"><em>x</em></span> to <span class="emphasis"><em>p</em></span> or <span class="emphasis"><em>q</em></span>
+            and back again. These tests have quite generous tolerances: in general
+            both the incomplete gamma, and its inverses, change so rapidly that round
+            tripping to more than a couple of significant digits isn't possible.
+            This is especially true when <span class="emphasis"><em>p</em></span> or <span class="emphasis"><em>q</em></span>
+            is very near one: in this case there isn't enough "information content"
+            in the input to the inverse function to get back where you started.
+          </li>
+<li>
+            Accuracy checks using high precision test values. These measure the accuracy
+            of the result, given exact input values.
+          </li>
+</ul></div>
+<a name="math_toolkit.special.sf_gamma.igamma_inv.implementation"></a><h5>
+<a name="id714358"></a>
+          <a class="link" href="igamma_inv.html#math_toolkit.special.sf_gamma.igamma_inv.implementation">Implementation</a>
+        </h5>
+<p>
+          The functions gamma_p_inv and gamma_q_inv
+          share a common implementation.
+        </p>
+<p>
+          First an initial approximation is computed using the methodology described
+          in:
+        </p>
+<p>
+          <a href="http://portal.acm.org/citation.cfm?id=23109&amp;coll=portal&amp;dl=ACM" target="_top">A.
+          R. Didonato and A. H. Morris, Computation of the Incomplete Gamma Function
+          Ratios and their Inverse, ACM Trans. Math. Software 12 (1986), 377-393.</a>
+        </p>
+<p>
+          Finally, the last few bits are cleaned up using Halley iteration, the iteration
+          limit is set to 2/3 of the number of bits in T, which by experiment is
+          sufficient to ensure that the inverses are at least as accurate as the
+          normal incomplete gamma functions. In testing, no more than 3 iterations
+          are required to produce a result as accurate as the forward incomplete
+          gamma function, and in many cases only one iteration is required.
+        </p>
+<p>
+          The functions gamma_p_inva and gamma_q_inva also share a common implementation
+          but are handled separately from gamma_p_inv and gamma_q_inv.
+        </p>
+<p>
+          An initial approximation for <span class="emphasis"><em>a</em></span> is computed very crudely
+          so that <span class="emphasis"><em>gamma_p(a, x) ~ 0.5</em></span>, this value is then used
+          as a starting point for a generic derivative-free root finding algorithm.
+          As a consequence, these two functions are rather more expensive to compute
+          than the gamma_p_inv or gamma_q_inv functions. Even so, the root is usually
+          found in fewer than 10 iterations.
+        </p>
+</div>
+<table xmlns:rev="http://www.cs.rpi.edu/~gregod/boost/tools/doc/revision" width="100%"><tr>
+<td align="left"></td>
+<td align="right"><div class="copyright-footer">Copyright © 2006 , 2007, 2008 John Maddock, Paul A. Bristow, Hubert
+      Holin, Xiaogang Zhang, Bruno Lalande and Gautam Sewani<p>
+        Distributed under the Boost Software License, Version 1.0. (See accompanying
+        file LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_0.txt)
+      </p>
+</div></td>
+</tr></table>
+<hr>
+<div class="spirit-nav">
+<a accesskey="p" href="igamma.html"><img src="../../../../../doc/html/images/prev.png" alt="Prev"></a><a accesskey="u" href="../sf_gamma.html"><img src="../../../../../doc/html/images/up.png" alt="Up"></a><a accesskey="h" href="../../../index.html"><img src="../../../../../doc/html/images/home.png" alt="Home"></a><a accesskey="n" href="gamma_derivatives.html"><img src="../../../../../doc/html/images/next.png" alt="Next"></a>
+</div>
+</body>
+</html>

Added: sandbox/tools/auto_index/example/math/doc/sf_and_dist/html/math_toolkit/special/sf_gamma/lgamma.html
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+++ sandbox/tools/auto_index/example/math/doc/sf_and_dist/html/math_toolkit/special/sf_gamma/lgamma.html	2008-11-28 05:25:28 EST (Fri, 28 Nov 2008)
@@ -0,0 +1,487 @@
+<html>
+<head>
+<meta http-equiv="Content-Type" content="text/html; charset=ISO-8859-1">
+<title>Log Gamma</title>
+<link rel="stylesheet" href="../../../boostbook.css" type="text/css">
+<meta name="generator" content="DocBook XSL Stylesheets Vsnapshot_8125">
+<link rel="home" href="../../../index.html" title="Math Toolkit">
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+<hr>
+<div class="spirit-nav">
+<a accesskey="p" href="tgamma.html"><img src="../../../../../doc/html/images/prev.png" alt="Prev"></a><a accesskey="u" href="../sf_gamma.html"><img src="../../../../../doc/html/images/up.png" alt="Up"></a><a accesskey="h" href="../../../index.html"><img src="../../../../../doc/html/images/home.png" alt="Home"></a><a accesskey="n" href="digamma.html"><img src="../../../../../doc/html/images/next.png" alt="Next"></a>
+</div>
+<div class="section" lang="en">
+<div class="titlepage"><div><div><h4 class="title">
+<a name="math_toolkit.special.sf_gamma.lgamma"></a><a class="link" href="lgamma.html" title="Log Gamma"> Log Gamma</a>
+</h4></div></div></div>
+<a name="math_toolkit.special.sf_gamma.lgamma.synopsis"></a><h5>
+<a name="id700758"></a>
+          <a class="link" href="lgamma.html#math_toolkit.special.sf_gamma.lgamma.synopsis">Synopsis</a>
+        </h5>
+<p>
+          
+</p>
+<pre class="programlisting"><span class="preprocessor">#include</span> <span class="special">&lt;</span><span class="identifier">boost</span><span class="special">/</span><span class="identifier">math</span><span class="special">/</span><span class="identifier">special_functions</span><span class="special">/</span><span class="identifier">gamma</span><span class="special">.</span><span class="identifier">hpp</span><span class="special">&gt;</span>
+</pre>
+<p>
+        </p>
+<pre class="programlisting"><span class="keyword">namespace</span> <span class="identifier">boost</span><span class="special">{</span> <span class="keyword">namespace</span> <span class="identifier">math</span><span class="special">{</span>
+
+<span class="keyword">template</span> <span class="special">&lt;</span><span class="keyword">class</span> <span class="identifier">T</span><span class="special">&gt;</span>
+<a class="link" href="../../main_overview/result_type.html" title="Calculation of the Type of the Result"><span class="emphasis"><em>calculated-result-type</em></span></a> <span class="identifier">lgamma</span><span class="special">(</span><span class="identifier">T</span> <span class="identifier">z</span><span class="special">);</span>
+
+<span class="keyword">template</span> <span class="special">&lt;</span><span class="keyword">class</span> <span class="identifier">T</span><span class="special">,</span> <span class="keyword">class</span> <a class="link" href="../../policy.html" title="Policies">Policy</a><span class="special">&gt;</span>
+<a class="link" href="../../main_overview/result_type.html" title="Calculation of the Type of the Result"><span class="emphasis"><em>calculated-result-type</em></span></a> <span class="identifier">lgamma</span><span class="special">(</span><span class="identifier">T</span> <span class="identifier">z</span><span class="special">,</span> <span class="keyword">const</span> <a class="link" href="../../policy.html" title="Policies">Policy</a><span class="special">&amp;);</span>
+
+<span class="keyword">template</span> <span class="special">&lt;</span><span class="keyword">class</span> <span class="identifier">T</span><span class="special">&gt;</span>
+<a class="link" href="../../main_overview/result_type.html" title="Calculation of the Type of the Result"><span class="emphasis"><em>calculated-result-type</em></span></a> <span class="identifier">lgamma</span><span class="special">(</span><span class="identifier">T</span> <span class="identifier">z</span><span class="special">,</span> <span class="keyword">int</span><span class="special">*</span> <span class="identifier">sign</span><span class="special">);</span>
+
+<span class="keyword">template</span> <span class="special">&lt;</span><span class="keyword">class</span> <span class="identifier">T</span><span class="special">,</span> <span class="keyword">class</span> <a class="link" href="../../policy.html" title="Policies">Policy</a><span class="special">&gt;</span>
+<a class="link" href="../../main_overview/result_type.html" title="Calculation of the Type of the Result"><span class="emphasis"><em>calculated-result-type</em></span></a> <span class="identifier">lgamma</span><span class="special">(</span><span class="identifier">T</span> <span class="identifier">z</span><span class="special">,</span> <span class="keyword">int</span><span class="special">*</span> <span class="identifier">sign</span><span class="special">,</span> <span class="keyword">const</span> <a class="link" href="../../policy.html" title="Policies">Policy</a><span class="special">&amp;);</span>
+
+<span class="special">}}</span> <span class="comment">// namespaces
+</span></pre>
+<a name="math_toolkit.special.sf_gamma.lgamma.description"></a><h5>
+<a name="id701294"></a>
+          <a class="link" href="lgamma.html#math_toolkit.special.sf_gamma.lgamma.description">Description</a>
+        </h5>
+<p>
+          The lgamma function
+          is defined by:
+        </p>
+<p>
+          <span class="inlinemediaobject"><img src="../../../../equations/lgamm1.png"></span>
+        </p>
+<p>
+          The second form of the function takes a pointer to an integer, which if
+          non-null is set on output to the sign of tgamma(z).
+        </p>
+<p>
+          </p>
+<p>
+            The final <a class="link" href="../../policy.html" title="Policies">Policy</a> argument
+            is optional and can be used to control the behaviour of the function:
+            how it handles errors, what level of precision to use etc. Refer to the
+            <a class="link" href="../../policy.html" title="Policies">policy documentation for more details</a>.
+          </p>
+<p>
+        </p>
+<p>
+          <span class="inlinemediaobject"><img src="../../../../graphs/lgamma.png" align="middle"></span>
+        </p>
+<p>
+          There are effectively two versions of this function internally: a fully
+          generic version that is slow, but reasonably accurate, and a much more
+          efficient approximation that is used where the number of digits in the
+          significand of T correspond to a certain <a class="link" href="../../backgrounders/lanczos.html" title="The Lanczos Approximation">Lanczos
+          approximation</a>. In practice, any built-in floating-point type you
+          will encounter has an appropriate <a class="link" href="../../backgrounders/lanczos.html" title="The Lanczos Approximation">Lanczos
+          approximation</a> defined for it. It is also possible, given enough
+          machine time, to generate further <a class="link" href="../../backgrounders/lanczos.html" title="The Lanczos Approximation">Lanczos
+          approximation</a>'s using the program libs/math/tools/lanczos_generator.cpp.
+        </p>
+<p>
+          The return type of these functions is computed using the <a class="link" href="../../main_overview/result_type.html" title="Calculation of the Type of the Result"><span class="emphasis"><em>result
+          type calculation rules</em></span></a>: the result is of type <code class="computeroutput"><span class="keyword">double</span></code> if T is an integer type, or type
+          T otherwise.
+        </p>
+<a name="math_toolkit.special.sf_gamma.lgamma.accuracy"></a><h5>
+<a name="id701510"></a>
+          <a class="link" href="lgamma.html#math_toolkit.special.sf_gamma.lgamma.accuracy">Accuracy</a>
+        </h5>
+<p>
+          The following table shows the peak errors (in units of epsilon) found on
+          various platforms with various floating point types, along with comparisons
+          to the GSL-1.9,
+          GNU C Lib, HP-UX C Library
+          and Cephes libraries.
+          Unless otherwise specified any floating point type that is narrower than
+          the one shown will have <a class="link" href="../../backgrounders/relative_error.html#zero_error">effectively zero error</a>.
+        </p>
+<p>
+          Note that while the relative errors near the positive roots of lgamma are
+          very low, the lgamma function has an infinite number of irrational roots
+          for negative arguments: very close to these negative roots only a low absolute
+          error can be guaranteed.
+        </p>
+<div class="informaltable"><table class="table">
+<colgroup>
+<col>
+<col>
+<col>
+<col>
+<col>
+<col>
+</colgroup>
+<thead><tr>
+<th>
+                <p>
+                  Significand Size
+                </p>
+                </th>
+<th>
+                <p>
+                  Platform and Compiler
+                </p>
+                </th>
+<th>
+                <p>
+                  Factorials and Half factorials
+                </p>
+                </th>
+<th>
+                <p>
+                  Values Near Zero
+                </p>
+                </th>
+<th>
+                <p>
+                  Values Near 1 or 2
+                </p>
+                </th>
+<th>
+                <p>
+                  Values Near a Negative Pole
+                </p>
+                </th>
+</tr></thead>
+<tbody>
+<tr>
+<td>
+                <p>
+                  53
+                </p>
+                </td>
+<td>
+                <p>
+                  Win32 Visual C++ 8
+                </p>
+                </td>
+<td>
+                <p>
+                  Peak=0.88 Mean=0.14
+                </p>
+                <p>
+                  (GSL=33) (Cephes=1.5)
+                </p>
+                </td>
+<td>
+                <p>
+                  Peak=0.96 Mean=0.46
+                </p>
+                <p>
+                  (GSL=5.2) (Cephes=1.1)
+                </p>
+                </td>
+<td>
+                <p>
+                  Peak=0.86 Mean=0.46
+                </p>
+                <p>
+                  (GSL=1168) (Cephes~500000)
+                </p>
+                </td>
+<td>
+                <p>
+                  Peak=4.2 Mean=1.3
+                </p>
+                <p>
+                  (GSL=25) (Cephes=1.6)
+                </p>
+                </td>
+</tr>
+<tr>
+<td>
+                <p>
+                  64
+                </p>
+                </td>
+<td>
+                <p>
+                  Linux IA32 / GCC
+                </p>
+                </td>
+<td>
+                <p>
+                  Peak=1.9 Mean=0.43
+                </p>
+                <p>
+                  (GNU C Lib
+                  Peak=1.7 Mean=0.49)
+                </p>
+                </td>
+<td>
+                <p>
+                  Peak=1.4 Mean=0.57
+                </p>
+                <p>
+                  (GNU C Lib
+                  Peak= 0.96 Mean=0.54)
+                </p>
+                </td>
+<td>
+                <p>
+                  Peak=0.86 Mean=0.35
+                </p>
+                <p>
+                  (GNU C Lib
+                  Peak=0.74 Mean=0.26)
+                </p>
+                </td>
+<td>
+                <p>
+                  Peak=6.0 Mean=1.8
+                </p>
+                <p>
+                  (GNU C Lib
+                  Peak=3.0 Mean=0.86)
+                </p>
+                </td>
+</tr>
+<tr>
+<td>
+                <p>
+                  64
+                </p>
+                </td>
+<td>
+                <p>
+                  Linux IA64 / GCC
+                </p>
+                </td>
+<td>
+                <p>
+                  Peak=0.99 Mean=0.12
+                </p>
+                <p>
+                  (GNU C Lib
+                  Peak 0)
+                </p>
+                </td>
+<td>
+                <p>
+                  Pek=1.2 Mean=0.6
+                </p>
+                <p>
+                  (GNU C Lib
+                  Peak 0)
+                </p>
+                </td>
+<td>
+                <p>
+                  Peak=0.86 Mean=0.16
+                </p>
+                <p>
+                  (GNU C Lib
+                  Peak 0)
+                </p>
+                </td>
+<td>
+                <p>
+                  Peak=2.3 Mean=0.69
+                </p>
+                <p>
+                  (GNU C Lib
+                  Peak 0)
+                </p>
+                </td>
+</tr>
+<tr>
+<td>
+                <p>
+                  113
+                </p>
+                </td>
+<td>
+                <p>
+                  HPUX IA64, aCC A.06.06
+                </p>
+                </td>
+<td>
+                <p>
+                  Peak=0.96 Mean=0.13
+                </p>
+                <p>
+                  (<a href="http://docs.hp.com/en/B9106-90010/index.html" target="_top">HP-UX
+                  C Library</a> Peak 0)
+                </p>
+                </td>
+<td>
+                <p>
+                  Peak=0.99 Mean=0.53
+                </p>
+                <p>
+                  (<a href="http://docs.hp.com/en/B9106-90010/index.html" target="_top">HP-UX
+                  C Library</a> Peak 0)
+                </p>
+                </td>
+<td>
+                <p>
+                  Peak=0.9 Mean=0.4
+                </p>
+                <p>
+                  (<a href="http://docs.hp.com/en/B9106-90010/index.html" target="_top">HP-UX
+                  C Library</a> Peak 0)
+                </p>
+                </td>
+<td>
+                <p>
+                  Peak=3.0 Mean=0.9
+                </p>
+                <p>
+                  (<a href="http://docs.hp.com/en/B9106-90010/index.html" target="_top">HP-UX
+                  C Library</a> Peak 0)
+                </p>
+                </td>
+</tr>
+</tbody>
+</table></div>
+<a name="math_toolkit.special.sf_gamma.lgamma.testing"></a><h5>
+<a name="id702077"></a>
+          <a class="link" href="lgamma.html#math_toolkit.special.sf_gamma.lgamma.testing">Testing</a>
+        </h5>
+<p>
+          The main tests for this function involve comparisons against the logs of
+          the factorials which can be independently calculated to very high accuracy.
+        </p>
+<p>
+          Random tests in key problem areas are also used.
+        </p>
+<a name="math_toolkit.special.sf_gamma.lgamma.implementation"></a><h5>
+<a name="id702117"></a>
+          <a class="link" href="lgamma.html#math_toolkit.special.sf_gamma.lgamma.implementation">Implementation</a>
+        </h5>
+<p>
+          The generic version of this function is implemented by combining the series
+          and continued fraction representations for the incomplete gamma function:
+        </p>
+<p>
+          <span class="inlinemediaobject"><img src="../../../../equations/lgamm2.png"></span>
+        </p>
+<p>
+          where <span class="emphasis"><em>l</em></span> is an arbitrary integration limit: choosing
+          <code class="literal">l = max(10, a)</code> seems to work fairly well. For negative
+          <span class="emphasis"><em>z</em></span> the logarithm version of the reflection formula
+          is used:
+        </p>
+<p>
+          <span class="inlinemediaobject"><img src="../../../../equations/lgamm3.png"></span>
+        </p>
+<p>
+          For types of known precision, the <a class="link" href="../../backgrounders/lanczos.html" title="The Lanczos Approximation">Lanczos
+          approximation</a> is used, a traits class <code class="computeroutput"><span class="identifier">boost</span><span class="special">::</span><span class="identifier">math</span><span class="special">::</span><span class="identifier">lanczos</span><span class="special">::</span><span class="identifier">lanczos_traits</span></code>
+          maps type T to an appropriate approximation. The logarithmic version of
+          the <a class="link" href="../../backgrounders/lanczos.html" title="The Lanczos Approximation">Lanczos approximation</a>
+          is:
+        </p>
+<p>
+          <span class="inlinemediaobject"><img src="../../../../equations/lgamm4.png"></span>
+        </p>
+<p>
+          Where L<sub>e,g</sub> is the Lanczos sum, scaled by e<sup>g</sup>.
+        </p>
+<p>
+          As before the reflection formula is used for <span class="emphasis"><em>z &lt; 0</em></span>.
+        </p>
+<p>
+          When z is very near 1 or 2, then the logarithmic version of the <a class="link" href="../../backgrounders/lanczos.html" title="The Lanczos Approximation">Lanczos
+          approximation</a> suffers very badly from cancellation error: indeed
+          for values sufficiently close to 1 or 2, arbitrarily large relative errors
+          can be obtained (even though the absolute error is tiny).
+        </p>
+<p>
+          For types with up to 113 bits of precision (up to and including 128-bit
+          long doubles), root-preserving rational approximations <a class="link" href="../../backgrounders/implementation.html#math_toolkit.backgrounders.implementation.rational_approximations_used">devised
+          by JM</a> are used over the intervals [1,2] and [2,3]. Over the interval
+          [2,3] the approximation form used is:
+        </p>
+<pre class="programlisting"><span class="identifier">lgamma</span><span class="special">(</span><span class="identifier">z</span><span class="special">)</span> <span class="special">=</span> <span class="special">(</span><span class="identifier">z</span><span class="special">-</span><span class="number">2</span><span class="special">)(</span><span class="identifier">z</span><span class="special">+</span><span class="number">1</span><span class="special">)(</span><span class="identifier">Y</span> <span class="special">+</span> <span class="identifier">R</span><span class="special">(</span><span class="identifier">z</span><span class="special">-</span><span class="number">2</span><span class="special">));</span>
+</pre>
+<p>
+          Where Y is a constant, and R(z-2) is the rational approximation: optimised
+          so that it's absolute error is tiny compared to Y. In addition small values
+          of z greater than 3 can handled by argument reduction using the recurrence
+          relation:
+        </p>
+<pre class="programlisting"><span class="identifier">lgamma</span><span class="special">(</span><span class="identifier">z</span><span class="special">+</span><span class="number">1</span><span class="special">)</span> <span class="special">=</span> <span class="identifier">log</span><span class="special">(</span><span class="identifier">z</span><span class="special">)</span> <span class="special">+</span> <span class="identifier">lgamma</span><span class="special">(</span><span class="identifier">z</span><span class="special">);</span>
+</pre>
+<p>
+          Over the interval [1,2] two approximations have to be used, one for small
+          z uses:
+        </p>
+<pre class="programlisting"><span class="identifier">lgamma</span><span class="special">(</span><span class="identifier">z</span><span class="special">)</span> <span class="special">=</span> <span class="special">(</span><span class="identifier">z</span><span class="special">-</span><span class="number">1</span><span class="special">)(</span><span class="identifier">z</span><span class="special">-</span><span class="number">2</span><span class="special">)(</span><span class="identifier">Y</span> <span class="special">+</span> <span class="identifier">R</span><span class="special">(</span><span class="identifier">z</span><span class="special">-</span><span class="number">1</span><span class="special">));</span>
+</pre>
+<p>
+          Once again Y is a constant, and R(z-1) is optimised for low absolute error
+          compared to Y. For z &gt; 1.5 the above form wouldn't converge to a minimax
+          solution but this similar form does:
+        </p>
+<pre class="programlisting"><span class="identifier">lgamma</span><span class="special">(</span><span class="identifier">z</span><span class="special">)</span> <span class="special">=</span> <span class="special">(</span><span class="number">2</span><span class="special">-</span><span class="identifier">z</span><span class="special">)(</span><span class="number">1</span><span class="special">-</span><span class="identifier">z</span><span class="special">)(</span><span class="identifier">Y</span> <span class="special">+</span> <span class="identifier">R</span><span class="special">(</span><span class="number">2</span><span class="special">-</span><span class="identifier">z</span><span class="special">));</span>
+</pre>
+<p>
+          Finally for z &lt; 1 the recurrence relation can be used to move to z &gt;
+          1:
+        </p>
+<pre class="programlisting"><span class="identifier">lgamma</span><span class="special">(</span><span class="identifier">z</span><span class="special">)</span> <span class="special">=</span> <span class="identifier">lgamma</span><span class="special">(</span><span class="identifier">z</span><span class="special">+</span><span class="number">1</span><span class="special">)</span> <span class="special">-</span> <span class="identifier">log</span><span class="special">(</span><span class="identifier">z</span><span class="special">);</span>
+</pre>
+<p>
+          Note that while this involves a subtraction, it appears not to suffer from
+          cancellation error: as z decreases from 1 the <code class="computeroutput"><span class="special">-</span><span class="identifier">log</span><span class="special">(</span><span class="identifier">z</span><span class="special">)</span></code> term
+          grows positive much more rapidly than the <code class="computeroutput"><span class="identifier">lgamma</span><span class="special">(</span><span class="identifier">z</span><span class="special">+</span><span class="number">1</span><span class="special">)</span></code> term becomes
+          negative. So in this specific case, significant digits are preserved, rather
+          than cancelled.
+        </p>
+<p>
+          For other types which do have a <a class="link" href="../../backgrounders/lanczos.html" title="The Lanczos Approximation">Lanczos
+          approximation</a> defined for them the current solution is as follows:
+          imagine we balance the two terms in the <a class="link" href="../../backgrounders/lanczos.html" title="The Lanczos Approximation">Lanczos
+          approximation</a> by dividing the power term by its value at <span class="emphasis"><em>z
+          = 1</em></span>, and then multiplying the Lanczos coefficients by the same
+          value. Now each term will take the value 1 at <span class="emphasis"><em>z = 1</em></span>
+          and we can rearrange the power terms in terms of log1p. Likewise if we
+          subtract 1 from the Lanczos sum part (algebraically, by subtracting the
+          value of each term at <span class="emphasis"><em>z = 1</em></span>), we obtain a new summation
+          that can be also be fed into log1p. Crucially, all of the terms tend to
+          zero, as <span class="emphasis"><em>z -&gt; 1</em></span>:
+        </p>
+<p>
+          <span class="inlinemediaobject"><img src="../../../../equations/lgamm5.png"></span>
+        </p>
+<p>
+          The C<sub>k</sub> terms in the above are the same as in the <a class="link" href="../../backgrounders/lanczos.html" title="The Lanczos Approximation">Lanczos
+          approximation</a>.
+        </p>
+<p>
+          A similar rearrangement can be performed at <span class="emphasis"><em>z = 2</em></span>:
+        </p>
+<p>
+          <span class="inlinemediaobject"><img src="../../../../equations/lgamm6.png"></span>
+        </p>
+</div>
+<table xmlns:rev="http://www.cs.rpi.edu/~gregod/boost/tools/doc/revision" width="100%"><tr>
+<td align="left"></td>
+<td align="right"><div class="copyright-footer">Copyright © 2006 , 2007, 2008 John Maddock, Paul A. Bristow, Hubert
+      Holin, Xiaogang Zhang, Bruno Lalande and Gautam Sewani<p>
+        Distributed under the Boost Software License, Version 1.0. (See accompanying
+        file LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_0.txt)
+      </p>
+</div></td>
+</tr></table>
+<hr>
+<div class="spirit-nav">
+<a accesskey="p" href="tgamma.html"><img src="../../../../../doc/html/images/prev.png" alt="Prev"></a><a accesskey="u" href="../sf_gamma.html"><img src="../../../../../doc/html/images/up.png" alt="Up"></a><a accesskey="h" href="../../../index.html"><img src="../../../../../doc/html/images/home.png" alt="Home"></a><a accesskey="n" href="digamma.html"><img src="../../../../../doc/html/images/next.png" alt="Next"></a>
+</div>
+</body>
+</html>

Added: sandbox/tools/auto_index/example/math/doc/sf_and_dist/html/math_toolkit/special/sf_gamma/tgamma.html
==============================================================================
--- (empty file)
+++ sandbox/tools/auto_index/example/math/doc/sf_and_dist/html/math_toolkit/special/sf_gamma/tgamma.html	2008-11-28 05:25:28 EST (Fri, 28 Nov 2008)
@@ -0,0 +1,479 @@
+<html>
+<head>
+<meta http-equiv="Content-Type" content="text/html; charset=ISO-8859-1">
+<title>Gamma</title>
+<link rel="stylesheet" href="../../../boostbook.css" type="text/css">
+<meta name="generator" content="DocBook XSL Stylesheets Vsnapshot_8125">
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+<hr>
+<div class="spirit-nav">
+<a accesskey="p" href="../sf_gamma.html"><img src="../../../../../doc/html/images/prev.png" alt="Prev"></a><a accesskey="u" href="../sf_gamma.html"><img src="../../../../../doc/html/images/up.png" alt="Up"></a><a accesskey="h" href="../../../index.html"><img src="../../../../../doc/html/images/home.png" alt="Home"></a><a accesskey="n" href="lgamma.html"><img src="../../../../../doc/html/images/next.png" alt="Next"></a>
+</div>
+<div class="section" lang="en">
+<div class="titlepage"><div><div><h4 class="title">
+<a name="math_toolkit.special.sf_gamma.tgamma"></a><a class="link" href="tgamma.html" title="Gamma"> Gamma</a>
+</h4></div></div></div>
+<a name="math_toolkit.special.sf_gamma.tgamma.synopsis"></a><h5>
+<a name="id698257"></a>
+          <a class="link" href="tgamma.html#math_toolkit.special.sf_gamma.tgamma.synopsis">Synopsis</a>
+        </h5>
+<p>
+          
+</p>
+<pre class="programlisting"><span class="preprocessor">#include</span> <span class="special">&lt;</span><span class="identifier">boost</span><span class="special">/</span><span class="identifier">math</span><span class="special">/</span><span class="identifier">special_functions</span><span class="special">/</span><span class="identifier">gamma</span><span class="special">.</span><span class="identifier">hpp</span><span class="special">&gt;</span>
+</pre>
+<p>
+        </p>
+<pre class="programlisting"><span class="keyword">namespace</span> <span class="identifier">boost</span><span class="special">{</span> <span class="keyword">namespace</span> <span class="identifier">math</span><span class="special">{</span>
+
+<span class="keyword">template</span> <span class="special">&lt;</span><span class="keyword">class</span> <span class="identifier">T</span><span class="special">&gt;</span>
+<a class="link" href="../../main_overview/result_type.html" title="Calculation of the Type of the Result"><span class="emphasis"><em>calculated-result-type</em></span></a> <span class="identifier">tgamma</span><span class="special">(</span><span class="identifier">T</span> <span class="identifier">z</span><span class="special">);</span>
+
+<span class="keyword">template</span> <span class="special">&lt;</span><span class="keyword">class</span> <span class="identifier">T</span><span class="special">,</span> <span class="keyword">class</span> <a class="link" href="../../policy.html" title="Policies">Policy</a><span class="special">&gt;</span>
+<a class="link" href="../../main_overview/result_type.html" title="Calculation of the Type of the Result"><span class="emphasis"><em>calculated-result-type</em></span></a> <span class="identifier">tgamma</span><span class="special">(</span><span class="identifier">T</span> <span class="identifier">z</span><span class="special">,</span> <span class="keyword">const</span> <a class="link" href="../../policy.html" title="Policies">Policy</a><span class="special">&amp;);</span>
+
+<span class="keyword">template</span> <span class="special">&lt;</span><span class="keyword">class</span> <span class="identifier">T</span><span class="special">&gt;</span>
+<a class="link" href="../../main_overview/result_type.html" title="Calculation of the Type of the Result"><span class="emphasis"><em>calculated-result-type</em></span></a> <span class="identifier">tgamma1pm1</span><span class="special">(</span><span class="identifier">T</span> <span class="identifier">dz</span><span class="special">);</span>
+
+<span class="keyword">template</span> <span class="special">&lt;</span><span class="keyword">class</span> <span class="identifier">T</span><span class="special">,</span> <span class="keyword">class</span> <a class="link" href="../../policy.html" title="Policies">Policy</a><span class="special">&gt;</span>
+<a class="link" href="../../main_overview/result_type.html" title="Calculation of the Type of the Result"><span class="emphasis"><em>calculated-result-type</em></span></a> <span class="identifier">tgamma1pm1</span><span class="special">(</span><span class="identifier">T</span> <span class="identifier">dz</span><span class="special">,</span> <span class="keyword">const</span> <a class="link" href="../../policy.html" title="Policies">Policy</a><span class="special">&amp;);</span>
+
+<span class="special">}}</span> <span class="comment">// namespaces
+</span></pre>
+<a name="math_toolkit.special.sf_gamma.tgamma.description"></a><h5>
+<a name="id698749"></a>
+          <a class="link" href="tgamma.html#math_toolkit.special.sf_gamma.tgamma.description">Description</a>
+        </h5>
+<pre class="programlisting"><span class="keyword">template</span> <span class="special">&lt;</span><span class="keyword">class</span> <span class="identifier">T</span><span class="special">&gt;</span>
+<a class="link" href="../../main_overview/result_type.html" title="Calculation of the Type of the Result"><span class="emphasis"><em>calculated-result-type</em></span></a> <span class="identifier">tgamma</span><span class="special">(</span><span class="identifier">T</span> <span class="identifier">z</span><span class="special">);</span>
+
+<span class="keyword">template</span> <span class="special">&lt;</span><span class="keyword">class</span> <span class="identifier">T</span><span class="special">,</span> <span class="keyword">class</span> <a class="link" href="../../policy.html" title="Policies">Policy</a><span class="special">&gt;</span>
+<a class="link" href="../../main_overview/result_type.html" title="Calculation of the Type of the Result"><span class="emphasis"><em>calculated-result-type</em></span></a> <span class="identifier">tgamma</span><span class="special">(</span><span class="identifier">T</span> <span class="identifier">z</span><span class="special">,</span> <span class="keyword">const</span> <a class="link" href="../../policy.html" title="Policies">Policy</a><span class="special">&amp;);</span>
+</pre>
+<p>
+          Returns the "true gamma" (hence name tgamma) of value z:
+        </p>
+<p>
+          <span class="inlinemediaobject"><img src="../../../../equations/gamm1.png"></span>
+        </p>
+<p>
+          <span class="inlinemediaobject"><img src="../../../../graphs/tgamma.png" align="middle"></span>
+        </p>
+<p>
+          </p>
+<p>
+            The final <a class="link" href="../../policy.html" title="Policies">Policy</a> argument
+            is optional and can be used to control the behaviour of the function:
+            how it handles errors, what level of precision to use etc. Refer to the
+            <a class="link" href="../../policy.html" title="Policies">policy documentation for more details</a>.
+          </p>
+<p>
+        </p>
+<p>
+          There are effectively two versions of the tgamma
+          function internally: a fully generic version that is slow, but reasonably
+          accurate, and a much more efficient approximation that is used where the
+          number of digits in the significand of T correspond to a certain <a class="link" href="../../backgrounders/lanczos.html" title="The Lanczos Approximation">Lanczos approximation</a>.
+          In practice any built in floating point type you will encounter has an
+          appropriate <a class="link" href="../../backgrounders/lanczos.html" title="The Lanczos Approximation">Lanczos
+          approximation</a> defined for it. It is also possible, given enough
+          machine time, to generate further <a class="link" href="../../backgrounders/lanczos.html" title="The Lanczos Approximation">Lanczos
+          approximation</a>'s using the program libs/math/tools/lanczos_generator.cpp.
+        </p>
+<p>
+          The return type of this function is computed using the <a class="link" href="../../main_overview/result_type.html" title="Calculation of the Type of the Result"><span class="emphasis"><em>result
+          type calculation rules</em></span></a>: the result is <code class="computeroutput"><span class="keyword">double</span></code>
+          when T is an integer type, and T otherwise.
+        </p>
+<pre class="programlisting"><span class="keyword">template</span> <span class="special">&lt;</span><span class="keyword">class</span> <span class="identifier">T</span><span class="special">&gt;</span>
+<a class="link" href="../../main_overview/result_type.html" title="Calculation of the Type of the Result"><span class="emphasis"><em>calculated-result-type</em></span></a> <span class="identifier">tgamma1pm1</span><span class="special">(</span><span class="identifier">T</span> <span class="identifier">dz</span><span class="special">);</span>
+
+<span class="keyword">template</span> <span class="special">&lt;</span><span class="keyword">class</span> <span class="identifier">T</span><span class="special">,</span> <span class="keyword">class</span> <a class="link" href="../../policy.html" title="Policies">Policy</a><span class="special">&gt;</span>
+<a class="link" href="../../main_overview/result_type.html" title="Calculation of the Type of the Result"><span class="emphasis"><em>calculated-result-type</em></span></a> <span class="identifier">tgamma1pm1</span><span class="special">(</span><span class="identifier">T</span> <span class="identifier">dz</span><span class="special">,</span> <span class="keyword">const</span> <a class="link" href="../../policy.html" title="Policies">Policy</a><span class="special">&amp;);</span>
+</pre>
+<p>
+          Returns <code class="computeroutput"><span class="identifier">tgamma</span><span class="special">(</span><span class="identifier">dz</span> <span class="special">+</span> <span class="number">1</span><span class="special">)</span> <span class="special">-</span>
+          <span class="number">1</span></code>. Internally the implementation
+          does not make use of the addition and subtraction implied by the definition,
+          leading to accurate results even for very small <code class="computeroutput"><span class="identifier">dz</span></code>.
+          However, the implementation is capped to either 35 digit accuracy, or to
+          the precision of the <a class="link" href="../../backgrounders/lanczos.html" title="The Lanczos Approximation">Lanczos
+          approximation</a> associated with type T, whichever is more accurate.
+        </p>
+<p>
+          The return type of this function is computed using the <a class="link" href="../../main_overview/result_type.html" title="Calculation of the Type of the Result"><span class="emphasis"><em>result
+          type calculation rules</em></span></a>: the result is <code class="computeroutput"><span class="keyword">double</span></code>
+          when T is an integer type, and T otherwise.
+        </p>
+<p>
+          </p>
+<p>
+            The final <a class="link" href="../../policy.html" title="Policies">Policy</a> argument
+            is optional and can be used to control the behaviour of the function:
+            how it handles errors, what level of precision to use etc. Refer to the
+            <a class="link" href="../../policy.html" title="Policies">policy documentation for more details</a>.
+          </p>
+<p>
+        </p>
+<a name="math_toolkit.special.sf_gamma.tgamma.accuracy"></a><h5>
+<a name="id699460"></a>
+          <a class="link" href="tgamma.html#math_toolkit.special.sf_gamma.tgamma.accuracy">Accuracy</a>
+        </h5>
+<p>
+          The following table shows the peak errors (in units of epsilon) found on
+          various platforms with various floating point types, along with comparisons
+          to the GSL-1.9,
+          GNU C Lib, HP-UX C Library
+          and Cephes libraries.
+          Unless otherwise specified any floating point type that is narrower than
+          the one shown will have <a class="link" href="../../backgrounders/relative_error.html#zero_error">effectively zero error</a>.
+        </p>
+<div class="informaltable"><table class="table">
+<colgroup>
+<col>
+<col>
+<col>
+<col>
+<col>
+<col>
+</colgroup>
+<thead><tr>
+<th>
+                <p>
+                  Significand Size
+                </p>
+                </th>
+<th>
+                <p>
+                  Platform and Compiler
+                </p>
+                </th>
+<th>
+                <p>
+                  Factorials and Half factorials
+                </p>
+                </th>
+<th>
+                <p>
+                  Values Near Zero
+                </p>
+                </th>
+<th>
+                <p>
+                  Values Near 1 or 2
+                </p>
+                </th>
+<th>
+                <p>
+                  Values Near a Negative Pole
+                </p>
+                </th>
+</tr></thead>
+<tbody>
+<tr>
+<td>
+                <p>
+                  53
+                </p>
+                </td>
+<td>
+                <p>
+                  Win32 Visual C++ 8
+                </p>
+                </td>
+<td>
+                <p>
+                  Peak=1.9 Mean=0.7
+                </p>
+                <p>
+                  (GSL=3.9)
+                </p>
+                <p>
+                  (Cephes=3.0)
+                </p>
+                </td>
+<td>
+                <p>
+                  Peak=2.0 Mean=1.1
+                </p>
+                <p>
+                  (GSL=4.5)
+                </p>
+                <p>
+                  (Cephes=1)
+                </p>
+                </td>
+<td>
+                <p>
+                  Peak=2.0 Mean=1.1
+                </p>
+                <p>
+                  (GSL=7.9)
+                </p>
+                <p>
+                  (Cephes=1.0)
+                </p>
+                </td>
+<td>
+                <p>
+                  Peak=2.6 Mean=1.3
+                </p>
+                <p>
+                  (GSL=2.5)
+                </p>
+                <p>
+                  (Cephes=2.7)
+                </p>
+                </td>
+</tr>
+<tr>
+<td>
+                <p>
+                  64
+                </p>
+                </td>
+<td>
+                <p>
+                  Linux IA32 / GCC
+                </p>
+                </td>
+<td>
+                <p>
+                  Peak=300 Mean=49.5
+                </p>
+                <p>
+                  (GNU C Lib
+                  Peak=395 Mean=89)
+                </p>
+                </td>
+<td>
+                <p>
+                  Peak=3.0 Mean=1.4
+                </p>
+                <p>
+                  (GNU C Lib
+                  Peak=11 Mean=3.3)
+                </p>
+                </td>
+<td>
+                <p>
+                  Peak=5.0 Mean=1.8
+                </p>
+                <p>
+                  (GNU C Lib
+                  Peak=0.92 Mean=0.2)
+                </p>
+                </td>
+<td>
+                <p>
+                  Peak=157 Mean=65
+                </p>
+                <p>
+                  (GNU C Lib
+                  Peak=205 Mean=108)
+                </p>
+                </td>
+</tr>
+<tr>
+<td>
+                <p>
+                  64
+                </p>
+                </td>
+<td>
+                <p>
+                  Linux IA64 / GCC
+                </p>
+                </td>
+<td>
+                <p>
+                  GNU C Lib
+                  Peak 2.8 Mean=0.9
+                </p>
+                <p>
+                  (GNU C Lib
+                  Peak 0.7)
+                </p>
+                </td>
+<td>
+                <p>
+                  Peak=4.8 Mean=1.5
+                </p>
+                <p>
+                  (GNU C Lib
+                  Peak 0)
+                </p>
+                </td>
+<td>
+                <p>
+                  Peak=4.8 Mean=1.5
+                </p>
+                <p>
+                  (GNU C Lib
+                  Peak 0)
+                </p>
+                </td>
+<td>
+                <p>
+                  Peak=5.0 Mean=1.7 (<a href="http://www.gnu.org/software/libc/" target="_top">GNU
+                  C Lib</a> Peak 0)
+                </p>
+                </td>
+</tr>
+<tr>
+<td>
+                <p>
+                  113
+                </p>
+                </td>
+<td>
+                <p>
+                  HPUX IA64, aCC A.06.06
+                </p>
+                </td>
+<td>
+                <p>
+                  Peak=2.5 Mean=1.1
+                </p>
+                <p>
+                  (<a href="http://docs.hp.com/en/B9106-90010/index.html" target="_top">HP-UX
+                  C Library</a> Peak 0)
+                </p>
+                </td>
+<td>
+                <p>
+                  Peak=3.5 Mean=1.7
+                </p>
+                <p>
+                  (<a href="http://docs.hp.com/en/B9106-90010/index.html" target="_top">HP-UX
+                  C Library</a> Peak 0)
+                </p>
+                </td>
+<td>
+                <p>
+                  Peak=3.5 Mean=1.6
+                </p>
+                <p>
+                  (<a href="http://docs.hp.com/en/B9106-90010/index.html" target="_top">HP-UX
+                  C Library</a> Peak 0)
+                </p>
+                </td>
+<td>
+                <p>
+                  Peak=5.2 Mean=1.92
+                </p>
+                <p>
+                  (<a href="http://docs.hp.com/en/B9106-90010/index.html" target="_top">HP-UX
+                  C Library</a> Peak 0)
+                </p>
+                </td>
+</tr>
+</tbody>
+</table></div>
+<a name="math_toolkit.special.sf_gamma.tgamma.testing"></a><h5>
+<a name="id700042"></a>
+          <a class="link" href="tgamma.html#math_toolkit.special.sf_gamma.tgamma.testing">Testing</a>
+        </h5>
+<p>
+          The gamma is relatively easy to test: factorials and half-integer factorials
+          can be calculated exactly by other means and compared with the gamma function.
+          In addition, some accuracy tests in known tricky areas were computed at
+          high precision using the generic version of this function.
+        </p>
+<p>
+          The function <code class="computeroutput"><span class="identifier">tgamma1pm1</span></code>
+          is tested against values calculated very naively using the formula <code class="computeroutput"><span class="identifier">tgamma</span><span class="special">(</span><span class="number">1</span><span class="special">+</span><span class="identifier">dz</span><span class="special">)-</span><span class="number">1</span></code> with
+          a lanczos approximation accurate to around 100 decimal digits.
+        </p>
+<a name="math_toolkit.special.sf_gamma.tgamma.implementation"></a><h5>
+<a name="id700136"></a>
+          <a class="link" href="tgamma.html#math_toolkit.special.sf_gamma.tgamma.implementation">Implementation</a>
+        </h5>
+<p>
+          The generic version of the <code class="computeroutput"><span class="identifier">tgamma</span></code>
+          function is implemented by combining the series and continued fraction
+          representations for the incomplete gamma function:
+        </p>
+<p>
+          <span class="inlinemediaobject"><img src="../../../../equations/gamm2.png"></span>
+        </p>
+<p>
+          where <span class="emphasis"><em>l</em></span> is an arbitrary integration limit: choosing
+          <code class="literal">l = max(10, a)</code> seems to work fairly well.
+        </p>
+<p>
+          For types of known precision the <a class="link" href="../../backgrounders/lanczos.html" title="The Lanczos Approximation">Lanczos
+          approximation</a> is used, a traits class <code class="computeroutput"><span class="identifier">boost</span><span class="special">::</span><span class="identifier">math</span><span class="special">::</span><span class="identifier">lanczos</span><span class="special">::</span><span class="identifier">lanczos_traits</span></code>
+          maps type T to an appropriate approximation.
+        </p>
+<p>
+          For z in the range -20 &lt; z &lt; 1 then recursion is used to shift to
+          z &gt; 1 via:
+        </p>
+<p>
+          <span class="inlinemediaobject"><img src="../../../../equations/gamm3.png"></span>
+        </p>
+<p>
+          For very small z, this helps to preserve the identity:
+        </p>
+<p>
+          <span class="inlinemediaobject"><img src="../../../../equations/gamm4.png"></span>
+        </p>
+<p>
+          For z &lt; -20 the reflection formula:
+        </p>
+<p>
+          <span class="inlinemediaobject"><img src="../../../../equations/gamm5.png"></span>
+        </p>
+<p>
+          is used. Particular care has to be taken to evaluate the <code class="computeroutput"><span class="identifier">z</span> <span class="special">*</span> <span class="identifier">sin</span><span class="special">([</span><span class="identifier">pi</span><span class="special">][</span><span class="identifier">space</span><span class="special">]</span> <span class="special">*</span> <span class="identifier">z</span><span class="special">)</span></code>
+          part: a special routine is used to reduce z prior to multiplying by &#960; to
+          ensure that the result in is the range [0, &#960;/2]. Without this an excessive
+          amount of error occurs in this region (which is hard enough already, as
+          the rate of change near a negative pole is <span class="emphasis"><em>exceptionally</em></span>
+          high).
+        </p>
+<p>
+          Finally if the argument is a small integer then table lookup of the factorial
+          is used.
+        </p>
+<p>
+          The function <code class="computeroutput"><span class="identifier">tgamma1pm1</span></code>
+          is implemented using rational approximations <a class="link" href="../../backgrounders/implementation.html#math_toolkit.backgrounders.implementation.rational_approximations_used">devised
+          by JM</a> in the region <code class="computeroutput"><span class="special">-</span><span class="number">0.5</span> <span class="special">&lt;</span> <span class="identifier">dz</span> <span class="special">&lt;</span> <span class="number">2</span></code>. These are the same approximations (and
+          internal routines) that are used for <a class="link" href="lgamma.html" title="Log Gamma">lgamma</a>,
+          and so aren't detailed further here. The result of the approximation is
+          <code class="computeroutput"><span class="identifier">log</span><span class="special">(</span><span class="identifier">tgamma</span><span class="special">(</span><span class="identifier">dz</span><span class="special">+</span><span class="number">1</span><span class="special">))</span></code> which can fed into <a class="link" href="../powers/expm1.html" title="expm1">expm1</a>
+          to give the desired result. Outside the range <code class="computeroutput"><span class="special">-</span><span class="number">0.5</span> <span class="special">&lt;</span> <span class="identifier">dz</span> <span class="special">&lt;</span> <span class="number">2</span></code> then the naive formula <code class="computeroutput"><span class="identifier">tgamma1pm1</span><span class="special">(</span><span class="identifier">dz</span><span class="special">)</span>
+          <span class="special">=</span> <span class="identifier">tgamma</span><span class="special">(</span><span class="identifier">dz</span><span class="special">+</span><span class="number">1</span><span class="special">)-</span><span class="number">1</span></code>
+          can be used directly.
+        </p>
+</div>
+<table xmlns:rev="http://www.cs.rpi.edu/~gregod/boost/tools/doc/revision" width="100%"><tr>
+<td align="left"></td>
+<td align="right"><div class="copyright-footer">Copyright © 2006 , 2007, 2008 John Maddock, Paul A. Bristow, Hubert
+      Holin, Xiaogang Zhang, Bruno Lalande and Gautam Sewani<p>
+        Distributed under the Boost Software License, Version 1.0. (See accompanying
+        file LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_0.txt)
+      </p>
+</div></td>
+</tr></table>
+<hr>
+<div class="spirit-nav">
+<a accesskey="p" href="../sf_gamma.html"><img src="../../../../../doc/html/images/prev.png" alt="Prev"></a><a accesskey="u" href="../sf_gamma.html"><img src="../../../../../doc/html/images/up.png" alt="Up"></a><a accesskey="h" href="../../../index.html"><img src="../../../../../doc/html/images/home.png" alt="Home"></a><a accesskey="n" href="lgamma.html"><img src="../../../../../doc/html/images/next.png" alt="Next"></a>
+</div>
+</body>
+</html>

Added: sandbox/tools/auto_index/example/math/doc/sf_and_dist/html/math_toolkit/special/sf_poly.html
==============================================================================
--- (empty file)
+++ sandbox/tools/auto_index/example/math/doc/sf_and_dist/html/math_toolkit/special/sf_poly.html	2008-11-28 05:25:28 EST (Fri, 28 Nov 2008)
@@ -0,0 +1,52 @@
+<html>
+<head>
+<meta http-equiv="Content-Type" content="text/html; charset=ISO-8859-1">
+<title>Polynomials</title>
+<link rel="stylesheet" href="../../boostbook.css" type="text/css">
+<meta name="generator" content="DocBook XSL Stylesheets Vsnapshot_8125">
+<link rel="home" href="../../index.html" title="Math Toolkit">
+<link rel="up" href="../special.html" title="Special Functions">
+<link rel="prev" href="sf_erf/error_inv.html" title="Error Function Inverses">
+<link rel="next" href="sf_poly/legendre.html" title="Legendre (and Associated) Polynomials">
+</head>
+<body bgcolor="white" text="black" link="#0000FF" vlink="#840084" alink="#0000FF">
+<table cellpadding="2" width="100%"><tr>
+<td valign="top"><img alt="Boost C++ Libraries" width="277" height="86" src="../../../../boost.png"></td>
+<td align="center">Home</td>
+<td align="center">Libraries</td>
+<td align="center">People</td>
+<td align="center">FAQ</td>
+<td align="center">More</td>
+</tr></table>
+<hr>
+<div class="spirit-nav">
+<a accesskey="p" href="sf_erf/error_inv.html"><img src="../../../../doc/html/images/prev.png" alt="Prev"></a><a accesskey="u" href="../special.html"><img src="../../../../doc/html/images/up.png" alt="Up"></a><a accesskey="h" href="../../index.html"><img src="../../../../doc/html/images/home.png" alt="Home"></a><a accesskey="n" href="sf_poly/legendre.html"><img src="../../../../doc/html/images/next.png" alt="Next"></a>
+</div>
+<div class="section" lang="en">
+<div class="titlepage"><div><div><h3 class="title">
+<a name="math_toolkit.special.sf_poly"></a><a class="link" href="sf_poly.html" title="Polynomials"> Polynomials</a>
+</h3></div></div></div>
+<div class="toc"><dl>
+<dt><span class="section"><a href="sf_poly/legendre.html"> Legendre (and
+        Associated) Polynomials</a></span></dt>
+<dt><span class="section"><a href="sf_poly/laguerre.html"> Laguerre (and
+        Associated) Polynomials</a></span></dt>
+<dt><span class="section"> Hermite Polynomials</span></dt>
+<dt><span class="section"> Spherical Harmonics</span></dt>
+</dl></div>
+</div>
+<table xmlns:rev="http://www.cs.rpi.edu/~gregod/boost/tools/doc/revision" width="100%"><tr>
+<td align="left"></td>
+<td align="right"><div class="copyright-footer">Copyright © 2006 , 2007, 2008 John Maddock, Paul A. Bristow, Hubert
+      Holin, Xiaogang Zhang, Bruno Lalande and Gautam Sewani<p>
+        Distributed under the Boost Software License, Version 1.0. (See accompanying
+        file LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_0.txt)
+      </p>
+</div></td>
+</tr></table>
+<hr>
+<div class="spirit-nav">
+<a accesskey="p" href="sf_erf/error_inv.html"><img src="../../../../doc/html/images/prev.png" alt="Prev"></a><a accesskey="u" href="../special.html"><img src="../../../../doc/html/images/up.png" alt="Up"></a><a accesskey="h" href="../../index.html"><img src="../../../../doc/html/images/home.png" alt="Home"></a><a accesskey="n" href="sf_poly/legendre.html"><img src="../../../../doc/html/images/next.png" alt="Next"></a>
+</div>
+</body>
+</html>

Added: sandbox/tools/auto_index/example/math/doc/sf_and_dist/html/math_toolkit/special/sf_poly/hermite.html
==============================================================================
--- (empty file)
+++ sandbox/tools/auto_index/example/math/doc/sf_and_dist/html/math_toolkit/special/sf_poly/hermite.html	2008-11-28 05:25:28 EST (Fri, 28 Nov 2008)
@@ -0,0 +1,289 @@
+<html>
+<head>
+<meta http-equiv="Content-Type" content="text/html; charset=ISO-8859-1">
+<title>Hermite Polynomials</title>
+<link rel="stylesheet" href="../../../boostbook.css" type="text/css">
+<meta name="generator" content="DocBook XSL Stylesheets Vsnapshot_8125">
+<link rel="home" href="../../../index.html" title="Math Toolkit">
+<link rel="up" href="../sf_poly.html" title="Polynomials">
+<link rel="prev" href="laguerre.html" title="Laguerre (and Associated) Polynomials">
+<link rel="next" href="sph_harm.html" title="Spherical Harmonics">
+</head>
+<body bgcolor="white" text="black" link="#0000FF" vlink="#840084" alink="#0000FF">
+<table cellpadding="2" width="100%"><tr>
+<td valign="top"><img alt="Boost C++ Libraries" width="277" height="86" src="../../../../../boost.png"></td>
+<td align="center">Home</td>
+<td align="center">Libraries</td>
+<td align="center">People</td>
+<td align="center">FAQ</td>
+<td align="center">More</td>
+</tr></table>
+<hr>
+<div class="spirit-nav">
+<a accesskey="p" href="laguerre.html"><img src="../../../../../doc/html/images/prev.png" alt="Prev"></a><a accesskey="u" href="../sf_poly.html"><img src="../../../../../doc/html/images/up.png" alt="Up"></a><a accesskey="h" href="../../../index.html"><img src="../../../../../doc/html/images/home.png" alt="Home"></a><a accesskey="n" href="sph_harm.html"><img src="../../../../../doc/html/images/next.png" alt="Next"></a>
+</div>
+<div class="section" lang="en">
+<div class="titlepage"><div><div><h4 class="title">
+<a name="math_toolkit.special.sf_poly.hermite"></a><a class="link" href="hermite.html" title="Hermite Polynomials"> Hermite Polynomials</a>
+</h4></div></div></div>
+<a name="math_toolkit.special.sf_poly.hermite.synopsis"></a><h5>
+<a name="id750175"></a>
+          <a class="link" href="hermite.html#math_toolkit.special.sf_poly.hermite.synopsis">Synopsis</a>
+        </h5>
+<p>
+          
+</p>
+<pre class="programlisting"><span class="preprocessor">#include</span> <span class="special">&lt;</span><span class="identifier">boost</span><span class="special">/</span><span class="identifier">math</span><span class="special">/</span><span class="identifier">special_functions</span><span class="special">/</span><span class="identifier">hermite</span><span class="special">.</span><span class="identifier">hpp</span><span class="special">&gt;</span>
+</pre>
+<p>
+        </p>
+<pre class="programlisting"><span class="keyword">namespace</span> <span class="identifier">boost</span><span class="special">{</span> <span class="keyword">namespace</span> <span class="identifier">math</span><span class="special">{</span>
+
+<span class="keyword">template</span> <span class="special">&lt;</span><span class="keyword">class</span> <span class="identifier">T</span><span class="special">&gt;</span>
+<a class="link" href="../../main_overview/result_type.html" title="Calculation of the Type of the Result"><span class="emphasis"><em>calculated-result-type</em></span></a> <span class="identifier">hermite</span><span class="special">(</span><span class="keyword">unsigned</span> <span class="identifier">n</span><span class="special">,</span> <span class="identifier">T</span> <span class="identifier">x</span><span class="special">);</span>
+
+<span class="keyword">template</span> <span class="special">&lt;</span><span class="keyword">class</span> <span class="identifier">T</span><span class="special">,</span> <span class="keyword">class</span> <a class="link" href="../../policy.html" title="Policies">Policy</a><span class="special">&gt;</span>
+<a class="link" href="../../main_overview/result_type.html" title="Calculation of the Type of the Result"><span class="emphasis"><em>calculated-result-type</em></span></a> <span class="identifier">hermite</span><span class="special">(</span><span class="keyword">unsigned</span> <span class="identifier">n</span><span class="special">,</span> <span class="identifier">T</span> <span class="identifier">x</span><span class="special">,</span> <span class="keyword">const</span> <a class="link" href="../../policy.html" title="Policies">Policy</a><span class="special">&amp;);</span>
+
+<span class="keyword">template</span> <span class="special">&lt;</span><span class="keyword">class</span> <span class="identifier">T1</span><span class="special">,</span> <span class="keyword">class</span> <span class="identifier">T2</span><span class="special">,</span> <span class="keyword">class</span> <span class="identifier">T3</span><span class="special">&gt;</span>
+<a class="link" href="../../main_overview/result_type.html" title="Calculation of the Type of the Result"><span class="emphasis"><em>calculated-result-type</em></span></a> <span class="identifier">hermite_next</span><span class="special">(</span><span class="keyword">unsigned</span> <span class="identifier">n</span><span class="special">,</span> <span class="identifier">T1</span> <span class="identifier">x</span><span class="special">,</span> <span class="identifier">T2</span> <span class="identifier">Hn</span><span class="special">,</span> <span class="identifier">T3</span> <span class="identifier">Hnm1</span><span class="special">);</span>
+   
+<span class="special">}}</span> <span class="comment">// namespaces
+</span></pre>
+<a name="math_toolkit.special.sf_poly.hermite.description"></a><h5>
+<a name="id750685"></a>
+          <a class="link" href="hermite.html#math_toolkit.special.sf_poly.hermite.description">Description</a>
+        </h5>
+<p>
+          The return type of these functions is computed using the <a class="link" href="../../main_overview/result_type.html" title="Calculation of the Type of the Result"><span class="emphasis"><em>result
+          type calculation rules</em></span></a>: note than when there is a single
+          template argument the result is the same type as that argument or <code class="computeroutput"><span class="keyword">double</span></code> if the template argument is an integer
+          type.
+        </p>
+<pre class="programlisting"><span class="keyword">template</span> <span class="special">&lt;</span><span class="keyword">class</span> <span class="identifier">T</span><span class="special">&gt;</span>
+<a class="link" href="../../main_overview/result_type.html" title="Calculation of the Type of the Result"><span class="emphasis"><em>calculated-result-type</em></span></a> <span class="identifier">hermite</span><span class="special">(</span><span class="keyword">unsigned</span> <span class="identifier">n</span><span class="special">,</span> <span class="identifier">T</span> <span class="identifier">x</span><span class="special">);</span>
+
+<span class="keyword">template</span> <span class="special">&lt;</span><span class="keyword">class</span> <span class="identifier">T</span><span class="special">,</span> <span class="keyword">class</span> <a class="link" href="../../policy.html" title="Policies">Policy</a><span class="special">&gt;</span>
+<a class="link" href="../../main_overview/result_type.html" title="Calculation of the Type of the Result"><span class="emphasis"><em>calculated-result-type</em></span></a> <span class="identifier">hermite</span><span class="special">(</span><span class="keyword">unsigned</span> <span class="identifier">n</span><span class="special">,</span> <span class="identifier">T</span> <span class="identifier">x</span><span class="special">,</span> <span class="keyword">const</span> <a class="link" href="../../policy.html" title="Policies">Policy</a><span class="special">&amp;);</span>
+</pre>
+<p>
+          Returns the value of the Hermite Polynomial of order <span class="emphasis"><em>n</em></span>
+          at point <span class="emphasis"><em>x</em></span>:
+        </p>
+<p>
+          <span class="inlinemediaobject"><img src="../../../../equations/hermite_0.png"></span>
+        </p>
+<p>
+          </p>
+<p>
+            The final <a class="link" href="../../policy.html" title="Policies">Policy</a> argument
+            is optional and can be used to control the behaviour of the function:
+            how it handles errors, what level of precision to use etc. Refer to the
+            <a class="link" href="../../policy.html" title="Policies">policy documentation for more details</a>.
+          </p>
+<p>
+        </p>
+<p>
+          The following graph illustrates the behaviour of the first few Hermite
+          Polynomials:
+        </p>
+<p>
+          <span class="inlinemediaobject"><img src="../../../../graphs/hermite.png" align="middle"></span>
+        </p>
+<pre class="programlisting"><span class="keyword">template</span> <span class="special">&lt;</span><span class="keyword">class</span> <span class="identifier">T1</span><span class="special">,</span> <span class="keyword">class</span> <span class="identifier">T2</span><span class="special">,</span> <span class="keyword">class</span> <span class="identifier">T3</span><span class="special">&gt;</span>
+<a class="link" href="../../main_overview/result_type.html" title="Calculation of the Type of the Result"><span class="emphasis"><em>calculated-result-type</em></span></a> <span class="identifier">hermite_next</span><span class="special">(</span><span class="keyword">unsigned</span> <span class="identifier">n</span><span class="special">,</span> <span class="identifier">T1</span> <span class="identifier">x</span><span class="special">,</span> <span class="identifier">T2</span> <span class="identifier">Hn</span><span class="special">,</span> <span class="identifier">T3</span> <span class="identifier">Hnm1</span><span class="special">);</span>
+</pre>
+<p>
+          Implements the three term recurrence relation for the Hermite polynomials,
+          this function can be used to create a sequence of values evaluated at the
+          same <span class="emphasis"><em>x</em></span>, and for rising <span class="emphasis"><em>n</em></span>.
+        </p>
+<p>
+          <span class="inlinemediaobject"><img src="../../../../equations/hermite_1.png"></span>
+        </p>
+<p>
+          For example we could produce a vector of the first 10 polynomial values
+          using:
+        </p>
+<pre class="programlisting"><span class="keyword">double</span> <span class="identifier">x</span> <span class="special">=</span> <span class="number">0.5</span><span class="special">;</span>  <span class="comment">// Abscissa value
+</span><span class="identifier">vector</span><span class="special">&lt;</span><span class="keyword">double</span><span class="special">&gt;</span> <span class="identifier">v</span><span class="special">;</span>
+<span class="identifier">v</span><span class="special">.</span><span class="identifier">push_back</span><span class="special">(</span><span class="identifier">hermite</span><span class="special">(</span><span class="number">0</span><span class="special">,</span> <span class="identifier">x</span><span class="special">)).</span><span class="identifier">push_back</span><span class="special">(</span><span class="identifier">hermite</span><span class="special">(</span><span class="number">1</span><span class="special">,</span> <span class="identifier">x</span><span class="special">));</span>
+<span class="keyword">for</span><span class="special">(</span><span class="keyword">unsigned</span> <span class="identifier">l</span> <span class="special">=</span> <span class="number">1</span><span class="special">;</span> <span class="identifier">l</span> <span class="special">&lt;</span> <span class="number">10</span><span class="special">;</span> <span class="special">++</span><span class="identifier">l</span><span class="special">)</span>
+   <span class="identifier">v</span><span class="special">.</span><span class="identifier">push_back</span><span class="special">(</span><span class="identifier">hermite_next</span><span class="special">(</span><span class="identifier">l</span><span class="special">,</span> <span class="identifier">x</span><span class="special">,</span> <span class="identifier">v</span><span class="special">[</span><span class="identifier">l</span><span class="special">],</span> <span class="identifier">v</span><span class="special">[</span><span class="identifier">l</span><span class="special">-</span><span class="number">1</span><span class="special">]));</span>
+</pre>
+<p>
+          Formally the arguments are:
+        </p>
+<div class="variablelist">
+<p class="title"><b></b></p>
+<dl>
+<dt><span class="term">n</span></dt>
+<dd><p>
+              The degree <span class="emphasis"><em>n</em></span> of the last polynomial calculated.
+            </p></dd>
+<dt><span class="term">x</span></dt>
+<dd><p>
+              The abscissa value
+            </p></dd>
+<dt><span class="term">Hn</span></dt>
+<dd><p>
+              The value of the polynomial evaluated at degree <span class="emphasis"><em>n</em></span>.
+            </p></dd>
+<dt><span class="term">Hnm1</span></dt>
+<dd><p>
+              The value of the polynomial evaluated at degree <span class="emphasis"><em>n-1</em></span>.
+            </p></dd>
+</dl>
+</div>
+<a name="math_toolkit.special.sf_poly.hermite.accuracy"></a><h5>
+<a name="id751716"></a>
+          <a class="link" href="hermite.html#math_toolkit.special.sf_poly.hermite.accuracy">Accuracy</a>
+        </h5>
+<p>
+          The following table shows peak errors (in units of epsilon) for various
+          domains of input arguments. Note that only results for the widest floating
+          point type on the system are given as narrower types have <a class="link" href="../../backgrounders/relative_error.html#zero_error">effectively
+          zero error</a>.
+        </p>
+<div class="table">
+<a name="id751750"></a><p class="title"><b>Table 34. Peak Errors In the Hermite Polynomial</b></p>
+<div class="table-contents"><table class="table" summary="Peak Errors In the Hermite Polynomial">
+<colgroup>
+<col>
+<col>
+<col>
+</colgroup>
+<thead><tr>
+<th>
+              <p>
+                Significand Size
+              </p>
+              </th>
+<th>
+              <p>
+                Platform and Compiler
+              </p>
+              </th>
+<th>
+              <p>
+                Errors in range
+              </p>
+              <p>
+                0 &lt; l &lt; 20
+              </p>
+              </th>
+</tr></thead>
+<tbody>
+<tr>
+<td>
+              <p>
+                53
+              </p>
+              </td>
+<td>
+              <p>
+                Win32, Visual C++ 8
+              </p>
+              </td>
+<td>
+              <p>
+                Peak=4.5 Mean=1.5
+              </p>
+              </td>
+</tr>
+<tr>
+<td>
+              <p>
+                64
+              </p>
+              </td>
+<td>
+              <p>
+                Red Hat Linux IA32, g++ 4.1
+              </p>
+              </td>
+<td>
+              <p>
+                Peak=6 Mean=2
+              </p>
+              </td>
+</tr>
+<tr>
+<td>
+              <p>
+                64
+              </p>
+              </td>
+<td>
+              <p>
+                Red Hat Linux IA64, g++ 3.4.4
+              </p>
+              </td>
+<td>
+              <p>
+                Peak=6 Mean=2
+              </p>
+              </td>
+</tr>
+<tr>
+<td>
+              <p>
+                113
+              </p>
+              </td>
+<td>
+              <p>
+                HPUX IA64, aCC A.06.06
+              </p>
+              </td>
+<td>
+              <p>
+                Peak=6 Mean=4
+              </p>
+              </td>
+</tr>
+</tbody>
+</table></div>
+</div>
+<br class="table-break"><p>
+          Note that the worst errors occur when the degree increases, values greater
+          than ~120 are very unlikely to produce sensible results, especially in
+          the associated polynomial case when the order is also large. Further the
+          relative errors are likely to grow arbitrarily large when the function
+          is very close to a root.
+        </p>
+<a name="math_toolkit.special.sf_poly.hermite.testing"></a><h5>
+<a name="id751943"></a>
+          <a class="link" href="hermite.html#math_toolkit.special.sf_poly.hermite.testing">Testing</a>
+        </h5>
+<p>
+          A mixture of spot tests of values calculated using functions.wolfram.com,
+          and randomly generated test data are used: the test data was computed using
+          NTL::RR at 1000-bit
+          precision.
+        </p>
+<a name="math_toolkit.special.sf_poly.hermite.implementation"></a><h5>
+<a name="id751984"></a>
+          <a class="link" href="hermite.html#math_toolkit.special.sf_poly.hermite.implementation">Implementation</a>
+        </h5>
+<p>
+          These functions are implemented using the stable three term recurrence
+          relations. These relations guarentee low absolute error but cannot guarentee
+          low relative error near one of the roots of the polynomials.
+        </p>
+</div>
+<table xmlns:rev="http://www.cs.rpi.edu/~gregod/boost/tools/doc/revision" width="100%"><tr>
+<td align="left"></td>
+<td align="right"><div class="copyright-footer">Copyright © 2006 , 2007, 2008 John Maddock, Paul A. Bristow, Hubert
+      Holin, Xiaogang Zhang, Bruno Lalande and Gautam Sewani<p>
+        Distributed under the Boost Software License, Version 1.0. (See accompanying
+        file LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_0.txt)
+      </p>
+</div></td>
+</tr></table>
+<hr>
+<div class="spirit-nav">
+<a accesskey="p" href="laguerre.html"><img src="../../../../../doc/html/images/prev.png" alt="Prev"></a><a accesskey="u" href="../sf_poly.html"><img src="../../../../../doc/html/images/up.png" alt="Up"></a><a accesskey="h" href="../../../index.html"><img src="../../../../../doc/html/images/home.png" alt="Home"></a><a accesskey="n" href="sph_harm.html"><img src="../../../../../doc/html/images/next.png" alt="Next"></a>
+</div>
+</body>
+</html>

Added: sandbox/tools/auto_index/example/math/doc/sf_and_dist/html/math_toolkit/special/sf_poly/laguerre.html
==============================================================================
--- (empty file)
+++ sandbox/tools/auto_index/example/math/doc/sf_and_dist/html/math_toolkit/special/sf_poly/laguerre.html	2008-11-28 05:25:28 EST (Fri, 28 Nov 2008)
@@ -0,0 +1,465 @@
+<html>
+<head>
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+</div>
+<div class="section" lang="en">
+<div class="titlepage"><div><div><h4 class="title">
+<a name="math_toolkit.special.sf_poly.laguerre"></a><a class="link" href="laguerre.html" title="Laguerre (and Associated) Polynomials"> Laguerre (and
+        Associated) Polynomials</a>
+</h4></div></div></div>
+<a name="math_toolkit.special.sf_poly.laguerre.synopsis"></a><h5>
+<a name="id746691"></a>
+          <a class="link" href="laguerre.html#math_toolkit.special.sf_poly.laguerre.synopsis">Synopsis</a>
+        </h5>
+<p>
+          
+</p>
+<pre class="programlisting"><span class="preprocessor">#include</span> <span class="special">&lt;</span><span class="identifier">boost</span><span class="special">/</span><span class="identifier">math</span><span class="special">/</span><span class="identifier">special_functions</span><span class="special">/</span><span class="identifier">laguerre</span><span class="special">.</span><span class="identifier">hpp</span><span class="special">&gt;</span>
+</pre>
+<p>
+        </p>
+<pre class="programlisting"><span class="keyword">namespace</span> <span class="identifier">boost</span><span class="special">{</span> <span class="keyword">namespace</span> <span class="identifier">math</span><span class="special">{</span>
+
+<span class="keyword">template</span> <span class="special">&lt;</span><span class="keyword">class</span> <span class="identifier">T</span><span class="special">&gt;</span>
+<a class="link" href="../../main_overview/result_type.html" title="Calculation of the Type of the Result"><span class="emphasis"><em>calculated-result-type</em></span></a> <span class="identifier">laguerre</span><span class="special">(</span><span class="keyword">unsigned</span> <span class="identifier">n</span><span class="special">,</span> <span class="identifier">T</span> <span class="identifier">x</span><span class="special">);</span>
+
+<span class="keyword">template</span> <span class="special">&lt;</span><span class="keyword">class</span> <span class="identifier">T</span><span class="special">,</span> <span class="keyword">class</span> <a class="link" href="../../policy.html" title="Policies">Policy</a><span class="special">&gt;</span>
+<a class="link" href="../../main_overview/result_type.html" title="Calculation of the Type of the Result"><span class="emphasis"><em>calculated-result-type</em></span></a> <span class="identifier">laguerre</span><span class="special">(</span><span class="keyword">unsigned</span> <span class="identifier">n</span><span class="special">,</span> <span class="identifier">T</span> <span class="identifier">x</span><span class="special">,</span> <span class="keyword">const</span> <a class="link" href="../../policy.html" title="Policies">Policy</a><span class="special">&amp;);</span>
+
+<span class="keyword">template</span> <span class="special">&lt;</span><span class="keyword">class</span> <span class="identifier">T</span><span class="special">&gt;</span>
+<a class="link" href="../../main_overview/result_type.html" title="Calculation of the Type of the Result"><span class="emphasis"><em>calculated-result-type</em></span></a> <span class="identifier">laguerre</span><span class="special">(</span><span class="keyword">unsigned</span> <span class="identifier">n</span><span class="special">,</span> <span class="keyword">unsigned</span> <span class="identifier">m</span><span class="special">,</span> <span class="identifier">T</span> <span class="identifier">x</span><span class="special">);</span>
+
+<span class="keyword">template</span> <span class="special">&lt;</span><span class="keyword">class</span> <span class="identifier">T</span><span class="special">,</span> <span class="keyword">class</span> <a class="link" href="../../policy.html" title="Policies">Policy</a><span class="special">&gt;</span>
+<a class="link" href="../../main_overview/result_type.html" title="Calculation of the Type of the Result"><span class="emphasis"><em>calculated-result-type</em></span></a> <span class="identifier">laguerre</span><span class="special">(</span><span class="keyword">unsigned</span> <span class="identifier">n</span><span class="special">,</span> <span class="keyword">unsigned</span> <span class="identifier">m</span><span class="special">,</span> <span class="identifier">T</span> <span class="identifier">x</span><span class="special">,</span> <span class="keyword">const</span> <a class="link" href="../../policy.html" title="Policies">Policy</a><span class="special">&amp;);</span>
+
+<span class="keyword">template</span> <span class="special">&lt;</span><span class="keyword">class</span> <span class="identifier">T1</span><span class="special">,</span> <span class="keyword">class</span> <span class="identifier">T2</span><span class="special">,</span> <span class="keyword">class</span> <span class="identifier">T3</span><span class="special">&gt;</span>
+<a class="link" href="../../main_overview/result_type.html" title="Calculation of the Type of the Result"><span class="emphasis"><em>calculated-result-type</em></span></a> <span class="identifier">laguerre_next</span><span class="special">(</span><span class="keyword">unsigned</span> <span class="identifier">n</span><span class="special">,</span> <span class="identifier">T1</span> <span class="identifier">x</span><span class="special">,</span> <span class="identifier">T2</span> <span class="identifier">Ln</span><span class="special">,</span> <span class="identifier">T3</span> <span class="identifier">Lnm1</span><span class="special">);</span>
+
+<span class="keyword">template</span> <span class="special">&lt;</span><span class="keyword">class</span> <span class="identifier">T1</span><span class="special">,</span> <span class="keyword">class</span> <span class="identifier">T2</span><span class="special">,</span> <span class="keyword">class</span> <span class="identifier">T3</span><span class="special">&gt;</span>
+<a class="link" href="../../main_overview/result_type.html" title="Calculation of the Type of the Result"><span class="emphasis"><em>calculated-result-type</em></span></a> <span class="identifier">laguerre_next</span><span class="special">(</span><span class="keyword">unsigned</span> <span class="identifier">n</span><span class="special">,</span> <span class="keyword">unsigned</span> <span class="identifier">m</span><span class="special">,</span> <span class="identifier">T1</span> <span class="identifier">x</span><span class="special">,</span> <span class="identifier">T2</span> <span class="identifier">Ln</span><span class="special">,</span> <span class="identifier">T3</span> <span class="identifier">Lnm1</span><span class="special">);</span>
+
+
+<span class="special">}}</span> <span class="comment">// namespaces
+</span></pre>
+<a name="math_toolkit.special.sf_poly.laguerre.description"></a><h5>
+<a name="id747612"></a>
+          <a class="link" href="laguerre.html#math_toolkit.special.sf_poly.laguerre.description">Description</a>
+        </h5>
+<p>
+          The return type of these functions is computed using the <a class="link" href="../../main_overview/result_type.html" title="Calculation of the Type of the Result"><span class="emphasis"><em>result
+          type calculation rules</em></span></a>: note than when there is a single
+          template argument the result is the same type as that argument or <code class="computeroutput"><span class="keyword">double</span></code> if the template argument is an integer
+          type.
+        </p>
+<p>
+          </p>
+<p>
+            The final <a class="link" href="../../policy.html" title="Policies">Policy</a> argument
+            is optional and can be used to control the behaviour of the function:
+            how it handles errors, what level of precision to use etc. Refer to the
+            <a class="link" href="../../policy.html" title="Policies">policy documentation for more details</a>.
+          </p>
+<p>
+        </p>
+<pre class="programlisting"><span class="keyword">template</span> <span class="special">&lt;</span><span class="keyword">class</span> <span class="identifier">T</span><span class="special">&gt;</span>
+<a class="link" href="../../main_overview/result_type.html" title="Calculation of the Type of the Result"><span class="emphasis"><em>calculated-result-type</em></span></a> <span class="identifier">laguerre</span><span class="special">(</span><span class="keyword">unsigned</span> <span class="identifier">n</span><span class="special">,</span> <span class="identifier">T</span> <span class="identifier">x</span><span class="special">);</span>
+
+<span class="keyword">template</span> <span class="special">&lt;</span><span class="keyword">class</span> <span class="identifier">T</span><span class="special">,</span> <span class="keyword">class</span> <a class="link" href="../../policy.html" title="Policies">Policy</a><span class="special">&gt;</span>
+<a class="link" href="../../main_overview/result_type.html" title="Calculation of the Type of the Result"><span class="emphasis"><em>calculated-result-type</em></span></a> <span class="identifier">laguerre</span><span class="special">(</span><span class="keyword">unsigned</span> <span class="identifier">n</span><span class="special">,</span> <span class="identifier">T</span> <span class="identifier">x</span><span class="special">,</span> <span class="keyword">const</span> <a class="link" href="../../policy.html" title="Policies">Policy</a><span class="special">&amp;);</span>
+</pre>
+<p>
+          Returns the value of the Laguerre Polynomial of order <span class="emphasis"><em>n</em></span>
+          at point <span class="emphasis"><em>x</em></span>:
+        </p>
+<p>
+          <span class="inlinemediaobject"><img src="../../../../equations/laguerre_0.png"></span>
+        </p>
+<p>
+          The following graph illustrates the behaviour of the first few Laguerre
+          Polynomials:
+        </p>
+<p>
+          <span class="inlinemediaobject"><img src="../../../../graphs/laguerre.png" align="middle"></span>
+        </p>
+<pre class="programlisting"><span class="keyword">template</span> <span class="special">&lt;</span><span class="keyword">class</span> <span class="identifier">T</span><span class="special">&gt;</span>
+<a class="link" href="../../main_overview/result_type.html" title="Calculation of the Type of the Result"><span class="emphasis"><em>calculated-result-type</em></span></a> <span class="identifier">laguerre</span><span class="special">(</span><span class="keyword">unsigned</span> <span class="identifier">n</span><span class="special">,</span> <span class="keyword">unsigned</span> <span class="identifier">m</span><span class="special">,</span> <span class="identifier">T</span> <span class="identifier">x</span><span class="special">);</span>
+
+<span class="keyword">template</span> <span class="special">&lt;</span><span class="keyword">class</span> <span class="identifier">T</span><span class="special">,</span> <span class="keyword">class</span> <a class="link" href="../../policy.html" title="Policies">Policy</a><span class="special">&gt;</span>
+<a class="link" href="../../main_overview/result_type.html" title="Calculation of the Type of the Result"><span class="emphasis"><em>calculated-result-type</em></span></a> <span class="identifier">laguerre</span><span class="special">(</span><span class="keyword">unsigned</span> <span class="identifier">n</span><span class="special">,</span> <span class="keyword">unsigned</span> <span class="identifier">m</span><span class="special">,</span> <span class="identifier">T</span> <span class="identifier">x</span><span class="special">,</span> <span class="keyword">const</span> <a class="link" href="../../policy.html" title="Policies">Policy</a><span class="special">&amp;);</span>
+</pre>
+<p>
+          Returns the Associated Laguerre polynomial of degree <span class="emphasis"><em>n</em></span>
+          and order <span class="emphasis"><em>m</em></span> at point <span class="emphasis"><em>x</em></span>:
+        </p>
+<p>
+          <span class="inlinemediaobject"><img src="../../../../equations/laguerre_1.png"></span>
+        </p>
+<pre class="programlisting"><span class="keyword">template</span> <span class="special">&lt;</span><span class="keyword">class</span> <span class="identifier">T1</span><span class="special">,</span> <span class="keyword">class</span> <span class="identifier">T2</span><span class="special">,</span> <span class="keyword">class</span> <span class="identifier">T3</span><span class="special">&gt;</span>
+<a class="link" href="../../main_overview/result_type.html" title="Calculation of the Type of the Result"><span class="emphasis"><em>calculated-result-type</em></span></a> <span class="identifier">laguerre_next</span><span class="special">(</span><span class="keyword">unsigned</span> <span class="identifier">n</span><span class="special">,</span> <span class="identifier">T1</span> <span class="identifier">x</span><span class="special">,</span> <span class="identifier">T2</span> <span class="identifier">Ln</span><span class="special">,</span> <span class="identifier">T3</span> <span class="identifier">Lnm1</span><span class="special">);</span>
+</pre>
+<p>
+          Implements the three term recurrence relation for the Laguerre polynomials,
+          this function can be used to create a sequence of values evaluated at the
+          same <span class="emphasis"><em>x</em></span>, and for rising <span class="emphasis"><em>n</em></span>.
+        </p>
+<p>
+          <span class="inlinemediaobject"><img src="../../../../equations/laguerre_2.png"></span>
+        </p>
+<p>
+          For example we could produce a vector of the first 10 polynomial values
+          using:
+        </p>
+<pre class="programlisting"><span class="keyword">double</span> <span class="identifier">x</span> <span class="special">=</span> <span class="number">0.5</span><span class="special">;</span>  <span class="comment">// Abscissa value
+</span><span class="identifier">vector</span><span class="special">&lt;</span><span class="keyword">double</span><span class="special">&gt;</span> <span class="identifier">v</span><span class="special">;</span>
+<span class="identifier">v</span><span class="special">.</span><span class="identifier">push_back</span><span class="special">(</span><span class="identifier">laguerre</span><span class="special">(</span><span class="number">0</span><span class="special">,</span> <span class="identifier">x</span><span class="special">)).</span><span class="identifier">push_back</span><span class="special">(</span><span class="identifier">laguerre</span><span class="special">(</span><span class="number">1</span><span class="special">,</span> <span class="identifier">x</span><span class="special">));</span>
+<span class="keyword">for</span><span class="special">(</span><span class="keyword">unsigned</span> <span class="identifier">l</span> <span class="special">=</span> <span class="number">1</span><span class="special">;</span> <span class="identifier">l</span> <span class="special">&lt;</span> <span class="number">10</span><span class="special">;</span> <span class="special">++</span><span class="identifier">l</span><span class="special">)</span>
+   <span class="identifier">v</span><span class="special">.</span><span class="identifier">push_back</span><span class="special">(</span><span class="identifier">laguerre_next</span><span class="special">(</span><span class="identifier">l</span><span class="special">,</span> <span class="identifier">x</span><span class="special">,</span> <span class="identifier">v</span><span class="special">[</span><span class="identifier">l</span><span class="special">],</span> <span class="identifier">v</span><span class="special">[</span><span class="identifier">l</span><span class="special">-</span><span class="number">1</span><span class="special">]));</span>
+</pre>
+<p>
+          Formally the arguments are:
+        </p>
+<div class="variablelist">
+<p class="title"><b></b></p>
+<dl>
+<dt><span class="term">n</span></dt>
+<dd><p>
+              The degree <span class="emphasis"><em>n</em></span> of the last polynomial calculated.
+            </p></dd>
+<dt><span class="term">x</span></dt>
+<dd><p>
+              The abscissa value
+            </p></dd>
+<dt><span class="term">Ln</span></dt>
+<dd><p>
+              The value of the polynomial evaluated at degree <span class="emphasis"><em>n</em></span>.
+            </p></dd>
+<dt><span class="term">Lnm1</span></dt>
+<dd><p>
+              The value of the polynomial evaluated at degree <span class="emphasis"><em>n-1</em></span>.
+            </p></dd>
+</dl>
+</div>
+<pre class="programlisting"><span class="keyword">template</span> <span class="special">&lt;</span><span class="keyword">class</span> <span class="identifier">T1</span><span class="special">,</span> <span class="keyword">class</span> <span class="identifier">T2</span><span class="special">,</span> <span class="keyword">class</span> <span class="identifier">T3</span><span class="special">&gt;</span>
+<a class="link" href="../../main_overview/result_type.html" title="Calculation of the Type of the Result"><span class="emphasis"><em>calculated-result-type</em></span></a> <span class="identifier">laguerre_next</span><span class="special">(</span><span class="keyword">unsigned</span> <span class="identifier">n</span><span class="special">,</span> <span class="keyword">unsigned</span> <span class="identifier">m</span><span class="special">,</span> <span class="identifier">T1</span> <span class="identifier">x</span><span class="special">,</span> <span class="identifier">T2</span> <span class="identifier">Ln</span><span class="special">,</span> <span class="identifier">T3</span> <span class="identifier">Lnm1</span><span class="special">);</span>
+</pre>
+<p>
+          Implements the three term recurrence relation for the Associated Laguerre
+          polynomials, this function can be used to create a sequence of values evaluated
+          at the same <span class="emphasis"><em>x</em></span>, and for rising degree <span class="emphasis"><em>n</em></span>.
+        </p>
+<p>
+          <span class="inlinemediaobject"><img src="../../../../equations/laguerre_3.png"></span>
+        </p>
+<p>
+          For example we could produce a vector of the first 10 polynomial values
+          using:
+        </p>
+<pre class="programlisting"><span class="keyword">double</span> <span class="identifier">x</span> <span class="special">=</span> <span class="number">0.5</span><span class="special">;</span>  <span class="comment">// Abscissa value
+</span><span class="keyword">int</span> <span class="identifier">m</span> <span class="special">=</span> <span class="number">10</span><span class="special">;</span>      <span class="comment">// order
+</span><span class="identifier">vector</span><span class="special">&lt;</span><span class="keyword">double</span><span class="special">&gt;</span> <span class="identifier">v</span><span class="special">;</span>
+<span class="identifier">v</span><span class="special">.</span><span class="identifier">push_back</span><span class="special">(</span><span class="identifier">laguerre</span><span class="special">(</span><span class="number">0</span><span class="special">,</span> <span class="identifier">m</span><span class="special">,</span> <span class="identifier">x</span><span class="special">)).</span><span class="identifier">push_back</span><span class="special">(</span><span class="identifier">laguerre</span><span class="special">(</span><span class="number">1</span><span class="special">,</span> <span class="identifier">m</span><span class="special">,</span> <span class="identifier">x</span><span class="special">));</span>
+<span class="keyword">for</span><span class="special">(</span><span class="keyword">unsigned</span> <span class="identifier">l</span> <span class="special">=</span> <span class="number">1</span><span class="special">;</span> <span class="identifier">l</span> <span class="special">&lt;</span> <span class="number">10</span><span class="special">;</span> <span class="special">++</span><span class="identifier">l</span><span class="special">)</span>
+   <span class="identifier">v</span><span class="special">.</span><span class="identifier">push_back</span><span class="special">(</span><span class="identifier">laguerre_next</span><span class="special">(</span><span class="identifier">l</span><span class="special">,</span> <span class="identifier">m</span><span class="special">,</span> <span class="identifier">x</span><span class="special">,</span> <span class="identifier">v</span><span class="special">[</span><span class="identifier">l</span><span class="special">],</span> <span class="identifier">v</span><span class="special">[</span><span class="identifier">l</span><span class="special">-</span><span class="number">1</span><span class="special">]));</span>
+</pre>
+<p>
+          Formally the arguments are:
+        </p>
+<div class="variablelist">
+<p class="title"><b></b></p>
+<dl>
+<dt><span class="term">n</span></dt>
+<dd><p>
+              The degree of the last polynomial calculated.
+            </p></dd>
+<dt><span class="term">m</span></dt>
+<dd><p>
+              The order of the Associated Polynomial.
+            </p></dd>
+<dt><span class="term">x</span></dt>
+<dd><p>
+              The abscissa value.
+            </p></dd>
+<dt><span class="term">Ln</span></dt>
+<dd><p>
+              The value of the polynomial evaluated at degree <span class="emphasis"><em>n</em></span>.
+            </p></dd>
+<dt><span class="term">Lnm1</span></dt>
+<dd><p>
+              The value of the polynomial evaluated at degree <span class="emphasis"><em>n-1</em></span>.
+            </p></dd>
+</dl>
+</div>
+<a name="math_toolkit.special.sf_poly.laguerre.accuracy"></a><h5>
+<a name="id749679"></a>
+          <a class="link" href="laguerre.html#math_toolkit.special.sf_poly.laguerre.accuracy">Accuracy</a>
+        </h5>
+<p>
+          The following table shows peak errors (in units of epsilon) for various
+          domains of input arguments. Note that only results for the widest floating
+          point type on the system are given as narrower types have <a class="link" href="../../backgrounders/relative_error.html#zero_error">effectively
+          zero error</a>.
+        </p>
+<div class="table">
+<a name="id749708"></a><p class="title"><b>Table 32. Peak Errors In the Laguerre Polynomial</b></p>
+<div class="table-contents"><table class="table" summary="Peak Errors In the Laguerre Polynomial">
+<colgroup>
+<col>
+<col>
+<col>
+</colgroup>
+<thead><tr>
+<th>
+              <p>
+                Significand Size
+              </p>
+              </th>
+<th>
+              <p>
+                Platform and Compiler
+              </p>
+              </th>
+<th>
+              <p>
+                Errors in range
+              </p>
+              <p>
+                0 &lt; l &lt; 20
+              </p>
+              </th>
+</tr></thead>
+<tbody>
+<tr>
+<td>
+              <p>
+                53
+              </p>
+              </td>
+<td>
+              <p>
+                Win32, Visual C++ 8
+              </p>
+              </td>
+<td>
+              <p>
+                Peak=3000 Mean=185
+              </p>
+              </td>
+</tr>
+<tr>
+<td>
+              <p>
+                64
+              </p>
+              </td>
+<td>
+              <p>
+                SUSE Linux IA32, g++ 4.1
+              </p>
+              </td>
+<td>
+              <p>
+                Peak=1x10<sup>4</sup> Mean=828
+              </p>
+              </td>
+</tr>
+<tr>
+<td>
+              <p>
+                64
+              </p>
+              </td>
+<td>
+              <p>
+                Red Hat Linux IA64, g++ 3.4.4
+              </p>
+              </td>
+<td>
+              <p>
+                Peak=1x10<sup>4</sup> Mean=828
+              </p>
+              </td>
+</tr>
+<tr>
+<td>
+              <p>
+                113
+              </p>
+              </td>
+<td>
+              <p>
+                HPUX IA64, aCC A.06.06
+              </p>
+              </td>
+<td>
+              <p>
+                Peak=680 Mean=40
+              </p>
+              </td>
+</tr>
+</tbody>
+</table></div>
+</div>
+<br class="table-break"><div class="table">
+<a name="id749882"></a><p class="title"><b>Table 33. Peak Errors In the Associated Laguerre
+        Polynomial</b></p>
+<div class="table-contents"><table class="table" summary="Peak Errors In the Associated Laguerre
+        Polynomial">
+<colgroup>
+<col>
+<col>
+<col>
+</colgroup>
+<thead><tr>
+<th>
+              <p>
+                Significand Size
+              </p>
+              </th>
+<th>
+              <p>
+                Platform and Compiler
+              </p>
+              </th>
+<th>
+              <p>
+                Errors in range
+              </p>
+              <p>
+                0 &lt; l &lt; 20
+              </p>
+              </th>
+</tr></thead>
+<tbody>
+<tr>
+<td>
+              <p>
+                53
+              </p>
+              </td>
+<td>
+              <p>
+                Win32, Visual C++ 8
+              </p>
+              </td>
+<td>
+              <p>
+                Peak=433 Mean=11
+              </p>
+              </td>
+</tr>
+<tr>
+<td>
+              <p>
+                64
+              </p>
+              </td>
+<td>
+              <p>
+                SUSE Linux IA32, g++ 4.1
+              </p>
+              </td>
+<td>
+              <p>
+                Peak=61.4 Mean=19.5
+              </p>
+              </td>
+</tr>
+<tr>
+<td>
+              <p>
+                64
+              </p>
+              </td>
+<td>
+              <p>
+                Red Hat Linux IA64, g++ 3.4.4
+              </p>
+              </td>
+<td>
+              <p>
+                Peak=61.4 Mean=19.5
+              </p>
+              </td>
+</tr>
+<tr>
+<td>
+              <p>
+                113
+              </p>
+              </td>
+<td>
+              <p>
+                HPUX IA64, aCC A.06.06
+              </p>
+              </td>
+<td>
+              <p>
+                Peak=540 Mean=13.94
+              </p>
+              </td>
+</tr>
+</tbody>
+</table></div>
+</div>
+<br class="table-break"><p>
+          Note that the worst errors occur when the degree increases, values greater
+          than ~120 are very unlikely to produce sensible results, especially in
+          the associated polynomial case when the order is also large. Further the
+          relative errors are likely to grow arbitrarily large when the function
+          is very close to a root.
+        </p>
+<a name="math_toolkit.special.sf_poly.laguerre.testing"></a><h5>
+<a name="id750079"></a>
+          <a class="link" href="laguerre.html#math_toolkit.special.sf_poly.laguerre.testing">Testing</a>
+        </h5>
+<p>
+          A mixture of spot tests of values calculated using functions.wolfram.com,
+          and randomly generated test data are used: the test data was computed using
+          NTL::RR at 1000-bit
+          precision.
+        </p>
+<a name="math_toolkit.special.sf_poly.laguerre.implementation"></a><h5>
+<a name="id750121"></a>
+          <a class="link" href="laguerre.html#math_toolkit.special.sf_poly.laguerre.implementation">Implementation</a>
+        </h5>
+<p>
+          These functions are implemented using the stable three term recurrence
+          relations. These relations guarentee low absolute error but cannot guarentee
+          low relative error near one of the roots of the polynomials.
+        </p>
+</div>
+<table xmlns:rev="http://www.cs.rpi.edu/~gregod/boost/tools/doc/revision" width="100%"><tr>
+<td align="left"></td>
+<td align="right"><div class="copyright-footer">Copyright © 2006 , 2007, 2008 John Maddock, Paul A. Bristow, Hubert
+      Holin, Xiaogang Zhang, Bruno Lalande and Gautam Sewani<p>
+        Distributed under the Boost Software License, Version 1.0. (See accompanying
+        file LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_0.txt)
+      </p>
+</div></td>
+</tr></table>
+<hr>
+<div class="spirit-nav">
+<a accesskey="p" href="legendre.html"><img src="../../../../../doc/html/images/prev.png" alt="Prev"></a><a accesskey="u" href="../sf_poly.html"><img src="../../../../../doc/html/images/up.png" alt="Up"></a><a accesskey="h" href="../../../index.html"><img src="../../../../../doc/html/images/home.png" alt="Home"></a><a accesskey="n" href="hermite.html"><img src="../../../../../doc/html/images/next.png" alt="Next"></a>
+</div>
+</body>
+</html>

Added: sandbox/tools/auto_index/example/math/doc/sf_and_dist/html/math_toolkit/special/sf_poly/legendre.html
==============================================================================
--- (empty file)
+++ sandbox/tools/auto_index/example/math/doc/sf_and_dist/html/math_toolkit/special/sf_poly/legendre.html	2008-11-28 05:25:28 EST (Fri, 28 Nov 2008)
@@ -0,0 +1,711 @@
+<html>
+<head>
+<meta http-equiv="Content-Type" content="text/html; charset=ISO-8859-1">
+<title>Legendre (and Associated) Polynomials</title>
+<link rel="stylesheet" href="../../../boostbook.css" type="text/css">
+<meta name="generator" content="DocBook XSL Stylesheets Vsnapshot_8125">
+<link rel="home" href="../../../index.html" title="Math Toolkit">
+<link rel="up" href="../sf_poly.html" title="Polynomials">
+<link rel="prev" href="../sf_poly.html" title="Polynomials">
+<link rel="next" href="laguerre.html" title="Laguerre (and Associated) Polynomials">
+</head>
+<body bgcolor="white" text="black" link="#0000FF" vlink="#840084" alink="#0000FF">
+<table cellpadding="2" width="100%"><tr>
+<td valign="top"><img alt="Boost C++ Libraries" width="277" height="86" src="../../../../../boost.png"></td>
+<td align="center">Home</td>
+<td align="center">Libraries</td>
+<td align="center">People</td>
+<td align="center">FAQ</td>
+<td align="center">More</td>
+</tr></table>
+<hr>
+<div class="spirit-nav">
+<a accesskey="p" href="../sf_poly.html"><img src="../../../../../doc/html/images/prev.png" alt="Prev"></a><a accesskey="u" href="../sf_poly.html"><img src="../../../../../doc/html/images/up.png" alt="Up"></a><a accesskey="h" href="../../../index.html"><img src="../../../../../doc/html/images/home.png" alt="Home"></a><a accesskey="n" href="laguerre.html"><img src="../../../../../doc/html/images/next.png" alt="Next"></a>
+</div>
+<div class="section" lang="en">
+<div class="titlepage"><div><div><h4 class="title">
+<a name="math_toolkit.special.sf_poly.legendre"></a><a class="link" href="legendre.html" title="Legendre (and Associated) Polynomials"> Legendre (and
+        Associated) Polynomials</a>
+</h4></div></div></div>
+<a name="math_toolkit.special.sf_poly.legendre.synopsis"></a><h5>
+<a name="id742240"></a>
+          <a class="link" href="legendre.html#math_toolkit.special.sf_poly.legendre.synopsis">Synopsis</a>
+        </h5>
+<p>
+          
+</p>
+<pre class="programlisting"><span class="preprocessor">#include</span> <span class="special">&lt;</span><span class="identifier">boost</span><span class="special">/</span><span class="identifier">math</span><span class="special">/</span><span class="identifier">special_functions</span><span class="special">/</span><span class="identifier">legendre</span><span class="special">.</span><span class="identifier">hpp</span><span class="special">&gt;</span>
+</pre>
+<p>
+        </p>
+<pre class="programlisting"><span class="keyword">namespace</span> <span class="identifier">boost</span><span class="special">{</span> <span class="keyword">namespace</span> <span class="identifier">math</span><span class="special">{</span>
+
+<span class="keyword">template</span> <span class="special">&lt;</span><span class="keyword">class</span> <span class="identifier">T</span><span class="special">&gt;</span>
+<a class="link" href="../../main_overview/result_type.html" title="Calculation of the Type of the Result"><span class="emphasis"><em>calculated-result-type</em></span></a> <span class="identifier">legendre_p</span><span class="special">(</span><span class="keyword">int</span> <span class="identifier">n</span><span class="special">,</span> <span class="identifier">T</span> <span class="identifier">x</span><span class="special">);</span>
+
+<span class="keyword">template</span> <span class="special">&lt;</span><span class="keyword">class</span> <span class="identifier">T</span><span class="special">,</span> <span class="keyword">class</span> <a class="link" href="../../policy.html" title="Policies">Policy</a><span class="special">&gt;</span>
+<a class="link" href="../../main_overview/result_type.html" title="Calculation of the Type of the Result"><span class="emphasis"><em>calculated-result-type</em></span></a> <span class="identifier">legendre_p</span><span class="special">(</span><span class="keyword">int</span> <span class="identifier">n</span><span class="special">,</span> <span class="identifier">T</span> <span class="identifier">x</span><span class="special">,</span> <span class="keyword">const</span> <a class="link" href="../../policy.html" title="Policies">Policy</a><span class="special">&amp;);</span>
+
+<span class="keyword">template</span> <span class="special">&lt;</span><span class="keyword">class</span> <span class="identifier">T</span><span class="special">&gt;</span>
+<a class="link" href="../../main_overview/result_type.html" title="Calculation of the Type of the Result"><span class="emphasis"><em>calculated-result-type</em></span></a> <span class="identifier">legendre_p</span><span class="special">(</span><span class="keyword">int</span> <span class="identifier">n</span><span class="special">,</span> <span class="keyword">int</span> <span class="identifier">m</span><span class="special">,</span> <span class="identifier">T</span> <span class="identifier">x</span><span class="special">);</span>
+
+<span class="keyword">template</span> <span class="special">&lt;</span><span class="keyword">class</span> <span class="identifier">T</span><span class="special">,</span> <span class="keyword">class</span> <a class="link" href="../../policy.html" title="Policies">Policy</a><span class="special">&gt;</span>
+<a class="link" href="../../main_overview/result_type.html" title="Calculation of the Type of the Result"><span class="emphasis"><em>calculated-result-type</em></span></a> <span class="identifier">legendre_p</span><span class="special">(</span><span class="keyword">int</span> <span class="identifier">n</span><span class="special">,</span> <span class="keyword">int</span> <span class="identifier">m</span><span class="special">,</span> <span class="identifier">T</span> <span class="identifier">x</span><span class="special">,</span> <span class="keyword">const</span> <a class="link" href="../../policy.html" title="Policies">Policy</a><span class="special">&amp;);</span>
+
+<span class="keyword">template</span> <span class="special">&lt;</span><span class="keyword">class</span> <span class="identifier">T</span><span class="special">&gt;</span>
+<a class="link" href="../../main_overview/result_type.html" title="Calculation of the Type of the Result"><span class="emphasis"><em>calculated-result-type</em></span></a> <span class="identifier">legendre_q</span><span class="special">(</span><span class="keyword">unsigned</span> <span class="identifier">n</span><span class="special">,</span> <span class="identifier">T</span> <span class="identifier">x</span><span class="special">);</span>
+
+<span class="keyword">template</span> <span class="special">&lt;</span><span class="keyword">class</span> <span class="identifier">T</span><span class="special">,</span> <span class="keyword">class</span> <a class="link" href="../../policy.html" title="Policies">Policy</a><span class="special">&gt;</span>
+<a class="link" href="../../main_overview/result_type.html" title="Calculation of the Type of the Result"><span class="emphasis"><em>calculated-result-type</em></span></a> <span class="identifier">legendre_q</span><span class="special">(</span><span class="keyword">unsigned</span> <span class="identifier">n</span><span class="special">,</span> <span class="identifier">T</span> <span class="identifier">x</span><span class="special">,</span> <span class="keyword">const</span> <a class="link" href="../../policy.html" title="Policies">Policy</a><span class="special">&amp;);</span>
+
+<span class="keyword">template</span> <span class="special">&lt;</span><span class="keyword">class</span> <span class="identifier">T1</span><span class="special">,</span> <span class="keyword">class</span> <span class="identifier">T2</span><span class="special">,</span> <span class="keyword">class</span> <span class="identifier">T3</span><span class="special">&gt;</span>
+<a class="link" href="../../main_overview/result_type.html" title="Calculation of the Type of the Result"><span class="emphasis"><em>calculated-result-type</em></span></a> <span class="identifier">legendre_next</span><span class="special">(</span><span class="keyword">unsigned</span> <span class="identifier">l</span><span class="special">,</span> <span class="identifier">T1</span> <span class="identifier">x</span><span class="special">,</span> <span class="identifier">T2</span> <span class="identifier">Pl</span><span class="special">,</span> <span class="identifier">T3</span> <span class="identifier">Plm1</span><span class="special">);</span>
+
+<span class="keyword">template</span> <span class="special">&lt;</span><span class="keyword">class</span> <span class="identifier">T1</span><span class="special">,</span> <span class="keyword">class</span> <span class="identifier">T2</span><span class="special">,</span> <span class="keyword">class</span> <span class="identifier">T3</span><span class="special">&gt;</span>
+<a class="link" href="../../main_overview/result_type.html" title="Calculation of the Type of the Result"><span class="emphasis"><em>calculated-result-type</em></span></a> <span class="identifier">legendre_next</span><span class="special">(</span><span class="keyword">unsigned</span> <span class="identifier">l</span><span class="special">,</span> <span class="keyword">unsigned</span> <span class="identifier">m</span><span class="special">,</span> <span class="identifier">T1</span> <span class="identifier">x</span><span class="special">,</span> <span class="identifier">T2</span> <span class="identifier">Pl</span><span class="special">,</span> <span class="identifier">T3</span> <span class="identifier">Plm1</span><span class="special">);</span>
+
+
+<span class="special">}}</span> <span class="comment">// namespaces
+</span></pre>
+<p>
+          The return type of these functions is computed using the <a class="link" href="../../main_overview/result_type.html" title="Calculation of the Type of the Result"><span class="emphasis"><em>result
+          type calculation rules</em></span></a>: note than when there is a single
+          template argument the result is the same type as that argument or <code class="computeroutput"><span class="keyword">double</span></code> if the template argument is an integer
+          type.
+        </p>
+<p>
+          </p>
+<p>
+            The final <a class="link" href="../../policy.html" title="Policies">Policy</a> argument
+            is optional and can be used to control the behaviour of the function:
+            how it handles errors, what level of precision to use etc. Refer to the
+            <a class="link" href="../../policy.html" title="Policies">policy documentation for more details</a>.
+          </p>
+<p>
+        </p>
+<a name="math_toolkit.special.sf_poly.legendre.description"></a><h5>
+<a name="id743427"></a>
+          <a class="link" href="legendre.html#math_toolkit.special.sf_poly.legendre.description">Description</a>
+        </h5>
+<pre class="programlisting"><span class="keyword">template</span> <span class="special">&lt;</span><span class="keyword">class</span> <span class="identifier">T</span><span class="special">&gt;</span>
+<a class="link" href="../../main_overview/result_type.html" title="Calculation of the Type of the Result"><span class="emphasis"><em>calculated-result-type</em></span></a> <span class="identifier">legendre_p</span><span class="special">(</span><span class="keyword">int</span> <span class="identifier">l</span><span class="special">,</span> <span class="identifier">T</span> <span class="identifier">x</span><span class="special">);</span>
+
+<span class="keyword">template</span> <span class="special">&lt;</span><span class="keyword">class</span> <span class="identifier">T</span><span class="special">,</span> <span class="keyword">class</span> <a class="link" href="../../policy.html" title="Policies">Policy</a><span class="special">&gt;</span>
+<a class="link" href="../../main_overview/result_type.html" title="Calculation of the Type of the Result"><span class="emphasis"><em>calculated-result-type</em></span></a> <span class="identifier">legendre_p</span><span class="special">(</span><span class="keyword">int</span> <span class="identifier">l</span><span class="special">,</span> <span class="identifier">T</span> <span class="identifier">x</span><span class="special">,</span> <span class="keyword">const</span> <a class="link" href="../../policy.html" title="Policies">Policy</a><span class="special">&amp;);</span>
+</pre>
+<p>
+          Returns the Legendre Polynomial of the first kind:
+        </p>
+<p>
+          <span class="inlinemediaobject"><img src="../../../../equations/legendre_0.png"></span>
+        </p>
+<p>
+          Requires -1 &lt;= x &lt;= 1, otherwise returns the result of <a class="link" href="../../main_overview/error_handling.html#domain_error">domain_error</a>.
+        </p>
+<p>
+          Negative orders are handled via the reflection formula:
+        </p>
+<p>
+          P<sub>-l-1</sub>(x) = P<sub>l</sub>(x)
+        </p>
+<p>
+          The following graph illustrates the behaviour of the first few Legendre
+          Polynomials:
+        </p>
+<p>
+          <span class="inlinemediaobject"><img src="../../../../graphs/legendre_p.png" align="middle"></span>
+        </p>
+<pre class="programlisting"><span class="keyword">template</span> <span class="special">&lt;</span><span class="keyword">class</span> <span class="identifier">T</span><span class="special">&gt;</span>
+<a class="link" href="../../main_overview/result_type.html" title="Calculation of the Type of the Result"><span class="emphasis"><em>calculated-result-type</em></span></a> <span class="identifier">legendre_p</span><span class="special">(</span><span class="keyword">int</span> <span class="identifier">l</span><span class="special">,</span> <span class="keyword">int</span> <span class="identifier">m</span><span class="special">,</span> <span class="identifier">T</span> <span class="identifier">x</span><span class="special">);</span>
+
+<span class="keyword">template</span> <span class="special">&lt;</span><span class="keyword">class</span> <span class="identifier">T</span><span class="special">,</span> <span class="keyword">class</span> <a class="link" href="../../policy.html" title="Policies">Policy</a><span class="special">&gt;</span>
+<a class="link" href="../../main_overview/result_type.html" title="Calculation of the Type of the Result"><span class="emphasis"><em>calculated-result-type</em></span></a> <span class="identifier">legendre_p</span><span class="special">(</span><span class="keyword">int</span> <span class="identifier">l</span><span class="special">,</span> <span class="keyword">int</span> <span class="identifier">m</span><span class="special">,</span> <span class="identifier">T</span> <span class="identifier">x</span><span class="special">,</span> <span class="keyword">const</span> <a class="link" href="../../policy.html" title="Policies">Policy</a><span class="special">&amp;);</span>
+</pre>
+<p>
+          Returns the associated Legendre polynomial of the first kind:
+        </p>
+<p>
+          <span class="inlinemediaobject"><img src="../../../../equations/legendre_1.png"></span>
+        </p>
+<p>
+          Requires -1 &lt;= x &lt;= 1, otherwise returns the result of <a class="link" href="../../main_overview/error_handling.html#domain_error">domain_error</a>.
+        </p>
+<p>
+          Negative values of <span class="emphasis"><em>l</em></span> and <span class="emphasis"><em>m</em></span> are
+          handled via the identity relations:
+        </p>
+<p>
+          <span class="inlinemediaobject"><img src="../../../../equations/legendre_3.png"></span>
+        </p>
+<div class="caution"><table border="0" summary="Caution">
+<tr>
+<td rowspan="2" align="center" valign="top" width="25"><img alt="[Caution]" src="../../../../../doc/html/images/caution.png"></td>
+<th align="left">Caution</th>
+</tr>
+<tr><td align="left" valign="top">
+<p>
+            The definition of the associated Legendre polynomial used here includes
+            a leading Condon-Shortley phase term of (-1)<sup>m</sup>. This matches the definition
+            given by Abramowitz and Stegun (8.6.6) and that used by Mathworld
+            and <a href="http://documents.wolfram.com/mathematica/functions/LegendreP" target="_top">Mathematica's
+            LegendreP function</a>. However, uses in the literature do not always
+            include this phase term, and strangely the specification for the associated
+            Legendre function in the C++ TR1 (assoc_legendre) also omits it, in spite
+            of stating that it uses Abramowitz and Stegun as the final arbiter on
+            these matters.
+          </p>
+<p>
+            See:
+          </p>
+<p>
+            <a href="http://mathworld.wolfram.com/LegendrePolynomial.html" target="_top">Weisstein,
+            Eric W. "Legendre Polynomial." From MathWorld--A Wolfram Web
+            Resource</a>.
+          </p>
+<p>
+            Abramowitz, M. and Stegun, I. A. (Eds.). "Legendre Functions"
+            and "Orthogonal Polynomials." Ch. 22 in Chs. 8 and 22 in Handbook
+            of Mathematical Functions with Formulas, Graphs, and Mathematical Tables,
+            9th printing. New York: Dover, pp. 331-339 and 771-802, 1972.
+          </p>
+</td></tr>
+</table></div>
+<pre class="programlisting"><span class="keyword">template</span> <span class="special">&lt;</span><span class="keyword">class</span> <span class="identifier">T</span><span class="special">&gt;</span>
+<a class="link" href="../../main_overview/result_type.html" title="Calculation of the Type of the Result"><span class="emphasis"><em>calculated-result-type</em></span></a> <span class="identifier">legendre_q</span><span class="special">(</span><span class="keyword">unsigned</span> <span class="identifier">n</span><span class="special">,</span> <span class="identifier">T</span> <span class="identifier">x</span><span class="special">);</span>
+
+<span class="keyword">template</span> <span class="special">&lt;</span><span class="keyword">class</span> <span class="identifier">T</span><span class="special">,</span> <span class="keyword">class</span> <a class="link" href="../../policy.html" title="Policies">Policy</a><span class="special">&gt;</span>
+<a class="link" href="../../main_overview/result_type.html" title="Calculation of the Type of the Result"><span class="emphasis"><em>calculated-result-type</em></span></a> <span class="identifier">legendre_q</span><span class="special">(</span><span class="keyword">unsigned</span> <span class="identifier">n</span><span class="special">,</span> <span class="identifier">T</span> <span class="identifier">x</span><span class="special">,</span> <span class="keyword">const</span> <a class="link" href="../../policy.html" title="Policies">Policy</a><span class="special">&amp;);</span>
+</pre>
+<p>
+          Returns the value of the Legendre polynomial that is the second solution
+          to the Legendre differential equation, for example:
+        </p>
+<p>
+          <span class="inlinemediaobject"><img src="../../../../equations/legendre_2.png"></span>
+        </p>
+<p>
+          Requires -1 &lt;= x &lt;= 1, otherwise <a class="link" href="../../main_overview/error_handling.html#domain_error">domain_error</a>
+          is called.
+        </p>
+<p>
+          The following graph illustrates the first few Legendre functions of the
+          second kind:
+        </p>
+<p>
+          <span class="inlinemediaobject"><img src="../../../../graphs/legendre_q.png" align="middle"></span>
+        </p>
+<pre class="programlisting"><span class="keyword">template</span> <span class="special">&lt;</span><span class="keyword">class</span> <span class="identifier">T1</span><span class="special">,</span> <span class="keyword">class</span> <span class="identifier">T2</span><span class="special">,</span> <span class="keyword">class</span> <span class="identifier">T3</span><span class="special">&gt;</span>
+<a class="link" href="../../main_overview/result_type.html" title="Calculation of the Type of the Result"><span class="emphasis"><em>calculated-result-type</em></span></a> <span class="identifier">legendre_next</span><span class="special">(</span><span class="keyword">unsigned</span> <span class="identifier">l</span><span class="special">,</span> <span class="identifier">T1</span> <span class="identifier">x</span><span class="special">,</span> <span class="identifier">T2</span> <span class="identifier">Pl</span><span class="special">,</span> <span class="identifier">T3</span> <span class="identifier">Plm1</span><span class="special">);</span>
+</pre>
+<p>
+          Implements the three term recurrence relation for the Legendre polynomials,
+          this function can be used to create a sequence of values evaluated at the
+          same <span class="emphasis"><em>x</em></span>, and for rising <span class="emphasis"><em>l</em></span>. This
+          recurrence relation holds for Legendre Polynomials of both the first and
+          second kinds.
+        </p>
+<p>
+          <span class="inlinemediaobject"><img src="../../../../equations/legendre_4.png"></span>
+        </p>
+<p>
+          For example we could produce a vector of the first 10 polynomial values
+          using:
+        </p>
+<pre class="programlisting"><span class="keyword">double</span> <span class="identifier">x</span> <span class="special">=</span> <span class="number">0.5</span><span class="special">;</span>  <span class="comment">// Abscissa value
+</span><span class="identifier">vector</span><span class="special">&lt;</span><span class="keyword">double</span><span class="special">&gt;</span> <span class="identifier">v</span><span class="special">;</span>
+<span class="identifier">v</span><span class="special">.</span><span class="identifier">push_back</span><span class="special">(</span><span class="identifier">legendre_p</span><span class="special">(</span><span class="number">0</span><span class="special">,</span> <span class="identifier">x</span><span class="special">)).</span><span class="identifier">push_back</span><span class="special">(</span><span class="identifier">legendre_p</span><span class="special">(</span><span class="number">1</span><span class="special">,</span> <span class="identifier">x</span><span class="special">));</span>
+<span class="keyword">for</span><span class="special">(</span><span class="keyword">unsigned</span> <span class="identifier">l</span> <span class="special">=</span> <span class="number">1</span><span class="special">;</span> <span class="identifier">l</span> <span class="special">&lt;</span> <span class="number">10</span><span class="special">;</span> <span class="special">++</span><span class="identifier">l</span><span class="special">)</span>
+   <span class="identifier">v</span><span class="special">.</span><span class="identifier">push_back</span><span class="special">(</span><span class="identifier">legendre_next</span><span class="special">(</span><span class="identifier">l</span><span class="special">,</span> <span class="identifier">x</span><span class="special">,</span> <span class="identifier">v</span><span class="special">[</span><span class="identifier">l</span><span class="special">],</span> <span class="identifier">v</span><span class="special">[</span><span class="identifier">l</span><span class="special">-</span><span class="number">1</span><span class="special">]));</span>
+</pre>
+<p>
+          Formally the arguments are:
+        </p>
+<div class="variablelist">
+<p class="title"><b></b></p>
+<dl>
+<dt><span class="term">l</span></dt>
+<dd><p>
+              The degree of the last polynomial calculated.
+            </p></dd>
+<dt><span class="term">x</span></dt>
+<dd><p>
+              The abscissa value
+            </p></dd>
+<dt><span class="term">Pl</span></dt>
+<dd><p>
+              The value of the polynomial evaluated at degree <span class="emphasis"><em>l</em></span>.
+            </p></dd>
+<dt><span class="term">Plm1</span></dt>
+<dd><p>
+              The value of the polynomial evaluated at degree <span class="emphasis"><em>l-1</em></span>.
+            </p></dd>
+</dl>
+</div>
+<pre class="programlisting"><span class="keyword">template</span> <span class="special">&lt;</span><span class="keyword">class</span> <span class="identifier">T1</span><span class="special">,</span> <span class="keyword">class</span> <span class="identifier">T2</span><span class="special">,</span> <span class="keyword">class</span> <span class="identifier">T3</span><span class="special">&gt;</span>
+<a class="link" href="../../main_overview/result_type.html" title="Calculation of the Type of the Result"><span class="emphasis"><em>calculated-result-type</em></span></a> <span class="identifier">legendre_next</span><span class="special">(</span><span class="keyword">unsigned</span> <span class="identifier">l</span><span class="special">,</span> <span class="keyword">unsigned</span> <span class="identifier">m</span><span class="special">,</span> <span class="identifier">T1</span> <span class="identifier">x</span><span class="special">,</span> <span class="identifier">T2</span> <span class="identifier">Pl</span><span class="special">,</span> <span class="identifier">T3</span> <span class="identifier">Plm1</span><span class="special">);</span>
+</pre>
+<p>
+          Implements the three term recurrence relation for the Associated Legendre
+          polynomials, this function can be used to create a sequence of values evaluated
+          at the same <span class="emphasis"><em>x</em></span>, and for rising <span class="emphasis"><em>l</em></span>.
+        </p>
+<p>
+          <span class="inlinemediaobject"><img src="../../../../equations/legendre_5.png"></span>
+        </p>
+<p>
+          For example we could produce a vector of the first m+10 polynomial values
+          using:
+        </p>
+<pre class="programlisting"><span class="keyword">double</span> <span class="identifier">x</span> <span class="special">=</span> <span class="number">0.5</span><span class="special">;</span>  <span class="comment">// Abscissa value
+</span><span class="keyword">int</span> <span class="identifier">m</span> <span class="special">=</span> <span class="number">10</span><span class="special">;</span>      <span class="comment">// order
+</span><span class="identifier">vector</span><span class="special">&lt;</span><span class="keyword">double</span><span class="special">&gt;</span> <span class="identifier">v</span><span class="special">;</span>
+<span class="identifier">v</span><span class="special">.</span><span class="identifier">push_back</span><span class="special">(</span><span class="identifier">legendre_p</span><span class="special">(</span><span class="identifier">m</span><span class="special">,</span> <span class="identifier">m</span><span class="special">,</span> <span class="identifier">x</span><span class="special">)).</span><span class="identifier">push_back</span><span class="special">(</span><span class="identifier">legendre_p</span><span class="special">(</span><span class="number">1</span> <span class="special">+</span> <span class="identifier">m</span><span class="special">,</span> <span class="identifier">m</span><span class="special">,</span> <span class="identifier">x</span><span class="special">));</span>
+<span class="keyword">for</span><span class="special">(</span><span class="keyword">unsigned</span> <span class="identifier">l</span> <span class="special">=</span> <span class="number">1</span> <span class="special">+</span> <span class="identifier">m</span><span class="special">;</span> <span class="identifier">l</span> <span class="special">&lt;</span> <span class="identifier">m</span> <span class="special">+</span> <span class="number">10</span><span class="special">;</span> <span class="special">++</span><span class="identifier">l</span><span class="special">)</span>
+   <span class="identifier">v</span><span class="special">.</span><span class="identifier">push_back</span><span class="special">(</span><span class="identifier">legendre_next</span><span class="special">(</span><span class="identifier">l</span><span class="special">,</span> <span class="identifier">m</span><span class="special">,</span> <span class="identifier">x</span><span class="special">,</span> <span class="identifier">v</span><span class="special">[</span><span class="identifier">l</span><span class="special">],</span> <span class="identifier">v</span><span class="special">[</span><span class="identifier">l</span><span class="special">-</span><span class="number">1</span><span class="special">]));</span>
+</pre>
+<p>
+          Formally the arguments are:
+        </p>
+<div class="variablelist">
+<p class="title"><b></b></p>
+<dl>
+<dt><span class="term">l</span></dt>
+<dd><p>
+              The degree of the last polynomial calculated.
+            </p></dd>
+<dt><span class="term">m</span></dt>
+<dd><p>
+              The order of the Associated Polynomial.
+            </p></dd>
+<dt><span class="term">x</span></dt>
+<dd><p>
+              The abscissa value
+            </p></dd>
+<dt><span class="term">Pl</span></dt>
+<dd><p>
+              The value of the polynomial evaluated at degree <span class="emphasis"><em>l</em></span>.
+            </p></dd>
+<dt><span class="term">Plm1</span></dt>
+<dd><p>
+              The value of the polynomial evaluated at degree <span class="emphasis"><em>l-1</em></span>.
+            </p></dd>
+</dl>
+</div>
+<a name="math_toolkit.special.sf_poly.legendre.accuracy"></a><h5>
+<a name="id745921"></a>
+          <a class="link" href="legendre.html#math_toolkit.special.sf_poly.legendre.accuracy">Accuracy</a>
+        </h5>
+<p>
+          The following table shows peak errors (in units of epsilon) for various
+          domains of input arguments. Note that only results for the widest floating
+          point type on the system are given as narrower types have <a class="link" href="../../backgrounders/relative_error.html#zero_error">effectively
+          zero error</a>.
+        </p>
+<div class="table">
+<a name="id745955"></a><p class="title"><b>Table 29. Peak Errors In the Legendre P Function</b></p>
+<div class="table-contents"><table class="table" summary="Peak Errors In the Legendre P Function">
+<colgroup>
+<col>
+<col>
+<col>
+<col>
+</colgroup>
+<thead><tr>
+<th>
+              <p>
+                Significand Size
+              </p>
+              </th>
+<th>
+              <p>
+                Platform and Compiler
+              </p>
+              </th>
+<th>
+              <p>
+                Errors in range
+              </p>
+              <p>
+                0 &lt; l &lt; 20
+              </p>
+              </th>
+<th>
+              <p>
+                Errors in range
+              </p>
+              <p>
+                20 &lt; l &lt; 120
+              </p>
+              </th>
+</tr></thead>
+<tbody>
+<tr>
+<td>
+              <p>
+                53
+              </p>
+              </td>
+<td>
+              <p>
+                Win32, Visual C++ 8
+              </p>
+              </td>
+<td>
+              <p>
+                Peak=211 Mean=20
+              </p>
+              </td>
+<td>
+              <p>
+                Peak=300 Mean=33
+              </p>
+              </td>
+</tr>
+<tr>
+<td>
+              <p>
+                64
+              </p>
+              </td>
+<td>
+              <p>
+                SUSE Linux IA32, g++ 4.1
+              </p>
+              </td>
+<td>
+              <p>
+                Peak=70 Mean=10
+              </p>
+              </td>
+<td>
+              <p>
+                Peak=700 Mean=60
+              </p>
+              </td>
+</tr>
+<tr>
+<td>
+              <p>
+                64
+              </p>
+              </td>
+<td>
+              <p>
+                Red Hat Linux IA64, g++ 3.4.4
+              </p>
+              </td>
+<td>
+              <p>
+                Peak=70 Mean=10
+              </p>
+              </td>
+<td>
+              <p>
+                Peak=700 Mean=60
+              </p>
+              </td>
+</tr>
+<tr>
+<td>
+              <p>
+                113
+              </p>
+              </td>
+<td>
+              <p>
+                HPUX IA64, aCC A.06.06
+              </p>
+              </td>
+<td>
+              <p>
+                Peak=35 Mean=6
+              </p>
+              </td>
+<td>
+              <p>
+                Peak=292 Mean=41
+              </p>
+              </td>
+</tr>
+</tbody>
+</table></div>
+</div>
+<br class="table-break"><div class="table">
+<a name="id746168"></a><p class="title"><b>Table 30. Peak Errors In the Associated Legendre
+        P Function</b></p>
+<div class="table-contents"><table class="table" summary="Peak Errors In the Associated Legendre
+        P Function">
+<colgroup>
+<col>
+<col>
+<col>
+</colgroup>
+<thead><tr>
+<th>
+              <p>
+                Significand Size
+              </p>
+              </th>
+<th>
+              <p>
+                Platform and Compiler
+              </p>
+              </th>
+<th>
+              <p>
+                Errors in range
+              </p>
+              <p>
+                0 &lt; l &lt; 20
+              </p>
+              </th>
+</tr></thead>
+<tbody>
+<tr>
+<td>
+              <p>
+                53
+              </p>
+              </td>
+<td>
+              <p>
+                Win32, Visual C++ 8
+              </p>
+              </td>
+<td>
+              <p>
+                Peak=1200 Mean=7
+              </p>
+              </td>
+</tr>
+<tr>
+<td>
+              <p>
+                64
+              </p>
+              </td>
+<td>
+              <p>
+                SUSE Linux IA32, g++ 4.1
+              </p>
+              </td>
+<td>
+              <p>
+                Peak=80 Mean=5
+              </p>
+              </td>
+</tr>
+<tr>
+<td>
+              <p>
+                64
+              </p>
+              </td>
+<td>
+              <p>
+                Red Hat Linux IA64, g++ 3.4.4
+              </p>
+              </td>
+<td>
+              <p>
+                Peak=80 Mean=5
+              </p>
+              </td>
+</tr>
+<tr>
+<td>
+              <p>
+                113
+              </p>
+              </td>
+<td>
+              <p>
+                HPUX IA64, aCC A.06.06
+              </p>
+              </td>
+<td>
+              <p>
+                Peak=42 Mean=4
+              </p>
+              </td>
+</tr>
+</tbody>
+</table></div>
+</div>
+<br class="table-break"><div class="table">
+<a name="id746339"></a><p class="title"><b>Table 31. Peak Errors In the Legendre Q Function</b></p>
+<div class="table-contents"><table class="table" summary="Peak Errors In the Legendre Q Function">
+<colgroup>
+<col>
+<col>
+<col>
+<col>
+</colgroup>
+<thead><tr>
+<th>
+              <p>
+                Significand Size
+              </p>
+              </th>
+<th>
+              <p>
+                Platform and Compiler
+              </p>
+              </th>
+<th>
+              <p>
+                Errors in range
+              </p>
+              <p>
+                0 &lt; l &lt; 20
+              </p>
+              </th>
+<th>
+              <p>
+                Errors in range
+              </p>
+              <p>
+                20 &lt; l &lt; 120
+              </p>
+              </th>
+</tr></thead>
+<tbody>
+<tr>
+<td>
+              <p>
+                53
+              </p>
+              </td>
+<td>
+              <p>
+                Win32, Visual C++ 8
+              </p>
+              </td>
+<td>
+              <p>
+                Peak=50 Mean=7
+              </p>
+              </td>
+<td>
+              <p>
+                Peak=4600 Mean=370
+              </p>
+              </td>
+</tr>
+<tr>
+<td>
+              <p>
+                64
+              </p>
+              </td>
+<td>
+              <p>
+                SUSE Linux IA32, g++ 4.1
+              </p>
+              </td>
+<td>
+              <p>
+                Peak=51 Mean=8
+              </p>
+              </td>
+<td>
+              <p>
+                Peak=6000 Mean=480
+              </p>
+              </td>
+</tr>
+<tr>
+<td>
+              <p>
+                64
+              </p>
+              </td>
+<td>
+              <p>
+                Red Hat Linux IA64, g++ 3.4.4
+              </p>
+              </td>
+<td>
+              <p>
+                Peak=51 Mean=8
+              </p>
+              </td>
+<td>
+              <p>
+                Peak=6000 Mean=480
+              </p>
+              </td>
+</tr>
+<tr>
+<td>
+              <p>
+                113
+              </p>
+              </td>
+<td>
+              <p>
+                HPUX IA64, aCC A.06.06
+              </p>
+              </td>
+<td>
+              <p>
+                Peak=90 Mean=10
+              </p>
+              </td>
+<td>
+              <p>
+                Peak=1700 Mean=140
+              </p>
+              </td>
+</tr>
+</tbody>
+</table></div>
+</div>
+<br class="table-break"><p>
+          Note that the worst errors occur when the order increases, values greater
+          than ~120 are very unlikely to produce sensible results, especially in
+          the associated polynomial case when the degree is also large. Further the
+          relative errors are likely to grow arbitrarily large when the function
+          is very close to a root.
+        </p>
+<p>
+          No comparisons to other libraries are shown here: there appears to be only
+          one viable implementation method for these functions, the comparisons to
+          other libraries that have been run show identical error rates to those
+          given here.
+        </p>
+<a name="math_toolkit.special.sf_poly.legendre.testing"></a><h5>
+<a name="id746592"></a>
+          <a class="link" href="legendre.html#math_toolkit.special.sf_poly.legendre.testing">Testing</a>
+        </h5>
+<p>
+          A mixture of spot tests of values calculated using functions.wolfram.com,
+          and randomly generated test data are used: the test data was computed using
+          NTL::RR at 1000-bit
+          precision.
+        </p>
+<a name="math_toolkit.special.sf_poly.legendre.implementation"></a><h5>
+<a name="id746634"></a>
+          <a class="link" href="legendre.html#math_toolkit.special.sf_poly.legendre.implementation">Implementation</a>
+        </h5>
+<p>
+          These functions are implemented using the stable three term recurrence
+          relations. These relations guarentee low absolute error but cannot guarentee
+          low relative error near one of the roots of the polynomials.
+        </p>
+</div>
+<table xmlns:rev="http://www.cs.rpi.edu/~gregod/boost/tools/doc/revision" width="100%"><tr>
+<td align="left"></td>
+<td align="right"><div class="copyright-footer">Copyright © 2006 , 2007, 2008 John Maddock, Paul A. Bristow, Hubert
+      Holin, Xiaogang Zhang, Bruno Lalande and Gautam Sewani<p>
+        Distributed under the Boost Software License, Version 1.0. (See accompanying
+        file LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_0.txt)
+      </p>
+</div></td>
+</tr></table>
+<hr>
+<div class="spirit-nav">
+<a accesskey="p" href="../sf_poly.html"><img src="../../../../../doc/html/images/prev.png" alt="Prev"></a><a accesskey="u" href="../sf_poly.html"><img src="../../../../../doc/html/images/up.png" alt="Up"></a><a accesskey="h" href="../../../index.html"><img src="../../../../../doc/html/images/home.png" alt="Home"></a><a accesskey="n" href="laguerre.html"><img src="../../../../../doc/html/images/next.png" alt="Next"></a>
+</div>
+</body>
+</html>

Added: sandbox/tools/auto_index/example/math/doc/sf_and_dist/html/math_toolkit/special/sf_poly/sph_harm.html
==============================================================================
--- (empty file)
+++ sandbox/tools/auto_index/example/math/doc/sf_and_dist/html/math_toolkit/special/sf_poly/sph_harm.html	2008-11-28 05:25:28 EST (Fri, 28 Nov 2008)
@@ -0,0 +1,316 @@
+<html>
+<head>
+<meta http-equiv="Content-Type" content="text/html; charset=ISO-8859-1">
+<title>Spherical Harmonics</title>
+<link rel="stylesheet" href="../../../boostbook.css" type="text/css">
+<meta name="generator" content="DocBook XSL Stylesheets Vsnapshot_8125">
+<link rel="home" href="../../../index.html" title="Math Toolkit">
+<link rel="up" href="../sf_poly.html" title="Polynomials">
+<link rel="prev" href="hermite.html" title="Hermite Polynomials">
+<link rel="next" href="../bessel.html" title="Bessel Functions">
+</head>
+<body bgcolor="white" text="black" link="#0000FF" vlink="#840084" alink="#0000FF">
+<table cellpadding="2" width="100%"><tr>
+<td valign="top"><img alt="Boost C++ Libraries" width="277" height="86" src="../../../../../boost.png"></td>
+<td align="center">Home</td>
+<td align="center">Libraries</td>
+<td align="center">People</td>
+<td align="center">FAQ</td>
+<td align="center">More</td>
+</tr></table>
+<hr>
+<div class="spirit-nav">
+<a accesskey="p" href="hermite.html"><img src="../../../../../doc/html/images/prev.png" alt="Prev"></a><a accesskey="u" href="../sf_poly.html"><img src="../../../../../doc/html/images/up.png" alt="Up"></a><a accesskey="h" href="../../../index.html"><img src="../../../../../doc/html/images/home.png" alt="Home"></a><a accesskey="n" href="../bessel.html"><img src="../../../../../doc/html/images/next.png" alt="Next"></a>
+</div>
+<div class="section" lang="en">
+<div class="titlepage"><div><div><h4 class="title">
+<a name="math_toolkit.special.sf_poly.sph_harm"></a><a class="link" href="sph_harm.html" title="Spherical Harmonics"> Spherical Harmonics</a>
+</h4></div></div></div>
+<a name="math_toolkit.special.sf_poly.sph_harm.synopsis"></a><h5>
+<a name="id752040"></a>
+          <a class="link" href="sph_harm.html#math_toolkit.special.sf_poly.sph_harm.synopsis">Synopsis</a>
+        </h5>
+<p>
+          
+</p>
+<pre class="programlisting"><span class="preprocessor">#include</span> <span class="special">&lt;</span><span class="identifier">boost</span><span class="special">/</span><span class="identifier">math</span><span class="special">/</span><span class="identifier">special_functions</span><span class="special">/</span><span class="identifier">spheric_harmonic</span><span class="special">.</span><span class="identifier">hpp</span><span class="special">&gt;</span>
+</pre>
+<p>
+        </p>
+<pre class="programlisting"><span class="keyword">namespace</span> <span class="identifier">boost</span><span class="special">{</span> <span class="keyword">namespace</span> <span class="identifier">math</span><span class="special">{</span>
+
+<span class="keyword">template</span> <span class="special">&lt;</span><span class="keyword">class</span> <span class="identifier">T1</span><span class="special">,</span> <span class="keyword">class</span> <span class="identifier">T2</span><span class="special">&gt;</span>
+<span class="identifier">std</span><span class="special">::</span><span class="identifier">complex</span><span class="special">&lt;</span><a class="link" href="../../main_overview/result_type.html" title="Calculation of the Type of the Result"><span class="emphasis"><em>calculated-result-type</em></span></a><span class="special">&gt;</span> <span class="identifier">spherical_harmonic</span><span class="special">(</span><span class="keyword">unsigned</span> <span class="identifier">n</span><span class="special">,</span> <span class="keyword">int</span> <span class="identifier">m</span><span class="special">,</span> <span class="identifier">T1</span> <span class="identifier">theta</span><span class="special">,</span> <span class="identifier">T2</span> <span class="identifier">phi</span><span class="special">);</span>
+
+<span class="keyword">template</span> <span class="special">&lt;</span><span class="keyword">class</span> <span class="identifier">T1</span><span class="special">,</span> <span class="keyword">class</span> <span class="identifier">T2</span><span class="special">,</span> <span class="keyword">class</span> <a class="link" href="../../policy.html" title="Policies">Policy</a><span class="special">&gt;</span>
+<span class="identifier">std</span><span class="special">::</span><span class="identifier">complex</span><span class="special">&lt;</span><a class="link" href="../../main_overview/result_type.html" title="Calculation of the Type of the Result"><span class="emphasis"><em>calculated-result-type</em></span></a><span class="special">&gt;</span> <span class="identifier">spherical_harmonic</span><span class="special">(</span><span class="keyword">unsigned</span> <span class="identifier">n</span><span class="special">,</span> <span class="keyword">int</span> <span class="identifier">m</span><span class="special">,</span> <span class="identifier">T1</span> <span class="identifier">theta</span><span class="special">,</span> <span class="identifier">T2</span> <span class="identifier">phi</span><span class="special">,</span> <span class="keyword">const</span> <a class="link" href="../../policy.html" title="Policies">Policy</a><span class="special">&amp;);</span>
+
+<span class="keyword">template</span> <span class="special">&lt;</span><span class="keyword">class</span> <span class="identifier">T1</span><span class="special">,</span> <span class="keyword">class</span> <span class="identifier">T2</span><span class="special">&gt;</span>
+<a class="link" href="../../main_overview/result_type.html" title="Calculation of the Type of the Result"><span class="emphasis"><em>calculated-result-type</em></span></a> <span class="identifier">spherical_harmonic_r</span><span class="special">(</span><span class="keyword">unsigned</span> <span class="identifier">n</span><span class="special">,</span> <span class="keyword">int</span> <span class="identifier">m</span><span class="special">,</span> <span class="identifier">T1</span> <span class="identifier">theta</span><span class="special">,</span> <span class="identifier">T2</span> <span class="identifier">phi</span><span class="special">);</span>
+
+<span class="keyword">template</span> <span class="special">&lt;</span><span class="keyword">class</span> <span class="identifier">T1</span><span class="special">,</span> <span class="keyword">class</span> <span class="identifier">T2</span><span class="special">,</span> <span class="keyword">class</span> <a class="link" href="../../policy.html" title="Policies">Policy</a><span class="special">&gt;</span>
+<a class="link" href="../../main_overview/result_type.html" title="Calculation of the Type of the Result"><span class="emphasis"><em>calculated-result-type</em></span></a> <span class="identifier">spherical_harmonic_r</span><span class="special">(</span><span class="keyword">unsigned</span> <span class="identifier">n</span><span class="special">,</span> <span class="keyword">int</span> <span class="identifier">m</span><span class="special">,</span> <span class="identifier">T1</span> <span class="identifier">theta</span><span class="special">,</span> <span class="identifier">T2</span> <span class="identifier">phi</span><span class="special">,</span> <span class="keyword">const</span> <a class="link" href="../../policy.html" title="Policies">Policy</a><span class="special">&amp;);</span>
+
+<span class="keyword">template</span> <span class="special">&lt;</span><span class="keyword">class</span> <span class="identifier">T1</span><span class="special">,</span> <span class="keyword">class</span> <span class="identifier">T2</span><span class="special">&gt;</span>
+<a class="link" href="../../main_overview/result_type.html" title="Calculation of the Type of the Result"><span class="emphasis"><em>calculated-result-type</em></span></a> <span class="identifier">spherical_harmonic_i</span><span class="special">(</span><span class="keyword">unsigned</span> <span class="identifier">n</span><span class="special">,</span> <span class="keyword">int</span> <span class="identifier">m</span><span class="special">,</span> <span class="identifier">T1</span> <span class="identifier">theta</span><span class="special">,</span> <span class="identifier">T2</span> <span class="identifier">phi</span><span class="special">);</span>
+   
+<span class="keyword">template</span> <span class="special">&lt;</span><span class="keyword">class</span> <span class="identifier">T1</span><span class="special">,</span> <span class="keyword">class</span> <span class="identifier">T2</span><span class="special">,</span> <span class="keyword">class</span> <a class="link" href="../../policy.html" title="Policies">Policy</a><span class="special">&gt;</span>
+<a class="link" href="../../main_overview/result_type.html" title="Calculation of the Type of the Result"><span class="emphasis"><em>calculated-result-type</em></span></a> <span class="identifier">spherical_harmonic_i</span><span class="special">(</span><span class="keyword">unsigned</span> <span class="identifier">n</span><span class="special">,</span> <span class="keyword">int</span> <span class="identifier">m</span><span class="special">,</span> <span class="identifier">T1</span> <span class="identifier">theta</span><span class="special">,</span> <span class="identifier">T2</span> <span class="identifier">phi</span><span class="special">,</span> <span class="keyword">const</span> <a class="link" href="../../policy.html" title="Policies">Policy</a><span class="special">&amp;);</span>
+   
+<span class="special">}}</span> <span class="comment">// namespaces
+</span></pre>
+<a name="math_toolkit.special.sf_poly.sph_harm.description"></a><h5>
+<a name="id753168"></a>
+          <a class="link" href="sph_harm.html#math_toolkit.special.sf_poly.sph_harm.description">Description</a>
+        </h5>
+<p>
+          The return type of these functions is computed using the <a class="link" href="../../main_overview/result_type.html" title="Calculation of the Type of the Result"><span class="emphasis"><em>result
+          type calculation rules</em></span></a> when T1 and T2 are different types.
+        </p>
+<p>
+          </p>
+<p>
+            The final <a class="link" href="../../policy.html" title="Policies">Policy</a> argument
+            is optional and can be used to control the behaviour of the function:
+            how it handles errors, what level of precision to use etc. Refer to the
+            <a class="link" href="../../policy.html" title="Policies">policy documentation for more details</a>.
+          </p>
+<p>
+        </p>
+<pre class="programlisting"><span class="keyword">template</span> <span class="special">&lt;</span><span class="keyword">class</span> <span class="identifier">T1</span><span class="special">,</span> <span class="keyword">class</span> <span class="identifier">T2</span><span class="special">&gt;</span>
+<span class="identifier">std</span><span class="special">::</span><span class="identifier">complex</span><span class="special">&lt;</span><a class="link" href="../../main_overview/result_type.html" title="Calculation of the Type of the Result"><span class="emphasis"><em>calculated-result-type</em></span></a><span class="special">&gt;</span> <span class="identifier">spherical_harmonic</span><span class="special">(</span><span class="keyword">unsigned</span> <span class="identifier">n</span><span class="special">,</span> <span class="keyword">int</span> <span class="identifier">m</span><span class="special">,</span> <span class="identifier">T1</span> <span class="identifier">theta</span><span class="special">,</span> <span class="identifier">T2</span> <span class="identifier">phi</span><span class="special">);</span>
+
+<span class="keyword">template</span> <span class="special">&lt;</span><span class="keyword">class</span> <span class="identifier">T1</span><span class="special">,</span> <span class="keyword">class</span> <span class="identifier">T2</span><span class="special">,</span> <span class="keyword">class</span> <a class="link" href="../../policy.html" title="Policies">Policy</a><span class="special">&gt;</span>
+<span class="identifier">std</span><span class="special">::</span><span class="identifier">complex</span><span class="special">&lt;</span><a class="link" href="../../main_overview/result_type.html" title="Calculation of the Type of the Result"><span class="emphasis"><em>calculated-result-type</em></span></a><span class="special">&gt;</span> <span class="identifier">spherical_harmonic</span><span class="special">(</span><span class="keyword">unsigned</span> <span class="identifier">n</span><span class="special">,</span> <span class="keyword">int</span> <span class="identifier">m</span><span class="special">,</span> <span class="identifier">T1</span> <span class="identifier">theta</span><span class="special">,</span> <span class="identifier">T2</span> <span class="identifier">phi</span><span class="special">,</span> <span class="keyword">const</span> <a class="link" href="../../policy.html" title="Policies">Policy</a><span class="special">&amp;);</span>
+</pre>
+<p>
+          Returns the value of the Spherical Harmonic Y<sub>n</sub><sup>m</sup>(theta, phi):
+        </p>
+<p>
+          <span class="inlinemediaobject"><img src="../../../../equations/spherical_0.png"></span>
+        </p>
+<p>
+          The spherical harmonics Y<sub>n</sub><sup>m</sup>(theta, phi) are the angular portion of the
+          solution to Laplace's equation in spherical coordinates where azimuthal
+          symmetry is not present.
+        </p>
+<div class="caution"><table border="0" summary="Caution">
+<tr>
+<td rowspan="2" align="center" valign="top" width="25"><img alt="[Caution]" src="../../../../../doc/html/images/caution.png"></td>
+<th align="left">Caution</th>
+</tr>
+<tr><td align="left" valign="top">
+<p>
+            Care must be taken in correctly identifying the arguments to this function:
+            &#952; is taken as the polar (colatitudinal) coordinate with &#952; in [0, &#960;], and &#966; as
+            the azimuthal (longitudinal) coordinate with &#966; in [0,2&#960;). This is the convention
+            used in Physics, and matches the definition used by <a href="http://documents.wolfram.com/mathematica/functions/SphericalHarmonicY" target="_top">Mathematica
+            in the function SpericalHarmonicY</a>, but is opposite to the usual
+            mathematical conventions.
+          </p>
+<p>
+            Some other sources include an additional Condon-Shortley phase term of
+            (-1)<sup>m</sup> in the definition of this function: note however that our definition
+            of the associated Legendre polynomial already includes this term.
+          </p>
+<p>
+            This implementation returns zero for m &gt; n
+          </p>
+<p>
+            For &#952; outside [0, &#960;] and &#966; outside [0, 2&#960;] this implementation follows the
+            convention used by Mathematica: the function is periodic with period
+            &#960; in &#952; and 2&#960; in &#966;. Please note that this is not the behaviour one would get
+            from a casual application of the function's definition. Cautious users
+            should keep &#952; and &#966; to the range [0, &#960;] and [0, 2&#960;] respectively.
+          </p>
+<p>
+            See: <a href="http://mathworld.wolfram.com/SphericalHarmonic.html" target="_top">Weisstein,
+            Eric W. "Spherical Harmonic." From MathWorld--A Wolfram Web
+            Resource</a>.
+          </p>
+</td></tr>
+</table></div>
+<pre class="programlisting"><span class="keyword">template</span> <span class="special">&lt;</span><span class="keyword">class</span> <span class="identifier">T1</span><span class="special">,</span> <span class="keyword">class</span> <span class="identifier">T2</span><span class="special">&gt;</span>
+<a class="link" href="../../main_overview/result_type.html" title="Calculation of the Type of the Result"><span class="emphasis"><em>calculated-result-type</em></span></a> <span class="identifier">spherical_harmonic_r</span><span class="special">(</span><span class="keyword">unsigned</span> <span class="identifier">n</span><span class="special">,</span> <span class="keyword">int</span> <span class="identifier">m</span><span class="special">,</span> <span class="identifier">T1</span> <span class="identifier">theta</span><span class="special">,</span> <span class="identifier">T2</span> <span class="identifier">phi</span><span class="special">);</span>
+
+<span class="keyword">template</span> <span class="special">&lt;</span><span class="keyword">class</span> <span class="identifier">T1</span><span class="special">,</span> <span class="keyword">class</span> <span class="identifier">T2</span><span class="special">,</span> <span class="keyword">class</span> <a class="link" href="../../policy.html" title="Policies">Policy</a><span class="special">&gt;</span>
+<a class="link" href="../../main_overview/result_type.html" title="Calculation of the Type of the Result"><span class="emphasis"><em>calculated-result-type</em></span></a> <span class="identifier">spherical_harmonic_r</span><span class="special">(</span><span class="keyword">unsigned</span> <span class="identifier">n</span><span class="special">,</span> <span class="keyword">int</span> <span class="identifier">m</span><span class="special">,</span> <span class="identifier">T1</span> <span class="identifier">theta</span><span class="special">,</span> <span class="identifier">T2</span> <span class="identifier">phi</span><span class="special">,</span> <span class="keyword">const</span> <a class="link" href="../../policy.html" title="Policies">Policy</a><span class="special">&amp;);</span>
+</pre>
+<p>
+          Returns the real part of Y<sub>n</sub><sup>m</sup>(theta, phi):
+        </p>
+<p>
+          <span class="inlinemediaobject"><img src="../../../../equations/spherical_1.png"></span>
+        </p>
+<pre class="programlisting"><span class="keyword">template</span> <span class="special">&lt;</span><span class="keyword">class</span> <span class="identifier">T1</span><span class="special">,</span> <span class="keyword">class</span> <span class="identifier">T2</span><span class="special">&gt;</span>
+<a class="link" href="../../main_overview/result_type.html" title="Calculation of the Type of the Result"><span class="emphasis"><em>calculated-result-type</em></span></a> <span class="identifier">spherical_harmonic_i</span><span class="special">(</span><span class="keyword">unsigned</span> <span class="identifier">n</span><span class="special">,</span> <span class="keyword">int</span> <span class="identifier">m</span><span class="special">,</span> <span class="identifier">T1</span> <span class="identifier">theta</span><span class="special">,</span> <span class="identifier">T2</span> <span class="identifier">phi</span><span class="special">);</span>
+
+<span class="keyword">template</span> <span class="special">&lt;</span><span class="keyword">class</span> <span class="identifier">T1</span><span class="special">,</span> <span class="keyword">class</span> <span class="identifier">T2</span><span class="special">,</span> <span class="keyword">class</span> <a class="link" href="../../policy.html" title="Policies">Policy</a><span class="special">&gt;</span>
+<a class="link" href="../../main_overview/result_type.html" title="Calculation of the Type of the Result"><span class="emphasis"><em>calculated-result-type</em></span></a> <span class="identifier">spherical_harmonic_i</span><span class="special">(</span><span class="keyword">unsigned</span> <span class="identifier">n</span><span class="special">,</span> <span class="keyword">int</span> <span class="identifier">m</span><span class="special">,</span> <span class="identifier">T1</span> <span class="identifier">theta</span><span class="special">,</span> <span class="identifier">T2</span> <span class="identifier">phi</span><span class="special">,</span> <span class="keyword">const</span> <a class="link" href="../../policy.html" title="Policies">Policy</a><span class="special">&amp;);</span>
+</pre>
+<p>
+          Returns the imaginary part of Y<sub>n</sub><sup>m</sup>(theta, phi):
+        </p>
+<p>
+          <span class="inlinemediaobject"><img src="../../../../equations/spherical_2.png"></span>
+        </p>
+<a name="math_toolkit.special.sf_poly.sph_harm.accuracy"></a><h5>
+<a name="id754461"></a>
+          <a class="link" href="sph_harm.html#math_toolkit.special.sf_poly.sph_harm.accuracy">Accuracy</a>
+        </h5>
+<p>
+          The following table shows peak errors for various domains of input arguments.
+          Note that only results for the widest floating point type on the system
+          are given as narrower types have <a class="link" href="../../backgrounders/relative_error.html#zero_error">effectively
+          zero error</a>. Peak errors are the same for both the real and imaginary
+          parts, as the error is dominated by calculation of the associated Legendre
+          polynomials: especially near the roots of the associated Legendre function.
+        </p>
+<p>
+          All values are in units of epsilon.
+        </p>
+<div class="table">
+<a name="id754507"></a><p class="title"><b>Table 35. Peak Errors In the Sperical Harmonic Functions</b></p>
+<div class="table-contents"><table class="table" summary="Peak Errors In the Sperical Harmonic Functions">
+<colgroup>
+<col>
+<col>
+<col>
+</colgroup>
+<thead><tr>
+<th>
+              <p>
+                Significand Size
+              </p>
+              </th>
+<th>
+              <p>
+                Platform and Compiler
+              </p>
+              </th>
+<th>
+              <p>
+                Errors in range
+              </p>
+              <p>
+                0 &lt; l &lt; 20
+              </p>
+              </th>
+</tr></thead>
+<tbody>
+<tr>
+<td>
+              <p>
+                53
+              </p>
+              </td>
+<td>
+              <p>
+                Win32, Visual C++ 8
+              </p>
+              </td>
+<td>
+              <p>
+                Peak=2x10<sup>4</sup> Mean=700
+              </p>
+              </td>
+</tr>
+<tr>
+<td>
+              <p>
+                64
+              </p>
+              </td>
+<td>
+              <p>
+                SUSE Linux IA32, g++ 4.1
+              </p>
+              </td>
+<td>
+              <p>
+                Peak=2900 Mean=100
+              </p>
+              </td>
+</tr>
+<tr>
+<td>
+              <p>
+                64
+              </p>
+              </td>
+<td>
+              <p>
+                Red Hat Linux IA64, g++ 3.4.4
+              </p>
+              </td>
+<td>
+              <p>
+                Peak=2900 Mean=100
+              </p>
+              </td>
+</tr>
+<tr>
+<td>
+              <p>
+                113
+              </p>
+              </td>
+<td>
+              <p>
+                HPUX IA64, aCC A.06.06
+              </p>
+              </td>
+<td>
+              <p>
+                Peak=6700 Mean=230
+              </p>
+              </td>
+</tr>
+</tbody>
+</table></div>
+</div>
+<br class="table-break"><p>
+          Note that the worst errors occur when the degree increases, values greater
+          than ~120 are very unlikely to produce sensible results, especially when
+          the order is also large. Further the relative errors are likely to grow
+          arbitrarily large when the function is very close to a root.
+        </p>
+<a name="math_toolkit.special.sf_poly.sph_harm.testing"></a><h5>
+<a name="id754697"></a>
+          <a class="link" href="sph_harm.html#math_toolkit.special.sf_poly.sph_harm.testing">Testing</a>
+        </h5>
+<p>
+          A mixture of spot tests of values calculated using functions.wolfram.com,
+          and randomly generated test data are used: the test data was computed using
+          NTL::RR at 1000-bit
+          precision.
+        </p>
+<a name="math_toolkit.special.sf_poly.sph_harm.implementation"></a><h5>
+<a name="id754738"></a>
+          <a class="link" href="sph_harm.html#math_toolkit.special.sf_poly.sph_harm.implementation">Implementation</a>
+        </h5>
+<p>
+          These functions are implemented fairly naively using the formulae given
+          above. Some extra care is taken to prevent roundoff error when converting
+          from polar coordinates (so for example the <span class="emphasis"><em>1-x<sup>2</sup></em></span> term
+          used by the associated Legendre functions is calculated without roundoff
+          error using <span class="emphasis"><em>x = cos(theta)</em></span>, and <span class="emphasis"><em>1-x<sup>2</sup> = sin<sup>2</sup>(theta)</em></span>).
+          The limiting factor in the error rates for these functions is the need
+          to calculate values near the roots of the associated Legendre functions.
+        </p>
+</div>
+<table xmlns:rev="http://www.cs.rpi.edu/~gregod/boost/tools/doc/revision" width="100%"><tr>
+<td align="left"></td>
+<td align="right"><div class="copyright-footer">Copyright © 2006 , 2007, 2008 John Maddock, Paul A. Bristow, Hubert
+      Holin, Xiaogang Zhang, Bruno Lalande and Gautam Sewani<p>
+        Distributed under the Boost Software License, Version 1.0. (See accompanying
+        file LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_0.txt)
+      </p>
+</div></td>
+</tr></table>
+<hr>
+<div class="spirit-nav">
+<a accesskey="p" href="hermite.html"><img src="../../../../../doc/html/images/prev.png" alt="Prev"></a><a accesskey="u" href="../sf_poly.html"><img src="../../../../../doc/html/images/up.png" alt="Up"></a><a accesskey="h" href="../../../index.html"><img src="../../../../../doc/html/images/home.png" alt="Home"></a><a accesskey="n" href="../bessel.html"><img src="../../../../../doc/html/images/next.png" alt="Next"></a>
+</div>
+</body>
+</html>

Added: sandbox/tools/auto_index/example/math/doc/sf_and_dist/html/math_toolkit/special/sinc.html
==============================================================================
--- (empty file)
+++ sandbox/tools/auto_index/example/math/doc/sf_and_dist/html/math_toolkit/special/sinc.html	2008-11-28 05:25:28 EST (Fri, 28 Nov 2008)
@@ -0,0 +1,51 @@
+<html>
+<head>
+<meta http-equiv="Content-Type" content="text/html; charset=ISO-8859-1">
+<title>Sinus Cardinal and Hyperbolic Sinus Cardinal Functions</title>
+<link rel="stylesheet" href="../../boostbook.css" type="text/css">
+<meta name="generator" content="DocBook XSL Stylesheets Vsnapshot_8125">
+<link rel="home" href="../../index.html" title="Math Toolkit">
+<link rel="up" href="../special.html" title="Special Functions">
+<link rel="prev" href="powers/ct_pow.html" title="Compile Time Power of a Runtime Base">
+<link rel="next" href="sinc/sinc_overview.html" title="Sinus Cardinal and Hyperbolic Sinus Cardinal Functions Overview">
+</head>
+<body bgcolor="white" text="black" link="#0000FF" vlink="#840084" alink="#0000FF">
+<table cellpadding="2" width="100%"><tr>
+<td valign="top"><img alt="Boost C++ Libraries" width="277" height="86" src="../../../../boost.png"></td>
+<td align="center">Home</td>
+<td align="center">Libraries</td>
+<td align="center">People</td>
+<td align="center">FAQ</td>
+<td align="center">More</td>
+</tr></table>
+<hr>
+<div class="spirit-nav">
+<a accesskey="p" href="powers/ct_pow.html"><img src="../../../../doc/html/images/prev.png" alt="Prev"></a><a accesskey="u" href="../special.html"><img src="../../../../doc/html/images/up.png" alt="Up"></a><a accesskey="h" href="../../index.html"><img src="../../../../doc/html/images/home.png" alt="Home"></a><a accesskey="n" href="sinc/sinc_overview.html"><img src="../../../../doc/html/images/next.png" alt="Next"></a>
+</div>
+<div class="section" lang="en">
+<div class="titlepage"><div><div><h3 class="title">
+<a name="math_toolkit.special.sinc"></a><a class="link" href="sinc.html" title="Sinus Cardinal and Hyperbolic Sinus Cardinal Functions"> Sinus Cardinal and Hyperbolic
+      Sinus Cardinal Functions</a>
+</h3></div></div></div>
+<div class="toc"><dl>
+<dt><span class="section"><a href="sinc/sinc_overview.html"> Sinus Cardinal
+        and Hyperbolic Sinus Cardinal Functions Overview</a></span></dt>
+<dt><span class="section">sinc_pi</span></dt>
+<dt><span class="section">sinhc_pi</span></dt>
+</dl></div>
+</div>
+<table xmlns:rev="http://www.cs.rpi.edu/~gregod/boost/tools/doc/revision" width="100%"><tr>
+<td align="left"></td>
+<td align="right"><div class="copyright-footer">Copyright © 2006 , 2007, 2008 John Maddock, Paul A. Bristow, Hubert
+      Holin, Xiaogang Zhang, Bruno Lalande and Gautam Sewani<p>
+        Distributed under the Boost Software License, Version 1.0. (See accompanying
+        file LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_0.txt)
+      </p>
+</div></td>
+</tr></table>
+<hr>
+<div class="spirit-nav">
+<a accesskey="p" href="powers/ct_pow.html"><img src="../../../../doc/html/images/prev.png" alt="Prev"></a><a accesskey="u" href="../special.html"><img src="../../../../doc/html/images/up.png" alt="Up"></a><a accesskey="h" href="../../index.html"><img src="../../../../doc/html/images/home.png" alt="Home"></a><a accesskey="n" href="sinc/sinc_overview.html"><img src="../../../../doc/html/images/next.png" alt="Next"></a>
+</div>
+</body>
+</html>

Added: sandbox/tools/auto_index/example/math/doc/sf_and_dist/html/math_toolkit/special/sinc/sinc_overview.html
==============================================================================
--- (empty file)
+++ sandbox/tools/auto_index/example/math/doc/sf_and_dist/html/math_toolkit/special/sinc/sinc_overview.html	2008-11-28 05:25:28 EST (Fri, 28 Nov 2008)
@@ -0,0 +1,93 @@
+<html>
+<head>
+<meta http-equiv="Content-Type" content="text/html; charset=ISO-8859-1">
+<title>Sinus Cardinal and Hyperbolic Sinus Cardinal Functions Overview</title>
+<link rel="stylesheet" href="../../../boostbook.css" type="text/css">
+<meta name="generator" content="DocBook XSL Stylesheets Vsnapshot_8125">
+<link rel="home" href="../../../index.html" title="Math Toolkit">
+<link rel="up" href="../sinc.html" title="Sinus Cardinal and Hyperbolic Sinus Cardinal Functions">
+<link rel="prev" href="../sinc.html" title="Sinus Cardinal and Hyperbolic Sinus Cardinal Functions">
+<link rel="next" href="sinc_pi.html" title="sinc_pi">
+</head>
+<body bgcolor="white" text="black" link="#0000FF" vlink="#840084" alink="#0000FF">
+<table cellpadding="2" width="100%"><tr>
+<td valign="top"><img alt="Boost C++ Libraries" width="277" height="86" src="../../../../../boost.png"></td>
+<td align="center">Home</td>
+<td align="center">Libraries</td>
+<td align="center">People</td>
+<td align="center">FAQ</td>
+<td align="center">More</td>
+</tr></table>
+<hr>
+<div class="spirit-nav">
+<a accesskey="p" href="../sinc.html"><img src="../../../../../doc/html/images/prev.png" alt="Prev"></a><a accesskey="u" href="../sinc.html"><img src="../../../../../doc/html/images/up.png" alt="Up"></a><a accesskey="h" href="../../../index.html"><img src="../../../../../doc/html/images/home.png" alt="Home"></a><a accesskey="n" href="sinc_pi.html"><img src="../../../../../doc/html/images/next.png" alt="Next"></a>
+</div>
+<div class="section" lang="en">
+<div class="titlepage"><div><div><h4 class="title">
+<a name="math_toolkit.special.sinc.sinc_overview"></a><a class="link" href="sinc_overview.html" title="Sinus Cardinal and Hyperbolic Sinus Cardinal Functions Overview"> Sinus Cardinal
+        and Hyperbolic Sinus Cardinal Functions Overview</a>
+</h4></div></div></div>
+<p>
+          The <a href="http://mathworld.wolfram.com/SincFunction.html" target="_top">Sinus Cardinal
+          family of functions</a> (indexed by the family of indices <code class="literal">a
+          &gt; 0</code>) is defined by
+        </p>
+<p>
+          <span class="inlinemediaobject"><img src="../../../../equations/special_functions_blurb20.png"></span>
+        </p>
+<p>
+          it sees heavy use in signal processing tasks.
+        </p>
+<p>
+          By analogy, the <a href="http://mathworld.wolfram.com/SinhcFunction.htm" target="_top">Hyperbolic
+          Sinus Cardinal</a> family of functions (also indexed by the family
+          of indices <code class="literal">a &gt; 0</code>) is defined by
+        </p>
+<p>
+          <span class="inlinemediaobject"><img src="../../../../equations/special_functions_blurb22.png"></span>
+        </p>
+<p>
+          These two families of functions are composed of entire functions.
+        </p>
+<p>
+          These functions (<a class="link" href="sinc_pi.html" title="sinc_pi">sinc_pi</a>
+          and <a class="link" href="sinhc_pi.html" title="sinhc_pi">sinhc_pi</a>)
+          are needed by <a href="http://www.boost.org/libs/math/quaternion/quaternion.html" target="_top">our
+          implementation</a> of quaternions
+          and octonions.
+        </p>
+<div class="blockquote"><blockquote class="blockquote">
+<p>
+            </p>
+<p>
+              <span class="emphasis"><em><span class="bold"><strong>Sinus Cardinal of index pi (purple)
+              and Hyperbolic Sinus Cardinal of index pi (red) on R</strong></span></em></span>
+            </p>
+<p>
+          </p>
+</blockquote></div>
+<div class="blockquote"><blockquote class="blockquote">
+<p>
+            </p>
+<p>
+              <span class="inlinemediaobject"><img src="../../../../graphs/sinc_pi_and_sinhc_pi_on_r.png" alt="sinc_pi_and_sinhc_pi_on_r"></span>
+            </p>
+<p>
+          </p>
+</blockquote></div>
+</div>
+<table xmlns:rev="http://www.cs.rpi.edu/~gregod/boost/tools/doc/revision" width="100%"><tr>
+<td align="left"></td>
+<td align="right"><div class="copyright-footer">Copyright © 2006 , 2007, 2008 John Maddock, Paul A. Bristow, Hubert
+      Holin, Xiaogang Zhang, Bruno Lalande and Gautam Sewani<p>
+        Distributed under the Boost Software License, Version 1.0. (See accompanying
+        file LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_0.txt)
+      </p>
+</div></td>
+</tr></table>
+<hr>
+<div class="spirit-nav">
+<a accesskey="p" href="../sinc.html"><img src="../../../../../doc/html/images/prev.png" alt="Prev"></a><a accesskey="u" href="../sinc.html"><img src="../../../../../doc/html/images/up.png" alt="Up"></a><a accesskey="h" href="../../../index.html"><img src="../../../../../doc/html/images/home.png" alt="Home"></a><a accesskey="n" href="sinc_pi.html"><img src="../../../../../doc/html/images/next.png" alt="Next"></a>
+</div>
+</body>
+</html>

Added: sandbox/tools/auto_index/example/math/doc/sf_and_dist/html/math_toolkit/special/sinc/sinc_pi.html
==============================================================================
--- (empty file)
+++ sandbox/tools/auto_index/example/math/doc/sf_and_dist/html/math_toolkit/special/sinc/sinc_pi.html	2008-11-28 05:25:28 EST (Fri, 28 Nov 2008)
@@ -0,0 +1,86 @@
+<html>
+<head>
+<meta http-equiv="Content-Type" content="text/html; charset=ISO-8859-1">
+<title>sinc_pi</title>
+<link rel="stylesheet" href="../../../boostbook.css" type="text/css">
+<meta name="generator" content="DocBook XSL Stylesheets Vsnapshot_8125">
+<link rel="home" href="../../../index.html" title="Math Toolkit">
+<link rel="up" href="../sinc.html" title="Sinus Cardinal and Hyperbolic Sinus Cardinal Functions">
+<link rel="prev" href="sinc_overview.html" title="Sinus Cardinal and Hyperbolic Sinus Cardinal Functions Overview">
+<link rel="next" href="sinhc_pi.html" title="sinhc_pi">
+</head>
+<body bgcolor="white" text="black" link="#0000FF" vlink="#840084" alink="#0000FF">
+<table cellpadding="2" width="100%"><tr>
+<td valign="top"><img alt="Boost C++ Libraries" width="277" height="86" src="../../../../../boost.png"></td>
+<td align="center">Home</td>
+<td align="center">Libraries</td>
+<td align="center">People</td>
+<td align="center">FAQ</td>
+<td align="center">More</td>
+</tr></table>
+<hr>
+<div class="spirit-nav">
+<a accesskey="p" href="sinc_overview.html"><img src="../../../../../doc/html/images/prev.png" alt="Prev"></a><a accesskey="u" href="../sinc.html"><img src="../../../../../doc/html/images/up.png" alt="Up"></a><a accesskey="h" href="../../../index.html"><img src="../../../../../doc/html/images/home.png" alt="Home"></a><a accesskey="n" href="sinhc_pi.html"><img src="../../../../../doc/html/images/next.png" alt="Next"></a>
+</div>
+<div class="section" lang="en">
+<div class="titlepage"><div><div><h4 class="title">
+<a name="math_toolkit.special.sinc.sinc_pi"></a><a class="link" href="sinc_pi.html" title="sinc_pi">sinc_pi</a>
+</h4></div></div></div>
+<p>
+          
+</p>
+<pre class="programlisting"><span class="preprocessor">#include</span> <span class="special">&lt;</span><span class="identifier">boost</span><span class="special">/</span><span class="identifier">math</span><span class="special">/</span><span class="identifier">special_functions</span><span class="special">/</span><span class="identifier">sinc</span><span class="special">.</span><span class="identifier">hpp</span><span class="special">&gt;</span>
+</pre>
+<p>
+        </p>
+<pre class="programlisting"><span class="keyword">template</span><span class="special">&lt;</span><span class="keyword">class</span> <span class="identifier">T</span><span class="special">&gt;</span> 
+<a class="link" href="../../main_overview/result_type.html" title="Calculation of the Type of the Result"><span class="emphasis"><em>calculated-result-type</em></span></a> <span class="identifier">sinc_pi</span><span class="special">(</span><span class="keyword">const</span> <span class="identifier">T</span> <span class="identifier">x</span><span class="special">);</span>
+
+<span class="keyword">template</span><span class="special">&lt;</span><span class="keyword">class</span> <span class="identifier">T</span><span class="special">,</span> <span class="keyword">class</span> <a class="link" href="../../policy.html" title="Policies">Policy</a><span class="special">&gt;</span> 
+<a class="link" href="../../main_overview/result_type.html" title="Calculation of the Type of the Result"><span class="emphasis"><em>calculated-result-type</em></span></a> <span class="identifier">sinc_pi</span><span class="special">(</span><span class="keyword">const</span> <span class="identifier">T</span> <span class="identifier">x</span><span class="special">,</span> <span class="keyword">const</span> <a class="link" href="../../policy.html" title="Policies">Policy</a><span class="special">&amp;);</span>
+
+<span class="keyword">template</span><span class="special">&lt;</span><span class="keyword">class</span> <span class="identifier">T</span><span class="special">,</span> <span class="keyword">template</span><span class="special">&lt;</span><span class="keyword">typename</span><span class="special">&gt;</span> <span class="keyword">class</span> <span class="identifier">U</span><span class="special">&gt;</span> 
+<span class="identifier">U</span><span class="special">&lt;</span><span class="identifier">T</span><span class="special">&gt;</span> <span class="identifier">sinc_pi</span><span class="special">(</span><span class="keyword">const</span> <span class="identifier">U</span><span class="special">&lt;</span><span class="identifier">T</span><span class="special">&gt;</span> <span class="identifier">x</span><span class="special">);</span>
+
+<span class="keyword">template</span><span class="special">&lt;</span><span class="keyword">class</span> <span class="identifier">T</span><span class="special">,</span> <span class="keyword">template</span><span class="special">&lt;</span><span class="keyword">typename</span><span class="special">&gt;</span> <span class="keyword">class</span> <span class="identifier">U</span><span class="special">,</span> <span class="keyword">class</span> <a class="link" href="../../policy.html" title="Policies">Policy</a><span class="special">&gt;</span> 
+<span class="identifier">U</span><span class="special">&lt;</span><span class="identifier">T</span><span class="special">&gt;</span> <span class="identifier">sinc_pi</span><span class="special">(</span><span class="keyword">const</span> <span class="identifier">U</span><span class="special">&lt;</span><span class="identifier">T</span><span class="special">&gt;</span> <span class="identifier">x</span><span class="special">,</span> <span class="keyword">const</span> <a class="link" href="../../policy.html" title="Policies">Policy</a><span class="special">&amp;);</span>
+</pre>
+<p>
+          Computes <a class="link" href="sinc_overview.html" title="Sinus Cardinal and Hyperbolic Sinus Cardinal Functions Overview">the Sinus
+          Cardinal</a> of x:
+        </p>
+<pre class="programlisting"><span class="identifier">sinc_pi</span><span class="special">(</span><span class="identifier">x</span><span class="special">)</span> <span class="special">=</span> <span class="identifier">sin</span><span class="special">(</span><span class="identifier">x</span><span class="special">)</span> <span class="special">/</span> <span class="identifier">x</span>
+</pre>
+<p>
+          The second form is for complex numbers, quaternions, octonions etc. Taylor
+          series are used at the origin to ensure accuracy.
+        </p>
+<p>
+          <span class="inlinemediaobject"><img src="../../../../graphs/sinc_pi.png" align="middle"></span>
+        </p>
+<p>
+          </p>
+<p>
+            The final <a class="link" href="../../policy.html" title="Policies">Policy</a> argument
+            is optional and can be used to control the behaviour of the function:
+            how it handles errors, what level of precision to use etc. Refer to the
+            <a class="link" href="../../policy.html" title="Policies">policy documentation for more details</a>.
+          </p>
+<p>
+        </p>
+</div>
+<table xmlns:rev="http://www.cs.rpi.edu/~gregod/boost/tools/doc/revision" width="100%"><tr>
+<td align="left"></td>
+<td align="right"><div class="copyright-footer">Copyright © 2006 , 2007, 2008 John Maddock, Paul A. Bristow, Hubert
+      Holin, Xiaogang Zhang, Bruno Lalande and Gautam Sewani<p>
+        Distributed under the Boost Software License, Version 1.0. (See accompanying
+        file LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_0.txt)
+      </p>
+</div></td>
+</tr></table>
+<hr>
+<div class="spirit-nav">
+<a accesskey="p" href="sinc_overview.html"><img src="../../../../../doc/html/images/prev.png" alt="Prev"></a><a accesskey="u" href="../sinc.html"><img src="../../../../../doc/html/images/up.png" alt="Up"></a><a accesskey="h" href="../../../index.html"><img src="../../../../../doc/html/images/home.png" alt="Home"></a><a accesskey="n" href="sinhc_pi.html"><img src="../../../../../doc/html/images/next.png" alt="Next"></a>
+</div>
+</body>
+</html>

Added: sandbox/tools/auto_index/example/math/doc/sf_and_dist/html/math_toolkit/special/sinc/sinhc_pi.html
==============================================================================
--- (empty file)
+++ sandbox/tools/auto_index/example/math/doc/sf_and_dist/html/math_toolkit/special/sinc/sinhc_pi.html	2008-11-28 05:25:28 EST (Fri, 28 Nov 2008)
@@ -0,0 +1,90 @@
+<html>
+<head>
+<meta http-equiv="Content-Type" content="text/html; charset=ISO-8859-1">
+<title>sinhc_pi</title>
+<link rel="stylesheet" href="../../../boostbook.css" type="text/css">
+<meta name="generator" content="DocBook XSL Stylesheets Vsnapshot_8125">
+<link rel="home" href="../../../index.html" title="Math Toolkit">
+<link rel="up" href="../sinc.html" title="Sinus Cardinal and Hyperbolic Sinus Cardinal Functions">
+<link rel="prev" href="sinc_pi.html" title="sinc_pi">
+<link rel="next" href="../inv_hyper.html" title="Inverse Hyperbolic Functions">
+</head>
+<body bgcolor="white" text="black" link="#0000FF" vlink="#840084" alink="#0000FF">
+<table cellpadding="2" width="100%"><tr>
+<td valign="top"><img alt="Boost C++ Libraries" width="277" height="86" src="../../../../../boost.png"></td>
+<td align="center">Home</td>
+<td align="center">Libraries</td>
+<td align="center">People</td>
+<td align="center">FAQ</td>
+<td align="center">More</td>
+</tr></table>
+<hr>
+<div class="spirit-nav">
+<a accesskey="p" href="sinc_pi.html"><img src="../../../../../doc/html/images/prev.png" alt="Prev"></a><a accesskey="u" href="../sinc.html"><img src="../../../../../doc/html/images/up.png" alt="Up"></a><a accesskey="h" href="../../../index.html"><img src="../../../../../doc/html/images/home.png" alt="Home"></a><a accesskey="n" href="../inv_hyper.html"><img src="../../../../../doc/html/images/next.png" alt="Next"></a>
+</div>
+<div class="section" lang="en">
+<div class="titlepage"><div><div><h4 class="title">
+<a name="math_toolkit.special.sinc.sinhc_pi"></a><a class="link" href="sinhc_pi.html" title="sinhc_pi">sinhc_pi</a>
+</h4></div></div></div>
+<p>
+          
+</p>
+<pre class="programlisting"><span class="preprocessor">#include</span> <span class="special">&lt;</span><span class="identifier">boost</span><span class="special">/</span><span class="identifier">math</span><span class="special">/</span><span class="identifier">special_functions</span><span class="special">/</span><span class="identifier">sinhc</span><span class="special">.</span><span class="identifier">hpp</span><span class="special">&gt;</span>
+</pre>
+<p>
+        </p>
+<pre class="programlisting"><span class="keyword">template</span><span class="special">&lt;</span><span class="keyword">class</span> <span class="identifier">T</span><span class="special">&gt;</span> 
+<a class="link" href="../../main_overview/result_type.html" title="Calculation of the Type of the Result"><span class="emphasis"><em>calculated-result-type</em></span></a> <span class="identifier">sinhc_pi</span><span class="special">(</span><span class="keyword">const</span> <span class="identifier">T</span> <span class="identifier">x</span><span class="special">);</span>
+
+<span class="keyword">template</span><span class="special">&lt;</span><span class="keyword">class</span> <span class="identifier">T</span><span class="special">,</span> <span class="keyword">class</span> <a class="link" href="../../policy.html" title="Policies">Policy</a><span class="special">&gt;</span> 
+<a class="link" href="../../main_overview/result_type.html" title="Calculation of the Type of the Result"><span class="emphasis"><em>calculated-result-type</em></span></a> <span class="identifier">sinhc_pi</span><span class="special">(</span><span class="keyword">const</span> <span class="identifier">T</span> <span class="identifier">x</span><span class="special">,</span> <span class="keyword">const</span> <a class="link" href="../../policy.html" title="Policies">Policy</a><span class="special">&amp;);</span>
+
+<span class="keyword">template</span><span class="special">&lt;</span><span class="keyword">typename</span> <span class="identifier">T</span><span class="special">,</span> <span class="keyword">template</span><span class="special">&lt;</span><span class="keyword">typename</span><span class="special">&gt;</span> <span class="keyword">class</span> <span class="identifier">U</span><span class="special">&gt;</span> 
+<span class="identifier">U</span><span class="special">&lt;</span><span class="identifier">T</span><span class="special">&gt;</span> <span class="identifier">sinhc_pi</span><span class="special">(</span><span class="keyword">const</span> <span class="identifier">U</span><span class="special">&lt;</span><span class="identifier">T</span><span class="special">&gt;</span> <span class="identifier">x</span><span class="special">);</span>
+
+<span class="keyword">template</span><span class="special">&lt;</span><span class="keyword">class</span> <span class="identifier">T</span><span class="special">,</span> <span class="keyword">template</span><span class="special">&lt;</span><span class="keyword">typename</span><span class="special">&gt;</span> <span class="keyword">class</span> <span class="identifier">U</span><span class="special">,</span> <span class="keyword">class</span> <a class="link" href="../../policy.html" title="Policies">Policy</a><span class="special">&gt;</span> 
+<span class="identifier">U</span><span class="special">&lt;</span><span class="identifier">T</span><span class="special">&gt;</span> <span class="identifier">sinhc_pi</span><span class="special">(</span><span class="keyword">const</span> <span class="identifier">U</span><span class="special">&lt;</span><span class="identifier">T</span><span class="special">&gt;</span> <span class="identifier">x</span><span class="special">,</span> <span class="keyword">const</span> <a class="link" href="../../policy.html" title="Policies">Policy</a><span class="special">&amp;);</span>
+</pre>
+<p>
+          Computes http://mathworld.wolfram.com/SinhcFunction.html <a class="link" href="sinc_overview.html" title="Sinus Cardinal and Hyperbolic Sinus Cardinal Functions Overview">the
+          Hyperbolic Sinus Cardinal</a> of x:
+        </p>
+<pre class="programlisting"><span class="identifier">sinhc_pi</span><span class="special">(</span><span class="identifier">x</span><span class="special">)</span> <span class="special">=</span> <span class="identifier">sinh</span><span class="special">(</span><span class="identifier">x</span><span class="special">)</span> <span class="special">/</span> <span class="identifier">x</span>
+</pre>
+<p>
+          The second form is for complex numbers, quaternions, octonions etc. Taylor
+          series are used at the origin to ensure accuracy.
+        </p>
+<p>
+          The return type of the first form is computed using the <a class="link" href="../../main_overview/result_type.html" title="Calculation of the Type of the Result"><span class="emphasis"><em>result
+          type calculation rules</em></span></a> when T is an integer type.
+        </p>
+<p>
+          </p>
+<p>
+            The final <a class="link" href="../../policy.html" title="Policies">Policy</a> argument
+            is optional and can be used to control the behaviour of the function:
+            how it handles errors, what level of precision to use etc. Refer to the
+            <a class="link" href="../../policy.html" title="Policies">policy documentation for more details</a>.
+          </p>
+<p>
+        </p>
+<p>
+          <span class="inlinemediaobject"><img src="../../../../graphs/sinhc_pi.png" align="middle"></span>
+        </p>
+</div>
+<table xmlns:rev="http://www.cs.rpi.edu/~gregod/boost/tools/doc/revision" width="100%"><tr>
+<td align="left"></td>
+<td align="right"><div class="copyright-footer">Copyright © 2006 , 2007, 2008 John Maddock, Paul A. Bristow, Hubert
+      Holin, Xiaogang Zhang, Bruno Lalande and Gautam Sewani<p>
+        Distributed under the Boost Software License, Version 1.0. (See accompanying
+        file LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_0.txt)
+      </p>
+</div></td>
+</tr></table>
+<hr>
+<div class="spirit-nav">
+<a accesskey="p" href="sinc_pi.html"><img src="../../../../../doc/html/images/prev.png" alt="Prev"></a><a accesskey="u" href="../sinc.html"><img src="../../../../../doc/html/images/up.png" alt="Up"></a><a accesskey="h" href="../../../index.html"><img src="../../../../../doc/html/images/home.png" alt="Home"></a><a accesskey="n" href="../inv_hyper.html"><img src="../../../../../doc/html/images/next.png" alt="Next"></a>
+</div>
+</body>
+</html>

Added: sandbox/tools/auto_index/example/math/doc/sf_and_dist/html/math_toolkit/special/zetas.html
==============================================================================
--- (empty file)
+++ sandbox/tools/auto_index/example/math/doc/sf_and_dist/html/math_toolkit/special/zetas.html	2008-11-28 05:25:28 EST (Fri, 28 Nov 2008)
@@ -0,0 +1,45 @@
+<html>
+<head>
+<meta http-equiv="Content-Type" content="text/html; charset=ISO-8859-1">
+<title>Zeta Functions</title>
+<link rel="stylesheet" href="../../boostbook.css" type="text/css">
+<meta name="generator" content="DocBook XSL Stylesheets Vsnapshot_8125">
+<link rel="home" href="../../index.html" title="Math Toolkit">
+<link rel="up" href="../special.html" title="Special Functions">
+<link rel="prev" href="ellint/ellint_3.html" title="Elliptic Integrals of the Third Kind - Legendre Form">
+<link rel="next" href="zetas/zeta.html" title="Riemann Zeta Function">
+</head>
+<body bgcolor="white" text="black" link="#0000FF" vlink="#840084" alink="#0000FF">
+<table cellpadding="2" width="100%"><tr>
+<td valign="top"><img alt="Boost C++ Libraries" width="277" height="86" src="../../../../boost.png"></td>
+<td align="center">Home</td>
+<td align="center">Libraries</td>
+<td align="center">People</td>
+<td align="center">FAQ</td>
+<td align="center">More</td>
+</tr></table>
+<hr>
+<div class="spirit-nav">
+<a accesskey="p" href="ellint/ellint_3.html"><img src="../../../../doc/html/images/prev.png" alt="Prev"></a><a accesskey="u" href="../special.html"><img src="../../../../doc/html/images/up.png" alt="Up"></a><a accesskey="h" href="../../index.html"><img src="../../../../doc/html/images/home.png" alt="Home"></a><a accesskey="n" href="zetas/zeta.html"><img src="../../../../doc/html/images/next.png" alt="Next"></a>
+</div>
+<div class="section" lang="en">
+<div class="titlepage"><div><div><h3 class="title">
+<a name="math_toolkit.special.zetas"></a><a class="link" href="zetas.html" title="Zeta Functions"> Zeta Functions</a>
+</h3></div></div></div>
+<div class="toc"><dl><dt><span class="section"> Riemann Zeta Function</span></dt></dl></div>
+</div>
+<table xmlns:rev="http://www.cs.rpi.edu/~gregod/boost/tools/doc/revision" width="100%"><tr>
+<td align="left"></td>
+<td align="right"><div class="copyright-footer">Copyright © 2006 , 2007, 2008 John Maddock, Paul A. Bristow, Hubert
+      Holin, Xiaogang Zhang, Bruno Lalande and Gautam Sewani<p>
+        Distributed under the Boost Software License, Version 1.0. (See accompanying
+        file LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_0.txt)
+      </p>
+</div></td>
+</tr></table>
+<hr>
+<div class="spirit-nav">
+<a accesskey="p" href="ellint/ellint_3.html"><img src="../../../../doc/html/images/prev.png" alt="Prev"></a><a accesskey="u" href="../special.html"><img src="../../../../doc/html/images/up.png" alt="Up"></a><a accesskey="h" href="../../index.html"><img src="../../../../doc/html/images/home.png" alt="Home"></a><a accesskey="n" href="zetas/zeta.html"><img src="../../../../doc/html/images/next.png" alt="Next"></a>
+</div>
+</body>
+</html>

Added: sandbox/tools/auto_index/example/math/doc/sf_and_dist/html/math_toolkit/special/zetas/zeta.html
==============================================================================
--- (empty file)
+++ sandbox/tools/auto_index/example/math/doc/sf_and_dist/html/math_toolkit/special/zetas/zeta.html	2008-11-28 05:25:28 EST (Fri, 28 Nov 2008)
@@ -0,0 +1,332 @@
+<html>
+<head>
+<meta http-equiv="Content-Type" content="text/html; charset=ISO-8859-1">
+<title>Riemann Zeta Function</title>
+<link rel="stylesheet" href="../../../boostbook.css" type="text/css">
+<meta name="generator" content="DocBook XSL Stylesheets Vsnapshot_8125">
+<link rel="home" href="../../../index.html" title="Math Toolkit">
+<link rel="up" href="../zetas.html" title="Zeta Functions">
+<link rel="prev" href="../zetas.html" title="Zeta Functions">
+<link rel="next" href="../expint.html" title="Exponential Integrals">
+</head>
+<body bgcolor="white" text="black" link="#0000FF" vlink="#840084" alink="#0000FF">
+<table cellpadding="2" width="100%"><tr>
+<td valign="top"><img alt="Boost C++ Libraries" width="277" height="86" src="../../../../../boost.png"></td>
+<td align="center">Home</td>
+<td align="center">Libraries</td>
+<td align="center">People</td>
+<td align="center">FAQ</td>
+<td align="center">More</td>
+</tr></table>
+<hr>
+<div class="spirit-nav">
+<a accesskey="p" href="../zetas.html"><img src="../../../../../doc/html/images/prev.png" alt="Prev"></a><a accesskey="u" href="../zetas.html"><img src="../../../../../doc/html/images/up.png" alt="Up"></a><a accesskey="h" href="../../../index.html"><img src="../../../../../doc/html/images/home.png" alt="Home"></a><a accesskey="n" href="../expint.html"><img src="../../../../../doc/html/images/next.png" alt="Next"></a>
+</div>
+<div class="section" lang="en">
+<div class="titlepage"><div><div><h4 class="title">
+<a name="math_toolkit.special.zetas.zeta"></a><a class="link" href="zeta.html" title="Riemann Zeta Function"> Riemann Zeta Function</a>
+</h4></div></div></div>
+<a name="math_toolkit.special.zetas.zeta.synopsis"></a><h5>
+<a name="id772622"></a>
+          <a class="link" href="zeta.html#math_toolkit.special.zetas.zeta.synopsis">Synopsis</a>
+        </h5>
+<p>
+          
+</p>
+<pre class="programlisting"><span class="preprocessor">#include</span> <span class="special">&lt;</span><span class="identifier">boost</span><span class="special">/</span><span class="identifier">math</span><span class="special">/</span><span class="identifier">special_functions</span><span class="special">/</span><span class="identifier">zeta</span><span class="special">.</span><span class="identifier">hpp</span><span class="special">&gt;</span>
+</pre>
+<p>
+        </p>
+<pre class="programlisting"><span class="keyword">namespace</span> <span class="identifier">boost</span><span class="special">{</span> <span class="keyword">namespace</span> <span class="identifier">math</span><span class="special">{</span>
+
+<span class="keyword">template</span> <span class="special">&lt;</span><span class="keyword">class</span> <span class="identifier">T</span><span class="special">&gt;</span>
+<a class="link" href="../../main_overview/result_type.html" title="Calculation of the Type of the Result"><span class="emphasis"><em>calculated-result-type</em></span></a> <span class="identifier">zeta</span><span class="special">(</span><span class="identifier">T</span> <span class="identifier">z</span><span class="special">);</span>
+
+<span class="keyword">template</span> <span class="special">&lt;</span><span class="keyword">class</span> <span class="identifier">T</span><span class="special">,</span> <span class="keyword">class</span> <a class="link" href="../../policy.html" title="Policies">Policy</a><span class="special">&gt;</span>
+<a class="link" href="../../main_overview/result_type.html" title="Calculation of the Type of the Result"><span class="emphasis"><em>calculated-result-type</em></span></a> <span class="identifier">zeta</span><span class="special">(</span><span class="identifier">T</span> <span class="identifier">z</span><span class="special">,</span> <span class="keyword">const</span> <a class="link" href="../../policy.html" title="Policies">Policy</a><span class="special">&amp;);</span>
+
+<span class="special">}}</span> <span class="comment">// namespaces
+</span></pre>
+<p>
+          The return type of these functions is computed using the <a class="link" href="../../main_overview/result_type.html" title="Calculation of the Type of the Result"><span class="emphasis"><em>result
+          type calculation rules</em></span></a>: the return type is <code class="computeroutput"><span class="keyword">double</span></code> if T is an integer type, and T otherwise.
+        </p>
+<p>
+          </p>
+<p>
+            The final <a class="link" href="../../policy.html" title="Policies">Policy</a> argument
+            is optional and can be used to control the behaviour of the function:
+            how it handles errors, what level of precision to use etc. Refer to the
+            <a class="link" href="../../policy.html" title="Policies">policy documentation for more details</a>.
+          </p>
+<p>
+        </p>
+<a name="math_toolkit.special.zetas.zeta.description"></a><h5>
+<a name="id773001"></a>
+          <a class="link" href="zeta.html#math_toolkit.special.zetas.zeta.description">Description</a>
+        </h5>
+<pre class="programlisting"><span class="keyword">template</span> <span class="special">&lt;</span><span class="keyword">class</span> <span class="identifier">T</span><span class="special">&gt;</span>
+<a class="link" href="../../main_overview/result_type.html" title="Calculation of the Type of the Result"><span class="emphasis"><em>calculated-result-type</em></span></a> <span class="identifier">zeta</span><span class="special">(</span><span class="identifier">T</span> <span class="identifier">z</span><span class="special">);</span>
+
+<span class="keyword">template</span> <span class="special">&lt;</span><span class="keyword">class</span> <span class="identifier">T</span><span class="special">,</span> <span class="keyword">class</span> <a class="link" href="../../policy.html" title="Policies">Policy</a><span class="special">&gt;</span>
+<a class="link" href="../../main_overview/result_type.html" title="Calculation of the Type of the Result"><span class="emphasis"><em>calculated-result-type</em></span></a> <span class="identifier">zeta</span><span class="special">(</span><span class="identifier">T</span> <span class="identifier">z</span><span class="special">,</span> <span class="keyword">const</span> <a class="link" href="../../policy.html" title="Policies">Policy</a><span class="special">&amp;);</span>
+</pre>
+<p>
+          Returns the <a href="http://mathworld.wolfram.com/RiemannZetaFunction.html" target="_top">zeta
+          function</a> of z:
+        </p>
+<p>
+          <span class="inlinemediaobject"><img src="../../../../equations/zeta1.png"></span>
+        </p>
+<p>
+          <span class="inlinemediaobject"><img src="../../../../graphs/zeta1.png" align="middle"></span>
+        </p>
+<p>
+          <span class="inlinemediaobject"><img src="../../../../graphs/zeta2.png" align="middle"></span>
+        </p>
+<a name="math_toolkit.special.zetas.zeta.accuracy"></a><h5>
+<a name="id773313"></a>
+          <a class="link" href="zeta.html#math_toolkit.special.zetas.zeta.accuracy">Accuracy</a>
+        </h5>
+<p>
+          The following table shows the peak errors (in units of epsilon) found on
+          various platforms with various floating point types, along with comparisons
+          to the GSL-1.9 and
+          Cephes libraries. Unless
+          otherwise specified any floating point type that is narrower than the one
+          shown will have <a class="link" href="../../backgrounders/relative_error.html#zero_error">effectively zero error</a>.
+        </p>
+<div class="table">
+<a name="id773364"></a><p class="title"><b>Table 44. Errors In the Function zeta(z)</b></p>
+<div class="table-contents"><table class="table" summary="Errors In the Function zeta(z)">
+<colgroup>
+<col>
+<col>
+<col>
+<col>
+</colgroup>
+<thead><tr>
+<th>
+              <p>
+                Significand Size
+              </p>
+              </th>
+<th>
+              <p>
+                Platform and Compiler
+              </p>
+              </th>
+<th>
+              <p>
+                z &gt; 0
+              </p>
+              </th>
+<th>
+              <p>
+                z &lt; 0
+              </p>
+              </th>
+</tr></thead>
+<tbody>
+<tr>
+<td>
+              <p>
+                53
+              </p>
+              </td>
+<td>
+              <p>
+                Win32, Visual C++ 8
+              </p>
+              </td>
+<td>
+              <p>
+                Peak=0.99 Mean=0.1
+              </p>
+              <p>
+                GSL Peak=8.7 Mean=1.0
+              </p>
+              <p>
+                Cephes Peak=2.1
+                Mean=1.1
+              </p>
+              </td>
+<td>
+              <p>
+                Peak=7.1 Mean=3.0
+              </p>
+              <p>
+                GSL Peak=137 Mean=14
+              </p>
+              <p>
+                Cephes Peak=5084
+                Mean=470
+              </p>
+              </td>
+</tr>
+<tr>
+<td>
+              <p>
+                64
+              </p>
+              </td>
+<td>
+              <p>
+                RedHat Linux IA_EM64, gcc-4.1
+              </p>
+              </td>
+<td>
+              <p>
+                Peak=0.99 Mean=0.5
+              </p>
+              </td>
+<td>
+              <p>
+                Peak=570 Mean=60
+              </p>
+              </td>
+</tr>
+<tr>
+<td>
+              <p>
+                64
+              </p>
+              </td>
+<td>
+              <p>
+                Redhat Linux IA64, gcc-4.1
+              </p>
+              </td>
+<td>
+              <p>
+                Peak=0.99 Mean=0.5
+              </p>
+              </td>
+<td>
+              <p>
+                Peak=559 Mean=56
+              </p>
+              </td>
+</tr>
+<tr>
+<td>
+              <p>
+                113
+              </p>
+              </td>
+<td>
+              <p>
+                HPUX IA64, aCC A.06.06
+              </p>
+              </td>
+<td>
+              <p>
+                Peak=1.0 Mean=0.4
+              </p>
+              </td>
+<td>
+              <p>
+                Peak=1018 Mean=79
+              </p>
+              </td>
+</tr>
+</tbody>
+</table></div>
+</div>
+<br class="table-break"><a name="math_toolkit.special.zetas.zeta.testing"></a><h5>
+<a name="id773607"></a>
+          <a class="link" href="zeta.html#math_toolkit.special.zetas.zeta.testing">Testing</a>
+        </h5>
+<p>
+          The tests for these functions come in two parts: basic sanity checks use
+          spot values calculated using <a href="http://functions.wolfram.com/webMathematica/FunctionEvaluation.jsp?name=Zeta" target="_top">Mathworld's
+          online evaluator</a>, while accuracy checks use high-precision test
+          values calculated at 1000-bit precision with NTL::RR
+          and this implementation. Note that the generic and type-specific versions
+          of these functions use differing implementations internally, so this gives
+          us reasonably independent test data. Using our test data to test other
+          "known good" implementations also provides an additional sanity
+          check.
+        </p>
+<a name="math_toolkit.special.zetas.zeta.implementation"></a><h5>
+<a name="id773671"></a>
+          <a class="link" href="zeta.html#math_toolkit.special.zetas.zeta.implementation">Implementation</a>
+        </h5>
+<p>
+          All versions of these functions first use the usual reflection formulas
+          to make their arguments positive:
+        </p>
+<p>
+          <span class="inlinemediaobject"><img src="../../../../equations/zeta3.png"></span>
+        </p>
+<p>
+          The generic versions of these functions are implemented using the series:
+        </p>
+<p>
+          <span class="inlinemediaobject"><img src="../../../../equations/zeta1.png"></span>
+        </p>
+<p>
+          for large z, and using the globally convergent series:
+        </p>
+<p>
+          <span class="inlinemediaobject"><img src="../../../../equations/zeta2.png"></span>
+        </p>
+<p>
+          In all other cases. The crossover point for these is chosen so that the
+          first series is used only if it will converge reasonably quickly, the problem
+          with this series is that convergence become slower the more terms you take,
+          so we really do have to be certain of convergence before using this series,
+          even though the alternative is often quite slow.
+        </p>
+<p>
+          When the significand (mantissa) size is recognised (currently for 53, 64
+          and 113-bit reals, plus single-precision 24-bit handled via promotion to
+          double) then a series of rational approximations <a class="link" href="../../backgrounders/implementation.html#math_toolkit.backgrounders.implementation.rational_approximations_used">devised
+          by JM</a> are used.
+        </p>
+<p>
+          For 0 &lt; z &lt; 1 the approximating form is:
+        </p>
+<p>
+          <span class="inlinemediaobject"><img src="../../../../equations/zeta4.png"></span>
+        </p>
+<p>
+          For a rational approximation R(1-z) and a constant C.
+        </p>
+<p>
+          For 1 &lt; z &lt; 4 the approximating form is:
+        </p>
+<p>
+          <span class="inlinemediaobject"><img src="../../../../equations/zeta5.png"></span>
+        </p>
+<p>
+          For a rational approximation R(n-z) and a constant C and integer n.
+        </p>
+<p>
+          For z &gt; 4 the approximating form is:
+        </p>
+<p>
+          &#950;(z) = 1 + e<sup>R(z - n)</sup>
+        </p>
+<p>
+          For a rational approximation R(z-n) and integer n, note that the accuracy
+          required for R(z-n) is not full machine precision, but an absolute error
+          of: &#949;/R(0). This saves us quite a few digits when dealing with large z,
+          especially when &#949; is small.
+        </p>
+</div>
+<table xmlns:rev="http://www.cs.rpi.edu/~gregod/boost/tools/doc/revision" width="100%"><tr>
+<td align="left"></td>
+<td align="right"><div class="copyright-footer">Copyright © 2006 , 2007, 2008 John Maddock, Paul A. Bristow, Hubert
+      Holin, Xiaogang Zhang, Bruno Lalande and Gautam Sewani<p>
+        Distributed under the Boost Software License, Version 1.0. (See accompanying
+        file LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_0.txt)
+      </p>
+</div></td>
+</tr></table>
+<hr>
+<div class="spirit-nav">
+<a accesskey="p" href="../zetas.html"><img src="../../../../../doc/html/images/prev.png" alt="Prev"></a><a accesskey="u" href="../zetas.html"><img src="../../../../../doc/html/images/up.png" alt="Up"></a><a accesskey="h" href="../../../index.html"><img src="../../../../../doc/html/images/home.png" alt="Home"></a><a accesskey="n" href="../expint.html"><img src="../../../../../doc/html/images/next.png" alt="Next"></a>
+</div>
+</body>
+</html>

Added: sandbox/tools/auto_index/example/math/doc/sf_and_dist/html/math_toolkit/status.html
==============================================================================
--- (empty file)
+++ sandbox/tools/auto_index/example/math/doc/sf_and_dist/html/math_toolkit/status.html	2008-11-28 05:25:28 EST (Fri, 28 Nov 2008)
@@ -0,0 +1,50 @@
+<html>
+<head>
+<meta http-equiv="Content-Type" content="text/html; charset=ISO-8859-1">
+<title>Library Status</title>
+<link rel="stylesheet" href="../boostbook.css" type="text/css">
+<meta name="generator" content="DocBook XSL Stylesheets Vsnapshot_8125">
+<link rel="home" href="../index.html" title="Math Toolkit">
+<link rel="up" href="../index.html" title="Math Toolkit">
+<link rel="prev" href="backgrounders/refs.html" title="References">
+<link rel="next" href="status/history1.html" title="History and What's New">
+</head>
+<body bgcolor="white" text="black" link="#0000FF" vlink="#840084" alink="#0000FF">
+<table cellpadding="2" width="100%"><tr>
+<td valign="top"><img alt="Boost C++ Libraries" width="277" height="86" src="../../../boost.png"></td>
+<td align="center">Home</td>
+<td align="center">Libraries</td>
+<td align="center">People</td>
+<td align="center">FAQ</td>
+<td align="center">More</td>
+</tr></table>
+<hr>
+<div class="spirit-nav">
+<a accesskey="p" href="backgrounders/refs.html"><img src="../../../doc/html/images/prev.png" alt="Prev"></a><a accesskey="u" href="../index.html"><img src="../../../doc/html/images/up.png" alt="Up"></a><a accesskey="h" href="../index.html"><img src="../../../doc/html/images/home.png" alt="Home"></a><a accesskey="n" href="status/history1.html"><img src="../../../doc/html/images/next.png" alt="Next"></a>
+</div>
+<div class="section" lang="en">
+<div class="titlepage"><div><div><h2 class="title" style="clear: both">
+<a name="math_toolkit.status"></a><a class="link" href="status.html" title="Library Status"> Library Status</a>
+</h2></div></div></div>
+<div class="toc"><dl>
+<dt><span class="section"> History and What's New</span></dt>
+<dt><span class="section"> Compilers</span></dt>
+<dt><span class="section"> Known Issues, and Todo List</span></dt>
+<dt><span class="section"> Credits and Acknowledgements</span></dt>
+</dl></div>
+</div>
+<table xmlns:rev="http://www.cs.rpi.edu/~gregod/boost/tools/doc/revision" width="100%"><tr>
+<td align="left"></td>
+<td align="right"><div class="copyright-footer">Copyright © 2006 , 2007, 2008 John Maddock, Paul A. Bristow, Hubert
+      Holin, Xiaogang Zhang, Bruno Lalande and Gautam Sewani<p>
+        Distributed under the Boost Software License, Version 1.0. (See accompanying
+        file LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_0.txt)
+      </p>
+</div></td>
+</tr></table>
+<hr>
+<div class="spirit-nav">
+<a accesskey="p" href="backgrounders/refs.html"><img src="../../../doc/html/images/prev.png" alt="Prev"></a><a accesskey="u" href="../index.html"><img src="../../../doc/html/images/up.png" alt="Up"></a><a accesskey="h" href="../index.html"><img src="../../../doc/html/images/home.png" alt="Home"></a><a accesskey="n" href="status/history1.html"><img src="../../../doc/html/images/next.png" alt="Next"></a>
+</div>
+</body>
+</html>

Added: sandbox/tools/auto_index/example/math/doc/sf_and_dist/html/math_toolkit/status/compilers.html
==============================================================================
--- (empty file)
+++ sandbox/tools/auto_index/example/math/doc/sf_and_dist/html/math_toolkit/status/compilers.html	2008-11-28 05:25:28 EST (Fri, 28 Nov 2008)
@@ -0,0 +1,629 @@
+<html>
+<head>
+<meta http-equiv="Content-Type" content="text/html; charset=ISO-8859-1">
+<title>Compilers</title>
+<link rel="stylesheet" href="../../boostbook.css" type="text/css">
+<meta name="generator" content="DocBook XSL Stylesheets Vsnapshot_8125">
+<link rel="home" href="../../index.html" title="Math Toolkit">
+<link rel="up" href="../status.html" title="Library Status">
+<link rel="prev" href="history1.html" title="History and What's New">
+<link rel="next" href="issues.html" title="Known Issues, and Todo List">
+</head>
+<body bgcolor="white" text="black" link="#0000FF" vlink="#840084" alink="#0000FF">
+<table cellpadding="2" width="100%"><tr>
+<td valign="top"><img alt="Boost C++ Libraries" width="277" height="86" src="../../../../boost.png"></td>
+<td align="center">Home</td>
+<td align="center">Libraries</td>
+<td align="center">People</td>
+<td align="center">FAQ</td>
+<td align="center">More</td>
+</tr></table>
+<hr>
+<div class="spirit-nav">
+<a accesskey="p" href="history1.html"><img src="../../../../doc/html/images/prev.png" alt="Prev"></a><a accesskey="u" href="../status.html"><img src="../../../../doc/html/images/up.png" alt="Up"></a><a accesskey="h" href="../../index.html"><img src="../../../../doc/html/images/home.png" alt="Home"></a><a accesskey="n" href="issues.html"><img src="../../../../doc/html/images/next.png" alt="Next"></a>
+</div>
+<div class="section" lang="en">
+<div class="titlepage"><div><div><h3 class="title">
+<a name="math_toolkit.status.compilers"></a><a class="link" href="compilers.html" title="Compilers"> Compilers</a>
+</h3></div></div></div>
+<p>
+        </p>
+<p>
+          This section contains some information about how various compilers work
+          with this library. It is not comprehensive and updated experiences are
+          always welcome. Some effort has been made to suppress unhelpful warnings
+          but it is difficult to achieve this on all systems.
+        </p>
+<p>
+        </p>
+<div class="table">
+<a name="id919720"></a><p class="title"><b>Table 55. Supported/Tested Compilers</b></p>
+<div class="table-contents"><table class="table" summary="Supported/Tested Compilers">
+<colgroup>
+<col>
+<col>
+<col>
+<col>
+</colgroup>
+<thead><tr>
+<th>
+              <p>
+                Platform
+              </p>
+              </th>
+<th>
+              <p>
+                Compiler
+              </p>
+              </th>
+<th>
+              <p>
+                Has long double support
+              </p>
+              </th>
+<th>
+              <p>
+                Notes
+              </p>
+              </th>
+</tr></thead>
+<tbody>
+<tr>
+<td>
+              <p>
+                Windows
+              </p>
+              </td>
+<td>
+              <p>
+                MSVC 7.1 and later
+              </p>
+              </td>
+<td>
+              <p>
+                Yes
+              </p>
+              </td>
+<td>
+              <p>
+                All tests OK.
+              </p>
+              <p>
+                We aim to keep our headers warning free at level 4 with this compiler.
+              </p>
+              </td>
+</tr>
+<tr>
+<td>
+              <p>
+                Windows
+              </p>
+              </td>
+<td>
+              <p>
+                Intel 8.1 and later
+              </p>
+              </td>
+<td>
+              <p>
+                Yes
+              </p>
+              </td>
+<td>
+              <p>
+                All tests OK.
+              </p>
+              <p>
+                We aim to keep our headers warning free at level 4 with this compiler.
+                However, The tests cases tend to generate a lot of warnings relating
+                to numeric underflow of the test data: these are harmless.
+              </p>
+              </td>
+</tr>
+<tr>
+<td>
+              <p>
+                Windows
+              </p>
+              </td>
+<td>
+              <p>
+                GNU Mingw32 C++
+              </p>
+              </td>
+<td>
+              <p>
+                Yes
+              </p>
+              </td>
+<td>
+              <p>
+                All tests OK.
+              </p>
+              <p>
+                We aim to keep our headers warning free with -Wall with this compiler.
+              </p>
+              </td>
+</tr>
+<tr>
+<td>
+              <p>
+                Windows
+              </p>
+              </td>
+<td>
+              <p>
+                GNU Cygwin C++
+              </p>
+              </td>
+<td>
+              <p>
+                No
+              </p>
+              </td>
+<td>
+              <p>
+                All tests OK.
+              </p>
+              <p>
+                We aim to keep our headers warning free with -Wall with this compiler.
+              </p>
+              <p>
+                Long double support has been disabled because there are no native
+                long double C std library functions available.
+              </p>
+              </td>
+</tr>
+<tr>
+<td>
+              <p>
+                Windows
+              </p>
+              </td>
+<td>
+              <p>
+                Borland C++ 5.8.2 (Developer studio 2006)
+              </p>
+              </td>
+<td>
+              <p>
+                No
+              </p>
+              </td>
+<td>
+              <p>
+                We have only partial compatability with this compiler:
+              </p>
+              <p>
+                Long double support has been disabled because the native long double
+                C standard library functions really only forward to the double versions.
+                This can result in unpredictable behaviour when using the long double
+                overloads: for example <code class="computeroutput"><span class="identifier">sqrtl</span></code>
+                applied to a finite value, can result in an infinite result.
+              </p>
+              <p>
+                Some functions still fail to compile, there are no known workarounds
+                at present.
+              </p>
+              </td>
+</tr>
+<tr>
+<td>
+              <p>
+                Linux
+              </p>
+              </td>
+<td>
+              <p>
+                GNU C++ 3.4 and later
+              </p>
+              </td>
+<td>
+              <p>
+                Yes
+              </p>
+              </td>
+<td>
+              <p>
+                All tests OK.
+              </p>
+              <p>
+                We aim to keep our headers warning free with -Wall with this compiler.
+              </p>
+              </td>
+</tr>
+<tr>
+<td>
+              <p>
+                Linux
+              </p>
+              </td>
+<td>
+              <p>
+                Intel C++ 10.0 and later
+              </p>
+              </td>
+<td>
+              <p>
+                Yes
+              </p>
+              </td>
+<td>
+              <p>
+                All tests OK.
+              </p>
+              <p>
+                We aim to keep our headers warning free with -Wall with this compiler.
+                However, The tests cases tend to generate a lot of warnings relating
+                to numeric underflow of the test data: these are harmless.
+              </p>
+              </td>
+</tr>
+<tr>
+<td>
+              <p>
+                Linux
+              </p>
+              </td>
+<td>
+              <p>
+                Intel C++ 8.1 and 9.1
+              </p>
+              </td>
+<td>
+              <p>
+                No
+              </p>
+              </td>
+<td>
+              <p>
+                All tests OK.
+              </p>
+              <p>
+                Long double support has been disabled with these compiler releases
+                because calling the standard library long double math functions can
+                result in a segfault. The issue is Linux distribution and glibc version
+                specific and is Intel bug report #409291. Fully up to date releases
+                of Intel 9.1 (post version l_cc_c_9.1.046) shouldn't have this problem.
+                If you need long double support with this compiler, then comment
+                out the define of BOOST_MATH_NO_LONG_DOUBLE_MATH_FUNCTIONS at line
+                55 of boost/math/tools/config.hpp.
+              </p>
+              <p>
+                We aim to keep our headers warning free with -Wall with this compiler.
+                However, The tests cases tend to generate a lot of warnings relating
+                to numeric underflow of the test data: these are harmless.
+              </p>
+              </td>
+</tr>
+<tr>
+<td>
+              <p>
+                Linux
+              </p>
+              </td>
+<td>
+              <p>
+                QLogic PathScale 3.0
+              </p>
+              </td>
+<td>
+              <p>
+                Yes
+              </p>
+              </td>
+<td>
+              <p>
+                Some tests involving conceptual checks fail to build, otherwise there
+                appear to be no issues.
+              </p>
+              </td>
+</tr>
+<tr>
+<td>
+              <p>
+                Linux
+              </p>
+              </td>
+<td>
+              <p>
+                Sun Studio 12
+              </p>
+              </td>
+<td>
+              <p>
+                Yes
+              </p>
+              </td>
+<td>
+              <p>
+                Some tests involving function overload resolution fail to build,
+                these issues should be rairly encountered in practice.
+              </p>
+              </td>
+</tr>
+<tr>
+<td>
+              <p>
+                Solaris
+              </p>
+              </td>
+<td>
+              <p>
+                Sun Studio 12
+              </p>
+              </td>
+<td>
+              <p>
+                Yes
+              </p>
+              </td>
+<td>
+              <p>
+                Some tests involving function overload resolution fail to build,
+                these issues should be rairly encountered in practice.
+              </p>
+              </td>
+</tr>
+<tr>
+<td>
+              <p>
+                Solaris
+              </p>
+              </td>
+<td>
+              <p>
+                GNU C++ 4.x
+              </p>
+              </td>
+<td>
+              <p>
+                Yes
+              </p>
+              </td>
+<td>
+              <p>
+                All tests OK.
+              </p>
+              <p>
+                We aim to keep our headers warning free with -Wall with this compiler.
+              </p>
+              </td>
+</tr>
+<tr>
+<td>
+              <p>
+                HP Tru64
+              </p>
+              </td>
+<td>
+              <p>
+                Compaq C++ 7.1
+              </p>
+              </td>
+<td>
+              <p>
+                Yes
+              </p>
+              </td>
+<td>
+              <p>
+                All tests OK.
+              </p>
+              </td>
+</tr>
+<tr>
+<td>
+              <p>
+                HP-UX Itanium
+              </p>
+              </td>
+<td>
+              <p>
+                HP aCC 6.x
+              </p>
+              </td>
+<td>
+              <p>
+                Yes
+              </p>
+              </td>
+<td>
+              <p>
+                All tests OK.
+              </p>
+              <p>
+                Unfortunately this compiler emits quite a few warnings from libraries
+                upon which we depend (TR1, Array etc).
+              </p>
+              </td>
+</tr>
+<tr>
+<td>
+              <p>
+                HP-UX PA-RISC
+              </p>
+              </td>
+<td>
+              <p>
+                GNU C++ 3.4
+              </p>
+              </td>
+<td>
+              <p>
+                No
+              </p>
+              </td>
+<td>
+              <p>
+                All tests OK.
+              </p>
+              </td>
+</tr>
+<tr>
+<td>
+              <p>
+                Apple Mac OS X, Intel
+              </p>
+              </td>
+<td>
+              <p>
+                Darwin/GNU C++ 4.x
+              </p>
+              </td>
+<td>
+              <p>
+                Yes
+              </p>
+              </td>
+<td>
+              <p>
+                All tests OK.
+              </p>
+              </td>
+</tr>
+<tr>
+<td>
+              <p>
+                Apple Mac OS X, PowerPC
+              </p>
+              </td>
+<td>
+              <p>
+                Darwin/GNU C++ 4.x
+              </p>
+              </td>
+<td>
+              <p>
+                No
+              </p>
+              </td>
+<td>
+              <p>
+                All tests OK.
+              </p>
+              <p>
+                Long double support has been disabled on this platform due to the
+                rather strange nature of Darwin's 106-bit long double implementation.
+                It should be possible to make this work if someone is prepared to
+                offer assistance.
+              </p>
+              </td>
+</tr>
+<tr>
+<td>
+              <p>
+                IMB AIX
+              </p>
+              </td>
+<td>
+              <p>
+                IBM xlc 5.3
+              </p>
+              </td>
+<td>
+              <p>
+                Yes
+              </p>
+              </td>
+<td>
+              <p>
+                All tests pass except for our fpclassify tests which fail due to
+                a bug in <code class="computeroutput"><span class="identifier">std</span><span class="special">::</span><span class="identifier">numeric_limits</span></code>, the bug effects
+                the test code, not fpclassify itself. The IBM compiler group are
+                aware of the problem.
+              </p>
+              </td>
+</tr>
+</tbody>
+</table></div>
+</div>
+<p><br class="table-break"> </p>
+<div class="table">
+<a name="id920599"></a><p class="title"><b>Table 56. Unsupported Compilers</b></p>
+<div class="table-contents"><table class="table" summary="Unsupported Compilers">
+<colgroup>
+<col>
+<col>
+</colgroup>
+<thead><tr>
+<th>
+              <p>
+                Platform
+              </p>
+              </th>
+<th>
+              <p>
+                Compiler
+              </p>
+              </th>
+</tr></thead>
+<tbody>
+<tr>
+<td>
+              <p>
+                Windows
+              </p>
+              </td>
+<td>
+              <p>
+                Borland C++ 5.9.2 (Borland Developer Studio 2007)
+              </p>
+              </td>
+</tr>
+<tr>
+<td>
+              <p>
+                Windows
+              </p>
+              </td>
+<td>
+              <p>
+                MSVC 6 and 7
+              </p>
+              </td>
+</tr>
+</tbody>
+</table></div>
+</div>
+<p><br class="table-break">
+        </p>
+<p>
+          If you're compiler or platform is not listed above, please try running
+          the regression tests: cd into boost-root/libs/math/test and do a:
+        </p>
+<p>
+        
+</p>
+<pre class="programlisting"><span class="identifier">bjam</span> <span class="identifier">mytoolset</span>
+</pre>
+<p>
+        </p>
+<p>
+          where "mytoolset" is the name of the Boost.Build
+          toolset used for your compiler. The chances are that <span class="bold"><strong>many
+          of the accuracy tests will fail at this stage</strong></span> - don't panic
+          - the default acceptable error tolerances are quite tight, especially for
+          long double types with an extended exponent range (these cause more extreme
+          test cases to be executed for some functions). You will need to cast an
+          eye over the output from the failing tests and make a judgement as to whether
+          the error rates are acceptable or not.
+        </p>
+<p>
+      </p>
+</div>
+<table xmlns:rev="http://www.cs.rpi.edu/~gregod/boost/tools/doc/revision" width="100%"><tr>
+<td align="left"></td>
+<td align="right"><div class="copyright-footer">Copyright © 2006 , 2007, 2008 John Maddock, Paul A. Bristow, Hubert
+      Holin, Xiaogang Zhang, Bruno Lalande and Gautam Sewani<p>
+        Distributed under the Boost Software License, Version 1.0. (See accompanying
+        file LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_0.txt)
+      </p>
+</div></td>
+</tr></table>
+<hr>
+<div class="spirit-nav">
+<a accesskey="p" href="history1.html"><img src="../../../../doc/html/images/prev.png" alt="Prev"></a><a accesskey="u" href="../status.html"><img src="../../../../doc/html/images/up.png" alt="Up"></a><a accesskey="h" href="../../index.html"><img src="../../../../doc/html/images/home.png" alt="Home"></a><a accesskey="n" href="issues.html"><img src="../../../../doc/html/images/next.png" alt="Next"></a>
+</div>
+</body>
+</html>

Added: sandbox/tools/auto_index/example/math/doc/sf_and_dist/html/math_toolkit/status/credits.html
==============================================================================
--- (empty file)
+++ sandbox/tools/auto_index/example/math/doc/sf_and_dist/html/math_toolkit/status/credits.html	2008-11-28 05:25:28 EST (Fri, 28 Nov 2008)
@@ -0,0 +1,103 @@
+<html>
+<head>
+<meta http-equiv="Content-Type" content="text/html; charset=ISO-8859-1">
+<title>Credits and Acknowledgements</title>
+<link rel="stylesheet" href="../../boostbook.css" type="text/css">
+<meta name="generator" content="DocBook XSL Stylesheets Vsnapshot_8125">
+<link rel="home" href="../../index.html" title="Math Toolkit">
+<link rel="up" href="../status.html" title="Library Status">
+<link rel="prev" href="issues.html" title="Known Issues, and Todo List">
+<link rel="next" href="../../index/s10.html" title="Class Index">
+</head>
+<body bgcolor="white" text="black" link="#0000FF" vlink="#840084" alink="#0000FF">
+<table cellpadding="2" width="100%"><tr>
+<td valign="top"><img alt="Boost C++ Libraries" width="277" height="86" src="../../../../boost.png"></td>
+<td align="center">Home</td>
+<td align="center">Libraries</td>
+<td align="center">People</td>
+<td align="center">FAQ</td>
+<td align="center">More</td>
+</tr></table>
+<hr>
+<div class="spirit-nav">
+<a accesskey="p" href="issues.html"><img src="../../../../doc/html/images/prev.png" alt="Prev"></a><a accesskey="u" href="../status.html"><img src="../../../../doc/html/images/up.png" alt="Up"></a><a accesskey="h" href="../../index.html"><img src="../../../../doc/html/images/home.png" alt="Home"></a><a accesskey="n" href="../../index/s10.html"><img src="../../../../doc/html/images/next.png" alt="Next"></a>
+</div>
+<div class="section" lang="en">
+<div class="titlepage"><div><div><h3 class="title">
+<a name="math_toolkit.status.credits"></a><a class="link" href="credits.html" title="Credits and Acknowledgements"> Credits and Acknowledgements</a>
+</h3></div></div></div>
+<p>
+        Hubert Holin started the Boost.Math library. The inverse hyperbolic functions,
+        and the sinus cardinal functions are his.
+      </p>
+<p>
+        John Maddock started this library, the beta, gamma, erf, polynomial, and
+        factorial functions are his, as is the "Toolkit" section, and many
+        of the statistical distributions.
+      </p>
+<p>
+        Paul A. Bristow threw down the challenge in <a href="http://www2.open-std.org/JTC1/SC22/WG21/docs/papers/2004/n1668.pdf" target="_top">A
+        Proposal to add Mathematical Functions for Statistics to the C++ Standard
+        Library</a> to add the key math functions, especially those essential
+        for statistics. After JM accepted and solved the difficult problems, not
+        only numerically, but in full C++ template style, PAB implemented a few of
+        the statistical distributions. PAB also tirelessly proof-read everything
+        that JM threw at him (so that all remaining editorial mistakes are his fault).
+      </p>
+<p>
+        Xiaogang Zhang worked on the Bessel functions and elliptic integrals for
+        his Google Summer of Code project 2006.
+      </p>
+<p>
+        Bruno Lalande submitted the "compile time power of a runtime base"
+        code.
+      </p>
+<p>
+        Gautam Sewani coded the logistic distribution as part of a Google Summer
+        of Code project 2008.
+      </p>
+<p>
+        Professor Nico Temme for advice on the inverse incomplete beta function.
+      </p>
+<p>
+        Victor Shoup for NTL, without which
+        it would have much more difficult to produce high accuracy constants, and
+        especially the tables of accurate values for testing.
+      </p>
+<p>
+        We are grateful to Joel Guzman for helping us stress-test his Boost.Quickbook
+        program used to generate the html and pdf versions of this document, adding
+        several new features en route.
+      </p>
+<p>
+        Plots of the functions and distributions were prepared in W3C
+        standard Scalable Vector Graphic (SVG)
+        format using a program created by Jacob Voytko during a <a href="http://code.google.com/soc/2007/" target="_top">Google
+        Summer of Code (2007)</a>. Since browser support for rendering SVG is
+        still not universal (Microsoft Internet Explorer, even IE 8 beta, still lacks
+        native SVG support but can be made to work with <a href="http://www.adobe.com/svg/viewer/install/" target="_top">Adobe's
+        free SVG viewer</a> plugin), so the SVG files were batch converted to
+        JPEG using Inkscape.
+      </p>
+<p>
+        We are also indebted to Matthias Schabel for managing the formal Boost-review
+        of this library, and to all the reviewers - including Guillaume Melquiond,
+        Arnaldur Gylfason, John Phillips, Stephan Tolksdorf and Jeff Garland - for
+        their many helpful comments.
+      </p>
+</div>
+<table xmlns:rev="http://www.cs.rpi.edu/~gregod/boost/tools/doc/revision" width="100%"><tr>
+<td align="left"></td>
+<td align="right"><div class="copyright-footer">Copyright © 2006 , 2007, 2008 John Maddock, Paul A. Bristow, Hubert
+      Holin, Xiaogang Zhang, Bruno Lalande and Gautam Sewani<p>
+        Distributed under the Boost Software License, Version 1.0. (See accompanying
+        file LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_0.txt)
+      </p>
+</div></td>
+</tr></table>
+<hr>
+<div class="spirit-nav">
+<a accesskey="p" href="issues.html"><img src="../../../../doc/html/images/prev.png" alt="Prev"></a><a accesskey="u" href="../status.html"><img src="../../../../doc/html/images/up.png" alt="Up"></a><a accesskey="h" href="../../index.html"><img src="../../../../doc/html/images/home.png" alt="Home"></a><a accesskey="n" href="../../index/s10.html"><img src="../../../../doc/html/images/next.png" alt="Next"></a>
+</div>
+</body>
+</html>

Added: sandbox/tools/auto_index/example/math/doc/sf_and_dist/html/math_toolkit/status/history1.html
==============================================================================
--- (empty file)
+++ sandbox/tools/auto_index/example/math/doc/sf_and_dist/html/math_toolkit/status/history1.html	2008-11-28 05:25:28 EST (Fri, 28 Nov 2008)
@@ -0,0 +1,286 @@
+<html>
+<head>
+<meta http-equiv="Content-Type" content="text/html; charset=ISO-8859-1">
+<title>History and What's New</title>
+<link rel="stylesheet" href="../../boostbook.css" type="text/css">
+<meta name="generator" content="DocBook XSL Stylesheets Vsnapshot_8125">
+<link rel="home" href="../../index.html" title="Math Toolkit">
+<link rel="up" href="../status.html" title="Library Status">
+<link rel="prev" href="../status.html" title="Library Status">
+<link rel="next" href="compilers.html" title="Compilers">
+</head>
+<body bgcolor="white" text="black" link="#0000FF" vlink="#840084" alink="#0000FF">
+<table cellpadding="2" width="100%"><tr>
+<td valign="top"><img alt="Boost C++ Libraries" width="277" height="86" src="../../../../boost.png"></td>
+<td align="center">Home</td>
+<td align="center">Libraries</td>
+<td align="center">People</td>
+<td align="center">FAQ</td>
+<td align="center">More</td>
+</tr></table>
+<hr>
+<div class="spirit-nav">
+<a accesskey="p" href="../status.html"><img src="../../../../doc/html/images/prev.png" alt="Prev"></a><a accesskey="u" href="../status.html"><img src="../../../../doc/html/images/up.png" alt="Up"></a><a accesskey="h" href="../../index.html"><img src="../../../../doc/html/images/home.png" alt="Home"></a><a accesskey="n" href="compilers.html"><img src="../../../../doc/html/images/next.png" alt="Next"></a>
+</div>
+<div class="section" lang="en">
+<div class="titlepage"><div><div><h3 class="title">
+<a name="math_toolkit.status.history1"></a><a class="link" href="history1.html" title="History and What's New"> History and What's New</a>
+</h3></div></div></div>
+<p>
+        <a name="math_toolkit.status.history1.boost_1_38_0"></a>
+        </p>
+<h5>
+<a name="id919138"></a>
+          <a class="link" href="history1.html#math_toolkit.status.history1.boost_1_38_0">Boost-1.38.0</a>
+        </h5>
+<p>
+        </p>
+<div class="itemizedlist"><ul type="disc">
+<li>
+            Added support for MPFR as a bignum type.
+          </li>
+<li>
+            Added some full specializations of the policy classes to reduce compile
+            times.
+          </li>
+<li>
+            Added logistic distribution, from Gautam Sewani's Google Summer of Code
+            project.
+          </li>
+</ul></div>
+<p>
+        <a name="math_toolkit.status.history1.boost_1_37_0"></a>
+        </p>
+<h5>
+<a name="id919183"></a>
+          <a class="link" href="history1.html#math_toolkit.status.history1.boost_1_37_0">Boost-1.37.0</a>
+        </h5>
+<p>
+        </p>
+<div class="itemizedlist"><ul type="disc"><li>
+            Improved accuracy and testing of the inverse hypergeometric functions.
+          </li></ul></div>
+<p>
+        <a name="math_toolkit.status.history1.boost_1_36_0"></a>
+        </p>
+<h5>
+<a name="id919218"></a>
+          <a class="link" href="history1.html#math_toolkit.status.history1.boost_1_36_0">Boost-1.36.0</a>
+        </h5>
+<p>
+        </p>
+<div class="itemizedlist"><ul type="disc">
+<li>
+            Added Noncentral Chi Squared Distribution.
+          </li>
+<li>
+            Added Noncentral Beta Distribution.
+          </li>
+<li>
+            Added Noncentral F Distribution.
+          </li>
+<li>
+            Added Noncentral T Distribution.
+          </li>
+<li>
+            Added Exponential Integral Functions.
+          </li>
+<li>
+            Added Zeta Function.
+          </li>
+<li>
+            Added Rounding and Truncation functions.
+          </li>
+<li>
+            Added Compile time powers of runtime bases.
+          </li>
+</ul></div>
+<p>
+        <a name="math_toolkit.status.history1.boost_1_35_0__post_review_first_official_release"></a>
+        </p>
+<h5>
+<a name="id919293"></a>
+          <a class="link" href="history1.html#math_toolkit.status.history1.boost_1_35_0__post_review_first_official_release">Boost-1.35.0:
+          Post Review First Official Release</a>
+        </h5>
+<p>
+        </p>
+<div class="itemizedlist"><ul type="disc">
+<li>
+            Added Policy based framework that allows fine grained control over function
+            behaviour.
+          </li>
+<li>
+<span class="bold"><strong>Breaking change:</strong></span> Changed default behaviour
+            for domain, pole and overflow errors to throw an exception (based on
+            review feedback), this behaviour can be customised using <a class="link" href="../policy.html" title="Policies">Policy</a>'s.
+          </li>
+<li>
+<span class="bold"><strong>Breaking change:</strong></span> Changed exception thrown
+            when an internal evaluation error occurs to boost::math::evaluation_error.
+          </li>
+<li>
+<span class="bold"><strong>Breaking change:</strong></span> Changed discrete quantiles
+            to return an integer result: this is anything up to 20 times faster than
+            finding the true root, this behaviour can be customised using <a class="link" href="../policy.html" title="Policies">Policy</a>'s.
+          </li>
+<li>
+            Polynomial/rational function evaluation is now customisable and hopefully
+            faster than before.
+          </li>
+<li>
+            Added performance test program.
+          </li>
+</ul></div>
+<p>
+        <a name="math_toolkit.status.history1.milestone_4__second_review_candidate__1st_march_2007_"></a>
+        </p>
+<h5>
+<a name="id919405"></a>
+          <a class="link" href="history1.html#math_toolkit.status.history1.milestone_4__second_review_candidate__1st_march_2007_">Milestone
+          4: Second Review Candidate (1st March 2007)</a>
+        </h5>
+<p>
+        </p>
+<div class="itemizedlist"><ul type="disc">
+<li>
+            Moved Xiaogang Zhang's Bessel Functions code into the library, and brought
+            them into line with the rest of the code.
+          </li>
+<li>
+            Added C# "Distribution Explorer" demo application.
+          </li>
+</ul></div>
+<p>
+        <a name="math_toolkit.status.history1.milestone_3__first_review_candidate__31st_dec_2006_"></a>
+        </p>
+<h5>
+<a name="id919452"></a>
+          <a class="link" href="history1.html#math_toolkit.status.history1.milestone_3__first_review_candidate__31st_dec_2006_">Milestone
+          3: First Review Candidate (31st Dec 2006)</a>
+        </h5>
+<p>
+        </p>
+<div class="itemizedlist"><ul type="disc">
+<li>
+            Implemented the main probability distribution and density functions.
+          </li>
+<li>
+            Implemented digamma.
+          </li>
+<li>
+            Added more factorial functions.
+          </li>
+<li>
+            Implemented the Hermite, Legendre and Laguerre polynomials plus the spherical
+            harmonic functions from TR1.
+          </li>
+<li>
+            Moved Xiaogang Zhang's elliptic integral code into the library, and brought
+            them into line with the rest of the code.
+          </li>
+<li>
+            Moved Hubert Holin's existing Boost.Math special functions into this
+            library and brought them into line with the rest of the code.
+          </li>
+</ul></div>
+<p>
+        <a name="math_toolkit.status.history1.milestone_2__released_september_10th_2006"></a>
+        </p>
+<h5>
+<a name="id919529"></a>
+          <a class="link" href="history1.html#math_toolkit.status.history1.milestone_2__released_september_10th_2006">Milestone
+          2: Released September 10th 2006</a>
+        </h5>
+<p>
+        </p>
+<div class="itemizedlist"><ul type="disc">
+<li>
+            Implement preview release of the statistical distributions.
+          </li>
+<li>
+            Added statistical distributions tutorial.
+          </li>
+<li>
+            Implemented root finding algorithms.
+          </li>
+<li>
+            Implemented the inverses of the incomplete gamma and beta functions.
+          </li>
+<li>
+            Rewrite erf/erfc as rational approximations (valid to 128-bit precision).
+          </li>
+<li>
+            Integrated the statistical results generated from the test data with
+            Boost.Test: uses a database of expected results, indexed by test, floating
+            point type, platform, and compiler.
+          </li>
+<li>
+            Improved lgamma near 1 and 2 (rational approximations).
+          </li>
+<li>
+            Improved erf/erfc inverses (rational approximations).
+          </li>
+<li>
+            Implemented Rational function generation (the Remez method).
+          </li>
+</ul></div>
+<p>
+        <a name="math_toolkit.status.history1.milestone_1__released_march_31st_2006"></a>
+        </p>
+<h5>
+<a name="id919618"></a>
+          <a class="link" href="history1.html#math_toolkit.status.history1.milestone_1__released_march_31st_2006">Milestone
+          1: Released March 31st 2006</a>
+        </h5>
+<p>
+        </p>
+<div class="itemizedlist"><ul type="disc">
+<li>
+            Implement gamma/beta/erf functions along with their incomplete counterparts.
+          </li>
+<li>
+            Generate high quality test data, against which future improvements can
+            be judged.
+          </li>
+<li>
+            Provide tools for the evaluation of infinite series, continued fractions,
+            and rational functions.
+          </li>
+<li>
+            Provide tools for testing against tabulated test data, and collecting
+            statistics on error rates.
+          </li>
+<li>
+            Provide sufficient docs for people to be able to find their way around
+            the library.
+          </li>
+</ul></div>
+<p>
+        </p>
+<p>
+          SVN Revisions:
+        </p>
+<p>
+        </p>
+<p>
+          Sandbox and trunk last synchonised at revision: 48300.
+        </p>
+<p>
+      </p>
+</div>
+<table xmlns:rev="http://www.cs.rpi.edu/~gregod/boost/tools/doc/revision" width="100%"><tr>
+<td align="left"></td>
+<td align="right"><div class="copyright-footer">Copyright © 2006 , 2007, 2008 John Maddock, Paul A. Bristow, Hubert
+      Holin, Xiaogang Zhang, Bruno Lalande and Gautam Sewani<p>
+        Distributed under the Boost Software License, Version 1.0. (See accompanying
+        file LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_0.txt)
+      </p>
+</div></td>
+</tr></table>
+<hr>
+<div class="spirit-nav">
+<a accesskey="p" href="../status.html"><img src="../../../../doc/html/images/prev.png" alt="Prev"></a><a accesskey="u" href="../status.html"><img src="../../../../doc/html/images/up.png" alt="Up"></a><a accesskey="h" href="../../index.html"><img src="../../../../doc/html/images/home.png" alt="Home"></a><a accesskey="n" href="compilers.html"><img src="../../../../doc/html/images/next.png" alt="Next"></a>
+</div>
+</body>
+</html>

Added: sandbox/tools/auto_index/example/math/doc/sf_and_dist/html/math_toolkit/status/issues.html
==============================================================================
--- (empty file)
+++ sandbox/tools/auto_index/example/math/doc/sf_and_dist/html/math_toolkit/status/issues.html	2008-11-28 05:25:28 EST (Fri, 28 Nov 2008)
@@ -0,0 +1,1317 @@
+<html>
+<head>
+<meta http-equiv="Content-Type" content="text/html; charset=ISO-8859-1">
+<title>Known Issues, and Todo List</title>
+<link rel="stylesheet" href="../../boostbook.css" type="text/css">
+<meta name="generator" content="DocBook XSL Stylesheets Vsnapshot_8125">
+<link rel="home" href="../../index.html" title="Math Toolkit">
+<link rel="up" href="../status.html" title="Library Status">
+<link rel="prev" href="compilers.html" title="Compilers">
+<link rel="next" href="credits.html" title="Credits and Acknowledgements">
+</head>
+<body bgcolor="white" text="black" link="#0000FF" vlink="#840084" alink="#0000FF">
+<table cellpadding="2" width="100%"><tr>
+<td valign="top"><img alt="Boost C++ Libraries" width="277" height="86" src="../../../../boost.png"></td>
+<td align="center">Home</td>
+<td align="center">Libraries</td>
+<td align="center">People</td>
+<td align="center">FAQ</td>
+<td align="center">More</td>
+</tr></table>
+<hr>
+<div class="spirit-nav">
+<a accesskey="p" href="compilers.html"><img src="../../../../doc/html/images/prev.png" alt="Prev"></a><a accesskey="u" href="../status.html"><img src="../../../../doc/html/images/up.png" alt="Up"></a><a accesskey="h" href="../../index.html"><img src="../../../../doc/html/images/home.png" alt="Home"></a><a accesskey="n" href="credits.html"><img src="../../../../doc/html/images/next.png" alt="Next"></a>
+</div>
+<div class="section" lang="en">
+<div class="titlepage"><div><div><h3 class="title">
+<a name="math_toolkit.status.issues"></a><a class="link" href="issues.html" title="Known Issues, and Todo List"> Known Issues, and Todo List</a>
+</h3></div></div></div>
+<p>
+        This section lists those issues that are known about.
+      </p>
+<p>
+        Predominantly this is a TODO list, or a list of possible future enhancements.
+        Items labled "High Priority" effect the proper functioning of the
+        component, and should be fixed as soon as possible. Items labled "Medium
+        Priority" are desirable enhancements, often pertaining to the performance
+        of the component, but do not effect it's accuracy or functionality. Items
+        labled "Low Priority" should probably be investigated at some point.
+        Such classifications are obviously highly subjective.
+      </p>
+<p>
+        If you don't see a component listed here, then we don't have any known issues
+        with it.
+      </p>
+<a name="math_toolkit.status.issues.tgamma"></a><h5>
+<a name="id920808"></a>
+        <a class="link" href="issues.html#math_toolkit.status.issues.tgamma">tgamma</a>
+      </h5>
+<div class="itemizedlist"><ul type="disc"><li>
+          Can the <a class="link" href="../backgrounders/lanczos.html" title="The Lanczos Approximation">Lanczos approximation</a>
+          be optimized any further? (low priority)
+        </li></ul></div>
+<a name="math_toolkit.status.issues.incomplete_beta"></a><h5>
+<a name="id920851"></a>
+        <a class="link" href="issues.html#math_toolkit.status.issues.incomplete_beta">Incomplete Beta</a>
+      </h5>
+<div class="itemizedlist"><ul type="disc"><li>
+          Investigate Didonato and Morris' asymptotic expansion for large a and b
+          (medium priority).
+        </li></ul></div>
+<a name="math_toolkit.status.issues.inverse_gamma"></a><h5>
+<a name="id920886"></a>
+        <a class="link" href="issues.html#math_toolkit.status.issues.inverse_gamma">Inverse Gamma</a>
+      </h5>
+<div class="itemizedlist"><ul type="disc"><li>
+          Investigate whether we can skip iteration altogether if the first approximation
+          is good enough (Medium Priority).
+        </li></ul></div>
+<a name="math_toolkit.status.issues.polynomials"></a><h5>
+<a name="id920920"></a>
+        <a class="link" href="issues.html#math_toolkit.status.issues.polynomials">Polynomials</a>
+      </h5>
+<div class="itemizedlist"><ul type="disc"><li>
+          The Legendre and Laguerre Polynomials have surprisingly different error
+          rates on different platforms, considering they are evaluated with only
+          basic arithmetic operations. Maybe this is telling us something, or maybe
+          not (Low Priority).
+        </li></ul></div>
+<a name="math_toolkit.status.issues.elliptic_integrals"></a><h5>
+<a name="id920952"></a>
+        <a class="link" href="issues.html#math_toolkit.status.issues.elliptic_integrals">Elliptic Integrals</a>
+      </h5>
+<div class="itemizedlist"><ul type="disc">
+<li>
+          Carlson's algorithms are essentially unchanged from Xiaogang Zhang's Google
+          Summer of Code student project, and are based on Carlson's original papers.
+          However, Carlson has revised his algorithms since then (refer to the references
+          in the elliptic integral docs for a list), to improve performance and accuracy,
+          we may be able to take advantage of these improvements too (Low Priority).
+        </li>
+<li>
+<p>Carlson's algorithms (mainly R<sub>J</sub>) are somewhat prone to internal overflow/underflow
+          when the arguments are very large or small. The homogeneity relations:</p>
+<p>R<sub>F</sub>(ka,
+          kb, kc) = k<sup>-1/2</sup> R<sub>F</sub>(a, b, c)</p>
+<p>and</p>
+<p>R<sub>J</sub>(ka, kb, kc, kr) = k<sup>-3/2</sup> R<sub>J</sub>(a, b, c, r)</p>
+<p>could
+          be used to sidestep trouble here: provided the problem domains can be accurately
+          identified. (Medium Priority).</p>
+</li>
+<li>
+          Carlson's R<sub>C</sub> can be reduced to elementary funtions (asin and log), would
+          it be more efficient evaluated this way, rather than by Carlson's algorithms?
+          (Low Priority).
+        </li>
+<li>
+          Should we add an implementation of Carlson's R<sub>G</sub>? It's not required for
+          the Legendre form integrals, but some people may find it useful (Low Priority).
+        </li>
+<li>
+          There are a several other integrals: D(&#966;, k), Z(&#946;, k), &#923;<sub>0</sub>(&#946;, k) and Bulirsch's
+          <span class="emphasis"><em>el</em></span> functions that could be implemented using Carlson's
+          integrals (Low Priority).
+        </li>
+<li>
+          The integrals K(k) and E(k) could be implemented using rational approximations
+          (both for efficiency and accuracy), assuming we can find them. (Medium
+          Priority).
+        </li>
+<li>
+          There is a sub-domain of <a class="link" href="../special/ellint/ellint_3.html" title="Elliptic Integrals of the Third Kind - Legendre Form">ellint_3</a>
+          that is unimplemented (see the docs for details), currently it's not clear
+          how to solve this issue, or if it's ever likely to be an real problem in
+          practice - especially as most other implementations don't support this
+          domain either (Medium Priority).
+        </li>
+</ul></div>
+<a name="math_toolkit.status.issues.inverse_hyperbolic_functions"></a><h5>
+<a name="id921134"></a>
+        <a class="link" href="issues.html#math_toolkit.status.issues.inverse_hyperbolic_functions">Inverse
+        Hyperbolic Functions</a>
+      </h5>
+<div class="itemizedlist"><ul type="disc"><li>
+          These functions are inherited from previous Boost versions, before <a class="link" href="../special/powers/log1p.html" title="log1p">log1p</a> became widely
+          available. Would they be better expressed in terms of this function? This
+          is probably only an issue for very high precision types (Low Priority).
+        </li></ul></div>
+<a name="math_toolkit.status.issues.statistical_distributions"></a><h5>
+<a name="id921181"></a>
+        <a class="link" href="issues.html#math_toolkit.status.issues.statistical_distributions">Statistical
+        distributions</a>
+      </h5>
+<div class="itemizedlist"><ul type="disc"><li>
+          Student's t Perhaps switch to normal distribution as a better approximation
+          for very large degrees of freedom?
+        </li></ul></div>
+<a name="math_toolkit.status.issues.feature_requests"></a><h5>
+<a name="id921218"></a>
+        <a class="link" href="issues.html#math_toolkit.status.issues.feature_requests">Feature Requests</a>
+      </h5>
+<p>
+        The following table lists distributions that are found in other packages
+        but which are not yet present here, the more frequently the distribution
+        is found, the higher the priority for implementing it:
+      </p>
+<div class="informaltable"><table class="table">
+<colgroup>
+<col>
+<col>
+<col>
+<col>
+<col>
+<col>
+</colgroup>
+<thead><tr>
+<th>
+              <p>
+                Distribution
+              </p>
+              </th>
+<th>
+              <p>
+                R
+              </p>
+              </th>
+<th>
+              <p>
+                Mathematica 6
+              </p>
+              </th>
+<th>
+              <p>
+                NIST
+              </p>
+              </th>
+<th>
+              <p>
+                Regress+
+              </p>
+              </th>
+<th>
+              <p>
+                Matlab
+              </p>
+              </th>
+</tr></thead>
+<tbody>
+<tr>
+<td>
+              <p>
+                Hypergeometric
+              </p>
+              </td>
+<td>
+              <p>
+                X
+              </p>
+              </td>
+<td>
+              <p>
+                X
+              </p>
+              </td>
+<td>
+              <p>
+                -
+              </p>
+              </td>
+<td>
+              <p>
+                X
+              </p>
+              </td>
+<td>
+              <p>
+                X
+              </p>
+              </td>
+</tr>
+<tr>
+<td>
+              <p>
+                Inverse Gausian / Inverse Normal
+              </p>
+              </td>
+<td>
+              <p>
+                -
+              </p>
+              </td>
+<td>
+              <p>
+                X
+              </p>
+              </td>
+<td>
+              <p>
+                -
+              </p>
+              </td>
+<td>
+              <p>
+                X
+              </p>
+              </td>
+<td>
+              <p>
+                X
+              </p>
+              </td>
+</tr>
+<tr>
+<td>
+              <p>
+                Geometric
+              </p>
+              </td>
+<td>
+              <p>
+                X
+              </p>
+              </td>
+<td>
+              <p>
+                X
+              </p>
+              </td>
+<td>
+              <p>
+                -
+              </p>
+              </td>
+<td>
+              <p>
+                -
+              </p>
+              </td>
+<td>
+              <p>
+                X
+              </p>
+              </td>
+</tr>
+<tr>
+<td>
+              <p>
+                Multinomial
+              </p>
+              </td>
+<td>
+              <p>
+                X
+              </p>
+              </td>
+<td>
+              <p>
+                -
+              </p>
+              </td>
+<td>
+              <p>
+                -
+              </p>
+              </td>
+<td>
+              <p>
+                -
+              </p>
+              </td>
+<td>
+              <p>
+                X
+              </p>
+              </td>
+</tr>
+<tr>
+<td>
+              <p>
+                Tukey Lambda
+              </p>
+              </td>
+<td>
+              <p>
+                X
+              </p>
+              </td>
+<td>
+              <p>
+                -
+              </p>
+              </td>
+<td>
+              <p>
+                X
+              </p>
+              </td>
+<td>
+              <p>
+                -
+              </p>
+              </td>
+<td>
+              <p>
+                -
+              </p>
+              </td>
+</tr>
+<tr>
+<td>
+              <p>
+                Half Normal / Folded Normal
+              </p>
+              </td>
+<td>
+              <p>
+                -
+              </p>
+              </td>
+<td>
+              <p>
+                X
+              </p>
+              </td>
+<td>
+              <p>
+                -
+              </p>
+              </td>
+<td>
+              <p>
+                X
+              </p>
+              </td>
+<td>
+              <p>
+                -
+              </p>
+              </td>
+</tr>
+<tr>
+<td>
+              <p>
+                Chi
+              </p>
+              </td>
+<td>
+              <p>
+                -
+              </p>
+              </td>
+<td>
+              <p>
+                X
+              </p>
+              </td>
+<td>
+              <p>
+                -
+              </p>
+              </td>
+<td>
+              <p>
+                X
+              </p>
+              </td>
+<td>
+              <p>
+                -
+              </p>
+              </td>
+</tr>
+<tr>
+<td>
+              <p>
+                Gumbel
+              </p>
+              </td>
+<td>
+              <p>
+                -
+              </p>
+              </td>
+<td>
+              <p>
+                X
+              </p>
+              </td>
+<td>
+              <p>
+                -
+              </p>
+              </td>
+<td>
+              <p>
+                X
+              </p>
+              </td>
+<td>
+              <p>
+                -
+              </p>
+              </td>
+</tr>
+<tr>
+<td>
+              <p>
+                Discrete Uniform
+              </p>
+              </td>
+<td>
+              <p>
+                -
+              </p>
+              </td>
+<td>
+              <p>
+                X
+              </p>
+              </td>
+<td>
+              <p>
+                -
+              </p>
+              </td>
+<td>
+              <p>
+                -
+              </p>
+              </td>
+<td>
+              <p>
+                X
+              </p>
+              </td>
+</tr>
+<tr>
+<td>
+              <p>
+                Log Series
+              </p>
+              </td>
+<td>
+              <p>
+                -
+              </p>
+              </td>
+<td>
+              <p>
+                X
+              </p>
+              </td>
+<td>
+              <p>
+                -
+              </p>
+              </td>
+<td>
+              <p>
+                X
+              </p>
+              </td>
+<td>
+              <p>
+                -
+              </p>
+              </td>
+</tr>
+<tr>
+<td>
+              <p>
+                Nakagami (generalised Chi)
+              </p>
+              </td>
+<td>
+              <p>
+                -
+              </p>
+              </td>
+<td>
+              <p>
+                -
+              </p>
+              </td>
+<td>
+              <p>
+                -
+              </p>
+              </td>
+<td>
+              <p>
+                X
+              </p>
+              </td>
+<td>
+              <p>
+                X
+              </p>
+              </td>
+</tr>
+<tr>
+<td>
+              <p>
+                Log Logistic
+              </p>
+              </td>
+<td>
+              <p>
+                -
+              </p>
+              </td>
+<td>
+              <p>
+                -
+              </p>
+              </td>
+<td>
+              <p>
+                -
+              </p>
+              </td>
+<td>
+              <p>
+                -
+              </p>
+              </td>
+<td>
+              <p>
+                X
+              </p>
+              </td>
+</tr>
+<tr>
+<td>
+              <p>
+                Tukey (Studentized range)
+              </p>
+              </td>
+<td>
+              <p>
+                X
+              </p>
+              </td>
+<td>
+              <p>
+                -
+              </p>
+              </td>
+<td>
+              <p>
+                -
+              </p>
+              </td>
+<td>
+              <p>
+                -
+              </p>
+              </td>
+<td>
+              <p>
+                -
+              </p>
+              </td>
+</tr>
+<tr>
+<td>
+              <p>
+                Wilcoxon rank sum
+              </p>
+              </td>
+<td>
+              <p>
+                X
+              </p>
+              </td>
+<td>
+              <p>
+                -
+              </p>
+              </td>
+<td>
+              <p>
+                -
+              </p>
+              </td>
+<td>
+              <p>
+                -
+              </p>
+              </td>
+<td>
+              <p>
+                -
+              </p>
+              </td>
+</tr>
+<tr>
+<td>
+              <p>
+                Wincoxon signed rank
+              </p>
+              </td>
+<td>
+              <p>
+                X
+              </p>
+              </td>
+<td>
+              <p>
+                -
+              </p>
+              </td>
+<td>
+              <p>
+                -
+              </p>
+              </td>
+<td>
+              <p>
+                -
+              </p>
+              </td>
+<td>
+              <p>
+                -
+              </p>
+              </td>
+</tr>
+<tr>
+<td>
+              <p>
+                Non-central Beta
+              </p>
+              </td>
+<td>
+              <p>
+                X
+              </p>
+              </td>
+<td>
+              <p>
+                -
+              </p>
+              </td>
+<td>
+              <p>
+                -
+              </p>
+              </td>
+<td>
+              <p>
+                -
+              </p>
+              </td>
+<td>
+              <p>
+                -
+              </p>
+              </td>
+</tr>
+<tr>
+<td>
+              <p>
+                Laplace
+              </p>
+              </td>
+<td>
+              <p>
+                -
+              </p>
+              </td>
+<td>
+              <p>
+                X
+              </p>
+              </td>
+<td>
+              <p>
+                -
+              </p>
+              </td>
+<td>
+              <p>
+                -
+              </p>
+              </td>
+<td>
+              <p>
+                -
+              </p>
+              </td>
+</tr>
+<tr>
+<td>
+              <p>
+                Maxwell
+              </p>
+              </td>
+<td>
+              <p>
+                -
+              </p>
+              </td>
+<td>
+              <p>
+                X
+              </p>
+              </td>
+<td>
+              <p>
+                -
+              </p>
+              </td>
+<td>
+              <p>
+                -
+              </p>
+              </td>
+<td>
+              <p>
+                -
+              </p>
+              </td>
+</tr>
+<tr>
+<td>
+              <p>
+                Beta-Binomial
+              </p>
+              </td>
+<td>
+              <p>
+                -
+              </p>
+              </td>
+<td>
+              <p>
+                X
+              </p>
+              </td>
+<td>
+              <p>
+                -
+              </p>
+              </td>
+<td>
+              <p>
+                -
+              </p>
+              </td>
+<td>
+              <p>
+                -
+              </p>
+              </td>
+</tr>
+<tr>
+<td>
+              <p>
+                Beta-negative Binomial
+              </p>
+              </td>
+<td>
+              <p>
+                -
+              </p>
+              </td>
+<td>
+              <p>
+                X
+              </p>
+              </td>
+<td>
+              <p>
+                -
+              </p>
+              </td>
+<td>
+              <p>
+                -
+              </p>
+              </td>
+<td>
+              <p>
+                -
+              </p>
+              </td>
+</tr>
+<tr>
+<td>
+              <p>
+                Zipf
+              </p>
+              </td>
+<td>
+              <p>
+                -
+              </p>
+              </td>
+<td>
+              <p>
+                X
+              </p>
+              </td>
+<td>
+              <p>
+                -
+              </p>
+              </td>
+<td>
+              <p>
+                -
+              </p>
+              </td>
+<td>
+              <p>
+                -
+              </p>
+              </td>
+</tr>
+<tr>
+<td>
+              <p>
+                Birnbaum-Saunders / Fatigue Life
+              </p>
+              </td>
+<td>
+              <p>
+                -
+              </p>
+              </td>
+<td>
+              <p>
+                -
+              </p>
+              </td>
+<td>
+              <p>
+                X
+              </p>
+              </td>
+<td>
+              <p>
+                -
+              </p>
+              </td>
+<td>
+              <p>
+                -
+              </p>
+              </td>
+</tr>
+<tr>
+<td>
+              <p>
+                Double Exponential
+              </p>
+              </td>
+<td>
+              <p>
+                -
+              </p>
+              </td>
+<td>
+              <p>
+                -
+              </p>
+              </td>
+<td>
+              <p>
+                X
+              </p>
+              </td>
+<td>
+              <p>
+                -
+              </p>
+              </td>
+<td>
+              <p>
+                -
+              </p>
+              </td>
+</tr>
+<tr>
+<td>
+              <p>
+                Power Normal
+              </p>
+              </td>
+<td>
+              <p>
+                -
+              </p>
+              </td>
+<td>
+              <p>
+                -
+              </p>
+              </td>
+<td>
+              <p>
+                X
+              </p>
+              </td>
+<td>
+              <p>
+                -
+              </p>
+              </td>
+<td>
+              <p>
+                -
+              </p>
+              </td>
+</tr>
+<tr>
+<td>
+              <p>
+                Power Lognormal
+              </p>
+              </td>
+<td>
+              <p>
+                -
+              </p>
+              </td>
+<td>
+              <p>
+                -
+              </p>
+              </td>
+<td>
+              <p>
+                X
+              </p>
+              </td>
+<td>
+              <p>
+                -
+              </p>
+              </td>
+<td>
+              <p>
+                -
+              </p>
+              </td>
+</tr>
+<tr>
+<td>
+              <p>
+                Cosine
+              </p>
+              </td>
+<td>
+              <p>
+                -
+              </p>
+              </td>
+<td>
+              <p>
+                -
+              </p>
+              </td>
+<td>
+              <p>
+                -
+              </p>
+              </td>
+<td>
+              <p>
+                X
+              </p>
+              </td>
+<td>
+              <p>
+                -
+              </p>
+              </td>
+</tr>
+<tr>
+<td>
+              <p>
+                Double Gamma
+              </p>
+              </td>
+<td>
+              <p>
+                -
+              </p>
+              </td>
+<td>
+              <p>
+                -
+              </p>
+              </td>
+<td>
+              <p>
+                -
+              </p>
+              </td>
+<td>
+              <p>
+                X
+              </p>
+              </td>
+<td>
+              <p>
+                -
+              </p>
+              </td>
+</tr>
+<tr>
+<td>
+              <p>
+                Double Weibul
+              </p>
+              </td>
+<td>
+              <p>
+                -
+              </p>
+              </td>
+<td>
+              <p>
+                -
+              </p>
+              </td>
+<td>
+              <p>
+                -
+              </p>
+              </td>
+<td>
+              <p>
+                X
+              </p>
+              </td>
+<td>
+              <p>
+                -
+              </p>
+              </td>
+</tr>
+<tr>
+<td>
+              <p>
+                Hyperbolic Secant
+              </p>
+              </td>
+<td>
+              <p>
+                -
+              </p>
+              </td>
+<td>
+              <p>
+                -
+              </p>
+              </td>
+<td>
+              <p>
+                -
+              </p>
+              </td>
+<td>
+              <p>
+                X
+              </p>
+              </td>
+<td>
+              <p>
+                -
+              </p>
+              </td>
+</tr>
+<tr>
+<td>
+              <p>
+                Laplace
+              </p>
+              </td>
+<td>
+              <p>
+                -
+              </p>
+              </td>
+<td>
+              <p>
+                -
+              </p>
+              </td>
+<td>
+              <p>
+                -
+              </p>
+              </td>
+<td>
+              <p>
+                X
+              </p>
+              </td>
+<td>
+              <p>
+                -
+              </p>
+              </td>
+</tr>
+<tr>
+<td>
+              <p>
+                Semicircular
+              </p>
+              </td>
+<td>
+              <p>
+                -
+              </p>
+              </td>
+<td>
+              <p>
+                -
+              </p>
+              </td>
+<td>
+              <p>
+                -
+              </p>
+              </td>
+<td>
+              <p>
+                X
+              </p>
+              </td>
+<td>
+              <p>
+                -
+              </p>
+              </td>
+</tr>
+<tr>
+<td>
+              <p>
+                Bradford
+              </p>
+              </td>
+<td>
+              <p>
+                -
+              </p>
+              </td>
+<td>
+              <p>
+                -
+              </p>
+              </td>
+<td>
+              <p>
+                -
+              </p>
+              </td>
+<td>
+              <p>
+                X
+              </p>
+              </td>
+<td>
+              <p>
+                -
+              </p>
+              </td>
+</tr>
+<tr>
+<td>
+              <p>
+                Birr / Fisk
+              </p>
+              </td>
+<td>
+              <p>
+                -
+              </p>
+              </td>
+<td>
+              <p>
+                -
+              </p>
+              </td>
+<td>
+              <p>
+                -
+              </p>
+              </td>
+<td>
+              <p>
+                X
+              </p>
+              </td>
+<td>
+              <p>
+                -
+              </p>
+              </td>
+</tr>
+<tr>
+<td>
+              <p>
+                Reciprocal
+              </p>
+              </td>
+<td>
+              <p>
+                -
+              </p>
+              </td>
+<td>
+              <p>
+                -
+              </p>
+              </td>
+<td>
+              <p>
+                -
+              </p>
+              </td>
+<td>
+              <p>
+                X
+              </p>
+              </td>
+<td>
+              <p>
+                -
+              </p>
+              </td>
+</tr>
+</tbody>
+</table></div>
+<p>
+        Also asked for more than once:
+      </p>
+<div class="itemizedlist"><ul type="disc">
+<li>
+          Add support for interpolated distributions, possibly combine with numeric
+          integration and differentiation.
+        </li>
+<li>
+          Add support for bivariate and multivariate distributions: most especially
+          the normal.
+        </li>
+</ul></div>
+</div>
+<table xmlns:rev="http://www.cs.rpi.edu/~gregod/boost/tools/doc/revision" width="100%"><tr>
+<td align="left"></td>
+<td align="right"><div class="copyright-footer">Copyright © 2006 , 2007, 2008 John Maddock, Paul A. Bristow, Hubert
+      Holin, Xiaogang Zhang, Bruno Lalande and Gautam Sewani<p>
+        Distributed under the Boost Software License, Version 1.0. (See accompanying
+        file LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_0.txt)
+      </p>
+</div></td>
+</tr></table>
+<hr>
+<div class="spirit-nav">
+<a accesskey="p" href="compilers.html"><img src="../../../../doc/html/images/prev.png" alt="Prev"></a><a accesskey="u" href="../status.html"><img src="../../../../doc/html/images/up.png" alt="Up"></a><a accesskey="h" href="../../index.html"><img src="../../../../doc/html/images/home.png" alt="Home"></a><a accesskey="n" href="credits.html"><img src="../../../../doc/html/images/next.png" alt="Next"></a>
+</div>
+</body>
+</html>

Added: sandbox/tools/auto_index/example/math/doc/sf_and_dist/html/math_toolkit/toolkit.html
==============================================================================
--- (empty file)
+++ sandbox/tools/auto_index/example/math/doc/sf_and_dist/html/math_toolkit/toolkit.html	2008-11-28 05:25:28 EST (Fri, 28 Nov 2008)
@@ -0,0 +1,74 @@
+<html>
+<head>
+<meta http-equiv="Content-Type" content="text/html; charset=ISO-8859-1">
+<title>Internal Details and Tools (Experimental)</title>
+<link rel="stylesheet" href="../boostbook.css" type="text/css">
+<meta name="generator" content="DocBook XSL Stylesheets Vsnapshot_8125">
+<link rel="home" href="../index.html" title="Math Toolkit">
+<link rel="up" href="../index.html" title="Math Toolkit">
+<link rel="prev" href="special/extern_c/tr1_ref.html" title="TR1 C Functions Quick Reference">
+<link rel="next" href="toolkit/internals_overview.html" title="Overview">
+</head>
+<body bgcolor="white" text="black" link="#0000FF" vlink="#840084" alink="#0000FF">
+<table cellpadding="2" width="100%"><tr>
+<td valign="top"><img alt="Boost C++ Libraries" width="277" height="86" src="../../../boost.png"></td>
+<td align="center">Home</td>
+<td align="center">Libraries</td>
+<td align="center">People</td>
+<td align="center">FAQ</td>
+<td align="center">More</td>
+</tr></table>
+<hr>
+<div class="spirit-nav">
+<a accesskey="p" href="special/extern_c/tr1_ref.html"><img src="../../../doc/html/images/prev.png" alt="Prev"></a><a accesskey="u" href="../index.html"><img src="../../../doc/html/images/up.png" alt="Up"></a><a accesskey="h" href="../index.html"><img src="../../../doc/html/images/home.png" alt="Home"></a><a accesskey="n" href="toolkit/internals_overview.html"><img src="../../../doc/html/images/next.png" alt="Next"></a>
+</div>
+<div class="section" lang="en">
+<div class="titlepage"><div><div><h2 class="title" style="clear: both">
+<a name="math_toolkit.toolkit"></a><a class="link" href="toolkit.html" title="Internal Details and Tools (Experimental)"> Internal Details and Tools (Experimental)</a>
+</h2></div></div></div>
+<div class="toc"><dl>
+<dt><span class="section"> Overview</span></dt>
+<dt><span class="section"> Reused Utilities</span></dt>
+<dd><dl>
+<dt><span class="section"><a href="toolkit/internals1/constants.html"> Numeric
+        Constants</a></span></dt>
+<dt><span class="section"><a href="toolkit/internals1/series_evaluation.html">
+        Series Evaluation</a></span></dt>
+<dt><span class="section"><a href="toolkit/internals1/cf.html"> Continued Fraction
+        Evaluation</a></span></dt>
+<dt><span class="section"><a href="toolkit/internals1/rational.html"> Polynomial
+        and Rational Function Evaluation</a></span></dt>
+<dt><span class="section"><a href="toolkit/internals1/roots.html"> Root Finding
+        With Derivatives</a></span></dt>
+<dt><span class="section"><a href="toolkit/internals1/roots2.html"> Root Finding
+        Without Derivatives</a></span></dt>
+<dt><span class="section"><a href="toolkit/internals1/minima.html"> Locating Function
+        Minima</a></span></dt>
+</dl></dd>
+<dt><span class="section"> Testing and Development</span></dt>
+<dd><dl>
+<dt><span class="section"> Polynomials</span></dt>
+<dt><span class="section"><a href="toolkit/internals2/minimax.html"> Minimax Approximations
+        and the Remez Algorithm</a></span></dt>
+<dt><span class="section"><a href="toolkit/internals2/error_test.html"> Relative
+        Error and Testing</a></span></dt>
+<dt><span class="section"><a href="toolkit/internals2/test_data.html"> Graphing,
+        Profiling, and Generating Test Data for Special Functions</a></span></dt>
+</dl></dd>
+</dl></div>
+</div>
+<table xmlns:rev="http://www.cs.rpi.edu/~gregod/boost/tools/doc/revision" width="100%"><tr>
+<td align="left"></td>
+<td align="right"><div class="copyright-footer">Copyright © 2006 , 2007, 2008 John Maddock, Paul A. Bristow, Hubert
+      Holin, Xiaogang Zhang, Bruno Lalande and Gautam Sewani<p>
+        Distributed under the Boost Software License, Version 1.0. (See accompanying
+        file LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_0.txt)
+      </p>
+</div></td>
+</tr></table>
+<hr>
+<div class="spirit-nav">
+<a accesskey="p" href="special/extern_c/tr1_ref.html"><img src="../../../doc/html/images/prev.png" alt="Prev"></a><a accesskey="u" href="../index.html"><img src="../../../doc/html/images/up.png" alt="Up"></a><a accesskey="h" href="../index.html"><img src="../../../doc/html/images/home.png" alt="Home"></a><a accesskey="n" href="toolkit/internals_overview.html"><img src="../../../doc/html/images/next.png" alt="Next"></a>
+</div>
+</body>
+</html>

Added: sandbox/tools/auto_index/example/math/doc/sf_and_dist/html/math_toolkit/toolkit/internals1.html
==============================================================================
--- (empty file)
+++ sandbox/tools/auto_index/example/math/doc/sf_and_dist/html/math_toolkit/toolkit/internals1.html	2008-11-28 05:25:28 EST (Fri, 28 Nov 2008)
@@ -0,0 +1,60 @@
+<html>
+<head>
+<meta http-equiv="Content-Type" content="text/html; charset=ISO-8859-1">
+<title>Reused Utilities</title>
+<link rel="stylesheet" href="../../boostbook.css" type="text/css">
+<meta name="generator" content="DocBook XSL Stylesheets Vsnapshot_8125">
+<link rel="home" href="../../index.html" title="Math Toolkit">
+<link rel="up" href="../toolkit.html" title="Internal Details and Tools (Experimental)">
+<link rel="prev" href="internals_overview.html" title="Overview">
+<link rel="next" href="internals1/constants.html" title="Numeric Constants">
+</head>
+<body bgcolor="white" text="black" link="#0000FF" vlink="#840084" alink="#0000FF">
+<table cellpadding="2" width="100%"><tr>
+<td valign="top"><img alt="Boost C++ Libraries" width="277" height="86" src="../../../../boost.png"></td>
+<td align="center">Home</td>
+<td align="center">Libraries</td>
+<td align="center">People</td>
+<td align="center">FAQ</td>
+<td align="center">More</td>
+</tr></table>
+<hr>
+<div class="spirit-nav">
+<a accesskey="p" href="internals_overview.html"><img src="../../../../doc/html/images/prev.png" alt="Prev"></a><a accesskey="u" href="../toolkit.html"><img src="../../../../doc/html/images/up.png" alt="Up"></a><a accesskey="h" href="../../index.html"><img src="../../../../doc/html/images/home.png" alt="Home"></a><a accesskey="n" href="internals1/constants.html"><img src="../../../../doc/html/images/next.png" alt="Next"></a>
+</div>
+<div class="section" lang="en">
+<div class="titlepage"><div><div><h3 class="title">
+<a name="math_toolkit.toolkit.internals1"></a><a class="link" href="internals1.html" title="Reused Utilities"> Reused Utilities</a>
+</h3></div></div></div>
+<div class="toc"><dl>
+<dt><span class="section"><a href="internals1/constants.html"> Numeric
+        Constants</a></span></dt>
+<dt><span class="section"><a href="internals1/series_evaluation.html">
+        Series Evaluation</a></span></dt>
+<dt><span class="section"><a href="internals1/cf.html"> Continued Fraction
+        Evaluation</a></span></dt>
+<dt><span class="section"><a href="internals1/rational.html"> Polynomial
+        and Rational Function Evaluation</a></span></dt>
+<dt><span class="section"><a href="internals1/roots.html"> Root Finding
+        With Derivatives</a></span></dt>
+<dt><span class="section"><a href="internals1/roots2.html"> Root Finding
+        Without Derivatives</a></span></dt>
+<dt><span class="section"><a href="internals1/minima.html"> Locating Function
+        Minima</a></span></dt>
+</dl></div>
+</div>
+<table xmlns:rev="http://www.cs.rpi.edu/~gregod/boost/tools/doc/revision" width="100%"><tr>
+<td align="left"></td>
+<td align="right"><div class="copyright-footer">Copyright © 2006 , 2007, 2008 John Maddock, Paul A. Bristow, Hubert
+      Holin, Xiaogang Zhang, Bruno Lalande and Gautam Sewani<p>
+        Distributed under the Boost Software License, Version 1.0. (See accompanying
+        file LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_0.txt)
+      </p>
+</div></td>
+</tr></table>
+<hr>
+<div class="spirit-nav">
+<a accesskey="p" href="internals_overview.html"><img src="../../../../doc/html/images/prev.png" alt="Prev"></a><a accesskey="u" href="../toolkit.html"><img src="../../../../doc/html/images/up.png" alt="Up"></a><a accesskey="h" href="../../index.html"><img src="../../../../doc/html/images/home.png" alt="Home"></a><a accesskey="n" href="internals1/constants.html"><img src="../../../../doc/html/images/next.png" alt="Next"></a>
+</div>
+</body>
+</html>

Added: sandbox/tools/auto_index/example/math/doc/sf_and_dist/html/math_toolkit/toolkit/internals1/cf.html
==============================================================================
--- (empty file)
+++ sandbox/tools/auto_index/example/math/doc/sf_and_dist/html/math_toolkit/toolkit/internals1/cf.html	2008-11-28 05:25:28 EST (Fri, 28 Nov 2008)
@@ -0,0 +1,265 @@
+<html>
+<head>
+<meta http-equiv="Content-Type" content="text/html; charset=ISO-8859-1">
+<title>Continued Fraction Evaluation</title>
+<link rel="stylesheet" href="../../../boostbook.css" type="text/css">
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+</div>
+<div class="section" lang="en">
+<div class="titlepage"><div><div><h4 class="title">
+<a name="math_toolkit.toolkit.internals1.cf"></a><a class="link" href="cf.html" title="Continued Fraction Evaluation"> Continued Fraction
+        Evaluation</a>
+</h4></div></div></div>
+<a name="math_toolkit.toolkit.internals1.cf.synopsis"></a><h5>
+<a name="id824898"></a>
+          <a class="link" href="cf.html#math_toolkit.toolkit.internals1.cf.synopsis">Synopsis</a>
+        </h5>
+<p>
+          
+</p>
+<pre class="programlisting"><span class="preprocessor">#include</span> <span class="special">&lt;</span><span class="identifier">boost</span><span class="special">/</span><span class="identifier">math</span><span class="special">/</span><span class="identifier">tools</span><span class="special">/</span><span class="identifier">fraction</span><span class="special">.</span><span class="identifier">hpp</span><span class="special">&gt;</span>
+</pre>
+<p>
+        </p>
+<pre class="programlisting"><span class="keyword">namespace</span> <span class="identifier">boost</span><span class="special">{</span> <span class="keyword">namespace</span> <span class="identifier">math</span><span class="special">{</span> <span class="keyword">namespace</span> <span class="identifier">tools</span><span class="special">{</span>
+
+<span class="keyword">template</span> <span class="special">&lt;</span><span class="keyword">class</span> <span class="identifier">Gen</span><span class="special">&gt;</span>
+<span class="keyword">typename</span> <span class="identifier">detail</span><span class="special">::</span><span class="identifier">fraction_traits</span><span class="special">&lt;</span><span class="identifier">Gen</span><span class="special">&gt;::</span><span class="identifier">result_type</span> 
+   <span class="identifier">continued_fraction_b</span><span class="special">(</span><span class="identifier">Gen</span><span class="special">&amp;</span> <span class="identifier">g</span><span class="special">,</span> <span class="keyword">int</span> <span class="identifier">bits</span><span class="special">);</span>
+
+<span class="keyword">template</span> <span class="special">&lt;</span><span class="keyword">class</span> <span class="identifier">Gen</span><span class="special">&gt;</span>
+<span class="keyword">typename</span> <span class="identifier">detail</span><span class="special">::</span><span class="identifier">fraction_traits</span><span class="special">&lt;</span><span class="identifier">Gen</span><span class="special">&gt;::</span><span class="identifier">result_type</span> 
+   <span class="identifier">continued_fraction_b</span><span class="special">(</span><span class="identifier">Gen</span><span class="special">&amp;</span> <span class="identifier">g</span><span class="special">,</span> <span class="keyword">int</span> <span class="identifier">bits</span><span class="special">,</span> <span class="identifier">boost</span><span class="special">::</span><span class="identifier">uintmax_t</span><span class="special">&amp;</span> <span class="identifier">max_terms</span><span class="special">);</span>
+
+<span class="keyword">template</span> <span class="special">&lt;</span><span class="keyword">class</span> <span class="identifier">Gen</span><span class="special">&gt;</span>
+<span class="keyword">typename</span> <span class="identifier">detail</span><span class="special">::</span><span class="identifier">fraction_traits</span><span class="special">&lt;</span><span class="identifier">Gen</span><span class="special">&gt;::</span><span class="identifier">result_type</span> 
+   <span class="identifier">continued_fraction_a</span><span class="special">(</span><span class="identifier">Gen</span><span class="special">&amp;</span> <span class="identifier">g</span><span class="special">,</span> <span class="keyword">int</span> <span class="identifier">bits</span><span class="special">);</span>
+   
+<span class="keyword">template</span> <span class="special">&lt;</span><span class="keyword">class</span> <span class="identifier">Gen</span><span class="special">&gt;</span>
+<span class="keyword">typename</span> <span class="identifier">detail</span><span class="special">::</span><span class="identifier">fraction_traits</span><span class="special">&lt;</span><span class="identifier">Gen</span><span class="special">&gt;::</span><span class="identifier">result_type</span> 
+   <span class="identifier">continued_fraction_a</span><span class="special">(</span><span class="identifier">Gen</span><span class="special">&amp;</span> <span class="identifier">g</span><span class="special">,</span> <span class="keyword">int</span> <span class="identifier">bits</span><span class="special">,</span> <span class="identifier">boost</span><span class="special">::</span><span class="identifier">uintmax_t</span><span class="special">&amp;</span> <span class="identifier">max_terms</span><span class="special">);</span>
+   
+<span class="special">}}}</span> <span class="comment">// namespaces
+</span></pre>
+<a name="math_toolkit.toolkit.internals1.cf.description"></a><h5>
+<a name="id825624"></a>
+          <a class="link" href="cf.html#math_toolkit.toolkit.internals1.cf.description">Description</a>
+        </h5>
+<p>
+          <a href="http://en.wikipedia.org/wiki/Continued_fraction" target="_top">Continued
+          fractions are a common method of approximation. </a> These functions
+          all evaluate the continued fraction described by the <span class="emphasis"><em>generator</em></span>
+          type argument. The functions with an "_a" suffix evaluate the
+          fraction:
+        </p>
+<p>
+          <span class="inlinemediaobject"><img src="../../../../equations/fraction2.png"></span>
+        </p>
+<p>
+          and those with a "_b" suffix evaluate the fraction:
+        </p>
+<p>
+          <span class="inlinemediaobject"><img src="../../../../equations/fraction1.png"></span>
+        </p>
+<p>
+          This latter form is somewhat more natural in that it corresponds with the
+          usual definition of a continued fraction, but note that the first <span class="emphasis"><em>a</em></span>
+          value returned by the generator is discarded. Further, often the first
+          <span class="emphasis"><em>a</em></span> and <span class="emphasis"><em>b</em></span> values in a continued
+          fraction have different defining equations to the remaining terms, which
+          may make the "_a" suffixed form more appropriate.
+        </p>
+<p>
+          The generator type should be a function object which supports the following
+          operations:
+        </p>
+<div class="informaltable"><table class="table">
+<colgroup>
+<col>
+<col>
+</colgroup>
+<thead><tr>
+<th>
+                <p>
+                  Expression
+                </p>
+                </th>
+<th>
+                <p>
+                  Description
+                </p>
+                </th>
+</tr></thead>
+<tbody>
+<tr>
+<td>
+                <p>
+                  Gen::result_type
+                </p>
+                </td>
+<td>
+                <p>
+                  The type that is the result of invoking operator(). This can be
+                  either an arithmetic type, or a std::pair&lt;&gt; of arithmetic
+                  types.
+                </p>
+                </td>
+</tr>
+<tr>
+<td>
+                <p>
+                  g()
+                </p>
+                </td>
+<td>
+                <p>
+                  Returns an object of type Gen::result_type.
+                </p>
+                <p>
+                  Each time this operator is called then the next pair of <span class="emphasis"><em>a</em></span>
+                  and <span class="emphasis"><em>b</em></span> values is returned. Or, if result_type
+                  is an arithmetic type, then the next <span class="emphasis"><em>b</em></span> value
+                  is returned and all the <span class="emphasis"><em>a</em></span> values are assumed
+                  to 1.
+                </p>
+                </td>
+</tr>
+</tbody>
+</table></div>
+<p>
+          In all the continued fraction evaluation functions the <span class="emphasis"><em>bits</em></span>
+          parameter is the number of bits precision desired in the result, evaluation
+          of the fraction will continue until the last term evaluated leaves the
+          first <span class="emphasis"><em>bits</em></span> bits in the result unchanged.
+        </p>
+<p>
+          If the optional <span class="emphasis"><em>max_terms</em></span> parameter is specified then
+          no more than <span class="emphasis"><em>max_terms</em></span> calls to the generator will
+          be made, and on output, <span class="emphasis"><em>max_terms</em></span> will be set to actual
+          number of calls made. This facility is particularly useful when profiling
+          a continued fraction for convergence.
+        </p>
+<a name="math_toolkit.toolkit.internals1.cf.implementation"></a><h5>
+<a name="id825926"></a>
+          <a class="link" href="cf.html#math_toolkit.toolkit.internals1.cf.implementation">Implementation</a>
+        </h5>
+<p>
+          Internally these algorithms all use the modified Lentz algorithm: refer
+          to Numeric Recipes in C++, W. H. Press et all, chapter 5, (especially 5.2
+          Evaluation of continued fractions, p 175 - 179) for more information, also
+          Lentz, W.J. 1976, Applied Optics, vol. 15, pp. 668-671.
+        </p>
+<a name="math_toolkit.toolkit.internals1.cf.examples"></a><h5>
+<a name="id825961"></a>
+          <a class="link" href="cf.html#math_toolkit.toolkit.internals1.cf.examples">Examples</a>
+        </h5>
+<p>
+          The <a href="http://en.wikipedia.org/wiki/Golden_ratio" target="_top">golden ratio
+          phi = 1.618033989...</a> can be computed from the simplest continued
+          fraction of all:
+        </p>
+<p>
+          <span class="inlinemediaobject"><img src="../../../../equations/fraction3.png"></span>
+        </p>
+<p>
+          We begin by defining a generator function:
+        </p>
+<pre class="programlisting"><span class="keyword">template</span> <span class="special">&lt;</span><span class="keyword">class</span> <span class="identifier">T</span><span class="special">&gt;</span>
+<span class="keyword">struct</span> <span class="identifier">golden_ratio_fraction</span>
+<span class="special">{</span>
+   <span class="keyword">typedef</span> <span class="identifier">T</span> <span class="identifier">result_type</span><span class="special">;</span>
+   
+   <span class="identifier">result_type</span> <span class="keyword">operator</span><span class="special">()</span>
+   <span class="special">{</span>
+      <span class="keyword">return</span> <span class="number">1</span><span class="special">;</span>
+   <span class="special">}</span>
+<span class="special">};</span>
+</pre>
+<p>
+          The golden ratio can then be computed to double precision using:
+        </p>
+<pre class="programlisting"><span class="identifier">continued_fraction_a</span><span class="special">(</span>
+   <span class="identifier">golden_ratio_fraction</span><span class="special">&lt;</span><span class="keyword">double</span><span class="special">&gt;(),</span>
+   <span class="identifier">std</span><span class="special">::</span><span class="identifier">numeric_limits</span><span class="special">&lt;</span><span class="keyword">double</span><span class="special">&gt;::</span><span class="identifier">digits</span><span class="special">);</span>
+</pre>
+<p>
+          It's more usual though to have to define both the <span class="emphasis"><em>a</em></span>'s
+          and the <span class="emphasis"><em>b</em></span>'s when evaluating special functions by continued
+          fractions, for example the tan function is defined by:
+        </p>
+<p>
+          <span class="inlinemediaobject"><img src="../../../../equations/fraction4.png"></span>
+        </p>
+<p>
+          So it's generator object would look like:
+        </p>
+<pre class="programlisting"><span class="keyword">template</span> <span class="special">&lt;</span><span class="keyword">class</span> <span class="identifier">T</span><span class="special">&gt;</span>
+<span class="keyword">struct</span> <span class="identifier">tan_fraction</span>
+<span class="special">{</span>
+<span class="keyword">private</span><span class="special">:</span>
+   <span class="identifier">T</span> <span class="identifier">a</span><span class="special">,</span> <span class="identifier">b</span><span class="special">;</span>
+<span class="keyword">public</span><span class="special">:</span>
+   <span class="identifier">tan_fraction</span><span class="special">(</span><span class="identifier">T</span> <span class="identifier">v</span><span class="special">)</span>
+      <span class="special">:</span> <span class="identifier">a</span><span class="special">(-</span><span class="identifier">v</span><span class="special">*</span><span class="identifier">v</span><span class="special">),</span> <span class="identifier">b</span><span class="special">(-</span><span class="number">1</span><span class="special">)</span>
+   <span class="special">{}</span>
+
+   <span class="keyword">typedef</span> <span class="identifier">std</span><span class="special">::</span><span class="identifier">pair</span><span class="special">&lt;</span><span class="identifier">T</span><span class="special">,</span><span class="identifier">T</span><span class="special">&gt;</span> <span class="identifier">result_type</span><span class="special">;</span>
+
+   <span class="identifier">std</span><span class="special">::</span><span class="identifier">pair</span><span class="special">&lt;</span><span class="identifier">T</span><span class="special">,</span><span class="identifier">T</span><span class="special">&gt;</span> <span class="keyword">operator</span><span class="special">()()</span>
+   <span class="special">{</span>
+      <span class="identifier">b</span> <span class="special">+=</span> <span class="number">2</span><span class="special">;</span>
+      <span class="keyword">return</span> <span class="identifier">std</span><span class="special">::</span><span class="identifier">make_pair</span><span class="special">(</span><span class="identifier">a</span><span class="special">,</span> <span class="identifier">b</span><span class="special">);</span>
+   <span class="special">}</span>
+<span class="special">};</span>
+</pre>
+<p>
+          Notice that if the continuant is subtracted from the <span class="emphasis"><em>b</em></span>
+          terms, as is the case here, then all the <span class="emphasis"><em>a</em></span> terms returned
+          by the generator will be negative. The tangent function can now be evaluated
+          using:
+        </p>
+<pre class="programlisting"><span class="keyword">template</span> <span class="special">&lt;</span><span class="keyword">class</span> <span class="identifier">T</span><span class="special">&gt;</span>
+<span class="identifier">T</span> <span class="identifier">tan</span><span class="special">(</span><span class="identifier">T</span> <span class="identifier">a</span><span class="special">)</span>
+<span class="special">{</span>
+   <span class="identifier">tan_fraction</span><span class="special">&lt;</span><span class="identifier">T</span><span class="special">&gt;</span> <span class="identifier">fract</span><span class="special">(</span><span class="identifier">a</span><span class="special">);</span>
+   <span class="keyword">return</span> <span class="identifier">a</span> <span class="special">/</span> <span class="identifier">continued_fraction_b</span><span class="special">(</span><span class="identifier">fract</span><span class="special">,</span> <span class="identifier">std</span><span class="special">::</span><span class="identifier">numeric_limits</span><span class="special">&lt;</span><span class="identifier">T</span><span class="special">&gt;::</span><span class="identifier">digits</span><span class="special">);</span>
+<span class="special">}</span>
+</pre>
+<p>
+          Notice that this time we're using the "_b" suffixed version to
+          evaluate the fraction: we're removing the leading <span class="emphasis"><em>a</em></span>
+          term during fraction evaluation as it's different from all the others.
+        </p>
+</div>
+<table xmlns:rev="http://www.cs.rpi.edu/~gregod/boost/tools/doc/revision" width="100%"><tr>
+<td align="left"></td>
+<td align="right"><div class="copyright-footer">Copyright © 2006 , 2007, 2008 John Maddock, Paul A. Bristow, Hubert
+      Holin, Xiaogang Zhang, Bruno Lalande and Gautam Sewani<p>
+        Distributed under the Boost Software License, Version 1.0. (See accompanying
+        file LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_0.txt)
+      </p>
+</div></td>
+</tr></table>
+<hr>
+<div class="spirit-nav">
+<a accesskey="p" href="series_evaluation.html"><img src="../../../../../doc/html/images/prev.png" alt="Prev"></a><a accesskey="u" href="../internals1.html"><img src="../../../../../doc/html/images/up.png" alt="Up"></a><a accesskey="h" href="../../../index.html"><img src="../../../../../doc/html/images/home.png" alt="Home"></a><a accesskey="n" href="rational.html"><img src="../../../../../doc/html/images/next.png" alt="Next"></a>
+</div>
+</body>
+</html>

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+++ sandbox/tools/auto_index/example/math/doc/sf_and_dist/html/math_toolkit/toolkit/internals1/constants.html	2008-11-28 05:25:28 EST (Fri, 28 Nov 2008)
@@ -0,0 +1,383 @@
+<html>
+<head>
+<meta http-equiv="Content-Type" content="text/html; charset=ISO-8859-1">
+<title>Numeric Constants</title>
+<link rel="stylesheet" href="../../../boostbook.css" type="text/css">
+<meta name="generator" content="DocBook XSL Stylesheets Vsnapshot_8125">
+<link rel="home" href="../../../index.html" title="Math Toolkit">
+<link rel="up" href="../internals1.html" title="Reused Utilities">
+<link rel="prev" href="../internals1.html" title="Reused Utilities">
+<link rel="next" href="series_evaluation.html" title="Series Evaluation">
+</head>
+<body bgcolor="white" text="black" link="#0000FF" vlink="#840084" alink="#0000FF">
+<table cellpadding="2" width="100%"><tr>
+<td valign="top"><img alt="Boost C++ Libraries" width="277" height="86" src="../../../../../boost.png"></td>
+<td align="center">Home</td>
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+<a accesskey="p" href="../internals1.html"><img src="../../../../../doc/html/images/prev.png" alt="Prev"></a><a accesskey="u" href="../internals1.html"><img src="../../../../../doc/html/images/up.png" alt="Up"></a><a accesskey="h" href="../../../index.html"><img src="../../../../../doc/html/images/home.png" alt="Home"></a><a accesskey="n" href="series_evaluation.html"><img src="../../../../../doc/html/images/next.png" alt="Next"></a>
+</div>
+<div class="section" lang="en">
+<div class="titlepage"><div><div><h4 class="title">
+<a name="math_toolkit.toolkit.internals1.constants"></a><a class="link" href="constants.html" title="Numeric Constants"> Numeric
+        Constants</a>
+</h4></div></div></div>
+<a name="math_toolkit.toolkit.internals1.constants.synopsis"></a><h5>
+<a name="id821382"></a>
+          <a class="link" href="constants.html#math_toolkit.toolkit.internals1.constants.synopsis">Synopsis</a>
+        </h5>
+<p>
+          
+</p>
+<pre class="programlisting"><span class="preprocessor">#include</span> <span class="special">&lt;</span><span class="identifier">boost</span><span class="special">/</span><span class="identifier">math</span><span class="special">/</span><span class="identifier">constants</span><span class="special">/</span><span class="identifier">constants</span><span class="special">.</span><span class="identifier">hpp</span><span class="special">&gt;</span>
+</pre>
+<p>
+        </p>
+<pre class="programlisting"><span class="keyword">namespace</span> <span class="identifier">boost</span><span class="special">{</span> <span class="keyword">namespace</span> <span class="identifier">math</span><span class="special">{</span> <span class="keyword">namespace</span> <span class="identifier">constants</span><span class="special">{</span>
+
+<span class="keyword">template</span> <span class="special">&lt;</span><span class="keyword">class</span> <span class="identifier">T</span><span class="special">&gt;</span> <span class="identifier">T</span> <span class="identifier">pi</span><span class="special">();</span>
+<span class="keyword">template</span> <span class="special">&lt;</span><span class="keyword">class</span> <span class="identifier">T</span><span class="special">&gt;</span> <span class="identifier">T</span> <span class="identifier">root_pi</span><span class="special">();</span>
+<span class="keyword">template</span> <span class="special">&lt;</span><span class="keyword">class</span> <span class="identifier">T</span><span class="special">&gt;</span> <span class="identifier">T</span> <span class="identifier">root_half_pi</span><span class="special">();</span>
+<span class="keyword">template</span> <span class="special">&lt;</span><span class="keyword">class</span> <span class="identifier">T</span><span class="special">&gt;</span> <span class="identifier">T</span> <span class="identifier">root_two_pi</span><span class="special">();</span>
+<span class="keyword">template</span> <span class="special">&lt;</span><span class="keyword">class</span> <span class="identifier">T</span><span class="special">&gt;</span> <span class="identifier">T</span> <span class="identifier">root_ln_four</span><span class="special">();</span>
+<span class="keyword">template</span> <span class="special">&lt;</span><span class="keyword">class</span> <span class="identifier">T</span><span class="special">&gt;</span> <span class="identifier">T</span> <span class="identifier">e</span><span class="special">();</span>
+<span class="keyword">template</span> <span class="special">&lt;</span><span class="keyword">class</span> <span class="identifier">T</span><span class="special">&gt;</span> <span class="identifier">T</span> <span class="identifier">half</span><span class="special">();</span>
+<span class="keyword">template</span> <span class="special">&lt;</span><span class="keyword">class</span> <span class="identifier">T</span><span class="special">&gt;</span> <span class="identifier">T</span> <span class="identifier">euler</span><span class="special">();</span>
+<span class="keyword">template</span> <span class="special">&lt;</span><span class="keyword">class</span> <span class="identifier">T</span><span class="special">&gt;</span> <span class="identifier">T</span> <span class="identifier">root_two</span><span class="special">();</span>
+<span class="keyword">template</span> <span class="special">&lt;</span><span class="keyword">class</span> <span class="identifier">T</span><span class="special">&gt;</span> <span class="identifier">T</span> <span class="identifier">ln_two</span><span class="special">();</span>
+<span class="keyword">template</span> <span class="special">&lt;</span><span class="keyword">class</span> <span class="identifier">T</span><span class="special">&gt;</span> <span class="identifier">T</span> <span class="identifier">ln_ln_two</span><span class="special">();</span>
+<span class="keyword">template</span> <span class="special">&lt;</span><span class="keyword">class</span> <span class="identifier">T</span><span class="special">&gt;</span> <span class="identifier">T</span> <span class="identifier">third</span><span class="special">();</span>
+<span class="keyword">template</span> <span class="special">&lt;</span><span class="keyword">class</span> <span class="identifier">T</span><span class="special">&gt;</span> <span class="identifier">T</span> <span class="identifier">twothirds</span><span class="special">();</span>
+<span class="keyword">template</span> <span class="special">&lt;</span><span class="keyword">class</span> <span class="identifier">T</span><span class="special">&gt;</span> <span class="identifier">T</span> <span class="identifier">pi_minus_three</span><span class="special">();</span>
+<span class="keyword">template</span> <span class="special">&lt;</span><span class="keyword">class</span> <span class="identifier">T</span><span class="special">&gt;</span> <span class="identifier">T</span> <span class="identifier">four_minus_pi</span><span class="special">();</span>
+
+<span class="special">}}}</span> <span class="comment">// namespaces
+</span></pre>
+<a name="math_toolkit.toolkit.internals1.constants.description"></a><h5>
+<a name="id822246"></a>
+          <a class="link" href="constants.html#math_toolkit.toolkit.internals1.constants.description">Description</a>
+        </h5>
+<p>
+          The header <code class="computeroutput"><span class="identifier">boost</span><span class="special">/</span><span class="identifier">math</span><span class="special">/</span><span class="identifier">constants</span><span class="special">/</span><span class="identifier">constants</span><span class="special">.</span><span class="identifier">hpp</span></code> contains some numeric constants that
+          we have found useful in the development of this library. New constants
+          are added on an ad-hock basis based on need.
+        </p>
+<p>
+          Usage is like this:
+        </p>
+<pre class="programlisting"><span class="keyword">template</span> <span class="special">&lt;</span><span class="keyword">class</span> <span class="identifier">T</span><span class="special">&gt;</span>
+<span class="identifier">T</span> <span class="identifier">circumference</span><span class="special">(</span><span class="identifier">T</span> <span class="identifier">r</span><span class="special">)</span>
+<span class="special">{</span>
+   <span class="keyword">return</span> <span class="number">2</span> <span class="special">*</span> <span class="identifier">boost</span><span class="special">::</span><span class="identifier">math</span><span class="special">::</span><span class="identifier">constants</span><span class="special">::</span><span class="identifier">pi</span><span class="special">&lt;</span><span class="identifier">T</span><span class="special">&gt;()</span> <span class="special">*</span> <span class="identifier">r</span><span class="special">;</span>
+<span class="special">}</span>
+</pre>
+<p>
+          All the constants are accurate to at least the 34 decimal digits required
+          for 128-bit long doubles, and most are accurate to 100 digits or more when
+          used with a suitable arbitrary precision type.
+        </p>
+<p>
+          The following table summarises the constants we have at present:
+        </p>
+<div class="informaltable"><table class="table">
+<colgroup>
+<col>
+<col>
+<col>
+</colgroup>
+<thead><tr>
+<th>
+                <p>
+                  Constant
+                </p>
+                </th>
+<th>
+                <p>
+                  Meaning
+                </p>
+                </th>
+<th>
+                <p>
+                  Value
+                </p>
+                </th>
+</tr></thead>
+<tbody>
+<tr>
+<td>
+                <p>
+                  pi
+                </p>
+                </td>
+<td>
+                <p>
+                  &#960;
+                </p>
+                </td>
+<td>
+                <p>
+                  3.1415926535897932384...
+                </p>
+                </td>
+</tr>
+<tr>
+<td>
+                <p>
+                  root_pi
+                </p>
+                </td>
+<td>
+                <p>
+                  &#8730;&#960;
+                </p>
+                </td>
+<td>
+                <p>
+                  1.772453850905516027...
+                </p>
+                </td>
+</tr>
+<tr>
+<td>
+                <p>
+                  root_half_pi
+                </p>
+                </td>
+<td>
+                <p>
+                  &#8730;(&#960;/2)
+                </p>
+                </td>
+<td>
+                <p>
+                  1.253314137315500251...
+                </p>
+                </td>
+</tr>
+<tr>
+<td>
+                <p>
+                  root_two_pi
+                </p>
+                </td>
+<td>
+                <p>
+                  &#8730;(2*&#960;)
+                </p>
+                </td>
+<td>
+                <p>
+                  2.506628274631000502...
+                </p>
+                </td>
+</tr>
+<tr>
+<td>
+                <p>
+                  root_ln_four
+                </p>
+                </td>
+<td>
+                <p>
+                  &#8730;(ln(4))
+                </p>
+                </td>
+<td>
+                <p>
+                  1.17741002251547469...
+                </p>
+                </td>
+</tr>
+<tr>
+<td>
+                <p>
+                  e
+                </p>
+                </td>
+<td>
+                <p>
+                  <span class="emphasis"><em>e</em></span>
+                </p>
+                </td>
+<td>
+                <p>
+                  2.71828182845904523536...
+                </p>
+                </td>
+</tr>
+<tr>
+<td>
+                <p>
+                  half
+                </p>
+                </td>
+<td>
+                <p>
+                  0.5
+                </p>
+                </td>
+<td>
+                <p>
+                  0.5
+                </p>
+                </td>
+</tr>
+<tr>
+<td>
+                <p>
+                  euler
+                </p>
+                </td>
+<td>
+                <p>
+                  Euler's constant
+                </p>
+                </td>
+<td>
+                <p>
+                  0.577215664901532860606
+                </p>
+                </td>
+</tr>
+<tr>
+<td>
+                <p>
+                  root_two
+                </p>
+                </td>
+<td>
+                <p>
+                  &#8730;2
+                </p>
+                </td>
+<td>
+                <p>
+                  1.4142135623730950488...
+                </p>
+                </td>
+</tr>
+<tr>
+<td>
+                <p>
+                  ln_two
+                </p>
+                </td>
+<td>
+                <p>
+                  ln(2)
+                </p>
+                </td>
+<td>
+                <p>
+                  0.6931471805599453094...
+                </p>
+                </td>
+</tr>
+<tr>
+<td>
+                <p>
+                  ln_ln_two
+                </p>
+                </td>
+<td>
+                <p>
+                  ln(ln(2))
+                </p>
+                </td>
+<td>
+                <p>
+                  -0.3665129205816643...
+                </p>
+                </td>
+</tr>
+<tr>
+<td>
+                <p>
+                  third
+                </p>
+                </td>
+<td>
+                <p>
+                  1/3
+                </p>
+                </td>
+<td>
+                <p>
+                  0.333333333333333333...
+                </p>
+                </td>
+</tr>
+<tr>
+<td>
+                <p>
+                  twothirds
+                </p>
+                </td>
+<td>
+                <p>
+                  2/3
+                </p>
+                </td>
+<td>
+                <p>
+                  0.666666666666666666...
+                </p>
+                </td>
+</tr>
+<tr>
+<td>
+                <p>
+                  pi_minus_three
+                </p>
+                </td>
+<td>
+                <p>
+                  &#960;-3
+                </p>
+                </td>
+<td>
+                <p>
+                  0.14159265358979323846...
+                </p>
+                </td>
+</tr>
+<tr>
+<td>
+                <p>
+                  four_minus_pi
+                </p>
+                </td>
+<td>
+                <p>
+                  4-&#960;
+                </p>
+                </td>
+<td>
+                <p>
+                  0.85840734641020676153735...
+                </p>
+                </td>
+</tr>
+</tbody>
+</table></div>
+</div>
+<table xmlns:rev="http://www.cs.rpi.edu/~gregod/boost/tools/doc/revision" width="100%"><tr>
+<td align="left"></td>
+<td align="right"><div class="copyright-footer">Copyright © 2006 , 2007, 2008 John Maddock, Paul A. Bristow, Hubert
+      Holin, Xiaogang Zhang, Bruno Lalande and Gautam Sewani<p>
+        Distributed under the Boost Software License, Version 1.0. (See accompanying
+        file LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_0.txt)
+      </p>
+</div></td>
+</tr></table>
+<hr>
+<div class="spirit-nav">
+<a accesskey="p" href="../internals1.html"><img src="../../../../../doc/html/images/prev.png" alt="Prev"></a><a accesskey="u" href="../internals1.html"><img src="../../../../../doc/html/images/up.png" alt="Up"></a><a accesskey="h" href="../../../index.html"><img src="../../../../../doc/html/images/home.png" alt="Home"></a><a accesskey="n" href="series_evaluation.html"><img src="../../../../../doc/html/images/next.png" alt="Next"></a>
+</div>
+</body>
+</html>

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+++ sandbox/tools/auto_index/example/math/doc/sf_and_dist/html/math_toolkit/toolkit/internals1/minima.html	2008-11-28 05:25:28 EST (Fri, 28 Nov 2008)
@@ -0,0 +1,126 @@
+<html>
+<head>
+<meta http-equiv="Content-Type" content="text/html; charset=ISO-8859-1">
+<title>Locating Function Minima</title>
+<link rel="stylesheet" href="../../../boostbook.css" type="text/css">
+<meta name="generator" content="DocBook XSL Stylesheets Vsnapshot_8125">
+<link rel="home" href="../../../index.html" title="Math Toolkit">
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+<table cellpadding="2" width="100%"><tr>
+<td valign="top"><img alt="Boost C++ Libraries" width="277" height="86" src="../../../../../boost.png"></td>
+<td align="center">Home</td>
+<td align="center">Libraries</td>
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+<td align="center">FAQ</td>
+<td align="center">More</td>
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+<hr>
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+<a accesskey="p" href="roots2.html"><img src="../../../../../doc/html/images/prev.png" alt="Prev"></a><a accesskey="u" href="../internals1.html"><img src="../../../../../doc/html/images/up.png" alt="Up"></a><a accesskey="h" href="../../../index.html"><img src="../../../../../doc/html/images/home.png" alt="Home"></a><a accesskey="n" href="../internals2.html"><img src="../../../../../doc/html/images/next.png" alt="Next"></a>
+</div>
+<div class="section" lang="en">
+<div class="titlepage"><div><div><h4 class="title">
+<a name="math_toolkit.toolkit.internals1.minima"></a><a class="link" href="minima.html" title="Locating Function Minima"> Locating Function
+        Minima</a>
+</h4></div></div></div>
+<a name="math_toolkit.toolkit.internals1.minima.synopsis"></a><h5>
+<a name="id842998"></a>
+          <a class="link" href="minima.html#math_toolkit.toolkit.internals1.minima.synopsis">synopsis</a>
+        </h5>
+<p>
+          
+</p>
+<pre class="programlisting"><span class="preprocessor">#include</span> <span class="special">&lt;</span><span class="identifier">boost</span><span class="special">/</span><span class="identifier">math</span><span class="special">/</span><span class="identifier">tools</span><span class="special">/</span><span class="identifier">minima</span><span class="special">.</span><span class="identifier">hpp</span><span class="special">&gt;</span>
+</pre>
+<p>
+        </p>
+<pre class="programlisting"><span class="keyword">template</span> <span class="special">&lt;</span><span class="keyword">class</span> <span class="identifier">F</span><span class="special">,</span> <span class="keyword">class</span> <span class="identifier">T</span><span class="special">&gt;</span>
+<span class="identifier">std</span><span class="special">::</span><span class="identifier">pair</span><span class="special">&lt;</span><span class="identifier">T</span><span class="special">,</span> <span class="identifier">T</span><span class="special">&gt;</span> <span class="identifier">brent_find_minima</span><span class="special">(</span><span class="identifier">F</span> <span class="identifier">f</span><span class="special">,</span> <span class="identifier">T</span> <span class="identifier">min</span><span class="special">,</span> <span class="identifier">T</span> <span class="identifier">max</span><span class="special">,</span> <span class="keyword">int</span> <span class="identifier">bits</span><span class="special">);</span>
+
+<span class="keyword">template</span> <span class="special">&lt;</span><span class="keyword">class</span> <span class="identifier">F</span><span class="special">,</span> <span class="keyword">class</span> <span class="identifier">T</span><span class="special">&gt;</span>
+<span class="identifier">std</span><span class="special">::</span><span class="identifier">pair</span><span class="special">&lt;</span><span class="identifier">T</span><span class="special">,</span> <span class="identifier">T</span><span class="special">&gt;</span> <span class="identifier">brent_find_minima</span><span class="special">(</span><span class="identifier">F</span> <span class="identifier">f</span><span class="special">,</span> <span class="identifier">T</span> <span class="identifier">min</span><span class="special">,</span> <span class="identifier">T</span> <span class="identifier">max</span><span class="special">,</span> <span class="keyword">int</span> <span class="identifier">bits</span><span class="special">,</span> <span class="identifier">boost</span><span class="special">::</span><span class="identifier">uintmax_t</span><span class="special">&amp;</span> <span class="identifier">max_iter</span><span class="special">);</span>
+</pre>
+<a name="math_toolkit.toolkit.internals1.minima.description"></a><h5>
+<a name="id843469"></a>
+          <a class="link" href="minima.html#math_toolkit.toolkit.internals1.minima.description">Description</a>
+        </h5>
+<p>
+          These two functions locate the minima of the continuous function <span class="emphasis"><em>f</em></span>
+          using Brent's algorithm. Parameters are:
+        </p>
+<div class="variablelist">
+<p class="title"><b></b></p>
+<dl>
+<dt><span class="term">f</span></dt>
+<dd><p>
+              The function to minimise. The function should be smooth over the range
+              [min,max], with no maxima occurring in that interval.
+            </p></dd>
+<dt><span class="term">min</span></dt>
+<dd><p>
+              The lower endpoint of the range in which to search for the minima.
+            </p></dd>
+<dt><span class="term">max</span></dt>
+<dd><p>
+              The upper endpoint of the range in which to search for the minima.
+            </p></dd>
+<dt><span class="term">bits</span></dt>
+<dd><p>
+              The number of bits precision to which the minima should be found. Note
+              that in principle, the minima can not be located to greater accuracy
+              than the square root of machine epsilon, therefore if <span class="emphasis"><em>bits</em></span>
+              is set to a value greater than one half of the bits in type T, then
+              the value will be ignored.
+            </p></dd>
+<dt><span class="term">max_iter</span></dt>
+<dd><p>
+              The maximum number of iterations to use in the algorithm, if not provided
+              the algorithm will just keep on going until the minima is found.
+            </p></dd>
+</dl>
+</div>
+<p>
+          <span class="bold"><strong>Returns:</strong></span> a pair containing the value of
+          the abscissa at the minima and the value of f(x) at the minima.
+        </p>
+<a name="math_toolkit.toolkit.internals1.minima.implementation"></a><h5>
+<a name="id843623"></a>
+          <a class="link" href="minima.html#math_toolkit.toolkit.internals1.minima.implementation">Implementation</a>
+        </h5>
+<p>
+          This is a reasonably faithful implementation of Brent's algorithm, refer
+          to:
+        </p>
+<p>
+          Brent, R.P. 1973, Algorithms for Minimization without Derivatives (Englewood
+          Cliffs, NJ: Prentice-Hall), Chapter 5.
+        </p>
+<p>
+          Numerical Recipes in C, The Art of Scientific Computing, Second Edition,
+          William H. Press, Saul A. Teukolsky, William T. Vetterling, and Brian P.
+          Flannery. Cambridge University Press. 1988, 1992.
+        </p>
+<p>
+          An algorithm with guaranteed convergence for finding a zero of a function,
+          R. P. Brent, The Computer Journal, Vol 44, 1971.
+        </p>
+</div>
+<table xmlns:rev="http://www.cs.rpi.edu/~gregod/boost/tools/doc/revision" width="100%"><tr>
+<td align="left"></td>
+<td align="right"><div class="copyright-footer">Copyright © 2006 , 2007, 2008 John Maddock, Paul A. Bristow, Hubert
+      Holin, Xiaogang Zhang, Bruno Lalande and Gautam Sewani<p>
+        Distributed under the Boost Software License, Version 1.0. (See accompanying
+        file LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_0.txt)
+      </p>
+</div></td>
+</tr></table>
+<hr>
+<div class="spirit-nav">
+<a accesskey="p" href="roots2.html"><img src="../../../../../doc/html/images/prev.png" alt="Prev"></a><a accesskey="u" href="../internals1.html"><img src="../../../../../doc/html/images/up.png" alt="Up"></a><a accesskey="h" href="../../../index.html"><img src="../../../../../doc/html/images/home.png" alt="Home"></a><a accesskey="n" href="../internals2.html"><img src="../../../../../doc/html/images/next.png" alt="Next"></a>
+</div>
+</body>
+</html>

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+++ sandbox/tools/auto_index/example/math/doc/sf_and_dist/html/math_toolkit/toolkit/internals1/rational.html	2008-11-28 05:25:28 EST (Fri, 28 Nov 2008)
@@ -0,0 +1,237 @@
+<html>
+<head>
+<meta http-equiv="Content-Type" content="text/html; charset=ISO-8859-1">
+<title>Polynomial and Rational Function Evaluation</title>
+<link rel="stylesheet" href="../../../boostbook.css" type="text/css">
+<meta name="generator" content="DocBook XSL Stylesheets Vsnapshot_8125">
+<link rel="home" href="../../../index.html" title="Math Toolkit">
+<link rel="up" href="../internals1.html" title="Reused Utilities">
+<link rel="prev" href="cf.html" title="Continued Fraction Evaluation">
+<link rel="next" href="roots.html" title="Root Finding With Derivatives">
+</head>
+<body bgcolor="white" text="black" link="#0000FF" vlink="#840084" alink="#0000FF">
+<table cellpadding="2" width="100%"><tr>
+<td valign="top"><img alt="Boost C++ Libraries" width="277" height="86" src="../../../../../boost.png"></td>
+<td align="center">Home</td>
+<td align="center">Libraries</td>
+<td align="center">People</td>
+<td align="center">FAQ</td>
+<td align="center">More</td>
+</tr></table>
+<hr>
+<div class="spirit-nav">
+<a accesskey="p" href="cf.html"><img src="../../../../../doc/html/images/prev.png" alt="Prev"></a><a accesskey="u" href="../internals1.html"><img src="../../../../../doc/html/images/up.png" alt="Up"></a><a accesskey="h" href="../../../index.html"><img src="../../../../../doc/html/images/home.png" alt="Home"></a><a accesskey="n" href="roots.html"><img src="../../../../../doc/html/images/next.png" alt="Next"></a>
+</div>
+<div class="section" lang="en">
+<div class="titlepage"><div><div><h4 class="title">
+<a name="math_toolkit.toolkit.internals1.rational"></a><a class="link" href="rational.html" title="Polynomial and Rational Function Evaluation"> Polynomial
+        and Rational Function Evaluation</a>
+</h4></div></div></div>
+<a name="math_toolkit.toolkit.internals1.rational.synopsis"></a><h5>
+<a name="id826961"></a>
+          <a class="link" href="rational.html#math_toolkit.toolkit.internals1.rational.synopsis">synopsis</a>
+        </h5>
+<p>
+          
+</p>
+<pre class="programlisting"><span class="preprocessor">#include</span> <span class="special">&lt;</span><span class="identifier">boost</span><span class="special">/</span><span class="identifier">math</span><span class="special">/</span><span class="identifier">tools</span><span class="special">/</span><span class="identifier">rational</span><span class="special">.</span><span class="identifier">hpp</span><span class="special">&gt;</span>
+</pre>
+<p>
+        </p>
+<pre class="programlisting"><span class="comment">// Polynomials:
+</span><span class="keyword">template</span> <span class="special">&lt;</span><span class="identifier">std</span><span class="special">::</span><span class="identifier">size_t</span> <span class="identifier">N</span><span class="special">,</span> <span class="keyword">class</span> <span class="identifier">T</span><span class="special">,</span> <span class="keyword">class</span> <span class="identifier">V</span><span class="special">&gt;</span>
+<span class="identifier">V</span> <span class="identifier">evaluate_polynomial</span><span class="special">(</span><span class="keyword">const</span> <span class="identifier">T</span><span class="special">(&amp;</span><span class="identifier">poly</span><span class="special">)[</span><span class="identifier">N</span><span class="special">],</span> <span class="keyword">const</span> <span class="identifier">V</span><span class="special">&amp;</span> <span class="identifier">val</span><span class="special">);</span>
+
+<span class="keyword">template</span> <span class="special">&lt;</span><span class="identifier">std</span><span class="special">::</span><span class="identifier">size_t</span> <span class="identifier">N</span><span class="special">,</span> <span class="keyword">class</span> <span class="identifier">T</span><span class="special">,</span> <span class="keyword">class</span> <span class="identifier">V</span><span class="special">&gt;</span>
+<span class="identifier">V</span> <span class="identifier">evaluate_polynomial</span><span class="special">(</span><span class="keyword">const</span> <span class="identifier">boost</span><span class="special">::</span><span class="identifier">array</span><span class="special">&lt;</span><span class="identifier">T</span><span class="special">,</span><span class="identifier">N</span><span class="special">&gt;&amp;</span> <span class="identifier">poly</span><span class="special">,</span> <span class="keyword">const</span> <span class="identifier">V</span><span class="special">&amp;</span> <span class="identifier">val</span><span class="special">);</span>
+
+<span class="keyword">template</span> <span class="special">&lt;</span><span class="keyword">class</span> <span class="identifier">T</span><span class="special">,</span> <span class="keyword">class</span> <span class="identifier">U</span><span class="special">&gt;</span>
+<span class="identifier">U</span> <span class="identifier">evaluate_polynomial</span><span class="special">(</span><span class="keyword">const</span> <span class="identifier">T</span><span class="special">*</span> <span class="identifier">poly</span><span class="special">,</span> <span class="identifier">U</span> <span class="identifier">z</span><span class="special">,</span> <span class="identifier">std</span><span class="special">::</span><span class="identifier">size_t</span> <span class="identifier">count</span><span class="special">);</span>
+
+<span class="comment">// Even polynomials:
+</span><span class="keyword">template</span> <span class="special">&lt;</span><span class="identifier">std</span><span class="special">::</span><span class="identifier">size_t</span> <span class="identifier">N</span><span class="special">,</span> <span class="keyword">class</span> <span class="identifier">T</span><span class="special">,</span> <span class="keyword">class</span> <span class="identifier">V</span><span class="special">&gt;</span>
+<span class="identifier">V</span> <span class="identifier">evaluate_even_polynomial</span><span class="special">(</span><span class="keyword">const</span> <span class="identifier">T</span><span class="special">(&amp;</span><span class="identifier">poly</span><span class="special">)[</span><span class="identifier">N</span><span class="special">],</span> <span class="keyword">const</span> <span class="identifier">V</span><span class="special">&amp;</span> <span class="identifier">z</span><span class="special">);</span>
+
+<span class="keyword">template</span> <span class="special">&lt;</span><span class="identifier">std</span><span class="special">::</span><span class="identifier">size_t</span> <span class="identifier">N</span><span class="special">,</span> <span class="keyword">class</span> <span class="identifier">T</span><span class="special">,</span> <span class="keyword">class</span> <span class="identifier">V</span><span class="special">&gt;</span>
+<span class="identifier">V</span> <span class="identifier">evaluate_even_polynomial</span><span class="special">(</span><span class="keyword">const</span> <span class="identifier">boost</span><span class="special">::</span><span class="identifier">array</span><span class="special">&lt;</span><span class="identifier">T</span><span class="special">,</span><span class="identifier">N</span><span class="special">&gt;&amp;</span> <span class="identifier">poly</span><span class="special">,</span> <span class="keyword">const</span> <span class="identifier">V</span><span class="special">&amp;</span> <span class="identifier">z</span><span class="special">);</span>
+
+<span class="keyword">template</span> <span class="special">&lt;</span><span class="keyword">class</span> <span class="identifier">T</span><span class="special">,</span> <span class="keyword">class</span> <span class="identifier">U</span><span class="special">&gt;</span>
+<span class="identifier">U</span> <span class="identifier">evaluate_even_polynomial</span><span class="special">(</span><span class="keyword">const</span> <span class="identifier">T</span><span class="special">*</span> <span class="identifier">poly</span><span class="special">,</span> <span class="identifier">U</span> <span class="identifier">z</span><span class="special">,</span> <span class="identifier">std</span><span class="special">::</span><span class="identifier">size_t</span> <span class="identifier">count</span><span class="special">);</span>
+
+<span class="comment">// Odd polynomials   
+</span><span class="keyword">template</span> <span class="special">&lt;</span><span class="identifier">std</span><span class="special">::</span><span class="identifier">size_t</span> <span class="identifier">N</span><span class="special">,</span> <span class="keyword">class</span> <span class="identifier">T</span><span class="special">,</span> <span class="keyword">class</span> <span class="identifier">V</span><span class="special">&gt;</span>
+<span class="identifier">V</span> <span class="identifier">evaluate_odd_polynomial</span><span class="special">(</span><span class="keyword">const</span> <span class="identifier">T</span><span class="special">(&amp;</span><span class="identifier">a</span><span class="special">)[</span><span class="identifier">N</span><span class="special">],</span> <span class="keyword">const</span> <span class="identifier">V</span><span class="special">&amp;</span> <span class="identifier">z</span><span class="special">);</span>
+
+<span class="keyword">template</span> <span class="special">&lt;</span><span class="identifier">std</span><span class="special">::</span><span class="identifier">size_t</span> <span class="identifier">N</span><span class="special">,</span> <span class="keyword">class</span> <span class="identifier">T</span><span class="special">,</span> <span class="keyword">class</span> <span class="identifier">V</span><span class="special">&gt;</span>
+<span class="identifier">V</span> <span class="identifier">evaluate_odd_polynomial</span><span class="special">(</span><span class="keyword">const</span> <span class="identifier">boost</span><span class="special">::</span><span class="identifier">array</span><span class="special">&lt;</span><span class="identifier">T</span><span class="special">,</span><span class="identifier">N</span><span class="special">&gt;&amp;</span> <span class="identifier">a</span><span class="special">,</span> <span class="keyword">const</span> <span class="identifier">V</span><span class="special">&amp;</span> <span class="identifier">z</span><span class="special">);</span>
+
+<span class="keyword">template</span> <span class="special">&lt;</span><span class="keyword">class</span> <span class="identifier">T</span><span class="special">,</span> <span class="keyword">class</span> <span class="identifier">U</span><span class="special">&gt;</span>
+<span class="identifier">U</span> <span class="identifier">evaluate_odd_polynomial</span><span class="special">(</span><span class="keyword">const</span> <span class="identifier">T</span><span class="special">*</span> <span class="identifier">poly</span><span class="special">,</span> <span class="identifier">U</span> <span class="identifier">z</span><span class="special">,</span> <span class="identifier">std</span><span class="special">::</span><span class="identifier">size_t</span> <span class="identifier">count</span><span class="special">);</span>
+
+<span class="comment">// Rational Functions:
+</span><span class="keyword">template</span> <span class="special">&lt;</span><span class="identifier">std</span><span class="special">::</span><span class="identifier">size_t</span> <span class="identifier">N</span><span class="special">,</span> <span class="keyword">class</span> <span class="identifier">T</span><span class="special">,</span> <span class="keyword">class</span> <span class="identifier">V</span><span class="special">&gt;</span>
+<span class="identifier">V</span> <span class="identifier">evaluate_rational</span><span class="special">(</span><span class="keyword">const</span> <span class="identifier">T</span><span class="special">(&amp;</span><span class="identifier">a</span><span class="special">)[</span><span class="identifier">N</span><span class="special">],</span> <span class="keyword">const</span> <span class="identifier">T</span><span class="special">(&amp;</span><span class="identifier">b</span><span class="special">)[</span><span class="identifier">N</span><span class="special">],</span> <span class="keyword">const</span> <span class="identifier">V</span><span class="special">&amp;</span> <span class="identifier">z</span><span class="special">);</span>
+
+<span class="keyword">template</span> <span class="special">&lt;</span><span class="identifier">std</span><span class="special">::</span><span class="identifier">size_t</span> <span class="identifier">N</span><span class="special">,</span> <span class="keyword">class</span> <span class="identifier">T</span><span class="special">,</span> <span class="keyword">class</span> <span class="identifier">V</span><span class="special">&gt;</span>
+<span class="identifier">V</span> <span class="identifier">evaluate_rational</span><span class="special">(</span><span class="keyword">const</span> <span class="identifier">boost</span><span class="special">::</span><span class="identifier">array</span><span class="special">&lt;</span><span class="identifier">T</span><span class="special">,</span><span class="identifier">N</span><span class="special">&gt;&amp;</span> <span class="identifier">a</span><span class="special">,</span> <span class="keyword">const</span> <span class="identifier">boost</span><span class="special">::</span><span class="identifier">array</span><span class="special">&lt;</span><span class="identifier">T</span><span class="special">,</span><span class="identifier">N</span><span class="special">&gt;&amp;</span> <span class="identifier">b</span><span class="special">,</span> <span class="keyword">const</span> <span class="identifier">V</span><span class="special">&amp;</span> <span class="identifier">z</span><span class="special">);</spa
n>
+
+<span class="keyword">template</span> <span class="special">&lt;</span><span class="keyword">class</span> <span class="identifier">T</span><span class="special">,</span> <span class="keyword">class</span> <span class="identifier">U</span><span class="special">,</span> <span class="keyword">class</span> <span class="identifier">V</span><span class="special">&gt;</span>
+<span class="identifier">V</span> <span class="identifier">evaluate_rational</span><span class="special">(</span><span class="keyword">const</span> <span class="identifier">T</span><span class="special">*</span> <span class="identifier">num</span><span class="special">,</span> <span class="keyword">const</span> <span class="identifier">U</span><span class="special">*</span> <span class="identifier">denom</span><span class="special">,</span> <span class="identifier">V</span> <span class="identifier">z</span><span class="special">,</span> <span class="keyword">unsigned</span> <span class="identifier">count</span><span class="special">);</span>
+</pre>
+<a name="math_toolkit.toolkit.internals1.rational.description"></a><h5>
+<a name="id829090"></a>
+          <a class="link" href="rational.html#math_toolkit.toolkit.internals1.rational.description">Description</a>
+        </h5>
+<p>
+          Each of the functions come in three variants: a pair of overloaded functions
+          where the order of the polynomial or rational function is evaluated at
+          compile time, and an overload that accepts a runtime variable for the size
+          of the coefficient array. Generally speaking, compile time evaluation of
+          the array size results in better type safety, is less prone to programmer
+          errors, and may result in better optimised code. The polynomial evaluation
+          functions in particular, are specialised for various array sizes, allowing
+          for loop unrolling, and one hopes, optimal inline expansion.
+        </p>
+<pre class="programlisting"><span class="keyword">template</span> <span class="special">&lt;</span><span class="identifier">std</span><span class="special">::</span><span class="identifier">size_t</span> <span class="identifier">N</span><span class="special">,</span> <span class="keyword">class</span> <span class="identifier">T</span><span class="special">,</span> <span class="keyword">class</span> <span class="identifier">V</span><span class="special">&gt;</span>
+<span class="identifier">V</span> <span class="identifier">evaluate_polynomial</span><span class="special">(</span><span class="keyword">const</span> <span class="identifier">T</span><span class="special">(&amp;</span><span class="identifier">poly</span><span class="special">)[</span><span class="identifier">N</span><span class="special">],</span> <span class="keyword">const</span> <span class="identifier">V</span><span class="special">&amp;</span> <span class="identifier">val</span><span class="special">);</span>
+
+<span class="keyword">template</span> <span class="special">&lt;</span><span class="identifier">std</span><span class="special">::</span><span class="identifier">size_t</span> <span class="identifier">N</span><span class="special">,</span> <span class="keyword">class</span> <span class="identifier">T</span><span class="special">,</span> <span class="keyword">class</span> <span class="identifier">V</span><span class="special">&gt;</span>
+<span class="identifier">V</span> <span class="identifier">evaluate_polynomial</span><span class="special">(</span><span class="keyword">const</span> <span class="identifier">boost</span><span class="special">::</span><span class="identifier">array</span><span class="special">&lt;</span><span class="identifier">T</span><span class="special">,</span><span class="identifier">N</span><span class="special">&gt;&amp;</span> <span class="identifier">poly</span><span class="special">,</span> <span class="keyword">const</span> <span class="identifier">V</span><span class="special">&amp;</span> <span class="identifier">val</span><span class="special">);</span>
+
+<span class="keyword">template</span> <span class="special">&lt;</span><span class="keyword">class</span> <span class="identifier">T</span><span class="special">,</span> <span class="keyword">class</span> <span class="identifier">U</span><span class="special">&gt;</span>
+<span class="identifier">U</span> <span class="identifier">evaluate_polynomial</span><span class="special">(</span><span class="keyword">const</span> <span class="identifier">T</span><span class="special">*</span> <span class="identifier">poly</span><span class="special">,</span> <span class="identifier">U</span> <span class="identifier">z</span><span class="special">,</span> <span class="identifier">std</span><span class="special">::</span><span class="identifier">size_t</span> <span class="identifier">count</span><span class="special">);</span>
+</pre>
+<p>
+          Evaluates the polynomial
+          described by the coefficients stored in <span class="emphasis"><em>poly</em></span>.
+        </p>
+<p>
+          If the size of the array is specified at runtime, then the polynomial most
+          have order <span class="emphasis"><em>count-1</em></span> with <span class="emphasis"><em>count</em></span>
+          coefficients. Otherwise it has order <span class="emphasis"><em>N-1</em></span> with <span class="emphasis"><em>N</em></span>
+          coefficients.
+        </p>
+<p>
+          Coefficients should be stored such that the coefficients for the x<sup>i </sup> terms
+          are in poly[i].
+        </p>
+<p>
+          The types of the coefficients and of variable <span class="emphasis"><em>z</em></span> may
+          differ as long as <span class="emphasis"><em>*poly</em></span> is convertible to type <span class="emphasis"><em>U</em></span>.
+          This allows, for example, for the coefficient table to be a table of integers
+          if this is appropriate.
+        </p>
+<pre class="programlisting"><span class="keyword">template</span> <span class="special">&lt;</span><span class="identifier">std</span><span class="special">::</span><span class="identifier">size_t</span> <span class="identifier">N</span><span class="special">,</span> <span class="keyword">class</span> <span class="identifier">T</span><span class="special">,</span> <span class="keyword">class</span> <span class="identifier">V</span><span class="special">&gt;</span>
+<span class="identifier">V</span> <span class="identifier">evaluate_even_polynomial</span><span class="special">(</span><span class="keyword">const</span> <span class="identifier">T</span><span class="special">(&amp;</span><span class="identifier">poly</span><span class="special">)[</span><span class="identifier">N</span><span class="special">],</span> <span class="keyword">const</span> <span class="identifier">V</span><span class="special">&amp;</span> <span class="identifier">z</span><span class="special">);</span>
+
+<span class="keyword">template</span> <span class="special">&lt;</span><span class="identifier">std</span><span class="special">::</span><span class="identifier">size_t</span> <span class="identifier">N</span><span class="special">,</span> <span class="keyword">class</span> <span class="identifier">T</span><span class="special">,</span> <span class="keyword">class</span> <span class="identifier">V</span><span class="special">&gt;</span>
+<span class="identifier">V</span> <span class="identifier">evaluate_even_polynomial</span><span class="special">(</span><span class="keyword">const</span> <span class="identifier">boost</span><span class="special">::</span><span class="identifier">array</span><span class="special">&lt;</span><span class="identifier">T</span><span class="special">,</span><span class="identifier">N</span><span class="special">&gt;&amp;</span> <span class="identifier">poly</span><span class="special">,</span> <span class="keyword">const</span> <span class="identifier">V</span><span class="special">&amp;</span> <span class="identifier">z</span><span class="special">);</span>
+
+<span class="keyword">template</span> <span class="special">&lt;</span><span class="keyword">class</span> <span class="identifier">T</span><span class="special">,</span> <span class="keyword">class</span> <span class="identifier">U</span><span class="special">&gt;</span>
+<span class="identifier">U</span> <span class="identifier">evaluate_even_polynomial</span><span class="special">(</span><span class="keyword">const</span> <span class="identifier">T</span><span class="special">*</span> <span class="identifier">poly</span><span class="special">,</span> <span class="identifier">U</span> <span class="identifier">z</span><span class="special">,</span> <span class="identifier">std</span><span class="special">::</span><span class="identifier">size_t</span> <span class="identifier">count</span><span class="special">);</span>
+</pre>
+<p>
+          As above, but evaluates an even polynomial: one where all the powers of
+          <span class="emphasis"><em>z</em></span> are even numbers. Equivalent to calling <code class="computeroutput"><span class="identifier">evaluate_polynomial</span><span class="special">(</span><span class="identifier">poly</span><span class="special">,</span> <span class="identifier">z</span><span class="special">*</span><span class="identifier">z</span><span class="special">,</span> <span class="identifier">count</span><span class="special">)</span></code>.
+        </p>
+<pre class="programlisting"><span class="keyword">template</span> <span class="special">&lt;</span><span class="identifier">std</span><span class="special">::</span><span class="identifier">size_t</span> <span class="identifier">N</span><span class="special">,</span> <span class="keyword">class</span> <span class="identifier">T</span><span class="special">,</span> <span class="keyword">class</span> <span class="identifier">V</span><span class="special">&gt;</span>
+<span class="identifier">V</span> <span class="identifier">evaluate_odd_polynomial</span><span class="special">(</span><span class="keyword">const</span> <span class="identifier">T</span><span class="special">(&amp;</span><span class="identifier">a</span><span class="special">)[</span><span class="identifier">N</span><span class="special">],</span> <span class="keyword">const</span> <span class="identifier">V</span><span class="special">&amp;</span> <span class="identifier">z</span><span class="special">);</span>
+
+<span class="keyword">template</span> <span class="special">&lt;</span><span class="identifier">std</span><span class="special">::</span><span class="identifier">size_t</span> <span class="identifier">N</span><span class="special">,</span> <span class="keyword">class</span> <span class="identifier">T</span><span class="special">,</span> <span class="keyword">class</span> <span class="identifier">V</span><span class="special">&gt;</span>
+<span class="identifier">V</span> <span class="identifier">evaluate_odd_polynomial</span><span class="special">(</span><span class="keyword">const</span> <span class="identifier">boost</span><span class="special">::</span><span class="identifier">array</span><span class="special">&lt;</span><span class="identifier">T</span><span class="special">,</span><span class="identifier">N</span><span class="special">&gt;&amp;</span> <span class="identifier">a</span><span class="special">,</span> <span class="keyword">const</span> <span class="identifier">V</span><span class="special">&amp;</span> <span class="identifier">z</span><span class="special">);</span>
+
+<span class="keyword">template</span> <span class="special">&lt;</span><span class="keyword">class</span> <span class="identifier">T</span><span class="special">,</span> <span class="keyword">class</span> <span class="identifier">U</span><span class="special">&gt;</span>
+<span class="identifier">U</span> <span class="identifier">evaluate_odd_polynomial</span><span class="special">(</span><span class="keyword">const</span> <span class="identifier">T</span><span class="special">*</span> <span class="identifier">poly</span><span class="special">,</span> <span class="identifier">U</span> <span class="identifier">z</span><span class="special">,</span> <span class="identifier">std</span><span class="special">::</span><span class="identifier">size_t</span> <span class="identifier">count</span><span class="special">);</span>
+</pre>
+<p>
+          As above but evaluates a polynomial where all the powers are odd numbers.
+          Equivalent to <code class="computeroutput"><span class="identifier">evaluate_polynomial</span><span class="special">(</span><span class="identifier">poly</span><span class="special">+</span><span class="number">1</span><span class="special">,</span>
+          <span class="identifier">z</span><span class="special">*</span><span class="identifier">z</span><span class="special">,</span> <span class="identifier">count</span><span class="special">-</span><span class="number">1</span><span class="special">)</span>
+          <span class="special">*</span> <span class="identifier">z</span>
+          <span class="special">+</span> <span class="identifier">poly</span><span class="special">[</span><span class="number">0</span><span class="special">]</span></code>.
+        </p>
+<pre class="programlisting"><span class="keyword">template</span> <span class="special">&lt;</span><span class="identifier">std</span><span class="special">::</span><span class="identifier">size_t</span> <span class="identifier">N</span><span class="special">,</span> <span class="keyword">class</span> <span class="identifier">T</span><span class="special">,</span> <span class="keyword">class</span> <span class="identifier">U</span><span class="special">,</span> <span class="keyword">class</span> <span class="identifier">V</span><span class="special">&gt;</span>
+<span class="identifier">V</span> <span class="identifier">evaluate_rational</span><span class="special">(</span><span class="keyword">const</span> <span class="identifier">T</span><span class="special">(&amp;</span><span class="identifier">num</span><span class="special">)[</span><span class="identifier">N</span><span class="special">],</span> <span class="keyword">const</span> <span class="identifier">U</span><span class="special">(&amp;</span><span class="identifier">denom</span><span class="special">)[</span><span class="identifier">N</span><span class="special">],</span> <span class="keyword">const</span> <span class="identifier">V</span><span class="special">&amp;</span> <span class="identifier">z</span><span class="special">);</span>
+
+<span class="keyword">template</span> <span class="special">&lt;</span><span class="identifier">std</span><span class="special">::</span><span class="identifier">size_t</span> <span class="identifier">N</span><span class="special">,</span> <span class="keyword">class</span> <span class="identifier">T</span><span class="special">,</span> <span class="keyword">class</span> <span class="identifier">U</span><span class="special">,</span> <span class="keyword">class</span> <span class="identifier">V</span><span class="special">&gt;</span>
+<span class="identifier">V</span> <span class="identifier">evaluate_rational</span><span class="special">(</span><span class="keyword">const</span> <span class="identifier">boost</span><span class="special">::</span><span class="identifier">array</span><span class="special">&lt;</span><span class="identifier">T</span><span class="special">,</span><span class="identifier">N</span><span class="special">&gt;&amp;</span> <span class="identifier">num</span><span class="special">,</span> <span class="keyword">const</span> <span class="identifier">boost</span><span class="special">::</span><span class="identifier">array</span><span class="special">&lt;</span><span class="identifier">U</span><span class="special">,</span><span class="identifier">N</span><span class="special">&gt;&amp;</span> <span class="identifier">denom</span><span class="special">,</span> <span class="keyword">const</span> <span class="identifier">V</span><span class="special">&amp;</span> <span class="identifier">z</span><span class="special">)
;</span>
+
+<span class="keyword">template</span> <span class="special">&lt;</span><span class="keyword">class</span> <span class="identifier">T</span><span class="special">,</span> <span class="keyword">class</span> <span class="identifier">U</span><span class="special">,</span> <span class="keyword">class</span> <span class="identifier">V</span><span class="special">&gt;</span>
+<span class="identifier">V</span> <span class="identifier">evaluate_rational</span><span class="special">(</span><span class="keyword">const</span> <span class="identifier">T</span><span class="special">*</span> <span class="identifier">num</span><span class="special">,</span> <span class="keyword">const</span> <span class="identifier">U</span><span class="special">*</span> <span class="identifier">denom</span><span class="special">,</span> <span class="identifier">V</span> <span class="identifier">z</span><span class="special">,</span> <span class="keyword">unsigned</span> <span class="identifier">count</span><span class="special">);</span>
+</pre>
+<p>
+          Evaluates the rational function (the ratio of two polynomials) described
+          by the coefficients stored in <span class="emphasis"><em>num</em></span> and <span class="emphasis"><em>demom</em></span>.
+        </p>
+<p>
+          If the size of the array is specified at runtime then both polynomials
+          most have order <span class="emphasis"><em>count-1</em></span> with <span class="emphasis"><em>count</em></span>
+          coefficients. Otherwise both polynomials have order <span class="emphasis"><em>N-1</em></span>
+          with <span class="emphasis"><em>N</em></span> coefficients.
+        </p>
+<p>
+          Array <span class="emphasis"><em>num</em></span> describes the numerator, and <span class="emphasis"><em>demon</em></span>
+          the denominator.
+        </p>
+<p>
+          Coefficients should be stored such that the coefficients for the x<sup>i </sup> terms
+          are in num[i] and denom[i].
+        </p>
+<p>
+          The types of the coefficients and of variable <span class="emphasis"><em>v</em></span> may
+          differ as long as <span class="emphasis"><em>*num</em></span> and <span class="emphasis"><em>*denom</em></span>
+          are convertible to type <span class="emphasis"><em>V</em></span>. This allows, for example,
+          for one or both of the coefficient tables to be a table of integers if
+          this is appropriate.
+        </p>
+<p>
+          These functions are designed to safely evaluate the result, even when the
+          value <span class="emphasis"><em>z</em></span> is very large. As such they do not take advantage
+          of compile time array sizes to make any optimisations. These functions
+          are best reserved for situations where <span class="emphasis"><em>z</em></span> may be large:
+          if you can be sure that numerical overflow will not occur then polynomial
+          evaluation with compile-time array sizes may offer slightly better performance.
+        </p>
+<a name="math_toolkit.toolkit.internals1.rational.implementation"></a><h5>
+<a name="id831578"></a>
+          <a class="link" href="rational.html#math_toolkit.toolkit.internals1.rational.implementation">Implementation</a>
+        </h5>
+<p>
+          Polynomials are evaluated by <a href="http://en.wikipedia.org/wiki/Horner_algorithm" target="_top">Horners
+          method</a>. If the array size is known at compile time then the functions
+          dispatch to size-specific implementations that unroll the evaluation loop.
+        </p>
+<p>
+          Rational evaluation is by <a href="http://en.wikipedia.org/wiki/Horner_algorithm" target="_top">Horners
+          method</a>: with the two polynomials being evaluated in parallel to
+          make the most of the processors floating-point pipeline. If <span class="emphasis"><em>v</em></span>
+          is greater than one, then the polynomials are evaluated in reverse order
+          as polynomials in <span class="emphasis"><em>1/v</em></span>: this avoids unnecessary numerical
+          overflow when the coefficients are large.
+        </p>
+<p>
+          Both the polynomial and rational function evaluation algorithms can be
+          tuned using various configuration macros to provide optimal performance
+          for a particular combination of compiler and platform. This includes support
+          for second-order Horner's methods. The various options are <a class="link" href="../../perf/tuning.html" title="Performance Tuning Macros">documented
+          here</a>. However, the performance benefits to be gained from these
+          are marginal on most current hardware, consequently it's best to run the
+          <a class="link" href="../../perf/perf_test_app.html" title="The Performance Test Application">performance test application</a>
+          before changing the default settings.
+        </p>
+</div>
+<table xmlns:rev="http://www.cs.rpi.edu/~gregod/boost/tools/doc/revision" width="100%"><tr>
+<td align="left"></td>
+<td align="right"><div class="copyright-footer">Copyright © 2006 , 2007, 2008 John Maddock, Paul A. Bristow, Hubert
+      Holin, Xiaogang Zhang, Bruno Lalande and Gautam Sewani<p>
+        Distributed under the Boost Software License, Version 1.0. (See accompanying
+        file LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_0.txt)
+      </p>
+</div></td>
+</tr></table>
+<hr>
+<div class="spirit-nav">
+<a accesskey="p" href="cf.html"><img src="../../../../../doc/html/images/prev.png" alt="Prev"></a><a accesskey="u" href="../internals1.html"><img src="../../../../../doc/html/images/up.png" alt="Up"></a><a accesskey="h" href="../../../index.html"><img src="../../../../../doc/html/images/home.png" alt="Home"></a><a accesskey="n" href="roots.html"><img src="../../../../../doc/html/images/next.png" alt="Next"></a>
+</div>
+</body>
+</html>

Added: sandbox/tools/auto_index/example/math/doc/sf_and_dist/html/math_toolkit/toolkit/internals1/roots.html
==============================================================================
--- (empty file)
+++ sandbox/tools/auto_index/example/math/doc/sf_and_dist/html/math_toolkit/toolkit/internals1/roots.html	2008-11-28 05:25:28 EST (Fri, 28 Nov 2008)
@@ -0,0 +1,384 @@
+<html>
+<head>
+<meta http-equiv="Content-Type" content="text/html; charset=ISO-8859-1">
+<title>Root Finding With Derivatives</title>
+<link rel="stylesheet" href="../../../boostbook.css" type="text/css">
+<meta name="generator" content="DocBook XSL Stylesheets Vsnapshot_8125">
+<link rel="home" href="../../../index.html" title="Math Toolkit">
+<link rel="up" href="../internals1.html" title="Reused Utilities">
+<link rel="prev" href="rational.html" title="Polynomial and Rational Function Evaluation">
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+<body bgcolor="white" text="black" link="#0000FF" vlink="#840084" alink="#0000FF">
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+</div>
+<div class="section" lang="en">
+<div class="titlepage"><div><div><h4 class="title">
+<a name="math_toolkit.toolkit.internals1.roots"></a><a class="link" href="roots.html" title="Root Finding With Derivatives"> Root Finding
+        With Derivatives</a>
+</h4></div></div></div>
+<a name="math_toolkit.toolkit.internals1.roots.synopsis"></a><h5>
+<a name="id831710"></a>
+          <a class="link" href="roots.html#math_toolkit.toolkit.internals1.roots.synopsis">Synopsis</a>
+        </h5>
+<p>
+          
+</p>
+<pre class="programlisting"><span class="preprocessor">#include</span> <span class="special">&lt;</span><span class="identifier">boost</span><span class="special">/</span><span class="identifier">math</span><span class="special">/</span><span class="identifier">tools</span><span class="special">/</span><span class="identifier">roots</span><span class="special">.</span><span class="identifier">hpp</span><span class="special">&gt;</span>
+</pre>
+<p>
+        </p>
+<pre class="programlisting"><span class="keyword">namespace</span> <span class="identifier">boost</span><span class="special">{</span> <span class="keyword">namespace</span> <span class="identifier">math</span><span class="special">{</span> <span class="keyword">namespace</span> <span class="identifier">tools</span><span class="special">{</span>
+
+<span class="keyword">template</span> <span class="special">&lt;</span><span class="keyword">class</span> <span class="identifier">F</span><span class="special">,</span> <span class="keyword">class</span> <span class="identifier">T</span><span class="special">&gt;</span>
+<span class="identifier">T</span> <span class="identifier">newton_raphson_iterate</span><span class="special">(</span><span class="identifier">F</span> <span class="identifier">f</span><span class="special">,</span> <span class="identifier">T</span> <span class="identifier">guess</span><span class="special">,</span> <span class="identifier">T</span> <span class="identifier">min</span><span class="special">,</span> <span class="identifier">T</span> <span class="identifier">max</span><span class="special">,</span> <span class="keyword">int</span> <span class="identifier">digits</span><span class="special">);</span>
+
+<span class="keyword">template</span> <span class="special">&lt;</span><span class="keyword">class</span> <span class="identifier">F</span><span class="special">,</span> <span class="keyword">class</span> <span class="identifier">T</span><span class="special">&gt;</span>
+<span class="identifier">T</span> <span class="identifier">newton_raphson_iterate</span><span class="special">(</span><span class="identifier">F</span> <span class="identifier">f</span><span class="special">,</span> <span class="identifier">T</span> <span class="identifier">guess</span><span class="special">,</span> <span class="identifier">T</span> <span class="identifier">min</span><span class="special">,</span> <span class="identifier">T</span> <span class="identifier">max</span><span class="special">,</span> <span class="keyword">int</span> <span class="identifier">digits</span><span class="special">,</span> <span class="identifier">boost</span><span class="special">::</span><span class="identifier">uintmax_t</span><span class="special">&amp;</span> <span class="identifier">max_iter</span><span class="special">);</span>
+
+<span class="keyword">template</span> <span class="special">&lt;</span><span class="keyword">class</span> <span class="identifier">F</span><span class="special">,</span> <span class="keyword">class</span> <span class="identifier">T</span><span class="special">&gt;</span>
+<span class="identifier">T</span> <span class="identifier">halley_iterate</span><span class="special">(</span><span class="identifier">F</span> <span class="identifier">f</span><span class="special">,</span> <span class="identifier">T</span> <span class="identifier">guess</span><span class="special">,</span> <span class="identifier">T</span> <span class="identifier">min</span><span class="special">,</span> <span class="identifier">T</span> <span class="identifier">max</span><span class="special">,</span> <span class="keyword">int</span> <span class="identifier">digits</span><span class="special">);</span>
+
+<span class="keyword">template</span> <span class="special">&lt;</span><span class="keyword">class</span> <span class="identifier">F</span><span class="special">,</span> <span class="keyword">class</span> <span class="identifier">T</span><span class="special">&gt;</span>
+<span class="identifier">T</span> <span class="identifier">halley_iterate</span><span class="special">(</span><span class="identifier">F</span> <span class="identifier">f</span><span class="special">,</span> <span class="identifier">T</span> <span class="identifier">guess</span><span class="special">,</span> <span class="identifier">T</span> <span class="identifier">min</span><span class="special">,</span> <span class="identifier">T</span> <span class="identifier">max</span><span class="special">,</span> <span class="keyword">int</span> <span class="identifier">digits</span><span class="special">,</span> <span class="identifier">boost</span><span class="special">::</span><span class="identifier">uintmax_t</span><span class="special">&amp;</span> <span class="identifier">max_iter</span><span class="special">);</span>
+
+<span class="keyword">template</span> <span class="special">&lt;</span><span class="keyword">class</span> <span class="identifier">F</span><span class="special">,</span> <span class="keyword">class</span> <span class="identifier">T</span><span class="special">&gt;</span>
+<span class="identifier">T</span> <span class="identifier">schroeder_iterate</span><span class="special">(</span><span class="identifier">F</span> <span class="identifier">f</span><span class="special">,</span> <span class="identifier">T</span> <span class="identifier">guess</span><span class="special">,</span> <span class="identifier">T</span> <span class="identifier">min</span><span class="special">,</span> <span class="identifier">T</span> <span class="identifier">max</span><span class="special">,</span> <span class="keyword">int</span> <span class="identifier">digits</span><span class="special">);</span>
+
+<span class="keyword">template</span> <span class="special">&lt;</span><span class="keyword">class</span> <span class="identifier">F</span><span class="special">,</span> <span class="keyword">class</span> <span class="identifier">T</span><span class="special">&gt;</span>
+<span class="identifier">T</span> <span class="identifier">schroeder_iterate</span><span class="special">(</span><span class="identifier">F</span> <span class="identifier">f</span><span class="special">,</span> <span class="identifier">T</span> <span class="identifier">guess</span><span class="special">,</span> <span class="identifier">T</span> <span class="identifier">min</span><span class="special">,</span> <span class="identifier">T</span> <span class="identifier">max</span><span class="special">,</span> <span class="keyword">int</span> <span class="identifier">digits</span><span class="special">,</span> <span class="identifier">boost</span><span class="special">::</span><span class="identifier">uintmax_t</span><span class="special">&amp;</span> <span class="identifier">max_iter</span><span class="special">);</span>
+
+<span class="special">}}}</span> <span class="comment">// namespaces
+</span></pre>
+<a name="math_toolkit.toolkit.internals1.roots.description"></a><h5>
+<a name="id832868"></a>
+          <a class="link" href="roots.html#math_toolkit.toolkit.internals1.roots.description">Description</a>
+        </h5>
+<p>
+          These functions all perform iterative root finding: <code class="computeroutput"><span class="identifier">newton_raphson_iterate</span></code>
+          performs second order <a class="link" href="roots.html#newton">Newton Raphson iteration</a>,
+          while <code class="computeroutput"><span class="identifier">halley_iterate</span></code> and
+          <code class="computeroutput"><span class="identifier">schroeder_iterate</span></code> perform
+          third order <a class="link" href="roots.html#halley">Halley</a> and <a class="link" href="roots.html#schroeder">Schroeder</a>
+          iteration respectively.
+        </p>
+<p>
+          The functions all take the same parameters:
+        </p>
+<div class="variablelist">
+<p class="title"><b>Parameters of the root finding functions</b></p>
+<dl>
+<dt><span class="term">F
+          f</span></dt>
+<dd>
+<p>
+              Type F must be a callable function object that accepts one parameter
+              and returns a tuple:
+            </p>
+<p>
+              For the second order iterative methods (Newton Raphson) the tuple should
+              have two elements containing the evaluation of the function and it's
+              first derivative.
+            </p>
+<p>
+              For the third order methods (Halley and Schroeder) the tuple should
+              have three elements containing the evaluation of the function and its
+              first and second derivatives.
+            </p>
+</dd>
+<dt><span class="term">T guess</span></dt>
+<dd><p>
+              The initial starting value.
+            </p></dd>
+<dt><span class="term">T min</span></dt>
+<dd><p>
+              The minimum possible value for the result, this is used as an initial
+              lower bracket.
+            </p></dd>
+<dt><span class="term">T max</span></dt>
+<dd><p>
+              The maximum possible value for the result, this is used as an initial
+              upper bracket.
+            </p></dd>
+<dt><span class="term">int digits</span></dt>
+<dd><p>
+              The desired number of binary digits.
+            </p></dd>
+<dt><span class="term">uintmax_t max_iter</span></dt>
+<dd><p>
+              An optional maximum number of iterations to perform.
+            </p></dd>
+</dl>
+</div>
+<p>
+          When using these functions you should note that:
+        </p>
+<div class="itemizedlist"><ul type="disc">
+<li>
+            They may be very sensitive to the initial guess, typically they converge
+            very rapidly if the initial guess has two or three decimal digits correct.
+            However convergence can be no better than bisection, or in some rare
+            cases even worse than bisection if the initial guess is a long way from
+            the correct value and the derivatives are close to zero.
+          </li>
+<li>
+            These functions include special cases to handle zero first (and second
+            where appropriate) derivatives, and fall back to bisection in this case.
+            However, it is helpful if F is defined to return an arbitrarily small
+            value <span class="emphasis"><em>of the correct sign</em></span> rather than zero.
+          </li>
+<li>
+            If the derivative at the current best guess for the result is infinite
+            (or very close to being infinite) then these functions may terminate
+            prematurely. A large first derivative leads to a very small next step,
+            triggering the termination condition. Derivative based iteration may
+            not be appropriate in such cases.
+          </li>
+<li>
+            These functions fall back to bisection if the next computed step would
+            take the next value out of bounds. The bounds are updated after each
+            step to ensure this leads to convergence. However, a good initial guess
+            backed up by asymptotically-tight bounds will improve performance no
+            end rather than relying on bisection.
+          </li>
+<li>
+            The value of <span class="emphasis"><em>digits</em></span> is crucial to good performance
+            of these functions, if it is set too high then at best you will get one
+            extra (unnecessary) iteration, and at worst the last few steps will proceed
+            by bisection. Remember that the returned value can never be more accurate
+            than f(x) can be evaluated, and that if f(x) suffers from cancellation
+            errors as it tends to zero then the computed steps will be effectively
+            random. The value of <span class="emphasis"><em>digits</em></span> should be set so that
+            iteration terminates before this point: remember that for second and
+            third order methods the number of correct digits in the result is increasing
+            quite substantially with each iteration, <span class="emphasis"><em>digits</em></span>
+            should be set by experiment so that the final iteration just takes the
+            next value into the zone where f(x) becomes inaccurate.
+          </li>
+<li>
+            Finally: you may well be able to do better than these functions by hand-coding
+            the heuristics used so that they are tailored to a specific function.
+            You may also be able to compute the ratio of derivatives used by these
+            methods more efficiently than computing the derivatives themselves. As
+            ever, algebraic simplification can be a big win.
+          </li>
+</ul></div>
+<a name="newton"></a><p>
+        </p>
+<a name="math_toolkit.toolkit.internals1.roots.newton_raphson_method"></a><h5>
+<a name="id833247"></a>
+          <a class="link" href="roots.html#math_toolkit.toolkit.internals1.roots.newton_raphson_method">Newton
+          Raphson Method</a>
+        </h5>
+<p>
+          Given an initial guess x0 the subsequent values are computed using:
+        </p>
+<p>
+          <span class="inlinemediaobject"><img src="../../../../equations/roots1.png"></span>
+        </p>
+<p>
+          Out of bounds steps revert to bisection of the current bounds.
+        </p>
+<p>
+          Under ideal conditions, the number of correct digits doubles with each
+          iteration.
+        </p>
+<a name="halley"></a><p>
+        </p>
+<a name="math_toolkit.toolkit.internals1.roots.halley_s_method"></a><h5>
+<a name="id833332"></a>
+          <a class="link" href="roots.html#math_toolkit.toolkit.internals1.roots.halley_s_method">Halley's
+          Method</a>
+        </h5>
+<p>
+          Given an initial guess x0 the subsequent values are computed using:
+        </p>
+<p>
+          <span class="inlinemediaobject"><img src="../../../../equations/roots2.png"></span>
+        </p>
+<p>
+          Over-compensation by the second derivative (one which would proceed in
+          the wrong direction) causes the method to revert to a Newton-Raphson step.
+        </p>
+<p>
+          Out of bounds steps revert to bisection of the current bounds.
+        </p>
+<p>
+          Under ideal conditions, the number of correct digits trebles with each
+          iteration.
+        </p>
+<a name="schroeder"></a><p>
+        </p>
+<a name="math_toolkit.toolkit.internals1.roots.schroeder_s_method"></a><h5>
+<a name="id833428"></a>
+          <a class="link" href="roots.html#math_toolkit.toolkit.internals1.roots.schroeder_s_method">Schroeder's
+          Method</a>
+        </h5>
+<p>
+          Given an initial guess x0 the subsequent values are computed using:
+        </p>
+<p>
+          <span class="inlinemediaobject"><img src="../../../../equations/roots3.png"></span>
+        </p>
+<p>
+          Over-compensation by the second derivative (one which would proceed in
+          the wrong direction) causes the method to revert to a Newton-Raphson step.
+          Likewise a Newton step is used whenever that Newton step would change the
+          next value by more than 10%.
+        </p>
+<p>
+          Out of bounds steps revert to bisection of the current bounds.
+        </p>
+<p>
+          Under ideal conditions, the number of correct digits trebles with each
+          iteration.
+        </p>
+<a name="math_toolkit.toolkit.internals1.roots.example"></a><h5>
+<a name="id833513"></a>
+          <a class="link" href="roots.html#math_toolkit.toolkit.internals1.roots.example">Example</a>
+        </h5>
+<p>
+          Lets suppose we want to find the cube root of a number, the equation we
+          want to solve along with its derivatives are:
+        </p>
+<p>
+          <span class="inlinemediaobject"><img src="../../../../equations/roots4.png"></span>
+        </p>
+<p>
+          To begin with lets solve the problem using Newton Raphson iterations, we'll
+          begin be defining a function object that returns the evaluation of the
+          function to solve, along with its first derivative:
+        </p>
+<pre class="programlisting"><span class="keyword">template</span> <span class="special">&lt;</span><span class="keyword">class</span> <span class="identifier">T</span><span class="special">&gt;</span>
+<span class="keyword">struct</span> <span class="identifier">cbrt_functor</span>
+<span class="special">{</span>
+   <span class="identifier">cbrt_functor</span><span class="special">(</span><span class="identifier">T</span> <span class="keyword">const</span><span class="special">&amp;</span> <span class="identifier">target</span><span class="special">)</span> <span class="special">:</span> <span class="identifier">a</span><span class="special">(</span><span class="identifier">target</span><span class="special">){}</span>
+   <span class="identifier">std</span><span class="special">::</span><span class="identifier">tr1</span><span class="special">::</span><span class="identifier">tuple</span><span class="special">&lt;</span><span class="identifier">T</span><span class="special">,</span> <span class="identifier">T</span><span class="special">&gt;</span> <span class="keyword">operator</span><span class="special">()(</span><span class="identifier">T</span> <span class="keyword">const</span><span class="special">&amp;</span> <span class="identifier">z</span><span class="special">)</span>
+   <span class="special">{</span>
+      <span class="identifier">T</span> <span class="identifier">sqr</span> <span class="special">=</span> <span class="identifier">z</span> <span class="special">*</span> <span class="identifier">z</span><span class="special">;</span>
+      <span class="keyword">return</span> <span class="identifier">std</span><span class="special">::</span><span class="identifier">tr1</span><span class="special">::</span><span class="identifier">make_tuple</span><span class="special">(</span><span class="identifier">sqr</span> <span class="special">*</span> <span class="identifier">z</span> <span class="special">-</span> <span class="identifier">a</span><span class="special">,</span> <span class="number">3</span> <span class="special">*</span> <span class="identifier">sqr</span><span class="special">);</span>
+   <span class="special">}</span>
+<span class="keyword">private</span><span class="special">:</span>
+   <span class="identifier">T</span> <span class="identifier">a</span><span class="special">;</span>
+<span class="special">};</span>
+</pre>
+<p>
+          Implementing the cube root is fairly trivial now, the hardest part is finding
+          a good approximation to begin with: in this case we'll just divide the
+          exponent by three:
+        </p>
+<pre class="programlisting"><span class="keyword">template</span> <span class="special">&lt;</span><span class="keyword">class</span> <span class="identifier">T</span><span class="special">&gt;</span>
+<span class="identifier">T</span> <span class="identifier">cbrt</span><span class="special">(</span><span class="identifier">T</span> <span class="identifier">z</span><span class="special">)</span>
+<span class="special">{</span>
+   <span class="keyword">using</span> <span class="keyword">namespace</span> <span class="identifier">std</span><span class="special">;</span>
+   <span class="keyword">int</span> <span class="identifier">exp</span><span class="special">;</span>
+   <span class="identifier">frexp</span><span class="special">(</span><span class="identifier">z</span><span class="special">,</span> <span class="special">&amp;</span><span class="identifier">exp</span><span class="special">);</span>
+   <span class="identifier">T</span> <span class="identifier">min</span> <span class="special">=</span> <span class="identifier">ldexp</span><span class="special">(</span><span class="number">0.5</span><span class="special">,</span> <span class="identifier">exp</span><span class="special">/</span><span class="number">3</span><span class="special">);</span>
+   <span class="identifier">T</span> <span class="identifier">max</span> <span class="special">=</span> <span class="identifier">ldexp</span><span class="special">(</span><span class="number">2.0</span><span class="special">,</span> <span class="identifier">exp</span><span class="special">/</span><span class="number">3</span><span class="special">);</span>
+   <span class="identifier">T</span> <span class="identifier">guess</span> <span class="special">=</span> <span class="identifier">ldexp</span><span class="special">(</span><span class="number">1.0</span><span class="special">,</span> <span class="identifier">exp</span><span class="special">/</span><span class="number">3</span><span class="special">);</span>
+   <span class="keyword">int</span> <span class="identifier">digits</span> <span class="special">=</span> <span class="identifier">std</span><span class="special">::</span><span class="identifier">numeric_limits</span><span class="special">&lt;</span><span class="identifier">T</span><span class="special">&gt;::</span><span class="identifier">digits</span><span class="special">;</span>
+   <span class="keyword">return</span> <span class="identifier">tools</span><span class="special">::</span><span class="identifier">newton_raphson_iterate</span><span class="special">(</span><span class="identifier">detail</span><span class="special">::</span><span class="identifier">cbrt_functor</span><span class="special">&lt;</span><span class="identifier">T</span><span class="special">&gt;(</span><span class="identifier">z</span><span class="special">),</span> <span class="identifier">guess</span><span class="special">,</span> <span class="identifier">min</span><span class="special">,</span> <span class="identifier">max</span><span class="special">,</span> <span class="identifier">digits</span><span class="special">);</span>
+<span class="special">}</span>
+</pre>
+<p>
+          Using the test data in libs/math/test/cbrt_test.cpp this found the cube
+          root exact to the last digit in every case, and in no more than 6 iterations
+          at double precision. However, you will note that a high precision was used
+          in this example, exactly what was warned against earlier on in these docs!
+          In this particular case its possible to compute f(x) exactly and without
+          undue cancellation error, so a high limit is not too much of an issue.
+          However, reducing the limit to <code class="computeroutput"><span class="identifier">std</span><span class="special">::</span><span class="identifier">numeric_limits</span><span class="special">&lt;</span><span class="identifier">T</span><span class="special">&gt;::</span><span class="identifier">digits</span>
+          <span class="special">*</span> <span class="number">2</span> <span class="special">/</span> <span class="number">3</span></code> gave
+          full precision in all but one of the test cases (and that one was out by
+          just one bit). The maximum number of iterations remained 6, but in most
+          cases was reduced by one.
+        </p>
+<p>
+          Note also that the above code omits error handling, and does not handle
+          negative values of z correctly. That will be left as an exercise for the
+          reader!
+        </p>
+<p>
+          Now lets adapt the functor slightly to return the second derivative as
+          well:
+        </p>
+<pre class="programlisting"><span class="keyword">template</span> <span class="special">&lt;</span><span class="keyword">class</span> <span class="identifier">T</span><span class="special">&gt;</span>
+<span class="keyword">struct</span> <span class="identifier">cbrt_functor</span>
+<span class="special">{</span>
+   <span class="identifier">cbrt_functor</span><span class="special">(</span><span class="identifier">T</span> <span class="keyword">const</span><span class="special">&amp;</span> <span class="identifier">target</span><span class="special">)</span> <span class="special">:</span> <span class="identifier">a</span><span class="special">(</span><span class="identifier">target</span><span class="special">){}</span>
+   <span class="identifier">std</span><span class="special">::</span><span class="identifier">tr1</span><span class="special">::</span><span class="identifier">tuple</span><span class="special">&lt;</span><span class="identifier">T</span><span class="special">,</span> <span class="identifier">T</span><span class="special">,</span> <span class="identifier">T</span><span class="special">&gt;</span> <span class="keyword">operator</span><span class="special">()(</span><span class="identifier">T</span> <span class="keyword">const</span><span class="special">&amp;</span> <span class="identifier">z</span><span class="special">)</span>
+   <span class="special">{</span>
+      <span class="identifier">T</span> <span class="identifier">sqr</span> <span class="special">=</span> <span class="identifier">z</span> <span class="special">*</span> <span class="identifier">z</span><span class="special">;</span>
+      <span class="keyword">return</span> <span class="identifier">std</span><span class="special">::</span><span class="identifier">tr1</span><span class="special">::</span><span class="identifier">make_tuple</span><span class="special">(</span><span class="identifier">sqr</span> <span class="special">*</span> <span class="identifier">z</span> <span class="special">-</span> <span class="identifier">a</span><span class="special">,</span> <span class="number">3</span> <span class="special">*</span> <span class="identifier">sqr</span><span class="special">,</span> <span class="number">6</span> <span class="special">*</span> <span class="identifier">z</span><span class="special">);</span>
+   <span class="special">}</span>
+<span class="keyword">private</span><span class="special">:</span>
+   <span class="identifier">T</span> <span class="identifier">a</span><span class="special">;</span>
+<span class="special">};</span>
+</pre>
+<p>
+          And then adapt the <code class="computeroutput"><span class="identifier">cbrt</span></code>
+          function to use Halley iterations:
+        </p>
+<pre class="programlisting"><span class="keyword">template</span> <span class="special">&lt;</span><span class="keyword">class</span> <span class="identifier">T</span><span class="special">&gt;</span>
+<span class="identifier">T</span> <span class="identifier">cbrt</span><span class="special">(</span><span class="identifier">T</span> <span class="identifier">z</span><span class="special">)</span>
+<span class="special">{</span>
+   <span class="keyword">using</span> <span class="keyword">namespace</span> <span class="identifier">std</span><span class="special">;</span>
+   <span class="keyword">int</span> <span class="identifier">exp</span><span class="special">;</span>
+   <span class="identifier">frexp</span><span class="special">(</span><span class="identifier">z</span><span class="special">,</span> <span class="special">&amp;</span><span class="identifier">exp</span><span class="special">);</span>
+   <span class="identifier">T</span> <span class="identifier">min</span> <span class="special">=</span> <span class="identifier">ldexp</span><span class="special">(</span><span class="number">0.5</span><span class="special">,</span> <span class="identifier">exp</span><span class="special">/</span><span class="number">3</span><span class="special">);</span>
+   <span class="identifier">T</span> <span class="identifier">max</span> <span class="special">=</span> <span class="identifier">ldexp</span><span class="special">(</span><span class="number">2.0</span><span class="special">,</span> <span class="identifier">exp</span><span class="special">/</span><span class="number">3</span><span class="special">);</span>
+   <span class="identifier">T</span> <span class="identifier">guess</span> <span class="special">=</span> <span class="identifier">ldexp</span><span class="special">(</span><span class="number">1.0</span><span class="special">,</span> <span class="identifier">exp</span><span class="special">/</span><span class="number">3</span><span class="special">);</span>
+   <span class="keyword">int</span> <span class="identifier">digits</span> <span class="special">=</span> <span class="identifier">std</span><span class="special">::</span><span class="identifier">numeric_limits</span><span class="special">&lt;</span><span class="identifier">T</span><span class="special">&gt;::</span><span class="identifier">digits</span> <span class="special">/</span> <span class="number">2</span><span class="special">;</span>
+   <span class="keyword">return</span> <span class="identifier">tools</span><span class="special">::</span><span class="identifier">halley_iterate</span><span class="special">(</span><span class="identifier">detail</span><span class="special">::</span><span class="identifier">cbrt_functor</span><span class="special">&lt;</span><span class="identifier">T</span><span class="special">&gt;(</span><span class="identifier">z</span><span class="special">),</span> <span class="identifier">guess</span><span class="special">,</span> <span class="identifier">min</span><span class="special">,</span> <span class="identifier">max</span><span class="special">,</span> <span class="identifier">digits</span><span class="special">);</span>
+<span class="special">}</span>
+</pre>
+<p>
+          Note that the iterations are set to stop at just one-half of full precision,
+          and yet even so not one of the test cases had a single bit wrong. What's
+          more, the maximum number of iterations was now just 4.
+        </p>
+<p>
+          Just to complete the picture, we could have called <code class="computeroutput"><span class="identifier">schroeder_iterate</span></code>
+          in the last example: and in fact it makes no difference to the accuracy
+          or number of iterations in this particular case. However, the relative
+          performance of these two methods may vary depending upon the nature of
+          f(x), and the accuracy to which the initial guess can be computed. There
+          appear to be no generalisations that can be made except "try them
+          and see".
+        </p>
+<p>
+          Finally, had we called cbrt with NTL::RR
+          set to 1000 bit precision, then full precision can be obtained with just
+          7 iterations. To put that in perspective an increase in precision by a
+          factor of 20, has less than doubled the number of iterations. That just
+          goes to emphasise that most of the iterations are used up getting the first
+          few digits correct: after that these methods can churn out further digits
+          with remarkable efficiency. Or to put it another way: <span class="emphasis"><em>nothing
+          beats a really good initial guess!</em></span>
+        </p>
+</div>
+<table xmlns:rev="http://www.cs.rpi.edu/~gregod/boost/tools/doc/revision" width="100%"><tr>
+<td align="left"></td>
+<td align="right"><div class="copyright-footer">Copyright © 2006 , 2007, 2008 John Maddock, Paul A. Bristow, Hubert
+      Holin, Xiaogang Zhang, Bruno Lalande and Gautam Sewani<p>
+        Distributed under the Boost Software License, Version 1.0. (See accompanying
+        file LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_0.txt)
+      </p>
+</div></td>
+</tr></table>
+<hr>
+<div class="spirit-nav">
+<a accesskey="p" href="rational.html"><img src="../../../../../doc/html/images/prev.png" alt="Prev"></a><a accesskey="u" href="../internals1.html"><img src="../../../../../doc/html/images/up.png" alt="Up"></a><a accesskey="h" href="../../../index.html"><img src="../../../../../doc/html/images/home.png" alt="Home"></a><a accesskey="n" href="roots2.html"><img src="../../../../../doc/html/images/next.png" alt="Next"></a>
+</div>
+</body>
+</html>

Added: sandbox/tools/auto_index/example/math/doc/sf_and_dist/html/math_toolkit/toolkit/internals1/roots2.html
==============================================================================
--- (empty file)
+++ sandbox/tools/auto_index/example/math/doc/sf_and_dist/html/math_toolkit/toolkit/internals1/roots2.html	2008-11-28 05:25:28 EST (Fri, 28 Nov 2008)
@@ -0,0 +1,592 @@
+<html>
+<head>
+<meta http-equiv="Content-Type" content="text/html; charset=ISO-8859-1">
+<title>Root Finding Without Derivatives</title>
+<link rel="stylesheet" href="../../../boostbook.css" type="text/css">
+<meta name="generator" content="DocBook XSL Stylesheets Vsnapshot_8125">
+<link rel="home" href="../../../index.html" title="Math Toolkit">
+<link rel="up" href="../internals1.html" title="Reused Utilities">
+<link rel="prev" href="roots.html" title="Root Finding With Derivatives">
+<link rel="next" href="minima.html" title="Locating Function Minima">
+</head>
+<body bgcolor="white" text="black" link="#0000FF" vlink="#840084" alink="#0000FF">
+<table cellpadding="2" width="100%"><tr>
+<td valign="top"><img alt="Boost C++ Libraries" width="277" height="86" src="../../../../../boost.png"></td>
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+<a accesskey="p" href="roots.html"><img src="../../../../../doc/html/images/prev.png" alt="Prev"></a><a accesskey="u" href="../internals1.html"><img src="../../../../../doc/html/images/up.png" alt="Up"></a><a accesskey="h" href="../../../index.html"><img src="../../../../../doc/html/images/home.png" alt="Home"></a><a accesskey="n" href="minima.html"><img src="../../../../../doc/html/images/next.png" alt="Next"></a>
+</div>
+<div class="section" lang="en">
+<div class="titlepage"><div><div><h4 class="title">
+<a name="math_toolkit.toolkit.internals1.roots2"></a><a class="link" href="roots2.html" title="Root Finding Without Derivatives"> Root Finding
+        Without Derivatives</a>
+</h4></div></div></div>
+<a name="math_toolkit.toolkit.internals1.roots2.synopsis"></a><h5>
+<a name="id835661"></a>
+          <a class="link" href="roots2.html#math_toolkit.toolkit.internals1.roots2.synopsis">Synopsis</a>
+        </h5>
+<p>
+          
+</p>
+<pre class="programlisting"><span class="preprocessor">#include</span> <span class="special">&lt;</span><span class="identifier">boost</span><span class="special">/</span><span class="identifier">math</span><span class="special">/</span><span class="identifier">tools</span><span class="special">/</span><span class="identifier">roots</span><span class="special">.</span><span class="identifier">hpp</span><span class="special">&gt;</span>
+</pre>
+<p>
+        </p>
+<pre class="programlisting"><span class="keyword">namespace</span> <span class="identifier">boost</span><span class="special">{</span> <span class="keyword">namespace</span> <span class="identifier">math</span><span class="special">{</span> <span class="keyword">namespace</span> <span class="identifier">tools</span><span class="special">{</span>
+
+<span class="keyword">template</span> <span class="special">&lt;</span><span class="keyword">class</span> <span class="identifier">F</span><span class="special">,</span> <span class="keyword">class</span> <span class="identifier">T</span><span class="special">,</span> <span class="keyword">class</span> <span class="identifier">Tol</span><span class="special">&gt;</span>
+<span class="identifier">std</span><span class="special">::</span><span class="identifier">pair</span><span class="special">&lt;</span><span class="identifier">T</span><span class="special">,</span> <span class="identifier">T</span><span class="special">&gt;</span> 
+   <span class="identifier">bisect</span><span class="special">(</span>
+      <span class="identifier">F</span> <span class="identifier">f</span><span class="special">,</span> 
+      <span class="identifier">T</span> <span class="identifier">min</span><span class="special">,</span> 
+      <span class="identifier">T</span> <span class="identifier">max</span><span class="special">,</span> 
+      <span class="identifier">Tol</span> <span class="identifier">tol</span><span class="special">,</span> 
+      <span class="identifier">boost</span><span class="special">::</span><span class="identifier">uintmax_t</span><span class="special">&amp;</span> <span class="identifier">max_iter</span><span class="special">);</span>
+
+<span class="keyword">template</span> <span class="special">&lt;</span><span class="keyword">class</span> <span class="identifier">F</span><span class="special">,</span> <span class="keyword">class</span> <span class="identifier">T</span><span class="special">,</span> <span class="keyword">class</span> <span class="identifier">Tol</span><span class="special">&gt;</span>
+<span class="identifier">std</span><span class="special">::</span><span class="identifier">pair</span><span class="special">&lt;</span><span class="identifier">T</span><span class="special">,</span> <span class="identifier">T</span><span class="special">&gt;</span> 
+   <span class="identifier">bisect</span><span class="special">(</span>
+      <span class="identifier">F</span> <span class="identifier">f</span><span class="special">,</span> 
+      <span class="identifier">T</span> <span class="identifier">min</span><span class="special">,</span> 
+      <span class="identifier">T</span> <span class="identifier">max</span><span class="special">,</span> 
+      <span class="identifier">Tol</span> <span class="identifier">tol</span><span class="special">);</span>
+
+<span class="keyword">template</span> <span class="special">&lt;</span><span class="keyword">class</span> <span class="identifier">F</span><span class="special">,</span> <span class="keyword">class</span> <span class="identifier">T</span><span class="special">,</span> <span class="keyword">class</span> <span class="identifier">Tol</span><span class="special">,</span> <span class="keyword">class</span> <a class="link" href="../../policy.html" title="Policies">Policy</a><span class="special">&gt;</span>
+<span class="identifier">std</span><span class="special">::</span><span class="identifier">pair</span><span class="special">&lt;</span><span class="identifier">T</span><span class="special">,</span> <span class="identifier">T</span><span class="special">&gt;</span> 
+   <span class="identifier">bisect</span><span class="special">(</span>
+      <span class="identifier">F</span> <span class="identifier">f</span><span class="special">,</span> 
+      <span class="identifier">T</span> <span class="identifier">min</span><span class="special">,</span> 
+      <span class="identifier">T</span> <span class="identifier">max</span><span class="special">,</span> 
+      <span class="identifier">Tol</span> <span class="identifier">tol</span><span class="special">,</span> 
+      <span class="identifier">boost</span><span class="special">::</span><span class="identifier">uintmax_t</span><span class="special">&amp;</span> <span class="identifier">max_iter</span><span class="special">,</span>
+      <span class="keyword">const</span> <a class="link" href="../../policy.html" title="Policies">Policy</a><span class="special">&amp;);</span>
+
+<span class="keyword">template</span> <span class="special">&lt;</span><span class="keyword">class</span> <span class="identifier">F</span><span class="special">,</span> <span class="keyword">class</span> <span class="identifier">T</span><span class="special">,</span> <span class="keyword">class</span> <span class="identifier">Tol</span><span class="special">&gt;</span>
+<span class="identifier">std</span><span class="special">::</span><span class="identifier">pair</span><span class="special">&lt;</span><span class="identifier">T</span><span class="special">,</span> <span class="identifier">T</span><span class="special">&gt;</span> 
+   <span class="identifier">bracket_and_solve_root</span><span class="special">(</span>
+      <span class="identifier">F</span> <span class="identifier">f</span><span class="special">,</span> 
+      <span class="keyword">const</span> <span class="identifier">T</span><span class="special">&amp;</span> <span class="identifier">guess</span><span class="special">,</span> 
+      <span class="keyword">const</span> <span class="identifier">T</span><span class="special">&amp;</span> <span class="identifier">factor</span><span class="special">,</span> 
+      <span class="keyword">bool</span> <span class="identifier">rising</span><span class="special">,</span> 
+      <span class="identifier">Tol</span> <span class="identifier">tol</span><span class="special">,</span> 
+      <span class="identifier">boost</span><span class="special">::</span><span class="identifier">uintmax_t</span><span class="special">&amp;</span> <span class="identifier">max_iter</span><span class="special">);</span>
+
+<span class="keyword">template</span> <span class="special">&lt;</span><span class="keyword">class</span> <span class="identifier">F</span><span class="special">,</span> <span class="keyword">class</span> <span class="identifier">T</span><span class="special">,</span> <span class="keyword">class</span> <span class="identifier">Tol</span><span class="special">,</span> <span class="keyword">class</span> <a class="link" href="../../policy.html" title="Policies">Policy</a><span class="special">&gt;</span>
+<span class="identifier">std</span><span class="special">::</span><span class="identifier">pair</span><span class="special">&lt;</span><span class="identifier">T</span><span class="special">,</span> <span class="identifier">T</span><span class="special">&gt;</span> 
+   <span class="identifier">bracket_and_solve_root</span><span class="special">(</span>
+      <span class="identifier">F</span> <span class="identifier">f</span><span class="special">,</span> 
+      <span class="keyword">const</span> <span class="identifier">T</span><span class="special">&amp;</span> <span class="identifier">guess</span><span class="special">,</span> 
+      <span class="keyword">const</span> <span class="identifier">T</span><span class="special">&amp;</span> <span class="identifier">factor</span><span class="special">,</span> 
+      <span class="keyword">bool</span> <span class="identifier">rising</span><span class="special">,</span> 
+      <span class="identifier">Tol</span> <span class="identifier">tol</span><span class="special">,</span> 
+      <span class="identifier">boost</span><span class="special">::</span><span class="identifier">uintmax_t</span><span class="special">&amp;</span> <span class="identifier">max_iter</span><span class="special">,</span>
+      <span class="keyword">const</span> <a class="link" href="../../policy.html" title="Policies">Policy</a><span class="special">&amp;);</span>
+
+<span class="keyword">template</span> <span class="special">&lt;</span><span class="keyword">class</span> <span class="identifier">F</span><span class="special">,</span> <span class="keyword">class</span> <span class="identifier">T</span><span class="special">,</span> <span class="keyword">class</span> <span class="identifier">Tol</span><span class="special">&gt;</span>
+<span class="identifier">std</span><span class="special">::</span><span class="identifier">pair</span><span class="special">&lt;</span><span class="identifier">T</span><span class="special">,</span> <span class="identifier">T</span><span class="special">&gt;</span> 
+   <span class="identifier">toms748_solve</span><span class="special">(</span>
+      <span class="identifier">F</span> <span class="identifier">f</span><span class="special">,</span> 
+      <span class="keyword">const</span> <span class="identifier">T</span><span class="special">&amp;</span> <span class="identifier">a</span><span class="special">,</span> 
+      <span class="keyword">const</span> <span class="identifier">T</span><span class="special">&amp;</span> <span class="identifier">b</span><span class="special">,</span> 
+      <span class="identifier">Tol</span> <span class="identifier">tol</span><span class="special">,</span> 
+      <span class="identifier">boost</span><span class="special">::</span><span class="identifier">uintmax_t</span><span class="special">&amp;</span> <span class="identifier">max_iter</span><span class="special">);</span>
+
+<span class="keyword">template</span> <span class="special">&lt;</span><span class="keyword">class</span> <span class="identifier">F</span><span class="special">,</span> <span class="keyword">class</span> <span class="identifier">T</span><span class="special">,</span> <span class="keyword">class</span> <span class="identifier">Tol</span><span class="special">,</span> <span class="keyword">class</span> <a class="link" href="../../policy.html" title="Policies">Policy</a><span class="special">&gt;</span>
+<span class="identifier">std</span><span class="special">::</span><span class="identifier">pair</span><span class="special">&lt;</span><span class="identifier">T</span><span class="special">,</span> <span class="identifier">T</span><span class="special">&gt;</span> 
+   <span class="identifier">toms748_solve</span><span class="special">(</span>
+      <span class="identifier">F</span> <span class="identifier">f</span><span class="special">,</span> 
+      <span class="keyword">const</span> <span class="identifier">T</span><span class="special">&amp;</span> <span class="identifier">a</span><span class="special">,</span> 
+      <span class="keyword">const</span> <span class="identifier">T</span><span class="special">&amp;</span> <span class="identifier">b</span><span class="special">,</span> 
+      <span class="identifier">Tol</span> <span class="identifier">tol</span><span class="special">,</span> 
+      <span class="identifier">boost</span><span class="special">::</span><span class="identifier">uintmax_t</span><span class="special">&amp;</span> <span class="identifier">max_iter</span><span class="special">,</span>
+      <span class="keyword">const</span> <a class="link" href="../../policy.html" title="Policies">Policy</a><span class="special">&amp;);</span>
+
+<span class="keyword">template</span> <span class="special">&lt;</span><span class="keyword">class</span> <span class="identifier">F</span><span class="special">,</span> <span class="keyword">class</span> <span class="identifier">T</span><span class="special">,</span> <span class="keyword">class</span> <span class="identifier">Tol</span><span class="special">&gt;</span>
+<span class="identifier">std</span><span class="special">::</span><span class="identifier">pair</span><span class="special">&lt;</span><span class="identifier">T</span><span class="special">,</span> <span class="identifier">T</span><span class="special">&gt;</span> 
+   <span class="identifier">toms748_solve</span><span class="special">(</span>
+      <span class="identifier">F</span> <span class="identifier">f</span><span class="special">,</span> 
+      <span class="keyword">const</span> <span class="identifier">T</span><span class="special">&amp;</span> <span class="identifier">a</span><span class="special">,</span> 
+      <span class="keyword">const</span> <span class="identifier">T</span><span class="special">&amp;</span> <span class="identifier">b</span><span class="special">,</span> 
+      <span class="keyword">const</span> <span class="identifier">T</span><span class="special">&amp;</span> <span class="identifier">fa</span><span class="special">,</span> 
+      <span class="keyword">const</span> <span class="identifier">T</span><span class="special">&amp;</span> <span class="identifier">fb</span><span class="special">,</span> 
+      <span class="identifier">Tol</span> <span class="identifier">tol</span><span class="special">,</span> 
+      <span class="identifier">boost</span><span class="special">::</span><span class="identifier">uintmax_t</span><span class="special">&amp;</span> <span class="identifier">max_iter</span><span class="special">);</span>
+
+<span class="keyword">template</span> <span class="special">&lt;</span><span class="keyword">class</span> <span class="identifier">F</span><span class="special">,</span> <span class="keyword">class</span> <span class="identifier">T</span><span class="special">,</span> <span class="keyword">class</span> <span class="identifier">Tol</span><span class="special">,</span> <span class="keyword">class</span> <a class="link" href="../../policy.html" title="Policies">Policy</a><span class="special">&gt;</span>
+<span class="identifier">std</span><span class="special">::</span><span class="identifier">pair</span><span class="special">&lt;</span><span class="identifier">T</span><span class="special">,</span> <span class="identifier">T</span><span class="special">&gt;</span> 
+   <span class="identifier">toms748_solve</span><span class="special">(</span>
+      <span class="identifier">F</span> <span class="identifier">f</span><span class="special">,</span> 
+      <span class="keyword">const</span> <span class="identifier">T</span><span class="special">&amp;</span> <span class="identifier">a</span><span class="special">,</span> 
+      <span class="keyword">const</span> <span class="identifier">T</span><span class="special">&amp;</span> <span class="identifier">b</span><span class="special">,</span> 
+      <span class="keyword">const</span> <span class="identifier">T</span><span class="special">&amp;</span> <span class="identifier">fa</span><span class="special">,</span> 
+      <span class="keyword">const</span> <span class="identifier">T</span><span class="special">&amp;</span> <span class="identifier">fb</span><span class="special">,</span> 
+      <span class="identifier">Tol</span> <span class="identifier">tol</span><span class="special">,</span> 
+      <span class="identifier">boost</span><span class="special">::</span><span class="identifier">uintmax_t</span><span class="special">&amp;</span> <span class="identifier">max_iter</span><span class="special">,</span>
+      <span class="keyword">const</span> <a class="link" href="../../policy.html" title="Policies">Policy</a><span class="special">&amp;);</span>
+
+<span class="comment">// Termination conditions:
+</span><span class="keyword">template</span> <span class="special">&lt;</span><span class="keyword">class</span> <span class="identifier">T</span><span class="special">&gt;</span>
+<span class="keyword">struct</span> <span class="identifier">eps_tolerance</span><span class="special">;</span>
+
+<span class="keyword">struct</span> <span class="identifier">equal_floor</span><span class="special">;</span>
+<span class="keyword">struct</span> <span class="identifier">equal_ceil</span><span class="special">;</span>
+<span class="keyword">struct</span> <span class="identifier">equal_nearest_integer</span><span class="special">;</span>
+
+<span class="special">}}}</span> <span class="comment">// namespaces
+</span></pre>
+<a name="math_toolkit.toolkit.internals1.roots2.description"></a><h5>
+<a name="id838333"></a>
+          <a class="link" href="roots2.html#math_toolkit.toolkit.internals1.roots2.description">Description</a>
+        </h5>
+<p>
+          These functions solve the root of some function <span class="emphasis"><em>f(x)</em></span>
+          without the need for the derivatives of <span class="emphasis"><em>f(x)</em></span>. The
+          functions here that use TOMS Algorithm 748 are asymptotically the most
+          efficient known, and have been shown to be optimal for a certain classes
+          of smooth functions.
+        </p>
+<p>
+          Alternatively, there is a simple bisection routine which can be useful
+          in its own right in some situations, or alternatively for narrowing down
+          the range containing the root, prior to calling a more advanced algorithm.
+        </p>
+<p>
+          All the algorithms in this section reduce the diameter of the enclosing
+          interval with the same asymptotic efficiency with which they locate the
+          root. This is in contrast to the derivative based methods which may <span class="emphasis"><em>never</em></span>
+          significantly reduce the enclosing interval, even though they rapidly approach
+          the root. This is also in contrast to some other derivative-free methods
+          (for example the methods of <a href="http://en.wikipedia.org/wiki/Brent%27s_method" target="_top">Brent
+          or Dekker)</a> which only reduce the enclosing interval on the final
+          step. Therefore these methods return a std::pair containing the enclosing
+          interval found, and accept a function object specifying the termination
+          condition. Three function objects are provided for ready-made termination
+          conditions: <span class="emphasis"><em>eps_tolerance</em></span> causes termination when
+          the relative error in the enclosing interval is below a certain threshold,
+          while <span class="emphasis"><em>equal_floor</em></span> and <span class="emphasis"><em>equal_ceil</em></span>
+          are useful for certain statistical applications where the result is known
+          to be an integer. Other user-defined termination conditions are likely
+          to be used only rarely, but may be useful in some specific circumstances.
+        </p>
+<pre class="programlisting"><span class="keyword">template</span> <span class="special">&lt;</span><span class="keyword">class</span> <span class="identifier">F</span><span class="special">,</span> <span class="keyword">class</span> <span class="identifier">T</span><span class="special">,</span> <span class="keyword">class</span> <span class="identifier">Tol</span><span class="special">&gt;</span>
+<span class="identifier">std</span><span class="special">::</span><span class="identifier">pair</span><span class="special">&lt;</span><span class="identifier">T</span><span class="special">,</span> <span class="identifier">T</span><span class="special">&gt;</span> 
+   <span class="identifier">bisect</span><span class="special">(</span>
+      <span class="identifier">F</span> <span class="identifier">f</span><span class="special">,</span> 
+      <span class="identifier">T</span> <span class="identifier">min</span><span class="special">,</span> 
+      <span class="identifier">T</span> <span class="identifier">max</span><span class="special">,</span> 
+      <span class="identifier">Tol</span> <span class="identifier">tol</span><span class="special">,</span> 
+      <span class="identifier">boost</span><span class="special">::</span><span class="identifier">uintmax_t</span><span class="special">&amp;</span> <span class="identifier">max_iter</span><span class="special">);</span>
+
+<span class="keyword">template</span> <span class="special">&lt;</span><span class="keyword">class</span> <span class="identifier">F</span><span class="special">,</span> <span class="keyword">class</span> <span class="identifier">T</span><span class="special">,</span> <span class="keyword">class</span> <span class="identifier">Tol</span><span class="special">&gt;</span>
+<span class="identifier">std</span><span class="special">::</span><span class="identifier">pair</span><span class="special">&lt;</span><span class="identifier">T</span><span class="special">,</span> <span class="identifier">T</span><span class="special">&gt;</span> 
+   <span class="identifier">bisect</span><span class="special">(</span>
+      <span class="identifier">F</span> <span class="identifier">f</span><span class="special">,</span> 
+      <span class="identifier">T</span> <span class="identifier">min</span><span class="special">,</span> 
+      <span class="identifier">T</span> <span class="identifier">max</span><span class="special">,</span> 
+      <span class="identifier">Tol</span> <span class="identifier">tol</span><span class="special">);</span>
+
+<span class="keyword">template</span> <span class="special">&lt;</span><span class="keyword">class</span> <span class="identifier">F</span><span class="special">,</span> <span class="keyword">class</span> <span class="identifier">T</span><span class="special">,</span> <span class="keyword">class</span> <span class="identifier">Tol</span><span class="special">,</span> <span class="keyword">class</span> <a class="link" href="../../policy.html" title="Policies">Policy</a><span class="special">&gt;</span>
+<span class="identifier">std</span><span class="special">::</span><span class="identifier">pair</span><span class="special">&lt;</span><span class="identifier">T</span><span class="special">,</span> <span class="identifier">T</span><span class="special">&gt;</span> 
+   <span class="identifier">bisect</span><span class="special">(</span>
+      <span class="identifier">F</span> <span class="identifier">f</span><span class="special">,</span> 
+      <span class="identifier">T</span> <span class="identifier">min</span><span class="special">,</span> 
+      <span class="identifier">T</span> <span class="identifier">max</span><span class="special">,</span> 
+      <span class="identifier">Tol</span> <span class="identifier">tol</span><span class="special">,</span> 
+      <span class="identifier">boost</span><span class="special">::</span><span class="identifier">uintmax_t</span><span class="special">&amp;</span> <span class="identifier">max_iter</span><span class="special">,</span>
+      <span class="keyword">const</span> <a class="link" href="../../policy.html" title="Policies">Policy</a><span class="special">&amp;);</span>
+</pre>
+<p>
+          These functions locate the root using bisection, function arguments are:
+        </p>
+<div class="variablelist">
+<p class="title"><b></b></p>
+<dl>
+<dt><span class="term">f</span></dt>
+<dd><p>
+              A unary functor which is the function whose root is to be found.
+            </p></dd>
+<dt><span class="term">min</span></dt>
+<dd><p>
+              The left bracket of the interval known to contain the root.
+            </p></dd>
+<dt><span class="term">max</span></dt>
+<dd><p>
+              The right bracket of the interval known to contain the root. It is
+              a precondition that <span class="emphasis"><em>min &lt; max</em></span> and <span class="emphasis"><em>f(min)*f(max)
+              &lt;= 0</em></span>, the function signals evaluation error if these
+              preconditions are violated. The action taken is controlled by the evaluation
+              error policy. A best guess may be returned, perhaps significantly wrong.
+            </p></dd>
+<dt><span class="term">tol</span></dt>
+<dd><p>
+              A binary functor that specifies the termination condition: the function
+              will return the current brackets enclosing the root when <span class="emphasis"><em>tol(min,max)</em></span>
+              becomes true.
+            </p></dd>
+<dt><span class="term">max_iter</span></dt>
+<dd><p>
+              The maximum number of invocations of <span class="emphasis"><em>f(x)</em></span> to make
+              while searching for the root.
+            </p></dd>
+</dl>
+</div>
+<p>
+          </p>
+<p>
+            The final <a class="link" href="../../policy.html" title="Policies">Policy</a> argument
+            is optional and can be used to control the behaviour of the function:
+            how it handles errors, what level of precision to use etc. Refer to the
+            <a class="link" href="../../policy.html" title="Policies">policy documentation for more details</a>.
+          </p>
+<p>
+        </p>
+<p>
+          Returns: a pair of values <span class="emphasis"><em>r</em></span> that bracket the root
+          so that:
+        </p>
+<pre class="programlisting"><span class="identifier">f</span><span class="special">(</span><span class="identifier">r</span><span class="special">.</span><span class="identifier">first</span><span class="special">)</span> <span class="special">*</span> <span class="identifier">f</span><span class="special">(</span><span class="identifier">r</span><span class="special">.</span><span class="identifier">second</span><span class="special">)</span> <span class="special">&lt;=</span> <span class="number">0</span>
+</pre>
+<p>
+          and either
+        </p>
+<pre class="programlisting"><span class="identifier">tol</span><span class="special">(</span><span class="identifier">r</span><span class="special">.</span><span class="identifier">first</span><span class="special">,</span> <span class="identifier">r</span><span class="special">.</span><span class="identifier">second</span><span class="special">)</span> <span class="special">==</span> <span class="keyword">true</span>
+</pre>
+<p>
+          or
+        </p>
+<pre class="programlisting"><span class="identifier">max_iter</span> <span class="special">&gt;=</span> <span class="identifier">m</span>
+</pre>
+<p>
+          where <span class="emphasis"><em>m</em></span> is the initial value of <span class="emphasis"><em>max_iter</em></span>
+          passed to the function.
+        </p>
+<p>
+          In other words, it's up to the caller to verify whether termination occurred
+          as a result of exceeding <span class="emphasis"><em>max_iter</em></span> function invocations
+          (easily done by checking the value of <span class="emphasis"><em>max_iter</em></span> when
+          the function returns), rather than because the termination condition <span class="emphasis"><em>tol</em></span>
+          was satisfied.
+        </p>
+<pre class="programlisting"><span class="keyword">template</span> <span class="special">&lt;</span><span class="keyword">class</span> <span class="identifier">F</span><span class="special">,</span> <span class="keyword">class</span> <span class="identifier">T</span><span class="special">,</span> <span class="keyword">class</span> <span class="identifier">Tol</span><span class="special">&gt;</span>
+<span class="identifier">std</span><span class="special">::</span><span class="identifier">pair</span><span class="special">&lt;</span><span class="identifier">T</span><span class="special">,</span> <span class="identifier">T</span><span class="special">&gt;</span> 
+   <span class="identifier">bracket_and_solve_root</span><span class="special">(</span>
+      <span class="identifier">F</span> <span class="identifier">f</span><span class="special">,</span> 
+      <span class="keyword">const</span> <span class="identifier">T</span><span class="special">&amp;</span> <span class="identifier">guess</span><span class="special">,</span> 
+      <span class="keyword">const</span> <span class="identifier">T</span><span class="special">&amp;</span> <span class="identifier">factor</span><span class="special">,</span> 
+      <span class="keyword">bool</span> <span class="identifier">rising</span><span class="special">,</span> 
+      <span class="identifier">Tol</span> <span class="identifier">tol</span><span class="special">,</span> 
+      <span class="identifier">boost</span><span class="special">::</span><span class="identifier">uintmax_t</span><span class="special">&amp;</span> <span class="identifier">max_iter</span><span class="special">);</span>
+
+<span class="keyword">template</span> <span class="special">&lt;</span><span class="keyword">class</span> <span class="identifier">F</span><span class="special">,</span> <span class="keyword">class</span> <span class="identifier">T</span><span class="special">,</span> <span class="keyword">class</span> <span class="identifier">Tol</span><span class="special">,</span> <span class="keyword">class</span> <a class="link" href="../../policy.html" title="Policies">Policy</a><span class="special">&gt;</span>
+<span class="identifier">std</span><span class="special">::</span><span class="identifier">pair</span><span class="special">&lt;</span><span class="identifier">T</span><span class="special">,</span> <span class="identifier">T</span><span class="special">&gt;</span> 
+   <span class="identifier">bracket_and_solve_root</span><span class="special">(</span>
+      <span class="identifier">F</span> <span class="identifier">f</span><span class="special">,</span> 
+      <span class="keyword">const</span> <span class="identifier">T</span><span class="special">&amp;</span> <span class="identifier">guess</span><span class="special">,</span> 
+      <span class="keyword">const</span> <span class="identifier">T</span><span class="special">&amp;</span> <span class="identifier">factor</span><span class="special">,</span> 
+      <span class="keyword">bool</span> <span class="identifier">rising</span><span class="special">,</span> 
+      <span class="identifier">Tol</span> <span class="identifier">tol</span><span class="special">,</span> 
+      <span class="identifier">boost</span><span class="special">::</span><span class="identifier">uintmax_t</span><span class="special">&amp;</span> <span class="identifier">max_iter</span><span class="special">,</span>
+      <span class="keyword">const</span> <a class="link" href="../../policy.html" title="Policies">Policy</a><span class="special">&amp;);</span>
+</pre>
+<p>
+          This is a convenience function that calls <span class="emphasis"><em>toms748_solve</em></span>
+          internally to find the root of <span class="emphasis"><em>f(x)</em></span>. It's usable only
+          when <span class="emphasis"><em>f(x)</em></span> is a monotonic function, and the location
+          of the root is known approximately, and in particular it is known whether
+          the root is occurs for positive or negative <span class="emphasis"><em>x</em></span>. The
+          parameters are:
+        </p>
+<div class="variablelist">
+<p class="title"><b></b></p>
+<dl>
+<dt><span class="term">f</span></dt>
+<dd><p>
+              A unary functor that is the function whose root is to be solved. f(x)
+              must be uniformly increasing or decreasing on <span class="emphasis"><em>x</em></span>.
+            </p></dd>
+<dt><span class="term">guess</span></dt>
+<dd><p>
+              An initial approximation to the root
+            </p></dd>
+<dt><span class="term">factor</span></dt>
+<dd><p>
+              A scaling factor that is used to bracket the root: the value <span class="emphasis"><em>guess</em></span>
+              is multiplied (or divided as appropriate) by <span class="emphasis"><em>factor</em></span>
+              until two values are found that bracket the root. A value such as 2
+              is a typical choice for <span class="emphasis"><em>factor</em></span>.
+            </p></dd>
+<dt><span class="term">rising</span></dt>
+<dd><p>
+              Set to <span class="emphasis"><em>true</em></span> if <span class="emphasis"><em>f(x)</em></span> is rising
+              on <span class="emphasis"><em>x</em></span> and <span class="emphasis"><em>false</em></span> if <span class="emphasis"><em>f(x)</em></span>
+              is falling on <span class="emphasis"><em>x</em></span>. This value is used along with
+              the result of <span class="emphasis"><em>f(guess)</em></span> to determine if <span class="emphasis"><em>guess</em></span>
+              is above or below the root.
+            </p></dd>
+<dt><span class="term">tol</span></dt>
+<dd><p>
+              A binary functor that determines the termination condition for the
+              search for the root. <span class="emphasis"><em>tol</em></span> is passed the current
+              brackets at each step, when it returns true then the current brackets
+              are returned as the result.
+            </p></dd>
+<dt><span class="term">max_iter</span></dt>
+<dd><p>
+              The maximum number of function invocations to perform in the search
+              for the root.
+            </p></dd>
+</dl>
+</div>
+<p>
+          </p>
+<p>
+            The final <a class="link" href="../../policy.html" title="Policies">Policy</a> argument
+            is optional and can be used to control the behaviour of the function:
+            how it handles errors, what level of precision to use etc. Refer to the
+            <a class="link" href="../../policy.html" title="Policies">policy documentation for more details</a>.
+          </p>
+<p>
+        </p>
+<p>
+          Returns: a pair of values <span class="emphasis"><em>r</em></span> that bracket the root
+          so that:
+        </p>
+<pre class="programlisting"><span class="identifier">f</span><span class="special">(</span><span class="identifier">r</span><span class="special">.</span><span class="identifier">first</span><span class="special">)</span> <span class="special">*</span> <span class="identifier">f</span><span class="special">(</span><span class="identifier">r</span><span class="special">.</span><span class="identifier">second</span><span class="special">)</span> <span class="special">&lt;=</span> <span class="number">0</span>
+</pre>
+<p>
+          and either
+        </p>
+<pre class="programlisting"><span class="identifier">tol</span><span class="special">(</span><span class="identifier">r</span><span class="special">.</span><span class="identifier">first</span><span class="special">,</span> <span class="identifier">r</span><span class="special">.</span><span class="identifier">second</span><span class="special">)</span> <span class="special">==</span> <span class="keyword">true</span>
+</pre>
+<p>
+          or
+        </p>
+<pre class="programlisting"><span class="identifier">max_iter</span> <span class="special">&gt;=</span> <span class="identifier">m</span>
+</pre>
+<p>
+          where <span class="emphasis"><em>m</em></span> is the initial value of <span class="emphasis"><em>max_iter</em></span>
+          passed to the function.
+        </p>
+<p>
+          In other words, it's up to the caller to verify whether termination occurred
+          as a result of exceeding <span class="emphasis"><em>max_iter</em></span> function invocations
+          (easily done by checking the value of <span class="emphasis"><em>max_iter</em></span> when
+          the function returns), rather than because the termination condition <span class="emphasis"><em>tol</em></span>
+          was satisfied.
+        </p>
+<pre class="programlisting"><span class="keyword">template</span> <span class="special">&lt;</span><span class="keyword">class</span> <span class="identifier">F</span><span class="special">,</span> <span class="keyword">class</span> <span class="identifier">T</span><span class="special">,</span> <span class="keyword">class</span> <span class="identifier">Tol</span><span class="special">&gt;</span>
+<span class="identifier">std</span><span class="special">::</span><span class="identifier">pair</span><span class="special">&lt;</span><span class="identifier">T</span><span class="special">,</span> <span class="identifier">T</span><span class="special">&gt;</span> 
+   <span class="identifier">toms748_solve</span><span class="special">(</span>
+      <span class="identifier">F</span> <span class="identifier">f</span><span class="special">,</span> 
+      <span class="keyword">const</span> <span class="identifier">T</span><span class="special">&amp;</span> <span class="identifier">a</span><span class="special">,</span> 
+      <span class="keyword">const</span> <span class="identifier">T</span><span class="special">&amp;</span> <span class="identifier">b</span><span class="special">,</span> 
+      <span class="identifier">Tol</span> <span class="identifier">tol</span><span class="special">,</span> 
+      <span class="identifier">boost</span><span class="special">::</span><span class="identifier">uintmax_t</span><span class="special">&amp;</span> <span class="identifier">max_iter</span><span class="special">);</span>
+
+<span class="keyword">template</span> <span class="special">&lt;</span><span class="keyword">class</span> <span class="identifier">F</span><span class="special">,</span> <span class="keyword">class</span> <span class="identifier">T</span><span class="special">,</span> <span class="keyword">class</span> <span class="identifier">Tol</span><span class="special">,</span> <span class="keyword">class</span> <a class="link" href="../../policy.html" title="Policies">Policy</a><span class="special">&gt;</span>
+<span class="identifier">std</span><span class="special">::</span><span class="identifier">pair</span><span class="special">&lt;</span><span class="identifier">T</span><span class="special">,</span> <span class="identifier">T</span><span class="special">&gt;</span> 
+   <span class="identifier">toms748_solve</span><span class="special">(</span>
+      <span class="identifier">F</span> <span class="identifier">f</span><span class="special">,</span> 
+      <span class="keyword">const</span> <span class="identifier">T</span><span class="special">&amp;</span> <span class="identifier">a</span><span class="special">,</span> 
+      <span class="keyword">const</span> <span class="identifier">T</span><span class="special">&amp;</span> <span class="identifier">b</span><span class="special">,</span> 
+      <span class="identifier">Tol</span> <span class="identifier">tol</span><span class="special">,</span> 
+      <span class="identifier">boost</span><span class="special">::</span><span class="identifier">uintmax_t</span><span class="special">&amp;</span> <span class="identifier">max_iter</span><span class="special">,</span>
+      <span class="keyword">const</span> <a class="link" href="../../policy.html" title="Policies">Policy</a><span class="special">&amp;);</span>
+
+<span class="keyword">template</span> <span class="special">&lt;</span><span class="keyword">class</span> <span class="identifier">F</span><span class="special">,</span> <span class="keyword">class</span> <span class="identifier">T</span><span class="special">,</span> <span class="keyword">class</span> <span class="identifier">Tol</span><span class="special">&gt;</span>
+<span class="identifier">std</span><span class="special">::</span><span class="identifier">pair</span><span class="special">&lt;</span><span class="identifier">T</span><span class="special">,</span> <span class="identifier">T</span><span class="special">&gt;</span> 
+   <span class="identifier">toms748_solve</span><span class="special">(</span>
+      <span class="identifier">F</span> <span class="identifier">f</span><span class="special">,</span> 
+      <span class="keyword">const</span> <span class="identifier">T</span><span class="special">&amp;</span> <span class="identifier">a</span><span class="special">,</span> 
+      <span class="keyword">const</span> <span class="identifier">T</span><span class="special">&amp;</span> <span class="identifier">b</span><span class="special">,</span> 
+      <span class="keyword">const</span> <span class="identifier">T</span><span class="special">&amp;</span> <span class="identifier">fa</span><span class="special">,</span> 
+      <span class="keyword">const</span> <span class="identifier">T</span><span class="special">&amp;</span> <span class="identifier">fb</span><span class="special">,</span> 
+      <span class="identifier">Tol</span> <span class="identifier">tol</span><span class="special">,</span> 
+      <span class="identifier">boost</span><span class="special">::</span><span class="identifier">uintmax_t</span><span class="special">&amp;</span> <span class="identifier">max_iter</span><span class="special">);</span>
+      
+<span class="keyword">template</span> <span class="special">&lt;</span><span class="keyword">class</span> <span class="identifier">F</span><span class="special">,</span> <span class="keyword">class</span> <span class="identifier">T</span><span class="special">,</span> <span class="keyword">class</span> <span class="identifier">Tol</span><span class="special">,</span> <span class="keyword">class</span> <a class="link" href="../../policy.html" title="Policies">Policy</a><span class="special">&gt;</span>
+<span class="identifier">std</span><span class="special">::</span><span class="identifier">pair</span><span class="special">&lt;</span><span class="identifier">T</span><span class="special">,</span> <span class="identifier">T</span><span class="special">&gt;</span> 
+   <span class="identifier">toms748_solve</span><span class="special">(</span>
+      <span class="identifier">F</span> <span class="identifier">f</span><span class="special">,</span> 
+      <span class="keyword">const</span> <span class="identifier">T</span><span class="special">&amp;</span> <span class="identifier">a</span><span class="special">,</span> 
+      <span class="keyword">const</span> <span class="identifier">T</span><span class="special">&amp;</span> <span class="identifier">b</span><span class="special">,</span> 
+      <span class="keyword">const</span> <span class="identifier">T</span><span class="special">&amp;</span> <span class="identifier">fa</span><span class="special">,</span> 
+      <span class="keyword">const</span> <span class="identifier">T</span><span class="special">&amp;</span> <span class="identifier">fb</span><span class="special">,</span> 
+      <span class="identifier">Tol</span> <span class="identifier">tol</span><span class="special">,</span> 
+      <span class="identifier">boost</span><span class="special">::</span><span class="identifier">uintmax_t</span><span class="special">&amp;</span> <span class="identifier">max_iter</span><span class="special">,</span>
+      <span class="keyword">const</span> <a class="link" href="../../policy.html" title="Policies">Policy</a><span class="special">&amp;);</span>
+</pre>
+<p>
+          These two functions implement TOMS Algorithm 748: it uses a mixture of
+          cubic, quadratic and linear (secant) interpolation to locate the root of
+          <span class="emphasis"><em>f(x)</em></span>. The two functions differ only by whether values
+          for <span class="emphasis"><em>f(a)</em></span> and <span class="emphasis"><em>f(b)</em></span> are already
+          available. The parameters are:
+        </p>
+<div class="variablelist">
+<p class="title"><b></b></p>
+<dl>
+<dt><span class="term">f</span></dt>
+<dd><p>
+              A unary functor that is the function whose root is to be solved. f(x)
+              need not be uniformly increasing or decreasing on <span class="emphasis"><em>x</em></span>
+              and may have multiple roots.
+            </p></dd>
+<dt><span class="term">a</span></dt>
+<dd><p>
+              The lower bound for the initial bracket of the root.
+            </p></dd>
+<dt><span class="term">b</span></dt>
+<dd><p>
+              The upper bound for the initial bracket of the root. It is a precondition
+              that <span class="emphasis"><em>a &lt; b</em></span> and that <span class="emphasis"><em>a</em></span>
+              and <span class="emphasis"><em>b</em></span> bracket the root to find so that <span class="emphasis"><em>f(a)*f(b)
+              &lt; 0</em></span>.
+            </p></dd>
+<dt><span class="term">fa</span></dt>
+<dd><p>
+              Optional: the value of <span class="emphasis"><em>f(a)</em></span>.
+            </p></dd>
+<dt><span class="term">fb</span></dt>
+<dd><p>
+              Optional: the value of <span class="emphasis"><em>f(b)</em></span>.
+            </p></dd>
+<dt><span class="term">tol</span></dt>
+<dd><p>
+              A binary functor that determines the termination condition for the
+              search for the root. <span class="emphasis"><em>tol</em></span> is passed the current
+              brackets at each step, when it returns true then the current brackets
+              are returned as the result.
+            </p></dd>
+<dt><span class="term">max_iter</span></dt>
+<dd><p>
+              The maximum number of function invocations to perform in the search
+              for the root. On exit <span class="emphasis"><em>max_iter</em></span> is set to actual
+              number of function invocations used.
+            </p></dd>
+</dl>
+</div>
+<p>
+          </p>
+<p>
+            The final <a class="link" href="../../policy.html" title="Policies">Policy</a> argument
+            is optional and can be used to control the behaviour of the function:
+            how it handles errors, what level of precision to use etc. Refer to the
+            <a class="link" href="../../policy.html" title="Policies">policy documentation for more details</a>.
+          </p>
+<p>
+        </p>
+<p>
+          Returns: a pair of values <span class="emphasis"><em>r</em></span> that bracket the root
+          so that:
+        </p>
+<pre class="programlisting"><span class="identifier">f</span><span class="special">(</span><span class="identifier">r</span><span class="special">.</span><span class="identifier">first</span><span class="special">)</span> <span class="special">*</span> <span class="identifier">f</span><span class="special">(</span><span class="identifier">r</span><span class="special">.</span><span class="identifier">second</span><span class="special">)</span> <span class="special">&lt;=</span> <span class="number">0</span>
+</pre>
+<p>
+          and either
+        </p>
+<pre class="programlisting"><span class="identifier">tol</span><span class="special">(</span><span class="identifier">r</span><span class="special">.</span><span class="identifier">first</span><span class="special">,</span> <span class="identifier">r</span><span class="special">.</span><span class="identifier">second</span><span class="special">)</span> <span class="special">==</span> <span class="keyword">true</span>
+</pre>
+<p>
+          or
+        </p>
+<pre class="programlisting"><span class="identifier">max_iter</span> <span class="special">&gt;=</span> <span class="identifier">m</span>
+</pre>
+<p>
+          where <span class="emphasis"><em>m</em></span> is the initial value of <span class="emphasis"><em>max_iter</em></span>
+          passed to the function.
+        </p>
+<p>
+          In other words, it's up to the caller to verify whether termination occurred
+          as a result of exceeding <span class="emphasis"><em>max_iter</em></span> function invocations
+          (easily done by checking the value of <span class="emphasis"><em>max_iter</em></span>), rather
+          than because the termination condition <span class="emphasis"><em>tol</em></span> was satisfied.
+        </p>
+<pre class="programlisting"><span class="keyword">template</span> <span class="special">&lt;</span><span class="keyword">class</span> <span class="identifier">T</span><span class="special">&gt;</span>
+<span class="keyword">struct</span> <span class="identifier">eps_tolerance</span>
+<span class="special">{</span>
+   <span class="identifier">eps_tolerance</span><span class="special">(</span><span class="keyword">int</span> <span class="identifier">bits</span><span class="special">);</span>
+   <span class="keyword">bool</span> <span class="keyword">operator</span><span class="special">()(</span><span class="keyword">const</span> <span class="identifier">T</span><span class="special">&amp;</span> <span class="identifier">a</span><span class="special">,</span> <span class="keyword">const</span> <span class="identifier">T</span><span class="special">&amp;</span> <span class="identifier">b</span><span class="special">)</span><span class="keyword">const</span><span class="special">;</span>
+<span class="special">};</span>
+</pre>
+<p>
+          This is the usual termination condition used with these root finding functions.
+          Its operator() will return true when the relative distance between <span class="emphasis"><em>a</em></span>
+          and <span class="emphasis"><em>b</em></span> is less than twice the machine epsilon for T,
+          or 2<sup>1-bits</sup>, whichever is the larger. In other words you set <span class="emphasis"><em>bits</em></span>
+          to the number of bits of precision you want in the result. The minimal
+          tolerance of twice the machine epsilon of T is required to ensure that
+          we get back a bracketing interval: since this must clearly be at least
+          1 epsilon in size.
+        </p>
+<pre class="programlisting"><span class="keyword">struct</span> <span class="identifier">equal_floor</span>
+<span class="special">{</span>
+   <span class="identifier">equal_floor</span><span class="special">();</span>
+   <span class="keyword">template</span> <span class="special">&lt;</span><span class="keyword">class</span> <span class="identifier">T</span><span class="special">&gt;</span> <span class="keyword">bool</span> <span class="keyword">operator</span><span class="special">()(</span><span class="keyword">const</span> <span class="identifier">T</span><span class="special">&amp;</span> <span class="identifier">a</span><span class="special">,</span> <span class="keyword">const</span> <span class="identifier">T</span><span class="special">&amp;</span> <span class="identifier">b</span><span class="special">)</span><span class="keyword">const</span><span class="special">;</span>
+<span class="special">};</span>
+</pre>
+<p>
+          This termination condition is used when you want to find an integer result
+          that is the <span class="emphasis"><em>floor</em></span> of the true root. It will terminate
+          as soon as both ends of the interval have the same <span class="emphasis"><em>floor</em></span>.
+        </p>
+<pre class="programlisting"><span class="keyword">struct</span> <span class="identifier">equal_ceil</span>
+<span class="special">{</span>
+   <span class="identifier">equal_ceil</span><span class="special">();</span>
+   <span class="keyword">template</span> <span class="special">&lt;</span><span class="keyword">class</span> <span class="identifier">T</span><span class="special">&gt;</span> <span class="keyword">bool</span> <span class="keyword">operator</span><span class="special">()(</span><span class="keyword">const</span> <span class="identifier">T</span><span class="special">&amp;</span> <span class="identifier">a</span><span class="special">,</span> <span class="keyword">const</span> <span class="identifier">T</span><span class="special">&amp;</span> <span class="identifier">b</span><span class="special">)</span><span class="keyword">const</span><span class="special">;</span>
+<span class="special">};</span>
+</pre>
+<p>
+          This termination condition is used when you want to find an integer result
+          that is the <span class="emphasis"><em>ceil</em></span> of the true root. It will terminate
+          as soon as both ends of the interval have the same <span class="emphasis"><em>ceil</em></span>.
+        </p>
+<pre class="programlisting"><span class="keyword">struct</span> <span class="identifier">equal_nearest_integer</span>
+<span class="special">{</span>
+   <span class="identifier">equal_nearest_integer</span><span class="special">();</span>
+   <span class="keyword">template</span> <span class="special">&lt;</span><span class="keyword">class</span> <span class="identifier">T</span><span class="special">&gt;</span> <span class="keyword">bool</span> <span class="keyword">operator</span><span class="special">()(</span><span class="keyword">const</span> <span class="identifier">T</span><span class="special">&amp;</span> <span class="identifier">a</span><span class="special">,</span> <span class="keyword">const</span> <span class="identifier">T</span><span class="special">&amp;</span> <span class="identifier">b</span><span class="special">)</span><span class="keyword">const</span><span class="special">;</span>
+<span class="special">};</span>
+</pre>
+<p>
+          This termination condition is used when you want to find an integer result
+          that is the <span class="emphasis"><em>closest</em></span> to the true root. It will terminate
+          as soon as both ends of the interval round to the same nearest integer.
+        </p>
+<a name="math_toolkit.toolkit.internals1.roots2.implementation"></a><h5>
+<a name="id842924"></a>
+          <a class="link" href="roots2.html#math_toolkit.toolkit.internals1.roots2.implementation">Implementation</a>
+        </h5>
+<p>
+          The implementation of the bisection algorithm is extremely straightforward
+          and not detailed here. TOMS algorithm 748 is described in detail in:
+        </p>
+<p>
+          <span class="emphasis"><em>Algorithm 748: Enclosing Zeros of Continuous Functions, G. E.
+          Alefeld, F. A. Potra and Yixun Shi, ACM Transactions on Mathematica1 Software,
+          Vol. 21. No. 3. September 1995. Pages 327-344.</em></span>
+        </p>
+<p>
+          The implementation here is a faithful translation of this paper into C++.
+        </p>
+</div>
+<table xmlns:rev="http://www.cs.rpi.edu/~gregod/boost/tools/doc/revision" width="100%"><tr>
+<td align="left"></td>
+<td align="right"><div class="copyright-footer">Copyright © 2006 , 2007, 2008 John Maddock, Paul A. Bristow, Hubert
+      Holin, Xiaogang Zhang, Bruno Lalande and Gautam Sewani<p>
+        Distributed under the Boost Software License, Version 1.0. (See accompanying
+        file LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_0.txt)
+      </p>
+</div></td>
+</tr></table>
+<hr>
+<div class="spirit-nav">
+<a accesskey="p" href="roots.html"><img src="../../../../../doc/html/images/prev.png" alt="Prev"></a><a accesskey="u" href="../internals1.html"><img src="../../../../../doc/html/images/up.png" alt="Up"></a><a accesskey="h" href="../../../index.html"><img src="../../../../../doc/html/images/home.png" alt="Home"></a><a accesskey="n" href="minima.html"><img src="../../../../../doc/html/images/next.png" alt="Next"></a>
+</div>
+</body>
+</html>

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+++ sandbox/tools/auto_index/example/math/doc/sf_and_dist/html/math_toolkit/toolkit/internals1/series_evaluation.html	2008-11-28 05:25:28 EST (Fri, 28 Nov 2008)
@@ -0,0 +1,190 @@
+<html>
+<head>
+<meta http-equiv="Content-Type" content="text/html; charset=ISO-8859-1">
+<title>Series Evaluation</title>
+<link rel="stylesheet" href="../../../boostbook.css" type="text/css">
+<meta name="generator" content="DocBook XSL Stylesheets Vsnapshot_8125">
+<link rel="home" href="../../../index.html" title="Math Toolkit">
+<link rel="up" href="../internals1.html" title="Reused Utilities">
+<link rel="prev" href="constants.html" title="Numeric Constants">
+<link rel="next" href="cf.html" title="Continued Fraction Evaluation">
+</head>
+<body bgcolor="white" text="black" link="#0000FF" vlink="#840084" alink="#0000FF">
+<table cellpadding="2" width="100%"><tr>
+<td valign="top"><img alt="Boost C++ Libraries" width="277" height="86" src="../../../../../boost.png"></td>
+<td align="center">Home</td>
+<td align="center">Libraries</td>
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+<hr>
+<div class="spirit-nav">
+<a accesskey="p" href="constants.html"><img src="../../../../../doc/html/images/prev.png" alt="Prev"></a><a accesskey="u" href="../internals1.html"><img src="../../../../../doc/html/images/up.png" alt="Up"></a><a accesskey="h" href="../../../index.html"><img src="../../../../../doc/html/images/home.png" alt="Home"></a><a accesskey="n" href="cf.html"><img src="../../../../../doc/html/images/next.png" alt="Next"></a>
+</div>
+<div class="section" lang="en">
+<div class="titlepage"><div><div><h4 class="title">
+<a name="math_toolkit.toolkit.internals1.series_evaluation"></a><a class="link" href="series_evaluation.html" title="Series Evaluation">
+        Series Evaluation</a>
+</h4></div></div></div>
+<a name="math_toolkit.toolkit.internals1.series_evaluation.synopsis"></a><h5>
+<a name="id823011"></a>
+          <a class="link" href="series_evaluation.html#math_toolkit.toolkit.internals1.series_evaluation.synopsis">Synopsis</a>
+        </h5>
+<p>
+          
+</p>
+<pre class="programlisting"><span class="preprocessor">#include</span> <span class="special">&lt;</span><span class="identifier">boost</span><span class="special">/</span><span class="identifier">math</span><span class="special">/</span><span class="identifier">tools</span><span class="special">/</span><span class="identifier">series</span><span class="special">.</span><span class="identifier">hpp</span><span class="special">&gt;</span>
+</pre>
+<p>
+        </p>
+<pre class="programlisting"><span class="keyword">namespace</span> <span class="identifier">boost</span><span class="special">{</span> <span class="keyword">namespace</span> <span class="identifier">math</span><span class="special">{</span> <span class="keyword">namespace</span> <span class="identifier">tools</span><span class="special">{</span>
+
+<span class="keyword">template</span> <span class="special">&lt;</span><span class="keyword">class</span> <span class="identifier">Functor</span><span class="special">&gt;</span>
+<span class="keyword">typename</span> <span class="identifier">Functor</span><span class="special">::</span><span class="identifier">result_type</span> <span class="identifier">sum_series</span><span class="special">(</span><span class="identifier">Functor</span><span class="special">&amp;</span> <span class="identifier">func</span><span class="special">,</span> <span class="keyword">int</span> <span class="identifier">bits</span><span class="special">);</span>
+
+<span class="keyword">template</span> <span class="special">&lt;</span><span class="keyword">class</span> <span class="identifier">Functor</span><span class="special">&gt;</span>
+<span class="keyword">typename</span> <span class="identifier">Functor</span><span class="special">::</span><span class="identifier">result_type</span> <span class="identifier">sum_series</span><span class="special">(</span><span class="identifier">Functor</span><span class="special">&amp;</span> <span class="identifier">func</span><span class="special">,</span> <span class="keyword">int</span> <span class="identifier">bits</span><span class="special">,</span> <span class="identifier">boost</span><span class="special">::</span><span class="identifier">uintmax_t</span><span class="special">&amp;</span> <span class="identifier">max_terms</span><span class="special">);</span>
+
+<span class="keyword">template</span> <span class="special">&lt;</span><span class="keyword">class</span> <span class="identifier">Functor</span><span class="special">,</span> <span class="keyword">class</span> <span class="identifier">U</span><span class="special">&gt;</span>
+<span class="keyword">typename</span> <span class="identifier">Functor</span><span class="special">::</span><span class="identifier">result_type</span> <span class="identifier">sum_series</span><span class="special">(</span><span class="identifier">Functor</span><span class="special">&amp;</span> <span class="identifier">func</span><span class="special">,</span> <span class="keyword">int</span> <span class="identifier">bits</span><span class="special">,</span> <span class="identifier">U</span> <span class="identifier">init_value</span><span class="special">);</span>
+
+<span class="keyword">template</span> <span class="special">&lt;</span><span class="keyword">class</span> <span class="identifier">Functor</span><span class="special">,</span> <span class="keyword">class</span> <span class="identifier">U</span><span class="special">&gt;</span>
+<span class="keyword">typename</span> <span class="identifier">Functor</span><span class="special">::</span><span class="identifier">result_type</span> <span class="identifier">sum_series</span><span class="special">(</span><span class="identifier">Functor</span><span class="special">&amp;</span> <span class="identifier">func</span><span class="special">,</span> <span class="keyword">int</span> <span class="identifier">bits</span><span class="special">,</span> <span class="identifier">boost</span><span class="special">::</span><span class="identifier">uintmax_t</span><span class="special">&amp;</span> <span class="identifier">max_terms</span><span class="special">,</span> <span class="identifier">U</span> <span class="identifier">init_value</span><span class="special">);</span>
+
+<span class="keyword">template</span> <span class="special">&lt;</span><span class="keyword">class</span> <span class="identifier">Functor</span><span class="special">&gt;</span>
+<span class="keyword">typename</span> <span class="identifier">Functor</span><span class="special">::</span><span class="identifier">result_type</span> <span class="identifier">kahan_sum_series</span><span class="special">(</span><span class="identifier">Functor</span><span class="special">&amp;</span> <span class="identifier">func</span><span class="special">,</span> <span class="keyword">int</span> <span class="identifier">bits</span><span class="special">);</span>
+
+<span class="keyword">template</span> <span class="special">&lt;</span><span class="keyword">class</span> <span class="identifier">Functor</span><span class="special">&gt;</span>
+<span class="keyword">typename</span> <span class="identifier">Functor</span><span class="special">::</span><span class="identifier">result_type</span> <span class="identifier">kahan_sum_series</span><span class="special">(</span><span class="identifier">Functor</span><span class="special">&amp;</span> <span class="identifier">func</span><span class="special">,</span> <span class="keyword">int</span> <span class="identifier">bits</span><span class="special">,</span> <span class="identifier">boost</span><span class="special">::</span><span class="identifier">uintmax_t</span><span class="special">&amp;</span> <span class="identifier">max_terms</span><span class="special">);</span>
+
+<span class="special">}}}</span> <span class="comment">// namespaces
+</span></pre>
+<a name="math_toolkit.toolkit.internals1.series_evaluation.description"></a><h5>
+<a name="id823963"></a>
+          <a class="link" href="series_evaluation.html#math_toolkit.toolkit.internals1.series_evaluation.description">Description</a>
+        </h5>
+<p>
+          These algorithms are intended for the <a href="http://en.wikipedia.org/wiki/Series_%28mathematics%29" target="_top">summation
+          of infinite series</a>.
+        </p>
+<p>
+          Each of the algorithms takes a nullary-function object as the first argument:
+          the function object will be repeatedly invoked to pull successive terms
+          from the series being summed.
+        </p>
+<p>
+          The second argument is the number of binary bits of precision required,
+          summation will stop when the next term is too small to have any effect
+          on the first <span class="emphasis"><em>bits</em></span> bits of the result.
+        </p>
+<p>
+          The optional third argument <span class="emphasis"><em>max_terms</em></span> sets an upper
+          limit on the number of terms of the series to evaluate. In addition, on
+          exit the function will set <span class="emphasis"><em>max_terms</em></span> to the actual
+          number of terms of the series that were evaluated: this is particularly
+          useful for profiling the convergence properties of a new series.
+        </p>
+<p>
+          The final optional argument <span class="emphasis"><em>init_value</em></span> is the initial
+          value of the sum to which the terms of the series should be added. This
+          is useful in two situations:
+        </p>
+<div class="itemizedlist"><ul type="disc">
+<li>
+            Where the first value of the series has a different formula to successive
+            terms. In this case the first value in the series can be passed as the
+            last argument and the logic of the function object can then be simplified
+            to return subsequent terms.
+          </li>
+<li>
+            Where the series is being added (or subtracted) from some other value:
+            termination of the series will likely occur much more rapidly if that
+            other value is passed as the last argument. For example, there are several
+            functions that can be expressed as <span class="emphasis"><em>1 - S(z)</em></span> where
+            S(z) is an infinite series. In this case, pass -1 as the last argument
+            and then negate the result of the summation to get the result of <span class="emphasis"><em>1
+            - S(z)</em></span>.
+          </li>
+</ul></div>
+<p>
+          The two <span class="emphasis"><em>kahan_sum_series</em></span> variants of these algorithms
+          maintain a carry term that corrects for roundoff error during summation.
+          They are inspired by the <a href="http://en.wikipedia.org/wiki/Kahan_Summation_Algorithm" target="_top"><span class="emphasis"><em>Kahan
+          Summation Formula</em></span></a> that appears in <a href="http://docs.sun.com/source/806-3568/ncg_goldberg.html" target="_top">What
+          Every Computer Scientist Should Know About Floating-Point Arithmetic</a>.
+          However, it should be pointed out that there are very few series that require
+          summation in this way.
+        </p>
+<a name="math_toolkit.toolkit.internals1.series_evaluation.example"></a><h5>
+<a name="id824124"></a>
+          <a class="link" href="series_evaluation.html#math_toolkit.toolkit.internals1.series_evaluation.example">Example</a>
+        </h5>
+<p>
+          Let's suppose we want to implement <span class="emphasis"><em>log(1+x)</em></span> via its
+          infinite series,
+        </p>
+<p>
+          <span class="inlinemediaobject"><img src="../../../../equations/log1pseries.png"></span>
+        </p>
+<p>
+          We begin by writing a small function object to return successive terms
+          of the series:
+        </p>
+<pre class="programlisting"><span class="keyword">template</span> <span class="special">&lt;</span><span class="keyword">class</span> <span class="identifier">T</span><span class="special">&gt;</span>
+<span class="keyword">struct</span> <span class="identifier">log1p_series</span>
+<span class="special">{</span>
+   <span class="comment">// we must define a result_type typedef:
+</span>   <span class="keyword">typedef</span> <span class="identifier">T</span> <span class="identifier">result_type</span><span class="special">;</span>
+
+   <span class="identifier">log1p_series</span><span class="special">(</span><span class="identifier">T</span> <span class="identifier">x</span><span class="special">)</span>
+      <span class="special">:</span> <span class="identifier">k</span><span class="special">(</span><span class="number">0</span><span class="special">),</span> <span class="identifier">m_mult</span><span class="special">(-</span><span class="identifier">x</span><span class="special">),</span> <span class="identifier">m_prod</span><span class="special">(-</span><span class="number">1</span><span class="special">){}</span>
+
+   <span class="identifier">T</span> <span class="keyword">operator</span><span class="special">()()</span>
+   <span class="special">{</span>
+      <span class="comment">// This is the function operator invoked by the summation
+</span>      <span class="comment">// algorithm, the first call to this operator should return
+</span>      <span class="comment">// the first term of the series, the second call the second 
+</span>      <span class="comment">// term and so on.
+</span>      <span class="identifier">m_prod</span> <span class="special">*=</span> <span class="identifier">m_mult</span><span class="special">;</span>
+      <span class="keyword">return</span> <span class="identifier">m_prod</span> <span class="special">/</span> <span class="special">++</span><span class="identifier">k</span><span class="special">;</span> 
+   <span class="special">}</span>
+
+<span class="keyword">private</span><span class="special">:</span>
+   <span class="keyword">int</span> <span class="identifier">k</span><span class="special">;</span>
+   <span class="keyword">const</span> <span class="identifier">T</span> <span class="identifier">m_mult</span><span class="special">;</span>
+   <span class="identifier">T</span> <span class="identifier">m_prod</span><span class="special">;</span>
+<span class="special">};</span>
+</pre>
+<p>
+          Implementing log(1+x) is now fairly trivial:
+        </p>
+<pre class="programlisting"><span class="keyword">template</span> <span class="special">&lt;</span><span class="keyword">class</span> <span class="identifier">T</span><span class="special">&gt;</span>
+<span class="identifier">T</span> <span class="identifier">log1p</span><span class="special">(</span><span class="identifier">T</span> <span class="identifier">x</span><span class="special">)</span>
+<span class="special">{</span>
+   <span class="comment">// We really should add some error checking on x here!
+</span>   <span class="identifier">assert</span><span class="special">(</span><span class="identifier">std</span><span class="special">::</span><span class="identifier">fabs</span><span class="special">(</span><span class="identifier">x</span><span class="special">)</span> <span class="special">&lt;</span> <span class="number">1</span><span class="special">);</span>
+   
+   <span class="comment">// construct the series functor:
+</span>   <span class="identifier">log1p_series</span><span class="special">&lt;</span><span class="identifier">T</span><span class="special">&gt;</span> <span class="identifier">s</span><span class="special">(</span><span class="identifier">x</span><span class="special">);</span>
+   <span class="comment">// and add it up, with enough digits for full machine precision
+</span>   <span class="comment">// plus a couple more for luck.... !
+</span>   <span class="keyword">return</span> <span class="identifier">tools</span><span class="special">::</span><span class="identifier">sum_series</span><span class="special">(</span><span class="identifier">s</span><span class="special">,</span> <span class="identifier">tools</span><span class="special">::</span><span class="identifier">digits</span><span class="special">(</span><span class="identifier">x</span><span class="special">)</span> <span class="special">+</span> <span class="number">2</span><span class="special">);</span>
+<span class="special">}</span>
+</pre>
+</div>
+<table xmlns:rev="http://www.cs.rpi.edu/~gregod/boost/tools/doc/revision" width="100%"><tr>
+<td align="left"></td>
+<td align="right"><div class="copyright-footer">Copyright © 2006 , 2007, 2008 John Maddock, Paul A. Bristow, Hubert
+      Holin, Xiaogang Zhang, Bruno Lalande and Gautam Sewani<p>
+        Distributed under the Boost Software License, Version 1.0. (See accompanying
+        file LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_0.txt)
+      </p>
+</div></td>
+</tr></table>
+<hr>
+<div class="spirit-nav">
+<a accesskey="p" href="constants.html"><img src="../../../../../doc/html/images/prev.png" alt="Prev"></a><a accesskey="u" href="../internals1.html"><img src="../../../../../doc/html/images/up.png" alt="Up"></a><a accesskey="h" href="../../../index.html"><img src="../../../../../doc/html/images/home.png" alt="Home"></a><a accesskey="n" href="cf.html"><img src="../../../../../doc/html/images/next.png" alt="Next"></a>
+</div>
+</body>
+</html>

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@@ -0,0 +1,53 @@
+<html>
+<head>
+<meta http-equiv="Content-Type" content="text/html; charset=ISO-8859-1">
+<title>Testing and Development</title>
+<link rel="stylesheet" href="../../boostbook.css" type="text/css">
+<meta name="generator" content="DocBook XSL Stylesheets Vsnapshot_8125">
+<link rel="home" href="../../index.html" title="Math Toolkit">
+<link rel="up" href="../toolkit.html" title="Internal Details and Tools (Experimental)">
+<link rel="prev" href="internals1/minima.html" title="Locating Function Minima">
+<link rel="next" href="internals2/polynomials.html" title="Polynomials">
+</head>
+<body bgcolor="white" text="black" link="#0000FF" vlink="#840084" alink="#0000FF">
+<table cellpadding="2" width="100%"><tr>
+<td valign="top"><img alt="Boost C++ Libraries" width="277" height="86" src="../../../../boost.png"></td>
+<td align="center">Home</td>
+<td align="center">Libraries</td>
+<td align="center">People</td>
+<td align="center">FAQ</td>
+<td align="center">More</td>
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+<a accesskey="p" href="internals1/minima.html"><img src="../../../../doc/html/images/prev.png" alt="Prev"></a><a accesskey="u" href="../toolkit.html"><img src="../../../../doc/html/images/up.png" alt="Up"></a><a accesskey="h" href="../../index.html"><img src="../../../../doc/html/images/home.png" alt="Home"></a><a accesskey="n" href="internals2/polynomials.html"><img src="../../../../doc/html/images/next.png" alt="Next"></a>
+</div>
+<div class="section" lang="en">
+<div class="titlepage"><div><div><h3 class="title">
+<a name="math_toolkit.toolkit.internals2"></a><a class="link" href="internals2.html" title="Testing and Development"> Testing and Development</a>
+</h3></div></div></div>
+<div class="toc"><dl>
+<dt><span class="section"> Polynomials</span></dt>
+<dt><span class="section"><a href="internals2/minimax.html"> Minimax Approximations
+        and the Remez Algorithm</a></span></dt>
+<dt><span class="section"><a href="internals2/error_test.html"> Relative
+        Error and Testing</a></span></dt>
+<dt><span class="section"><a href="internals2/test_data.html"> Graphing,
+        Profiling, and Generating Test Data for Special Functions</a></span></dt>
+</dl></div>
+</div>
+<table xmlns:rev="http://www.cs.rpi.edu/~gregod/boost/tools/doc/revision" width="100%"><tr>
+<td align="left"></td>
+<td align="right"><div class="copyright-footer">Copyright © 2006 , 2007, 2008 John Maddock, Paul A. Bristow, Hubert
+      Holin, Xiaogang Zhang, Bruno Lalande and Gautam Sewani<p>
+        Distributed under the Boost Software License, Version 1.0. (See accompanying
+        file LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_0.txt)
+      </p>
+</div></td>
+</tr></table>
+<hr>
+<div class="spirit-nav">
+<a accesskey="p" href="internals1/minima.html"><img src="../../../../doc/html/images/prev.png" alt="Prev"></a><a accesskey="u" href="../toolkit.html"><img src="../../../../doc/html/images/up.png" alt="Up"></a><a accesskey="h" href="../../index.html"><img src="../../../../doc/html/images/home.png" alt="Home"></a><a accesskey="n" href="internals2/polynomials.html"><img src="../../../../doc/html/images/next.png" alt="Next"></a>
+</div>
+</body>
+</html>

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@@ -0,0 +1,235 @@
+<html>
+<head>
+<meta http-equiv="Content-Type" content="text/html; charset=ISO-8859-1">
+<title>Relative Error and Testing</title>
+<link rel="stylesheet" href="../../../boostbook.css" type="text/css">
+<meta name="generator" content="DocBook XSL Stylesheets Vsnapshot_8125">
+<link rel="home" href="../../../index.html" title="Math Toolkit">
+<link rel="up" href="../internals2.html" title="Testing and Development">
+<link rel="prev" href="minimax.html" title="Minimax Approximations and the Remez Algorithm">
+<link rel="next" href="test_data.html" title="Graphing, Profiling, and Generating Test Data for Special Functions">
+</head>
+<body bgcolor="white" text="black" link="#0000FF" vlink="#840084" alink="#0000FF">
+<table cellpadding="2" width="100%"><tr>
+<td valign="top"><img alt="Boost C++ Libraries" width="277" height="86" src="../../../../../boost.png"></td>
+<td align="center">Home</td>
+<td align="center">Libraries</td>
+<td align="center">People</td>
+<td align="center">FAQ</td>
+<td align="center">More</td>
+</tr></table>
+<hr>
+<div class="spirit-nav">
+<a accesskey="p" href="minimax.html"><img src="../../../../../doc/html/images/prev.png" alt="Prev"></a><a accesskey="u" href="../internals2.html"><img src="../../../../../doc/html/images/up.png" alt="Up"></a><a accesskey="h" href="../../../index.html"><img src="../../../../../doc/html/images/home.png" alt="Home"></a><a accesskey="n" href="test_data.html"><img src="../../../../../doc/html/images/next.png" alt="Next"></a>
+</div>
+<div class="section" lang="en">
+<div class="titlepage"><div><div><h4 class="title">
+<a name="math_toolkit.toolkit.internals2.error_test"></a><a class="link" href="error_test.html" title="Relative Error and Testing"> Relative
+        Error and Testing</a>
+</h4></div></div></div>
+<a name="math_toolkit.toolkit.internals2.error_test.synopsis"></a><h5>
+<a name="id847822"></a>
+          <a class="link" href="error_test.html#math_toolkit.toolkit.internals2.error_test.synopsis">Synopsis</a>
+        </h5>
+<p>
+          
+</p>
+<pre class="programlisting"><span class="preprocessor">#include</span> <span class="special">&lt;</span><span class="identifier">boost</span><span class="special">/</span><span class="identifier">math</span><span class="special">/</span><span class="identifier">tools</span><span class="special">/</span><span class="identifier">test</span><span class="special">.</span><span class="identifier">hpp</span><span class="special">&gt;</span>
+</pre>
+<p>
+        </p>
+<pre class="programlisting"><span class="keyword">template</span> <span class="special">&lt;</span><span class="keyword">class</span> <span class="identifier">T</span><span class="special">&gt;</span>
+<span class="identifier">T</span> <span class="identifier">relative_error</span><span class="special">(</span><span class="identifier">T</span> <span class="identifier">a</span><span class="special">,</span> <span class="identifier">T</span> <span class="identifier">b</span><span class="special">);</span>
+
+<span class="keyword">template</span> <span class="special">&lt;</span><span class="keyword">class</span> <span class="identifier">A</span><span class="special">,</span> <span class="keyword">class</span> <span class="identifier">F1</span><span class="special">,</span> <span class="keyword">class</span> <span class="identifier">F2</span><span class="special">&gt;</span>
+<span class="identifier">test_result</span><span class="special">&lt;</span><span class="identifier">see</span><span class="special">-</span><span class="identifier">below</span><span class="special">&gt;</span> <span class="identifier">test</span><span class="special">(</span><span class="keyword">const</span> <span class="identifier">A</span><span class="special">&amp;</span> <span class="identifier">a</span><span class="special">,</span> <span class="identifier">F1</span> <span class="identifier">test_func</span><span class="special">,</span> <span class="identifier">F2</span> <span class="identifier">expect_func</span><span class="special">);</span>
+</pre>
+<a name="math_toolkit.toolkit.internals2.error_test.description"></a><h5>
+<a name="id848175"></a>
+          <a class="link" href="error_test.html#math_toolkit.toolkit.internals2.error_test.description">Description</a>
+        </h5>
+<pre class="programlisting"><span class="keyword">template</span> <span class="special">&lt;</span><span class="keyword">class</span> <span class="identifier">T</span><span class="special">&gt;</span>
+<span class="identifier">T</span> <span class="identifier">relative_error</span><span class="special">(</span><span class="identifier">T</span> <span class="identifier">a</span><span class="special">,</span> <span class="identifier">T</span> <span class="identifier">v</span><span class="special">);</span>
+</pre>
+<p>
+          Returns the relative error between <span class="emphasis"><em>a</em></span> and <span class="emphasis"><em>v</em></span>
+          using the usual formula:
+        </p>
+<p>
+          <span class="inlinemediaobject"><img src="../../../../equations/error1.png"></span>
+        </p>
+<p>
+          In addition the value returned is zero if:
+        </p>
+<div class="itemizedlist"><ul type="disc">
+<li>
+            Both <span class="emphasis"><em>a</em></span> and <span class="emphasis"><em>v</em></span> are infinite.
+          </li>
+<li>
+            Both <span class="emphasis"><em>a</em></span> and <span class="emphasis"><em>v</em></span> are denormalised
+            numbers or zero.
+          </li>
+</ul></div>
+<p>
+          Otherwise if only one of <span class="emphasis"><em>a</em></span> and <span class="emphasis"><em>v</em></span>
+          is zero then the value returned is 1.
+        </p>
+<pre class="programlisting"><span class="keyword">template</span> <span class="special">&lt;</span><span class="keyword">class</span> <span class="identifier">A</span><span class="special">,</span> <span class="keyword">class</span> <span class="identifier">F1</span><span class="special">,</span> <span class="keyword">class</span> <span class="identifier">F2</span><span class="special">&gt;</span>
+<span class="identifier">test_result</span><span class="special">&lt;</span><span class="identifier">see</span><span class="special">-</span><span class="identifier">below</span><span class="special">&gt;</span> <span class="identifier">test</span><span class="special">(</span><span class="keyword">const</span> <span class="identifier">A</span><span class="special">&amp;</span> <span class="identifier">a</span><span class="special">,</span> <span class="identifier">F1</span> <span class="identifier">test_func</span><span class="special">,</span> <span class="identifier">F2</span> <span class="identifier">expect_func</span><span class="special">);</span>
+</pre>
+<p>
+          This function is used for testing a function against tabulated test data.
+        </p>
+<p>
+          The return type contains statistical data on the relative errors (max,
+          mean, variance, and the number of test cases etc), as well as the row of
+          test data that caused the largest relative error. Public members of type
+          test_result are:
+        </p>
+<div class="variablelist">
+<p class="title"><b></b></p>
+<dl>
+<dt><span class="term"><code class="computeroutput"><span class="keyword">unsigned</span>
+          <span class="identifier">worst</span><span class="special">()</span><span class="keyword">const</span><span class="special">;</span></code></span></dt>
+<dd><p>
+              Returns the row at which the worst error occurred.
+            </p></dd>
+<dt><span class="term"><code class="computeroutput"><span class="identifier">T</span>
+          <span class="identifier">min</span><span class="special">()</span><span class="keyword">const</span><span class="special">;</span></code></span></dt>
+<dd><p>
+              Returns the smallest relative error found.
+            </p></dd>
+<dt><span class="term"><code class="computeroutput"><span class="identifier">T</span>
+          <span class="identifier">max</span><span class="special">()</span><span class="keyword">const</span><span class="special">;</span></code></span></dt>
+<dd><p>
+              Returns the largest relative error found.
+            </p></dd>
+<dt><span class="term"><code class="computeroutput"><span class="identifier">T</span>
+          <span class="identifier">mean</span><span class="special">()</span><span class="keyword">const</span><span class="special">;</span></code></span></dt>
+<dd><p>
+              Returns the mean error found.
+            </p></dd>
+<dt><span class="term"><code class="computeroutput"><span class="identifier">boost</span><span class="special">::</span><span class="identifier">uintmax_t</span>
+          <span class="identifier">count</span><span class="special">()</span><span class="keyword">const</span><span class="special">;</span></code></span></dt>
+<dd><p>
+              Returns the number of test cases.
+            </p></dd>
+<dt><span class="term"><code class="computeroutput"><span class="identifier">T</span>
+          <span class="identifier">variance</span><span class="special">()</span><span class="keyword">const</span><span class="special">;</span></code></span></dt>
+<dd><p>
+              Returns the variance of the errors found.
+            </p></dd>
+<dt><span class="term"><code class="computeroutput"><span class="identifier">T</span>
+          <span class="identifier">variance1</span><span class="special">()</span><span class="keyword">const</span><span class="special">;</span></code></span></dt>
+<dd><p>
+              Returns the unbiased variance of the errors found.
+            </p></dd>
+<dt><span class="term"><code class="computeroutput"><span class="identifier">T</span>
+          <span class="identifier">rms</span><span class="special">()</span><span class="keyword">const</span></code></span></dt>
+<dd><p>
+              Returns the Root Mean Square, or quadratic mean of the errors.
+            </p></dd>
+<dt><span class="term"><code class="computeroutput"><span class="identifier">test_result</span><span class="special">&amp;</span> <span class="keyword">operator</span><span class="special">+=(</span><span class="keyword">const</span> <span class="identifier">test_result</span><span class="special">&amp;</span>
+          <span class="identifier">t</span><span class="special">)</span></code></span></dt>
+<dd><p>
+              Combines two test_result's into a single result.
+            </p></dd>
+</dl>
+</div>
+<p>
+          The template parameter of test_result, is the same type as the values in
+          the two dimensional array passed to function <span class="emphasis"><em>test</em></span>,
+          roughly that's <code class="computeroutput"><span class="identifier">A</span><span class="special">::</span><span class="identifier">value_type</span><span class="special">::</span><span class="identifier">value_type</span></code>.
+        </p>
+<p>
+          Parameter <span class="emphasis"><em>a</em></span> is a matrix of test data: and must be
+          a standard library Sequence type, that contains another Sequence type:
+          typically it will be a two dimensional instance of <code class="literal">boost::array</code>.
+          Each row of <span class="emphasis"><em>a</em></span> should contain all the parameters that
+          are passed to the function under test as well as the expected result.
+        </p>
+<p>
+          Parameter <span class="emphasis"><em>test_func</em></span> is the function under test, it
+          is invoked with each row of test data in <span class="emphasis"><em>a</em></span>. Typically
+          type F1 is created with Boost.Lambda: see the example below.
+        </p>
+<p>
+          Parameter <span class="emphasis"><em>expect_func</em></span> is a functor that extracts the
+          expected result from a row of test data in <span class="emphasis"><em>a</em></span>. Typically
+          type F2 is created with Boost.Lambda: see the example below.
+        </p>
+<p>
+          If the function under test returns a non-finite value when a finite result
+          is expected, or if a gross error is found, then a message is sent to <code class="computeroutput"><span class="identifier">std</span><span class="special">::</span><span class="identifier">cerr</span></code>, and a call to BOOST_ERROR() made
+          (which means that including this header requires you use Boost.Test). This
+          is mainly a debugging/development aid (and a good place for a breakpoint).
+        </p>
+<a name="math_toolkit.toolkit.internals2.error_test.example"></a><h5>
+<a name="id849159"></a>
+          <a class="link" href="error_test.html#math_toolkit.toolkit.internals2.error_test.example">Example</a>
+        </h5>
+<p>
+          Suppose we want to test the tgamma and lgamma functions, we can create
+          a two dimensional matrix of test data, each row is one test case, and contains
+          three elements: the input value, and the expected results for the tgamma
+          and lgamma functions respectively.
+        </p>
+<pre class="programlisting"><span class="keyword">static</span> <span class="keyword">const</span> <span class="identifier">boost</span><span class="special">::</span><span class="identifier">array</span><span class="special">&lt;</span><span class="identifier">boost</span><span class="special">::</span><span class="identifier">array</span><span class="special">&lt;</span><span class="identifier">TestType</span><span class="special">,</span> <span class="number">3</span><span class="special">&gt;,</span> <span class="identifier">NumberOfTests</span><span class="special">&gt;</span> 
+   <span class="identifier">factorials</span> <span class="special">=</span> <span class="special">{</span>
+      <span class="comment">/* big array of test data goes here */</span>
+   <span class="special">};</span>
+</pre>
+<p>
+          Now we can invoke the test function to test tgamma:
+        </p>
+<pre class="programlisting"><span class="keyword">using</span> <span class="keyword">namespace</span> <span class="identifier">boost</span><span class="special">::</span><span class="identifier">math</span><span class="special">::</span><span class="identifier">tools</span><span class="special">;</span>
+<span class="keyword">using</span> <span class="keyword">namespace</span> <span class="identifier">boost</span><span class="special">::</span><span class="identifier">lambda</span><span class="special">;</span>
+
+<span class="comment">// get a pointer to the function under test:
+</span><span class="identifier">TestType</span> <span class="special">(*</span><span class="identifier">funcp</span><span class="special">)(</span><span class="identifier">TestType</span><span class="special">)</span> <span class="special">=</span> <span class="identifier">boost</span><span class="special">::</span><span class="identifier">math</span><span class="special">::</span><span class="identifier">tgamma</span><span class="special">;</span>
+
+<span class="comment">// declare something to hold the result:
+</span><span class="identifier">test_result</span><span class="special">&lt;</span><span class="identifier">TestType</span><span class="special">&gt;</span> <span class="identifier">result</span><span class="special">;</span>
+<span class="comment">//
+</span><span class="comment">// and test tgamma against data:
+</span><span class="comment">//
+</span><span class="identifier">result</span> <span class="special">=</span> <span class="identifier">test</span><span class="special">(</span>
+   <span class="identifier">factorials</span><span class="special">,</span> 
+   <span class="identifier">bind</span><span class="special">(</span><span class="identifier">funcp</span><span class="special">,</span> <span class="identifier">ret</span><span class="special">&lt;</span><span class="identifier">TestType</span><span class="special">&gt;(</span><span class="identifier">_1</span><span class="special">[</span><span class="number">0</span><span class="special">])),</span> <span class="comment">// calls tgamma with factorials[row][0]
+</span>   <span class="identifier">ret</span><span class="special">&lt;</span><span class="identifier">TestType</span><span class="special">&gt;(</span><span class="identifier">_1</span><span class="special">[</span><span class="number">1</span><span class="special">])</span>               <span class="comment">// extracts the expected result from factorials[row][1]
+</span><span class="special">);</span>
+<span class="comment">//
+</span><span class="comment">// Print out some results:
+</span><span class="comment">//
+</span><span class="identifier">std</span><span class="special">::</span><span class="identifier">cout</span> <span class="special">&lt;&lt;</span> <span class="string">"The Mean was "</span> <span class="special">&lt;&lt;</span> <span class="identifier">result</span><span class="special">.</span><span class="identifier">mean</span><span class="special">()</span> <span class="special">&lt;&lt;</span> <span class="identifier">std</span><span class="special">::</span><span class="identifier">endl</span><span class="special">;</span>
+<span class="identifier">std</span><span class="special">::</span><span class="identifier">cout</span> <span class="special">&lt;&lt;</span> <span class="string">"The worst error was "</span> <span class="special">&lt;&lt;</span> <span class="special">(</span><span class="identifier">result</span><span class="special">.</span><span class="identifier">max</span><span class="special">)()</span> <span class="special">&lt;&lt;</span> <span class="identifier">std</span><span class="special">::</span><span class="identifier">endl</span><span class="special">;</span>
+<span class="identifier">std</span><span class="special">::</span><span class="identifier">cout</span> <span class="special">&lt;&lt;</span> <span class="string">"The worst error was at row "</span> <span class="special">&lt;&lt;</span> <span class="identifier">result</span><span class="special">.</span><span class="identifier">worst_case</span><span class="special">()</span> <span class="special">&lt;&lt;</span> <span class="identifier">std</span><span class="special">::</span><span class="identifier">endl</span><span class="special">;</span>
+<span class="comment">//
+</span><span class="comment">// same again with lgamma this time:
+</span><span class="comment">//
+</span><span class="identifier">funcp</span> <span class="special">=</span> <span class="identifier">boost</span><span class="special">::</span><span class="identifier">math</span><span class="special">::</span><span class="identifier">lgamma</span><span class="special">;</span>
+<span class="identifier">result</span> <span class="special">=</span> <span class="identifier">test</span><span class="special">(</span>
+   <span class="identifier">factorials</span><span class="special">,</span> 
+   <span class="identifier">bind</span><span class="special">(</span><span class="identifier">funcp</span><span class="special">,</span> <span class="identifier">ret</span><span class="special">&lt;</span><span class="identifier">TestType</span><span class="special">&gt;(</span><span class="identifier">_1</span><span class="special">[</span><span class="number">0</span><span class="special">])),</span> <span class="comment">// calls tgamma with factorials[row][0]
+</span>   <span class="identifier">ret</span><span class="special">&lt;</span><span class="identifier">TestType</span><span class="special">&gt;(</span><span class="identifier">_1</span><span class="special">[</span><span class="number">2</span><span class="special">])</span>               <span class="comment">// extracts the expected result from factorials[row][2]
+</span><span class="special">);</span>
+<span class="comment">//
+</span><span class="comment">// etc ...
+</span><span class="comment">//
+</span></pre>
+</div>
+<table xmlns:rev="http://www.cs.rpi.edu/~gregod/boost/tools/doc/revision" width="100%"><tr>
+<td align="left"></td>
+<td align="right"><div class="copyright-footer">Copyright © 2006 , 2007, 2008 John Maddock, Paul A. Bristow, Hubert
+      Holin, Xiaogang Zhang, Bruno Lalande and Gautam Sewani<p>
+        Distributed under the Boost Software License, Version 1.0. (See accompanying
+        file LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_0.txt)
+      </p>
+</div></td>
+</tr></table>
+<hr>
+<div class="spirit-nav">
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+</div>
+</body>
+</html>

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@@ -0,0 +1,282 @@
+<html>
+<head>
+<meta http-equiv="Content-Type" content="text/html; charset=ISO-8859-1">
+<title>Minimax Approximations and the Remez Algorithm</title>
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+</div>
+<div class="section" lang="en">
+<div class="titlepage"><div><div><h4 class="title">
+<a name="math_toolkit.toolkit.internals2.minimax"></a><a class="link" href="minimax.html" title="Minimax Approximations and the Remez Algorithm"> Minimax Approximations
+        and the Remez Algorithm</a>
+</h4></div></div></div>
+<p>
+          The directory libs/math/minimax contains a command line driven program
+          for the generation of minimax approximations using the Remez algorithm.
+          Both polynomial and rational approximations are supported, although the
+          latter are tricky to converge: it is not uncommon for convergence of rational
+          forms to fail. No such limitations are present for polynomial approximations
+          which should always converge smoothly.
+        </p>
+<p>
+          It's worth stressing that developing rational approximations to functions
+          is often not an easy task, and one to which many books have been devoted.
+          To use this tool, you will need to have a reasonable grasp of what the
+          Remez algorithm is, and the general form of the approximation you want
+          to achieve.
+        </p>
+<p>
+          Unless you already familar with the Remez method you should first read
+          the <a class="link" href="../../backgrounders/remez.html" title="The Remez Method">brief background article
+          explaining the principals behind the Remez algorithm</a>.
+        </p>
+<p>
+          The program consists of two parts:
+        </p>
+<div class="variablelist">
+<p class="title"><b></b></p>
+<dl>
+<dt><span class="term">main.cpp</span></dt>
+<dd><p>
+              Contains the command line parser, and all the calls to the Remez code.
+            </p></dd>
+<dt><span class="term">f.cpp</span></dt>
+<dd><p>
+              Contains the function to approximate.
+            </p></dd>
+</dl>
+</div>
+<p>
+          Therefore to use this tool, you must modify f.cpp to return the function
+          to approximate. The tools supports multiple function approximations within
+          the same compiled program: each as a separate variant:
+        </p>
+<pre class="programlisting"><span class="identifier">NTL</span><span class="special">::</span><span class="identifier">RR</span> <span class="identifier">f</span><span class="special">(</span><span class="keyword">const</span> <span class="identifier">NTL</span><span class="special">::</span><span class="identifier">RR</span><span class="special">&amp;</span> <span class="identifier">x</span><span class="special">,</span> <span class="keyword">int</span> <span class="identifier">variant</span><span class="special">);</span>
+</pre>
+<p>
+          Returns the value of the function <span class="emphasis"><em>variant</em></span> at point
+          <span class="emphasis"><em>x</em></span>. So if you wish you can just add the function to
+          approximate as a new variant after the existing examples.
+        </p>
+<p>
+          In addition to those two files, the program needs to be linked to a <a class="link" href="../../using_udt/use_ntl.html" title="Using With NTL - a High-Precision Floating-Point Library">patched NTL library to compile</a>.
+        </p>
+<p>
+          Note that the function <span class="emphasis"><em>f</em></span> must return the rational
+          part of the approximation: for example if you are approximating a function
+          <span class="emphasis"><em>f(x)</em></span> then it is quite common to use:
+        </p>
+<pre class="programlisting"><span class="identifier">f</span><span class="special">(</span><span class="identifier">x</span><span class="special">)</span> <span class="special">=</span> <span class="identifier">g</span><span class="special">(</span><span class="identifier">x</span><span class="special">)(</span><span class="identifier">Y</span> <span class="special">+</span> <span class="identifier">R</span><span class="special">(</span><span class="identifier">x</span><span class="special">))</span>
+</pre>
+<p>
+          where <span class="emphasis"><em>g(x)</em></span> is the dominant part of <span class="emphasis"><em>f(x)</em></span>,
+          <span class="emphasis"><em>Y</em></span> is some constant, and <span class="emphasis"><em>R(x)</em></span>
+          is the rational approximation part, usually optimised for a low absolute
+          error compared to |Y|.
+        </p>
+<p>
+          In this case you would define <span class="emphasis"><em>f</em></span> to return <span class="emphasis"><em>f(x)/g(x)</em></span>
+          and then set the y-offset of the approximation to <span class="emphasis"><em>Y</em></span>
+          (see command line options below).
+        </p>
+<p>
+          Many other forms are possible, but in all cases the objective is to split
+          <span class="emphasis"><em>f(x)</em></span> into a dominant part that you can evaluate easily
+          using standard math functions, and a smooth and slowly changing rational
+          approximation part. Refer to your favourite textbook for more examples.
+        </p>
+<p>
+          Command line options for the program are as follows:
+        </p>
+<div class="variablelist">
+<p class="title"><b></b></p>
+<dl>
+<dt><span class="term">variant N</span></dt>
+<dd><p>
+              Sets the current function variant to N. This allows multiple functions
+              that are to be approximated to be compiled into the same executable.
+              Defaults to 0.
+            </p></dd>
+<dt><span class="term">range a b</span></dt>
+<dd><p>
+              Sets the domain for the approximation to the range [a,b], defaults
+              to [0,1].
+            </p></dd>
+<dt><span class="term">relative</span></dt>
+<dd><p>
+              Sets the Remez code to optimise for relative error. This is the default
+              at program startup. Note that relative error can only be used if f(x)
+              has no roots over the range being optimised.
+            </p></dd>
+<dt><span class="term">absolute</span></dt>
+<dd><p>
+              Sets the Remez code to optimise for absolute error.
+            </p></dd>
+<dt><span class="term">pin [true|false]</span></dt>
+<dd><p>
+              "Pins" the code so that the rational approximation passes
+              through the origin. Obviously only set this to <span class="emphasis"><em>true</em></span>
+              if R(0) must be zero. This is typically used when trying to preserve
+              a root at [0,0] while also optimising for relative error.
+            </p></dd>
+<dt><span class="term">order N D</span></dt>
+<dd><p>
+              Sets the order of the approximation to <span class="emphasis"><em>N</em></span> in the
+              numerator and <span class="emphasis"><em>D</em></span> in the denominator. If <span class="emphasis"><em>D</em></span>
+              is zero then the result will be a polynomial approximation. There will
+              be N+D+2 coefficients in total, the first coefficient of the numerator
+              is zero if <span class="emphasis"><em>pin</em></span> was set to true, and the first
+              coefficient of the denominator is always one.
+            </p></dd>
+<dt><span class="term">working-precision N</span></dt>
+<dd><p>
+              Sets the working precision of NTL::RR to <span class="emphasis"><em>N</em></span> binary
+              digits. Defaults to 250.
+            </p></dd>
+<dt><span class="term">target-precision N</span></dt>
+<dd><p>
+              Sets the precision of printed output to <span class="emphasis"><em>N</em></span> binary
+              digits: set to the same number of digits as the type that will be used
+              to evaluate the approximation. Defaults to 53 (for double precision).
+            </p></dd>
+<dt><span class="term">skew val</span></dt>
+<dd><p>
+              "Skews" the initial interpolated control points towards one
+              end or the other of the range. Positive values skew the initial control
+              points towards the left hand side of the range, and negative values
+              towards the right hand side. If an approximation won't converge (a
+              common situation) try adjusting the skew parameter until the first
+              step yields the smallest possible error. <span class="emphasis"><em>val</em></span> should
+              be in the range [-100,+100], the default is zero.
+            </p></dd>
+<dt><span class="term">brake val</span></dt>
+<dd><p>
+              Sets a brake on each step so that the change in the control points
+              is braked by <span class="emphasis"><em>val%</em></span>. Defaults to 50, try a higher
+              value if an approximation won't converge, or a lower value to get speedier
+              convergence.
+            </p></dd>
+<dt><span class="term">x-offset val</span></dt>
+<dd><p>
+              Sets the x-offset to <span class="emphasis"><em>val</em></span>: the approximation will
+              be generated for <code class="computeroutput"><span class="identifier">f</span><span class="special">(</span><span class="identifier">S</span> <span class="special">*</span> <span class="special">(</span><span class="identifier">x</span> <span class="special">+</span> <span class="identifier">X</span><span class="special">))</span> <span class="special">+</span> <span class="identifier">Y</span></code>
+              where <span class="emphasis"><em>X</em></span> is the x-offset, <span class="emphasis"><em>S</em></span>
+              is the x-scale and <span class="emphasis"><em>Y</em></span> is the y-offset. Defaults
+              to zero. To avoid rounding errors, take care to specify a value that
+              can be exactly represented as a floating point number.
+            </p></dd>
+<dt><span class="term">x-scale val</span></dt>
+<dd><p>
+              Sets the x-scale to <span class="emphasis"><em>val</em></span>: the approximation will
+              be generated for <code class="computeroutput"><span class="identifier">f</span><span class="special">(</span><span class="identifier">S</span> <span class="special">*</span> <span class="special">(</span><span class="identifier">x</span> <span class="special">+</span> <span class="identifier">X</span><span class="special">))</span> <span class="special">+</span> <span class="identifier">Y</span></code>
+              where <span class="emphasis"><em>S</em></span> is the x-scale, <span class="emphasis"><em>X</em></span>
+              is the x-offset and <span class="emphasis"><em>Y</em></span> is the y-offset. Defaults
+              to one. To avoid rounding errors, take care to specify a value that
+              can be exactly represented as a floating point number.
+            </p></dd>
+<dt><span class="term">y-offset val</span></dt>
+<dd><p>
+              Sets the y-offset to <span class="emphasis"><em>val</em></span>: the approximation will
+              be generated for <code class="computeroutput"><span class="identifier">f</span><span class="special">(</span><span class="identifier">S</span> <span class="special">*</span> <span class="special">(</span><span class="identifier">x</span> <span class="special">+</span> <span class="identifier">X</span><span class="special">))</span> <span class="special">+</span> <span class="identifier">Y</span></code>
+              where <span class="emphasis"><em>X</em></span> is the x-offset, <span class="emphasis"><em>S</em></span>
+              is the x-scale and <span class="emphasis"><em>Y</em></span> is the y-offset. Defaults
+              to zero. To avoid rounding errors, take care to specify a value that
+              can be exactly represented as a floating point number.
+            </p></dd>
+<dt><span class="term">y-offset auto</span></dt>
+<dd><p>
+              Sets the y-offset to the average value of f(x) evaluated at the two
+              endpoints of the range plus the midpoint of the range. The calculated
+              value is deliberately truncated to <span class="emphasis"><em>float</em></span> precision
+              (and should be stored as a <span class="emphasis"><em>float</em></span> in your code).
+              The approximation will be generated for <code class="computeroutput"><span class="identifier">f</span><span class="special">(</span><span class="identifier">x</span> <span class="special">+</span> <span class="identifier">X</span><span class="special">)</span> <span class="special">+</span> <span class="identifier">Y</span></code> where <span class="emphasis"><em>X</em></span> is
+              the x-offset and <span class="emphasis"><em>Y</em></span> is the y-offset. Defaults to
+              zero.
+            </p></dd>
+<dt><span class="term">graph N</span></dt>
+<dd><p>
+              Prints N evaluations of f(x) at evenly spaced points over the range
+              being optimised. If unspecified then <span class="emphasis"><em>N</em></span> defaults
+              to 3. Use to check that f(x) is indeed smooth over the range of interest.
+            </p></dd>
+<dt><span class="term">step N</span></dt>
+<dd><p>
+              Performs <span class="emphasis"><em>N</em></span> steps, or one step if <span class="emphasis"><em>N</em></span>
+              is unspecified. After each step prints: the peek error at the extrema
+              of the error function of the approximation, the theoretical error term
+              solved for on the last step, and the maximum relative change in the
+              location of the Chebyshev control points. The approximation is converged
+              on the minimax solution when the two error terms are (approximately)
+              equal, and the change in the control points has decreased to a suitably
+              small value.
+            </p></dd>
+<dt><span class="term">test [float|double|long]</span></dt>
+<dd><p>
+              Tests the current approximation at float, double, or long double precision.
+              Useful to check for rounding errors in evaluating the approximation
+              at fixed precision. Tests are conducted at the extrema of the error
+              function of the approximation, and at the zeros of the error function.
+            </p></dd>
+<dt><span class="term">test [float|double|long] N</span></dt>
+<dd><p>
+              Tests the current approximation at float, double, or long double precision.
+              Useful to check for rounding errors in evaluating the approximation
+              at fixed precision. Tests are conducted at N evenly spaced points over
+              the range of the approximation. If none of [float|double|long] are
+              specified then tests using NTL::RR, this can be used to obtain the
+              error function of the approximation.
+            </p></dd>
+<dt><span class="term">rescale a b</span></dt>
+<dd><p>
+              Takes the current Chebeshev control points, and rescales them over
+              a new interval [a,b]. Sometimes this can be used to obtain starting
+              control points for an approximation that can not otherwise be converged.
+            </p></dd>
+<dt><span class="term">rotate</span></dt>
+<dd><p>
+              Moves one term from the numerator to the denominator, but keeps the
+              Chebyshev control points the same. Sometimes this can be used to obtain
+              starting control points for an approximation that can not otherwise
+              be converged.
+            </p></dd>
+<dt><span class="term">info</span></dt>
+<dd><p>
+              Prints out the current approximation: the location of the zeros of
+              the error function, the location of the Chebyshev control points, the
+              x and y offsets, and of course the coefficients of the polynomials.
+            </p></dd>
+</dl>
+</div>
+</div>
+<table xmlns:rev="http://www.cs.rpi.edu/~gregod/boost/tools/doc/revision" width="100%"><tr>
+<td align="left"></td>
+<td align="right"><div class="copyright-footer">Copyright © 2006 , 2007, 2008 John Maddock, Paul A. Bristow, Hubert
+      Holin, Xiaogang Zhang, Bruno Lalande and Gautam Sewani<p>
+        Distributed under the Boost Software License, Version 1.0. (See accompanying
+        file LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_0.txt)
+      </p>
+</div></td>
+</tr></table>
+<hr>
+<div class="spirit-nav">
+<a accesskey="p" href="polynomials.html"><img src="../../../../../doc/html/images/prev.png" alt="Prev"></a><a accesskey="u" href="../internals2.html"><img src="../../../../../doc/html/images/up.png" alt="Up"></a><a accesskey="h" href="../../../index.html"><img src="../../../../../doc/html/images/home.png" alt="Home"></a><a accesskey="n" href="error_test.html"><img src="../../../../../doc/html/images/next.png" alt="Next"></a>
+</div>
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+++ sandbox/tools/auto_index/example/math/doc/sf_and_dist/html/math_toolkit/toolkit/internals2/polynomials.html	2008-11-28 05:25:28 EST (Fri, 28 Nov 2008)
@@ -0,0 +1,137 @@
+<html>
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+<a name="math_toolkit.toolkit.internals2.polynomials"></a><a class="link" href="polynomials.html" title="Polynomials"> Polynomials</a>
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+          <a class="link" href="polynomials.html#math_toolkit.toolkit.internals2.polynomials.synopsis">Synopsis</a>
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+          
+</p>
+<pre class="programlisting"><span class="preprocessor">#include</span> <span class="special">&lt;</span><span class="identifier">boost</span><span class="special">/</span><span class="identifier">math</span><span class="special">/</span><span class="identifier">tools</span><span class="special">/</span><span class="identifier">polynomial</span><span class="special">.</span><span class="identifier">hpp</span><span class="special">&gt;</span>
+</pre>
+<p>
+        </p>
+<pre class="programlisting"><span class="keyword">namespace</span> <span class="identifier">boost</span><span class="special">{</span> <span class="keyword">namespace</span> <span class="identifier">math</span><span class="special">{</span> <span class="keyword">namespace</span> <span class="identifier">tools</span><span class="special">{</span>
+
+<span class="keyword">template</span> <span class="special">&lt;</span><span class="keyword">class</span> <span class="identifier">T</span><span class="special">&gt;</span>
+<span class="keyword">class</span> <span class="identifier">polynomial</span>
+<span class="special">{</span>
+<span class="keyword">public</span><span class="special">:</span>
+   <span class="comment">// typedefs:
+</span>   <span class="keyword">typedef</span> <span class="keyword">typename</span> <span class="identifier">std</span><span class="special">::</span><span class="identifier">vector</span><span class="special">&lt;</span><span class="identifier">T</span><span class="special">&gt;::</span><span class="identifier">value_type</span> <span class="identifier">value_type</span><span class="special">;</span>
+   <span class="keyword">typedef</span> <span class="keyword">typename</span> <span class="identifier">std</span><span class="special">::</span><span class="identifier">vector</span><span class="special">&lt;</span><span class="identifier">T</span><span class="special">&gt;::</span><span class="identifier">size_type</span>  <span class="identifier">size_type</span><span class="special">;</span>
+
+   <span class="comment">// construct:
+</span>   <span class="identifier">polynomial</span><span class="special">(){}</span>
+   <span class="keyword">template</span> <span class="special">&lt;</span><span class="keyword">class</span> <span class="identifier">U</span><span class="special">&gt;</span>
+   <span class="identifier">polynomial</span><span class="special">(</span><span class="keyword">const</span> <span class="identifier">U</span><span class="special">*</span> <span class="identifier">data</span><span class="special">,</span> <span class="keyword">unsigned</span> <span class="identifier">order</span><span class="special">);</span>
+   <span class="keyword">template</span> <span class="special">&lt;</span><span class="keyword">class</span> <span class="identifier">U</span><span class="special">&gt;</span>
+   <span class="identifier">polynomial</span><span class="special">(</span><span class="keyword">const</span> <span class="identifier">U</span><span class="special">&amp;</span> <span class="identifier">point</span><span class="special">);</span>
+   
+   <span class="comment">// access:
+</span>   <span class="identifier">size_type</span> <span class="identifier">size</span><span class="special">()</span><span class="keyword">const</span><span class="special">;</span>
+   <span class="identifier">size_type</span> <span class="identifier">degree</span><span class="special">()</span><span class="keyword">const</span><span class="special">;</span>
+   <span class="identifier">value_type</span><span class="special">&amp;</span> <span class="keyword">operator</span><span class="special">[](</span><span class="identifier">size_type</span> <span class="identifier">i</span><span class="special">);</span>
+   <span class="keyword">const</span> <span class="identifier">value_type</span><span class="special">&amp;</span> <span class="keyword">operator</span><span class="special">[](</span><span class="identifier">size_type</span> <span class="identifier">i</span><span class="special">)</span><span class="keyword">const</span><span class="special">;</span>
+
+   <span class="comment">// operators:
+</span>   <span class="keyword">template</span> <span class="special">&lt;</span><span class="keyword">class</span> <span class="identifier">U</span><span class="special">&gt;</span>
+   <span class="identifier">polynomial</span><span class="special">&amp;</span> <span class="keyword">operator</span> <span class="special">+=(</span><span class="keyword">const</span> <span class="identifier">U</span><span class="special">&amp;</span> <span class="identifier">value</span><span class="special">);</span>
+   <span class="keyword">template</span> <span class="special">&lt;</span><span class="keyword">class</span> <span class="identifier">U</span><span class="special">&gt;</span>
+   <span class="identifier">polynomial</span><span class="special">&amp;</span> <span class="keyword">operator</span> <span class="special">-=(</span><span class="keyword">const</span> <span class="identifier">U</span><span class="special">&amp;</span> <span class="identifier">value</span><span class="special">);</span>
+   <span class="keyword">template</span> <span class="special">&lt;</span><span class="keyword">class</span> <span class="identifier">U</span><span class="special">&gt;</span>
+   <span class="identifier">polynomial</span><span class="special">&amp;</span> <span class="keyword">operator</span> <span class="special">*=(</span><span class="keyword">const</span> <span class="identifier">U</span><span class="special">&amp;</span> <span class="identifier">value</span><span class="special">);</span>
+   <span class="keyword">template</span> <span class="special">&lt;</span><span class="keyword">class</span> <span class="identifier">U</span><span class="special">&gt;</span>
+   <span class="identifier">polynomial</span><span class="special">&amp;</span> <span class="keyword">operator</span> <span class="special">+=(</span><span class="keyword">const</span> <span class="identifier">polynomial</span><span class="special">&lt;</span><span class="identifier">U</span><span class="special">&gt;&amp;</span> <span class="identifier">value</span><span class="special">);</span>
+   <span class="keyword">template</span> <span class="special">&lt;</span><span class="keyword">class</span> <span class="identifier">U</span><span class="special">&gt;</span>
+   <span class="identifier">polynomial</span><span class="special">&amp;</span> <span class="keyword">operator</span> <span class="special">-=(</span><span class="keyword">const</span> <span class="identifier">polynomial</span><span class="special">&lt;</span><span class="identifier">U</span><span class="special">&gt;&amp;</span> <span class="identifier">value</span><span class="special">);</span>
+   <span class="keyword">template</span> <span class="special">&lt;</span><span class="keyword">class</span> <span class="identifier">U</span><span class="special">&gt;</span>
+   <span class="identifier">polynomial</span><span class="special">&amp;</span> <span class="keyword">operator</span> <span class="special">*=(</span><span class="keyword">const</span> <span class="identifier">polynomial</span><span class="special">&lt;</span><span class="identifier">U</span><span class="special">&gt;&amp;</span> <span class="identifier">value</span><span class="special">);</span>
+<span class="special">};</span>
+
+<span class="keyword">template</span> <span class="special">&lt;</span><span class="keyword">class</span> <span class="identifier">T</span><span class="special">&gt;</span>
+<span class="identifier">polynomial</span><span class="special">&lt;</span><span class="identifier">T</span><span class="special">&gt;</span> <span class="keyword">operator</span> <span class="special">+</span> <span class="special">(</span><span class="keyword">const</span> <span class="identifier">polynomial</span><span class="special">&lt;</span><span class="identifier">T</span><span class="special">&gt;&amp;</span> <span class="identifier">a</span><span class="special">,</span> <span class="keyword">const</span> <span class="identifier">polynomial</span><span class="special">&lt;</span><span class="identifier">T</span><span class="special">&gt;&amp;</span> <span class="identifier">b</span><span class="special">);</span>
+<span class="keyword">template</span> <span class="special">&lt;</span><span class="keyword">class</span> <span class="identifier">T</span><span class="special">&gt;</span>
+<span class="identifier">polynomial</span><span class="special">&lt;</span><span class="identifier">T</span><span class="special">&gt;</span> <span class="keyword">operator</span> <span class="special">-</span> <span class="special">(</span><span class="keyword">const</span> <span class="identifier">polynomial</span><span class="special">&lt;</span><span class="identifier">T</span><span class="special">&gt;&amp;</span> <span class="identifier">a</span><span class="special">,</span> <span class="keyword">const</span> <span class="identifier">polynomial</span><span class="special">&lt;</span><span class="identifier">T</span><span class="special">&gt;&amp;</span> <span class="identifier">b</span><span class="special">);</span>
+<span class="keyword">template</span> <span class="special">&lt;</span><span class="keyword">class</span> <span class="identifier">T</span><span class="special">&gt;</span>
+<span class="identifier">polynomial</span><span class="special">&lt;</span><span class="identifier">T</span><span class="special">&gt;</span> <span class="keyword">operator</span> <span class="special">*</span> <span class="special">(</span><span class="keyword">const</span> <span class="identifier">polynomial</span><span class="special">&lt;</span><span class="identifier">T</span><span class="special">&gt;&amp;</span> <span class="identifier">a</span><span class="special">,</span> <span class="keyword">const</span> <span class="identifier">polynomial</span><span class="special">&lt;</span><span class="identifier">T</span><span class="special">&gt;&amp;</span> <span class="identifier">b</span><span class="special">);</span>
+
+<span class="keyword">template</span> <span class="special">&lt;</span><span class="keyword">class</span> <span class="identifier">T</span><span class="special">,</span> <span class="keyword">class</span> <span class="identifier">U</span><span class="special">&gt;</span>
+<span class="identifier">polynomial</span><span class="special">&lt;</span><span class="identifier">T</span><span class="special">&gt;</span> <span class="keyword">operator</span> <span class="special">+</span> <span class="special">(</span><span class="keyword">const</span> <span class="identifier">polynomial</span><span class="special">&lt;</span><span class="identifier">T</span><span class="special">&gt;&amp;</span> <span class="identifier">a</span><span class="special">,</span> <span class="keyword">const</span> <span class="identifier">U</span><span class="special">&amp;</span> <span class="identifier">b</span><span class="special">);</span>
+<span class="keyword">template</span> <span class="special">&lt;</span><span class="keyword">class</span> <span class="identifier">T</span><span class="special">,</span> <span class="keyword">class</span> <span class="identifier">U</span><span class="special">&gt;</span>
+<span class="identifier">polynomial</span><span class="special">&lt;</span><span class="identifier">T</span><span class="special">&gt;</span> <span class="keyword">operator</span> <span class="special">-</span> <span class="special">(</span><span class="keyword">const</span> <span class="identifier">polynomial</span><span class="special">&lt;</span><span class="identifier">T</span><span class="special">&gt;&amp;</span> <span class="identifier">a</span><span class="special">,</span> <span class="keyword">const</span> <span class="identifier">U</span><span class="special">&amp;</span> <span class="identifier">b</span><span class="special">);</span>
+<span class="keyword">template</span> <span class="special">&lt;</span><span class="keyword">class</span> <span class="identifier">T</span><span class="special">,</span> <span class="keyword">class</span> <span class="identifier">U</span><span class="special">&gt;</span>
+<span class="identifier">polynomial</span><span class="special">&lt;</span><span class="identifier">T</span><span class="special">&gt;</span> <span class="keyword">operator</span> <span class="special">*</span> <span class="special">(</span><span class="keyword">const</span> <span class="identifier">polynomial</span><span class="special">&lt;</span><span class="identifier">T</span><span class="special">&gt;&amp;</span> <span class="identifier">a</span><span class="special">,</span> <span class="keyword">const</span> <span class="identifier">U</span><span class="special">&amp;</span> <span class="identifier">b</span><span class="special">);</span>
+
+<span class="keyword">template</span> <span class="special">&lt;</span><span class="keyword">class</span> <span class="identifier">U</span><span class="special">,</span> <span class="keyword">class</span> <span class="identifier">T</span><span class="special">&gt;</span>
+<span class="identifier">polynomial</span><span class="special">&lt;</span><span class="identifier">T</span><span class="special">&gt;</span> <span class="keyword">operator</span> <span class="special">+</span> <span class="special">(</span><span class="keyword">const</span> <span class="identifier">U</span><span class="special">&amp;</span> <span class="identifier">a</span><span class="special">,</span> <span class="keyword">const</span> <span class="identifier">polynomial</span><span class="special">&lt;</span><span class="identifier">T</span><span class="special">&gt;&amp;</span> <span class="identifier">b</span><span class="special">);</span>
+<span class="keyword">template</span> <span class="special">&lt;</span><span class="keyword">class</span> <span class="identifier">U</span><span class="special">,</span> <span class="keyword">class</span> <span class="identifier">T</span><span class="special">&gt;</span>
+<span class="identifier">polynomial</span><span class="special">&lt;</span><span class="identifier">T</span><span class="special">&gt;</span> <span class="keyword">operator</span> <span class="special">-</span> <span class="special">(</span><span class="keyword">const</span> <span class="identifier">U</span><span class="special">&amp;</span> <span class="identifier">a</span><span class="special">,</span> <span class="keyword">const</span> <span class="identifier">polynomial</span><span class="special">&lt;</span><span class="identifier">T</span><span class="special">&gt;&amp;</span> <span class="identifier">b</span><span class="special">);</span>
+<span class="keyword">template</span> <span class="special">&lt;</span><span class="keyword">class</span> <span class="identifier">U</span><span class="special">,</span> <span class="keyword">class</span> <span class="identifier">T</span><span class="special">&gt;</span>
+<span class="identifier">polynomial</span><span class="special">&lt;</span><span class="identifier">T</span><span class="special">&gt;</span> <span class="keyword">operator</span> <span class="special">*</span> <span class="special">(</span><span class="keyword">const</span> <span class="identifier">U</span><span class="special">&amp;</span> <span class="identifier">a</span><span class="special">,</span> <span class="keyword">const</span> <span class="identifier">polynomial</span><span class="special">&lt;</span><span class="identifier">T</span><span class="special">&gt;&amp;</span> <span class="identifier">b</span><span class="special">);</span>
+
+<span class="keyword">template</span> <span class="special">&lt;</span><span class="keyword">class</span> <span class="identifier">charT</span><span class="special">,</span> <span class="keyword">class</span> <span class="identifier">traits</span><span class="special">,</span> <span class="keyword">class</span> <span class="identifier">T</span><span class="special">&gt;</span>
+<span class="identifier">std</span><span class="special">::</span><span class="identifier">basic_ostream</span><span class="special">&lt;</span><span class="identifier">charT</span><span class="special">,</span> <span class="identifier">traits</span><span class="special">&gt;&amp;</span> <span class="keyword">operator</span> <span class="special">&lt;&lt;</span> 
+   <span class="special">(</span><span class="identifier">std</span><span class="special">::</span><span class="identifier">basic_ostream</span><span class="special">&lt;</span><span class="identifier">charT</span><span class="special">,</span> <span class="identifier">traits</span><span class="special">&gt;&amp;</span> <span class="identifier">os</span><span class="special">,</span> <span class="keyword">const</span> <span class="identifier">polynomial</span><span class="special">&lt;</span><span class="identifier">T</span><span class="special">&gt;&amp;</span> <span class="identifier">poly</span><span class="special">);</span>
+
+<span class="special">}}}</span> <span class="comment">// namespaces
+</span></pre>
+<a name="math_toolkit.toolkit.internals2.polynomials.description"></a><h5>
+<a name="id846499"></a>
+          <a class="link" href="polynomials.html#math_toolkit.toolkit.internals2.polynomials.description">Description</a>
+        </h5>
+<p>
+          This is a fairly trivial class for polynomial manipulation.
+        </p>
+<p>
+          Implementation is currently of the "naive" variety, with O(N^2)
+          multiplication for example. This class should not be used in high-performance
+          computing environments: it is intended for the simple manipulation of small
+          polynomials, typically generated for special function approximation.
+        </p>
+<p>
+          Advanced manipulations: the FFT, division, GCD, factorisation etc are not
+          currently provided. Submissions for these are of course welcome :-)
+        </p>
+</div>
+<table xmlns:rev="http://www.cs.rpi.edu/~gregod/boost/tools/doc/revision" width="100%"><tr>
+<td align="left"></td>
+<td align="right"><div class="copyright-footer">Copyright © 2006 , 2007, 2008 John Maddock, Paul A. Bristow, Hubert
+      Holin, Xiaogang Zhang, Bruno Lalande and Gautam Sewani<p>
+        Distributed under the Boost Software License, Version 1.0. (See accompanying
+        file LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_0.txt)
+      </p>
+</div></td>
+</tr></table>
+<hr>
+<div class="spirit-nav">
+<a accesskey="p" href="../internals2.html"><img src="../../../../../doc/html/images/prev.png" alt="Prev"></a><a accesskey="u" href="../internals2.html"><img src="../../../../../doc/html/images/up.png" alt="Up"></a><a accesskey="h" href="../../../index.html"><img src="../../../../../doc/html/images/home.png" alt="Home"></a><a accesskey="n" href="minimax.html"><img src="../../../../../doc/html/images/next.png" alt="Next"></a>
+</div>
+</body>
+</html>

Added: sandbox/tools/auto_index/example/math/doc/sf_and_dist/html/math_toolkit/toolkit/internals2/test_data.html
==============================================================================
--- (empty file)
+++ sandbox/tools/auto_index/example/math/doc/sf_and_dist/html/math_toolkit/toolkit/internals2/test_data.html	2008-11-28 05:25:28 EST (Fri, 28 Nov 2008)
@@ -0,0 +1,549 @@
+<html>
+<head>
+<meta http-equiv="Content-Type" content="text/html; charset=ISO-8859-1">
+<title>Graphing, Profiling, and Generating Test Data for Special Functions</title>
+<link rel="stylesheet" href="../../../boostbook.css" type="text/css">
+<meta name="generator" content="DocBook XSL Stylesheets Vsnapshot_8125">
+<link rel="home" href="../../../index.html" title="Math Toolkit">
+<link rel="up" href="../internals2.html" title="Testing and Development">
+<link rel="prev" href="error_test.html" title="Relative Error and Testing">
+<link rel="next" href="../../using_udt.html" title="Use with User-Defined Floating-Point Types">
+</head>
+<body bgcolor="white" text="black" link="#0000FF" vlink="#840084" alink="#0000FF">
+<table cellpadding="2" width="100%"><tr>
+<td valign="top"><img alt="Boost C++ Libraries" width="277" height="86" src="../../../../../boost.png"></td>
+<td align="center">Home</td>
+<td align="center">Libraries</td>
+<td align="center">People</td>
+<td align="center">FAQ</td>
+<td align="center">More</td>
+</tr></table>
+<hr>
+<div class="spirit-nav">
+<a accesskey="p" href="error_test.html"><img src="../../../../../doc/html/images/prev.png" alt="Prev"></a><a accesskey="u" href="../internals2.html"><img src="../../../../../doc/html/images/up.png" alt="Up"></a><a accesskey="h" href="../../../index.html"><img src="../../../../../doc/html/images/home.png" alt="Home"></a><a accesskey="n" href="../../using_udt.html"><img src="../../../../../doc/html/images/next.png" alt="Next"></a>
+</div>
+<div class="section" lang="en">
+<div class="titlepage"><div><div><h4 class="title">
+<a name="math_toolkit.toolkit.internals2.test_data"></a><a class="link" href="test_data.html" title="Graphing, Profiling, and Generating Test Data for Special Functions"> Graphing,
+        Profiling, and Generating Test Data for Special Functions</a>
+</h4></div></div></div>
+<p>
+          The class <code class="computeroutput"><span class="identifier">test_data</span></code> and
+          associated helper functions are designed so that in just a few lines of
+          code you should be able to:
+        </p>
+<div class="itemizedlist"><ul type="disc">
+<li>
+            Profile a continued fraction, or infinite series for convergence and
+            accuracy.
+          </li>
+<li>
+            Generate csv data from a special function that can be imported into your
+            favorite graphing program (or spreadsheet) for further analysis.
+          </li>
+<li>
+            Generate high precision test data.
+          </li>
+</ul></div>
+<a name="math_toolkit.toolkit.internals2.test_data.synopsis"></a><h5>
+<a name="id850270"></a>
+          <a class="link" href="test_data.html#math_toolkit.toolkit.internals2.test_data.synopsis">Synopsis</a>
+        </h5>
+<pre class="programlisting"><span class="keyword">namespace</span> <span class="identifier">boost</span><span class="special">{</span> <span class="keyword">namespace</span> <span class="identifier">math</span><span class="special">{</span> <span class="keyword">namespace</span> <span class="identifier">tools</span><span class="special">{</span>
+
+<span class="keyword">enum</span> <span class="identifier">parameter_type</span>
+<span class="special">{</span>
+   <span class="identifier">random_in_range</span> <span class="special">=</span> <span class="number">0</span><span class="special">,</span>
+   <span class="identifier">periodic_in_range</span> <span class="special">=</span> <span class="number">1</span><span class="special">,</span>
+   <span class="identifier">power_series</span> <span class="special">=</span> <span class="number">2</span><span class="special">,</span>
+   <span class="identifier">dummy_param</span> <span class="special">=</span> <span class="number">0x80</span><span class="special">,</span>
+<span class="special">};</span>
+
+<span class="keyword">template</span> <span class="special">&lt;</span><span class="keyword">class</span> <span class="identifier">T</span><span class="special">&gt;</span>
+<span class="keyword">struct</span> <span class="identifier">parameter_info</span><span class="special">;</span>
+
+<span class="keyword">template</span> <span class="special">&lt;</span><span class="keyword">class</span> <span class="identifier">T</span><span class="special">&gt;</span>
+<span class="identifier">parameter_info</span><span class="special">&lt;</span><span class="identifier">T</span><span class="special">&gt;</span> <span class="identifier">make_random_param</span><span class="special">(</span><span class="identifier">T</span> <span class="identifier">start_range</span><span class="special">,</span> <span class="identifier">T</span> <span class="identifier">end_range</span><span class="special">,</span> <span class="keyword">int</span> <span class="identifier">n_points</span><span class="special">);</span>
+
+<span class="keyword">template</span> <span class="special">&lt;</span><span class="keyword">class</span> <span class="identifier">T</span><span class="special">&gt;</span>
+<span class="identifier">parameter_info</span><span class="special">&lt;</span><span class="identifier">T</span><span class="special">&gt;</span> <span class="identifier">make_periodic_param</span><span class="special">(</span><span class="identifier">T</span> <span class="identifier">start_range</span><span class="special">,</span> <span class="identifier">T</span> <span class="identifier">end_range</span><span class="special">,</span> <span class="keyword">int</span> <span class="identifier">n_points</span><span class="special">);</span>
+
+<span class="keyword">template</span> <span class="special">&lt;</span><span class="keyword">class</span> <span class="identifier">T</span><span class="special">&gt;</span>
+<span class="identifier">parameter_info</span><span class="special">&lt;</span><span class="identifier">T</span><span class="special">&gt;</span> <span class="identifier">make_power_param</span><span class="special">(</span><span class="identifier">T</span> <span class="identifier">basis</span><span class="special">,</span> <span class="keyword">int</span> <span class="identifier">start_exponent</span><span class="special">,</span> <span class="keyword">int</span> <span class="identifier">end_exponent</span><span class="special">);</span>
+
+<span class="keyword">template</span> <span class="special">&lt;</span><span class="keyword">class</span> <span class="identifier">T</span><span class="special">&gt;</span>
+<span class="keyword">bool</span> <span class="identifier">get_user_parameter_info</span><span class="special">(</span><span class="identifier">parameter_info</span><span class="special">&lt;</span><span class="identifier">T</span><span class="special">&gt;&amp;</span> <span class="identifier">info</span><span class="special">,</span> <span class="keyword">const</span> <span class="keyword">char</span><span class="special">*</span> <span class="identifier">param_name</span><span class="special">);</span>
+
+<span class="keyword">template</span> <span class="special">&lt;</span><span class="keyword">class</span> <span class="identifier">T</span><span class="special">&gt;</span>
+<span class="keyword">class</span> <span class="identifier">test_data</span>
+<span class="special">{</span>
+<span class="keyword">public</span><span class="special">:</span>
+   <span class="keyword">typedef</span> <span class="identifier">std</span><span class="special">::</span><span class="identifier">vector</span><span class="special">&lt;</span><span class="identifier">T</span><span class="special">&gt;</span> <span class="identifier">row_type</span><span class="special">;</span>
+   <span class="keyword">typedef</span> <span class="identifier">row_type</span> <span class="identifier">value_type</span><span class="special">;</span>
+<span class="keyword">private</span><span class="special">:</span>
+   <span class="keyword">typedef</span> <span class="identifier">std</span><span class="special">::</span><span class="identifier">set</span><span class="special">&lt;</span><span class="identifier">row_type</span><span class="special">&gt;</span> <span class="identifier">container_type</span><span class="special">;</span>
+<span class="keyword">public</span><span class="special">:</span>
+   <span class="keyword">typedef</span> <span class="keyword">typename</span> <span class="identifier">container_type</span><span class="special">::</span><span class="identifier">reference</span> <span class="identifier">reference</span><span class="special">;</span>
+   <span class="keyword">typedef</span> <span class="keyword">typename</span> <span class="identifier">container_type</span><span class="special">::</span><span class="identifier">const_reference</span> <span class="identifier">const_reference</span><span class="special">;</span>
+   <span class="keyword">typedef</span> <span class="keyword">typename</span> <span class="identifier">container_type</span><span class="special">::</span><span class="identifier">iterator</span> <span class="identifier">iterator</span><span class="special">;</span>
+   <span class="keyword">typedef</span> <span class="keyword">typename</span> <span class="identifier">container_type</span><span class="special">::</span><span class="identifier">const_iterator</span> <span class="identifier">const_iterator</span><span class="special">;</span>
+   <span class="keyword">typedef</span> <span class="keyword">typename</span> <span class="identifier">container_type</span><span class="special">::</span><span class="identifier">difference_type</span> <span class="identifier">difference_type</span><span class="special">;</span>
+   <span class="keyword">typedef</span> <span class="keyword">typename</span> <span class="identifier">container_type</span><span class="special">::</span><span class="identifier">size_type</span> <span class="identifier">size_type</span><span class="special">;</span>
+
+   <span class="comment">// creation:
+</span>   <span class="identifier">test_data</span><span class="special">(){}</span>
+   <span class="keyword">template</span> <span class="special">&lt;</span><span class="keyword">class</span> <span class="identifier">F</span><span class="special">&gt;</span>
+   <span class="identifier">test_data</span><span class="special">(</span><span class="identifier">F</span> <span class="identifier">func</span><span class="special">,</span> <span class="keyword">const</span> <span class="identifier">parameter_info</span><span class="special">&lt;</span><span class="identifier">T</span><span class="special">&gt;&amp;</span> <span class="identifier">arg1</span><span class="special">);</span>
+
+   <span class="comment">// insertion:
+</span>   <span class="keyword">template</span> <span class="special">&lt;</span><span class="keyword">class</span> <span class="identifier">F</span><span class="special">&gt;</span>
+   <span class="identifier">test_data</span><span class="special">&amp;</span> <span class="identifier">insert</span><span class="special">(</span><span class="identifier">F</span> <span class="identifier">func</span><span class="special">,</span> <span class="keyword">const</span> <span class="identifier">parameter_info</span><span class="special">&lt;</span><span class="identifier">T</span><span class="special">&gt;&amp;</span> <span class="identifier">arg1</span><span class="special">);</span>
+
+   <span class="keyword">template</span> <span class="special">&lt;</span><span class="keyword">class</span> <span class="identifier">F</span><span class="special">&gt;</span>
+   <span class="identifier">test_data</span><span class="special">&amp;</span> <span class="identifier">insert</span><span class="special">(</span><span class="identifier">F</span> <span class="identifier">func</span><span class="special">,</span> <span class="keyword">const</span> <span class="identifier">parameter_info</span><span class="special">&lt;</span><span class="identifier">T</span><span class="special">&gt;&amp;</span> <span class="identifier">arg1</span><span class="special">,</span> 
+                     <span class="keyword">const</span> <span class="identifier">parameter_info</span><span class="special">&lt;</span><span class="identifier">T</span><span class="special">&gt;&amp;</span> <span class="identifier">arg2</span><span class="special">);</span>
+
+   <span class="keyword">template</span> <span class="special">&lt;</span><span class="keyword">class</span> <span class="identifier">F</span><span class="special">&gt;</span>
+   <span class="identifier">test_data</span><span class="special">&amp;</span> <span class="identifier">insert</span><span class="special">(</span><span class="identifier">F</span> <span class="identifier">func</span><span class="special">,</span> <span class="keyword">const</span> <span class="identifier">parameter_info</span><span class="special">&lt;</span><span class="identifier">T</span><span class="special">&gt;&amp;</span> <span class="identifier">arg1</span><span class="special">,</span> 
+                     <span class="keyword">const</span> <span class="identifier">parameter_info</span><span class="special">&lt;</span><span class="identifier">T</span><span class="special">&gt;&amp;</span> <span class="identifier">arg2</span><span class="special">,</span> 
+                     <span class="keyword">const</span> <span class="identifier">parameter_info</span><span class="special">&lt;</span><span class="identifier">T</span><span class="special">&gt;&amp;</span> <span class="identifier">arg3</span><span class="special">);</span>
+
+   <span class="keyword">void</span> <span class="identifier">clear</span><span class="special">();</span>
+
+   <span class="comment">// access:
+</span>   <span class="identifier">iterator</span> <span class="identifier">begin</span><span class="special">();</span>
+   <span class="identifier">iterator</span> <span class="identifier">end</span><span class="special">();</span>
+   <span class="identifier">const_iterator</span> <span class="identifier">begin</span><span class="special">()</span><span class="keyword">const</span><span class="special">;</span>
+   <span class="identifier">const_iterator</span> <span class="identifier">end</span><span class="special">()</span><span class="keyword">const</span><span class="special">;</span>
+   <span class="keyword">bool</span> <span class="keyword">operator</span><span class="special">==(</span><span class="keyword">const</span> <span class="identifier">test_data</span><span class="special">&amp;</span> <span class="identifier">d</span><span class="special">)</span><span class="keyword">const</span><span class="special">;</span>
+   <span class="keyword">bool</span> <span class="keyword">operator</span><span class="special">!=(</span><span class="keyword">const</span> <span class="identifier">test_data</span><span class="special">&amp;</span> <span class="identifier">d</span><span class="special">)</span><span class="keyword">const</span><span class="special">;</span>
+   <span class="keyword">void</span> <span class="identifier">swap</span><span class="special">(</span><span class="identifier">test_data</span><span class="special">&amp;</span> <span class="identifier">other</span><span class="special">);</span>
+   <span class="identifier">size_type</span> <span class="identifier">size</span><span class="special">()</span><span class="keyword">const</span><span class="special">;</span>
+   <span class="identifier">size_type</span> <span class="identifier">max_size</span><span class="special">()</span><span class="keyword">const</span><span class="special">;</span>
+   <span class="keyword">bool</span> <span class="identifier">empty</span><span class="special">()</span><span class="keyword">const</span><span class="special">;</span>
+
+   <span class="keyword">bool</span> <span class="keyword">operator</span> <span class="special">&lt;</span> <span class="special">(</span><span class="keyword">const</span> <span class="identifier">test_data</span><span class="special">&amp;</span> <span class="identifier">dat</span><span class="special">)</span><span class="keyword">const</span><span class="special">;</span>
+   <span class="keyword">bool</span> <span class="keyword">operator</span> <span class="special">&lt;=</span> <span class="special">(</span><span class="keyword">const</span> <span class="identifier">test_data</span><span class="special">&amp;</span> <span class="identifier">dat</span><span class="special">)</span><span class="keyword">const</span><span class="special">;</span>
+   <span class="keyword">bool</span> <span class="keyword">operator</span> <span class="special">&gt;</span> <span class="special">(</span><span class="keyword">const</span> <span class="identifier">test_data</span><span class="special">&amp;</span> <span class="identifier">dat</span><span class="special">)</span><span class="keyword">const</span><span class="special">;</span>
+   <span class="keyword">bool</span> <span class="keyword">operator</span> <span class="special">&gt;=</span> <span class="special">(</span><span class="keyword">const</span> <span class="identifier">test_data</span><span class="special">&amp;</span> <span class="identifier">dat</span><span class="special">)</span><span class="keyword">const</span><span class="special">;</span>
+<span class="special">};</span>
+
+<span class="keyword">template</span> <span class="special">&lt;</span><span class="keyword">class</span> <span class="identifier">charT</span><span class="special">,</span> <span class="keyword">class</span> <span class="identifier">traits</span><span class="special">,</span> <span class="keyword">class</span> <span class="identifier">T</span><span class="special">&gt;</span>
+<span class="identifier">std</span><span class="special">::</span><span class="identifier">basic_ostream</span><span class="special">&lt;</span><span class="identifier">charT</span><span class="special">,</span> <span class="identifier">traits</span><span class="special">&gt;&amp;</span> <span class="identifier">write_csv</span><span class="special">(</span>
+            <span class="identifier">std</span><span class="special">::</span><span class="identifier">basic_ostream</span><span class="special">&lt;</span><span class="identifier">charT</span><span class="special">,</span> <span class="identifier">traits</span><span class="special">&gt;&amp;</span> <span class="identifier">os</span><span class="special">,</span>
+            <span class="keyword">const</span> <span class="identifier">test_data</span><span class="special">&lt;</span><span class="identifier">T</span><span class="special">&gt;&amp;</span> <span class="identifier">data</span><span class="special">);</span>
+
+<span class="keyword">template</span> <span class="special">&lt;</span><span class="keyword">class</span> <span class="identifier">charT</span><span class="special">,</span> <span class="keyword">class</span> <span class="identifier">traits</span><span class="special">,</span> <span class="keyword">class</span> <span class="identifier">T</span><span class="special">&gt;</span>
+<span class="identifier">std</span><span class="special">::</span><span class="identifier">basic_ostream</span><span class="special">&lt;</span><span class="identifier">charT</span><span class="special">,</span> <span class="identifier">traits</span><span class="special">&gt;&amp;</span> <span class="identifier">write_csv</span><span class="special">(</span>
+            <span class="identifier">std</span><span class="special">::</span><span class="identifier">basic_ostream</span><span class="special">&lt;</span><span class="identifier">charT</span><span class="special">,</span> <span class="identifier">traits</span><span class="special">&gt;&amp;</span> <span class="identifier">os</span><span class="special">,</span>
+            <span class="keyword">const</span> <span class="identifier">test_data</span><span class="special">&lt;</span><span class="identifier">T</span><span class="special">&gt;&amp;</span> <span class="identifier">data</span><span class="special">,</span>
+            <span class="keyword">const</span> <span class="identifier">charT</span><span class="special">*</span> <span class="identifier">separator</span><span class="special">);</span>
+
+<span class="keyword">template</span> <span class="special">&lt;</span><span class="keyword">class</span> <span class="identifier">T</span><span class="special">&gt;</span>
+<span class="identifier">std</span><span class="special">::</span><span class="identifier">ostream</span><span class="special">&amp;</span> <span class="identifier">write_code</span><span class="special">(</span><span class="identifier">std</span><span class="special">::</span><span class="identifier">ostream</span><span class="special">&amp;</span> <span class="identifier">os</span><span class="special">,</span>
+                         <span class="keyword">const</span> <span class="identifier">test_data</span><span class="special">&lt;</span><span class="identifier">T</span><span class="special">&gt;&amp;</span> <span class="identifier">data</span><span class="special">,</span> 
+                         <span class="keyword">const</span> <span class="keyword">char</span><span class="special">*</span> <span class="identifier">name</span><span class="special">);</span>
+                         
+<span class="special">}}}</span> <span class="comment">// namespaces
+</span></pre>
+<a name="math_toolkit.toolkit.internals2.test_data.description"></a><h5>
+<a name="id853205"></a>
+          <a class="link" href="test_data.html#math_toolkit.toolkit.internals2.test_data.description">Description</a>
+        </h5>
+<p>
+          This tool is best illustrated with the following series of examples.
+        </p>
+<p>
+          The functionality of test_data is split into the following parts:
+        </p>
+<div class="itemizedlist"><ul type="disc">
+<li>
+            A functor that implements the function for which data is being generated:
+            this is the bit you have to write.
+          </li>
+<li>
+            One of more parameters that are to be passed to the functor, these are
+            described in fairly abstract terms: give me N points distributed like
+            <span class="emphasis"><em>this</em></span> etc.
+          </li>
+<li>
+            The class test_data, that takes the functor and descriptions of the parameters
+            and computes how ever many output points have been requested, these are
+            stored in a sorted container.
+          </li>
+<li>
+            Routines to iterate over the test_data container and output the data
+            in either csv format, or as C++ source code (as a table using Boost.Array).
+          </li>
+</ul></div>
+<a name="math_toolkit.toolkit.internals2.test_data.example_1__output_data_for_graph_plotting"></a><h6>
+<a name="id853290"></a>
+          <a class="link" href="test_data.html#math_toolkit.toolkit.internals2.test_data.example_1__output_data_for_graph_plotting">Example
+          1: Output Data for Graph Plotting</a>
+        </h6>
+<p>
+          For example, lets say we want to graph the lgamma function between -3 and
+          100, one could do this like so:
+        </p>
+<pre class="programlisting"><span class="preprocessor">#include</span> <span class="special">&lt;</span><span class="identifier">boost</span><span class="special">/</span><span class="identifier">math</span><span class="special">/</span><span class="identifier">tools</span><span class="special">/</span><span class="identifier">test_data</span><span class="special">.</span><span class="identifier">hpp</span><span class="special">&gt;</span>
+<span class="preprocessor">#include</span> <span class="special">&lt;</span><span class="identifier">boost</span><span class="special">/</span><span class="identifier">math</span><span class="special">/</span><span class="identifier">special_functions</span><span class="special">/</span><span class="identifier">gamma</span><span class="special">.</span><span class="identifier">hpp</span><span class="special">&gt;</span>
+
+<span class="keyword">int</span> <span class="identifier">main</span><span class="special">()</span>
+<span class="special">{</span>
+   <span class="keyword">using</span> <span class="keyword">namespace</span> <span class="identifier">boost</span><span class="special">::</span><span class="identifier">math</span><span class="special">::</span><span class="identifier">tools</span><span class="special">;</span>
+   
+   <span class="comment">// create an object to hold the data:
+</span>   <span class="identifier">test_data</span><span class="special">&lt;</span><span class="keyword">double</span><span class="special">&gt;</span> <span class="identifier">data</span><span class="special">;</span>
+   
+   <span class="comment">// insert 500 points at uniform intervals between just after -3 and 100:
+</span>   <span class="keyword">double</span> <span class="special">(*</span><span class="identifier">pf</span><span class="special">)(</span><span class="keyword">double</span><span class="special">)</span> <span class="special">=</span> <span class="identifier">boost</span><span class="special">::</span><span class="identifier">math</span><span class="special">::</span><span class="identifier">lgamma</span><span class="special">;</span>
+   <span class="identifier">data</span><span class="special">.</span><span class="identifier">insert</span><span class="special">(</span><span class="identifier">pf</span><span class="special">,</span> <span class="identifier">make_periodic_param</span><span class="special">(-</span><span class="number">3.0</span> <span class="special">+</span> <span class="number">0.00001</span><span class="special">,</span> <span class="number">100.0</span><span class="special">,</span> <span class="number">500</span><span class="special">));</span>
+   
+   <span class="comment">// print out in csv format:
+</span>   <span class="identifier">write_csv</span><span class="special">(</span><span class="identifier">std</span><span class="special">::</span><span class="identifier">cout</span><span class="special">,</span> <span class="identifier">data</span><span class="special">,</span> <span class="string">", "</span><span class="special">);</span>
+   <span class="keyword">return</span> <span class="number">0</span><span class="special">;</span>
+<span class="special">}</span>
+</pre>
+<p>
+          Which, when plotted, results in:
+        </p>
+<p>
+          <span class="inlinemediaobject"><img src="../../../../graphs/lgamma.png" align="middle"></span>
+        </p>
+<a name="math_toolkit.toolkit.internals2.test_data.example_2__creating_test_data"></a><h6>
+<a name="id853858"></a>
+          <a class="link" href="test_data.html#math_toolkit.toolkit.internals2.test_data.example_2__creating_test_data">Example
+          2: Creating Test Data</a>
+        </h6>
+<p>
+          As a second example, let's suppose we want to create highly accurate test
+          data for a special function. Since many special functions have two or more
+          independent parameters, it's very hard to effectively cover all of the
+          possible parameter space without generating gigabytes of data at great
+          computational expense. A second best approach is to provide the tools by
+          which a user (or the library maintainer) can quickly generate more data
+          on demand to probe the function over a particular domain of interest.
+        </p>
+<p>
+          In this example we'll generate test data for the beta function using NTL::RR at 1000 bit precision.
+          Rather than call our generic version of the beta function, we'll implement
+          a deliberately naive version of the beta function using lgamma, and rely
+          on the high precision of the data type used to get results accurate to
+          at least 128-bit precision. In this way our test data is independent of
+          whatever clever tricks we may wish to use inside the our beta function.
+        </p>
+<p>
+          To start with then, here's the function object that creates the test data:
+        </p>
+<pre class="programlisting"><span class="preprocessor">#include</span> <span class="special">&lt;</span><span class="identifier">boost</span><span class="special">/</span><span class="identifier">math</span><span class="special">/</span><span class="identifier">tools</span><span class="special">/</span><span class="identifier">ntl</span><span class="special">.</span><span class="identifier">hpp</span><span class="special">&gt;</span>
+<span class="preprocessor">#include</span> <span class="special">&lt;</span><span class="identifier">boost</span><span class="special">/</span><span class="identifier">math</span><span class="special">/</span><span class="identifier">special_functions</span><span class="special">/</span><span class="identifier">gamma</span><span class="special">.</span><span class="identifier">hpp</span><span class="special">&gt;</span>
+<span class="preprocessor">#include</span> <span class="special">&lt;</span><span class="identifier">boost</span><span class="special">/</span><span class="identifier">math</span><span class="special">/</span><span class="identifier">tools</span><span class="special">/</span><span class="identifier">test_data</span><span class="special">.</span><span class="identifier">hpp</span><span class="special">&gt;</span>
+<span class="preprocessor">#include</span> <span class="special">&lt;</span><span class="identifier">fstream</span><span class="special">&gt;</span>
+
+<span class="preprocessor">#include</span> <span class="special">&lt;</span><span class="identifier">boost</span><span class="special">/</span><span class="identifier">math</span><span class="special">/</span><span class="identifier">tools</span><span class="special">/</span><span class="identifier">test_data</span><span class="special">.</span><span class="identifier">hpp</span><span class="special">&gt;</span>
+
+<span class="keyword">using</span> <span class="keyword">namespace</span> <span class="identifier">boost</span><span class="special">::</span><span class="identifier">math</span><span class="special">::</span><span class="identifier">tools</span><span class="special">;</span>
+
+<span class="keyword">struct</span> <span class="identifier">beta_data_generator</span>
+<span class="special">{</span>
+   <span class="identifier">NTL</span><span class="special">::</span><span class="identifier">RR</span> <span class="keyword">operator</span><span class="special">()(</span><span class="identifier">NTL</span><span class="special">::</span><span class="identifier">RR</span> <span class="identifier">a</span><span class="special">,</span> <span class="identifier">NTL</span><span class="special">::</span><span class="identifier">RR</span> <span class="identifier">b</span><span class="special">)</span>
+   <span class="special">{</span>
+      <span class="comment">//
+</span>      <span class="comment">// If we throw a domain error then test_data will
+</span>      <span class="comment">// ignore this input point. We'll use this to filter
+</span>      <span class="comment">// out all cases where a &lt; b since the beta function
+</span>      <span class="comment">// is symmetrical in a and b:
+</span>      <span class="comment">//
+</span>      <span class="keyword">if</span><span class="special">(</span><span class="identifier">a</span> <span class="special">&lt;</span> <span class="identifier">b</span><span class="special">)</span>
+         <span class="keyword">throw</span> <span class="identifier">std</span><span class="special">::</span><span class="identifier">domain_error</span><span class="special">(</span><span class="string">""</span><span class="special">);</span>
+         
+      <span class="comment">// very naively calculate spots with lgamma:
+</span>      <span class="identifier">NTL</span><span class="special">::</span><span class="identifier">RR</span> <span class="identifier">g1</span><span class="special">,</span> <span class="identifier">g2</span><span class="special">,</span> <span class="identifier">g3</span><span class="special">;</span>
+      <span class="keyword">int</span> <span class="identifier">s1</span><span class="special">,</span> <span class="identifier">s2</span><span class="special">,</span> <span class="identifier">s3</span><span class="special">;</span>
+      <span class="identifier">g1</span> <span class="special">=</span> <span class="identifier">boost</span><span class="special">::</span><span class="identifier">math</span><span class="special">::</span><span class="identifier">lgamma</span><span class="special">(</span><span class="identifier">a</span><span class="special">,</span> <span class="special">&amp;</span><span class="identifier">s1</span><span class="special">);</span>
+      <span class="identifier">g2</span> <span class="special">=</span> <span class="identifier">boost</span><span class="special">::</span><span class="identifier">math</span><span class="special">::</span><span class="identifier">lgamma</span><span class="special">(</span><span class="identifier">b</span><span class="special">,</span> <span class="special">&amp;</span><span class="identifier">s2</span><span class="special">);</span>
+      <span class="identifier">g3</span> <span class="special">=</span> <span class="identifier">boost</span><span class="special">::</span><span class="identifier">math</span><span class="special">::</span><span class="identifier">lgamma</span><span class="special">(</span><span class="identifier">a</span><span class="special">+</span><span class="identifier">b</span><span class="special">,</span> <span class="special">&amp;</span><span class="identifier">s3</span><span class="special">);</span>
+      <span class="identifier">g1</span> <span class="special">+=</span> <span class="identifier">g2</span> <span class="special">-</span> <span class="identifier">g3</span><span class="special">;</span>
+      <span class="identifier">g1</span> <span class="special">=</span> <span class="identifier">exp</span><span class="special">(</span><span class="identifier">g1</span><span class="special">);</span>
+      <span class="identifier">g1</span> <span class="special">*=</span> <span class="identifier">s1</span> <span class="special">*</span> <span class="identifier">s2</span> <span class="special">*</span> <span class="identifier">s3</span><span class="special">;</span>
+      <span class="keyword">return</span> <span class="identifier">g1</span><span class="special">;</span>
+   <span class="special">}</span>
+<span class="special">};</span>
+</pre>
+<p>
+          To create the data, we'll need to input the domains for a and b for which
+          the function will be tested: the function <code class="computeroutput"><span class="identifier">get_user_parameter_info</span></code>
+          is designed for just that purpose. The start of main will look something
+          like:
+        </p>
+<pre class="programlisting"><span class="comment">// Set the precision on RR:
+</span><span class="identifier">NTL</span><span class="special">::</span><span class="identifier">RR</span><span class="special">::</span><span class="identifier">SetPrecision</span><span class="special">(</span><span class="number">1000</span><span class="special">);</span> <span class="comment">// bits.
+</span><span class="identifier">NTL</span><span class="special">::</span><span class="identifier">RR</span><span class="special">::</span><span class="identifier">SetOutputPrecision</span><span class="special">(</span><span class="number">40</span><span class="special">);</span> <span class="comment">// decimal digits.
+</span>
+<span class="identifier">parameter_info</span><span class="special">&lt;</span><span class="identifier">NTL</span><span class="special">::</span><span class="identifier">RR</span><span class="special">&gt;</span> <span class="identifier">arg1</span><span class="special">,</span> <span class="identifier">arg2</span><span class="special">;</span>
+<span class="identifier">test_data</span><span class="special">&lt;</span><span class="identifier">NTL</span><span class="special">::</span><span class="identifier">RR</span><span class="special">&gt;</span> <span class="identifier">data</span><span class="special">;</span>
+
+<span class="identifier">std</span><span class="special">::</span><span class="identifier">cout</span> <span class="special">&lt;&lt;</span> <span class="string">"Welcome.\n"</span>
+   <span class="string">"This program will generate spot tests for the beta function:\n"</span>
+   <span class="string">"  beta(a, b)\n\n"</span><span class="special">;</span>
+
+<span class="keyword">bool</span> <span class="identifier">cont</span><span class="special">;</span>
+<span class="identifier">std</span><span class="special">::</span><span class="identifier">string</span> <span class="identifier">line</span><span class="special">;</span>
+
+<span class="keyword">do</span><span class="special">{</span>
+   <span class="comment">// prompt the user for the domain of a and b to test:
+</span>   <span class="identifier">get_user_parameter_info</span><span class="special">(</span><span class="identifier">arg1</span><span class="special">,</span> <span class="string">"a"</span><span class="special">);</span>
+   <span class="identifier">get_user_parameter_info</span><span class="special">(</span><span class="identifier">arg2</span><span class="special">,</span> <span class="string">"b"</span><span class="special">);</span>
+   
+   <span class="comment">// create the data:
+</span>   <span class="identifier">data</span><span class="special">.</span><span class="identifier">insert</span><span class="special">(</span><span class="identifier">beta_data_generator</span><span class="special">(),</span> <span class="identifier">arg1</span><span class="special">,</span> <span class="identifier">arg2</span><span class="special">);</span>
+   
+   <span class="comment">// see if the user want's any more domains tested:
+</span>   <span class="identifier">std</span><span class="special">::</span><span class="identifier">cout</span> <span class="special">&lt;&lt;</span> <span class="string">"Any more data [y/n]?"</span><span class="special">;</span>
+   <span class="identifier">std</span><span class="special">::</span><span class="identifier">getline</span><span class="special">(</span><span class="identifier">std</span><span class="special">::</span><span class="identifier">cin</span><span class="special">,</span> <span class="identifier">line</span><span class="special">);</span>
+   <span class="identifier">boost</span><span class="special">::</span><span class="identifier">algorithm</span><span class="special">::</span><span class="identifier">trim</span><span class="special">(</span><span class="identifier">line</span><span class="special">);</span>
+   <span class="identifier">cont</span> <span class="special">=</span> <span class="special">(</span><span class="identifier">line</span> <span class="special">==</span> <span class="string">"y"</span><span class="special">);</span>
+<span class="special">}</span><span class="keyword">while</span><span class="special">(</span><span class="identifier">cont</span><span class="special">);</span>
+</pre>
+<div class="caution"><table border="0" summary="Caution">
+<tr>
+<td rowspan="2" align="center" valign="top" width="25"><img alt="[Caution]" src="../../../../../doc/html/images/caution.png"></td>
+<th align="left">Caution</th>
+</tr>
+<tr><td align="left" valign="top"><p>
+            At this point one potential stumbling block should be mentioned: test_data&lt;&gt;::insert
+            will create a matrix of test data when there are two or more parameters,
+            so if we have two parameters and we're asked for a thousand points on
+            each, that's a <span class="emphasis"><em>million test points in total</em></span>. Don't
+            say you weren't warned!
+          </p></td></tr>
+</table></div>
+<p>
+          There's just one final step now, and that's to write the test data to file:
+        </p>
+<pre class="programlisting"><span class="identifier">std</span><span class="special">::</span><span class="identifier">cout</span> <span class="special">&lt;&lt;</span> <span class="string">"Enter name of test data file [default=beta_data.ipp]"</span><span class="special">;</span>
+<span class="identifier">std</span><span class="special">::</span><span class="identifier">getline</span><span class="special">(</span><span class="identifier">std</span><span class="special">::</span><span class="identifier">cin</span><span class="special">,</span> <span class="identifier">line</span><span class="special">);</span>
+<span class="identifier">boost</span><span class="special">::</span><span class="identifier">algorithm</span><span class="special">::</span><span class="identifier">trim</span><span class="special">(</span><span class="identifier">line</span><span class="special">);</span>
+<span class="keyword">if</span><span class="special">(</span><span class="identifier">line</span> <span class="special">==</span> <span class="string">""</span><span class="special">)</span>
+   <span class="identifier">line</span> <span class="special">=</span> <span class="string">"beta_data.ipp"</span><span class="special">;</span>
+<span class="identifier">std</span><span class="special">::</span><span class="identifier">ofstream</span> <span class="identifier">ofs</span><span class="special">(</span><span class="identifier">line</span><span class="special">.</span><span class="identifier">c_str</span><span class="special">());</span>
+<span class="identifier">write_code</span><span class="special">(</span><span class="identifier">ofs</span><span class="special">,</span> <span class="identifier">data</span><span class="special">,</span> <span class="string">"beta_data"</span><span class="special">);</span>
+</pre>
+<p>
+          The format of the test data looks something like:
+        </p>
+<pre class="programlisting"><span class="preprocessor">#define</span> <span class="identifier">SC_</span><span class="special">(</span><span class="identifier">x</span><span class="special">)</span> <span class="keyword">static_cast</span><span class="special">&lt;</span><span class="identifier">T</span><span class="special">&gt;(</span><span class="identifier">BOOST_JOIN</span><span class="special">(</span><span class="identifier">x</span><span class="special">,</span> <span class="identifier">L</span><span class="special">))</span>
+   <span class="keyword">static</span> <span class="keyword">const</span> <span class="identifier">boost</span><span class="special">::</span><span class="identifier">array</span><span class="special">&lt;</span><span class="identifier">boost</span><span class="special">::</span><span class="identifier">array</span><span class="special">&lt;</span><span class="identifier">T</span><span class="special">,</span> <span class="number">3</span><span class="special">&gt;,</span> <span class="number">1830</span><span class="special">&gt;</span>
+   <span class="identifier">beta_med_data</span> <span class="special">=</span> <span class="special">{</span>
+      <span class="identifier">SC_</span><span class="special">(</span><span class="number">0.4883005917072296142578125</span><span class="special">),</span>
+      <span class="identifier">SC_</span><span class="special">(</span><span class="number">0.4883005917072296142578125</span><span class="special">),</span>
+      <span class="identifier">SC_</span><span class="special">(</span><span class="number">3.245912809500479157065104747353807392371</span><span class="special">),</span> 
+      <span class="identifier">SC_</span><span class="special">(</span><span class="number">3.5808107852935791015625</span><span class="special">),</span>
+      <span class="identifier">SC_</span><span class="special">(</span><span class="number">0.4883005917072296142578125</span><span class="special">),</span>
+      <span class="identifier">SC_</span><span class="special">(</span><span class="number">1.007653173802923954909901438393379243537</span><span class="special">),</span> 
+      <span class="comment">/* ... lots of rows skipped */</span>
+<span class="special">};</span>
+</pre>
+<p>
+          The first two values in each row are the input parameters that were passed
+          to our functor and the last value is the return value from the functor.
+          Had our functor returned a tuple rather than a value, then we would have
+          had one entry for each element in the tuple in addition to the input parameters.
+        </p>
+<p>
+          The first #define serves two purposes:
+        </p>
+<div class="itemizedlist"><ul type="disc">
+<li>
+            It reduces the file sizes considerably: all those <code class="computeroutput"><span class="keyword">static_cast</span></code>'s
+            add up to a lot of bytes otherwise (they are needed to suppress compiler
+            warnings when <code class="computeroutput"><span class="identifier">T</span></code> is narrower
+            than a <code class="computeroutput"><span class="keyword">long</span> <span class="keyword">double</span></code>).
+          </li>
+<li>
+            It provides a useful customisation point: for example if we were testing
+            a user-defined type that has more precision than a <code class="computeroutput"><span class="keyword">long</span>
+            <span class="keyword">double</span></code> we could change it to:
+          </li>
+</ul></div>
+<p>
+          <code class="literal">#define SC_(x) lexical_cast&lt;T&gt;(BOOST_STRINGIZE(x))</code>
+        </p>
+<p>
+          in order to ensure that no truncation of the values occurs prior to conversion
+          to <code class="computeroutput"><span class="identifier">T</span></code>. Note that this isn't
+          used by default as it's rather hard on the compiler when the table is large.
+        </p>
+<a name="math_toolkit.toolkit.internals2.test_data.example_3__profiling_a_continued_fraction_for_convergence_and_accuracy"></a><h6>
+<a name="id856384"></a>
+          <a class="link" href="test_data.html#math_toolkit.toolkit.internals2.test_data.example_3__profiling_a_continued_fraction_for_convergence_and_accuracy">Example
+          3: Profiling a Continued Fraction for Convergence and Accuracy</a>
+        </h6>
+<p>
+          Alternatively, lets say we want to profile a continued fraction for convergence
+          and error. As an example, we'll use the continued fraction for the upper
+          incomplete gamma function, the following function object returns the next
+          a<sub>N </sub> and b<sub>N </sub> of the continued fraction each time it's invoked:
+        </p>
+<pre class="programlisting"><span class="keyword">template</span> <span class="special">&lt;</span><span class="keyword">class</span> <span class="identifier">T</span><span class="special">&gt;</span>
+<span class="keyword">struct</span> <span class="identifier">upper_incomplete_gamma_fract</span>
+<span class="special">{</span>
+<span class="keyword">private</span><span class="special">:</span>
+   <span class="identifier">T</span> <span class="identifier">z</span><span class="special">,</span> <span class="identifier">a</span><span class="special">;</span>
+   <span class="keyword">int</span> <span class="identifier">k</span><span class="special">;</span>
+<span class="keyword">public</span><span class="special">:</span>
+   <span class="keyword">typedef</span> <span class="identifier">std</span><span class="special">::</span><span class="identifier">pair</span><span class="special">&lt;</span><span class="identifier">T</span><span class="special">,</span><span class="identifier">T</span><span class="special">&gt;</span> <span class="identifier">result_type</span><span class="special">;</span>
+
+   <span class="identifier">upper_incomplete_gamma_fract</span><span class="special">(</span><span class="identifier">T</span> <span class="identifier">a1</span><span class="special">,</span> <span class="identifier">T</span> <span class="identifier">z1</span><span class="special">)</span>
+      <span class="special">:</span> <span class="identifier">z</span><span class="special">(</span><span class="identifier">z1</span><span class="special">-</span><span class="identifier">a1</span><span class="special">+</span><span class="number">1</span><span class="special">),</span> <span class="identifier">a</span><span class="special">(</span><span class="identifier">a1</span><span class="special">),</span> <span class="identifier">k</span><span class="special">(</span><span class="number">0</span><span class="special">)</span>
+   <span class="special">{</span>
+   <span class="special">}</span>
+
+   <span class="identifier">result_type</span> <span class="keyword">operator</span><span class="special">()()</span>
+   <span class="special">{</span>
+      <span class="special">++</span><span class="identifier">k</span><span class="special">;</span>
+      <span class="identifier">z</span> <span class="special">+=</span> <span class="number">2</span><span class="special">;</span>
+      <span class="keyword">return</span> <span class="identifier">result_type</span><span class="special">(</span><span class="identifier">k</span> <span class="special">*</span> <span class="special">(</span><span class="identifier">a</span> <span class="special">-</span> <span class="identifier">k</span><span class="special">),</span> <span class="identifier">z</span><span class="special">);</span>
+   <span class="special">}</span>
+<span class="special">};</span>
+</pre>
+<p>
+          We want to measure both the relative error, and the rate of convergence
+          of this fraction, so we'll write a functor that returns both as a tuple:
+          class test_data will unpack the tuple for us, and create one column of
+          data for each element in the tuple (in addition to the input parameters):
+        </p>
+<pre class="programlisting"><span class="preprocessor">#include</span> <span class="special">&lt;</span><span class="identifier">boost</span><span class="special">/</span><span class="identifier">math</span><span class="special">/</span><span class="identifier">tools</span><span class="special">/</span><span class="identifier">test_data</span><span class="special">.</span><span class="identifier">hpp</span><span class="special">&gt;</span>
+<span class="preprocessor">#include</span> <span class="special">&lt;</span><span class="identifier">boost</span><span class="special">/</span><span class="identifier">math</span><span class="special">/</span><span class="identifier">tools</span><span class="special">/</span><span class="identifier">test</span><span class="special">.</span><span class="identifier">hpp</span><span class="special">&gt;</span>
+<span class="preprocessor">#include</span> <span class="special">&lt;</span><span class="identifier">boost</span><span class="special">/</span><span class="identifier">math</span><span class="special">/</span><span class="identifier">special_functions</span><span class="special">/</span><span class="identifier">gamma</span><span class="special">.</span><span class="identifier">hpp</span><span class="special">&gt;</span>
+<span class="preprocessor">#include</span> <span class="special">&lt;</span><span class="identifier">boost</span><span class="special">/</span><span class="identifier">math</span><span class="special">/</span><span class="identifier">tools</span><span class="special">/</span><span class="identifier">ntl</span><span class="special">.</span><span class="identifier">hpp</span><span class="special">&gt;</span>
+<span class="preprocessor">#include</span> <span class="special">&lt;</span><span class="identifier">boost</span><span class="special">/</span><span class="identifier">tr1</span><span class="special">/</span><span class="identifier">tuple</span><span class="special">.</span><span class="identifier">hpp</span><span class="special">&gt;</span>
+
+<span class="keyword">template</span> <span class="special">&lt;</span><span class="keyword">class</span> <span class="identifier">T</span><span class="special">&gt;</span>
+<span class="keyword">struct</span> <span class="identifier">profile_gamma_fraction</span>
+<span class="special">{</span>
+   <span class="keyword">typedef</span> <span class="identifier">std</span><span class="special">::</span><span class="identifier">tr1</span><span class="special">::</span><span class="identifier">tuple</span><span class="special">&lt;</span><span class="identifier">T</span><span class="special">,</span> <span class="identifier">T</span><span class="special">&gt;</span> <span class="identifier">result_type</span><span class="special">;</span>
+
+   <span class="identifier">result_type</span> <span class="keyword">operator</span><span class="special">()(</span><span class="identifier">T</span> <span class="identifier">val</span><span class="special">)</span>
+   <span class="special">{</span>
+      <span class="keyword">using</span> <span class="keyword">namespace</span> <span class="identifier">boost</span><span class="special">::</span><span class="identifier">math</span><span class="special">::</span><span class="identifier">tools</span><span class="special">;</span>
+      <span class="comment">// estimate the true value, using arbitary precision
+</span>      <span class="comment">// arithmetic and NTL::RR:
+</span>      <span class="identifier">NTL</span><span class="special">::</span><span class="identifier">RR</span> <span class="identifier">rval</span><span class="special">(</span><span class="identifier">val</span><span class="special">);</span>
+      <span class="identifier">upper_incomplete_gamma_fract</span><span class="special">&lt;</span><span class="identifier">NTL</span><span class="special">::</span><span class="identifier">RR</span><span class="special">&gt;</span> <span class="identifier">f1</span><span class="special">(</span><span class="identifier">rval</span><span class="special">,</span> <span class="identifier">rval</span><span class="special">);</span>
+      <span class="identifier">NTL</span><span class="special">::</span><span class="identifier">RR</span> <span class="identifier">true_val</span> <span class="special">=</span> <span class="identifier">continued_fraction_a</span><span class="special">(</span><span class="identifier">f1</span><span class="special">,</span> <span class="number">1000</span><span class="special">);</span>
+      <span class="comment">//
+</span>      <span class="comment">// Now get the aproximation at double precision, along with the number of
+</span>      <span class="comment">// iterations required:
+</span>      <span class="identifier">boost</span><span class="special">::</span><span class="identifier">uintmax_t</span> <span class="identifier">iters</span> <span class="special">=</span> <span class="identifier">std</span><span class="special">::</span><span class="identifier">numeric_limits</span><span class="special">&lt;</span><span class="identifier">boost</span><span class="special">::</span><span class="identifier">uintmax_t</span><span class="special">&gt;::</span><span class="identifier">max</span><span class="special">();</span>
+      <span class="identifier">upper_incomplete_gamma_fract</span><span class="special">&lt;</span><span class="identifier">T</span><span class="special">&gt;</span> <span class="identifier">f2</span><span class="special">(</span><span class="identifier">val</span><span class="special">,</span> <span class="identifier">val</span><span class="special">);</span>
+      <span class="identifier">T</span> <span class="identifier">found_val</span> <span class="special">=</span> <span class="identifier">continued_fraction_a</span><span class="special">(</span><span class="identifier">f2</span><span class="special">,</span> <span class="identifier">std</span><span class="special">::</span><span class="identifier">numeric_limits</span><span class="special">&lt;</span><span class="identifier">T</span><span class="special">&gt;::</span><span class="identifier">digits</span><span class="special">,</span> <span class="identifier">iters</span><span class="special">);</span>
+      <span class="comment">//
+</span>      <span class="comment">// Work out the relative error, as measured in units of epsilon:
+</span>      <span class="identifier">T</span> <span class="identifier">err</span> <span class="special">=</span> <span class="identifier">real_cast</span><span class="special">&lt;</span><span class="identifier">T</span><span class="special">&gt;(</span><span class="identifier">relative_error</span><span class="special">(</span><span class="identifier">true_val</span><span class="special">,</span> <span class="identifier">NTL</span><span class="special">::</span><span class="identifier">RR</span><span class="special">(</span><span class="identifier">found_val</span><span class="special">))</span> <span class="special">/</span> <span class="identifier">std</span><span class="special">::</span><span class="identifier">numeric_limits</span><span class="special">&lt;</span><span class="identifier">T</span><span class="special">&gt;::</span><span class="identifier">epsilon</span><span class="special">());</span>
+      <span class="comment">//
+</span>      <span class="comment">// now just return the results as a tuple:
+</span>      <span class="keyword">return</span> <span class="identifier">std</span><span class="special">::</span><span class="identifier">tr1</span><span class="special">::</span><span class="identifier">make_tuple</span><span class="special">(</span><span class="identifier">err</span><span class="special">,</span> <span class="identifier">iters</span><span class="special">);</span>
+   <span class="special">}</span>
+<span class="special">};</span>
+</pre>
+<p>
+          Feeding that functor into test_data allows rapid output of csv data, for
+          whatever type <code class="computeroutput"><span class="identifier">T</span></code> we may
+          be interested in:
+        </p>
+<pre class="programlisting"><span class="keyword">int</span> <span class="identifier">main</span><span class="special">()</span>
+<span class="special">{</span>
+   <span class="keyword">using</span> <span class="keyword">namespace</span> <span class="identifier">boost</span><span class="special">::</span><span class="identifier">math</span><span class="special">::</span><span class="identifier">tools</span><span class="special">;</span>
+   <span class="comment">// create an object to hold the data:
+</span>   <span class="identifier">test_data</span><span class="special">&lt;</span><span class="keyword">double</span><span class="special">&gt;</span> <span class="identifier">data</span><span class="special">;</span>
+   <span class="comment">// insert 500 points at uniform intervals between just after 0 and 100:
+</span>   <span class="identifier">data</span><span class="special">.</span><span class="identifier">insert</span><span class="special">(</span><span class="identifier">profile_gamma_fraction</span><span class="special">&lt;</span><span class="keyword">double</span><span class="special">&gt;(),</span> <span class="identifier">make_periodic_param</span><span class="special">(</span><span class="number">0.01</span><span class="special">,</span> <span class="number">100.0</span><span class="special">,</span> <span class="number">100</span><span class="special">));</span>
+   <span class="comment">// print out in csv format:
+</span>   <span class="identifier">write_csv</span><span class="special">(</span><span class="identifier">std</span><span class="special">::</span><span class="identifier">cout</span><span class="special">,</span> <span class="identifier">data</span><span class="special">,</span> <span class="string">", "</span><span class="special">);</span>
+   <span class="keyword">return</span> <span class="number">0</span><span class="special">;</span>
+<span class="special">}</span>
+</pre>
+<p>
+          This time there's no need to plot a graph, the first few rows are:
+        </p>
+<pre class="programlisting"><span class="identifier">a</span> <span class="keyword">and</span> <span class="identifier">z</span><span class="special">,</span>  <span class="identifier">Error</span><span class="special">/</span><span class="identifier">epsilon</span><span class="special">,</span>  <span class="identifier">Iterations</span> <span class="identifier">required</span>
+
+<span class="number">0.01</span><span class="special">,</span>     <span class="number">9723.14</span><span class="special">,</span>        <span class="number">4726</span>
+<span class="number">1.0099</span><span class="special">,</span>   <span class="number">9.54818</span><span class="special">,</span>        <span class="number">87</span>
+<span class="number">2.0098</span><span class="special">,</span>   <span class="number">3.84777</span><span class="special">,</span>        <span class="number">40</span>
+<span class="number">3.0097</span><span class="special">,</span>   <span class="number">0.728358</span><span class="special">,</span>       <span class="number">25</span>
+<span class="number">4.0096</span><span class="special">,</span>   <span class="number">2.39712</span><span class="special">,</span>        <span class="number">21</span>
+<span class="number">5.0095</span><span class="special">,</span>   <span class="number">0.233263</span><span class="special">,</span>       <span class="number">16</span>
+</pre>
+<p>
+          So it's pretty clear that this fraction shouldn't be used for small values
+          of a and z.
+        </p>
+<a name="math_toolkit.toolkit.internals2.test_data.reference"></a><h5>
+<a name="id858651"></a>
+          <a class="link" href="test_data.html#math_toolkit.toolkit.internals2.test_data.reference">reference</a>
+        </h5>
+<a name="test_data_reference"></a><p>
+        </p>
+<p>
+          Most of this tool has been described already in the examples above, we'll
+          just add the following notes on the non-member functions:
+        </p>
+<pre class="programlisting"><span class="keyword">template</span> <span class="special">&lt;</span><span class="keyword">class</span> <span class="identifier">T</span><span class="special">&gt;</span>
+<span class="identifier">parameter_info</span><span class="special">&lt;</span><span class="identifier">T</span><span class="special">&gt;</span> <span class="identifier">make_random_param</span><span class="special">(</span><span class="identifier">T</span> <span class="identifier">start_range</span><span class="special">,</span> <span class="identifier">T</span> <span class="identifier">end_range</span><span class="special">,</span> <span class="keyword">int</span> <span class="identifier">n_points</span><span class="special">);</span>
+</pre>
+<p>
+          Tells class test_data to test <span class="emphasis"><em>n_points</em></span> random values
+          in the range [start_range,end_range].
+        </p>
+<pre class="programlisting"><span class="keyword">template</span> <span class="special">&lt;</span><span class="keyword">class</span> <span class="identifier">T</span><span class="special">&gt;</span>
+<span class="identifier">parameter_info</span><span class="special">&lt;</span><span class="identifier">T</span><span class="special">&gt;</span> <span class="identifier">make_periodic_param</span><span class="special">(</span><span class="identifier">T</span> <span class="identifier">start_range</span><span class="special">,</span> <span class="identifier">T</span> <span class="identifier">end_range</span><span class="special">,</span> <span class="keyword">int</span> <span class="identifier">n_points</span><span class="special">);</span>
+</pre>
+<p>
+          Tells class test_data to test <span class="emphasis"><em>n_points</em></span> evenly spaced
+          values in the range [start_range,end_range].
+        </p>
+<pre class="programlisting"><span class="keyword">template</span> <span class="special">&lt;</span><span class="keyword">class</span> <span class="identifier">T</span><span class="special">&gt;</span>
+<span class="identifier">parameter_info</span><span class="special">&lt;</span><span class="identifier">T</span><span class="special">&gt;</span> <span class="identifier">make_power_param</span><span class="special">(</span><span class="identifier">T</span> <span class="identifier">basis</span><span class="special">,</span> <span class="keyword">int</span> <span class="identifier">start_exponent</span><span class="special">,</span> <span class="keyword">int</span> <span class="identifier">end_exponent</span><span class="special">);</span>
+</pre>
+<p>
+          Tells class test_data to test points of the form <span class="emphasis"><em>basis + R *
+          2<sup>expon</sup></em></span> for each <span class="emphasis"><em>expon</em></span> in the range [start_exponent,
+          end_exponent], and <span class="emphasis"><em>R</em></span> a random number in [0.5, 1].
+        </p>
+<pre class="programlisting"><span class="keyword">template</span> <span class="special">&lt;</span><span class="keyword">class</span> <span class="identifier">T</span><span class="special">&gt;</span>
+<span class="keyword">bool</span> <span class="identifier">get_user_parameter_info</span><span class="special">(</span><span class="identifier">parameter_info</span><span class="special">&lt;</span><span class="identifier">T</span><span class="special">&gt;&amp;</span> <span class="identifier">info</span><span class="special">,</span> <span class="keyword">const</span> <span class="keyword">char</span><span class="special">*</span> <span class="identifier">param_name</span><span class="special">);</span>
+</pre>
+<p>
+          Prompts the user for the parameter range and form to use.
+        </p>
+<p>
+          Finally, if we don't want the parameter to be included in the output, we
+          can tell test_data by setting it a "dummy parameter":
+        </p>
+<pre class="programlisting"><span class="identifier">parameter_info</span><span class="special">&lt;</span><span class="keyword">double</span><span class="special">&gt;</span> <span class="identifier">p</span> <span class="special">=</span> <span class="identifier">make_random_param</span><span class="special">(</span><span class="number">2.0</span><span class="special">,</span> <span class="number">5.0</span><span class="special">,</span> <span class="number">10</span><span class="special">);</span>
+<span class="identifier">p</span><span class="special">.</span><span class="identifier">type</span> <span class="special">|=</span> <span class="identifier">dummy_param</span><span class="special">;</span>
+</pre>
+<p>
+          This is useful when the functor used transforms the parameter in some way
+          before passing it to the function under test, usually the functor will
+          then return both the transformed input and the result in a tuple, so there's
+          no need for the original pseudo-parameter to be included in program output.
+        </p>
+</div>
+<table xmlns:rev="http://www.cs.rpi.edu/~gregod/boost/tools/doc/revision" width="100%"><tr>
+<td align="left"></td>
+<td align="right"><div class="copyright-footer">Copyright © 2006 , 2007, 2008 John Maddock, Paul A. Bristow, Hubert
+      Holin, Xiaogang Zhang, Bruno Lalande and Gautam Sewani<p>
+        Distributed under the Boost Software License, Version 1.0. (See accompanying
+        file LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_0.txt)
+      </p>
+</div></td>
+</tr></table>
+<hr>
+<div class="spirit-nav">
+<a accesskey="p" href="error_test.html"><img src="../../../../../doc/html/images/prev.png" alt="Prev"></a><a accesskey="u" href="../internals2.html"><img src="../../../../../doc/html/images/up.png" alt="Up"></a><a accesskey="h" href="../../../index.html"><img src="../../../../../doc/html/images/home.png" alt="Home"></a><a accesskey="n" href="../../using_udt.html"><img src="../../../../../doc/html/images/next.png" alt="Next"></a>
+</div>
+</body>
+</html>

Added: sandbox/tools/auto_index/example/math/doc/sf_and_dist/html/math_toolkit/toolkit/internals_overview.html
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--- (empty file)
+++ sandbox/tools/auto_index/example/math/doc/sf_and_dist/html/math_toolkit/toolkit/internals_overview.html	2008-11-28 05:25:28 EST (Fri, 28 Nov 2008)
@@ -0,0 +1,58 @@
+<html>
+<head>
+<meta http-equiv="Content-Type" content="text/html; charset=ISO-8859-1">
+<title>Overview</title>
+<link rel="stylesheet" href="../../boostbook.css" type="text/css">
+<meta name="generator" content="DocBook XSL Stylesheets Vsnapshot_8125">
+<link rel="home" href="../../index.html" title="Math Toolkit">
+<link rel="up" href="../toolkit.html" title="Internal Details and Tools (Experimental)">
+<link rel="prev" href="../toolkit.html" title="Internal Details and Tools (Experimental)">
+<link rel="next" href="internals1.html" title="Reused Utilities">
+</head>
+<body bgcolor="white" text="black" link="#0000FF" vlink="#840084" alink="#0000FF">
+<table cellpadding="2" width="100%"><tr>
+<td valign="top"><img alt="Boost C++ Libraries" width="277" height="86" src="../../../../boost.png"></td>
+<td align="center">Home</td>
+<td align="center">Libraries</td>
+<td align="center">People</td>
+<td align="center">FAQ</td>
+<td align="center">More</td>
+</tr></table>
+<hr>
+<div class="spirit-nav">
+<a accesskey="p" href="../toolkit.html"><img src="../../../../doc/html/images/prev.png" alt="Prev"></a><a accesskey="u" href="../toolkit.html"><img src="../../../../doc/html/images/up.png" alt="Up"></a><a accesskey="h" href="../../index.html"><img src="../../../../doc/html/images/home.png" alt="Home"></a><a accesskey="n" href="internals1.html"><img src="../../../../doc/html/images/next.png" alt="Next"></a>
+</div>
+<div class="section" lang="en">
+<div class="titlepage"><div><div><h3 class="title">
+<a name="math_toolkit.toolkit.internals_overview"></a><a class="link" href="internals_overview.html" title="Overview"> Overview</a>
+</h3></div></div></div>
+<p>
+        This section contains internal utilities used by the library's implementation
+        along with tools used in development and testing. These tools have only minimal
+        documentation, and crucially <span class="emphasis"><em>do not have stable interfaces</em></span>.
+      </p>
+<p>
+        There is no doubt that these components can be improved, but they are also
+        largely incidental to the main purpose of this library.
+      </p>
+<p>
+        These tools are designed to "just get the job done", and receive
+        minimal documentation here, in the hopes that they will help stimulate further
+        submissions to this library.
+      </p>
+</div>
+<table xmlns:rev="http://www.cs.rpi.edu/~gregod/boost/tools/doc/revision" width="100%"><tr>
+<td align="left"></td>
+<td align="right"><div class="copyright-footer">Copyright © 2006 , 2007, 2008 John Maddock, Paul A. Bristow, Hubert
+      Holin, Xiaogang Zhang, Bruno Lalande and Gautam Sewani<p>
+        Distributed under the Boost Software License, Version 1.0. (See accompanying
+        file LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_0.txt)
+      </p>
+</div></td>
+</tr></table>
+<hr>
+<div class="spirit-nav">
+<a accesskey="p" href="../toolkit.html"><img src="../../../../doc/html/images/prev.png" alt="Prev"></a><a accesskey="u" href="../toolkit.html"><img src="../../../../doc/html/images/up.png" alt="Up"></a><a accesskey="h" href="../../index.html"><img src="../../../../doc/html/images/home.png" alt="Home"></a><a accesskey="n" href="internals1.html"><img src="../../../../doc/html/images/next.png" alt="Next"></a>
+</div>
+</body>
+</html>

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+++ sandbox/tools/auto_index/example/math/doc/sf_and_dist/html/math_toolkit/using_udt.html	2008-11-28 05:25:28 EST (Fri, 28 Nov 2008)
@@ -0,0 +1,57 @@
+<html>
+<head>
+<meta http-equiv="Content-Type" content="text/html; charset=ISO-8859-1">
+<title>Use with User-Defined Floating-Point Types</title>
+<link rel="stylesheet" href="../boostbook.css" type="text/css">
+<meta name="generator" content="DocBook XSL Stylesheets Vsnapshot_8125">
+<link rel="home" href="../index.html" title="Math Toolkit">
+<link rel="up" href="../index.html" title="Math Toolkit">
+<link rel="prev" href="toolkit/internals2/test_data.html" title="Graphing, Profiling, and Generating Test Data for Special Functions">
+<link rel="next" href="using_udt/use_ntl.html" title="Using With NTL - a High-Precision Floating-Point Library">
+</head>
+<body bgcolor="white" text="black" link="#0000FF" vlink="#840084" alink="#0000FF">
+<table cellpadding="2" width="100%"><tr>
+<td valign="top"><img alt="Boost C++ Libraries" width="277" height="86" src="../../../boost.png"></td>
+<td align="center">Home</td>
+<td align="center">Libraries</td>
+<td align="center">People</td>
+<td align="center">FAQ</td>
+<td align="center">More</td>
+</tr></table>
+<hr>
+<div class="spirit-nav">
+<a accesskey="p" href="toolkit/internals2/test_data.html"><img src="../../../doc/html/images/prev.png" alt="Prev"></a><a accesskey="u" href="../index.html"><img src="../../../doc/html/images/up.png" alt="Up"></a><a accesskey="h" href="../index.html"><img src="../../../doc/html/images/home.png" alt="Home"></a><a accesskey="n" href="using_udt/use_ntl.html"><img src="../../../doc/html/images/next.png" alt="Next"></a>
+</div>
+<div class="section" lang="en">
+<div class="titlepage"><div><div><h2 class="title" style="clear: both">
+<a name="math_toolkit.using_udt"></a><a class="link" href="using_udt.html" title="Use with User-Defined Floating-Point Types"> Use with User-Defined Floating-Point
+    Types</a>
+</h2></div></div></div>
+<div class="toc"><dl>
+<dt><span class="section"><a href="using_udt/use_ntl.html"> Using With NTL - a High-Precision
+      Floating-Point Library</a></span></dt>
+<dt><span class="section"><a href="using_udt/use_mpfr.html"> Using With MPFR / GMP
+      - a High-Precision Floating-Point Library</a></span></dt>
+<dt><span class="section"><a href="using_udt/concepts.html"> Conceptual Requirements
+      for Real Number Types</a></span></dt>
+<dt><span class="section"><a href="using_udt/dist_concept.html"> Conceptual Requirements
+      for Distribution Types</a></span></dt>
+<dt><span class="section"><a href="using_udt/archetypes.html"> Conceptual Archetypes
+      and Testing</a></span></dt>
+</dl></div>
+</div>
+<table xmlns:rev="http://www.cs.rpi.edu/~gregod/boost/tools/doc/revision" width="100%"><tr>
+<td align="left"></td>
+<td align="right"><div class="copyright-footer">Copyright © 2006 , 2007, 2008 John Maddock, Paul A. Bristow, Hubert
+      Holin, Xiaogang Zhang, Bruno Lalande and Gautam Sewani<p>
+        Distributed under the Boost Software License, Version 1.0. (See accompanying
+        file LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_0.txt)
+      </p>
+</div></td>
+</tr></table>
+<hr>
+<div class="spirit-nav">
+<a accesskey="p" href="toolkit/internals2/test_data.html"><img src="../../../doc/html/images/prev.png" alt="Prev"></a><a accesskey="u" href="../index.html"><img src="../../../doc/html/images/up.png" alt="Up"></a><a accesskey="h" href="../index.html"><img src="../../../doc/html/images/home.png" alt="Home"></a><a accesskey="n" href="using_udt/use_ntl.html"><img src="../../../doc/html/images/next.png" alt="Next"></a>
+</div>
+</body>
+</html>

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--- (empty file)
+++ sandbox/tools/auto_index/example/math/doc/sf_and_dist/html/math_toolkit/using_udt/archetypes.html	2008-11-28 05:25:28 EST (Fri, 28 Nov 2008)
@@ -0,0 +1,178 @@
+<html>
+<head>
+<meta http-equiv="Content-Type" content="text/html; charset=ISO-8859-1">
+<title>Conceptual Archetypes and Testing</title>
+<link rel="stylesheet" href="../../boostbook.css" type="text/css">
+<meta name="generator" content="DocBook XSL Stylesheets Vsnapshot_8125">
+<link rel="home" href="../../index.html" title="Math Toolkit">
+<link rel="up" href="../using_udt.html" title="Use with User-Defined Floating-Point Types">
+<link rel="prev" href="dist_concept.html" title="Conceptual Requirements for Distribution Types">
+<link rel="next" href="../policy.html" title="Policies">
+</head>
+<body bgcolor="white" text="black" link="#0000FF" vlink="#840084" alink="#0000FF">
+<table cellpadding="2" width="100%"><tr>
+<td valign="top"><img alt="Boost C++ Libraries" width="277" height="86" src="../../../../boost.png"></td>
+<td align="center">Home</td>
+<td align="center">Libraries</td>
+<td align="center">People</td>
+<td align="center">FAQ</td>
+<td align="center">More</td>
+</tr></table>
+<hr>
+<div class="spirit-nav">
+<a accesskey="p" href="dist_concept.html"><img src="../../../../doc/html/images/prev.png" alt="Prev"></a><a accesskey="u" href="../using_udt.html"><img src="../../../../doc/html/images/up.png" alt="Up"></a><a accesskey="h" href="../../index.html"><img src="../../../../doc/html/images/home.png" alt="Home"></a><a accesskey="n" href="../policy.html"><img src="../../../../doc/html/images/next.png" alt="Next"></a>
+</div>
+<div class="section" lang="en">
+<div class="titlepage"><div><div><h3 class="title">
+<a name="math_toolkit.using_udt.archetypes"></a><a class="link" href="archetypes.html" title="Conceptual Archetypes and Testing"> Conceptual Archetypes
+      and Testing</a>
+</h3></div></div></div>
+<p>
+        There are several concept archetypes available:
+      </p>
+<p>
+        
+</p>
+<pre class="programlisting"><span class="preprocessor">#include</span> <span class="special">&lt;</span><span class="identifier">boost</span><span class="special">/</span><span class="identifier">concepts</span><span class="special">/</span><span class="identifier">std_real_concept</span><span class="special">.</span><span class="identifier">hpp</span><span class="special">&gt;</span></pre>
+<p>
+      </p>
+<pre class="programlisting"><span class="keyword">namespace</span> <span class="identifier">boost</span><span class="special">{</span>
+<span class="keyword">namespace</span> <span class="identifier">math</span><span class="special">{</span>
+<span class="keyword">namespace</span> <span class="identifier">concepts</span><span class="special">{</span>
+
+<span class="keyword">class</span> <span class="identifier">std_real_concept</span><span class="special">;</span>
+
+<span class="special">}}}</span> <span class="comment">// namespaces
+</span></pre>
+<p>
+        <code class="computeroutput"><span class="identifier">std_real_concept</span></code> is an archetype
+        for the built-in Real types.
+      </p>
+<p>
+        The main purpose in providing this type is to verify that standard library
+        functions are found via a using declaration - bringing those functions into
+        the current scope - and not just because they happen to be in global scope.
+      </p>
+<p>
+        In order to ensure that a call to say <code class="computeroutput"><span class="identifier">pow</span></code>
+        can be found either via argument dependent lookup, or failing that then in
+        the std namespace: all calls to standard library functions are unqualified,
+        with the std:: versions found via a using declaration to make them visible
+        in the current scope. Unfortunately it's all to easy to forget the using
+        declaration, and call the double version of the function that happens to
+        be in the global scope by mistake.
+      </p>
+<p>
+        For example if the code calls ::pow rather than std::pow, the code will cleanly
+        compile, but truncation of long doubles to double will cause a significant
+        loss of precision. In contrast a template instantiated with std_real_concept
+        will <span class="bold"><strong>only</strong></span> compile if the all the standard
+        library functions used have been brought into the current scope with a using
+        declaration.
+      </p>
+<p>
+        There is a test program libs/math/test/std_real_concept_check.cpp
+        that instantiates every template in this library with type <code class="computeroutput"><span class="identifier">std_real_concept</span></code> to verify it's usage of
+        standard library functions.
+      </p>
+<p>
+        
+</p>
+<pre class="programlisting"><span class="preprocessor">#include</span> <span class="special">&lt;</span><span class="identifier">boost</span><span class="special">/</span><span class="identifier">math</span><span class="special">/</span><span class="identifier">concepts</span><span class="special">/</span><span class="identifier">real_concept</span><span class="special">.</span><span class="identifier">hpp</span><span class="special">&gt;</span></pre>
+<p>
+      </p>
+<pre class="programlisting"><span class="keyword">namespace</span> <span class="identifier">boost</span><span class="special">{</span> 
+<span class="keyword">namespace</span> <span class="identifier">math</span><span class="special">{</span> 
+<span class="keyword">namespace</span> <span class="identifier">concepts</span><span class="special">{</span>
+
+<span class="keyword">class</span> <span class="identifier">real_concept</span><span class="special">;</span>
+
+<span class="special">}}}</span> <span class="comment">// namespaces
+</span></pre>
+<p>
+        <code class="computeroutput"><span class="identifier">real_concept</span></code> is an archetype
+        for <a class="link" href="concepts.html" title="Conceptual Requirements for Real Number Types">user defined real types</a>,
+        it declares it's standard library functions in it's own namespace: these
+        will only be found if they are called unqualified allowing argument dependent
+        lookup to locate them. In addition this type is useable at runtime: this
+        allows code that would not otherwise be exercised by the built-in floating
+        point types to be tested. There is no std::numeric_limits&lt;&gt; support
+        for this type, since this is not a conceptual requirement for <a class="link" href="concepts.html" title="Conceptual Requirements for Real Number Types">RealType</a>'s.
+      </p>
+<p>
+        NTL RR is an example of a type meeting the requirements that this type models,
+        but note that use of a thin wrapper class is required: refer to <a class="link" href="use_ntl.html" title="Using With NTL - a High-Precision Floating-Point Library">"Using
+        With NTL - a High-Precision Floating-Point Library"</a>.
+      </p>
+<p>
+        There is no specific test case for type <code class="computeroutput"><span class="identifier">real_concept</span></code>,
+        instead, since this type is usable at runtime, each individual test case
+        as well as testing <code class="computeroutput"><span class="keyword">float</span></code>, <code class="computeroutput"><span class="keyword">double</span></code> and <code class="computeroutput"><span class="keyword">long</span>
+        <span class="keyword">double</span></code>, also tests <code class="computeroutput"><span class="identifier">real_concept</span></code>.
+      </p>
+<p>
+        
+</p>
+<pre class="programlisting"><span class="preprocessor">#include</span> <span class="special">&lt;</span><span class="identifier">boost</span><span class="special">/</span><span class="identifier">math</span><span class="special">/</span><span class="identifier">concepts</span><span class="special">/</span><span class="identifier">distribution</span><span class="special">.</span><span class="identifier">hpp</span><span class="special">&gt;</span></pre>
+<p>
+      </p>
+<pre class="programlisting"><span class="keyword">namespace</span> <span class="identifier">boost</span><span class="special">{</span>
+<span class="keyword">namespace</span> <span class="identifier">math</span><span class="special">{</span>
+<span class="keyword">namespace</span> <span class="identifier">concepts</span><span class="special">{</span>
+
+<span class="keyword">template</span> <span class="special">&lt;</span><span class="keyword">class</span> <span class="identifier">RealType</span><span class="special">&gt;</span>
+<span class="keyword">class</span> <span class="identifier">distribution_archetype</span><span class="special">;</span>
+
+<span class="keyword">template</span> <span class="special">&lt;</span><span class="keyword">class</span> <span class="identifier">Distribution</span><span class="special">&gt;</span>
+<span class="keyword">struct</span> <span class="identifier">DistributionConcept</span><span class="special">;</span>
+
+<span class="special">}}}</span> <span class="comment">// namespaces
+</span></pre>
+<p>
+        The class template <code class="computeroutput"><span class="identifier">distribution_archetype</span></code>
+        is a model of the <a class="link" href="dist_concept.html" title="Conceptual Requirements for Distribution Types">Distribution
+        concept</a>.
+      </p>
+<p>
+        The class template <code class="computeroutput"><span class="identifier">DistributionConcept</span></code>
+        is a <a href="../../../../../../../libs/concept_check/index.html" target="_top">concept checking
+        class</a> for distribution types.
+      </p>
+<p>
+        The test program distribution_concept_check.cpp
+        is responsible for using <code class="computeroutput"><span class="identifier">DistributionConcept</span></code>
+        to verify that all the distributions in this library conform to the <a class="link" href="dist_concept.html" title="Conceptual Requirements for Distribution Types">Distribution concept</a>.
+      </p>
+<p>
+        The class template <code class="computeroutput"><span class="identifier">DistributionConcept</span></code>
+        verifies the existence (but not proper function) of the non-member accessors
+        required by the <a class="link" href="dist_concept.html" title="Conceptual Requirements for Distribution Types">Distribution
+        concept</a>. These are checked by calls like
+      </p>
+<p>
+        v = pdf(dist, x); // (Result v is ignored).
+      </p>
+<p>
+        And in addition, those that accept two arguments do the right thing when
+        the arguments are of different types (the result type is always the same
+        as the distribution's value_type). (This is implemented by some additional
+        forwarding-functions in derived_accessors.hpp, so that there is no need for
+        any code changes. Likewise boilerplate versions of the hazard/chf/coefficient_of_variation
+        functions are implemented in there too.)
+      </p>
+</div>
+<table xmlns:rev="http://www.cs.rpi.edu/~gregod/boost/tools/doc/revision" width="100%"><tr>
+<td align="left"></td>
+<td align="right"><div class="copyright-footer">Copyright © 2006 , 2007, 2008 John Maddock, Paul A. Bristow, Hubert
+      Holin, Xiaogang Zhang, Bruno Lalande and Gautam Sewani<p>
+        Distributed under the Boost Software License, Version 1.0. (See accompanying
+        file LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_0.txt)
+      </p>
+</div></td>
+</tr></table>
+<hr>
+<div class="spirit-nav">
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@@ -0,0 +1,1364 @@
+<html>
+<head>
+<meta http-equiv="Content-Type" content="text/html; charset=ISO-8859-1">
+<title>Conceptual Requirements for Real Number Types</title>
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+</div>
+<div class="section" lang="en">
+<div class="titlepage"><div><div><h3 class="title">
+<a name="math_toolkit.using_udt.concepts"></a><a class="link" href="concepts.html" title="Conceptual Requirements for Real Number Types"> Conceptual Requirements
+      for Real Number Types</a>
+</h3></div></div></div>
+<p>
+        The functions, and statistical distributions in this library can be used
+        with any type <span class="emphasis"><em>RealType</em></span> that meets the conceptual requirements
+        given below. All the built in floating point types will meet these requirements.
+        User defined types that meet the requirements can also be used. For example,
+        with <a class="link" href="use_ntl.html" title="Using With NTL - a High-Precision Floating-Point Library">a thin wrapper class</a>
+        one of the types provided with NTL (RR)
+        can be used. Submissions of binding to other extended precision types would
+        also be most welcome!
+      </p>
+<p>
+        The guiding principal behind these requirements, is that a <span class="emphasis"><em>RealType</em></span>
+        behaves just like a built in floating point type.
+      </p>
+<a name="math_toolkit.using_udt.concepts.basic_arithmetic_requirements"></a><h5>
+<a name="id860217"></a>
+        <a class="link" href="concepts.html#math_toolkit.using_udt.concepts.basic_arithmetic_requirements">Basic
+        Arithmetic Requirements</a>
+      </h5>
+<p>
+        These requirements are common to all of the functions in this library.
+      </p>
+<p>
+        In the following table <span class="emphasis"><em>r</em></span> is an object of type <code class="computeroutput"><span class="identifier">RealType</span></code>, <span class="emphasis"><em>cr</em></span> and
+        <span class="emphasis"><em>cr2</em></span> are objects of type <code class="computeroutput"><span class="keyword">const</span>
+        <span class="identifier">RealType</span></code>, and <span class="emphasis"><em>ca</em></span>
+        is an object of type <code class="computeroutput"><span class="keyword">const</span> <span class="identifier">arithmetic</span><span class="special">-</span><span class="identifier">type</span></code> (arithmetic types include all the
+        built in integers and floating point types).
+      </p>
+<div class="informaltable"><table class="table">
+<colgroup>
+<col>
+<col>
+<col>
+</colgroup>
+<thead><tr>
+<th>
+              <p>
+                Expression
+              </p>
+              </th>
+<th>
+              <p>
+                Result Type
+              </p>
+              </th>
+<th>
+              <p>
+                Notes
+              </p>
+              </th>
+</tr></thead>
+<tbody>
+<tr>
+<td>
+              <p>
+                <code class="computeroutput"><span class="identifier">RealType</span><span class="special">(</span><span class="identifier">cr</span><span class="special">)</span></code>
+              </p>
+              </td>
+<td>
+              <p>
+                RealType
+              </p>
+              </td>
+<td>
+              <p>
+                RealType is copy constructible.
+              </p>
+              </td>
+</tr>
+<tr>
+<td>
+              <p>
+                <code class="computeroutput"><span class="identifier">RealType</span><span class="special">(</span><span class="identifier">ca</span><span class="special">)</span></code>
+              </p>
+              </td>
+<td>
+              <p>
+                RealType
+              </p>
+              </td>
+<td>
+              <p>
+                RealType is copy constructible from the arithmetic types.
+              </p>
+              </td>
+</tr>
+<tr>
+<td>
+              <p>
+                <code class="computeroutput"><span class="identifier">r</span> <span class="special">=</span>
+                <span class="identifier">cr</span></code>
+              </p>
+              </td>
+<td>
+              <p>
+                RealType&amp;
+              </p>
+              </td>
+<td>
+              <p>
+                Assignment operator.
+              </p>
+              </td>
+</tr>
+<tr>
+<td>
+              <p>
+                <code class="computeroutput"><span class="identifier">r</span> <span class="special">=</span>
+                <span class="identifier">ca</span></code>
+              </p>
+              </td>
+<td>
+              <p>
+                RealType&amp;
+              </p>
+              </td>
+<td>
+              <p>
+                Assignment operator from the arithmetic types.
+              </p>
+              </td>
+</tr>
+<tr>
+<td>
+              <p>
+                <code class="computeroutput"><span class="identifier">r</span> <span class="special">+=</span>
+                <span class="identifier">cr</span></code>
+              </p>
+              </td>
+<td>
+              <p>
+                RealType&amp;
+              </p>
+              </td>
+<td>
+              <p>
+                Adds cr to r.
+              </p>
+              </td>
+</tr>
+<tr>
+<td>
+              <p>
+                <code class="computeroutput"><span class="identifier">r</span> <span class="special">+=</span>
+                <span class="identifier">ca</span></code>
+              </p>
+              </td>
+<td>
+              <p>
+                RealType&amp;
+              </p>
+              </td>
+<td>
+              <p>
+                Adds ar to r.
+              </p>
+              </td>
+</tr>
+<tr>
+<td>
+              <p>
+                <code class="computeroutput"><span class="identifier">r</span> <span class="special">-=</span>
+                <span class="identifier">cr</span></code>
+              </p>
+              </td>
+<td>
+              <p>
+                RealType&amp;
+              </p>
+              </td>
+<td>
+              <p>
+                Subtracts cr from r.
+              </p>
+              </td>
+</tr>
+<tr>
+<td>
+              <p>
+                <code class="computeroutput"><span class="identifier">r</span> <span class="special">-=</span>
+                <span class="identifier">ca</span></code>
+              </p>
+              </td>
+<td>
+              <p>
+                RealType&amp;
+              </p>
+              </td>
+<td>
+              <p>
+                Subtracts ca from r.
+              </p>
+              </td>
+</tr>
+<tr>
+<td>
+              <p>
+                <code class="computeroutput"><span class="identifier">r</span> <span class="special">*=</span>
+                <span class="identifier">cr</span></code>
+              </p>
+              </td>
+<td>
+              <p>
+                RealType&amp;
+              </p>
+              </td>
+<td>
+              <p>
+                Multiplies r by cr.
+              </p>
+              </td>
+</tr>
+<tr>
+<td>
+              <p>
+                <code class="computeroutput"><span class="identifier">r</span> <span class="special">*=</span>
+                <span class="identifier">ca</span></code>
+              </p>
+              </td>
+<td>
+              <p>
+                RealType&amp;
+              </p>
+              </td>
+<td>
+              <p>
+                Multiplies r by ca.
+              </p>
+              </td>
+</tr>
+<tr>
+<td>
+              <p>
+                <code class="computeroutput"><span class="identifier">r</span> <span class="special">/=</span>
+                <span class="identifier">cr</span></code>
+              </p>
+              </td>
+<td>
+              <p>
+                RealType&amp;
+              </p>
+              </td>
+<td>
+              <p>
+                Divides r by cr.
+              </p>
+              </td>
+</tr>
+<tr>
+<td>
+              <p>
+                <code class="computeroutput"><span class="identifier">r</span> <span class="special">/=</span>
+                <span class="identifier">ca</span></code>
+              </p>
+              </td>
+<td>
+              <p>
+                RealType&amp;
+              </p>
+              </td>
+<td>
+              <p>
+                Divides r by ca.
+              </p>
+              </td>
+</tr>
+<tr>
+<td>
+              <p>
+                <code class="computeroutput"><span class="special">-</span><span class="identifier">r</span></code>
+              </p>
+              </td>
+<td>
+              <p>
+                RealType
+              </p>
+              </td>
+<td>
+              <p>
+                Unary Negation.
+              </p>
+              </td>
+</tr>
+<tr>
+<td>
+              <p>
+                <code class="computeroutput"><span class="special">+</span><span class="identifier">r</span></code>
+              </p>
+              </td>
+<td>
+              <p>
+                RealType&amp;
+              </p>
+              </td>
+<td>
+              <p>
+                Identity Operation.
+              </p>
+              </td>
+</tr>
+<tr>
+<td>
+              <p>
+                <code class="computeroutput"><span class="identifier">cr</span> <span class="special">+</span>
+                <span class="identifier">cr2</span></code>
+              </p>
+              </td>
+<td>
+              <p>
+                RealType
+              </p>
+              </td>
+<td>
+              <p>
+                Binary Addition
+              </p>
+              </td>
+</tr>
+<tr>
+<td>
+              <p>
+                <code class="computeroutput"><span class="identifier">cr</span> <span class="special">+</span>
+                <span class="identifier">ca</span></code>
+              </p>
+              </td>
+<td>
+              <p>
+                RealType
+              </p>
+              </td>
+<td>
+              <p>
+                Binary Addition
+              </p>
+              </td>
+</tr>
+<tr>
+<td>
+              <p>
+                <code class="computeroutput"><span class="identifier">ca</span> <span class="special">+</span>
+                <span class="identifier">cr</span></code>
+              </p>
+              </td>
+<td>
+              <p>
+                RealType
+              </p>
+              </td>
+<td>
+              <p>
+                Binary Addition
+              </p>
+              </td>
+</tr>
+<tr>
+<td>
+              <p>
+                <code class="computeroutput"><span class="identifier">cr</span> <span class="special">-</span>
+                <span class="identifier">cr2</span></code>
+              </p>
+              </td>
+<td>
+              <p>
+                RealType
+              </p>
+              </td>
+<td>
+              <p>
+                Binary Subtraction
+              </p>
+              </td>
+</tr>
+<tr>
+<td>
+              <p>
+                <code class="computeroutput"><span class="identifier">cr</span> <span class="special">-</span>
+                <span class="identifier">ca</span></code>
+              </p>
+              </td>
+<td>
+              <p>
+                RealType
+              </p>
+              </td>
+<td>
+              <p>
+                Binary Subtraction
+              </p>
+              </td>
+</tr>
+<tr>
+<td>
+              <p>
+                <code class="computeroutput"><span class="identifier">ca</span> <span class="special">-</span>
+                <span class="identifier">cr</span></code>
+              </p>
+              </td>
+<td>
+              <p>
+                RealType
+              </p>
+              </td>
+<td>
+              <p>
+                Binary Subtraction
+              </p>
+              </td>
+</tr>
+<tr>
+<td>
+              <p>
+                <code class="computeroutput"><span class="identifier">cr</span> <span class="special">*</span>
+                <span class="identifier">cr2</span></code>
+              </p>
+              </td>
+<td>
+              <p>
+                RealType
+              </p>
+              </td>
+<td>
+              <p>
+                Binary Multiplication
+              </p>
+              </td>
+</tr>
+<tr>
+<td>
+              <p>
+                <code class="computeroutput"><span class="identifier">cr</span> <span class="special">*</span>
+                <span class="identifier">ca</span></code>
+              </p>
+              </td>
+<td>
+              <p>
+                RealType
+              </p>
+              </td>
+<td>
+              <p>
+                Binary Multiplication
+              </p>
+              </td>
+</tr>
+<tr>
+<td>
+              <p>
+                <code class="computeroutput"><span class="identifier">ca</span> <span class="special">*</span>
+                <span class="identifier">cr</span></code>
+              </p>
+              </td>
+<td>
+              <p>
+                RealType
+              </p>
+              </td>
+<td>
+              <p>
+                Binary Multiplication
+              </p>
+              </td>
+</tr>
+<tr>
+<td>
+              <p>
+                <code class="computeroutput"><span class="identifier">cr</span> <span class="special">/</span>
+                <span class="identifier">cr2</span></code>
+              </p>
+              </td>
+<td>
+              <p>
+                RealType
+              </p>
+              </td>
+<td>
+              <p>
+                Binary Subtraction
+              </p>
+              </td>
+</tr>
+<tr>
+<td>
+              <p>
+                <code class="computeroutput"><span class="identifier">cr</span> <span class="special">/</span>
+                <span class="identifier">ca</span></code>
+              </p>
+              </td>
+<td>
+              <p>
+                RealType
+              </p>
+              </td>
+<td>
+              <p>
+                Binary Subtraction
+              </p>
+              </td>
+</tr>
+<tr>
+<td>
+              <p>
+                <code class="computeroutput"><span class="identifier">ca</span> <span class="special">/</span>
+                <span class="identifier">cr</span></code>
+              </p>
+              </td>
+<td>
+              <p>
+                RealType
+              </p>
+              </td>
+<td>
+              <p>
+                Binary Subtraction
+              </p>
+              </td>
+</tr>
+<tr>
+<td>
+              <p>
+                <code class="computeroutput"><span class="identifier">cr</span> <span class="special">==</span>
+                <span class="identifier">cr2</span></code>
+              </p>
+              </td>
+<td>
+              <p>
+                bool
+              </p>
+              </td>
+<td>
+              <p>
+                Equality Comparison
+              </p>
+              </td>
+</tr>
+<tr>
+<td>
+              <p>
+                <code class="computeroutput"><span class="identifier">cr</span> <span class="special">==</span>
+                <span class="identifier">ca</span></code>
+              </p>
+              </td>
+<td>
+              <p>
+                bool
+              </p>
+              </td>
+<td>
+              <p>
+                Equality Comparison
+              </p>
+              </td>
+</tr>
+<tr>
+<td>
+              <p>
+                <code class="computeroutput"><span class="identifier">ca</span> <span class="special">==</span>
+                <span class="identifier">cr</span></code>
+              </p>
+              </td>
+<td>
+              <p>
+                bool
+              </p>
+              </td>
+<td>
+              <p>
+                Equality Comparison
+              </p>
+              </td>
+</tr>
+<tr>
+<td>
+              <p>
+                <code class="computeroutput"><span class="identifier">cr</span> <span class="special">!=</span>
+                <span class="identifier">cr2</span></code>
+              </p>
+              </td>
+<td>
+              <p>
+                bool
+              </p>
+              </td>
+<td>
+              <p>
+                Inequality Comparison
+              </p>
+              </td>
+</tr>
+<tr>
+<td>
+              <p>
+                <code class="computeroutput"><span class="identifier">cr</span> <span class="special">!=</span>
+                <span class="identifier">ca</span></code>
+              </p>
+              </td>
+<td>
+              <p>
+                bool
+              </p>
+              </td>
+<td>
+              <p>
+                Inequality Comparison
+              </p>
+              </td>
+</tr>
+<tr>
+<td>
+              <p>
+                <code class="computeroutput"><span class="identifier">ca</span> <span class="special">!=</span>
+                <span class="identifier">cr</span></code>
+              </p>
+              </td>
+<td>
+              <p>
+                bool
+              </p>
+              </td>
+<td>
+              <p>
+                Inequality Comparison
+              </p>
+              </td>
+</tr>
+<tr>
+<td>
+              <p>
+                <code class="computeroutput"><span class="identifier">cr</span> <span class="special">&lt;=</span>
+                <span class="identifier">cr2</span></code>
+              </p>
+              </td>
+<td>
+              <p>
+                bool
+              </p>
+              </td>
+<td>
+              <p>
+                Less than equal to.
+              </p>
+              </td>
+</tr>
+<tr>
+<td>
+              <p>
+                <code class="computeroutput"><span class="identifier">cr</span> <span class="special">&lt;=</span>
+                <span class="identifier">ca</span></code>
+              </p>
+              </td>
+<td>
+              <p>
+                bool
+              </p>
+              </td>
+<td>
+              <p>
+                Less than equal to.
+              </p>
+              </td>
+</tr>
+<tr>
+<td>
+              <p>
+                <code class="computeroutput"><span class="identifier">ca</span> <span class="special">&lt;=</span>
+                <span class="identifier">cr</span></code>
+              </p>
+              </td>
+<td>
+              <p>
+                bool
+              </p>
+              </td>
+<td>
+              <p>
+                Less than equal to.
+              </p>
+              </td>
+</tr>
+<tr>
+<td>
+              <p>
+                <code class="computeroutput"><span class="identifier">cr</span> <span class="special">&gt;=</span>
+                <span class="identifier">cr2</span></code>
+              </p>
+              </td>
+<td>
+              <p>
+                bool
+              </p>
+              </td>
+<td>
+              <p>
+                Greater than equal to.
+              </p>
+              </td>
+</tr>
+<tr>
+<td>
+              <p>
+                <code class="computeroutput"><span class="identifier">cr</span> <span class="special">&gt;=</span>
+                <span class="identifier">ca</span></code>
+              </p>
+              </td>
+<td>
+              <p>
+                bool
+              </p>
+              </td>
+<td>
+              <p>
+                Greater than equal to.
+              </p>
+              </td>
+</tr>
+<tr>
+<td>
+              <p>
+                <code class="computeroutput"><span class="identifier">ca</span> <span class="special">&gt;=</span>
+                <span class="identifier">cr</span></code>
+              </p>
+              </td>
+<td>
+              <p>
+                bool
+              </p>
+              </td>
+<td>
+              <p>
+                Greater than equal to.
+              </p>
+              </td>
+</tr>
+<tr>
+<td>
+              <p>
+                <code class="computeroutput"><span class="identifier">cr</span> <span class="special">&lt;</span>
+                <span class="identifier">cr2</span></code>
+              </p>
+              </td>
+<td>
+              <p>
+                bool
+              </p>
+              </td>
+<td>
+              <p>
+                Less than comparison.
+              </p>
+              </td>
+</tr>
+<tr>
+<td>
+              <p>
+                <code class="computeroutput"><span class="identifier">cr</span> <span class="special">&lt;</span>
+                <span class="identifier">ca</span></code>
+              </p>
+              </td>
+<td>
+              <p>
+                bool
+              </p>
+              </td>
+<td>
+              <p>
+                Less than comparison.
+              </p>
+              </td>
+</tr>
+<tr>
+<td>
+              <p>
+                <code class="computeroutput"><span class="identifier">ca</span> <span class="special">&lt;</span>
+                <span class="identifier">cr</span></code>
+              </p>
+              </td>
+<td>
+              <p>
+                bool
+              </p>
+              </td>
+<td>
+              <p>
+                Less than comparison.
+              </p>
+              </td>
+</tr>
+<tr>
+<td>
+              <p>
+                <code class="computeroutput"><span class="identifier">cr</span> <span class="special">&gt;</span>
+                <span class="identifier">cr2</span></code>
+              </p>
+              </td>
+<td>
+              <p>
+                bool
+              </p>
+              </td>
+<td>
+              <p>
+                Greater than comparison.
+              </p>
+              </td>
+</tr>
+<tr>
+<td>
+              <p>
+                <code class="computeroutput"><span class="identifier">cr</span> <span class="special">&gt;</span>
+                <span class="identifier">ca</span></code>
+              </p>
+              </td>
+<td>
+              <p>
+                bool
+              </p>
+              </td>
+<td>
+              <p>
+                Greater than comparison.
+              </p>
+              </td>
+</tr>
+<tr>
+<td>
+              <p>
+                <code class="computeroutput"><span class="identifier">ca</span> <span class="special">&gt;</span>
+                <span class="identifier">cr</span></code>
+              </p>
+              </td>
+<td>
+              <p>
+                bool
+              </p>
+              </td>
+<td>
+              <p>
+                Greater than comparison.
+              </p>
+              </td>
+</tr>
+<tr>
+<td>
+              <p>
+                <code class="computeroutput"><span class="identifier">boost</span><span class="special">::</span><span class="identifier">math</span><span class="special">::</span><span class="identifier">tools</span><span class="special">::</span><span class="identifier">digits</span><span class="special">&lt;</span><span class="identifier">RealType</span><span class="special">&gt;()</span></code>
+              </p>
+              </td>
+<td>
+              <p>
+                int
+              </p>
+              </td>
+<td>
+              <p>
+                The number of digits in the significand of RealType.
+              </p>
+              </td>
+</tr>
+<tr>
+<td>
+              <p>
+                <code class="computeroutput"><span class="identifier">boost</span><span class="special">::</span><span class="identifier">math</span><span class="special">::</span><span class="identifier">tools</span><span class="special">::</span><span class="identifier">max_value</span><span class="special">&lt;</span><span class="identifier">RealType</span><span class="special">&gt;()</span></code>
+              </p>
+              </td>
+<td>
+              <p>
+                RealType
+              </p>
+              </td>
+<td>
+              <p>
+                The largest representable number by type RealType.
+              </p>
+              </td>
+</tr>
+<tr>
+<td>
+              <p>
+                <code class="computeroutput"><span class="identifier">boost</span><span class="special">::</span><span class="identifier">math</span><span class="special">::</span><span class="identifier">tools</span><span class="special">::</span><span class="identifier">min_value</span><span class="special">&lt;</span><span class="identifier">RealType</span><span class="special">&gt;()</span></code>
+              </p>
+              </td>
+<td>
+              <p>
+                RealType
+              </p>
+              </td>
+<td>
+              <p>
+                The smallest representable number by type RealType.
+              </p>
+              </td>
+</tr>
+<tr>
+<td>
+              <p>
+                <code class="computeroutput"><span class="identifier">boost</span><span class="special">::</span><span class="identifier">math</span><span class="special">::</span><span class="identifier">tools</span><span class="special">::</span><span class="identifier">log_max_value</span><span class="special">&lt;</span><span class="identifier">RealType</span><span class="special">&gt;()</span></code>
+              </p>
+              </td>
+<td>
+              <p>
+                RealType
+              </p>
+              </td>
+<td>
+              <p>
+                The natural logarithm of the largest representable number by type
+                RealType.
+              </p>
+              </td>
+</tr>
+<tr>
+<td>
+              <p>
+                <code class="computeroutput"><span class="identifier">boost</span><span class="special">::</span><span class="identifier">math</span><span class="special">::</span><span class="identifier">tools</span><span class="special">::</span><span class="identifier">log_min_value</span><span class="special">&lt;</span><span class="identifier">RealType</span><span class="special">&gt;()</span></code>
+              </p>
+              </td>
+<td>
+              <p>
+                RealType
+              </p>
+              </td>
+<td>
+              <p>
+                The natural logarithm of the smallest representable number by type
+                RealType.
+              </p>
+              </td>
+</tr>
+<tr>
+<td>
+              <p>
+                <code class="computeroutput"><span class="identifier">boost</span><span class="special">::</span><span class="identifier">math</span><span class="special">::</span><span class="identifier">tools</span><span class="special">::</span><span class="identifier">epsilon</span><span class="special">&lt;</span><span class="identifier">RealType</span><span class="special">&gt;()</span></code>
+              </p>
+              </td>
+<td>
+              <p>
+                RealType
+              </p>
+              </td>
+<td>
+              <p>
+                The machine epsilon of RealType.
+              </p>
+              </td>
+</tr>
+</tbody>
+</table></div>
+<p>
+        Note that:
+      </p>
+<div class="orderedlist"><ol type="1">
+<li>
+          The functions <code class="computeroutput"><span class="identifier">log_max_value</span></code>
+          and <code class="computeroutput"><span class="identifier">log_min_value</span></code> can be
+          synthesised from the others, and so no explicit specialisation is required.
+        </li>
+<li>
+          The function <code class="computeroutput"><span class="identifier">epsilon</span></code> can
+          be synthesised from the others, so no explicit specialisation is required
+          provided the precision of RealType does not vary at runtime (see the header
+          boost/math/bindings/rr.hpp
+          for an example where the precision does vary at runtime).
+        </li>
+<li>
+          The functions <code class="computeroutput"><span class="identifier">digits</span></code>,
+          <code class="computeroutput"><span class="identifier">max_value</span></code> and <code class="computeroutput"><span class="identifier">min_value</span></code>, all get synthesised automatically
+          from <code class="computeroutput"><span class="identifier">std</span><span class="special">::</span><span class="identifier">numeric_limits</span></code>. However, if <code class="computeroutput"><span class="identifier">numeric_limits</span></code> is not specialised for
+          type RealType, then you will get a compiler error when code tries to use
+          these functions, <span class="emphasis"><em>unless</em></span> you explicitly specialise
+          them. For example if the precision of RealType varies at runtime, then
+          <code class="computeroutput"><span class="identifier">numeric_limits</span></code> support
+          may not be appropriate, see boost/math/bindings/rr.hpp
+          for examples.
+        </li>
+</ol></div>
+<div class="warning"><table border="0" summary="Warning">
+<tr>
+<td rowspan="2" align="center" valign="top" width="25"><img alt="[Warning]" src="../../../../doc/html/images/warning.png"></td>
+<th align="left">Warning</th>
+</tr>
+<tr><td align="left" valign="top">
+<p>
+          If <code class="computeroutput"><span class="identifier">std</span><span class="special">::</span><span class="identifier">numeric_limits</span><span class="special">&lt;&gt;</span></code>
+          is <span class="bold"><strong>not specialized</strong></span> for type <span class="emphasis"><em>RealType</em></span>
+          then the default float precision of 6 decimal digits will be used by other
+          Boost programs including:
+        </p>
+<p>
+          Boost.Test: giving misleading error messages like
+        </p>
+<p>
+          <span class="emphasis"><em>"difference between {9.79796} and {9.79796} exceeds 5.42101e-19%".</em></span>
+        </p>
+<p>
+          Boost.LexicalCast and Boost.Serialization when converting the number to
+          a string, causing potentially serious loss of accuracy on output.
+        </p>
+<p>
+          Although it might seem obvious that RealType should require <code class="computeroutput"><span class="identifier">std</span><span class="special">::</span><span class="identifier">numeric_limits</span></code> to be specialized, this
+          is not sensible for <code class="computeroutput"><span class="identifier">NTL</span><span class="special">::</span><span class="identifier">RR</span></code>
+          and similar classes where the number of digits is a runtime parameter (where
+          as for <code class="computeroutput"><span class="identifier">numeric_limits</span></code> it
+          has to be fixed at compile time).
+        </p>
+</td></tr>
+</table></div>
+<a name="math_toolkit.using_udt.concepts.standard_library_support_requirements"></a><h5>
+<a name="id863386"></a>
+        <a class="link" href="concepts.html#math_toolkit.using_udt.concepts.standard_library_support_requirements">Standard
+        Library Support Requirements</a>
+      </h5>
+<p>
+        Many (though not all) of the functions in this library make calls to standard
+        library functions, the following table summarises the requirements. Note
+        that most of the functions in this library will only call a small subset
+        of the functions listed here, so if in doubt whether a user defined type
+        has enough standard library support to be useable the best advise is to try
+        it and see!
+      </p>
+<p>
+        In the following table <span class="emphasis"><em>r</em></span> is an object of type <code class="computeroutput"><span class="identifier">RealType</span></code>, <span class="emphasis"><em>cr1</em></span> and
+        <span class="emphasis"><em>cr2</em></span> are objects of type <code class="computeroutput"><span class="keyword">const</span>
+        <span class="identifier">RealType</span></code>, and <span class="emphasis"><em>i</em></span>
+        is an object of type <code class="computeroutput"><span class="keyword">int</span></code>.
+      </p>
+<div class="informaltable"><table class="table">
+<colgroup>
+<col>
+<col>
+</colgroup>
+<thead><tr>
+<th>
+              <p>
+                Expression
+              </p>
+              </th>
+<th>
+              <p>
+                Result Type
+              </p>
+              </th>
+</tr></thead>
+<tbody>
+<tr>
+<td>
+              <p>
+                <code class="computeroutput"><span class="identifier">fabs</span><span class="special">(</span><span class="identifier">cr1</span><span class="special">)</span></code>
+              </p>
+              </td>
+<td>
+              <p>
+                RealType
+              </p>
+              </td>
+</tr>
+<tr>
+<td>
+              <p>
+                <code class="computeroutput"><span class="identifier">abs</span><span class="special">(</span><span class="identifier">cr1</span><span class="special">)</span></code>
+              </p>
+              </td>
+<td>
+              <p>
+                RealType
+              </p>
+              </td>
+</tr>
+<tr>
+<td>
+              <p>
+                <code class="computeroutput"><span class="identifier">ceil</span><span class="special">(</span><span class="identifier">cr1</span><span class="special">)</span></code>
+              </p>
+              </td>
+<td>
+              <p>
+                RealType
+              </p>
+              </td>
+</tr>
+<tr>
+<td>
+              <p>
+                <code class="computeroutput"><span class="identifier">floor</span><span class="special">(</span><span class="identifier">cr1</span><span class="special">)</span></code>
+              </p>
+              </td>
+<td>
+              <p>
+                RealType
+              </p>
+              </td>
+</tr>
+<tr>
+<td>
+              <p>
+                <code class="computeroutput"><span class="identifier">exp</span><span class="special">(</span><span class="identifier">cr1</span><span class="special">)</span></code>
+              </p>
+              </td>
+<td>
+              <p>
+                RealType
+              </p>
+              </td>
+</tr>
+<tr>
+<td>
+              <p>
+                <code class="computeroutput"><span class="identifier">pow</span><span class="special">(</span><span class="identifier">cr1</span><span class="special">,</span>
+                <span class="identifier">cr2</span><span class="special">)</span></code>
+              </p>
+              </td>
+<td>
+              <p>
+                RealType
+              </p>
+              </td>
+</tr>
+<tr>
+<td>
+              <p>
+                <code class="computeroutput"><span class="identifier">sqrt</span><span class="special">(</span><span class="identifier">cr1</span><span class="special">)</span></code>
+              </p>
+              </td>
+<td>
+              <p>
+                RealType
+              </p>
+              </td>
+</tr>
+<tr>
+<td>
+              <p>
+                <code class="computeroutput"><span class="identifier">log</span><span class="special">(</span><span class="identifier">cr1</span><span class="special">)</span></code>
+              </p>
+              </td>
+<td>
+              <p>
+                RealType
+              </p>
+              </td>
+</tr>
+<tr>
+<td>
+              <p>
+                <code class="computeroutput"><span class="identifier">frexp</span><span class="special">(</span><span class="identifier">cr1</span><span class="special">,</span>
+                <span class="special">&amp;</span><span class="identifier">i</span><span class="special">)</span></code>
+              </p>
+              </td>
+<td>
+              <p>
+                RealType
+              </p>
+              </td>
+</tr>
+<tr>
+<td>
+              <p>
+                <code class="computeroutput"><span class="identifier">ldexp</span><span class="special">(</span><span class="identifier">cr1</span><span class="special">,</span>
+                <span class="identifier">i</span><span class="special">)</span></code>
+              </p>
+              </td>
+<td>
+              <p>
+                RealType
+              </p>
+              </td>
+</tr>
+<tr>
+<td>
+              <p>
+                <code class="computeroutput"><span class="identifier">cos</span><span class="special">(</span><span class="identifier">cr1</span><span class="special">)</span></code>
+              </p>
+              </td>
+<td>
+              <p>
+                RealType
+              </p>
+              </td>
+</tr>
+<tr>
+<td>
+              <p>
+                <code class="computeroutput"><span class="identifier">sin</span><span class="special">(</span><span class="identifier">cr1</span><span class="special">)</span></code>
+              </p>
+              </td>
+<td>
+              <p>
+                RealType
+              </p>
+              </td>
+</tr>
+<tr>
+<td>
+              <p>
+                <code class="computeroutput"><span class="identifier">asin</span><span class="special">(</span><span class="identifier">cr1</span><span class="special">)</span></code>
+              </p>
+              </td>
+<td>
+              <p>
+                RealType
+              </p>
+              </td>
+</tr>
+<tr>
+<td>
+              <p>
+                <code class="computeroutput"><span class="identifier">tan</span><span class="special">(</span><span class="identifier">cr1</span><span class="special">)</span></code>
+              </p>
+              </td>
+<td>
+              <p>
+                RealType
+              </p>
+              </td>
+</tr>
+<tr>
+<td>
+              <p>
+                <code class="computeroutput"><span class="identifier">atan</span><span class="special">(</span><span class="identifier">cr1</span><span class="special">)</span></code>
+              </p>
+              </td>
+<td>
+              <p>
+                RealType
+              </p>
+              </td>
+</tr>
+<tr>
+<td>
+              <p>
+                <code class="computeroutput"><span class="identifier">fmod</span><span class="special">(</span><span class="identifier">cr1</span><span class="special">)</span></code>
+              </p>
+              </td>
+<td>
+              <p>
+                RealType
+              </p>
+              </td>
+</tr>
+<tr>
+<td>
+              <p>
+                <code class="computeroutput"><span class="identifier">round</span><span class="special">(</span><span class="identifier">cr1</span><span class="special">)</span></code>
+              </p>
+              </td>
+<td>
+              <p>
+                RealType
+              </p>
+              </td>
+</tr>
+<tr>
+<td>
+              <p>
+                <code class="computeroutput"><span class="identifier">iround</span><span class="special">(</span><span class="identifier">cr1</span><span class="special">)</span></code>
+              </p>
+              </td>
+<td>
+              <p>
+                int
+              </p>
+              </td>
+</tr>
+<tr>
+<td>
+              <p>
+                <code class="computeroutput"><span class="identifier">trunc</span><span class="special">(</span><span class="identifier">cr1</span><span class="special">)</span></code>
+              </p>
+              </td>
+<td>
+              <p>
+                RealType
+              </p>
+              </td>
+</tr>
+<tr>
+<td>
+              <p>
+                <code class="computeroutput"><span class="identifier">itrunc</span><span class="special">(</span><span class="identifier">cr1</span><span class="special">)</span></code>
+              </p>
+              </td>
+<td>
+              <p>
+                int
+              </p>
+              </td>
+</tr>
+</tbody>
+</table></div>
+<p>
+        Note that the table above lists only those standard library functions known
+        to be used (or likely to be used in the near future) by this library. The
+        following functions: <code class="computeroutput"><span class="identifier">acos</span></code>,
+        <code class="computeroutput"><span class="identifier">atan2</span></code>, <code class="computeroutput"><span class="identifier">fmod</span></code>,
+        <code class="computeroutput"><span class="identifier">cosh</span></code>, <code class="computeroutput"><span class="identifier">sinh</span></code>,
+        <code class="computeroutput"><span class="identifier">tanh</span></code>, <code class="computeroutput"><span class="identifier">log10</span></code>,
+        <code class="computeroutput"><span class="identifier">lround</span></code>, <code class="computeroutput"><span class="identifier">llround</span></code>,
+        ltrunc<code class="computeroutput"><span class="special">,</span> </code>lltrunc<code class="computeroutput"> <span class="keyword">and</span> </code>modf` are not currently used, but may
+        be if further special functions are added.
+      </p>
+<p>
+        Note that the <code class="computeroutput"><span class="identifier">round</span></code>, <code class="computeroutput"><span class="identifier">trunc</span></code> and <code class="computeroutput"><span class="identifier">modf</span></code>
+        functions are not part of the current C++ standard: they are part of the
+        additions added to C99 which will likely be in the next C++ standard. There
+        are Boost versions of these provided as a backup, and the functions are always
+        called unqualified so that argument-dependent-lookup can take place.
+      </p>
+<p>
+        In addition, for efficient and accurate results, a <a class="link" href="../backgrounders/lanczos.html" title="The Lanczos Approximation">Lanczos
+        approximation</a> is highly desirable. You may be able to adapt an existing
+        approximation from boost/math/special_functions/lanczos.hpp
+        or libs/math/tools/ntl_rr_lanczos.hpp:
+        you will need change static_cast's to lexical_cast's, and the constants to
+        <span class="emphasis"><em>strings</em></span> (in order to ensure the coefficients aren't
+        truncated to long double) and then specialise <code class="computeroutput"><span class="identifier">lanczos_traits</span></code>
+        for type T. Otherwise you may have to hack libs/math/tools/lanczos_generator.cpp
+        to find a suitable approximation for your RealType. The code will still compile
+        if you don't do this, but both accuracy and efficiency will be greatly compromised
+        in any function that makes use of the gamma/beta/erf family of functions.
+      </p>
+</div>
+<table xmlns:rev="http://www.cs.rpi.edu/~gregod/boost/tools/doc/revision" width="100%"><tr>
+<td align="left"></td>
+<td align="right"><div class="copyright-footer">Copyright © 2006 , 2007, 2008 John Maddock, Paul A. Bristow, Hubert
+      Holin, Xiaogang Zhang, Bruno Lalande and Gautam Sewani<p>
+        Distributed under the Boost Software License, Version 1.0. (See accompanying
+        file LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_0.txt)
+      </p>
+</div></td>
+</tr></table>
+<hr>
+<div class="spirit-nav">
+<a accesskey="p" href="use_mpfr.html"><img src="../../../../doc/html/images/prev.png" alt="Prev"></a><a accesskey="u" href="../using_udt.html"><img src="../../../../doc/html/images/up.png" alt="Up"></a><a accesskey="h" href="../../index.html"><img src="../../../../doc/html/images/home.png" alt="Home"></a><a accesskey="n" href="dist_concept.html"><img src="../../../../doc/html/images/next.png" alt="Next"></a>
+</div>
+</body>
+</html>

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--- (empty file)
+++ sandbox/tools/auto_index/example/math/doc/sf_and_dist/html/math_toolkit/using_udt/dist_concept.html	2008-11-28 05:25:28 EST (Fri, 28 Nov 2008)
@@ -0,0 +1,396 @@
+<html>
+<head>
+<meta http-equiv="Content-Type" content="text/html; charset=ISO-8859-1">
+<title>Conceptual Requirements for Distribution Types</title>
+<link rel="stylesheet" href="../../boostbook.css" type="text/css">
+<meta name="generator" content="DocBook XSL Stylesheets Vsnapshot_8125">
+<link rel="home" href="../../index.html" title="Math Toolkit">
+<link rel="up" href="../using_udt.html" title="Use with User-Defined Floating-Point Types">
+<link rel="prev" href="concepts.html" title="Conceptual Requirements for Real Number Types">
+<link rel="next" href="archetypes.html" title="Conceptual Archetypes and Testing">
+</head>
+<body bgcolor="white" text="black" link="#0000FF" vlink="#840084" alink="#0000FF">
+<table cellpadding="2" width="100%"><tr>
+<td valign="top"><img alt="Boost C++ Libraries" width="277" height="86" src="../../../../boost.png"></td>
+<td align="center">Home</td>
+<td align="center">Libraries</td>
+<td align="center">People</td>
+<td align="center">FAQ</td>
+<td align="center">More</td>
+</tr></table>
+<hr>
+<div class="spirit-nav">
+<a accesskey="p" href="concepts.html"><img src="../../../../doc/html/images/prev.png" alt="Prev"></a><a accesskey="u" href="../using_udt.html"><img src="../../../../doc/html/images/up.png" alt="Up"></a><a accesskey="h" href="../../index.html"><img src="../../../../doc/html/images/home.png" alt="Home"></a><a accesskey="n" href="archetypes.html"><img src="../../../../doc/html/images/next.png" alt="Next"></a>
+</div>
+<div class="section" lang="en">
+<div class="titlepage"><div><div><h3 class="title">
+<a name="math_toolkit.using_udt.dist_concept"></a><a class="link" href="dist_concept.html" title="Conceptual Requirements for Distribution Types"> Conceptual Requirements
+      for Distribution Types</a>
+</h3></div></div></div>
+<p>
+        A <span class="emphasis"><em>DistributionType</em></span> is a type that implements the following
+        conceptual requirements, and encapsulates a statistical distribution.
+      </p>
+<p>
+        Please note that this documentation should not be used as a substitute for
+        the <a class="link" href="../dist/dist_ref.html" title="Statistical Distributions Reference">reference documentation</a>,
+        and <a class="link" href="../dist/stat_tut.html" title="Statistical Distributions Tutorial">tutorial</a> of the statistical
+        distributions.
+      </p>
+<p>
+        In the following table, <span class="emphasis"><em>d</em></span> is an object of type <code class="computeroutput"><span class="identifier">DistributionType</span></code>, <span class="emphasis"><em>cd</em></span>
+        is an object of type <code class="computeroutput"><span class="keyword">const</span> <span class="identifier">DistributionType</span></code> and <span class="emphasis"><em>cr</em></span>
+        is an object of a type convertible to <code class="computeroutput"><span class="identifier">RealType</span></code>.
+      </p>
+<div class="informaltable"><table class="table">
+<colgroup>
+<col>
+<col>
+<col>
+</colgroup>
+<thead><tr>
+<th>
+              <p>
+                Expression
+              </p>
+              </th>
+<th>
+              <p>
+                Result Type
+              </p>
+              </th>
+<th>
+              <p>
+                Notes
+              </p>
+              </th>
+</tr></thead>
+<tbody>
+<tr>
+<td>
+              <p>
+                DistributionType::value_type
+              </p>
+              </td>
+<td>
+              <p>
+                RealType
+              </p>
+              </td>
+<td>
+              <p>
+                The real-number type <span class="emphasis"><em>RealType</em></span> upon which the
+                distribution operates.
+              </p>
+              </td>
+</tr>
+<tr>
+<td>
+              <p>
+                DistributionType::policy_type
+              </p>
+              </td>
+<td>
+              <p>
+                RealType
+              </p>
+              </td>
+<td>
+              <p>
+                The <a class="link" href="../policy.html" title="Policies">Policy</a> to use when
+                evaluating functions that depend on this distribution.
+              </p>
+              </td>
+</tr>
+<tr>
+<td>
+              <p>
+                d = cd
+              </p>
+              </td>
+<td>
+              <p>
+                Distribution&amp;
+              </p>
+              </td>
+<td>
+              <p>
+                Distribution types are assignable.
+              </p>
+              </td>
+</tr>
+<tr>
+<td>
+              <p>
+                Distribution(cd)
+              </p>
+              </td>
+<td>
+              <p>
+                Distribution
+              </p>
+              </td>
+<td>
+              <p>
+                Distribution types are copy constructible.
+              </p>
+              </td>
+</tr>
+<tr>
+<td>
+              <p>
+                pdf(cd, cr)
+              </p>
+              </td>
+<td>
+              <p>
+                RealType
+              </p>
+              </td>
+<td>
+              <p>
+                Returns the PDF of the distribution.
+              </p>
+              </td>
+</tr>
+<tr>
+<td>
+              <p>
+                cdf(cd, cr)
+              </p>
+              </td>
+<td>
+              <p>
+                RealType
+              </p>
+              </td>
+<td>
+              <p>
+                Returns the CDF of the distribution.
+              </p>
+              </td>
+</tr>
+<tr>
+<td>
+              <p>
+                cdf(complement(cd, cr))
+              </p>
+              </td>
+<td>
+              <p>
+                RealType
+              </p>
+              </td>
+<td>
+              <p>
+                Returns the complement of the CDF of the distribution, the same as:
+                <code class="computeroutput"><span class="number">1</span><span class="special">-</span><span class="identifier">cdf</span><span class="special">(</span><span class="identifier">cd</span><span class="special">,</span> <span class="identifier">cr</span><span class="special">)</span></code>
+              </p>
+              </td>
+</tr>
+<tr>
+<td>
+              <p>
+                quantile(cd, cr)
+              </p>
+              </td>
+<td>
+              <p>
+                RealType
+              </p>
+              </td>
+<td>
+              <p>
+                Returns the quantile of the distribution.
+              </p>
+              </td>
+</tr>
+<tr>
+<td>
+              <p>
+                quantile(complement(cd, cr))
+              </p>
+              </td>
+<td>
+              <p>
+                RealType
+              </p>
+              </td>
+<td>
+              <p>
+                Returns the quantile of the distribution, starting from the complement
+                of the probability, the same as: <code class="computeroutput"><span class="identifier">quantile</span><span class="special">(</span><span class="identifier">cd</span><span class="special">,</span> <span class="number">1</span><span class="special">-</span><span class="identifier">cr</span><span class="special">)</span></code>
+              </p>
+              </td>
+</tr>
+<tr>
+<td>
+              <p>
+                chf(cd, cr)
+              </p>
+              </td>
+<td>
+              <p>
+                RealType
+              </p>
+              </td>
+<td>
+              <p>
+                Returns the cumulative hazard function of the distribution.
+              </p>
+              </td>
+</tr>
+<tr>
+<td>
+              <p>
+                hazard(cd, cr)
+              </p>
+              </td>
+<td>
+              <p>
+                RealType
+              </p>
+              </td>
+<td>
+              <p>
+                Returns the hazard function of the distribution.
+              </p>
+              </td>
+</tr>
+<tr>
+<td>
+              <p>
+                kurtosis(cd)
+              </p>
+              </td>
+<td>
+              <p>
+                RealType
+              </p>
+              </td>
+<td>
+              <p>
+                Returns the kurtosis of the distribution.
+              </p>
+              </td>
+</tr>
+<tr>
+<td>
+              <p>
+                kurtosis_excess(cd)
+              </p>
+              </td>
+<td>
+              <p>
+                RealType
+              </p>
+              </td>
+<td>
+              <p>
+                Returns the kurtosis excess of the distribution.
+              </p>
+              </td>
+</tr>
+<tr>
+<td>
+              <p>
+                mean(cd)
+              </p>
+              </td>
+<td>
+              <p>
+                RealType
+              </p>
+              </td>
+<td>
+              <p>
+                Returns the mean of the distribution.
+              </p>
+              </td>
+</tr>
+<tr>
+<td>
+              <p>
+                mode(cd)
+              </p>
+              </td>
+<td>
+              <p>
+                RealType
+              </p>
+              </td>
+<td>
+              <p>
+                Returns the mode of the distribution.
+              </p>
+              </td>
+</tr>
+<tr>
+<td>
+              <p>
+                skewness(cd)
+              </p>
+              </td>
+<td>
+              <p>
+                RealType
+              </p>
+              </td>
+<td>
+              <p>
+                Returns the skewness of the distribution.
+              </p>
+              </td>
+</tr>
+<tr>
+<td>
+              <p>
+                standard_deviation(cd)
+              </p>
+              </td>
+<td>
+              <p>
+                RealType
+              </p>
+              </td>
+<td>
+              <p>
+                Returns the standard deviation of the distribution.
+              </p>
+              </td>
+</tr>
+<tr>
+<td>
+              <p>
+                variance(cd)
+              </p>
+              </td>
+<td>
+              <p>
+                RealType
+              </p>
+              </td>
+<td>
+              <p>
+                Returns the variance of the distribution.
+              </p>
+              </td>
+</tr>
+</tbody>
+</table></div>
+</div>
+<table xmlns:rev="http://www.cs.rpi.edu/~gregod/boost/tools/doc/revision" width="100%"><tr>
+<td align="left"></td>
+<td align="right"><div class="copyright-footer">Copyright © 2006 , 2007, 2008 John Maddock, Paul A. Bristow, Hubert
+      Holin, Xiaogang Zhang, Bruno Lalande and Gautam Sewani<p>
+        Distributed under the Boost Software License, Version 1.0. (See accompanying
+        file LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_0.txt)
+      </p>
+</div></td>
+</tr></table>
+<hr>
+<div class="spirit-nav">
+<a accesskey="p" href="concepts.html"><img src="../../../../doc/html/images/prev.png" alt="Prev"></a><a accesskey="u" href="../using_udt.html"><img src="../../../../doc/html/images/up.png" alt="Up"></a><a accesskey="h" href="../../index.html"><img src="../../../../doc/html/images/home.png" alt="Home"></a><a accesskey="n" href="archetypes.html"><img src="../../../../doc/html/images/next.png" alt="Next"></a>
+</div>
+</body>
+</html>

Added: sandbox/tools/auto_index/example/math/doc/sf_and_dist/html/math_toolkit/using_udt/use_mpfr.html
==============================================================================
--- (empty file)
+++ sandbox/tools/auto_index/example/math/doc/sf_and_dist/html/math_toolkit/using_udt/use_mpfr.html	2008-11-28 05:25:28 EST (Fri, 28 Nov 2008)
@@ -0,0 +1,89 @@
+<html>
+<head>
+<meta http-equiv="Content-Type" content="text/html; charset=ISO-8859-1">
+<title>Using With MPFR / GMP - a High-Precision Floating-Point Library</title>
+<link rel="stylesheet" href="../../boostbook.css" type="text/css">
+<meta name="generator" content="DocBook XSL Stylesheets Vsnapshot_8125">
+<link rel="home" href="../../index.html" title="Math Toolkit">
+<link rel="up" href="../using_udt.html" title="Use with User-Defined Floating-Point Types">
+<link rel="prev" href="use_ntl.html" title="Using With NTL - a High-Precision Floating-Point Library">
+<link rel="next" href="concepts.html" title="Conceptual Requirements for Real Number Types">
+</head>
+<body bgcolor="white" text="black" link="#0000FF" vlink="#840084" alink="#0000FF">
+<table cellpadding="2" width="100%"><tr>
+<td valign="top"><img alt="Boost C++ Libraries" width="277" height="86" src="../../../../boost.png"></td>
+<td align="center">Home</td>
+<td align="center">Libraries</td>
+<td align="center">People</td>
+<td align="center">FAQ</td>
+<td align="center">More</td>
+</tr></table>
+<hr>
+<div class="spirit-nav">
+<a accesskey="p" href="use_ntl.html"><img src="../../../../doc/html/images/prev.png" alt="Prev"></a><a accesskey="u" href="../using_udt.html"><img src="../../../../doc/html/images/up.png" alt="Up"></a><a accesskey="h" href="../../index.html"><img src="../../../../doc/html/images/home.png" alt="Home"></a><a accesskey="n" href="concepts.html"><img src="../../../../doc/html/images/next.png" alt="Next"></a>
+</div>
+<div class="section" lang="en">
+<div class="titlepage"><div><div><h3 class="title">
+<a name="math_toolkit.using_udt.use_mpfr"></a><a class="link" href="use_mpfr.html" title="Using With MPFR / GMP - a High-Precision Floating-Point Library"> Using With MPFR / GMP
+      - a High-Precision Floating-Point Library</a>
+</h3></div></div></div>
+<p>
+        The special functions and tools in this library can be used with <a href="http://www.mpfr.org" target="_top">MPFR
+        (an arbitrary precision number type based on the GMP library)</a>, via
+        the bindings in boost/math/bindings/mpfr.hpp.
+      </p>
+<p>
+        In order to use these binings you will need to have installed MPFR
+        plus it's dependency the GMP library
+        and the C++ wrapper for MPFR known as <a href="http://math.berkeley.edu/~wilken/code/gmpfrxx/" target="_top">gmpfrxx
+        (or mpfr_class)</a>.
+      </p>
+<p>
+        Unfortunately <code class="computeroutput"><span class="identifier">mpfr_class</span></code>
+        doesn't quite satisfy our conceptual requirements, so there is a very thin
+        set of additional interfaces and some helper traits defined in boost/math/bindings/mpfr.hpp
+        that you should use in place of including 'gmpfrxx.h' directly. The existing
+        mpfr_class is then usable unchanged once this header is included, so it's
+        performance-enhancing expression templates are preserved and fully supported
+        by this library:
+      </p>
+<pre class="programlisting"><span class="preprocessor">#include</span> <span class="special">&lt;</span><span class="identifier">boost</span><span class="special">/</span><span class="identifier">math</span><span class="special">/</span><span class="identifier">bindings</span><span class="special">/</span><span class="identifier">mpfr</span><span class="special">.</span><span class="identifier">hpp</span><span class="special">&gt;</span>
+<span class="preprocessor">#include</span> <span class="special">&lt;</span><span class="identifier">boost</span><span class="special">/</span><span class="identifier">math</span><span class="special">/</span><span class="identifier">special_functions</span><span class="special">/</span><span class="identifier">gamma</span><span class="special">.</span><span class="identifier">hpp</span><span class="special">&gt;</span>
+
+<span class="keyword">int</span> <span class="identifier">main</span><span class="special">()</span>
+<span class="special">{</span>
+   <span class="identifier">mpfr_class</span><span class="special">::</span><span class="identifier">set_dprec</span><span class="special">(</span><span class="number">500</span><span class="special">);</span> <span class="comment">// 500 bit precision
+</span>   <span class="comment">//
+</span>   <span class="comment">// Note that the argument to tgamma is an expression template,
+</span>   <span class="comment">// that's just fine here:
+</span>   <span class="comment">//
+</span>   <span class="identifier">mpfr_class</span> <span class="identifier">v</span> <span class="special">=</span> <span class="identifier">boost</span><span class="special">::</span><span class="identifier">math</span><span class="special">::</span><span class="identifier">tgamma</span><span class="special">(</span><span class="identifier">sqrt</span><span class="special">(</span><span class="identifier">mpfr_class</span><span class="special">(</span><span class="number">2</span><span class="special">)));</span>
+   <span class="identifier">std</span><span class="special">::</span><span class="identifier">cout</span> <span class="special">&lt;&lt;</span> <span class="identifier">std</span><span class="special">::</span><span class="identifier">setprecision</span><span class="special">(</span><span class="number">50</span><span class="special">)</span> <span class="special">&lt;&lt;</span> <span class="identifier">v</span> <span class="special">&lt;&lt;</span> <span class="identifier">std</span><span class="special">::</span><span class="identifier">endl</span><span class="special">;</span>
+<span class="special">}</span>
+</pre>
+<p>
+        For those functions that are based upon the <a class="link" href="../backgrounders/lanczos.html" title="The Lanczos Approximation">Lanczos
+        approximation</a>, the bindings defines a series of approximations with
+        up to 61 terms and accuracy up to approximately 3e-113. This therefore sets
+        the upper limit for accuracy to the majority of functions defined this library
+        when used with <code class="computeroutput"><span class="identifier">mpfr_class</span></code>.
+      </p>
+<p>
+        There is a concept checking test program for mpfr support here.
+      </p>
+</div>
+<table xmlns:rev="http://www.cs.rpi.edu/~gregod/boost/tools/doc/revision" width="100%"><tr>
+<td align="left"></td>
+<td align="right"><div class="copyright-footer">Copyright © 2006 , 2007, 2008 John Maddock, Paul A. Bristow, Hubert
+      Holin, Xiaogang Zhang, Bruno Lalande and Gautam Sewani<p>
+        Distributed under the Boost Software License, Version 1.0. (See accompanying
+        file LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_0.txt)
+      </p>
+</div></td>
+</tr></table>
+<hr>
+<div class="spirit-nav">
+<a accesskey="p" href="use_ntl.html"><img src="../../../../doc/html/images/prev.png" alt="Prev"></a><a accesskey="u" href="../using_udt.html"><img src="../../../../doc/html/images/up.png" alt="Up"></a><a accesskey="h" href="../../index.html"><img src="../../../../doc/html/images/home.png" alt="Home"></a><a accesskey="n" href="concepts.html"><img src="../../../../doc/html/images/next.png" alt="Next"></a>
+</div>
+</body>
+</html>

Added: sandbox/tools/auto_index/example/math/doc/sf_and_dist/html/math_toolkit/using_udt/use_ntl.html
==============================================================================
--- (empty file)
+++ sandbox/tools/auto_index/example/math/doc/sf_and_dist/html/math_toolkit/using_udt/use_ntl.html	2008-11-28 05:25:28 EST (Fri, 28 Nov 2008)
@@ -0,0 +1,69 @@
+<html>
+<head>
+<meta http-equiv="Content-Type" content="text/html; charset=ISO-8859-1">
+<title>Using With NTL - a High-Precision Floating-Point Library</title>
+<link rel="stylesheet" href="../../boostbook.css" type="text/css">
+<meta name="generator" content="DocBook XSL Stylesheets Vsnapshot_8125">
+<link rel="home" href="../../index.html" title="Math Toolkit">
+<link rel="up" href="../using_udt.html" title="Use with User-Defined Floating-Point Types">
+<link rel="prev" href="../using_udt.html" title="Use with User-Defined Floating-Point Types">
+<link rel="next" href="use_mpfr.html" title="Using With MPFR / GMP - a High-Precision Floating-Point Library">
+</head>
+<body bgcolor="white" text="black" link="#0000FF" vlink="#840084" alink="#0000FF">
+<table cellpadding="2" width="100%"><tr>
+<td valign="top"><img alt="Boost C++ Libraries" width="277" height="86" src="../../../../boost.png"></td>
+<td align="center">Home</td>
+<td align="center">Libraries</td>
+<td align="center">People</td>
+<td align="center">FAQ</td>
+<td align="center">More</td>
+</tr></table>
+<hr>
+<div class="spirit-nav">
+<a accesskey="p" href="../using_udt.html"><img src="../../../../doc/html/images/prev.png" alt="Prev"></a><a accesskey="u" href="../using_udt.html"><img src="../../../../doc/html/images/up.png" alt="Up"></a><a accesskey="h" href="../../index.html"><img src="../../../../doc/html/images/home.png" alt="Home"></a><a accesskey="n" href="use_mpfr.html"><img src="../../../../doc/html/images/next.png" alt="Next"></a>
+</div>
+<div class="section" lang="en">
+<div class="titlepage"><div><div><h3 class="title">
+<a name="math_toolkit.using_udt.use_ntl"></a><a class="link" href="use_ntl.html" title="Using With NTL - a High-Precision Floating-Point Library"> Using With NTL - a High-Precision
+      Floating-Point Library</a>
+</h3></div></div></div>
+<p>
+        The special functions and tools in this library can be used with <a href="http://shoup.net/ntl/doc/RR.txt" target="_top">NTL::RR
+        (an arbitrary precision number type)</a>, via the bindings in boost/math/bindings/rr.hpp.
+        <a href="http://shoup.net/ntl/" target="_top">See also NTL: A Library for doing Number
+        Theory by Victor Shoup</a>
+      </p>
+<p>
+        Unfortunately <code class="computeroutput"><span class="identifier">NTL</span><span class="special">::</span><span class="identifier">RR</span></code> doesn't quite satisfy our conceptual
+        requirements, so there is a very thin wrapper class <code class="computeroutput"><span class="identifier">boost</span><span class="special">::</span><span class="identifier">math</span><span class="special">::</span><span class="identifier">ntl</span><span class="special">::</span><span class="identifier">RR</span></code> defined in boost/math/bindings/rr.hpp
+        that you should use in place of <code class="computeroutput"><span class="identifier">NTL</span><span class="special">::</span><span class="identifier">RR</span></code>. The
+        class is intended to be a drop-in replacement for the "real" NTL::RR
+        that adds some syntactic sugar to keep this library happy, plus some of the
+        standard library functions not implemented in NTL.
+      </p>
+<p>
+        For those functions that are based upon the <a class="link" href="../backgrounders/lanczos.html" title="The Lanczos Approximation">Lanczos
+        approximation</a>, the bindings defines a series of approximations with
+        up to 61 terms and accuracy up to approximately 3e-113. This therefore sets
+        the upper limit for accuracy to the majority of functions defined this library
+        when used with <code class="computeroutput"><span class="identifier">NTL</span><span class="special">::</span><span class="identifier">RR</span></code>.
+      </p>
+<p>
+        There is a concept checking test program for NTL support here.
+      </p>
+</div>
+<table xmlns:rev="http://www.cs.rpi.edu/~gregod/boost/tools/doc/revision" width="100%"><tr>
+<td align="left"></td>
+<td align="right"><div class="copyright-footer">Copyright © 2006 , 2007, 2008 John Maddock, Paul A. Bristow, Hubert
+      Holin, Xiaogang Zhang, Bruno Lalande and Gautam Sewani<p>
+        Distributed under the Boost Software License, Version 1.0. (See accompanying
+        file LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_0.txt)
+      </p>
+</div></td>
+</tr></table>
+<hr>
+<div class="spirit-nav">
+<a accesskey="p" href="../using_udt.html"><img src="../../../../doc/html/images/prev.png" alt="Prev"></a><a accesskey="u" href="../using_udt.html"><img src="../../../../doc/html/images/up.png" alt="Up"></a><a accesskey="h" href="../../index.html"><img src="../../../../doc/html/images/home.png" alt="Home"></a><a accesskey="n" href="use_mpfr.html"><img src="../../../../doc/html/images/next.png" alt="Next"></a>
+</div>
+</body>
+</html>

Added: sandbox/tools/auto_index/example/math/doc/sf_and_dist/index.idx
==============================================================================
--- (empty file)
+++ sandbox/tools/auto_index/example/math/doc/sf_and_dist/index.idx	2008-11-28 05:25:28 EST (Fri, 28 Nov 2008)
@@ -0,0 +1,22 @@
+
+"Lanczos approximation" lanczos
+
+!scan-path ../../../../../../../trunk/boost/math .*\.hpp true
+
+!exclude policy precision apply evaluation polynomial name helper 
+!exclude true_type false_type polynomial type d reference terminate
+!exclude arg1 arg2 charT const_iterator const_reference container_type
+!exclude result_type difference_type dummy iterator max_value result_type
+!exclude row_type size_type tag traits 
+!exclude a abs acos add asin atan atan2 b begin bracket ceil check clear
+!exclude cos cosh digits end exp fabs floor fmod frexp g if in log log10
+!exclude modf pow real result sin sinh sqrt swap tan tanh
+
+!rewrite-name "(?i)(?:A|The)\s+(.*)" "\1"
+!rewrite-name "Additional Implementation Notes" "Implementation Notes"
+!rewrite-name "(?i)Calculating(?:\s+the)?\s+(.*)" "\1"
+!rewrite-id math_toolkit\.dist\.stat_tut\.weg.* Examples
+
+
+
+

Modified: sandbox/tools/auto_index/example/math/doc/sf_and_dist/math.qbk
==============================================================================
--- sandbox/tools/auto_index/example/math/doc/sf_and_dist/math.qbk	(original)
+++ sandbox/tools/auto_index/example/math/doc/sf_and_dist/math.qbk	2008-11-28 05:25:28 EST (Fri, 28 Nov 2008)
@@ -469,9 +469,26 @@
 
 [endsect] [/section:status Status and Roadmap] 
 
+'''
+  <index type="class_name">
+  <title>Class Index</title>
+  </index>
+  <index type="typedef_name">
+  <title>Typedef Index</title>
+  </index>
+  <index type="function_name">
+  <title>Function Index</title>
+  </index>
+  <index type="macro_name">
+  <title>Macro Index</title>
+  </index>
+  <index/>
+'''
+
 [/ math.qbk
   Copyright 2008 John Maddock and Paul A. Bristow.
   Distributed under the Boost Software License, Version 1.0.
   (See accompanying file LICENSE_1_0.txt or copy at
   http://www.boost.org/LICENSE_1_0.txt).
 ]
+