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Subject: [Boost-commit] svn:boost r83512 - in trunk: boost/math/distributions boost/math/tools libs/math/doc/sf_and_dist libs/math/doc/sf_and_dist/html libs/math/doc/sf_and_dist/html/index libs/math/doc/sf_and_dist/html/math_toolkit/backgrounders libs/math/doc/sf_and_dist/html/math_toolkit/main_overview libs/math/doc/sf_and_dist/html/math_toolkit/special/bessel libs/math/doc/sf_and_dist/html/math_toolkit/status libs/math/doc/sf_and_dist/html/math_toolkit/using_udt/high_precision libs/math/test
From: john_at_[hidden]
Date: 2013-03-21 09:01:53

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Author: johnmaddock
Date: 2013-03-21 09:01:50 EDT (Thu, 21 Mar 2013)
New Revision: 83512
URL: http://svn.boost.org/trac/boost/changeset/83512

Log:
Fix edge case in Halley iteration where the derivative is flatlining.
Fix edge cases in poisson distribution quantile.
Fixes #8314.
Fixes #8308.
Update and regenerate docs.
Text files modified:
   trunk/boost/math/distributions/poisson.hpp | 39 +-
   trunk/boost/math/tools/roots.hpp | 12
   trunk/libs/math/doc/sf_and_dist/html/index.html | 2
   trunk/libs/math/doc/sf_and_dist/html/index/s13.html | 6
   trunk/libs/math/doc/sf_and_dist/html/index/s14.html | 4
   trunk/libs/math/doc/sf_and_dist/html/index/s15.html | 4
   trunk/libs/math/doc/sf_and_dist/html/index/s16.html | 4
   trunk/libs/math/doc/sf_and_dist/html/index/s17.html | 10
   trunk/libs/math/doc/sf_and_dist/html/math_toolkit/backgrounders/refs.html | 14
   trunk/libs/math/doc/sf_and_dist/html/math_toolkit/main_overview/conventions.html | 2
   trunk/libs/math/doc/sf_and_dist/html/math_toolkit/main_overview/history1.html | 9
   trunk/libs/math/doc/sf_and_dist/html/math_toolkit/main_overview/navigation.html | 2
   trunk/libs/math/doc/sf_and_dist/html/math_toolkit/special/bessel/bessel0.html | 667 +++++++++++++++++++++++++++++----------
   trunk/libs/math/doc/sf_and_dist/html/math_toolkit/status/history1.html | 9
   trunk/libs/math/doc/sf_and_dist/html/math_toolkit/status/issues.html | 31 +
   trunk/libs/math/doc/sf_and_dist/html/math_toolkit/using_udt/high_precision/using_test.html | 6
   trunk/libs/math/doc/sf_and_dist/roadmap.qbk | 4
   trunk/libs/math/test/test_poisson.cpp | 20 +
   18 files changed, 622 insertions(+), 223 deletions(-)

Modified: trunk/boost/math/distributions/poisson.hpp
==============================================================================
--- trunk/boost/math/distributions/poisson.hpp (original)
+++ trunk/boost/math/distributions/poisson.hpp 2013-03-21 09:01:50 EDT (Thu, 21 Mar 2013)
@@ -443,9 +443,10 @@
 inline RealType quantile(const poisson_distribution<RealType, Policy>& dist, const RealType& p)
 { // Quantile (or Percent Point) Poisson function.
 // Return the number of expected events k for a given probability p.
+ static const char* function = "boost::math::quantile(const poisson_distribution<%1%>&, %1%)";
 RealType result = 0; // of Argument checks:
 if(false == poisson_detail::check_prob(
- "boost::math::quantile(const poisson_distribution<%1%>&, %1%)",
+ function,
 p,
 &result, Policy()))
 {
@@ -455,23 +456,21 @@
 if (dist.mean() == 0)
 { // if mean = 0 then p = 0, so k can be anything?
 if (false == poisson_detail::check_mean_NZ(
- "boost::math::quantile(const poisson_distribution<%1%>&, %1%)",
+ function,
 dist.mean(),
 &result, Policy()))
 {
 return result;
 }
 }
- /*
- BOOST_MATH_STD_USING // ADL of std functions.
- // if(p == 0) NOT necessarily zero!
- // Not necessarily any special value of k because is unlimited.
- if (p <= exp(-dist.mean()))
- { // if p <= cdf for 0 events (== pdf for 0 events), then quantile must be zero.
- return 0;
+ if(p == 0)
+ {
+ return 0; // Exact result regardless of discrete-quantile Policy
+ }
+ if(p == 1)
+ {
+ return policies::raise_overflow_error<RealType>(function, 0, Policy());
 }
- return gamma_q_inva(dist.mean(), p, Policy()) - 1;
- */
 typedef typename Policy::discrete_quantile_type discrete_type;
 boost::uintmax_t max_iter = policies::get_max_root_iterations<Policy>();
 RealType guess, factor = 8;
@@ -512,11 +511,12 @@
 // complement of the probability q.
 //
 // Error checks:
+ static const char* function = "boost::math::quantile(complement(const poisson_distribution<%1%>&, %1%))";
 RealType q = c.param;
 const poisson_distribution<RealType, Policy>& dist = c.dist;
 RealType result = 0; // of argument checks.
 if(false == poisson_detail::check_prob(
- "boost::math::quantile(const poisson_distribution<%1%>&, %1%)",
+ function,
 q,
 &result, Policy()))
 {
@@ -526,20 +526,21 @@
 if (dist.mean() == 0)
 { // if mean = 0 then p = 0, so k can be anything?
 if (false == poisson_detail::check_mean_NZ(
- "boost::math::quantile(const poisson_distribution<%1%>&, %1%)",
+ function,
 dist.mean(),
 &result, Policy()))
 {
 return result;
 }
 }
- /*
- if (-q <= boost::math::expm1(-dist.mean()))
- { // if q <= cdf(complement for 0 events, then quantile must be zero.
- return 0;
+ if(q == 0)
+ {
+ return policies::raise_overflow_error<RealType>(function, 0, Policy());
+ }
+ if(q == 1)
+ {
+ return 0; // Exact result regardless of discrete-quantile Policy
 }
- return gamma_p_inva(dist.mean(), q, Policy()) -1;
- */
 typedef typename Policy::discrete_quantile_type discrete_type;
 boost::uintmax_t max_iter = policies::get_max_root_iterations<Policy>();
 RealType guess, factor = 8;

Modified: trunk/boost/math/tools/roots.hpp
==============================================================================
--- trunk/boost/math/tools/roots.hpp (original)
+++ trunk/boost/math/tools/roots.hpp 2013-03-21 09:01:50 EDT (Thu, 21 Mar 2013)
@@ -329,8 +329,18 @@
 delta = denom / num;
 if(delta * f1 / f0 < 0)
 {
- // probably cancellation error, try a Newton step instead:
+ // Oh dear, we have a problem as Newton and Halley steps
+ // disagree about which way we should move. Probably
+ // there is cancelation error in the calculation of the
+ // Halley step, or else the derivatives are so small
+ // that their values are basically trash. We will move
+ // in the direction indicated by a Newton step, but
+ // by no more than twice the current guess value, otherwise
+ // we can jump way out of bounds if we're not careful.
+ // See https://svn.boost.org/trac/boost/ticket/8314.
 delta = f0 / f1;
+ if(fabs(delta) > 2 * fabs(guess))
+ delta = (delta < 0 ? -1 : 1) * 2 * fabs(guess);
 }
 }
 else

Modified: trunk/libs/math/doc/sf_and_dist/html/index.html
==============================================================================
--- trunk/libs/math/doc/sf_and_dist/html/index.html (original)
+++ trunk/libs/math/doc/sf_and_dist/html/index.html 2013-03-21 09:01:50 EDT (Thu, 21 Mar 2013)
@@ -599,7 +599,7 @@

</div>
<table xmlns:rev="http://www.cs.rpi.edu/~gregod/boost/tools/doc/revision" width="100%"><tr>
-<td align="left">Last revised: March 07, 2013 at 09:36:37 GMT</td>
+<td align="left">Last revised: March 21, 2013 at 12:24:21 GMT</td>
<td align="right"><div class="copyright-footer"></div></td>
</tr></table>
<hr>

Modified: trunk/libs/math/doc/sf_and_dist/html/index/s13.html
==============================================================================
--- trunk/libs/math/doc/sf_and_dist/html/index/s13.html (original)
+++ trunk/libs/math/doc/sf_and_dist/html/index/s13.html 2013-03-21 09:01:50 EDT (Thu, 21 Mar 2013)
@@ -22,9 +22,9 @@
<div class="spirit-nav">
<a accesskey="p" href="../math_toolkit/status/credits.html"><img src="../../../../../../doc/src/images/prev.png" alt="Prev"></a><a accesskey="u" href="../index.html"><img src="../../../../../../doc/src/images/up.png" alt="Up"></a><a accesskey="h" href="../index.html"><img src="../../../../../../doc/src/images/home.png" alt="Home"></a><a accesskey="n" href="s14.html"><img src="../../../../../../doc/src/images/next.png" alt="Next"></a>
</div>
-<div class="section id1346486">
+<div class="section id863386">
<div class="titlepage"><div><div><h2 class="title" style="clear: both">
-<a name="id1346486"></a>Function Index</h2></div></div></div>
+<a name="id863386"></a>Function Index</h2></div></div></div>
<a class="link" href="s13.html#idx_id_0">A</a> <a class="link" href="s13.html#idx_id_1">B</a> <a class="link" href="s13.html#idx_id_2">C</a> <a class="link" href="s13.html#idx_id_3">D</a> <a class="link" href="s13.html#idx_id_4">E</a> <a class="link" href="s13.html#idx_id_5">F</a> <a class="link" href="s13.html#idx_id_6">G</a> <a class="link" href="s13.html#idx_id_7">H</a> <a class="link" href="s13.html#idx_id_8">I</a> <a class="link" href="s13.html#idx_id_9">J</a> <a class="link" href="s13.html#idx_id_10">K</a> <a class="link" href="s13.html#idx_id_11">L</a> <a class="link" href="s13.html#idx_id_12">M</a> <a class="link" href="s13.html#idx_id_13">N</a> <a class="link" href="s13.html#idx_id_14">O</a> <a class="link" href="s13.html#idx_id_15">P</a> <a class="link" href="s13.html#idx_id_16">Q</a> <a class="link" href="s13.html#idx_id_17">R</a> <a class="link" href="s13.html#idx_id_18">S</a> <a class="link" href="s13.html#idx_id_19">T</a> <a class="link" href="s13.html#idx_id_20">U</a> <a class="link" href=
"s13.html#idx_id_21">V</a> <a class="link" href="s13.html#idx_id_22">W</a> <a class="link" href="s13.html#idx_id_23">Z</a>
<div class="variablelist"><dl class="variablelist">
<dt>
@@ -440,6 +440,7 @@
<li class="listitem" style="list-style-type: none"><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></li>
<li class="listitem" style="list-style-type: none"><a class="link" href="../math_toolkit/main_overview/tr1.html" title="C99 and C++ TR1 C-style Functions">C99 and C++ TR1 C-style Functions</a></li>
<li class="listitem" style="list-style-type: none"><a class="link" href="../math_toolkit/extern_c/tr1.html" title="C99 and TR1 C Functions Overview">C99 and TR1 C Functions Overview</a></li>
+<li class="listitem" style="list-style-type: none"><a class="link" href="../math_toolkit/status/issues.html" title="Known Issues, and TODO List">Known Issues, and TODO List</a></li>
<li class="listitem" style="list-style-type: none"><a class="link" href="../math_toolkit/extern_c/tr1_ref.html" title="TR1 C Functions Quick Reference">TR1 C Functions Quick Reference</a></li>
</ul></div>
</li>
@@ -494,6 +495,7 @@
<li class="listitem" style="list-style-type: none"><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></li>
<li class="listitem" style="list-style-type: none"><a class="link" href="../math_toolkit/main_overview/tr1.html" title="C99 and C++ TR1 C-style Functions">C99 and C++ TR1 C-style Functions</a></li>
<li class="listitem" style="list-style-type: none"><a class="link" href="../math_toolkit/extern_c/tr1.html" title="C99 and TR1 C Functions Overview">C99 and TR1 C Functions Overview</a></li>
+<li class="listitem" style="list-style-type: none"><a class="link" href="../math_toolkit/status/issues.html" title="Known Issues, and TODO List">Known Issues, and TODO List</a></li>
<li class="listitem" style="list-style-type: none"><a class="link" href="../math_toolkit/extern_c/tr1_ref.html" title="TR1 C Functions Quick Reference">TR1 C Functions Quick Reference</a></li>
</ul></div>
</li>

Modified: trunk/libs/math/doc/sf_and_dist/html/index/s14.html
==============================================================================
--- trunk/libs/math/doc/sf_and_dist/html/index/s14.html (original)
+++ trunk/libs/math/doc/sf_and_dist/html/index/s14.html 2013-03-21 09:01:50 EDT (Thu, 21 Mar 2013)
@@ -22,9 +22,9 @@
<div class="spirit-nav">
<a accesskey="p" href="s13.html"><img src="../../../../../../doc/src/images/prev.png" alt="Prev"></a><a accesskey="u" href="../index.html"><img src="../../../../../../doc/src/images/up.png" alt="Up"></a><a accesskey="h" href="../index.html"><img src="../../../../../../doc/src/images/home.png" alt="Home"></a><a accesskey="n" href="s15.html"><img src="../../../../../../doc/src/images/next.png" alt="Next"></a>
</div>
-<div class="section id1363831">
+<div class="section id1364536">
<div class="titlepage"><div><div><h2 class="title" style="clear: both">
-<a name="id1363831"></a>Class Index</h2></div></div></div>
+<a name="id1364536"></a>Class Index</h2></div></div></div>
<a class="link" href="s14.html#idx_id_25">B</a> <a class="link" href="s14.html#idx_id_26">C</a> <a class="link" href="s14.html#idx_id_27">D</a> <a class="link" href="s14.html#idx_id_28">E</a> <a class="link" href="s14.html#idx_id_29">F</a> <a class="link" href="s14.html#idx_id_30">G</a> <a class="link" href="s14.html#idx_id_31">H</a> <a class="link" href="s14.html#idx_id_32">I</a> <a class="link" href="s14.html#idx_id_35">L</a> <a class="link" href="s14.html#idx_id_36">M</a> <a class="link" href="s14.html#idx_id_37">N</a> <a class="link" href="s14.html#idx_id_39">P</a> <a class="link" href="s14.html#idx_id_41">R</a> <a class="link" href="s14.html#idx_id_42">S</a> <a class="link" href="s14.html#idx_id_43">T</a> <a class="link" href="s14.html#idx_id_44">U</a> <a class="link" href="s14.html#idx_id_46">W</a>
<div class="variablelist"><dl class="variablelist">
<dt>

Modified: trunk/libs/math/doc/sf_and_dist/html/index/s15.html
==============================================================================
--- trunk/libs/math/doc/sf_and_dist/html/index/s15.html (original)
+++ trunk/libs/math/doc/sf_and_dist/html/index/s15.html 2013-03-21 09:01:50 EDT (Thu, 21 Mar 2013)
@@ -22,9 +22,9 @@
<div class="spirit-nav">
<a accesskey="p" href="s14.html"><img src="../../../../../../doc/src/images/prev.png" alt="Prev"></a><a accesskey="u" href="../index.html"><img src="../../../../../../doc/src/images/up.png" alt="Up"></a><a accesskey="h" href="../index.html"><img src="../../../../../../doc/src/images/home.png" alt="Home"></a><a accesskey="n" href="s16.html"><img src="../../../../../../doc/src/images/next.png" alt="Next"></a>
</div>
-<div class="section id1364772">
+<div class="section id1368890">
<div class="titlepage"><div><div><h2 class="title" style="clear: both">
-<a name="id1364772"></a>Typedef Index</h2></div></div></div>
+<a name="id1368890"></a>Typedef Index</h2></div></div></div>
<a class="link" href="s15.html#idx_id_48">A</a> <a class="link" href="s15.html#idx_id_49">B</a> <a class="link" href="s15.html#idx_id_50">C</a> <a class="link" href="s15.html#idx_id_51">D</a> <a class="link" href="s15.html#idx_id_52">E</a> <a class="link" href="s15.html#idx_id_53">F</a> <a class="link" href="s15.html#idx_id_54">G</a> <a class="link" href="s15.html#idx_id_55">H</a> <a class="link" href="s15.html#idx_id_56">I</a> <a class="link" href="s15.html#idx_id_59">L</a> <a class="link" href="s15.html#idx_id_61">N</a> <a class="link" href="s15.html#idx_id_62">O</a> <a class="link" href="s15.html#idx_id_63">P</a> <a class="link" href="s15.html#idx_id_65">R</a> <a class="link" href="s15.html#idx_id_66">S</a> <a class="link" href="s15.html#idx_id_67">T</a> <a class="link" href="s15.html#idx_id_68">U</a> <a class="link" href="s15.html#idx_id_69">V</a> <a class="link" href="s15.html#idx_id_70">W</a>
<div class="variablelist"><dl class="variablelist">
<dt>

Modified: trunk/libs/math/doc/sf_and_dist/html/index/s16.html
==============================================================================
--- trunk/libs/math/doc/sf_and_dist/html/index/s16.html (original)
+++ trunk/libs/math/doc/sf_and_dist/html/index/s16.html 2013-03-21 09:01:50 EDT (Thu, 21 Mar 2013)
@@ -22,9 +22,9 @@
<div class="spirit-nav">
<a accesskey="p" href="s15.html"><img src="../../../../../../doc/src/images/prev.png" alt="Prev"></a><a accesskey="u" href="../index.html"><img src="../../../../../../doc/src/images/up.png" alt="Up"></a><a accesskey="h" href="../index.html"><img src="../../../../../../doc/src/images/home.png" alt="Home"></a><a accesskey="n" href="s17.html"><img src="../../../../../../doc/src/images/next.png" alt="Next"></a>
</div>
-<div class="section id1367681">
+<div class="section id1370708">
<div class="titlepage"><div><div><h2 class="title" style="clear: both">
-<a name="id1367681"></a>Macro Index</h2></div></div></div>
+<a name="id1370708"></a>Macro Index</h2></div></div></div>
<a class="link" href="s16.html#idx_id_73">B</a> <a class="link" href="s16.html#idx_id_77">F</a>
<div class="variablelist"><dl class="variablelist">
<dt>

Modified: trunk/libs/math/doc/sf_and_dist/html/index/s17.html
==============================================================================
--- trunk/libs/math/doc/sf_and_dist/html/index/s17.html (original)
+++ trunk/libs/math/doc/sf_and_dist/html/index/s17.html 2013-03-21 09:01:50 EDT (Thu, 21 Mar 2013)
@@ -21,9 +21,9 @@
<div class="spirit-nav">
<a accesskey="p" href="s16.html"><img src="../../../../../../doc/src/images/prev.png" alt="Prev"></a><a accesskey="u" href="../index.html"><img src="../../../../../../doc/src/images/up.png" alt="Up"></a><a accesskey="h" href="../index.html"><img src="../../../../../../doc/src/images/home.png" alt="Home"></a>
</div>
-<div class="section id855986">
+<div class="section id1371934">
<div class="titlepage"><div><div><h2 class="title" style="clear: both">
-<a name="id855986"></a>Index</h2></div></div></div>
+<a name="id1371934"></a>Index</h2></div></div></div>
<a class="link" href="s17.html#idx_id_96">A</a> <a class="link" href="s17.html#idx_id_97">B</a> <a class="link" href="s17.html#idx_id_98">C</a> <a class="link" href="s17.html#idx_id_99">D</a> <a class="link" href="s17.html#idx_id_100">E</a> <a class="link" href="s17.html#idx_id_101">F</a> <a class="link" href="s17.html#idx_id_102">G</a> <a class="link" href="s17.html#idx_id_103">H</a> <a class="link" href="s17.html#idx_id_104">I</a> <a class="link" href="s17.html#idx_id_105">J</a> <a class="link" href="s17.html#idx_id_106">K</a> <a class="link" href="s17.html#idx_id_107">L</a> <a class="link" href="s17.html#idx_id_108">M</a> <a class="link" href="s17.html#idx_id_109">N</a> <a class="link" href="s17.html#idx_id_110">O</a> <a class="link" href="s17.html#idx_id_111">P</a> <a class="link" href="s17.html#idx_id_112">Q</a> <a class="link" href="s17.html#idx_id_113">R</a> <a class="link" href="s17.html#idx_id_114">S</a> <a class="link" href="s17.html#idx_id_115">T</a> <a class="link" href="s17.html#idx_id_116">
U</a> <a class="link" href="s17.html#idx_id_117">V</a> <a class="link" href="s17.html#idx_id_118">W</a> <a class="link" href="s17.html#idx_id_119">Z</a>
<div class="variablelist"><dl class="variablelist">
<dt>
@@ -1416,6 +1416,7 @@
<li class="listitem" style="list-style-type: none"><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></li>
<li class="listitem" style="list-style-type: none"><a class="link" href="../math_toolkit/main_overview/tr1.html" title="C99 and C++ TR1 C-style Functions">C99 and C++ TR1 C-style Functions</a></li>
<li class="listitem" style="list-style-type: none"><a class="link" href="../math_toolkit/extern_c/tr1.html" title="C99 and TR1 C Functions Overview">C99 and TR1 C Functions Overview</a></li>
+<li class="listitem" style="list-style-type: none"><a class="link" href="../math_toolkit/status/issues.html" title="Known Issues, and TODO List">Known Issues, and TODO List</a></li>
<li class="listitem" style="list-style-type: none"><a class="link" href="../math_toolkit/extern_c/tr1_ref.html" title="TR1 C Functions Quick Reference">TR1 C Functions Quick Reference</a></li>
</ul></div>
</li>
@@ -1470,6 +1471,7 @@
<li class="listitem" style="list-style-type: none"><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></li>
<li class="listitem" style="list-style-type: none"><a class="link" href="../math_toolkit/main_overview/tr1.html" title="C99 and C++ TR1 C-style Functions">C99 and C++ TR1 C-style Functions</a></li>
<li class="listitem" style="list-style-type: none"><a class="link" href="../math_toolkit/extern_c/tr1.html" title="C99 and TR1 C Functions Overview">C99 and TR1 C Functions Overview</a></li>
+<li class="listitem" style="list-style-type: none"><a class="link" href="../math_toolkit/status/issues.html" title="Known Issues, and TODO List">Known Issues, and TODO List</a></li>
<li class="listitem" style="list-style-type: none"><a class="link" href="../math_toolkit/extern_c/tr1_ref.html" title="TR1 C Functions Quick Reference">TR1 C Functions Quick Reference</a></li>
</ul></div>
</li>
@@ -2026,6 +2028,7 @@
<li class="listitem" style="list-style-type: none"><a class="link" href="../math_toolkit/special/factorials/sf_factorial.html" title="Factorial">Factorial</a></li>
<li class="listitem" style="list-style-type: none"><a class="link" href="../math_toolkit/constants/FAQ.html" title="FAQs">FAQs</a></li>
<li class="listitem" style="list-style-type: none"><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></li>
+<li class="listitem" style="list-style-type: none"><a class="link" href="../math_toolkit/special/bessel/bessel0.html" title="Finding Zeros of Bessel Functions of the First and Second Kinds">Finding Zeros of Bessel Functions of the First and Second Kinds</a></li>
<li class="listitem" style="list-style-type: none"><a class="link" href="../math_toolkit/dist/dist_ref/dists/gamma_dist.html" title="Gamma (and Erlang) Distribution">Gamma (and Erlang) Distribution</a></li>
<li class="listitem" style="list-style-type: none"><a class="link" href="../math_toolkit/dist/stat_tut/weg/geometric_eg.html" title="Geometric Distribution Examples">Geometric Distribution Examples</a></li>
<li class="listitem" style="list-style-type: none"><a class="link" href="../math_toolkit/main_overview/history1.html" title="History and What's New">History and What's New</a></li>
@@ -2154,6 +2157,7 @@
<div class="index"><ul class="index" style="list-style-type: none; ">
<li class="listitem" style="list-style-type: none"><a class="link" href="../math_toolkit/special/bessel/bessel0.html" title="Finding Zeros of Bessel Functions of the First and Second Kinds">cyl_bessel_j_zero</a></li>
<li class="listitem" style="list-style-type: none"><a class="link" href="../math_toolkit/special/bessel/bessel0.html" title="Finding Zeros of Bessel Functions of the First and Second Kinds">cyl_neumann_zero</a></li>
+<li class="listitem" style="list-style-type: none"><a class="link" href="../math_toolkit/special/bessel/bessel0.html" title="Finding Zeros of Bessel Functions of the First and Second Kinds">expression</a></li>
</ul></div>
</li>
<li class="listitem" style="list-style-type: none">
@@ -2997,6 +3001,8 @@
<li class="listitem" style="list-style-type: none">
Known Issues, and TODO List
<div class="index"><ul class="index" style="list-style-type: none; ">
+<li class="listitem" style="list-style-type: none"><a class="link" href="../math_toolkit/status/issues.html" title="Known Issues, and TODO List">cyl_bessel_j</a></li>
+<li class="listitem" style="list-style-type: none"><a class="link" href="../math_toolkit/status/issues.html" title="Known Issues, and TODO List">cyl_neumann</a></li>
<li class="listitem" style="list-style-type: none"><a class="link" href="../math_toolkit/status/issues.html" title="Known Issues, and TODO List">Lanczos approximation</a></li>
<li class="listitem" style="list-style-type: none"><a class="link" href="../math_toolkit/status/issues.html" title="Known Issues, and TODO List">T</a></li>
</ul></div>

Modified: trunk/libs/math/doc/sf_and_dist/html/math_toolkit/backgrounders/refs.html
==============================================================================
--- trunk/libs/math/doc/sf_and_dist/html/math_toolkit/backgrounders/refs.html (original)
+++ trunk/libs/math/doc/sf_and_dist/html/math_toolkit/backgrounders/refs.html 2013-03-21 09:01:50 EDT (Thu, 21 Mar 2013)
@@ -47,14 +47,12 @@
 D.C.
 

- NIST Handbook of Mathematical Functions
- 
-
- Edited by: Frank W. J. Olver, University of Maryland and National Institute
- of Standards and Technology, Maryland, Daniel W. Lozier, National Institute
- of Standards and Technology, Maryland, Ronald F. Boisvert, National Institute
- of Standards and Technology, Maryland, Charles W. Clark, National Institute
- of Standards and Technology, Maryland and University of Maryland.
+ NIST Handbook of Mathematical Functions Edited by: Frank W. J. Olver, University
+ of Maryland and National Institute of Standards and Technology, Maryland,
+ Daniel W. Lozier, National Institute of Standards and Technology, Maryland,
+ Ronald F. Boisvert, National Institute of Standards and Technology, Maryland,
+ Charles W. Clark, National Institute of Standards and Technology, Maryland
+ and University of Maryland.
 

 ISBN: 978-0521140638 (paperback), 9780521192255 (hardback), July 2010, Cambridge

Modified: trunk/libs/math/doc/sf_and_dist/html/math_toolkit/main_overview/conventions.html
==============================================================================
--- trunk/libs/math/doc/sf_and_dist/html/math_toolkit/main_overview/conventions.html (original)
+++ trunk/libs/math/doc/sf_and_dist/html/math_toolkit/main_overview/conventions.html 2013-03-21 09:01:50 EDT (Thu, 21 Mar 2013)
@@ -27,7 +27,7 @@
<a name="math_toolkit.main_overview.conventions"></a><a class="link" href="conventions.html" title="Document Conventions">Document Conventions</a>
</h3></div></div></div>

- <a class="indexterm" name="id848638"></a>
+ <a class="indexterm" name="id855190"></a>


This documentation aims to use of the following naming and formatting conventions.

Modified: trunk/libs/math/doc/sf_and_dist/html/math_toolkit/main_overview/history1.html
==============================================================================
--- trunk/libs/math/doc/sf_and_dist/html/math_toolkit/main_overview/history1.html (original)
+++ trunk/libs/math/doc/sf_and_dist/html/math_toolkit/main_overview/history1.html 2013-03-21 09:01:50 EDT (Thu, 21 Mar 2013)
@@ -73,6 +73,15 @@
<li class="listitem">
Added minimal __float128 support.
</li>
+<li class="listitem">
+ Fixed bug in edge-cases of poisson quantile #8308.
+ </li>
+<li class="listitem">
+ Adjusted heuristics used in Halley iteration to cope with inverting the
+ incomplete beta in tricky regions where the derivative is flatlining.
+ Example is computing the quantile of the Fisher F distribution for probabilities
+ smaller than machine epsilon. See ticket #8314.
+ </li>
</ul></div>
<h5>
<a name="math_toolkit.main_overview.history1.h1"></a>

Modified: trunk/libs/math/doc/sf_and_dist/html/math_toolkit/main_overview/navigation.html
==============================================================================
--- trunk/libs/math/doc/sf_and_dist/html/math_toolkit/main_overview/navigation.html (original)
+++ trunk/libs/math/doc/sf_and_dist/html/math_toolkit/main_overview/navigation.html 2013-03-21 09:01:50 EDT (Thu, 21 Mar 2013)
@@ -27,7 +27,7 @@
<a name="math_toolkit.main_overview.navigation"></a><a class="link" href="navigation.html" title="Navigation">Navigation</a>
</h3></div></div></div>

- <a class="indexterm" name="id848509"></a>
+ <a class="indexterm" name="id855061"></a>


Boost.Math documentation is provided in both HTML and PDF formats.

Modified: trunk/libs/math/doc/sf_and_dist/html/math_toolkit/special/bessel/bessel0.html
==============================================================================
--- trunk/libs/math/doc/sf_and_dist/html/math_toolkit/special/bessel/bessel0.html (original)
+++ trunk/libs/math/doc/sf_and_dist/html/math_toolkit/special/bessel/bessel0.html 2013-03-21 09:01:50 EDT (Thu, 21 Mar 2013)
@@ -43,75 +43,127 @@
 The signature of the single value functions are:
 
<pre class="programlisting">template <class T>
-T cyl_bessel_j_zero(T v, // Floating-point value for Jv.
- int m); // 1-based index of zero.
+T cyl_bessel_j_zero(
+ T v, // Floating-point value for Jv.
+ int m); // 1-based index of zero.
+
template <class T>
-T cyl_neumann_zero(T v, // Floating-point value for Jv.
- int m); // 1-based index of zero.
+T cyl_neumann_zero(
+ T v, // Floating-point value for Jv.
+ int m); // 1-based index of zero.
</pre>

 and for multiple zeros:
 
<pre class="programlisting">template <class T, class OutputIterator>
-OutputIterator cyl_bessel_j_zero(T v, // Floating-point value for Jv.
- int start_index, // 1-based index of zero.
- unsigned number_of_zeros,
- OutputIterator out_it); //
+OutputIterator cyl_bessel_j_zero(
+ T v, // Floating-point value for Jv.
+ int start_index, // 1-based index of first zero.
+ unsigned number_of_zeros, // How many zeros to generate.
+ OutputIterator out_it); // Destination for zeros.
+
template <class T, class OutputIterator>
-OutputIterator cyl_neumann_zero(T v, // Floating-point value for Jv.
- int start_index, // 1-based index of zero.
- unsigned number_of_zeros,
- OutputIterator out_it); //
+OutputIterator cyl_neumann_zero(
+ T v, // Floating-point value for Jv.
+ int start_index, // 1-based index of zero.
+ unsigned number_of_zeros, // How many zeros to generate
+ OutputIterator out_it); // Destination for zeros.
</pre>

- There are also versions which allows control of the <a class="link" href="../../policy.html" title="Policies">Policies</a>
+ There are also versions which allow control of the <a class="link" href="../../policy.html" title="Policies">Policies</a>
 for error handling and precision.
 
-<pre class="programlisting">template <class T>
-T cyl_bessel_j_zero(T v, // Floating-point value for Jv.
- int m, // 1-based start index.
- const Policy& pol); // Policy
-template <class T>
-T cyl_neumann_zero(T v, // Floating-point value for Jv.
- int m, // 1-based start index.
- const Policy& pol); // Policy
-
-template <class T, class OutputIterator, class Policy>
-OutputIterator cyl_bessel_j_zero(T v, // Floating-point value for Jv.
- int start_index, // 1-based start index.
- unsigned number_of_zeros,
- OutputIterator out_it,
- const Policy& pol);
-template <class T, class OutputIterator, class Policy>
-OutputIterator cyl_neumann_zero(T v, // Floating-point value for Jv.
- int start_index, // 1-based start index.
- unsigned number_of_zeros,
- OutputIterator out_it,
- const Policy& pol);
+<pre class="programlisting"> template <class T>
+ T cyl_bessel_j_zero(
+ T v, // Floating-point value for Jv.
+ int m, // 1-based index of zero.
+ const Policy&); // Policy to use.
+
+ template <class T>
+ T cyl_neumann_zero(
+ T v, // Floating-point value for Jv.
+ int m, // 1-based index of zero.
+ const Policy&); // Policy to use.
+
+
+template <class T, class OutputIterator>
+OutputIterator cyl_bessel_j_zero(
+ T v, // Floating-point value for Jv.
+ int start_index, // 1-based index of first zero.
+ unsigned number_of_zeros, // How many zeros to generate.
+ OutputIterator out_it, // Destination for zeros.
+ const Policy& pol); // Policy to use.
+
+template <class T, class OutputIterator>
+OutputIterator cyl_neumann_zero(
+ T v, // Floating-point value for Jv.
+ int start_index, // 1-based index of zero.
+ unsigned number_of_zeros, // How many zeros to generate.
+ OutputIterator out_it, // Destination for zeros.
+ const Policy& pol); // Policy to use.
</pre>
<h5>
<a name="math_toolkit.special.bessel.bessel.h6"></a>
 <a name="math_toolkit.special.bessel.bessel.description0"></a><a class="link" href="bessel0.html#math_toolkit.special.bessel.bessel.description0">Description</a>
 </h5>

- The zeros or roots (values of x where the function crosses the y = 0 axis)
- of the Bessel and Neumann functions are computed by two functions, <code class="computeroutput">cyl_bessel_j_zero</code> and <code class="computeroutput">cyl_neumann_zero</code>.
+ Every real order ν cylindrical Bessel and Neumann functions have an infinite
+ number of zeros on the positive real axis. The real zeros on the positive
+ real axis can be found by solving for the roots of
+ 
+
+   Jν(jν, m) = 0
+ 
+
+   Yν(yν, m) = 0
+ 
+
+ Here, jν, m represents the mth
+ root of the cylindrical Bessel function of order ν,
+ and yν, m represents the mth root
+ of the cylindrical Neumann function of order ν.
 

- In each case the index of the zero returned is 1-based, which is to say:
+ The zeros or roots (values of <code class="computeroutput">x</code>
+ where the function crosses the horizontal <code class="computeroutput">y
+ = 0</code>
+ axis) of the Bessel and Neumann functions are computed by two functions,
+ <code class="computeroutput">cyl_bessel_j_zero</code> and
+ <code class="computeroutput">cyl_neumann_zero</code>.
+ 
+
+ In each case the index or rank of the zero returned is 1-based, which is
+ to say:
 
<pre class="programlisting">cyl_bessel_j_zero(v, 1);
</pre>

- returns the first zero of Bessel J, and
+ returns the first zero of Bessel J.
+ 
+
+ Passing an <code class="computeroutput">start_index <= 0</code> results
+ in a <code class="computeroutput">std::domain_error</code> being raised.
+ 
+
+ For certain parameters, however, the zero'th root is defined and it has
+ a value of zero. For example, the zero'th root of <code class="computeroutput">J[sub v](x)</code> is defined and it has a value of zero
+ for all values of <code class="computeroutput">v >
+ 0</code> and for negative integer values
+ of <code class="computeroutput">v =
+ -n</code>.
+ Similar cases are described in the implementation details below.
 
-<pre class="programlisting">cyl_bessel_j_zero(v, 0);
-</pre>

- results in a <a class="link" href="../../main_overview/error_handling.html#domain_error">domain_error</a> being raised.
+ The order <code class="computeroutput">v</code> of <code class="computeroutput">J</code> can be positive, negative and zero
+ for the <code class="computeroutput">cyl_bessel_j</code> and
+ <code class="computeroutput">cyl_neumann</code> functions,
+ but not infinite nor NaN.
 

- <img src="../../../../graphs/bessel_zeros.png" align="middle">
+ <img src="../../../../graphs/bessel_j_zeros.png" align="middle">
+ 
+
+ <img src="../../../../graphs/neumann_y_zeros.png" align="middle">
 
<h5>
<a name="math_toolkit.special.bessel.bessel.h7"></a>
@@ -119,10 +171,10 @@
 of finding Bessel and Neumann zeros</a>
 </h5>

- This example demonstrates calculating zeros of the Bessel, Neumann and
- Airy functions. It also shows how Boost.Math and Boost.Multiprecision can
- be combined to provide a many decimal digit precision. For 50 decimal digit
- precision we need to include
+ This example demonstrates calculating zeros of the Bessel and Neumann functions.
+ It also shows how Boost.Math and Boost.Multiprecision can be combined to
+ provide a many decimal digit precision. For 50 decimal digit precision
+ we need to include
 


@@ -167,40 +219,8 @@

 This example shows obtaining both a single zero of the Bessel function,
 and then placing multiple zeros into a container like <code class="computeroutput">std::vector</code>
- by providing an iterator. The signature of the single value function is:
- 
-<pre class="programlisting">template <class T>
-inline typename detail::bessel_traits<T, T, policies::policy<> >::result_type
- cyl_bessel_j_zero(T v, // Floating-point value for Jv.
- int m); // start index.
-</pre>
-
- The result type is controlled by the floating-point type of parameter
- <code class="computeroutput">v</code> (but subject to the usual
- <a class="link" href="../../policy/pol_ref/precision_pol.html" title="Precision Policies">precision policy</a>
- and <a class="link" href="../../policy/pol_ref/internal_promotion.html" title="Internal Floating-point Promotion Policies">internal
- promotion policy</a>).
- 
-
- The signature of multiple zeros function is:
- 
-<pre class="programlisting">template <class T, class OutputIterator>
-inline OutputIterator cyl_bessel_j_zero(T v, // Floating-point value for Jv.
- int start_index, // 1-based start index.
- unsigned number_of_zeros,
- OutputIterator out_it); // iterator into container for zeros.
-</pre>
-
- There is also a version which allows control of the <a class="link" href="../../policy.html" title="Policies">Policies</a>
- for error handling and precision.
+ by providing an iterator.
 
-<pre class="programlisting">template <class T, class OutputIterator, class Policy>
-inline OutputIterator cyl_bessel_j_zero(T v, // Floating-point value for Jv.
- int start_index, // 1-based start index.
- unsigned number_of_zeros,
- OutputIterator out_it,
- const Policy& pol); // iterator into container for zeros.
-</pre>
<div class="tip"><table border="0" summary="Tip">
<tr>
<td rowspan="2" align="center" valign="top" width="25"><img alt="[Tip]" src="../../../../../../../../doc/src/images/tip.png"></td>
@@ -208,7 +228,7 @@
</tr>
<tr><td align="left" valign="top">
 It is always wise to place code using Boost.Math inside try'n'catch blocks;
- this will ensure that helpful error messages can be shown when exceptional
+ this will ensure that helpful error messages are shown when exceptional
 conditions arise.
 </td></tr>
</table></div>
@@ -224,12 +244,12 @@
 


-<pre class="programlisting">double root = boost::math::cyl_bessel_j_zero(0.0, 1);
-// Displaying with default precision of 6 decimal digits:
-std::cout << "boost::math::cyl_bessel_j_zero(0.0, 1) " << root << std::endl; // 2.40483
-// And with all the guaranteed (15) digits:
-std::cout.precision(std::numeric_limits<double>::digits10);
-std::cout << "boost::math::cyl_bessel_j_zero(0.0, 1) " << root << std::endl; // 2.40482555769577
+<pre class="programlisting">// double root = boost::math::cyl_bessel_j_zero(0.0, 1);
+// // Displaying with default precision of 6 decimal digits:
+// std::cout << "boost::math::cyl_bessel_j_zero(0.0, 1) " << root << std::endl; // 2.40483
+// // And with all the guaranteed (15) digits:
+// std::cout.precision(std::numeric_limits<double>::digits10);
+// std::cout << "boost::math::cyl_bessel_j_zero(0.0, 1) " << root << std::endl; // 2.40482555769577
</pre>

 
@@ -255,30 +275,37 @@
 handling</a>).
 

- To create a (possibly unwise!) policy that ignores all errors:
+ To create a (possibly unwise!) policy <code class="computeroutput">ignore_all_policy</code>
+ that ignores all errors:
 


-<pre class="programlisting">typedef boost::math::policies::policy
- <
- boost::math::policies::domain_error<boost::math::policies::ignore_error>,
- boost::math::policies::overflow_error<boost::math::policies::ignore_error>,
- boost::math::policies::underflow_error<boost::math::policies::ignore_error>,
- boost::math::policies::denorm_error<boost::math::policies::ignore_error>,
- boost::math::policies::pole_error<boost::math::policies::ignore_error>,
- boost::math::policies::evaluation_error<boost::math::policies::ignore_error>
- > ignore_all_policy;
-
- double inf = std::numeric_limits<double>::infinity();
- double nan = std::numeric_limits<double>::quiet_NaN();
-
- std::cout << "boost::math::cyl_bessel_j_zero(-1.0, 0) " << std::endl;
- double dodgy_root = boost::math::cyl_bessel_j_zero(-1.0, 0, ignore_all_policy());
- std::cout << "boost::math::cyl_bessel_j_zero(-1.0, 1) " << dodgy_root << std::endl; // 1.#QNAN
- double inf_root = boost::math::cyl_bessel_j_zero(inf, 1, ignore_all_policy());
- std::cout << "boost::math::cyl_bessel_j_zero(inf, 1) " << inf_root << std::endl; // 1.#QNAN
- double nan_root = boost::math::cyl_bessel_j_zero(nan, 1, ignore_all_policy());
- std::cout << "boost::math::cyl_bessel_j_zero(nan, 1) " << nan_root << std::endl; // 1.#QNAN
+<pre class="programlisting">typedef boost::math::policies::policy<
+ boost::math::policies::domain_error<boost::math::policies::ignore_error>,
+ boost::math::policies::overflow_error<boost::math::policies::ignore_error>,
+ boost::math::policies::underflow_error<boost::math::policies::ignore_error>,
+ boost::math::policies::denorm_error<boost::math::policies::ignore_error>,
+ boost::math::policies::pole_error<boost::math::policies::ignore_error>,
+ boost::math::policies::evaluation_error<boost::math::policies::ignore_error>
+ > ignore_all_policy;
+</pre>
+
+ 
+
+ Examples of use of this <code class="computeroutput">ignore_all_policy</code>
+ are
+ 
+
+
+<pre class="programlisting">double inf = std::numeric_limits<double>::infinity();
+double nan = std::numeric_limits<double>::quiet_NaN();
+
+double dodgy_root = boost::math::cyl_bessel_j_zero(-1.0, 1, ignore_all_policy());
+std::cout << "boost::math::cyl_bessel_j_zero(-1.0, 1) " << dodgy_root << std::endl; // 1.#QNAN
+double inf_root = boost::math::cyl_bessel_j_zero(inf, 1, ignore_all_policy());
+std::cout << "boost::math::cyl_bessel_j_zero(inf, 1) " << inf_root << std::endl; // 1.#QNAN
+double nan_root = boost::math::cyl_bessel_j_zero(nan, 1, ignore_all_policy());
+std::cout << "boost::math::cyl_bessel_j_zero(nan, 1) " << nan_root << std::endl; // 1.#QNAN
</pre>

 
@@ -286,11 +313,9 @@
 Another version of <code class="computeroutput">cyl_bessel_j_zero</code>
 allows calculation of multiple zeros with one call, placing the results
 in a container, often <code class="computeroutput">std::vector</code>.
- For example, generate five <code class="computeroutput">double</code>
- roots of Jv for integral order 2.
- 
-
- As column J2(x) in table 1 of <a href="http://mathworld.wolfram.com/BesselFunctionZeros.html" target="_top">Wolfram
+ For example, generate and display the first five <code class="computeroutput">double</code>
+ roots of Jv for integral order 2, as column J2(x) in
+ table 1 of <a href="http://mathworld.wolfram.com/BesselFunctionZeros.html" target="_top">Wolfram
 Bessel Function Zeros</a>.
 

@@ -305,10 +330,13 @@

 

- Or generate 50 decimal digit roots of Jv for non-integral order <code class="computeroutput">v=71/19</code>.
+ Or we can use Boost.Multiprecision to generate 50 decimal digit roots of
+ Jv for non-integral order <code class="computeroutput">v= 71/19 == 3.736842</code>,
+ expressed as an exact-integer fraction to generate the most accurate value
+ possible for all floating-point types.
 

- We set the precision of the output stream and show trailing zeros to display
+ We set the precision of the output stream, and show trailing zeros to display
 a fixed 50 decimal digits.
 

@@ -333,48 +361,26 @@
</pre>

 
+<h6>
+<a name="math_toolkit.special.bessel.bessel.h8"></a>
+ <a name="math_toolkit.special.bessel.bessel.using_output_iterator_to_sum_zeros_of_bessel_functions"></a><a class="link" href="bessel0.html#math_toolkit.special.bessel.bessel.using_output_iterator_to_sum_zeros_of_bessel_functions">Using
+ Output Iterator to sum zeros of Bessel Functions</a>
+ </h6>

- The Neumann function zeros are evaluated very similarly:
+ This example demonstrates summing zeros of the Bessel functions. To use
+ the functions for finding zeros of the functions we need
 


-<pre class="programlisting">using boost::math::cyl_neumann_zero;
-
-double zn = cyl_neumann_zero(2., 1);
-
-std::cout << "cyl_neumann_zero(2., 1) = " << std::endl;
-//double zn0 = zn;
-// std::cout << "zn0 = " << std::endl;
-// std::cout << zn0 << std::endl;
-//
-std::cout << zn << std::endl;
-// std::cout << cyl_neumann_zero(2., 1) << std::endl;
-
-std::vector<float> nzeros(3); // Space for 3 zeros.
-cyl_neumann_zero<float>(2.F, 1, nzeros.size(), nzeros.begin());
-
-std::cout << "cyl_neumann_zero<float>(2.F, 1, " << std::endl;
-// Print the zeros to the output stream.
-std::copy(nzeros.begin(), nzeros.end(),
- std::ostream_iterator<float>(std::cout, "\n"));
-
-std::cout << cyl_neumann_zero(static_cast<float_type>(220)/100, 1) << std::endl;
-// 3.6154383428745996706772556069431792744372398748422
+<pre class="programlisting">#include <boost/math/special_functions/bessel.hpp>
</pre>

 

- Finally we show how the output iterator can be used to compute a sum of
- zeros.
- 
-
- (See <a href="http://dx.doi.org/10.1017/S2040618500034067" target="_top">Ian N. Sneddon,
- Infinite Sums of Bessel Zeros</a>, page 150 equation 40).
- 
-
 We use the <code class="computeroutput">cyl_bessel_j_zero</code>
 output iterator parameter <code class="computeroutput">out_it</code>
- to create a sum of 1/zeros2 by defining a custom output iterator:
+ to create a sum of 1/zeros2 by defining a custom output
+ iterator:
 


@@ -419,22 +425,112 @@
</pre>

 
+<h6>
+<a name="math_toolkit.special.bessel.bessel.h9"></a>
+ <a name="math_toolkit.special.bessel.bessel.calculating_zeros_of_the_neumann_function_"></a><a class="link" href="bessel0.html#math_toolkit.special.bessel.bessel.calculating_zeros_of_the_neumann_function_">Calculating
+ zeros of the Neumann function.</a>
+ </h6>
+
+ This example also shows how Boost.Math and Boost.Multiprecision can be
+ combined to provide a many decimal digit precision. For 50 decimal digit
+ precision we need to include
+ 
+
+
+<pre class="programlisting">#include <boost/multiprecision/cpp_dec_float.hpp>
+</pre>
+
+ 
+
+ and a <code class="computeroutput">typedef</code> for <code class="computeroutput">float_type</code> may be convenient (allowing
+ a quick switch to re-compute at built-in <code class="computeroutput">double</code>
+ or other precision)
+ 
+
+
+<pre class="programlisting">typedef boost::multiprecision::cpp_dec_float_50 float_type;
+</pre>
+
+ 
+
+ To use the functions for finding zeros of the <code class="computeroutput">cyl_neumann</code>
+ function we need:
+ 
+
+
+<pre class="programlisting">#include <boost/math/special_functions/bessel.hpp>
+</pre>
+
+ 
+
+ The Neumann (Bessel Y) function zeros are evaluated very similarly:
+ 
+
+
+<pre class="programlisting">using boost::math::cyl_neumann_zero;
+double zn = cyl_neumann_zero(2., 1);
+std::cout << "cyl_neumann_zero(2., 1) = " << zn << std::endl;
+
+std::vector<float> nzeros(3); // Space for 3 zeros.
+cyl_neumann_zero<float>(2.F, 1, nzeros.size(), nzeros.begin());
+
+std::cout << "cyl_neumann_zero<float>(2.F, 1, ";
+// Print the zeros to the output stream.
+std::copy(nzeros.begin(), nzeros.end(),
+ std::ostream_iterator<float>(std::cout, ", "));
+
+std::cout << "\n""cyl_neumann_zero(static_cast<float_type>(220)/100, 1) = "
+ << cyl_neumann_zero(static_cast<float_type>(220)/100, 1) << std::endl;
+// 3.6154383428745996706772556069431792744372398748422
+</pre>
+
+ 
+<h6>
+<a name="math_toolkit.special.bessel.bessel.h10"></a>
+ <a name="math_toolkit.special.bessel.bessel.error_messages_from__bad__input"></a><a class="link" href="bessel0.html#math_toolkit.special.bessel.bessel.error_messages_from__bad__input">Error
+ messages from 'bad' input</a>
+ </h6>
+
+ Another example demonstrates calculating zeros of the Bessel functions
+ showing the error messages from 'bad' input is handled by throwing exceptions.
+ 
+
+ To use the functions for finding zeros of the functions we need:
+ 
+
+
+<pre class="programlisting">#include <boost/math/special_functions/bessel.hpp>
+#include <boost/math/special_functions/airy.hpp>
+</pre>
+
+ 
+<div class="tip"><table border="0" summary="Tip">
+<tr>
+<td rowspan="2" align="center" valign="top" width="25"><img alt="[Tip]" src="../../../../../../../../doc/src/images/tip.png"></td>
+<th align="left">Tip</th>
+</tr>
+<tr><td align="left" valign="top">
+ It is always wise to place all code using Boost.Math inside try'n'catch
+ blocks; this will ensure that helpful error messages can be shown when
+ exceptional conditions arise.
+ </td></tr>
+</table></div>

- Examples below show effect of 'bad' arguments that throw a <code class="computeroutput">domain_error</code> exception.
+ Examples below show messages from several 'bad' arguments that throw a
+ <code class="computeroutput">domain_error</code> exception.
 


<pre class="programlisting">try
-{ // Try a negative rank m.
- std::cout << "boost::math::cyl_bessel_j_zero(-1.F, -1) " << std::endl;
- float dodgy_root = boost::math::cyl_bessel_j_zero(-1.F, -1);
- std::cout << "boost::math::cyl_bessel_j_zero(-1.F, -1) " << dodgy_root << std::endl;
- // Throw exception Error in function boost::math::cyl_bessel_j_zero<double>(double, int):
- // Order argument is -1, but must be >= 0 !
+{ // Try a zero order v.
+ float dodgy_root = boost::math::cyl_bessel_j_zero(0.F, 0);
+ std::cout << "boost::math::cyl_bessel_j_zero(0.F, 0) " << dodgy_root << std::endl;
+ // Thrown exception Error in function boost::math::cyl_bessel_j_zero<double>(double, int):
+ // Requested the 0'th zero of J0, but the rank must be > 0 !
}
catch (std::exception& ex)
{
- std::cout << "Throw exception " << ex.what() << std::endl;
+ std::cout << "Thrown exception " << ex.what() << std::endl;
}
</pre>

@@ -445,8 +541,8 @@
<th align="left">Note</th>
</tr>
<tr><td align="left" valign="top">
- The type shown is the type after promotion,
- using <a class="link" href="../../policy/pol_ref/precision_pol.html" title="Precision Policies">precision
+ The type shown in the error message is the type after
+ promotion, using <a class="link" href="../../policy/pol_ref/precision_pol.html" title="Precision Policies">precision
 policy</a> and <a class="link" href="../../policy/pol_ref/internal_promotion.html" title="Internal Floating-point Promotion Policies">internal
 promotion policy</a>, from <code class="computeroutput">float</code>
 to <code class="computeroutput">double</code> in this case.
@@ -470,8 +566,8 @@
 - so that's the precision we want (and the type that will be returned).
 </li>
<li class="listitem">
- Evaluate internally as <code class="computeroutput">long
- double</code> for full <code class="computeroutput">double</code> precision.
+ Evaluate internally as <code class="computeroutput">double</code>
+ for full <code class="computeroutput">float</code> precision.
 </li>
</ol></div>

@@ -479,24 +575,253 @@
 to <code class="computeroutput">long double</code>.
 

- The full code (and output) for this example for Bessel <code class="computeroutput">cyl_bessel_j_zeros</code>
- is at <a href="../../../../../../example/bessel_zeros_example.cpp" target="_top">Bessel, Neumann
- and Airy zeros</a>.
+ Other examples of 'bad' inputs like infinity and NaN are below. Some compiler
+ warnings indicate that 'bad' values are detected at compile time.
 
-<h5>
-<a name="math_toolkit.special.bessel.bessel.h8"></a>
+
+
+<pre class="programlisting">try
+{ // order v = inf
+ std::cout << "boost::math::cyl_bessel_j_zero(inf, 1) " << std::endl;
+ double inf = std::numeric_limits<double>::infinity();
+ double inf_root = boost::math::cyl_bessel_j_zero(inf, 1);
+ std::cout << "boost::math::cyl_bessel_j_zero(inf, 1) " << inf_root << std::endl;
+ // Throw exception Error in function boost::math::cyl_bessel_j_zero<long double>(long double, unsigned):
+ // Order argument is 1.#INF, but must be finite >= 0 !
+}
+catch (std::exception& ex)
+{
+ std::cout << "Thrown exception " << ex.what() << std::endl;
+}
+
+try
+{ // order v = NaN, rank m = 1
+ std::cout << "boost::math::cyl_bessel_j_zero(nan, 1) " << std::endl;
+ double nan = std::numeric_limits<double>::quiet_NaN();
+ double nan_root = boost::math::cyl_bessel_j_zero(nan, 1);
+ std::cout << "boost::math::cyl_bessel_j_zero(nan, 1) " << nan_root << std::endl;
+ // Throw exception Error in function boost::math::cyl_bessel_j_zero<long double>(long double, unsigned):
+ // Order argument is 1.#QNAN, but must be finite >= 0 !
+}
+catch (std::exception& ex)
+{
+ std::cout << "Thrown exception " << ex.what() << std::endl;
+}
+</pre>
+
+ 
+
+ The output from other examples are shown appended to the full code listing.
+ 
+
+ The full code (and output) for these examples is at <a href="../../../../../../example/bessel_zeros_example_1.cpp" target="_top">Bessel
+ zeros</a>, <a href="../../../../../../example/bessel_zeros_interator_example.cpp" target="_top">Bessel
+ zeros iterator</a>, <a href="../../../../../../example/neumann_zeros_example_1.cpp" target="_top">Neumann
+ zeros</a>, <a href="../../../../../../example/bessel_errors_example.cpp" target="_top">Bessel
+ error messages</a>.
+ 
+<h4>
+<a name="math_toolkit.special.bessel.bessel.h11"></a>
 <a name="math_toolkit.special.bessel.bessel.implementation0"></a><a class="link" href="bessel0.html#math_toolkit.special.bessel.bessel.implementation0">Implementation</a>
- </h5>
+ </h4>

- The method uses Newton-Raphson method starting with McMahon's approximation.
- See "Handbook of Mathematical Functions", M. Abramowitz and I.
- A. Stegan, section 9.5. Also: NIST Digital Library of Mathematical Functions,
- Bessel Function Zeros.
+ Various methods are used to compute initial estimates for jν,
+ m and yν, m ; these are described in detail
+ below.
 
-<h5>
-<a name="math_toolkit.special.bessel.bessel.h9"></a>
+
+ After finding the initial estimate of a given root, its precision is subsequently
+ refined to the desired level using Newton-Raphson iteration from Boost.Math's
+ <a class="link" href="../../toolkit/internals1/roots.html" title="Root Finding With Derivatives: Newton-Raphson, Halley & Schroeder">root-finding with
+ derivatives</a> utilities combined with 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>.
+ 
+
+ Newton iteration requires both Jν(x) or Yν(x)
+ as well as its derivative. The derivatives of Jν(x)
+ and Yν(x) with respect to x are
+ given by M. Abramowitz and I. A. Stegun, Handbook of Mathematical Functions,
+ NBS (1964). In particular,
+ 
+
+   d/dx Jν(x) = Jν-1(x) -
+ ν Jν(x) / x
+ 
+
+   d/dx Yν(x) = Yν-1(x) -
+ ν Yν(x) / x
+ 
+
+ Enumeration of the rank of a root (in other words the index of a root)
+ begins with one and counts up, in other words m,=1,2,3,…
+ The value of the first root is always greater than zero.
+ 
+
+ For certain special parameters, cylindrical Bessel functions and cylindrical
+ Neumann functions have a root at the origin. For example, Jν(x)
+ has a root at the origin for every positive order ν > 0,
+ and for every negative integer order ν = -n with n
+ ∈ ℕ + and n ≠ 0.
+ 
+
+ In addition, Yν(x) has a root at the origin for every
+ negative half-integer order ν = -n/2, with n
+ ∈ ℕ + and and n ≠ 0.
+ 
+
+ For these special parameter values, the origin with a value of x
+ = 0 is provided as the 0th root generated
+ by <code class="computeroutput">cyl_bessel_j_zero()</code>
+ and <code class="computeroutput">cyl_neumann_zero()</code>.
+ 
+
+ When calculating initial estimates for the roots of Bessel functions, a
+ distinction is made between positive order and negative order, and different
+ methods are used for these. In addition, different algorithms are used
+ for the first root m = 1 and for subsequent roots
+ with higher rank m ≥ 2. Furthermore, estimates of the
+ roots for Bessel functions with order above and below a cutoff at ν =
+ 2.2 are calculated with different methods.
+ 
+
+ Calculations of the estimates of jν,1 and yν,1
+ with 0 ≤ ν < 2.2 use empirically tabulated values.
+ The coefficients for these have been generated by a computer algebra system.
+ 
+
+ Calculations of the estimates of jν,1 and yν,1
+ with ν≥ 2.2 use Eqs.9.5.14 and 9.5.15 in M. Abramowitz
+ and I. A. Stegun, Handbook of Mathematical Functions, NBS (1964).
+ 
+
+ In particular,
+ 
+
+   jν,1 ≅ ν + 1.85575 ν⅓ + 1.033150 ν-⅓ - 0.00397 ν-1 - 0.0908 ν-5/3 + 0.043 ν-7/3 +
+ …
+ 
+
+ and
+ 
+
+   yν,1 ≅ ν + 0.93157 ν⅓ + 0.26035 ν-⅓ + 0.01198 ν-1 - 0.0060 ν-5/3 - 0.001 ν-7/3 +
+ …
+ 
+
+ Calculations of the estimates of jν, m and yν,
+ m with rank m > 2 and 0 ≤ ν <
+ 2.2 use McMahon's approximation, as described in M. Abramowitz
+ and I. A. Stegan, Section 9.5 and 9.5.12. In particular,
+ 
+
+   jν,m, yν,m ≅ β - (μ-1) / 8β
+ 
+
+       - 4(μ-1)(7μ - 31) / 3(8β)3
+ 
+
+       -32(μ-1)(83μ² - 982μ + 3779) / 15(8β)5
+ 
+
+       -64(μ-1)(6949μ3 - 153855μ² + 1585743μ- 6277237) / 105(8a)7
+ 
+
+       - …     (5)
+ 
+
+ where μ = 4ν2 and β = (m + ½ν - ¼)π for
+ jν,m and β = (m + ½ν -¾)π for yν,m.
+ 
+
+ Calculations of the estimates of jν, m and yν,
+ m with ν ≥ 2.2 use one term in the asymptotic
+ expansion given in Eq.9.5.22 and top line of Eq.9.5.26 combined with Eq.
+ 9.3.39, all in M. Abramowitz and I. A. Stegun, Handbook of Mathematical
+ Functions, NBS (1964) explicit and easy-to-understand treatment for asymptotic
+ expansion of zeros. The latter two equations are expressed for argument
+ (x) greater than one. (Olver also gives the series
+ form of the equations in <a href="http://dlmf.nist.gov/10.21#vi" target="_top">§10.21(vi)
+ McMahon's Asymptotic Expansions for Large Zeros</a> - using slightly
+ different variable names).
+ 
+
+ In summary,
+ 
+
+   jν, m ∼ νx(-ζ) + f1(-ζ/ν)
+ 
+
+ where -ζ = ν-2/3am and am is the
+ absolute value of the mth root of Ai(x)
+ on the negative real axis.
+ 
+
+ Here x = x(-ζ) is the inverse of the function
+ 
+
+   ⅔(-ζ)3/2 = √(x² - 1) - cos⁻¹(1/x)     (7)
+ 
+
+ Furthermore,
+ 
+
+   f1(-ζ) = ½x(-ζ) {h(-ζ)}² ⋅ b0(-ζ)
+ 
+
+ where
+ 
+
+   h(-ζ) = {4(-ζ) / (x² - 1)}4
+ 
+
+ and
+ 
+
+   b0(-ζ) = -5/(48ζ²) + 1/(-ζ)½ ⋅ { 5/(24(x2-1)3/2) + 1/(8(x2-1)½)}
+ 
+
+ When solving for x(-ζ) in Eq. 7 above, the right-hand-side
+ is expanded to order 2 in a Taylor series for large x.
+ This results in
+ 
+
+   ⅔(-ζ)3/2 ≈ x + 1/2x - π/2
+ 
+
+ The positive root of the resulting quadratic equation is used to find an
+ initial estimate x(-ζ). This initial estimate is subsequently
+ refined with several steps of Newton-Raphson iteration in Eq. 7.
+ 
+
+ Estimates of the roots of cylindrical Bessel functions of negative order
+ on the positive real axis are found using interlacing relations. For example,
+ the mth root of the cylindrical Bessel function j-ν,m
+ is bracketed by the mth root and the (m+1)th
+ root of the Bessel function of corresponding positive integer order. In
+ other words,
+ 
+
+   jnν,m < j-ν,m < jnν,m+1
+ 
+
+ where m > 1 and nν represents
+ the integral floor of the absolute value of |-ν|.
+ 
+
+ Similar bracketing relations are used to find estimates of the roots of
+ Neumann functions of negative order, whereby a discontinuity at every negative
+ half-integer order needs to be handled.
+ 
+
+ Bracketing relations do not hold for the first root of cylindrical Bessel
+ functions and cylindrical Neumann functions with negative order. Therefore,
+ iterative algorithms combined with root-finding via bisection are used
+ to localize j-ν,1 and y-ν,1.
+ 
+<h4>
+<a name="math_toolkit.special.bessel.bessel.h12"></a>
 <a name="math_toolkit.special.bessel.bessel.testing0"></a><a class="link" href="bessel0.html#math_toolkit.special.bessel.bessel.testing0">Testing</a>
- </h5>
+ </h4>

 The precision of evaluation of zeros was tested at 50 decimal digits using
 <code class="computeroutput">cpp_dec_float_50</code> and found

Modified: trunk/libs/math/doc/sf_and_dist/html/math_toolkit/status/history1.html
==============================================================================
--- trunk/libs/math/doc/sf_and_dist/html/math_toolkit/status/history1.html (original)
+++ trunk/libs/math/doc/sf_and_dist/html/math_toolkit/status/history1.html 2013-03-21 09:01:50 EDT (Thu, 21 Mar 2013)
@@ -72,6 +72,15 @@
<li class="listitem">
Added minimal __float128 support.
</li>
+<li class="listitem">
+ Fixed bug in edge-cases of poisson quantile #8308.
+ </li>
+<li class="listitem">
+ Adjusted heuristics used in Halley iteration to cope with inverting the
+ incomplete beta in tricky regions where the derivative is flatlining.
+ Example is computing the quantile of the Fisher F distribution for probabilities
+ smaller than machine epsilon. See ticket #8314.
+ </li>
</ul></div>
<h5>
<a name="math_toolkit.status.history1.h1"></a>

Modified: trunk/libs/math/doc/sf_and_dist/html/math_toolkit/status/issues.html
==============================================================================
--- trunk/libs/math/doc/sf_and_dist/html/math_toolkit/status/issues.html (original)
+++ trunk/libs/math/doc/sf_and_dist/html/math_toolkit/status/issues.html 2013-03-21 09:01:50 EDT (Thu, 21 Mar 2013)
@@ -41,6 +41,21 @@
 
<h5>
<a name="math_toolkit.status.issues.h0"></a>
+ <a name="math_toolkit.status.issues.derivatives_of_bessel_functions__and_their_zeros_"></a><a class="link" href="issues.html#math_toolkit.status.issues.derivatives_of_bessel_functions__and_their_zeros_">Derivatives
+ of Bessel functions (and their zeros)</a>
+ </h5>
+
+ Potentially, there could be native support for <code class="computeroutput">cyl_bessel_j_prime()</code> and <code class="computeroutput">cyl_neumann_prime()</code>. One could also imagine supporting the
+ zeros thereof, but they might be slower to calculate since root bracketing
+ might be needed instead of Newton iteration (for the lack of 2nd derivatives).
+ 
+
+ Since Boost.Math's Bessel functions are so excellent, the quick way to <code class="computeroutput">cyl_bessel_j_prime()</code>
+ and <code class="computeroutput">cyl_neumann_prime()</code>
+ would be via relationship with <code class="computeroutput">cyl_bessel_j()</code> and <code class="computeroutput">cyl_neumann()</code>.
+ 
+<h5>
+<a name="math_toolkit.status.issues.h1"></a>
 <a name="math_toolkit.status.issues.tgamma"></a><a class="link" href="issues.html#math_toolkit.status.issues.tgamma">tgamma</a>
 </h5>
<div class="itemizedlist"><ul class="itemizedlist" style="list-style-type: disc; "><li class="listitem">
@@ -48,7 +63,7 @@
 be optimized any further? (low priority)
 </li></ul></div>
<h5>
-<a name="math_toolkit.status.issues.h1"></a>
+<a name="math_toolkit.status.issues.h2"></a>
 <a name="math_toolkit.status.issues.incomplete_beta"></a><a class="link" href="issues.html#math_toolkit.status.issues.incomplete_beta">Incomplete
 Beta</a>
 </h5>
@@ -57,7 +72,7 @@
 b (medium priority).
 </li></ul></div>
<h5>
-<a name="math_toolkit.status.issues.h2"></a>
+<a name="math_toolkit.status.issues.h3"></a>
 <a name="math_toolkit.status.issues.inverse_gamma"></a><a class="link" href="issues.html#math_toolkit.status.issues.inverse_gamma">Inverse
 Gamma</a>
 </h5>
@@ -66,7 +81,7 @@
 is good enough (Medium Priority).
 </li></ul></div>
<h5>
-<a name="math_toolkit.status.issues.h3"></a>
+<a name="math_toolkit.status.issues.h4"></a>
 <a name="math_toolkit.status.issues.polynomials"></a><a class="link" href="issues.html#math_toolkit.status.issues.polynomials">Polynomials</a>
 </h5>
<div class="itemizedlist"><ul class="itemizedlist" style="list-style-type: disc; "><li class="listitem">
@@ -76,7 +91,7 @@
 not (Low Priority).
 </li></ul></div>
<h5>
-<a name="math_toolkit.status.issues.h4"></a>
+<a name="math_toolkit.status.issues.h5"></a>
 <a name="math_toolkit.status.issues.elliptic_integrals"></a><a class="link" href="issues.html#math_toolkit.status.issues.elliptic_integrals">Elliptic
 Integrals</a>
 </h5>
@@ -129,7 +144,7 @@
 </li>
</ul></div>
<h5>
-<a name="math_toolkit.status.issues.h5"></a>
+<a name="math_toolkit.status.issues.h6"></a>
 <a name="math_toolkit.status.issues.owen_s_t_function"></a><a class="link" href="issues.html#math_toolkit.status.issues.owen_s_t_function">Owen's
 T Function</a>
 </h5>
@@ -145,7 +160,7 @@
 but it remains elusive at present.
 
<h5>
-<a name="math_toolkit.status.issues.h6"></a>
+<a name="math_toolkit.status.issues.h7"></a>
 <a name="math_toolkit.status.issues.jocobi_elliptic_functions"></a><a class="link" href="issues.html#math_toolkit.status.issues.jocobi_elliptic_functions">Jocobi elliptic
 functions</a>
 </h5>
@@ -154,7 +169,7 @@
 these.
 
<h5>
-<a name="math_toolkit.status.issues.h7"></a>
+<a name="math_toolkit.status.issues.h8"></a>
 <a name="math_toolkit.status.issues.statistical_distributions"></a><a class="link" href="issues.html#math_toolkit.status.issues.statistical_distributions">Statistical
 distributions</a>
 </h5>
@@ -163,7 +178,7 @@
 for very large degrees of freedom?
 </li></ul></div>
<h5>
-<a name="math_toolkit.status.issues.h8"></a>
+<a name="math_toolkit.status.issues.h9"></a>
 <a name="math_toolkit.status.issues.feature_requests"></a><a class="link" href="issues.html#math_toolkit.status.issues.feature_requests">Feature
 Requests</a>
 </h5>

Modified: trunk/libs/math/doc/sf_and_dist/html/math_toolkit/using_udt/high_precision/using_test.html
==============================================================================
--- trunk/libs/math/doc/sf_and_dist/html/math_toolkit/using_udt/high_precision/using_test.html (original)
+++ trunk/libs/math/doc/sf_and_dist/html/math_toolkit/using_udt/high_precision/using_test.html 2013-03-21 09:01:50 EDT (Thu, 21 Mar 2013)
@@ -65,7 +65,7 @@
 with <code class="computeroutput">boost::multiprecision::et_off</code>, an enumerated type.
 
<pre class="programlisting">typedef boost::multiprecision::number<boost::multiprecision::cpp_dec_float<50>, boost::multiprecision::et_off>
-cpp_dec_float_50_noet;`
+cpp_dec_float_50_noet;
</pre>

 You can reduce typing with a <code class="computeroutput">using</code>
@@ -101,8 +101,8 @@

 std::cout <<"a = " << a << ",\nb = " << b << ",\neps = " << eps << std::endl;

- BOOST_CHECK_CLOSE(a, b, eps); // Expected to pass (because tolerance is as percent).
- BOOST_CHECK_CLOSE_FRACTION(a, b, eps); // Expected to fail.
+ BOOST_CHECK_CLOSE(a, b, eps * 100); // Expected to pass (because tolerance is as percent).
+ BOOST_CHECK_CLOSE_FRACTION(a, b, eps); // Expected to pass (because tolerance is as fraction).
</pre>

Modified: trunk/libs/math/doc/sf_and_dist/roadmap.qbk
==============================================================================
--- trunk/libs/math/doc/sf_and_dist/roadmap.qbk (original)
+++ trunk/libs/math/doc/sf_and_dist/roadmap.qbk 2013-03-21 09:01:50 EDT (Thu, 21 Mar 2013)
@@ -17,6 +17,10 @@
* Fixed bug in __tgamma that caused spurious overflow for arguments between 142.5 and 143.
* Fixed bug in raise_rounding_error that caused it to return an incorrect result when throwing an exception is turned off [@https://svn.boost.org/trac/boost/ticket/7905 #7905].
* Added minimal __float128 support.
+* Fixed bug in edge-cases of poisson quantile [@https://svn.boost.org/trac/boost/ticket/8308 #8308].
+* Adjusted heuristics used in Halley iteration to cope with inverting the incomplete beta in tricky regions
+where the derivative is flatlining. Example is computing the quantile of the Fisher F distribution for probabilities
+smaller than machine epsilon. See ticket [@https://svn.boost.org/trac/boost/ticket/8314 #8314].

[h4 Boost-1.53]

Modified: trunk/libs/math/test/test_poisson.cpp
==============================================================================
--- trunk/libs/math/test/test_poisson.cpp (original)
+++ trunk/libs/math/test/test_poisson.cpp 2013-03-21 09:01:50 EDT (Thu, 21 Mar 2013)
@@ -146,6 +146,26 @@
 static_cast<RealType>(-1)), // bad probability.
 std::domain_error);

+ BOOST_CHECK_THROW(
+ quantile(poisson_distribution<RealType>(static_cast<RealType>(1)),
+ static_cast<RealType>(1)), // bad probability.
+ std::overflow_error);
+
+ BOOST_CHECK_THROW(
+ quantile(complement(poisson_distribution<RealType>(static_cast<RealType>(1)),
+ static_cast<RealType>(0))), // bad probability.
+ std::overflow_error);
+
+ BOOST_CHECK_EQUAL(
+ quantile(poisson_distribution<RealType>(static_cast<RealType>(1)),
+ static_cast<RealType>(0)), // bad probability.
+ 0);
+
+ BOOST_CHECK_EQUAL(
+ quantile(complement(poisson_distribution<RealType>(static_cast<RealType>(1)),
+ static_cast<RealType>(1))), // bad probability.
+ 0);
+
 // Check some test values.

 BOOST_CHECK_CLOSE( // mode

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