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Subject: [Boost-commit] svn:boost r66944 - in sandbox/math_constants: boost/math/constants libs/math/doc libs/math/doc/html libs/math/doc/html/images libs/math/doc/html/images/callouts libs/math/doc/html/math_constants
From: john_at_[hidden]
Date: 2010-12-01 08:46:13

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Author: johnmaddock
Date: 2010-12-01 08:46:11 EST (Wed, 01 Dec 2010)
New Revision: 66944
URL: http://svn.boost.org/trac/boost/changeset/66944

Log:
Add docs, tweak constexp support.
Added:
   sandbox/math_constants/libs/math/doc/
   sandbox/math_constants/libs/math/doc/Jamfile.v2 (contents, props changed)
   sandbox/math_constants/libs/math/doc/constants.qbk (contents, props changed)
   sandbox/math_constants/libs/math/doc/html/
   sandbox/math_constants/libs/math/doc/html/boostbook.css (contents, props changed)
   sandbox/math_constants/libs/math/doc/html/images/
   sandbox/math_constants/libs/math/doc/html/images/alert.png (contents, props changed)
   sandbox/math_constants/libs/math/doc/html/images/blank.png (contents, props changed)
   sandbox/math_constants/libs/math/doc/html/images/callouts/
   sandbox/math_constants/libs/math/doc/html/images/callouts/1.png (contents, props changed)
   sandbox/math_constants/libs/math/doc/html/images/callouts/1.svg (contents, props changed)
   sandbox/math_constants/libs/math/doc/html/images/callouts/10.png (contents, props changed)
   sandbox/math_constants/libs/math/doc/html/images/callouts/10.svg (contents, props changed)
   sandbox/math_constants/libs/math/doc/html/images/callouts/11.png (contents, props changed)
   sandbox/math_constants/libs/math/doc/html/images/callouts/11.svg (contents, props changed)
   sandbox/math_constants/libs/math/doc/html/images/callouts/12.png (contents, props changed)
   sandbox/math_constants/libs/math/doc/html/images/callouts/12.svg (contents, props changed)
   sandbox/math_constants/libs/math/doc/html/images/callouts/13.png (contents, props changed)
   sandbox/math_constants/libs/math/doc/html/images/callouts/13.svg (contents, props changed)
   sandbox/math_constants/libs/math/doc/html/images/callouts/14.png (contents, props changed)
   sandbox/math_constants/libs/math/doc/html/images/callouts/14.svg (contents, props changed)
   sandbox/math_constants/libs/math/doc/html/images/callouts/15.png (contents, props changed)
   sandbox/math_constants/libs/math/doc/html/images/callouts/15.svg (contents, props changed)
   sandbox/math_constants/libs/math/doc/html/images/callouts/16.svg (contents, props changed)
   sandbox/math_constants/libs/math/doc/html/images/callouts/17.svg (contents, props changed)
   sandbox/math_constants/libs/math/doc/html/images/callouts/18.svg (contents, props changed)
   sandbox/math_constants/libs/math/doc/html/images/callouts/19.svg (contents, props changed)
   sandbox/math_constants/libs/math/doc/html/images/callouts/2.png (contents, props changed)
   sandbox/math_constants/libs/math/doc/html/images/callouts/2.svg (contents, props changed)
   sandbox/math_constants/libs/math/doc/html/images/callouts/20.svg (contents, props changed)
   sandbox/math_constants/libs/math/doc/html/images/callouts/21.svg (contents, props changed)
   sandbox/math_constants/libs/math/doc/html/images/callouts/22.svg (contents, props changed)
   sandbox/math_constants/libs/math/doc/html/images/callouts/23.svg (contents, props changed)
   sandbox/math_constants/libs/math/doc/html/images/callouts/24.svg (contents, props changed)
   sandbox/math_constants/libs/math/doc/html/images/callouts/25.svg (contents, props changed)
   sandbox/math_constants/libs/math/doc/html/images/callouts/26.svg (contents, props changed)
   sandbox/math_constants/libs/math/doc/html/images/callouts/27.svg (contents, props changed)
   sandbox/math_constants/libs/math/doc/html/images/callouts/28.svg (contents, props changed)
   sandbox/math_constants/libs/math/doc/html/images/callouts/29.svg (contents, props changed)
   sandbox/math_constants/libs/math/doc/html/images/callouts/3.png (contents, props changed)
   sandbox/math_constants/libs/math/doc/html/images/callouts/3.svg (contents, props changed)
   sandbox/math_constants/libs/math/doc/html/images/callouts/30.svg (contents, props changed)
   sandbox/math_constants/libs/math/doc/html/images/callouts/4.png (contents, props changed)
   sandbox/math_constants/libs/math/doc/html/images/callouts/4.svg (contents, props changed)
   sandbox/math_constants/libs/math/doc/html/images/callouts/5.png (contents, props changed)
   sandbox/math_constants/libs/math/doc/html/images/callouts/5.svg (contents, props changed)
   sandbox/math_constants/libs/math/doc/html/images/callouts/6.png (contents, props changed)
   sandbox/math_constants/libs/math/doc/html/images/callouts/6.svg (contents, props changed)
   sandbox/math_constants/libs/math/doc/html/images/callouts/7.png (contents, props changed)
   sandbox/math_constants/libs/math/doc/html/images/callouts/7.svg (contents, props changed)
   sandbox/math_constants/libs/math/doc/html/images/callouts/8.png (contents, props changed)
   sandbox/math_constants/libs/math/doc/html/images/callouts/8.svg (contents, props changed)
   sandbox/math_constants/libs/math/doc/html/images/callouts/9.png (contents, props changed)
   sandbox/math_constants/libs/math/doc/html/images/callouts/9.svg (contents, props changed)
   sandbox/math_constants/libs/math/doc/html/images/caution.png (contents, props changed)
   sandbox/math_constants/libs/math/doc/html/images/caution.svg (contents, props changed)
   sandbox/math_constants/libs/math/doc/html/images/draft.png (contents, props changed)
   sandbox/math_constants/libs/math/doc/html/images/home.png (contents, props changed)
   sandbox/math_constants/libs/math/doc/html/images/home.svg (contents, props changed)
   sandbox/math_constants/libs/math/doc/html/images/important.png (contents, props changed)
   sandbox/math_constants/libs/math/doc/html/images/important.svg (contents, props changed)
   sandbox/math_constants/libs/math/doc/html/images/next.png (contents, props changed)
   sandbox/math_constants/libs/math/doc/html/images/next.svg (contents, props changed)
   sandbox/math_constants/libs/math/doc/html/images/next_disabled.png (contents, props changed)
   sandbox/math_constants/libs/math/doc/html/images/note.png (contents, props changed)
   sandbox/math_constants/libs/math/doc/html/images/note.svg (contents, props changed)
   sandbox/math_constants/libs/math/doc/html/images/prev.png (contents, props changed)
   sandbox/math_constants/libs/math/doc/html/images/prev.svg (contents, props changed)
   sandbox/math_constants/libs/math/doc/html/images/prev_disabled.png (contents, props changed)
   sandbox/math_constants/libs/math/doc/html/images/smiley.png (contents, props changed)
   sandbox/math_constants/libs/math/doc/html/images/tip.png (contents, props changed)
   sandbox/math_constants/libs/math/doc/html/images/tip.svg (contents, props changed)
   sandbox/math_constants/libs/math/doc/html/images/toc-blank.png (contents, props changed)
   sandbox/math_constants/libs/math/doc/html/images/toc-minus.png (contents, props changed)
   sandbox/math_constants/libs/math/doc/html/images/toc-plus.png (contents, props changed)
   sandbox/math_constants/libs/math/doc/html/images/up.png (contents, props changed)
   sandbox/math_constants/libs/math/doc/html/images/up.svg (contents, props changed)
   sandbox/math_constants/libs/math/doc/html/images/up_disabled.png (contents, props changed)
   sandbox/math_constants/libs/math/doc/html/images/warning.png (contents, props changed)
   sandbox/math_constants/libs/math/doc/html/images/warning.svg (contents, props changed)
   sandbox/math_constants/libs/math/doc/html/index.html (contents, props changed)
   sandbox/math_constants/libs/math/doc/html/math_constants/
   sandbox/math_constants/libs/math/doc/html/math_constants/tutorial.html (contents, props changed)
Text files modified:
   sandbox/math_constants/boost/math/constants/constants.hpp | 12 ++++++------
   1 files changed, 6 insertions(+), 6 deletions(-)

Modified: sandbox/math_constants/boost/math/constants/constants.hpp
==============================================================================
--- sandbox/math_constants/boost/math/constants/constants.hpp (original)
+++ sandbox/math_constants/boost/math/constants/constants.hpp 2010-12-01 08:46:11 EST (Wed, 01 Dec 2010)
@@ -110,11 +110,11 @@
 BOOST_MATH_CONSTANT_THREAD_HELPER(name, string_)\
 return BOOST_JOIN(string_get_, name)<T>();\
 }\
- template <class T> inline T BOOST_JOIN(get_, name)(const mpl::int_<construct_from_float>& BOOST_MATH_APPEND_EXPLICIT_TEMPLATE_TYPE_SPEC(T))\
+ template <class T> inline BOOST_CONSTEXPR T BOOST_JOIN(get_, name)(const mpl::int_<construct_from_float>& BOOST_MATH_APPEND_EXPLICIT_TEMPLATE_TYPE_SPEC(T))\
 { return BOOST_JOIN(BOOST_JOIN(x, BOOST_JOIN(e, exp)), F); }\
- template <class T> inline T BOOST_JOIN(get_, name)(const mpl::int_<construct_from_double>& BOOST_MATH_APPEND_EXPLICIT_TEMPLATE_TYPE_SPEC(T))\
+ template <class T> inline BOOST_CONSTEXPR T BOOST_JOIN(get_, name)(const mpl::int_<construct_from_double>& BOOST_MATH_APPEND_EXPLICIT_TEMPLATE_TYPE_SPEC(T))\
 { return BOOST_JOIN(x, BOOST_JOIN(e, exp)); }\
- template <class T> inline T BOOST_JOIN(get_, name)(const mpl::int_<construct_from_long_double>& BOOST_MATH_APPEND_EXPLICIT_TEMPLATE_TYPE_SPEC(T))\
+ template <class T> inline BOOST_CONSTEXPR T BOOST_JOIN(get_, name)(const mpl::int_<construct_from_long_double>& BOOST_MATH_APPEND_EXPLICIT_TEMPLATE_TYPE_SPEC(T))\
 { return BOOST_JOIN(BOOST_JOIN(x, BOOST_JOIN(e, exp)), L); }\
 /* This one is for very high precision that is none the less known at compile time: */ \
 template <class T, int N> inline T BOOST_JOIN(compute_get_, name)(BOOST_MATH_EXPLICIT_TEMPLATE_TYPE_SPEC(mpl::int_<N>) BOOST_MATH_APPEND_EXPLICIT_TEMPLATE_TYPE_SPEC(T))\
@@ -122,7 +122,7 @@
 template <class T, int N> inline T BOOST_JOIN(get_, name)(const mpl::int_<N>& n BOOST_MATH_APPEND_EXPLICIT_TEMPLATE_TYPE_SPEC(T))\
 {\
 BOOST_MATH_CONSTANT_THREAD_HELPER(name, compute_)\
- BOOST_JOIN(compute_get_, name)<T, N>(); \
+ return BOOST_JOIN(compute_get_, name)<T, N>(); \
 }\
 /* This one is for true arbitary precision, which may well vary at runtime: */ \
 template <class T> inline T BOOST_JOIN(get_, name)(const mpl::int_<0>& n BOOST_MATH_APPEND_EXPLICIT_TEMPLATE_TYPE_SPEC(T))\
@@ -131,9 +131,9 @@
 \
 \
 /* The actual forwarding function: */ \
- template <class T, class Policy> inline T name(BOOST_MATH_EXPLICIT_TEMPLATE_TYPE_SPEC(T) BOOST_MATH_APPEND_EXPLICIT_TEMPLATE_TYPE_SPEC(Policy))\
+ template <class T, class Policy> inline BOOST_CONSTEXPR T name(BOOST_MATH_EXPLICIT_TEMPLATE_TYPE_SPEC(T) BOOST_MATH_APPEND_EXPLICIT_TEMPLATE_TYPE_SPEC(Policy))\
 { return detail:: BOOST_JOIN(get_, name)<T>(typename construction_traits<T, Policy>::type()); }\
- template <class T> inline T name(BOOST_MATH_EXPLICIT_TEMPLATE_TYPE_SPEC(T))\
+ template <class T> inline BOOST_CONSTEXPR T name(BOOST_MATH_EXPLICIT_TEMPLATE_TYPE_SPEC(T))\
 { return name<T, boost::math::policies::policy<> >(); }\
 \
 \

Added: sandbox/math_constants/libs/math/doc/Jamfile.v2
==============================================================================
--- (empty file)
+++ sandbox/math_constants/libs/math/doc/Jamfile.v2 2010-12-01 08:46:11 EST (Wed, 01 Dec 2010)
@@ -0,0 +1,68 @@
+
+# Copyright John Maddock 2005. Use, modification, and distribution are
+# subject to 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)
+
+using quickbook ;
+
+path-constant images_location : html ;
+
+xml constants : constants.qbk ;
+boostbook standalone
+ :
+ constants
+ :
+ # Path for links to Boost:
+ #<xsl:param>boost.root=../../../../..
+
+ # Some general style settings:
+ <xsl:param>table.footnote.number.format=1
+ <xsl:param>footnote.number.format=1
+
+ # HTML options first:
+ # Use graphics not text for navigation:
+ <xsl:param>navig.graphics=1
+ # How far down we chunk nested sections, basically all of them:
+ <xsl:param>chunk.section.depth=0
+ # Don't put the first section on the same page as the TOC:
+ <xsl:param>chunk.first.sections=0
+ # How far down sections get TOC's
+ <xsl:param>toc.section.depth=10
+ # Max depth in each TOC:
+ <xsl:param>toc.max.depth=4
+ # How far down we go with TOC's
+ #<xsl:param>generate.section.toc.level=0
+ # Index on type:
+ <xsl:param>index.on.type=1
+
+ # PDF Options:
+ # TOC Generation: this is needed for FOP-0.9 and later:
+ <xsl:param>fop1.extensions=0
+ <format>pdf:<xsl:param>xep.extensions=1
+ # TOC generation: this is needed for FOP 0.2, but must not be set to zero for FOP-0.9!
+ <format>pdf:<xsl:param>fop.extensions=0
+ <format>pdf:<xsl:param>fop1.extensions=0
+ # No indent on body text:
+ <format>pdf:<xsl:param>body.start.indent=0pt
+ # Margin size:
+ <format>pdf:<xsl:param>page.margin.inner=0.5in
+ # Margin size:
+ <format>pdf:<xsl:param>page.margin.outer=0.5in
+ # Paper type = A4
+ <format>pdf:<xsl:param>paper.type=A4
+ # Yes, we want graphics for admonishments:
+ <xsl:param>admon.graphics=1
+ # Set this one for PDF generation *only*:
+ # default pnd graphics are awful in PDF form,
+ # better use SVG's instead:
+ <format>pdf:<xsl:param>admon.graphics.extension=".svg"
+ <format>pdf:<xsl:param>use.role.for.mediaobject=1
+ <format>pdf:<xsl:param>preferred.mediaobject.role=print
+ <format>pdf:<xsl:param>img.src.path=$(images_location)/
+ <format>pdf:<xsl:param>draft.mode="no"
+ <format>pdf:<xsl:param>boost.url.prefix=http://www.boost.org/doc/libs/release/libs/math/doc/sf_and_dist/html
+ ;
+
+install pdf-install : standalone : <location>. <install-type>PDF ;
+
+

Added: sandbox/math_constants/libs/math/doc/constants.qbk
==============================================================================
--- (empty file)
+++ sandbox/math_constants/libs/math/doc/constants.qbk 2010-12-01 08:46:11 EST (Wed, 01 Dec 2010)
@@ -0,0 +1,225 @@
+[article Math Constants
+ [quickbook 1.5]
+ [copyright 2010 John Maddock, Paul A. Bristow]
+ [/purpose ISBN 0-9504833-2-X 978-0-9504833-2-0, Classification 519.2-dc22]
+ [license
+ 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])
+ ]
+ [authors [Maddock, John], [Bristow, Paul A.]]
+ [/last-revision $Date: 2010-11-25 09:56:01 +0000 (Thu, 25 Nov 2010) $]
+]
+
+[section:tutorial Tutorial]
+
+[section:non_templ Use in non-template code]
+
+When using the constants at fixed precision in non-template code, you can simply
+add a using declaration to make the constants of the correct precision for your code
+visible in the current scope, and then use each constant as a simple variable:
+
+ #include <boost/math/constants.hpp>
+
+ double area(double r)
+ {
+ using boost::math::double_constants;
+ return pi * r * r;
+ }
+
+Had our function been written as taking a `float` rather than a `double`
+we could have written instead:
+
+ #include <boost/math/constants.hpp>
+
+ float area(float r)
+ {
+ using boost::math::float_constants;
+ return pi * r * r;
+ }
+
+Likewise constants that are suitable for use at `long double` precision
+are available in the namespace `boost::math::long_double_constants`.
+
+[endsect]
+[section:templ Use in template code]
+
+When using the constants inside a function template, we need to ensure that
+we use the a constant of the correct precision for our template parameters.
+We can do this by calling the function-template versions of the constants
+like this:
+
+ #include <boost/math/constants.hpp>
+
+ template <class Real>
+ Real area(Real r)
+ {
+ using namespace boost::math::constants;
+ return pi<Real>() * r * r;
+ }
+
+Although this syntax is a little less "cute" than the non-template version
+the code is no less efficient (at least for the builtin types float, double and long double)
+- the function template versions of the constants are simple inline functions that
+return a constant of the correct precision for the type used. In addition these
+functions are declared `constexp` for those compilers that support this, allowing
+the result to be used in constant-expressions provided the template argument is a literal type.
+
+[endsect]
+[section:user_def Use With User Defined Types]
+
+The syntax for using the constants with user-defined types is the same as it is in
+the template clase, which is to say we use:
+
+ #include <boost/math/constants.hpp>
+
+ boost::math::constants::pi<UserDefinedType>();
+
+However, since the precision of the user-defined type may be much greater than that
+of the builtin floating pointer types, how the value returned is created is as follows:
+
+* If the precision of the type is known at compile time:
+ * If the precision is less than or equal to that of a `float` and the type is constructable from a `float`
+ then our code returns a `float` literal. If the user-defined type is a literal type
+ then the function call that returns the constant will be a `constexp`.
+ * If the precision is less than or equal to that of a `double` and the type is constructable from a `double`
+ then our code returns a `double` literal. If the user-defined type is a literal type
+ then the function call that returns the constant will be a `constexp`.
+ * If the precision is less than or equal to that of a `long double` and the type is constructable from a `long double`
+ then our code returns a `long double` literal. If the user-defined type is a literal type
+ then the function call that returns the constant will be a `constexp`.
+ * If the precision is less than 100 decimal digits, then the constant will be constructed
+ (just the once, then cached in a thread safe manner) from a string representation of the constant.
+ * Otherwise the value is computed (just once, then cached in a thread safe manner).
+* If the precision is unknown at compile time then:
+ * If the runtime precision (obtained from a call to `boost::math::tools::digits<T>()`) is
+ less than 100 decimal digits, then the constant is constructed "on the fly" from the string
+ representation of the constant.
+ * Otherwise the value is constructed "on the fly" by calculating then value of the constant
+ using the current default precision of the type. Note that this can make use of the constants
+ rather expensive.
+
+In addition, it is possible to pass a "Policy" type as a second template argument, and use this to control
+the precision:
+
+ #include <boost/math/constants/constants.hpp>
+
+ typedef boost::math::policies::policy<boost::math::policies::digits2<80> > my_policy_type;
+ boost::math::constants::pi<MyType, my_policy_type>();
+
+Note that Boost.Math doesn't know how to control the internal precision of `MyType`, the policy
+just controls how the selection process above is carried out, and the calculation precision
+if the result is computed.
+
+It is also possible to control which method is used to construct the constant by specialising
+the traits class `construction_traits`:
+
+ namespace boost{ namespace math{ namespace constant{
+
+ template <class T, class Policy>
+ struct construction_traits
+ {
+ typedef mpl::int_<N> type;
+ };
+
+ }}} // namespaces
+
+Where /N/ takes one of the following values:
+
+[table
+[[N][Meaning]]
+[[0][The precision is unavailable at compile time, either construct from a string or calculate on the fly
+ depending upon the runtime precision.]]
+[[1][Return a float precision constant.]]
+[[2][Return a double precision constant.]]
+[[3][Return a long double precision constant.]]
+[[4][Construct the result from the string representation, and cache the result.]]
+[[Any other value N][Sets the compile time precision to N bits.]]
+]
+
+Finally, sice it can be tricky to diagnose what meta-programmed code is doing, there is a
+diagnostic routine that prints information about how this library will handle a specific type,
+it can be used like this:
+
+ #include <boost/math/constants/info.hpp>
+
+ int main()
+ {
+ boost::math::constants::print_info_on_type<MyType>();
+ }
+
+If you wish you can also pass an optional std::ostream argument to the `print_info_on_type` function.
+Typical output for a user-defined type looks like this:
+
+[pre
+Information on the Implementation and Handling of
+Mathematical Constants for Type class boost::math::concepts::real_concept
+
+Checking for std::numeric_limits<class boost::math::concepts::real_concept> specialisation: no
+boost::math::policies::precision<class boost::math::concepts::real_concept, Policy>
+reports that there is no compile type precision available.
+boost::math::tools::digits<class boost::math::concepts::real_concept>()
+reports that the current runtime precision is
+53 binary digits.
+No compile time precision is available, the construction method
+will be decided at runtime and results will not be cached
+- this may lead to poor runtime performance.
+Current runtime precision indicates that
+the constant will be constructed from a string on each call.
+]
+
+[endsect]
+[endsect]
+
+[section:constants The constants]
+
+TODO!!
+
+[endsect]
+
+[section:new_const Defining New Constants]
+
+The library provides some helper code to assist in defining new constants, the process
+for defining a constant called "boost" goes like this:
+
+1. Define a function that calculates the value of the constant, this should be a template
+function, and be placed in boost/math/constants/calculate_constants.hpp if the constant is to be
+added to this library, or else defined at the top of your source file if not. The function should look like this:
+
+ namespace boost{ namespace math{ namespace constants{ namespace detail{
+
+ template <class Real, int N>
+ Real calculate_boost((const mpl::int_<N>& BOOST_MATH_APPEND_EXPLICIT_TEMPLATE_TYPE_SPEC(T))
+ {
+ int required_precision = N ? N : tools::digits<Real>();
+ Real result = /* value computed to required_precision bits */ ;
+ return result;
+ }
+
+ }}}} // namespaces
+
+2. You will need an arbitary precision type to use to calculate the value - this library
+currently supports either NTL::RR or mpfr_class used via the bindings in boost/math/bindings.
+The default is to use NTL::RR unles you define `USE_MPFR` at the start of your program.
+
+3. The complete program to calculate the constant is then:
+
+ #define USE_MPFR // if required
+ #include <boost/math/constants/generate.hpp>
+
+ int main()
+ {
+ BOOST_CONSTANTS_GENERATE(boost);
+ }
+
+The output from the program is a snippet of C++ code (actually a macro call) that can be cut and pasted
+into boost/math/constants/constants.hpp or else into your own code:
+
+[pre
+BOOST_DEFINE_MATH_CONSTANT(boost, 3.141592653589793238462643383279502884, 19716939937510582097494459230781640628620899862803482534211706798, 0);
+]
+
+This code snippet declares the float, double and long double versions of the constant, plus a string representation correct to 100 decimal
+digits, and all the meta-programming machinary needed to select between them.
+
+[endsect]

Added: sandbox/math_constants/libs/math/doc/html/boostbook.css
==============================================================================
--- (empty file)
+++ sandbox/math_constants/libs/math/doc/html/boostbook.css 2010-12-01 08:46:11 EST (Wed, 01 Dec 2010)
@@ -0,0 +1,601 @@
+/*=============================================================================
+ Copyright (c) 2004 Joel de Guzman
+ http://spirit.sourceforge.net/
+
+ Distributed under the Boost Software License, Version 1.0. (See accompany-
+ ing file LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_0.txt)
+=============================================================================*/
+
+/*=============================================================================
+ Body defaults
+=============================================================================*/
+
+ body
+ {
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--- (empty file)
+++ sandbox/math_constants/libs/math/doc/html/index.html 2010-12-01 08:46:11 EST (Wed, 01 Dec 2010)
@@ -0,0 +1,432 @@
+<html>
+<head>
+<meta http-equiv="Content-Type" content="text/html; charset=US-ASCII">
+<title>Math Constants</title>
+<link rel="stylesheet" href="boostbook.css" type="text/css">
+<meta name="generator" content="DocBook XSL Stylesheets V1.74.0">
+<link rel="home" href="index.html" title="Math Constants">
+</head>
+<body bgcolor="white" text="black" link="#0000FF" vlink="#840084" alink="#0000FF">
+<table cellpadding="2" width="100%"><tr><td valign="top"></td></tr></table>
+<hr>
+<div class="spirit-nav"></div>
+<div class="article" lang="en">
+<div class="titlepage">
+<div>
+<div><h2 class="title">
+<a name="math_constants"></a>Math Constants</h2></div>
+<div><div class="authorgroup">
+<div class="author"><h3 class="author">
+John Maddock
+</h3></div>
+<div class="author"><h3 class="author">
+Paul A. Bristow
+</h3></div>
+</div></div>
+<div>Copyright © 2010 John Maddock, Paul A. Bristow</div>
+<div><div class="legalnotice">
+<a name="id978745"></a>
+ 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)
+ 
+</div></div>
+</div>
+<hr>
+</div>
+<div class="toc">
+Table of Contents
+<dl>
+<dt> Tutorial</dt>
+<dd><dl>
+<dt><a href="index.html#math_constants.tutorial.non_templ"> Use in non-template
+ code</a></dt>
+<dt> Use in template code</dt>
+<dt><a href="index.html#math_constants.tutorial.user_def"> Use With User Defined
+ Types</a></dt>
+</dl></dd>
+<dt> The constants</dt>
+<dt> Defining New Constants</dt>
+</dl>
+</div>
+<div class="section" lang="en">
+<div class="titlepage"><div><div><h2 class="title" style="clear: both">
+<a name="math_constants.tutorial"></a><a class="link" href="index.html#math_constants.tutorial" title="Tutorial"> Tutorial</a>
+</h2></div></div></div>
+<div class="toc"><dl>
+<dt><a href="index.html#math_constants.tutorial.non_templ"> Use in non-template
+ code</a></dt>
+<dt> Use in template code</dt>
+<dt><a href="index.html#math_constants.tutorial.user_def"> Use With User Defined
+ Types</a></dt>
+</dl></div>
+<div class="section" lang="en">
+<div class="titlepage"><div><div><h3 class="title">
+<a name="math_constants.tutorial.non_templ"></a><a class="link" href="index.html#math_constants.tutorial.non_templ" title="Use in non-template code"> Use in non-template
+ code</a>
+</h3></div></div></div>
+
+ When using the constants at fixed precision in non-template code, you can
+ simply add a using declaration to make the constants of the correct precision
+ for your code visible in the current scope, and then use each constant as
+ a simple variable:
+ 
+<pre class="programlisting">#include <boost/math/constants.hpp>
+
+double area(double r)
+{
+ using boost::math::double_constants;
+ return pi * r * r;
+}
+</pre>
+
+ Had our function been written as taking a <code class="computeroutput">float</code>
+ rather than a <code class="computeroutput">double</code> we could
+ have written instead:
+ 
+<pre class="programlisting">#include <boost/math/constants.hpp>
+
+float area(float r)
+{
+ using boost::math::float_constants;
+ return pi * r * r;
+}
+</pre>
+
+ Likewise constants that are suitable for use at <code class="computeroutput">long
+ double</code> precision are available in
+ the namespace <code class="computeroutput">boost::math::long_double_constants</code>.
+ 
+</div>
+<div class="section" lang="en">
+<div class="titlepage"><div><div><h3 class="title">
+<a name="math_constants.tutorial.templ"></a><a class="link" href="index.html#math_constants.tutorial.templ" title="Use in template code"> Use in template code</a>
+</h3></div></div></div>
+
+ When using the constants inside a function template, we need to ensure that
+ we use the a constant of the correct precision for our template parameters.
+ We can do this by calling the function-template versions of the constants
+ like this:
+ 
+<pre class="programlisting">#include <boost/math/constants.hpp>
+
+template <class Real>
+Real area(Real r)
+{
+ using namespace boost::math::constants;
+ return pi<Real>() * r * r;
+}
+</pre>
+
+ Although this syntax is a little less "cute" than the non-template
+ version the code is no less efficient (at least for the builtin types float,
+ double and long double) - the function template versions of the constants
+ are simple inline functions that return a constant of the correct precision
+ for the type used. In addition these functions are declared <code class="computeroutput">constexp</code> for those compilers that support
+ this, allowing the result to be used in constant-expressions provided the
+ template argument is a literal type.
+ 
+</div>
+<div class="section" lang="en">
+<div class="titlepage"><div><div><h3 class="title">
+<a name="math_constants.tutorial.user_def"></a><a class="link" href="index.html#math_constants.tutorial.user_def" title="Use With User Defined Types"> Use With User Defined
+ Types</a>
+</h3></div></div></div>
+
+ The syntax for using the constants with user-defined types is the same as
+ it is in the template clase, which is to say we use:
+ 
+<pre class="programlisting">#include <boost/math/constants.hpp>
+
+boost::math::constants::pi<UserDefinedType>();
+</pre>
+
+ However, since the precision of the user-defined type may be much greater
+ than that of the builtin floating pointer types, how the value returned is
+ created is as follows:
+ 
+<div class="itemizedlist"><ul type="disc">
+<li>
+ If the precision of the type is known at compile time:
+ <div class="itemizedlist"><ul type="circle">
+<li>
+ If the precision is less than or equal to that of a <code class="computeroutput">float</code> and the type is constructable
+ from a <code class="computeroutput">float</code> then
+ our code returns a <code class="computeroutput">float</code>
+ literal. If the user-defined type is a literal type then the function
+ call that returns the constant will be a <code class="computeroutput">constexp</code>.
+ </li>
+<li>
+ If the precision is less than or equal to that of a <code class="computeroutput">double</code> and the type is constructable
+ from a <code class="computeroutput">double</code> then
+ our code returns a <code class="computeroutput">double</code>
+ literal. If the user-defined type is a literal type then the function
+ call that returns the constant will be a <code class="computeroutput">constexp</code>.
+ </li>
+<li>
+ If the precision is less than or equal to that of a <code class="computeroutput">long double</code>
+ and the type is constructable from a <code class="computeroutput">long
+ double</code> then our code returns
+ a <code class="computeroutput">long double</code>
+ literal. If the user-defined type is a literal type then the function
+ call that returns the constant will be a <code class="computeroutput">constexp</code>.
+ </li>
+<li>
+ If the precision is less than 100 decimal digits, then the constant
+ will be constructed (just the once, then cached in a thread safe
+ manner) from a string representation of the constant.
+ </li>
+<li>
+ Otherwise the value is computed (just once, then cached in a thread
+ safe manner).
+ </li>
+</ul></div>
+ </li>
+<li>
+ If the precision is unknown at compile time then:
+ <div class="itemizedlist"><ul type="circle">
+<li>
+ If the runtime precision (obtained from a call to <code class="computeroutput">boost::math::tools::digits<T>()</code>)
+ is less than 100 decimal digits, then the constant is constructed
+ "on the fly" from the string representation of the constant.
+ </li>
+<li>
+ Otherwise the value is constructed "on the fly" by calculating
+ then value of the constant using the current default precision
+ of the type. Note that this can make use of the constants rather
+ expensive.
+ </li>
+</ul></div>
+ </li>
+</ul></div>
+
+ In addition, it is possible to pass a "Policy" type as a second
+ template argument, and use this to control the precision:
+ 
+<pre class="programlisting">#include <boost/math/constants/constants.hpp>
+
+typedef boost::math::policies::policy<boost::math::policies::digits2<80> > my_policy_type;
+boost::math::constants::pi<MyType, my_policy_type>();
+</pre>
+
+ Note that Boost.Math doesn't know how to control the internal precision of
+ <code class="computeroutput">MyType</code>, the policy just controls
+ how the selection process above is carried out, and the calculation precision
+ if the result is computed.
+ 
+
+ It is also possible to control which method is used to construct the constant
+ by specialising the traits class <code class="computeroutput">construction_traits</code>:
+ 
+<pre class="programlisting">namespace boost{ namespace math{ namespace constant{
+
+template <class T, class Policy>
+struct construction_traits
+{
+ typedef mpl::int_<N> type;
+};
+
+}}} // namespaces
+</pre>
+
+ Where N takes one of the following values:
+ 
+<div class="informaltable"><table class="table">
+<colgroup>
+<col>
+<col>
+</colgroup>
+<thead><tr>
+<th>
+ 
+ N
+ 
+ </th>
+<th>
+ 
+ Meaning
+ 
+ </th>
+</tr></thead>
+<tbody>
+<tr>
+<td>
+ 
+ 0
+ 
+ </td>
+<td>
+ 
+ The precision is unavailable at compile time, either construct
+ from a string or calculate on the fly depending upon the runtime
+ precision.
+ 
+ </td>
+</tr>
+<tr>
+<td>
+ 
+ 1
+ 
+ </td>
+<td>
+ 
+ Return a float precision constant.
+ 
+ </td>
+</tr>
+<tr>
+<td>
+ 
+ 2
+ 
+ </td>
+<td>
+ 
+ Return a double precision constant.
+ 
+ </td>
+</tr>
+<tr>
+<td>
+ 
+ 3
+ 
+ </td>
+<td>
+ 
+ Return a long double precision constant.
+ 
+ </td>
+</tr>
+<tr>
+<td>
+ 
+ 4
+ 
+ </td>
+<td>
+ 
+ Construct the result from the string representation, and cache
+ the result.
+ 
+ </td>
+</tr>
+<tr>
+<td>
+ 
+ Any other value N
+ 
+ </td>
+<td>
+ 
+ Sets the compile time precision to N bits.
+ 
+ </td>
+</tr>
+</tbody>
+</table></div>
+
+ Finally, sice it can be tricky to diagnose what meta-programmed code is doing,
+ there is a diagnostic routine that prints information about how this library
+ will handle a specific type, it can be used like this:
+ 
+<pre class="programlisting">#include <boost/math/constants/info.hpp>
+
+int main()
+{
+ boost::math::constants::print_info_on_type<MyType>();
+}
+</pre>
+
+ If you wish you can also pass an optional std::ostream argument to the <code class="computeroutput">print_info_on_type</code> function. Typical output
+ for a user-defined type looks like this:
+ 
+<pre class="programlisting">Information on the Implementation and Handling of
+Mathematical Constants for Type class boost::math::concepts::real_concept
+
+Checking for std::numeric_limits<class boost::math::concepts::real_concept> specialisation: no
+boost::math::policies::precision<class boost::math::concepts::real_concept, Policy>
+reports that there is no compile type precision available.
+boost::math::tools::digits<class boost::math::concepts::real_concept>()
+reports that the current runtime precision is
+53 binary digits.
+No compile time precision is available, the construction method
+will be decided at runtime and results will not be cached
+- this may lead to poor runtime performance.
+Current runtime precision indicates that
+the constant will be constructed from a string on each call.
+</pre>
+</div>
+</div>
+<div class="section" lang="en">
+<div class="titlepage"><div><div><h2 class="title" style="clear: both">
+<a name="math_constants.constants"></a><a class="link" href="index.html#math_constants.constants" title="The constants"> The constants</a>
+</h2></div></div></div>
+
+ TODO!!
+ 
+</div>
+<div class="section" lang="en">
+<div class="titlepage"><div><div><h2 class="title" style="clear: both">
+<a name="math_constants.new_const"></a><a class="link" href="index.html#math_constants.new_const" title="Defining New Constants"> Defining New Constants</a>
+</h2></div></div></div>
+
+ The library provides some helper code to assist in defining new constants,
+ the process for defining a constant called "boost" goes like this:
+ 
+
+ 1. Define a function that calculates the value of the constant, this should
+ be a template function, and be placed in boost/math/constants/calculate_constants.hpp
+ if the constant is to be added to this library, or else defined at the top
+ of your source file if not. The function should look like this:
+ 
+<pre class="programlisting">namespace boost{ namespace math{ namespace constants{ namespace detail{
+
+template <class Real, int N>
+Real calculate_boost((const mpl::int_<N>& BOOST_MATH_APPEND_EXPLICIT_TEMPLATE_TYPE_SPEC(T))
+{
+ int required_precision = N ? N : tools::digits<Real>();
+ Real result = /* value computed to required_precision bits */ ;
+ return result;
+}
+
+}}}} // namespaces
+</pre>
+
+ 2. You will need an arbitary precision type to use to calculate the value -
+ this library currently supports either NTL::RR or mpfr_class used via the bindings
+ in boost/math/bindings. The default is to use NTL::RR unles you define <code class="computeroutput">USE_MPFR</code> at the start of your program.
+ 
+
+ 3. The complete program to calculate the constant is then:
+ 
+<pre class="programlisting">#define USE_MPFR // if required
+#include <boost/math/constants/generate.hpp>
+
+int main()
+{
+ BOOST_CONSTANTS_GENERATE(boost);
+}
+</pre>
+
+ The output from the program is a snippet of C++ code (actually a macro call)
+ that can be cut and pasted into boost/math/constants/constants.hpp or else
+ into your own code:
+ 
+<pre class="programlisting">BOOST_DEFINE_MATH_CONSTANT(boost, 3.141592653589793238462643383279502884, 19716939937510582097494459230781640628620899862803482534211706798, 0);
+</pre>
+
+ This code snippet declares the float, double and long double versions of the
+ constant, plus a string representation correct to 100 decimal digits, and all
+ the meta-programming machinary needed to select between them.
+ 
+</div>
+</div>
+<table xmlns:rev="http://www.cs.rpi.edu/~gregod/boost/tools/doc/revision" width="100%"><tr>
+<td align="left">Last revised: December 01, 2010 at 13:39:54 GMT</td>
+<td align="right"><div class="copyright-footer"></div></td>
+</tr></table>
+<hr>
+<div class="spirit-nav"></div>
+</body>
+</html>

Added: sandbox/math_constants/libs/math/doc/html/math_constants/tutorial.html
==============================================================================
--- (empty file)
+++ sandbox/math_constants/libs/math/doc/html/math_constants/tutorial.html 2010-12-01 08:46:11 EST (Wed, 01 Dec 2010)
@@ -0,0 +1,172 @@
+<html>
+<head>
+<meta http-equiv="Content-Type" content="text/html; charset=US-ASCII">
+<title>Tutorial</title>
+<link rel="stylesheet" href="../boostbook.css" type="text/css">
+<meta name="generator" content="DocBook XSL Stylesheets V1.74.0">
+<link rel="home" href="../index.html" title="Math Constants">
+<link rel="up" href="../index.html" title="Math Constants">
+<link rel="prev" href="../index.html" title="Math Constants">
+</head>
+<body bgcolor="white" text="black" link="#0000FF" vlink="#840084" alink="#0000FF">
+<table cellpadding="2" width="100%"><tr><td valign="top"></td></tr></table>
+<hr>
+<div class="spirit-nav">
+<a accesskey="p" href="../index.html"><img src="../images/prev.png" alt="Prev"></a><a accesskey="u" href="../index.html"><img src="../images/up.png" alt="Up"></a><a accesskey="h" href="../index.html"><img src="../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="math_constants.tutorial"></a><a class="link" href="tutorial.html" title="Tutorial"> Tutorial</a>
+</h2></div></div></div>
+<a name="math_constants.tutorial.use_in_non_template_code"></a><h5>
+<a name="id1012468"></a>
+ <a class="link" href="tutorial.html#math_constants.tutorial.use_in_non_template_code">Use in non-template
+ code</a>
+ </h5>
+
+ When using the constants at fixed precision in non-template code, you can simply
+ add a using declaration to make the constants of the correct precision for
+ your code visible in the current scope, and then use each constant as a simple
+ variable:
+ 
+<pre class="programlisting">#include <boost/math/constants.hpp>
+
+double area(double r)
+{
+ using boost::math::double_constants;
+ return pi * r * r;
+}
+</pre>
+
+ Had our function been written as taking a <code class="computeroutput">float</code>
+ rather than a <code class="computeroutput">double</code> we could
+ have written instead:
+ 
+<pre class="programlisting">#include <boost/math/constants.hpp>
+
+float area(float r)
+{
+ using boost::math::float_constants;
+ return pi * r * r;
+}
+</pre>
+
+ Likewise constants that are suitable for use at <code class="computeroutput">long
+ double</code> precision are available in the
+ namespace <code class="computeroutput">boost::math::long_double_constants</code>.
+ 
+<a name="math_constants.tutorial.use_in_template_code"></a><h5>
+<a name="id1012814"></a>
+ <a class="link" href="tutorial.html#math_constants.tutorial.use_in_template_code">Use in template
+ code</a>
+ </h5>
+
+ When using the constants inside a function template, we need to ensure that
+ we use the a constant of the correct precision for our template parameters.
+ We can do this by calling the function-template versions of the constants like
+ this:
+ 
+<pre class="programlisting">#include <boost/math/constants.hpp>
+
+template <class Real>
+Real area(Real r)
+{
+ using namespace boost::math::constants;
+ return pi<Real>() * r * r;
+}
+</pre>
+
+ Although this syntax is a little less "cute" than the non-template
+ version the code is no less efficient (at least for the builtin types float,
+ double and long double) - the function template versions of the constants are
+ simple inline functions that return a constant of the correct precision for
+ the type used. In addition these functions are declared <code class="computeroutput">constexp</code>
+ for those compilers that support this, allowing the result to be used in constant-expressions
+ provided the template argument is a literal type.
+ 
+<a name="math_constants.tutorial.use_with_user_defined_types"></a><h5>
+<a name="id1013016"></a>
+ <a class="link" href="tutorial.html#math_constants.tutorial.use_with_user_defined_types">Use With
+ User Defined Types</a>
+ </h5>
+
+ The syntax for using the constants with user-defined types is the same as it
+ is in the template clase, which is to say we use:
+ 
+<pre class="programlisting">#include <boost/math/constants.hpp>
+
+boost::math::constants::pi<UserDefinedType>();
+</pre>
+
+ However, since the precision of the user-defined type may be much greater than
+ that of the builtin floating pointer types, how the value returned is created
+ is as follows:
+ 
+<div class="itemizedlist"><ul type="disc">
+<li>
+ If the precision of the type is known at compile time:
+ <div class="itemizedlist"><ul type="circle">
+<li>
+ If the precision is less than or equal to that of a <code class="computeroutput">float</code> and the type is constructable
+ from a <code class="computeroutput">float</code> then our
+ code returns a <code class="computeroutput">float</code>
+ literal. If the user-defined type is a literal type then the function
+ call that returns the constant will be a <code class="computeroutput">constexp</code>.
+ </li>
+<li>
+ If the precision is less than or equal to that of a <code class="computeroutput">double</code> and the type is constructable
+ from a <code class="computeroutput">double</code> then our
+ code returns a <code class="computeroutput">double</code>
+ literal. If the user-defined type is a literal type then the function
+ call that returns the constant will be a <code class="computeroutput">constexp</code>.
+ </li>
+<li>
+ If the precision is less than or equal to that of a <code class="computeroutput">long double</code>
+ and the type is constructable from a <code class="computeroutput">long
+ double</code> then our code returns
+ a <code class="computeroutput">long double</code>
+ literal. If the user-defined type is a literal type then the function
+ call that returns the constant will be a <code class="computeroutput">constexp</code>.
+ </li>
+<li>
+ If the precision is less than 100 decimal digits, then the constant
+ will be constructed (just the once, then cached in a thread safe
+ manner) from a string representation of the constant.
+ </li>
+<li>
+ Otherwise the value is computed (just once, then cached in a thread
+ safe manner).
+ </li>
+</ul></div>
+ </li>
+<li>
+ If the precision is unknown at compile time then:
+ <div class="itemizedlist"><ul type="circle">
+<li>
+ If the runtime precision (obtained from a call to <code class="computeroutput">boost::math::tools::digits<T>()</code>) is less than 100 decimal digits,
+ then the constant is constructed "on the fly" from the
+ string representation of the constant.
+ </li>
+<li>
+ Otherwise the value is constructed "on the fly" by calculating
+ then value of the constant using the current default precision of
+ the type. Note that this can make use of the constants rather expensive.
+ </li>
+</ul></div>
+ </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 © 2010 John Maddock, 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)
+ 
+</div></td>
+</tr></table>
+<hr>
+<div class="spirit-nav">
+<a accesskey="p" href="../index.html"><img src="../images/prev.png" alt="Prev"></a><a accesskey="u" href="../index.html"><img src="../images/up.png" alt="Up"></a><a accesskey="h" href="../index.html"><img src="../images/home.png" alt="Home"></a>
+</div>
+</body>
+</html>

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