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  26 <div class="titlepage"><div><div><h3 class="title">
  27 <a name="math_toolkit.high_precision.use_mpfr"></a><a class="link" href="use_mpfr.html" title="Using With MPFR or GMP - High-Precision Floating-Point Library">Using With MPFR
  28       or GMP - High-Precision Floating-Point Library</a>
  29 </h3></div></div></div>
  30 <p>
  31         The special functions and tools in this library can be used with <a href="http://www.mpfr.org" target="_top">MPFR</a>
  32         (an arbitrary precision number type based on the <a href="http://gmplib.org/" target="_top">GNU
  33         Multiple Precision Arithmetic Library</a>), either via the bindings in
  34         <a href="../../../../../../boost/math/bindings/mpfr.hpp" target="_top">boost/math/bindings/mpfr.hpp</a>,
  35         or via <a href="../../../../../../boost/math/bindings/mpfr.hpp" target="_top">boost/math/bindings/mpreal.hpp</a>.
  36       </p>
  37 <p>
  38         <span class="bold"><strong>New projects are recommended to use <a href="../../../../../../libs/multiprecision/doc/html/index.html" target="_top">Boost.Multiprecision</a>
  39         with GMP/MPFR backend instead.</strong></span>
  40       </p>
  41 <p>
  42         In order to use these bindings you will need to have installed <a href="http://www.mpfr.org" target="_top">MPFR</a>
  43         plus its dependency the <a href="http://gmplib.org" target="_top">GMP library</a>.
  44         You will also need one of the two supported C++ wrappers for MPFR: <a href="http://math.berkeley.edu/~wilken/code/gmpfrxx/" target="_top">gmpfrxx (or mpfr_class)</a>,
  45         or <a href="http://www.holoborodko.com/pavel/mpfr/" target="_top">mpfr-C++ (mpreal)</a>.
  46       </p>
  47 <p>
  48         Unfortunately neither <code class="computeroutput"><span class="identifier">mpfr_class</span></code>
  49         nor <code class="computeroutput"><span class="identifier">mpreal</span></code> quite satisfy
  50         our conceptual requirements, so there is a very thin set of additional interfaces
  51         and some helper traits defined in <a href="../../../../../../boost/math/bindings/mpfr.hpp" target="_top">boost/math/bindings/mpfr.hpp</a>
  52         and <a href="../../../../../../boost/math/bindings/mpreal.hpp" target="_top">boost/math/bindings/mpreal.hpp</a>
  53         that you should use in place of including 'gmpfrxx.h' or 'mpreal.h' directly.
  54         The classes <code class="computeroutput"><span class="identifier">mpfr_class</span></code> or
  55         <code class="computeroutput"><span class="identifier">mpreal</span></code> are then usable unchanged
  56         once this header is included, so for example <code class="computeroutput"><span class="identifier">mpfr_class</span></code>'s
  57         performance-enhancing expression templates are preserved and fully supported
  58         by this library:
  59       </p>
  60 <pre class="programlisting"><span class="preprocessor">#include</span> <span class="special">&lt;</span><span class="identifier">boost</span><span class="special">/</span><span class="identifier">math</span><span class="special">/</span><span class="identifier">bindings</span><span class="special">/</span><span class="identifier">mpfr</span><span class="special">.</span><span class="identifier">hpp</span><span class="special">&gt;</span>
  61 <span class="preprocessor">#include</span> <span class="special">&lt;</span><span class="identifier">boost</span><span class="special">/</span><span class="identifier">math</span><span class="special">/</span><span class="identifier">special_functions</span><span class="special">/</span><span class="identifier">gamma</span><span class="special">.</span><span class="identifier">hpp</span><span class="special">&gt;</span>
  62
  63 <span class="keyword">int</span> <span class="identifier">main</span><span class="special">()</span>
  64 <span class="special">{</span>
  65    <span class="identifier">mpfr_class</span><span class="special">::</span><span class="identifier">set_dprec</span><span class="special">(</span><span class="number">500</span><span class="special">);</span> <span class="comment">// 500 bit precision</span>
  66    <span class="comment">//</span>
  67    <span class="comment">// Note that the argument to tgamma is</span>
  68    <span class="comment">// an expression template - that's just fine here.</span>
  69    <span class="comment">//</span>
  70    <span class="identifier">mpfr_class</span> <span class="identifier">v</span> <span class="special">=</span> <span class="identifier">boost</span><span class="special">::</span><span class="identifier">math</span><span class="special">::</span><span class="identifier">tgamma</span><span class="special">(</span><span class="identifier">sqrt</span><span class="special">(</span><span class="identifier">mpfr_class</span><span class="special">(</span><span class="number">2</span><span class="special">)));</span>
  71    <span class="identifier">std</span><span class="special">::</span><span class="identifier">cout</span> <span class="special">&lt;&lt;</span> <span class="identifier">std</span><span class="special">::</span><span class="identifier">setprecision</span><span class="special">(</span><span class="number">50</span><span class="special">)</span> <span class="special">&lt;&lt;</span> <span class="identifier">v</span> <span class="special">&lt;&lt;</span> <span class="identifier">std</span><span class="special">::</span><span class="identifier">endl</span><span class="special">;</span>
  72 <span class="special">}</span>
  73 </pre>
  74 <p>
  75         Alternatively use with <code class="computeroutput"><span class="identifier">mpreal</span></code>
  76         would look like:
  77       </p>
  78 <pre class="programlisting"><span class="preprocessor">#include</span> <span class="special">&lt;</span><span class="identifier">boost</span><span class="special">/</span><span class="identifier">math</span><span class="special">/</span><span class="identifier">bindings</span><span class="special">/</span><span class="identifier">mpreal</span><span class="special">.</span><span class="identifier">hpp</span><span class="special">&gt;</span>
  79 <span class="preprocessor">#include</span> <span class="special">&lt;</span><span class="identifier">boost</span><span class="special">/</span><span class="identifier">math</span><span class="special">/</span><span class="identifier">special_functions</span><span class="special">/</span><span class="identifier">gamma</span><span class="special">.</span><span class="identifier">hpp</span><span class="special">&gt;</span>
  80
  81 <span class="keyword">int</span> <span class="identifier">main</span><span class="special">()</span>
  82 <span class="special">{</span>
  83    <span class="identifier">mpfr</span><span class="special">::</span><span class="identifier">mpreal</span><span class="special">::</span><span class="identifier">set_precision</span><span class="special">(</span><span class="number">500</span><span class="special">);</span> <span class="comment">// 500 bit precision</span>
  84    <span class="identifier">mpfr</span><span class="special">::</span><span class="identifier">mpreal</span> <span class="identifier">v</span> <span class="special">=</span> <span class="identifier">boost</span><span class="special">::</span><span class="identifier">math</span><span class="special">::</span><span class="identifier">tgamma</span><span class="special">(</span><span class="identifier">sqrt</span><span class="special">(</span><span class="identifier">mpfr</span><span class="special">::</span><span class="identifier">mpreal</span><span class="special">(</span><span class="number">2</span><span class="special">)));</span>
  85    <span class="identifier">std</span><span class="special">::</span><span class="identifier">cout</span> <span class="special">&lt;&lt;</span> <span class="identifier">std</span><span class="special">::</span><span class="identifier">setprecision</span><span class="special">(</span><span class="number">50</span><span class="special">)</span> <span class="special">&lt;&lt;</span> <span class="identifier">v</span> <span class="special">&lt;&lt;</span> <span class="identifier">std</span><span class="special">::</span><span class="identifier">endl</span><span class="special">;</span>
  86 <span class="special">}</span>
  87 </pre>
  88 <p>
  89         For those functions that are based upon the <a class="link" href="../lanczos.html" title="The Lanczos Approximation">Lanczos
  90         approximation</a>, the bindings defines a series of approximations with
  91         up to 61 terms and accuracy up to approximately 3e-113. This therefore sets
  92         the upper limit for accuracy to the majority of functions defined this library
  93         when used with either <code class="computeroutput"><span class="identifier">mpfr_class</span></code>
  94         or <code class="computeroutput"><span class="identifier">mpreal</span></code>.
  95       </p>
  96 <p>
  97         There is a concept checking test program for mpfr support <a href="../../../../../../libs/math/test/mpfr_concept_check.cpp" target="_top">here</a>
  98         and <a href="../../../../../../libs/math/test/mpreal_concept_check.cpp" target="_top">here</a>.
  99       </p>
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 101 <table xmlns:rev="http://www.cs.rpi.edu/~gregod/boost/tools/doc/revision" width="100%"><tr>
 102 <td align="left"></td>
 103 <td align="right"><div class="copyright-footer">Copyright &#169; 2006-2010, 2012-2014 Nikhar Agrawal,
 104       Anton Bikineev, Paul A. Bristow, Marco Guazzone, Christopher Kormanyos, Hubert
 105       Holin, Bruno Lalande, John Maddock, Jeremy Murphy, Johan R&#229;de, Gautam Sewani,
 106       Benjamin Sobotta, Thijs van den Berg, Daryle Walker and Xiaogang Zhang<p>
 107         Distributed under the Boost Software License, Version 1.0. (See accompanying
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