| <html> |
| <head> |
| <meta http-equiv="Content-Type" content="text/html; charset=US-ASCII"> |
| <title>mpfr_float</title> |
| <link rel="stylesheet" href="../../../../../../../doc/src/boostbook.css" type="text/css"> |
| <meta name="generator" content="DocBook XSL Stylesheets V1.77.1"> |
| <link rel="home" href="../../../index.html" title="Chapter 1. Boost.Multiprecision"> |
| <link rel="up" href="../floats.html" title="Floating Point Numbers"> |
| <link rel="prev" href="gmp_float.html" title="gmp_float"> |
| <link rel="next" href="float128.html" title="float128"> |
| </head> |
| <body bgcolor="white" text="black" link="#0000FF" vlink="#840084" alink="#0000FF"> |
| <table cellpadding="2" width="100%"><tr> |
| <td valign="top"><img alt="Boost C++ Libraries" width="277" height="86" src="../../../../../../../boost.png"></td> |
| <td align="center"><a href="../../../../../../../index.html">Home</a></td> |
| <td align="center"><a href="../../../../../../../libs/libraries.htm">Libraries</a></td> |
| <td align="center"><a href="http://www.boost.org/users/people.html">People</a></td> |
| <td align="center"><a href="http://www.boost.org/users/faq.html">FAQ</a></td> |
| <td align="center"><a href="../../../../../../../more/index.htm">More</a></td> |
| </tr></table> |
| <hr> |
| <div class="spirit-nav"> |
| <a accesskey="p" href="gmp_float.html"><img src="../../../../../../../doc/src/images/prev.png" alt="Prev"></a><a accesskey="u" href="../floats.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="float128.html"><img src="../../../../../../../doc/src/images/next.png" alt="Next"></a> |
| </div> |
| <div class="section"> |
| <div class="titlepage"><div><div><h4 class="title"> |
| <a name="boost_multiprecision.tut.floats.mpfr_float"></a><a class="link" href="mpfr_float.html" title="mpfr_float">mpfr_float</a> |
| </h4></div></div></div> |
| <p> |
| <code class="computeroutput"><span class="preprocessor">#include</span> <span class="special"><</span><span class="identifier">boost</span><span class="special">/</span><span class="identifier">multiprecision</span><span class="special">/</span><span class="identifier">mpfr</span><span class="special">.</span><span class="identifier">hpp</span><span class="special">></span></code> |
| </p> |
| <pre class="programlisting"><span class="keyword">namespace</span> <span class="identifier">boost</span><span class="special">{</span> <span class="keyword">namespace</span> <span class="identifier">multiprecision</span><span class="special">{</span> |
| |
| <span class="keyword">enum</span> <span class="identifier">mpfr_allocation_type</span> |
| <span class="special">{</span> |
| <span class="identifier">allocate_stack</span><span class="special">,</span> |
| <span class="identifier">allocate_dynamic</span> |
| <span class="special">};</span> |
| |
| <span class="keyword">template</span> <span class="special"><</span><span class="keyword">unsigned</span> <span class="identifier">Digits10</span><span class="special">,</span> <span class="identifier">mpfr_allocation_type</span> <span class="identifier">AllocateType</span> <span class="special">=</span> <span class="identifier">allocate_dynamic</span><span class="special">></span> |
| <span class="keyword">class</span> <span class="identifier">mpfr_float_backend</span><span class="special">;</span> |
| |
| <span class="keyword">typedef</span> <span class="identifier">number</span><span class="special"><</span><span class="identifier">mpfr_float_backend</span><span class="special"><</span><span class="number">50</span><span class="special">></span> <span class="special">></span> <span class="identifier">mpfr_float_50</span><span class="special">;</span> |
| <span class="keyword">typedef</span> <span class="identifier">number</span><span class="special"><</span><span class="identifier">mpfr_float_backend</span><span class="special"><</span><span class="number">100</span><span class="special">></span> <span class="special">></span> <span class="identifier">mpfr_float_100</span><span class="special">;</span> |
| <span class="keyword">typedef</span> <span class="identifier">number</span><span class="special"><</span><span class="identifier">mpfr_float_backend</span><span class="special"><</span><span class="number">500</span><span class="special">></span> <span class="special">></span> <span class="identifier">mpfr_float_500</span><span class="special">;</span> |
| <span class="keyword">typedef</span> <span class="identifier">number</span><span class="special"><</span><span class="identifier">mpfr_float_backend</span><span class="special"><</span><span class="number">1000</span><span class="special">></span> <span class="special">></span> <span class="identifier">mpfr_float_1000</span><span class="special">;</span> |
| <span class="keyword">typedef</span> <span class="identifier">number</span><span class="special"><</span><span class="identifier">mpfr_float_backend</span><span class="special"><</span><span class="number">0</span><span class="special">></span> <span class="special">></span> <span class="identifier">mpfr_float</span><span class="special">;</span> |
| |
| <span class="keyword">typedef</span> <span class="identifier">number</span><span class="special"><</span><span class="identifier">mpfr_float_backend</span><span class="special"><</span><span class="number">50</span><span class="special">,</span> <span class="identifier">allocate_stack</span><span class="special">></span> <span class="special">></span> <span class="identifier">static_mpfr_float_50</span><span class="special">;</span> |
| <span class="keyword">typedef</span> <span class="identifier">number</span><span class="special"><</span><span class="identifier">mpfr_float_backend</span><span class="special"><</span><span class="number">100</span><span class="special">,</span> <span class="identifier">allocate_stack</span><span class="special">></span> <span class="special">></span> <span class="identifier">static_mpfr_float_100</span><span class="special">;</span> |
| |
| <span class="special">}}</span> <span class="comment">// namespaces</span> |
| </pre> |
| <p> |
| The <code class="computeroutput"><span class="identifier">mpfr_float_backend</span></code> |
| type is used in conjunction with <code class="computeroutput"><span class="identifier">number</span></code>: |
| It acts as a thin wrapper around the <a href="http://www.mpfr.org" target="_top">MPFR</a> |
| <code class="computeroutput"><span class="identifier">mpfr_t</span></code> to provide an real-number |
| type that is a drop-in replacement for the native C++ floating-point types, |
| but with much greater precision. |
| </p> |
| <p> |
| Type <code class="computeroutput"><span class="identifier">mpfr_float_backend</span></code> |
| can be used at fixed precision by specifying a non-zero <code class="computeroutput"><span class="identifier">Digits10</span></code> |
| template parameter, or at variable precision by setting the template argument |
| to zero. The typedefs mpfr_float_50, mpfr_float_100, mpfr_float_500, mpfr_float_1000 |
| provide arithmetic types at 50, 100, 500 and 1000 decimal digits precision |
| respectively. The typedef mpfr_float provides a variable precision type |
| whose precision can be controlled via the <code class="computeroutput"><span class="identifier">number</span></code>s |
| member functions. |
| </p> |
| <p> |
| In addition the second template parameter lets you choose between dynamic |
| allocation (the default, and uses MPFR's normal allocation routines), or |
| stack allocation (where all the memory required for the underlying data |
| types is stored within <code class="computeroutput"><span class="identifier">mpfr_float_backend</span></code>). |
| The latter option can result in significantly faster code, at the expense |
| of growing the size of <code class="computeroutput"><span class="identifier">mpfr_float_backend</span></code>. |
| It can only be used at fixed precision, and should only be used for lower |
| digit counts. Note that we can not guarantee that using <code class="computeroutput"><span class="identifier">allocate_stack</span></code> |
| won't cause any calls to mpfr's allocation routines, as mpfr may call these |
| inside it's own code. The following table gives an idea of the performance |
| tradeoff's at 50 decimal digits precision<a href="#ftn.boost_multiprecision.tut.floats.mpfr_float.f0" class="footnote"><sup class="footnote"><a name="boost_multiprecision.tut.floats.mpfr_float.f0"></a>[2]</sup></a>: |
| </p> |
| <div class="informaltable"><table class="table"> |
| <colgroup> |
| <col> |
| <col> |
| </colgroup> |
| <thead><tr> |
| <th> |
| <p> |
| Type |
| </p> |
| </th> |
| <th> |
| <p> |
| Bessel function evaluation, relative times |
| </p> |
| </th> |
| </tr></thead> |
| <tbody> |
| <tr> |
| <td> |
| <p> |
| <code class="computeroutput"><span class="identifier">number</span><span class="special"><</span><span class="identifier">mpfr_float_backend</span><span class="special"><</span><span class="number">50</span><span class="special">,</span> <span class="identifier">allocate_static</span><span class="special">>,</span> |
| <span class="identifier">et_on</span><span class="special">></span></code> |
| </p> |
| </td> |
| <td> |
| <p> |
| 1.0 (5.5s) |
| </p> |
| </td> |
| </tr> |
| <tr> |
| <td> |
| <p> |
| <code class="computeroutput"><span class="identifier">number</span><span class="special"><</span><span class="identifier">mpfr_float_backend</span><span class="special"><</span><span class="number">50</span><span class="special">,</span> <span class="identifier">allocate_static</span><span class="special">>,</span> |
| <span class="identifier">et_off</span><span class="special">></span></code> |
| </p> |
| </td> |
| <td> |
| <p> |
| 1.05 (5.8s) |
| </p> |
| </td> |
| </tr> |
| <tr> |
| <td> |
| <p> |
| <code class="computeroutput"><span class="identifier">number</span><span class="special"><</span><span class="identifier">mpfr_float_backend</span><span class="special"><</span><span class="number">50</span><span class="special">,</span> <span class="identifier">allocate_dynamic</span><span class="special">>,</span> |
| <span class="identifier">et_on</span><span class="special">></span></code> |
| </p> |
| </td> |
| <td> |
| <p> |
| 1.05 (5.8s) |
| </p> |
| </td> |
| </tr> |
| <tr> |
| <td> |
| <p> |
| <code class="computeroutput"><span class="identifier">number</span><span class="special"><</span><span class="identifier">mpfr_float_backend</span><span class="special"><</span><span class="number">50</span><span class="special">,</span> <span class="identifier">allocate_dynamic</span><span class="special">>,</span> |
| <span class="identifier">et_off</span><span class="special">></span></code> |
| </p> |
| </td> |
| <td> |
| <p> |
| 1.16 (6.4s) |
| </p> |
| </td> |
| </tr> |
| </tbody> |
| </table></div> |
| <div class="note"><table border="0" summary="Note"> |
| <tr> |
| <td rowspan="2" align="center" valign="top" width="25"><img alt="[Note]" src="../../../../../../../doc/src/images/note.png"></td> |
| <th align="left">Note</th> |
| </tr> |
| <tr><td align="left" valign="top"><p> |
| This type only provides <code class="computeroutput"><span class="identifier">numeric_limits</span></code> |
| support when the precision is fixed at compile time. |
| </p></td></tr> |
| </table></div> |
| <p> |
| As well as the usual conversions from arithmetic and string types, instances |
| of <code class="computeroutput"><span class="identifier">number</span><span class="special"><</span><span class="identifier">mpfr_float_backend</span><span class="special"><</span><span class="identifier">N</span><span class="special">></span> <span class="special">></span></code> are copy constructible and assignable |
| from: |
| </p> |
| <div class="itemizedlist"><ul class="itemizedlist" style="list-style-type: disc; "> |
| <li class="listitem"> |
| The <a href="http://gmplib.org" target="_top">GMP</a> native types <code class="computeroutput"><span class="identifier">mpf_t</span></code>, <code class="computeroutput"><span class="identifier">mpz_t</span></code>, |
| <code class="computeroutput"><span class="identifier">mpq_t</span></code>. |
| </li> |
| <li class="listitem"> |
| The <a href="http://www.mpfr.org" target="_top">MPFR</a> native type <code class="computeroutput"><span class="identifier">mpfr_t</span></code>. |
| </li> |
| <li class="listitem"> |
| The <code class="computeroutput"><span class="identifier">number</span></code> wrappers |
| around those types: <code class="computeroutput"><span class="identifier">number</span><span class="special"><</span><span class="identifier">mpfr_float_backend</span><span class="special"><</span><span class="identifier">M</span><span class="special">></span> <span class="special">></span></code>, |
| <code class="computeroutput"><span class="identifier">number</span><span class="special"><</span><span class="identifier">mpf_float</span><span class="special"><</span><span class="identifier">M</span><span class="special">></span> <span class="special">></span></code>, <code class="computeroutput"><span class="identifier">number</span><span class="special"><</span><span class="identifier">gmp_int</span><span class="special">></span></code>, <code class="computeroutput"><span class="identifier">number</span><span class="special"><</span><span class="identifier">gmp_rational</span><span class="special">></span></code>. |
| </li> |
| </ul></div> |
| <p> |
| It's also possible to access the underlying <code class="computeroutput"><span class="identifier">mpfr_t</span></code> |
| via the data() member function of <code class="computeroutput"><span class="identifier">mpfr_float_backend</span></code>. |
| </p> |
| <p> |
| Things you should know when using this type: |
| </p> |
| <div class="itemizedlist"><ul class="itemizedlist" style="list-style-type: disc; "> |
| <li class="listitem"> |
| A default constructed <code class="computeroutput"><span class="identifier">mpfr_float_backend</span></code> |
| is set to a NaN (this is the default <a href="http://www.mpfr.org" target="_top">MPFR</a> |
| behavior). |
| </li> |
| <li class="listitem"> |
| All operations use round to nearest. |
| </li> |
| <li class="listitem"> |
| No changes are made to <a href="http://gmplib.org" target="_top">GMP</a> or |
| <a href="http://www.mpfr.org" target="_top">MPFR</a> global settings, so this |
| type can coexist with existing <a href="http://www.mpfr.org" target="_top">MPFR</a> |
| or <a href="http://gmplib.org" target="_top">GMP</a> code. |
| </li> |
| <li class="listitem"> |
| The code can equally use <a href="http://mpir.org/" target="_top">MPIR</a> |
| in place of <a href="http://gmplib.org" target="_top">GMP</a> - indeed that |
| is the preferred option on Win32. |
| </li> |
| <li class="listitem"> |
| This backend supports rvalue-references and is move-aware, making instantiations |
| of <code class="computeroutput"><span class="identifier">number</span></code> on this backend |
| move aware. |
| </li> |
| <li class="listitem"> |
| Conversion from a string results in a <code class="computeroutput"><span class="identifier">std</span><span class="special">::</span><span class="identifier">runtime_error</span></code> |
| being thrown if the string can not be interpreted as a valid floating |
| point number. |
| </li> |
| <li class="listitem"> |
| Division by zero results in an infinity. |
| </li> |
| </ul></div> |
| <h6> |
| <a name="boost_multiprecision.tut.floats.mpfr_float.h0"></a> |
| <span class="phrase"><a name="boost_multiprecision.tut.floats.mpfr_float.mpfr_example"></a></span><a class="link" href="mpfr_float.html#boost_multiprecision.tut.floats.mpfr_float.mpfr_example"> MPFR example:</a> |
| </h6> |
| <pre class="programlisting"><span class="preprocessor">#include</span> <span class="special"><</span><span class="identifier">boost</span><span class="special">/</span><span class="identifier">multiprecision</span><span class="special">/</span><span class="identifier">mpfr</span><span class="special">.</span><span class="identifier">hpp</span><span class="special">></span> |
| <span class="preprocessor">#include</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">special_functions</span><span class="special">/</span><span class="identifier">gamma</span><span class="special">.</span><span class="identifier">hpp</span><span class="special">></span> |
| <span class="preprocessor">#include</span> <span class="special"><</span><span class="identifier">iostream</span><span class="special">></span> |
| |
| <span class="keyword">int</span> <span class="identifier">main</span><span class="special">()</span> |
| <span class="special">{</span> |
| <span class="keyword">using</span> <span class="keyword">namespace</span> <span class="identifier">boost</span><span class="special">::</span><span class="identifier">multiprecision</span><span class="special">;</span> |
| |
| <span class="comment">// Operations at variable precision and no numeric_limits support:</span> |
| <span class="identifier">mpfr_float</span> <span class="identifier">a</span> <span class="special">=</span> <span class="number">2</span><span class="special">;</span> |
| <span class="identifier">mpfr_float</span><span class="special">::</span><span class="identifier">default_precision</span><span class="special">(</span><span class="number">1000</span><span class="special">);</span> |
| <span class="identifier">std</span><span class="special">::</span><span class="identifier">cout</span> <span class="special"><<</span> <span class="identifier">mpfr_float</span><span class="special">::</span><span class="identifier">default_precision</span><span class="special">()</span> <span class="special"><<</span> <span class="identifier">std</span><span class="special">::</span><span class="identifier">endl</span><span class="special">;</span> |
| <span class="identifier">std</span><span class="special">::</span><span class="identifier">cout</span> <span class="special"><<</span> <span class="identifier">sqrt</span><span class="special">(</span><span class="identifier">a</span><span class="special">)</span> <span class="special"><<</span> <span class="identifier">std</span><span class="special">::</span><span class="identifier">endl</span><span class="special">;</span> <span class="comment">// print root-2</span> |
| |
| <span class="comment">// Operations at fixed precision and full numeric_limits support:</span> |
| <span class="identifier">mpfr_float_100</span> <span class="identifier">b</span> <span class="special">=</span> <span class="number">2</span><span class="special">;</span> |
| <span class="identifier">std</span><span class="special">::</span><span class="identifier">cout</span> <span class="special"><<</span> <span class="identifier">std</span><span class="special">::</span><span class="identifier">numeric_limits</span><span class="special"><</span><span class="identifier">mpfr_float_100</span><span class="special">>::</span><span class="identifier">digits</span> <span class="special"><<</span> <span class="identifier">std</span><span class="special">::</span><span class="identifier">endl</span><span class="special">;</span> |
| <span class="comment">// We can use any C++ std lib function:</span> |
| <span class="identifier">std</span><span class="special">::</span><span class="identifier">cout</span> <span class="special"><<</span> <span class="identifier">log</span><span class="special">(</span><span class="identifier">b</span><span class="special">)</span> <span class="special"><<</span> <span class="identifier">std</span><span class="special">::</span><span class="identifier">endl</span><span class="special">;</span> <span class="comment">// print log(2)</span> |
| <span class="comment">// We can also use any function from Boost.Math:</span> |
| <span class="identifier">std</span><span class="special">::</span><span class="identifier">cout</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">b</span><span class="special">)</span> <span class="special"><<</span> <span class="identifier">std</span><span class="special">::</span><span class="identifier">endl</span><span class="special">;</span> |
| <span class="comment">// These even work when the argument is an expression template:</span> |
| <span class="identifier">std</span><span class="special">::</span><span class="identifier">cout</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">b</span> <span class="special">*</span> <span class="identifier">b</span><span class="special">)</span> <span class="special"><<</span> <span class="identifier">std</span><span class="special">::</span><span class="identifier">endl</span><span class="special">;</span> |
| |
| <span class="comment">// Access the underlying data:</span> |
| <span class="identifier">mpfr_t</span> <span class="identifier">r</span><span class="special">;</span> |
| <span class="identifier">mpfr_init</span><span class="special">(</span><span class="identifier">r</span><span class="special">);</span> |
| <span class="identifier">mpfr_set</span><span class="special">(</span><span class="identifier">r</span><span class="special">,</span> <span class="identifier">b</span><span class="special">.</span><span class="identifier">backend</span><span class="special">().</span><span class="identifier">data</span><span class="special">(),</span> <span class="identifier">GMP_RNDN</span><span class="special">);</span> |
| <span class="identifier">mpfr_clear</span><span class="special">(</span><span class="identifier">r</span><span class="special">);</span> |
| <span class="keyword">return</span> <span class="number">0</span><span class="special">;</span> |
| <span class="special">}</span> |
| </pre> |
| <div class="footnotes"> |
| <br><hr style="width:100; align:left;"> |
| <div id="ftn.boost_multiprecision.tut.floats.mpfr_float.f0" class="footnote"><p><a href="#boost_multiprecision.tut.floats.mpfr_float.f0" class="para"><sup class="para">[2] </sup></a> |
| Compiled with VC++10 and /Ox, with MPFR-3.0.0 and MPIR-2.3.0 |
| </p></div> |
| </div> |
| </div> |
| <table xmlns:rev="http://www.cs.rpi.edu/~gregod/boost/tools/doc/revision" width="100%"><tr> |
| <td align="left"></td> |
| <td align="right"><div class="copyright-footer">Copyright © 2002-2013 John Maddock and Christopher Kormanyos<p> |
| Distributed under the Boost Software License, Version 1.0. (See accompanying |
| file LICENSE_1_0.txt or copy at <a href="http://www.boost.org/LICENSE_1_0.txt" target="_top">http://www.boost.org/LICENSE_1_0.txt</a>) |
| </p> |
| </div></td> |
| </tr></table> |
| <hr> |
| <div class="spirit-nav"> |
| <a accesskey="p" href="gmp_float.html"><img src="../../../../../../../doc/src/images/prev.png" alt="Prev"></a><a accesskey="u" href="../floats.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="float128.html"><img src="../../../../../../../doc/src/images/next.png" alt="Next"></a> |
| </div> |
| </body> |
| </html> |
