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boost-react-native-bundle

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<html> <head> <meta http-equiv="Content-Type" content="text/html; charset=US-ASCII"> <title>Reference</title> <link rel="stylesheet" href="../../../doc/src/boostbook.css" type="text/css"> <meta name="generator" content="DocBook XSL Stylesheets V1.78.1"> <link rel="home" href="../index.html" title="The Boost C++ Libraries BoostBook Documentation Subset"> <link rel="up" href="../ratio.html" title="Chapter&#160;25.&#160;Boost.Ratio 2.1.0"> <link rel="prev" href="users_guide.html" title="User's Guide"> <link rel="next" href="appendices.html" title="Appendices"> </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="users_guide.html"><img src="../../../doc/src/images/prev.png" alt="Prev"></a><a accesskey="u" href="../ratio.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="appendices.html"><img src="../../../doc/src/images/next.png" alt="Next"></a> </div> <div class="section"> <div class="titlepage"><div><div><h2 class="title" style="clear: both"> <a name="ratio.reference"></a><a class="link" href="reference.html" title="Reference">Reference </a> </h2></div></div></div> <div class="toc"><dl class="toc"> <dt><span class="section"><a href="reference.html#ratio.reference.config_hpp">Header <code class="computeroutput"><span class="special">&lt;</span><span class="identifier">boost</span><span class="special">/</span><span class="identifier">ratio</span><span class="special">/</span><span class="identifier">config</span><span class="special">.</span><span class="identifier">hpp</span><span class="special">&gt;</span></code></a></span></dt> <dt><span class="section"><a href="reference.html#ratio.reference.std">C++0x Recommendation</a></span></dt> <dt><span class="section"><a href="reference.html#ratio.reference.io">Ratio I/O</a></span></dt> <dt><span class="section"><a href="reference.html#ratio.reference.mpl">Rational Constant</a></span></dt> </dl></div> <div class="section"> <div class="titlepage"><div><div><h3 class="title"> <a name="ratio.reference.config_hpp"></a><a class="link" href="reference.html#ratio.reference.config_hpp" title="Header &lt;boost/ratio/config.hpp&gt;">Header <code class="computeroutput"><span class="special">&lt;</span><span class="identifier">boost</span><span class="special">/</span><span class="identifier">ratio</span><span class="special">/</span><span class="identifier">config</span><span class="special">.</span><span class="identifier">hpp</span><span class="special">&gt;</span></code></a> </h3></div></div></div> <div class="toc"><dl class="toc"> <dt><span class="section"><a href="reference.html#ratio.reference.config_hpp.ext">Extensions</a></span></dt> <dt><span class="section"><a href="reference.html#ratio.reference.config_hpp.deprecated">Deprecated</a></span></dt> <dt><span class="section"><a href="reference.html#ratio.reference.config_hpp.version">Version</a></span></dt> <dt><span class="section"><a href="reference.html#ratio.reference.config_hpp.assert">Static Assert</a></span></dt> </dl></div> <pre class="programlisting"><span class="comment">// Configuration macros</span> <span class="preprocessor">#define</span> <a class="link" href="reference.html#ratio.reference.config_hpp.version" title="Version"><code class="computeroutput"><span class="identifier">BOOST_RATIO_VERSION</span> </code></a> <span class="preprocessor">#define</span> <a class="link" href="reference.html#ratio.reference.config_hpp.ext" title="Extensions"><code class="computeroutput"><span class="identifier">BOOST_RATIO_EXTENSIONS</span></code></a> <span class="preprocessor">#define</span> <a class="link" href="reference.html#ratio.reference.config_hpp.deprecated" title="Deprecated"><code class="computeroutput"><span class="identifier">BOOST_RATIO_PROVIDES_DEPRECATED_FEATURES_SINCE_V2_0_0</span></code></a> <span class="preprocessor">#define</span> <a class="link" href="reference.html#ratio.reference.config_hpp.deprecated" title="Deprecated"><code class="computeroutput"><span class="identifier">BOOST_RATIO_DONT_PROVIDE_DEPRECATED_FEATURES_SINCE_V2_0_0</span> </code></a> <span class="preprocessor">#define</span> <a class="link" href="reference.html#ratio.reference.config_hpp.assert" title="Static Assert"><code class="computeroutput"><span class="identifier">BOOST_RATIO_USES_STATIC_ASSERT</span></code></a> <span class="preprocessor">#define</span> <a class="link" href="reference.html#ratio.reference.config_hpp.assert" title="Static Assert"><code class="computeroutput"><span class="identifier">BOOST_RATIO_USES_MPL_ASSERT</span></code></a> <span class="preprocessor">#define</span> <a class="link" href="reference.html#ratio.reference.config_hpp.assert" title="Static Assert"><code class="computeroutput"><span class="identifier">BOOST_RATIO_USES_ARRAY_ASSERT</span></code></a> </pre> <div class="section"> <div class="titlepage"><div><div><h4 class="title"> <a name="ratio.reference.config_hpp.ext"></a><a class="link" href="reference.html#ratio.reference.config_hpp.ext" title="Extensions">Extensions</a> </h4></div></div></div> <p> When <a class="link" href="reference.html#ratio.reference.config_hpp.ext" title="Extensions"><code class="computeroutput"><span class="identifier">BOOST_RATIO_EXTENSIONS</span></code></a> is defined, <span class="bold"><strong>Boost.Ratio</strong></span> provides in addition some extension to the C++ standard, see below. </p> </div> <div class="section"> <div class="titlepage"><div><div><h4 class="title"> <a name="ratio.reference.config_hpp.deprecated"></a><a class="link" href="reference.html#ratio.reference.config_hpp.deprecated" title="Deprecated">Deprecated</a> </h4></div></div></div> <p> When <a class="link" href="reference.html#ratio.reference.config_hpp.deprecated" title="Deprecated"><code class="computeroutput"><span class="identifier">BOOST_RATIO_PROVIDES_DEPRECATED_FEATURES_SINCE_V2_0_0</span></code></a> is defined the deprecated features stated as DEPRECATED V2 are provided. </p> <p> When <a class="link" href="reference.html#ratio.reference.config_hpp.deprecated" title="Deprecated"><code class="computeroutput"><span class="identifier">BOOST_RATIO_DONT_PROVIDE_DEPRECATED_FEATURES_SINCE_V2_0_0</span> </code></a> is defined the deprecated features stated as DEPRECATED V2 are NOT provided. </p> </div> <div class="section"> <div class="titlepage"><div><div><h4 class="title"> <a name="ratio.reference.config_hpp.version"></a><a class="link" href="reference.html#ratio.reference.config_hpp.version" title="Version">Version</a> </h4></div></div></div> <p> <a class="link" href="reference.html#ratio.reference.config_hpp.version" title="Version"><code class="computeroutput"><span class="identifier">BOOST_RATIO_VERSION</span> </code></a> stands for the Boost.Ratio version which can be 1 or 2. The default up to 1.55 is version 1. Since 1.56 it will be 2. </p> <p> When <a class="link" href="reference.html#ratio.reference.config_hpp.version" title="Version"><code class="computeroutput"><span class="identifier">BOOST_RATIO_VERSION</span> </code></a> is 1 <a class="link" href="reference.html#ratio.reference.config_hpp.deprecated" title="Deprecated"><code class="computeroutput"><span class="identifier">BOOST_RATIO_PROVIDES_DEPRECATED_FEATURES_SINCE_V2_0_0</span></code></a> is defined by default. </p> <p> When <a class="link" href="reference.html#ratio.reference.config_hpp.version" title="Version"><code class="computeroutput"><span class="identifier">BOOST_RATIO_VERSION</span> </code></a> is 2 <a class="link" href="reference.html#ratio.reference.config_hpp.deprecated" title="Deprecated"><code class="computeroutput"><span class="identifier">BOOST_RATIO_DONT_PROVIDE_DEPRECATED_FEATURES_SINCE_V2_0_0</span> </code></a> is defined by default. </p> </div> <div class="section"> <div class="titlepage"><div><div><h4 class="title"> <a name="ratio.reference.config_hpp.assert"></a><a class="link" href="reference.html#ratio.reference.config_hpp.assert" title="Static Assert">Static Assert</a> </h4></div></div></div> <p> When BOOST_NO_STATIC_ASSERT is defined, the user can select the way static assertions are reported. Define </p> <div class="itemizedlist"><ul class="itemizedlist" style="list-style-type: disc; "> <li class="listitem"> <a class="link" href="reference.html#ratio.reference.config_hpp.assert" title="Static Assert"><code class="computeroutput"><span class="identifier">BOOST_RATIO_USES_STATIC_ASSERT</span></code></a> to use Boost.StaticAssert. </li> <li class="listitem"> <a class="link" href="reference.html#ratio.reference.config_hpp.assert" title="Static Assert"><code class="computeroutput"><span class="identifier">BOOST_RATIO_USES_MPL_ASSERT</span></code></a> to use <span class="bold"><strong>Boost.MPL</strong></span> static assertions. </li> <li class="listitem"> <a class="link" href="reference.html#ratio.reference.config_hpp.assert" title="Static Assert"><code class="computeroutput"><span class="identifier">BOOST_RATIO_USES_ARRAY_ASSERT</span></code></a> to use <span class="bold"><strong>Boost.Ratio</strong></span> internal static assertions. </li> </ul></div> <p> The default behavior is as if <a class="link" href="reference.html#ratio.reference.config_hpp.assert" title="Static Assert"><code class="computeroutput"><span class="identifier">BOOST_RATIO_USES_ARRAY_ASSERT</span></code></a> was defined. </p> <p> When <a class="link" href="reference.html#ratio.reference.config_hpp.assert" title="Static Assert"><code class="computeroutput"><span class="identifier">BOOST_RATIO_USES_MPL_ASSERT</span></code></a> is not defined the following symbols are defined as shown: </p> <pre class="programlisting"><span class="preprocessor">#define</span> <span class="identifier">BOOST_RATIO_OVERFLOW_IN_ADD</span> <span class="string">"overflow in ratio add"</span> <span class="preprocessor">#define</span> <span class="identifier">BOOST_RATIO_OVERFLOW_IN_SUB</span> <span class="string">"overflow in ratio sub"</span> <span class="preprocessor">#define</span> <span class="identifier">BOOST_RATIO_OVERFLOW_IN_MUL</span> <span class="string">"overflow in ratio mul"</span> <span class="preprocessor">#define</span> <span class="identifier">BOOST_RATIO_OVERFLOW_IN_DIV</span> <span class="string">"overflow in ratio div"</span> <span class="preprocessor">#define</span> <span class="identifier">BOOST_RATIO_NUMERATOR_IS_OUT_OF_RANGE</span> <span class="string">"ratio numerator is out of range"</span> <span class="preprocessor">#define</span> <span class="identifier">BOOST_RATIO_DIVIDE_BY_0</span> <span class="string">"ratio divide by 0"</span> <span class="preprocessor">#define</span> <span class="identifier">BOOST_RATIO_DENOMINATOR_IS_OUT_OF_RANGE</span> <span class="string">"ratio denominator is out of range"</span> </pre> <p> Depending upon the static assertion system used, a hint as to the failing assertion will appear in some form in the compiler diagnostic output. </p> </div> </div> <div class="section"> <div class="titlepage"><div><div><h3 class="title"> <a name="ratio.reference.std"></a><a class="link" href="reference.html#ratio.reference.std" title="C++0x Recommendation">C++0x Recommendation</a> </h3></div></div></div> <div class="toc"><dl class="toc"> <dt><span class="section"><a href="reference.html#ratio.reference.std.ratio_ratio_hpp">Header <code class="computeroutput"><span class="special">&lt;</span><span class="identifier">boost</span><span class="special">/</span><span class="identifier">ratio</span><span class="special">.</span><span class="identifier">hpp</span><span class="special">&gt;</span></code></a></span></dt> <dt><span class="section"><a href="reference.html#ratio.reference.std.ratio_fwdhpp">Header <code class="computeroutput"><span class="special">&lt;</span><span class="identifier">boost</span><span class="special">/</span><span class="identifier">ratio</span><span class="special">/</span><span class="identifier">ratio_fwd</span><span class="special">.</span><span class="identifier">hpp</span><span class="special">&gt;</span></code></a></span></dt> <dt><span class="section"><a href="reference.html#ratio.reference.std.ratio_hpp">Header <code class="computeroutput"><span class="special">&lt;</span><span class="identifier">boost</span><span class="special">/</span><span class="identifier">ratio</span><span class="special">/</span><span class="identifier">ratio</span><span class="special">.</span><span class="identifier">hpp</span><span class="special">&gt;</span></code></a></span></dt> </dl></div> <div class="section"> <div class="titlepage"><div><div><h4 class="title"> <a name="ratio.reference.std.ratio_ratio_hpp"></a><a class="link" href="reference.html#ratio.reference.std.ratio_ratio_hpp" title="Header &lt;boost/ratio.hpp&gt;">Header <code class="computeroutput"><span class="special">&lt;</span><span class="identifier">boost</span><span class="special">/</span><span class="identifier">ratio</span><span class="special">.</span><span class="identifier">hpp</span><span class="special">&gt;</span></code></a> </h4></div></div></div> <p> This header includes all the ratio related header files </p> <pre class="programlisting"><span class="preprocessor">#include</span> <span class="special">&lt;</span><span class="identifier">boost</span><span class="special">/</span><span class="identifier">ratio</span><span class="special">/</span><span class="identifier">ratio</span><span class="special">.</span><span class="identifier">hpp</span><span class="special">&gt;</span> <span class="preprocessor">#include</span> <span class="special">&lt;</span><span class="identifier">boost</span><span class="special">/</span><span class="identifier">ratio</span><span class="special">/</span><span class="identifier">ratio_io</span><span class="special">.</span><span class="identifier">hpp</span><span class="special">&gt;</span> <span class="preprocessor">#include</span> <span class="special">&lt;</span><span class="identifier">boost</span><span class="special">/</span><span class="identifier">ratio</span><span class="special">/</span><span class="identifier">rational_constant</span><span class="special">.</span><span class="identifier">hpp</span><span class="special">&gt;</span> </pre> </div> <div class="section"> <div class="titlepage"><div><div><h4 class="title"> <a name="ratio.reference.std.ratio_fwdhpp"></a><a class="link" href="reference.html#ratio.reference.std.ratio_fwdhpp" title="Header &lt;boost/ratio/ratio_fwd.hpp&gt;">Header <code class="computeroutput"><span class="special">&lt;</span><span class="identifier">boost</span><span class="special">/</span><span class="identifier">ratio</span><span class="special">/</span><span class="identifier">ratio_fwd</span><span class="special">.</span><span class="identifier">hpp</span><span class="special">&gt;</span></code></a> </h4></div></div></div> <p> This header provides forward declarations for the <code class="computeroutput"><span class="special">&lt;</span><span class="identifier">boost</span><span class="special">/</span><span class="identifier">ratio</span><span class="special">/</span><span class="identifier">ratio</span><span class="special">.</span><span class="identifier">hpp</span><span class="special">&gt;</span></code> file. </p> <pre class="programlisting"><span class="keyword">namespace</span> <span class="identifier">boost</span> <span class="special">{</span> <span class="keyword">template</span> <span class="special">&lt;</span><span class="identifier">boost</span><span class="special">::</span><span class="identifier">intmax_t</span> <span class="identifier">N</span><span class="special">,</span> <span class="identifier">boost</span><span class="special">::</span><span class="identifier">intmax_t</span> <span class="identifier">D</span> <span class="special">=</span> <span class="number">1</span><span class="special">&gt;</span> <span class="keyword">class</span> <a class="link" href="reference.html#ratio.reference.std.ratio_hpp.ratio" title="Class Template ratio&lt;&gt;"><code class="computeroutput"><span class="identifier">ratio</span></code></a><span class="special">;</span> <span class="comment">// ratio arithmetic</span> <span class="keyword">template</span> <span class="special">&lt;</span><span class="keyword">class</span> <span class="identifier">R1</span><span class="special">,</span> <span class="keyword">class</span> <span class="identifier">R2</span><span class="special">&gt;</span> <span class="keyword">struct</span> <a class="link" href="reference.html#ratio.reference.std.ratio_hpp.ratio_arithmetic" title="ratio Arithmetic"><code class="computeroutput"><span class="identifier">ratio_add</span></code></a><span class="special">;</span> <span class="keyword">template</span> <span class="special">&lt;</span><span class="keyword">class</span> <span class="identifier">R1</span><span class="special">,</span> <span class="keyword">class</span> <span class="identifier">R2</span><span class="special">&gt;</span> <span class="keyword">struct</span> <a class="link" href="reference.html#ratio.reference.std.ratio_hpp.ratio_arithmetic" title="ratio Arithmetic"><code class="computeroutput"><span class="identifier">ratio_subtract</span></code></a><span class="special">;</span> <span class="keyword">template</span> <span class="special">&lt;</span><span class="keyword">class</span> <span class="identifier">R1</span><span class="special">,</span> <span class="keyword">class</span> <span class="identifier">R2</span><span class="special">&gt;</span> <span class="keyword">struct</span> <a class="link" href="reference.html#ratio.reference.std.ratio_hpp.ratio_arithmetic" title="ratio Arithmetic"><code class="computeroutput"><span class="identifier">ratio_multiply</span></code></a><span class="special">;</span> <span class="keyword">template</span> <span class="special">&lt;</span><span class="keyword">class</span> <span class="identifier">R1</span><span class="special">,</span> <span class="keyword">class</span> <span class="identifier">R2</span><span class="special">&gt;</span> <span class="keyword">struct</span> <a class="link" href="reference.html#ratio.reference.std.ratio_hpp.ratio_arithmetic" title="ratio Arithmetic"><code class="computeroutput"><span class="identifier">ratio_divide</span></code></a><span class="special">;</span> <span class="preprocessor">#ifdef</span> <span class="identifier">BOOST_RATIO_EXTENSIONS</span> <span class="keyword">template</span> <span class="special">&lt;</span><span class="keyword">class</span> <span class="identifier">R</span><span class="special">,</span><span class="keyword">int</span> <span class="identifier">P</span><span class="special">&gt;</span> <span class="keyword">struct</span> <a class="link" href="reference.html#ratio.reference.std.ratio_hpp.ratio_arithmetic" title="ratio Arithmetic"><code class="computeroutput"><span class="identifier">ratio_power</span></code></a><span class="special">;</span> <span class="keyword">template</span> <span class="special">&lt;</span><span class="keyword">class</span> <span class="identifier">R</span><span class="special">&gt;</span> <span class="keyword">struct</span> <a class="link" href="reference.html#ratio.reference.std.ratio_hpp.ratio_arithmetic" title="ratio Arithmetic"><code class="computeroutput"><span class="identifier">ratio_negate</span></code></a><span class="special">;</span> <span class="keyword">template</span> <span class="special">&lt;</span><span class="keyword">class</span> <span class="identifier">R</span><span class="special">&gt;</span> <span class="keyword">struct</span> <a class="link" href="reference.html#ratio.reference.std.ratio_hpp.ratio_arithmetic" title="ratio Arithmetic"><code class="computeroutput"><span class="identifier">ratio_sign</span></code></a><span class="special">;</span> <span class="keyword">template</span> <span class="special">&lt;</span><span class="keyword">class</span> <span class="identifier">R</span><span class="special">&gt;</span> <span class="keyword">struct</span> <a class="link" href="reference.html#ratio.reference.std.ratio_hpp.ratio_arithmetic" title="ratio Arithmetic"><code class="computeroutput"><span class="identifier">ratio_abs</span></code></a><span class="special">;</span> <span class="keyword">template</span> <span class="special">&lt;</span><span class="keyword">class</span> <span class="identifier">R1</span><span class="special">,</span> <span class="keyword">class</span> <span class="identifier">R2</span><span class="special">&gt;</span> <span class="keyword">struct</span> <a class="link" href="reference.html#ratio.reference.std.ratio_hpp.ratio_arithmetic" title="ratio Arithmetic"><code class="computeroutput"><span class="identifier">ratio_gcd</span></code></a><span class="special">;</span> <span class="keyword">template</span> <span class="special">&lt;</span><span class="keyword">class</span> <span class="identifier">R1</span><span class="special">,</span> <span class="keyword">class</span> <span class="identifier">R2</span><span class="special">&gt;</span> <span class="keyword">struct</span> <a class="link" href="reference.html#ratio.reference.std.ratio_hpp.ratio_arithmetic" title="ratio Arithmetic"><code class="computeroutput"><span class="identifier">ratio_lcm</span></code></a><span class="special">;</span> <span class="preprocessor">#endif</span> <span class="comment">// ratio comparison</span> <span class="keyword">template</span> <span class="special">&lt;</span><span class="keyword">class</span> <span class="identifier">R1</span><span class="special">,</span> <span class="keyword">class</span> <span class="identifier">R2</span><span class="special">&gt;</span> <span class="keyword">struct</span> <a class="link" href="reference.html#ratio.reference.std.ratio_hpp.ratio_comparison" title="ratio Comparison"><code class="computeroutput"><span class="identifier">ratio_equal</span></code></a><span class="special">;</span> <span class="keyword">template</span> <span class="special">&lt;</span><span class="keyword">class</span> <span class="identifier">R1</span><span class="special">,</span> <span class="keyword">class</span> <span class="identifier">R2</span><span class="special">&gt;</span> <span class="keyword">struct</span> <a class="link" href="reference.html#ratio.reference.std.ratio_hpp.ratio_comparison" title="ratio Comparison"><code class="computeroutput"><span class="identifier">ratio_not_equal</span></code></a><span class="special">;</span> <span class="keyword">template</span> <span class="special">&lt;</span><span class="keyword">class</span> <span class="identifier">R1</span><span class="special">,</span> <span class="keyword">class</span> <span class="identifier">R2</span><span class="special">&gt;</span> <span class="keyword">struct</span> <a class="link" href="reference.html#ratio.reference.std.ratio_hpp.ratio_comparison" title="ratio Comparison"><code class="computeroutput"><span class="identifier">ratio_less</span></code></a><span class="special">;</span> <span class="keyword">template</span> <span class="special">&lt;</span><span class="keyword">class</span> <span class="identifier">R1</span><span class="special">,</span> <span class="keyword">class</span> <span class="identifier">R2</span><span class="special">&gt;</span> <span class="keyword">struct</span> <a class="link" href="reference.html#ratio.reference.std.ratio_hpp.ratio_comparison" title="ratio Comparison"><code class="computeroutput"><span class="identifier">ratio_less_equal</span></code></a><span class="special">;</span> <span class="keyword">template</span> <span class="special">&lt;</span><span class="keyword">class</span> <span class="identifier">R1</span><span class="special">,</span> <span class="keyword">class</span> <span class="identifier">R2</span><span class="special">&gt;</span> <span class="keyword">struct</span> <a class="link" href="reference.html#ratio.reference.std.ratio_hpp.ratio_comparison" title="ratio Comparison"><code class="computeroutput"><span class="identifier">ratio_greater</span></code></a><span class="special">;</span> <span class="keyword">template</span> <span class="special">&lt;</span><span class="keyword">class</span> <span class="identifier">R1</span><span class="special">,</span> <span class="keyword">class</span> <span class="identifier">R2</span><span class="special">&gt;</span> <span class="keyword">struct</span> <a class="link" href="reference.html#ratio.reference.std.ratio_hpp.ratio_comparison" title="ratio Comparison"><code class="computeroutput"><span class="identifier">ratio_greater_equal</span></code></a><span class="special">;</span> <span class="comment">// convenience SI typedefs</span> <span class="keyword">typedef</span> <span class="identifier">ratio</span><span class="special">&lt;</span><span class="number">1LL</span><span class="special">,</span> <span class="number">1000000000000000000LL</span><span class="special">&gt;</span> <a class="link" href="reference.html#ratio.reference.std.ratio_hpp.ratio_si_typedefs" title="SI typedefs"><code class="computeroutput"><span class="identifier">atto</span></code></a><span class="special">;</span> <span class="keyword">typedef</span> <span class="identifier">ratio</span><span class="special">&lt;</span><span class="number">1LL</span><span class="special">,</span> <span class="number">1000000000000000LL</span><span class="special">&gt;</span> <a class="link" href="reference.html#ratio.reference.std.ratio_hpp.ratio_si_typedefs" title="SI typedefs"><code class="computeroutput"><span class="identifier">femto</span></code></a><span class="special">;</span> <span class="keyword">typedef</span> <span class="identifier">ratio</span><span class="special">&lt;</span><span class="number">1LL</span><span class="special">,</span> <span class="number">1000000000000LL</span><span class="special">&gt;</span> <a class="link" href="reference.html#ratio.reference.std.ratio_hpp.ratio_si_typedefs" title="SI typedefs"><code class="computeroutput"><span class="identifier">pico</span></code></a><span class="special">;</span> <span class="keyword">typedef</span> <span class="identifier">ratio</span><span class="special">&lt;</span><span class="number">1LL</span><span class="special">,</span> <span class="number">1000000000LL</span><span class="special">&gt;</span> <a class="link" href="reference.html#ratio.reference.std.ratio_hpp.ratio_si_typedefs" title="SI typedefs"><code class="computeroutput"><span class="identifier">nano</span></code></a><span class="special">;</span> <span class="keyword">typedef</span> <span class="identifier">ratio</span><span class="special">&lt;</span><span class="number">1LL</span><span class="special">,</span> <span class="number">1000000LL</span><span class="special">&gt;</span> <a class="link" href="reference.html#ratio.reference.std.ratio_hpp.ratio_si_typedefs" title="SI typedefs"><code class="computeroutput"><span class="identifier">micro</span></code></a><span class="special">;</span> <span class="keyword">typedef</span> <span class="identifier">ratio</span><span class="special">&lt;</span><span class="number">1LL</span><span class="special">,</span> <span class="number">1000LL</span><span class="special">&gt;</span> <a class="link" href="reference.html#ratio.reference.std.ratio_hpp.ratio_si_typedefs" title="SI typedefs"><code class="computeroutput"><span class="identifier">milli</span></code></a><span class="special">;</span> <span class="keyword">typedef</span> <span class="identifier">ratio</span><span class="special">&lt;</span><span class="number">1LL</span><span class="special">,</span> <span class="number">100LL</span><span class="special">&gt;</span> <a class="link" href="reference.html#ratio.reference.std.ratio_hpp.ratio_si_typedefs" title="SI typedefs"><code class="computeroutput"><span class="identifier">centi</span></code></a><span class="special">;</span> <span class="keyword">typedef</span> <span class="identifier">ratio</span><span class="special">&lt;</span><span class="number">1LL</span><span class="special">,</span> <span class="number">10LL</span><span class="special">&gt;</span> <a class="link" href="reference.html#ratio.reference.std.ratio_hpp.ratio_si_typedefs" title="SI typedefs"><code class="computeroutput"><span class="identifier">deci</span></code></a><span class="special">;</span> <span class="keyword">typedef</span> <span class="identifier">ratio</span><span class="special">&lt;</span> <span class="number">10LL</span><span class="special">,</span> <span class="number">1LL</span><span class="special">&gt;</span> <a class="link" href="reference.html#ratio.reference.std.ratio_hpp.ratio_si_typedefs" title="SI typedefs"><code class="computeroutput"><span class="identifier">deca</span></code></a><span class="special">;</span> <span class="keyword">typedef</span> <span class="identifier">ratio</span><span class="special">&lt;</span> <span class="number">100LL</span><span class="special">,</span> <span class="number">1LL</span><span class="special">&gt;</span> <a class="link" href="reference.html#ratio.reference.std.ratio_hpp.ratio_si_typedefs" title="SI typedefs"><code class="computeroutput"><span class="identifier">hecto</span></code></a><span class="special">;</span> <span class="keyword">typedef</span> <span class="identifier">ratio</span><span class="special">&lt;</span> <span class="number">1000LL</span><span class="special">,</span> <span class="number">1LL</span><span class="special">&gt;</span> <a class="link" href="reference.html#ratio.reference.std.ratio_hpp.ratio_si_typedefs" title="SI typedefs"><code class="computeroutput"><span class="identifier">kilo</span></code></a><span class="special">;</span> <span class="keyword">typedef</span> <span class="identifier">ratio</span><span class="special">&lt;</span> <span class="number">1000000LL</span><span class="special">,</span> <span class="number">1LL</span><span class="special">&gt;</span> <a class="link" href="reference.html#ratio.reference.std.ratio_hpp.ratio_si_typedefs" title="SI typedefs"><code class="computeroutput"><span class="identifier">mega</span></code></a><span class="special">;</span> <span class="keyword">typedef</span> <span class="identifier">ratio</span><span class="special">&lt;</span> <span class="number">1000000000LL</span><span class="special">,</span> <span class="number">1LL</span><span class="special">&gt;</span> <a class="link" href="reference.html#ratio.reference.std.ratio_hpp.ratio_si_typedefs" title="SI typedefs"><code class="computeroutput"><span class="identifier">giga</span></code></a><span class="special">;</span> <span class="keyword">typedef</span> <span class="identifier">ratio</span><span class="special">&lt;</span> <span class="number">1000000000000LL</span><span class="special">,</span> <span class="number">1LL</span><span class="special">&gt;</span> <a class="link" href="reference.html#ratio.reference.std.ratio_hpp.ratio_si_typedefs" title="SI typedefs"><code class="computeroutput"><span class="identifier">tera</span></code></a><span class="special">;</span> <span class="keyword">typedef</span> <span class="identifier">ratio</span><span class="special">&lt;</span> <span class="number">1000000000000000LL</span><span class="special">,</span> <span class="number">1LL</span><span class="special">&gt;</span> <a class="link" href="reference.html#ratio.reference.std.ratio_hpp.ratio_si_typedefs" title="SI typedefs"><code class="computeroutput"><span class="identifier">peta</span></code></a><span class="special">;</span> <span class="keyword">typedef</span> <span class="identifier">ratio</span><span class="special">&lt;</span><span class="number">1000000000000000000LL</span><span class="special">,</span> <span class="number">1LL</span><span class="special">&gt;</span> <a class="link" href="reference.html#ratio.reference.std.ratio_hpp.ratio_si_typedefs" title="SI typedefs"><code class="computeroutput"><span class="identifier">exa</span></code></a><span class="special">;</span> <span class="preprocessor">#ifdef</span> <span class="identifier">BOOST_RATIO_EXTENSIONS</span> <span class="comment">// convenience IEC typedefs</span> <span class="keyword">typedef</span> <span class="identifier">ratio</span><span class="special">&lt;</span> <span class="number">1024LL</span><span class="special">&gt;</span> <a class="link" href="reference.html#ratio.reference.std.ratio_hpp.ratio_iec_typedefs" title="IEC typedefs"><code class="computeroutput"><span class="identifier">kibi</span></code></a><span class="special">;</span> <span class="keyword">typedef</span> <span class="identifier">ratio</span><span class="special">&lt;</span> <span class="number">1024LL</span><span class="special">*</span><span class="number">1024LL</span><span class="special">&gt;</span> <a class="link" href="reference.html#ratio.reference.std.ratio_hpp.ratio_iec_typedefs" title="IEC typedefs"><code class="computeroutput"><span class="identifier">mebi</span></code></a><span class="special">;</span> <span class="keyword">typedef</span> <span class="identifier">ratio</span><span class="special">&lt;</span> <span class="number">1024LL</span><span class="special">*</span><span class="number">1024LL</span><span class="special">*</span><span class="number">1024LL</span><span class="special">&gt;</span> <a class="link" href="reference.html#ratio.reference.std.ratio_hpp.ratio_iec_typedefs" title="IEC typedefs"><code class="computeroutput"><span class="identifier">gibi</span></code></a><span class="special">;</span> <span class="keyword">typedef</span> <span class="identifier">ratio</span><span class="special">&lt;</span> <span class="number">1024LL</span><span class="special">*</span><span class="number">1024LL</span><span class="special">*</span><span class="number">1024LL</span><span class="special">*</span><span class="number">1024LL</span><span class="special">&gt;</span> <a class="link" href="reference.html#ratio.reference.std.ratio_hpp.ratio_iec_typedefs" title="IEC typedefs"><code class="computeroutput"><span class="identifier">tebi</span></code></a><span class="special">;</span> <span class="keyword">typedef</span> <span class="identifier">ratio</span><span class="special">&lt;</span> <span class="number">1024LL</span><span class="special">*</span><span class="number">1024LL</span><span class="special">*</span><span class="number">1024LL</span><span class="special">*</span><span class="number">1024LL</span><span class="special">*</span><span class="number">1024LL</span><span class="special">&gt;</span> <a class="link" href="reference.html#ratio.reference.std.ratio_hpp.ratio_iec_typedefs" title="IEC typedefs"><code class="computeroutput"><span class="identifier">pebi</span></code></a><span class="special">;</span> <span class="keyword">typedef</span> <span class="identifier">ratio</span><span class="special">&lt;</span><span class="number">1024LL</span><span class="special">*</span><span class="number">1024LL</span><span class="special">*</span><span class="number">1024LL</span><span class="special">*</span><span class="number">1024LL</span><span class="special">*</span><span class="number">1024LL</span><span class="special">*</span><span class="number">1024LL</span><span class="special">&gt;</span> <a class="link" href="reference.html#ratio.reference.std.ratio_hpp.ratio_iec_typedefs" title="IEC typedefs"><code class="computeroutput"><span class="identifier">exbi</span></code></a><span class="special">;</span> <span class="preprocessor">#endif</span> <span class="special">}</span> </pre> </div> <div class="section"> <div class="titlepage"><div><div><h4 class="title"> <a name="ratio.reference.std.ratio_hpp"></a><a class="link" href="reference.html#ratio.reference.std.ratio_hpp" title="Header &lt;boost/ratio/ratio.hpp&gt;">Header <code class="computeroutput"><span class="special">&lt;</span><span class="identifier">boost</span><span class="special">/</span><span class="identifier">ratio</span><span class="special">/</span><span class="identifier">ratio</span><span class="special">.</span><span class="identifier">hpp</span><span class="special">&gt;</span></code></a> </h4></div></div></div> <div class="toc"><dl class="toc"> <dt><span class="section"><a href="reference.html#ratio.reference.std.ratio_hpp.ratio">Class Template <code class="computeroutput"><span class="identifier">ratio</span><span class="special">&lt;&gt;</span></code></a></span></dt> <dt><span class="section"><a href="reference.html#ratio.reference.std.ratio_hpp.ratio_arithmetic"><code class="computeroutput"><span class="identifier">ratio</span></code> Arithmetic</a></span></dt> <dt><span class="section"><a href="reference.html#ratio.reference.std.ratio_hpp.ratio_comparison"><code class="computeroutput"><span class="identifier">ratio</span></code> Comparison</a></span></dt> <dt><span class="section"><a href="reference.html#ratio.reference.std.ratio_hpp.ratio_si_typedefs">SI typedefs</a></span></dt> <dt><span class="section"><a href="reference.html#ratio.reference.std.ratio_hpp.ratio_iec_typedefs">IEC typedefs</a></span></dt> <dt><span class="section"><a href="reference.html#ratio.reference.std.ratio_hpp.limitations">Limitations</a></span></dt> <dt><span class="section"><a href="reference.html#ratio.reference.std.ratio_hpp.extensions">Extensions</a></span></dt> </dl></div> <p> <a class="link" href="reference.html#ratio.reference.std.ratio_hpp.ratio" title="Class Template ratio&lt;&gt;"><code class="computeroutput"><span class="identifier">ratio</span></code></a> is a facility which is useful in specifying compile-time rational constants. Compile-time rational arithmetic is supported with protection against overflow and divide by zero. Such a facility is very handy to efficiently represent 1/3 of a nanosecond, or to specify an inch in terms of meters (for example 254/10000 meters - which <a class="link" href="reference.html#ratio.reference.std.ratio_hpp.ratio" title="Class Template ratio&lt;&gt;"><code class="computeroutput"><span class="identifier">ratio</span></code></a> will reduce to 127/5000 meters). </p> <div class="section"> <div class="titlepage"><div><div><h5 class="title"> <a name="ratio.reference.std.ratio_hpp.ratio"></a><a class="link" href="reference.html#ratio.reference.std.ratio_hpp.ratio" title="Class Template ratio&lt;&gt;">Class Template <code class="computeroutput"><span class="identifier">ratio</span><span class="special">&lt;&gt;</span></code></a> </h5></div></div></div> <pre class="programlisting"><span class="keyword">template</span> <span class="special">&lt;</span><span class="identifier">boost</span><span class="special">::</span><span class="identifier">intmax_t</span> <span class="identifier">N</span><span class="special">,</span> <span class="identifier">boost</span><span class="special">::</span><span class="identifier">intmax_t</span> <span class="identifier">D</span><span class="special">&gt;</span> <span class="keyword">class</span> <span class="identifier">ratio</span> <span class="special">{</span> <span class="keyword">public</span><span class="special">:</span> <span class="keyword">static</span> <span class="keyword">const</span> <span class="identifier">boost</span><span class="special">::</span><span class="identifier">intmax_t</span> <span class="identifier">num</span><span class="special">;</span> <span class="keyword">static</span> <span class="keyword">const</span> <span class="identifier">boost</span><span class="special">::</span><span class="identifier">intmax_t</span> <span class="identifier">den</span><span class="special">;</span> <span class="keyword">typedef</span> <span class="identifier">ratio</span><span class="special">&lt;</span><span class="identifier">num</span><span class="special">,</span> <span class="identifier">den</span><span class="special">&gt;</span> <span class="identifier">type</span><span class="special">;</span> <span class="preprocessor">#ifdef</span> <a class="link" href="reference.html#ratio.reference.config_hpp.ext" title="Extensions"><code class="computeroutput"><span class="identifier">BOOST_RATIO_EXTENSIONS</span></code></a> <span class="keyword">typedef</span> <span class="identifier">mpl</span><span class="special">::</span><span class="identifier">rational_c_tag</span> <span class="identifier">tag</span><span class="special">;</span> <span class="keyword">typedef</span> <span class="identifier">boost</span><span class="special">::</span><span class="identifier">rational</span><span class="special">&lt;</span><span class="identifier">boost</span><span class="special">::</span><span class="identifier">intmax_t</span><span class="special">&gt;</span> <span class="identifier">value_type</span><span class="special">;</span> <span class="keyword">typedef</span> <span class="identifier">boost</span><span class="special">::</span><span class="identifier">intmax_t</span> <span class="identifier">num_type</span><span class="special">;</span> <span class="keyword">typedef</span> <span class="identifier">boost</span><span class="special">::</span><span class="identifier">intmax_t</span> <span class="identifier">den_type</span><span class="special">;</span> <span class="identifier">ratio</span><span class="special">()</span> <span class="special">=</span> <span class="keyword">default</span><span class="special">;</span> <span class="keyword">template</span> <span class="special">&lt;</span><span class="identifier">intmax_t</span> <span class="identifier">_N2</span><span class="special">,</span> <span class="identifier">intmax_t</span> <span class="identifier">_D2</span><span class="special">&gt;</span> <span class="identifier">ratio</span><span class="special">(</span><span class="keyword">const</span> <span class="identifier">ratio</span><span class="special">&lt;</span><span class="identifier">_N2</span><span class="special">,</span> <span class="identifier">_D2</span><span class="special">&gt;&amp;);</span> <span class="keyword">template</span> <span class="special">&lt;</span><span class="identifier">intmax_t</span> <span class="identifier">_N2</span><span class="special">,</span> <span class="identifier">intmax_t</span> <span class="identifier">_D2</span><span class="special">&gt;</span> <span class="identifier">ratio</span><span class="special">&amp;</span> <span class="keyword">operator</span><span class="special">=(</span><span class="keyword">const</span> <span class="identifier">ratio</span><span class="special">&lt;</span><span class="identifier">_N2</span><span class="special">,</span> <span class="identifier">_D2</span><span class="special">&gt;&amp;);</span> <span class="keyword">static</span> <span class="identifier">value_type</span> <span class="identifier">value</span><span class="special">();</span> <span class="identifier">value_type</span> <span class="keyword">operator</span><span class="special">()()</span> <span class="keyword">const</span><span class="special">;</span> <span class="preprocessor">#endif</span> <span class="special">};</span> </pre> <p> A diagnostic will be emitted if <a class="link" href="reference.html#ratio.reference.std.ratio_hpp.ratio" title="Class Template ratio&lt;&gt;"><code class="computeroutput"><span class="identifier">ratio</span></code></a> is instantiated with <code class="computeroutput"><span class="identifier">D</span> <span class="special">==</span> <span class="number">0</span></code>, or if the absolute value of <code class="computeroutput"><span class="identifier">N</span></code> or <code class="computeroutput"><span class="identifier">D</span></code> cannot be represented. <span class="bold"><strong>Note:</strong></span> These rules ensure that infinite ratios are avoided and that for any negative input, there exists a representable value of its absolute value which is positive. In a two's complement representation, this excludes the most negative value. </p> <p> The members num and den will be normalized values of the template arguments N and D computed as follows. Let <code class="computeroutput"><span class="identifier">gcd</span></code> denote the greatest common divisor of <code class="computeroutput"><span class="identifier">N</span></code>'s absolute value and of <code class="computeroutput"><span class="identifier">D</span></code>'s absolute value. Then: </p> <div class="itemizedlist"><ul class="itemizedlist" style="list-style-type: disc; "> <li class="listitem"> <code class="computeroutput"><span class="identifier">num</span></code> has the value <code class="computeroutput"><span class="identifier">sign</span><span class="special">(</span><span class="identifier">N</span><span class="special">)*</span><span class="identifier">sign</span><span class="special">(</span><span class="identifier">D</span><span class="special">)*</span><span class="identifier">abs</span><span class="special">(</span><span class="identifier">N</span><span class="special">)/</span><span class="identifier">gcd</span></code>. </li> <li class="listitem"> <code class="computeroutput"><span class="identifier">den</span></code> has the value <code class="computeroutput"><span class="identifier">abs</span><span class="special">(</span><span class="identifier">D</span><span class="special">)/</span><span class="identifier">gcd</span></code>. </li> </ul></div> <p> The nested typedef <code class="computeroutput"><span class="identifier">type</span></code> denotes the normalized form of this <a class="link" href="reference.html#ratio.reference.std.ratio_hpp.ratio" title="Class Template ratio&lt;&gt;"><code class="computeroutput"><span class="identifier">ratio</span></code></a> type. It should be used when the normalized form of the template arguments are required, since the arguments are not necessarily normalized. </p> <p> Two <a class="link" href="reference.html#ratio.reference.std.ratio_hpp.ratio" title="Class Template ratio&lt;&gt;"><code class="computeroutput"><span class="identifier">ratio</span></code></a> classes <code class="computeroutput"><a class="link" href="reference.html#ratio.reference.std.ratio_hpp.ratio" title="Class Template ratio&lt;&gt;"><code class="computeroutput"><span class="identifier">ratio</span></code></a><span class="special">&lt;</span><span class="identifier">N1</span><span class="special">,</span><span class="identifier">D1</span><span class="special">&gt;</span></code> and <code class="computeroutput"><a class="link" href="reference.html#ratio.reference.std.ratio_hpp.ratio" title="Class Template ratio&lt;&gt;"><code class="computeroutput"><span class="identifier">ratio</span></code></a><span class="special">&lt;</span><span class="identifier">N2</span><span class="special">,</span><span class="identifier">D2</span><span class="special">&gt;</span></code> have the same normalized form if <code class="computeroutput"><a class="link" href="reference.html#ratio.reference.std.ratio_hpp.ratio" title="Class Template ratio&lt;&gt;"><code class="computeroutput"><span class="identifier">ratio</span></code></a><span class="special">&lt;</span><span class="identifier">N1</span><span class="special">,</span><span class="identifier">D1</span><span class="special">&gt;::</span><span class="identifier">type</span></code> is the same type as <code class="computeroutput"><a class="link" href="reference.html#ratio.reference.std.ratio_hpp.ratio" title="Class Template ratio&lt;&gt;"><code class="computeroutput"><span class="identifier">ratio</span></code></a><span class="special">&lt;</span><span class="identifier">N2</span><span class="special">,</span><span class="identifier">D2</span><span class="special">&gt;::</span><span class="identifier">type</span></code> </p> <div class="section"> <div class="titlepage"><div><div><h6 class="title"> <a name="ratio.reference.std.ratio_hpp.ratio.ca"></a><a class="link" href="reference.html#ratio.reference.std.ratio_hpp.ratio.ca" title="Construction and Assignment">Construction