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  26 <div class="titlepage"><div><div><h2 class="title" style="clear: both">
  27 <a name="math_toolkit.exact_typdefs"></a><a class="link" href="exact_typdefs.html" title="Exact-Width Floating-Point typedefs">Exact-Width Floating-Point
  28     <code class="computeroutput"><span class="keyword">typedef</span></code>s</a>
  29 </h2></div></div></div>
  30 <p>
  31       The <code class="computeroutput"><span class="keyword">typedef</span> <span class="keyword">float</span><span class="special">#</span><span class="identifier">_t</span></code>, with
  32       # replaced by the width, designates a floating-point type of exactly # bits.
  33       For example <code class="computeroutput"><span class="identifier">float32_t</span></code> denotes
  34       a single-precision floating-point type with approximately 7 decimal digits
  35       of precision (equivalent to binary32 in <a href="http://en.wikipedia.org/wiki/IEEE_floating_point" target="_top">IEEE_floating_point</a>).
  36     </p>
  37 <p>
  38       Floating-point types in C and C++ are specified to be allowed to have (optionally)
  39       implementation-specific widths and formats. However, if a platform supports
  40       underlying floating-point types (conformant with <a href="http://en.wikipedia.org/wiki/IEEE_floating_point" target="_top">IEEE_floating_point</a>)
  41       with widths of 16, 32, 64, 80, 128 bits, or any combination thereof, then
  42       <code class="computeroutput"><span class="special">&lt;</span><span class="identifier">boost</span><span class="special">/</span><span class="identifier">cstdfloat</span><span class="special">.</span><span class="identifier">hpp</span><span class="special">&gt;</span></code>
  43       does provide the corresponding <code class="computeroutput"><span class="keyword">typedef</span></code>s
  44       <code class="computeroutput"><span class="identifier">float16_t</span><span class="special">,</span>
  45       <span class="identifier">float32_t</span><span class="special">,</span>
  46       <span class="identifier">float64_t</span><span class="special">,</span>
  47       <span class="identifier">float80_t</span><span class="special">,</span>
  48       <span class="identifier">float128_t</span><span class="special">,</span></code>
  49       their corresponding least and fast types, and the corresponding maximum-width
  50       type.
  51     </p>
  52 <h5>
  53 <a name="math_toolkit.exact_typdefs.h0"></a>
  54       <span class="phrase"><a name="math_toolkit.exact_typdefs.how_to_tell_which_widths_are_sup"></a></span><a class="link" href="exact_typdefs.html#math_toolkit.exact_typdefs.how_to_tell_which_widths_are_sup">How to
  55       tell which widths are supported</a>
  56     </h5>
  57 <p>
  58       The definition (or not) of a <a class="link" href="macros.html" title="Floating-Point Constant Macros">floating-point
  59       constant macro</a> is a way to test if a <span class="bold"><strong>specific
  60       width floating-point</strong></span> is available on a platform.
  61     </p>
  62 <pre class="programlisting"><span class="preprocessor">#if</span> <span class="identifier">defined</span><span class="special">(</span><span class="identifier">BOOST_FLOAT16_C</span><span class="special">)</span>
  63 <span class="comment">// Can use boost::float16_t, perhaps a proposed __short_float.</span>
  64 <span class="comment">// P0192R1, Adding Fundamental Type for Short Float,</span>
  65 <span class="comment">// Boris Fomitchev, Sergei Nikolaev, Olivier Giroux, Lawrence Crowl, 2016 Feb14</span>
  66 <span class="comment">// http://www.open-std.org/jtc1/sc22/wg14/www/docs/n2016.pdf</span>
  67 <span class="preprocessor">#endif</span>
  68
  69 <span class="preprocessor">#if</span> <span class="identifier">defined</span><span class="special">(</span><span class="identifier">BOOST_FLOAT32_C</span><span class="special">)</span>
  70 <span class="comment">// Can use boost::float32_t, usually type `float`.</span>
  71 <span class="preprocessor">#endif</span>
  72
  73 <span class="preprocessor">#if</span> <span class="identifier">defined</span><span class="special">(</span><span class="identifier">BOOST_FLOAT64_C</span><span class="special">)</span>
  74 <span class="comment">// Can use boost::float64_t, usually type `double`, and sometimes also type `long double`.</span>
  75 <span class="preprocessor">#endif</span>
  76
  77 <span class="preprocessor">#if</span> <span class="identifier">defined</span><span class="special">(</span><span class="identifier">BOOST_FLOAT80_C</span><span class="special">)</span>
  78 <span class="comment">// Can use boost::float80_t, sometimes type `long double`.</span>
  79 <span class="preprocessor">#endif</span>
  80
  81 <span class="preprocessor">#if</span> <span class="identifier">defined</span><span class="special">(</span><span class="identifier">BOOST_FLOAT128_C</span><span class="special">)</span>
  82 <span class="comment">// Can use boost::float128_t. Sometimes type `__float128` or `_Quad`.</span>
  83 <span class="preprocessor">#endif</span>
  84 </pre>
  85 <p>
  86       This can be used to write code which will compile and run (albeit differently)
  87       on several platforms. Without these tests, if a width, say <code class="computeroutput"><span class="identifier">float128_t</span></code>
  88       is not supported, then compilation would fail. (It is, of course, rare for
  89       <code class="computeroutput"><span class="identifier">float64_t</span></code> or <code class="computeroutput"><span class="identifier">float32_t</span></code> not to be supported).
  90     </p>
  91 <p>
  92       The number of bits in just the significand can be determined using:
  93     </p>
  94 <pre class="programlisting"><span class="identifier">std</span><span class="special">::</span><span class="identifier">numeric_limits</span><span class="special">&lt;</span><span class="identifier">boost</span><span class="special">::</span><span class="identifier">floatmax_t</span><span class="special">&gt;::</span><span class="identifier">digits</span>
  95 </pre>
  96 <p>
  97       and from this one can safely infer the total number of bits because the type
  98       must be IEEE754 format, <code class="computeroutput"><span class="identifier">std</span><span class="special">::</span><span class="identifier">numeric_limits</span><span class="special">&lt;</span><span class="identifier">boost</span><span class="special">::</span><span class="identifier">floatmax_t</span><span class="special">&gt;::</span><span class="identifier">is_iec559</span>
  99       <span class="special">==</span> <span class="keyword">true</span></code>,
 100       so, for example, if <code class="computeroutput"><span class="identifier">std</span><span class="special">::</span><span class="identifier">numeric_limits</span><span class="special">&lt;</span><span class="identifier">boost</span><span class="special">::</span><span class="identifier">floatmax_t</span><span class="special">&gt;::</span><span class="identifier">digits</span> <span class="special">==</span> <span class="number">113</span></code>, then
 101       <code class="computeroutput"><span class="identifier">floatmax_t</span></code> must be<code class="computeroutput"> <span class="identifier">float128_t</span></code>.
 102     </p>
 103 <p>
 104       The <span class="bold"><strong>total</strong></span> number of bits using <code class="computeroutput"><span class="identifier">floatmax_t</span></code> can be found thus:
 105     </p>
 106 <pre class="programlisting"><span class="keyword">const</span> <span class="keyword">int</span> <span class="identifier">fpbits</span> <span class="special">=</span>
 107   <span class="special">(</span><span class="identifier">std</span><span class="special">::</span><span class="identifier">numeric_limits</span><span class="special">&lt;</span><span class="identifier">boost</span><span class="special">::</span><span class="identifier">floatmax_t</span><span class="special">&gt;::</span><span class="identifier">digits</span> <span class="special">==</span> <span class="number">113</span><span class="special">)</span> <span class="special">?</span> <span class="number">128</span> <span class="special">:</span>
 108   <span class="special">(</span><span class="identifier">std</span><span class="special">::</span><span class="identifier">numeric_limits</span><span class="special">&lt;</span><span class="identifier">boost</span><span class="special">::</span><span class="identifier">floatmax_t</span><span class="special">&gt;::</span><span class="identifier">digits</span> <span class="special">==</span> <span class="number">64</span><span class="special">)</span> <span class="special">?</span> <span class="number">80</span> <span class="special">:</span>
 109   <span class="special">(</span><span class="identifier">std</span><span class="special">::</span><span class="identifier">numeric_limits</span><span class="special">&lt;</span><span class="identifier">boost</span><span class="special">::</span><span class="identifier">floatmax_t</span><span class="special">&gt;::</span><span class="identifier">digits</span> <span class="special">==</span> <span class="number">53</span><span class="special">)</span> <span class="special">?</span> <span class="number">64</span> <span class="special">:</span>
 110   <span class="special">(</span><span class="identifier">std</span><span class="special">::</span><span class="identifier">numeric_limits</span><span class="special">&lt;</span><span class="identifier">boost</span><span class="special">::</span><span class="identifier">floatmax_t</span><span class="special">&gt;::</span><span class="identifier">digits</span> <span class="special">==</span> <span class="number">24</span><span class="special">)</span> <span class="special">?</span> <span class="number">32</span> <span class="special">:</span>
 111   <span class="special">(</span><span class="identifier">std</span><span class="special">::</span><span class="identifier">numeric_limits</span><span class="special">&lt;</span><span class="identifier">boost</span><span class="special">::</span><span class="identifier">floatmax_t</span><span class="special">&gt;::</span><span class="identifier">digits</span> <span class="special">==</span> <span class="number">11</span><span class="special">)</span> <span class="special">?</span> <span class="number">16</span> <span class="special">:</span>
 112   <span class="number">0</span><span class="special">;</span> <span class="comment">// Unknown - not IEEE754 format.</span>
 113  <span class="identifier">std</span><span class="special">::</span><span class="identifier">cout</span> <span class="special">&lt;&lt;</span> <span class="identifier">fpbits</span> <span class="special">&lt;&lt;</span> <span class="string">" bits."</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>
 114 </pre>
 115 <p>
 116       and the number of 'guaranteed' decimal digits using
 117     </p>
 118 <pre class="programlisting"><span class="identifier">std</span><span class="special">::</span><span class="identifier">numeric_limits</span><span class="special">&lt;</span><span class="identifier">boost</span><span class="special">::</span><span class="identifier">floatmax_t</span><span class="special">&gt;::</span><span class="identifier">digits10</span>
 119 </pre>
 120 <p>
 121       and the maximum number of possibly significant decimal digits using
 122     </p>
 123 <pre class="programlisting"><span class="identifier">std</span><span class="special">::</span><span class="identifier">numeric_limits</span><span class="special">&lt;</span><span class="identifier">boost</span><span class="special">::</span><span class="identifier">floatmax_t</span><span class="special">&gt;::</span><span class="identifier">max_digits10</span>
 124 </pre>
 125 <div class="tip"><table border="0" summary="Tip">
 126 <tr>
 127 <td rowspan="2" align="center" valign="top" width="25"><img alt="[Tip]" src="../../../../../doc/src/images/tip.png"></td>
 128 <th align="left">Tip</th>
 129 </tr>
 130 <tr><td align="left" valign="top"><p>
 131         <code class="computeroutput"><span class="identifier">max_digits10</span></code> is not always
 132         supported, but can be calculated at compile-time using the Kahan formula,
 133         <code class="computeroutput"><span class="number">2</span> <span class="special">+</span>
 134         <span class="identifier">binary_digits</span> <span class="special">*</span>
 135         <span class="number">0.3010</span></code> which can be calculated <span class="bold"><strong>at compile time</strong></span> using <code class="computeroutput"><span class="number">2</span>
 136         <span class="special">+</span> <span class="identifier">binary_digits</span>
 137         <span class="special">*</span> <span class="number">3010</span><span class="special">/</span><span class="number">10000</span></code>.
 138       </p></td></tr>
 139 </table></div>
 140 <div class="note"><table border="0" summary="Note">
 141 <tr>
 142 <td rowspan="2" align="center" valign="top" width="25"><img alt="[Note]" src="../../../../../doc/src/images/note.png"></td>
 143 <th align="left">Note</th>
 144 </tr>
 145 <tr><td align="left" valign="top">
 146 <p>
 147         One could test that
 148       </p>
 149 <p>
 150         std::is_same&lt;boost::floatmax_t, boost::float128_t&gt;::value == true
 151       </p>
 152 <p>
 153         but this would fail to compile on a platform where <code class="computeroutput"><span class="identifier">boost</span><span class="special">::</span><span class="identifier">float128_t</span></code>
 154         is not defined. So it is better to use the MACROs <code class="computeroutput"><span class="identifier">BOOST_FLOATnnn_C</span></code>.
 155       </p>
 156 </td></tr>
 157 </table></div>
 158 </div>
 159 <table xmlns:rev="http://www.cs.rpi.edu/~gregod/boost/tools/doc/revision" width="100%"><tr>
 160 <td align="left"></td>
 161 <td align="right"><div class="copyright-footer">Copyright &#169; 2006-2010, 2012-2014 Nikhar Agrawal,
 162       Anton Bikineev, Paul A. Bristow, Marco Guazzone, Christopher Kormanyos, Hubert
 163       Holin, Bruno Lalande, John Maddock, Jeremy Murphy, Johan R&#229;de, Gautam Sewani,
 164       Benjamin Sobotta, Thijs van den Berg, Daryle Walker and Xiaogang Zhang<p>
 165         Distributed under the Boost Software License, Version 1.0. (See accompanying
 166         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>)
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