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| 24 | </div> | |
| 25 | <div class="section"> | |
| 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"><</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">></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"><</span><span class="identifier">boost</span><span class="special">::</span><span class="identifier">floatmax_t</span><span class="special">>::</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"><</span><span class="identifier">boost</span><span class="special">::</span><span class="identifier">floatmax_t</span><span class="special">>::</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"><</span><span class="identifier">boost</span><span class="special">::</span><span class="identifier">floatmax_t</span><span class="special">>::</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"><</span><span class="identifier">boost</span><span class="special">::</span><span class="identifier">floatmax_t</span><span class="special">>::</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"><</span><span class="identifier">boost</span><span class="special">::</span><span class="identifier">floatmax_t</span><span class="special">>::</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"><</span><span class="identifier">boost</span><span class="special">::</span><span class="identifier">floatmax_t</span><span class="special">>::</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"><</span><span class="identifier">boost</span><span class="special">::</span><span class="identifier">floatmax_t</span><span class="special">>::</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"><</span><span class="identifier">boost</span><span class="special">::</span><span class="identifier">floatmax_t</span><span class="special">>::</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"><<</span> <span class="identifier">fpbits</span> <span class="special"><<</span> <span class="string">" bits."</span> <span class="special"><<</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"><</span><span class="identifier">boost</span><span class="special">::</span><span class="identifier">floatmax_t</span><span class="special">>::</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"><</span><span class="identifier">boost</span><span class="special">::</span><span class="identifier">floatmax_t</span><span class="special">>::</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<boost::floatmax_t, boost::float128_t>::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 © 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 Råde, 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>) | |
| 167 | </p> | |
| 168 | </div></td> | |
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