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| <div class="titlepage"><div><div><h2 class="title" style="clear: both"> |
| <a name="math_toolkit.exact_typdefs"></a><a class="link" href="exact_typdefs.html" title="Exact-Width Floating-Point typedefs">Exact-Width Floating-Point |
| <code class="computeroutput"><span class="keyword">typedef</span></code>s</a> |
| </h2></div></div></div> |
| <p> |
| 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 |
| # replaced by the width, designates a floating-point type of exactly # bits. |
| For example <code class="computeroutput"><span class="identifier">float32_t</span></code> denotes |
| a single-precision floating-point type with approximately 7 decimal digits |
| of precision (equivalent to binary32 in <a href="http://en.wikipedia.org/wiki/IEEE_floating_point" target="_top">IEEE_floating_point</a>). |
| </p> |
| <p> |
| Floating-point types in C and C++ are specified to be allowed to have (optionally) |
| implementation-specific widths and formats. However, if a platform supports |
| underlying floating-point types (conformant with <a href="http://en.wikipedia.org/wiki/IEEE_floating_point" target="_top">IEEE_floating_point</a>) |
| with widths of 16, 32, 64, 80, 128 bits, or any combination thereof, then |
| <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> |
| does provide the corresponding <code class="computeroutput"><span class="keyword">typedef</span></code>s |
| <code class="computeroutput"><span class="identifier">float16_t</span><span class="special">,</span> |
| <span class="identifier">float32_t</span><span class="special">,</span> |
| <span class="identifier">float64_t</span><span class="special">,</span> |
| <span class="identifier">float80_t</span><span class="special">,</span> |
| <span class="identifier">float128_t</span><span class="special">,</span></code> |
| their corresponding least and fast types, and the corresponding maximum-width |
| type. |
| </p> |
| <h5> |
| <a name="math_toolkit.exact_typdefs.h0"></a> |
| <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 |
| tell which widths are supported</a> |
| </h5> |
| <p> |
| The definition (or not) of a <a class="link" href="macros.html" title="Floating-Point Constant Macros">floating-point |
| constant macro</a> is the way to test if a specific width is available on |
| a platform. |
| </p> |
| <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> |
| <span class="comment">// Can use boost::float16_t.</span> |
| <span class="preprocessor">#endif</span> |
| |
| <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> |
| <span class="comment">// Can use boost::float32_t.</span> |
| <span class="preprocessor">#endif</span> |
| |
| <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> |
| <span class="comment">// Can use boost::float64_t.</span> |
| <span class="preprocessor">#endif</span> |
| |
| <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> |
| <span class="comment">// Can use boost::float80_t.</span> |
| <span class="preprocessor">#endif</span> |
| |
| <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> |
| <span class="comment">// Can use boost::float128_t.</span> |
| <span class="preprocessor">#endif</span> |
| </pre> |
| <p> |
| This can be used to write code which will compile and run (albeit differently) |
| on several platforms. Without these tests, if a width, say <code class="computeroutput"><span class="identifier">float128_t</span></code> |
| is not supported, then compilation would fail. (It is of course, rare for |
| <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). |
| </p> |
| <p> |
| The number of bits in just the significand can be determined using: |
| </p> |
| <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> |
| </pre> |
| <p> |
| and from this one can safely infer the total number of bits because the type |
| must be IEEE754 format, 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 |
| <code class="computeroutput"><span class="identifier">floatmax_t</span></code> must be<code class="computeroutput"> <span class="identifier">float128_t</span></code>. |
| </p> |
| <p> |
| 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: |
| </p> |
| <pre class="programlisting"><span class="keyword">const</span> <span class="keyword">int</span> <span class="identifier">fpbits</span> <span class="special">=</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">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> |
| <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> |
| <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> |
| <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> |
| <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> |
| <span class="number">0</span><span class="special">;</span> <span class="comment">// Unknown - not IEEE754 format.</span> |
| <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> |
| </pre> |
| <p> |
| and the number of 'guaranteed' decimal digits using |
| </p> |
| <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> |
| </pre> |
| <p> |
| and the maximum number of possibly significant decimal digits using |
| </p> |
| <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> |
| </pre> |
| <div class="tip"><table border="0" summary="Tip"> |
| <tr> |
| <td rowspan="2" align="center" valign="top" width="25"><img alt="[Tip]" src="../../../../../doc/src/images/tip.png"></td> |
| <th align="left">Tip</th> |
| </tr> |
| <tr><td align="left" valign="top"><p> |
| <code class="computeroutput"><span class="identifier">max_digits10</span></code> is not always |
| supported, but can be calculated at compile-time using the Kahan formula. |
| </p></td></tr> |
| </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> |
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| <p> |
| One could test |
| </p> |
| <p> |
| std::is_same<boost::floatmax_t, boost::float128_t>::value == true |
| </p> |
| <p> |
| 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> |
| is not defined. So use the MACROs BOOST_FLOATnnn_C. |
| </p> |
| </td></tr> |
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| Thijs van den Berg, Daryle Walker and Xiaogang Zhang<p> |
| Distributed under the Boost Software License, Version 1.0. (See accompanying |
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