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<title>Exact-Width Floating-Point typedefs</title>
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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">&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>
      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 a way to test if a <span class="bold"><strong>specific
      width floating-point</strong></span> 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, perhaps a proposed __short_float.</span>
<span class="comment">// P0192R1, Adding Fundamental Type for Short Float,</span>
<span class="comment">// Boris Fomitchev, Sergei Nikolaev, Olivier Giroux, Lawrence Crowl, 2016 Feb14</span>
<span class="comment">// http://www.open-std.org/jtc1/sc22/wg14/www/docs/n2016.pdf</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, usually type `float`.</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, usually type `double`, and sometimes also type `long double`.</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, sometimes type `long double`.</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. Sometimes type `__float128` or `_Quad`.</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">&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>
</pre>
<p>
      and from this one can safely infer the total number of bits because the type
      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>
      <span class="special">==</span> <span class="keyword">true</span></code>,
      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
      <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">&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>
  <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>
  <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>
  <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>
  <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>
  <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">&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>
</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">&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>
</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">&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>
</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,
        <code class="computeroutput"><span class="number">2</span> <span class="special">+</span>
        <span class="identifier">binary_digits</span> <span class="special">*</span>
        <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>
        <span class="special">+</span> <span class="identifier">binary_digits</span>
        <span class="special">*</span> <span class="number">3010</span><span class="special">/</span><span class="number">10000</span></code>.
      </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>
</tr>
<tr><td align="left" valign="top">
<p>
        One could test that
      </p>
<p>
        std::is_same&lt;boost::floatmax_t, boost::float128_t&gt;::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 it is better to use the MACROs <code class="computeroutput"><span class="identifier">BOOST_FLOATnnn_C</span></code>.
      </p>
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        Distributed under the Boost Software License, Version 1.0. (See accompanying
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