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  27 <a name="math_toolkit.float128"></a><a class="link" href="float128.html" title="Implementation of Float128 type">Implementation of Float128 type</a>
  28 </h2></div></div></div>
  29 <div class="toc"><dl class="toc">
  30 <dt><span class="section"><a href="float128/overloading.html">Overloading template
  31       functions with float128_t</a></span></dt>
  32 <dt><span class="section"><a href="float128/exp_function.html">Exponential function</a></span></dt>
  33 <dt><span class="section"><a href="float128/typeinfo.html"><code class="computeroutput"><span class="identifier">typeinfo</span></code></a></span></dt>
  34 </dl></div>
  35 <p>
  36       Since few compilers implement a true 128-bit floating-point, and language features
  37       like the suffix Q (which may need an option <code class="computeroutput"><span class="special">-</span><span class="identifier">fext</span><span class="special">-</span><span class="identifier">numeric</span><span class="special">-</span><span class="identifier">literals</span></code>
  38       to enable), and C++ Standard library functions are as-yet missing or incomplete
  39       in C++11, this Boost.Math implementation wraps <code class="computeroutput"><span class="identifier">__float128</span></code>
  40       provided by the GCC compiler <a href="https://gcc.gnu.org/onlinedocs/gcc/Floating-Types.html" target="_top">GCC
  41       floating-point types</a> or the <code class="computeroutput"><span class="identifier">_Quad</span></code>
  42       type provided by the Intel compiler.
  43     </p>
  44 <p>
  45       This is provided to in order to demonstrate, and users to evaluate, the feasibility
  46       and benefits of higher-precision floating-point, especially to allow use of
  47       the full &lt;cmath&gt; and Boost.Math library of functions and distributions
  48       at high precision.
  49     </p>
  50 <p>
  51       (It is also possible to use Boost.Math with Boost.Multiprecision decimal and
  52       binary, but since these are entirely software solutions, allowing much higher
  53       precision or arbitrary precision, they are likely to be slower).
  54     </p>
  55 <p>
  56       We also provide (we believe full) support for <code class="computeroutput"><span class="special">&lt;</span><span class="identifier">limits</span><span class="special">&gt;,</span> <span class="special">&lt;</span><span class="identifier">cmath</span><span class="special">&gt;</span></code>, I/O stream operations in <code class="computeroutput"><span class="special">&lt;</span><span class="identifier">iostream</span><span class="special">&gt;</span></code>, and <code class="computeroutput"><span class="special">&lt;</span><span class="identifier">complex</span><span class="special">&gt;</span></code>.
  57     </p>
  58 <p>
  59       As a prototype for a future C++ standard, we place all these in <code class="computeroutput"><span class="keyword">namespace</span> <span class="identifier">std</span></code>.
  60       This contravenes the existing C++ standard of course, so selecting any compiler
  61       that promises to check conformance will fail.
  62     </p>
  63 <div class="tip"><table border="0" summary="Tip">
  64 <tr>
  65 <td rowspan="2" align="center" valign="top" width="25"><img alt="[Tip]" src="../../../../../doc/src/images/tip.png"></td>
  66 <th align="left">Tip</th>
  67 </tr>
  68 <tr><td align="left" valign="top"><p>
  69         For GCC, compile with <code class="computeroutput"><span class="special">-</span><span class="identifier">std</span><span class="special">=</span><span class="identifier">gnu</span><span class="special">++</span><span class="number">11</span></code> or <code class="computeroutput"><span class="special">-</span><span class="identifier">std</span><span class="special">=</span><span class="identifier">gnu</span><span class="special">++</span><span class="number">03</span></code> and do
  70         not use <code class="computeroutput"><span class="special">-</span><span class="identifier">std</span><span class="special">=</span><span class="identifier">stdc</span><span class="special">++</span><span class="number">11</span></code> or any 'strict' options, as these turn off
  71         full support for <code class="computeroutput"><span class="identifier">__float128</span></code>.
  72         These requirements also apply to the Intel compiler on Linux, for Intel on
  73         Windows you need to compile with <code class="computeroutput"><span class="special">-</span><span class="identifier">Qoption</span><span class="special">,</span><span class="identifier">cpp</span><span class="special">,--</span><span class="identifier">extended_float_type</span> <span class="special">-</span><span class="identifier">DBOOST_MATH_USE_FLOAT128</span></code> in order to activate
  74         128-bit floating point support.
  75       </p></td></tr>
  76 </table></div>
  77 <p>
  78       The <code class="computeroutput"><span class="identifier">__float128</span></code> type is provided
  79       by the <a href="http://gcc.gnu.org/onlinedocs/libquadmath/" target="_top">libquadmath
  80       library</a> on GCC or by Intel's FORTRAN library with Intel C++. They also
  81       provide a full set of <code class="computeroutput"><span class="special">&lt;</span><span class="identifier">cmath</span><span class="special">&gt;</span></code> functions in <code class="computeroutput"><span class="keyword">namespace</span>
  82       <span class="identifier">std</span></code>.
  83     </p>
  84 <h5>
  85 <a name="math_toolkit.float128.h0"></a>
  86       <span class="phrase"><a name="math_toolkit.float128.using_c_float128_quadmath_type"></a></span><a class="link" href="float128.html#math_toolkit.float128.using_c_float128_quadmath_type">Using
  87       C __float128 quadmath type</a>
  88     </h5>
  89 <p>
  90       The source code is at <a href="https://gcc.gnu.org/onlinedocs/gcc-9.1.0/libquadmath/quadmath_005fsnprintf.html#quadmath_005fsnprintf" target="_top">quadmath_snprintf.c</a>.
  91     </p>
  92 <h5>
  93 <a name="math_toolkit.float128.h1"></a>
  94       <span class="phrase"><a name="math_toolkit.float128.using_c_float128_quadmath_type0"></a></span><a class="link" href="float128.html#math_toolkit.float128.using_c_float128_quadmath_type0">Using
  95       C++ <code class="computeroutput"><span class="identifier">float128</span></code> quadmath type</a>
  96     </h5>
  97 <p>
  98       For C++ programs, you will want to use the C++ type <code class="computeroutput"><span class="identifier">float128</span></code>
  99     </p>
 100 <p>
 101       See example at <a href="../../../example/cstdfloat_example.cpp" target="_top">cstdfloat_example.cpp</a>.
 102     </p>
 103 <p>
 104       A typical invocation of the compiler is
 105     </p>
 106 <pre class="programlisting"><span class="identifier">g</span><span class="special">++</span> <span class="special">-</span><span class="identifier">O3</span> <span class="special">-</span><span class="identifier">std</span><span class="special">=</span><span class="identifier">gnu</span><span class="special">++</span><span class="number">11</span> <span class="identifier">test</span><span class="special">.</span><span class="identifier">cpp</span> <span class="special">-</span><span class="identifier">I</span><span class="special">/</span><span class="identifier">c</span><span class="special">/</span><span class="identifier">modular</span><span class="special">-</span><span class="identifier">boost</span> <span class="special">-</span><span class="identifier">lquadmath</span> <span class="special">-</span><span class="identifier">o</span> <span class="identifier">test</span><span class="special">.</span><span class="identifier">exe</span>
 107 </pre>
 108 <div class="tip"><table border="0" summary="Tip">
 109 <tr>
 110 <td rowspan="2" align="center" valign="top" width="25"><img alt="[Tip]" src="../../../../../doc/src/images/tip.png"></td>
 111 <th align="left">Tip</th>
 112 </tr>
 113 <tr><td align="left" valign="top"><p>
 114         If you are trying to use the develop branch of Boost.Math, then make <code class="computeroutput"><span class="special">-</span><span class="identifier">I</span><span class="special">/</span><span class="identifier">c</span><span class="special">/</span><span class="identifier">modular</span><span class="special">-</span><span class="identifier">boost</span><span class="special">/</span><span class="identifier">libs</span><span class="special">/</span><span class="identifier">math</span><span class="special">/</span><span class="identifier">include</span></code>
 115         the <span class="bold"><strong>first</strong></span> include directory.
 116       </p></td></tr>
 117 </table></div>
 118 <pre class="programlisting"><span class="identifier">g</span><span class="special">++</span> <span class="special">-</span><span class="identifier">O3</span> <span class="special">-</span><span class="identifier">std</span><span class="special">=</span><span class="identifier">gnu</span><span class="special">++</span><span class="number">11</span> <span class="identifier">test</span><span class="special">.</span><span class="identifier">cpp</span> <span class="special">-</span><span class="identifier">I</span><span class="special">/</span><span class="identifier">c</span><span class="special">/</span><span class="identifier">modular</span><span class="special">-</span><span class="identifier">boost</span><span class="special">/</span><span class="identifier">libs</span><span class="special">/</span><span class="identifier">math</span><span class="special">/</span><span class="identifier">include</span> <span class="special">-</span><span class="identifier">I</span><span class="special">/</span><span class="identifier">c</span><span class="special">/</span><span class="identifier">modular</span><span class="special">-</span><span class="identifier">boost</span> <span class="special">-</span><span class="identifier">lquadmath</span> <span class="special">-</span><span class="identifier">o</span> <span class="identifier">test</span><span class="special">.</span><span class="identifier">exe</span>
 119 </pre>
 120 <div class="note"><table border="0" summary="Note">
 121 <tr>
 122 <td rowspan="2" align="center" valign="top" width="25"><img alt="[Note]" src="../../../../../doc/src/images/note.png"></td>
 123 <th align="left">Note</th>
 124 </tr>
 125 <tr><td align="left" valign="top">
 126 <p>
 127         So far, the only missing detail that we had noted was in trying to use <code class="computeroutput"><span class="special">&lt;</span><span class="identifier">typeinfo</span><span class="special">&gt;</span></code>, for example for <code class="computeroutput"><span class="identifier">std</span><span class="special">::</span><span class="identifier">cout</span> <span class="special">&lt;&lt;</span> <span class="keyword">typeid</span><span class="special">&lt;</span><span class="identifier">__float_128</span><span class="special">&gt;.</span><span class="identifier">name</span><span class="special">();</span></code>.
 128       </p>
 129 <pre class="programlisting"><span class="identifier">Link</span> <span class="identifier">fails</span><span class="special">:</span> <span class="identifier">undefined</span> <span class="identifier">reference</span> <span class="identifier">to</span> <span class="identifier">typeinfo</span> <span class="keyword">for</span> <span class="identifier">__float128</span><span class="special">.</span>
 130 </pre>
 131 <p>
 132         See <a href="http://gcc.gnu.org/bugzilla/show_bug.cgi?id=43622" target="_top">GCC Bug
 133         43622 - no C++ typeinfo for __float128</a>. But this is reported (Marc
 134         Glisse 2015-04-04 ) fixed in GCC 5 (and above).
 135       </p>
 136 <p>
 137         For example, with GCC6.1.1 this works as expected to a <span class="bold"><strong>mangled</strong></span>
 138         string name, and output (if possible - not always).
 139       </p>
 140 <pre class="programlisting"><span class="keyword">const</span> <span class="identifier">std</span><span class="special">::</span><span class="identifier">type_info</span><span class="special">&amp;</span> <span class="identifier">tifu128</span> <span class="special">=</span> <span class="keyword">typeid</span><span class="special">(</span><span class="identifier">__float128</span><span class="special">);</span> <span class="comment">// OK.</span>
 141 <span class="comment">//std::cout &lt;&lt; tifu128.name() &lt;&lt; std::endl; // On GCC, aborts (because not printable string).</span>
 142 <span class="comment">//std::cout &lt;&lt; typeid(__float128).name() &lt;&lt; std::endl; // Aborts - string name cannot be output.</span>
 143
 144 <span class="keyword">const</span> <span class="identifier">std</span><span class="special">::</span><span class="identifier">type_info</span><span class="special">&amp;</span> <span class="identifier">tif128</span> <span class="special">=</span> <span class="keyword">typeid</span><span class="special">(</span><span class="identifier">float128</span><span class="special">);</span> <span class="comment">// OK.</span>
 145 <span class="identifier">std</span><span class="special">::</span><span class="identifier">cout</span> <span class="special">&lt;&lt;</span> <span class="identifier">tif128</span><span class="special">.</span><span class="identifier">name</span><span class="special">()</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> <span class="comment">// OK.</span>
 146 <span class="identifier">std</span><span class="special">::</span><span class="identifier">cout</span> <span class="special">&lt;&lt;</span> <span class="keyword">typeid</span><span class="special">(</span><span class="identifier">float128</span><span class="special">).</span><span class="identifier">name</span><span class="special">()</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> <span class="comment">// OK.</span>
 147
 148 <span class="keyword">const</span> <span class="identifier">std</span><span class="special">::</span><span class="identifier">type_info</span><span class="special">&amp;</span> <span class="identifier">tpi</span> <span class="special">=</span> <span class="keyword">typeid</span><span class="special">(</span><span class="identifier">pi1</span><span class="special">);</span> <span class="comment">// OK GCC 6.1.1 (from GCC 5 according to http://gcc.gnu.org/bugzilla/show_bug.cgi?id=43622)</span>
 149 <span class="identifier">std</span><span class="special">::</span><span class="identifier">cout</span> <span class="special">&lt;&lt;</span> <span class="identifier">tpi</span><span class="special">.</span><span class="identifier">name</span><span class="special">()</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> <span class="comment">// Output mangled name:</span>
 150
 151 <span class="comment">// N5boost14multiprecision6numberINS0_8backends16float128_backendELNS0_26expression_template_optionE0EEE</span>
 152 </pre>
 153 </td></tr>
 154 </table></div>
 155 </div>
 156 <table xmlns:rev="http://www.cs.rpi.edu/~gregod/boost/tools/doc/revision" width="100%"><tr>
 157 <td align="left"></td>
 158 <td align="right"><div class="copyright-footer">Copyright &#169; 2006-2019 Nikhar
 159       Agrawal, Anton Bikineev, Paul A. Bristow, Marco Guazzone, Christopher Kormanyos,
 160       Hubert Holin, Bruno Lalande, John Maddock, Jeremy Murphy, Matthew Pulver, Johan
 161       R&#229;de, Gautam Sewani, Benjamin Sobotta, Nicholas Thompson, Thijs van den Berg,
 162       Daryle Walker and Xiaogang Zhang<p>
 163         Distributed under the Boost Software License, Version 1.0. (See accompanying
 164         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>)
 165       </p>
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