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  26 <div class="titlepage"><div><div><h4 class="title">
  27 <a name="boost_multiprecision.tut.floats.float128"></a><a class="link" href="float128.html" title="float128">float128</a>
  28 </h4></div></div></div>
  29 <p>
  30           <code class="computeroutput"><span class="preprocessor">#include</span> <span class="special">&lt;</span><span class="identifier">boost</span><span class="special">/</span><span class="identifier">multiprecision</span><span class="special">/</span><span class="identifier">float128</span><span class="special">.</span><span class="identifier">hpp</span><span class="special">&gt;</span></code>
  31         </p>
  32 <pre class="programlisting"><span class="keyword">namespace</span> <span class="identifier">boost</span><span class="special">{</span> <span class="keyword">namespace</span> <span class="identifier">multiprecision</span><span class="special">{</span>
  33
  34 <span class="keyword">class</span> <span class="identifier">float128_backend</span><span class="special">;</span>
  35
  36 <span class="keyword">typedef</span> <span class="identifier">number</span><span class="special">&lt;</span><span class="identifier">float128_backend</span><span class="special">,</span> <span class="identifier">et_off</span><span class="special">&gt;</span>    <span class="identifier">float128</span><span class="special">;</span>
  37
  38 <span class="special">}}</span> <span class="comment">// namespaces</span>
  39 </pre>
  40 <p>
  41           The <code class="computeroutput"><span class="identifier">float128</span></code> number type
  42           is a very thin wrapper around GCC's <code class="computeroutput"><a class="link" href="float128.html" title="float128">float128</a></code>
  43           or Intel's <code class="computeroutput"><span class="identifier">_Quad</span></code> data types
  44           and provides an real-number type that is a drop-in replacement for the
  45           native C++ floating-point types, but with a 113 bit mantissa, and compatible
  46           with FORTRAN's 128-bit QUAD real.
  47         </p>
  48 <p>
  49           All the usual standard library and <code class="computeroutput"><span class="identifier">numeric_limits</span></code>
  50           support are available, performance should be equivalent to the underlying
  51           native types: for example the LINPACK benchmarks for GCC's <code class="computeroutput"><a class="link" href="float128.html" title="float128">float128</a></code>
  52           and <code class="computeroutput"><span class="identifier">boost</span><span class="special">::</span><span class="identifier">multiprecision</span><span class="special">::</span><span class="identifier">float128</span></code> both achieved 5.6 MFLOPS<a href="#ftn.boost_multiprecision.tut.floats.float128.f0" class="footnote" name="boost_multiprecision.tut.floats.float128.f0"><sup class="footnote">[3]</sup></a>.
  53         </p>
  54 <p>
  55           As well as the usual conversions from arithmetic and string types, instances
  56           of <code class="computeroutput"><span class="identifier">float128</span></code> are copy constructible
  57           and assignable from GCC's <code class="computeroutput"><a class="link" href="float128.html" title="float128">float128</a></code>
  58           and Intel's <code class="computeroutput"><span class="identifier">_Quad</span></code> data
  59           types.
  60         </p>
  61 <p>
  62           It's also possible to access the underlying <code class="computeroutput"><a class="link" href="float128.html" title="float128">float128</a></code>
  63           or <code class="computeroutput"><span class="identifier">_Quad</span></code> type via the
  64           <code class="computeroutput"><span class="identifier">data</span><span class="special">()</span></code>
  65           member function of <code class="computeroutput"><span class="identifier">float128_backend</span></code>.
  66         </p>
  67 <p>
  68           Things you should know when using this type:
  69         </p>
  70 <div class="itemizedlist"><ul class="itemizedlist" style="list-style-type: disc; ">
  71 <li class="listitem">
  72               Default constructed <code class="computeroutput"><span class="identifier">float128</span></code>s
  73               have the value zero.
  74             </li>
  75 <li class="listitem">
  76               This backend supports rvalue-references and is move-aware, making instantiations
  77               of <code class="computeroutput"><span class="identifier">number</span></code> on this backend
  78               move aware.
  79             </li>
  80 <li class="listitem">
  81               This type is fully <code class="computeroutput"><span class="keyword">constexpr</span></code>
  82               aware - basic constexpr arithmetic is supported from C++14 and onwards,
  83               comparisons, plus the functions <code class="computeroutput"><span class="identifier">fabs</span></code>,
  84               <code class="computeroutput"><span class="identifier">abs</span></code>, <code class="computeroutput"><span class="identifier">fpclassify</span></code>, <code class="computeroutput"><span class="identifier">isnormal</span></code>,
  85               <code class="computeroutput"><span class="identifier">isfinite</span></code>, <code class="computeroutput"><span class="identifier">isinf</span></code> and <code class="computeroutput"><span class="identifier">isnan</span></code>
  86               are also supported if either the compiler implements C++20's <code class="computeroutput"><span class="identifier">std</span><span class="special">::</span><span class="identifier">is_constant_evaluated</span><span class="special">()</span></code>,
  87               or if the compiler is GCC.
  88             </li>
  89 <li class="listitem">
  90               It is not possible to round-trip objects of this type to and from a
  91               string and get back exactly the same value when compiled with Intel's
  92               C++ compiler and using <code class="computeroutput"><span class="identifier">_Quad</span></code>
  93               as the underlying type: this is a current limitation of our code. Round
  94               tripping when using <code class="computeroutput"><a class="link" href="float128.html" title="float128">float128</a></code>
  95               as the underlying type is possible (both for GCC and Intel).
  96             </li>
  97 <li class="listitem">
  98               Conversion from a string results in a <code class="computeroutput"><span class="identifier">std</span><span class="special">::</span><span class="identifier">runtime_error</span></code>
  99               being thrown if the string can not be interpreted as a valid floating-point
 100               number.
 101             </li>
 102 <li class="listitem">
 103               Division by zero results in an infinity being produced.
 104             </li>
 105 <li class="listitem">
 106               Type <code class="computeroutput"><span class="identifier">float128</span></code> can be
 107               used as a literal type (constexpr support).
 108             </li>
 109 <li class="listitem">
 110               Type <code class="computeroutput"><span class="identifier">float128</span></code> can be
 111               used for full <code class="computeroutput"><span class="keyword">constexpr</span></code>
 112               arithmetic from C++14 and later with GCC. The functions <code class="computeroutput"><span class="identifier">abs</span></code>, <code class="computeroutput"><span class="identifier">fabs</span></code>,
 113               <code class="computeroutput"><span class="identifier">fpclassify</span></code>, <code class="computeroutput"><span class="identifier">isnan</span></code>, <code class="computeroutput"><span class="identifier">isinf</span></code>,
 114               <code class="computeroutput"><span class="identifier">isfinite</span></code> and <code class="computeroutput"><span class="identifier">isnormal</span></code> are also <code class="computeroutput"><span class="keyword">constexpr</span></code>,
 115               but the transcendental functions are not.
 116             </li>
 117 <li class="listitem">
 118               When using the Intel compiler, the underlying type defaults to <code class="computeroutput"><a class="link" href="float128.html" title="float128">float128</a></code>
 119               if it's available and <code class="computeroutput"><span class="identifier">_Quad</span></code>
 120               if not. You can override the default by defining either <code class="computeroutput"><span class="identifier">BOOST_MP_USE_FLOAT128</span></code> or <code class="computeroutput"><span class="identifier">BOOST_MP_USE_QUAD</span></code>.
 121             </li>
 122 <li class="listitem">
 123               When the underlying type is Intel's <code class="computeroutput"><span class="identifier">_Quad</span></code>
 124               type, the code must be compiled with the compiler option <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></code>.
 125             </li>
 126 <li class="listitem">
 127               When compiling with <code class="computeroutput"><span class="identifier">gcc</span></code>,
 128               you need to use the flag <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><span class="special">/</span><span class="number">14</span><span class="special">/</span><span class="number">17</span></code>,
 129               as the suffix 'Q' is a GNU extension. Compilation fails with the flag
 130               <code class="computeroutput"><span class="special">--</span><span class="identifier">std</span><span class="special">=</span><span class="identifier">c</span><span class="special">++</span><span class="number">11</span><span class="special">/</span><span class="number">14</span><span class="special">/</span><span class="number">17</span></code> unless you also use <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>.
 131             </li>
 132 </ul></div>
 133 <h6>
 134 <a name="boost_multiprecision.tut.floats.float128.h0"></a>
 135           <span class="phrase"><a name="boost_multiprecision.tut.floats.float128.float128_example"></a></span><a class="link" href="float128.html#boost_multiprecision.tut.floats.float128.float128_example">float128
 136           example:</a>
 137         </h6>
 138 <pre class="programlisting"><span class="preprocessor">#include</span> <span class="special">&lt;</span><span class="identifier">boost</span><span class="special">/</span><span class="identifier">multiprecision</span><span class="special">/</span><span class="identifier">float128</span><span class="special">.</span><span class="identifier">hpp</span><span class="special">&gt;</span>
 139 <span class="preprocessor">#include</span> <span class="special">&lt;</span><span class="identifier">boost</span><span class="special">/</span><span class="identifier">math</span><span class="special">/</span><span class="identifier">special_functions</span><span class="special">/</span><span class="identifier">gamma</span><span class="special">.</span><span class="identifier">hpp</span><span class="special">&gt;</span>
 140 <span class="preprocessor">#include</span> <span class="special">&lt;</span><span class="identifier">iostream</span><span class="special">&gt;</span>
 141
 142 <span class="keyword">int</span> <span class="identifier">main</span><span class="special">()</span>
 143 <span class="special">{</span>
 144    <span class="keyword">using</span> <span class="keyword">namespace</span> <span class="identifier">boost</span><span class="special">::</span><span class="identifier">multiprecision</span><span class="special">;</span>
 145
 146    <span class="comment">// Operations at 128-bit precision and full numeric_limits support:</span>
 147    <span class="identifier">float128</span> <span class="identifier">b</span> <span class="special">=</span> <span class="number">2</span><span class="special">;</span>
 148    <span class="comment">// There are 113-bits of precision:</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">std</span><span class="special">::</span><span class="identifier">numeric_limits</span><span class="special">&lt;</span><span class="identifier">float128</span><span class="special">&gt;::</span><span class="identifier">digits</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>
 150    <span class="comment">// Or 34 decimal places:</span>
 151    <span class="identifier">std</span><span class="special">::</span><span class="identifier">cout</span> <span class="special">&lt;&lt;</span> <span class="identifier">std</span><span class="special">::</span><span class="identifier">numeric_limits</span><span class="special">&lt;</span><span class="identifier">float128</span><span class="special">&gt;::</span><span class="identifier">digits10</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>
 152    <span class="comment">// We can use any C++ std lib function, lets print all the digits as well:</span>
 153    <span class="identifier">std</span><span class="special">::</span><span class="identifier">cout</span> <span class="special">&lt;&lt;</span> <span class="identifier">std</span><span class="special">::</span><span class="identifier">setprecision</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">float128</span><span class="special">&gt;::</span><span class="identifier">max_digits10</span><span class="special">)</span>
 154       <span class="special">&lt;&lt;</span> <span class="identifier">log</span><span class="special">(</span><span class="identifier">b</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">// print log(2) = 0.693147180559945309417232121458176575</span>
 155    <span class="comment">// We can also use any function from Boost.Math:</span>
 156    <span class="identifier">std</span><span class="special">::</span><span class="identifier">cout</span> <span class="special">&lt;&lt;</span> <span class="identifier">boost</span><span class="special">::</span><span class="identifier">math</span><span class="special">::</span><span class="identifier">tgamma</span><span class="special">(</span><span class="identifier">b</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>
 157    <span class="comment">// And since we have an extended exponent range we can generate some really large </span>
 158    <span class="comment">// numbers here (4.02387260077093773543702433923004111e+2564):</span>
 159    <span class="identifier">std</span><span class="special">::</span><span class="identifier">cout</span> <span class="special">&lt;&lt;</span> <span class="identifier">boost</span><span class="special">::</span><span class="identifier">math</span><span class="special">::</span><span class="identifier">tgamma</span><span class="special">(</span><span class="identifier">float128</span><span class="special">(</span><span class="number">1000</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>
 160    <span class="comment">//</span>
 161    <span class="comment">// We can declare constants using GCC or Intel's native types, and the Q suffix,</span>
 162    <span class="comment">// these can be declared constexpr if required:</span>
 163
 164    <span class="keyword">constexpr</span> <span class="identifier">float128</span> <span class="identifier">pi</span> <span class="special">=</span> <span class="number">3.1415926535897932384626433832795028841971693993751058</span><span class="identifier">Q</span><span class="special">;</span>
 165
 166    <span class="keyword">return</span> <span class="number">0</span><span class="special">;</span>
 167 <span class="special">}</span>
 168 </pre>
 169 <div class="footnotes">
 170 <br><hr style="width:100; text-align:left;margin-left: 0">
 171 <div id="ftn.boost_multiprecision.tut.floats.float128.f0" class="footnote"><p><a href="#boost_multiprecision.tut.floats.float128.f0" class="para"><sup class="para">[3] </sup></a>
 172             On 64-bit Ubuntu 11.10, GCC-4.8.0, Intel Core 2 Duo T5800.
 173           </p></div>
 174 </div>
 175 </div>
 176 <table xmlns:rev="http://www.cs.rpi.edu/~gregod/boost/tools/doc/revision" width="100%"><tr>
 177 <td align="left"></td>
 178 <td align="right"><div class="copyright-footer">Copyright &#169; 2002-2019 John Maddock
 179       and Christopher Kormanyos<p>
 180         Distributed under the Boost Software License, Version 1.0. (See accompanying
 181         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>)
 182       </p>
 183 </div></td>
 184 </tr></table>
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