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<div class="titlepage"><div><div><h4 class="title">
<a name="boost_multiprecision.tut.floats.float128"></a><a class="link" href="float128.html" title="float128">float128</a>
</h4></div></div></div>
<p>
          <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>
        </p>
<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>

<span class="keyword">class</span> <span class="identifier">float128_backend</span><span class="special">;</span>

<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>

<span class="special">}}</span> <span class="comment">// namespaces</span>
</pre>
<p>
          The <code class="computeroutput"><span class="identifier">float128</span></code> number type
          is a very thin wrapper around GCC's <code class="computeroutput"><a class="link" href="float128.html" title="float128">float128</a></code>
          or Intel's <code class="computeroutput"><span class="identifier">_Quad</span></code> data types
          and provides an real-number type that is a drop-in replacement for the
          native C++ floating-point types, but with a 113 bit mantissa, and compatible
          with FORTRAN's 128-bit QUAD real.
        </p>
<p>
          All the usual standard library and <code class="computeroutput"><span class="identifier">numeric_limits</span></code>
          support are available, performance should be equivalent to the underlying
          native types: for example the LINPACK benchmarks for GCC's <code class="computeroutput"><a class="link" href="float128.html" title="float128">float128</a></code>
          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>.
        </p>
<p>
          As well as the usual conversions from arithmetic and string types, instances
          of <code class="computeroutput"><span class="identifier">float128</span></code> are copy constructible
          and assignable from GCC's <code class="computeroutput"><a class="link" href="float128.html" title="float128">float128</a></code>
          and Intel's <code class="computeroutput"><span class="identifier">_Quad</span></code> data
          types.
        </p>
<p>
          It's also possible to access the underlying <code class="computeroutput"><a class="link" href="float128.html" title="float128">float128</a></code>
          or <code class="computeroutput"><span class="identifier">_Quad</span></code> type via the
          <code class="computeroutput"><span class="identifier">data</span><span class="special">()</span></code>
          member function of <code class="computeroutput"><span class="identifier">float128_backend</span></code>.
        </p>
<p>
          Things you should know when using this type:
        </p>
<div class="itemizedlist"><ul class="itemizedlist" style="list-style-type: disc; ">
<li class="listitem">
              Default constructed <code class="computeroutput"><span class="identifier">float128</span></code>s
              have the value zero.
            </li>
<li class="listitem">
              This backend supports rvalue-references and is move-aware, making instantiations
              of <code class="computeroutput"><span class="identifier">number</span></code> on this backend
              move aware.
            </li>
<li class="listitem">
              This type is fully <code class="computeroutput"><span class="keyword">constexpr</span></code>
              aware - basic constexpr arithmetic is supported from C++14 and onwards,
              comparisons, plus the functions <code class="computeroutput"><span class="identifier">fabs</span></code>,
              <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>,
              <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>
              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>,
              or if the compiler is GCC.
            </li>
<li class="listitem">
              It is not possible to round-trip objects of this type to and from a
              string and get back exactly the same value when compiled with Intel's
              C++ compiler and using <code class="computeroutput"><span class="identifier">_Quad</span></code>
              as the underlying type: this is a current limitation of our code. Round
              tripping when using <code class="computeroutput"><a class="link" href="float128.html" title="float128">float128</a></code>
              as the underlying type is possible (both for GCC and Intel).
            </li>
<li class="listitem">
              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>
              being thrown if the string can not be interpreted as a valid floating-point
              number.
            </li>
<li class="listitem">
              Division by zero results in an infinity being produced.
            </li>
<li class="listitem">
              Type <code class="computeroutput"><span class="identifier">float128</span></code> can be
              used as a literal type (constexpr support).
            </li>
<li class="listitem">
              Type <code class="computeroutput"><span class="identifier">float128</span></code> can be
              used for full <code class="computeroutput"><span class="keyword">constexpr</span></code>
              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>,
              <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>,
              <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>,
              but the transcendental functions are not.
            </li>
<li class="listitem">
              When using the Intel compiler, the underlying type defaults to <code class="computeroutput"><a class="link" href="float128.html" title="float128">float128</a></code>
              if it's available and <code class="computeroutput"><span class="identifier">_Quad</span></code>
              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>.
            </li>
<li class="listitem">
              When the underlying type is Intel's <code class="computeroutput"><span class="identifier">_Quad</span></code>
              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>.
            </li>
<li class="listitem">
              When compiling with <code class="computeroutput"><span class="identifier">gcc</span></code>,
              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>,
              as the suffix 'Q' is a GNU extension. Compilation fails with the flag
              <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>.
            </li>
</ul></div>
<h6>
<a name="boost_multiprecision.tut.floats.float128.h0"></a>
          <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
          example:</a>
        </h6>
<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>
<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>
<span class="preprocessor">#include</span> <span class="special">&lt;</span><span class="identifier">iostream</span><span class="special">&gt;</span>

<span class="keyword">int</span> <span class="identifier">main</span><span class="special">()</span>
<span class="special">{</span>
   <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>

   <span class="comment">// Operations at 128-bit precision and full numeric_limits support:</span>
   <span class="identifier">float128</span> <span class="identifier">b</span> <span class="special">=</span> <span class="number">2</span><span class="special">;</span>
   <span class="comment">// There are 113-bits of precision:</span>
   <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>
   <span class="comment">// Or 34 decimal places:</span>
   <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>
   <span class="comment">// We can use any C++ std lib function, lets print all the digits as well:</span>
   <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>
      <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>
   <span class="comment">// We can also use any function from Boost.Math:</span>
   <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>
   <span class="comment">// And since we have an extended exponent range we can generate some really large </span>
   <span class="comment">// numbers here (4.02387260077093773543702433923004111e+2564):</span>
   <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>
   <span class="comment">//</span>
   <span class="comment">// We can declare constants using GCC or Intel's native types, and the Q suffix,</span>
   <span class="comment">// these can be declared constexpr if required:</span>

   <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>

   <span class="keyword">return</span> <span class="number">0</span><span class="special">;</span>
<span class="special">}</span>
</pre>
<div class="footnotes">
<br><hr style="width:100; text-align:left;margin-left: 0">
<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>
            On 64-bit Ubuntu 11.10, GCC-4.8.0, Intel Core 2 Duo T5800.
          </p></div>
</div>
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<td align="right"><div class="copyright-footer">Copyright &#169; 2002-2019 John Maddock
      and Christopher Kormanyos<p>
        Distributed under the Boost Software License, Version 1.0. (See accompanying
        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>)
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