191 lines
19 KiB
HTML
191 lines
19 KiB
HTML
<html>
|
|
<head>
|
|
<meta http-equiv="Content-Type" content="text/html; charset=US-ASCII">
|
|
<title>float128</title>
|
|
<link rel="stylesheet" href="../../../multiprecision.css" type="text/css">
|
|
<meta name="generator" content="DocBook XSL Stylesheets V1.79.1">
|
|
<link rel="home" href="../../../index.html" title="Chapter 1. Boost.Multiprecision">
|
|
<link rel="up" href="../floats.html" title="floating-point Numbers">
|
|
<link rel="prev" href="mpfr_float.html" title="mpfr_float">
|
|
<link rel="next" href="fp_eg.html" title="Examples">
|
|
</head>
|
|
<body bgcolor="white" text="black" link="#0000FF" vlink="#840084" alink="#0000FF">
|
|
<table cellpadding="2" width="100%"><tr>
|
|
<td valign="top"><img alt="Boost C++ Libraries" width="277" height="86" src="../../../../../../../boost.png"></td>
|
|
<td align="center"><a href="../../../../../../../index.html">Home</a></td>
|
|
<td align="center"><a href="../../../../../../../libs/libraries.htm">Libraries</a></td>
|
|
<td align="center"><a href="http://www.boost.org/users/people.html">People</a></td>
|
|
<td align="center"><a href="http://www.boost.org/users/faq.html">FAQ</a></td>
|
|
<td align="center"><a href="../../../../../../../more/index.htm">More</a></td>
|
|
</tr></table>
|
|
<hr>
|
|
<div class="spirit-nav">
|
|
<a accesskey="p" href="mpfr_float.html"><img src="../../../../../../../doc/src/images/prev.png" alt="Prev"></a><a accesskey="u" href="../floats.html"><img src="../../../../../../../doc/src/images/up.png" alt="Up"></a><a accesskey="h" href="../../../index.html"><img src="../../../../../../../doc/src/images/home.png" alt="Home"></a><a accesskey="n" href="fp_eg.html"><img src="../../../../../../../doc/src/images/next.png" alt="Next"></a>
|
|
</div>
|
|
<div class="section">
|
|
<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"><</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">></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"><</span><span class="identifier">float128_backend</span><span class="special">,</span> <span class="identifier">et_off</span><span class="special">></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"><</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">></span>
|
|
<span class="preprocessor">#include</span> <span class="special"><</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">></span>
|
|
<span class="preprocessor">#include</span> <span class="special"><</span><span class="identifier">iostream</span><span class="special">></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"><<</span> <span class="identifier">std</span><span class="special">::</span><span class="identifier">numeric_limits</span><span class="special"><</span><span class="identifier">float128</span><span class="special">>::</span><span class="identifier">digits</span> <span class="special"><<</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"><<</span> <span class="identifier">std</span><span class="special">::</span><span class="identifier">numeric_limits</span><span class="special"><</span><span class="identifier">float128</span><span class="special">>::</span><span class="identifier">digits10</span> <span class="special"><<</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"><<</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"><</span><span class="identifier">float128</span><span class="special">>::</span><span class="identifier">max_digits10</span><span class="special">)</span>
|
|
<span class="special"><<</span> <span class="identifier">log</span><span class="special">(</span><span class="identifier">b</span><span class="special">)</span> <span class="special"><<</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"><<</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"><<</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"><<</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"><<</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>
|
|
</div>
|
|
<table xmlns:rev="http://www.cs.rpi.edu/~gregod/boost/tools/doc/revision" width="100%"><tr>
|
|
<td align="left"></td>
|
|
<td align="right"><div class="copyright-footer">Copyright © 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>)
|
|
</p>
|
|
</div></td>
|
|
</tr></table>
|
|
<hr>
|
|
<div class="spirit-nav">
|
|
<a accesskey="p" href="mpfr_float.html"><img src="../../../../../../../doc/src/images/prev.png" alt="Prev"></a><a accesskey="u" href="../floats.html"><img src="../../../../../../../doc/src/images/up.png" alt="Up"></a><a accesskey="h" href="../../../index.html"><img src="../../../../../../../doc/src/images/home.png" alt="Home"></a><a accesskey="n" href="fp_eg.html"><img src="../../../../../../../doc/src/images/next.png" alt="Next"></a>
|
|
</div>
|
|
</body>
|
|
</html>
|