1<html> 2<head> 3<meta http-equiv="Content-Type" content="text/html; charset=UTF-8"> 4<title>float128</title> 5<link rel="stylesheet" href="../../../multiprecision.css" type="text/css"> 6<meta name="generator" content="DocBook XSL Stylesheets V1.79.1"> 7<link rel="home" href="../../../index.html" title="Chapter 1. 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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> 24</div> 25<div class="section"> 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"><</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> 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"><</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> 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"><span class="identifier">__float128</span></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">std</span><span class="special">::</span><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"><span class="identifier">__float128</span></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> 52 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"><span class="identifier">__float128</span></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"><span class="identifier">__float128</span></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"><span class="identifier">__float128</span></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"><span class="identifier">__float128</span></code> if it's available and 119 <code class="computeroutput"><span class="identifier">_Quad</span></code> if not. You can 120 override the default by defining either <code class="computeroutput"><span class="identifier">BOOST_MP_USE_FLOAT128</span></code> 121 or <code class="computeroutput"><span class="identifier">BOOST_MP_USE_QUAD</span></code>. 122 </li> 123<li class="listitem"> 124 When the underlying type is Intel's <code class="computeroutput"><span class="identifier">_Quad</span></code> 125 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>. 126 </li> 127<li class="listitem"> 128 When compiling with <code class="computeroutput"><span class="identifier">gcc</span></code>, 129 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>, 130 as the suffix 'Q' is a GNU extension. Compilation fails with the flag 131 <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>. 132 </li> 133<li class="listitem"> 134 You will need to link to <code class="computeroutput"><span class="identifier">libquadmath</span><span class="special">.</span><span class="identifier">dll</span></code> 135 with the link command <code class="computeroutput"><span class="special">-</span><span class="identifier">lquadmath</span></code> and ensure that the DLL 136 is visible by the linker. If you are using the B2/bjam build system 137 then commands<code class="computeroutput"><span class="special"><</span><span class="identifier">linkflags</span><span class="special">>-</span><span class="identifier">lQUADMATH</span></code> 138 and <code class="computeroutput"><span class="special"><</span><span class="identifier">linkflags</span><span class="special">>-</span><span class="identifier">L</span><span class="string">"path/to/lib"</span></code> will be needed. 139 </li> 140<li class="listitem"> 141 The values shown by <code class="computeroutput"><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></code> and extremely close <span class="emphasis"><em>but 142 not identical</em></span> to those from the equivalent precision and 143 range multiprecision types <code class="computeroutput"><span class="identifier">std</span><span class="special">::</span><span class="identifier">numeric_limits</span><span class="special"><</span><span class="identifier">cpp_bin_float_quad</span><span class="special">></span></code> and <code class="computeroutput"><span class="identifier">std</span><span class="special">::</span><span class="identifier">numeric_limits</span><span class="special"><</span><span class="identifier">cpp_dec_float_quad</span><span class="special">></span></code>. 144 </li> 145</ul></div> 146<h6> 147<a name="boost_multiprecision.tut.floats.float128.h0"></a> 148 <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 149 example:</a> 150 </h6> 151<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> 152<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> 153<span class="preprocessor">#include</span> <span class="special"><</span><span class="identifier">iostream</span><span class="special">></span> 154 155<span class="keyword">int</span> <span class="identifier">main</span><span class="special">()</span> 156<span class="special">{</span> 157 <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">// Potential to cause name collisions?</span> 158 <span class="comment">// using boost::multiprecision::float128; // is safer.</span> 159</pre> 160<p> 161 The type float128 provides operations at 128-bit precision with <a href="https://en.wikipedia.org/wiki/Quadruple-precision_floating-point_format#IEEE_754_quadruple-precision_binary_floating-point_format:_binary128" target="_top">Quadruple-precision 162 floating-point format</a> and have full <code class="computeroutput"><span class="identifier">std</span><span class="special">::</span><span class="identifier">numeric_limits</span></code> 163 support: 164 </p> 165<pre class="programlisting"><span class="identifier">float128</span> <span class="identifier">b</span> <span class="special">=</span> <span class="number">2</span><span class="special">;</span> 166</pre> 167<p> 168 There are 15 bits of (biased) binary exponent and 113-bits of significand 169 precision 170 </p> 171<pre class="programlisting"><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> 172</pre> 173<p> 174 or 33 decimal places: 175 </p> 176<pre class="programlisting"><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> 177</pre> 178<p> 179 We can use any C++ std library function, so let's show all the at-most 180 36 potentially significant digits, and any trailing zeros, as well: 181 </p> 182<pre class="programlisting"> <span class="identifier">std</span><span class="special">::</span><span class="identifier">cout</span><span class="special">.</span><span class="identifier">setf</span><span class="special">(</span><span class="identifier">std</span><span class="special">::</span><span class="identifier">ios_base</span><span class="special">::</span><span class="identifier">showpoint</span><span class="special">);</span> <span class="comment">// Include any trailing zeros.</span> 183<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> 184 <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">// Shows log(2) = 0.693147180559945309417232121458176575</span> 185</pre> 186<p> 187 We can also use any function from Boost.Math, for example, the 'true gamma' 188 function <code class="computeroutput"><span class="identifier">tgamma</span></code>: 189 </p> 190<pre class="programlisting"><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> 191</pre> 192<p> 193 And since we have an extended exponent range, we can generate some really 194 large numbers here (4.02387260077093773543702433923004111e+2564): 195 </p> 196<pre class="programlisting"><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> 197</pre> 198<p> 199 We can declare constants using GCC or Intel's native types, and literals 200 with the Q suffix, and these can be declared <code class="computeroutput"><span class="keyword">constexpr</span></code> 201 if required: 202 </p> 203<pre class="programlisting"><span class="comment">// std::numeric_limits<float128>::max_digits10 = 36</span> 204<span class="keyword">constexpr</span> <span class="identifier">float128</span> <span class="identifier">pi</span> <span class="special">=</span> <span class="number">3.14159265358979323846264338327950288</span><span class="identifier">Q</span><span class="special">;</span> 205<span class="identifier">std</span><span class="special">::</span><span class="identifier">cout</span><span class="special">.</span><span class="identifier">precision</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> 206<span class="identifier">std</span><span class="special">::</span><span class="identifier">cout</span> <span class="special"><<</span> <span class="string">"pi = "</span> <span class="special"><<</span> <span class="identifier">pi</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">//pi = 3.14159265358979323846264338327950280</span> 207</pre> 208<p> 209 Values for <code class="computeroutput"><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></code> 210 are: 211 </p> 212<pre class="programlisting"><span class="identifier">GCC</span> <span class="number">8.1</span><span class="special">.</span><span class="number">0</span> 213 214<span class="identifier">Type</span> <span class="identifier">name</span> <span class="identifier">is</span> <span class="identifier">float128_t</span><span class="special">:</span> 215<span class="identifier">Type</span> <span class="identifier">is</span> <span class="identifier">g</span> 216<span class="identifier">std</span><span class="special">::</span><span class="identifier">is_fundamental</span><span class="special"><></span> <span class="special">=</span> <span class="keyword">true</span> 217<span class="identifier">std</span><span class="special">::</span><span class="identifier">is_signed</span><span class="special"><></span> <span class="special">=</span> <span class="keyword">true</span> 218<span class="identifier">std</span><span class="special">::</span><span class="identifier">is_unsigned</span><span class="special"><></span> <span class="special">=</span> <span class="keyword">false</span> 219<span class="identifier">std</span><span class="special">::</span><span class="identifier">is_integral</span><span class="special"><></span> <span class="special">=</span> <span class="keyword">false</span> 220<span class="identifier">std</span><span class="special">::</span><span class="identifier">is_arithmetic</span><span class="special"><></span> <span class="special">=</span> <span class="keyword">true</span> 221<span class="identifier">std</span><span class="special">::</span><span class="identifier">is_const</span><span class="special"><></span> <span class="special">=</span> <span class="keyword">false</span> 222<span class="identifier">std</span><span class="special">::</span><span class="identifier">is_trivial</span><span class="special"><></span> <span class="special">=</span> <span class="keyword">true</span> 223<span class="identifier">std</span><span class="special">::</span><span class="identifier">is_standard_layout</span><span class="special"><></span> <span class="special">=</span> <span class="keyword">true</span> 224<span class="identifier">std</span><span class="special">::</span><span class="identifier">is_pod</span><span class="special"><></span> <span class="special">=</span> <span class="keyword">true</span> 225<span class="identifier">std</span><span class="special">::</span><span class="identifier">numeric_limits</span><span class="special">::<></span><span class="identifier">is_exact</span> <span class="special">=</span> <span class="keyword">false</span> 226<span class="identifier">std</span><span class="special">::</span><span class="identifier">numeric_limits</span><span class="special">::<></span><span class="identifier">is</span> <span class="identifier">bounded</span> <span class="special">=</span> <span class="keyword">true</span> 227<span class="identifier">std</span><span class="special">::</span><span class="identifier">numeric_limits</span><span class="special">::<></span><span class="identifier">is_modulo</span> <span class="special">=</span> <span class="keyword">false</span> 228<span class="identifier">std</span><span class="special">::</span><span class="identifier">numeric_limits</span><span class="special">::<></span><span class="identifier">is_iec559</span> <span class="special">=</span> <span class="keyword">true</span> 229<span class="identifier">std</span><span class="special">::</span><span class="identifier">numeric_limits</span><span class="special">::<></span><span class="identifier">traps</span> <span class="special">=</span> <span class="keyword">false</span> 230<span class="identifier">std</span><span class="special">::</span><span class="identifier">numeric_limits</span><span class="special">::<></span><span class="identifier">tinyness_before</span> <span class="special">=</span> <span class="keyword">false</span> 231<span class="identifier">std</span><span class="special">::</span><span class="identifier">numeric_limits</span><span class="special">::<></span><span class="identifier">max</span><span class="special">()</span> <span class="special">=</span> <span class="number">1.18973149535723176508575932662800702e+4932</span> 232<span class="identifier">std</span><span class="special">::</span><span class="identifier">numeric_limits</span><span class="special">::<></span><span class="identifier">min</span><span class="special">()</span> <span class="special">=</span> <span class="number">3.36210314311209350626267781732175260e-4932</span> 233<span class="identifier">std</span><span class="special">::</span><span class="identifier">numeric_limits</span><span class="special">::<></span><span class="identifier">lowest</span><span class="special">()</span> <span class="special">=</span> <span class="special">-</span><span class="number">1.18973149535723176508575932662800702e+4932</span> 234<span class="identifier">std</span><span class="special">::</span><span class="identifier">numeric_limits</span><span class="special">::<></span><span class="identifier">min_exponent</span> <span class="special">=</span> <span class="special">-</span><span class="number">16381</span> 235<span class="identifier">std</span><span class="special">::</span><span class="identifier">numeric_limits</span><span class="special">::<></span><span class="identifier">max_exponent</span> <span class="special">=</span> <span class="number">16384</span> 236<span class="identifier">std</span><span class="special">::</span><span class="identifier">numeric_limits</span><span class="special">::<></span><span class="identifier">epsilon</span><span class="special">()</span> <span class="special">=</span> <span class="number">1.92592994438723585305597794258492732e-34</span> 237<span class="identifier">std</span><span class="special">::</span><span class="identifier">numeric_limits</span><span class="special">::<></span><span class="identifier">radix</span> <span class="special">=</span> <span class="number">2</span> 238<span class="identifier">std</span><span class="special">::</span><span class="identifier">numeric_limits</span><span class="special">::<></span><span class="identifier">digits</span> <span class="special">=</span> <span class="number">113</span> 239<span class="identifier">std</span><span class="special">::</span><span class="identifier">numeric_limits</span><span class="special">::<></span><span class="identifier">digits10</span> <span class="special">=</span> <span class="number">33</span> 240<span class="identifier">std</span><span class="special">::</span><span class="identifier">numeric_limits</span><span class="special">::<></span><span class="identifier">max_digits10</span> <span class="special">=</span> <span class="number">36</span> 241<span class="identifier">std</span><span class="special">::</span><span class="identifier">numeric_limits</span><span class="special">::<></span><span class="identifier">has</span> <span class="identifier">denorm</span> <span class="special">=</span> <span class="keyword">true</span> 242<span class="identifier">std</span><span class="special">::</span><span class="identifier">numeric_limits</span><span class="special">::<></span><span class="identifier">denorm</span> <span class="identifier">min</span> <span class="special">=</span> <span class="number">6.47517511943802511092443895822764655e-4966</span> 243<span class="identifier">std</span><span class="special">::</span><span class="identifier">denorm_loss</span> <span class="special">=</span> <span class="keyword">false</span> 244<span class="identifier">limits</span><span class="special">::</span><span class="identifier">has_signaling_NaN</span> <span class="special">==</span> <span class="keyword">false</span> 245<span class="identifier">std</span><span class="special">::</span><span class="identifier">numeric_limits</span><span class="special">::<></span><span class="identifier">quiet_NaN</span> <span class="special">=</span> <span class="identifier">nan</span> 246<span class="identifier">std</span><span class="special">::</span><span class="identifier">numeric_limits</span><span class="special">::<></span><span class="identifier">infinity</span> <span class="special">=</span> <span class="identifier">inf</span> 247</pre> 248<div class="footnotes"> 249<br><hr style="width:100; text-align:left;margin-left: 0"> 250<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> 251 On 64-bit Ubuntu 11.10, GCC-4.8.0, Intel Core 2 Duo T5800. 252 </p></div> 253</div> 254</div> 255<table xmlns:rev="http://www.cs.rpi.edu/~gregod/boost/tools/doc/revision" width="100%"><tr> 256<td align="left"></td> 257<td align="right"><div class="copyright-footer">Copyright © 2002-2020 John 258 Maddock and Christopher Kormanyos<p> 259 Distributed under the Boost Software License, Version 1.0. (See accompanying 260 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>) 261 </p> 262</div></td> 263</tr></table> 264<hr> 265<div class="spirit-nav"> 266<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> 267</div> 268</body> 269</html> 270
