1<html> 2<head> 3<meta http-equiv="Content-Type" content="text/html; charset=UTF-8"> 4<title>mpfi_float</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. Boost.Multiprecision"> 8<link rel="up" href="../interval.html" title="Interval Number Types"> 9<link rel="prev" href="../interval.html" title="Interval Number Types"> 10<link rel="next" href="../complex.html" title="Complex Number Types"> 11</head> 12<body bgcolor="white" text="black" link="#0000FF" vlink="#840084" alink="#0000FF"> 13<table cellpadding="2" width="100%"><tr> 14<td valign="top"><img alt="Boost C++ Libraries" width="277" height="86" src="../../../../../../../boost.png"></td> 15<td align="center"><a href="../../../../../../../index.html">Home</a></td> 16<td align="center"><a href="../../../../../../../libs/libraries.htm">Libraries</a></td> 17<td align="center"><a href="http://www.boost.org/users/people.html">People</a></td> 18<td align="center"><a href="http://www.boost.org/users/faq.html">FAQ</a></td> 19<td align="center"><a href="../../../../../../../more/index.htm">More</a></td> 20</tr></table> 21<hr> 22<div class="spirit-nav"> 23<a accesskey="p" href="../interval.html"><img src="../../../../../../../doc/src/images/prev.png" alt="Prev"></a><a accesskey="u" href="../interval.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="../complex.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.interval.mpfi"></a><a class="link" href="mpfi.html" title="mpfi_float">mpfi_float</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">mpfi</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">template</span> <span class="special"><</span><span class="keyword">unsigned</span> <span class="identifier">Digits10</span><span class="special">></span> 35<span class="keyword">class</span> <span class="identifier">mpfi_float_backend</span><span class="special">;</span> 36 37<span class="keyword">typedef</span> <span class="identifier">number</span><span class="special"><</span><span class="identifier">mpfi_float_backend</span><span class="special"><</span><span class="number">50</span><span class="special">></span> <span class="special">></span> <span class="identifier">mpfi_float_50</span><span class="special">;</span> 38<span class="keyword">typedef</span> <span class="identifier">number</span><span class="special"><</span><span class="identifier">mpfi_float_backend</span><span class="special"><</span><span class="number">100</span><span class="special">></span> <span class="special">></span> <span class="identifier">mpfifloat_100</span><span class="special">;</span> 39<span class="keyword">typedef</span> <span class="identifier">number</span><span class="special"><</span><span class="identifier">mpfi_float_backend</span><span class="special"><</span><span class="number">500</span><span class="special">></span> <span class="special">></span> <span class="identifier">mpfifloat_500</span><span class="special">;</span> 40<span class="keyword">typedef</span> <span class="identifier">number</span><span class="special"><</span><span class="identifier">mpfi_float_backend</span><span class="special"><</span><span class="number">1000</span><span class="special">></span> <span class="special">></span> <span class="identifier">mpfi_float_1000</span><span class="special">;</span> 41<span class="keyword">typedef</span> <span class="identifier">number</span><span class="special"><</span><span class="identifier">mpfi_float_backend</span><span class="special"><</span><span class="number">0</span><span class="special">></span> <span class="special">></span> <span class="identifier">mpfi_float</span><span class="special">;</span> 42 43<span class="special">}}</span> <span class="comment">// namespaces</span> 44</pre> 45<p> 46 The <code class="computeroutput"><span class="identifier">mpfi_float_backend</span></code> 47 type is used in conjunction with <code class="computeroutput"><span class="identifier">number</span></code>: 48 It acts as a thin wrapper around the <a href="http://perso.ens-lyon.fr/nathalie.revol/software.html" target="_top">MPFI</a> 49 <code class="computeroutput"><span class="identifier">mpfi_t</span></code> to provide an real-number 50 type that is a drop-in replacement for the native C++ floating-point types, 51 but with much greater precision and implementing interval arithmetic. 52 </p> 53<p> 54 Type <code class="computeroutput"><span class="identifier">mpfi_float_backend</span></code> 55 can be used at fixed precision by specifying a non-zero <code class="computeroutput"><span class="identifier">Digits10</span></code> 56 template parameter, or at variable precision by setting the template argument 57 to zero. The <code class="computeroutput"><span class="keyword">typedef</span></code>s <code class="computeroutput"><span class="identifier">mpfi_float_50</span></code>, <code class="computeroutput"><span class="identifier">mpfi_float_100</span></code>, 58 <code class="computeroutput"><span class="identifier">mpfi_float_500</span></code>, <code class="computeroutput"><span class="identifier">mpfi_float_1000</span></code> provide arithmetic types 59 at 50, 100, 500 and 1000 decimal digits precision respectively. The <code class="computeroutput"><span class="keyword">typedef</span> <span class="identifier">mpfi_float</span></code> 60 provides a variable precision type whose precision can be controlled via 61 theF <code class="computeroutput"><span class="identifier">number</span></code>s member functions. 62 </p> 63<div class="note"><table border="0" summary="Note"> 64<tr> 65<td rowspan="2" align="center" valign="top" width="25"><img alt="[Note]" src="../../../../../../../doc/src/images/note.png"></td> 66<th align="left">Note</th> 67</tr> 68<tr><td align="left" valign="top"><p> 69 This type only provides <code class="computeroutput"><span class="identifier">numeric_limits</span></code> 70 support when the precision is fixed at compile time. 71 </p></td></tr> 72</table></div> 73<p> 74 As well as the usual conversions from arithmetic and string types, instances 75 of <code class="computeroutput"><span class="identifier">number</span><span class="special"><</span><span class="identifier">mpfi_float_backend</span><span class="special"><</span><span class="identifier">N</span><span class="special">></span> <span class="special">></span></code> are copy constructible and assignable 76 from: 77 </p> 78<div class="itemizedlist"><ul class="itemizedlist" style="list-style-type: disc; "> 79<li class="listitem"> 80 The <a href="http://perso.ens-lyon.fr/nathalie.revol/software.html" target="_top">MPFI</a> 81 native type <code class="computeroutput"><span class="identifier">mpfi_t</span></code>. 82 </li> 83<li class="listitem"> 84 The <code class="computeroutput"><span class="identifier">number</span></code> wrappers 85 around <a href="http://perso.ens-lyon.fr/nathalie.revol/software.html" target="_top">MPFI</a> 86 or <a href="http://www.mpfr.org" target="_top">MPFR</a>: <code class="computeroutput"><span class="identifier">number</span><span class="special"><</span><span class="identifier">mpfi_float_backend</span><span class="special"><</span><span class="identifier">M</span><span class="special">></span> <span class="special">></span></code> 87 and <code class="computeroutput"><span class="identifier">number</span><span class="special"><</span><span class="identifier">mpfr_float</span><span class="special"><</span><span class="identifier">M</span><span class="special">></span> <span class="special">></span></code>. 88 </li> 89<li class="listitem"> 90 There is a two argument constructor taking two <code class="computeroutput"><span class="identifier">number</span><span class="special"><</span><span class="identifier">mpfr_float</span><span class="special"><</span><span class="identifier">M</span><span class="special">></span> <span class="special">></span></code> 91 arguments specifying the interval. 92 </li> 93</ul></div> 94<p> 95 It's also possible to access the underlying <code class="computeroutput"><span class="identifier">mpfi_t</span></code> 96 via the <code class="computeroutput"><span class="identifier">data</span><span class="special">()</span></code> 97 member function of <code class="computeroutput"><span class="identifier">mpfi_float_backend</span></code>. 98 </p> 99<p> 100 Things you should know when using this type: 101 </p> 102<div class="itemizedlist"><ul class="itemizedlist" style="list-style-type: disc; "> 103<li class="listitem"> 104 A default constructed <code class="computeroutput"><span class="identifier">mpfi_float_backend</span></code> 105 is set to zero (<span class="emphasis"><em>Note that this is <span class="bold"><strong>not</strong></span> 106 the default <a href="http://perso.ens-lyon.fr/nathalie.revol/software.html" target="_top">MPFI</a> 107 behavior</em></span>). 108 </li> 109<li class="listitem"> 110 No changes are made to <a href="http://gmplib.org" target="_top">GMP</a> or 111 <a href="http://www.mpfr.org" target="_top">MPFR</a> global settings, so this 112 type can coexist with existing <a href="http://www.mpfr.org" target="_top">MPFR</a> 113 or <a href="http://gmplib.org" target="_top">GMP</a> code. 114 </li> 115<li class="listitem"> 116 The code can equally use <a href="http://mpir.org/" target="_top">MPIR</a> 117 in place of <a href="http://gmplib.org" target="_top">GMP</a> - indeed that 118 is the preferred option on Win32. 119 </li> 120<li class="listitem"> 121 This backend supports rvalue-references and is move-aware, making instantiations 122 of <code class="computeroutput"><span class="identifier">number</span></code> on this backend 123 move aware. 124 </li> 125<li class="listitem"> 126 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> 127 being thrown if the string can not be interpreted as a valid floating-point 128 number. 129 </li> 130<li class="listitem"> 131 Division by zero results in an infinity. 132 </li> 133</ul></div> 134<p> 135 There are some additional non member functions for working on intervals: 136 </p> 137<pre class="programlisting"><span class="keyword">template</span> <span class="special"><</span><span class="keyword">unsigned</span> <span class="identifier">Digits10</span><span class="special">,</span> <span class="identifier">expression_template_option</span> <span class="identifier">ExpressionTemplates</span><span class="special">></span> 138<span class="identifier">number</span><span class="special"><</span><span class="identifier">mpfr_float_backend</span><span class="special"><</span><span class="identifier">Digits10</span><span class="special">>,</span> <span class="identifier">ExpressionTemplates</span><span class="special">></span> <span class="identifier">lower</span><span class="special">(</span><span class="keyword">const</span> <span class="identifier">number</span><span class="special"><</span><span class="identifier">mpfi_float_backend</span><span class="special"><</span><span class="identifier">Digits10</span><span class="special">>,</span> <span class="identifier">ExpressionTemplates</span><span class="special">>&</span> <span class="identifier">val</span><span class="special">);</span> 139</pre> 140<p> 141 Returns the lower end of the interval. 142 </p> 143<pre class="programlisting"><span class="keyword">template</span> <span class="special"><</span><span class="keyword">unsigned</span> <span class="identifier">Digits10</span><span class="special">,</span> <span class="identifier">expression_template_option</span> <span class="identifier">ExpressionTemplates</span><span class="special">></span> 144<span class="identifier">number</span><span class="special"><</span><span class="identifier">mpfr_float_backend</span><span class="special"><</span><span class="identifier">Digits10</span><span class="special">>,</span> <span class="identifier">ExpressionTemplates</span><span class="special">></span> <span class="identifier">upper</span><span class="special">(</span><span class="keyword">const</span> <span class="identifier">number</span><span class="special"><</span><span class="identifier">mpfi_float_backend</span><span class="special"><</span><span class="identifier">Digits10</span><span class="special">>,</span> <span class="identifier">ExpressionTemplates</span><span class="special">>&</span> <span class="identifier">val</span><span class="special">);</span> 145</pre> 146<p> 147 Returns the upper end of the interval. 148 </p> 149<pre class="programlisting"><span class="keyword">template</span> <span class="special"><</span><span class="keyword">unsigned</span> <span class="identifier">Digits10</span><span class="special">,</span> <span class="identifier">expression_template_option</span> <span class="identifier">ExpressionTemplates</span><span class="special">></span> 150<span class="identifier">number</span><span class="special"><</span><span class="identifier">mpfr_float_backend</span><span class="special"><</span><span class="identifier">Digits10</span><span class="special">>,</span> <span class="identifier">ExpressionTemplates</span><span class="special">></span> <span class="identifier">median</span><span class="special">(</span><span class="keyword">const</span> <span class="identifier">number</span><span class="special"><</span><span class="identifier">mpfi_float_backend</span><span class="special"><</span><span class="identifier">Digits10</span><span class="special">>,</span> <span class="identifier">ExpressionTemplates</span><span class="special">>&</span> <span class="identifier">val</span><span class="special">);</span> 151</pre> 152<p> 153 Returns the mid point of the interval. 154 </p> 155<pre class="programlisting"><span class="keyword">template</span> <span class="special"><</span><span class="keyword">unsigned</span> <span class="identifier">Digits10</span><span class="special">,</span> <span class="identifier">expression_template_option</span> <span class="identifier">ExpressionTemplates</span><span class="special">></span> 156<span class="identifier">number</span><span class="special"><</span><span class="identifier">mpfr_float_backend</span><span class="special"><</span><span class="identifier">Digits10</span><span class="special">>,</span> <span class="identifier">ExpressionTemplates</span><span class="special">></span> <span class="identifier">width</span><span class="special">(</span><span class="keyword">const</span> <span class="identifier">number</span><span class="special"><</span><span class="identifier">mpfi_float_backend</span><span class="special"><</span><span class="identifier">Digits10</span><span class="special">>,</span> <span class="identifier">ExpressionTemplates</span><span class="special">>&</span> <span class="identifier">val</span><span class="special">);</span> 157</pre> 158<p> 159 Returns the absolute width of the interval. 160 </p> 161<pre class="programlisting"><span class="keyword">template</span> <span class="special"><</span><span class="keyword">unsigned</span> <span class="identifier">Digits10</span><span class="special">,</span> <span class="identifier">expression_template_option</span> <span class="identifier">ExpressionTemplates</span><span class="special">></span> 162<span class="identifier">number</span><span class="special"><</span><span class="identifier">mpfi_float_backend</span><span class="special"><</span><span class="identifier">Digits10</span><span class="special">>,</span> <span class="identifier">ExpressionTemplates</span><span class="special">></span> <span class="identifier">intersect</span><span class="special">(</span> 163 <span class="keyword">const</span> <span class="identifier">number</span><span class="special"><</span><span class="identifier">mpfi_float_backend</span><span class="special"><</span><span class="identifier">Digits10</span><span class="special">>,</span> <span class="identifier">ExpressionTemplates</span><span class="special">>&</span> <span class="identifier">a</span><span class="special">,</span> 164 <span class="keyword">const</span> <span class="identifier">number</span><span class="special"><</span><span class="identifier">mpfi_float_backend</span><span class="special"><</span><span class="identifier">Digits10</span><span class="special">>,</span> <span class="identifier">ExpressionTemplates</span><span class="special">>&</span> <span class="identifier">b</span><span class="special">);</span> 165</pre> 166<p> 167 Returns the interval which is the intersection of the <span class="emphasis"><em>a</em></span> 168 and <span class="emphasis"><em>b</em></span>. Returns an unspecified empty interval if there 169 is no such intersection. 170 </p> 171<pre class="programlisting"><span class="keyword">template</span> <span class="special"><</span><span class="keyword">unsigned</span> <span class="identifier">Digits10</span><span class="special">,</span> <span class="identifier">expression_template_option</span> <span class="identifier">ExpressionTemplates</span><span class="special">></span> 172<span class="identifier">number</span><span class="special"><</span><span class="identifier">mpfi_float_backend</span><span class="special"><</span><span class="identifier">Digits10</span><span class="special">>,</span> <span class="identifier">ExpressionTemplates</span><span class="special">></span> <span class="identifier">hull</span><span class="special">(</span> 173 <span class="keyword">const</span> <span class="identifier">number</span><span class="special"><</span><span class="identifier">mpfi_float_backend</span><span class="special"><</span><span class="identifier">Digits10</span><span class="special">>,</span> <span class="identifier">ExpressionTemplates</span><span class="special">>&</span> <span class="identifier">a</span><span class="special">,</span> 174 <span class="keyword">const</span> <span class="identifier">number</span><span class="special"><</span><span class="identifier">mpfi_float_backend</span><span class="special"><</span><span class="identifier">Digits10</span><span class="special">>,</span> <span class="identifier">ExpressionTemplates</span><span class="special">>&</span> <span class="identifier">b</span><span class="special">);</span> 175</pre> 176<p> 177 Returns the interval which is the union of <span class="emphasis"><em>a</em></span> and 178 <span class="emphasis"><em>b</em></span>. 179 </p> 180<pre class="programlisting"><span class="keyword">template</span> <span class="special"><</span><span class="keyword">unsigned</span> <span class="identifier">Digits10</span><span class="special">,</span> <span class="identifier">expression_template_option</span> <span class="identifier">ExpressionTemplates</span><span class="special">></span> 181<span class="keyword">bool</span> <span class="identifier">overlap</span><span class="special">(</span><span class="keyword">const</span> <span class="identifier">number</span><span class="special"><</span><span class="identifier">mpfi_float_backend</span><span class="special"><</span><span class="identifier">Digits10</span><span class="special">>,</span> <span class="identifier">ExpressionTemplates</span><span class="special">>&</span> <span class="identifier">a</span><span class="special">,</span> 182 <span class="keyword">const</span> <span class="identifier">number</span><span class="special"><</span><span class="identifier">mpfi_float_backend</span><span class="special"><</span><span class="identifier">Digits10</span><span class="special">>,</span> <span class="identifier">ExpressionTemplates</span><span class="special">>&</span> <span class="identifier">b</span><span class="special">);</span> 183</pre> 184<p> 185 Returns <code class="computeroutput"><span class="keyword">true</span></code> only if the intervals 186 <span class="emphasis"><em>a</em></span> and <span class="emphasis"><em>b</em></span> overlap. 187 </p> 188<pre class="programlisting"><span class="keyword">template</span> <span class="special"><</span><span class="keyword">unsigned</span> <span class="identifier">Digits10</span><span class="special">,</span> <span class="identifier">expression_template_option</span> <span class="identifier">ExpressionTemplates1</span><span class="special">,</span> <span class="identifier">expression_template_option</span> <span class="identifier">ExpressionTemplates2</span><span class="special">></span> 189<span class="keyword">bool</span> <span class="identifier">in</span><span class="special">(</span><span class="keyword">const</span> <span class="identifier">number</span><span class="special"><</span><span class="identifier">mpfr_float_backend</span><span class="special"><</span><span class="identifier">Digits10</span><span class="special">>,</span> <span class="identifier">ExpressionTemplates1</span><span class="special">>&</span> <span class="identifier">a</span><span class="special">,</span> 190 <span class="keyword">const</span> <span class="identifier">number</span><span class="special"><</span><span class="identifier">mpfi_float_backend</span><span class="special"><</span><span class="identifier">Digits10</span><span class="special">>,</span> <span class="identifier">ExpressionTemplates2</span><span class="special">>&</span> <span class="identifier">b</span><span class="special">);</span> 191</pre> 192<p> 193 Returns <code class="computeroutput"><span class="keyword">true</span></code> only if point 194 <span class="emphasis"><em>a</em></span> is contained within the interval <span class="emphasis"><em>b</em></span>. 195 </p> 196<pre class="programlisting"><span class="keyword">template</span> <span class="special"><</span><span class="keyword">unsigned</span> <span class="identifier">Digits10</span><span class="special">,</span> <span class="identifier">expression_template_option</span> <span class="identifier">ExpressionTemplates</span><span class="special">></span> 197<span class="keyword">bool</span> <span class="identifier">zero_in</span><span class="special">(</span><span class="keyword">const</span> <span class="identifier">number</span><span class="special"><</span><span class="identifier">mpfi_float_backend</span><span class="special"><</span><span class="identifier">Digits10</span><span class="special">>,</span> <span class="identifier">ExpressionTemplates</span><span class="special">>&</span> <span class="identifier">a</span><span class="special">);</span> 198</pre> 199<p> 200 Returns <code class="computeroutput"><span class="keyword">true</span></code> only if the interval 201 <span class="emphasis"><em>a</em></span> contains the value zero. 202 </p> 203<pre class="programlisting"><span class="keyword">template</span> <span class="special"><</span><span class="keyword">unsigned</span> <span class="identifier">Digits10</span><span class="special">,</span> <span class="identifier">expression_template_option</span> <span class="identifier">ExpressionTemplates</span><span class="special">></span> 204<span class="keyword">bool</span> <span class="identifier">subset</span><span class="special">(</span><span class="keyword">const</span> <span class="identifier">number</span><span class="special"><</span><span class="identifier">mpfi_float_backend</span><span class="special"><</span><span class="identifier">Digits10</span><span class="special">>,</span> <span class="identifier">ExpressionTemplates</span><span class="special">>&</span> <span class="identifier">a</span><span class="special">,</span> 205 <span class="keyword">const</span> <span class="identifier">number</span><span class="special"><</span><span class="identifier">mpfi_float_backend</span><span class="special"><</span><span class="identifier">Digits10</span><span class="special">>,</span> <span class="identifier">ExpressionTemplates</span><span class="special">>&</span> <span class="identifier">b</span><span class="special">);</span> 206</pre> 207<p> 208 Returns <code class="computeroutput"><span class="keyword">true</span></code> only if <span class="emphasis"><em>a</em></span> 209 is a subset of <span class="emphasis"><em>b</em></span>. 210 </p> 211<pre class="programlisting"><span class="keyword">template</span> <span class="special"><</span><span class="keyword">unsigned</span> <span class="identifier">Digits10</span><span class="special">,</span> <span class="identifier">expression_template_option</span> <span class="identifier">ExpressionTemplates</span><span class="special">></span> 212<span class="keyword">bool</span> <span class="identifier">proper_subset</span><span class="special">(</span><span class="keyword">const</span> <span class="identifier">number</span><span class="special"><</span><span class="identifier">mpfi_float_backend</span><span class="special"><</span><span class="identifier">Digits10</span><span class="special">>,</span> <span class="identifier">ExpressionTemplates</span><span class="special">>&</span> <span class="identifier">a</span><span class="special">,</span> 213 <span class="keyword">const</span> <span class="identifier">number</span><span class="special"><</span><span class="identifier">mpfi_float_backend</span><span class="special"><</span><span class="identifier">Digits10</span><span class="special">>,</span> <span class="identifier">ExpressionTemplates</span><span class="special">>&</span> <span class="identifier">b</span><span class="special">);</span> 214</pre> 215<p> 216 Returns <code class="computeroutput"><span class="keyword">true</span></code> only if <span class="emphasis"><em>a</em></span> 217 is a proper subset of <span class="emphasis"><em>b</em></span>. 218 </p> 219<pre class="programlisting"><span class="keyword">template</span> <span class="special"><</span><span class="keyword">unsigned</span> <span class="identifier">Digits10</span><span class="special">,</span> <span class="identifier">expression_template_option</span> <span class="identifier">ExpressionTemplates</span><span class="special">></span> 220<span class="keyword">bool</span> <span class="identifier">empty</span><span class="special">(</span><span class="keyword">const</span> <span class="identifier">number</span><span class="special"><</span><span class="identifier">mpfi_float_backend</span><span class="special"><</span><span class="identifier">Digits10</span><span class="special">>,</span> <span class="identifier">ExpressionTemplates</span><span class="special">>&</span> <span class="identifier">a</span><span class="special">);</span> 221</pre> 222<p> 223 Returns <code class="computeroutput"><span class="keyword">true</span></code> only if <span class="emphasis"><em>a</em></span> 224 is an empty interval, equivalent to <code class="computeroutput"><span class="identifier">upper</span><span class="special">(</span><span class="identifier">a</span><span class="special">)</span> 225 <span class="special"><</span> <span class="identifier">lower</span><span class="special">(</span><span class="identifier">a</span><span class="special">)</span></code>. 226 </p> 227<pre class="programlisting"><span class="keyword">template</span> <span class="special"><</span><span class="keyword">unsigned</span> <span class="identifier">Digits10</span><span class="special">,</span> <span class="identifier">expression_template_option</span> <span class="identifier">ExpressionTemplates</span><span class="special">></span> 228<span class="keyword">bool</span> <span class="identifier">singleton</span><span class="special">(</span><span class="keyword">const</span> <span class="identifier">number</span><span class="special"><</span><span class="identifier">mpfi_float_backend</span><span class="special"><</span><span class="identifier">Digits10</span><span class="special">>,</span> <span class="identifier">ExpressionTemplates</span><span class="special">>&</span> <span class="identifier">a</span><span class="special">);</span> 229</pre> 230<p> 231 Returns <code class="computeroutput"><span class="keyword">true</span></code> if <code class="computeroutput"><span class="identifier">lower</span><span class="special">(</span><span class="identifier">a</span><span class="special">)</span> <span class="special">==</span> 232 <span class="identifier">upper</span><span class="special">(</span><span class="identifier">a</span><span class="special">)</span></code>. 233 </p> 234<h6> 235<a name="boost_multiprecision.tut.interval.mpfi.h0"></a> 236 <span class="phrase"><a name="boost_multiprecision.tut.interval.mpfi.mpfi_example"></a></span><a class="link" href="mpfi.html#boost_multiprecision.tut.interval.mpfi.mpfi_example"> MPFI 237 example:</a> 238 </h6> 239<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">mpfi</span><span class="special">.</span><span class="identifier">hpp</span><span class="special">></span> 240<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> 241<span class="preprocessor">#include</span> <span class="special"><</span><span class="identifier">iostream</span><span class="special">></span> 242 243<span class="keyword">int</span> <span class="identifier">main</span><span class="special">()</span> 244<span class="special">{</span> 245 <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> 246 247 <span class="comment">// Operations at variable precision and no numeric_limits support:</span> 248 <span class="identifier">mpfi_float</span> <span class="identifier">a</span> <span class="special">=</span> <span class="number">2</span><span class="special">;</span> 249 <span class="identifier">mpfi_float</span><span class="special">::</span><span class="identifier">default_precision</span><span class="special">(</span><span class="number">1000</span><span class="special">);</span> 250 <span class="identifier">std</span><span class="special">::</span><span class="identifier">cout</span> <span class="special"><<</span> <span class="identifier">mpfi_float</span><span class="special">::</span><span class="identifier">default_precision</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> 251 <span class="identifier">std</span><span class="special">::</span><span class="identifier">cout</span> <span class="special"><<</span> <span class="identifier">sqrt</span><span class="special">(</span><span class="identifier">a</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 root-2</span> 252 253 <span class="comment">// Operations at fixed precision and full numeric_limits support:</span> 254 <span class="identifier">mpfi_float_100</span> <span class="identifier">b</span> <span class="special">=</span> <span class="number">2</span><span class="special">;</span> 255 <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">mpfi_float_100</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> 256 <span class="comment">// We can use any C++ std lib function:</span> 257 <span class="identifier">std</span><span class="special">::</span><span class="identifier">cout</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)</span> 258 259 <span class="comment">// Access the underlying data:</span> 260 <span class="identifier">mpfi_t</span> <span class="identifier">r</span><span class="special">;</span> 261 <span class="identifier">mpfi_init</span><span class="special">(</span><span class="identifier">r</span><span class="special">);</span> 262 <span class="identifier">mpfi_set</span><span class="special">(</span><span class="identifier">r</span><span class="special">,</span> <span class="identifier">b</span><span class="special">.</span><span class="identifier">backend</span><span class="special">().</span><span class="identifier">data</span><span class="special">());</span> 263 264 <span class="comment">// Construct some explicit intervals and perform set operations:</span> 265 <span class="identifier">mpfi_float_50</span> <span class="identifier">i1</span><span class="special">(</span><span class="number">1</span><span class="special">,</span> <span class="number">2</span><span class="special">),</span> <span class="identifier">i2</span><span class="special">(</span><span class="number">1.5</span><span class="special">,</span> <span class="number">2.5</span><span class="special">);</span> 266 <span class="identifier">std</span><span class="special">::</span><span class="identifier">cout</span> <span class="special"><<</span> <span class="identifier">intersect</span><span class="special">(</span><span class="identifier">i1</span><span class="special">,</span> <span class="identifier">i2</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> 267 <span class="identifier">std</span><span class="special">::</span><span class="identifier">cout</span> <span class="special"><<</span> <span class="identifier">hull</span><span class="special">(</span><span class="identifier">i1</span><span class="special">,</span> <span class="identifier">i2</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> 268 <span class="identifier">std</span><span class="special">::</span><span class="identifier">cout</span> <span class="special"><<</span> <span class="identifier">overlap</span><span class="special">(</span><span class="identifier">i1</span><span class="special">,</span> <span class="identifier">i2</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> 269 <span class="identifier">std</span><span class="special">::</span><span class="identifier">cout</span> <span class="special"><<</span> <span class="identifier">subset</span><span class="special">(</span><span class="identifier">i1</span><span class="special">,</span> <span class="identifier">i2</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> 270 <span class="identifier">mpfi_clear</span><span class="special">(</span><span class="identifier">r</span><span class="special">);</span> 271 <span class="keyword">return</span> <span class="number">0</span><span class="special">;</span> 272<span class="special">}</span> 273</pre> 274</div> 275<table xmlns:rev="http://www.cs.rpi.edu/~gregod/boost/tools/doc/revision" width="100%"><tr> 276<td align="left"></td> 277<td align="right"><div class="copyright-footer">Copyright © 2002-2020 John 278 Maddock and Christopher Kormanyos<p> 279 Distributed under the Boost Software License, Version 1.0. (See accompanying 280 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>) 281 </p> 282</div></td> 283</tr></table> 284<hr> 285<div class="spirit-nav"> 286<a accesskey="p" href="../interval.html"><img src="../../../../../../../doc/src/images/prev.png" alt="Prev"></a><a accesskey="u" href="../interval.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="../complex.html"><img src="../../../../../../../doc/src/images/next.png" alt="Next"></a> 287</div> 288</body> 289</html> 290
