libs/multiprecision/doc/html/boost_multiprecision/tut/gen_int.html

   1 <html>
   2 <head>
   3 <meta http-equiv="Content-Type" content="text/html; charset=US-ASCII">
   4 <title>Generic Integer Operations</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&#160;1.&#160;Boost.Multiprecision">
   8 <link rel="up" href="../tut.html" title="Tutorial">
   9 <link rel="prev" href="mixed.html" title="Mixed Precision Arithmetic">
  10 <link rel="next" href="serial.html" title="Boost.Serialization Support">
  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="mixed.html"><img src="../../../../../../doc/src/images/prev.png" alt="Prev"></a><a accesskey="u" href="../tut.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="serial.html"><img src="../../../../../../doc/src/images/next.png" alt="Next"></a>
  24 </div>
  25 <div class="section">
  26 <div class="titlepage"><div><div><h3 class="title">
  27 <a name="boost_multiprecision.tut.gen_int"></a><a class="link" href="gen_int.html" title="Generic Integer Operations">Generic Integer Operations</a>
  28 </h3></div></div></div>
  29 <p>
  30         All of the <a class="link" href="../ref/number.html#boost_multiprecision.ref.number.integer_functions">non-member
  31         integer operations</a> are overloaded for the built in integer types in
  32         <code class="computeroutput"><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">integer</span><span class="special">.</span><span class="identifier">hpp</span><span class="special">&gt;</span></code>.
  33         Where these operations require a temporary increase in precision (such as
  34         for <code class="computeroutput"><span class="identifier">powm</span></code>), then if no built
  35         in type is available, a <a class="link" href="ints/cpp_int.html" title="cpp_int">cpp_int</a>
  36         of appropriate precision will be used.
  37       </p>
  38 <p>
  39         Some of these functions are trivial, others use compiler intrinsics (where
  40         available) to ensure optimal evaluation.
  41       </p>
  42 <p>
  43         The overloaded functions are:
  44       </p>
  45 <pre class="programlisting"><span class="keyword">template</span> <span class="special">&lt;</span><span class="keyword">class</span> <span class="identifier">Integer</span><span class="special">,</span> <span class="keyword">class</span> <span class="identifier">I2</span><span class="special">&gt;</span>
  46 <span class="identifier">Integer</span><span class="special">&amp;</span> <span class="identifier">multiply</span><span class="special">(</span><span class="identifier">Integer</span><span class="special">&amp;</span> <span class="identifier">result</span><span class="special">,</span> <span class="keyword">const</span> <span class="identifier">I2</span><span class="special">&amp;</span> <span class="identifier">a</span><span class="special">,</span> <span class="keyword">const</span> <span class="identifier">I2</span><span class="special">&amp;</span> <span class="identifier">b</span><span class="special">);</span>
  47 </pre>
  48 <p>
  49         Multiplies two <code class="computeroutput"><span class="identifier">I2</span></code> values,
  50         to produce a wider <code class="computeroutput"><span class="identifier">Integer</span></code>
  51         result.
  52       </p>
  53 <p>
  54         Returns <code class="computeroutput"><span class="identifier">result</span> <span class="special">=</span>
  55         <span class="identifier">a</span> <span class="special">*</span> <span class="identifier">b</span></code> without overflow or loss of precision
  56         in the multiplication.
  57       </p>
  58 <pre class="programlisting"><span class="keyword">template</span> <span class="special">&lt;</span><span class="keyword">class</span> <span class="identifier">Integer</span><span class="special">,</span> <span class="keyword">class</span> <span class="identifier">I2</span><span class="special">&gt;</span>
  59 <span class="identifier">Integer</span><span class="special">&amp;</span> <span class="identifier">add</span><span class="special">(</span><span class="identifier">Integer</span><span class="special">&amp;</span> <span class="identifier">result</span><span class="special">,</span> <span class="keyword">const</span> <span class="identifier">I2</span><span class="special">&amp;</span> <span class="identifier">a</span><span class="special">,</span> <span class="keyword">const</span> <span class="identifier">I2</span><span class="special">&amp;</span> <span class="identifier">b</span><span class="special">);</span>
  60 </pre>
  61 <p>
  62         Adds two <code class="computeroutput"><span class="identifier">I2</span></code> values, to produce
  63         a wider <code class="computeroutput"><span class="identifier">Integer</span></code> result.
  64       </p>
  65 <p>
  66         Returns <code class="computeroutput"><span class="identifier">result</span> <span class="special">=</span>
  67         <span class="identifier">a</span> <span class="special">+</span> <span class="identifier">b</span></code> without overflow or loss of precision
  68         in the addition.
  69       </p>
  70 <pre class="programlisting"><span class="keyword">template</span> <span class="special">&lt;</span><span class="keyword">class</span> <span class="identifier">Integer</span><span class="special">,</span> <span class="keyword">class</span> <span class="identifier">I2</span><span class="special">&gt;</span>
  71 <span class="identifier">Integer</span><span class="special">&amp;</span> <span class="identifier">subtract</span><span class="special">(</span><span class="identifier">Integer</span><span class="special">&amp;</span> <span class="identifier">result</span><span class="special">,</span> <span class="keyword">const</span> <span class="identifier">I2</span><span class="special">&amp;</span> <span class="identifier">a</span><span class="special">,</span> <span class="keyword">const</span> <span class="identifier">I2</span><span class="special">&amp;</span> <span class="identifier">b</span><span class="special">);</span>
  72 </pre>
  73 <p>
  74         Subtracts two <code class="computeroutput"><span class="identifier">I2</span></code> values,
  75         to produce a wider <code class="computeroutput"><span class="identifier">Integer</span></code>
  76         result.
  77       </p>
  78 <p>
  79         Returns <code class="computeroutput"><span class="identifier">result</span> <span class="special">=</span>
  80         <span class="identifier">a</span> <span class="special">-</span> <span class="identifier">b</span></code> without overflow or loss of precision
  81         in the subtraction.
  82       </p>
  83 <pre class="programlisting"><span class="keyword">template</span> <span class="special">&lt;</span><span class="keyword">class</span> <span class="identifier">Integer</span><span class="special">&gt;</span>
  84 <span class="identifier">Integer</span> <span class="identifier">powm</span><span class="special">(</span><span class="keyword">const</span> <span class="identifier">Integer</span><span class="special">&amp;</span> <span class="identifier">b</span><span class="special">,</span> <span class="keyword">const</span> <span class="identifier">Integer</span><span class="special">&amp;</span> <span class="identifier">p</span><span class="special">,</span> <span class="keyword">const</span> <span class="identifier">Integer</span><span class="special">&amp;</span> <span class="identifier">m</span><span class="special">);</span>
  85 </pre>
  86 <p>
  87         Returns b<sup>p</sup> % m.
  88       </p>
  89 <pre class="programlisting"><span class="keyword">template</span> <span class="special">&lt;</span><span class="keyword">class</span> <span class="identifier">Integer</span><span class="special">&gt;</span>
  90 <span class="keyword">void</span> <span class="identifier">divide_qr</span><span class="special">(</span><span class="keyword">const</span> <span class="identifier">Integer</span><span class="special">&amp;</span> <span class="identifier">x</span><span class="special">,</span> <span class="keyword">const</span> <span class="identifier">Integer</span><span class="special">&amp;</span> <span class="identifier">y</span><span class="special">,</span> <span class="identifier">Integer</span><span class="special">&amp;</span> <span class="identifier">q</span><span class="special">,</span> <span class="identifier">Integer</span><span class="special">&amp;</span> <span class="identifier">r</span><span class="special">);</span>
  91 </pre>
  92 <p>
  93         Sets <code class="computeroutput"><span class="identifier">q</span> <span class="special">=</span>
  94         <span class="identifier">x</span> <span class="special">/</span> <span class="identifier">y</span></code> and <code class="computeroutput"><span class="identifier">r</span>
  95         <span class="special">=</span> <span class="identifier">x</span> <span class="special">%</span> <span class="identifier">y</span></code>.
  96       </p>
  97 <pre class="programlisting"><span class="keyword">template</span> <span class="special">&lt;</span><span class="keyword">class</span> <span class="identifier">Integer1</span><span class="special">,</span> <span class="keyword">class</span> <span class="identifier">Integer2</span><span class="special">&gt;</span>
  98 <span class="identifier">Integer2</span> <span class="identifier">integer_modulus</span><span class="special">(</span><span class="keyword">const</span> <span class="identifier">Integer1</span><span class="special">&amp;</span> <span class="identifier">x</span><span class="special">,</span> <span class="identifier">Integer2</span> <span class="identifier">val</span><span class="special">);</span>
  99 </pre>
 100 <p>
 101         Returns x % val;
 102       </p>
 103 <pre class="programlisting"><span class="keyword">template</span> <span class="special">&lt;</span><span class="keyword">class</span> <span class="identifier">Integer</span><span class="special">&gt;</span>
 104 <span class="keyword">unsigned</span> <span class="identifier">lsb</span><span class="special">(</span><span class="keyword">const</span> <span class="identifier">Integer</span><span class="special">&amp;</span> <span class="identifier">x</span><span class="special">);</span>
 105 </pre>
 106 <p>
 107         Returns the (zero-based) index of the least significant bit of <code class="computeroutput"><span class="identifier">x</span></code>.
 108       </p>
 109 <p>
 110         Throws a <code class="computeroutput"><span class="identifier">std</span><span class="special">::</span><span class="identifier">domain_error</span></code> if <code class="computeroutput"><span class="identifier">x</span>
 111         <span class="special">&lt;=</span> <span class="number">0</span></code>.
 112       </p>
 113 <pre class="programlisting"><span class="keyword">template</span> <span class="special">&lt;</span><span class="keyword">class</span> <span class="identifier">Integer</span><span class="special">&gt;</span>
 114 <span class="keyword">unsigned</span> <span class="identifier">msb</span><span class="special">(</span><span class="keyword">const</span> <span class="identifier">Integer</span><span class="special">&amp;</span> <span class="identifier">x</span><span class="special">);</span>
 115 </pre>
 116 <p>
 117         Returns the (zero-based) index of the most significant bit of <code class="computeroutput"><span class="identifier">x</span></code>.
 118       </p>
 119 <p>
 120         Throws a <code class="computeroutput"><span class="identifier">std</span><span class="special">::</span><span class="identifier">domain_error</span></code> if <code class="computeroutput"><span class="identifier">x</span>
 121         <span class="special">&lt;=</span> <span class="number">0</span></code>.
 122       </p>
 123 <pre class="programlisting"><span class="keyword">template</span> <span class="special">&lt;</span><span class="keyword">class</span> <span class="identifier">Integer</span><span class="special">&gt;</span>
 124 <span class="keyword">bool</span> <span class="identifier">bit_test</span><span class="special">(</span><span class="keyword">const</span> <span class="identifier">Integer</span><span class="special">&amp;</span> <span class="identifier">val</span><span class="special">,</span> <span class="keyword">unsigned</span> <span class="identifier">index</span><span class="special">);</span>
 125 </pre>
 126 <p>
 127         Returns <code class="computeroutput"><span class="keyword">true</span></code> if bit <code class="computeroutput"><span class="identifier">index</span></code> is set in <code class="computeroutput"><span class="identifier">val</span></code>.
 128       </p>
 129 <pre class="programlisting"><span class="keyword">template</span> <span class="special">&lt;</span><span class="keyword">class</span> <span class="identifier">Integer</span><span class="special">&gt;</span>
 130 <span class="identifier">Integer</span><span class="special">&amp;</span> <span class="identifier">bit_set</span><span class="special">(</span><span class="identifier">Integer</span><span class="special">&amp;</span> <span class="identifier">val</span><span class="special">,</span> <span class="keyword">unsigned</span> <span class="identifier">index</span><span class="special">);</span>
 131 </pre>
 132 <p>
 133         Sets the <code class="computeroutput"><span class="identifier">index</span></code> bit in <code class="computeroutput"><span class="identifier">val</span></code>.
 134       </p>
 135 <pre class="programlisting"><span class="keyword">template</span> <span class="special">&lt;</span><span class="keyword">class</span> <span class="identifier">Integer</span><span class="special">&gt;</span>
 136 <span class="identifier">Integer</span><span class="special">&amp;</span> <span class="identifier">bit_unset</span><span class="special">(</span><span class="identifier">Integer</span><span class="special">&amp;</span> <span class="identifier">val</span><span class="special">,</span> <span class="keyword">unsigned</span> <span class="identifier">index</span><span class="special">);</span>
 137 </pre>
 138 <p>
 139         Unsets the <code class="computeroutput"><span class="identifier">index</span></code> bit in
 140         <code class="computeroutput"><span class="identifier">val</span></code>.
 141       </p>
 142 <pre class="programlisting"><span class="keyword">template</span> <span class="special">&lt;</span><span class="keyword">class</span> <span class="identifier">Integer</span><span class="special">&gt;</span>
 143 <span class="identifier">Integer</span><span class="special">&amp;</span> <span class="identifier">bit_flip</span><span class="special">(</span><span class="identifier">Integer</span><span class="special">&amp;</span> <span class="identifier">val</span><span class="special">,</span> <span class="keyword">unsigned</span> <span class="identifier">index</span><span class="special">);</span>
 144 </pre>
 145 <p>
 146         Flips the <code class="computeroutput"><span class="identifier">index</span></code> bit in <code class="computeroutput"><span class="identifier">val</span></code>.
 147       </p>
 148 <pre class="programlisting"><span class="keyword">template</span> <span class="special">&lt;</span><span class="keyword">class</span> <span class="identifier">Integer</span><span class="special">&gt;</span>
 149 <span class="identifier">Integer</span> <span class="identifier">sqrt</span><span class="special">(</span><span class="keyword">const</span> <span class="identifier">Integer</span><span class="special">&amp;</span> <span class="identifier">x</span><span class="special">);</span>
 150 <span class="keyword">template</span> <span class="special">&lt;</span><span class="keyword">class</span> <span class="identifier">Integer</span><span class="special">&gt;</span>
 151 <span class="identifier">Integer</span> <span class="identifier">sqrt</span><span class="special">(</span><span class="keyword">const</span> <span class="identifier">Integer</span><span class="special">&amp;</span> <span class="identifier">x</span><span class="special">,</span> <span class="identifier">Integer</span><span class="special">&amp;</span> <span class="identifier">r</span><span class="special">);</span>
 152 </pre>
 153 <p>
 154         Returns the integer square root <code class="computeroutput"><span class="identifier">s</span></code>
 155         of x and sets <code class="computeroutput"><span class="identifier">r</span></code> to the remainder
 156         <span class="emphasis"><em>x - s<sup>2</sup></em></span>.
 157       </p>
 158 <pre class="programlisting"><span class="keyword">template</span> <span class="special">&lt;</span><span class="keyword">class</span> <span class="identifier">Engine</span><span class="special">&gt;</span>
 159 <span class="keyword">bool</span> <span class="identifier">miller_rabin_test</span><span class="special">(</span><span class="keyword">const</span> <span class="identifier">number</span><span class="special">-</span><span class="keyword">or</span><span class="special">-</span><span class="identifier">expression</span><span class="special">-</span><span class="keyword">template</span><span class="special">-</span><span class="identifier">type</span><span class="special">&amp;</span> <span class="identifier">n</span><span class="special">,</span> <span class="keyword">unsigned</span> <span class="identifier">trials</span><span class="special">,</span> <span class="identifier">Engine</span><span class="special">&amp;</span> <span class="identifier">gen</span><span class="special">);</span>
 160 <span class="keyword">bool</span> <span class="identifier">miller_rabin_test</span><span class="special">(</span><span class="keyword">const</span> <span class="identifier">number</span><span class="special">-</span><span class="keyword">or</span><span class="special">-</span><span class="identifier">expression</span><span class="special">-</span><span class="keyword">template</span><span class="special">-</span><span class="identifier">type</span><span class="special">&amp;</span> <span class="identifier">n</span><span class="special">,</span> <span class="keyword">unsigned</span> <span class="identifier">trials</span><span class="special">);</span>
 161 </pre>
 162 <p>
 163         The regular Miller-Rabin functions in <code class="computeroutput"><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">miller_rabin</span><span class="special">.</span><span class="identifier">hpp</span><span class="special">&gt;</span></code>
 164         are defined in terms of the above generic operations, and so function equally
 165         well for built-in or __fundamental_types and multiprecision types.
 166       </p>
 167 </div>
 168 <table xmlns:rev="http://www.cs.rpi.edu/~gregod/boost/tools/doc/revision" width="100%"><tr>
 169 <td align="left"></td>
 170 <td align="right"><div class="copyright-footer">Copyright &#169; 2002-2019 John Maddock
 171       and Christopher Kormanyos<p>
 172         Distributed under the Boost Software License, Version 1.0. (See accompanying
 173         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>)
 174       </p>
 175 </div></td>
 176 </tr></table>
 177 <hr>
 178 <div class="spirit-nav">
 179 <a accesskey="p" href="mixed.html"><img src="../../../../../../doc/src/images/prev.png" alt="Prev"></a><a accesskey="u" href="../tut.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="serial.html"><img src="../../../../../../doc/src/images/next.png" alt="Next"></a>
 180 </div>
 181 </body>
 182 </html>