1<html> 2<head> 3<meta http-equiv="Content-Type" content="text/html; charset=UTF-8"> 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 1. 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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 <a href="https://en.cppreference.com/w/cpp/language/types" target="_top">fundamental 32 (built-in)</a> integer types in <code class="computeroutput"><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">integer</span><span class="special">.</span><span class="identifier">hpp</span><span class="special">></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 <a href="https://en.cppreference.com/w/cpp/language/types" target="_top">fundamental (built-in)</a> 35 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"><</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">></span> 46<span class="identifier">Integer</span><span class="special">&</span> <span class="identifier">multiply</span><span class="special">(</span><span class="identifier">Integer</span><span class="special">&</span> <span class="identifier">result</span><span class="special">,</span> <span class="keyword">const</span> <span class="identifier">I2</span><span class="special">&</span> <span class="identifier">a</span><span class="special">,</span> <span class="keyword">const</span> <span class="identifier">I2</span><span class="special">&</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"><</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">></span> 59<span class="identifier">Integer</span><span class="special">&</span> <span class="identifier">add</span><span class="special">(</span><span class="identifier">Integer</span><span class="special">&</span> <span class="identifier">result</span><span class="special">,</span> <span class="keyword">const</span> <span class="identifier">I2</span><span class="special">&</span> <span class="identifier">a</span><span class="special">,</span> <span class="keyword">const</span> <span class="identifier">I2</span><span class="special">&</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"><</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">></span> 71<span class="identifier">Integer</span><span class="special">&</span> <span class="identifier">subtract</span><span class="special">(</span><span class="identifier">Integer</span><span class="special">&</span> <span class="identifier">result</span><span class="special">,</span> <span class="keyword">const</span> <span class="identifier">I2</span><span class="special">&</span> <span class="identifier">a</span><span class="special">,</span> <span class="keyword">const</span> <span class="identifier">I2</span><span class="special">&</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"><</span><span class="keyword">class</span> <span class="identifier">Integer</span><span class="special">></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">&</span> <span class="identifier">b</span><span class="special">,</span> <span class="keyword">const</span> <span class="identifier">Integer</span><span class="special">&</span> <span class="identifier">p</span><span class="special">,</span> <span class="keyword">const</span> <span class="identifier">Integer</span><span class="special">&</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"><</span><span class="keyword">class</span> <span class="identifier">Integer</span><span class="special">></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">&</span> <span class="identifier">x</span><span class="special">,</span> <span class="keyword">const</span> <span class="identifier">Integer</span><span class="special">&</span> <span class="identifier">y</span><span class="special">,</span> <span class="identifier">Integer</span><span class="special">&</span> <span class="identifier">q</span><span class="special">,</span> <span class="identifier">Integer</span><span class="special">&</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"><</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">></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">&</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"><</span><span class="keyword">class</span> <span class="identifier">Integer</span><span class="special">></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">&</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"><=</span> <span class="number">0</span></code>. 112 </p> 113<pre class="programlisting"><span class="keyword">template</span> <span class="special"><</span><span class="keyword">class</span> <span class="identifier">Integer</span><span class="special">></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">&</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"><=</span> <span class="number">0</span></code>. 122 </p> 123<pre class="programlisting"><span class="keyword">template</span> <span class="special"><</span><span class="keyword">class</span> <span class="identifier">Integer</span><span class="special">></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">&</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"><</span><span class="keyword">class</span> <span class="identifier">Integer</span><span class="special">></span> 130<span class="identifier">Integer</span><span class="special">&</span> <span class="identifier">bit_set</span><span class="special">(</span><span class="identifier">Integer</span><span class="special">&</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"><</span><span class="keyword">class</span> <span class="identifier">Integer</span><span class="special">></span> 136<span class="identifier">Integer</span><span class="special">&</span> <span class="identifier">bit_unset</span><span class="special">(</span><span class="identifier">Integer</span><span class="special">&</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"><</span><span class="keyword">class</span> <span class="identifier">Integer</span><span class="special">></span> 143<span class="identifier">Integer</span><span class="special">&</span> <span class="identifier">bit_flip</span><span class="special">(</span><span class="identifier">Integer</span><span class="special">&</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"><</span><span class="keyword">class</span> <span class="identifier">Integer</span><span class="special">></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">&</span> <span class="identifier">x</span><span class="special">);</span> 150<span class="keyword">template</span> <span class="special"><</span><span class="keyword">class</span> <span class="identifier">Integer</span><span class="special">></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">&</span> <span class="identifier">x</span><span class="special">,</span> <span class="identifier">Integer</span><span class="special">&</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"><</span><span class="keyword">class</span> <span class="identifier">Engine</span><span class="special">></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">&</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">&</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">&</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"><</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">></span></code> 164 are defined in terms of the above generic operations, and so function equally 165 well for <a href="https://en.cppreference.com/w/cpp/language/types" target="_top">fundamental 166 (built-in) types</a> and multiprecision types. 167 </p> 168</div> 169<table xmlns:rev="http://www.cs.rpi.edu/~gregod/boost/tools/doc/revision" width="100%"><tr> 170<td align="left"></td> 171<td align="right"><div class="copyright-footer">Copyright © 2002-2020 John 172 Maddock and Christopher Kormanyos<p> 173 Distributed under the Boost Software License, Version 1.0. (See accompanying 174 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>) 175 </p> 176</div></td> 177</tr></table> 178<hr> 179<div class="spirit-nav"> 180<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> 181</div> 182</body> 183</html> 184
