feedc0de/boost_integer
1
0
Fork 0
forked from boostorg/integer
Code Pull Requests Activity

Regenerate documentation.

Browse Source
This commit is contained in:
Nick Thompson
2018-11-02 13:45:45 -06:00
parent 9a7f24e8ca
commit cad4623876
11 changed files with 319 additions and 65 deletions
Download Patch File Download Diff File Expand all files Collapse all files

2
doc/html/boost_integer/cstdint.html
View File

@ -3,7 +3,7 @@
<meta http-equiv="Content-Type" content="text/html; charset=US-ASCII">
<title>Removed from library: Standard Integer Types</title>
<link rel="stylesheet" href="../../../../../doc/src/boostbook.css" type="text/css">
<meta name="generator" content="DocBook XSL Stylesheets V1.77.1">
<meta name="generator" content="DocBook XSL Stylesheets V1.79.1">
<link rel="home" href="../index.html" title="Boost.Integer">
<link rel="up" href="../index.html" title="Boost.Integer">
<link rel="prev" href="history.html" title="History">

109
doc/html/boost_integer/extended_euclidean.html Normal file
View File

@ -0,0 +1,109 @@
<html>
<head>
<meta http-equiv="Content-Type" content="text/html; charset=US-ASCII">
<title>Extended Euclidean Algorithm</title>
<link rel="stylesheet" href="../../../../../doc/src/boostbook.css" type="text/css">
<meta name="generator" content="DocBook XSL Stylesheets V1.79.1">
<link rel="home" href="../index.html" title="Boost.Integer">
<link rel="up" href="../index.html" title="Boost.Integer">
<link rel="prev" href="gcd_lcm.html" title="Greatest Common Divisor and Least Common Multiple">
<link rel="next" href="mod_inverse.html" title="Modular Multiplicative Inverse">
</head>
<body bgcolor="white" text="black" link="#0000FF" vlink="#840084" alink="#0000FF">
<table cellpadding="2" width="100%"><tr>
<td valign="top"><img alt="Boost C++ Libraries" width="277" height="86" src="../../../../../boost.png"></td>
<td align="center"><a href="../../../../../index.html">Home</a></td>
<td align="center"><a href="../../../../../libs/libraries.htm">Libraries</a></td>
<td align="center"><a href="http://www.boost.org/users/people.html">People</a></td>
<td align="center"><a href="http://www.boost.org/users/faq.html">FAQ</a></td>
<td align="center"><a href="../../../../../more/index.htm">More</a></td>
</tr></table>
<hr>
<div class="spirit-nav">
<a accesskey="p" href="gcd_lcm.html"><img src="../../../../../doc/src/images/prev.png" alt="Prev"></a><a accesskey="u" href="../index.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="mod_inverse.html"><img src="../../../../../doc/src/images/next.png" alt="Next"></a>
</div>
<div class="section">
<div class="titlepage"><div><div><h2 class="title" style="clear: both">
<a name="boost_integer.extended_euclidean"></a><a class="link" href="extended_euclidean.html" title="Extended Euclidean Algorithm">Extended Euclidean Algorithm</a>
</h2></div></div></div>
<div class="toc"><dl class="toc">
<dt><span class="section"><a href="extended_euclidean.html#boost_integer.extended_euclidean.introduction">Introduction</a></span></dt>
<dt><span class="section"><a href="extended_euclidean.html#boost_integer.extended_euclidean.synopsis">Synopsis</a></span></dt>
<dt><span class="section"><a href="extended_euclidean.html#boost_integer.extended_euclidean.usage">Usage</a></span></dt>
<dt><span class="section"><a href="extended_euclidean.html#boost_integer.extended_euclidean.references">References</a></span></dt>
</dl></div>
<div class="section">
<div class="titlepage"><div><div><h3 class="title">
<a name="boost_integer.extended_euclidean.introduction"></a><a class="link" href="extended_euclidean.html#boost_integer.extended_euclidean.introduction" title="Introduction">Introduction</a>
</h3></div></div></div>
<p>
The extended Euclidean algorithm solves the integer relation <span class="emphasis"><em>mx
+ ny</em></span> = gcd(<span class="emphasis"><em>m</em></span>, <span class="emphasis"><em>n</em></span>) for
<span class="emphasis"><em>x</em></span> and <span class="emphasis"><em>y</em></span>.
</p>
</div>
<div class="section">
<div class="titlepage"><div><div><h3 class="title">
<a name="boost_integer.extended_euclidean.synopsis"></a><a class="link" href="extended_euclidean.html#boost_integer.extended_euclidean.synopsis" title="Synopsis">Synopsis</a>
</h3></div></div></div>
<pre class="programlisting"><span class="preprocessor">#include</span> <span class="special">&lt;</span><span class="identifier">boost</span><span class="special">/</span><span class="identifier">integer</span><span class="special">/</span><span class="identifier">extended_euclidean</span><span class="special">.</span><span class="identifier">hpp</span><span class="special">&gt;</span>
<span class="keyword">namespace</span> <span class="identifier">boost</span> <span class="special">{</span> <span class="keyword">namespace</span> <span class="identifier">integer</span> <span class="special">{</span>
<span class="keyword">template</span><span class="special">&lt;</span><span class="keyword">class</span> <span class="identifier">Z</span><span class="special">&gt;</span>
<span class="keyword">struct</span> <span class="identifier">euclidean_result_t</span> <span class="special">{</span>
<span class="identifier">Z</span> <span class="identifier">gcd</span><span class="special">;</span>
<span class="identifier">Z</span> <span class="identifier">x</span><span class="special">;</span>
<span class="identifier">Z</span> <span class="identifier">y</span><span class="special">;</span>
<span class="special">};</span>
<span class="keyword">template</span><span class="special">&lt;</span><span class="keyword">class</span> <span class="identifier">Z</span><span class="special">&gt;</span>
<span class="identifier">euclidean_result_t</span><span class="special">&lt;</span><span class="identifier">Z</span><span class="special">&gt;</span> <span class="identifier">extended_euclidean</span><span class="special">(</span><span class="identifier">Z</span> <span class="identifier">m</span><span class="special">,</span> <span class="identifier">Z</span> <span class="identifier">n</span><span class="special">);</span>
<span class="special">}}</span>
</pre>
</div>
<div class="section">
<div class="titlepage"><div><div><h3 class="title">
<a name="boost_integer.extended_euclidean.usage"></a><a class="link" href="extended_euclidean.html#boost_integer.extended_euclidean.usage" title="Usage">Usage</a>
</h3></div></div></div>
<pre class="programlisting"><span class="keyword">int</span> <span class="identifier">m</span> <span class="special">=</span> <span class="number">12</span><span class="special">;</span>
<span class="keyword">int</span> <span class="identifier">n</span> <span class="special">=</span> <span class="number">15</span><span class="special">;</span>
<span class="keyword">auto</span> <span class="identifier">res</span> <span class="special">=</span> <span class="identifier">extended_euclidean</span><span class="special">(</span><span class="identifier">m</span><span class="special">,</span> <span class="identifier">n</span><span class="special">);</span>
<span class="keyword">int</span> <span class="identifier">gcd</span> <span class="special">=</span> <span class="identifier">res</span><span class="special">.</span><span class="identifier">gcd</span><span class="special">;</span>
<span class="keyword">int</span> <span class="identifier">x</span> <span class="special">=</span> <span class="identifier">res</span><span class="special">.</span><span class="identifier">x</span><span class="special">;</span>
<span class="keyword">int</span> <span class="identifier">y</span> <span class="special">=</span> <span class="identifier">res</span><span class="special">.</span><span class="identifier">y</span><span class="special">;</span>
<span class="comment">// mx + ny = gcd(m,n) should now hold</span>
</pre>
<p>
Unlike most of the library, the extended Euclidean algorithm requires C++11
features.
</p>
</div>
<div class="section">
<div class="titlepage"><div><div><h3 class="title">
<a name="boost_integer.extended_euclidean.references"></a><a class="link" href="extended_euclidean.html#boost_integer.extended_euclidean.references" title="References">References</a>
</h3></div></div></div>
<p>
Wagstaff, Samuel S., <span class="emphasis"><em>The Joy of Factoring</em></span>, Vol. 68.
American Mathematical Soc., 2013.
</p>
</div>
</div>
<table xmlns:rev="http://www.cs.rpi.edu/~gregod/boost/tools/doc/revision" width="100%"><tr>
<td align="left"></td>
<td align="right"><div class="copyright-footer">Copyright &#169; 2001-2009 Beman
Dawes, Daryle Walker, Gennaro Prota, John Maddock<p>
Distributed under the Boost Software License, Version 1.0. (See accompanying
file LICENSE_1_0.txt or copy at <a href="http://www.boost.org/LICENSE_1_0.txt" target="_top">http://www.boost.org/LICENSE_1_0.txt</a>)
</p>
</div></td>
</tr></table>
<hr>
<div class="spirit-nav">
<a accesskey="p" href="gcd_lcm.html"><img src="../../../../../doc/src/images/prev.png" alt="Prev"></a><a accesskey="u" href="../index.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="mod_inverse.html"><img src="../../../../../doc/src/images/next.png" alt="Next"></a>
</div>
</body>
</html>

90
doc/html/boost_integer/gcd_lcm.html
View File

@ -3,11 +3,11 @@
<meta http-equiv="Content-Type" content="text/html; charset=US-ASCII">
<title>Greatest Common Divisor and Least Common Multiple</title>
<link rel="stylesheet" href="../../../../../doc/src/boostbook.css" type="text/css">
<meta name="generator" content="DocBook XSL Stylesheets V1.77.1">
<meta name="generator" content="DocBook XSL Stylesheets V1.79.1">
<link rel="home" href="../index.html" title="Boost.Integer">
<link rel="up" href="../index.html" title="Boost.Integer">
<link rel="prev" href="integer.html" title="Integer Type Selection">
<link rel="next" href="mask.html" title="Integer Masks">
<link rel="next" href="extended_euclidean.html" title="Extended Euclidean Algorithm">
</head>
<body bgcolor="white" text="black" link="#0000FF" vlink="#840084" alink="#0000FF">
<table cellpadding="2" width="100%"><tr>
@ -20,14 +20,14 @@
</tr></table>
<hr>
<div class="spirit-nav">
<a accesskey="p" href="integer.html"><img src="../../../../../doc/src/images/prev.png" alt="Prev"></a><a accesskey="u" href="../index.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="mask.html"><img src="../../../../../doc/src/images/next.png" alt="Next"></a>
<a accesskey="p" href="integer.html"><img src="../../../../../doc/src/images/prev.png" alt="Prev"></a><a accesskey="u" href="../index.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="extended_euclidean.html"><img src="../../../../../doc/src/images/next.png" alt="Next"></a>
</div>
<div class="section">
<div class="titlepage"><div><div><h2 class="title" style="clear: both">
<a name="boost_integer.gcd_lcm"></a><a class="link" href="gcd_lcm.html" title="Greatest Common Divisor and Least Common Multiple">Greatest Common Divisor and Least
Common Multiple</a>
</h2></div></div></div>
<div class="toc"><dl>
<div class="toc"><dl class="toc">
<dt><span class="section"><a href="gcd_lcm.html#boost_integer.gcd_lcm.introduction">Introduction</a></span></dt>
<dt><span class="section"><a href="gcd_lcm.html#boost_integer.gcd_lcm.synopsis">Synopsis</a></span></dt>
<dt><span class="section"><a href="gcd_lcm.html#boost_integer.gcd_lcm.gcd_function_object">GCD Function
@ -38,7 +38,7 @@
Determination</a></span></dt>
<dt><span class="section"><a href="gcd_lcm.html#boost_integer.gcd_lcm.compile_time">Compile time GCD
and LCM determination</a></span></dt>
<dt><span class="section"><a href="gcd_lcm.html#boost_integer.gcd_lcm.gcd_header">Header &lt;boost/math/common_factor.hpp&gt;</a></span></dt>
<dt><span class="section"><a href="gcd_lcm.html#boost_integer.gcd_lcm.gcd_header">Header &lt;boost/integer/common_factor.hpp&gt;</a></span></dt>
<dt><span class="section"><a href="gcd_lcm.html#boost_integer.gcd_lcm.demo">Demonstration Program</a></span></dt>
<dt><span class="section"><a href="gcd_lcm.html#boost_integer.gcd_lcm.rationale">Rationale</a></span></dt>
<dt><span class="section"><a href="gcd_lcm.html#boost_integer.gcd_lcm.gcd_history">History</a></span></dt>
@ -61,7 +61,7 @@
</h3></div></div></div>
<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">math</span>
<span class="keyword">namespace</span> <span class="identifier">integer</span>
<span class="special">{</span>
<span class="keyword">template</span> <span class="special">&lt;</span> <span class="keyword">typename</span> <span class="identifier">IntegerType</span> <span class="special">&gt;</span>
@ -102,10 +102,10 @@
Object</a>
</h3></div></div></div>
<p>
<span class="bold"><strong>Header: </strong></span> <a href="../../../../../boost/math/common_factor_rt.hpp" target="_top">&lt;boost/math/common_factor_rt.hpp&gt;</a>
<span class="bold"><strong>Header: </strong></span> <a href="../../../../../boost/integer/common_factor_rt.hpp" target="_top">&lt;boost/integer/common_factor_rt.hpp&gt;</a>
</p>
<pre class="programlisting"><span class="keyword">template</span> <span class="special">&lt;</span> <span class="keyword">typename</span> <span class="identifier">IntegerType</span> <span class="special">&gt;</span>
<span class="keyword">class</span> <span class="identifier">boost</span><span class="special">::</span><span class="identifier">math</span><span class="special">::</span><span class="identifier">gcd_evaluator</span>
<span class="keyword">class</span> <span class="identifier">boost</span><span class="special">::</span><span class="identifier">integer</span><span class="special">::</span><span class="identifier">gcd_evaluator</span>
<span class="special">{</span>
<span class="keyword">public</span><span class="special">:</span>
<span class="comment">// Types</span>
@ -120,11 +120,11 @@
<span class="special">};</span>
</pre>
<p>
The boost::math::gcd_evaluator class template defines a function object class
to return the greatest common divisor of two integers. The template is parameterized
by a single type, called IntegerType here. This type should be a numeric
type that represents integers. The result of the function object is always
nonnegative, even if either of the operator arguments is negative.
The boost::integer::gcd_evaluator class template defines a function object
class to return the greatest common divisor of two integers. The template
is parameterized by a single type, called IntegerType here. This type should
be a numeric type that represents integers. The result of the function object
is always nonnegative, even if either of the operator arguments is negative.
</p>
<p>
This function object class template is used in the corresponding version
@ -144,10 +144,10 @@
Object</a>
</h3></div></div></div>
<p>
<span class="bold"><strong>Header: </strong></span> <a href="../../../../../boost/math/common_factor_rt.hpp" target="_top">&lt;boost/math/common_factor_rt.hpp&gt;</a>
<span class="bold"><strong>Header: </strong></span> <a href="../../../../../boost/integer/common_factor_rt.hpp" target="_top">&lt;boost/integer/common_factor_rt.hpp&gt;</a>
</p>
<pre class="programlisting"><span class="keyword">template</span> <span class="special">&lt;</span> <span class="keyword">typename</span> <span class="identifier">IntegerType</span> <span class="special">&gt;</span>
<span class="keyword">class</span> <span class="identifier">boost</span><span class="special">::</span><span class="identifier">math</span><span class="special">::</span><span class="identifier">lcm_evaluator</span>
<span class="keyword">class</span> <span class="identifier">boost</span><span class="special">::</span><span class="identifier">integer</span><span class="special">::</span><span class="identifier">lcm_evaluator</span>
<span class="special">{</span>
<span class="keyword">public</span><span class="special">:</span>
<span class="comment">// Types</span>
@ -162,13 +162,13 @@
<span class="special">};</span>
</pre>
<p>
The boost::math::lcm_evaluator class template defines a function object class
to return the least common multiple of two integers. The template is parameterized
by a single type, called IntegerType here. This type should be a numeric
type that represents integers. The result of the function object is always
nonnegative, even if either of the operator arguments is negative. If the
least common multiple is beyond the range of the integer type, the results
are undefined.
The boost::integer::lcm_evaluator class template defines a function object
class to return the least common multiple of two integers. The template is
parameterized by a single type, called IntegerType here. This type should
be a numeric type that represents integers. The result of the function object
is always nonnegative, even if either of the operator arguments is negative.
If the least common multiple is beyond the range of the integer type, the
results are undefined.
</p>
<p>
This function object class template is used in the corresponding version
@ -188,13 +188,13 @@
Determination</a>
</h3></div></div></div>
<p>
<span class="bold"><strong>Header: </strong></span> <a href="../../../../../boost/math/common_factor_rt.hpp" target="_top">&lt;boost/math/common_factor_rt.hpp&gt;</a>
<span class="bold"><strong>Header: </strong></span> <a href="../../../../../boost/integer/common_factor_rt.hpp" target="_top">&lt;boost/integer/common_factor_rt.hpp&gt;</a>
</p>
<pre class="programlisting"><span class="keyword">template</span> <span class="special">&lt;</span> <span class="keyword">typename</span> <span class="identifier">IntegerType</span> <span class="special">&gt;</span>
<span class="keyword">constexpr</span> <span class="identifier">IntegerType</span> <span class="identifier">boost</span><span class="special">::</span><span class="identifier">math</span><span class="special">::</span><span class="identifier">gcd</span><span class="special">(</span> <span class="identifier">IntegerType</span> <span class="keyword">const</span> <span class="special">&amp;</span><span class="identifier">a</span><span class="special">,</span> <span class="identifier">IntegerType</span> <span class="keyword">const</span> <span class="special">&amp;</span><span class="identifier">b</span> <span class="special">);</span>
<span class="keyword">constexpr</span> <span class="identifier">IntegerType</span> <span class="identifier">boost</span><span class="special">::</span><span class="identifier">integer</span><span class="special">::</span><span class="identifier">gcd</span><span class="special">(</span> <span class="identifier">IntegerType</span> <span class="keyword">const</span> <span class="special">&amp;</span><span class="identifier">a</span><span class="special">,</span> <span class="identifier">IntegerType</span> <span class="keyword">const</span> <span class="special">&amp;</span><span class="identifier">b</span> <span class="special">);</span>
<span class="keyword">template</span> <span class="special">&lt;</span> <span class="keyword">typename</span> <span class="identifier">IntegerType</span> <span class="special">&gt;</span>
<span class="keyword">constexpr</span> <span class="identifier">IntegerType</span> <span class="identifier">boost</span><span class="special">::</span><span class="identifier">math</span><span class="special">::</span><span class="identifier">lcm</span><span class="special">(</span> <span class="identifier">IntegerType</span> <span class="keyword">const</span> <span class="special">&amp;</span><span class="identifier">a</span><span class="special">,</span> <span class="identifier">IntegerType</span> <span class="keyword">const</span> <span class="special">&amp;</span><span class="identifier">b</span> <span class="special">);</span>
<span class="keyword">constexpr</span> <span class="identifier">IntegerType</span> <span class="identifier">boost</span><span class="special">::</span><span class="identifier">integer</span><span class="special">::</span><span class="identifier">lcm</span><span class="special">(</span> <span class="identifier">IntegerType</span> <span class="keyword">const</span> <span class="special">&amp;</span><span class="identifier">a</span><span class="special">,</span> <span class="identifier">IntegerType</span> <span class="keyword">const</span> <span class="special">&amp;</span><span class="identifier">b</span> <span class="special">);</span>
<span class="keyword">template</span> <span class="special">&lt;</span> <span class="keyword">typename</span> <span class="identifier">IntegerType</span><span class="special">,</span> <span class="keyword">typename</span><span class="special">...</span> <span class="identifier">Args</span> <span class="special">&gt;</span>
<span class="keyword">constexpr</span> <span class="identifier">IntegerType</span> <span class="identifier">gcd</span><span class="special">(</span> <span class="identifier">IntegerType</span> <span class="keyword">const</span> <span class="special">&amp;</span><span class="identifier">a</span><span class="special">,</span> <span class="identifier">IntegerType</span> <span class="keyword">const</span> <span class="special">&amp;</span><span class="identifier">b</span><span class="special">,</span> <span class="identifier">Args</span> <span class="keyword">const</span><span class="special">&amp;...</span> <span class="special">);</span>
@ -211,8 +211,8 @@
<span class="identifier">lcm_range</span><span class="special">(</span><span class="identifier">I</span> <span class="identifier">first</span><span class="special">,</span> <span class="identifier">I</span> <span class="identifier">last</span><span class="special">);</span>
</pre>
<p>
The boost::math::gcd function template returns the greatest common (nonnegative)
divisor of the two integers passed to it. <code class="computeroutput"><span class="identifier">boost</span><span class="special">::</span><span class="identifier">math</span><span class="special">::</span><span class="identifier">gcd_range</span></code>
The boost::integer::gcd function template returns the greatest common (nonnegative)
divisor of the two integers passed to it. <code class="computeroutput"><span class="identifier">boost</span><span class="special">::</span><span class="identifier">integer</span><span class="special">::</span><span class="identifier">gcd_range</span></code>
is the iteration of the above gcd algorithm over a range, returning the greatest
common divisor of all the elements. The algorithm terminates when the gcd
reaches unity or the end of the range. Thus it also returns the iterator
@ -222,7 +222,7 @@
to reach unity.
</p>
<p>
The boost::math::lcm function template returns the least common (nonnegative)
The boost::integer::lcm function template returns the least common (nonnegative)
multiple of the two integers passed to it. As with gcd, there are range and
variadic versions of the function for more than 2 arguments.
</p>
@ -249,17 +249,17 @@
</p></td></tr>
</table></div>
<p>
<span class="bold"><strong>Header: </strong></span> <a href="../../../../../boost/math/common_factor_ct.hpp" target="_top">&lt;boost/math/common_factor_ct.hpp&gt;</a>
<span class="bold"><strong>Header: </strong></span> <a href="../../../../../boost/integer/common_factor_ct.hpp" target="_top">&lt;boost/integer/common_factor_ct.hpp&gt;</a>
</p>
<pre class="programlisting"><span class="keyword">typedef</span> <span class="emphasis"><em>unspecified</em></span> <span class="identifier">static_gcd_type</span><span class="special">;</span>
<span class="keyword">template</span> <span class="special">&lt;</span> <span class="identifier">static_gcd_type</span> <span class="identifier">Value1</span><span class="special">,</span> <span class="identifier">static_gcd_type</span> <span class="identifier">Value2</span> <span class="special">&gt;</span>
<span class="keyword">struct</span> <span class="identifier">boost</span><span class="special">::</span><span class="identifier">math</span><span class="special">::</span><span class="identifier">static_gcd</span> <span class="special">:</span> <span class="keyword">public</span> <span class="identifier">mpl</span><span class="special">::</span><span class="identifier">integral_c</span><span class="special">&lt;</span><span class="identifier">static_gcd_type</span><span class="special">,</span> <span class="identifier">implementation_defined</span><span class="special">&gt;</span>
<span class="keyword">struct</span> <span class="identifier">boost</span><span class="special">::</span><span class="identifier">integer</span><span class="special">::</span><span class="identifier">static_gcd</span> <span class="special">:</span> <span class="keyword">public</span> <span class="identifier">mpl</span><span class="special">::</span><span class="identifier">integral_c</span><span class="special">&lt;</span><span class="identifier">static_gcd_type</span><span class="special">,</span> <span class="identifier">implementation_defined</span><span class="special">&gt;</span>
<span class="special">{</span>
<span class="special">};</span>
<span class="keyword">template</span> <span class="special">&lt;</span> <span class="identifier">static_gcd_type</span> <span class="identifier">Value1</span><span class="special">,</span> <span class="identifier">static_gcd_type</span> <span class="identifier">Value2</span> <span class="special">&gt;</span>
<span class="keyword">struct</span> <span class="identifier">boost</span><span class="special">::</span><span class="identifier">math</span><span class="special">::</span><span class="identifier">static_lcm</span> <span class="special">:</span> <span class="keyword">public</span> <span class="identifier">mpl</span><span class="special">::</span><span class="identifier">integral_c</span><span class="special">&lt;</span><span class="identifier">static_gcd_type</span><span class="special">,</span> <span class="identifier">implementation_defined</span><span class="special">&gt;</span>
<span class="keyword">struct</span> <span class="identifier">boost</span><span class="special">::</span><span class="identifier">integer</span><span class="special">::</span><span class="identifier">static_lcm</span> <span class="special">:</span> <span class="keyword">public</span> <span class="identifier">mpl</span><span class="special">::</span><span class="identifier">integral_c</span><span class="special">&lt;</span><span class="identifier">static_gcd_type</span><span class="special">,</span> <span class="identifier">implementation_defined</span><span class="special">&gt;</span>
<span class="special">{</span>
<span class="special">};</span>
</pre>
@ -271,8 +271,8 @@
<span class="keyword">long</span></code> for some older compilers.
</p>
<p>
The boost::math::static_gcd and boost::math::static_lcm class templates take
two value-based template parameters of the <span class="emphasis"><em>static_gcd_type</em></span>
The boost::integer::static_gcd and boost::integer::static_lcm class templates
take two value-based template parameters of the <span class="emphasis"><em>static_gcd_type</em></span>
type and inherit from the type <code class="computeroutput"><span class="identifier">boost</span><span class="special">::</span><span class="identifier">mpl</span><span class="special">::</span><span class="identifier">integral_c</span></code>. Inherited from the base class,
they have a member <span class="emphasis"><em>value</em></span> that is the greatest common
factor or least common multiple, respectively, of the template arguments.
@ -283,7 +283,7 @@
<a name="boost_integer.gcd_lcm.compile_time.h0"></a>
<span class="phrase"><a name="boost_integer.gcd_lcm.compile_time.example"></a></span><a class="link" href="gcd_lcm.html#boost_integer.gcd_lcm.compile_time.example">Example</a>
</h4>
<pre class="programlisting"><span class="preprocessor">#include</span> <span class="special">&lt;</span><span class="identifier">boost</span><span class="special">/</span><span class="identifier">math</span><span class="special">/</span><span class="identifier">common_factor</span><span class="special">.</span><span class="identifier">hpp</span><span class="special">&gt;</span>
<pre class="programlisting"><span class="preprocessor">#include</span> <span class="special">&lt;</span><span class="identifier">boost</span><span class="special">/</span><span class="identifier">integer</span><span class="special">/</span><span class="identifier">common_factor</span><span class="special">.</span><span class="identifier">hpp</span><span class="special">&gt;</span>
<span class="preprocessor">#include</span> <span class="special">&lt;</span><span class="identifier">algorithm</span><span class="special">&gt;</span>
<span class="preprocessor">#include</span> <span class="special">&lt;</span><span class="identifier">iterator</span><span class="special">&gt;</span>
<span class="preprocessor">#include</span> <span class="special">&lt;</span><span class="identifier">iostream</span><span class="special">&gt;</span>
@ -294,29 +294,29 @@
<span class="keyword">using</span> <span class="identifier">std</span><span class="special">::</span><span class="identifier">endl</span><span class="special">;</span>
<span class="identifier">cout</span> <span class="special">&lt;&lt;</span> <span class="string">"The GCD and LCM of 6 and 15 are "</span>
<span class="special">&lt;&lt;</span> <span class="identifier">boost</span><span class="special">::</span><span class="identifier">math</span><span class="special">::</span><span class="identifier">gcd</span><span class="special">(</span><span class="number">6</span><span class="special">,</span> <span class="number">15</span><span class="special">)</span> <span class="special">&lt;&lt;</span> <span class="string">" and "</span>
<span class="special">&lt;&lt;</span> <span class="identifier">boost</span><span class="special">::</span><span class="identifier">math</span><span class="special">::</span><span class="identifier">lcm</span><span class="special">(</span><span class="number">6</span><span class="special">,</span> <span class="number">15</span><span class="special">)</span> <span class="special">&lt;&lt;</span> <span class="string">", respectively."</span>
<span class="special">&lt;&lt;</span> <span class="identifier">boost</span><span class="special">::</span><span class="identifier">integer</span><span class="special">::</span><span class="identifier">gcd</span><span class="special">(</span><span class="number">6</span><span class="special">,</span> <span class="number">15</span><span class="special">)</span> <span class="special">&lt;&lt;</span> <span class="string">" and "</span>
<span class="special">&lt;&lt;</span> <span class="identifier">boost</span><span class="special">::</span><span class="identifier">integer</span><span class="special">::</span><span class="identifier">lcm</span><span class="special">(</span><span class="number">6</span><span class="special">,</span> <span class="number">15</span><span class="special">)</span> <span class="special">&lt;&lt;</span> <span class="string">", respectively."</span>
<span class="special">&lt;&lt;</span> <span class="identifier">endl</span><span class="special">;</span>
<span class="identifier">cout</span> <span class="special">&lt;&lt;</span> <span class="string">"The GCD and LCM of 8 and 9 are "</span>
<span class="special">&lt;&lt;</span> <span class="identifier">boost</span><span class="special">::</span><span class="identifier">math</span><span class="special">::</span><span class="identifier">static_gcd</span><span class="special">&lt;</span><span class="number">8</span><span class="special">,</span> <span class="number">9</span><span class="special">&gt;::</span><span class="identifier">value</span>
<span class="special">&lt;&lt;</span> <span class="identifier">boost</span><span class="special">::</span><span class="identifier">integer</span><span class="special">::</span><span class="identifier">static_gcd</span><span class="special">&lt;</span><span class="number">8</span><span class="special">,</span> <span class="number">9</span><span class="special">&gt;::</span><span class="identifier">value</span>
<span class="special">&lt;&lt;</span> <span class="string">" and "</span>
<span class="special">&lt;&lt;</span> <span class="identifier">boost</span><span class="special">::</span><span class="identifier">math</span><span class="special">::</span><span class="identifier">static_lcm</span><span class="special">&lt;</span><span class="number">8</span><span class="special">,</span> <span class="number">9</span><span class="special">&gt;::</span><span class="identifier">value</span>
<span class="special">&lt;&lt;</span> <span class="identifier">boost</span><span class="special">::</span><span class="identifier">integer</span><span class="special">::</span><span class="identifier">static_lcm</span><span class="special">&lt;</span><span class="number">8</span><span class="special">,</span> <span class="number">9</span><span class="special">&gt;::</span><span class="identifier">value</span>
<span class="special">&lt;&lt;</span> <span class="string">", respectively."</span> <span class="special">&lt;&lt;</span> <span class="identifier">endl</span><span class="special">;</span>
<span class="keyword">int</span> <span class="identifier">a</span><span class="special">[]</span> <span class="special">=</span> <span class="special">{</span> <span class="number">4</span><span class="special">,</span> <span class="number">5</span><span class="special">,</span> <span class="number">6</span> <span class="special">},</span> <span class="identifier">b</span><span class="special">[]</span> <span class="special">=</span> <span class="special">{</span> <span class="number">7</span><span class="special">,</span> <span class="number">8</span><span class="special">,</span> <span class="number">9</span> <span class="special">},</span> <span class="identifier">c</span><span class="special">[</span><span class="number">3</span><span class="special">];</span>
<span class="identifier">std</span><span class="special">::</span><span class="identifier">transform</span><span class="special">(</span> <span class="identifier">a</span><span class="special">,</span> <span class="identifier">a</span> <span class="special">+</span> <span class="number">3</span><span class="special">,</span> <span class="identifier">b</span><span class="special">,</span> <span class="identifier">c</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">gcd_evaluator</span><span class="special">&lt;</span><span class="keyword">int</span><span class="special">&gt;()</span> <span class="special">);</span>
<span class="identifier">std</span><span class="special">::</span><span class="identifier">transform</span><span class="special">(</span> <span class="identifier">a</span><span class="special">,</span> <span class="identifier">a</span> <span class="special">+</span> <span class="number">3</span><span class="special">,</span> <span class="identifier">b</span><span class="special">,</span> <span class="identifier">c</span><span class="special">,</span> <span class="identifier">boost</span><span class="special">::</span><span class="identifier">integer</span><span class="special">::</span><span class="identifier">gcd_evaluator</span><span class="special">&lt;</span><span class="keyword">int</span><span class="special">&gt;()</span> <span class="special">);</span>
<span class="identifier">std</span><span class="special">::</span><span class="identifier">copy</span><span class="special">(</span> <span class="identifier">c</span><span class="special">,</span> <span class="identifier">c</span> <span class="special">+</span> <span class="number">3</span><span class="special">,</span> <span class="identifier">std</span><span class="special">::</span><span class="identifier">ostream_iterator</span><span class="special">&lt;</span><span class="keyword">int</span><span class="special">&gt;(</span><span class="identifier">cout</span><span class="special">,</span> <span class="string">" "</span><span class="special">)</span> <span class="special">);</span>
<span class="special">}</span>
</pre>
</div>
<div class="section">
<div class="titlepage"><div><div><h3 class="title">
<a name="boost_integer.gcd_lcm.gcd_header"></a><a class="link" href="gcd_lcm.html#boost_integer.gcd_lcm.gcd_header" title="Header &lt;boost/math/common_factor.hpp&gt;">Header &lt;boost/math/common_factor.hpp&gt;</a>
<a name="boost_integer.gcd_lcm.gcd_header"></a><a class="link" href="gcd_lcm.html#boost_integer.gcd_lcm.gcd_header" title="Header &lt;boost/integer/common_factor.hpp&gt;">Header &lt;boost/integer/common_factor.hpp&gt;</a>
</h3></div></div></div>
<p>
This header simply includes the headers <a href="../../../../../boost/math/common_factor_ct.hpp" target="_top">&lt;boost/math/common_factor_ct.hpp&gt;</a>
and <a href="../../../../../boost/math/common_factor_rt.hpp" target="_top">&lt;boost/math/common_factor_rt.hpp&gt;</a>.
This header simply includes the headers <a href="../../../../../boost/integer/common_factor_ct.hpp" target="_top">&lt;boost/integer/common_factor_ct.hpp&gt;</a>
and <a href="../../../../../boost/integer/common_factor_rt.hpp" target="_top">&lt;boost/integer/common_factor_rt.hpp&gt;</a>.
</p>
<p>
Note this is a legacy header: it used to contain the actual implementation,
@ -329,7 +329,7 @@
<a name="boost_integer.gcd_lcm.demo"></a><a class="link" href="gcd_lcm.html#boost_integer.gcd_lcm.demo" title="Demonstration Program">Demonstration Program</a>
</h3></div></div></div>
<p>
The program <a href="../../../../../libs/math/test/common_factor_test.cpp" target="_top">common_factor_test.cpp</a>
The program <a href="../../../../../libs/integer/test/common_factor_test.cpp" target="_top">common_factor_test.cpp</a>
is a demonstration of the results from instantiating various examples of
the run-time GCD and LCM function templates and the compile-time GCD and
LCM class templates. (The run-time GCD and LCM class templates are tested
@ -344,7 +344,7 @@
The greatest common divisor and least common multiple functions are greatly
used in some numeric contexts, including some of the other Boost libraries.
Centralizing these functions to one header improves code factoring and eases
maintainence.
maintenance.
</p>
</div>
<div class="section">
@ -394,7 +394,7 @@
</tr></table>
<hr>
<div class="spirit-nav">
<a accesskey="p" href="integer.html"><img src="../../../../../doc/src/images/prev.png" alt="Prev"></a><a accesskey="u" href="../index.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="mask.html"><img src="../../../../../doc/src/images/next.png" alt="Next"></a>
<a accesskey="p" href="integer.html"><img src="../../../../../doc/src/images/prev.png" alt="Prev"></a><a accesskey="u" href="../index.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="extended_euclidean.html"><img src="../../../../../doc/src/images/next.png" alt="Next"></a>
</div>
</body>
</html>

2
doc/html/boost_integer/history.html
View File

@ -3,7 +3,7 @@
<meta http-equiv="Content-Type" content="text/html; charset=US-ASCII">
<title>History</title>
<link rel="stylesheet" href="../../../../../doc/src/boostbook.css" type="text/css">
<meta name="generator" content="DocBook XSL Stylesheets V1.77.1">
<meta name="generator" content="DocBook XSL Stylesheets V1.79.1">
<link rel="home" href="../index.html" title="Boost.Integer">
<link rel="up" href="../index.html" title="Boost.Integer">
<link rel="prev" href="minmax.html" title="Compile time min/max calculation">

8
doc/html/boost_integer/integer.html
View File

@ -3,7 +3,7 @@
<meta http-equiv="Content-Type" content="text/html; charset=US-ASCII">
<title>Integer Type Selection</title>
<link rel="stylesheet" href="../../../../../doc/src/boostbook.css" type="text/css">
<meta name="generator" content="DocBook XSL Stylesheets V1.77.1">
<meta name="generator" content="DocBook XSL Stylesheets V1.79.1">
<link rel="home" href="../index.html" title="Boost.Integer">
<link rel="up" href="../index.html" title="Boost.Integer">
<link rel="prev" href="traits.html" title="Integer Traits">
@ -26,7 +26,7 @@
<div class="titlepage"><div><div><h2 class="title" style="clear: both">
<a name="boost_integer.integer"></a><a class="link" href="integer.html" title="Integer Type Selection">Integer Type Selection</a>
</h2></div></div></div>
<div class="toc"><dl>
<div class="toc"><dl class="toc">
<dt><span class="section"><a href="integer.html#boost_integer.integer.synopsis">Synopsis</a></span></dt>
<dt><span class="section"><a href="integer.html#boost_integer.integer.easiest">Easiest-to-Manipulate
Types</a></span></dt>
@ -353,10 +353,10 @@
<span class="special">{</span>
<span class="identifier">boost</span><span class="special">::</span><span class="identifier">int_t</span><span class="special">&lt;</span><span class="number">24</span><span class="special">&gt;::</span><span class="identifier">least</span> <span class="identifier">my_var</span><span class="special">;</span> <span class="comment">// my_var has at least 24-bits</span>
<span class="comment">//...</span>
<span class="comment">// This one is guarenteed not to be truncated:</span>
<span class="comment">// This one is guaranteed not to be truncated:</span>
<span class="identifier">boost</span><span class="special">::</span><span class="identifier">int_max_value_t</span><span class="special">&lt;</span><span class="number">1000</span><span class="special">&gt;::</span><span class="identifier">least</span> <span class="identifier">my1000</span> <span class="special">=</span> <span class="number">1000</span><span class="special">;</span>
<span class="comment">//...</span>
<span class="comment">// This one is guarenteed not to be truncated, and as fast</span>
<span class="comment">// This one is guaranteed not to be truncated, and as fast</span>
<span class="comment">// to manipulate as possible, its size may be greater than</span>
<span class="comment">// that of my1000:</span>
<span class="identifier">boost</span><span class="special">::</span><span class="identifier">int_max_value_t</span><span class="special">&lt;</span><span class="number">1000</span><span class="special">&gt;::</span><span class="identifier">fast</span> <span class="identifier">my_fast1000</span> <span class="special">=</span> <span class="number">1000</span><span class="special">;</span>

4
doc/html/boost_integer/log2.html
View File

@ -3,7 +3,7 @@
<meta http-equiv="Content-Type" content="text/html; charset=US-ASCII">
<title>Compile Time log2 Calculation</title>
<link rel="stylesheet" href="../../../../../doc/src/boostbook.css" type="text/css">
<meta name="generator" content="DocBook XSL Stylesheets V1.77.1">
<meta name="generator" content="DocBook XSL Stylesheets V1.79.1">
<link rel="home" href="../index.html" title="Boost.Integer">
<link rel="up" href="../index.html" title="Boost.Integer">
<link rel="prev" href="mask.html" title="Integer Masks">
@ -26,7 +26,7 @@
<div class="titlepage"><div><div><h2 class="title" style="clear: both">
<a name="boost_integer.log2"></a><a class="link" href="log2.html" title="Compile Time log2 Calculation">Compile Time log2 Calculation</a>
</h2></div></div></div>
<div class="toc"><dl>
<div class="toc"><dl class="toc">
<dt><span class="section"><a href="log2.html#boost_integer.log2.synopsis">Synopsis</a></span></dt>
<dt><span class="section"><a href="log2.html#boost_integer.log2.usage">Usage</a></span></dt>
<dt><span class="section"><a href="log2.html#boost_integer.log2.demonstration_program">Demonstration

10
doc/html/boost_integer/mask.html
View File

@ -3,10 +3,10 @@
<meta http-equiv="Content-Type" content="text/html; charset=US-ASCII">
<title>Integer Masks</title>
<link rel="stylesheet" href="../../../../../doc/src/boostbook.css" type="text/css">
<meta name="generator" content="DocBook XSL Stylesheets V1.77.1">
<meta name="generator" content="DocBook XSL Stylesheets V1.79.1">
<link rel="home" href="../index.html" title="Boost.Integer">
<link rel="up" href="../index.html" title="Boost.Integer">
<link rel="prev" href="gcd_lcm.html" title="Greatest Common Divisor and Least Common Multiple">
<link rel="prev" href="mod_inverse.html" title="Modular Multiplicative Inverse">
<link rel="next" href="log2.html" title="Compile Time log2 Calculation">
</head>
<body bgcolor="white" text="black" link="#0000FF" vlink="#840084" alink="#0000FF">
@ -20,13 +20,13 @@
</tr></table>
<hr>
<div class="spirit-nav">
<a accesskey="p" href="gcd_lcm.html"><img src="../../../../../doc/src/images/prev.png" alt="Prev"></a><a accesskey="u" href="../index.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="log2.html"><img src="../../../../../doc/src/images/next.png" alt="Next"></a>
<a accesskey="p" href="mod_inverse.html"><img src="../../../../../doc/src/images/prev.png" alt="Prev"></a><a accesskey="u" href="../index.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="log2.html"><img src="../../../../../doc/src/images/next.png" alt="Next"></a>
</div>
<div class="section">
<div class="titlepage"><div><div><h2 class="title" style="clear: both">
<a name="boost_integer.mask"></a><a class="link" href="mask.html" title="Integer Masks">Integer Masks</a>
</h2></div></div></div>
<div class="toc"><dl>
<div class="toc"><dl class="toc">
<dt><span class="section"><a href="mask.html#boost_integer.mask.overview">Overview</a></span></dt>
<dt><span class="section"><a href="mask.html#boost_integer.mask.synopsis">Synopsis</a></span></dt>
<dt><span class="section"><a href="mask.html#boost_integer.mask.single_bit_mask_class_template">Single
@ -374,7 +374,7 @@
</tr></table>
<hr>
<div class="spirit-nav">
<a accesskey="p" href="gcd_lcm.html"><img src="../../../../../doc/src/images/prev.png" alt="Prev"></a><a accesskey="u" href="../index.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="log2.html"><img src="../../../../../doc/src/images/next.png" alt="Next"></a>
<a accesskey="p" href="mod_inverse.html"><img src="../../../../../doc/src/images/prev.png" alt="Prev"></a><a accesskey="u" href="../index.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="log2.html"><img src="../../../../../doc/src/images/next.png" alt="Next"></a>
</div>
</body>
</html>

4
doc/html/boost_integer/minmax.html
View File

@ -3,7 +3,7 @@
<meta http-equiv="Content-Type" content="text/html; charset=US-ASCII">
<title>Compile time min/max calculation</title>
<link rel="stylesheet" href="../../../../../doc/src/boostbook.css" type="text/css">
<meta name="generator" content="DocBook XSL Stylesheets V1.77.1">
<meta name="generator" content="DocBook XSL Stylesheets V1.79.1">
<link rel="home" href="../index.html" title="Boost.Integer">
<link rel="up" href="../index.html" title="Boost.Integer">
<link rel="prev" href="log2.html" title="Compile Time log2 Calculation">
@ -26,7 +26,7 @@
<div class="titlepage"><div><div><h2 class="title" style="clear: both">
<a name="boost_integer.minmax"></a><a class="link" href="minmax.html" title="Compile time min/max calculation">Compile time min/max calculation</a>
</h2></div></div></div>
<div class="toc"><dl>
<div class="toc"><dl class="toc">
<dt><span class="section"><a href="minmax.html#boost_integer.minmax.synopsis">Synopsis</a></span></dt>
<dt><span class="section"><a href="minmax.html#boost_integer.minmax.usage">Usage</a></span></dt>
<dt><span class="section"><a href="minmax.html#boost_integer.minmax.example">Example</a></span></dt>

105
doc/html/boost_integer/mod_inverse.html Normal file
View File

@ -0,0 +1,105 @@
<html>
<head>
<meta http-equiv="Content-Type" content="text/html; charset=US-ASCII">
<title>Modular Multiplicative Inverse</title>
<link rel="stylesheet" href="../../../../../doc/src/boostbook.css" type="text/css">
<meta name="generator" content="DocBook XSL Stylesheets V1.79.1">
<link rel="home" href="../index.html" title="Boost.Integer">
<link rel="up" href="../index.html" title="Boost.Integer">
<link rel="prev" href="extended_euclidean.html" title="Extended Euclidean Algorithm">
<link rel="next" href="mask.html" title="Integer Masks">
</head>
<body bgcolor="white" text="black" link="#0000FF" vlink="#840084" alink="#0000FF">
<table cellpadding="2" width="100%"><tr>
<td valign="top"><img alt="Boost C++ Libraries" width="277" height="86" src="../../../../../boost.png"></td>
<td align="center"><a href="../../../../../index.html">Home</a></td>
<td align="center"><a href="../../../../../libs/libraries.htm">Libraries</a></td>
<td align="center"><a href="http://www.boost.org/users/people.html">People</a></td>
<td align="center"><a href="http://www.boost.org/users/faq.html">FAQ</a></td>
<td align="center"><a href="../../../../../more/index.htm">More</a></td>
</tr></table>
<hr>
<div class="spirit-nav">
<a accesskey="p" href="extended_euclidean.html"><img src="../../../../../doc/src/images/prev.png" alt="Prev"></a><a accesskey="u" href="../index.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="mask.html"><img src="../../../../../doc/src/images/next.png" alt="Next"></a>
</div>
<div class="section">
<div class="titlepage"><div><div><h2 class="title" style="clear: both">
<a name="boost_integer.mod_inverse"></a><a class="link" href="mod_inverse.html" title="Modular Multiplicative Inverse">Modular Multiplicative Inverse</a>
</h2></div></div></div>
<div class="toc"><dl class="toc">
<dt><span class="section"><a href="mod_inverse.html#boost_integer.mod_inverse.introduction">Introduction</a></span></dt>
<dt><span class="section"><a href="mod_inverse.html#boost_integer.mod_inverse.synopsis">Synopsis</a></span></dt>
<dt><span class="section"><a href="mod_inverse.html#boost_integer.mod_inverse.usage">Usage</a></span></dt>
<dt><span class="section"><a href="mod_inverse.html#boost_integer.mod_inverse.references">References</a></span></dt>
</dl></div>
<div class="section">
<div class="titlepage"><div><div><h3 class="title">
<a name="boost_integer.mod_inverse.introduction"></a><a class="link" href="mod_inverse.html#boost_integer.mod_inverse.introduction" title="Introduction">Introduction</a>
</h3></div></div></div>
<p>
The modular multiplicative inverse of a number <span class="emphasis"><em>a</em></span> is
that number <span class="emphasis"><em>x</em></span> which satisfies <span class="emphasis"><em>ax</em></span>
= 1 mod <span class="emphasis"><em>p</em></span>. A fast algorithm for computing modular multiplicative
inverses based on the extended Euclidean algorithm exists and is provided
by Boost.
</p>
</div>
<div class="section">
<div class="titlepage"><div><div><h3 class="title">
<a name="boost_integer.mod_inverse.synopsis"></a><a class="link" href="mod_inverse.html#boost_integer.mod_inverse.synopsis" title="Synopsis">Synopsis</a>
</h3></div></div></div>
<pre class="programlisting"><span class="preprocessor">#include</span> <span class="special">&lt;</span><span class="identifier">boost</span><span class="special">/</span><span class="identifier">integer</span><span class="special">/</span><span class="identifier">mod_inverse</span><span class="special">.</span><span class="identifier">hpp</span><span class="special">&gt;</span>
<span class="keyword">namespace</span> <span class="identifier">boost</span> <span class="special">{</span> <span class="keyword">namespace</span> <span class="identifier">integer</span> <span class="special">{</span>
<span class="keyword">template</span><span class="special">&lt;</span><span class="keyword">class</span> <span class="identifier">Z</span><span class="special">&gt;</span>
<span class="identifier">boost</span><span class="special">::</span><span class="identifier">optional</span><span class="special">&lt;</span><span class="identifier">Z</span><span class="special">&gt;</span> <span class="identifier">mod_inverse</span><span class="special">(</span><span class="identifier">Z</span> <span class="identifier">a</span><span class="special">,</span> <span class="identifier">Z</span> <span class="identifier">m</span><span class="special">);</span>
<span class="special">}}</span>
</pre>
</div>
<div class="section">
<div class="titlepage"><div><div><h3 class="title">
<a name="boost_integer.mod_inverse.usage"></a><a class="link" href="mod_inverse.html#boost_integer.mod_inverse.usage" title="Usage">Usage</a>
</h3></div></div></div>
<p>
Multiplicative modular inverses exist if and only if <span class="emphasis"><em>a</em></span>
and <span class="emphasis"><em>m</em></span> are coprime. So for example
</p>
<pre class="programlisting"><span class="keyword">auto</span> <span class="identifier">x</span> <span class="special">=</span> <span class="identifier">mod_inverse</span><span class="special">(</span><span class="number">2</span><span class="special">,</span> <span class="number">5</span><span class="special">);</span>
<span class="keyword">if</span> <span class="special">(</span><span class="identifier">x</span><span class="special">)</span>
<span class="special">{</span>
<span class="keyword">int</span> <span class="identifier">should_be_three</span> <span class="special">=</span> <span class="identifier">x</span><span class="special">.</span><span class="identifier">value</span><span class="special">();</span>
<span class="special">}</span>
<span class="keyword">auto</span> <span class="identifier">y</span> <span class="special">=</span> <span class="identifier">mod_inverse</span><span class="special">(</span><span class="number">2</span><span class="special">,</span> <span class="number">4</span><span class="special">);</span>
<span class="keyword">if</span> <span class="special">(!</span><span class="identifier">y</span><span class="special">)</span>
<span class="special">{</span>
<span class="identifier">std</span><span class="special">::</span><span class="identifier">cout</span> <span class="special">&lt;&lt;</span> <span class="string">"There is no inverse of 2 mod 4\n"</span><span class="special">;</span>
<span class="special">}</span>
</pre>
</div>
<div class="section">
<div class="titlepage"><div><div><h3 class="title">
<a name="boost_integer.mod_inverse.references"></a><a class="link" href="mod_inverse.html#boost_integer.mod_inverse.references" title="References">References</a>
</h3></div></div></div>
<p>
Wagstaff, Samuel S., <span class="emphasis"><em>The Joy of Factoring</em></span>, Vol. 68.
American Mathematical Soc., 2013.
</p>
</div>
</div>
<table xmlns:rev="http://www.cs.rpi.edu/~gregod/boost/tools/doc/revision" width="100%"><tr>
<td align="left"></td>
<td align="right"><div class="copyright-footer">Copyright &#169; 2001-2009 Beman
Dawes, Daryle Walker, Gennaro Prota, John Maddock<p>
Distributed under the Boost Software License, Version 1.0. (See accompanying
file LICENSE_1_0.txt or copy at <a href="http://www.boost.org/LICENSE_1_0.txt" target="_top">http://www.boost.org/LICENSE_1_0.txt</a>)
</p>
</div></td>
</tr></table>
<hr>
<div class="spirit-nav">
<a accesskey="p" href="extended_euclidean.html"><img src="../../../../../doc/src/images/prev.png" alt="Prev"></a><a accesskey="u" href="../index.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="mask.html"><img src="../../../../../doc/src/images/next.png" alt="Next"></a>
</div>
</body>
</html>

4
doc/html/boost_integer/traits.html
View File

@ -3,7 +3,7 @@
<meta http-equiv="Content-Type" content="text/html; charset=US-ASCII">
<title>Integer Traits</title>
<link rel="stylesheet" href="../../../../../doc/src/boostbook.css" type="text/css">
<meta name="generator" content="DocBook XSL Stylesheets V1.77.1">
<meta name="generator" content="DocBook XSL Stylesheets V1.79.1">
<link rel="home" href="../index.html" title="Boost.Integer">
<link rel="up" href="../index.html" title="Boost.Integer">
<link rel="prev" href="../index.html" title="Boost.Integer">
@ -26,7 +26,7 @@
<div class="titlepage"><div><div><h2 class="title" style="clear: both">
<a name="boost_integer.traits"></a><a class="link" href="traits.html" title="Integer Traits">Integer Traits</a>
</h2></div></div></div>
<div class="toc"><dl>
<div class="toc"><dl class="toc">
<dt><span class="section"><a href="traits.html#boost_integer.traits.motivation">Motivation</a></span></dt>
<dt><span class="section"><a href="traits.html#boost_integer.traits.synopsis">Synopsis</a></span></dt>
<dt><span class="section"><a href="traits.html#boost_integer.traits.description">Description</a></span></dt>

46
doc/html/index.html
View File

@ -3,7 +3,7 @@
<meta http-equiv="Content-Type" content="text/html; charset=US-ASCII">
<title>Boost.Integer</title>
<link rel="stylesheet" href="../../../../doc/src/boostbook.css" type="text/css">
<meta name="generator" content="DocBook XSL Stylesheets V1.77.1">
<meta name="generator" content="DocBook XSL Stylesheets V1.79.1">
<link rel="home" href="index.html" title="Boost.Integer">
<link rel="next" href="boost_integer/traits.html" title="Integer Traits">
</head>
@ -50,12 +50,14 @@
</div>
<div class="toc">
<p><b>Table of Contents</b></p>
<dl>
<dl class="toc">
<dt><span class="section"><a href="index.html#boost_integer.overview">Overview</a></span></dt>
<dt><span class="section"><a href="boost_integer/traits.html">Integer Traits</a></span></dt>
<dt><span class="section"><a href="boost_integer/integer.html">Integer Type Selection</a></span></dt>
<dt><span class="section"><a href="boost_integer/gcd_lcm.html">Greatest Common Divisor and Least
Common Multiple</a></span></dt>
<dt><span class="section"><a href="boost_integer/extended_euclidean.html">Extended Euclidean Algorithm</a></span></dt>
<dt><span class="section"><a href="boost_integer/mod_inverse.html">Modular Multiplicative Inverse</a></span></dt>
<dt><span class="section"><a href="boost_integer/mask.html">Integer Masks</a></span></dt>
<dt><span class="section"><a href="boost_integer/log2.html">Compile Time log2 Calculation</a></span></dt>
<dt><span class="section"><a href="boost_integer/minmax.html">Compile time min/max calculation</a></span></dt>
@ -237,12 +239,50 @@
</p>
</td>
</tr>
<tr>
<td>
<p>
<a class="link" href="boost_integer/extended_euclidean.html" title="Extended Euclidean Algorithm">Extended Euclidean
algorithm</a>.
</p>
</td>
<td>
<p>
<code class="literal"><a href="../../../../boost/integer/extended_euclidean.hpp" target="_top">&lt;boost/integer/extended_euclidean.hpp&gt;</a></code>
</p>
</td>
<td>
<p>
Solves <span class="emphasis"><em>mx + ny = gcd(x,y)</em></span> for <span class="emphasis"><em>x</em></span>
and <span class="emphasis"><em>y</em></span>.
</p>
</td>
</tr>
<tr>
<td>
<p>
<a class="link" href="boost_integer/mod_inverse.html" title="Modular Multiplicative Inverse">Modular multiplicative
inverse</a>.
</p>
</td>
<td>
<p>
<code class="literal"><a href="../../../../boost/integer/mod_inverse.hpp" target="_top">&lt;boost/integer/mod_inverse.hpp&gt;</a></code>
</p>
</td>
<td>
<p>
Given <span class="emphasis"><em>a</em></span> and <span class="emphasis"><em>m</em></span>, solves
<span class="emphasis"><em>ax</em></span> = 1 mod <span class="emphasis"><em>m</em></span> for <span class="emphasis"><em>x</em></span>.
</p>
</td>
</tr>
</tbody>
</table></div>
</div>
</div>
<table xmlns:rev="http://www.cs.rpi.edu/~gregod/boost/tools/doc/revision" width="100%"><tr>
<td align="left"><p><small>Last revised: April 24, 2017 at 17:49:59 GMT</small></p></td>
<td align="left"><p><small>Last revised: November 02, 2018 at 19:38:28 GMT</small></p></td>
<td align="right"><div class="copyright-footer"></div></td>
</tr></table>
<hr>