401 lines
40 KiB
HTML
401 lines
40 KiB
HTML
<html>
|
|
<head>
|
|
<meta http-equiv="Content-Type" content="text/html; charset=UTF-8">
|
|
<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 V1.79.1">
|
|
<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="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>
|
|
<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="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 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
|
|
Object</a></span></dt>
|
|
<dt><span class="section"><a href="gcd_lcm.html#boost_integer.gcd_lcm.lcm_function_object">LCM Function
|
|
Object</a></span></dt>
|
|
<dt><span class="section"><a href="gcd_lcm.html#boost_integer.gcd_lcm.run_time">Run-time GCD & LCM
|
|
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 <boost/integer/common_factor.hpp></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>
|
|
<dt><span class="section"><a href="gcd_lcm.html#boost_integer.gcd_lcm.gcd_credits">Credits</a></span></dt>
|
|
</dl></div>
|
|
<div class="section">
|
|
<div class="titlepage"><div><div><h3 class="title">
|
|
<a name="boost_integer.gcd_lcm.introduction"></a><a class="link" href="gcd_lcm.html#boost_integer.gcd_lcm.introduction" title="Introduction">Introduction</a>
|
|
</h3></div></div></div>
|
|
<p>
|
|
The class and function templates in <boost/math/common_factor.hpp>
|
|
provide run-time and compile-time evaluation of the greatest common divisor
|
|
(GCD) or least common multiple (LCM) of two integers. These facilities are
|
|
useful for many numeric-oriented generic programming problems.
|
|
</p>
|
|
</div>
|
|
<div class="section">
|
|
<div class="titlepage"><div><div><h3 class="title">
|
|
<a name="boost_integer.gcd_lcm.synopsis"></a><a class="link" href="gcd_lcm.html#boost_integer.gcd_lcm.synopsis" title="Synopsis">Synopsis</a>
|
|
</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">integer</span>
|
|
<span class="special">{</span>
|
|
|
|
<span class="keyword">template</span> <span class="special"><</span> <span class="keyword">typename</span> <span class="identifier">IntegerType</span> <span class="special">></span>
|
|
<span class="keyword">class</span> <span class="identifier">gcd_evaluator</span><span class="special">;</span>
|
|
<span class="keyword">template</span> <span class="special"><</span> <span class="keyword">typename</span> <span class="identifier">IntegerType</span> <span class="special">></span>
|
|
<span class="keyword">class</span> <span class="identifier">lcm_evaluator</span><span class="special">;</span>
|
|
|
|
<span class="keyword">template</span> <span class="special"><</span> <span class="keyword">typename</span> <span class="identifier">IntegerType</span> <span class="special">></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">&</span><span class="identifier">a</span><span class="special">,</span> <span class="identifier">IntegerType</span> <span class="keyword">const</span> <span class="special">&</span><span class="identifier">b</span> <span class="special">);</span>
|
|
<span class="keyword">template</span> <span class="special"><</span> <span class="keyword">typename</span> <span class="identifier">IntegerType</span> <span class="special">></span>
|
|
<span class="keyword">constexpr</span> <span class="identifier">IntegerType</span> <span class="identifier">lcm</span><span class="special">(</span> <span class="identifier">IntegerType</span> <span class="keyword">const</span> <span class="special">&</span><span class="identifier">a</span><span class="special">,</span> <span class="identifier">IntegerType</span> <span class="keyword">const</span> <span class="special">&</span><span class="identifier">b</span> <span class="special">);</span>
|
|
<span class="keyword">template</span> <span class="special"><</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">></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">&</span><span class="identifier">a</span><span class="special">,</span> <span class="identifier">IntegerType</span> <span class="keyword">const</span> <span class="special">&</span><span class="identifier">b</span><span class="special">,</span> <span class="identifier">Args</span> <span class="keyword">const</span><span class="special">&...</span> <span class="special">);</span>
|
|
<span class="keyword">template</span> <span class="special"><</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">></span>
|
|
<span class="keyword">constexpr</span> <span class="identifier">IntegerType</span> <span class="identifier">lcm</span><span class="special">(</span> <span class="identifier">IntegerType</span> <span class="keyword">const</span> <span class="special">&</span><span class="identifier">a</span><span class="special">,</span> <span class="identifier">IntegerType</span> <span class="keyword">const</span> <span class="special">&</span><span class="identifier">b</span><span class="special">,</span> <span class="identifier">Args</span> <span class="keyword">const</span><span class="special">&...</span> <span class="special">);</span>
|
|
|
|
<span class="keyword">template</span> <span class="special"><</span><span class="keyword">typename</span> <span class="identifier">I</span><span class="special">></span>
|
|
<span class="identifier">std</span><span class="special">::</span><span class="identifier">pair</span><span class="special"><</span><span class="keyword">typename</span> <span class="identifier">std</span><span class="special">::</span><span class="identifier">iterator_traits</span><span class="special"><</span><span class="identifier">I</span><span class="special">>::</span><span class="identifier">value_type</span><span class="special">,</span> <span class="identifier">I</span><span class="special">></span>
|
|
<span class="identifier">gcd_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>
|
|
<span class="keyword">template</span> <span class="special"><</span><span class="keyword">typename</span> <span class="identifier">I</span><span class="special">></span>
|
|
<span class="identifier">std</span><span class="special">::</span><span class="identifier">pair</span><span class="special"><</span><span class="keyword">typename</span> <span class="identifier">std</span><span class="special">::</span><span class="identifier">iterator_traits</span><span class="special"><</span><span class="identifier">I</span><span class="special">>::</span><span class="identifier">value_type</span><span class="special">,</span> <span class="identifier">I</span><span class="special">></span>
|
|
<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>
|
|
|
|
<span class="keyword">typedef</span> <span class="emphasis"><em>see-below</em></span> <span class="identifier">static_gcd_type</span><span class="special">;</span>
|
|
|
|
<span class="keyword">template</span> <span class="special"><</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">></span>
|
|
<span class="keyword">struct</span> <span class="identifier">static_gcd</span><span class="special">;</span>
|
|
<span class="keyword">template</span> <span class="special"><</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">></span>
|
|
<span class="keyword">struct</span> <span class="identifier">static_lcm</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_function_object"></a><a class="link" href="gcd_lcm.html#boost_integer.gcd_lcm.gcd_function_object" title="GCD Function Object">GCD Function
|
|
Object</a>
|
|
</h3></div></div></div>
|
|
<p>
|
|
<span class="bold"><strong>Header: </strong></span> <a href="../../../../../boost/integer/common_factor_rt.hpp" target="_top"><boost/integer/common_factor_rt.hpp></a>
|
|
</p>
|
|
<pre class="programlisting"><span class="keyword">template</span> <span class="special"><</span> <span class="keyword">typename</span> <span class="identifier">IntegerType</span> <span class="special">></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>
|
|
<span class="keyword">typedef</span> <span class="identifier">IntegerType</span> <span class="identifier">result_type</span><span class="special">;</span>
|
|
<span class="keyword">typedef</span> <span class="identifier">IntegerType</span> <span class="identifier">first_argument_type</span><span class="special">;</span>
|
|
<span class="keyword">typedef</span> <span class="identifier">IntegerType</span> <span class="identifier">second_argument_type</span><span class="special">;</span>
|
|
|
|
<span class="comment">// Function object interface</span>
|
|
<span class="keyword">constexpr</span> <span class="identifier">result_type</span> <span class="keyword">operator</span> <span class="special">()(</span>
|
|
<span class="identifier">first_argument_type</span> <span class="keyword">const</span> <span class="special">&</span><span class="identifier">a</span><span class="special">,</span>
|
|
<span class="identifier">second_argument_type</span> <span class="keyword">const</span> <span class="special">&</span><span class="identifier">b</span> <span class="special">)</span> <span class="keyword">const</span><span class="special">;</span>
|
|
<span class="special">};</span>
|
|
</pre>
|
|
<p>
|
|
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
|
|
of the GCD function template. If a numeric type wants to customize evaluations
|
|
of its greatest common divisors, then the type should specialize on the gcd_evaluator
|
|
class template.
|
|
</p>
|
|
<p>
|
|
Note that these function objects are <code class="computeroutput"><span class="keyword">constexpr</span></code>
|
|
in C++14 and later only. They are also declared <code class="computeroutput"><span class="keyword">noexcept</span></code>
|
|
when appropriate.
|
|
</p>
|
|
</div>
|
|
<div class="section">
|
|
<div class="titlepage"><div><div><h3 class="title">
|
|
<a name="boost_integer.gcd_lcm.lcm_function_object"></a><a class="link" href="gcd_lcm.html#boost_integer.gcd_lcm.lcm_function_object" title="LCM Function Object">LCM Function
|
|
Object</a>
|
|
</h3></div></div></div>
|
|
<p>
|
|
<span class="bold"><strong>Header: </strong></span> <a href="../../../../../boost/integer/common_factor_rt.hpp" target="_top"><boost/integer/common_factor_rt.hpp></a>
|
|
</p>
|
|
<pre class="programlisting"><span class="keyword">template</span> <span class="special"><</span> <span class="keyword">typename</span> <span class="identifier">IntegerType</span> <span class="special">></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>
|
|
<span class="keyword">typedef</span> <span class="identifier">IntegerType</span> <span class="identifier">result_type</span><span class="special">;</span>
|
|
<span class="keyword">typedef</span> <span class="identifier">IntegerType</span> <span class="identifier">first_argument_type</span><span class="special">;</span>
|
|
<span class="keyword">typedef</span> <span class="identifier">IntegerType</span> <span class="identifier">second_argument_type</span><span class="special">;</span>
|
|
|
|
<span class="comment">// Function object interface</span>
|
|
<span class="keyword">constexpr</span> <span class="identifier">result_type</span> <span class="keyword">operator</span> <span class="special">()(</span>
|
|
<span class="identifier">first_argument_type</span> <span class="keyword">const</span> <span class="special">&</span><span class="identifier">a</span><span class="special">,</span>
|
|
<span class="identifier">second_argument_type</span> <span class="keyword">const</span> <span class="special">&</span><span class="identifier">b</span> <span class="special">)</span> <span class="keyword">const</span><span class="special">;</span>
|
|
<span class="special">};</span>
|
|
</pre>
|
|
<p>
|
|
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
|
|
of the LCM function template. If a numeric type wants to customize evaluations
|
|
of its least common multiples, then the type should specialize on the lcm_evaluator
|
|
class template.
|
|
</p>
|
|
<p>
|
|
Note that these function objects are constexpr in C++14 and later only. They
|
|
are also declared <code class="computeroutput"><span class="keyword">noexcept</span></code> when
|
|
appropriate.
|
|
</p>
|
|
</div>
|
|
<div class="section">
|
|
<div class="titlepage"><div><div><h3 class="title">
|
|
<a name="boost_integer.gcd_lcm.run_time"></a><a class="link" href="gcd_lcm.html#boost_integer.gcd_lcm.run_time" title="Run-time GCD & LCM Determination">Run-time GCD & LCM
|
|
Determination</a>
|
|
</h3></div></div></div>
|
|
<p>
|
|
<span class="bold"><strong>Header: </strong></span> <a href="../../../../../boost/integer/common_factor_rt.hpp" target="_top"><boost/integer/common_factor_rt.hpp></a>
|
|
</p>
|
|
<pre class="programlisting"><span class="keyword">template</span> <span class="special"><</span> <span class="keyword">typename</span> <span class="identifier">IntegerType</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">&</span><span class="identifier">a</span><span class="special">,</span> <span class="identifier">IntegerType</span> <span class="keyword">const</span> <span class="special">&</span><span class="identifier">b</span> <span class="special">);</span>
|
|
|
|
<span class="keyword">template</span> <span class="special"><</span> <span class="keyword">typename</span> <span class="identifier">IntegerType</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">&</span><span class="identifier">a</span><span class="special">,</span> <span class="identifier">IntegerType</span> <span class="keyword">const</span> <span class="special">&</span><span class="identifier">b</span> <span class="special">);</span>
|
|
|
|
<span class="keyword">template</span> <span class="special"><</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">></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">&</span><span class="identifier">a</span><span class="special">,</span> <span class="identifier">IntegerType</span> <span class="keyword">const</span> <span class="special">&</span><span class="identifier">b</span><span class="special">,</span> <span class="identifier">Args</span> <span class="keyword">const</span><span class="special">&...</span> <span class="special">);</span>
|
|
|
|
<span class="keyword">template</span> <span class="special"><</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">></span>
|
|
<span class="keyword">constexpr</span> <span class="identifier">IntegerType</span> <span class="identifier">lcm</span><span class="special">(</span> <span class="identifier">IntegerType</span> <span class="keyword">const</span> <span class="special">&</span><span class="identifier">a</span><span class="special">,</span> <span class="identifier">IntegerType</span> <span class="keyword">const</span> <span class="special">&</span><span class="identifier">b</span><span class="special">,</span> <span class="identifier">Args</span> <span class="keyword">const</span><span class="special">&...</span> <span class="special">);</span>
|
|
|
|
<span class="keyword">template</span> <span class="special"><</span><span class="keyword">typename</span> <span class="identifier">I</span><span class="special">></span>
|
|
<span class="identifier">std</span><span class="special">::</span><span class="identifier">pair</span><span class="special"><</span><span class="keyword">typename</span> <span class="identifier">std</span><span class="special">::</span><span class="identifier">iterator_traits</span><span class="special"><</span><span class="identifier">I</span><span class="special">>::</span><span class="identifier">value_type</span><span class="special">,</span> <span class="identifier">I</span><span class="special">></span>
|
|
<span class="identifier">gcd_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>
|
|
|
|
<span class="keyword">template</span> <span class="special"><</span><span class="keyword">typename</span> <span class="identifier">I</span><span class="special">></span>
|
|
<span class="identifier">std</span><span class="special">::</span><span class="identifier">pair</span><span class="special"><</span><span class="keyword">typename</span> <span class="identifier">std</span><span class="special">::</span><span class="identifier">iterator_traits</span><span class="special"><</span><span class="identifier">I</span><span class="special">>::</span><span class="identifier">value_type</span><span class="special">,</span> <span class="identifier">I</span><span class="special">></span>
|
|
<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::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
|
|
after the last element inspected because this may not be equal to the end
|
|
of the range. The variadic version of <code class="computeroutput"><span class="identifier">gcd</span></code>
|
|
behaves similarly but does not indicate which input value caused the gcd
|
|
to reach unity.
|
|
</p>
|
|
<p>
|
|
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>
|
|
<p>
|
|
Note that these functions are constexpr in C++14 and later only. They are
|
|
also declared <code class="computeroutput"><span class="keyword">noexcept</span></code> when
|
|
appropriate.
|
|
</p>
|
|
</div>
|
|
<div class="section">
|
|
<div class="titlepage"><div><div><h3 class="title">
|
|
<a name="boost_integer.gcd_lcm.compile_time"></a><a class="link" href="gcd_lcm.html#boost_integer.gcd_lcm.compile_time" title="Compile time GCD and LCM determination">Compile time GCD
|
|
and LCM determination</a>
|
|
</h3></div></div></div>
|
|
<div class="note"><table border="0" summary="Note">
|
|
<tr>
|
|
<td rowspan="2" align="center" valign="top" width="25"><img alt="[Note]" src="../../../../../doc/src/images/note.png"></td>
|
|
<th align="left">Note</th>
|
|
</tr>
|
|
<tr><td align="left" valign="top"><p>
|
|
These functions are deprecated in favor of constexpr <code class="computeroutput"><span class="identifier">gcd</span></code>
|
|
and <code class="computeroutput"><span class="identifier">lcm</span></code> on C++14 capable
|
|
compilers.
|
|
</p></td></tr>
|
|
</table></div>
|
|
<p>
|
|
<span class="bold"><strong>Header: </strong></span> <a href="../../../../../boost/integer/common_factor_ct.hpp" target="_top"><boost/integer/common_factor_ct.hpp></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"><</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">></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"><</span><span class="identifier">static_gcd_type</span><span class="special">,</span> <span class="identifier">implementation_defined</span><span class="special">></span>
|
|
<span class="special">{</span>
|
|
<span class="special">};</span>
|
|
|
|
<span class="keyword">template</span> <span class="special"><</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">></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"><</span><span class="identifier">static_gcd_type</span><span class="special">,</span> <span class="identifier">implementation_defined</span><span class="special">></span>
|
|
<span class="special">{</span>
|
|
<span class="special">};</span>
|
|
</pre>
|
|
<p>
|
|
The type <code class="computeroutput"><span class="identifier">static_gcd_type</span></code>
|
|
is the widest unsigned-integer-type that is supported for use in integral-constant-expressions
|
|
by the compiler. Usually this the same type as <code class="computeroutput"><span class="identifier">boost</span><span class="special">::</span><span class="identifier">uintmax_t</span></code>,
|
|
but may fall back to being <code class="computeroutput"><span class="keyword">unsigned</span>
|
|
<span class="keyword">long</span></code> for some older compilers.
|
|
</p>
|
|
<p>
|
|
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.
|
|
A compile-time error will occur if the least common multiple is beyond the
|
|
range of <code class="computeroutput"><span class="identifier">static_gcd_type</span></code>.
|
|
</p>
|
|
<h4>
|
|
<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"><</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">></span>
|
|
<span class="preprocessor">#include</span> <span class="special"><</span><span class="identifier">algorithm</span><span class="special">></span>
|
|
<span class="preprocessor">#include</span> <span class="special"><</span><span class="identifier">iterator</span><span class="special">></span>
|
|
<span class="preprocessor">#include</span> <span class="special"><</span><span class="identifier">iostream</span><span class="special">></span>
|
|
|
|
<span class="keyword">int</span> <span class="identifier">main</span><span class="special">()</span>
|
|
<span class="special">{</span>
|
|
<span class="keyword">using</span> <span class="identifier">std</span><span class="special">::</span><span class="identifier">cout</span><span class="special">;</span>
|
|
<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"><<</span> <span class="string">"The GCD and LCM of 6 and 15 are "</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</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"><<</span> <span class="string">" and "</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">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"><<</span> <span class="string">", respectively."</span>
|
|
<span class="special"><<</span> <span class="identifier">endl</span><span class="special">;</span>
|
|
|
|
<span class="identifier">cout</span> <span class="special"><<</span> <span class="string">"The GCD and LCM of 8 and 9 are "</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">static_gcd</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">value</span>
|
|
<span class="special"><<</span> <span class="string">" and "</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">static_lcm</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">value</span>
|
|
<span class="special"><<</span> <span class="string">", respectively."</span> <span class="special"><<</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">integer</span><span class="special">::</span><span class="identifier">gcd_evaluator</span><span class="special"><</span><span class="keyword">int</span><span class="special">>()</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"><</span><span class="keyword">int</span><span class="special">>(</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 <boost/integer/common_factor.hpp>">Header <boost/integer/common_factor.hpp></a>
|
|
</h3></div></div></div>
|
|
<p>
|
|
This header simply includes the headers <a href="../../../../../boost/integer/common_factor_ct.hpp" target="_top"><boost/integer/common_factor_ct.hpp></a>
|
|
and <a href="../../../../../boost/integer/common_factor_rt.hpp" target="_top"><boost/integer/common_factor_rt.hpp></a>.
|
|
</p>
|
|
<p>
|
|
Note this is a legacy header: it used to contain the actual implementation,
|
|
but the compile-time and run-time facilities were moved to separate headers
|
|
(since they were independent of each other).
|
|
</p>
|
|
</div>
|
|
<div class="section">
|
|
<div class="titlepage"><div><div><h3 class="title">
|
|
<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/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
|
|
indirectly through the run-time function templates.)
|
|
</p>
|
|
</div>
|
|
<div class="section">
|
|
<div class="titlepage"><div><div><h3 class="title">
|
|
<a name="boost_integer.gcd_lcm.rationale"></a><a class="link" href="gcd_lcm.html#boost_integer.gcd_lcm.rationale" title="Rationale">Rationale</a>
|
|
</h3></div></div></div>
|
|
<p>
|
|
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
|
|
maintenance.
|
|
</p>
|
|
</div>
|
|
<div class="section">
|
|
<div class="titlepage"><div><div><h3 class="title">
|
|
<a name="boost_integer.gcd_lcm.gcd_history"></a><a class="link" href="gcd_lcm.html#boost_integer.gcd_lcm.gcd_history" title="History">History</a>
|
|
</h3></div></div></div>
|
|
<div class="itemizedlist"><ul class="itemizedlist" style="list-style-type: disc; ">
|
|
<li class="listitem">
|
|
24th April 2017 Moved to Jeremy Murphy's improved algorithms, added constexpr
|
|
and noexcept support, added compiler intrinsic support, added variadic
|
|
and range based versions of the algorithms.
|
|
</li>
|
|
<li class="listitem">
|
|
13 May 2013 Moved into main Boost.Math Quickbook documentation.
|
|
</li>
|
|
<li class="listitem">
|
|
17 Dec 2005: Converted documentation to Quickbook Format.
|
|
</li>
|
|
<li class="listitem">
|
|
2 Jul 2002: Compile-time and run-time items separated to new headers.
|
|
</li>
|
|
<li class="listitem">
|
|
7 Nov 2001: Initial version
|
|
</li>
|
|
</ul></div>
|
|
</div>
|
|
<div class="section">
|
|
<div class="titlepage"><div><div><h3 class="title">
|
|
<a name="boost_integer.gcd_lcm.gcd_credits"></a><a class="link" href="gcd_lcm.html#boost_integer.gcd_lcm.gcd_credits" title="Credits">Credits</a>
|
|
</h3></div></div></div>
|
|
<p>
|
|
The author of the Boost compilation of GCD and LCM computations is Daryle
|
|
Walker. The code was prompted by existing code hiding in the implementations
|
|
of Paul Moore's rational library and Steve Cleary's pool library. The code
|
|
had updates by Helmut Zeisel.
|
|
</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 © 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="https://www.boost.org/LICENSE_1_0.txt" target="_top">https://www.boost.org/LICENSE_1_0.txt</a>)
|
|
</p>
|
|
</div></td>
|
|
</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="extended_euclidean.html"><img src="../../../../../doc/src/images/next.png" alt="Next"></a>
|
|
</div>
|
|
</body>
|
|
</html>
|