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<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="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="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>