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Update docs to match new gcd/lcm code.

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@ -1,5 +1,5 @@
[mathpart gcd_lcm Integer Utilities (Greatest Common Divisor and Least Common Multiple)]
[section:gcd_lcm Greatest Common Divisor and Least Common Multiple]
[section Introduction]
@ -27,6 +27,17 @@ programming problems.
constexpr IntegerType gcd( IntegerType const &a, IntegerType const &b );
template < typename IntegerType >
constexpr IntegerType lcm( IntegerType const &a, IntegerType const &b );
template < typename IntegerType, typename... Args >
constexpr IntegerType gcd( IntegerType const &a, IntegerType const &b, Args const&... );
template < typename IntegerType, typename... Args >
constexpr IntegerType lcm( IntegerType const &a, IntegerType const &b, Args const&... );
template <typename I>
std::pair<typename std::iterator_traits<I>::value_type, I>
gcd_range(I first, I last);
template <typename I>
std::pair<typename std::iterator_traits<I>::value_type, I>
lcm_range(I first, I last);
typedef ``['see-below]`` static_gcd_type;
@ -123,14 +134,33 @@ They are also declared `noexcept` when appropriate.
template < typename IntegerType >
constexpr IntegerType boost::math::lcm( IntegerType const &a, IntegerType const &b );
template < typename IntegerType, typename... Args >
constexpr IntegerType gcd( IntegerType const &a, IntegerType const &b, Args const&... );
template < typename IntegerType, typename... Args >
constexpr IntegerType lcm( IntegerType const &a, IntegerType const &b, Args const&... );
template <typename I>
std::pair<typename std::iterator_traits<I>::value_type, I>
gcd_range(I first, I last);
template <typename I>
std::pair<typename std::iterator_traits<I>::value_type, I>
lcm_range(I first, I last);
The boost::math::gcd function template returns the greatest common
(nonnegative) divisor of the two integers passed to it.
`boost::math::gcd_range` 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 `gcd` behaves similarly
but does not indicate which input value caused the gcd to reach unity.
The boost::math::lcm function template returns the least common
(nonnegative) multiple of the two integers passed to it.
The function templates are parameterized on the function arguments'
IntegerType, which is also the return type. Internally, these function
templates use an object of the corresponding version of the
gcd_evaluator and lcm_evaluator class templates, respectively.
As with gcd, there are range and variadic versions of the function for
more than 2 arguments.
Note that these functions are constexpr in C++14 and later only.
They are also declared `noexcept` when appropriate.
@ -139,6 +169,8 @@ They are also declared `noexcept` when appropriate.
[section:compile_time Compile time GCD and LCM determination]
[note These functions are deprecated in favor of constexpr `gcd` and `lcm` on C++14 capable compilers.]
[*Header: ] [@../../../../boost/math/common_factor_ct.hpp <boost/math/common_factor_ct.hpp>]
typedef ``['unspecified]`` static_gcd_type;
@ -246,7 +278,7 @@ pool library. The code had updates by Helmut Zeisel.
[endsect]
[endmathpart]
[endsect]
[/
Copyright 2005, 2013 Daryle Walker.

395
doc/html/boost_integer/gcd_lcm.html Normal file
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@ -0,0 +1,395 @@
<html>
<head>
<meta http-equiv="Content-Type" content="text/html; charset=US-ASCII">
<title>Greatest Common Divisor and Least Common Multiple</title>
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<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>
<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 &amp; 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 &lt;boost/math/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>
<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 &lt;boost/math/common_factor.hpp&gt;
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">math</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">class</span> <span class="identifier">gcd_evaluator</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">class</span> <span class="identifier">lcm_evaluator</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">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">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>
<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">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="identifier">Args</span> <span class="keyword">const</span><span class="special">&amp;...</span> <span class="special">);</span>
<span class="keyword">template</span> <span class="special">&lt;</span><span class="keyword">typename</span> <span class="identifier">I</span><span class="special">&gt;</span>
<span class="identifier">std</span><span class="special">::</span><span class="identifier">pair</span><span class="special">&lt;</span><span class="keyword">typename</span> <span class="identifier">std</span><span class="special">::</span><span class="identifier">iterator_traits</span><span class="special">&lt;</span><span class="identifier">I</span><span class="special">&gt;::</span><span class="identifier">value_type</span><span class="special">,</span> <span class="identifier">I</span><span class="special">&gt;</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">&lt;</span><span class="keyword">typename</span> <span class="identifier">I</span><span class="special">&gt;</span>
<span class="identifier">std</span><span class="special">::</span><span class="identifier">pair</span><span class="special">&lt;</span><span class="keyword">typename</span> <span class="identifier">std</span><span class="special">::</span><span class="identifier">iterator_traits</span><span class="special">&lt;</span><span class="identifier">I</span><span class="special">&gt;::</span><span class="identifier">value_type</span><span class="special">,</span> <span class="identifier">I</span><span class="special">&gt;</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">&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">static_gcd</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">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/math/common_factor_rt.hpp" target="_top">&lt;boost/math/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="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">&amp;</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">&amp;</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::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.
</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/math/common_factor_rt.hpp" target="_top">&lt;boost/math/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="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">&amp;</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">&amp;</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::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.
</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 &amp; LCM Determination">Run-time GCD &amp; LCM
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>
</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">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">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>
<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">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="identifier">Args</span> <span class="keyword">const</span><span class="special">&amp;...</span> <span class="special">);</span>
<span class="keyword">template</span> <span class="special">&lt;</span><span class="keyword">typename</span> <span class="identifier">I</span><span class="special">&gt;</span>
<span class="identifier">std</span><span class="special">::</span><span class="identifier">pair</span><span class="special">&lt;</span><span class="keyword">typename</span> <span class="identifier">std</span><span class="special">::</span><span class="identifier">iterator_traits</span><span class="special">&lt;</span><span class="identifier">I</span><span class="special">&gt;::</span><span class="identifier">value_type</span><span class="special">,</span> <span class="identifier">I</span><span class="special">&gt;</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">&lt;</span><span class="keyword">typename</span> <span class="identifier">I</span><span class="special">&gt;</span>
<span class="identifier">std</span><span class="special">::</span><span class="identifier">pair</span><span class="special">&lt;</span><span class="keyword">typename</span> <span class="identifier">std</span><span class="special">::</span><span class="identifier">iterator_traits</span><span class="special">&lt;</span><span class="identifier">I</span><span class="special">&gt;::</span><span class="identifier">value_type</span><span class="special">,</span> <span class="identifier">I</span><span class="special">&gt;</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::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>
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::math::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/math/common_factor_ct.hpp" target="_top">&lt;boost/math/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="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="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::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>
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">&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>
<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>
<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">&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">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="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="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">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>
</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>.
</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/math/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
maintainence.
</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">
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 &#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>
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@ -54,6 +54,8 @@
<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/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>
@ -158,6 +160,27 @@
</td>
</tr>
<tr>
<td>
<p>
<a class="link" href="boost_integer/gcd_lcm.html" title="Greatest Common Divisor and Least Common Multiple">Greatest Common Divisor and
Least Common Multiple</a>.
</p>
</td>
<td>
<p>
<code class="literal"><a href="../../../../boost/integer/common_factor_rt.hpp" target="_top">&lt;boost/integer/common_factor_rt.hpp&gt;</a></code>
and <code class="literal"><a href="../../../../boost/integer/common_factor_ct.hpp" target="_top">&lt;boost/integer/common_factor_ct.hpp&gt;</a></code>
</p>
</td>
<td>
<p>
Functions <code class="computeroutput"><span class="identifier">gcd</span></code> and
<code class="computeroutput"><span class="identifier">lcm</span></code> plus function
objects and compile time versions.
</p>
</td>
</tr>
<tr>
<td>
<p>
<a class="link" href="boost_integer/mask.html" title="Integer Masks">Integer Masks</a>.
@ -219,7 +242,7 @@
</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: March 28, 2017 at 17:56:42 GMT</small></p></td>
<td align="left"><p><small>Last revised: April 24, 2017 at 12:00:17 GMT</small></p></td>
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6
doc/integer.qbk
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@ -42,6 +42,11 @@ compile-time value; and computing min and max of constant expressions.
Use to select the type of an integer when some property such as maximum value or number of bits is known.
Useful for generic programming. ]
]
[
[[link boost_integer.gcd_lcm Greatest Common Divisor and Least Common Multiple].]
[[^[@../../../../boost/integer/common_factor_rt.hpp <boost/integer/common_factor_rt.hpp>]] and [^[@../../../../boost/integer/common_factor_ct.hpp <boost/integer/common_factor_ct.hpp>]]]
[Functions `gcd` and `lcm` plus function objects and compile time versions.]
]
[
[[link boost_integer.mask Integer Masks].]
[[^[@../../../../boost/integer/integer_mask.hpp <boost/integer/integer_mask.hpp>]]]
@ -358,6 +363,7 @@ for sharing their designs for similar templates.
[endsect]
[endsect]
[include gcd/math-gcd.qbk]
[section:mask Integer Masks]