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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
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- </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">
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