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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 & 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/math/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">math</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/math/common_factor_rt.hpp" target="_top"><boost/math/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">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">&</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::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"><boost/math/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">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">&</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::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 & LCM Determination">Run-time GCD & 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"><boost/math/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">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">&</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">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">&</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::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"><boost/math/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">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"><</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">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"><</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::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"><</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">></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">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"><<</span> <span class="string">" and "</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">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">math</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">math</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">math</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/math/common_factor.hpp>">Header <boost/math/common_factor.hpp></a> |
| </h3></div></div></div> |
| <p> |
| This header simply includes the headers <a href="../../../../../boost/math/common_factor_ct.hpp" target="_top"><boost/math/common_factor_ct.hpp></a> |
| and <a href="../../../../../boost/math/common_factor_rt.hpp" target="_top"><boost/math/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/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"> |
| 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> |
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