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<!DOCTYPE HTML PUBLIC "-//W3C//DTD HTML 3.2//EN">
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<title>Boost GCD & LCM Library</title>
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</head>
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<body bgcolor="white" text="black" link="blue" alink="red" vlink="purple">
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<h1>
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<img src="../../../boost.png" alt="boost.png (6897 bytes)"
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align="left" width="277" height="86">Greatest Common Divisor<br>
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Least
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Common Multiple<br>
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</h1>
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<p>The class and function templates in <cite><a
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href="../../../boost/math/common_factor.hpp"><boost/math/common_factor.hpp></a>
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</cite> provide run-time and compile-time evaluation of the greatest
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common divisor (GCD) or least common multiple (LCM) of two integers.
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These facilities are useful for many numeric-oriented generic
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programming problems.</p>
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<h2><a name="contents">Contents</a></h2>
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<ul>
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<li><a href="#contents">Contents</a></li>
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<li>Header <cite><a href="#cf_hpp"><boost/math/common_factor.hpp></a></cite>
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<ul>
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<li><a href="#synopsis">Synopsis</a></li>
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</ul></li>
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<li>Header <cite><a href="#cfrt_hpp"><boost/math/common_factor_rt.hpp></a></cite>
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<ul>
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<li><a href="#gcd_obj">GCD Function Object</a></li>
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<li><a href="#lcm_obj">LCM Function Object</a></li>
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<li><a href="#run_gcd_lcm">Run-time GCD & LCM Determination</a></li>
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</ul></li>
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<li>Header <cite><a href="#cfct_hpp"><boost/math/common_factor_ct.hpp></a></cite></li>
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<li><a href="#example">Example</a></li>
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<li><a href="#demo">Demonstration Program</a></li>
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<li><a href="#rationale">Rationale</a></li>
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<li><a href="#history">History</a></li>
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<li><a href="#credits">Credits</a></li>
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</ul>
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<h2>Header <cite><a name="cf_hpp" href="../../../boost/math/common_factor.hpp"><boost/math/common_factor.hpp></a></cite></h2>
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<p>This header simply includes the headers <cite><a
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href="../../../boost/math/common_factor_ct.hpp"><boost/math/common_factor_ct.hpp></a></cite>
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and <cite><a
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href="../../../boost/math/common_factor_rt.hpp"><boost/math/common_factor_rt.hpp></a></cite>.
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It used to contain the code, but the compile-time and run-time
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facilities were moved to separate headers (since they were independent),
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and this header maintains compatibility.</p>
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<h3><a name="synopsis">Synopsis</a></h3>
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<blockquote><pre>namespace boost
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{
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namespace math
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{
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template < typename IntegerType >
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class gcd_evaluator;
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template < typename IntegerType >
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class lcm_evaluator;
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template < typename IntegerType >
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IntegerType gcd( IntegerType const &a, IntegerType const &b );
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template < typename IntegerType >
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IntegerType lcm( IntegerType const &a, IntegerType const &b );
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template < unsigned long Value1, unsigned long Value2 >
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struct static_gcd;
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template < unsigned long Value1, unsigned long Value2 >
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struct static_lcm;
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}
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}
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</pre></blockquote>
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<h2>Header <cite><a name="cfrt_hpp" href="../../../boost/math/common_factor_rt.hpp"><boost/math/common_factor_rt.hpp></a></cite></h2>
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<h3><a name="gcd_obj">GCD Function Object</a></h3>
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<blockquote><pre>template < typename IntegerType >
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class boost::math::gcd_evaluator
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{
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public:
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// Types
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typedef IntegerType result_type;
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typedef IntegerType first_argument_type;
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typedef IntegerType second_argument_type;
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// Function object interface
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result_type operator ()( first_argument_type const &a,
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second_argument_type const &b ) const;
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};
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</pre></blockquote>
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<p>The <code>boost::math::gcd_evaluator</code> class template defines a
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function object class to return the greatest common divisor of two
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integers. The template is parameterized by a single type, called
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<code>IntegerType</code> here. This type should be a numeric type that
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represents integers. The result of the function object is always
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nonnegative, even if either of the operator arguments is negative.</p>
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<p>This function object class template is used in the corresponding
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version of the <a href="#run_gcd_lcm">GCD function template</a>. If a
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numeric type wants to customize evaluations of its greatest common
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divisors, then the type should specialize on the
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<code>gcd_evaluator</code> class template.</p>
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<h3><a name="lcm_obj">LCM Function Object</a></h3>
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<blockquote><pre>template < typename IntegerType >
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class boost::math::lcm_evaluator
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{
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public:
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// Types
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typedef IntegerType result_type;
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typedef IntegerType first_argument_type;
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typedef IntegerType second_argument_type;
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// Function object interface
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result_type operator ()( first_argument_type const &a,
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second_argument_type const &b ) const;
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};
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</pre></blockquote>
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<p>The <code>boost::math::lcm_evaluator</code> class template defines a
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function object class to return the least common multiple of two
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integers. The template is parameterized by a single type, called
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<code>IntegerType</code> here. This type should be a numeric type that
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represents integers. The result of the function object is always
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nonnegative, even if either of the operator arguments is negative. If
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the least common multiple is beyond the range of the integer type, the
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results are undefined.</p>
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<p>This function object class template is used in the corresponding
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version of the <a href="#run_gcd_lcm">LCM function template</a>. If a
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numeric type wants to customize evaluations of its least common
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multiples, then the type should specialize on the
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<code>lcm_evaluator</code> class template.</p>
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<h3><a name="run_gcd_lcm">Run-time GCD & LCM Determination</a></h3>
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<blockquote><pre>template < typename IntegerType >
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IntegerType boost::math::gcd( IntegerType const &a, IntegerType const &b );
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template < typename IntegerType >
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IntegerType boost::math::lcm( IntegerType const &a, IntegerType const &b );
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</pre></blockquote>
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<p>The <code>boost::math::gcd</code> function template returns the
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greatest common (nonnegative) divisor of the two integers passed to it.
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The <code>boost::math::lcm</code> function template returns the least
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common (nonnegative) multiple of the two integers passed to it. The
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function templates are parameterized on the function arguments'
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<var>IntegerType</var>, which is also the return type. Internally,
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these function templates use an object of the corresponding version of
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the <code><a href="#gcd_obj">gcd_evaluator</a></code> and <code><a
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href="#lcm_obj">lcm_evaluator</a></code> class templates,
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respectively.</p>
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<h2>Header <cite><a name="cfct_hpp" href="../../../boost/math/common_factor_ct.hpp"><boost/math/common_factor_ct.hpp></a></cite></h2>
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<blockquote><pre>template < unsigned long Value1, unsigned long Value2 >
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struct boost::math::static_gcd
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{
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static unsigned long const value = <em>implementation_defined</em>;
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};
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template < unsigned long Value1, unsigned long Value2 >
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struct boost::math::static_lcm
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{
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static unsigned long const value = <em>implementation_defined</em>;
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};
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</pre></blockquote>
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<p>The <code>boost::math::static_gcd</code> and
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<code>boost::math::static_lcm</code> class templates take two
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value-based template parameters of the <code>unsigned long</code> type
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and have a single static constant data member, <code>value</code>, of
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that same type. The value of that member is the greatest common factor
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or least common multiple, respectively, of the template arguments. A
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compile-time error will occur if the least common multiple is beyond the
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range of an <code>unsigned long</code>.</p>
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<h2><a name="example">Example</a></h2>
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<blockquote><pre>#include <boost/math/common_factor.hpp>
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#include <algorithm>
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#include <iterator>
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int main()
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{
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using std::cout;
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using std::endl;
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cout << "The GCD and LCM of 6 and 15 are "
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<< boost::math::gcd(6, 15) << " and "
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<< boost::math::lcm(6, 15) << ", respectively."
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<< endl;
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cout << "The GCD and LCM of 8 and 9 are "
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<< boost::math::static_gcd<8, 9>::value
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<< " and "
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<< boost::math::static_lcm<8, 9>::value
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<< ", respectively." << endl;
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int a[] = { 4, 5, 6 }, b[] = { 7, 8, 9 }, c[3];
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std::transform( a, a + 3, b, c, boost::math::gcd_evaluator<int>() );
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std::copy( c, c + 3, std::ostream_iterator<int>(cout, " ") );
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}
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</pre></blockquote>
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<h2><a name="demo">Demonstration Program</a></h2>
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<p>The program <a
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href="../test/common_factor_test.cpp">common_factor_test.cpp</a> is a
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demonstration of the results from instantiating various examples of the
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run-time GCD and LCM function templates and the compile-time GCD and
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LCM class templates. (The run-time GCD and LCM class templates are
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tested indirectly through the run-time function templates.)</p>
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<h2><a name="rationale">Rationale</a></h2>
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<p>The greatest common divisor and least common multiple functions are
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greatly used in some numeric contexts, including some of the other Boost
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libraries. Centralizing these functions to one header improves code
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factoring and eases maintainence.</p>
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<h2><a name="history">History</a></h2>
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<dl>
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<dt>2 Jul 2002
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<dd>Compile-time and run-time items separated to new headers.
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<dt>7 Nov 2001
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<dd>Initial version
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</dl>
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<h2><a name="credits">Credits</a></h2>
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<p>The author of the Boost compilation of GCD and LCM computations is <a
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href="../../../people/daryle_walker.html">Daryle Walker</a>. The code was
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prompted by existing code hiding in the implementations of <a
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href="../../../people/paul_moore.htm">Paul Moore</a>'s <a
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href="../../rational/index.html">rational</a> library and Steve Cleary's <a
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href="../../pool/doc/index.html">pool</a> library. The code had updates by
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Helmut Zeisel.</p>
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<hr>
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<p>Revised July 2, 2002</p>
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<p>© Copyright Daryle Walker 2001-2002. Permission to copy, use,
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modify, sell and distribute this document is granted provided this
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copyright notice appears in all copies. This document is provided
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"as is" without express or implied warranty, and with no claim
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as to its suitability for any purpose.</p>
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</body>
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</html> |