531 lines
13 KiB
C++
531 lines
13 KiB
C++
// Boost common_factor_rt.hpp header file ----------------------------------//
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// (C) Copyright Daryle Walker and Paul Moore 2001-2002. Permission to copy,
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// use, modify, sell and distribute this software is granted provided this
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// copyright notice appears in all copies. This software is provided "as is"
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// without express or implied warranty, and with no claim as to its suitability
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// for any purpose.
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// boostinspect:nolicense (don't complain about the lack of a Boost license)
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// (Paul Moore hasn't been in contact for years, so there's no way to change the
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// license.)
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// See http://www.boost.org for updates, documentation, and revision history.
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#ifndef BOOST_MATH_COMMON_FACTOR_RT_HPP
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#define BOOST_MATH_COMMON_FACTOR_RT_HPP
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#include <boost/math_fwd.hpp> // self include
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#include <boost/config.hpp> // for BOOST_NESTED_TEMPLATE, etc.
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#include <boost/limits.hpp> // for std::numeric_limits
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#include <climits> // for CHAR_MIN
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#include <boost/detail/workaround.hpp>
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#ifdef BOOST_MSVC
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#pragma warning(push)
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#pragma warning(disable:4127 4244) // Conditional expression is constant
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#endif
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namespace boost
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{
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namespace math
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{
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// Forward declarations for function templates -----------------------------//
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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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// Greatest common divisor evaluator class declaration ---------------------//
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template < typename IntegerType >
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class gcd_evaluator
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{
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public:
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// Types
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typedef IntegerType result_type, first_argument_type, 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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}; // boost::math::gcd_evaluator
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// Least common multiple evaluator class declaration -----------------------//
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template < typename IntegerType >
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class lcm_evaluator
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{
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public:
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// Types
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typedef IntegerType result_type, first_argument_type, 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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}; // boost::math::lcm_evaluator
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// Implementation details --------------------------------------------------//
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namespace detail
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{
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// Greatest common divisor for rings (including unsigned integers)
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template < typename RingType >
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RingType
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gcd_euclidean
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(
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RingType a,
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RingType b
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)
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{
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// Avoid repeated construction
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#ifndef __BORLANDC__
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RingType const zero = static_cast<RingType>( 0 );
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#else
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RingType zero = static_cast<RingType>( 0 );
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#endif
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// Reduce by GCD-remainder property [GCD(a,b) == GCD(b,a MOD b)]
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while ( true )
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{
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if ( a == zero )
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return b;
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b %= a;
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if ( b == zero )
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return a;
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a %= b;
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}
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}
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// Greatest common divisor for (signed) integers
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template < typename IntegerType >
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inline
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IntegerType
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gcd_integer
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(
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IntegerType const & a,
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IntegerType const & b
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)
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{
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// Avoid repeated construction
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IntegerType const zero = static_cast<IntegerType>( 0 );
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IntegerType const result = gcd_euclidean( a, b );
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return ( result < zero ) ? static_cast<IntegerType>(-result) : result;
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}
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// Greatest common divisor for unsigned binary integers
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template < typename BuiltInUnsigned >
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BuiltInUnsigned
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gcd_binary
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(
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BuiltInUnsigned u,
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BuiltInUnsigned v
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)
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{
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if ( u && v )
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{
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// Shift out common factors of 2
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unsigned shifts = 0;
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while ( !(u & 1u) && !(v & 1u) )
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{
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++shifts;
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u >>= 1;
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v >>= 1;
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}
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// Start with the still-even one, if any
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BuiltInUnsigned r[] = { u, v };
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unsigned which = static_cast<bool>( u & 1u );
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// Whittle down the values via their differences
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do
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{
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#if BOOST_WORKAROUND(__BORLANDC__, BOOST_TESTED_AT(0x582))
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while ( !(r[ which ] & 1u) )
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{
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r[ which ] = (r[which] >> 1);
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}
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#else
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// Remove factors of two from the even one
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while ( !(r[ which ] & 1u) )
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{
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r[ which ] >>= 1;
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}
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#endif
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// Replace the larger of the two with their difference
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if ( r[!which] > r[which] )
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{
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which ^= 1u;
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}
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r[ which ] -= r[ !which ];
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}
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while ( r[which] );
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// Shift-in the common factor of 2 to the residues' GCD
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return r[ !which ] << shifts;
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}
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else
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{
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// At least one input is zero, return the other
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// (adding since zero is the additive identity)
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// or zero if both are zero.
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return u + v;
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}
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}
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// Least common multiple for rings (including unsigned integers)
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template < typename RingType >
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inline
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RingType
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lcm_euclidean
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(
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RingType const & a,
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RingType const & b
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)
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{
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RingType const zero = static_cast<RingType>( 0 );
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RingType const temp = gcd_euclidean( a, b );
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return ( temp != zero ) ? ( a / temp * b ) : zero;
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}
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// Least common multiple for (signed) integers
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template < typename IntegerType >
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inline
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IntegerType
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lcm_integer
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(
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IntegerType const & a,
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IntegerType const & b
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)
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{
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// Avoid repeated construction
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IntegerType const zero = static_cast<IntegerType>( 0 );
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IntegerType const result = lcm_euclidean( a, b );
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return ( result < zero ) ? static_cast<IntegerType>(-result) : result;
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}
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// Function objects to find the best way of computing GCD or LCM
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#ifndef BOOST_NO_LIMITS_COMPILE_TIME_CONSTANTS
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#ifndef BOOST_NO_TEMPLATE_PARTIAL_SPECIALIZATION
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template < typename T, bool IsSpecialized, bool IsSigned >
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struct gcd_optimal_evaluator_helper_t
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{
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T operator ()( T const &a, T const &b )
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{
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return gcd_euclidean( a, b );
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}
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};
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template < typename T >
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struct gcd_optimal_evaluator_helper_t< T, true, true >
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{
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T operator ()( T const &a, T const &b )
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{
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return gcd_integer( a, b );
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}
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};
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#else
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template < bool IsSpecialized, bool IsSigned >
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struct gcd_optimal_evaluator_helper2_t
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{
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template < typename T >
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struct helper
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{
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T operator ()( T const &a, T const &b )
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{
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return gcd_euclidean( a, b );
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}
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};
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};
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template < >
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struct gcd_optimal_evaluator_helper2_t< true, true >
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{
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template < typename T >
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struct helper
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{
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T operator ()( T const &a, T const &b )
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{
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return gcd_integer( a, b );
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}
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};
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};
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template < typename T, bool IsSpecialized, bool IsSigned >
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struct gcd_optimal_evaluator_helper_t
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: gcd_optimal_evaluator_helper2_t<IsSpecialized, IsSigned>
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::BOOST_NESTED_TEMPLATE helper<T>
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{
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};
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#endif
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template < typename T >
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struct gcd_optimal_evaluator
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{
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T operator ()( T const &a, T const &b )
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{
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typedef ::std::numeric_limits<T> limits_type;
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typedef gcd_optimal_evaluator_helper_t<T,
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limits_type::is_specialized, limits_type::is_signed> helper_type;
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helper_type solver;
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return solver( a, b );
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}
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};
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#else // BOOST_NO_LIMITS_COMPILE_TIME_CONSTANTS
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template < typename T >
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struct gcd_optimal_evaluator
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{
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T operator ()( T const &a, T const &b )
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{
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return gcd_integer( a, b );
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}
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};
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#endif
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// Specialize for the built-in integers
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#define BOOST_PRIVATE_GCD_UF( Ut ) \
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template < > struct gcd_optimal_evaluator<Ut> \
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{ Ut operator ()( Ut a, Ut b ) const { return gcd_binary( a, b ); } }
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BOOST_PRIVATE_GCD_UF( unsigned char );
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BOOST_PRIVATE_GCD_UF( unsigned short );
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BOOST_PRIVATE_GCD_UF( unsigned );
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BOOST_PRIVATE_GCD_UF( unsigned long );
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#ifdef BOOST_HAS_LONG_LONG
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BOOST_PRIVATE_GCD_UF( boost::ulong_long_type );
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#elif defined(BOOST_HAS_MS_INT64)
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BOOST_PRIVATE_GCD_UF( unsigned __int64 );
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#endif
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#if CHAR_MIN == 0
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BOOST_PRIVATE_GCD_UF( char ); // char is unsigned
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#endif
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#undef BOOST_PRIVATE_GCD_UF
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#define BOOST_PRIVATE_GCD_SF( St, Ut ) \
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template < > struct gcd_optimal_evaluator<St> \
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{ St operator ()( St a, St b ) const { Ut const a_abs = \
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static_cast<Ut>( a < 0 ? -a : +a ), b_abs = static_cast<Ut>( \
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b < 0 ? -b : +b ); return static_cast<St>( \
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gcd_optimal_evaluator<Ut>()(a_abs, b_abs) ); } }
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BOOST_PRIVATE_GCD_SF( signed char, unsigned char );
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BOOST_PRIVATE_GCD_SF( short, unsigned short );
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BOOST_PRIVATE_GCD_SF( int, unsigned );
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BOOST_PRIVATE_GCD_SF( long, unsigned long );
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#if CHAR_MIN < 0
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BOOST_PRIVATE_GCD_SF( char, unsigned char ); // char is signed
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#endif
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#ifdef BOOST_HAS_LONG_LONG
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BOOST_PRIVATE_GCD_SF( boost::long_long_type, boost::ulong_long_type );
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#elif defined(BOOST_HAS_MS_INT64)
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BOOST_PRIVATE_GCD_SF( __int64, unsigned __int64 );
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#endif
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#undef BOOST_PRIVATE_GCD_SF
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#ifndef BOOST_NO_LIMITS_COMPILE_TIME_CONSTANTS
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#ifndef BOOST_NO_TEMPLATE_PARTIAL_SPECIALIZATION
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template < typename T, bool IsSpecialized, bool IsSigned >
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struct lcm_optimal_evaluator_helper_t
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{
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T operator ()( T const &a, T const &b )
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{
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return lcm_euclidean( a, b );
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}
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};
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template < typename T >
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struct lcm_optimal_evaluator_helper_t< T, true, true >
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{
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T operator ()( T const &a, T const &b )
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{
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return lcm_integer( a, b );
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}
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};
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#else
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template < bool IsSpecialized, bool IsSigned >
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struct lcm_optimal_evaluator_helper2_t
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{
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template < typename T >
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struct helper
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{
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T operator ()( T const &a, T const &b )
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{
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return lcm_euclidean( a, b );
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}
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};
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};
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template < >
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struct lcm_optimal_evaluator_helper2_t< true, true >
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{
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template < typename T >
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struct helper
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{
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T operator ()( T const &a, T const &b )
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{
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return lcm_integer( a, b );
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}
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};
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};
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template < typename T, bool IsSpecialized, bool IsSigned >
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struct lcm_optimal_evaluator_helper_t
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: lcm_optimal_evaluator_helper2_t<IsSpecialized, IsSigned>
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::BOOST_NESTED_TEMPLATE helper<T>
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{
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};
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#endif
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template < typename T >
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struct lcm_optimal_evaluator
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{
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T operator ()( T const &a, T const &b )
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{
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typedef ::std::numeric_limits<T> limits_type;
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typedef lcm_optimal_evaluator_helper_t<T,
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limits_type::is_specialized, limits_type::is_signed> helper_type;
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helper_type solver;
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return solver( a, b );
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}
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};
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#else // BOOST_NO_LIMITS_COMPILE_TIME_CONSTANTS
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template < typename T >
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struct lcm_optimal_evaluator
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{
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T operator ()( T const &a, T const &b )
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{
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return lcm_integer( a, b );
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}
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};
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#endif
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// Functions to find the GCD or LCM in the best way
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template < typename T >
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inline
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T
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gcd_optimal
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(
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T const & a,
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T const & b
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)
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{
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gcd_optimal_evaluator<T> solver;
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return solver( a, b );
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}
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template < typename T >
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inline
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T
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lcm_optimal
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(
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T const & a,
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T const & b
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)
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{
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lcm_optimal_evaluator<T> solver;
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return solver( a, b );
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}
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} // namespace detail
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// Greatest common divisor evaluator member function definition ------------//
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template < typename IntegerType >
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inline
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typename gcd_evaluator<IntegerType>::result_type
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gcd_evaluator<IntegerType>::operator ()
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(
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first_argument_type const & a,
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second_argument_type const & b
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) const
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{
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return detail::gcd_optimal( a, b );
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}
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// Least common multiple evaluator member function definition --------------//
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template < typename IntegerType >
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inline
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typename lcm_evaluator<IntegerType>::result_type
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lcm_evaluator<IntegerType>::operator ()
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(
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first_argument_type const & a,
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second_argument_type const & b
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) const
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{
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return detail::lcm_optimal( a, b );
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}
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// Greatest common divisor and least common multiple function definitions --//
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template < typename IntegerType >
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inline
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IntegerType
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gcd
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(
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IntegerType const & a,
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IntegerType const & b
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)
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{
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gcd_evaluator<IntegerType> solver;
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return solver( a, b );
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}
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template < typename IntegerType >
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inline
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IntegerType
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lcm
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(
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IntegerType const & a,
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IntegerType const & b
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)
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{
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lcm_evaluator<IntegerType> solver;
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return solver( a, b );
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}
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} // namespace math
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} // namespace boost
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#ifdef BOOST_MSVC
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#pragma warning(pop)
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#endif
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#endif // BOOST_MATH_COMMON_FACTOR_RT_HPP
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