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561 lines
14 KiB
C++
561 lines
14 KiB
C++
// Boost common_factor.hpp header file -------------------------------------//
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// (C) Copyright Daryle Walker, Stephen Cleary, Paul Moore 2001. Permission
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// to copy, use, modify, sell and distribute this software is granted provided
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// this copyright notice appears in all copies. This software is provided "as
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// is" without express or implied warranty, and with no claim as to its
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// suitability for any purpose.
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// See http://www.boost.org for updates, documentation, and revision history.
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#ifndef BOOST_MATH_COMMON_FACTOR_HPP
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#define BOOST_MATH_COMMON_FACTOR_HPP
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#include <boost/math_fwd.hpp> // self include
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#include <boost/config.hpp> // for BOOST_STATIC_CONSTANT, etc.
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#include <boost/limits.hpp> // for std::numeric_limits
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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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#ifndef BOOST_NO_TEMPLATE_PARTIAL_SPECIALIZATION
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// Build GCD with Euclid's recursive algorithm
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template < unsigned long Value1, unsigned long Value2 >
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struct static_gcd_helper_t
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{
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private:
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BOOST_STATIC_CONSTANT( unsigned long, new_value1 = Value2 );
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BOOST_STATIC_CONSTANT( unsigned long, new_value2 = Value1 % Value2 );
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#ifndef __BORLANDC__
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#define BOOST_DETAIL_GCD_HELPER_VAL(Value) Value
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#else
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typedef static_gcd_helper_t self_type;
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#define BOOST_DETAIL_GCD_HELPER_VAL(Value) (self_type:: Value )
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#endif
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typedef static_gcd_helper_t< BOOST_DETAIL_GCD_HELPER_VAL(new_value1),
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BOOST_DETAIL_GCD_HELPER_VAL(new_value2) > next_step_type;
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#undef BOOST_DETAIL_GCD_HELPER_VAL
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public:
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BOOST_STATIC_CONSTANT( unsigned long, value = next_step_type::value );
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};
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// Non-recursive case
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template < unsigned long Value1 >
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struct static_gcd_helper_t< Value1, 0UL >
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{
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BOOST_STATIC_CONSTANT( unsigned long, value = Value1 );
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};
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#else
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// Use inner class template workaround from Peter Dimov
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template < unsigned long Value1 >
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struct static_gcd_helper2_t
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{
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template < unsigned long Value2 >
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struct helper
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{
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BOOST_STATIC_CONSTANT( unsigned long, value
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= static_gcd_helper2_t<Value2>::helper<Value1 % Value2>::value );
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};
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template < >
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struct helper< 0UL >
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{
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BOOST_STATIC_CONSTANT( unsigned long, value = Value1 );
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};
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};
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// Special case
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template < >
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struct static_gcd_helper2_t< 0UL >
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{
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template < unsigned long Value2 >
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struct helper
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{
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BOOST_STATIC_CONSTANT( unsigned long, value = Value2 );
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};
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};
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// Build the GCD from the above template(s)
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template < unsigned long Value1, unsigned long Value2 >
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struct static_gcd_helper_t
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{
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BOOST_STATIC_CONSTANT( unsigned long, value
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= static_gcd_helper2_t<Value1>::BOOST_NESTED_TEMPLATE
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helper<Value2>::value );
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};
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#endif
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#ifndef BOOST_NO_TEMPLATE_PARTIAL_SPECIALIZATION
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// Build the LCM from the GCD
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template < unsigned long Value1, unsigned long Value2 >
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struct static_lcm_helper_t
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{
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typedef static_gcd_helper_t<Value1, Value2> gcd_type;
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BOOST_STATIC_CONSTANT( unsigned long, value = Value1 / gcd_type::value
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* Value2 );
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};
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// Special case for zero-GCD values
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template < >
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struct static_lcm_helper_t< 0UL, 0UL >
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{
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BOOST_STATIC_CONSTANT( unsigned long, value = 0UL );
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};
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#else
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// Adapt GCD's inner class template workaround for LCM
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template < unsigned long Value1 >
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struct static_lcm_helper2_t
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{
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template < unsigned long Value2 >
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struct helper
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{
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typedef static_gcd_helper_t<Value1, Value2> gcd_type;
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BOOST_STATIC_CONSTANT( unsigned long, value = Value1
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/ gcd_type::value * Value2 );
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};
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template < >
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struct helper< 0UL >
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{
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BOOST_STATIC_CONSTANT( unsigned long, value = 0UL );
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};
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};
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// Special case
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template < >
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struct static_lcm_helper2_t< 0UL >
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{
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template < unsigned long Value2 >
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struct helper
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{
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BOOST_STATIC_CONSTANT( unsigned long, value = 0UL );
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};
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};
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// Build the LCM from the above template(s)
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template < unsigned long Value1, unsigned long Value2 >
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struct static_lcm_helper_t
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{
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BOOST_STATIC_CONSTANT( unsigned long, value
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= static_lcm_helper2_t<Value1>::BOOST_NESTED_TEMPLATE
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helper<Value2>::value );
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};
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#endif
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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 ) ? -result : result;
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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 ) ? -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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#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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// Compile-time greatest common divisor evaluator class declaration --------//
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template < unsigned long Value1, unsigned long Value2 >
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struct static_gcd
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{
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BOOST_STATIC_CONSTANT( unsigned long, value
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= (detail::static_gcd_helper_t<Value1, Value2>::value) );
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}; // boost::math::static_gcd
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// Compile-time least common multiple evaluator class declaration ----------//
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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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BOOST_STATIC_CONSTANT( unsigned long, value
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= (detail::static_lcm_helper_t<Value1, Value2>::value) );
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}; // boost::math::static_lcm
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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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#endif // BOOST_MATH_COMMON_FACTOR_HPP
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