boostorg/integer
1
0
Fork 1
mirror of https://github.com/boostorg/integer.git synced 2025-10-31 16:21:37 +01:00
Code Issues Packages Projects Releases Wiki Activity
Files
217fa37de2cbe8a58c0d2128e4b731f687981d03
integer/include/boost/math/common_factor_rt.hpp
John Maddock 307fee457a Fix Borland infinite looping issue. 
[SVN r39723]
2015-01-13 19:41:27 +02:00

513 lines
13 KiB
C++
Raw Blame History

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