Sprout/sprout/math/gcd.hpp
2013-03-22 14:24:19 +09:00

251 lines
9 KiB
C++

#ifndef SPROUT_MATH_GCD_HPP
#define SPROUT_MATH_GCD_HPP
#include <climits>
#include <limits>
#include <sprout/config.hpp>
#include <sprout/array/array.hpp>
#include <sprout/cstdlib/abs.hpp>
#ifdef SPROUT_WORKAROUND_NOT_TERMINATE_RECURSIVE_CONSTEXPR_FUNCTION_TEMPLATE
# include <sprout/workaround/recursive_function_template.hpp>
#endif
namespace sprout {
namespace math {
namespace detail {
template<typename RingType>
inline SPROUT_CONSTEXPR RingType
gcd_euclidean(RingType a, RingType b) {
return a == static_cast<RingType>(0) ? b
: b % a == static_cast<RingType>(0) ? a
: sprout::math::detail::gcd_euclidean(a % (b % a), b % a)
;
}
template<typename IntType>
inline SPROUT_CONSTEXPR IntType
gcd_integer_impl(IntType result) {
return result < static_cast<IntType>(0) ? -result : result;
}
template<typename IntType>
inline SPROUT_CONSTEXPR IntType
gcd_integer(IntType const& a, IntType const& b) {
return sprout::math::detail::gcd_integer_impl(
sprout::math::detail::gcd_euclidean(a, b)
);
}
#ifdef SPROUT_WORKAROUND_NOT_TERMINATE_RECURSIVE_CONSTEXPR_FUNCTION_TEMPLATE
template<int D = 16, typename BuiltInUnsigned, SPROUT_RECURSIVE_FUNCTION_TEMPLATE_CONTINUE(D)>
inline SPROUT_CONSTEXPR BuiltInUnsigned
gcd_binary_2_1(unsigned shifts, sprout::array<BuiltInUnsigned, 2> const& r, unsigned which);
template<int D = 16, typename BuiltInUnsigned, SPROUT_RECURSIVE_FUNCTION_TEMPLATE_BREAK(D)>
inline SPROUT_CONSTEXPR BuiltInUnsigned
gcd_binary_2_1(unsigned shifts, sprout::array<BuiltInUnsigned, 2> const& r, unsigned which);
template<int D, typename BuiltInUnsigned, SPROUT_RECURSIVE_FUNCTION_TEMPLATE_CONTINUE(D)>
inline SPROUT_CONSTEXPR BuiltInUnsigned
gcd_binary_2_2(unsigned shifts, sprout::array<BuiltInUnsigned, 2> const& r, unsigned which) {
return r[which] ? sprout::math::detail::gcd_binary_2_1<D + 1>(shifts, r, which)
: r[!which] << shifts
;
}
template<int D, typename BuiltInUnsigned, SPROUT_RECURSIVE_FUNCTION_TEMPLATE_BREAK(D)>
inline SPROUT_CONSTEXPR BuiltInUnsigned
gcd_binary_2_2(unsigned shifts, sprout::array<BuiltInUnsigned, 2> const& r, unsigned which) {
return sprout::throw_recursive_function_template_instantiation_exeeded();
}
template<int D, typename BuiltInUnsigned, SPROUT_RECURSIVE_FUNCTION_TEMPLATE_CONTINUE_DECL(D)>
inline SPROUT_CONSTEXPR BuiltInUnsigned
gcd_binary_2_1(unsigned shifts, sprout::array<BuiltInUnsigned, 2> const& r, unsigned which) {
return !(r[which] & 1u) ? sprout::math::detail::gcd_binary_2_1<D + 2>(
shifts,
which ? sprout::array<BuiltInUnsigned, 2>{{r[0], BuiltInUnsigned(r[1] >> 1)}}
: sprout::array<BuiltInUnsigned, 2>{{BuiltInUnsigned(r[0] >> 1), r[1]}}
,
which
)
: r[!which] > r[which] ? sprout::math::detail::gcd_binary_2_2<D + 1>(
shifts,
which ^ 1u ? sprout::array<BuiltInUnsigned, 2>{{r[0], BuiltInUnsigned(r[1] - r[0])}}
: sprout::array<BuiltInUnsigned, 2>{{BuiltInUnsigned(r[0] - r[1]), r[1]}}
,
which ^ 1u
)
: sprout::math::detail::gcd_binary_2_2<D + 1>(
shifts,
which ? sprout::array<BuiltInUnsigned, 2>{{r[0], BuiltInUnsigned(r[1] - r[0])}}
: sprout::array<BuiltInUnsigned, 2>{{BuiltInUnsigned(r[0] - r[1]), r[1]}}
,
which
)
;
}
template<int D, typename BuiltInUnsigned, SPROUT_RECURSIVE_FUNCTION_TEMPLATE_BREAK_DECL(D)>
inline SPROUT_CONSTEXPR BuiltInUnsigned
gcd_binary_2_1(unsigned shifts, sprout::array<BuiltInUnsigned, 2> const& r, unsigned which) {
return sprout::throw_recursive_function_template_instantiation_exeeded();
}
#else
template<typename BuiltInUnsigned>
inline SPROUT_CONSTEXPR BuiltInUnsigned
gcd_binary_2_1(unsigned shifts, sprout::array<BuiltInUnsigned, 2> const& r, unsigned which);
template<typename BuiltInUnsigned>
inline SPROUT_CONSTEXPR BuiltInUnsigned
gcd_binary_2_2(unsigned shifts, sprout::array<BuiltInUnsigned, 2> const& r, unsigned which) {
return r[which] ? sprout::math::detail::gcd_binary_2_1(shifts, r, which)
: r[!which] << shifts
;
}
template<typename BuiltInUnsigned>
inline SPROUT_CONSTEXPR BuiltInUnsigned
gcd_binary_2_1(unsigned shifts, sprout::array<BuiltInUnsigned, 2> const& r, unsigned which) {
return !(r[which] & 1u) ? sprout::math::detail::gcd_binary_2_1(
shifts,
which ? sprout::array<BuiltInUnsigned, 2>{{r[0], BuiltInUnsigned(r[1] >> 1)}}
: sprout::array<BuiltInUnsigned, 2>{{BuiltInUnsigned(r[0] >> 1), r[1]}}
,
which
)
: r[!which] > r[which] ? sprout::math::detail::gcd_binary_2_2(
shifts,
which ^ 1u ? sprout::array<BuiltInUnsigned, 2>{{r[0], BuiltInUnsigned(r[1] - r[0])}}
: sprout::array<BuiltInUnsigned, 2>{{BuiltInUnsigned(r[0] - r[1]), r[1]}}
,
which ^ 1u
)
: sprout::math::detail::gcd_binary_2_2(
shifts,
which ? sprout::array<BuiltInUnsigned, 2>{{r[0], BuiltInUnsigned(r[1] - r[0])}}
: sprout::array<BuiltInUnsigned, 2>{{BuiltInUnsigned(r[0] - r[1]), r[1]}}
,
which
)
;
}
#endif
template<typename BuiltInUnsigned>
inline SPROUT_CONSTEXPR BuiltInUnsigned
gcd_binary_1(BuiltInUnsigned u, BuiltInUnsigned v, unsigned shifts = 0) {
return (!(u & 1u) && !(v & 1u)) ? sprout::math::detail::gcd_binary_1(u >> 1, v >> 1, shifts + 1)
: sprout::math::detail::gcd_binary_2_1(
shifts, sprout::array<BuiltInUnsigned, 2>{{u, v}}, static_cast<bool>(u & 1u)
)
;
}
template<typename BuiltInUnsigned>
inline SPROUT_CONSTEXPR BuiltInUnsigned
gcd_binary(BuiltInUnsigned u, BuiltInUnsigned v) {
return u && v ? sprout::math::detail::gcd_binary_1(u, v)
: u + v
;
}
template<typename T, bool IsSpecialized, bool IsSigned>
struct gcd_optimal_evaluator_helper_t {
public:
SPROUT_CONSTEXPR T operator()(T const& a, T const& b) const {
return sprout::math::detail::gcd_euclidean(a, b);
}
};
template<typename T>
struct gcd_optimal_evaluator_helper_t<T, true, true> {
public:
SPROUT_CONSTEXPR T operator()(T const& a, T const& b) const {
return sprout::math::detail::gcd_integer(a, b);
}
};
template<typename T>
struct gcd_optimal_evaluator {
public:
SPROUT_CONSTEXPR T operator()(T const& a, T const& b) const {
typedef std::numeric_limits<T> limits_type;
typedef sprout::math::detail::gcd_optimal_evaluator_helper_t<
T, limits_type::is_specialized, limits_type::is_signed
> helper_type;
return helper_type().operator()(a, b);
}
};
# define SPROUT_PRIVATE_GCD_UF(Ut) \
template<> \
struct gcd_optimal_evaluator<Ut> { \
public: \
SPROUT_CONSTEXPR Ut operator()(Ut a, Ut b) const { \
return sprout::math::detail::gcd_binary(a, b); \
} \
}
SPROUT_PRIVATE_GCD_UF(unsigned char);
SPROUT_PRIVATE_GCD_UF(unsigned short);
SPROUT_PRIVATE_GCD_UF(unsigned);
SPROUT_PRIVATE_GCD_UF(unsigned long);
SPROUT_PRIVATE_GCD_UF(unsigned long long);
# if CHAR_MIN == 0
SPROUT_PRIVATE_GCD_UF(char);
# endif
#undef SPROUT_PRIVATE_GCD_UF
# define SPROUT_PRIVATE_GCD_SF(St, Ut) \
template<> \
struct gcd_optimal_evaluator<St> { \
public: \
SPROUT_CONSTEXPR St operator()(St a, St b) const { \
using sprout::abs; \
return static_cast<St>(sprout::math::detail::gcd_optimal_evaluator<Ut>().operator()( \
static_cast<Ut>(abs(a)), static_cast<Ut>(abs(b)) \
)); \
} \
}
SPROUT_PRIVATE_GCD_SF(signed char, unsigned char);
SPROUT_PRIVATE_GCD_SF(short, unsigned short);
SPROUT_PRIVATE_GCD_SF(int, unsigned);
SPROUT_PRIVATE_GCD_SF(long, unsigned long);
# if CHAR_MIN < 0
SPROUT_PRIVATE_GCD_SF(char, unsigned char);
# endif
SPROUT_PRIVATE_GCD_SF(long long, unsigned long long);
#undef SPROUT_PRIVATE_GCD_SF
template<typename T>
inline SPROUT_CONSTEXPR T
gcd_optimal(T const& a, T const& b) {
return sprout::math::detail::gcd_optimal_evaluator<T>().operator()(a, b);
}
} // namespace detail
//
// gcd_evaluator
//
template<typename IntType = void>
class gcd_evaluator {
public:
typedef IntType result_type;
typedef IntType first_argument_type;
typedef IntType second_argument_type;
public:
SPROUT_CONSTEXPR IntType
operator()(IntType const& a, IntType const& b) const {
return sprout::math::detail::gcd_optimal(a, b);
}
};
template<>
class gcd_evaluator<void> {
public:
template<typename IntType>
SPROUT_CONSTEXPR IntType
operator()(IntType const& a, IntType const& b) const {
return sprout::math::detail::gcd_optimal(a, b);
}
};
//
// gcd
//
template<typename IntType>
inline SPROUT_CONSTEXPR IntType
gcd(IntType const& a, IntType const& b) {
return sprout::math::gcd_evaluator<IntType>().operator()(a, b);
}
} // namespace math
} // namespace boost
#endif // #ifndef SPROUT_MATH_GCD_HPP