mirror of
https://github.com/bolero-MURAKAMI/Sprout.git
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260 lines
9.5 KiB
C++
260 lines
9.5 KiB
C++
/*=============================================================================
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Copyright (c) 2011-2014 Bolero MURAKAMI
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https://github.com/bolero-MURAKAMI/Sprout
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Distributed under the Boost Software License, Version 1.0. (See accompanying
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file LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_0.txt)
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=============================================================================*/
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#ifndef SPROUT_MATH_GCD_HPP
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#define SPROUT_MATH_GCD_HPP
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#include <climits>
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#include <sprout/config.hpp>
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#include <sprout/limits.hpp>
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#include <sprout/array/array.hpp>
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#include <sprout/cstdlib/abs.hpp>
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#ifdef SPROUT_WORKAROUND_NOT_TERMINATE_RECURSIVE_CONSTEXPR_FUNCTION_TEMPLATE
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# include <sprout/workaround/recursive_function_template.hpp>
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#endif
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namespace sprout {
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namespace math {
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namespace detail {
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template<typename RingType>
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inline SPROUT_CONSTEXPR RingType
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gcd_euclidean(RingType a, RingType b) {
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return a == static_cast<RingType>(0) ? b
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: b % a == static_cast<RingType>(0) ? a
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: sprout::math::detail::gcd_euclidean(a % (b % a), b % a)
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;
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}
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template<typename IntType>
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inline SPROUT_CONSTEXPR IntType
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gcd_integer_impl(IntType result) {
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return result < static_cast<IntType>(0) ? -result : result;
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}
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template<typename IntType>
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inline SPROUT_CONSTEXPR IntType
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gcd_integer(IntType const& a, IntType const& b) {
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return sprout::math::detail::gcd_integer_impl(
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sprout::math::detail::gcd_euclidean(a, b)
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);
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}
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#ifdef SPROUT_WORKAROUND_NOT_TERMINATE_RECURSIVE_CONSTEXPR_FUNCTION_TEMPLATE
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template<int D = 16, typename BuiltInUnsigned, SPROUT_RECURSIVE_FUNCTION_TEMPLATE_CONTINUE(D)>
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inline SPROUT_CONSTEXPR BuiltInUnsigned
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gcd_binary_2_1(unsigned shifts, sprout::array<BuiltInUnsigned, 2> const& r, unsigned which);
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template<int D = 16, typename BuiltInUnsigned, SPROUT_RECURSIVE_FUNCTION_TEMPLATE_BREAK(D)>
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inline SPROUT_CONSTEXPR BuiltInUnsigned
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gcd_binary_2_1(unsigned shifts, sprout::array<BuiltInUnsigned, 2> const& r, unsigned which);
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template<int D, typename BuiltInUnsigned, SPROUT_RECURSIVE_FUNCTION_TEMPLATE_CONTINUE(D)>
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inline SPROUT_CONSTEXPR BuiltInUnsigned
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gcd_binary_2_2(unsigned shifts, sprout::array<BuiltInUnsigned, 2> const& r, unsigned which) {
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return r[which] ? sprout::math::detail::gcd_binary_2_1<D + 1>(shifts, r, which)
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: r[!which] << shifts
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;
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}
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template<int D, typename BuiltInUnsigned, SPROUT_RECURSIVE_FUNCTION_TEMPLATE_BREAK(D)>
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inline SPROUT_CONSTEXPR BuiltInUnsigned
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gcd_binary_2_2(unsigned, sprout::array<BuiltInUnsigned, 2> const&, unsigned) {
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return sprout::throw_recursive_function_template_instantiation_exeeded();
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}
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template<int D, typename BuiltInUnsigned, SPROUT_RECURSIVE_FUNCTION_TEMPLATE_CONTINUE_DECL(D)>
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inline SPROUT_CONSTEXPR BuiltInUnsigned
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gcd_binary_2_1(unsigned shifts, sprout::array<BuiltInUnsigned, 2> const& r, unsigned which) {
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return !(r[which] & 1u) ? sprout::math::detail::gcd_binary_2_1<D + 2>(
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shifts,
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which ? sprout::array<BuiltInUnsigned, 2>{{r[0], BuiltInUnsigned(r[1] >> 1)}}
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: sprout::array<BuiltInUnsigned, 2>{{BuiltInUnsigned(r[0] >> 1), r[1]}}
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,
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which
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)
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: r[!which] > r[which] ? sprout::math::detail::gcd_binary_2_2<D + 1>(
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shifts,
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which ^ 1u ? sprout::array<BuiltInUnsigned, 2>{{r[0], BuiltInUnsigned(r[1] - r[0])}}
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: sprout::array<BuiltInUnsigned, 2>{{BuiltInUnsigned(r[0] - r[1]), r[1]}}
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,
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which ^ 1u
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)
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: sprout::math::detail::gcd_binary_2_2<D + 1>(
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shifts,
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which ? sprout::array<BuiltInUnsigned, 2>{{r[0], BuiltInUnsigned(r[1] - r[0])}}
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: sprout::array<BuiltInUnsigned, 2>{{BuiltInUnsigned(r[0] - r[1]), r[1]}}
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,
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which
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)
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;
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}
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template<int D, typename BuiltInUnsigned, SPROUT_RECURSIVE_FUNCTION_TEMPLATE_BREAK_DECL(D)>
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inline SPROUT_CONSTEXPR BuiltInUnsigned
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gcd_binary_2_1(unsigned, sprout::array<BuiltInUnsigned, 2> const&, unsigned) {
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return sprout::throw_recursive_function_template_instantiation_exeeded();
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}
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#else
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template<typename BuiltInUnsigned>
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inline SPROUT_CONSTEXPR BuiltInUnsigned
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gcd_binary_2_1(unsigned shifts, sprout::array<BuiltInUnsigned, 2> const& r, unsigned which);
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template<typename BuiltInUnsigned>
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inline SPROUT_CONSTEXPR BuiltInUnsigned
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gcd_binary_2_2(unsigned shifts, sprout::array<BuiltInUnsigned, 2> const& r, unsigned which) {
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return r[which] ? sprout::math::detail::gcd_binary_2_1(shifts, r, which)
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: r[!which] << shifts
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;
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}
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template<typename BuiltInUnsigned>
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inline SPROUT_CONSTEXPR BuiltInUnsigned
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gcd_binary_2_1(unsigned shifts, sprout::array<BuiltInUnsigned, 2> const& r, unsigned which) {
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return !(r[which] & 1u) ? sprout::math::detail::gcd_binary_2_1(
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shifts,
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which ? sprout::array<BuiltInUnsigned, 2>{{r[0], BuiltInUnsigned(r[1] >> 1)}}
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: sprout::array<BuiltInUnsigned, 2>{{BuiltInUnsigned(r[0] >> 1), r[1]}}
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,
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which
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)
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: r[!which] > r[which] ? sprout::math::detail::gcd_binary_2_2(
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shifts,
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which ^ 1u ? sprout::array<BuiltInUnsigned, 2>{{r[0], BuiltInUnsigned(r[1] - r[0])}}
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: sprout::array<BuiltInUnsigned, 2>{{BuiltInUnsigned(r[0] - r[1]), r[1]}}
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,
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which ^ 1u
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)
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: sprout::math::detail::gcd_binary_2_2(
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shifts,
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which ? sprout::array<BuiltInUnsigned, 2>{{r[0], BuiltInUnsigned(r[1] - r[0])}}
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: sprout::array<BuiltInUnsigned, 2>{{BuiltInUnsigned(r[0] - r[1]), r[1]}}
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,
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which
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)
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;
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}
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#endif
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template<typename BuiltInUnsigned>
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inline SPROUT_CONSTEXPR BuiltInUnsigned
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gcd_binary_1(BuiltInUnsigned u, BuiltInUnsigned v, unsigned shifts = 0) {
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return (!(u & 1u) && !(v & 1u)) ? sprout::math::detail::gcd_binary_1(u >> 1, v >> 1, shifts + 1)
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: sprout::math::detail::gcd_binary_2_1(
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shifts, sprout::array<BuiltInUnsigned, 2>{{u, v}}, static_cast<bool>(u & 1u)
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)
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;
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}
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template<typename BuiltInUnsigned>
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inline SPROUT_CONSTEXPR BuiltInUnsigned
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gcd_binary(BuiltInUnsigned u, BuiltInUnsigned v) {
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return u && v ? sprout::math::detail::gcd_binary_1(u, v)
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: u + v
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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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public:
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SPROUT_CONSTEXPR T operator()(T const& a, T const& b) const {
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return sprout::math::detail::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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public:
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SPROUT_CONSTEXPR T operator()(T const& a, T const& b) const {
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return sprout::math::detail::gcd_integer(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 {
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public:
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SPROUT_CONSTEXPR T operator()(T const& a, T const& b) const {
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typedef sprout::numeric_limits<T> limits_type;
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typedef sprout::math::detail::gcd_optimal_evaluator_helper_t<
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T, limits_type::is_specialized, limits_type::is_signed
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> helper_type;
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return helper_type().operator()(a, b);
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}
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};
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# define SPROUT_PRIVATE_GCD_UF(Ut) \
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template<> \
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struct gcd_optimal_evaluator<Ut> { \
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public: \
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SPROUT_CONSTEXPR Ut operator()(Ut a, Ut b) const { \
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return sprout::math::detail::gcd_binary(a, b); \
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} \
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}
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SPROUT_PRIVATE_GCD_UF(unsigned char);
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SPROUT_PRIVATE_GCD_UF(unsigned short);
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SPROUT_PRIVATE_GCD_UF(unsigned);
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SPROUT_PRIVATE_GCD_UF(unsigned long);
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SPROUT_PRIVATE_GCD_UF(unsigned long long);
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# if CHAR_MIN == 0
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SPROUT_PRIVATE_GCD_UF(char);
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# endif
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#undef SPROUT_PRIVATE_GCD_UF
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# define SPROUT_PRIVATE_GCD_SF(St, Ut) \
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template<> \
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struct gcd_optimal_evaluator<St> { \
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public: \
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SPROUT_CONSTEXPR St operator()(St a, St b) const { \
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using sprout::abs; \
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return static_cast<St>(sprout::math::detail::gcd_optimal_evaluator<Ut>().operator()( \
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static_cast<Ut>(abs(a)), static_cast<Ut>(abs(b)) \
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)); \
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} \
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}
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SPROUT_PRIVATE_GCD_SF(signed char, unsigned char);
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SPROUT_PRIVATE_GCD_SF(short, unsigned short);
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SPROUT_PRIVATE_GCD_SF(int, unsigned);
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SPROUT_PRIVATE_GCD_SF(long, unsigned long);
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# if CHAR_MIN < 0
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SPROUT_PRIVATE_GCD_SF(char, unsigned char);
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# endif
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SPROUT_PRIVATE_GCD_SF(long long, unsigned long long);
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#undef SPROUT_PRIVATE_GCD_SF
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template<typename T>
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inline SPROUT_CONSTEXPR T
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gcd_optimal(T const& a, T const& b) {
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return sprout::math::detail::gcd_optimal_evaluator<T>().operator()(a, b);
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}
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} // namespace detail
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//
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// gcd_evaluator
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//
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template<typename IntType = void>
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class gcd_evaluator {
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public:
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typedef IntType result_type;
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typedef IntType first_argument_type;
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typedef IntType second_argument_type;
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public:
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SPROUT_CONSTEXPR IntType
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operator()(IntType const& a, IntType const& b) const {
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return sprout::math::detail::gcd_optimal(a, b);
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}
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};
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template<>
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class gcd_evaluator<void> {
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public:
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template<typename IntType>
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SPROUT_CONSTEXPR IntType
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operator()(IntType const& a, IntType const& b) const {
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return sprout::math::detail::gcd_optimal(a, b);
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}
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};
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//
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// gcd
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//
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template<typename IntType>
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inline SPROUT_CONSTEXPR IntType
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gcd(IntType const& a, IntType const& b) {
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return sprout::math::gcd_evaluator<IntType>().operator()(a, b);
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}
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} // namespace math
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using sprout::math::gcd;
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} // namespace sprout
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#endif // #ifndef SPROUT_MATH_GCD_HPP
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