| // -*- C++ -*- |
| //===----------------------------------------------------------------------===// |
| // |
| // Part of the LLVM Project, under the Apache License v2.0 with LLVM Exceptions. |
| // See https://llvm.org/LICENSE.txt for license information. |
| // SPDX-License-Identifier: Apache-2.0 WITH LLVM-exception |
| // |
| //===----------------------------------------------------------------------===// |
| |
| #ifndef _LIBCPP___NUMERIC_GCD_LCM_H |
| #define _LIBCPP___NUMERIC_GCD_LCM_H |
| |
| #include <__algorithm/min.h> |
| #include <__assert> |
| #include <__bit/countr.h> |
| #include <__config> |
| #include <__type_traits/common_type.h> |
| #include <__type_traits/is_integral.h> |
| #include <__type_traits/is_same.h> |
| #include <__type_traits/is_signed.h> |
| #include <__type_traits/make_unsigned.h> |
| #include <limits> |
| |
| #if !defined(_LIBCPP_HAS_NO_PRAGMA_SYSTEM_HEADER) |
| # pragma GCC system_header |
| #endif |
| |
| _LIBCPP_PUSH_MACROS |
| #include <__undef_macros> |
| |
| _LIBCPP_BEGIN_NAMESPACE_STD |
| |
| #if _LIBCPP_STD_VER >= 17 |
| |
| template <typename _Result, typename _Source, bool _IsSigned = is_signed<_Source>::value> |
| struct __ct_abs; |
| |
| template <typename _Result, typename _Source> |
| struct __ct_abs<_Result, _Source, true> { |
| constexpr _LIBCPP_HIDE_FROM_ABI _Result operator()(_Source __t) const noexcept { |
| if (__t >= 0) |
| return __t; |
| if (__t == numeric_limits<_Source>::min()) |
| return -static_cast<_Result>(__t); |
| return -__t; |
| } |
| }; |
| |
| template <typename _Result, typename _Source> |
| struct __ct_abs<_Result, _Source, false> { |
| constexpr _LIBCPP_HIDE_FROM_ABI _Result operator()(_Source __t) const noexcept { return __t; } |
| }; |
| |
| template <class _Tp> |
| constexpr _LIBCPP_HIDDEN _Tp __gcd(_Tp __a, _Tp __b) { |
| static_assert(!is_signed<_Tp>::value, ""); |
| |
| // Using Binary GCD algorithm https://en.wikipedia.org/wiki/Binary_GCD_algorithm, based on an implementation |
| // from https://lemire.me/blog/2024/04/13/greatest-common-divisor-the-extended-euclidean-algorithm-and-speed/ |
| // |
| // If power of two divides both numbers, we can push it out. |
| // - gcd( 2^x * a, 2^x * b) = 2^x * gcd(a, b) |
| // |
| // If and only if exactly one number is even, we can divide that number by that power. |
| // - if a, b are odd, then gcd(2^x * a, b) = gcd(a, b) |
| // |
| // And standard gcd algorithm where instead of modulo, minus is used. |
| |
| if (__a < __b) { |
| _Tp __tmp = __b; |
| __b = __a; |
| __a = __tmp; |
| } |
| if (__b == 0) |
| return __a; |
| __a %= __b; // Make both argument of the same size, and early result in the easy case. |
| if (__a == 0) |
| return __b; |
| |
| _Tp __c = __a | __b; |
| int __shift = std::__countr_zero(__c); |
| __a >>= std::__countr_zero(__a); |
| do { |
| _Tp __t = __b >> std::__countr_zero(__b); |
| if (__a > __t) { |
| __b = __a - __t; |
| __a = __t; |
| } else { |
| __b = __t - __a; |
| } |
| } while (__b != 0); |
| return __a << __shift; |
| } |
| |
| template <class _Tp, class _Up> |
| constexpr _LIBCPP_HIDE_FROM_ABI common_type_t<_Tp, _Up> gcd(_Tp __m, _Up __n) { |
| static_assert(is_integral<_Tp>::value && is_integral<_Up>::value, "Arguments to gcd must be integer types"); |
| static_assert(!is_same<__remove_cv_t<_Tp>, bool>::value, "First argument to gcd cannot be bool"); |
| static_assert(!is_same<__remove_cv_t<_Up>, bool>::value, "Second argument to gcd cannot be bool"); |
| using _Rp = common_type_t<_Tp, _Up>; |
| using _Wp = make_unsigned_t<_Rp>; |
| return static_cast<_Rp>( |
| std::__gcd(static_cast<_Wp>(__ct_abs<_Rp, _Tp>()(__m)), static_cast<_Wp>(__ct_abs<_Rp, _Up>()(__n)))); |
| } |
| |
| template <class _Tp, class _Up> |
| constexpr _LIBCPP_HIDE_FROM_ABI common_type_t<_Tp, _Up> lcm(_Tp __m, _Up __n) { |
| static_assert(is_integral<_Tp>::value && is_integral<_Up>::value, "Arguments to lcm must be integer types"); |
| static_assert(!is_same<__remove_cv_t<_Tp>, bool>::value, "First argument to lcm cannot be bool"); |
| static_assert(!is_same<__remove_cv_t<_Up>, bool>::value, "Second argument to lcm cannot be bool"); |
| if (__m == 0 || __n == 0) |
| return 0; |
| |
| using _Rp = common_type_t<_Tp, _Up>; |
| _Rp __val1 = __ct_abs<_Rp, _Tp>()(__m) / std::gcd(__m, __n); |
| _Rp __val2 = __ct_abs<_Rp, _Up>()(__n); |
| _Rp __res; |
| [[maybe_unused]] bool __overflow = __builtin_mul_overflow(__val1, __val2, &__res); |
| _LIBCPP_ASSERT_ARGUMENT_WITHIN_DOMAIN(!__overflow, "Overflow in lcm"); |
| return __res; |
| } |
| |
| #endif // _LIBCPP_STD_VER >= 17 |
| |
| _LIBCPP_END_NAMESPACE_STD |
| |
| _LIBCPP_POP_MACROS |
| |
| #endif // _LIBCPP___NUMERIC_GCD_LCM_H |