1 // -*- C++ -*- 2 //===----------------------------------------------------------------------===// 3 // 4 // Part of the LLVM Project, under the Apache License v2.0 with LLVM Exceptions. 5 // See https://llvm.org/LICENSE.txt for license information. 6 // SPDX-License-Identifier: Apache-2.0 WITH LLVM-exception 7 // 8 //===----------------------------------------------------------------------===// 9 10 #ifndef _LIBCPP___NUMERIC_GCD_LCM_H 11 #define _LIBCPP___NUMERIC_GCD_LCM_H 12 13 #include <__algorithm/min.h> 14 #include <__assert> 15 #include <__bit/countr.h> 16 #include <__config> 17 #include <__type_traits/common_type.h> 18 #include <__type_traits/is_integral.h> 19 #include <__type_traits/is_same.h> 20 #include <__type_traits/is_signed.h> 21 #include <__type_traits/make_unsigned.h> 22 #include <limits> 23 24 #if !defined(_LIBCPP_HAS_NO_PRAGMA_SYSTEM_HEADER) 25 # pragma GCC system_header 26 #endif 27 28 _LIBCPP_PUSH_MACROS 29 #include <__undef_macros> 30 31 _LIBCPP_BEGIN_NAMESPACE_STD 32 33 #if _LIBCPP_STD_VER >= 17 34 35 template <typename _Result, typename _Source, bool _IsSigned = is_signed<_Source>::value> 36 struct __ct_abs; 37 38 template <typename _Result, typename _Source> 39 struct __ct_abs<_Result, _Source, true> { 40 constexpr _LIBCPP_HIDE_FROM_ABI _Result operator()(_Source __t) const noexcept { 41 if (__t >= 0) 42 return __t; 43 if (__t == numeric_limits<_Source>::min()) 44 return -static_cast<_Result>(__t); 45 return -__t; 46 } 47 }; 48 49 template <typename _Result, typename _Source> 50 struct __ct_abs<_Result, _Source, false> { 51 constexpr _LIBCPP_HIDE_FROM_ABI _Result operator()(_Source __t) const noexcept { return __t; } 52 }; 53 54 template <class _Tp> 55 constexpr _LIBCPP_HIDDEN _Tp __gcd(_Tp __a, _Tp __b) { 56 static_assert(!is_signed<_Tp>::value, ""); 57 58 // Using Binary GCD algorithm https://en.wikipedia.org/wiki/Binary_GCD_algorithm, based on an implementation 59 // from https://lemire.me/blog/2024/04/13/greatest-common-divisor-the-extended-euclidean-algorithm-and-speed/ 60 // 61 // If power of two divides both numbers, we can push it out. 62 // - gcd( 2^x * a, 2^x * b) = 2^x * gcd(a, b) 63 // 64 // If and only if exactly one number is even, we can divide that number by that power. 65 // - if a, b are odd, then gcd(2^x * a, b) = gcd(a, b) 66 // 67 // And standard gcd algorithm where instead of modulo, minus is used. 68 69 if (__a < __b) { 70 _Tp __tmp = __b; 71 __b = __a; 72 __a = __tmp; 73 } 74 if (__b == 0) 75 return __a; 76 __a %= __b; // Make both argument of the same size, and early result in the easy case. 77 if (__a == 0) 78 return __b; 79 80 _Tp __c = __a | __b; 81 int __shift = std::__countr_zero(__c); 82 __a >>= std::__countr_zero(__a); 83 do { 84 _Tp __t = __b >> std::__countr_zero(__b); 85 if (__a > __t) { 86 __b = __a - __t; 87 __a = __t; 88 } else { 89 __b = __t - __a; 90 } 91 } while (__b != 0); 92 return __a << __shift; 93 } 94 95 template <class _Tp, class _Up> 96 constexpr _LIBCPP_HIDE_FROM_ABI common_type_t<_Tp, _Up> gcd(_Tp __m, _Up __n) { 97 static_assert(is_integral<_Tp>::value && is_integral<_Up>::value, "Arguments to gcd must be integer types"); 98 static_assert(!is_same<__remove_cv_t<_Tp>, bool>::value, "First argument to gcd cannot be bool"); 99 static_assert(!is_same<__remove_cv_t<_Up>, bool>::value, "Second argument to gcd cannot be bool"); 100 using _Rp = common_type_t<_Tp, _Up>; 101 using _Wp = make_unsigned_t<_Rp>; 102 return static_cast<_Rp>( 103 std::__gcd(static_cast<_Wp>(__ct_abs<_Rp, _Tp>()(__m)), static_cast<_Wp>(__ct_abs<_Rp, _Up>()(__n)))); 104 } 105 106 template <class _Tp, class _Up> 107 constexpr _LIBCPP_HIDE_FROM_ABI common_type_t<_Tp, _Up> lcm(_Tp __m, _Up __n) { 108 static_assert(is_integral<_Tp>::value && is_integral<_Up>::value, "Arguments to lcm must be integer types"); 109 static_assert(!is_same<__remove_cv_t<_Tp>, bool>::value, "First argument to lcm cannot be bool"); 110 static_assert(!is_same<__remove_cv_t<_Up>, bool>::value, "Second argument to lcm cannot be bool"); 111 if (__m == 0 || __n == 0) 112 return 0; 113 114 using _Rp = common_type_t<_Tp, _Up>; 115 _Rp __val1 = __ct_abs<_Rp, _Tp>()(__m) / std::gcd(__m, __n); 116 _Rp __val2 = __ct_abs<_Rp, _Up>()(__n); 117 _Rp __res; 118 [[maybe_unused]] bool __overflow = __builtin_mul_overflow(__val1, __val2, &__res); 119 _LIBCPP_ASSERT_ARGUMENT_WITHIN_DOMAIN(!__overflow, "Overflow in lcm"); 120 return __res; 121 } 122 123 #endif // _LIBCPP_STD_VER >= 17 124 125 _LIBCPP_END_NAMESPACE_STD 126 127 _LIBCPP_POP_MACROS 128 129 #endif // _LIBCPP___NUMERIC_GCD_LCM_H 130