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
35template <typename _Result, typename _Source, bool _IsSigned = is_signed<_Source>::value>
36struct __ct_abs;
37
38template <typename _Result, typename _Source>
39struct __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
49template <typename _Result, typename _Source>
50struct __ct_abs<_Result, _Source, false> {
51 constexpr _LIBCPP_HIDE_FROM_ABI _Result operator()(_Source __t) const noexcept { return __t; }
52};
53
54template <class _Tp>
55constexpr _LIBCPP_HIDDEN _Tp __gcd(_Tp __a, _Tp __b) {
56 static_assert(!is_signed<_Tp>::value, "");
57
58 // From: https://lemire.me/blog/2013/12/26/fastest-way-to-compute-the-greatest-common-divisor
59 //
60 // If power of two divides both numbers, we can push it out.
61 // - gcd( 2^x * a, 2^x * b) = 2^x * gcd(a, b)
62 //
63 // If and only if exactly one number is even, we can divide that number by that power.
64 // - if a, b are odd, then gcd(2^x * a, b) = gcd(a, b)
65 //
66 // And standard gcd algorithm where instead of modulo, minus is used.
67
68 if (__a < __b) {
69 _Tp __tmp = __b;
70 __b = __a;
71 __a = __tmp;
72 }
73 if (__b == 0)
74 return __a;
75 __a %= __b; // Make both argument of the same size, and early result in the easy case.
76 if (__a == 0)
77 return __b;
78
79 int __az = std::__countr_zero(__a);
80 int __bz = std::__countr_zero(__b);
81 int __shift = std::min(a: __az, b: __bz);
82 __a >>= __az;
83 __b >>= __bz;
84 do {
85 _Tp __diff = __a - __b;
86 if (__a > __b) {
87 __a = __b;
88 __b = __diff;
89 } else {
90 __b = __b - __a;
91 }
92 if (__diff != 0)
93 __b >>= std::__countr_zero(__diff);
94 } while (__b != 0);
95 return __a << __shift;
96}
97
98template <class _Tp, class _Up>
99constexpr _LIBCPP_HIDE_FROM_ABI common_type_t<_Tp, _Up> gcd(_Tp __m, _Up __n) {
100 static_assert(is_integral<_Tp>::value && is_integral<_Up>::value, "Arguments to gcd must be integer types");
101 static_assert(!is_same<__remove_cv_t<_Tp>, bool>::value, "First argument to gcd cannot be bool");
102 static_assert(!is_same<__remove_cv_t<_Up>, bool>::value, "Second argument to gcd cannot be bool");
103 using _Rp = common_type_t<_Tp, _Up>;
104 using _Wp = make_unsigned_t<_Rp>;
105 return static_cast<_Rp>(
106 std::__gcd(static_cast<_Wp>(__ct_abs<_Rp, _Tp>()(__m)), static_cast<_Wp>(__ct_abs<_Rp, _Up>()(__n))));
107}
108
109template <class _Tp, class _Up>
110constexpr _LIBCPP_HIDE_FROM_ABI common_type_t<_Tp, _Up> lcm(_Tp __m, _Up __n) {
111 static_assert(is_integral<_Tp>::value && is_integral<_Up>::value, "Arguments to lcm must be integer types");
112 static_assert(!is_same<__remove_cv_t<_Tp>, bool>::value, "First argument to lcm cannot be bool");
113 static_assert(!is_same<__remove_cv_t<_Up>, bool>::value, "Second argument to lcm cannot be bool");
114 if (__m == 0 || __n == 0)
115 return 0;
116
117 using _Rp = common_type_t<_Tp, _Up>;
118 _Rp __val1 = __ct_abs<_Rp, _Tp>()(__m) / std::gcd(__m, __n);
119 _Rp __val2 = __ct_abs<_Rp, _Up>()(__n);
120 _Rp __res;
121 [[maybe_unused]] bool __overflow = __builtin_mul_overflow(__val1, __val2, &__res);
122 _LIBCPP_ASSERT_ARGUMENT_WITHIN_DOMAIN(!__overflow, "Overflow in lcm");
123 return __res;
124}
125
126#endif // _LIBCPP_STD_VER >= 17
127
128_LIBCPP_END_NAMESPACE_STD
129
130_LIBCPP_POP_MACROS
131
132#endif // _LIBCPP___NUMERIC_GCD_LCM_H
133