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