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 <class _Result, class _Source>
37constexpr _LIBCPP_HIDE_FROM_ABI _Result __abs_in_type(_Source __t) noexcept {
38 if constexpr (is_signed_v<_Source>) {
39 if (__t >= 0)
40 return __t;
41 if (__t == numeric_limits<_Source>::min())
42 return -static_cast<_Result>(__t);
43 return -__t;
44 } else {
45 return __t;
46 }
47}
48
49template <class _Tp, class _Up>
50constexpr _LIBCPP_HIDE_FROM_ABI common_type_t<_Tp, _Up> gcd(_Tp __m, _Up __n) {
51 static_assert(is_integral<_Tp>::value && is_integral<_Up>::value, "Arguments to gcd must be integer types");
52 static_assert(!is_same<__remove_cv_t<_Tp>, bool>::value, "First argument to gcd cannot be bool");
53 static_assert(!is_same<__remove_cv_t<_Up>, bool>::value, "Second argument to gcd cannot be bool");
54 using _Rp = common_type_t<_Tp, _Up>;
55 using _Wp = make_unsigned_t<_Rp>;
56
57 // Using Binary GCD algorithm https://en.wikipedia.org/wiki/Binary_GCD_algorithm, based on an implementation
58 // from https://lemire.me/blog/2024/04/13/greatest-common-divisor-the-extended-euclidean-algorithm-and-speed/
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 auto __a = static_cast<_Wp>(std::__abs_in_type<_Rp>(__m));
69 auto __b = static_cast<_Wp>(std::__abs_in_type<_Rp>(__n));
70
71 if (__a < __b) {
72 _Wp __tmp = __b;
73 __b = __a;
74 __a = __tmp;
75 }
76 if (__b == 0)
77 return static_cast<_Rp>(__a);
78 __a %= __b; // Make both argument of the same size, and early result in the easy case.
79 if (__a == 0)
80 return static_cast<_Rp>(__b);
81
82 _Wp __c = __a | __b;
83 int __shift = std::__countr_zero(__c);
84 __a >>= std::__countr_zero(__a);
85 do {
86 _Wp __t = __b >> std::__countr_zero(__b);
87 if (__a > __t) {
88 __b = __a - __t;
89 __a = __t;
90 } else {
91 __b = __t - __a;
92 }
93 } while (__b != 0);
94 return static_cast<_Rp>(__a << __shift);
95}
96
97template <class _Tp, class _Up>
98constexpr _LIBCPP_HIDE_FROM_ABI common_type_t<_Tp, _Up> lcm(_Tp __m, _Up __n) {
99 static_assert(is_integral<_Tp>::value && is_integral<_Up>::value, "Arguments to lcm must be integer types");
100 static_assert(!is_same<__remove_cv_t<_Tp>, bool>::value, "First argument to lcm cannot be bool");
101 static_assert(!is_same<__remove_cv_t<_Up>, bool>::value, "Second argument to lcm cannot be bool");
102 if (__m == 0 || __n == 0)
103 return 0;
104
105 using _Rp = common_type_t<_Tp, _Up>;
106 _Rp __val1 = std::__abs_in_type<_Rp>(__m) / std::gcd(__m, __n);
107 _Rp __val2 = std::__abs_in_type<_Rp>(__n);
108 _Rp __res;
109 [[maybe_unused]] bool __overflow = __builtin_mul_overflow(__val1, __val2, std::addressof(__res));
110 _LIBCPP_ASSERT_ARGUMENT_WITHIN_DOMAIN(!__overflow, "Overflow in lcm");
111 return __res;
112}
113
114#endif // _LIBCPP_STD_VER >= 17
115
116_LIBCPP_END_NAMESPACE_STD
117
118_LIBCPP_POP_MACROS
119
120#endif // _LIBCPP___NUMERIC_GCD_LCM_H
121