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// -*- 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
|
