mirror of
https://github.com/jart/cosmopolitan.git
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132 lines
4.2 KiB
C++
132 lines
4.2 KiB
C++
// -*- C++ -*-
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//===----------------------------------------------------------------------===//
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//
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// Part of the LLVM Project, under the Apache License v2.0 with LLVM Exceptions.
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// See https://llvm.org/LICENSE.txt for license information.
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// SPDX-License-Identifier: Apache-2.0 WITH LLVM-exception
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//
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//===----------------------------------------------------------------------===//
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#ifndef _LIBCPP___NUMERIC_GCD_LCM_H
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#define _LIBCPP___NUMERIC_GCD_LCM_H
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#include <__algorithm/min.h>
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#include <__assert>
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#include <__bit/countr.h>
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#include <__config>
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#include <__type_traits/common_type.h>
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#include <__type_traits/is_integral.h>
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#include <__type_traits/is_same.h>
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#include <__type_traits/is_signed.h>
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#include <__type_traits/make_unsigned.h>
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#include <limits>
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#if !defined(_LIBCPP_HAS_NO_PRAGMA_SYSTEM_HEADER)
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# pragma GCC system_header
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#endif
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_LIBCPP_PUSH_MACROS
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#include <__undef_macros>
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_LIBCPP_BEGIN_NAMESPACE_STD
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#if _LIBCPP_STD_VER >= 17
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template <typename _Result, typename _Source, bool _IsSigned = is_signed<_Source>::value>
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struct __ct_abs;
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template <typename _Result, typename _Source>
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struct __ct_abs<_Result, _Source, true> {
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constexpr _LIBCPP_HIDE_FROM_ABI _Result operator()(_Source __t) const noexcept {
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if (__t >= 0)
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return __t;
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if (__t == numeric_limits<_Source>::min())
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return -static_cast<_Result>(__t);
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return -__t;
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}
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};
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template <typename _Result, typename _Source>
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struct __ct_abs<_Result, _Source, false> {
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constexpr _LIBCPP_HIDE_FROM_ABI _Result operator()(_Source __t) const noexcept { return __t; }
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};
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template <class _Tp>
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constexpr _LIBCPP_HIDDEN _Tp __gcd(_Tp __a, _Tp __b) {
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static_assert(!is_signed<_Tp>::value, "");
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// From: https://lemire.me/blog/2013/12/26/fastest-way-to-compute-the-greatest-common-divisor
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//
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// If power of two divides both numbers, we can push it out.
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// - gcd( 2^x * a, 2^x * b) = 2^x * gcd(a, b)
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//
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// If and only if exactly one number is even, we can divide that number by that power.
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// - if a, b are odd, then gcd(2^x * a, b) = gcd(a, b)
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//
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// And standard gcd algorithm where instead of modulo, minus is used.
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if (__a < __b) {
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_Tp __tmp = __b;
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__b = __a;
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__a = __tmp;
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}
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if (__b == 0)
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return __a;
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__a %= __b; // Make both argument of the same size, and early result in the easy case.
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if (__a == 0)
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return __b;
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int __az = std::__countr_zero(__a);
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int __bz = std::__countr_zero(__b);
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int __shift = std::min(__az, __bz);
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__a >>= __az;
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__b >>= __bz;
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do {
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_Tp __diff = __a - __b;
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if (__a > __b) {
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__a = __b;
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__b = __diff;
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} else {
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__b = __b - __a;
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}
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if (__diff != 0)
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__b >>= std::__countr_zero(__diff);
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} while (__b != 0);
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return __a << __shift;
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}
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template <class _Tp, class _Up>
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constexpr _LIBCPP_HIDE_FROM_ABI common_type_t<_Tp, _Up> gcd(_Tp __m, _Up __n) {
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static_assert(is_integral<_Tp>::value && is_integral<_Up>::value, "Arguments to gcd must be integer types");
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static_assert(!is_same<__remove_cv_t<_Tp>, bool>::value, "First argument to gcd cannot be bool");
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static_assert(!is_same<__remove_cv_t<_Up>, bool>::value, "Second argument to gcd cannot be bool");
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using _Rp = common_type_t<_Tp, _Up>;
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using _Wp = make_unsigned_t<_Rp>;
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return static_cast<_Rp>(
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std::__gcd(static_cast<_Wp>(__ct_abs<_Rp, _Tp>()(__m)), static_cast<_Wp>(__ct_abs<_Rp, _Up>()(__n))));
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}
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template <class _Tp, class _Up>
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constexpr _LIBCPP_HIDE_FROM_ABI common_type_t<_Tp, _Up> lcm(_Tp __m, _Up __n) {
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static_assert(is_integral<_Tp>::value && is_integral<_Up>::value, "Arguments to lcm must be integer types");
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static_assert(!is_same<__remove_cv_t<_Tp>, bool>::value, "First argument to lcm cannot be bool");
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static_assert(!is_same<__remove_cv_t<_Up>, bool>::value, "Second argument to lcm cannot be bool");
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if (__m == 0 || __n == 0)
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return 0;
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using _Rp = common_type_t<_Tp, _Up>;
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_Rp __val1 = __ct_abs<_Rp, _Tp>()(__m) / std::gcd(__m, __n);
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_Rp __val2 = __ct_abs<_Rp, _Up>()(__n);
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_Rp __res;
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[[maybe_unused]] bool __overflow = __builtin_mul_overflow(__val1, __val2, &__res);
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_LIBCPP_ASSERT_ARGUMENT_WITHIN_DOMAIN(!__overflow, "Overflow in lcm");
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return __res;
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}
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#endif // _LIBCPP_STD_VER >= 17
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_LIBCPP_END_NAMESPACE_STD
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_LIBCPP_POP_MACROS
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#endif // _LIBCPP___NUMERIC_GCD_LCM_H
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