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lcm.hpp
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lcm.hpp
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/*################################################################################
##
## Copyright (C) 2016-2024 Keith O'Hara
##
## This file is part of the GCE-Math C++ library.
##
## Licensed under the Apache License, Version 2.0 (the "License");
## you may not use this file except in compliance with the License.
## You may obtain a copy of the License at
##
## http://www.apache.org/licenses/LICENSE-2.0
##
## Unless required by applicable law or agreed to in writing, software
## distributed under the License is distributed on an "AS IS" BASIS,
## WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
## See the License for the specific language governing permissions and
## limitations under the License.
##
################################################################################*/
#ifndef _gcem_lcm_HPP
#define _gcem_lcm_HPP
namespace internal
{
template<typename T>
constexpr
T
lcm_compute(const T a, const T b)
noexcept
{
return abs(a * (b / gcd(a,b)));
}
template<typename T1, typename T2, typename TC = common_t<T1,T2>>
constexpr
TC
lcm_type_check(const T1 a, const T2 b)
noexcept
{
return lcm_compute(static_cast<TC>(a),static_cast<TC>(b));
}
}
/**
* Compile-time least common multiple (LCM) function
*
* @param a integral-valued input.
* @param b integral-valued input.
* @return the least common multiple between integers \c a and \c b using the representation \f[ \text{lcm}(a,b) = \dfrac{| a b |}{\text{gcd}(a,b)} \f]
* where \f$ \text{gcd}(a,b) \f$ denotes the greatest common divisor between \f$ a \f$ and \f$ b \f$.
*/
template<typename T1, typename T2>
constexpr
common_t<T1,T2>
lcm(const T1 a, const T2 b)
noexcept
{
return internal::lcm_type_check(a,b);
}
#endif