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floor.hpp
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floor.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_floor_HPP
#define _gcem_floor_HPP
namespace internal
{
template<typename T>
constexpr
int
floor_resid(const T x, const T x_whole)
noexcept
{
return( (x < T(0)) && (x < x_whole) );
}
template<typename T>
constexpr
T
floor_int(const T x, const T x_whole)
noexcept
{
return( x_whole - static_cast<T>(floor_resid(x,x_whole)) );
}
template<typename T>
constexpr
T
floor_check_internal(const T x)
noexcept
{
return x;
}
template<>
constexpr
float
floor_check_internal<float>(const float x)
noexcept
{
return( abs(x) >= 8388608.f ? \
// if
x : \
// else
floor_int(x, float(static_cast<int>(x))) );
}
template<>
constexpr
double
floor_check_internal<double>(const double x)
noexcept
{
return( abs(x) >= 4503599627370496. ? \
// if
x : \
// else
floor_int(x, double(static_cast<llint_t>(x))) );
}
template<>
constexpr
long double
floor_check_internal<long double>(const long double x)
noexcept
{
return( abs(x) >= 9223372036854775808.l ? \
// if
x : \
// else
floor_int(x, ((long double)static_cast<ullint_t>(abs(x))) * sgn(x)) );
}
template<typename T>
constexpr
T
floor_check(const T x)
noexcept
{
return( // NaN check
is_nan(x) ? \
GCLIM<T>::quiet_NaN() :
// +/- infinite
!is_finite(x) ? \
x :
// signed-zero cases
GCLIM<T>::min() > abs(x) ? \
x :
// else
floor_check_internal(x) );
}
}
/**
* Compile-time floor function
*
* @param x a real-valued input.
* @return computes the floor-value of the input.
*/
template<typename T>
constexpr
return_t<T>
floor(const T x)
noexcept
{
return internal::floor_check( static_cast<return_t<T>>(x) );
}
#endif