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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.
##
################################################################################*/
/*
* compile-time sine function using tan(x/2)
*
* see eq. 5.4.8 in Numerical Recipes
*/
#ifndef _gcem_sin_HPP
#define _gcem_sin_HPP
#include <cmath>
#include <type_traits>
namespace gcem
{
namespace internal
{
template<typename T>
constexpr
T
sin_compute(const T x)
noexcept
{
return T(2)*x/(T(1) + x*x);
}
template<typename T>
constexpr
T
sin_check(const T x)
noexcept
{
return( // NaN check
is_nan(x) ? \
GCLIM<T>::quiet_NaN() :
// indistinguishable from zero
GCLIM<T>::min() > abs(x) ? \
T(0) :
// special cases: pi/2 and pi
GCLIM<T>::min() > abs(x - T(GCEM_HALF_PI)) ? \
T(1) :
GCLIM<T>::min() > abs(x + T(GCEM_HALF_PI)) ? \
- T(1) :
GCLIM<T>::min() > abs(x - T(GCEM_PI)) ? \
T(0) :
GCLIM<T>::min() > abs(x + T(GCEM_PI)) ? \
- T(0) :
// else
sin_compute( tan(x/T(2)) ) );
}
}
/**
* Compile-time sine function
*
* @param x a real-valued input.
* @return the sine function using \f[ \sin(x) = \frac{2\tan(x/2)}{1+\tan^2(x/2)} \f]
*/
template<typename T>
constexpr
return_t<T>
sin(const T x)
noexcept
{
if (std::is_constant_evaluated()) {
return internal::sin_check( static_cast<return_t<T>>(x) );
} else {
return std::sin(x);
}
}
}
#endif