cos.hpp

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/*################################################################################
  ##
  ##   Copyright (C) 2016-2022 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 cosine function using tan(x/2)
 */
 
#ifndef _gcem_cos_HPP
#define _gcem_cos_HPP
 
namespace internal
{
 
template<typename T>
constexpr
T
cos_compute(const T x)
noexcept
{
    return( T(1) - x*x)/(T(1) + x*x );
}
 
template<typename T>
constexpr
T
cos_check(const T x)
noexcept
{
    return( // NaN check
            is_nan(x) ? \
                GCLIM<T>::quiet_NaN() :
            // indistinguishable from 0
            GCLIM<T>::min() > abs(x) ? 
                T(1) :
            // special cases: pi/2 and pi
            GCLIM<T>::min() > abs(x - T(GCEM_HALF_PI)) ? \
                T(0) :
            GCLIM<T>::min() > abs(x + T(GCEM_HALF_PI)) ? \
                T(0) :
            GCLIM<T>::min() > abs(x - T(GCEM_PI)) ? \
                - T(1) :
            GCLIM<T>::min() > abs(x + T(GCEM_PI)) ? \
                - T(1) :
            // else
                cos_compute( tan(x/T(2)) ) );
}
 
}
 
/**
 * Compile-time cosine function
 *
 * @param x a real-valued input.
 * @return the cosine function using \f[ \cos(x) = \frac{1-\tan^2(x/2)}{1+\tan^2(x/2)} \f]
 */
 
template<typename T>
constexpr
return_t<T>
cos(const T x)
noexcept
{
    return internal::cos_check( static_cast<return_t<T>>(x) );
}
 
#endif