math/special_functions/cos_pi.hpp

0001 //  Copyright (c) 2007 John Maddock
0002 //  Copyright (c) 2024 Matt Borland
0003 //  Use, modification and distribution are subject to the
0004 //  Boost Software License, Version 1.0. (See accompanying file
0005 //  LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_0.txt)
0006
0007 #ifndef BOOST_MATH_COS_PI_HPP
0008 #define BOOST_MATH_COS_PI_HPP
0009
0010 #ifdef _MSC_VER
0011 #pragma once
0012 #endif
0013
0014 #include <boost/math/tools/config.hpp>
0015
0016 #ifndef BOOST_MATH_HAS_NVRTC
0017
0018 #include <cmath>
0019 #include <limits>
0020 #include <boost/math/tools/numeric_limits.hpp>
0021 #include <boost/math/special_functions/math_fwd.hpp>
0022 #include <boost/math/special_functions/trunc.hpp>
0023 #include <boost/math/tools/promotion.hpp>
0024 #include <boost/math/constants/constants.hpp>
0025
0026 namespace boost{ namespace math{ namespace detail{
0027
0028 template <class T, class Policy>
0029 BOOST_MATH_GPU_ENABLED T cos_pi_imp(T x, const Policy&)
0030 {
0031    BOOST_MATH_STD_USING // ADL of std names
0032    // cos of pi*x:
0033    bool invert = false;
0034    if(fabs(x) < T(0.25))
0035       return cos(constants::pi<T>() * x);
0036
0037    if(x < 0)
0038    {
0039       x = -x;
0040    }
0041    T rem = floor(x);
0042    if(abs(floor(rem/2)*2 - rem) > boost::math::numeric_limits<T>::epsilon())
0043    {
0044       invert = !invert;
0045    }
0046    rem = x - rem;
0047    if(rem > 0.5f)
0048    {
0049       rem = 1 - rem;
0050       invert = !invert;
0051    }
0052    if(rem == 0.5f)
0053       return 0;
0054
0055    if(rem > 0.25f)
0056    {
0057       rem = 0.5f - rem;
0058       rem = sin(constants::pi<T>() * rem);
0059    }
0060    else
0061       rem = cos(constants::pi<T>() * rem);
0062    return invert ? T(-rem) : rem;
0063 }
0064
0065 } // namespace detail
0066
0067 template <class T, class Policy>
0068 BOOST_MATH_GPU_ENABLED inline typename tools::promote_args<T>::type cos_pi(T x, const Policy&)
0069 {
0070    typedef typename tools::promote_args<T>::type result_type;
0071    typedef typename policies::evaluation<result_type, Policy>::type value_type;
0072    typedef typename policies::normalise<
0073       Policy,
0074       policies::promote_float<false>,
0075       policies::promote_double<false>,
0076       policies::discrete_quantile<>,
0077       policies::assert_undefined<>,
0078       // We want to ignore overflows since the result is in [-1,1] and the
0079       // check slows the code down considerably.
0080       policies::overflow_error<policies::ignore_error> >::type forwarding_policy;
0081    return policies::checked_narrowing_cast<result_type, forwarding_policy>(boost::math::detail::cos_pi_imp<value_type>(x, forwarding_policy()), "cos_pi");
0082 }
0083
0084 template <class T>
0085 BOOST_MATH_GPU_ENABLED inline typename tools::promote_args<T>::type cos_pi(T x)
0086 {
0087    return boost::math::cos_pi(x, policies::policy<>());
0088 }
0089
0090 } // namespace math
0091 } // namespace boost
0092
0093 #else // Special handling for NVRTC
0094
0095 namespace boost {
0096 namespace math {
0097
0098 template <typename T>
0099 BOOST_MATH_GPU_ENABLED auto cos_pi(T x)
0100 {
0101    return ::cospi(x);
0102 }
0103
0104 template <>
0105 BOOST_MATH_GPU_ENABLED auto cos_pi(float x)
0106 {
0107    return ::cospif(x);
0108 }
0109
0110 template <typename T, typename Policy>
0111 BOOST_MATH_GPU_ENABLED auto cos_pi(T x, const Policy&)
0112 {
0113    return ::cospi(x);
0114 }
0115
0116 template <typename Policy>
0117 BOOST_MATH_GPU_ENABLED auto cos_pi(float x, const Policy&)
0118 {
0119    return ::cospif(x);
0120 }
0121
0122 } // namespace math
0123 } // namespace boost
0124
0125 #endif // BOOST_MATH_HAS_NVRTC
0126
0127 #endif
0128