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author | Mark Benvenuto <mark.benvenuto@mongodb.com> | 2016-03-31 15:09:29 -0400 |
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committer | Mark Benvenuto <mark.benvenuto@mongodb.com> | 2016-03-31 15:09:29 -0400 |
commit | 869912de45bfec53f8fd15c4f716b49ac2ca7aa4 (patch) | |
tree | 97934f62054ebb1f1c78812196f7c7bded1fc1b3 /src/third_party/boost-1.60.0/boost/math/special_functions/sinc.hpp | |
parent | 319e895cc28b4aade6fa843583e0fd2ea96cd7a0 (diff) | |
download | mongo-869912de45bfec53f8fd15c4f716b49ac2ca7aa4.tar.gz |
SERVER-17294 Boost 1.60
Diffstat (limited to 'src/third_party/boost-1.60.0/boost/math/special_functions/sinc.hpp')
-rw-r--r-- | src/third_party/boost-1.60.0/boost/math/special_functions/sinc.hpp | 145 |
1 files changed, 145 insertions, 0 deletions
diff --git a/src/third_party/boost-1.60.0/boost/math/special_functions/sinc.hpp b/src/third_party/boost-1.60.0/boost/math/special_functions/sinc.hpp new file mode 100644 index 00000000000..84fbf0e324a --- /dev/null +++ b/src/third_party/boost-1.60.0/boost/math/special_functions/sinc.hpp @@ -0,0 +1,145 @@ +// boost sinc.hpp header file + +// (C) Copyright Hubert Holin 2001. +// Distributed under the Boost Software License, Version 1.0. (See +// accompanying file LICENSE_1_0.txt or copy at +// http://www.boost.org/LICENSE_1_0.txt) + +// See http://www.boost.org for updates, documentation, and revision history. + +#ifndef BOOST_SINC_HPP +#define BOOST_SINC_HPP + + +#ifdef _MSC_VER +#pragma once +#endif + +#include <boost/math/tools/config.hpp> +#include <boost/math/tools/precision.hpp> +#include <boost/math/policies/policy.hpp> +#include <boost/math/special_functions/math_fwd.hpp> +#include <boost/config/no_tr1/cmath.hpp> +#include <boost/limits.hpp> +#include <string> +#include <stdexcept> + + +#include <boost/config.hpp> + + +// These are the the "Sinus Cardinal" functions. + +namespace boost +{ + namespace math + { + namespace detail + { + // This is the "Sinus Cardinal" of index Pi. + + template<typename T> + inline T sinc_pi_imp(const T x) + { + BOOST_MATH_STD_USING + + T const taylor_0_bound = tools::epsilon<T>(); + T const taylor_2_bound = tools::root_epsilon<T>(); + T const taylor_n_bound = tools::forth_root_epsilon<T>(); + + if (abs(x) >= taylor_n_bound) + { + return(sin(x)/x); + } + else + { + // approximation by taylor series in x at 0 up to order 0 + T result = static_cast<T>(1); + + if (abs(x) >= taylor_0_bound) + { + T x2 = x*x; + + // approximation by taylor series in x at 0 up to order 2 + result -= x2/static_cast<T>(6); + + if (abs(x) >= taylor_2_bound) + { + // approximation by taylor series in x at 0 up to order 4 + result += (x2*x2)/static_cast<T>(120); + } + } + + return(result); + } + } + + } // namespace detail + + template <class T> + inline typename tools::promote_args<T>::type sinc_pi(T x) + { + typedef typename tools::promote_args<T>::type result_type; + return detail::sinc_pi_imp(static_cast<result_type>(x)); + } + + template <class T, class Policy> + inline typename tools::promote_args<T>::type sinc_pi(T x, const Policy&) + { + typedef typename tools::promote_args<T>::type result_type; + return detail::sinc_pi_imp(static_cast<result_type>(x)); + } + +#ifndef BOOST_NO_TEMPLATE_TEMPLATES + template<typename T, template<typename> class U> + inline U<T> sinc_pi(const U<T> x) + { + BOOST_MATH_STD_USING + using ::std::numeric_limits; + + T const taylor_0_bound = tools::epsilon<T>(); + T const taylor_2_bound = tools::root_epsilon<T>(); + T const taylor_n_bound = tools::forth_root_epsilon<T>(); + + if (abs(x) >= taylor_n_bound) + { + return(sin(x)/x); + } + else + { + // approximation by taylor series in x at 0 up to order 0 +#ifdef __MWERKS__ + U<T> result = static_cast<U<T> >(1); +#else + U<T> result = U<T>(1); +#endif + + if (abs(x) >= taylor_0_bound) + { + U<T> x2 = x*x; + + // approximation by taylor series in x at 0 up to order 2 + result -= x2/static_cast<T>(6); + + if (abs(x) >= taylor_2_bound) + { + // approximation by taylor series in x at 0 up to order 4 + result += (x2*x2)/static_cast<T>(120); + } + } + + return(result); + } + } + + template<typename T, template<typename> class U, class Policy> + inline U<T> sinc_pi(const U<T> x, const Policy&) + { + return sinc_pi(x); + } +#endif /* BOOST_NO_TEMPLATE_TEMPLATES */ + } +} + +#endif /* BOOST_SINC_HPP */ + |