146 lines
4.2 KiB
C++
146 lines
4.2 KiB
C++
// boost sinc.hpp header file
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// (C) Copyright Hubert Holin 2001.
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// Distributed under the Boost Software License, Version 1.0. (See
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// accompanying file LICENSE_1_0.txt or copy at
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// http://www.boost.org/LICENSE_1_0.txt)
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// See http://www.boost.org for updates, documentation, and revision history.
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#ifndef BOOST_SINC_HPP
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#define BOOST_SINC_HPP
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#ifdef _MSC_VER
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#pragma once
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#endif
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#include <boost/math/tools/config.hpp>
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#include <boost/math/tools/precision.hpp>
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#include <boost/math/policies/policy.hpp>
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#include <boost/math/special_functions/math_fwd.hpp>
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#include <boost/config/no_tr1/cmath.hpp>
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#include <boost/limits.hpp>
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#include <string>
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#include <stdexcept>
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#include <boost/config.hpp>
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// These are the the "Sinus Cardinal" functions.
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namespace boost
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{
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namespace math
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{
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namespace detail
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{
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// This is the "Sinus Cardinal" of index Pi.
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template<typename T>
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inline T sinc_pi_imp(const T x)
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{
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BOOST_MATH_STD_USING
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T const taylor_0_bound = tools::epsilon<T>();
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T const taylor_2_bound = tools::root_epsilon<T>();
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T const taylor_n_bound = tools::forth_root_epsilon<T>();
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if (abs(x) >= taylor_n_bound)
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{
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return(sin(x)/x);
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}
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else
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{
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// approximation by taylor series in x at 0 up to order 0
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T result = static_cast<T>(1);
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if (abs(x) >= taylor_0_bound)
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{
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T x2 = x*x;
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// approximation by taylor series in x at 0 up to order 2
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result -= x2/static_cast<T>(6);
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if (abs(x) >= taylor_2_bound)
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{
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// approximation by taylor series in x at 0 up to order 4
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result += (x2*x2)/static_cast<T>(120);
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}
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}
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return(result);
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}
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}
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} // namespace detail
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template <class T>
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inline typename tools::promote_args<T>::type sinc_pi(T x)
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{
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typedef typename tools::promote_args<T>::type result_type;
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return detail::sinc_pi_imp(static_cast<result_type>(x));
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}
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template <class T, class Policy>
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inline typename tools::promote_args<T>::type sinc_pi(T x, const Policy&)
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{
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typedef typename tools::promote_args<T>::type result_type;
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return detail::sinc_pi_imp(static_cast<result_type>(x));
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}
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#ifndef BOOST_NO_TEMPLATE_TEMPLATES
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template<typename T, template<typename> class U>
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inline U<T> sinc_pi(const U<T> x)
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{
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BOOST_MATH_STD_USING
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using ::std::numeric_limits;
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T const taylor_0_bound = tools::epsilon<T>();
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T const taylor_2_bound = tools::root_epsilon<T>();
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T const taylor_n_bound = tools::forth_root_epsilon<T>();
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if (abs(x) >= taylor_n_bound)
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{
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return(sin(x)/x);
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}
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else
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{
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// approximation by taylor series in x at 0 up to order 0
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#ifdef __MWERKS__
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U<T> result = static_cast<U<T> >(1);
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#else
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U<T> result = U<T>(1);
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#endif
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if (abs(x) >= taylor_0_bound)
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{
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U<T> x2 = x*x;
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// approximation by taylor series in x at 0 up to order 2
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result -= x2/static_cast<T>(6);
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if (abs(x) >= taylor_2_bound)
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{
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// approximation by taylor series in x at 0 up to order 4
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result += (x2*x2)/static_cast<T>(120);
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}
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}
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return(result);
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}
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}
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template<typename T, template<typename> class U, class Policy>
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inline U<T> sinc_pi(const U<T> x, const Policy&)
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{
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return sinc_pi(x);
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}
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#endif /* BOOST_NO_TEMPLATE_TEMPLATES */
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}
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}
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#endif /* BOOST_SINC_HPP */
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