summaryrefslogtreecommitdiff log msg author committer range
 ```1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100 101 102 103 104 105 106 107 108 109 110 111 112 113 114 115 116 117 118 119 120 121 122 123 124 125 126 127 128 129 130 131 132 133 134 135 136 137 138 139 140 141 142 143 144 145 ``` ``````// 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 #include #include #include #include #include #include #include #include // These are the the "Sinus Cardinal" functions. namespace boost { namespace math { namespace detail { // This is the "Sinus Cardinal" of index Pi. template inline T sinc_pi_imp(const T x) { BOOST_MATH_STD_USING T const taylor_0_bound = tools::epsilon(); T const taylor_2_bound = tools::root_epsilon(); T const taylor_n_bound = tools::forth_root_epsilon(); 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(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(6); if (abs(x) >= taylor_2_bound) { // approximation by taylor series in x at 0 up to order 4 result += (x2*x2)/static_cast(120); } } return(result); } } } // namespace detail template inline typename tools::promote_args::type sinc_pi(T x) { typedef typename tools::promote_args::type result_type; return detail::sinc_pi_imp(static_cast(x)); } template inline typename tools::promote_args::type sinc_pi(T x, const Policy&) { typedef typename tools::promote_args::type result_type; return detail::sinc_pi_imp(static_cast(x)); } #ifndef BOOST_NO_TEMPLATE_TEMPLATES template class U> inline U sinc_pi(const U x) { BOOST_MATH_STD_USING using ::std::numeric_limits; T const taylor_0_bound = tools::epsilon(); T const taylor_2_bound = tools::root_epsilon(); T const taylor_n_bound = tools::forth_root_epsilon(); 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 result = static_cast >(1); #else U result = U(1); #endif if (abs(x) >= taylor_0_bound) { U x2 = x*x; // approximation by taylor series in x at 0 up to order 2 result -= x2/static_cast(6); if (abs(x) >= taylor_2_bound) { // approximation by taylor series in x at 0 up to order 4 result += (x2*x2)/static_cast(120); } } return(result); } } template class U, class Policy> inline U sinc_pi(const U x, const Policy&) { return sinc_pi(x); } #endif /* BOOST_NO_TEMPLATE_TEMPLATES */ } } #endif /* BOOST_SINC_HPP */ ``````