]>
Commit | Line | Data |
---|---|---|
7c673cae FG |
1 | // boost sinc.hpp header file |
2 | ||
3 | // (C) Copyright Hubert Holin 2001. | |
4 | // Distributed under the Boost Software License, Version 1.0. (See | |
5 | // accompanying file LICENSE_1_0.txt or copy at | |
6 | // http://www.boost.org/LICENSE_1_0.txt) | |
7 | ||
8 | // See http://www.boost.org for updates, documentation, and revision history. | |
9 | ||
10 | #ifndef BOOST_SINC_HPP | |
11 | #define BOOST_SINC_HPP | |
12 | ||
13 | ||
14 | #ifdef _MSC_VER | |
15 | #pragma once | |
16 | #endif | |
17 | ||
18 | #include <boost/math/tools/config.hpp> | |
19 | #include <boost/math/tools/precision.hpp> | |
20 | #include <boost/math/policies/policy.hpp> | |
21 | #include <boost/math/special_functions/math_fwd.hpp> | |
22 | #include <boost/config/no_tr1/cmath.hpp> | |
23 | #include <boost/limits.hpp> | |
24 | #include <string> | |
25 | #include <stdexcept> | |
26 | ||
27 | ||
28 | #include <boost/config.hpp> | |
29 | ||
30 | ||
31 | // These are the the "Sinus Cardinal" functions. | |
32 | ||
33 | namespace boost | |
34 | { | |
35 | namespace math | |
36 | { | |
37 | namespace detail | |
38 | { | |
39 | // This is the "Sinus Cardinal" of index Pi. | |
40 | ||
41 | template<typename T> | |
42 | inline T sinc_pi_imp(const T x) | |
43 | { | |
44 | BOOST_MATH_STD_USING | |
45 | ||
92f5a8d4 | 46 | if (abs(x) >= 3.3 * tools::forth_root_epsilon<T>()) |
7c673cae FG |
47 | { |
48 | return(sin(x)/x); | |
49 | } | |
50 | else | |
51 | { | |
92f5a8d4 TL |
52 | // |x| < (eps*120)^(1/4) |
53 | return 1 - x * x / 6; | |
7c673cae FG |
54 | } |
55 | } | |
56 | ||
57 | } // namespace detail | |
58 | ||
59 | template <class T> | |
60 | inline typename tools::promote_args<T>::type sinc_pi(T x) | |
61 | { | |
62 | typedef typename tools::promote_args<T>::type result_type; | |
63 | return detail::sinc_pi_imp(static_cast<result_type>(x)); | |
64 | } | |
65 | ||
66 | template <class T, class Policy> | |
67 | inline typename tools::promote_args<T>::type sinc_pi(T x, const Policy&) | |
68 | { | |
69 | typedef typename tools::promote_args<T>::type result_type; | |
70 | return detail::sinc_pi_imp(static_cast<result_type>(x)); | |
71 | } | |
72 | ||
73 | #ifndef BOOST_NO_TEMPLATE_TEMPLATES | |
74 | template<typename T, template<typename> class U> | |
75 | inline U<T> sinc_pi(const U<T> x) | |
76 | { | |
77 | BOOST_MATH_STD_USING | |
78 | using ::std::numeric_limits; | |
79 | ||
80 | T const taylor_0_bound = tools::epsilon<T>(); | |
81 | T const taylor_2_bound = tools::root_epsilon<T>(); | |
82 | T const taylor_n_bound = tools::forth_root_epsilon<T>(); | |
83 | ||
84 | if (abs(x) >= taylor_n_bound) | |
85 | { | |
86 | return(sin(x)/x); | |
87 | } | |
88 | else | |
89 | { | |
90 | // approximation by taylor series in x at 0 up to order 0 | |
91 | #ifdef __MWERKS__ | |
92 | U<T> result = static_cast<U<T> >(1); | |
93 | #else | |
94 | U<T> result = U<T>(1); | |
95 | #endif | |
96 | ||
97 | if (abs(x) >= taylor_0_bound) | |
98 | { | |
99 | U<T> x2 = x*x; | |
100 | ||
101 | // approximation by taylor series in x at 0 up to order 2 | |
102 | result -= x2/static_cast<T>(6); | |
103 | ||
104 | if (abs(x) >= taylor_2_bound) | |
105 | { | |
106 | // approximation by taylor series in x at 0 up to order 4 | |
107 | result += (x2*x2)/static_cast<T>(120); | |
108 | } | |
109 | } | |
110 | ||
111 | return(result); | |
112 | } | |
113 | } | |
114 | ||
115 | template<typename T, template<typename> class U, class Policy> | |
116 | inline U<T> sinc_pi(const U<T> x, const Policy&) | |
117 | { | |
118 | return sinc_pi(x); | |
119 | } | |
120 | #endif /* BOOST_NO_TEMPLATE_TEMPLATES */ | |
121 | } | |
122 | } | |
123 | ||
124 | #endif /* BOOST_SINC_HPP */ | |
125 |