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
33namespace 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
46 if (abs(x) >= 3.3 * tools::forth_root_epsilon<T>())
47 {
48 return(sin(x)/x);
49 }
50 else
51 {
52 // |x| < (eps*120)^(1/4)
53 return 1 - x * x / 6;
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
126

source code of include/boost/math/special_functions/sinc.hpp