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 <limits>
23 #include <string>
24 #include <stdexcept>
25 #include <cmath>
26 
27 // These are the the "Sinus Cardinal" functions.
28 
29 namespace boost
30 {
31     namespace math
32     {
33        namespace detail
34        {
35         // This is the "Sinus Cardinal" of index Pi.
36 
37         template<typename T>
sinc_pi_imp(const T x)38         inline T    sinc_pi_imp(const T x)
39         {
40             BOOST_MATH_STD_USING
41 
42             if    (abs(x) >= 3.3 * tools::forth_root_epsilon<T>())
43             {
44                 return(sin(x)/x);
45             }
46             else
47             {
48                 // |x| < (eps*120)^(1/4)
49                 return 1 - x * x / 6;
50             }
51         }
52 
53        } // namespace detail
54 
55        template <class T>
sinc_pi(T x)56        inline typename tools::promote_args<T>::type sinc_pi(T x)
57        {
58           typedef typename tools::promote_args<T>::type result_type;
59           return detail::sinc_pi_imp(static_cast<result_type>(x));
60        }
61 
62        template <class T, class Policy>
sinc_pi(T x,const Policy &)63        inline typename tools::promote_args<T>::type sinc_pi(T x, const Policy&)
64        {
65           typedef typename tools::promote_args<T>::type result_type;
66           return detail::sinc_pi_imp(static_cast<result_type>(x));
67        }
68 
69         template<typename T, template<typename> class U>
sinc_pi(const U<T> x)70         inline U<T>    sinc_pi(const U<T> x)
71         {
72             BOOST_MATH_STD_USING
73             using    ::std::numeric_limits;
74 
75             T const    taylor_0_bound = tools::epsilon<T>();
76             T const    taylor_2_bound = tools::root_epsilon<T>();
77             T const    taylor_n_bound = tools::forth_root_epsilon<T>();
78 
79             if    (abs(x) >= taylor_n_bound)
80             {
81                 return(sin(x)/x);
82             }
83             else
84             {
85                 // approximation by taylor series in x at 0 up to order 0
86 #ifdef __MWERKS__
87                 U<T>    result = static_cast<U<T> >(1);
88 #else
89                 U<T>    result = U<T>(1);
90 #endif
91 
92                 if    (abs(x) >= taylor_0_bound)
93                 {
94                     U<T>    x2 = x*x;
95 
96                     // approximation by taylor series in x at 0 up to order 2
97                     result -= x2/static_cast<T>(6);
98 
99                     if    (abs(x) >= taylor_2_bound)
100                     {
101                         // approximation by taylor series in x at 0 up to order 4
102                         result += (x2*x2)/static_cast<T>(120);
103                     }
104                 }
105 
106                 return(result);
107             }
108         }
109 
110         template<typename T, template<typename> class U, class Policy>
sinc_pi(const U<T> x,const Policy &)111         inline U<T>    sinc_pi(const U<T> x, const Policy&)
112         {
113            return sinc_pi(x);
114         }
115     }
116 }
117 
118 #endif /* BOOST_SINC_HPP */
119 
120