ceph/src/boost/boost/math/special_functions/sinc.hpp

   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>
  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>
  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>
  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>
  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>
 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