ceph/src/boost/libs/math/include/boost/math/special_functions/sinhc.hpp

   1 //  boost sinhc.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_SINHC_HPP
  11 #define BOOST_SINHC_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/special_functions/math_fwd.hpp>
  21 #include <boost/config/no_tr1/cmath.hpp>
  22 #include <boost/limits.hpp>
  23 #include <string>
  24 #include <stdexcept>
  25
  26 #include <boost/config.hpp>
  27
  28
  29 // These are the the "Hyperbolic Sinus Cardinal" functions.
  30
  31 namespace boost
  32 {
  33     namespace math
  34     {
  35        namespace detail
  36        {
  37         // This is the "Hyperbolic Sinus Cardinal" of index Pi.
  38
  39         template<typename T>
  40         inline T    sinhc_pi_imp(const T x)
  41         {
  42 #if defined(BOOST_NO_STDC_NAMESPACE) && !defined(__SUNPRO_CC)
  43             using    ::abs;
  44             using    ::sinh;
  45             using    ::sqrt;
  46 #else    /* BOOST_NO_STDC_NAMESPACE */
  47             using    ::std::abs;
  48             using    ::std::sinh;
  49             using    ::std::sqrt;
  50 #endif    /* BOOST_NO_STDC_NAMESPACE */
  51
  52             static T const    taylor_0_bound = tools::epsilon<T>();
  53             static T const    taylor_2_bound = sqrt(taylor_0_bound);
  54             static T const    taylor_n_bound = sqrt(taylor_2_bound);
  55
  56             if    (abs(x) >= taylor_n_bound)
  57             {
  58                 return(sinh(x)/x);
  59             }
  60             else
  61             {
  62                 // approximation by taylor series in x at 0 up to order 0
  63                 T    result = static_cast<T>(1);
  64
  65                 if    (abs(x) >= taylor_0_bound)
  66                 {
  67                     T    x2 = x*x;
  68
  69                     // approximation by taylor series in x at 0 up to order 2
  70                     result += x2/static_cast<T>(6);
  71
  72                     if    (abs(x) >= taylor_2_bound)
  73                     {
  74                         // approximation by taylor series in x at 0 up to order 4
  75                         result += (x2*x2)/static_cast<T>(120);
  76                     }
  77                 }
  78
  79                 return(result);
  80             }
  81         }
  82
  83        } // namespace detail
  84
  85        template <class T>
  86        inline typename tools::promote_args<T>::type sinhc_pi(T x)
  87        {
  88           typedef typename tools::promote_args<T>::type result_type;
  89           return detail::sinhc_pi_imp(static_cast<result_type>(x));
  90        }
  91
  92        template <class T, class Policy>
  93        inline typename tools::promote_args<T>::type sinhc_pi(T x, const Policy&)
  94        {
  95           return boost::math::sinhc_pi(x);
  96        }
  97
  98 #ifdef    BOOST_NO_TEMPLATE_TEMPLATES
  99 #else    /* BOOST_NO_TEMPLATE_TEMPLATES */
 100         template<typename T, template<typename> class U>
 101         inline U<T>    sinhc_pi(const U<T> x)
 102         {
 103 #if defined(BOOST_FUNCTION_SCOPE_USING_DECLARATION_BREAKS_ADL) || defined(__GNUC__)
 104             using namespace std;
 105 #elif    defined(BOOST_NO_STDC_NAMESPACE) && !defined(__SUNPRO_CC)
 106             using    ::abs;
 107             using    ::sinh;
 108             using    ::sqrt;
 109 #else    /* BOOST_NO_STDC_NAMESPACE */
 110             using    ::std::abs;
 111             using    ::std::sinh;
 112             using    ::std::sqrt;
 113 #endif    /* BOOST_NO_STDC_NAMESPACE */
 114
 115             using    ::std::numeric_limits;
 116
 117             static T const    taylor_0_bound = tools::epsilon<T>();
 118             static T const    taylor_2_bound = sqrt(taylor_0_bound);
 119             static T const    taylor_n_bound = sqrt(taylor_2_bound);
 120
 121             if    (abs(x) >= taylor_n_bound)
 122             {
 123                 return(sinh(x)/x);
 124             }
 125             else
 126             {
 127                 // approximation by taylor series in x at 0 up to order 0
 128 #ifdef __MWERKS__
 129                 U<T>    result = static_cast<U<T> >(1);
 130 #else
 131                 U<T>    result = U<T>(1);
 132 #endif
 133
 134                 if    (abs(x) >= taylor_0_bound)
 135                 {
 136                     U<T>    x2 = x*x;
 137
 138                     // approximation by taylor series in x at 0 up to order 2
 139                     result += x2/static_cast<T>(6);
 140
 141                     if    (abs(x) >= taylor_2_bound)
 142                     {
 143                         // approximation by taylor series in x at 0 up to order 4
 144                         result += (x2*x2)/static_cast<T>(120);
 145                     }
 146                 }
 147
 148                 return(result);
 149             }
 150         }
 151 #endif    /* BOOST_NO_TEMPLATE_TEMPLATES */
 152     }
 153 }
 154
 155 #endif /* BOOST_SINHC_HPP */
 156