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> sinhc_pi_imp(const T x)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> sinhc_pi(T x)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> sinhc_pi(T x,const 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> sinhc_pi(const U<T> x)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 */ 156 157