| // boost sinhc.hpp header file |
| |
| // (C) Copyright Hubert Holin 2001. |
| // Distributed under the Boost Software License, Version 1.0. (See |
| // accompanying file LICENSE_1_0.txt or copy at |
| // http://www.boost.org/LICENSE_1_0.txt) |
| |
| // See http://www.boost.org for updates, documentation, and revision history. |
| |
| #ifndef BOOST_SINHC_HPP |
| #define BOOST_SINHC_HPP |
| |
| |
| #ifdef _MSC_VER |
| #pragma once |
| #endif |
| |
| #include <boost/math/tools/config.hpp> |
| #include <boost/math/tools/precision.hpp> |
| #include <boost/math/special_functions/math_fwd.hpp> |
| #include <boost/config/no_tr1/cmath.hpp> |
| #include <boost/limits.hpp> |
| #include <string> |
| #include <stdexcept> |
| |
| #include <boost/config.hpp> |
| |
| |
| // These are the the "Hyperbolic Sinus Cardinal" functions. |
| |
| namespace boost |
| { |
| namespace math |
| { |
| namespace detail |
| { |
| #if defined(__GNUC__) && (__GNUC__ < 3) |
| // gcc 2.x ignores function scope using declarations, |
| // put them in the scope of the enclosing namespace instead: |
| |
| using ::std::abs; |
| using ::std::sqrt; |
| using ::std::sinh; |
| |
| using ::std::numeric_limits; |
| #endif /* defined(__GNUC__) && (__GNUC__ < 3) */ |
| |
| // This is the "Hyperbolic Sinus Cardinal" of index Pi. |
| |
| template<typename T> |
| inline T sinhc_pi_imp(const T x) |
| { |
| #if defined(BOOST_NO_STDC_NAMESPACE) && !defined(__SUNPRO_CC) |
| using ::abs; |
| using ::sinh; |
| using ::sqrt; |
| #else /* BOOST_NO_STDC_NAMESPACE */ |
| using ::std::abs; |
| using ::std::sinh; |
| using ::std::sqrt; |
| #endif /* BOOST_NO_STDC_NAMESPACE */ |
| |
| static T const taylor_0_bound = tools::epsilon<T>(); |
| static T const taylor_2_bound = sqrt(taylor_0_bound); |
| static T const taylor_n_bound = sqrt(taylor_2_bound); |
| |
| if (abs(x) >= taylor_n_bound) |
| { |
| return(sinh(x)/x); |
| } |
| else |
| { |
| // approximation by taylor series in x at 0 up to order 0 |
| T result = static_cast<T>(1); |
| |
| if (abs(x) >= taylor_0_bound) |
| { |
| T x2 = x*x; |
| |
| // approximation by taylor series in x at 0 up to order 2 |
| result += x2/static_cast<T>(6); |
| |
| if (abs(x) >= taylor_2_bound) |
| { |
| // approximation by taylor series in x at 0 up to order 4 |
| result += (x2*x2)/static_cast<T>(120); |
| } |
| } |
| |
| return(result); |
| } |
| } |
| |
| } // namespace detail |
| |
| template <class T> |
| inline typename tools::promote_args<T>::type sinhc_pi(T x) |
| { |
| typedef typename tools::promote_args<T>::type result_type; |
| return detail::sinhc_pi_imp(static_cast<result_type>(x)); |
| } |
| |
| template <class T, class Policy> |
| inline typename tools::promote_args<T>::type sinhc_pi(T x, const Policy&) |
| { |
| return boost::math::sinhc_pi(x); |
| } |
| |
| #ifdef BOOST_NO_TEMPLATE_TEMPLATES |
| #else /* BOOST_NO_TEMPLATE_TEMPLATES */ |
| template<typename T, template<typename> class U> |
| inline U<T> sinhc_pi(const U<T> x) |
| { |
| #if defined(BOOST_FUNCTION_SCOPE_USING_DECLARATION_BREAKS_ADL) || defined(__GNUC__) |
| using namespace std; |
| #elif defined(BOOST_NO_STDC_NAMESPACE) && !defined(__SUNPRO_CC) |
| using ::abs; |
| using ::sinh; |
| using ::sqrt; |
| #else /* BOOST_NO_STDC_NAMESPACE */ |
| using ::std::abs; |
| using ::std::sinh; |
| using ::std::sqrt; |
| #endif /* BOOST_NO_STDC_NAMESPACE */ |
| |
| using ::std::numeric_limits; |
| |
| static T const taylor_0_bound = tools::epsilon<T>(); |
| static T const taylor_2_bound = sqrt(taylor_0_bound); |
| static T const taylor_n_bound = sqrt(taylor_2_bound); |
| |
| if (abs(x) >= taylor_n_bound) |
| { |
| return(sinh(x)/x); |
| } |
| else |
| { |
| // approximation by taylor series in x at 0 up to order 0 |
| #ifdef __MWERKS__ |
| U<T> result = static_cast<U<T> >(1); |
| #else |
| U<T> result = U<T>(1); |
| #endif |
| |
| if (abs(x) >= taylor_0_bound) |
| { |
| U<T> x2 = x*x; |
| |
| // approximation by taylor series in x at 0 up to order 2 |
| result += x2/static_cast<T>(6); |
| |
| if (abs(x) >= taylor_2_bound) |
| { |
| // approximation by taylor series in x at 0 up to order 4 |
| result += (x2*x2)/static_cast<T>(120); |
| } |
| } |
| |
| return(result); |
| } |
| } |
| #endif /* BOOST_NO_TEMPLATE_TEMPLATES */ |
| } |
| } |
| |
| #endif /* BOOST_SINHC_HPP */ |
| |