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