Boost C++ Libraries

boost/math/special_functions/sinhc.hpp

//  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/precision.hpp>
#include <boost/math/special_functions/math_fwd.hpp>
#include <limits>
#include <string>
#include <stdexcept>
#include <cmath>

// These are the the "Hyperbolic Sinus Cardinal" functions.

namespace boost
{
    namespace math
    {
       namespace detail
       {
        // This is the "Hyperbolic Sinus Cardinal" of index Pi.

        template<typename T>
        inline T    sinhc_pi_imp(const T x)
        {
            using    ::std::abs;
            using    ::std::sinh;
            using    ::std::sqrt;

            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);
       }

        template<typename T, template<typename> class U>
        inline U<T>    sinhc_pi(const U<T> x)
        {
            using std::abs;
            using std::sinh;
            using std::sqrt;

            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_SINHC_HPP */