//    boost asinh.hpp header file

//  (C) Copyright Eric Ford 2001 & Hubert Holin.

//  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_ACOSH_HPP

#define BOOST_ACOSH_HPP

#include <cmath>

#include <limits>

#include <string>

#include <stdexcept>

#include <boost/config.hpp>

// This is the inverse of the hyperbolic cosine function.

namespace boost

{

    namespace math

    {

#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::log;

        using    ::std::numeric_limits;

#endif

#if defined(BOOST_NO_TEMPLATE_PARTIAL_SPECIALIZATION)

        // This is the main fare

        template<typename T>

        inline T    acosh(const T x)

        {

            using    ::std::abs;

            using    ::std::sqrt;

            using    ::std::log;

            using    ::std::numeric_limits;

            T const    one = static_cast<T>(1);

            T const    two = static_cast<T>(2);

            static T const    taylor_2_bound = sqrt(numeric_limits<T>::epsilon());

            static T const    taylor_n_bound = sqrt(taylor_2_bound);

            static T const    upper_taylor_2_bound = one/taylor_2_bound;

            if        (x < one)

            {

                if    (numeric_limits<T>::has_quiet_NaN)

                {

                    return(numeric_limits<T>::quiet_NaN());

                }

                else

                {

                    ::std::string        error_reporting("Argument to atanh is strictly greater than +1 or strictly smaller than -1!");

                    ::std::domain_error  bad_argument(error_reporting);

                    throw(bad_argument);

                }

            }

            else if    (x >= taylor_n_bound)

            {

                if    (x > upper_taylor_2_bound)

                {

                    // approximation by laurent series in 1/x at 0+ order from -1 to 0

                    return( log( x*two) );

                }

                else

                {

                    return( log( x + sqrt(x*x-one) ) );

                }

            }

            else

            {

                T    y = sqrt(x-one);

                // approximation by taylor series in y at 0 up to order 2

                T    result = y;

                if    (y >= taylor_2_bound)

                {

                    T    y3 = y*y*y;

                    // approximation by taylor series in y at 0 up to order 4

                    result -= y3/static_cast<T>(12);

                }

                return(sqrt(static_cast<T>(2))*result);

            }

        }

#else

        // These are implementation details (for main fare see below)

        namespace detail

        {

            template    <

                            typename T,

                            bool QuietNanSupported

                        >

            struct    acosh_helper2_t

            {

                static T    get_NaN()

                {

                    return(::std::numeric_limits<T>::quiet_NaN());

                }

            };  // boost::detail::acosh_helper2_t

            template<typename T>

            struct    acosh_helper2_t<T, false>

            {

                static T    get_NaN()

                {

                    ::std::string        error_reporting("Argument to acosh is greater than or equal to +1!");

                    ::std::domain_error  bad_argument(error_reporting);

                    throw(bad_argument);

                }

            };  // boost::detail::acosh_helper2_t

        }  // boost::detail

        // This is the main fare

        template<typename T>

        inline T    acosh(const T x)

        {

            using    ::std::abs;

            using    ::std::sqrt;

            using    ::std::log;

            using    ::std::numeric_limits;

            typedef    detail::acosh_helper2_t<T, std::numeric_limits<T>::has_quiet_NaN>    helper2_type;

            T const    one = static_cast<T>(1);

            T const    two = static_cast<T>(2);

            static T const    taylor_2_bound = sqrt(numeric_limits<T>::epsilon());

            static T const    taylor_n_bound = sqrt(taylor_2_bound);

            static T const    upper_taylor_2_bound = one/taylor_2_bound;

            if        (x < one)

            {

                return(helper2_type::get_NaN());

            }

            else if    (x >= taylor_n_bound)

            {

                if    (x > upper_taylor_2_bound)

                {

                    // approximation by laurent series in 1/x at 0+ order from -1 to 0

                    return( log( x*two) );

                }

                else

                {

                    return( log( x + sqrt(x*x-one) ) );

                }

            }

            else

            {

                T    y = sqrt(x-one);

                // approximation by taylor series in y at 0 up to order 2

                T    result = y;

                if    (y >= taylor_2_bound)

                {

                    T    y3 = y*y*y;

                    // approximation by taylor series in y at 0 up to order 4

                    result -= y3/static_cast<T>(12);

                }

                return(sqrt(static_cast<T>(2))*result);

            }

        }

#endif /* defined(BOOST_NO_TEMPLATE_PARTIAL_SPECIALIZATION) */

    }

}

#endif /* BOOST_ACOSH_HPP */