Chris@16: //    boost asinh.hpp header file
Chris@16: 
Chris@16: //  (C) Copyright Eric Ford & Hubert Holin 2001.
Chris@16: //  (C) Copyright John Maddock 2008.
Chris@16: //  Distributed under the Boost Software License, Version 1.0. (See
Chris@16: //  accompanying file LICENSE_1_0.txt or copy at
Chris@16: //  http://www.boost.org/LICENSE_1_0.txt)
Chris@16: 
Chris@16: // See http://www.boost.org for updates, documentation, and revision history.
Chris@16: 
Chris@16: #ifndef BOOST_ASINH_HPP
Chris@16: #define BOOST_ASINH_HPP
Chris@16: 
Chris@16: #ifdef _MSC_VER
Chris@16: #pragma once
Chris@16: #endif
Chris@16: 
Chris@16: 
Chris@16: #include <boost/config/no_tr1/cmath.hpp>
Chris@16: #include <boost/config.hpp>
Chris@16: #include <boost/math/tools/precision.hpp>
Chris@16: #include <boost/math/special_functions/math_fwd.hpp>
Chris@16: #include <boost/math/special_functions/sqrt1pm1.hpp>
Chris@16: #include <boost/math/special_functions/log1p.hpp>
Chris@16: #include <boost/math/constants/constants.hpp>
Chris@16: 
Chris@16: // This is the inverse of the hyperbolic sine function.
Chris@16: 
Chris@16: namespace boost
Chris@16: {
Chris@16:     namespace math
Chris@16:     {
Chris@16:        namespace detail{
Chris@16:         template<typename T, class Policy>
Chris@16:         inline T    asinh_imp(const T x, const Policy& pol)
Chris@16:         {
Chris@16:             BOOST_MATH_STD_USING
Chris@16:             
Chris@16:             if        (x >= tools::forth_root_epsilon<T>())
Chris@16:             {
Chris@16:                if        (x > 1 / tools::root_epsilon<T>())
Chris@16:                 {
Chris@16:                     // http://functions.wolfram.com/ElementaryFunctions/ArcSinh/06/01/06/01/0001/
Chris@16:                     // approximation by laurent series in 1/x at 0+ order from -1 to 1
Chris@16:                     return constants::ln_two<T>() + log(x) + 1/ (4 * x * x);
Chris@16:                 }
Chris@16:                 else if(x < 0.5f)
Chris@16:                 {
Chris@16:                    // As below, but rearranged to preserve digits:
Chris@16:                    return boost::math::log1p(x + boost::math::sqrt1pm1(x * x, pol), pol);
Chris@16:                 }
Chris@16:                 else
Chris@16:                 {
Chris@16:                     // http://functions.wolfram.com/ElementaryFunctions/ArcSinh/02/
Chris@16:                     return( log( x + sqrt(x*x+1) ) );
Chris@16:                 }
Chris@16:             }
Chris@16:             else if    (x <= -tools::forth_root_epsilon<T>())
Chris@16:             {
Chris@16:                 return(-asinh(-x, pol));
Chris@16:             }
Chris@16:             else
Chris@16:             {
Chris@16:                 // http://functions.wolfram.com/ElementaryFunctions/ArcSinh/06/01/03/01/0001/
Chris@16:                 // approximation by taylor series in x at 0 up to order 2
Chris@16:                 T    result = x;
Chris@16:                 
Chris@16:                 if    (abs(x) >= tools::root_epsilon<T>())
Chris@16:                 {
Chris@16:                     T    x3 = x*x*x;
Chris@16:                     
Chris@16:                     // approximation by taylor series in x at 0 up to order 4
Chris@16:                     result -= x3/static_cast<T>(6);
Chris@16:                 }
Chris@16:                 
Chris@16:                 return(result);
Chris@16:             }
Chris@16:         }
Chris@16:        }
Chris@16: 
Chris@16:         template<typename T>
Chris@16:         inline typename tools::promote_args<T>::type asinh(T x)
Chris@16:         {
Chris@16:            return boost::math::asinh(x, policies::policy<>());
Chris@16:         }
Chris@16:         template<typename T, typename Policy>
Chris@16:         inline typename tools::promote_args<T>::type asinh(T x, const Policy&)
Chris@16:         {
Chris@16:             typedef typename tools::promote_args<T>::type result_type;
Chris@16:             typedef typename policies::evaluation<result_type, Policy>::type value_type;
Chris@16:             typedef typename policies::normalise<
Chris@16:                Policy, 
Chris@16:                policies::promote_float<false>, 
Chris@16:                policies::promote_double<false>, 
Chris@16:                policies::discrete_quantile<>,
Chris@16:                policies::assert_undefined<> >::type forwarding_policy;
Chris@16:            return policies::checked_narrowing_cast<result_type, forwarding_policy>(
Chris@16:               detail::asinh_imp(static_cast<value_type>(x), forwarding_policy()),
Chris@16:               "boost::math::asinh<%1%>(%1%)");
Chris@16:         }
Chris@16: 
Chris@16:     }
Chris@16: }
Chris@16: 
Chris@16: #endif /* BOOST_ASINH_HPP */
Chris@16: