Chris@16: //    boost asinh.hpp header file
Chris@16: 
Chris@16: //  (C) Copyright Eric Ford 2001 & Hubert Holin.
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_ACOSH_HPP
Chris@16: #define BOOST_ACOSH_HPP
Chris@16: 
Chris@16: #ifdef _MSC_VER
Chris@16: #pragma once
Chris@16: #endif
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/policies/error_handling.hpp>
Chris@16: #include <boost/math/special_functions/math_fwd.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 cosine function.
Chris@16: 
Chris@16: namespace boost
Chris@16: {
Chris@16:     namespace math
Chris@16:     {
Chris@16:        namespace detail
Chris@16:        {
Chris@16:         template<typename T, typename Policy>
Chris@16:         inline T    acosh_imp(const T x, const Policy& pol)
Chris@16:         {
Chris@16:             BOOST_MATH_STD_USING
Chris@16:             
Chris@16:             if(x < 1)
Chris@16:             {
Chris@16:                return policies::raise_domain_error<T>(
Chris@16:                   "boost::math::acosh<%1%>(%1%)",
Chris@16:                   "acosh requires x >= 1, but got x = %1%.", x, pol);
Chris@16:             }
Chris@16:             else if    ((x - 1) >= tools::root_epsilon<T>())
Chris@16:             {
Chris@16:                 if    (x > 1 / tools::root_epsilon<T>())
Chris@16:                 {
Chris@16:                     // http://functions.wolfram.com/ElementaryFunctions/ArcCosh/06/01/06/01/0001/
Chris@16:                     // approximation by laurent series in 1/x at 0+ order from -1 to 0
Chris@16:                     return log(x) + constants::ln_two<T>();
Chris@16:                 }
Chris@16:                 else if(x < 1.5f)
Chris@16:                 {
Chris@16:                    // This is just a rearrangement of the standard form below
Chris@16:                    // devised to minimse loss of precision when x ~ 1:
Chris@16:                    T y = x - 1;
Chris@16:                    return boost::math::log1p(y + sqrt(y * y + 2 * y), pol);
Chris@16:                 }
Chris@16:                 else
Chris@16:                 {
Chris@16:                     // http://functions.wolfram.com/ElementaryFunctions/ArcCosh/02/
Chris@16:                     return( log( x + sqrt(x * x - 1) ) );
Chris@16:                 }
Chris@16:             }
Chris@16:             else
Chris@16:             {
Chris@16:                 // see http://functions.wolfram.com/ElementaryFunctions/ArcCosh/06/01/04/01/0001/
Chris@16:                 T y = x - 1;
Chris@16:                 
Chris@16:                 // approximation by taylor series in y at 0 up to order 2
Chris@16:                 T result = sqrt(2 * y) * (1 - y /12 + 3 * y * y / 160);
Chris@16:                 return result;
Chris@16:             }
Chris@16:         }
Chris@16:        }
Chris@16: 
Chris@16:         template<typename T, typename Policy>
Chris@16:         inline typename tools::promote_args<T>::type acosh(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::acosh_imp(static_cast<value_type>(x), forwarding_policy()),
Chris@16:               "boost::math::acosh<%1%>(%1%)");
Chris@16:         }
Chris@16:         template<typename T>
Chris@16:         inline typename tools::promote_args<T>::type acosh(T x)
Chris@16:         {
Chris@16:            return boost::math::acosh(x, policies::policy<>());
Chris@16:         }
Chris@16: 
Chris@16:     }
Chris@16: }
Chris@16: 
Chris@16: #endif /* BOOST_ACOSH_HPP */
Chris@16: 
Chris@16: