// boost asinh.hpp header file // (C) Copyright Eric Ford 2001 & Hubert Holin. // (C) Copyright John Maddock 2008. // 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 #ifdef _MSC_VER #pragma once #endif #include #include #include #include #include #include #include // This is the inverse of the hyperbolic cosine function. namespace boost { namespace math { namespace detail { template inline T acosh_imp(const T x, const Policy& pol) { BOOST_MATH_STD_USING if(x < 1) { return policies::raise_domain_error( "boost::math::acosh<%1%>(%1%)", "acosh requires x >= 1, but got x = %1%.", x, pol); } else if ((x - 1) >= tools::root_epsilon()) { if (x > 1 / tools::root_epsilon()) { // http://functions.wolfram.com/ElementaryFunctions/ArcCosh/06/01/06/01/0001/ // approximation by laurent series in 1/x at 0+ order from -1 to 0 return log(x) + constants::ln_two(); } else if(x < 1.5f) { // This is just a rearrangement of the standard form below // devised to minimse loss of precision when x ~ 1: T y = x - 1; return boost::math::log1p(y + sqrt(y * y + 2 * y), pol); } else { // http://functions.wolfram.com/ElementaryFunctions/ArcCosh/02/ return( log( x + sqrt(x * x - 1) ) ); } } else { // see http://functions.wolfram.com/ElementaryFunctions/ArcCosh/06/01/04/01/0001/ T y = x - 1; // approximation by taylor series in y at 0 up to order 2 T result = sqrt(2 * y) * (1 - y /12 + 3 * y * y / 160); return result; } } } template inline typename tools::promote_args::type acosh(T x, const Policy&) { typedef typename tools::promote_args::type result_type; typedef typename policies::evaluation::type value_type; typedef typename policies::normalise< Policy, policies::promote_float, policies::promote_double, policies::discrete_quantile<>, policies::assert_undefined<> >::type forwarding_policy; return policies::checked_narrowing_cast( detail::acosh_imp(static_cast(x), forwarding_policy()), "boost::math::acosh<%1%>(%1%)"); } template inline typename tools::promote_args::type acosh(T x) { return boost::math::acosh(x, policies::policy<>()); } } } #endif /* BOOST_ACOSH_HPP */