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Diffstat (limited to 'boost/math/special_functions/acosh.hpp')
-rw-r--r-- | boost/math/special_functions/acosh.hpp | 114 |
1 files changed, 114 insertions, 0 deletions
diff --git a/boost/math/special_functions/acosh.hpp b/boost/math/special_functions/acosh.hpp new file mode 100644 index 0000000000..40ca985edc --- /dev/null +++ b/boost/math/special_functions/acosh.hpp @@ -0,0 +1,114 @@ +// 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 <boost/config/no_tr1/cmath.hpp> +#include <boost/config.hpp> +#include <boost/math/tools/precision.hpp> +#include <boost/math/policies/error_handling.hpp> +#include <boost/math/special_functions/math_fwd.hpp> +#include <boost/math/special_functions/log1p.hpp> + +// This is the inverse of the hyperbolic cosine function. + +namespace boost +{ + namespace math + { + namespace detail + { +#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 + + template<typename T, typename Policy> + inline T acosh_imp(const T x, const Policy& pol) + { + BOOST_MATH_STD_USING + + if(x < 1) + { + return policies::raise_domain_error<T>( + "boost::math::acosh<%1%>(%1%)", + "acosh requires x >= 1, but got x = %1%.", x, pol); + } + else if ((x - 1) >= tools::root_epsilon<T>()) + { + if (x > 1 / tools::root_epsilon<T>()) + { + // 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 * 2) ); + } + 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<typename T, typename Policy> + inline typename tools::promote_args<T>::type acosh(T x, const Policy&) + { + typedef typename tools::promote_args<T>::type result_type; + typedef typename policies::evaluation<result_type, Policy>::type value_type; + typedef typename policies::normalise< + Policy, + policies::promote_float<false>, + policies::promote_double<false>, + policies::discrete_quantile<>, + policies::assert_undefined<> >::type forwarding_policy; + return policies::checked_narrowing_cast<result_type, forwarding_policy>( + detail::acosh_imp(static_cast<value_type>(x), forwarding_policy()), + "boost::math::acosh<%1%>(%1%)"); + } + template<typename T> + inline typename tools::promote_args<T>::type acosh(T x) + { + return boost::math::acosh(x, policies::policy<>()); + } + + } +} + +#endif /* BOOST_ACOSH_HPP */ + + |