| // 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 */ |
| |
| |