| // boost atanh.hpp header file |
| |
| // (C) Copyright Hubert Holin 2001. |
| // (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_ATANH_HPP |
| #define BOOST_ATANH_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 tangent 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 |
| |
| // This is the main fare |
| |
| template<typename T, typename Policy> |
| inline T atanh_imp(const T x, const Policy& pol) |
| { |
| BOOST_MATH_STD_USING |
| static const char* function = "boost::math::atanh<%1%>(%1%)"; |
| |
| if(x < -1) |
| { |
| return policies::raise_domain_error<T>( |
| function, |
| "atanh requires x >= -1, but got x = %1%.", x, pol); |
| } |
| else if(x < -1 + tools::epsilon<T>()) |
| { |
| // -Infinity: |
| return -policies::raise_overflow_error<T>(function, 0, pol); |
| } |
| else if(x > 1 - tools::epsilon<T>()) |
| { |
| // Infinity: |
| return -policies::raise_overflow_error<T>(function, 0, pol); |
| } |
| else if(x > 1) |
| { |
| return policies::raise_domain_error<T>( |
| function, |
| "atanh requires x <= 1, but got x = %1%.", x, pol); |
| } |
| else if(abs(x) >= tools::forth_root_epsilon<T>()) |
| { |
| // http://functions.wolfram.com/ElementaryFunctions/ArcTanh/02/ |
| if(abs(x) < 0.5f) |
| return (boost::math::log1p(x, pol) - boost::math::log1p(-x, pol)) / 2; |
| return(log( (1 + x) / (1 - x) ) / 2); |
| } |
| else |
| { |
| // http://functions.wolfram.com/ElementaryFunctions/ArcTanh/06/01/03/01/ |
| // approximation by taylor series in x at 0 up to order 2 |
| T result = x; |
| |
| if (abs(x) >= tools::root_epsilon<T>()) |
| { |
| T x3 = x*x*x; |
| |
| // approximation by taylor series in x at 0 up to order 4 |
| result += x3/static_cast<T>(3); |
| } |
| |
| return(result); |
| } |
| } |
| } |
| |
| template<typename T, typename Policy> |
| inline typename tools::promote_args<T>::type atanh(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::atanh_imp(static_cast<value_type>(x), forwarding_policy()), |
| "boost::math::atanh<%1%>(%1%)"); |
| } |
| template<typename T> |
| inline typename tools::promote_args<T>::type atanh(T x) |
| { |
| return boost::math::atanh(x, policies::policy<>()); |
| } |
| |
| } |
| } |
| |
| #endif /* BOOST_ATANH_HPP */ |
| |
| |
| |