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Diffstat (limited to 'boost/math/special_functions/atanh.hpp')
-rw-r--r-- | boost/math/special_functions/atanh.hpp | 128 |
1 files changed, 128 insertions, 0 deletions
diff --git a/boost/math/special_functions/atanh.hpp b/boost/math/special_functions/atanh.hpp new file mode 100644 index 0000000000..d447e2057b --- /dev/null +++ b/boost/math/special_functions/atanh.hpp @@ -0,0 +1,128 @@ +// 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 */ + + + |