1 // boost atanh.hpp header file
3 // (C) Copyright Hubert Holin 2001.
4 // (C) Copyright John Maddock 2008.
5 // Distributed under the Boost Software License, Version 1.0. (See
6 // accompanying file LICENSE_1_0.txt or copy at
7 // http://www.boost.org/LICENSE_1_0.txt)
9 // See http://www.boost.org for updates, documentation, and revision history.
11 #ifndef BOOST_ATANH_HPP
12 #define BOOST_ATANH_HPP
19 #include <boost/math/tools/precision.hpp>
20 #include <boost/math/policies/error_handling.hpp>
21 #include <boost/math/special_functions/math_fwd.hpp>
22 #include <boost/math/special_functions/log1p.hpp>
23 #include <boost/math/special_functions/fpclassify.hpp>
25 // This is the inverse of the hyperbolic tangent function.
33 // This is the main fare
35 template<typename T, typename Policy>
36 inline T atanh_imp(const T x, const Policy& pol)
39 static const char* function = "boost::math::atanh<%1%>(%1%)";
43 return policies::raise_domain_error<T>(
45 "atanh requires x >= -1, but got x = %1%.", x, pol);
49 return policies::raise_domain_error<T>(
51 "atanh requires x <= 1, but got x = %1%.", x, pol);
53 else if((boost::math::isnan)(x))
55 return policies::raise_domain_error<T>(
57 "atanh requires -1 <= x <= 1, but got x = %1%.", x, pol);
59 else if(x < -1 + tools::epsilon<T>())
62 return -policies::raise_overflow_error<T>(function, 0, pol);
64 else if(x > 1 - tools::epsilon<T>())
67 return policies::raise_overflow_error<T>(function, 0, pol);
69 else if(abs(x) >= tools::forth_root_epsilon<T>())
71 // http://functions.wolfram.com/ElementaryFunctions/ArcTanh/02/
73 return (boost::math::log1p(x, pol) - boost::math::log1p(-x, pol)) / 2;
74 return(log( (1 + x) / (1 - x) ) / 2);
78 // http://functions.wolfram.com/ElementaryFunctions/ArcTanh/06/01/03/01/
79 // approximation by taylor series in x at 0 up to order 2
82 if (abs(x) >= tools::root_epsilon<T>())
86 // approximation by taylor series in x at 0 up to order 4
87 result += x3/static_cast<T>(3);
95 template<typename T, typename Policy>
96 inline typename tools::promote_args<T>::type atanh(T x, const Policy&)
98 typedef typename tools::promote_args<T>::type result_type;
99 typedef typename policies::evaluation<result_type, Policy>::type value_type;
100 typedef typename policies::normalise<
102 policies::promote_float<false>,
103 policies::promote_double<false>,
104 policies::discrete_quantile<>,
105 policies::assert_undefined<> >::type forwarding_policy;
106 return policies::checked_narrowing_cast<result_type, forwarding_policy>(
107 detail::atanh_imp(static_cast<value_type>(x), forwarding_policy()),
108 "boost::math::atanh<%1%>(%1%)");
111 inline typename tools::promote_args<T>::type atanh(T x)
113 return boost::math::atanh(x, policies::policy<>());
119 #endif /* BOOST_ATANH_HPP */