1// boost atanh.hpp header file
2
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)
8
9// See http://www.boost.org for updates, documentation, and revision history.
10
11#ifndef BOOST_ATANH_HPP
12#define BOOST_ATANH_HPP
13
14#ifdef _MSC_VER
15#pragma once
16#endif
17
18
19#include <boost/config/no_tr1/cmath.hpp>
20#include <boost/config.hpp>
21#include <boost/math/tools/precision.hpp>
22#include <boost/math/policies/error_handling.hpp>
23#include <boost/math/special_functions/math_fwd.hpp>
24#include <boost/math/special_functions/log1p.hpp>
25
26// This is the inverse of the hyperbolic tangent function.
27
28namespace boost
29{
30 namespace math
31 {
32 namespace detail
33 {
34 // This is the main fare
35
36 template<typename T, typename Policy>
37 inline T atanh_imp(const T x, const Policy& pol)
38 {
39 BOOST_MATH_STD_USING
40 static const char* function = "boost::math::atanh<%1%>(%1%)";
41
42 if(x < -1)
43 {
44 return policies::raise_domain_error<T>(
45 function,
46 "atanh requires x >= -1, but got x = %1%.", x, pol);
47 }
48 else if(x > 1)
49 {
50 return policies::raise_domain_error<T>(
51 function,
52 "atanh requires x <= 1, but got x = %1%.", x, pol);
53 }
54 else if((boost::math::isnan)(x))
55 {
56 return policies::raise_domain_error<T>(
57 function,
58 "atanh requires -1 <= x <= 1, but got x = %1%.", x, pol);
59 }
60 else if(x < -1 + tools::epsilon<T>())
61 {
62 // -Infinity:
63 return -policies::raise_overflow_error<T>(function, 0, pol);
64 }
65 else if(x > 1 - tools::epsilon<T>())
66 {
67 // Infinity:
68 return policies::raise_overflow_error<T>(function, 0, pol);
69 }
70 else if(abs(x) >= tools::forth_root_epsilon<T>())
71 {
72 // http://functions.wolfram.com/ElementaryFunctions/ArcTanh/02/
73 if(abs(x) < 0.5f)
74 return (boost::math::log1p(x, pol) - boost::math::log1p(-x, pol)) / 2;
75 return(log( (1 + x) / (1 - x) ) / 2);
76 }
77 else
78 {
79 // http://functions.wolfram.com/ElementaryFunctions/ArcTanh/06/01/03/01/
80 // approximation by taylor series in x at 0 up to order 2
81 T result = x;
82
83 if (abs(x) >= tools::root_epsilon<T>())
84 {
85 T x3 = x*x*x;
86
87 // approximation by taylor series in x at 0 up to order 4
88 result += x3/static_cast<T>(3);
89 }
90
91 return(result);
92 }
93 }
94 }
95
96 template<typename T, typename Policy>
97 inline typename tools::promote_args<T>::type atanh(T x, const Policy&)
98 {
99 typedef typename tools::promote_args<T>::type result_type;
100 typedef typename policies::evaluation<result_type, Policy>::type value_type;
101 typedef typename policies::normalise<
102 Policy,
103 policies::promote_float<false>,
104 policies::promote_double<false>,
105 policies::discrete_quantile<>,
106 policies::assert_undefined<> >::type forwarding_policy;
107 return policies::checked_narrowing_cast<result_type, forwarding_policy>(
108 detail::atanh_imp(static_cast<value_type>(x), forwarding_policy()),
109 "boost::math::atanh<%1%>(%1%)");
110 }
111 template<typename T>
112 inline typename tools::promote_args<T>::type atanh(T x)
113 {
114 return boost::math::atanh(x, policies::policy<>());
115 }
116
117 }
118}
119
120#endif /* BOOST_ATANH_HPP */
121
122
123
124

source code of include/boost/math/special_functions/atanh.hpp