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#include <cmath>
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>
24
25// This is the inverse of the hyperbolic tangent function.
26
27namespace boost
28{
29 namespace math
30 {
31 namespace detail
32 {
33 // This is the main fare
34
35 template<typename T, typename Policy>
36 inline T atanh_imp(const T x, const Policy& pol)
37 {
38 BOOST_MATH_STD_USING
39 static const char* function = "boost::math::atanh<%1%>(%1%)";
40
41 if(x < -1)
42 {
43 return policies::raise_domain_error<T>(
44 function,
45 "atanh requires x >= -1, but got x = %1%.", x, pol);
46 }
47 else if(x > 1)
48 {
49 return policies::raise_domain_error<T>(
50 function,
51 "atanh requires x <= 1, but got x = %1%.", x, pol);
52 }
53 else if((boost::math::isnan)(x))
54 {
55 return policies::raise_domain_error<T>(
56 function,
57 "atanh requires -1 <= x <= 1, but got x = %1%.", x, pol);
58 }
59 else if(x < -1 + tools::epsilon<T>())
60 {
61 // -Infinity:
62 return -policies::raise_overflow_error<T>(function, nullptr, pol);
63 }
64 else if(x > 1 - tools::epsilon<T>())
65 {
66 // Infinity:
67 return policies::raise_overflow_error<T>(function, nullptr, pol);
68 }
69 else if(abs(x) >= tools::forth_root_epsilon<T>())
70 {
71 // http://functions.wolfram.com/ElementaryFunctions/ArcTanh/02/
72 if(abs(x) < 0.5f)
73 return (boost::math::log1p(x, pol) - boost::math::log1p(-x, pol)) / 2;
74 return(log( (1 + x) / (1 - x) ) / 2);
75 }
76 else
77 {
78 // http://functions.wolfram.com/ElementaryFunctions/ArcTanh/06/01/03/01/
79 // approximation by taylor series in x at 0 up to order 2
80 T result = x;
81
82 if (abs(x) >= tools::root_epsilon<T>())
83 {
84 T x3 = x*x*x;
85
86 // approximation by taylor series in x at 0 up to order 4
87 result += x3/static_cast<T>(3);
88 }
89
90 return(result);
91 }
92 }
93 }
94
95 template<typename T, typename Policy>
96 inline typename tools::promote_args<T>::type atanh(T x, const Policy&)
97 {
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<
101 Policy,
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%)");
109 }
110 template<typename T>
111 inline typename tools::promote_args<T>::type atanh(T x)
112 {
113 return boost::math::atanh(x, policies::policy<>());
114 }
115
116 }
117}
118
119#endif /* BOOST_ATANH_HPP */
120
121
122
123

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