1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
79
80
81
82
83
84
85
86
87
88
89
90
91
92
93
94
95
96
97
98
99
100
101
102
103
104
105
106
107
108
109
110
111
112
113
114
115
116
117
118
119
120
121
122
123
|
// 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
{
// 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)
{
return policies::raise_domain_error<T>(
function,
"atanh requires x <= 1, but got x = %1%.", x, pol);
}
else if((boost::math::isnan)(x))
{
return policies::raise_domain_error<T>(
function,
"atanh requires -1 <= 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(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 */
|