1// boost asinh.hpp header file
2
3// (C) Copyright Eric Ford & 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_ASINH_HPP
12#define BOOST_ASINH_HPP
13
14#ifdef _MSC_VER
15#pragma once
16#endif
17
18
19#include <cmath>
20#include <boost/math/tools/precision.hpp>
21#include <boost/math/special_functions/math_fwd.hpp>
22#include <boost/math/special_functions/sqrt1pm1.hpp>
23#include <boost/math/special_functions/log1p.hpp>
24#include <boost/math/constants/constants.hpp>
25#include <boost/math/special_functions/fpclassify.hpp>
26
27// This is the inverse of the hyperbolic sine function.
28
29namespace boost
30{
31 namespace math
32 {
33 namespace detail{
34 template<typename T, class Policy>
35 inline T asinh_imp(const T x, const Policy& pol)
36 {
37 BOOST_MATH_STD_USING
38
39 if((boost::math::isnan)(x))
40 {
41 return policies::raise_domain_error<T>("boost::math::asinh<%1%>(%1%)", "asinh requires a finite argument, but got x = %1%.", x, pol);
42 }
43 if (x >= tools::forth_root_epsilon<T>())
44 {
45 if (x > 1 / tools::root_epsilon<T>())
46 {
47 // http://functions.wolfram.com/ElementaryFunctions/ArcSinh/06/01/06/01/0001/
48 // approximation by laurent series in 1/x at 0+ order from -1 to 1
49 return constants::ln_two<T>() + log(x) + 1/ (4 * x * x);
50 }
51 else if(x < 0.5f)
52 {
53 // As below, but rearranged to preserve digits:
54 return boost::math::log1p(x + boost::math::sqrt1pm1(x * x, pol), pol);
55 }
56 else
57 {
58 // http://functions.wolfram.com/ElementaryFunctions/ArcSinh/02/
59 return( log( x + sqrt(x*x+1) ) );
60 }
61 }
62 else if (x <= -tools::forth_root_epsilon<T>())
63 {
64 return(-asinh(-x, pol));
65 }
66 else
67 {
68 // http://functions.wolfram.com/ElementaryFunctions/ArcSinh/06/01/03/01/0001/
69 // approximation by taylor series in x at 0 up to order 2
70 T result = x;
71
72 if (abs(x) >= tools::root_epsilon<T>())
73 {
74 T x3 = x*x*x;
75
76 // approximation by taylor series in x at 0 up to order 4
77 result -= x3/static_cast<T>(6);
78 }
79
80 return(result);
81 }
82 }
83 }
84
85 template<typename T>
86 inline typename tools::promote_args<T>::type asinh(T x)
87 {
88 return boost::math::asinh(x, policies::policy<>());
89 }
90 template<typename T, typename Policy>
91 inline typename tools::promote_args<T>::type asinh(T x, const Policy&)
92 {
93 typedef typename tools::promote_args<T>::type result_type;
94 typedef typename policies::evaluation<result_type, Policy>::type value_type;
95 typedef typename policies::normalise<
96 Policy,
97 policies::promote_float<false>,
98 policies::promote_double<false>,
99 policies::discrete_quantile<>,
100 policies::assert_undefined<> >::type forwarding_policy;
101 return policies::checked_narrowing_cast<result_type, forwarding_policy>(
102 detail::asinh_imp(static_cast<value_type>(x), forwarding_policy()),
103 "boost::math::asinh<%1%>(%1%)");
104 }
105
106 }
107}
108
109#endif /* BOOST_ASINH_HPP */
110
111

source code of boost/libs/math/include/boost/math/special_functions/asinh.hpp