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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 <boost/config/no_tr1/cmath.hpp> | |
20 | #include <boost/config.hpp> | |
21 | #include <boost/math/tools/precision.hpp> | |
22 | #include <boost/math/special_functions/math_fwd.hpp> | |
23 | #include <boost/math/special_functions/sqrt1pm1.hpp> | |
24 | #include <boost/math/special_functions/log1p.hpp> | |
25 | #include <boost/math/constants/constants.hpp> | |
26 | ||
27 | // This is the inverse of the hyperbolic sine function. | |
28 | ||
29 | namespace 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 (x >= tools::forth_root_epsilon<T>()) | |
40 | { | |
41 | if (x > 1 / tools::root_epsilon<T>()) | |
42 | { | |
43 | // http://functions.wolfram.com/ElementaryFunctions/ArcSinh/06/01/06/01/0001/ | |
44 | // approximation by laurent series in 1/x at 0+ order from -1 to 1 | |
45 | return constants::ln_two<T>() + log(x) + 1/ (4 * x * x); | |
46 | } | |
47 | else if(x < 0.5f) | |
48 | { | |
49 | // As below, but rearranged to preserve digits: | |
50 | return boost::math::log1p(x + boost::math::sqrt1pm1(x * x, pol), pol); | |
51 | } | |
52 | else | |
53 | { | |
54 | // http://functions.wolfram.com/ElementaryFunctions/ArcSinh/02/ | |
55 | return( log( x + sqrt(x*x+1) ) ); | |
56 | } | |
57 | } | |
58 | else if (x <= -tools::forth_root_epsilon<T>()) | |
59 | { | |
60 | return(-asinh(-x, pol)); | |
61 | } | |
62 | else | |
63 | { | |
64 | // http://functions.wolfram.com/ElementaryFunctions/ArcSinh/06/01/03/01/0001/ | |
65 | // approximation by taylor series in x at 0 up to order 2 | |
66 | T result = x; | |
67 | ||
68 | if (abs(x) >= tools::root_epsilon<T>()) | |
69 | { | |
70 | T x3 = x*x*x; | |
71 | ||
72 | // approximation by taylor series in x at 0 up to order 4 | |
73 | result -= x3/static_cast<T>(6); | |
74 | } | |
75 | ||
76 | return(result); | |
77 | } | |
78 | } | |
79 | } | |
80 | ||
81 | template<typename T> | |
82 | inline typename tools::promote_args<T>::type asinh(T x) | |
83 | { | |
84 | return boost::math::asinh(x, policies::policy<>()); | |
85 | } | |
86 | template<typename T, typename Policy> | |
87 | inline typename tools::promote_args<T>::type asinh(T x, const Policy&) | |
88 | { | |
89 | typedef typename tools::promote_args<T>::type result_type; | |
90 | typedef typename policies::evaluation<result_type, Policy>::type value_type; | |
91 | typedef typename policies::normalise< | |
92 | Policy, | |
93 | policies::promote_float<false>, | |
94 | policies::promote_double<false>, | |
95 | policies::discrete_quantile<>, | |
96 | policies::assert_undefined<> >::type forwarding_policy; | |
97 | return policies::checked_narrowing_cast<result_type, forwarding_policy>( | |
98 | detail::asinh_imp(static_cast<value_type>(x), forwarding_policy()), | |
99 | "boost::math::asinh<%1%>(%1%)"); | |
100 | } | |
101 | ||
102 | } | |
103 | } | |
104 | ||
105 | #endif /* BOOST_ASINH_HPP */ | |
106 |