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1 | // boost asinh.hpp header file |
2 | ||
3 | // (C) Copyright Eric Ford 2001 & Hubert Holin. | |
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_ACOSH_HPP | |
12 | #define BOOST_ACOSH_HPP | |
13 | ||
14 | #ifdef _MSC_VER | |
15 | #pragma once | |
16 | #endif | |
17 | ||
18 | #include <boost/config/no_tr1/cmath.hpp> | |
19 | #include <boost/config.hpp> | |
20 | #include <boost/math/tools/precision.hpp> | |
21 | #include <boost/math/policies/error_handling.hpp> | |
22 | #include <boost/math/special_functions/math_fwd.hpp> | |
23 | #include <boost/math/special_functions/log1p.hpp> | |
24 | #include <boost/math/constants/constants.hpp> | |
25 | ||
26 | // This is the inverse of the hyperbolic cosine function. | |
27 | ||
28 | namespace boost | |
29 | { | |
30 | namespace math | |
31 | { | |
32 | namespace detail | |
33 | { | |
34 | template<typename T, typename Policy> | |
35 | inline T acosh_imp(const T x, const Policy& pol) | |
36 | { | |
37 | BOOST_MATH_STD_USING | |
38 | ||
39 | if(x < 1) | |
40 | { | |
41 | return policies::raise_domain_error<T>( | |
42 | "boost::math::acosh<%1%>(%1%)", | |
43 | "acosh requires x >= 1, but got x = %1%.", x, pol); | |
44 | } | |
45 | else if ((x - 1) >= tools::root_epsilon<T>()) | |
46 | { | |
47 | if (x > 1 / tools::root_epsilon<T>()) | |
48 | { | |
49 | // http://functions.wolfram.com/ElementaryFunctions/ArcCosh/06/01/06/01/0001/ | |
50 | // approximation by laurent series in 1/x at 0+ order from -1 to 0 | |
51 | return log(x) + constants::ln_two<T>(); | |
52 | } | |
53 | else if(x < 1.5f) | |
54 | { | |
55 | // This is just a rearrangement of the standard form below | |
56 | // devised to minimse loss of precision when x ~ 1: | |
57 | T y = x - 1; | |
58 | return boost::math::log1p(y + sqrt(y * y + 2 * y), pol); | |
59 | } | |
60 | else | |
61 | { | |
62 | // http://functions.wolfram.com/ElementaryFunctions/ArcCosh/02/ | |
63 | return( log( x + sqrt(x * x - 1) ) ); | |
64 | } | |
65 | } | |
66 | else | |
67 | { | |
68 | // see http://functions.wolfram.com/ElementaryFunctions/ArcCosh/06/01/04/01/0001/ | |
69 | T y = x - 1; | |
70 | ||
71 | // approximation by taylor series in y at 0 up to order 2 | |
72 | T result = sqrt(2 * y) * (1 - y /12 + 3 * y * y / 160); | |
73 | return result; | |
74 | } | |
75 | } | |
76 | } | |
77 | ||
78 | template<typename T, typename Policy> | |
79 | inline typename tools::promote_args<T>::type acosh(T x, const Policy&) | |
80 | { | |
81 | typedef typename tools::promote_args<T>::type result_type; | |
82 | typedef typename policies::evaluation<result_type, Policy>::type value_type; | |
83 | typedef typename policies::normalise< | |
84 | Policy, | |
85 | policies::promote_float<false>, | |
86 | policies::promote_double<false>, | |
87 | policies::discrete_quantile<>, | |
88 | policies::assert_undefined<> >::type forwarding_policy; | |
89 | return policies::checked_narrowing_cast<result_type, forwarding_policy>( | |
90 | detail::acosh_imp(static_cast<value_type>(x), forwarding_policy()), | |
91 | "boost::math::acosh<%1%>(%1%)"); | |
92 | } | |
93 | template<typename T> | |
94 | inline typename tools::promote_args<T>::type acosh(T x) | |
95 | { | |
96 | return boost::math::acosh(x, policies::policy<>()); | |
97 | } | |
98 | ||
99 | } | |
100 | } | |
101 | ||
102 | #endif /* BOOST_ACOSH_HPP */ | |
103 | ||
104 |