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 <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/constants/constants.hpp>
24#include <boost/math/special_functions/fpclassify.hpp>
25
26// This is the inverse of the hyperbolic cosine function.
27
28namespace 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) || (boost::math::isnan)(x))
40 {
41 return policies::raise_domain_error<T>("boost::math::acosh<%1%>(%1%)", "acosh requires x >= 1, but got x = %1%.", x, pol);
42 }
43 else if ((x - 1) >= tools::root_epsilon<T>())
44 {
45 if (x > 1 / tools::root_epsilon<T>())
46 {
47 // http://functions.wolfram.com/ElementaryFunctions/ArcCosh/06/01/06/01/0001/
48 // approximation by laurent series in 1/x at 0+ order from -1 to 0
49 return log(x) + constants::ln_two<T>();
50 }
51 else if(x < 1.5f)
52 {
53 // This is just a rearrangement of the standard form below
54 // devised to minimise loss of precision when x ~ 1:
55 T y = x - 1;
56 return boost::math::log1p(y + sqrt(y * y + 2 * y), pol);
57 }
58 else
59 {
60 // http://functions.wolfram.com/ElementaryFunctions/ArcCosh/02/
61 return( log( x + sqrt(x * x - 1) ) );
62 }
63 }
64 else
65 {
66 // see http://functions.wolfram.com/ElementaryFunctions/ArcCosh/06/01/04/01/0001/
67 T y = x - 1;
68
69 // approximation by taylor series in y at 0 up to order 2
70 T result = sqrt(2 * y) * (1 - y /12 + 3 * y * y / 160);
71 return result;
72 }
73 }
74 }
75
76 template<typename T, typename Policy>
77 inline typename tools::promote_args<T>::type acosh(T x, const Policy&)
78 {
79 typedef typename tools::promote_args<T>::type result_type;
80 typedef typename policies::evaluation<result_type, Policy>::type value_type;
81 typedef typename policies::normalise<
82 Policy,
83 policies::promote_float<false>,
84 policies::promote_double<false>,
85 policies::discrete_quantile<>,
86 policies::assert_undefined<> >::type forwarding_policy;
87 return policies::checked_narrowing_cast<result_type, forwarding_policy>(
88 detail::acosh_imp(static_cast<value_type>(x), forwarding_policy()),
89 "boost::math::acosh<%1%>(%1%)");
90 }
91 template<typename T>
92 inline typename tools::promote_args<T>::type acosh(T x)
93 {
94 return boost::math::acosh(x, policies::policy<>());
95 }
96
97 }
98}
99
100#endif /* BOOST_ACOSH_HPP */
101
102
103

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