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>
acosh_imp(const T x,const Policy & pol)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>
acosh(T x,const 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>
acosh(T x)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 
105