1 // boost asinh.hpp header file
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)
9 // See http://www.boost.org for updates, documentation, and revision history.
11 #ifndef BOOST_ASINH_HPP
12 #define BOOST_ASINH_HPP
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>
27 // This is the inverse of the hyperbolic sine function.
34 template<typename T, class Policy>
35 inline T asinh_imp(const T x, const Policy& pol)
39 if (x >= tools::forth_root_epsilon<T>())
41 if (x > 1 / tools::root_epsilon<T>())
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);
49 // As below, but rearranged to preserve digits:
50 return boost::math::log1p(x + boost::math::sqrt1pm1(x * x, pol), pol);
54 // http://functions.wolfram.com/ElementaryFunctions/ArcSinh/02/
55 return( log( x + sqrt(x*x+1) ) );
58 else if (x <= -tools::forth_root_epsilon<T>())
60 return(-asinh(-x, pol));
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
68 if (abs(x) >= tools::root_epsilon<T>())
72 // approximation by taylor series in x at 0 up to order 4
73 result -= x3/static_cast<T>(6);
82 inline typename tools::promote_args<T>::type asinh(T x)
84 return boost::math::asinh(x, policies::policy<>());
86 template<typename T, typename Policy>
87 inline typename tools::promote_args<T>::type asinh(T x, const Policy&)
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<
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%)");
105 #endif /* BOOST_ASINH_HPP */