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 #if defined(__GNUC__) && (__GNUC__ < 3)
35 // gcc 2.x ignores function scope using declarations,
36 // put them in the scope of the enclosing namespace instead:
42 using ::std::numeric_limits;
45 template<typename T, class Policy>
46 inline T asinh_imp(const T x, const Policy& pol)
50 if (x >= tools::forth_root_epsilon<T>())
52 if (x > 1 / tools::root_epsilon<T>())
54 // http://functions.wolfram.com/ElementaryFunctions/ArcSinh/06/01/06/01/0001/
55 // approximation by laurent series in 1/x at 0+ order from -1 to 1
56 return constants::ln_two<T>() + log(x) + 1/ (4 * x * x);
60 // As below, but rearranged to preserve digits:
61 return boost::math::log1p(x + boost::math::sqrt1pm1(x * x, pol), pol);
65 // http://functions.wolfram.com/ElementaryFunctions/ArcSinh/02/
66 return( log( x + sqrt(x*x+1) ) );
69 else if (x <= -tools::forth_root_epsilon<T>())
71 return(-asinh(-x, pol));
75 // http://functions.wolfram.com/ElementaryFunctions/ArcSinh/06/01/03/01/0001/
76 // approximation by taylor series in x at 0 up to order 2
79 if (abs(x) >= tools::root_epsilon<T>())
83 // approximation by taylor series in x at 0 up to order 4
84 result -= x3/static_cast<T>(6);
93 inline typename tools::promote_args<T>::type asinh(T x)
95 return boost::math::asinh(x, policies::policy<>());
97 template<typename T, typename Policy>
98 inline typename tools::promote_args<T>::type asinh(T x, const Policy&)
100 typedef typename tools::promote_args<T>::type result_type;
101 typedef typename policies::evaluation<result_type, Policy>::type value_type;
102 typedef typename policies::normalise<
104 policies::promote_float<false>,
105 policies::promote_double<false>,
106 policies::discrete_quantile<>,
107 policies::assert_undefined<> >::type forwarding_policy;
108 return policies::checked_narrowing_cast<result_type, forwarding_policy>(
109 detail::asinh_imp(static_cast<value_type>(x), forwarding_policy()),
110 "boost::math::asinh<%1%>(%1%)");
116 #endif /* BOOST_ASINH_HPP */