ceph/src/boost/boost/math/special_functions/asinh.hpp

   1 //    boost asinh.hpp header file
   2
   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)
   8
   9 // See http://www.boost.org for updates, documentation, and revision history.
  10
  11 #ifndef BOOST_ASINH_HPP
  12 #define BOOST_ASINH_HPP
  13
  14 #ifdef _MSC_VER
  15 #pragma once
  16 #endif
  17
  18
  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>
  26
  27 // This is the inverse of the hyperbolic sine function.
  28
  29 namespace boost
  30 {
  31     namespace math
  32     {
  33        namespace detail{
  34         template<typename T, class Policy>
  35         inline T    asinh_imp(const T x, const Policy& pol)
  36         {
  37             BOOST_MATH_STD_USING
  38
  39             if((boost::math::isnan)(x))
  40             {
  41                return policies::raise_domain_error<T>(
  42                   "boost::math::asinh<%1%>(%1%)",
  43                   "asinh requires a finite argument, but got x = %1%.", x, pol);
  44             }
  45             if        (x >= tools::forth_root_epsilon<T>())
  46             {
  47                if        (x > 1 / tools::root_epsilon<T>())
  48                 {
  49                     // http://functions.wolfram.com/ElementaryFunctions/ArcSinh/06/01/06/01/0001/
  50                     // approximation by laurent series in 1/x at 0+ order from -1 to 1
  51                     return constants::ln_two<T>() + log(x) + 1/ (4 * x * x);
  52                 }
  53                 else if(x < 0.5f)
  54                 {
  55                    // As below, but rearranged to preserve digits:
  56                    return boost::math::log1p(x + boost::math::sqrt1pm1(x * x, pol), pol);
  57                 }
  58                 else
  59                 {
  60                     // http://functions.wolfram.com/ElementaryFunctions/ArcSinh/02/
  61                     return( log( x + sqrt(x*x+1) ) );
  62                 }
  63             }
  64             else if    (x <= -tools::forth_root_epsilon<T>())
  65             {
  66                 return(-asinh(-x, pol));
  67             }
  68             else
  69             {
  70                 // http://functions.wolfram.com/ElementaryFunctions/ArcSinh/06/01/03/01/0001/
  71                 // approximation by taylor series in x at 0 up to order 2
  72                 T    result = x;
  73
  74                 if    (abs(x) >= tools::root_epsilon<T>())
  75                 {
  76                     T    x3 = x*x*x;
  77
  78                     // approximation by taylor series in x at 0 up to order 4
  79                     result -= x3/static_cast<T>(6);
  80                 }
  81
  82                 return(result);
  83             }
  84         }
  85        }
  86
  87         template<typename T>
  88         inline typename tools::promote_args<T>::type asinh(T x)
  89         {
  90            return boost::math::asinh(x, policies::policy<>());
  91         }
  92         template<typename T, typename Policy>
  93         inline typename tools::promote_args<T>::type asinh(T x, const Policy&)
  94         {
  95             typedef typename tools::promote_args<T>::type result_type;
  96             typedef typename policies::evaluation<result_type, Policy>::type value_type;
  97             typedef typename policies::normalise<
  98                Policy,
  99                policies::promote_float<false>,
 100                policies::promote_double<false>,
 101                policies::discrete_quantile<>,
 102                policies::assert_undefined<> >::type forwarding_policy;
 103            return policies::checked_narrowing_cast<result_type, forwarding_policy>(
 104               detail::asinh_imp(static_cast<value_type>(x), forwarding_policy()),
 105               "boost::math::asinh<%1%>(%1%)");
 106         }
 107
 108     }
 109 }
 110
 111 #endif /* BOOST_ASINH_HPP */
 112