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 #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:
  37
  38         using    ::std::abs;
  39         using    ::std::sqrt;
  40         using    ::std::log;
  41
  42         using    ::std::numeric_limits;
  43 #endif
  44
  45         template<typename T, class Policy>
  46         inline T    asinh_imp(const T x, const Policy& pol)
  47         {
  48             BOOST_MATH_STD_USING
  49
  50             if        (x >= tools::forth_root_epsilon<T>())
  51             {
  52                if        (x > 1 / tools::root_epsilon<T>())
  53                 {
  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);
  57                 }
  58                 else if(x < 0.5f)
  59                 {
  60                    // As below, but rearranged to preserve digits:
  61                    return boost::math::log1p(x + boost::math::sqrt1pm1(x * x, pol), pol);
  62                 }
  63                 else
  64                 {
  65                     // http://functions.wolfram.com/ElementaryFunctions/ArcSinh/02/
  66                     return( log( x + sqrt(x*x+1) ) );
  67                 }
  68             }
  69             else if    (x <= -tools::forth_root_epsilon<T>())
  70             {
  71                 return(-asinh(-x, pol));
  72             }
  73             else
  74             {
  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
  77                 T    result = x;
  78
  79                 if    (abs(x) >= tools::root_epsilon<T>())
  80                 {
  81                     T    x3 = x*x*x;
  82
  83                     // approximation by taylor series in x at 0 up to order 4
  84                     result -= x3/static_cast<T>(6);
  85                 }
  86
  87                 return(result);
  88             }
  89         }
  90        }
  91
  92         template<typename T>
  93         inline typename tools::promote_args<T>::type asinh(T x)
  94         {
  95            return boost::math::asinh(x, policies::policy<>());
  96         }
  97         template<typename T, typename Policy>
  98         inline typename tools::promote_args<T>::type asinh(T x, const Policy&)
  99         {
 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<
 103                Policy,
 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%)");
 111         }
 112
 113     }
 114 }
 115
 116 #endif /* BOOST_ASINH_HPP */
 117