boost/math/special_functions/atanh.hpp

   1 //    boost atanh.hpp header file
   2
   3 //  (C) Copyright 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_ATANH_HPP
  12 #define BOOST_ATANH_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/policies/error_handling.hpp>
  23 #include <boost/math/special_functions/math_fwd.hpp>
  24 #include <boost/math/special_functions/log1p.hpp>
  25
  26 // This is the inverse of the hyperbolic tangent function.
  27
  28 namespace boost
  29 {
  30     namespace math
  31     {
  32        namespace detail
  33        {
  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         // This is the main fare
  46
  47         template<typename T, typename Policy>
  48         inline T    atanh_imp(const T x, const Policy& pol)
  49         {
  50             BOOST_MATH_STD_USING
  51             static const char* function = "boost::math::atanh<%1%>(%1%)";
  52
  53             if(x < -1)
  54             {
  55                return policies::raise_domain_error<T>(
  56                   function,
  57                   "atanh requires x >= -1, but got x = %1%.", x, pol);
  58             }
  59             else if(x > 1)
  60             {
  61                return policies::raise_domain_error<T>(
  62                   function,
  63                   "atanh requires x <= 1, but got x = %1%.", x, pol);
  64             }
  65             else if(x < -1 + tools::epsilon<T>())
  66             {
  67                // -Infinity:
  68                return -policies::raise_overflow_error<T>(function, 0, pol);
  69             }
  70             else if(x > 1 - tools::epsilon<T>())
  71             {
  72                // Infinity:
  73                return policies::raise_overflow_error<T>(function, 0, pol);
  74             }
  75             else if(abs(x) >= tools::forth_root_epsilon<T>())
  76             {
  77                 // http://functions.wolfram.com/ElementaryFunctions/ArcTanh/02/
  78                 if(abs(x) < 0.5f)
  79                    return (boost::math::log1p(x, pol) - boost::math::log1p(-x, pol)) / 2;
  80                 return(log( (1 + x) / (1 - x) ) / 2);
  81             }
  82             else
  83             {
  84                 // http://functions.wolfram.com/ElementaryFunctions/ArcTanh/06/01/03/01/
  85                 // approximation by taylor series in x at 0 up to order 2
  86                 T    result = x;
  87
  88                 if    (abs(x) >= tools::root_epsilon<T>())
  89                 {
  90                     T    x3 = x*x*x;
  91
  92                     // approximation by taylor series in x at 0 up to order 4
  93                     result += x3/static_cast<T>(3);
  94                 }
  95
  96                 return(result);
  97             }
  98         }
  99        }
 100
 101         template<typename T, typename Policy>
 102         inline typename tools::promote_args<T>::type atanh(T x, const Policy&)
 103         {
 104             typedef typename tools::promote_args<T>::type result_type;
 105             typedef typename policies::evaluation<result_type, Policy>::type value_type;
 106             typedef typename policies::normalise<
 107                Policy,
 108                policies::promote_float<false>,
 109                policies::promote_double<false>,
 110                policies::discrete_quantile<>,
 111                policies::assert_undefined<> >::type forwarding_policy;
 112            return policies::checked_narrowing_cast<result_type, forwarding_policy>(
 113               detail::atanh_imp(static_cast<value_type>(x), forwarding_policy()),
 114               "boost::math::atanh<%1%>(%1%)");
 115         }
 116         template<typename T>
 117         inline typename tools::promote_args<T>::type atanh(T x)
 118         {
 119            return boost::math::atanh(x, policies::policy<>());
 120         }
 121
 122     }
 123 }
 124
 125 #endif /* BOOST_ATANH_HPP */
 126
 127
 128