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         // This is the main fare
  35
  36         template<typename T, typename Policy>
  37         inline T    atanh_imp(const T x, const Policy& pol)
  38         {
  39             BOOST_MATH_STD_USING
  40             static const char* function = "boost::math::atanh<%1%>(%1%)";
  41
  42             if(x < -1)
  43             {
  44                return policies::raise_domain_error<T>(
  45                   function,
  46                   "atanh requires x >= -1, but got x = %1%.", x, pol);
  47             }
  48             else if(x > 1)
  49             {
  50                return policies::raise_domain_error<T>(
  51                   function,
  52                   "atanh requires x <= 1, but got x = %1%.", x, pol);
  53             }
  54             else if((boost::math::isnan)(x))
  55             {
  56                return policies::raise_domain_error<T>(
  57                   function,
  58                   "atanh requires -1 <= x <= 1, but got x = %1%.", x, pol);
  59             }
  60             else if(x < -1 + tools::epsilon<T>())
  61             {
  62                // -Infinity:
  63                return -policies::raise_overflow_error<T>(function, 0, 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(abs(x) >= tools::forth_root_epsilon<T>())
  71             {
  72                 // http://functions.wolfram.com/ElementaryFunctions/ArcTanh/02/
  73                 if(abs(x) < 0.5f)
  74                    return (boost::math::log1p(x, pol) - boost::math::log1p(-x, pol)) / 2;
  75                 return(log( (1 + x) / (1 - x) ) / 2);
  76             }
  77             else
  78             {
  79                 // http://functions.wolfram.com/ElementaryFunctions/ArcTanh/06/01/03/01/
  80                 // approximation by taylor series in x at 0 up to order 2
  81                 T    result = x;
  82
  83                 if    (abs(x) >= tools::root_epsilon<T>())
  84                 {
  85                     T    x3 = x*x*x;
  86
  87                     // approximation by taylor series in x at 0 up to order 4
  88                     result += x3/static_cast<T>(3);
  89                 }
  90
  91                 return(result);
  92             }
  93         }
  94        }
  95
  96         template<typename T, typename Policy>
  97         inline typename tools::promote_args<T>::type atanh(T x, const Policy&)
  98         {
  99             typedef typename tools::promote_args<T>::type result_type;
 100             typedef typename policies::evaluation<result_type, Policy>::type value_type;
 101             typedef typename policies::normalise<
 102                Policy,
 103                policies::promote_float<false>,
 104                policies::promote_double<false>,
 105                policies::discrete_quantile<>,
 106                policies::assert_undefined<> >::type forwarding_policy;
 107            return policies::checked_narrowing_cast<result_type, forwarding_policy>(
 108               detail::atanh_imp(static_cast<value_type>(x), forwarding_policy()),
 109               "boost::math::atanh<%1%>(%1%)");
 110         }
 111         template<typename T>
 112         inline typename tools::promote_args<T>::type atanh(T x)
 113         {
 114            return boost::math::atanh(x, policies::policy<>());
 115         }
 116
 117     }
 118 }
 119
 120 #endif /* BOOST_ATANH_HPP */
 121
 122
 123