ceph/src/boost/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 #include <cmath>
  19 #include <boost/math/tools/precision.hpp>
  20 #include <boost/math/policies/error_handling.hpp>
  21 #include <boost/math/special_functions/math_fwd.hpp>
  22 #include <boost/math/special_functions/log1p.hpp>
  23 #include <boost/math/special_functions/fpclassify.hpp>
  24
  25 // This is the inverse of the hyperbolic tangent function.
  26
  27 namespace boost
  28 {
  29     namespace math
  30     {
  31        namespace detail
  32        {
  33         // This is the main fare
  34
  35         template<typename T, typename Policy>
  36         inline T    atanh_imp(const T x, const Policy& pol)
  37         {
  38             BOOST_MATH_STD_USING
  39             static const char* function = "boost::math::atanh<%1%>(%1%)";
  40
  41             if(x < -1)
  42             {
  43                return policies::raise_domain_error<T>(
  44                   function,
  45                   "atanh requires x >= -1, but got x = %1%.", x, pol);
  46             }
  47             else if(x > 1)
  48             {
  49                return policies::raise_domain_error<T>(
  50                   function,
  51                   "atanh requires x <= 1, but got x = %1%.", x, pol);
  52             }
  53             else if((boost::math::isnan)(x))
  54             {
  55                return policies::raise_domain_error<T>(
  56                   function,
  57                   "atanh requires -1 <= x <= 1, but got x = %1%.", x, pol);
  58             }
  59             else if(x < -1 + tools::epsilon<T>())
  60             {
  61                // -Infinity:
  62                return -policies::raise_overflow_error<T>(function, 0, pol);
  63             }
  64             else if(x > 1 - tools::epsilon<T>())
  65             {
  66                // Infinity:
  67                return policies::raise_overflow_error<T>(function, 0, pol);
  68             }
  69             else if(abs(x) >= tools::forth_root_epsilon<T>())
  70             {
  71                 // http://functions.wolfram.com/ElementaryFunctions/ArcTanh/02/
  72                 if(abs(x) < 0.5f)
  73                    return (boost::math::log1p(x, pol) - boost::math::log1p(-x, pol)) / 2;
  74                 return(log( (1 + x) / (1 - x) ) / 2);
  75             }
  76             else
  77             {
  78                 // http://functions.wolfram.com/ElementaryFunctions/ArcTanh/06/01/03/01/
  79                 // approximation by taylor series in x at 0 up to order 2
  80                 T    result = x;
  81
  82                 if    (abs(x) >= tools::root_epsilon<T>())
  83                 {
  84                     T    x3 = x*x*x;
  85
  86                     // approximation by taylor series in x at 0 up to order 4
  87                     result += x3/static_cast<T>(3);
  88                 }
  89
  90                 return(result);
  91             }
  92         }
  93        }
  94
  95         template<typename T, typename Policy>
  96         inline typename tools::promote_args<T>::type atanh(T x, const Policy&)
  97         {
  98             typedef typename tools::promote_args<T>::type result_type;
  99             typedef typename policies::evaluation<result_type, Policy>::type value_type;
 100             typedef typename policies::normalise<
 101                Policy,
 102                policies::promote_float<false>,
 103                policies::promote_double<false>,
 104                policies::discrete_quantile<>,
 105                policies::assert_undefined<> >::type forwarding_policy;
 106            return policies::checked_narrowing_cast<result_type, forwarding_policy>(
 107               detail::atanh_imp(static_cast<value_type>(x), forwarding_policy()),
 108               "boost::math::atanh<%1%>(%1%)");
 109         }
 110         template<typename T>
 111         inline typename tools::promote_args<T>::type atanh(T x)
 112         {
 113            return boost::math::atanh(x, policies::policy<>());
 114         }
 115
 116     }
 117 }
 118
 119 #endif /* BOOST_ATANH_HPP */
 120
 121
 122