ceph/src/boost/libs/math/include/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(x < -1 + tools::epsilon<T>())
  55             {
  56                // -Infinity:
  57                return -policies::raise_overflow_error<T>(function, 0, 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(abs(x) >= tools::forth_root_epsilon<T>())
  65             {
  66                 // http://functions.wolfram.com/ElementaryFunctions/ArcTanh/02/
  67                 if(abs(x) < 0.5f)
  68                    return (boost::math::log1p(x, pol) - boost::math::log1p(-x, pol)) / 2;
  69                 return(log( (1 + x) / (1 - x) ) / 2);
  70             }
  71             else
  72             {
  73                 // http://functions.wolfram.com/ElementaryFunctions/ArcTanh/06/01/03/01/
  74                 // approximation by taylor series in x at 0 up to order 2
  75                 T    result = x;
  76
  77                 if    (abs(x) >= tools::root_epsilon<T>())
  78                 {
  79                     T    x3 = x*x*x;
  80
  81                     // approximation by taylor series in x at 0 up to order 4
  82                     result += x3/static_cast<T>(3);
  83                 }
  84
  85                 return(result);
  86             }
  87         }
  88        }
  89
  90         template<typename T, typename Policy>
  91         inline typename tools::promote_args<T>::type atanh(T x, const Policy&)
  92         {
  93             typedef typename tools::promote_args<T>::type result_type;
  94             typedef typename policies::evaluation<result_type, Policy>::type value_type;
  95             typedef typename policies::normalise<
  96                Policy,
  97                policies::promote_float<false>,
  98                policies::promote_double<false>,
  99                policies::discrete_quantile<>,
 100                policies::assert_undefined<> >::type forwarding_policy;
 101            return policies::checked_narrowing_cast<result_type, forwarding_policy>(
 102               detail::atanh_imp(static_cast<value_type>(x), forwarding_policy()),
 103               "boost::math::atanh<%1%>(%1%)");
 104         }
 105         template<typename T>
 106         inline typename tools::promote_args<T>::type atanh(T x)
 107         {
 108            return boost::math::atanh(x, policies::policy<>());
 109         }
 110
 111     }
 112 }
 113
 114 #endif /* BOOST_ATANH_HPP */
 115
 116
 117