ceph/src/boost/libs/math/include/boost/math/special_functions/acosh.hpp

   1 //    boost asinh.hpp header file
   2
   3 //  (C) Copyright Eric Ford 2001 & Hubert Holin.
   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_ACOSH_HPP
  12 #define BOOST_ACOSH_HPP
  13
  14 #ifdef _MSC_VER
  15 #pragma once
  16 #endif
  17
  18 #include <boost/config/no_tr1/cmath.hpp>
  19 #include <boost/config.hpp>
  20 #include <boost/math/tools/precision.hpp>
  21 #include <boost/math/policies/error_handling.hpp>
  22 #include <boost/math/special_functions/math_fwd.hpp>
  23 #include <boost/math/special_functions/log1p.hpp>
  24 #include <boost/math/constants/constants.hpp>
  25
  26 // This is the inverse of the hyperbolic cosine function.
  27
  28 namespace boost
  29 {
  30     namespace math
  31     {
  32        namespace detail
  33        {
  34         template<typename T, typename Policy>
  35         inline T    acosh_imp(const T x, const Policy& pol)
  36         {
  37             BOOST_MATH_STD_USING
  38
  39             if(x < 1)
  40             {
  41                return policies::raise_domain_error<T>(
  42                   "boost::math::acosh<%1%>(%1%)",
  43                   "acosh requires x >= 1, but got x = %1%.", x, pol);
  44             }
  45             else if    ((x - 1) >= tools::root_epsilon<T>())
  46             {
  47                 if    (x > 1 / tools::root_epsilon<T>())
  48                 {
  49                     // http://functions.wolfram.com/ElementaryFunctions/ArcCosh/06/01/06/01/0001/
  50                     // approximation by laurent series in 1/x at 0+ order from -1 to 0
  51                     return log(x) + constants::ln_two<T>();
  52                 }
  53                 else if(x < 1.5f)
  54                 {
  55                    // This is just a rearrangement of the standard form below
  56                    // devised to minimse loss of precision when x ~ 1:
  57                    T y = x - 1;
  58                    return boost::math::log1p(y + sqrt(y * y + 2 * y), pol);
  59                 }
  60                 else
  61                 {
  62                     // http://functions.wolfram.com/ElementaryFunctions/ArcCosh/02/
  63                     return( log( x + sqrt(x * x - 1) ) );
  64                 }
  65             }
  66             else
  67             {
  68                 // see http://functions.wolfram.com/ElementaryFunctions/ArcCosh/06/01/04/01/0001/
  69                 T y = x - 1;
  70
  71                 // approximation by taylor series in y at 0 up to order 2
  72                 T result = sqrt(2 * y) * (1 - y /12 + 3 * y * y / 160);
  73                 return result;
  74             }
  75         }
  76        }
  77
  78         template<typename T, typename Policy>
  79         inline typename tools::promote_args<T>::type acosh(T x, const Policy&)
  80         {
  81             typedef typename tools::promote_args<T>::type result_type;
  82             typedef typename policies::evaluation<result_type, Policy>::type value_type;
  83             typedef typename policies::normalise<
  84                Policy,
  85                policies::promote_float<false>,
  86                policies::promote_double<false>,
  87                policies::discrete_quantile<>,
  88                policies::assert_undefined<> >::type forwarding_policy;
  89            return policies::checked_narrowing_cast<result_type, forwarding_policy>(
  90               detail::acosh_imp(static_cast<value_type>(x), forwarding_policy()),
  91               "boost::math::acosh<%1%>(%1%)");
  92         }
  93         template<typename T>
  94         inline typename tools::promote_args<T>::type acosh(T x)
  95         {
  96            return boost::math::acosh(x, policies::policy<>());
  97         }
  98
  99     }
 100 }
 101
 102 #endif /* BOOST_ACOSH_HPP */
 103
 104