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 #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         template<typename T, typename Policy>
  46         inline T    acosh_imp(const T x, const Policy& pol)
  47         {
  48             BOOST_MATH_STD_USING
  49
  50             if(x < 1)
  51             {
  52                return policies::raise_domain_error<T>(
  53                   "boost::math::acosh<%1%>(%1%)",
  54                   "acosh requires x >= 1, but got x = %1%.", x, pol);
  55             }
  56             else if    ((x - 1) >= tools::root_epsilon<T>())
  57             {
  58                 if    (x > 1 / tools::root_epsilon<T>())
  59                 {
  60                     // http://functions.wolfram.com/ElementaryFunctions/ArcCosh/06/01/06/01/0001/
  61                     // approximation by laurent series in 1/x at 0+ order from -1 to 0
  62                     return log(x) + constants::ln_two<T>();
  63                 }
  64                 else if(x < 1.5f)
  65                 {
  66                    // This is just a rearrangement of the standard form below
  67                    // devised to minimse loss of precision when x ~ 1:
  68                    T y = x - 1;
  69                    return boost::math::log1p(y + sqrt(y * y + 2 * y), pol);
  70                 }
  71                 else
  72                 {
  73                     // http://functions.wolfram.com/ElementaryFunctions/ArcCosh/02/
  74                     return( log( x + sqrt(x * x - 1) ) );
  75                 }
  76             }
  77             else
  78             {
  79                 // see http://functions.wolfram.com/ElementaryFunctions/ArcCosh/06/01/04/01/0001/
  80                 T y = x - 1;
  81
  82                 // approximation by taylor series in y at 0 up to order 2
  83                 T result = sqrt(2 * y) * (1 - y /12 + 3 * y * y / 160);
  84                 return result;
  85             }
  86         }
  87        }
  88
  89         template<typename T, typename Policy>
  90         inline typename tools::promote_args<T>::type acosh(T x, const Policy&)
  91         {
  92             typedef typename tools::promote_args<T>::type result_type;
  93             typedef typename policies::evaluation<result_type, Policy>::type value_type;
  94             typedef typename policies::normalise<
  95                Policy,
  96                policies::promote_float<false>,
  97                policies::promote_double<false>,
  98                policies::discrete_quantile<>,
  99                policies::assert_undefined<> >::type forwarding_policy;
 100            return policies::checked_narrowing_cast<result_type, forwarding_policy>(
 101               detail::acosh_imp(static_cast<value_type>(x), forwarding_policy()),
 102               "boost::math::acosh<%1%>(%1%)");
 103         }
 104         template<typename T>
 105         inline typename tools::promote_args<T>::type acosh(T x)
 106         {
 107            return boost::math::acosh(x, policies::policy<>());
 108         }
 109
 110     }
 111 }
 112
 113 #endif /* BOOST_ACOSH_HPP */
 114
 115