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

   1 //  Copyright (c) 2006 Xiaogang Zhang, 2015 John Maddock
   2 //  Use, modification and distribution are subject to the
   3 //  Boost Software License, Version 1.0. (See accompanying file
   4 //  LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_0.txt)
   5 //
   6 //  History:
   7 //  XZ wrote the original of this file as part of the Google
   8 //  Summer of Code 2006.  JM modified it to fit into the
   9 //  Boost.Math conceptual framework better, and to correctly
  10 //  handle the y < 0 case.
  11 //  Updated 2015 to use Carlson's latest methods.
  12 //
  13
  14 #ifndef BOOST_MATH_ELLINT_RC_HPP
  15 #define BOOST_MATH_ELLINT_RC_HPP
  16
  17 #ifdef _MSC_VER
  18 #pragma once
  19 #endif
  20
  21 #include <boost/math/policies/error_handling.hpp>
  22 #include <boost/math/tools/config.hpp>
  23 #include <boost/math/special_functions/math_fwd.hpp>
  24 #include <boost/math/special_functions/log1p.hpp>
  25 #include <boost/math/constants/constants.hpp>
  26 #include <iostream>
  27
  28 // Carlson's degenerate elliptic integral
  29 // R_C(x, y) = R_F(x, y, y) = 0.5 * \int_{0}^{\infty} (t+x)^{-1/2} (t+y)^{-1} dt
  30 // Carlson, Numerische Mathematik, vol 33, 1 (1979)
  31
  32 namespace boost { namespace math { namespace detail{
  33
  34 template <typename T, typename Policy>
  35 T ellint_rc_imp(T x, T y, const Policy& pol)
  36 {
  37     BOOST_MATH_STD_USING
  38
  39     static const char* function = "boost::math::ellint_rc<%1%>(%1%,%1%)";
  40
  41     if(x < 0)
  42     {
  43        return policies::raise_domain_error<T>(function,
  44             "Argument x must be non-negative but got %1%", x, pol);
  45     }
  46     if(y == 0)
  47     {
  48        return policies::raise_domain_error<T>(function,
  49             "Argument y must not be zero but got %1%", y, pol);
  50     }
  51
  52     // for y < 0, the integral is singular, return Cauchy principal value
  53     T prefix, result;
  54     if(y < 0)
  55     {
  56         prefix = sqrt(x / (x - y));
  57         x = x - y;
  58         y = -y;
  59     }
  60     else
  61        prefix = 1;
  62
  63     if(x == 0)
  64     {
  65        result = constants::half_pi<T>() / sqrt(y);
  66     }
  67     else if(x == y)
  68     {
  69        result = 1 / sqrt(x);
  70     }
  71     else if(y > x)
  72     {
  73        result = atan(sqrt((y - x) / x)) / sqrt(y - x);
  74     }
  75     else
  76     {
  77        if(y / x > 0.5)
  78        {
  79           T arg = sqrt((x - y) / x);
  80           result = (boost::math::log1p(arg) - boost::math::log1p(-arg)) / (2 * sqrt(x - y));
  81        }
  82        else
  83        {
  84           result = log((sqrt(x) + sqrt(x - y)) / sqrt(y)) / sqrt(x - y);
  85        }
  86     }
  87     return prefix * result;
  88 }
  89
  90 } // namespace detail
  91
  92 template <class T1, class T2, class Policy>
  93 inline typename tools::promote_args<T1, T2>::type
  94    ellint_rc(T1 x, T2 y, const Policy& pol)
  95 {
  96    typedef typename tools::promote_args<T1, T2>::type result_type;
  97    typedef typename policies::evaluation<result_type, Policy>::type value_type;
  98    return policies::checked_narrowing_cast<result_type, Policy>(
  99       detail::ellint_rc_imp(
 100          static_cast<value_type>(x),
 101          static_cast<value_type>(y), pol), "boost::math::ellint_rc<%1%>(%1%,%1%)");
 102 }
 103
 104 template <class T1, class T2>
 105 inline typename tools::promote_args<T1, T2>::type
 106    ellint_rc(T1 x, T2 y)
 107 {
 108    return ellint_rc(x, y, policies::policy<>());
 109 }
 110
 111 }} // namespaces
 112
 113 #endif // BOOST_MATH_ELLINT_RC_HPP
 114