Chris@101: //  Copyright (c) 2006 Xiaogang Zhang, 2015 John Maddock
Chris@16: //  Use, modification and distribution are subject to the
Chris@16: //  Boost Software License, Version 1.0. (See accompanying file
Chris@16: //  LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_0.txt)
Chris@16: //
Chris@16: //  History:
Chris@16: //  XZ wrote the original of this file as part of the Google
Chris@16: //  Summer of Code 2006.  JM modified it to fit into the
Chris@16: //  Boost.Math conceptual framework better, and to correctly
Chris@16: //  handle the y < 0 case.
Chris@101: //  Updated 2015 to use Carlson's latest methods.
Chris@16: //
Chris@16: 
Chris@16: #ifndef BOOST_MATH_ELLINT_RC_HPP
Chris@16: #define BOOST_MATH_ELLINT_RC_HPP
Chris@16: 
Chris@16: #ifdef _MSC_VER
Chris@16: #pragma once
Chris@16: #endif
Chris@16: 
Chris@16: #include <boost/math/policies/error_handling.hpp>
Chris@16: #include <boost/math/tools/config.hpp>
Chris@16: #include <boost/math/special_functions/math_fwd.hpp>
Chris@101: #include <boost/math/special_functions/log1p.hpp>
Chris@101: #include <boost/math/constants/constants.hpp>
Chris@101: #include <iostream>
Chris@16: 
Chris@16: // Carlson's degenerate elliptic integral
Chris@16: // R_C(x, y) = R_F(x, y, y) = 0.5 * \int_{0}^{\infty} (t+x)^{-1/2} (t+y)^{-1} dt
Chris@16: // Carlson, Numerische Mathematik, vol 33, 1 (1979)
Chris@16: 
Chris@16: namespace boost { namespace math { namespace detail{
Chris@16: 
Chris@16: template <typename T, typename Policy>
Chris@16: T ellint_rc_imp(T x, T y, const Policy& pol)
Chris@16: {
Chris@16:     BOOST_MATH_STD_USING
Chris@16: 
Chris@16:     static const char* function = "boost::math::ellint_rc<%1%>(%1%,%1%)";
Chris@16: 
Chris@16:     if(x < 0)
Chris@16:     {
Chris@16:        return policies::raise_domain_error<T>(function,
Chris@16:             "Argument x must be non-negative but got %1%", x, pol);
Chris@16:     }
Chris@16:     if(y == 0)
Chris@16:     {
Chris@16:        return policies::raise_domain_error<T>(function,
Chris@16:             "Argument y must not be zero but got %1%", y, pol);
Chris@16:     }
Chris@16: 
Chris@16:     // for y < 0, the integral is singular, return Cauchy principal value
Chris@101:     T prefix, result;
Chris@101:     if(y < 0)
Chris@16:     {
Chris@16:         prefix = sqrt(x / (x - y));
Chris@16:         x = x - y;
Chris@16:         y = -y;
Chris@16:     }
Chris@16:     else
Chris@16:        prefix = 1;
Chris@16: 
Chris@101:     if(x == 0)
Chris@16:     {
Chris@101:        result = constants::half_pi<T>() / sqrt(y);
Chris@101:     }
Chris@101:     else if(x == y)
Chris@101:     {
Chris@101:        result = 1 / sqrt(x);
Chris@101:     }
Chris@101:     else if(y > x)
Chris@101:     {
Chris@101:        result = atan(sqrt((y - x) / x)) / sqrt(y - x);
Chris@101:     }
Chris@101:     else
Chris@101:     {
Chris@101:        if(y / x > 0.5)
Chris@101:        {
Chris@101:           T arg = sqrt((x - y) / x);
Chris@101:           result = (boost::math::log1p(arg) - boost::math::log1p(-arg)) / (2 * sqrt(x - y));
Chris@101:        }
Chris@101:        else
Chris@101:        {
Chris@101:           result = log((sqrt(x) + sqrt(x - y)) / sqrt(y)) / sqrt(x - y);
Chris@101:        }
Chris@101:     }
Chris@101:     return prefix * result;
Chris@16: }
Chris@16: 
Chris@16: } // namespace detail
Chris@16: 
Chris@16: template <class T1, class T2, class Policy>
Chris@16: inline typename tools::promote_args<T1, T2>::type 
Chris@16:    ellint_rc(T1 x, T2 y, const Policy& pol)
Chris@16: {
Chris@16:    typedef typename tools::promote_args<T1, T2>::type result_type;
Chris@16:    typedef typename policies::evaluation<result_type, Policy>::type value_type;
Chris@16:    return policies::checked_narrowing_cast<result_type, Policy>(
Chris@16:       detail::ellint_rc_imp(
Chris@16:          static_cast<value_type>(x),
Chris@16:          static_cast<value_type>(y), pol), "boost::math::ellint_rc<%1%>(%1%,%1%)");
Chris@16: }
Chris@16: 
Chris@16: template <class T1, class T2>
Chris@16: inline typename tools::promote_args<T1, T2>::type 
Chris@16:    ellint_rc(T1 x, T2 y)
Chris@16: {
Chris@16:    return ellint_rc(x, y, policies::policy<>());
Chris@16: }
Chris@16: 
Chris@16: }} // namespaces
Chris@16: 
Chris@16: #endif // BOOST_MATH_ELLINT_RC_HPP
Chris@16: