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authorAnas Nashif <anas.nashif@intel.com>2012-10-30 19:57:26 (GMT)
committerAnas Nashif <anas.nashif@intel.com>2012-10-30 19:57:26 (GMT)
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Imported Upstream version 1.49.0upstream/1.49.0
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+// Copyright (c) 2006 Xiaogang Zhang
+// Use, modification and distribution are subject to the
+// Boost Software License, Version 1.0. (See accompanying file
+// LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_0.txt)
+//
+// History:
+// XZ wrote the original of this file as part of the Google
+// Summer of Code 2006. JM modified it slightly to fit into the
+// Boost.Math conceptual framework better.
+
+#ifndef BOOST_MATH_ELLINT_RD_HPP
+#define BOOST_MATH_ELLINT_RD_HPP
+
+#ifdef _MSC_VER
+#pragma once
+#endif
+
+#include <boost/math/special_functions/math_fwd.hpp>
+#include <boost/math/tools/config.hpp>
+#include <boost/math/policies/error_handling.hpp>
+
+// Carlson's elliptic integral of the second kind
+// R_D(x, y, z) = R_J(x, y, z, z) = 1.5 * \int_{0}^{\infty} [(t+x)(t+y)]^{-1/2} (t+z)^{-3/2} dt
+// Carlson, Numerische Mathematik, vol 33, 1 (1979)
+
+namespace boost { namespace math { namespace detail{
+
+template <typename T, typename Policy>
+T ellint_rd_imp(T x, T y, T z, const Policy& pol)
+{
+ T value, u, lambda, sigma, factor, tolerance;
+ T X, Y, Z, EA, EB, EC, ED, EE, S1, S2;
+ unsigned long k;
+
+ BOOST_MATH_STD_USING
+ using namespace boost::math::tools;
+
+ static const char* function = "boost::math::ellint_rd<%1%>(%1%,%1%,%1%)";
+
+ if (x < 0)
+ {
+ return policies::raise_domain_error<T>(function,
+ "Argument x must be >= 0, but got %1%", x, pol);
+ }
+ if (y < 0)
+ {
+ return policies::raise_domain_error<T>(function,
+ "Argument y must be >= 0, but got %1%", y, pol);
+ }
+ if (z <= 0)
+ {
+ return policies::raise_domain_error<T>(function,
+ "Argument z must be > 0, but got %1%", z, pol);
+ }
+ if (x + y == 0)
+ {
+ return policies::raise_domain_error<T>(function,
+ "At most one argument can be zero, but got, x + y = %1%", x+y, pol);
+ }
+
+ // error scales as the 6th power of tolerance
+ tolerance = pow(tools::epsilon<T>() / 3, T(1)/6);
+
+ // duplication
+ sigma = 0;
+ factor = 1;
+ k = 1;
+ do
+ {
+ u = (x + y + z + z + z) / 5;
+ X = (u - x) / u;
+ Y = (u - y) / u;
+ Z = (u - z) / u;
+ if ((tools::max)(abs(X), abs(Y), abs(Z)) < tolerance)
+ break;
+ T sx = sqrt(x);
+ T sy = sqrt(y);
+ T sz = sqrt(z);
+ lambda = sy * (sx + sz) + sz * sx; //sqrt(x * y) + sqrt(y * z) + sqrt(z * x);
+ sigma += factor / (sz * (z + lambda));
+ factor /= 4;
+ x = (x + lambda) / 4;
+ y = (y + lambda) / 4;
+ z = (z + lambda) / 4;
+ ++k;
+ }
+ while(k < policies::get_max_series_iterations<Policy>());
+
+ // Check to see if we gave up too soon:
+ policies::check_series_iterations<T>(function, k, pol);
+
+ // Taylor series expansion to the 5th order
+ EA = X * Y;
+ EB = Z * Z;
+ EC = EA - EB;
+ ED = EA - 6 * EB;
+ EE = ED + EC + EC;
+ S1 = ED * (ED * T(9) / 88 - Z * EE * T(9) / 52 - T(3) / 14);
+ S2 = Z * (EE / 6 + Z * (-EC * T(9) / 22 + Z * EA * T(3) / 26));
+ value = 3 * sigma + factor * (1 + S1 + S2) / (u * sqrt(u));
+
+ return value;
+}
+
+} // namespace detail
+
+template <class T1, class T2, class T3, class Policy>
+inline typename tools::promote_args<T1, T2, T3>::type
+ ellint_rd(T1 x, T2 y, T3 z, const Policy& pol)
+{
+ typedef typename tools::promote_args<T1, T2, T3>::type result_type;
+ typedef typename policies::evaluation<result_type, Policy>::type value_type;
+ return policies::checked_narrowing_cast<result_type, Policy>(
+ detail::ellint_rd_imp(
+ static_cast<value_type>(x),
+ static_cast<value_type>(y),
+ static_cast<value_type>(z), pol), "boost::math::ellint_rd<%1%>(%1%,%1%,%1%)");
+}
+
+template <class T1, class T2, class T3>
+inline typename tools::promote_args<T1, T2, T3>::type
+ ellint_rd(T1 x, T2 y, T3 z)
+{
+ return ellint_rd(x, y, z, policies::policy<>());
+}
+
+}} // namespaces
+
+#endif // BOOST_MATH_ELLINT_RD_HPP
+