Updated boost to v1.55.0

[rsem.git] / boost / math / special_functions / ellint_rc.hpp

diff --git a/boost/math/special_functions/ellint_rc.hpp b/boost/math/special_functions/ellint_rc.hpp
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+++ b/boost/math/special_functions/ellint_rc.hpp
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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 to fit into the
+//  Boost.Math conceptual framework better, and to correctly
+//  handle the y < 0 case.
+//
+
+#ifndef BOOST_MATH_ELLINT_RC_HPP
+#define BOOST_MATH_ELLINT_RC_HPP
+
+#ifdef _MSC_VER
+#pragma once
+#endif
+
+#include <boost/math/policies/error_handling.hpp>
+#include <boost/math/tools/config.hpp>
+#include <boost/math/special_functions/math_fwd.hpp>
+
+// Carlson's degenerate elliptic integral
+// R_C(x, y) = R_F(x, y, y) = 0.5 * \int_{0}^{\infty} (t+x)^{-1/2} (t+y)^{-1} dt
+// Carlson, Numerische Mathematik, vol 33, 1 (1979)
+
+namespace boost { namespace math { namespace detail{
+
+template <typename T, typename Policy>
+T ellint_rc_imp(T x, T y, const Policy& pol)
+{
+    T value, S, u, lambda, tolerance, prefix;
+    unsigned long k;
+
+    BOOST_MATH_STD_USING
+    using namespace boost::math::tools;
+
+    static const char* function = "boost::math::ellint_rc<%1%>(%1%,%1%)";
+
+    if(x < 0)
+    {
+       return policies::raise_domain_error<T>(function,
+            "Argument x must be non-negative but got %1%", x, pol);
+    }
+    if(y == 0)
+    {
+       return policies::raise_domain_error<T>(function,
+            "Argument y must not be zero but got %1%", y, pol);
+    }
+
+    // error scales as the 6th power of tolerance
+    tolerance = pow(4 * tools::epsilon<T>(), T(1) / 6);
+
+    // for y < 0, the integral is singular, return Cauchy principal value
+    if (y < 0)
+    {
+        prefix = sqrt(x / (x - y));
+        x = x - y;
+        y = -y;
+    }
+    else
+       prefix = 1;
+
+    // duplication:
+    k = 1;
+    do
+    {
+        u = (x + y + y) / 3;
+        S = y / u - 1;               // 1 - x / u = 2 * S
+
+        if (2 * abs(S) < tolerance) 
+           break;
+
+        T sx = sqrt(x);
+        T sy = sqrt(y);
+        lambda = 2 * sx * sy + y;
+        x = (x + lambda) / 4;
+        y = (y + 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
+    value = (1 + S * S * (T(3) / 10 + S * (T(1) / 7 + S * (T(3) / 8 + S * T(9) / 22)))) / sqrt(u);
+
+    return value * prefix;
+}
+
+} // namespace detail
+
+template <class T1, class T2, class Policy>
+inline typename tools::promote_args<T1, T2>::type 
+   ellint_rc(T1 x, T2 y, const Policy& pol)
+{
+   typedef typename tools::promote_args<T1, T2>::type result_type;
+   typedef typename policies::evaluation<result_type, Policy>::type value_type;
+   return policies::checked_narrowing_cast<result_type, Policy>(
+      detail::ellint_rc_imp(
+         static_cast<value_type>(x),
+         static_cast<value_type>(y), pol), "boost::math::ellint_rc<%1%>(%1%,%1%)");
+}
+
+template <class T1, class T2>
+inline typename tools::promote_args<T1, T2>::type 
+   ellint_rc(T1 x, T2 y)
+{
+   return ellint_rc(x, y, policies::policy<>());
+}
+
+}} // namespaces
+
+#endif // BOOST_MATH_ELLINT_RC_HPP
+