--- /dev/null
+// Copyright (c) 2006 Xiaogang Zhang
+// Copyright (c) 2006 John Maddock
+// 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 ensure
+// that the code continues to work no matter how many digits
+// type T has.
+
+#ifndef BOOST_MATH_ELLINT_1_HPP
+#define BOOST_MATH_ELLINT_1_HPP
+
+#ifdef _MSC_VER
+#pragma once
+#endif
+
+#include <boost/math/special_functions/ellint_rf.hpp>
+#include <boost/math/constants/constants.hpp>
+#include <boost/math/policies/error_handling.hpp>
+#include <boost/math/tools/workaround.hpp>
+#include <boost/math/special_functions/round.hpp>
+
+// Elliptic integrals (complete and incomplete) of the first kind
+// Carlson, Numerische Mathematik, vol 33, 1 (1979)
+
+namespace boost { namespace math {
+
+template <class T1, class T2, class Policy>
+typename tools::promote_args<T1, T2>::type ellint_1(T1 k, T2 phi, const Policy& pol);
+
+namespace detail{
+
+template <typename T, typename Policy>
+T ellint_k_imp(T k, const Policy& pol);
+
+// Elliptic integral (Legendre form) of the first kind
+template <typename T, typename Policy>
+T ellint_f_imp(T phi, T k, const Policy& pol)
+{
+ BOOST_MATH_STD_USING
+ using namespace boost::math::tools;
+ using namespace boost::math::constants;
+
+ static const char* function = "boost::math::ellint_f<%1%>(%1%,%1%)";
+ BOOST_MATH_INSTRUMENT_VARIABLE(phi);
+ BOOST_MATH_INSTRUMENT_VARIABLE(k);
+ BOOST_MATH_INSTRUMENT_VARIABLE(function);
+
+ if (abs(k) > 1)
+ {
+ return policies::raise_domain_error<T>(function,
+ "Got k = %1%, function requires |k| <= 1", k, pol);
+ }
+
+ bool invert = false;
+ if(phi < 0)
+ {
+ BOOST_MATH_INSTRUMENT_VARIABLE(phi);
+ phi = fabs(phi);
+ invert = true;
+ }
+
+ T result;
+
+ if(phi >= tools::max_value<T>())
+ {
+ // Need to handle infinity as a special case:
+ result = policies::raise_overflow_error<T>(function, 0, pol);
+ BOOST_MATH_INSTRUMENT_VARIABLE(result);
+ }
+ else if(phi > 1 / tools::epsilon<T>())
+ {
+ // Phi is so large that phi%pi is necessarily zero (or garbage),
+ // just return the second part of the duplication formula:
+ result = 2 * phi * ellint_k_imp(k, pol) / constants::pi<T>();
+ BOOST_MATH_INSTRUMENT_VARIABLE(result);
+ }
+ else
+ {
+ // Carlson's algorithm works only for |phi| <= pi/2,
+ // use the integrand's periodicity to normalize phi
+ //
+ // Xiaogang's original code used a cast to long long here
+ // but that fails if T has more digits than a long long,
+ // so rewritten to use fmod instead:
+ //
+ BOOST_MATH_INSTRUMENT_CODE("pi/2 = " << constants::pi<T>() / 2);
+ T rphi = boost::math::tools::fmod_workaround(phi, T(constants::half_pi<T>()));
+ BOOST_MATH_INSTRUMENT_VARIABLE(rphi);
+ T m = boost::math::round((phi - rphi) / constants::half_pi<T>());
+ BOOST_MATH_INSTRUMENT_VARIABLE(m);
+ int s = 1;
+ if(boost::math::tools::fmod_workaround(m, T(2)) > 0.5)
+ {
+ m += 1;
+ s = -1;
+ rphi = constants::half_pi<T>() - rphi;
+ BOOST_MATH_INSTRUMENT_VARIABLE(rphi);
+ }
+ T sinp = sin(rphi);
+ T cosp = cos(rphi);
+ BOOST_MATH_INSTRUMENT_VARIABLE(sinp);
+ BOOST_MATH_INSTRUMENT_VARIABLE(cosp);
+ result = s * sinp * ellint_rf_imp(T(cosp * cosp), T(1 - k * k * sinp * sinp), T(1), pol);
+ BOOST_MATH_INSTRUMENT_VARIABLE(result);
+ if(m != 0)
+ {
+ result += m * ellint_k_imp(k, pol);
+ BOOST_MATH_INSTRUMENT_VARIABLE(result);
+ }
+ }
+ return invert ? T(-result) : result;
+}
+
+// Complete elliptic integral (Legendre form) of the first kind
+template <typename T, typename Policy>
+T ellint_k_imp(T k, const Policy& pol)
+{
+ BOOST_MATH_STD_USING
+ using namespace boost::math::tools;
+
+ static const char* function = "boost::math::ellint_k<%1%>(%1%)";
+
+ if (abs(k) > 1)
+ {
+ return policies::raise_domain_error<T>(function,
+ "Got k = %1%, function requires |k| <= 1", k, pol);
+ }
+ if (abs(k) == 1)
+ {
+ return policies::raise_overflow_error<T>(function, 0, pol);
+ }
+
+ T x = 0;
+ T y = 1 - k * k;
+ T z = 1;
+ T value = ellint_rf_imp(x, y, z, pol);
+
+ return value;
+}
+
+template <typename T, typename Policy>
+inline typename tools::promote_args<T>::type ellint_1(T k, const Policy& pol, const mpl::true_&)
+{
+ typedef typename tools::promote_args<T>::type result_type;
+ typedef typename policies::evaluation<result_type, Policy>::type value_type;
+ return policies::checked_narrowing_cast<result_type, Policy>(detail::ellint_k_imp(static_cast<value_type>(k), pol), "boost::math::ellint_1<%1%>(%1%)");
+}
+
+template <class T1, class T2>
+inline typename tools::promote_args<T1, T2>::type ellint_1(T1 k, T2 phi, const mpl::false_&)
+{
+ return boost::math::ellint_1(k, phi, policies::policy<>());
+}
+
+}
+
+// Complete elliptic integral (Legendre form) of the first kind
+template <typename T>
+inline typename tools::promote_args<T>::type ellint_1(T k)
+{
+ return ellint_1(k, policies::policy<>());
+}
+
+// Elliptic integral (Legendre form) of the first kind
+template <class T1, class T2, class Policy>
+inline typename tools::promote_args<T1, T2>::type ellint_1(T1 k, T2 phi, 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_f_imp(static_cast<value_type>(phi), static_cast<value_type>(k), pol), "boost::math::ellint_1<%1%>(%1%,%1%)");
+}
+
+template <class T1, class T2>
+inline typename tools::promote_args<T1, T2>::type ellint_1(T1 k, T2 phi)
+{
+ typedef typename policies::is_policy<T2>::type tag_type;
+ return detail::ellint_1(k, phi, tag_type());
+}
+
+}} // namespaces
+
+#endif // BOOST_MATH_ELLINT_1_HPP
+
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