1 files changed, 468 insertions, 0 deletions
diff --git a/src/boost/libs/math/test/test_carlson.hpp b/src/boost/libs/math/test/test_carlson.hpp
new file mode 100644
index 00000000..48b68909
--- /dev/null
+++ b/src/boost/libs/math/test/test_carlson.hpp
@@ -0,0 +1,468 @@
+// Copyright John Maddock 2006.
+// Copyright Paul A. Bristow 2007, 2009
+//  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)
+
+#include <boost/math/concepts/real_concept.hpp>
+#define BOOST_TEST_MAIN
+#include <boost/test/unit_test.hpp>
+#include <boost/test/tools/floating_point_comparison.hpp>
+#include <boost/math/special_functions/math_fwd.hpp>
+#include <boost/math/constants/constants.hpp>
+#include <boost/array.hpp>
+#include <boost/random.hpp>
+#include "functor.hpp"
+
+#include "handle_test_result.hpp"
+#include "table_type.hpp"
+
+#ifndef SC_
+#define SC_(x) static_cast<typename table_type<T>::type>(BOOST_JOIN(x, L))
+#endif
+
+template <class Real, typename T>
+void do_test_ellint_rf(T& data, const char* type_name, const char* test)
+{
+#if !(defined(ERROR_REPORTING_MODE) && !defined(ELLINT_RF_FUNCTION_TO_TEST))
+   typedef Real                   value_type;
+
+   std::cout << "Testing: " << test << std::endl;
+
+#ifdef ELLINT_RF_FUNCTION_TO_TEST
+   value_type(*fp)(value_type, value_type, value_type) = ELLINT_RF_FUNCTION_TO_TEST;
+#elif defined(BOOST_MATH_NO_DEDUCED_FUNCTION_POINTERS)
+    value_type (*fp)(value_type, value_type, value_type) = boost::math::ellint_rf<value_type, value_type, value_type>;
+#else
+    value_type (*fp)(value_type, value_type, value_type) = boost::math::ellint_rf;
+#endif
+    boost::math::tools::test_result<value_type> result;
+ 
+    result = boost::math::tools::test_hetero<Real>(
+      data, 
+      bind_func<Real>(fp, 0, 1, 2),
+      extract_result<Real>(3));
+   handle_test_result(result, data[result.worst()], result.worst(), 
+      type_name, "ellint_rf", test);
+
+   std::cout << std::endl;
+#endif
+}
+
+template <class Real, typename T>
+void do_test_ellint_rc(T& data, const char* type_name, const char* test)
+{
+#if !(defined(ERROR_REPORTING_MODE) && !defined(ELLINT_RC_FUNCTION_TO_TEST))
+   typedef Real                   value_type;
+
+   std::cout << "Testing: " << test << std::endl;
+
+#ifdef ELLINT_RC_FUNCTION_TO_TEST
+   value_type(*fp)(value_type, value_type) = ELLINT_RC_FUNCTION_TO_TEST;
+#elif defined(BOOST_MATH_NO_DEDUCED_FUNCTION_POINTERS)
+    value_type (*fp)(value_type, value_type) = boost::math::ellint_rc<value_type, value_type>;
+#else
+    value_type (*fp)(value_type, value_type) = boost::math::ellint_rc;
+#endif
+    boost::math::tools::test_result<value_type> result;
+ 
+    result = boost::math::tools::test_hetero<Real>(
+      data, 
+      bind_func<Real>(fp, 0, 1),
+      extract_result<Real>(2));
+      handle_test_result(result, data[result.worst()], result.worst(), 
+      type_name, "ellint_rc", test);
+
+   std::cout << std::endl;
+#endif
+}
+
+template <class Real, typename T>
+void do_test_ellint_rj(T& data, const char* type_name, const char* test)
+{
+#if !(defined(ERROR_REPORTING_MODE) && !defined(ELLINT_RJ_FUNCTION_TO_TEST))
+   typedef Real                   value_type;
+
+   std::cout << "Testing: " << test << std::endl;
+
+#ifdef ELLINT_RJ_FUNCTION_TO_TEST
+   value_type(*fp)(value_type, value_type, value_type, value_type) = ELLINT_RJ_FUNCTION_TO_TEST;
+#elif defined(BOOST_MATH_NO_DEDUCED_FUNCTION_POINTERS)
+    value_type (*fp)(value_type, value_type, value_type, value_type) = boost::math::ellint_rj<value_type, value_type, value_type, value_type>;
+#else
+    value_type (*fp)(value_type, value_type, value_type, value_type) = boost::math::ellint_rj;
+#endif
+    boost::math::tools::test_result<value_type> result;
+ 
+    result = boost::math::tools::test_hetero<Real>(
+      data, 
+      bind_func<Real>(fp, 0, 1, 2, 3),
+      extract_result<Real>(4));
+      handle_test_result(result, data[result.worst()], result.worst(), 
+      type_name, "ellint_rj", test);
+
+   std::cout << std::endl;
+#endif
+}
+
+template <class Real, typename T>
+void do_test_ellint_rd(T& data, const char* type_name, const char* test)
+{
+#if !(defined(ERROR_REPORTING_MODE) && !defined(ELLINT_RD_FUNCTION_TO_TEST))
+   typedef Real                   value_type;
+
+   std::cout << "Testing: " << test << std::endl;
+
+#ifdef ELLINT_RD_FUNCTION_TO_TEST
+   value_type(*fp)(value_type, value_type, value_type) = ELLINT_RD_FUNCTION_TO_TEST;
+#elif defined(BOOST_MATH_NO_DEDUCED_FUNCTION_POINTERS)
+    value_type (*fp)(value_type, value_type, value_type) = boost::math::ellint_rd<value_type, value_type, value_type>;
+#else
+    value_type (*fp)(value_type, value_type, value_type) = boost::math::ellint_rd;
+#endif
+    boost::math::tools::test_result<value_type> result;
+ 
+    result = boost::math::tools::test_hetero<Real>(
+      data, 
+      bind_func<Real>(fp, 0, 1, 2),
+      extract_result<Real>(3));
+    handle_test_result(result, data[result.worst()], result.worst(), 
+      type_name, "ellint_rd", test);
+
+   std::cout << std::endl;
+#endif
+}
+
+template <class Real, typename T>
+void do_test_ellint_rg(T& data, const char* type_name, const char* test)
+{
+#if !(defined(ERROR_REPORTING_MODE) && !defined(ELLINT_RD_FUNCTION_TO_TEST))
+   typedef Real                   value_type;
+
+   std::cout << "Testing: " << test << std::endl;
+
+#ifdef ELLINT_RG_FUNCTION_TO_TEST
+   value_type(*fp)(value_type, value_type, value_type) = ELLINT_RG_FUNCTION_TO_TEST;
+#elif defined(BOOST_MATH_NO_DEDUCED_FUNCTION_POINTERS)
+   value_type(*fp)(value_type, value_type, value_type) = boost::math::ellint_rg<value_type, value_type, value_type>;
+#else
+   value_type(*fp)(value_type, value_type, value_type) = boost::math::ellint_rg;
+#endif
+   boost::math::tools::test_result<value_type> result;
+
+   result = boost::math::tools::test_hetero<Real>(
+      data,
+      bind_func<Real>(fp, 0, 1, 2),
+      extract_result<Real>(3));
+   handle_test_result(result, data[result.worst()], result.worst(),
+      type_name, "ellint_rg", test);
+
+   std::cout << std::endl;
+#endif
+}
+
+#if !defined(TEST1) && !defined(TEST2) && !defined(TEST3) && !defined(TEST4)
+#define TEST1
+#define TEST2
+#define TEST3
+#define TEST4
+#endif
+
+#ifdef TEST1
+
+template <typename T>
+void t1(T, const char* type_name)
+{
+#include "ellint_rf_data.ipp"
+
+   do_test_ellint_rf<T>(ellint_rf_data, type_name, "RF: Random data");
+}
+
+template <typename T>
+void t2(T, const char* type_name)
+{
+#include "ellint_rf_xxx.ipp"
+
+   do_test_ellint_rf<T>(ellint_rf_xxx, type_name, "RF: x = y = z");
+}
+
+template <typename T>
+void t3(T, const char* type_name)
+{
+#include "ellint_rf_xyy.ipp"
+
+   do_test_ellint_rf<T>(ellint_rf_xyy, type_name, "RF: x = y or y = z or x = z");
+}
+
+template <typename T>
+void t4(T, const char* type_name)
+{
+#include "ellint_rf_0yy.ipp"
+
+   do_test_ellint_rf<T>(ellint_rf_0yy, type_name, "RF: x = 0, y = z");
+}
+
+template <typename T>
+void t5(T, const char* type_name)
+{
+#include "ellint_rf_xy0.ipp"
+
+   do_test_ellint_rf<T>(ellint_rf_xy0, type_name, "RF: z = 0");
+}
+
+#endif
+#ifdef TEST2
+
+template <typename T>
+void t6(T, const char* type_name)
+{
+#include "ellint_rc_data.ipp"
+
+   do_test_ellint_rc<T>(ellint_rc_data, type_name, "RC: Random data");
+}
+
+template <typename T>
+void t7(T, const char* type_name)
+{
+#include "ellint_rj_data.ipp"
+
+   do_test_ellint_rj<T>(ellint_rj_data, type_name, "RJ: Random data");
+}
+
+template <typename T>
+void t8(T, const char* type_name)
+{
+#include "ellint_rj_e4.ipp"
+
+   do_test_ellint_rj<T>(ellint_rj_e4, type_name, "RJ: 4 Equal Values");
+}
+
+template <typename T>
+void t9(T, const char* type_name)
+{
+#include "ellint_rj_e3.ipp"
+
+   do_test_ellint_rj<T>(ellint_rj_e3, type_name, "RJ: 3 Equal Values");
+}
+
+template <typename T>
+void t10(T, const char* type_name)
+{
+#include "ellint_rj_e2.ipp"
+
+   do_test_ellint_rj<T>(ellint_rj_e2, type_name, "RJ: 2 Equal Values");
+}
+
+template <typename T>
+void t11(T, const char* type_name)
+{
+#include "ellint_rj_zp.ipp"
+
+   do_test_ellint_rj<T>(ellint_rj_zp, type_name, "RJ: Equal z and p");
+}
+
+#endif
+#ifdef TEST3
+
+template <typename T>
+void t12(T, const char* type_name)
+{
+#include "ellint_rd_data.ipp"
+
+   do_test_ellint_rd<T>(ellint_rd_data, type_name, "RD: Random data");
+}
+
+template <typename T>
+void t13(T, const char* type_name)
+{
+#include "ellint_rd_xyy.ipp"
+
+   do_test_ellint_rd<T>(ellint_rd_xyy, type_name, "RD: y = z");
+}
+
+template <typename T>
+void t14(T, const char* type_name)
+{
+#include "ellint_rd_xxz.ipp"
+
+   do_test_ellint_rd<T>(ellint_rd_xxz, type_name, "RD: x = y");
+}
+
+template <typename T>
+void t15(T, const char* type_name)
+{
+#include "ellint_rd_0yy.ipp"
+
+   do_test_ellint_rd<T>(ellint_rd_0yy, type_name, "RD: x = 0, y = z");
+}
+
+template <typename T>
+void t16(T, const char* type_name)
+{
+#include "ellint_rd_xxx.ipp"
+
+   do_test_ellint_rd<T>(ellint_rd_xxx, type_name, "RD: x = y = z");
+}
+
+template <typename T>
+void t17(T, const char* type_name)
+{
+#include "ellint_rd_0xy.ipp"
+
+   do_test_ellint_rd<T>(ellint_rd_0xy, type_name, "RD: x = 0");
+}
+
+#endif
+#ifdef TEST4
+
+template <typename T>
+void t18(T, const char* type_name)
+{
+#include "ellint_rg.ipp"
+
+   do_test_ellint_rg<T>(ellint_rg, type_name, "RG: Random Data");
+}
+
+template <typename T>
+void t19(T, const char* type_name)
+{
+#include "ellint_rg_00x.ipp"
+
+   do_test_ellint_rg<T>(ellint_rg_00x, type_name, "RG: two values 0");
+}
+
+template <typename T>
+void t20(T, const char* type_name)
+{
+#include "ellint_rg_xxx.ipp"
+
+   do_test_ellint_rg<T>(ellint_rg_xxx, type_name, "RG: All values the same or zero");
+}
+
+template <typename T>
+void t21(T, const char* type_name)
+{
+#include "ellint_rg_xyy.ipp"
+
+   do_test_ellint_rg<T>(ellint_rg_xyy, type_name, "RG: two values the same");
+}
+
+template <typename T>
+void t22(T, const char* type_name)
+{
+#include "ellint_rg_xy0.ipp"
+
+   do_test_ellint_rg<T>(ellint_rg_xy0, type_name, "RG: one value zero");
+}
+
+#endif
+
+template <typename T>
+void test_spots(T val, const char* type_name)
+{
+#ifndef TEST_UDT
+   using namespace boost::math;
+   using namespace std;
+   // Spot values from Numerical Computation of Real or Complex 
+   // Elliptic Integrals, B. C. Carlson: http://arxiv.org/abs/math.CA/9409227
+   // RF:
+   T tolerance = (std::max)(T(1e-13f), tools::epsilon<T>() * 5) * 100; // Note 5eps expressed as a persentage!!!
+   T eps2 = 5 * tools::epsilon<T>();
+   BOOST_CHECK_CLOSE(ellint_rf(T(1), T(2), T(0)), T(1.3110287771461), tolerance);
+   BOOST_CHECK_CLOSE(ellint_rf(T(0.5), T(1), T(0)), T(1.8540746773014), tolerance);
+   BOOST_CHECK_CLOSE(ellint_rf(T(2), T(3), T(4)), T(0.58408284167715), tolerance);
+   // RC:
+   BOOST_CHECK_CLOSE_FRACTION(ellint_rc(T(0), T(1)/4), boost::math::constants::pi<T>(), eps2);
+   BOOST_CHECK_CLOSE_FRACTION(ellint_rc(T(9)/4, T(2)), boost::math::constants::ln_two<T>(), eps2);
+   BOOST_CHECK_CLOSE_FRACTION(ellint_rc(T(1) / 4, T(-2)), boost::math::constants::ln_two<T>() / 3, eps2);
+   // RJ:
+   BOOST_CHECK_CLOSE(ellint_rj(T(0), T(1), T(2), T(3)), T(0.77688623778582), tolerance);
+   BOOST_CHECK_CLOSE(ellint_rj(T(2), T(3), T(4), T(5)), T(0.14297579667157), tolerance);
+   BOOST_CHECK_CLOSE(ellint_rj(T(2), T(3), T(4), T(-0.5)), T(0.24723819703052), tolerance);
+   BOOST_CHECK_CLOSE(ellint_rj(T(2), T(3), T(4), T(-5)), T(-0.12711230042964), tolerance);
+   // RD:
+   BOOST_CHECK_CLOSE(ellint_rd(T(0), T(2), T(1)), T(1.7972103521034), tolerance);
+   BOOST_CHECK_CLOSE(ellint_rd(T(2), T(3), T(4)), T(0.16510527294261), tolerance);
+
+   // Sanity/consistency checks from Numerical Computation of Real or Complex 
+   // Elliptic Integrals, B. C. Carlson: http://arxiv.org/abs/math.CA/9409227
+   boost::mt19937 ran;
+   boost::uniform_real<float> ur(0, 1000);
+   T eps40 = 40 * tools::epsilon<T>();
+
+   for(unsigned i = 0; i < 1000; ++i)
+   {
+      T x = ur(ran);
+      T y = ur(ran);
+      T z = ur(ran);
+      T lambda = ur(ran);
+      T mu = x * y / lambda;
+      // RF, eq 49:
+      T s1 = ellint_rf(x+lambda, y+lambda, lambda) + 
+         ellint_rf(x + mu, y + mu, mu);
+      T s2 = ellint_rf(x, y, T(0));
+      BOOST_CHECK_CLOSE_FRACTION(s1, s2, eps40);
+      // RC is degenerate case of RF:
+      s1 = ellint_rc(x, y);
+      s2 = ellint_rf(x, y, y);
+      BOOST_CHECK_CLOSE_FRACTION(s1, s2, eps40);
+      // RC, eq 50 (Note have to assume y = x):
+      T mu2 = x * x / lambda;
+      s1 = ellint_rc(lambda, x+lambda) 
+         + ellint_rc(mu2, x + mu2);
+      s2 = ellint_rc(T(0), x);
+      BOOST_CHECK_CLOSE_FRACTION(s1, s2, eps40);
+      /*
+      T p = ????; // no closed form for a, b and p???
+      s1 = ellint_rj(x+lambda, y+lambda, lambda, p+lambda)
+         + ellint_rj(x+mu, y+mu, mu, p+mu);
+      s2 = ellint_rj(x, y, T(0), p)
+         - 3 * ellint_rc(a, b);
+      */
+      // RD, eq 53:
+      s1 = ellint_rd(lambda, x+lambda, y+lambda)
+         + ellint_rd(mu, x+mu, y+mu);
+      s2 = ellint_rd(T(0), x, y)
+         - 3 / (y * sqrt(x+y+lambda+mu));
+      BOOST_CHECK_CLOSE_FRACTION(s1, s2, eps40);
+      // RD is degenerate case of RJ:
+      s1 = ellint_rd(x, y, z);
+      s2 = ellint_rj(x, y, z, z);
+      BOOST_CHECK_CLOSE_FRACTION(s1, s2, eps40);
+   }
+#endif
+   //
+   // Now random spot values:
+   //
+#ifdef TEST1
+   t1(val, type_name);
+   t2(val, type_name);
+   t3(val, type_name);
+   t4(val, type_name);
+   t5(val, type_name);
+#endif
+#ifdef TEST2
+   t6(val, type_name);
+   t7(val, type_name);
+   t8(val, type_name);
+   t9(val, type_name);
+   t10(val, type_name);
+   t11(val, type_name);
+#endif
+#ifdef TEST3
+   t12(val, type_name);
+   t13(val, type_name);
+   t14(val, type_name);
+   t15(val, type_name);
+   t16(val, type_name);
+   t17(val, type_name);
+#endif
+#ifdef TEST4
+   t18(val, type_name);
+   t19(val, type_name);
+   t20(val, type_name);
+   t21(val, type_name);
+   t22(val, type_name);
+#endif
+}
+