text: //  Copyright 2006 John Maddock
  // Copyright Paul A. Bristow 2007.
  
  //  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 <pch_light.hpp>
  #include "test_carlson.hpp"
  
  //
  // DESCRIPTION:
  // ~~~~~~~~~~~~
  //
  // This file tests the Carlson Elliptic Integrals.  
  // There are two sets of tests, spot
  // tests which compare our results with the published test values, 
  // in Numerical Computation of Real or Complex Elliptic Integrals,
  // B. C. Carlson: http://arxiv.org/abs/math.CA/9409227
  // However, the bulk of the accuracy tests
  // use values generated with NTL::RR at 1000-bit precision
  // and our generic versions of these functions.
  //
  // Note that when this file is first run on a new platform many of
  // these tests will fail: the default accuracy is 1 epsilon which
  // is too tight for most platforms.  In this situation you will 
  // need to cast a human eye over the error rates reported and make
  // a judgement as to whether they are acceptable.  Either way please
  // report the results to the Boost mailing list.  Acceptable rates of
  // error are marked up below as a series of regular expressions that
  // identify the compiler/stdlib/platform/data-type/test-data/test-function
  // along with the maximum expected peek and RMS mean errors for that
  // test.
  //
  
  void expected_results()
  {
     //
     // Define the max and mean errors expected for
     // various compilers and platforms.
     //
     const char* largest_type;
  #ifndef BOOST_MATH_NO_LONG_DOUBLE_MATH_FUNCTIONS
     if(boost::math::policies::digits<double, boost::math::policies::policy<> >() == boost::math::policies::digits<long double, boost::math::policies::policy<> >())
     {
        largest_type = "(long\\s+)?double";
     }
     else
     {
        largest_type = "long double";
     }
  #else
     largest_type = "(long\\s+)?double";
  #endif
     //
     // real long doubles:
     //
     if(boost::math::policies::digits<long double, boost::math::policies::policy<> >() > 53)
     {
        add_expected_result(
           ".*",                          // compiler
           ".*",                          // stdlib
           BOOST_PLATFORM,                          // platform
           largest_type,                  // test type(s)
           ".*RJ.*",      // test data group
           ".*", 1000, 50);  // test function
        add_expected_result(
           ".*",                          // compiler
           ".*",                          // stdlib
           BOOST_PLATFORM,                          // platform
           "real_concept",                  // test type(s)
           ".*RJ.*",      // test data group
           ".*", 1000, 50);  // test function
     }
     //
     // Catch all cases come last:
     //
     add_expected_result(
        ".*",                          // compiler
        ".*",                          // stdlib
        ".*",                          // platform
        largest_type,                  // test type(s)
        ".*RJ.*",      // test data group
        ".*", 180, 50);  // test function
     add_expected_result(
        ".*",                          // compiler
        ".*",                          // stdlib
        ".*",                          // platform
        "real_concept",                  // test type(s)
        ".*RJ.*",      // test data group
        ".*", 180, 50);  // test function
     add_expected_result(
        ".*",                          // compiler
        ".*",                          // stdlib
        ".*",                          // platform
        largest_type,                  // test type(s)
        ".*",      // test data group
        ".*", 15, 8);  // test function
     add_expected_result(
        ".*",                          // compiler
        ".*",                          // stdlib
        ".*",                          // platform
        "real_concept",                  // test type(s)
        ".*",      // test data group
        ".*", 15, 8);  // test function
     //
     // Finish off by printing out the compiler/stdlib/platform names,
     // we do this to make it easier to mark up expected error rates.
     //
     std::cout << "Tests run with " << BOOST_COMPILER << ", " 
        << BOOST_STDLIB << ", " << BOOST_PLATFORM << std::endl;
  }
  
  
  int test_main(int, char* [])
  {
      expected_results();
      BOOST_MATH_CONTROL_FP;
  
      boost::math::ellint_rj(1.778e-31, 1.407e+18, 10.05, -4.83e-10);
  
      test_spots(0.0F, "float");
      test_spots(0.0, "double");
  #ifndef BOOST_MATH_NO_LONG_DOUBLE_MATH_FUNCTIONS
      test_spots(0.0L, "long double");
  #ifndef BOOST_MATH_NO_REAL_CONCEPT_TESTS
      test_spots(boost::math::concepts::real_concept(0), "real_concept");
  #endif
  #else
     std::cout << "<note>The long double tests have been disabled on this platform "
        "either because the long double overloads of the usual math functions are "
        "not available at all, or because they are too inaccurate for these tests "
        "to pass.</note>" << std::cout;
  #endif
  
      return 0;
  }
  
  /*
  
  test_carlson.cpp
  Linking...
  Embedding manifest...
  Autorun "i:\boost-06-05-03-1300\libs\math\test\Math_test\debug\test_carlson.exe"
  Running 1 test case...
  Tests run with Microsoft Visual C++ version 8.0, Dinkumware standard library version 405, Win32
  Testing: RF: Random data
  boost::math::ellint_rf<float> Max = 0 RMS Mean=0
  Testing: RC: Random data
  boost::math::ellint_rc<float> Max = 0 RMS Mean=0
  Testing: RJ: Random data
  boost::math::ellint_rf<float> Max = 0 RMS Mean=0
  Testing: RD: Random data
  boost::math::ellint_rd<float> Max = 0 RMS Mean=0
  Testing: RF: Random data
  boost::math::ellint_rf<double> Max = 2.949 RMS Mean=0.7498
      worst case at row: 377
      { 3.418e+025, 2.594e-005, 3.264e-012, 6.169e-012 }
  Testing: RC: Random data
  boost::math::ellint_rc<double> Max = 2.396 RMS Mean=0.6283
      worst case at row: 10
      { 1.97e-029, 3.224e-025, 2.753e+012 }
  Testing: RJ: Random data
  boost::math::ellint_rf<double> Max = 152.9 RMS Mean=11.15
      worst case at row: 633
      { 1.876e+016, 0.000278, 3.796e-006, -4.412e-005, -1.656e-005 }
  Testing: RD: Random data
  boost::math::ellint_rd<double> Max = 2.586 RMS Mean=0.8614
      worst case at row: 45
      { 2.111e-020, 8.757e-026, 1.923e-023, 1.004e+033 }
  Testing: RF: Random data
  boost::math::ellint_rf<long double> Max = 2.949 RMS Mean=0.7498
      worst case at row: 377
      { 3.418e+025, 2.594e-005, 3.264e-012, 6.169e-012 }
  Testing: RC: Random data
  boost::math::ellint_rc<long double> Max = 2.396 RMS Mean=0.6283
      worst case at row: 10
      { 1.97e-029, 3.224e-025, 2.753e+012 }
  Testing: RJ: Random data
  boost::math::ellint_rf<long double> Max = 152.9 RMS Mean=11.15
      worst case at row: 633
      { 1.876e+016, 0.000278, 3.796e-006, -4.412e-005, -1.656e-005 }
  Testing: RD: Random data
  boost::math::ellint_rd<long double> Max = 2.586 RMS Mean=0.8614
      worst case at row: 45
      { 2.111e-020, 8.757e-026, 1.923e-023, 1.004e+033 }
  Testing: RF: Random data
  boost::math::ellint_rf<real_concept> Max = 2.949 RMS Mean=0.7498
      worst case at row: 377
      { 3.418e+025, 2.594e-005, 3.264e-012, 6.169e-012 }
  Testing: RC: Random data
  boost::math::ellint_rc<real_concept> Max = 2.396 RMS Mean=0.6283
      worst case at row: 10
      { 1.97e-029, 3.224e-025, 2.753e+012 }
  Testing: RJ: Random data
  boost::math::ellint_rf<real_concept> Max = 152.9 RMS Mean=11.15
      worst case at row: 633
      { 1.876e+016, 0.000278, 3.796e-006, -4.412e-005, -1.656e-005 }
  Testing: RD: Random data
  boost::math::ellint_rd<real_concept> Max = 2.586 RMS Mean=0.8614
      worst case at row: 45
      { 2.111e-020, 8.757e-026, 1.923e-023, 1.004e+033 }
  *** No errors detected
  
  */
  