//  (C) Copyright John Maddock 2006.
//  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_legendre.hpp"

//
// DESCRIPTION:
// ~~~~~~~~~~~~
//
// This file tests the legendre polynomials.
// There are two sets of tests, spot
// tests which compare our results with selected values computed
// using the online special function calculator at
// functions.wolfram.com, while 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
   //
   // Linux:
   //
   if((std::numeric_limits<long double>::digits <= 64)
      && (std::numeric_limits<long double>::digits != std::numeric_limits<double>::digits))
   {
#ifndef BOOST_MATH_NO_LONG_DOUBLE_MATH_FUNCTIONS
      add_expected_result(
         ".*",                          // compiler
         ".*",                          // stdlib
         ".*",                          // platform
         "double",                      // test type(s)
         ".*",                          // test data group
         ".*", 10, 5);                  // test function
#endif
   }
   if(std::numeric_limits<long double>::digits == 64)
   {
      add_expected_result(
         ".*",                          // compiler
         ".*",                          // stdlib
         ".*",                          // platform
         largest_type,                  // test type(s)
         "Legendre Polynomials.*Large.*",      // test data group
         "legendre_p", 1000, 200);  // test function
      add_expected_result(
         "Intel.*",                          // compiler
         ".*",                          // stdlib
         ".*",                          // platform
         largest_type,                  // test type(s)
         "Legendre Polynomials.*Large.*",      // test data group
         "legendre_q", 10000, 1000);  // test function
      add_expected_result(
         ".*",                          // compiler
         ".*",                          // stdlib
         ".*",                          // platform
         largest_type,                  // test type(s)
         "Legendre Polynomials.*Large.*",      // test data group
         "legendre_q", 7000, 1000);  // test function
      add_expected_result(
         ".*",                          // compiler
         ".*",                          // stdlib
         ".*",                          // platform
         "real_concept",                  // test type(s)
         "Legendre Polynomials.*Large.*",      // test data group
         "legendre_p", 1000, 200);  // test function
      add_expected_result(
         ".*",                          // compiler
         ".*",                          // stdlib
         ".*",                          // platform
         "real_concept",                  // test type(s)
         "Legendre Polynomials.*Large.*",      // test data group
         "legendre_q", 7000, 1000);  // test function
   }
   //
   // Catch all cases come last:
   //
   add_expected_result(
      ".*",                          // compiler
      ".*",                          // stdlib
      ".*",                          // platform
      largest_type,                  // test type(s)
      "Legendre Polynomials.*Large.*",      // test data group
      "legendre_p", 500, 200);  // test function
   add_expected_result(
      ".*",                          // compiler
      ".*",                          // stdlib
      ".*",                          // platform
      largest_type,                  // test type(s)
      "Legendre Polynomials.*Large.*",      // test data group
      "legendre_q", 5400, 500);  // test function
   add_expected_result(
      ".*",                          // compiler
      ".*",                          // stdlib
      ".*",                          // platform
      largest_type,                  // test type(s)
      "Legendre Polynomials.*",      // test data group
      "legendre_p", 300, 80);  // test function
   add_expected_result(
      ".*",                          // compiler
      ".*",                          // stdlib
      ".*",                          // platform
      largest_type,                  // test type(s)
      "Legendre Polynomials.*",      // test data group
      "legendre_q", 100, 50);  // test function
   add_expected_result(
      "Intel.*",                          // compiler
      ".*",                          // stdlib
      ".*",                          // platform
      largest_type,                  // test type(s)
      "Associated Legendre Polynomials.*",      // test data group
      ".*", 300, 20);  // test function
   add_expected_result(
      ".*",                          // compiler
      ".*",                          // stdlib
      ".*",                          // platform
      largest_type,                  // test type(s)
      "Associated Legendre Polynomials.*",      // test data group
      ".*", 200, 20);  // test function

   add_expected_result(
      ".*",                          // compiler
      ".*",                          // stdlib
      ".*",                          // platform
      "real_concept",                  // test type(s)
      "Legendre Polynomials.*Large.*",      // test data group
      "legendre_p", 500, 200);  // test function
   add_expected_result(
      ".*",                          // compiler
      ".*",                          // stdlib
      ".*",                          // platform
      "real_concept",                  // test type(s)
      "Legendre Polynomials.*Large.*",      // test data group
      "legendre_q", 5400, 500);  // test function
   add_expected_result(
      ".*",                          // compiler
      ".*",                          // stdlib
      ".*",                          // platform
      "real_concept",                  // test type(s)
      "Legendre Polynomials.*",      // test data group
      "legendre_p", 300, 80);  // test function
   add_expected_result(
      ".*",                          // compiler
      ".*",                          // stdlib
      ".*",                          // platform
      "real_concept",                  // test type(s)
      "Legendre Polynomials.*",      // test data group
      "legendre_q", 100, 50);  // test function
   add_expected_result(
      ".*",                          // compiler
      ".*",                          // stdlib
      ".*",                          // platform
      "real_concept",                  // test type(s)
      "Associated Legendre Polynomials.*",      // test data group
      ".*", 200, 20);  // 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;
}


BOOST_AUTO_TEST_CASE( test_main )
{
   BOOST_MATH_CONTROL_FP;
   test_spots(0.0F, "float");
   test_spots(0.0, "double");
#ifndef BOOST_MATH_NO_LONG_DOUBLE_MATH_FUNCTIONS
   test_spots(0.0L, "long double");
   test_spots(boost::math::concepts::real_concept(0.1), "real_concept");
#endif

   expected_results();

   test_legendre_p(0.1F, "float");
   test_legendre_p(0.1, "double");
#ifndef BOOST_MATH_NO_LONG_DOUBLE_MATH_FUNCTIONS
   test_legendre_p(0.1L, "long double");
#ifndef BOOST_MATH_NO_REAL_CONCEPT_TESTS
   test_legendre_p(boost::math::concepts::real_concept(0.1), "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::endl;
#endif

   test_legendre_p_prime<float>();
   test_legendre_p_prime<double>();
   test_legendre_p_prime<long double>();

   int ulp_distance = test_legendre_p_zeros_double_ulp(1, 100);
   BOOST_CHECK(ulp_distance <= 2);
   test_legendre_p_zeros<float>();
   test_legendre_p_zeros<double>();
   test_legendre_p_zeros<long double>();
}