text: //  (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_gamma.hpp"
  
  //
  // DESCRIPTION:
  // ~~~~~~~~~~~~
  //
  // This file tests the functions tgamma and lgamma, and the 
  // function tgamma1pm1.  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
     //
     // G++ on Darwin: results are just slightly worse than we might hope for
     // but still pretty good:
     //
     add_expected_result(
        ".*",                          // compiler
        ".*",                          // stdlib
        "Mac OS",                      // platform
        largest_type,                  // test type(s)
        "factorials",                  // test data group
        "boost::math::tgamma", 100, 15); // test function
  
     //
     // G++ on Linux, result vary a bit by processor type,
     // on Itanium results are *much* better than listed here,
     // but x86 appears to have much less accurate std::pow
     // that throws off the results:
     //
     add_expected_result(
        ".*",                          // compiler
        ".*",                          // stdlib
        "linux",                       // platform
        largest_type,                  // test type(s)
        "factorials",                  // test data group
        "boost::math::tgamma", 400, 200); // test function
     add_expected_result(
        ".*",                          // compiler
        ".*",                          // stdlib
        "linux",                          // platform
        largest_type,                  // test type(s)
        "factorials",                  // test data group
        "boost::math::lgamma", 30, 10);  // test function
     add_expected_result(
        ".*",                          // compiler
        ".*",                          // stdlib
        "linux",                       // platform
        largest_type,                  // test type(s)
        "near (1|2|-10)",              // test data group
        "boost::math::tgamma", 10, 5);  // test function
     add_expected_result(
        ".*",                          // compiler
        ".*",                          // stdlib
        "linux",                       // platform
        largest_type,                  // test type(s)
        "near (1|2|-10)",              // test data group
        "boost::math::lgamma", 50, 50);  // test function
     add_expected_result(
        ".*",                          // compiler
        ".*",                          // stdlib
        "linux",                       // platform
        largest_type,                  // test type(s)
        "tgamma1pm1.*",                // test data group
        "boost::math::tgamma1pm1", 50, 15);  // test function
     add_expected_result(
        ".*",                          // compiler
        ".*",                          // stdlib
        "linux",                       // platform
        "real_concept",                // test type(s)
        "factorials",                  // test data group
        "boost::math::tgamma", 220, 70);  // test function
     add_expected_result(
        ".*",                          // compiler
        ".*",                          // stdlib
        "linux",                       // platform
        "real_concept",                // test type(s)
        "near (0|-55)",                // test data group
        "boost::math::(t|l)gamma", 130, 80);  // test function
     add_expected_result(
        ".*",                          // compiler
        ".*",                          // stdlib
        "linux",                       // platform
        "real_concept",                // test type(s)
        "tgamma1pm1.*",                // test data group
        "boost::math::tgamma1pm1", 40, 10);  // test function
     //
     // HP-UX results:
     //
     add_expected_result(
        ".*",                          // compiler
        ".*",                          // stdlib
        "HP-UX",                          // platform
        largest_type,                  // test type(s)
        "factorials",                  // test data group
        "boost::math::tgamma", 5, 4);  // test function
     add_expected_result(
        ".*",                          // compiler
        ".*",                          // stdlib
        "HP-UX",                       // platform
        largest_type,                  // test type(s)
        "near (0|-55)",                // test data group
        "boost::math::tgamma", 10, 5);  // test function
     add_expected_result(
        ".*",                          // compiler
        ".*",                          // stdlib
        "HP-UX",                       // platform
        largest_type,                  // test type(s)
        "near (1|2|-10)",              // test data group
        "boost::math::lgamma", 250, 200);  // test function
     add_expected_result(
        ".*",                          // compiler
        ".*",                          // stdlib
        "HP-UX",                          // platform
        "real_concept",                // test type(s)
        "factorials",                  // test data group
        "boost::math::lgamma", 50, 20);  // test function
     add_expected_result(
        ".*",                          // compiler
        ".*",                          // stdlib
        "HP-UX",                          // platform
        "real_concept",                // test type(s)
        "tgamma1pm1.*",                // test data group
        "boost::math::tgamma1pm1", 200, 80);  // test function
     //
     // Tru64:
     //
     add_expected_result(
        ".*Tru64.*",                          // compiler
        ".*",                          // stdlib
        ".*",                          // platform
        "real_concept",                // test type(s)
        "factorials",                  // test data group
        "boost::math::lgamma", 50, 20);  // test function
     //
     // Sun OS:
     //
     add_expected_result(
        ".*",                          // compiler
        ".*",                          // stdlib
        "Sun.*",                       // platform
        largest_type,                  // test type(s)
        "factorials",                  // test data group
        "boost::math::tgamma", 300, 50); // test function
     add_expected_result(
        ".*",                          // compiler
        ".*",                          // stdlib
        "Sun.*",                       // platform
        "real_concept",                // test type(s)
        "factorials",                  // test data group
        "boost::math::tgamma", 300, 50); // test function
  
     //
     // Catch all cases come last:
     //
     add_expected_result(
        ".*",                          // compiler
        ".*",                          // stdlib
        ".*",                          // platform
        largest_type,                  // test type(s)
        "factorials",                  // test data group
        "boost::math::tgamma", 4, 1);  // test function
     add_expected_result(
        ".*",                          // compiler
        ".*",                          // stdlib
        ".*",                          // platform
        largest_type,                  // test type(s)
        "factorials",                  // test data group
        "boost::math::lgamma", 9, 1);  // test function
     add_expected_result(
        ".*",                          // compiler
        ".*",                          // stdlib
        ".*",                          // platform
        largest_type,                  // test type(s)
        "near (0|-55)",                // test data group
        "boost::math::(t|l)gamma", 200, 100);  // test function
     add_expected_result(
        ".*",                          // compiler
        ".*",                          // stdlib
        ".*",                          // platform
        largest_type,                  // test type(s)
        "near (1|2|-10)",              // test data group
        "boost::math::tgamma", 10, 5);  // test function
     add_expected_result(
        ".*",                          // compiler
        ".*",                          // stdlib
        ".*",                          // platform
        largest_type,                  // test type(s)
        "near (1|2|-10)",              // test data group
        "boost::math::lgamma", 14, 7);  // test function
     add_expected_result(
        ".*",                          // compiler
        ".*",                          // stdlib
        ".*",                          // platform
        largest_type,                  // test type(s)
        "tgamma1pm1.*",                // test data group
        "boost::math::tgamma1pm1", 30, 9);  // test function
  
     add_expected_result(
        ".*",                          // compiler
        ".*",                          // stdlib
        ".*",                          // platform
        "real_concept",                // test type(s)
        "factorials",                  // test data group
        "boost::math::tgamma", 70, 25);  // test function
     add_expected_result(
        ".*",                          // compiler
        ".*",                          // stdlib
        ".*",                          // platform
        "real_concept",                // test type(s)
        "factorials",                  // test data group
        "boost::math::lgamma", 40, 4);  // test function
     add_expected_result(
        ".*",                          // compiler
        ".*",                          // stdlib
        ".*",                          // platform
        "real_concept",                // test type(s)
        "near.*",                      // test data group
        "boost::math::tgamma", 80, 60);  // test function
     add_expected_result(
        ".*",                          // compiler
        ".*",                          // stdlib
        ".*",                          // platform
        "real_concept",                // test type(s)
        "near.*",                      // test data group
        "boost::math::lgamma", 10000000, 10000000);  // test function
     add_expected_result(
        ".*",                          // compiler
        ".*",                          // stdlib
        ".*",                          // platform
        "real_concept",                // test type(s)
        "tgamma1pm1.*",                // test data group
        "boost::math::tgamma1pm1", 20, 5);  // 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;
  
  #ifndef BOOST_MATH_BUGGY_LARGE_FLOAT_CONSTANTS
     test_spots(0.0F);
  #endif
     test_spots(0.0);
  #ifndef BOOST_MATH_NO_LONG_DOUBLE_MATH_FUNCTIONS
     test_spots(0.0L);
     test_spots(boost::math::concepts::real_concept(0.1));
  #endif
  
  #ifndef BOOST_MATH_BUGGY_LARGE_FLOAT_CONSTANTS
     test_gamma(0.1F, "float");
  #endif
     test_gamma(0.1, "double");
  #ifndef BOOST_MATH_NO_LONG_DOUBLE_MATH_FUNCTIONS
     test_gamma(0.1L, "long double");
  #ifndef BOOST_MATH_NO_REAL_CONCEPT_TESTS
  #if !BOOST_WORKAROUND(__BORLANDC__, BOOST_TESTED_AT(0x582))
     test_gamma(boost::math::concepts::real_concept(0.1), "real_concept");
  #endif
  #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;
  }
  
  
  
  