test_igamma.cpp

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//  (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)

#define BOOST_MATH_OVERFLOW_ERROR_POLICY ignore_error

#include <boost/math/concepts/real_concept.hpp>
#include <boost/math/special_functions/gamma.hpp>
#include <boost/test/included/test_exec_monitor.hpp>
#include <boost/test/floating_point_comparison.hpp>
#include <boost/math/tools/stats.hpp>
#include <boost/math/tools/test.hpp>
#include <boost/math/constants/constants.hpp>
#include <boost/type_traits/is_floating_point.hpp>
#include <boost/array.hpp>
#include "functor.hpp"

#include "test_gamma_hooks.hpp"
#include "handle_test_result.hpp"

//
// DESCRIPTION:
// ~~~~~~~~~~~~
//
// This file tests the incomplete gamma functions tgamma,
// tgamma_lower, gamma_p and gamma_q. 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:
   //
   // These should not really be needed, but on *some* Linux
   // versions these error rates are quite large and appear to
   // be related to the accuracy of powl and expl.  On Itanium
   // or Xeon machines the error rates are much lower than this.
   // Worst cases appear to be AMD64 machines.
   //
   add_expected_result(
      "[^|]*",                          // compiler
      "[^|]*",                          // stdlib
      "linux",                          // platform
      largest_type,                     // test type(s)
      "[^|]*medium[^|]*",               // test data group
      "[^|]*", 1000, 200);                 // test function
   add_expected_result(
      "[^|]*",                          // compiler
      "[^|]*",                          // stdlib
      "linux",                          // platform
      largest_type,                     // test type(s)
      "[^|]*integer[^|]*",               // test data group
      "[^|]*", 1000, 200);                 // test function
   add_expected_result(
      "[^|]*",                          // compiler
      "[^|]*",                          // stdlib
      "linux",                          // platform
      "real_concept",                   // test type(s)
      "[^|]*medium[^|]*",               // test data group
      "[^|]*", 600, 200);                // test function
   add_expected_result(
      "[^|]*",                          // compiler
      "[^|]*",                          // stdlib
      "linux",                          // platform
      "real_concept",                   // test type(s)
      "[^|]*integer[^|]*",               // test data group
      "[^|]*", 600, 200);                // test function

   //
   // Mac OS X:
   // It's not clear why these should be required, but see notes above
   // about Linux.
   //
   add_expected_result(
      "[^|]*",                          // compiler
      "[^|]*",                          // stdlib
      "Mac OS",                          // platform
      largest_type,                     // test type(s)
      "[^|]*medium[^|]*",               // test data group
      "[^|]*", 5000, 1000);                 // test function
   add_expected_result(
      "[^|]*",                          // compiler
      "[^|]*",                          // stdlib
      "Mac OS",                          // platform
      largest_type,                     // test type(s)
      "[^|]*small[^|]*",               // test data group
      "[^|]*", 40, 15);                 // test function
   add_expected_result(
      "[^|]*",                          // compiler
      "[^|]*",                          // stdlib
      "Mac OS",                          // platform
      largest_type,                     // test type(s)
      "[^|]*integer[^|]*",               // test data group
      "[^|]*", 2000, 300);                 // test function
   add_expected_result(
      "[^|]*",                          // compiler
      "[^|]*",                          // stdlib
      "Mac OS",                          // platform
      "real_concept",                   // test type(s)
      "[^|]*medium[^|]*",               // test data group
      "[^|]*", 5000, 1000);                // test function
   add_expected_result(
      "[^|]*",                          // compiler
      "[^|]*",                          // stdlib
      "Mac OS",                          // platform
      "real_concept",                     // test type(s)
      "[^|]*small[^|]*",               // test data group
      "[^|]*", 40, 15);                 // test function
   add_expected_result(
      "[^|]*",                          // compiler
      "[^|]*",                          // stdlib
      "Mac OS",                          // platform
      "real_concept",                   // test type(s)
      "[^|]*integer[^|]*",               // test data group
      "[^|]*", 2000, 300);                // test function
   //
   // HP-UX:
   //
   add_expected_result(
      "[^|]*",                          // compiler
      "[^|]*",                          // stdlib
      "HP-UX",                          // platform
      largest_type,                     // test type(s)
      "[^|]*medium[^|]*",               // test data group
      "[^|]*", 500, 50);                 // test function
   add_expected_result(
      "[^|]*",                          // compiler
      "[^|]*",                          // stdlib
      "HP-UX",                          // platform
      "real_concept",                   // test type(s)
      "[^|]*medium[^|]*",               // test data group
      "[^|]*", 500, 100);                // test function
   //
   // Sun OS:
   //
   add_expected_result(
      "[^|]*",                          // compiler
      "[^|]*",                          // stdlib
      "Sun.*",                          // platform
      largest_type,                     // test type(s)
      "[^|]*medium[^|]*",               // test data group
      "[^|]*", 500, 100);               // test function
   add_expected_result(
      "[^|]*",                          // compiler
      "[^|]*",                          // stdlib
      "Sun.*",                          // platform
      largest_type,                     // test type(s)
      "[^|]*integer[^|]*",              // test data group
      "[^|]*", 100, 30);                // test function
   add_expected_result(
      "[^|]*",                          // compiler
      "[^|]*",                          // stdlib
      "Sun.*",                          // platform
      "real_concept",                   // test type(s)
      "[^|]*medium[^|]*",               // test data group
      "[^|]*", 500, 100);                // test function
   add_expected_result(
      "[^|]*",                          // compiler
      "[^|]*",                          // stdlib
      "Sun.*",                          // platform
      "real_concept",                   // test type(s)
      "[^|]*integer[^|]*",               // test data group
      "[^|]*", 100, 30);                // test function

   //
   // Mac OS X:
   //
   add_expected_result(
      "[^|]*",                          // compiler
      "[^|]*",                          // stdlib
      "Mac OS",                          // platform
      largest_type,                     // test type(s)
      "[^|]*medium[^|]*",               // test data group
      "[^|]*", 100, 50);                 // test function

   //
   // Large exponent range causes more extreme test cases to be evaluated:
   //
   if(std::numeric_limits<long double>::max_exponent > std::numeric_limits<double>::max_exponent)
   {
      add_expected_result(
         "[^|]*",                          // compiler
         "[^|]*",                          // stdlib
         "[^|]*",                          // platform
         largest_type,                     // test type(s)
         "[^|]*large[^|]*",                // test data group
         ".*", 40000, 3000);  // test function
   }


   //
   // Catch all cases come last:
   //
   add_expected_result(
      "[^|]*",                          // compiler
      "[^|]*",                          // stdlib
      "[^|]*",                          // platform
      largest_type,                     // test type(s)
      "[^|]*medium[^|]*",               // test data group
      "[^|]*", 50, 20);                 // test function
   add_expected_result(
      "[^|]*",                          // compiler
      "[^|]*",                          // stdlib
      "[^|]*",                          // platform
      largest_type,                     // test type(s)
      "[^|]*small[^|]*",                // test data group
      "[^|]*", 20, 10);                  // test function
   add_expected_result(
      "[^|]*",                          // compiler
      "[^|]*",                          // stdlib
      "[^|]*",                          // platform
      largest_type,                     // test type(s)
      "[^|]*large[^|]*",                // test data group
      "boost::math::gamma_q", 500, 50);  // test function
   add_expected_result(
      "[^|]*",                          // compiler
      "[^|]*",                          // stdlib
      "Cygwin",                         // platform
      largest_type,                     // test type(s)
      "[^|]*large[^|]*",                // test data group
      "boost::math::gamma_p", 700, 50);  // test function
   add_expected_result(
      "[^|]*",                          // compiler
      "[^|]*",                          // stdlib
      "[^|]*",                          // platform
      largest_type,                     // test type(s)