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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)
#include <pch.hpp>
#include "test_binomial_coeff.hpp"
//
// DESCRIPTION:
// ~~~~~~~~~~~~
//
// This file tests the function binomial_coefficient<T>.
// The accuracy tests
// use values generated with NTL::RR at 1000-bit precision
// and our generic versions of these function.
//
// 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
add_expected_result(
".*", // compiler
".*", // stdlib
".*", // platform
largest_type, // test type(s)
".*large.*", // test data group
".*", 100, 20); // test function
add_expected_result(
".*", // compiler
".*", // stdlib
".*", // platform
"real_concept", // test type(s)
".*large.*", // test data group
".*", 250, 100); // test function
add_expected_result(
".*", // compiler
".*", // stdlib
".*", // platform
"real_concept", // test type(s)
".*", // test data group
".*", 150, 30); // test function
add_expected_result(
".*", // compiler
".*", // stdlib
".*", // platform
".*", // test type(s)
".*", // test data group
".*", 2, 1); // 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;
}
template <class T>
void test_spots(T, const char* name)
{
T tolerance = boost::math::tools::epsilon<T>() * 50 * 100; // 50 eps as a percentage
if(!std::numeric_limits<T>::is_specialized)
tolerance *= 10; // beta function not so accurate without lanczos support
std::cout << "Testing spot checks for type " << name << " with tolerance " << tolerance << "%\n";
BOOST_CHECK_EQUAL(boost::math::binomial_coefficient<T>(20, 0), static_cast<T>(1));
BOOST_CHECK_EQUAL(boost::math::binomial_coefficient<T>(20, 1), static_cast<T>(20));
BOOST_CHECK_EQUAL(boost::math::binomial_coefficient<T>(20, 2), static_cast<T>(190));
BOOST_CHECK_EQUAL(boost::math::binomial_coefficient<T>(20, 3), static_cast<T>(1140));
BOOST_CHECK_EQUAL(boost::math::binomial_coefficient<T>(20, 20), static_cast<T>(1));
BOOST_CHECK_EQUAL(boost::math::binomial_coefficient<T>(20, 19), static_cast<T>(20));
BOOST_CHECK_EQUAL(boost::math::binomial_coefficient<T>(20, 18), static_cast<T>(190));
BOOST_CHECK_EQUAL(boost::math::binomial_coefficient<T>(20, 17), static_cast<T>(1140));
BOOST_CHECK_EQUAL(boost::math::binomial_coefficient<T>(20, 10), static_cast<T>(184756L));
BOOST_CHECK_CLOSE(boost::math::binomial_coefficient<T>(100, 5), static_cast<T>(7.528752e7L), tolerance);
BOOST_CHECK_CLOSE(boost::math::binomial_coefficient<T>(100, 81), static_cast<T>(1.323415729392122674e20L), tolerance);
BOOST_CHECK_CLOSE(boost::math::binomial_coefficient<T>(300, 3), static_cast<T>(4.45510e6L), tolerance);
BOOST_CHECK_CLOSE(boost::math::binomial_coefficient<T>(300, 7), static_cast<T>(4.043855956140000e13L), tolerance);
BOOST_CHECK_CLOSE(boost::math::binomial_coefficient<T>(300, 290), static_cast<T>(1.3983202332417017700000000e18L), tolerance);
BOOST_CHECK_CLOSE(boost::math::binomial_coefficient<T>(300, 275), static_cast<T>(1.953265141442868389822364184842211512000000e36L), tolerance);
}
BOOST_AUTO_TEST_CASE( test_main )
{
expected_results();
BOOST_MATH_CONTROL_FP;
test_spots(1.0F, "float");
test_spots(1.0, "double");
#ifndef BOOST_MATH_NO_LONG_DOUBLE_MATH_FUNCTIONS
test_spots(1.0L, "long double");
#ifndef BOOST_MATH_NO_REAL_CONCEPT_TESTS
test_spots(boost::math::concepts::real_concept(), "real_concept");
#endif
#endif
test_binomial(1.0F, "float");
test_binomial(1.0, "double");
#ifndef BOOST_MATH_NO_LONG_DOUBLE_MATH_FUNCTIONS
test_binomial(1.0L, "long double");
#ifndef BOOST_MATH_NO_REAL_CONCEPT_TESTS
test_binomial(boost::math::concepts::real_concept(), "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
}
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