387 lines
17 KiB
C++
387 lines
17 KiB
C++
// Copyright John Maddock 2006.
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// Use, modification and distribution are subject to the
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// Boost Software License, Version 1.0. (See accompanying file
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// LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_0.txt)
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#include <pch.hpp>
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#ifdef _MSC_VER
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# pragma warning(disable: 4127) // conditional expression is constant.
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# pragma warning(disable: 4245) // int/unsigned int conversion
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#endif
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// Return infinities not exceptions:
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#define BOOST_MATH_OVERFLOW_ERROR_POLICY ignore_error
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#include <boost/math/concepts/real_concept.hpp>
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#define BOOST_TEST_MAIN
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#include <boost/test/unit_test.hpp>
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#include <boost/test/tools/floating_point_comparison.hpp>
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#include <boost/math/special_functions/factorials.hpp>
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#include <boost/math/special_functions/gamma.hpp>
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#include <boost/math/tools/stats.hpp>
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#include <boost/math/tools/test.hpp>
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#include <iostream>
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#include <iomanip>
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using std::cout;
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using std::endl;
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template <class T>
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T naive_falling_factorial(T x, unsigned n)
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{
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if(n == 0)
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return 1;
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T result = x;
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while(--n)
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{
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x -= 1;
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result *= x;
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}
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return result;
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}
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template <class T>
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void test_spots(T)
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{
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//
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// Basic sanity checks.
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//
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T tolerance = boost::math::tools::epsilon<T>() * 100 * 2; // 2 eps as a percent.
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BOOST_CHECK_CLOSE(
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::boost::math::factorial<T>(0),
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static_cast<T>(1), tolerance);
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BOOST_CHECK_CLOSE(
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::boost::math::factorial<T>(1),
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static_cast<T>(1), tolerance);
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BOOST_CHECK_CLOSE(
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::boost::math::factorial<T>(10),
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static_cast<T>(3628800L), tolerance);
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BOOST_CHECK_CLOSE(
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::boost::math::unchecked_factorial<T>(0),
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static_cast<T>(1), tolerance);
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BOOST_CHECK_CLOSE(
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::boost::math::unchecked_factorial<T>(1),
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static_cast<T>(1), tolerance);
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BOOST_CHECK_CLOSE(
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::boost::math::unchecked_factorial<T>(10),
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static_cast<T>(3628800L), tolerance);
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//
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// Try some double factorials:
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//
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BOOST_CHECK_CLOSE(
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::boost::math::double_factorial<T>(0),
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static_cast<T>(1), tolerance);
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BOOST_CHECK_CLOSE(
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::boost::math::double_factorial<T>(1),
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static_cast<T>(1), tolerance);
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BOOST_CHECK_CLOSE(
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::boost::math::double_factorial<T>(2),
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static_cast<T>(2), tolerance);
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BOOST_CHECK_CLOSE(
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::boost::math::double_factorial<T>(5),
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static_cast<T>(15), tolerance);
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BOOST_CHECK_CLOSE(
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::boost::math::double_factorial<T>(10),
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static_cast<T>(3840), tolerance);
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BOOST_CHECK_CLOSE(
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::boost::math::double_factorial<T>(19),
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static_cast<T>(6.547290750e8L), tolerance);
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BOOST_CHECK_CLOSE(
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::boost::math::double_factorial<T>(24),
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static_cast<T>(1.961990553600000e12L), tolerance);
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BOOST_CHECK_CLOSE(
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::boost::math::double_factorial<T>(33),
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static_cast<T>(6.33265987076285062500000e18L), tolerance);
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BOOST_CHECK_CLOSE(
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::boost::math::double_factorial<T>(42),
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static_cast<T>(1.0714547155728479551488000000e26L), tolerance);
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BOOST_CHECK_CLOSE(
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::boost::math::double_factorial<T>(47),
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static_cast<T>(1.19256819277443412353990764062500000e30L), tolerance);
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if((std::numeric_limits<T>::has_infinity) && (std::numeric_limits<T>::max_exponent <= 1024))
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{
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BOOST_CHECK_EQUAL(
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::boost::math::double_factorial<T>(320),
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std::numeric_limits<T>::infinity());
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BOOST_CHECK_EQUAL(
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::boost::math::double_factorial<T>(301),
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std::numeric_limits<T>::infinity());
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}
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//
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// Rising factorials:
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//
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tolerance = boost::math::tools::epsilon<T>() * 100 * 20; // 20 eps as a percent.
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if(std::numeric_limits<T>::is_specialized == 0)
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tolerance *= 5; // higher error rates without Lanczos support
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BOOST_CHECK_CLOSE(
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::boost::math::rising_factorial(static_cast<T>(3), 4),
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static_cast<T>(360), tolerance);
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BOOST_CHECK_CLOSE(
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::boost::math::rising_factorial(static_cast<T>(7), -4),
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static_cast<T>(0.00277777777777777777777777777777777777777777777777777777777778L), tolerance);
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BOOST_CHECK_CLOSE(
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::boost::math::rising_factorial(static_cast<T>(120.5f), 8),
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static_cast<T>(5.58187566784927180664062500e16L), tolerance);
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BOOST_CHECK_CLOSE(
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::boost::math::rising_factorial(static_cast<T>(120.5f), -4),
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static_cast<T>(5.15881498170104646868208445266116850161120996179812063177241e-9L), tolerance);
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BOOST_CHECK_CLOSE(
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::boost::math::rising_factorial(static_cast<T>(5000.25f), 8),
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static_cast<T>(3.92974581976666067544013393509103775024414062500000e29L), tolerance);
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BOOST_CHECK_CLOSE(
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::boost::math::rising_factorial(static_cast<T>(5000.25f), -7),
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static_cast<T>(1.28674092710208810281923019294164707555099052561945725535047e-26L), tolerance);
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BOOST_CHECK_CLOSE(
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::boost::math::rising_factorial(static_cast<T>(30.25), 21),
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static_cast<T>(3.93286957998925490693364184100209193343633629069699964020401e33L), tolerance * 2);
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BOOST_CHECK_CLOSE(
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::boost::math::rising_factorial(static_cast<T>(30.25), -21),
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static_cast<T>(3.35010902064291983728782493133164809108646650368560147505884e-27L), tolerance);
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BOOST_CHECK_CLOSE(
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::boost::math::rising_factorial(static_cast<T>(-30.25), 21),
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static_cast<T>(-9.76168312768123676601980433377916854311706629232503473758698e26L), tolerance * 2);
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BOOST_CHECK_CLOSE(
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::boost::math::rising_factorial(static_cast<T>(-30.25), -21),
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static_cast<T>(-1.50079704000923674318934280259377728203516775215430875839823e-34L), 2 * tolerance);
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BOOST_CHECK_CLOSE(
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::boost::math::rising_factorial(static_cast<T>(-30.25), 5),
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static_cast<T>(-1.78799177197265625000000e7L), tolerance);
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BOOST_CHECK_CLOSE(
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::boost::math::rising_factorial(static_cast<T>(-30.25), -5),
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static_cast<T>(-2.47177487004482195012362027432181137141899692171397467859150e-8L), tolerance);
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BOOST_CHECK_CLOSE(
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::boost::math::rising_factorial(static_cast<T>(-30.25), 6),
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static_cast<T>(4.5146792242309570312500000e8L), tolerance);
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BOOST_CHECK_CLOSE(
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::boost::math::rising_factorial(static_cast<T>(-30.25), -6),
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static_cast<T>(6.81868929667537089689274558433603136943171564610751635473516e-10L), tolerance);
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BOOST_CHECK_CLOSE(
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::boost::math::rising_factorial(static_cast<T>(-3), 6),
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static_cast<T>(0), tolerance);
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BOOST_CHECK_CLOSE(
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::boost::math::rising_factorial(static_cast<T>(-3.25), 6),
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static_cast<T>(2.99926757812500L), tolerance);
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BOOST_CHECK_CLOSE(
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::boost::math::rising_factorial(static_cast<T>(-5.25), 6),
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static_cast<T>(50.987548828125000000000000L), tolerance);
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BOOST_CHECK_CLOSE(
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::boost::math::rising_factorial(static_cast<T>(-5.25), 13),
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static_cast<T>(127230.91046623885631561279296875000L), tolerance);
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BOOST_CHECK_CLOSE(
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::boost::math::rising_factorial(static_cast<T>(-3.25), -6),
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static_cast<T>(0.0000129609865918182348202632178291407500332449622510474437452125L), tolerance);
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BOOST_CHECK_CLOSE(
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::boost::math::rising_factorial(static_cast<T>(-5.25), -6),
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static_cast<T>(2.50789821857946332294524052303699065683926911849535903362649e-6L), tolerance);
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BOOST_CHECK_CLOSE(
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::boost::math::rising_factorial(static_cast<T>(-5.25), -13),
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static_cast<T>(-1.38984989447269128946284683518361786049649013886981662962096e-14L), tolerance);
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//
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// More cases reported as bugs by Rocco Romeo:
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//
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BOOST_CHECK_EQUAL(::boost::math::rising_factorial(static_cast<T>(0), 1), static_cast<T>(0));
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BOOST_CHECK_EQUAL(::boost::math::rising_factorial(static_cast<T>(0), -1), static_cast<T>(-1));
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BOOST_CHECK_CLOSE(::boost::math::rising_factorial(static_cast<T>(0.5f), -1), static_cast<T>(-2), tolerance);
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BOOST_CHECK_CLOSE(::boost::math::rising_factorial(static_cast<T>(40.5), -41), static_cast<T>(-2.75643016796662963097096639854040835565778207128865739e-47L), tolerance);
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BOOST_CHECK_EQUAL(::boost::math::rising_factorial(static_cast<T>(-2), 3), static_cast<T>(0));
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BOOST_CHECK_EQUAL(::boost::math::rising_factorial(static_cast<T>(-2), 2), static_cast<T>(2));
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BOOST_CHECK_EQUAL(::boost::math::rising_factorial(static_cast<T>(-4), 3), static_cast<T>(-24));
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BOOST_CHECK_CLOSE(::boost::math::rising_factorial(static_cast<T>(-4), -3), static_cast<T>(-0.00476190476190476190476190476190476190476190476190476190476L), tolerance);
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if(ldexp(T(1), -150) != 0)
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{
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BOOST_CHECK_CLOSE(::boost::math::rising_factorial(ldexp(T(1), -150), 0), static_cast<T>(1), tolerance);
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BOOST_CHECK_CLOSE(::boost::math::rising_factorial(ldexp(T(1), -150), -1), static_cast<T>(-1.00000000000000000000000000000000000000000000070064923216241L), tolerance);
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BOOST_CHECK_CLOSE(::boost::math::rising_factorial(ldexp(T(1), -150), -2), static_cast<T>(0.500000000000000000000000000000000000000000000525486924121806L), tolerance);
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BOOST_CHECK_CLOSE(::boost::math::rising_factorial(ldexp(T(1), -150), -25), static_cast<T>(-6.44695028438447339619485321920468720529890442766578870603544e-26L), 15 * tolerance);
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if(std::numeric_limits<T>::min_exponent10 < -50)
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{
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BOOST_CHECK_CLOSE(::boost::math::rising_factorial(ldexp(T(1), -150), -40), static_cast<T>(1.22561743912838584942353998493975692372556196815242899727910e-48L), tolerance);
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}
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}
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//
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// Falling factorials:
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//
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BOOST_CHECK_CLOSE(
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::boost::math::falling_factorial(static_cast<T>(30.25), 0),
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static_cast<T>(naive_falling_factorial(30.25L, 0)),
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tolerance);
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BOOST_CHECK_CLOSE(
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::boost::math::falling_factorial(static_cast<T>(30.25), 1),
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static_cast<T>(naive_falling_factorial(30.25L, 1)),
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tolerance);
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BOOST_CHECK_CLOSE(
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::boost::math::falling_factorial(static_cast<T>(30.25), 2),
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static_cast<T>(naive_falling_factorial(30.25L, 2)),
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tolerance);
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BOOST_CHECK_CLOSE(
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::boost::math::falling_factorial(static_cast<T>(30.25), 5),
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static_cast<T>(naive_falling_factorial(30.25L, 5)),
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tolerance);
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BOOST_CHECK_CLOSE(
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::boost::math::falling_factorial(static_cast<T>(30.25), 22),
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static_cast<T>(naive_falling_factorial(30.25L, 22)),
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tolerance);
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BOOST_CHECK_CLOSE(
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::boost::math::falling_factorial(static_cast<T>(100.5), 6),
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static_cast<T>(naive_falling_factorial(100.5L, 6)),
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tolerance);
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BOOST_CHECK_CLOSE(
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::boost::math::falling_factorial(static_cast<T>(30.75), 30),
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static_cast<T>(naive_falling_factorial(30.75L, 30)),
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tolerance * 3);
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if(boost::math::policies::digits<T, boost::math::policies::policy<> >() > 50)
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{
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BOOST_CHECK_CLOSE(
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::boost::math::falling_factorial(static_cast<T>(-30.75L), 30),
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static_cast<T>(naive_falling_factorial(-30.75L, 30)),
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tolerance * 3);
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BOOST_CHECK_CLOSE(
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::boost::math::falling_factorial(static_cast<T>(-30.75L), 27),
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static_cast<T>(naive_falling_factorial(-30.75L, 27)),
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tolerance * 3);
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}
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BOOST_CHECK_CLOSE(
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::boost::math::falling_factorial(static_cast<T>(-12.0), 6),
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static_cast<T>(naive_falling_factorial(-12.0L, 6)),
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tolerance);
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BOOST_CHECK_CLOSE(
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::boost::math::falling_factorial(static_cast<T>(-12), 5),
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static_cast<T>(naive_falling_factorial(-12.0L, 5)),
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tolerance);
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BOOST_CHECK_CLOSE(
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::boost::math::falling_factorial(static_cast<T>(-3.0), 6),
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static_cast<T>(naive_falling_factorial(-3.0L, 6)),
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tolerance);
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BOOST_CHECK_CLOSE(
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::boost::math::falling_factorial(static_cast<T>(-3), 5),
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static_cast<T>(naive_falling_factorial(-3.0L, 5)),
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tolerance);
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BOOST_CHECK_CLOSE(
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::boost::math::falling_factorial(static_cast<T>(3.0), 6),
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static_cast<T>(naive_falling_factorial(3.0L, 6)),
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tolerance);
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BOOST_CHECK_CLOSE(
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::boost::math::falling_factorial(static_cast<T>(3), 5),
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static_cast<T>(naive_falling_factorial(3.0L, 5)),
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tolerance);
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BOOST_CHECK_CLOSE(
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::boost::math::falling_factorial(static_cast<T>(3.25), 4),
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static_cast<T>(naive_falling_factorial(3.25L, 4)),
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tolerance);
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BOOST_CHECK_CLOSE(
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::boost::math::falling_factorial(static_cast<T>(3.25), 5),
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static_cast<T>(naive_falling_factorial(3.25L, 5)),
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tolerance);
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BOOST_CHECK_CLOSE(
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::boost::math::falling_factorial(static_cast<T>(3.25), 6),
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static_cast<T>(naive_falling_factorial(3.25L, 6)),
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tolerance);
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BOOST_CHECK_CLOSE(
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::boost::math::falling_factorial(static_cast<T>(3.25), 7),
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static_cast<T>(naive_falling_factorial(3.25L, 7)),
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tolerance);
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BOOST_CHECK_CLOSE(
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::boost::math::falling_factorial(static_cast<T>(8.25), 12),
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static_cast<T>(naive_falling_factorial(8.25L, 12)),
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tolerance);
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//
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// More cases reported as bugs by Rocco Romeo:
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//
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BOOST_CHECK_EQUAL(::boost::math::falling_factorial(static_cast<T>(0), 1), static_cast<T>(0));
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BOOST_CHECK_CLOSE(::boost::math::falling_factorial(static_cast<T>(-2), 3), static_cast<T>(-24), tolerance);
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BOOST_CHECK_CLOSE(::boost::math::falling_factorial(static_cast<T>(-2), 2), static_cast<T>(6), tolerance);
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BOOST_CHECK_CLOSE(::boost::math::falling_factorial(static_cast<T>(-4), 3), static_cast<T>(-120), tolerance);
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if(ldexp(static_cast<T>(1), -100) != 0)
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{
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BOOST_CHECK_CLOSE(::boost::math::falling_factorial(ldexp(static_cast<T>(1), -100), 1), static_cast<T>(7.888609052210118054117285652827862296732064351090230047e-31L), tolerance);
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BOOST_CHECK_CLOSE(::boost::math::falling_factorial(ldexp(static_cast<T>(1), -100), 2), static_cast<T>(-7.88860905221011805411728565282163928145420320938308598e-31L), tolerance);
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BOOST_CHECK_CLOSE(::boost::math::falling_factorial(ldexp(static_cast<T>(1), -100), 3), static_cast<T>(1.577721810442023610823457130563705554763054527705902790e-30L), tolerance);
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BOOST_CHECK_CLOSE(::boost::math::falling_factorial(ldexp(static_cast<T>(1), -100), 35), static_cast<T>(2.32897613101315187323300837924676081371219290005311315885e8L), 35 * tolerance);
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}
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if((ldexp(static_cast<T>(1), -300) != 0) && (std::numeric_limits<T>::max_exponent10 > 290))
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{
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BOOST_CHECK_CLOSE(::boost::math::falling_factorial(ldexp(static_cast<T>(1), -300), 20), static_cast<T>(-5.97167167502482975928590631196751639118233432208390100e-74L), tolerance);
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BOOST_CHECK_CLOSE(::boost::math::falling_factorial(ldexp(static_cast<T>(1), -300), 200), static_cast<T>(-1.93579759151806711025267355739174942986011285920860098569075e282L), 10 * tolerance);
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}
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tolerance = boost::math::tools::epsilon<T>() * 100 * 20; // 20 eps as a percent.
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unsigned i = boost::math::max_factorial<T>::value;
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if((boost::is_floating_point<T>::value) && (sizeof(T) <= sizeof(double)))
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{
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// Without Lanczos support, tgamma isn't accurate enough for this test:
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BOOST_CHECK_CLOSE(
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::boost::math::unchecked_factorial<T>(i),
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boost::math::tgamma(static_cast<T>(i+1)), tolerance);
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}
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i += 10;
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while(boost::math::lgamma(static_cast<T>(i+1)) < boost::math::tools::log_max_value<T>())
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{
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BOOST_CHECK_CLOSE(
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::boost::math::factorial<T>(i),
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boost::math::tgamma(static_cast<T>(i+1)), tolerance);
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i += 10;
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}
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} // template <class T> void test_spots(T)
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BOOST_AUTO_TEST_CASE( test_main )
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{
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BOOST_MATH_CONTROL_FP;
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test_spots(0.0F);
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test_spots(0.0);
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#ifndef BOOST_MATH_NO_LONG_DOUBLE_MATH_FUNCTIONS
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test_spots(0.0L);
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#ifndef BOOST_MATH_NO_REAL_CONCEPT_TESTS
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test_spots(boost::math::concepts::real_concept(0.));
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#endif
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#else
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std::cout << "<note>The long double tests have been disabled on this platform "
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"either because the long double overloads of the usual math functions are "
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"not available at all, or because they are too inaccurate for these tests "
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"to pass.</note>" << std::endl;
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#endif
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if (std::numeric_limits<double>::digits == std::numeric_limits<long double>::digits)
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{
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cout << "Types double and long double have the same number of floating-point significand bits ("
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<< std::numeric_limits<long double>::digits << ") on this platform." << endl;
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}
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if (std::numeric_limits<float>::digits == std::numeric_limits<double>::digits)
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{
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cout << "Types float and double have the same number of floating-point significand bits ("
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<< std::numeric_limits<double>::digits << ") on this platform." << endl;
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}
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using boost::math::max_factorial;
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cout << "max factorial for float " << max_factorial<float>::value << endl;
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cout << "max factorial for double " << max_factorial<double>::value << endl;
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cout << "max factorial for long double " << max_factorial<long double>::value << endl;
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cout << "max factorial for real_concept " << max_factorial<boost::math::concepts::real_concept>::value << endl;
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}
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/*
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Output is:
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Running 1 test case...
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Types double and long double have the same number of floating-point significand bits (53) on this platform.
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max factorial for float 34
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max factorial for double 170
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max factorial for long double 170
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max factorial for real_concept 100
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*** No errors detected
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*/
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