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245 lines
11 KiB
C++
245 lines
11 KiB
C++
// Copyright Xiaogang Zhang 2006
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// Copyright John Maddock 2006, 2007
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// Copyright Paul A. Bristow 2007
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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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#ifdef _MSC_VER
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# pragma warning(disable : 4756) // overflow in constant arithmetic
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// Constants are too big for float case, but this doesn't matter for test.
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#endif
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#include <boost/math/concepts/real_concept.hpp>
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#include <boost/test/included/test_exec_monitor.hpp>
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#include <boost/test/floating_point_comparison.hpp>
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#include <boost/math/special_functions/ellint_3.hpp>
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#include <boost/array.hpp>
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#include <boost/lambda/lambda.hpp>
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#include <boost/lambda/bind.hpp>
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#include "handle_test_result.hpp"
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//
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// DESCRIPTION:
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// ~~~~~~~~~~~~
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//
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// This file tests the Elliptic Integrals of the third kind.
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// There are two sets of tests, spot
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// tests which compare our results with selected values computed
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// using the online special function calculator at
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// functions.wolfram.com, while the bulk of the accuracy tests
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// use values generated with NTL::RR at 1000-bit precision
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// and our generic versions of these functions.
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//
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// Note that when this file is first run on a new platform many of
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// these tests will fail: the default accuracy is 1 epsilon which
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// is too tight for most platforms. In this situation you will
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// need to cast a human eye over the error rates reported and make
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// a judgement as to whether they are acceptable. Either way please
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// report the results to the Boost mailing list. Acceptable rates of
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// error are marked up below as a series of regular expressions that
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// identify the compiler/stdlib/platform/data-type/test-data/test-function
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// along with the maximum expected peek and RMS mean errors for that
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// test.
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//
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void expected_results()
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{
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//
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// Define the max and mean errors expected for
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// various compilers and platforms.
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//
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const char* largest_type;
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#ifndef BOOST_MATH_NO_LONG_DOUBLE_MATH_FUNCTIONS
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if(boost::math::policies::digits<double, boost::math::policies::policy<> >() == boost::math::policies::digits<long double, boost::math::policies::policy<> >())
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{
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largest_type = "(long\\s+)?double";
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}
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else
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{
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largest_type = "long double";
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}
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#else
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largest_type = "(long\\s+)?double";
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#endif
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//
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// Catch all cases come last:
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//
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add_expected_result(
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".*", // compiler
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".*", // stdlib
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".*", // platform
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largest_type, // test type(s)
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".*Large.*", // test data group
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".*", 50, 20); // test function
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add_expected_result(
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".*", // compiler
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".*", // stdlib
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".*", // platform
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"real_concept", // test type(s)
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".*Large.*", // test data group
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".*", 50, 20); // test function
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add_expected_result(
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".*", // compiler
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".*", // stdlib
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".*", // platform
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largest_type, // test type(s)
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".*", // test data group
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".*", 15, 8); // test function
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add_expected_result(
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".*", // compiler
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".*", // stdlib
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".*", // platform
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"real_concept", // test type(s)
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".*", // test data group
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".*", 15, 8); // test function
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//
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// Finish off by printing out the compiler/stdlib/platform names,
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// we do this to make it easier to mark up expected error rates.
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//
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std::cout << "Tests run with " << BOOST_COMPILER << ", "
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<< BOOST_STDLIB << ", " << BOOST_PLATFORM << std::endl;
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}
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template <typename T>
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void do_test_ellint_pi3(T& data, const char* type_name, const char* test)
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{
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typedef typename T::value_type row_type;
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typedef typename row_type::value_type value_type;
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std::cout << "Testing: " << test << std::endl;
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value_type (*fp2)(value_type, value_type, value_type) = boost::math::ellint_3;
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boost::math::tools::test_result<value_type> result;
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result = boost::math::tools::test(
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data,
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boost::lambda::bind(fp2,
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boost::lambda::ret<value_type>(boost::lambda::_1[2]),
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boost::lambda::ret<value_type>(boost::lambda::_1[0]),
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boost::lambda::ret<value_type>(boost::lambda::_1[1])),
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boost::lambda::ret<value_type>(boost::lambda::_1[3]));
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handle_test_result(result, data[result.worst()], result.worst(),
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type_name, "boost::math::ellint_3", test);
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std::cout << std::endl;
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}
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template <typename T>
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void do_test_ellint_pi2(T& data, const char* type_name, const char* test)
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{
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typedef typename T::value_type row_type;
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typedef typename row_type::value_type value_type;
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std::cout << "Testing: " << test << std::endl;
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value_type (*fp2)(value_type, value_type) = boost::math::ellint_3;
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boost::math::tools::test_result<value_type> result;
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result = boost::math::tools::test(
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data,
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boost::lambda::bind(fp2,
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boost::lambda::ret<value_type>(boost::lambda::_1[1]),
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boost::lambda::ret<value_type>(boost::lambda::_1[0])),
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boost::lambda::ret<value_type>(boost::lambda::_1[2]));
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handle_test_result(result, data[result.worst()], result.worst(),
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type_name, "boost::math::ellint_3", test);
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std::cout << std::endl;
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}
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template <typename T>
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void test_spots(T, const char* type_name)
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{
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// function values calculated on http://functions.wolfram.com/
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#define SC_(x) static_cast<T>(BOOST_JOIN(x, L))
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static const boost::array<boost::array<T, 4>, 21> data1 = {
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SC_(1), SC_(-1), SC_(0), SC_(-1.557407724654902230506974807458360173087),
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SC_(0), SC_(-4), SC_(0.4), SC_(-4.153623371196831087495427530365430979011),
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SC_(0), SC_(8), SC_(-0.6), SC_(8.935930619078575123490612395578518914416),
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SC_(0), SC_(0.5), SC_(0.25), SC_(0.501246705365439492445236118603525029757890291780157969500480),
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SC_(0), SC_(0.5), SC_(0), SC_(0.5),
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SC_(-2), SC_(0.5), SC_(0), SC_(0.437501067017546278595664813509803743009132067629603474488486),
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SC_(0.25), SC_(0.5), SC_(0), SC_(0.510269830229213412212501938035914557628394166585442994564135),
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SC_(0.75), SC_(0.5), SC_(0), SC_(0.533293253875952645421201146925578536430596894471541312806165),
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SC_(0.75), SC_(0.75), SC_(0), SC_(0.871827580412760575085768367421866079353646112288567703061975),
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SC_(1), SC_(0.25), SC_(0), SC_(0.255341921221036266504482236490473678204201638800822621740476),
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SC_(2), SC_(0.25), SC_(0), SC_(0.261119051639220165094943572468224137699644963125853641716219),
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SC_(1023)/1024, SC_(1.5), SC_(0), SC_(13.2821612239764190363647953338544569682942329604483733197131),
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SC_(0.5), SC_(-1), SC_(0.5), SC_(-1.228014414316220642611298946293865487807),
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SC_(0.5), SC_(1e+10), SC_(0.5), SC_(1.536591003599172091573590441336982730551e+10),
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SC_(-1e+05), SC_(10), SC_(0.75), SC_(0.0347926099493147087821620459290460547131012904008557007934290),
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SC_(-1e+10), SC_(10), SC_(0.875), SC_(0.000109956202759561502329123384755016959364346382187364656768212),
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SC_(-1e+10), SC_(1e+20), SC_(0.875), SC_(1.00000626665567332602765201107198822183913978895904937646809e15),
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SC_(-1e+10), SC_(1608)/1024, SC_(0.875), SC_(0.0000157080616044072676127333183571107873332593142625043567690379),
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1-SC_(1) / 1024, SC_(1e+20), SC_(0.875), SC_(6.43274293944380717581167058274600202023334985100499739678963e21),
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SC_(50), SC_(0.1), SC_(0.25), SC_(0.124573770342749525407523258569507331686458866564082916835900),
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SC_(1.125), SC_(1), SC_(0.25), SC_(1.77299767784815770192352979665283069318388205110727241629752),
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//SC_(1.125), SC_(10), SC_(0.25), SC_(0.662467818678976949597336360256848770217429434745967677192487),
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//SC_(1.125), SC_(3), SC_(0.25), SC_(-0.142697285116693775525461312178015106079842313950476205580178),
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};
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#undef SC_
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do_test_ellint_pi3(data1, type_name, "Elliptic Integral PI: Mathworld Data");
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#include "ellint_pi3_data.ipp"
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do_test_ellint_pi3(ellint_pi3_data, type_name, "Elliptic Integral PI: Random Data");
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#include "ellint_pi3_large_data.ipp"
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do_test_ellint_pi3(ellint_pi3_large_data, type_name, "Elliptic Integral PI: Large Random Data");
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// function values calculated on http://functions.wolfram.com/
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#define SC_(x) static_cast<T>(BOOST_JOIN(x, L))
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static const boost::array<boost::array<T, 3>, 9> data2 = {
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SC_(0), SC_(0.2), SC_(1.586867847454166237308008033828114192951),
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SC_(0), SC_(0.4), SC_(1.639999865864511206865258329748601457626),
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SC_(0), SC_(0), SC_(1.57079632679489661923132169163975144209858469968755291048747),
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SC_(0.5), SC_(0), SC_(2.221441469079183123507940495030346849307),
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SC_(-4), SC_(0.3), SC_(0.712708870925620061597924858162260293305195624270730660081949),
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SC_(-1e+05), SC_(-0.5), SC_(0.00496944596485066055800109163256108604615568144080386919012831),
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SC_(-1e+10), SC_(-0.75), SC_(0.0000157080225184890546939710019277357161497407143903832703317801),
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SC_(1) / 1024, SC_(-0.875), SC_(2.18674503176462374414944618968850352696579451638002110619287),
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SC_(1023)/1024, SC_(-0.875), SC_(101.045289804941384100960063898569538919135722087486350366997),
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};
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#undef SC_
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do_test_ellint_pi2(data2, type_name, "Complete Elliptic Integral PI: Mathworld Data");
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#include "ellint_pi2_data.ipp"
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do_test_ellint_pi2(ellint_pi2_data, type_name, "Complete Elliptic Integral PI: Random Data");
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// Special cases, exceptions etc:
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BOOST_CHECK_THROW(boost::math::ellint_3(T(1.0001), T(-1), T(0)), std::domain_error);
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BOOST_CHECK_THROW(boost::math::ellint_3(T(0.5), T(20), T(1.5)), std::domain_error);
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BOOST_CHECK_THROW(boost::math::ellint_3(T(1.0001), T(-1)), std::domain_error);
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BOOST_CHECK_THROW(boost::math::ellint_3(T(0.5), T(1)), std::domain_error);
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BOOST_CHECK_THROW(boost::math::ellint_3(T(0.5), T(2)), std::domain_error);
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}
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int test_main(int, char* [])
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{
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expected_results();
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test_spots(0.0F, "float");
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test_spots(0.0, "double");
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#ifndef BOOST_MATH_NO_LONG_DOUBLE_MATH_FUNCTIONS
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test_spots(0.0L, "long double");
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#ifndef BOOST_MATH_NO_REAL_CONCEPT_TESTS
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test_spots(boost::math::concepts::real_concept(0), "real_concept");
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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::cout;
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#endif
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return 0;
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}
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