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27f5e4d59e
Added sinh and cosh to ntl.hpp. Fixed FreeBSD test failures (no real long long support). [SVN r3598]
197 lines
7.6 KiB
C++
197 lines
7.6 KiB
C++
// Copyright (c) 2006 Xiaogang Zhang
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// Copyright (c) 2006 John Maddock
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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 <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_2.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 second 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::tools::digits<double>() == boost::math::tools::digits<long double>())
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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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".*", // test data group
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".*", 15, 6); // 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, 6); // 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_e2(const 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_2;
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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_2", 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_e1(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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boost::math::tools::test_result<value_type> result;
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std::cout << "Testing: " << test << std::endl;
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value_type (*fp1)(value_type) = boost::math::ellint_2;
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result = boost::math::tools::test(
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data,
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boost::lambda::bind(fp1,
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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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handle_test_result(result, data[result.worst()], result.worst(),
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type_name, "boost::math::ellint_2", 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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// Note that Mathematica's EllipticE accepts k^2 as the second parameter.
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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>, 10> data1 = {
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SC_(0), SC_(0), SC_(0),
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SC_(-10), SC_(0), SC_(-10),
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SC_(-1), SC_(-1), SC_(-0.84147098480789650665250232163029899962256306079837),
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SC_(-4), SC_(900) / 1024, SC_(-3.1756145986492562317862928524528520686391383168377),
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SC_(8), SC_(-600) / 1024, SC_(7.2473147180505693037677015377802777959345489333465),
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SC_(1e-05), SC_(800) / 1024, SC_(9.999999999898274739584436515967055859383969942432E-6),
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SC_(1e+05), SC_(100) / 1024, SC_(99761.153306972066658135668386691227343323331995888),
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SC_(1e+10), SC_(-0.5), SC_(9.3421545766487137036576748555295222252286528414669e9),
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ldexp(SC_(1), 66), SC_(400) / 1024, SC_(7.0886102721911705466476846969992069994308167515242e19),
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ldexp(SC_(1), 166), SC_(900) / 1024, SC_(7.1259011068364515942912094521783688927118026465790e49),
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};
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#undef SC_
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do_test_ellint_e2(data1, type_name, "Elliptic Integral E: Mathworld Data");
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#include "ellint_e2_data.ipp"
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do_test_ellint_e2(ellint_e2_data, type_name, "Elliptic Integral E: Random Data");
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// Function values calculated on http://functions.wolfram.com/
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// Note that Mathematica's EllipticE accepts k^2 as the second parameter.
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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, 2>, 10> data2 = {
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SC_(-1), SC_(1),
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SC_(0), SC_(1.5707963267948966192313216916397514420985846996876),
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SC_(100) / 1024, SC_(1.5670445330545086723323795143598956428788609133377),
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SC_(200) / 1024, SC_(1.5557071588766556854463404816624361127847775545087),
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SC_(300) / 1024, SC_(1.5365278991162754883035625322482669608948678755743),
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SC_(400) / 1024, SC_(1.5090417763083482272165682786143770446401437564021),
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SC_(-0.5), SC_(1.4674622093394271554597952669909161360253617523272),
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SC_(-600) / 1024, SC_(1.4257538571071297192428217218834579920545946473778),
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SC_(-800) / 1024, SC_(1.2927868476159125056958680222998765985004489572909),
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SC_(-900) / 1024, SC_(1.1966864890248739524112920627353824133420353430982),
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};
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#undef SC_
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do_test_ellint_e1(data2, type_name, "Elliptic Integral E: Mathworld Data");
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#include "ellint_e_data.ipp"
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do_test_ellint_e1(ellint_e_data, type_name, "Elliptic Integral E: Random Data");
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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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test_spots(boost::math::concepts::real_concept(0), "real_concept");
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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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