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5b9e2ec5a8
Added more Remez code, and appoximations for erf/erfc inverses. Updated and refactored erf code to use new approximations. Added more test cases. [SVN r3210]
314 lines
12 KiB
C++
314 lines
12 KiB
C++
// (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 <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/erf.hpp>
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#include <boost/math/constants/constants.hpp>
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#include <boost/type_traits/is_floating_point.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 "test_erf_hooks.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 functions erf, erfc, and the inverses
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// erf_inv and erfc_inv. 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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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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"Erf Function:.*", // test data group
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"boost::math::erfc?", 20, 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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"Inverse Erfc.*", // test data group
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"boost::math::erfc_inv", 80, 10); // test function
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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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".*", // test type(s)
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"Erf Function:.*", // test data group
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"boost::math::erfc?", 2, 2); // test function
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add_expected_result(
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".*aCC.*", // compiler
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".*", // stdlib
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".*", // platform
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".*", // test type(s)
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"Inverse Erfc.*", // test data group
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"boost::math::erfc_inv", 80, 10); // 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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".*", // test type(s)
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"Inverse Erf.*", // test data group
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"boost::math::erfc?_inv", 18, 4); // 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 <class T>
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void do_test_erf(const T& data, const char* type_name, const char* test_name)
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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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typedef value_type (*pg)(value_type);
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pg funcp = boost::math::erf;
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boost::math::tools::test_result<value_type> result;
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std::cout << "Testing " << test_name << " with type " << type_name
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<< "\n~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~\n";
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//
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// test erf against data:
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//
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result = boost::math::tools::test(
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data,
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boost::lambda::bind(funcp,
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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(), type_name, "boost::math::erf", test_name);
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#ifdef TEST_OTHER
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if(::boost::is_floating_point<value_type>::value){
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funcp = other::erf;
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result = boost::math::tools::test(
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data,
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boost::lambda::bind(funcp,
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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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print_test_result(result, data[result.worst()], result.worst(), type_name, "other::erf");
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}
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#endif
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//
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// test erfc against data:
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//
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funcp = boost::math::erfc;
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result = boost::math::tools::test(
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data,
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boost::lambda::bind(funcp,
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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(), type_name, "boost::math::erfc", test_name);
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#ifdef TEST_OTHER
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if(::boost::is_floating_point<value_type>::value){
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funcp = other::erfc;
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result = boost::math::tools::test(
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data,
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boost::lambda::bind(funcp,
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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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print_test_result(result, data[result.worst()], result.worst(), type_name, "other::erfc");
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}
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#endif
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std::cout << std::endl;
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}
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template <class T>
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void do_test_erf_inv(const T& data, const char* type_name, const char* test_name)
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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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typedef value_type (*pg)(value_type);
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pg funcp = boost::math::erf;
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boost::math::tools::test_result<value_type> result;
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std::cout << "Testing " << test_name << " with type " << type_name
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<< "\n~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~\n";
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//
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// test erf_inv against data:
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//
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funcp = boost::math::erf_inv;
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result = boost::math::tools::test(
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data,
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boost::lambda::bind(funcp,
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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(), type_name, "boost::math::erf_inv", test_name);
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std::cout << std::endl;
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}
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template <class T>
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void do_test_erfc_inv(const T& data, const char* type_name, const char* test_name)
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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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typedef value_type (*pg)(value_type);
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pg funcp = boost::math::erf;
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boost::math::tools::test_result<value_type> result;
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std::cout << "Testing " << test_name << " with type " << type_name
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<< "\n~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~\n";
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//
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// test erfc_inv against data:
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//
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funcp = boost::math::erfc_inv;
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result = boost::math::tools::test(
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data,
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boost::lambda::bind(funcp,
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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(), type_name, "boost::math::erfc_inv", test_name);
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std::cout << std::endl;
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}
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template <class T>
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void test_erf(T, const char* name)
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{
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//
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// The actual test data is rather verbose, so it's in a separate file
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//
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// The contents are as follows, each row of data contains
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// three items, input value a, input value b and erf(a, b):
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//
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# include "erf_small_data.ipp"
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do_test_erf(erf_small_data, name, "Erf Function: Small Values");
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# include "erf_data.ipp"
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do_test_erf(erf_data, name, "Erf Function: Medium Values");
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# include "erf_large_data.ipp"
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do_test_erf(erf_large_data, name, "Erf Function: Large Values");
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# include "erf_inv_data.ipp"
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do_test_erf_inv(erf_inv_data, name, "Inverse Erf Function");
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# include "erfc_inv_data.ipp"
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do_test_erfc_inv(erfc_inv_data, name, "Inverse Erfc Function");
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# include "erfc_inv_big_data.ipp"
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if(std::numeric_limits<T>::min_exponent <= -4500)
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{
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do_test_erfc_inv(erfc_inv_big_data, name, "Inverse Erfc Function: extreme values");
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}
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}
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template <class T>
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void test_spots(T, const char* t)
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{
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std::cout << "Testing basic sanity checks for type " << t << std::endl;
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//
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// basic sanity checks, tolerance is 10 epsilon expressed as a percentage:
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//
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T tolerance = boost::math::tools::epsilon<T>() * 1000;
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BOOST_CHECK_CLOSE(::boost::math::erfc(static_cast<T>(0.125)), static_cast<T>(0.85968379519866618260697055347837660181302041685015L), tolerance);
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BOOST_CHECK_CLOSE(::boost::math::erfc(static_cast<T>(0.5)), static_cast<T>(0.47950012218695346231725334610803547126354842424204L), tolerance);
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BOOST_CHECK_CLOSE(::boost::math::erfc(static_cast<T>(1)), static_cast<T>(0.15729920705028513065877936491739074070393300203370L), tolerance);
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BOOST_CHECK_CLOSE(::boost::math::erfc(static_cast<T>(5)), static_cast<T>(1.5374597944280348501883434853833788901180503147234e-12L), tolerance);
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BOOST_CHECK_CLOSE(::boost::math::erfc(static_cast<T>(-0.125)), static_cast<T>(1.1403162048013338173930294465216233981869795831498L), tolerance);
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BOOST_CHECK_CLOSE(::boost::math::erfc(static_cast<T>(-0.5)), static_cast<T>(1.5204998778130465376827466538919645287364515757580L), tolerance);
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BOOST_CHECK_CLOSE(::boost::math::erfc(static_cast<T>(0)), static_cast<T>(1), tolerance);
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BOOST_CHECK_CLOSE(::boost::math::erf(static_cast<T>(0.125)), static_cast<T>(0.14031620480133381739302944652162339818697958314985L), tolerance);
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BOOST_CHECK_CLOSE(::boost::math::erf(static_cast<T>(0.5)), static_cast<T>(0.52049987781304653768274665389196452873645157575796L), tolerance);
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BOOST_CHECK_CLOSE(::boost::math::erf(static_cast<T>(1)), static_cast<T>(0.84270079294971486934122063508260925929606699796630L), tolerance);
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BOOST_CHECK_CLOSE(::boost::math::erf(static_cast<T>(5)), static_cast<T>(0.9999999999984625402055719651498116565146166211099L), tolerance);
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BOOST_CHECK_CLOSE(::boost::math::erf(static_cast<T>(-0.125)), static_cast<T>(-0.14031620480133381739302944652162339818697958314985L), tolerance);
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BOOST_CHECK_CLOSE(::boost::math::erf(static_cast<T>(-0.5)), static_cast<T>(-0.52049987781304653768274665389196452873645157575796L), tolerance);
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BOOST_CHECK_CLOSE(::boost::math::erf(static_cast<T>(0)), static_cast<T>(0), tolerance);
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tolerance = boost::math::tools::epsilon<T>() * 100 * 200; // 200 eps %.
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#if defined(__CYGWIN__)
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// some platforms long double is only reliably accurate to double precision:
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if(sizeof(T) == sizeof(long double))
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tolerance = boost::math::tools::epsilon<double>() * 100 * 200; // 200 eps %.
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#endif
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for(T i = -0.95f; i < 1; i += 0.125f)
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{
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T inv = boost::math::erf_inv(i);
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T b = boost::math::erf(inv);
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BOOST_CHECK_CLOSE(b, i, tolerance);
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}
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for(T j = 0.125f; j < 2; j += 0.125f)
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{
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T inv = boost::math::erfc_inv(j);
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T b = boost::math::erfc(inv);
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BOOST_CHECK_CLOSE(b, j, tolerance);
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}
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}
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int test_main(int, char* [])
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{
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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(0.1), "real_concept");
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#endif
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expected_results();
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test_erf(0.1F, "float");
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test_erf(0.1, "double");
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#ifndef BOOST_MATH_NO_LONG_DOUBLE_MATH_FUNCTIONS
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test_erf(0.1L, "long double");
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test_erf(boost::math::concepts::real_concept(0.1), "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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