// (C) Copyright John Maddock 2007.
// Use, modification and distribution are subject to the
// Boost Software License, Version 1.0. (See accompanying file
// LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_0.txt)
#include <pch_light.hpp>
#include "test_bessel_j.hpp"
//
// DESCRIPTION:
// ~~~~~~~~~~~~
//
// This file tests the bessel functions. There are two sets of tests, spot
// tests which compare our results with selected values computed
// using the online special function calculator at
// functions.wolfram.com, while the bulk of the accuracy tests
// use values generated with NTL::RR at 1000-bit precision
// and our generic versions of these functions.
//
// Note that when this file is first run on a new platform many of
// these tests will fail: the default accuracy is 1 epsilon which
// is too tight for most platforms. In this situation you will
// need to cast a human eye over the error rates reported and make
// a judgement as to whether they are acceptable. Either way please
// report the results to the Boost mailing list. Acceptable rates of
// error are marked up below as a series of regular expressions that
// identify the compiler/stdlib/platform/data-type/test-data/test-function
// along with the maximum expected peek and RMS mean errors for that
// test.
//
void expected_results()
{
//
// Define the max and mean errors expected for
// various compilers and platforms.
//
const char* largest_type;
#ifndef BOOST_MATH_NO_LONG_DOUBLE_MATH_FUNCTIONS
if(boost::math::policies::digits<double, boost::math::policies::policy<> >() == boost::math::policies::digits<long double, boost::math::policies::policy<> >())
{
largest_type = "(long\\s+)?double|real_concept";
}
else
{
largest_type = "long double|real_concept";
}
#else
largest_type = "(long\\s+)?double";
#endif
//
// HP-UX specific rates:
//
// Error rate for double precision are limited by the accuracy of
// the approximations use, which bracket rather than preserve the root.
//
add_expected_result(
".*", // compiler
".*", // stdlib
"HP-UX", // platform
largest_type, // test type(s)
".*J0.*Tricky.*", // test data group
".*", 80000000000LL, 80000000000LL); // test function
add_expected_result(
".*", // compiler
".*", // stdlib
"HP-UX", // platform
largest_type, // test type(s)
".*J1.*Tricky.*", // test data group
".*", 3000000, 2000000); // test function
add_expected_result(
".*", // compiler
".*", // stdlib
"HP-UX", // platform
"double", // test type(s)
".*Tricky.*", // test data group
".*", 100000, 100000); // test function
add_expected_result(
".*", // compiler
".*", // stdlib
"HP-UX", // platform
largest_type, // test type(s)
".*J.*Tricky.*", // test data group
".*", 3000, 500); // test function
//
// HP Tru64:
//
add_expected_result(
".*Tru64.*", // compiler
".*", // stdlib
".*", // platform
"double", // test type(s)
".*Tricky.*", // test data group
".*", 100000, 100000); // test function
add_expected_result(
".*Tru64.*", // compiler
".*", // stdlib
".*", // platform
largest_type, // test type(s)
".*Tricky large.*", // test data group
".*", 3000, 1000); // test function
//
// Solaris specific rates:
//
// Error rate for double precision are limited by the accuracy of
// the approximations use, which bracket rather than preserve the root.
//
add_expected_result(
".*", // compiler
".*", // stdlib
"Sun Solaris", // platform
largest_type, // test type(s)
"Bessel J: Random Data.*Tricky.*", // test data group
".*", 3000, 500); // test function
add_expected_result(
".*", // compiler
".*", // stdlib
"Sun Solaris", // platform
"double", // test type(s)
".*Tricky.*", // test data group
".*", 200000, 100000); // test function
add_expected_result(
".*", // compiler
".*", // stdlib
"Sun Solaris", // platform
largest_type, // test type(s)
".*J.*tricky.*", // test data group
".*", 400000000, 200000000); // test function
//
// Mac OS X:
//
add_expected_result(
".*", // compiler
".*", // stdlib
"Mac OS", // platform
largest_type, // test type(s)
".*J0.*Tricky.*", // test data group
".*", 400000000, 400000000); // test function
add_expected_result(
".*", // compiler
".*", // stdlib
"Mac OS", // platform
largest_type, // test type(s)
".*J1.*Tricky.*", // test data group
".*", 3000000, 2000000); // test function
add_expected_result(
".*", // compiler
".*", // stdlib
"Mac OS", // platform
largest_type, // test type(s)
"Bessel JN.*", // test data group
".*", 40000, 20000); // test function
add_expected_result(
".*", // compiler
".*", // stdlib
"Mac OS", // platform
largest_type, // test type(s)
"Bessel J:.*", // test data group
".*", 50000, 20000); // test function
//
// Linux specific results:
//
// sin and cos appear to have only double precision for large
// arguments on some linux distros:
//
add_expected_result(
".*", // compiler
".*", // stdlib
"linux", // platform
largest_type, // test type(s)
".*J:.*", // test data group
".*", 40000, 30000); // test function
#ifndef BOOST_MATH_NO_LONG_DOUBLE_MATH_FUNCTIONS
if((std::numeric_limits<double>::digits != std::numeric_limits<long double>::digits)
&& (std::numeric_limits<long double>::digits < 90))
{
// some errors spill over into type double as well:
add_expected_result(
".*", // compiler
".*", // stdlib
".*", // platform
"double", // test type(s)
".*J0.*Tricky.*", // test data group
".*", 400000, 400000); // test function
add_expected_result(
".*", // compiler
".*", // stdlib
".*", // platform
"double", // test type(s)
".*J1.*Tricky.*", // test data group
".*", 5000, 5000); // test function
add_expected_result(
".*", // compiler
".*", // stdlib
".*", // platform
"double", // test type(s)
".*(JN|j).*|.*Tricky.*", // test data group
".*", 50, 50); // test function
add_expected_result(
".*", // compiler
".*", // stdlib
".*", // platform
"double", // test type(s)
".*", // test data group
".*", 30, 30); // test function
//
// and we have a few cases with higher limits as well:
//
add_expected_result(
".*", // compiler
".*", // stdlib
".*", // platform
largest_type, // test type(s)
".*J0.*Tricky.*", // test data group
".*", 400000000, 400000000); // test function
add_expected_result(
".*", // compiler
".*", // stdlib
".*", // platform
largest_type, // test type(s)
".*J1.*Tricky.*", // test data group
".*", 5000000, 5000000); // test function
add_expected_result(
".*", // compiler
".*", // stdlib
".*", // platform
largest_type, // test type(s)
".*(JN|j).*|.*Tricky.*", // test data group
".*", 33000, 20000); // test function
}
#endif
add_expected_result(
".*", // compiler
".*", // stdlib
".*", // platform
largest_type, // test type(s)
".*J0.*Tricky.*", // test data group
".*", 400000000, 400000000); // test function
add_expected_result(
".*", // compiler
".*", // stdlib
".*", // platform
largest_type, // test type(s)
".*J1.*Tricky.*", // test data group
".*", 5000000, 5000000); // test function
add_expected_result(
".*", // compiler
".*", // stdlib
".*", // platform
largest_type, // test type(s)
"Bessel j:.*|Bessel JN: Mathworld.*|.*Tricky.*", // test data group
".*", 1500, 700); // test function
add_expected_result(
".*", // compiler
".*", // stdlib
".*", // platform
largest_type, // test type(s)
".*", // test data group
".*", 40, 20); // test function
//
// One set of float tests has inexact input values, so there is a slight error:
//
add_expected_result(
".*", // compiler
".*", // stdlib
".*", // platform
"float", // test type(s)
"Bessel J: Mathworld Data", // test data group
".*", 20, 20); // test function
//
// Finish off by printing out the compiler/stdlib/platform names,
// we do this to make it easier to mark up expected error rates.
//
std::cout << "Tests run with " << BOOST_COMPILER << ", "
<< BOOST_STDLIB << ", " << BOOST_PLATFORM << std::endl;
}
BOOST_AUTO_TEST_CASE( test_main )
{
#ifdef TEST_GSL
gsl_set_error_handler_off();
#endif
expected_results();
BOOST_MATH_CONTROL_FP;
test_bessel(0.1F, "float");
test_bessel(0.1, "double");
#ifndef BOOST_MATH_NO_LONG_DOUBLE_MATH_FUNCTIONS
test_bessel(0.1L, "long double");
#ifndef BOOST_MATH_NO_REAL_CONCEPT_TESTS
test_bessel(boost::math::concepts::real_concept(0.1), "real_concept");
#endif
#else
std::cout << "<note>The long double tests have been disabled on this platform "
"either because the long double overloads of the usual math functions are "
"not available at all, or because they are too inaccurate for these tests "
"to pass.</note>" << std::endl;
#endif
}