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// Copyright (c) 2013 Anton Bikineev
// 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_i_prime.hpp"
//
// DESCRIPTION:
// ~~~~~~~~~~~~
//
// This file tests the bessel I functions derivatives. 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 Boost.Multiprecision at 50 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";
}
else
{
largest_type = "long double";
}
#else
largest_type = "(long\\s+)?double";
#endif
//
// Mac OS has higher error rates, why?
//
add_expected_result(
".*", // compiler
".*", // stdlib
"Mac OS", // platform
largest_type, // test type(s)
".*", // test data group
#ifdef __aarch64__
// Error rates for M1 macs are higher than x86_64 macs
".*", 4000, 1500); // test function
#else
".*", 3500, 1500); // test function
#endif
//
// Cygwin:
//
add_expected_result(
"GNU.*", // Compiler
".*", // Stdlib
"Cygwin*", // Platform
largest_type, // test type(s)
".*", // test data group
".*", 3500, 1000); // test function
//
// G++ on Linux, results vary a bit by processor type,
// on Itanium results are *much* better than listed here,
// but x86 appears to have much less accurate std::pow
// that throws off the results for tgamma(long double)
// which then impacts on the Bessel functions:
//
add_expected_result(
".*", // compiler
".*", // stdlib
"linux", // platform
largest_type, // test type(s)
".*Random.*", // test data group
".*", 600, 200); // test function
add_expected_result(
"GNU.*", // compiler
".*", // stdlib
"Win32.*", // platform
largest_type, // test type(s)
".*Random.*", // test data group
".*", 500, 200); // test function
add_expected_result(
"GNU.*", // compiler
".*", // stdlib
"Win32.*", // platform
largest_type, // test type(s)
".*", // test data group
".*", 3500, 1000); // test function
add_expected_result(
".*", // compiler
".*", // stdlib
".*", // platform
largest_type, // test type(s)
".*I'v.*Mathworld.*", // test data group
".*", 4200, 2000); // test function
add_expected_result(
".*", // compiler
".*", // stdlib
".*Solaris.*", // platform
largest_type, // test type(s)
".*", // test data group
".*", 900, 300); // test function
add_expected_result(
".*", // compiler
".*", // stdlib
".*", // platform
largest_type, // test type(s)
".*", // test data group
".*", 40, 25); // test function
//
// Set error rates a little higher for real_concept -
// now that we use a series approximation for small z
// that relies on tgamma the error rates are a little
// higher only when a Lanczos approximation is not available.
// All other types are unaffected.
//
add_expected_result(
".*", // compiler
".*", // stdlib
".*", // platform
"real_concept", // test type(s)
".*I'v.*Mathworld.*", // test data group
".*", 4500, 2000); // test function
add_expected_result(
".*", // compiler
".*", // stdlib
".*Solaris.*", // platform
"real_concept", // test type(s)
".*", // test data group
".*", 800, 400); // test function
add_expected_result(
".*", // compiler
".*", // stdlib
".*", // platform
"real_concept", // test type(s)
".*", // test data group
".*", 600, 200); // test function
add_expected_result(
".*", // compiler
".*", // stdlib
".*", // platform
"double", // test type(s)
".*", // test data group
".*", 2, 1); // 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;
#ifndef BOOST_MATH_BUGGY_LARGE_FLOAT_CONSTANTS
test_bessel(0.1F, "float");
#endif
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
}
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