mirror of
https://github.com/boostorg/math.git
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4bdf0dd8f0
Added new optimisation config options (still need documenting). Tidied up use of instrumentation code so they all use BOOST_MATH_INSTRUMENT now. Various tweaks to inverse incomplete beta and gamma to reduce number of iterations. Changed incomplete gamma and beta to calculate derivative at the same time as the function (performance optimisation for inverses). Fixed MinGW failures. Refactored and extended rational / polynomial test cases. [SVN r4172]
492 lines
22 KiB
C++
492 lines
22 KiB
C++
// (C) Copyright John Maddock 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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#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/bessel.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 "handle_test_result.hpp"
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#include "test_bessel_hooks.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 bessel functions. 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|real_concept";
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}
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else
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{
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largest_type = "long double|real_concept";
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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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// HP-UX specific rates:
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//
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// Does this need more investigation or is test data limited????
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add_expected_result(
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".*", // compiler
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".*", // stdlib
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"HP-UX", // platform
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"double", // test type(s)
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".*Tricky.*", // test data group
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".*", 100000, 100000); // test function
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add_expected_result(
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".*", // compiler
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".*", // stdlib
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"HP-UX", // platform
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largest_type, // test type(s)
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".*J0.*Tricky.*", // test data group
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".*", 80000000000LL, 80000000000LL); // test function
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add_expected_result(
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".*", // compiler
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".*", // stdlib
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"HP-UX", // platform
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largest_type, // test type(s)
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".*J1.*Tricky.*", // test data group
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".*", 3000000, 2000000); // test function
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add_expected_result(
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".*", // compiler
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".*", // stdlib
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"HP-UX", // platform
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largest_type, // test type(s)
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".*J.*Tricky.*", // test data group
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".*", 3000, 500); // test function
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//
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// Mac OS X:
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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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"Mac OS", // platform
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largest_type, // test type(s)
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"Bessel JN.*", // test data group
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".*", 40000, 20000); // test function
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add_expected_result(
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".*", // compiler
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".*", // stdlib
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"Mac OS", // platform
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largest_type, // test type(s)
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"Bessel J:.*", // test data group
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".*", 50000, 20000); // test function
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// This shouldn't be required, could be limited test data precision
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// i.e. not enough bits in double input to get double result.
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add_expected_result(
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".*", // compiler
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".*", // stdlib
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"Mac OS", // platform
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"double", // test type(s)
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".*Tricky.*", // test data group
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".*", 100000, 100000); // test function
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//
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// Linux specific results:
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//
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// sin and cos appear to have only double precision for large
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// arguments on some linux distros:
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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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"linux", // platform
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largest_type, // test type(s)
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".*J:.*", // test data group
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".*", 40000, 30000); // test function
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if((std::numeric_limits<double>::digits != std::numeric_limits<long double>::digits)
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&& (std::numeric_limits<long double>::digits < 90))
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{
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// some errors spill over into type double as well:
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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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"double", // test type(s)
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".*J0.*Tricky.*", // test data group
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".*", 400000, 400000); // 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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"double", // test type(s)
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".*J1.*Tricky.*", // test data group
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".*", 5000, 5000); // 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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"double", // test type(s)
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".*(JN|j).*|.*Tricky.*", // test data group
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".*", 50, 50); // 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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"double", // test type(s)
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".*", // test data group
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".*", 30, 30); // test function
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//
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// and we have a few cases with higher limits as well:
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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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".*J0.*Tricky.*", // test data group
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".*", 400000000, 400000000); // 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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".*J1.*Tricky.*", // test data group
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".*", 5000000, 5000000); // 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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".*(JN|j).*|.*Tricky.*", // test data group
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".*", 33000, 20000); // test function
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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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".*J0.*Tricky.*", // test data group
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".*", 400000000, 400000000); // 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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".*J1.*Tricky.*", // test data group
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".*", 5000000, 5000000); // 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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".*JN.*Integer.*", // test data group
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".*", 30000, 10000); // 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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".*(JN|j).*|.*Tricky.*", // test data group
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".*", 1500, 700); // 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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".*", 40, 20); // 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_cyl_bessel_j(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, value_type);
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pg funcp = boost::math::cyl_bessel_j;
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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 cyl_bessel_j 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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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::cyl_bessel_j", test_name);
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std::cout << std::endl;
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#ifdef TEST_OTHER
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if(boost::is_floating_point<value_type>::value)
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{
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funcp = other::cyl_bessel_j;
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//
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// test other::cyl_bessel_j 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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boost::lambda::ret<value_type>(boost::lambda::_1[2]));
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handle_test_result(result, data[result.worst()], result.worst(), type_name, "other::cyl_bessel_j", test_name);
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std::cout << std::endl;
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}
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#endif
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}
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template <class T>
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T cyl_bessel_j_int_wrapper(T v, T x)
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{
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return static_cast<T>(boost::math::cyl_bessel_j(boost::math::tools::real_cast<int>(v), x));
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}
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template <class T>
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void do_test_cyl_bessel_j_int(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, value_type);
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pg funcp = cyl_bessel_j_int_wrapper;
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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 cyl_bessel_j 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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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::cyl_bessel_j", 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_sph_bessel_j(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)(unsigned, value_type);
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pg funcp = boost::math::sph_bessel;
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typedef int (*cast_t)(value_type);
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cast_t rc = &boost::math::tools::real_cast<int, value_type>;
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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 sph_bessel 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<int>(
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boost::lambda::bind(
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rc,
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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[2]));
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handle_test_result(result, data[result.worst()], result.worst(), type_name, "boost::math::sph_bessel", 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_bessel(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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// 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>, 8> j0_data = {{
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{ SC_(0), SC_(0), SC_(1) },
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{ SC_(0), SC_(1), SC_(0.7651976865579665514497175261026632209093) },
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{ SC_(0), SC_(-2), SC_(0.2238907791412356680518274546499486258252) },
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{ SC_(0), SC_(4), SC_(-0.3971498098638473722865907684516980419756) },
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{ SC_(0), SC_(-8), SC_(0.1716508071375539060908694078519720010684) },
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{ SC_(0), SC_(1e-05), SC_(0.999999999975000000000156249999999565972) },
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{ SC_(0), SC_(1e-10), SC_(0.999999999999999999997500000000000000000) },
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{ SC_(0), SC_(-1e+01), SC_(-0.2459357644513483351977608624853287538296) },
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}};
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static const boost::array<boost::array<T, 3>, 6> j0_tricky = {{
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// Big numbers make the accuracy of std::sin the limiting factor:
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{ SC_(0), SC_(1e+03), SC_(0.02478668615242017456133073111569370878617) },
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{ SC_(0), SC_(1e+05), SC_(-0.001719201116235972192570601477073201747532) },
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// test at the roots:
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{ SC_(0), SC_(2521642)/(1024 * 1024), SC_(1.80208819970046790002973759410972422387259992955354630042138e-7) },
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{ SC_(0), SC_(5788221)/(1024 * 1024), SC_(-1.37774249380686777043369399806210229535671843632174587432454e-7) },
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{ SC_(0), SC_(9074091)/(1024 * 1024), SC_(1.03553057441100845081018471279571355857520645127532785991335e-7) },
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{ SC_(0), SC_(12364320)/(1024 * 1024), SC_(-3.53017140778223781420794006033810387155048392363051866610931e-9) }
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}};
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static const boost::array<boost::array<T, 3>, 8> j1_data = {
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SC_(1), SC_(0), SC_(0),
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SC_(1), SC_(1), SC_(0.4400505857449335159596822037189149131274),
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SC_(1), SC_(-2), SC_(-0.5767248077568733872024482422691370869203),
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SC_(1), SC_(4), SC_(-6.604332802354913614318542080327502872742e-02),
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SC_(1), SC_(-8), SC_(-0.2346363468539146243812766515904546115488),
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SC_(1), SC_(1e-05), SC_(4.999999999937500000000260416666666124132e-06),
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SC_(1), SC_(1e-10), SC_(4.999999999999999999993750000000000000000e-11),
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SC_(1), SC_(-1e+01), SC_(-4.347274616886143666974876802585928830627e-02),
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};
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static const boost::array<boost::array<T, 3>, 5> j1_tricky = {
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// Big numbers make the accuracy of std::sin the limiting factor:
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SC_(1), SC_(1e+03), SC_(4.728311907089523917576071901216916285418e-03),
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SC_(1), SC_(1e+05), SC_(1.846757562882567716362123967114215743694e-03),
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// test zeros:
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SC_(1), SC_(4017834)/(1024*1024), SC_(3.53149033321258645807835062770856949751958513973522222203044e-7),
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SC_(1), SC_(7356375)/(1024*1024), SC_(-2.31227973111067286051984021150135526024117175836722748404342e-7),
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SC_(1), SC_(10667654)/(1024*1024), SC_(1.24591331097191900488116495350277530373473085499043086981229e-7),
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};
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static const boost::array<boost::array<T, 3>, 14> jn_data = {
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SC_(2), SC_(0), SC_(0),
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SC_(2), SC_(1e-02), SC_(1.249989583365885362413250958437642113452e-05),
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SC_(5), SC_(10), SC_(-0.2340615281867936404436949416457777864635),
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SC_(5), SC_(-10), SC_(0.2340615281867936404436949416457777864635),
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SC_(-5), SC_(1e+06), SC_(7.259643842453285052375779970433848914846e-04),
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SC_(5), SC_(1e+06), SC_(-0.000725964384245328505237577997043384891484649290328285235308619),
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SC_(-5), SC_(-1), SC_(2.497577302112344313750655409880451981584e-04),
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SC_(10), SC_(10), SC_(0.2074861066333588576972787235187534280327),
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SC_(10), SC_(-10), SC_(0.2074861066333588576972787235187534280327),
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SC_(10), SC_(-5), SC_(1.467802647310474131107532232606627020895e-03),
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SC_(-10), SC_(1e+06), SC_(-3.310793117604488741264958559035744460210e-04),
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SC_(10), SC_(1e+06), SC_(-0.000331079311760448874126495855903574446020957243277028930713243),
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SC_(1e+02), SC_(8e+01), SC_(4.606553064823477354141298259169874909670e-06),
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SC_(1e+03), SC_(1e+05), SC_(1.283178112502480365195139312635384057363e-03),
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};
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do_test_cyl_bessel_j(j0_data, name, "Bessel J0: Mathworld Data");
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do_test_cyl_bessel_j(j0_tricky, name, "Bessel J0: Mathworld Data (Tricky cases)");
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do_test_cyl_bessel_j(j1_data, name, "Bessel J1: Mathworld Data");
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do_test_cyl_bessel_j(j1_tricky, name, "Bessel J1: Mathworld Data (tricky cases)");
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do_test_cyl_bessel_j(jn_data, name, "Bessel JN: Mathworld Data");
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do_test_cyl_bessel_j_int(j0_data, name, "Bessel J0: Mathworld Data (Integer Version)");
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do_test_cyl_bessel_j_int(j0_tricky, name, "Bessel J0: Mathworld Data (Tricky cases) (Integer Version)");
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do_test_cyl_bessel_j_int(j1_data, name, "Bessel J1: Mathworld Data (Integer Version)");
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do_test_cyl_bessel_j_int(j1_tricky, name, "Bessel J1: Mathworld Data (tricky cases) (Integer Version)");
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do_test_cyl_bessel_j_int(jn_data, name, "Bessel JN: Mathworld Data (Integer Version)");
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static const boost::array<boost::array<T, 3>, 17> jv_data = {
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//SC_(-2.4), SC_(0), std::numeric_limits<T>::infinity(),
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SC_(2457)/1024, SC_(1)/1024, SC_(3.80739920118603335646474073457326714709615200130620574875292e-9),
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SC_(5.5), SC_(3217)/1024, SC_(0.0281933076257506091621579544064767140470089107926550720453038),
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SC_(-5.5), SC_(3217)/1024, SC_(-2.55820064470647911823175836997490971806135336759164272675969),
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SC_(-5.5), SC_(1e+04), SC_(2.449843111985605522111159013846599118397e-03),
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SC_(5.5), SC_(1e+04), SC_(0.00759343502722670361395585198154817047185480147294665270646578),
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SC_(5.5), SC_(1e+06), SC_(-0.000747424248595630177396350688505919533097973148718960064663632),
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SC_(5.125), SC_(1e+06), SC_(-0.000776600124835704280633640911329691642748783663198207360238214),
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SC_(5.875), SC_(1e+06), SC_(-0.000466322721115193071631008581529503095819705088484386434589780),
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SC_(0.5), SC_(101), SC_(0.0358874487875643822020496677692429287863419555699447066226409),
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SC_(-5.5), SC_(1e+04), SC_(0.00244984311198560552211115901384659911839737686676766460822577),
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SC_(-5.5), SC_(1e+06), SC_(0.000279243200433579511095229508894156656558211060453622750659554),
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|
SC_(-0.5), SC_(101), SC_(0.0708184798097594268482290389188138201440114881159344944791454),
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|
SC_(-10486074) / (1024*1024), SC_(1)/1024, SC_(1.41474013160494695750009004222225969090304185981836460288562e35),
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|
SC_(-10486074) / (1024*1024), SC_(15), SC_(-0.0902239288885423309568944543848111461724911781719692852541489),
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|
SC_(10486074) / (1024*1024), SC_(1e+02), SC_(-0.0547064914615137807616774867984047583596945624129838091326863),
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|
SC_(10486074) / (1024*1024), SC_(2e+04), SC_(-0.00556783614400875611650958980796060611309029233226596737701688),
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|
SC_(-10486074) / (1024*1024), SC_(1e+02), SC_(-0.0547613660316806551338637153942604550779513947674222863858713),
|
|
};
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do_test_cyl_bessel_j(jv_data, name, "Bessel J: Mathworld Data");
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|
|
|
#undef SC_
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#include "bessel_j_int_data.ipp"
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do_test_cyl_bessel_j(bessel_j_int_data, name, "Bessel JN: Random Data");
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|
|
|
#include "bessel_j_data.ipp"
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|
do_test_cyl_bessel_j(bessel_j_data, name, "Bessel J: Random Data");
|
|
|
|
#include "bessel_j_large_data.ipp"
|
|
do_test_cyl_bessel_j(bessel_j_large_data, name, "Bessel J: Random Data (Tricky large values)");
|
|
|
|
#include "sph_bessel_data.ipp"
|
|
do_test_sph_bessel_j(sph_bessel_data, name, "Bessel j: Random Data");
|
|
}
|
|
|
|
int test_main(int, char* [])
|
|
{
|
|
#ifdef TEST_GSL
|
|
gsl_set_error_handler_off();
|
|
#endif
|
|
expected_results();
|
|
|
|
test_bessel(0.1F, "float");
|
|
test_bessel(0.1, "double");
|
|
#ifndef BOOST_MATH_NO_LONG_DOUBLE_MATH_FUNCTIONS
|
|
test_bessel(0.1L, "long double");
|
|
test_bessel(boost::math::concepts::real_concept(0.1), "real_concept");
|
|
#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::cout;
|
|
#endif
|
|
return 0;
|
|
}
|
|
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