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296 lines
12 KiB
C++
296 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/laguerre.hpp>
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#include <boost/math/constants/constants.hpp>
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#include <boost/array.hpp>
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#if !BOOST_WORKAROUND(__BORLANDC__, BOOST_TESTED_AT(0x582))
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#include <boost/lambda/lambda.hpp>
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#include <boost/lambda/bind.hpp>
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#endif
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#include "handle_test_result.hpp"
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#include "test_legendre_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 Laguerre polynomials.
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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::policies::digits<double, boost::math::policies::policy<> >() == boost::math::policies::digits<long double, boost::math::policies::policy<> >())
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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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// Linux special cases, error rates seem to be much higer here
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// even though the implementation contains nothing but basic
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// arithmetic?
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//
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if((std::numeric_limits<long double>::digits <= 64)
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&& (std::numeric_limits<long double>::digits != std::numeric_limits<double>::digits))
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{
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#ifndef BOOST_MATH_NO_LONG_DOUBLE_MATH_FUNCTIONS
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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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".*", 10, 5); // test function
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#endif
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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.*|Mac OS|Sun.*", // platform
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largest_type, // test type(s)
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".*", // test data group
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".*", 40000, 1000); // test function
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add_expected_result(
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".*", // compiler
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".*", // stdlib
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"linux.*|Mac OS|Sun.*", // platform
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"real_concept", // test type(s)
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".*", // test data group
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".*", 40000, 1000); // test function
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add_expected_result(
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".*mingw.*", // 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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".*", 40000, 1000); // test function
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add_expected_result(
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".*mingw.*", // 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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".*", 40000, 1000); // 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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largest_type, // test type(s)
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".*", // test data group
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".*", 4000, 500); // 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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".*", 4000, 500); // 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_laguerre2(const T& data, const char* type_name, const char* test_name)
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{
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#if !BOOST_WORKAROUND(__BORLANDC__, BOOST_TESTED_AT(0x582))
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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::laguerre;
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typedef unsigned (*cast_t)(value_type);
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cast_t rc = &boost::math::tools::real_cast<unsigned, 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 laguerre 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<unsigned>(
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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::laguerre(n, x)", test_name);
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std::cout << std::endl;
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#endif
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}
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template <class T>
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void do_test_laguerre3(const T& data, const char* type_name, const char* test_name)
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{
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#if !BOOST_WORKAROUND(__BORLANDC__, BOOST_TESTED_AT(0x582))
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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, unsigned, value_type);
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pg funcp = boost::math::laguerre;
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typedef unsigned (*cast_t)(value_type);
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cast_t rc = &boost::math::tools::real_cast<unsigned, 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 laguerre 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<unsigned>(
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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<unsigned>(
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boost::lambda::bind(
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rc,
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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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boost::lambda::ret<value_type>(boost::lambda::_1[3]));
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handle_test_result(result, data[result.worst()], result.worst(), type_name, "boost::math::laguerre(n, m, x)", test_name);
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std::cout << std::endl;
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#endif
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}
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template <class T>
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void test_laguerre(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 "laguerre2.ipp"
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do_test_laguerre2(laguerre2, name, "Laguerre Polynomials");
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# include "laguerre3.ipp"
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do_test_laguerre3(laguerre3, name, "Associated Laguerre Polynomials");
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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 100 epsilon:
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//
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T tolerance = boost::math::tools::epsilon<T>() * 100;
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BOOST_CHECK_CLOSE_FRACTION(::boost::math::laguerre(1, static_cast<T>(0.5L)), static_cast<T>(0.5L), tolerance);
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BOOST_CHECK_CLOSE_FRACTION(::boost::math::laguerre(4, static_cast<T>(0.5L)), static_cast<T>(-0.3307291666666666666666666666666666666667L), tolerance);
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BOOST_CHECK_CLOSE_FRACTION(::boost::math::laguerre(7, static_cast<T>(0.5L)), static_cast<T>(-0.5183392237103174603174603174603174603175L), tolerance);
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BOOST_CHECK_CLOSE_FRACTION(::boost::math::laguerre(20, static_cast<T>(0.5L)), static_cast<T>(0.3120174870800154148915399248893113634676L), tolerance);
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BOOST_CHECK_CLOSE_FRACTION(::boost::math::laguerre(50, static_cast<T>(0.5L)), static_cast<T>(-0.3181388060269979064951118308575628226834L), tolerance);
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BOOST_CHECK_CLOSE_FRACTION(::boost::math::laguerre(1, static_cast<T>(-0.5L)), static_cast<T>(1.5L), tolerance);
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BOOST_CHECK_CLOSE_FRACTION(::boost::math::laguerre(4, static_cast<T>(-0.5L)), static_cast<T>(3.835937500000000000000000000000000000000L), tolerance);
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BOOST_CHECK_CLOSE_FRACTION(::boost::math::laguerre(7, static_cast<T>(-0.5L)), static_cast<T>(7.950934709821428571428571428571428571429L), tolerance);
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BOOST_CHECK_CLOSE_FRACTION(::boost::math::laguerre(20, static_cast<T>(-0.5L)), static_cast<T>(76.12915699869631476833699787070874048223L), tolerance);
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BOOST_CHECK_CLOSE_FRACTION(::boost::math::laguerre(50, static_cast<T>(-0.5L)), static_cast<T>(2307.428631277506570629232863491518399720L), tolerance);
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BOOST_CHECK_CLOSE_FRACTION(::boost::math::laguerre(1, static_cast<T>(4.5L)), static_cast<T>(-3.500000000000000000000000000000000000000L), tolerance);
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BOOST_CHECK_CLOSE_FRACTION(::boost::math::laguerre(4, static_cast<T>(4.5L)), static_cast<T>(0.08593750000000000000000000000000000000000L), tolerance);
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BOOST_CHECK_CLOSE_FRACTION(::boost::math::laguerre(7, static_cast<T>(4.5L)), static_cast<T>(-1.036928013392857142857142857142857142857L), tolerance);
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BOOST_CHECK_CLOSE_FRACTION(::boost::math::laguerre(20, static_cast<T>(4.5L)), static_cast<T>(1.437239150257817378525582974722170737587L), tolerance);
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BOOST_CHECK_CLOSE_FRACTION(::boost::math::laguerre(50, static_cast<T>(4.5L)), static_cast<T>(-0.7795068145562651416494321484050019245248L), tolerance);
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BOOST_CHECK_CLOSE_FRACTION(::boost::math::laguerre(4, 5, static_cast<T>(0.5L)), static_cast<T>(88.31510416666666666666666666666666666667L), tolerance);
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BOOST_CHECK_CLOSE_FRACTION(::boost::math::laguerre(10, 0, static_cast<T>(2.5L)), static_cast<T>(-0.8802526766660982969576719576719576719577L), tolerance);
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BOOST_CHECK_CLOSE_FRACTION(::boost::math::laguerre(10, 1, static_cast<T>(4.5L)), static_cast<T>(1.564311458042689732142857142857142857143L), tolerance);
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BOOST_CHECK_CLOSE_FRACTION(::boost::math::laguerre(10, 6, static_cast<T>(8.5L)), static_cast<T>(20.51596541066649098875661375661375661376L), tolerance);
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BOOST_CHECK_CLOSE_FRACTION(::boost::math::laguerre(10, 12, static_cast<T>(12.5L)), static_cast<T>(-199.5560968456234671241181657848324514991L), tolerance);
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BOOST_CHECK_CLOSE_FRACTION(::boost::math::laguerre(50, 40, static_cast<T>(12.5L)), static_cast<T>(-4.996769495006119488583146995907246595400e16L), tolerance);
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}
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int test_main(int, char* [])
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{
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#ifndef BOOST_MATH_BUGGY_LARGE_FLOAT_CONSTANTS
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test_spots(0.0F, "float");
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#endif
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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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#ifndef BOOST_MATH_BUGGY_LARGE_FLOAT_CONSTANTS
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test_laguerre(0.1F, "float");
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#endif
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test_laguerre(0.1, "double");
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#ifndef BOOST_MATH_NO_LONG_DOUBLE_MATH_FUNCTIONS
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test_laguerre(0.1L, "long double");
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#ifndef BOOST_MATH_NO_REAL_CONCEPT_TESTS
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test_laguerre(boost::math::concepts::real_concept(0.1), "real_concept");
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#endif
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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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