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401 lines
18 KiB
C++
401 lines
18 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/math/special_functions/gamma.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/tools/stats.hpp>
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#include <boost/math/tools/test.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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#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 "test_gamma_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 incomplete gamma function inverses
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// gamma_p_inv and gamma_q_inv. There are three sets of tests:
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// 1) Spot tests which compare our results with selected values
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// computed using the online special function calculator at
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// functions.wolfram.com,
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// 2) Accuracy tests use values generated with NTL::RR at
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// 1000-bit precision and our generic versions of these functions.
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// 3) Round trip sanity checks, use the test data for the forward
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// functions, and verify that we can get (approximately) back
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// where we started.
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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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// Large exponent range causes more extreme test cases to be evaluated:
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//
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if(std::numeric_limits<long double>::max_exponent > std::numeric_limits<double>::max_exponent)
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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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"[^|]*small[^|]*", // test data group
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"[^|]*", 200000, 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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"real_concept", // test type(s)
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"[^|]*small[^|]*", // test data group
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"[^|]*", 70000, 8000); // test function
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}
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//
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// These high error rates are seen on on some Linux
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// architectures:
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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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"[^|]*medium[^|]*", // test data group
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"[^|]*", 350, 5); // test function
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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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"[^|]*large[^|]*", // test data group
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"[^|]*", 150, 5); // 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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"[^|]*medium[^|]*", // test data group
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"[^|]*", 20, 5); // 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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"[^|]*large[^|]*", // test data group
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"[^|]*", 5, 2); // 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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"[^|]*small[^|]*", // test data group
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"[^|]*", 2100, 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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"float|double", // test type(s)
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"[^|]*small[^|]*", // test data group
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"boost::math::gamma_p_inv", 500, 60); // 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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"float|double", // test type(s)
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"[^|]*", // test data group
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"boost::math::gamma_q_inv", 350, 60); // 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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"float|double", // test type(s)
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"[^|]*", // test data group
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"[^|]*", 4, 2); // 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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"[^|]*medium[^|]*", // test data group
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"[^|]*", 20, 5); // 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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"[^|]*large[^|]*", // test data group
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"[^|]*", 1000, 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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"[^|]*small[^|]*", // test data group
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"[^|]*", 3500, 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_gamma_2(const T& data, const char* type_name, const char* test_name)
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{
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//
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// test gamma_p_inv(T, T) against data:
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//
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using namespace std;
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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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std::cout << test_name << " with type " << type_name << std::endl;
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//
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// These sanity checks test for a round trip accuracy of one half
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// of the bits in T, unless T is type float, in which case we check
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// for just one decimal digit. The problem here is the sensitivity
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// of the functions, not their accuracy. This test data was generated
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// for the forward functions, which means that when it is used as
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// the input to the inverses then it is necessarily inexact. This rounding
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// of the input is what makes the data unsuitable for use as an accuracy check,
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// and also demonstrates that you can't in general round-trip these functions.
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// It is however a useful sanity check.
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//
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value_type precision = static_cast<value_type>(ldexp(1.0, 1-boost::math::policies::digits<value_type, boost::math::policies::policy<> >()/2)) * 100;
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if(boost::math::policies::digits<value_type, boost::math::policies::policy<> >() < 50)
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precision = 1; // 1% or two decimal digits, all we can hope for when the input is truncated to float
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for(unsigned i = 0; i < data.size(); ++i)
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{
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//
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// These inverse tests are thrown off if the output of the
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// incomplete gamma is too close to 1: basically there is insuffient
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// information left in the value we're using as input to the inverse
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// to be able to get back to the original value.
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//
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if(data[i][5] == 0)
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BOOST_CHECK_EQUAL(boost::math::gamma_p_inv(data[i][0], data[i][5]), value_type(0));
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else if((1 - data[i][5] > 0.001) && (fabs(data[i][5]) >= boost::math::tools::min_value<value_type>()))
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{
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value_type inv = boost::math::gamma_p_inv(data[i][0], data[i][5]);
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BOOST_CHECK_CLOSE(data[i][1], inv, precision);
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}
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else if(1 == data[i][5])
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BOOST_CHECK_EQUAL(boost::math::gamma_p_inv(data[i][0], data[i][5]), boost::math::tools::max_value<value_type>());
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else
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{
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// not enough bits in our input to get back to x, but we should be in
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// the same ball park:
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value_type inv = boost::math::gamma_p_inv(data[i][0], data[i][5]);
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BOOST_CHECK_CLOSE(data[i][1], inv, 100000);
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}
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if(data[i][3] == 0)
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BOOST_CHECK_EQUAL(boost::math::gamma_q_inv(data[i][0], data[i][3]), boost::math::tools::max_value<value_type>());
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else if((1 - data[i][3] > 0.001) && (fabs(data[i][3]) >= boost::math::tools::min_value<value_type>()))
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{
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value_type inv = boost::math::gamma_q_inv(data[i][0], data[i][3]);
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BOOST_CHECK_CLOSE(data[i][1], inv, precision);
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}
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else if(1 == data[i][3])
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BOOST_CHECK_EQUAL(boost::math::gamma_q_inv(data[i][0], data[i][3]), value_type(0));
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else
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{
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// not enough bits in our input to get back to x, but we should be in
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// the same ball park:
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value_type inv = boost::math::gamma_q_inv(data[i][0], data[i][3]);
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BOOST_CHECK_CLOSE(data[i][1], inv, 100);
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}
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}
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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_gamma_inv(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)(value_type, value_type);
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pg funcp = boost::math::gamma_p_inv;
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using namespace boost::lambda;
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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 gamma_p_inv(T, T) against data:
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//
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result = boost::math::tools::test(
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data,
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bind(funcp, ret<value_type>(_1[0]), ret<value_type>(_1[1])),
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ret<value_type>(_1[2]));
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handle_test_result(result, data[result.worst()], result.worst(), type_name, "boost::math::gamma_p_inv", test_name);
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//
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// test gamma_q_inv(T, T) against data:
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//
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funcp = boost::math::gamma_q_inv;
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result = boost::math::tools::test(
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data,
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bind(funcp, ret<value_type>(_1[0]), ret<value_type>(_1[1])),
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ret<value_type>(_1[3]));
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handle_test_result(result, data[result.worst()], result.worst(), type_name, "boost::math::gamma_q_inv", test_name);
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#endif
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}
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template <class T>
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void test_gamma(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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// First the data for the incomplete gamma function, each
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// row has the following 6 entries:
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// Parameter a, parameter z,
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// Expected tgamma(a, z), Expected gamma_q(a, z)
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// Expected tgamma_lower(a, z), Expected gamma_p(a, z)
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//
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# include "igamma_med_data.ipp"
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do_test_gamma_2(igamma_med_data, name, "Running round trip sanity checks on incomplete gamma medium sized values");
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# include "igamma_small_data.ipp"
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do_test_gamma_2(igamma_small_data, name, "Running round trip sanity checks on incomplete gamma small values");
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# include "igamma_big_data.ipp"
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do_test_gamma_2(igamma_big_data, name, "Running round trip sanity checks on incomplete gamma large values");
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# include "gamma_inv_data.ipp"
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do_test_gamma_inv(gamma_inv_data, name, "incomplete gamma inverse(a, z) medium values");
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# include "gamma_inv_big_data.ipp"
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do_test_gamma_inv(gamma_inv_big_data, name, "incomplete gamma inverse(a, z) large values");
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# include "gamma_inv_small_data.ipp"
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do_test_gamma_inv(gamma_inv_small_data, name, "incomplete gamma inverse(a, z) small values");
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}
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template <class T>
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void test_spots(T, const char* type_name)
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{
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std::cout << "Running spot checks for type " << type_name << std::endl;
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//
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// basic sanity checks, tolerance is 100 epsilon expressed as a percentage:
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//
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T tolerance = boost::math::tools::epsilon<T>() * 10000;
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if(tolerance < 1e-25f)
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tolerance = 1e-25f; // limit of test data?
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BOOST_CHECK_CLOSE(::boost::math::gamma_q_inv(static_cast<T>(1)/100, static_cast<T>(1.0/128)), static_cast<T>(0.35767144525455121503672919307647515332256996883787L), tolerance);
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BOOST_CHECK_CLOSE(::boost::math::gamma_q_inv(static_cast<T>(1)/100, static_cast<T>(0.5)), static_cast<T>(4.4655350189103486773248562646452806745879516124613e-31L), tolerance*10);
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//
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// We can't test in this region against Mathworld's data as the results produced
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// by functions.wolfram.com appear to be in error, and do *not* round trip with
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// their own version of gamma_q. Using our output from the inverse as input to
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// their version of gamma_q *does* round trip however. It should be pointed out
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// that the functions in this area are very sensitive with nearly infinite
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// first derivatives, it's also questionable how useful these functions are
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// in this part of the domain.
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//
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//BOOST_CHECK_CLOSE(::boost::math::gamma_q_inv(static_cast<T>(1e-2), static_cast<T>(1.0-1.0/128)), static_cast<T>(3.8106736649978161389878528903698068142257930575497e-181L), tolerance);
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//
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BOOST_CHECK_CLOSE(::boost::math::gamma_q_inv(static_cast<T>(0.5), static_cast<T>(1.0/128)), static_cast<T>(3.5379794687984498627918583429482809311448951189097L), tolerance);
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BOOST_CHECK_CLOSE(::boost::math::gamma_q_inv(static_cast<T>(0.5), static_cast<T>(1.0/2)), static_cast<T>(0.22746821155978637597125832348982469815821055329511L), tolerance);
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BOOST_CHECK_CLOSE(::boost::math::gamma_q_inv(static_cast<T>(0.5), static_cast<T>(1.0-1.0/128)), static_cast<T>(0.000047938431649305382237483273209405461203600840052182L), tolerance);
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BOOST_CHECK_CLOSE(::boost::math::gamma_q_inv(static_cast<T>(10), static_cast<T>(1.0/128)), static_cast<T>(19.221865946801723949866005318845155649972164294057L), tolerance);
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BOOST_CHECK_CLOSE(::boost::math::gamma_q_inv(static_cast<T>(10), static_cast<T>(1.0/2)), static_cast<T>(9.6687146147141311517500637401166726067778162022664L), tolerance);
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BOOST_CHECK_CLOSE(::boost::math::gamma_q_inv(static_cast<T>(10), static_cast<T>(1.0-1.0/128)), static_cast<T>(3.9754602513640844712089002210120603689809432130520L), tolerance);
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BOOST_CHECK_CLOSE(::boost::math::gamma_q_inv(static_cast<T>(10000), static_cast<T>(1.0/128)), static_cast<T>(10243.369973939134157953734588122880006091919872879L), tolerance);
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BOOST_CHECK_CLOSE(::boost::math::gamma_q_inv(static_cast<T>(10000), static_cast<T>(1.0/2)), static_cast<T>(9999.6666686420474237369661574633153551436435884101L), tolerance);
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BOOST_CHECK_CLOSE(::boost::math::gamma_q_inv(static_cast<T>(10000), static_cast<T>(1.0-1.0/128)), static_cast<T>(9759.8597223369324083191194574874497413261589080204L), tolerance);
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}
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int test_main(int, char* [])
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{
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expected_results();
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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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#if !BOOST_WORKAROUND(__BORLANDC__, BOOST_TESTED_AT(0x582))
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test_spots(boost::math::concepts::real_concept(0.1), "real_concept");
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#endif
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#endif
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#ifndef BOOST_MATH_BUGGY_LARGE_FLOAT_CONSTANTS
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test_gamma(0.1F, "float");
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#endif
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test_gamma(0.1, "double");
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#ifndef BOOST_MATH_NO_LONG_DOUBLE_MATH_FUNCTIONS
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test_gamma(0.1L, "long double");
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#ifndef BOOST_MATH_NO_REAL_CONCEPT_TESTS
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#if !BOOST_WORKAROUND(__BORLANDC__, BOOST_TESTED_AT(0x582))
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test_gamma(boost::math::concepts::real_concept(0.1), "real_concept");
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#endif
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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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