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321 lines
23 KiB
C++
321 lines
23 KiB
C++
// Copyright John Maddock 2006.
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// Copyright Paul A. Bristow 2007, 2009
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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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#define BOOST_MATH_OVERFLOW_ERROR_POLICY ignore_error
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#include <boost/math/concepts/real_concept.hpp>
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#include <boost/math/special_functions/math_fwd.hpp>
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#include <boost/math/special_functions/gamma.hpp>
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#define BOOST_TEST_MAIN
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#include <boost/test/unit_test.hpp>
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#include <boost/test/tools/floating_point_comparison.hpp>
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#include "../include_private/boost/math/tools/test.hpp"
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#include <boost/math/tools/stats.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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#include "functor.hpp"
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#include "handle_test_result.hpp"
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#include "table_type.hpp"
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#ifndef SC_
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#define SC_(x) static_cast<typename table_type<T>::type>(BOOST_JOIN(x, L))
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#endif
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template <class Real, 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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typedef Real value_type;
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typedef value_type (*pg)(value_type, value_type);
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pg funcp;
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boost::math::tools::test_result<value_type> result;
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#if !(defined(ERROR_REPORTING_MODE) && !defined(IGAMMA_FUNCTION_TO_TEST))
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#ifdef IGAMMA_FUNCTION_TO_TEST
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funcp = IGAMMA_FUNCTION_TO_TEST;
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#elif defined(BOOST_MATH_NO_DEDUCED_FUNCTION_POINTERS)
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funcp = boost::math::tgamma<value_type, value_type>;
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#else
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funcp = boost::math::tgamma;
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#endif
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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 tgamma(T, T) against data:
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//
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if(Real(data[0][2]) > 0)
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{
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result = boost::math::tools::test_hetero<Real>(
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data,
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bind_func<Real>(funcp, 0, 1),
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extract_result<Real>(2));
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handle_test_result(result, data[result.worst()], result.worst(), type_name, "tgamma (incomplete)", test_name);
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//
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// test tgamma_lower(T, T) against data:
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//
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#ifdef IGAMMAL_FUNCTION_TO_TEST
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funcp = IGAMMAL_FUNCTION_TO_TEST;
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#elif defined(BOOST_MATH_NO_DEDUCED_FUNCTION_POINTERS)
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funcp = boost::math::tgamma_lower<value_type, value_type>;
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#else
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funcp = boost::math::tgamma_lower;
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#endif
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result = boost::math::tools::test_hetero<Real>(
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data,
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bind_func<Real>(funcp, 0, 1),
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extract_result<Real>(4));
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handle_test_result(result, data[result.worst()], result.worst(), type_name, "tgamma_lower", test_name);
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}
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#endif
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#if !(defined(ERROR_REPORTING_MODE) && !defined(GAMMAQ_FUNCTION_TO_TEST))
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//
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// test gamma_q(T, T) against data:
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//
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#ifdef GAMMAQ_FUNCTION_TO_TEST
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funcp = GAMMAQ_FUNCTION_TO_TEST;
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#elif defined(BOOST_MATH_NO_DEDUCED_FUNCTION_POINTERS)
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funcp = boost::math::gamma_q<value_type, value_type>;
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#else
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funcp = boost::math::gamma_q;
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#endif
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result = boost::math::tools::test_hetero<Real>(
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data,
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bind_func<Real>(funcp, 0, 1),
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extract_result<Real>(3));
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handle_test_result(result, data[result.worst()], result.worst(), type_name, "gamma_q", test_name);
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//
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// test gamma_p(T, T) against data:
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//
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#ifdef GAMMAP_FUNCTION_TO_TEST
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funcp = GAMMAP_FUNCTION_TO_TEST;
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#elif defined(BOOST_MATH_NO_DEDUCED_FUNCTION_POINTERS)
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funcp = boost::math::gamma_p<value_type, value_type>;
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#else
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funcp = boost::math::gamma_p;
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#endif
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result = boost::math::tools::test_hetero<Real>(
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data,
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bind_func<Real>(funcp, 0, 1),
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extract_result<Real>(5));
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handle_test_result(result, data[result.worst()], result.worst(), type_name, "gamma_p", 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_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<T>(igamma_med_data, name, "tgamma(a, z) medium values");
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# include "igamma_small_data.ipp"
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do_test_gamma_2<T>(igamma_small_data, name, "tgamma(a, z) small values");
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# include "igamma_big_data.ipp"
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do_test_gamma_2<T>(igamma_big_data, name, "tgamma(a, z) large values");
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# include "igamma_int_data.ipp"
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do_test_gamma_2<T>(igamma_int_data, name, "tgamma(a, z) integer and half integer values");
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}
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template <class T>
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void test_spots(T, const char* name = nullptr)
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{
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std::cout << "Testing spot values with type " << name << std::endl;
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//
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// basic sanity checks, tolerance is 10 epsilon expressed as a percentage:
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//
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T tolerance = boost::math::tools::epsilon<T>() * 1000;
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#if (defined(macintosh) || defined(__APPLE__) || defined(__APPLE_CC__))
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tolerance *= 10;
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#endif
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// An extra fudge factor for real_concept which has a less accurate tgamma:
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T tolerance_tgamma_extra = std::numeric_limits<T>::is_specialized ? 1 : 10;
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BOOST_CHECK_CLOSE(::boost::math::tgamma(static_cast<T>(5), static_cast<T>(1)), static_cast<T>(23.912163676143750903709045060494956383977723517065L), tolerance);
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BOOST_CHECK_CLOSE(::boost::math::tgamma(static_cast<T>(5), static_cast<T>(5)), static_cast<T>(10.571838841565097874621959975919877646444998907920L), tolerance);
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BOOST_CHECK_CLOSE(::boost::math::tgamma(static_cast<T>(5), static_cast<T>(10)), static_cast<T>(0.70206451384706574414638719662835463671916532623256L), tolerance);
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BOOST_CHECK_CLOSE(::boost::math::tgamma(static_cast<T>(5), static_cast<T>(100)), static_cast<T>(3.8734332808745531496973774140085644548465762343719e-36L), tolerance);
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BOOST_CHECK_CLOSE(::boost::math::tgamma(static_cast<T>(0.5), static_cast<T>(0.5)), static_cast<T>(0.56241823159440712427949495730204306902676756479651L), tolerance * tolerance_tgamma_extra);
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BOOST_CHECK_CLOSE(::boost::math::tgamma(static_cast<T>(0.5), static_cast<T>(9)/10), static_cast<T>(0.31853210360412109873859360390443790076576777747449L), tolerance*10);
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BOOST_CHECK_CLOSE(::boost::math::tgamma(static_cast<T>(0.5), static_cast<T>(5)), static_cast<T>(0.0027746032604128093194908357272603294120210079791437L), tolerance * tolerance_tgamma_extra);
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BOOST_CHECK_CLOSE(::boost::math::tgamma(static_cast<T>(0.5), static_cast<T>(100)), static_cast<T>(3.7017478604082789202535664481339075721362102520338e-45L), tolerance * tolerance_tgamma_extra);
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BOOST_CHECK_CLOSE(::boost::math::tgamma_lower(static_cast<T>(5), static_cast<T>(1)), static_cast<T>(0.087836323856249096290954939505043616022276482935091L), tolerance);
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BOOST_CHECK_CLOSE(::boost::math::tgamma_lower(static_cast<T>(5), static_cast<T>(5)), static_cast<T>(13.428161158434902125378040024080122353555001092080L), tolerance);
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BOOST_CHECK_CLOSE(::boost::math::tgamma_lower(static_cast<T>(5), static_cast<T>(10)), static_cast<T>(23.297935486152934255853612803371645363280834673767L), tolerance);
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BOOST_CHECK_CLOSE(::boost::math::tgamma_lower(static_cast<T>(5), static_cast<T>(100)), static_cast<T>(23.999999999999999999999999999999999996126566719125L), tolerance);
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BOOST_CHECK_CLOSE(::boost::math::gamma_q(static_cast<T>(5), static_cast<T>(1)), static_cast<T>(0.99634015317265628765454354418728984933240514654437L), tolerance);
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BOOST_CHECK_CLOSE(::boost::math::gamma_q(static_cast<T>(5), static_cast<T>(5)), static_cast<T>(0.44049328506521241144258166566332823526854162116334L), tolerance);
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BOOST_CHECK_CLOSE(::boost::math::gamma_q(static_cast<T>(5), static_cast<T>(10)), static_cast<T>(0.029252688076961072672766133192848109863298555259690L), tolerance);
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BOOST_CHECK_CLOSE(::boost::math::gamma_q(static_cast<T>(5), static_cast<T>(100)), static_cast<T>(1.6139305336977304790405739225035685228527400976549e-37L), tolerance);
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BOOST_CHECK_CLOSE(::boost::math::gamma_q(static_cast<T>(1.5), static_cast<T>(2)), static_cast<T>(0.26146412994911062220282207597592120190281060919079L), tolerance);
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BOOST_CHECK_CLOSE(::boost::math::gamma_q(static_cast<T>(20.5), static_cast<T>(22)), static_cast<T>(0.34575332043467326814971590879658406632570278929072L), tolerance);
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BOOST_CHECK_CLOSE(::boost::math::gamma_p(static_cast<T>(5), static_cast<T>(1)), static_cast<T>(0.0036598468273437123454564558127101506675948534556288L), tolerance);
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BOOST_CHECK_CLOSE(::boost::math::gamma_p(static_cast<T>(5), static_cast<T>(5)), static_cast<T>(0.55950671493478758855741833433667176473145837883666L), tolerance);
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BOOST_CHECK_CLOSE(::boost::math::gamma_p(static_cast<T>(5), static_cast<T>(10)), static_cast<T>(0.97074731192303892732723386680715189013670144474031L), tolerance);
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BOOST_CHECK_CLOSE(::boost::math::gamma_p(static_cast<T>(5), static_cast<T>(100)), static_cast<T>(0.9999999999999999999999999999999999998386069466302L), tolerance);
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BOOST_CHECK_CLOSE(::boost::math::gamma_p(static_cast<T>(1.5), static_cast<T>(2)), static_cast<T>(0.73853587005088937779717792402407879809718939080921L), tolerance);
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BOOST_CHECK_CLOSE(::boost::math::gamma_p(static_cast<T>(20.5), static_cast<T>(22)), static_cast<T>(0.65424667956532673185028409120341593367429721070928L), tolerance);
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// naive check on derivative function:
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using namespace std; // For ADL of std functions
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tolerance = boost::math::tools::epsilon<T>() * 5000; // 50 eps
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BOOST_CHECK_CLOSE(::boost::math::gamma_p_derivative(static_cast<T>(20.5), static_cast<T>(22)),
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exp(static_cast<T>(-22)) * pow(static_cast<T>(22), static_cast<T>(19.5)) / boost::math::tgamma(static_cast<T>(20.5)), tolerance);
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// Bug reports from Rocco Romeo:
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BOOST_CHECK_CLOSE(::boost::math::tgamma(static_cast<T>(20), ldexp(T(1), -40)), static_cast<T>(1.21645100408832000000e17L), tolerance);
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BOOST_CHECK_CLOSE(::boost::math::tgamma_lower(static_cast<T>(20), ldexp(T(1), -40)), static_cast<T>(7.498484069471659696438206828760307317022658816757448882e-243L), tolerance);
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BOOST_CHECK_CLOSE(::boost::math::gamma_p(static_cast<T>(20), ldexp(T(1), -40)), static_cast<T>(6.164230243774976473534975936127139110276824507876192062e-260L), tolerance);
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BOOST_CHECK_CLOSE(::boost::math::tgamma(static_cast<T>(30), ldexp(T(1), -30)), static_cast<T>(8.841761993739701954543616000000e30L), tolerance);
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BOOST_CHECK_CLOSE(::boost::math::tgamma_lower(static_cast<T>(30), ldexp(T(1), -30)), static_cast<T>(3.943507283668378474979245322638092813837393749566146974e-273L), tolerance);
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#ifdef __SUNPRO_CC
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BOOST_CHECK_CLOSE(::boost::math::gamma_p(static_cast<T>(30), ldexp(T(1), -30)), static_cast<T>(4.460092102072560946444018923090222645613009128135650652e-304L), tolerance * 8);
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#else
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BOOST_CHECK_CLOSE(::boost::math::gamma_p(static_cast<T>(30), ldexp(T(1), -30)), static_cast<T>(4.460092102072560946444018923090222645613009128135650652e-304L), tolerance);
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#endif
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BOOST_CHECK_CLOSE(::boost::math::gamma_p_derivative(static_cast<T>(2), ldexp(T(1), -575)), static_cast<T>(8.08634922390438981326119906687585206568664784377654648227177e-174L), tolerance);
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//typedef boost::math::policies::policy<boost::math::policies::overflow_error<boost::math::policies::throw_on_error> > throw_policy;
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BOOST_IF_CONSTEXPR(std::numeric_limits<T>::max_exponent <= 1024 && std::numeric_limits<T>::has_infinity)
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{
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BOOST_CHECK_EQUAL(::boost::math::tgamma(static_cast<T>(176), static_cast<T>(100)), std::numeric_limits<T>::infinity());
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//BOOST_MATH_CHECK_THROW(::boost::math::tgamma(static_cast<T>(176), static_cast<T>(100), throw_policy()), std::overflow_error);
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BOOST_CHECK_EQUAL(::boost::math::tgamma(static_cast<T>(530), static_cast<T>(2000)), std::numeric_limits<T>::infinity());
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BOOST_CHECK_EQUAL(::boost::math::tgamma(static_cast<T>(740), static_cast<T>(2500)), std::numeric_limits<T>::infinity());
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BOOST_CHECK_EQUAL(::boost::math::tgamma(static_cast<T>(530.5), static_cast<T>(2000)), std::numeric_limits<T>::infinity());
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BOOST_CHECK_EQUAL(::boost::math::tgamma(static_cast<T>(740.5), static_cast<T>(2500)), std::numeric_limits<T>::infinity());
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BOOST_CHECK_EQUAL(::boost::math::tgamma_lower(static_cast<T>(10000.0f), static_cast<T>(10000.0f / 4)), std::numeric_limits<T>::infinity());
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}
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BOOST_IF_CONSTEXPR(std::numeric_limits<T>::max_exponent >= 1024)
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{
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BOOST_CHECK_CLOSE(::boost::math::tgamma(static_cast<T>(170), static_cast<T>(165)), static_cast<T>(2.737338337642022829223832094019477918166996032112404370e304L), (std::numeric_limits<T>::digits > 100 ? 10 : 3) * tolerance);
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BOOST_CHECK_CLOSE(::boost::math::tgamma_lower(static_cast<T>(170), static_cast<T>(165)), static_cast<T>(1.531729671362682445715419794880088619901822603944331733e304L), 3 * tolerance);
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BOOST_CHECK_CLOSE(::boost::math::tgamma(static_cast<T>(170), static_cast<T>(170)), static_cast<T>(2.090991698081449410761040647015858316167077909285580375e304L), 10 * tolerance);
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BOOST_CHECK_CLOSE(::boost::math::tgamma_lower(static_cast<T>(170), static_cast<T>(170)), static_cast<T>(2.178076310923255864178211241883708221901740726771155728e304L), 10 * tolerance);
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BOOST_CHECK_CLOSE(::boost::math::tgamma(static_cast<T>(170), static_cast<T>(190)), static_cast<T>(2.8359275512790301602903689596273175148895758522893941392e303L), 10 * tolerance);
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BOOST_CHECK_CLOSE(::boost::math::tgamma_lower(static_cast<T>(170), static_cast<T>(190)), static_cast<T>(3.985475253876802258910214992936834786579861050827796689e304L), 10 * tolerance);
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BOOST_CHECK_CLOSE(::boost::math::tgamma(static_cast<T>(170), static_cast<T>(1000)), static_cast<T>(6.1067635957780723069200425769800190368662985052038980542e72L), 10 * tolerance);
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BOOST_CHECK_CLOSE(::boost::math::tgamma_lower(static_cast<T>(185), static_cast<T>(1)), static_cast<T>(0.001999286058955490074702037576083582139834300307968257924836L), tolerance);
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BOOST_CHECK_CLOSE(::boost::math::tgamma(static_cast<T>(185), static_cast<T>(1500)), static_cast<T>(1.037189524841404054867100938934493979112615962865368623e-67L), tolerance * 10);
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BOOST_CHECK_CLOSE(::boost::math::tgamma(static_cast<T>(36), ldexp(static_cast<T>(1), -26)), static_cast<T>(1.03331479663861449296666513375232000000e40L), tolerance * 10);
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BOOST_CHECK_CLOSE(::boost::math::tgamma(static_cast<T>(50.5), ldexp(static_cast<T>(1), -17)), static_cast<T>(4.2904629123519598109157551960589377e63L), tolerance * 10);
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BOOST_CHECK_CLOSE(::boost::math::tgamma(static_cast<T>(164.5), static_cast<T>(0.125)), static_cast<T>(2.5649307433687542701168405519538910e292L), tolerance * 10);
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}
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//
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// Check very large parameters, see: https://github.com/boostorg/math/issues/168
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//
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T max_val = boost::math::tools::max_value<T>();
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T large_val = max_val * 0.99f;
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BOOST_CHECK_EQUAL(::boost::math::tgamma(static_cast<T>(22.25), max_val), 0);
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BOOST_CHECK_EQUAL(::boost::math::tgamma(static_cast<T>(22.25), large_val), 0);
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BOOST_CHECK_EQUAL(::boost::math::tgamma_lower(static_cast<T>(22.25), max_val), boost::math::tgamma(static_cast<T>(22.25)));
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BOOST_CHECK_EQUAL(::boost::math::tgamma_lower(static_cast<T>(22.25), large_val), boost::math::tgamma(static_cast<T>(22.25)));
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BOOST_CHECK_EQUAL(::boost::math::gamma_q(static_cast<T>(22.25), max_val), 0);
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BOOST_CHECK_EQUAL(::boost::math::gamma_q(static_cast<T>(22.25), large_val), 0);
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BOOST_CHECK_EQUAL(::boost::math::gamma_p(static_cast<T>(22.25), max_val), 1);
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BOOST_CHECK_EQUAL(::boost::math::gamma_p(static_cast<T>(22.25), large_val), 1);
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if (std::numeric_limits<T>::has_infinity)
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{
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BOOST_CHECK_EQUAL(::boost::math::tgamma(static_cast<T>(22.25), std::numeric_limits<T>::infinity()), 0);
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BOOST_CHECK_EQUAL(::boost::math::tgamma_lower(static_cast<T>(22.25), std::numeric_limits<T>::infinity()), boost::math::tgamma(static_cast<T>(22.25)));
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BOOST_CHECK_EQUAL(::boost::math::gamma_q(static_cast<T>(22.25), std::numeric_limits<T>::infinity()), 0);
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BOOST_CHECK_EQUAL(::boost::math::gamma_p(static_cast<T>(22.25), std::numeric_limits<T>::infinity()), 1);
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}
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//
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// Large arguments and small parameters, see https://github.com/boostorg/math/issues/451:
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//
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BOOST_CHECK_EQUAL(::boost::math::gamma_q(static_cast<T>(1770), static_cast<T>(1e-12)), 1);
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BOOST_CHECK_EQUAL(::boost::math::gamma_p(static_cast<T>(1770), static_cast<T>(1e-12)), 0);
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//
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// Check that lgamma_q returns correct values with spot values calculated via wolframalpha log(Q[a, x])
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//
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BOOST_CHECK_CLOSE(::boost::math::lgamma_q(static_cast<T>(5), static_cast<T>(100)), static_cast<T>(-84.71697591169848944613823640968965801339401810393519310714864307L), tolerance);
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BOOST_CHECK_CLOSE(::boost::math::lgamma_q(static_cast<T>(22.5), static_cast<T>(2000)), static_cast<T>(-1883.489773203771543025750308264545743305089849873060383828767138L), tolerance);
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BOOST_CHECK_CLOSE(::boost::math::lgamma_q(static_cast<T>(501.25), static_cast<T>(2000)), static_cast<T>(-810.2453406781655559126505101822969531699112391075198076300675402L), tolerance);
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BOOST_CHECK_CLOSE(::boost::math::lgamma_q(static_cast<T>(20), static_cast<T>(0.25)), static_cast<T>(-2.946458104491857816330873290969917497748067639461638294404e-31L), tolerance);
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BOOST_CHECK_CLOSE(::boost::math::lgamma_q(static_cast<T>(40), static_cast<T>(0.75)), static_cast<T>(-5.930604927955460343652485525435087275997461623988991819824e-54L), tolerance);
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BOOST_CHECK_CLOSE(::boost::math::lgamma_q(static_cast<T>(50), static_cast<T>(2)), static_cast<T>(-5.214301903317168085381693412994550732094621576607843973832e-51L), tolerance);
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BOOST_CHECK_CLOSE(::boost::math::lgamma_q(static_cast<T>(500), static_cast<T>(10)), static_cast<T>(-3.79666711621207197039397438773960431648625558027046365463e-639L), tolerance * 3);
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BOOST_CHECK_CLOSE(::boost::math::lgamma_q(static_cast<T>(5), static_cast<T>(1000)), static_cast<T>(-975.5430287171020511929200293377669175923128826278957569928895945L), tolerance);
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// Pairs of tests that bisect the crossover condition in our code at double and then quad precision:
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BOOST_CHECK_CLOSE(::boost::math::lgamma_q(static_cast<T>(10), static_cast<T>(698.75)), static_cast<T>(-652.5952453102824132865663191324423994628428404928732148525545721L), tolerance);
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BOOST_CHECK_CLOSE(::boost::math::lgamma_q(static_cast<T>(10), static_cast<T>(699.25)), static_cast<T>(-653.0888168445921483147208556398158677077537551419551652934287016L), tolerance);
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BOOST_CHECK_CLOSE(::boost::math::lgamma_q(static_cast<T>(10), static_cast<T>(999.75)), static_cast<T>(-950.3752463850600415679327136010171192193400042422096029239012176L), tolerance);
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BOOST_CHECK_CLOSE(::boost::math::lgamma_q(static_cast<T>(10), static_cast<T>(1000.25)), static_cast<T>(-950.8707509166152482936275883547176592196662090187561681198668099L), tolerance);
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BOOST_CHECK_CLOSE(::boost::math::lgamma_q(static_cast<T>(50), static_cast<T>(698.75)), static_cast<T>(-522.3277960730837166223131189587863209730608668858212533099139269L), tolerance);
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BOOST_CHECK_CLOSE(::boost::math::lgamma_q(static_cast<T>(50), static_cast<T>(699.25)), static_cast<T>(-522.7927997457481265511084805522296021540768033975669071565674196L), tolerance);
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BOOST_CHECK_CLOSE(::boost::math::lgamma_q(static_cast<T>(50), static_cast<T>(999.75)), static_cast<T>(-805.7977867938474339107474131612354353193501692041340771552419902L), tolerance);
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BOOST_CHECK_CLOSE(::boost::math::lgamma_q(static_cast<T>(50), static_cast<T>(1000.25)), static_cast<T>(-806.2733124989172792095030711884568388681331032891850662521501582L), tolerance);
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BOOST_CHECK_CLOSE(::boost::math::lgamma_q(static_cast<T>(800), static_cast<T>(999.75)), static_cast<T>(-24.33274293617739453303937714319703386675839030466670622049929011L), tolerance * 2);
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BOOST_CHECK_CLOSE(::boost::math::lgamma_q(static_cast<T>(800), static_cast<T>(1000.25)), static_cast<T>(-24.43514173634027477093666725985191846106997808357863808910970142L), tolerance * (boost::math::tools::digits<T>() > 54 ? 20 : 1));
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// Once we get large a,x then error start to accumulate no matter what we do:
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BOOST_CHECK_CLOSE(::boost::math::lgamma_q(static_cast<T>(1200), static_cast<T>(1249.75)), static_cast<T>(-2.565496161584661216769813239648606145255794643472303927896044375L), tolerance * (std::is_floating_point<T>::value ? 1 : 4));
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BOOST_CHECK_CLOSE(::boost::math::lgamma_q(static_cast<T>(1200), static_cast<T>(1250.25)), static_cast<T>(-2.591934862117586205519309712218581885256650074210410262843591453L), tolerance * ((std::numeric_limits<T>::max_digits10 >= 36 || std::is_same<T, boost::math::concepts::real_concept>::value) ? 750 : (std::is_same<T, float>::value ? 1 : 50))); // Test fails on ARM64 and s390x long doubles and real_concept types unless tolerance is adjusted
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BOOST_CHECK_CLOSE(::boost::math::lgamma_q(static_cast<T>(2200), static_cast<T>(2249.75)), static_cast<T>(-1.933779894897391651410597618307863427927461116308937004149240320L), tolerance * (std::is_floating_point<T>::value ? 1 : 10));
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BOOST_CHECK_CLOSE(::boost::math::lgamma_q(static_cast<T>(2200), static_cast<T>(2250.25)), static_cast<T>(-1.950346484067948344620463026377077515919992808640737320057812268L), tolerance * (std::is_same<T, float>::value ? 1 : (std::is_floating_point<T>::value ? 100 : 200)));
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//
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// Coverage:
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//
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#ifndef BOOST_MATH_NO_EXCEPTIONS
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BOOST_CHECK_THROW(boost::math::gamma_p(static_cast<T>(-1), static_cast<T>(2)), std::domain_error);
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BOOST_CHECK_THROW(boost::math::gamma_q(static_cast<T>(-1), static_cast<T>(2)), std::domain_error);
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BOOST_CHECK_THROW(boost::math::gamma_p(static_cast<T>(1), static_cast<T>(-2)), std::domain_error);
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BOOST_CHECK_THROW(boost::math::gamma_q(static_cast<T>(1), static_cast<T>(-2)), std::domain_error);
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BOOST_CHECK_THROW(boost::math::gamma_p(static_cast<T>(0), static_cast<T>(2)), std::domain_error);
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BOOST_CHECK_THROW(boost::math::gamma_q(static_cast<T>(0), static_cast<T>(2)), std::domain_error);
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BOOST_CHECK_THROW(boost::math::lgamma_q(static_cast<T>(-1), static_cast<T>(2)), std::domain_error);
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BOOST_CHECK_THROW(boost::math::lgamma_q(static_cast<T>(1), static_cast<T>(-2)), std::domain_error);
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BOOST_CHECK_THROW(boost::math::lgamma_q(static_cast<T>(0), static_cast<T>(2)), std::domain_error);
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BOOST_CHECK_THROW(boost::math::gamma_p_derivative(static_cast<T>(-1), static_cast<T>(2)), std::domain_error);
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BOOST_CHECK_THROW(boost::math::gamma_p_derivative(static_cast<T>(1), static_cast<T>(-2)), std::domain_error);
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BOOST_CHECK_THROW(boost::math::gamma_p_derivative(static_cast<T>(0), static_cast<T>(2)), std::domain_error);
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#else
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BOOST_CHECK((boost::math::isnan)(boost::math::gamma_p(static_cast<T>(-1), static_cast<T>(2))));
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BOOST_CHECK((boost::math::isnan)(boost::math::gamma_q(static_cast<T>(-1), static_cast<T>(2))));
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BOOST_CHECK((boost::math::isnan)(boost::math::gamma_p(static_cast<T>(1), static_cast<T>(-2))));
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BOOST_CHECK((boost::math::isnan)(boost::math::gamma_q(static_cast<T>(1), static_cast<T>(-2))));
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BOOST_CHECK((boost::math::isnan)(boost::math::gamma_p(static_cast<T>(0), static_cast<T>(2))));
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BOOST_CHECK((boost::math::isnan)(boost::math::gamma_q(static_cast<T>(0), static_cast<T>(2))));
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BOOST_CHECK((boost::math::isnan)(boost::math::lgamma_q(static_cast<T>(-1), static_cast<T>(2))));
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BOOST_CHECK((boost::math::isnan)(boost::math::lgamma_q(static_cast<T>(1), static_cast<T>(-2))));
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BOOST_CHECK((boost::math::isnan)(boost::math::lgamma_q(static_cast<T>(0), static_cast<T>(2))));
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BOOST_CHECK((boost::math::isnan)(boost::math::gamma_p_derivative(static_cast<T>(-1), static_cast<T>(2))));
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BOOST_CHECK((boost::math::isnan)(boost::math::gamma_p_derivative(static_cast<T>(1), static_cast<T>(-2))));
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BOOST_CHECK((boost::math::isnan)(boost::math::gamma_p_derivative(static_cast<T>(0), static_cast<T>(2))));
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#endif
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}
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