📄 test.c
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/* p(x,nu) = (1/2)*(1+sign(x)*betaI(x^2/(nu+x^2),1/2,nu/2)) q(x,nu) = (1/2)*(1-sign(x)*betaI(x^2/(nu+x^2),1/2,nu/2)) */void test_tdist (void) { TEST (gsl_cdf_tdist_P, (0.0, 1.0), 0.5, TEST_TOL6); TEST (gsl_cdf_tdist_P, (1e-100, 1.0), 0.5, TEST_TOL6); TEST (gsl_cdf_tdist_P, (0.001, 1.0), 5.00318309780080559e-1, TEST_TOL6); TEST (gsl_cdf_tdist_P, (0.01, 1.0), 5.03182992764908255e-1, TEST_TOL6); TEST (gsl_cdf_tdist_P, (0.1, 1.0), 5.31725517430553569e-1, TEST_TOL6); TEST (gsl_cdf_tdist_P, (0.325, 1.0), 6.00023120032852123e-1, TEST_TOL6); TEST (gsl_cdf_tdist_P, (1.0, 1.0), 0.75000000000000000e0, TEST_TOL6); TEST (gsl_cdf_tdist_P, (1.5, 1.0), 8.12832958189001183e-1, TEST_TOL6); TEST (gsl_cdf_tdist_P, (2.0, 1.0), 8.52416382349566726e-1, TEST_TOL6); TEST (gsl_cdf_tdist_P, (10.0, 1.0), 9.68274482569446430e-1, TEST_TOL6); TEST (gsl_cdf_tdist_P, (20.0, 1.0), 9.84097748743823625e-1, TEST_TOL6); TEST (gsl_cdf_tdist_P, (100.0, 1.0), 9.96817007235091745e-1, TEST_TOL6); TEST (gsl_cdf_tdist_P, (1000.0, 1.0), 9.99681690219919441e-1, TEST_TOL6); TEST (gsl_cdf_tdist_P, (10000.0, 1.0), 9.99968169011487724e-1, TEST_TOL6); TEST (gsl_cdf_tdist_Q, (0.0, 1.0), 0.5, TEST_TOL6); TEST (gsl_cdf_tdist_Q, (1e-100, 1.0), 0.5, TEST_TOL6); TEST (gsl_cdf_tdist_Q, (0.001, 1.0), 4.99681690219919441e-1, TEST_TOL6); TEST (gsl_cdf_tdist_Q, (0.01, 1.0), 4.96817007235091745e-1, TEST_TOL6); TEST (gsl_cdf_tdist_Q, (0.1, 1.0), 4.68274482569446430e-1, TEST_TOL6); TEST (gsl_cdf_tdist_Q, (0.325, 1.0), 3.99976879967147876e-1, TEST_TOL6); TEST (gsl_cdf_tdist_Q, (1.0, 1.0), 2.5e-1, TEST_TOL6); TEST (gsl_cdf_tdist_Q, (1.5, 1.0), 1.87167041810998816e-1, TEST_TOL6); TEST (gsl_cdf_tdist_Q, (2.0, 1.0), 1.47583617650433274e-1, TEST_TOL6); TEST (gsl_cdf_tdist_Q, (10.0, 1.0), 3.17255174305535695e-2, TEST_TOL6); TEST (gsl_cdf_tdist_Q, (20.0, 1.0), 1.59022512561763752e-2, TEST_TOL6); TEST (gsl_cdf_tdist_Q, (100.0, 1.0), 3.18299276490825515e-3, TEST_TOL6); TEST (gsl_cdf_tdist_Q, (1000.0, 1.0), 3.18309780080558939e-4, TEST_TOL6); TEST (gsl_cdf_tdist_Q, (10000.0, 1.0), 3.18309885122757724e-5, TEST_TOL6); TEST (gsl_cdf_tdist_P, (-1e-100, 1.0), 0.5, TEST_TOL6); TEST (gsl_cdf_tdist_P, (-0.001, 1.0), 4.99681690219919441e-1, TEST_TOL6); TEST (gsl_cdf_tdist_P, (-0.01, 1.0), 4.96817007235091744e-1, TEST_TOL6); TEST (gsl_cdf_tdist_P, (-0.1, 1.0), 4.68274482569446430e-1, TEST_TOL6); TEST (gsl_cdf_tdist_P, (-0.325, 1.0), 3.99976879967147876e-1, TEST_TOL6); TEST (gsl_cdf_tdist_P, (-1.0, 1.0), 0.25, TEST_TOL6); TEST (gsl_cdf_tdist_P, (-1.5, 1.0), 1.87167041810998816e-1, TEST_TOL6); TEST (gsl_cdf_tdist_P, (-2.0, 1.0), 1.47583617650433274e-1, TEST_TOL6); TEST (gsl_cdf_tdist_P, (-10.0, 1.0), 3.17255174305535695e-2, TEST_TOL6); TEST (gsl_cdf_tdist_P, (-20.0, 1.0), 1.59022512561763751e-2, TEST_TOL6); TEST (gsl_cdf_tdist_P, (-100.0, 1.0), 3.18299276490825514e-3, TEST_TOL6); TEST (gsl_cdf_tdist_P, (-1000.0, 1.0), 3.18309780080558938e-4, TEST_TOL6); TEST (gsl_cdf_tdist_P, (-10000.0, 1.0), 3.18309885122757724e-5, TEST_TOL6); TEST (gsl_cdf_tdist_Q, (-1e-100, 1.0), 0.5, TEST_TOL6); TEST (gsl_cdf_tdist_Q, (-0.001, 1.0), 5.00318309780080559e-1, TEST_TOL6); TEST (gsl_cdf_tdist_Q, (-0.01, 1.0), 5.03182992764908255e-1, TEST_TOL6); TEST (gsl_cdf_tdist_Q, (-0.1, 1.0), 5.31725517430553570e-1, TEST_TOL6); TEST (gsl_cdf_tdist_Q, (-0.325, 1.0), 6.00023120032852124e-1, TEST_TOL6); TEST (gsl_cdf_tdist_Q, (-1.0, 1.0), 7.5e-1, TEST_TOL6); TEST (gsl_cdf_tdist_Q, (-1.5, 1.0), 8.12832958189001184e-1, TEST_TOL6); TEST (gsl_cdf_tdist_Q, (-2.0, 1.0), 8.52416382349566726e-1, TEST_TOL6); TEST (gsl_cdf_tdist_Q, (-10.0, 1.0), 9.68274482569446430e-1, TEST_TOL6); TEST (gsl_cdf_tdist_Q, (-20.0, 1.0), 9.84097748743823625e-1, TEST_TOL6); TEST (gsl_cdf_tdist_Q, (-100.0, 1.0), 9.96817007235091745e-1, TEST_TOL6); TEST (gsl_cdf_tdist_Q, (-1000.0, 1.0), 9.99681690219919441e-1, TEST_TOL6); TEST (gsl_cdf_tdist_Q, (-10000.0, 1.0), 9.99968169011487724e-1, TEST_TOL6); TEST (gsl_cdf_tdist_P, (0.0, 2.0), 5.00000000000000000e-01, TEST_TOL6); TEST (gsl_cdf_tdist_P, (1e-100, 2.0), 5.00000000000000000e-01, TEST_TOL6); TEST (gsl_cdf_tdist_P, (0.001, 2.0), 5.00353553302204959e-01, TEST_TOL6); TEST (gsl_cdf_tdist_P, (0.01, 2.0), 5.03535445520899514e-01, TEST_TOL6); TEST (gsl_cdf_tdist_P, (0.1, 2.0), 5.35267280792929913e-01, TEST_TOL6); TEST (gsl_cdf_tdist_P, (0.325, 2.0), 6.11985772746873767e-01, TEST_TOL6); TEST (gsl_cdf_tdist_P, (1.0, 2.0), 7.88675134594812882e-01, TEST_TOL6); TEST (gsl_cdf_tdist_P, (1.5, 2.0), 8.63803437554499460e-01, TEST_TOL6); TEST (gsl_cdf_tdist_P, (2.0, 2.0), 9.08248290463863016e-01, TEST_TOL6); TEST (gsl_cdf_tdist_P, (10.0, 2.0), 9.95073771488337154e-01, TEST_TOL6); TEST (gsl_cdf_tdist_P, (20.0, 2.0), 9.98754668053816452e-01, TEST_TOL6); TEST (gsl_cdf_tdist_P, (100.0, 2.0), 9.99950007498750219e-01, TEST_TOL6); TEST (gsl_cdf_tdist_P, (1000.0, 2.0), 9.99999500000749945e-01, TEST_TOL6); TEST (gsl_cdf_tdist_P, (10000.0, 2.0), 9.999999950000000739e-01, TEST_TOL6); TEST (gsl_cdf_tdist_Q, (0.0, 2.0), 5.00000000000000000e-01, TEST_TOL6); TEST (gsl_cdf_tdist_Q, (1e-100, 2.0), 5.00000000000000000e-01, TEST_TOL6); TEST (gsl_cdf_tdist_Q, (0.001, 2.0), 4.99646446697795041e-1, TEST_TOL6); TEST (gsl_cdf_tdist_Q, (0.01, 2.0), 4.96464554479100486e-1, TEST_TOL6); TEST (gsl_cdf_tdist_Q, (0.1, 2.0), 4.64732719207070087e-1, TEST_TOL6); TEST (gsl_cdf_tdist_Q, (0.325, 2.0), 3.88014227253126233e-1, TEST_TOL6); TEST (gsl_cdf_tdist_Q, (1.0, 2.0), 2.11324865405187118e-1, TEST_TOL6); TEST (gsl_cdf_tdist_Q, (1.5, 2.0), 1.36196562445500540e-1, TEST_TOL6); TEST (gsl_cdf_tdist_Q, (2.0, 2.0), 9.17517095361369836e-2, TEST_TOL6); TEST (gsl_cdf_tdist_Q, (10.0, 2.0), 4.92622851166284542e-3, TEST_TOL6); TEST (gsl_cdf_tdist_Q, (20.0, 2.0), 1.24533194618354849e-3, TEST_TOL6); TEST (gsl_cdf_tdist_Q, (100.0, 2.0), 4.99925012497812894e-5, TEST_TOL6); TEST (gsl_cdf_tdist_Q, (1000.0, 2.0), 4.99999250001249998e-7, TEST_TOL6); TEST (gsl_cdf_tdist_Q, (10000.0, 2.0), 4.99999992500000125e-9, TEST_TOL6); TEST (gsl_cdf_tdist_P, (-1e-100, 2.0), 5.00000000000000000e-01, TEST_TOL6); TEST (gsl_cdf_tdist_P, (-0.001, 2.0), 4.99646446697795041e-01, TEST_TOL6); TEST (gsl_cdf_tdist_P, (-0.01, 2.0), 4.96464554479100486e-01, TEST_TOL6); TEST (gsl_cdf_tdist_P, (-0.1, 2.0), 4.64732719207070087e-01, TEST_TOL6); TEST (gsl_cdf_tdist_P, (-0.325, 2.0), 3.88014227253126233e-01, TEST_TOL6); TEST (gsl_cdf_tdist_P, (-1.0, 2.0), 2.11324865405187118e-01, TEST_TOL6); TEST (gsl_cdf_tdist_P, (-1.5, 2.0), 1.36196562445500540e-01, TEST_TOL6); TEST (gsl_cdf_tdist_P, (-2.0, 2.0), 9.17517095361369836e-02, TEST_TOL6); TEST (gsl_cdf_tdist_P, (-10.0, 2.0), 4.92622851166284542e-03, TEST_TOL6); TEST (gsl_cdf_tdist_P, (-20.0, 2.0), 1.24533194618354849e-03, TEST_TOL6); TEST (gsl_cdf_tdist_P, (-100.0, 2.0), 4.99925012497812894e-05, TEST_TOL6); TEST (gsl_cdf_tdist_P, (-1000.0, 2.0), 4.99999250001249998e-07, TEST_TOL6); TEST (gsl_cdf_tdist_P, (-10000.0, 2.0), 4.99999992500000125e-09, TEST_TOL6); TEST (gsl_cdf_tdist_Q, (-1e-100, 2.0), 5.00000000000000000e-01, TEST_TOL6); TEST (gsl_cdf_tdist_Q, (-0.001, 2.0), 5.00353553302204959e-1, TEST_TOL6); TEST (gsl_cdf_tdist_Q, (-0.01, 2.0), 5.03535445520899514e-1, TEST_TOL6); TEST (gsl_cdf_tdist_Q, (-0.1, 2.0), 5.35267280792929913e-1, TEST_TOL6); TEST (gsl_cdf_tdist_Q, (-0.325, 2.0), 6.11985772746873767e-1, TEST_TOL6); TEST (gsl_cdf_tdist_Q, (-1.0, 2.0), 7.88675134594812882e-1, TEST_TOL6); TEST (gsl_cdf_tdist_Q, (-1.5, 2.0), 8.63803437554499460e-1, TEST_TOL6); TEST (gsl_cdf_tdist_Q, (-2.0, 2.0), 9.08248290463863016e-1, TEST_TOL6); TEST (gsl_cdf_tdist_Q, (-10.0, 2.0), 9.95073771488337155e-1, TEST_TOL6); TEST (gsl_cdf_tdist_Q, (-20.0, 2.0), 9.98754668053816452e-1, TEST_TOL6); TEST (gsl_cdf_tdist_Q, (-100.0, 2.0), 9.99950007498750219e-1, TEST_TOL6); TEST (gsl_cdf_tdist_Q, (-1000.0, 2.0), 9.99999500000749999e-1, TEST_TOL6); TEST (gsl_cdf_tdist_Q, (-10000.0, 2.0), 9.99999995000000075e-1, TEST_TOL6); TEST (gsl_cdf_tdist_P, (0.0, 300.0), 5.00000000000000000e-01, TEST_TOL6); TEST (gsl_cdf_tdist_P, (1e-100, 300.0), 5.00000000000000000e-01, TEST_TOL6); TEST (gsl_cdf_tdist_P, (0.001, 300.0), 5.00398609900942949e-01, TEST_TOL6); TEST (gsl_cdf_tdist_P, (0.01, 300.0), 5.03986033020559088e-01, TEST_TOL6); TEST (gsl_cdf_tdist_P, (0.1, 300.0), 5.39794441177768194e-01, TEST_TOL6); TEST (gsl_cdf_tdist_P, (0.325, 300.0), 6.27296201542523812e-01, TEST_TOL6); TEST (gsl_cdf_tdist_P, (1.0, 300.0), 8.40941797784686861e-01, TEST_TOL6); TEST (gsl_cdf_tdist_P, (1.5, 300.0), 9.32666983425369137e-01, TEST_TOL6); TEST (gsl_cdf_tdist_P, (2.0, 300.0), 9.76799239508425455e-01, TEST_TOL6); TEST (gsl_cdf_tdist_P, (10.0, 300.0), 1.00000000000000000e+00, TEST_TOL6); TEST (gsl_cdf_tdist_P, (20.0, 300.0), 1.00000000000000000e+00, TEST_TOL6); TEST (gsl_cdf_tdist_P, (100.0, 300.0), 1.00000000000000000e+00, TEST_TOL6); TEST (gsl_cdf_tdist_P, (1000.0, 300.0), 1.00000000000000000e+00, TEST_TOL6); TEST (gsl_cdf_tdist_P, (10000.0, 300.0), 1.00000000000000000e+00, TEST_TOL6); TEST (gsl_cdf_tdist_Q, (0.0, 300.0), 5.00000000000000000e-01, TEST_TOL6); TEST (gsl_cdf_tdist_Q, (1e-100, 300.0), 5.00000000000000000e-01, TEST_TOL6); TEST (gsl_cdf_tdist_Q, (0.001, 300.0), 4.99601390099057051e-1, TEST_TOL6); TEST (gsl_cdf_tdist_Q, (0.01, 300.0), 4.96013966979440912e-1, TEST_TOL6); TEST (gsl_cdf_tdist_Q, (0.1, 300.0), 4.60205558822231806e-1, TEST_TOL6); TEST (gsl_cdf_tdist_Q, (0.325, 300.0), 3.72703798457476188e-1, TEST_TOL6); TEST (gsl_cdf_tdist_Q, (1.0, 300.0), 1.59058202215313138e-1, TEST_TOL6); TEST (gsl_cdf_tdist_Q, (1.5, 300.0), 6.73330165746308628e-2, TEST_TOL6); TEST (gsl_cdf_tdist_Q, (2.0, 300.0), 2.32007604915745452e-2, TEST_TOL6); TEST (gsl_cdf_tdist_Q, (10.0, 300.0), 8.279313677e-21, TEST_TOL6); TEST (gsl_cdf_tdist_Q, (20.0, 300.0), 1.93159812815803978e-57, TEST_TOL6); TEST (gsl_cdf_tdist_Q, (100.0, 300.0), 1.02557519997736154e-232, TEST_TOL6); TEST (gsl_cdf_tdist_Q, (1000.0, 300.0), 0.00000000000000000e+00, 0.0); TEST (gsl_cdf_tdist_Q, (10000.0, 300.0), 0.00000000000000000e+00, 0.0); TEST (gsl_cdf_tdist_P, (-1e-100, 300.0), 5.00000000000000000e-01, TEST_TOL6); TEST (gsl_cdf_tdist_P, (-0.001, 300.0), 4.99601390099057051e-01, TEST_TOL6); TEST (gsl_cdf_tdist_P, (-0.01, 300.0), 4.96013966979440912e-01, TEST_TOL6); TEST (gsl_cdf_tdist_P, (-0.1, 300.0), 4.60205558822231806e-01, TEST_TOL6); TEST (gsl_cdf_tdist_P, (-0.325, 300.0), 3.72703798457476188e-01, TEST_TOL6); TEST (gsl_cdf_tdist_P, (-1.0, 300.0), 1.59058202215313138e-01, TEST_TOL6); TEST (gsl_cdf_tdist_P, (-1.5, 300.0), 6.73330165746308628e-02, TEST_TOL6); TEST (gsl_cdf_tdist_P, (-2.0, 300.0), 2.32007604915745452e-02, TEST_TOL6); TEST (gsl_cdf_tdist_P, (-10.0, 300.0), 8.279313675556272534e-21, TEST_TOL6); TEST (gsl_cdf_tdist_P, (-20.0, 300.0), 1.93159812815803978e-57, TEST_TOL6); TEST (gsl_cdf_tdist_P, (-100.0, 300.0), 1.02557519997736154e-232, TEST_TOL6); TEST (gsl_cdf_tdist_P, (-1000.0, 300.0), 0.0, 0.0); TEST (gsl_cdf_tdist_P, (-10000.0, 300.0), 0.0, 0.0); TEST (gsl_cdf_tdist_Q, (-1e-100, 300.0), 5.00000000000000000e-01, TEST_TOL6); TEST (gsl_cdf_tdist_Q, (-0.001, 300.0), 5.00398609900942949e-1, TEST_TOL6); TEST (gsl_cdf_tdist_Q, (-0.01, 300.0), 5.03986033020559088e-1, TEST_TOL6); TEST (gsl_cdf_tdist_Q, (-0.1, 300.0), 5.39794441177768194e-1, TEST_TOL6); TEST (gsl_cdf_tdist_Q, (-0.325, 300.0), 6.27296201542523812e-1, TEST_TOL6); TEST (gsl_cdf_tdist_Q, (-1.0, 300.0), 8.40941797784686862e-1, TEST_TOL6); TEST (gsl_cdf_tdist_Q, (-1.5, 300.0), 9.32666983425369137e-1, TEST_TOL6); TEST (gsl_cdf_tdist_Q, (-2.0, 300.0), 9.76799239508425455e-1, TEST_TOL6); TEST (gsl_cdf_tdist_Q, (-10.0, 300.0), 1.000000000000000000e0, TEST_TOL6); TEST (gsl_cdf_tdist_Q, (-20.0, 300.0), 1.0, TEST_TOL6); TEST (gsl_cdf_tdist_Q, (-100.0, 300.0), 1.0, TEST_TOL6); TEST (gsl_cdf_tdist_Q, (-1000.0, 300.0), 1.0, TEST_TOL6); TEST (gsl_cdf_tdist_Q, (-10000.0, 300.0), 1.0, TEST_TOL6);} /* Tests for F distribution */ /* p(x, nu1, nu2) := betaI(1 / (1 + nu2 / nu1 * x), nu1 / 2, nu2 / 2) */void test_fdist (void) { TEST (gsl_cdf_fdist_P, (0.0, 1.2, 1.3), 0.0, 0.0); TEST (gsl_cdf_fdist_P, (1e-100, 1.2, 1.3), 6.98194275525039002e-61, TEST_TOL6); TEST (gsl_cdf_fdist_P, (0.001, 1.2, 1.3), 1.10608485860238564e-2, TEST_TOL6); TEST (gsl_cdf_fdist_P, (0.01, 1.2, 1.3), 4.38636757068313850e-2, TEST_TOL6); TEST (gsl_cdf_fdist_P, (0.1, 1.2, 1.3), 1.68242392712840734e-1, TEST_TOL6); TEST (gsl_cdf_fdist_P, (0.325, 1.2, 1.3), 3.14130045246195449e-1, TEST_TOL6); TEST (gsl_cdf_fdist_P, (1.0, 1.2, 1.3), 5.09630779074755253e-01, TEST_TOL6); TEST (gsl_cdf_fdist_P, (1.5, 1.2, 1.3), 5.83998640641553852e-1, TEST_TOL6); TEST (gsl_cdf_fdist_P, (2.0, 1.2, 1.3), 6.34733581351938787e-1, TEST_TOL6); TEST (gsl_cdf_fdist_P, (10.0, 1.2, 1.3), 8.48446237879200975e-1, TEST_TOL6); TEST (gsl_cdf_fdist_P, (20.0, 1.2, 1.3), 9.00987726336875039e-1, TEST_TOL6); TEST (gsl_cdf_fdist_P, (100.0, 1.2, 1.3), 9.64489127047688435e-1, TEST_TOL6); TEST (gsl_cdf_fdist_P, (1000.0, 1.2, 1.3), 9.92012051694116388e-1, TEST_TOL6); TEST (gsl_cdf_fdist_P, (10000.0, 1.2, 1.3), 9.98210862808842585e-1, TEST_TOL6); TEST (gsl_cdf_fdist_Q, (0.0, 1.2, 1.3), 1.0, TEST_TOL6); TEST (gsl_cdf_fdist_Q, (1e-100, 1.2, 1.3), 1.0, TEST_TOL6); TEST (gsl_cdf_fdist_Q, (0.001, 1.2, 1.3), 9.88939151413976144e-1, TEST_TOL6); TEST (gsl_cdf_fdist_Q, (0.01, 1.2, 1.3), 9.56136324293168615e-1, TEST_TOL6); TEST (gsl_cdf_fdist_Q, (0.1, 1.2, 1.3), 8.31757607287159265e-1, TEST_TOL6); TEST (gsl_cdf_fdist_Q, (0.325, 1.2, 1.3), 6.85869954753804551e-1, TEST_TOL6); TEST (gsl_cdf_fdist_Q, (1.0, 1.2, 1.3), 4.90369220925244747e-1, TEST_TOL6); TEST (gsl_cdf_fdist_Q, (1.5, 1.2, 1.3), 4.16001359358446148e-1, TEST_TOL6); TEST (gsl_cdf_fdist_Q, (2.0, 1.2, 1.3), 3.65266418648061213e-1, TEST_TOL6); TEST (gsl_cdf_fdist_Q, (10.0, 1.2, 1.3), 1.51553762120799025e-1, TEST_TOL6); TEST (gsl_cdf_fdist_Q, (20.0, 1.2, 1.3), 9.90122736631249612e-2, TEST_TOL6); TEST (gsl_cdf_fdist_Q, (100.0, 1.2, 1.3), 3.55108729523115643e-2, TEST_TOL6); TEST (gsl_cdf_fdist_Q, (1000.0, 1.2, 1.3), 7.98794830588361109e-3, TEST_TOL6); TEST (gsl_cdf_fdist_Q, (10000.0, 1.2, 1.3), 1.7891371911574145e-3, TEST_TOL6); TEST (gsl_cdf_fdist_P, (0.0, 500.0, 1.3), 0.0, 0.0); TEST (gsl_cdf_fdist_P, (1e-100, 500.0, 1.3), 0.0, 0.0); TEST (gsl_cdf_fdist_P, (0.001, 500.0, 1.3), 9.83434460393304765e-141, TEST_TOL6); TEST (gsl_cdf_fdist_P, (0.01, 500.0, 1.3), 1.45915624888550014e-26, TEST_TOL6); TEST (gsl_cdf_fdist_P, (0.1, 500.0, 1.3), 5.89976509619688165e-4, TEST_TOL6); TEST (gsl_cdf_fdist_P, (0.325, 500.0, 1.3), 6.86110486051542533e-2, TEST_TOL6);
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