mirror of
https://github.com/vale981/arb
synced 2025-03-06 09:51:39 -05:00
99 lines
2.8 KiB
C
99 lines
2.8 KiB
C
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/*
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Copyright (C) 2017 Fredrik Johansson
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This file is part of Arb.
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Arb is free software: you can redistribute it and/or modify it under
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the terms of the GNU Lesser General Public License (LGPL) as published
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by the Free Software Foundation; either version 2.1 of the License, or
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(at your option) any later version. See <http://www.gnu.org/licenses/>.
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*/
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#include "arb_hypgeom.h"
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int main()
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{
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slong iter;
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flint_rand_t state;
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flint_printf("legendre_p_ui_deriv_bound....");
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fflush(stdout);
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flint_randinit(state);
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for (iter = 0; iter < 10000 * arb_test_multiplier(); iter++)
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{
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arb_t x, x2sub1, y, z;
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mag_t m1, m2, exact;
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ulong n;
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slong prec;
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arb_init(x);
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arb_init(x2sub1);
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arb_init(y);
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arb_init(z);
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mag_init(m1);
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mag_init(m2);
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mag_init(exact);
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n = n_randtest(state) % 10000;
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prec = 64;
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arb_randtest(x, state, 2 * prec, 0);
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mag_zero(arb_radref(x));
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while (arf_cmpabs_2exp_si(arb_midref(x), 0) >= 0)
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arb_mul_2exp_si(x, x, -1);
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arb_mul_2exp_si(x, x, -n_randint(state, 10));
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arb_mul(x2sub1, x, x, 2 * prec);
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arb_sub_ui(x2sub1, x2sub1, 1, 2 * prec);
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arb_neg(x2sub1, x2sub1);
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arb_hypgeom_legendre_p_ui_deriv_bound(m1, m2, n, x, x2sub1);
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arb_hypgeom_legendre_p_ui(y, z, n, x, prec);
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arb_get_mag_lower(exact, z);
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if (mag_cmp(m1, exact) < 0)
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{
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flint_printf("FAIL: first derivative\n\n");
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flint_printf("n = %wu\n\n", n);
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flint_printf("x = "); arb_printn(x, 50, 0); flint_printf("\n\n");
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flint_printf("z = "); arb_printn(z, 50, 0); flint_printf("\n\n");
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flint_printf("m1 = "); mag_printd(m1, 15); flint_printf("\n\n");
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flint_abort();
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}
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arb_mul(z, z, x, prec);
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arb_mul_2exp_si(z, z, 1);
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arb_mul_ui(y, y, n, prec);
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arb_mul_ui(y, y, n + 1, prec);
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arb_sub(z, z, y, prec);
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arb_div(z, z, x2sub1, prec);
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arb_get_mag_lower(exact, z);
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if (mag_cmp(m2, exact) < 0)
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{
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flint_printf("FAIL: second derivative\n\n");
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flint_printf("n = %wu\n\n", n);
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flint_printf("x = "); arb_printn(x, 50, 0); flint_printf("\n\n");
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flint_printf("z = "); arb_printn(z, 50, 0); flint_printf("\n\n");
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flint_printf("m2 = "); mag_printd(m2, 15); flint_printf("\n\n");
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flint_abort();
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}
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arb_clear(x);
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arb_clear(x2sub1);
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arb_clear(y);
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arb_clear(z);
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mag_clear(m1);
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mag_clear(m2);
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mag_clear(exact);
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}
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flint_randclear(state);
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flint_cleanup();
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flint_printf("PASS\n");
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return EXIT_SUCCESS;
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}
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