mirror of
https://github.com/vale981/arb
synced 2025-03-06 09:51:39 -05:00
6bf072eb59
This will allow us to not loose the julia session on error. See also https://github.com/wbhart/flint2/pull/243
216 lines
7 KiB
C
216 lines
7 KiB
C
/*
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Copyright (C) 2014 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 "acb_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("u_asymp....");
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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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acb_t a, b, a2, b2, z, U1, U2, t, u, M1, M2, am;
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acb_struct bm[2];
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ulong n1, n2;
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slong prec0, prec1, prec2;
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acb_init(a);
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acb_init(b);
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acb_init(a2);
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acb_init(b2);
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acb_init(z);
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acb_init(U1);
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acb_init(U2);
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acb_init(t);
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acb_init(u);
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acb_init(M1);
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acb_init(M2);
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acb_init(am);
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acb_init(bm);
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acb_init(bm + 1);
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if (n_randint(state, 4) == 0)
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{
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n1 = n_randint(state, 200);
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n2 = n_randint(state, 200);
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prec0 = 2 + n_randint(state, 1000);
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prec1 = 2 + n_randint(state, 1000);
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prec2 = 2 + n_randint(state, 1000);
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}
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else
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{
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n1 = n_randint(state, 40);
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n2 = n_randint(state, 40);
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prec0 = 2 + n_randint(state, 300);
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prec1 = 2 + n_randint(state, 300);
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prec2 = 2 + n_randint(state, 300);
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}
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acb_randtest_param(a, state, prec0, 1 + n_randint(state, 20));
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if (n_randint(state, 4) == 0)
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acb_add_ui(b, a, n_randint(state, 10), prec0);
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else
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acb_randtest_param(b, state, prec0, 1 + n_randint(state, 20));
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acb_randtest(z, state, prec0, 1 + n_randint(state, 20));
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/* Test Kummer's transformation */
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acb_sub(a2, a, b, prec0);
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acb_add_ui(a2, a2, 1, prec0);
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acb_sub_ui(b2, b, 2, prec0);
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acb_neg(b2, b2);
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acb_hypgeom_u_asymp(U1, a, b, z, n1, prec1);
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acb_hypgeom_u_asymp(U2, a2, b2, z, n2, prec2);
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if (!acb_overlaps(U1, U2))
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{
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flint_printf("FAIL (Kummer transformation)\n");
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flint_printf("iter = %wd\n", iter);
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flint_printf("a = "); acb_printd(a, 50); flint_printf("\n");
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flint_printf("b = "); acb_printd(b, 50); flint_printf("\n");
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flint_printf("z = "); acb_printd(z, 50); flint_printf("\n");
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flint_printf("n1 = %wd, n2 = %wd, prec1 = %wd, prec2 = %wd\n", n1, n2, prec1, prec2);
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flint_printf("U1 = "); acb_printd(U1, 100); flint_printf("\n");
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flint_printf("U2 = "); acb_printd(U2, 100); flint_printf("\n");
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flint_abort();
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}
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/* Check contiguous relation
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(b-a-1)U(a,b-1,z) + z U(a,b+1,z) + (1-b-z) U(a,b,z) = 0 */
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acb_one(t);
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acb_sub(t, t, b, prec0);
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acb_sub(t, t, z, prec0);
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acb_mul(u, U1, t, prec1);
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acb_add_ui(b2, b, 1, prec0);
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acb_hypgeom_u_asymp(U2, a, b2, z, n2, prec2);
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acb_addmul(u, U2, z, prec1);
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acb_sub_ui(b2, b, 1, prec0);
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acb_hypgeom_u_asymp(U2, a, b2, z, n2, prec2);
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acb_sub(t, b, a, prec0);
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acb_sub_ui(t, t, 1, prec0);
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acb_mul(t, t, U2, prec0);
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acb_add(t, t, u, prec0);
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if (!acb_contains_zero(t))
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{
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flint_printf("FAIL (contiguous relation)\n");
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flint_printf("iter = %wd\n", iter);
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flint_printf("a = "); acb_printd(a, 50); flint_printf("\n");
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flint_printf("b = "); acb_printd(b, 50); flint_printf("\n");
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flint_printf("z = "); acb_printd(z, 50); flint_printf("\n");
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flint_printf("n1 = %wd, n2 = %wd, prec1 = %wd, prec2 = %wd\n", n1, n2, prec1, prec2);
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flint_printf("U1 = "); acb_printd(U1, 100); flint_printf("\n");
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flint_printf("t = "); acb_printd(t, 100); flint_printf("\n");
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flint_abort();
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}
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/* Test U(a,b,z) = gamma(1-b)/gamma(a-b+1) M(a,b,z)
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+ gamma(b-1)/gamma(a) z^(1-b) M(a-b+1,2-b,z) */
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acb_set(am, a);
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acb_set(bm, b);
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acb_one(bm + 1);
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acb_hypgeom_pfq_direct(M1, am, 1, bm, 2, z, n2, prec2);
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acb_sub(am, a, b, prec2);
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acb_add_ui(am, am, 1, prec2);
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acb_sub_ui(bm, b, 2, prec2);
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acb_neg(bm, bm);
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acb_one(bm + 1);
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acb_hypgeom_pfq_direct(M2, am, 1, bm, 2, z, n2, prec2);
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acb_sub(am, a, b, prec2);
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acb_add_ui(am, am, 1, prec2);
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acb_rgamma(am, am, prec2);
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acb_mul(M1, M1, am, prec2);
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acb_sub_ui(am, b, 1, prec2);
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acb_neg(am, am);
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acb_gamma(am, am, prec2);
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acb_mul(M1, M1, am, prec2);
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acb_rgamma(am, a, prec2);
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acb_mul(M2, M2, am, prec2);
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acb_sub_ui(am, b, 1, prec2);
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acb_gamma(am, am, prec2);
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acb_mul(M2, M2, am, prec2);
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acb_sub_ui(am, b, 1, prec2);
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acb_neg(am, am);
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acb_pow(am, z, am, prec2);
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acb_mul(M2, M2, am, prec2);
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acb_add(U2, M1, M2, prec2);
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acb_pow(am, z, a, prec2);
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acb_mul(U2, U2, am, prec2);
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if (!acb_overlaps(U1, U2))
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{
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flint_printf("FAIL (U in terms of M)\n");
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flint_printf("iter = %wd\n", iter);
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flint_printf("a = "); acb_printd(a, 50); flint_printf("\n");
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flint_printf("b = "); acb_printd(b, 50); flint_printf("\n");
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flint_printf("z = "); acb_printd(z, 50); flint_printf("\n");
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flint_printf("n1 = %wd, n2 = %wd, prec1 = %wd, prec2 = %wd\n", n1, n2, prec1, prec2);
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flint_printf("U1 = "); acb_printd(U1, 100); flint_printf("\n");
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flint_printf("U2 = "); acb_printd(U2, 100); flint_printf("\n");
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flint_abort();
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}
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/* Test special value: b = a+1 */
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acb_add_ui(b, a, 1, prec0);
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acb_hypgeom_u_asymp(U1, a, b, z, n1, prec1);
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acb_one(U2);
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if (!acb_overlaps(U1, U2))
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{
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flint_printf("FAIL (special value)\n");
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flint_printf("iter = %wd\n", iter);
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flint_printf("a = "); acb_printd(a, 50); flint_printf("\n");
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flint_printf("b = "); acb_printd(b, 50); flint_printf("\n");
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flint_printf("z = "); acb_printd(z, 50); flint_printf("\n");
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flint_printf("n1 = %wd, n2 = %wd, prec1 = %wd, prec2 = %wd\n", n1, n2, prec1, prec2);
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flint_printf("U1 = "); acb_printd(U1, 100); flint_printf("\n");
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flint_printf("U2 = "); acb_printd(U2, 100); flint_printf("\n");
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flint_abort();
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}
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acb_clear(a);
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acb_clear(b);
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acb_clear(a2);
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acb_clear(b2);
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acb_clear(z);
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acb_clear(U1);
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acb_clear(U2);
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acb_clear(t);
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acb_clear(u);
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acb_clear(M1);
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acb_clear(M2);
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acb_clear(am);
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acb_clear(bm);
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acb_clear(bm + 1);
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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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