mirror of
https://github.com/vale981/arb
synced 2025-03-06 09:51:39 -05:00
136 lines
3.8 KiB
C
136 lines
3.8 KiB
C
/*=============================================================================
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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
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it under the terms of the GNU General Public License as published by
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the Free Software Foundation; either version 2 of the License, or
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(at your option) any later version.
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ARB is distributed in the hope that it will be useful,
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but WITHOUT ANY WARRANTY; without even the implied warranty of
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MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
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GNU General Public License for more details.
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You should have received a copy of the GNU General Public License
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along with ARB; if not, write to the Free Software
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Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA
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=============================================================================*/
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/******************************************************************************
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Copyright (C) 2016 Pascal Molin
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******************************************************************************/
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#include "acb_dirichlet.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("chi....");
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fflush(stdout);
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flint_randinit(state);
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for (iter = 0; iter < 10000; iter++)
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{
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acb_dirichlet_group_t G;
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acb_conrey_t x;
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ulong q, n, k, sum;
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long ref;
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/*int * bits;*/
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q = 1 + n_randint(state, 1000 * (1 + iter / 100));
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acb_dirichlet_group_init(G, q);
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acb_conrey_init(x, G);
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/* check group size and elements */
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acb_conrey_one(x, G);
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sum = 1;
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#if 1
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for (n = 1; acb_conrey_next(x, G) < G->num; n++)
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sum += x->n * x->n;
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#else
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/* iteration much faster than gcd below */
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n = 1;
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for (k = 2; k < G->q; k++)
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{
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if (n_gcd(k, G->q) > 1)
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continue;
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n++;
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sum += k * k;
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}
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#endif
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/* use http://oeis.org/A053818 to check all elements
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* are gone through */
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ref = (q % 4 == 2) ? -2 : 1;
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k = (G->neven == 2) ? 1 : 0;
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for (; k<G->num; k++)
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ref = - ref * G->primes[k];
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ref = ( G->phi_q * (2 * q * q + ref) ) / 6;
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if (n != G->phi_q)
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{
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flint_printf("FAIL: group size\n\n");
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flint_printf("q = %wu\n\n", q);
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flint_printf("phi(q) = %wu\n\n", G->phi_q);
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flint_printf("loop index = %wu\n\n", n);
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abort();
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}
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if (sum != ref && q > 1)
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{
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flint_printf("FAIL: sum test\n\n");
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flint_printf("q = %wu\n\n", q);
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flint_printf("sum k^2 = %wu\n\n", ref);
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flint_printf("sum obtained = %wu\n\n", sum);
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abort();
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}
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if (q % 4 == 2)
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continue;
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/* check primitive elements */
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if (q % 4 == 2)
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ref = 0;
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else
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{
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ref = 1;
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k = (G->neven == 2) ? 1 : 0;
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for (; k < G->num; k++)
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{
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ulong p = G->primes[k];
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if (G->exponents[k] == 1)
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ref *= p - 2;
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else
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ref *= (p * (p -2) + 1) * n_pow(p, G->exponents[k] - 2);
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}
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}
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acb_conrey_first_primitive(x, G);
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for (n = 1; (k=acb_conrey_next_primitive(x, G)) < G->num; n++);
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if (n != ref)
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{
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flint_printf("FAIL: number of primitive elements\n\n");
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flint_printf("q = %wu\n\n", q);
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flint_printf("# primitive = %wu\n\n", ref);
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flint_printf("loop index = %wu\n\n", n);
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abort();
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}
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acb_conrey_clear(x);
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acb_dirichlet_group_clear(G);
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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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