1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
79
80
81
|
/*
Copyright (C) 2016 Pascal Molin
This file is part of Arb.
Arb is free software: you can redistribute it and/or modify it under
the terms of the GNU Lesser General Public License (LGPL) as published
by the Free Software Foundation; either version 2.1 of the License, or
(at your option) any later version. See <http://www.gnu.org/licenses/>.
*/
#include "acb_dirichlet.h"
int main()
{
slong prec = 128;
ulong q;
flint_printf("gauss....");
fflush(stdout);
/* check Gauss sums */
for (q = 3; q < 250; q ++)
{
dirichlet_group_t G;
dirichlet_char_t chi;
acb_t s1, s2, s3, s4;
dirichlet_group_init(G, q);
dirichlet_char_init(chi, G);
acb_init(s1);
acb_init(s2);
acb_init(s3);
acb_init(s4);
dirichlet_char_one(chi, G);
while (1) {
acb_dirichlet_gauss_sum_naive(s1, G, chi, prec);
acb_dirichlet_gauss_sum(s2, G, chi, prec);
acb_dirichlet_gauss_sum_factor(s3, G, chi, prec);
if (dirichlet_conductor_char(G, chi) == G->q)
acb_dirichlet_gauss_sum_theta(s4, G, chi, prec);
else
acb_set(s4, s1);
if (!acb_overlaps(s1, s2)
|| !acb_overlaps(s1, s3)
|| !acb_overlaps(s1, s4))
{
flint_printf("FAIL: G(chi_%wu(%wu))\n\n", q, chi->n);
flint_printf("\nnaive ");
acb_printd(s1, 25);
flint_printf("\ndefault ");
acb_printd(s2, 25);
flint_printf("\nfactor ");
acb_printd(s3, 25);
flint_printf("\ntheta ");
acb_printd(s4, 25);
flint_abort();
}
if (dirichlet_char_next(chi, G) < 0)
break;
}
acb_clear(s1);
acb_clear(s2);
acb_clear(s3);
acb_clear(s4);
dirichlet_group_clear(G);
dirichlet_char_clear(chi);
}
flint_cleanup();
flint_printf("PASS\n");
return EXIT_SUCCESS;
}
|
