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
|
/*
Copyright (C) 2019 D.H.J Polymath
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"
static void
_mag_div_ui_ui(mag_t res, ulong a, ulong b)
{
mag_set_ui(res, a);
mag_div_ui(res, res, b);
}
ulong
acb_dirichlet_turing_method_bound(const fmpz_t p)
{
ulong result;
arb_t t;
fmpz_t k;
mag_t m, b1, b2, c;
arb_init(t);
fmpz_init(k);
mag_init(m);
mag_init(b1);
mag_init(b2);
mag_init(c);
acb_dirichlet_gram_point(t, p, NULL, NULL, FLINT_MAX(8, fmpz_bits(p)));
arb_get_mag(m, t);
mag_log(m, m);
/* b1 = 0.0061*log(gram(p))^2 + 0.08*log(gram(p)) */
_mag_div_ui_ui(c, 61, 10000);
mag_mul(b1, c, m);
_mag_div_ui_ui(c, 8, 100);
mag_add(b1, b1, c);
mag_mul(b1, b1, m);
/* b2 = 0.0031*log(gram(p))^2 + 0.11*log(gram(p)) */
_mag_div_ui_ui(c, 31, 10000);
mag_mul(b2, c, m);
_mag_div_ui_ui(c, 11, 100);
mag_add(b2, b2, c);
mag_mul(b2, b2, m);
/* result = ceil(min(b1, b2)) */
mag_min(m, b1, b2);
mag_get_fmpz(k, m);
result = fmpz_get_ui(k);
arb_clear(t);
fmpz_clear(k);
mag_clear(m);
mag_clear(b1);
mag_clear(b2);
mag_clear(c);
return result;
}
|
