mirror of
https://github.com/vale981/arb
synced 2025-03-05 09:21:38 -05:00
67 lines
1.5 KiB
C
67 lines
1.5 KiB
C
/*
|
|
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;
|
|
}
|