arb/acb_dirichlet/theta_length.c
2016-09-06 15:32:23 +02:00

39 lines
1,005 B
C

/*
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"
#include <math.h>
#define PI 3.14159265358
#define LOG2 0.69314718055
ulong
acb_dirichlet_theta_length_d(ulong q, double t, slong prec)
{
double a, la;
a = PI / (double)q * t * t;
la = (a < .3) ? -log(2*a*(1-a)) : .8;
la = ((double)prec * LOG2 + la) / a;
return ceil(sqrt(la)+.5);
}
ulong
acb_dirichlet_theta_length(ulong q, const arb_t t, slong prec)
{
double dt;
ulong len;
arf_t at;
arf_init(at);
arb_get_lbound_arf(at, t, 53);
dt = arf_get_d(at, ARF_RND_DOWN);
len = acb_dirichlet_theta_length_d(q, dt, prec);
arf_clear(at);
return len;
}