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/*
Copyright (C) 2014 Fredrik Johansson
This file is part of FLINT.
FLINT 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 3 of the License, or
(at your option) any later version. See <https://www.gnu.org/licenses/>.
*/
#include <math.h>
#include "acb_modular.h"
static inline int
d_is_ok(double x)
{
return (x > -1e15) && (x < 1e15);
}
void
acb_modular_fundamental_domain_approx_d(psl2z_t g,
double x, double y, double one_minus_eps)
{
double a, b, c, d, aa, bb, t;
int i;
a = d = 1;
b = c = 0;
for (i = 0; i < 20; i++)
{
if (!d_is_ok(x) || !d_is_ok(y) || !(y > 0.0))
{
psl2z_one(g);
return;
}
/* shift */
if (x < -0.5 || x > 0.5)
{
t = floor(x + 0.5);
x -= t;
a -= t * c;
b -= t * d;
/* too large to guarantee exactness */
if (!d_is_ok(a) || !d_is_ok(b))
{
psl2z_one(g);
return;
}
continue;
}
t = x*x + y*y;
/* can't divide by a too small number */
if (t < 1e-30)
{
psl2z_one(g);
break;
}
/* inversion */
if (t < one_minus_eps)
{
t = 1.0 / t;
x *= -t;
y *= t;
aa = a;
bb = b;
a = -c;
b = -d;
c = aa;
d = bb;
continue;
}
/* we're good */
break;
}
if (c < 0 || (c == 0 && d < 0))
{
a = -a;
b = -b;
c = -c;
d = -d;
}
fmpz_set_d(&g->a, a);
fmpz_set_d(&g->b, b);
fmpz_set_d(&g->c, c);
fmpz_set_d(&g->d, d);
}