void
mag_rfac_ui(mag_t z, ulong n)
{
if (n < MAG_FAC_TABLE_NUM)
{
_fmpz_demote(MAG_EXPREF(z));
MAG_EXP(z) = mag_rfac_tab[n * 2];
MAG_MAN(z) = mag_rfac_tab[n * 2 + 1];
}
else
{
double x = n;
x = ceil((((x+0.5)*mag_d_log_lower_bound(x) - x) * 1.4426950408889634074) * -0.9999999);
/* x + 1 could round down for huge x, but this doesn't matter
as long as the value was perturbed up above */
fmpz_set_d(MAG_EXPREF(z), x + 1);
MAG_MAN(z) = MAG_ONE_HALF;
}
}
void
dedekind_sum_coprime(fmpq_t s, const fmpz_t h, const fmpz_t k)
{
if (fmpz_cmp_ui(k, DOUBLE_CUTOFF) < 0)
{
double t;
t = dedekind_sum_coprime_d(*h, *k) * (6 * (*k));
/* Round to nearest after truncation */
if (t > 0)
t += 0.5;
else
t -= 0.5;
fmpz_set_d(fmpq_numref(s), t);
fmpz_set_ui(fmpq_denref(s), 6UL * (*k));
fmpq_canonicalise(s);
}
else
{
dedekind_sum_coprime_large(s, h, k);
}
}
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);
}
