void
_acb_poly_compose(acb_ptr res,
acb_srcptr poly1, slong len1,
acb_srcptr poly2, slong len2, slong prec)
{
if (len1 == 1)
{
acb_set_round(res, poly1, prec);
}
else if (len2 == 1)
{
_acb_poly_evaluate(res, poly1, len1, poly2, prec);
}
else if (_acb_vec_is_zero(poly2 + 1, len2 - 2))
{
_acb_poly_compose_axnc(res, poly1, len1, poly2, poly2 + len2 - 1, len2 - 1, prec);
}
else if (len1 <= 7)
{
_acb_poly_compose_horner(res, poly1, len1, poly2, len2, prec);
}
else
{
_acb_poly_compose_divconquer(res, poly1, len1, poly2, len2, prec);
}
}
void
_acb_poly_compose_series(acb_ptr res, acb_srcptr poly1, slong len1,
acb_srcptr poly2, slong len2, slong n, slong prec)
{
if (len2 == 1)
{
acb_set_round(res, poly1, prec);
_acb_vec_zero(res + 1, n - 1);
}
else if (_acb_vec_is_zero(poly2 + 1, len2 - 2)) /* poly2 is a monomial */
{
slong i, j;
acb_t t;
acb_init(t);
acb_set(t, poly2 + len2 - 1);
acb_set_round(res, poly1, prec);
for (i = 1, j = len2 - 1; i < len1 && j < n; i++, j += len2 - 1)
{
acb_mul(res + j, poly1 + i, t, prec);
if (i + 1 < len1 && j + len2 - 1 < n)
acb_mul(t, t, poly2 + len2 - 1, prec);
}
if (len2 != 2)
for (i = 1; i < n; i++)
if (i % (len2 - 1) != 0)
acb_zero(res + i);
acb_clear(t);
}
else if (len1 < 6 || n < 6)
{
_acb_poly_compose_series_horner(res, poly1, len1, poly2, len2, n, prec);
}
else
{
_acb_poly_compose_series_brent_kung(res, poly1, len1, poly2, len2, n, prec);
}
}
void
_acb_poly_sqrt_series(acb_ptr g,
acb_srcptr h, slong hlen, slong len, slong prec)
{
hlen = FLINT_MIN(hlen, len);
while (hlen > 0 && acb_is_zero(h + hlen - 1))
hlen--;
if (hlen <= 1)
{
acb_sqrt(g, h, prec);
_acb_vec_zero(g + 1, len - 1);
}
else if (len == 2)
{
acb_sqrt(g, h, prec);
acb_div(g + 1, h + 1, h, prec);
acb_mul(g + 1, g + 1, g, prec);
acb_mul_2exp_si(g + 1, g + 1, -1);
}
else if (_acb_vec_is_zero(h + 1, hlen - 2))
{
acb_t t;
acb_init(t);
arf_set_si_2exp_si(arb_midref(acb_realref(t)), 1, -1);
_acb_poly_binomial_pow_acb_series(g, h, hlen, t, len, prec);
acb_clear(t);
}
else
{
acb_ptr t;
t = _acb_vec_init(len);
_acb_poly_rsqrt_series(t, h, hlen, len, prec);
_acb_poly_mullow(g, t, len, h, hlen, len, prec);
_acb_vec_clear(t, len);
}
}