void
_arb_poly_inv_series(arb_ptr Qinv,
arb_srcptr Q, slong Qlen, slong len, slong prec)
{
arb_inv(Qinv, Q, prec);
if (Qlen == 1)
{
_arb_vec_zero(Qinv + 1, len - 1);
}
else if (len == 2)
{
arb_div(Qinv + 1, Qinv, Q, prec);
arb_mul(Qinv + 1, Qinv + 1, Q + 1, prec);
arb_neg(Qinv + 1, Qinv + 1);
}
else
{
slong Qnlen, Wlen, W2len;
arb_ptr W;
W = _arb_vec_init(len);
NEWTON_INIT(1, len)
NEWTON_LOOP(m, n)
Qnlen = FLINT_MIN(Qlen, n);
Wlen = FLINT_MIN(Qnlen + m - 1, n);
W2len = Wlen - m;
MULLOW(W, Q, Qnlen, Qinv, m, Wlen, prec);
MULLOW(Qinv + m, Qinv, m, W + m, W2len, n - m, prec);
_arb_vec_neg(Qinv + m, Qinv + m, n - m);
NEWTON_END_LOOP
NEWTON_END
_arb_vec_clear(W, len);
}
}
void
_arb_poly_inv_series(arb_ptr Qinv,
arb_srcptr Q, slong Qlen, slong len, slong prec)
{
Qlen = FLINT_MIN(Qlen, len);
arb_inv(Qinv, Q, prec);
if (Qlen == 1)
{
_arb_vec_zero(Qinv + 1, len - 1);
}
else if (len == 2)
{
arb_mul(Qinv + 1, Qinv, Qinv, prec);
arb_mul(Qinv + 1, Qinv + 1, Q + 1, prec);
arb_neg(Qinv + 1, Qinv + 1);
}
else
{
slong i, j, blen;
/* The basecase algorithm is faster for much larger Qlen or len than
this, but unfortunately also much less numerically stable. */
if (Qlen == 2 || len <= 8)
blen = len;
else
blen = FLINT_MIN(len, 4);
for (i = 1; i < blen; i++)
{
arb_mul(Qinv + i, Q + 1, Qinv + i - 1, prec);
for (j = 2; j < FLINT_MIN(i + 1, Qlen); j++)
arb_addmul(Qinv + i, Q + j, Qinv + i - j, prec);
if (!arb_is_one(Qinv))
arb_mul(Qinv + i, Qinv + i, Qinv, prec);
arb_neg(Qinv + i, Qinv + i);
}
if (len > blen)
{
slong Qnlen, Wlen, W2len;
arb_ptr W;
W = _arb_vec_init(len);
NEWTON_INIT(blen, len)
NEWTON_LOOP(m, n)
Qnlen = FLINT_MIN(Qlen, n);
Wlen = FLINT_MIN(Qnlen + m - 1, n);
W2len = Wlen - m;
MULLOW(W, Q, Qnlen, Qinv, m, Wlen, prec);
MULLOW(Qinv + m, Qinv, m, W + m, W2len, n - m, prec);
_arb_vec_neg(Qinv + m, Qinv + m, n - m);
NEWTON_END_LOOP
NEWTON_END
_arb_vec_clear(W, len);
}
}
}
