void _fmpz_mod_poly_radix(fmpz **B, const fmpz *F, fmpz **Rpow, fmpz **Rinv,
long degR, long k, long i, fmpz *W, const fmpz_t p)
{
if (i == -1)
{
_fmpz_vec_set(B[k], F, degR);
}
else
{
const long lenQ = (1L << i) * degR;
fmpz *Frev = W;
fmpz *Q = W + lenQ;
fmpz *S = W;
_fmpz_poly_reverse(Frev, F + lenQ, lenQ, lenQ);
_fmpz_mod_poly_mullow(Q, Frev, lenQ, Rinv[i], lenQ, p, lenQ);
_fmpz_poly_reverse(Q, Q, lenQ, lenQ);
_fmpz_mod_poly_radix(B, Q, Rpow, Rinv, degR, k + (1L << i), i-1, W, p);
_fmpz_mod_poly_mullow(S, Rpow[i], lenQ, Q, lenQ, p, lenQ);
_fmpz_mod_poly_sub(S, F, lenQ, S, lenQ, p);
_fmpz_mod_poly_radix(B, S, Rpow, Rinv, degR, k, i-1, W + lenQ, p);
}
}
void fmpq_poly_reverse(fmpq_poly_t res, const fmpq_poly_t poly, slong n)
{
slong len = FLINT_MIN(n, poly->length);
if (len == 0)
{
fmpq_poly_zero(res);
return;
}
fmpq_poly_fit_length(res, n);
_fmpz_poly_reverse(res->coeffs, poly->coeffs, len, n);
fmpz_set(res->den, poly->den);
_fmpq_poly_set_length(res, n);
fmpq_poly_canonicalise(res);
}
void
_fmpq_poly_inv_series_newton(fmpz * Qinv, fmpz_t Qinvden,
const fmpz * Q, const fmpz_t Qden, long n)
{
if (n == 1)
{
if (fmpz_sgn(Q) > 0)
{
fmpz_set(Qinv, Qden);
fmpz_set(Qinvden, Q);
}
else
{
fmpz_neg(Qinv, Qden);
fmpz_neg(Qinvden, Q);
}
}
else
{
const long alloc = FLINT_MAX(n, 3 * FMPQ_POLY_INV_NEWTON_CUTOFF);
long *a, i, m;
fmpz *W, *Wden;
W = _fmpz_vec_init(alloc + 1);
Wden = W + alloc;
for (i = 1; (1L << i) < n; i++) ;
a = (long *) flint_malloc(i * sizeof(long));
a[i = 0] = n;
while (n >= FMPQ_POLY_INV_NEWTON_CUTOFF)
a[++i] = (n = (n + 1) / 2);
/* Base case */
{
fmpz *rev = W + 2 * FMPQ_POLY_INV_NEWTON_CUTOFF;
_fmpz_poly_reverse(rev, Q, n, n);
_fmpz_vec_zero(W, 2*n - 2);
fmpz_one(W + (2*n - 2));
fmpz_one(Wden);
_fmpq_poly_div(Qinv, Qinvden, W, Wden, 2*n - 1, rev, Qden, n);
_fmpq_poly_canonicalise(Qinv, Qinvden, n);
_fmpz_poly_reverse(Qinv, Qinv, n, n);
}
for (i--; i >= 0; i--)
{
m = n;
n = a[i];
_fmpz_poly_mullow(W, Q, n, Qinv, m, n);
fmpz_mul(Wden, Qden, Qinvden);
_fmpz_poly_mullow(Qinv + m, Qinv, m, W + m, n - m, n - m);
fmpz_mul(Qinvden, Qinvden, Wden);
_fmpz_vec_scalar_mul_fmpz(Qinv, Qinv, m, Wden);
_fmpz_vec_neg(Qinv + m, Qinv + m, n - m);
_fmpq_poly_canonicalise(Qinv, Qinvden, n);
}
_fmpz_vec_clear(W, alloc + 1);
flint_free(a);
}
}
