void
nmod_poly_div_divconquer(nmod_poly_t Q,
const nmod_poly_t A, const nmod_poly_t B)
{
nmod_poly_t tQ;
mp_ptr q;
long Alen, Blen;
Blen = B->length;
if (Blen == 0)
{
printf("Exception: division by zero in nmod_poly_div_divconquer\n");
abort();
}
Alen = A->length;
if (Alen < Blen)
{
nmod_poly_zero(Q);
return;
}
if (Q == A || Q == B)
{
nmod_poly_init2(tQ, A->mod.n, Alen - Blen + 1);
q = tQ->coeffs;
}
else
{
nmod_poly_fit_length(Q, Alen - Blen + 1);
q = Q->coeffs;
}
_nmod_poly_div_divconquer(q, A->coeffs, Alen,
B->coeffs, Blen, A->mod);
if (Q == A || Q == B)
{
nmod_poly_swap(tQ, Q);
nmod_poly_clear(tQ);
}
Q->length = Alen - Blen + 1;
}
void
_nmod_poly_inv_series_basecase(mp_ptr Qinv,
mp_srcptr Q, long n, nmod_t mod)
{
mp_ptr X2n, Qrev;
X2n = _nmod_vec_init(2*n);
Qrev = X2n + n;
_nmod_poly_reverse(Qrev, Q, n, n);
X2n[n - 1] = 1;
mpn_zero(X2n, n - 1);
X2n -= (n - 1);
_nmod_poly_div_divconquer(Qinv, X2n, 2*n - 1, Qrev, n, mod);
_nmod_poly_reverse(Qinv, Qinv, n, n);
_nmod_vec_free(X2n + n - 1);
}
void
_nmod_poly_div_divconquer(mp_ptr Q, mp_srcptr A, long lenA,
mp_srcptr B, long lenB, nmod_t mod)
{
if (lenA < 2 * lenB - 1)
{
/*
Convert unbalanced division into a 2 n1 - 1 by n1 division
*/
const long n1 = lenA - lenB + 1;
const long n2 = lenB - n1;
mp_srcptr p1 = A + n2;
mp_srcptr d1 = B + n2;
mp_ptr V = _nmod_vec_init(n1 - 1 + NMOD_DIVREM_DC_ITCH(n1, mod));
mp_ptr W = V + NMOD_DIVREM_DC_ITCH(n1, mod);
_nmod_poly_div_divconquer_recursive(Q, W, V, p1, d1, n1, mod);
_nmod_vec_clear(V);
}
else if (lenA > 2 * lenB - 1)
{
/*
We shift A right until it is of length 2 lenB - 1, call this p1
*/
const long shift = lenA - 2 * lenB + 1;
mp_srcptr p1 = A + shift;
mp_ptr V = _nmod_vec_init(lenA + (3 * lenB - 2) + NMOD_DIVREM_DC_ITCH(lenB, mod));
mp_ptr R = V + NMOD_DIVREM_DC_ITCH(lenB, mod);
mp_ptr W = R + lenB - 1;
mp_ptr q1 = Q + shift;
mp_ptr q2 = Q;
mp_ptr dq1 = W;
mp_ptr d1q1 = dq1 + shift;
/*
Set q1 to p1 div B, a 2 lenB - 1 by lenB division, so q1 ends up
being of length lenB; set d1q1 = d1 * q1 of length 2 lenB - 1
*/
_nmod_poly_divrem_divconquer_recursive(q1, d1q1, R, V, p1, B, lenB, mod);
/*
We have dq1 = d1 * q1 * x^shift, of length lenA
Compute R = A - dq1; the first lenB coeffs represent remainder
terms (zero if division is exact), leaving lenA - lenB significant
terms which we use in the division
*/
mpn_copyi(dq1, A, shift);
_nmod_vec_sub(dq1 + shift, A + shift, dq1 + shift, lenB - 1, mod);
/*
Compute q2 = trunc(R) div B; it is a smaller division than the
original since len(trunc(R)) = lenA - lenB
*/
_nmod_poly_div_divconquer(q2, dq1, lenA - lenB, B, lenB, mod);
/*
We have Q = q1 * x^shift + q2; Q has length lenB + shift;
note q2 has length shift since the above division is
lenA - lenB by lenB
*/
_nmod_vec_clear(V);
}
else /* lenA = 2 * lenB - 1 */
{
mp_ptr V = _nmod_vec_init(lenB - 1 + NMOD_DIVREM_DC_ITCH(lenB, mod));
mp_ptr W = V + NMOD_DIVREM_DC_ITCH(lenB, mod);
_nmod_poly_div_divconquer_recursive(Q, W, V, A, B, lenB, mod);
_nmod_vec_clear(V);
}
}