void
_nmod_poly_divrem_divconquer_recursive(mp_ptr Q, mp_ptr BQ, mp_ptr W, mp_ptr V,
mp_srcptr A, mp_srcptr B, slong lenB, nmod_t mod)
{
if (lenB <= NMOD_DIVREM_DIVCONQUER_CUTOFF)
{
mp_ptr t = V;
mp_ptr w = t + 2*lenB - 1;
flint_mpn_copyi(t + lenB - 1, A + lenB - 1, lenB);
flint_mpn_zero(t, lenB - 1);
_nmod_poly_divrem_basecase(Q, BQ, w, t, 2 * lenB - 1, B, lenB, mod);
/* BQ = A - R */
_nmod_vec_neg(BQ, BQ, lenB - 1, mod);
}
else
{
const slong n2 = lenB / 2;
const slong n1 = lenB - n2;
mp_ptr W1 = W;
mp_ptr W2 = W + n2;
mp_srcptr p1 = A + 2 * n2;
mp_srcptr p2;
mp_srcptr d1 = B + n2;
mp_srcptr d2 = B;
mp_srcptr d3 = B + n1;
mp_srcptr d4 = B;
mp_ptr q1 = Q + n2;
mp_ptr q2 = Q;
mp_ptr dq1 = BQ + n2;
mp_ptr d1q1 = BQ + n2 - (n1 - 1);
mp_ptr d2q1, d3q2, d4q2, t;
/*
Set q1 to p1 div d1, a 2 n1 - 1 by n1 division so q1 ends up
being of length n1; low(d1q1) = d1 q1 is of length n1 - 1
*/
_nmod_poly_divrem_divconquer_recursive(q1, d1q1, W1, V, p1, d1, n1, mod);
/*
Compute bottom n1 + n2 - 1 coeffs of d2q1 = d2 q1
*/
d2q1 = W1;
_nmod_poly_mullow(d2q1, q1, n1, d2, n2, n1 + n2 - 1, mod);
/*
Compute dq1 = d1 q1 x^n2 + d2 q1, of length n1 + n2 - 1
Split it into a segment of length n1 - 1 at dq1 and a piece
of length n2 at BQ.
*/
flint_mpn_copyi(dq1, d2q1, n1 - 1);
if (n2 > n1 - 1)
BQ[0] = d2q1[n1 - 1];
_nmod_vec_add(d1q1, d1q1, d2q1 + n2, n1 - 1, mod);
/*
Compute t = A/x^n2 - dq1, which has length 2 n1 + n2 - 1, but we
are not interested in the top n1 coeffs as they will be zero, so
this has effective length n1 + n2 - 1
For the following division, we want to set {p2, 2 n2 - 1} to the
top 2 n2 - 1 coeffs of this
Since the bottom n2 - 1 coeffs of p2 are irrelevant for the
division, we in fact set {t, n2} to the relevant coeffs
*/
t = W1;
_nmod_vec_sub(t, A + n2 + (n1 - 1), BQ, n2, mod);
p2 = t - (n2 - 1);
/*
Compute q2 = t div d3, a 2 n2 - 1 by n2 division, so q2 will have
length n2; let low(d3q2) = d3 q2, of length n2 - 1
*/
d3q2 = BQ;
_nmod_poly_divrem_divconquer_recursive(q2, d3q2, W2, V, p2, d3, n2, mod);
/*
Compute d4q2 = d4 q2, of length n1 + n2 - 1
*/
d4q2 = W1;
_nmod_poly_mullow(d4q2, d4, n1, q2, n2, n1 + n2 - 1, mod);
/*
Compute dq2 = d3q2 x^n1 + d4q2, of length n1 + n2 - 1
*/
_nmod_vec_add(BQ + n1, BQ + n1, d3q2, n2 - 1, mod);
flint_mpn_copyi(BQ, d4q2, n2);
_nmod_vec_add(BQ + n2, BQ + n2, d4q2 + n2, n1 - 1, mod);
/*
Note Q = q1 x^n2 + q2, and BQ = dq1 x^n2 + dq2
*/
}
}
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);
}
}
void
_nmod_poly_div_divconquer_recursive(mp_ptr Q, mp_ptr W, mp_ptr V,
mp_srcptr A, mp_srcptr B, long lenB, nmod_t mod)
{
if (lenB <= NMOD_DIV_DIVCONQUER_CUTOFF)
{
_nmod_poly_div_basecase(Q, V, A, 2 * lenB - 1, B, lenB, mod);
}
else
{
const long n2 = lenB / 2;
const long n1 = lenB - n2;
mp_ptr W1 = W;
mp_ptr W2 = W + n2;
mp_srcptr p1 = A + 2 * n2;
mp_srcptr p2;
mp_srcptr d1 = B + n2;
mp_srcptr d2 = B;
mp_srcptr d3 = B + n1;
mp_ptr q1 = Q + n2;
mp_ptr q2 = Q;
mp_ptr d1q1 = q2 + n2 - (n1 - 1);
mp_ptr d2q1, t;
/*
Set q1 to p1 div d1, a 2 n1 - 1 by n1 division so q1 ends up
being of length n1; low(d1q1) = d1 q1 is of length n1 - 1
*/
_nmod_poly_divrem_divconquer_recursive(q1, d1q1, W1, V, p1, d1, n1, mod);
/*
Compute bottom n1 + n2 - 1 coeffs of d2q1 = d2 q1
*/
d2q1 = W1;
_nmod_poly_mullow(d2q1, q1, n1, d2, n2, n1 + n2 - 1, mod);
/*
Compute dq1 = d1 q1 x^n2 + d2 q1, of length n1 + n2 - 1
Split it into a segment of length n1 - 1 at which is ignored
and a piece of length n2 at BQ.
*/
if (n2 > n1 - 1)
W1[0] = d2q1[n1 - 1];
_nmod_vec_add(W1 + n2 - (n1 - 1), d1q1, d2q1 + n2, n1 - 1, mod);
/*
Compute t = A/x^n2 - dq1, which has length 2 n1 + n2 - 1, but we
are not interested in the top n1 coeffs as they will be zero, so
this has effective length n1 + n2 - 1
For the following division, we want to set {p2, 2 n2 - 1} to the
top 2 n2 - 1 coeffs of this
Since the bottom n2 - 1 coeffs of p2 are irrelevant for the
division, we in fact set {t, n2} to the relevant coeffs
*/
t = W1;
_nmod_vec_sub(t, A + n2 + (n1 - 1), t, n2, mod);
p2 = t - (n2 - 1);
/*
Compute q2 = t div d3, a 2 n2 - 1 by n2 division, so q2 will have
length n2;
*/
_nmod_poly_div_divconquer_recursive(q2, W2, V, p2, d3, n2, mod);
/*
Note Q = q1 x^n2 + q2
*/
}
}
