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/*
Copyright (C) 2008, 2009, 2019 William Hart
Copyright (C) 2010 Sebastian Pancratz
This file is part of FLINT.
FLINT is free software: you can redistribute it and/or modify it under
the terms of the GNU Lesser General Public License (LGPL) as published
by the Free Software Foundation; either version 3 of the License, or
(at your option) any later version. See <https://www.gnu.org/licenses/>.
*/
#include "fmpz.h"
#include "fmpz_vec.h"
#include "fmpz_poly.h"
#define FLINT_DIVREM_DIVCONQUER_CUTOFF 16
int
_fmpz_poly_divrem_divconquer_recursive(fmpz * Q, fmpz * BQ, fmpz * W,
const fmpz * A, const fmpz * B,
slong lenB, int exact)
{
if (lenB <= FLINT_DIVREM_DIVCONQUER_CUTOFF)
{
_fmpz_vec_zero(BQ, lenB - 1);
_fmpz_vec_set(BQ + (lenB - 1), A + (lenB - 1), lenB);
if (!_fmpz_poly_divrem_basecase(Q, BQ, BQ, 2 * lenB - 1, B, lenB, exact))
return 0;
_fmpz_vec_neg(BQ, BQ, lenB - 1);
_fmpz_vec_sub(BQ + (lenB - 1), A + (lenB - 1), BQ + (lenB - 1), lenB);
}
else
{
const slong n2 = lenB / 2;
const slong n1 = lenB - n2;
fmpz * W1 = W;
fmpz * W2 = W + lenB;
const fmpz * p1 = A + 2 * n2;
const fmpz * p2;
const fmpz * d1 = B + n2;
const fmpz * d2 = B;
const fmpz * d3 = B + n1;
const fmpz * d4 = B;
fmpz * q1 = Q + n2;
fmpz * q2 = Q;
fmpz * dq1 = BQ + n2;
fmpz * d1q1 = BQ + 2 * n2;
fmpz *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; d1q1 = d1 q1 is of length 2 n1 - 1
*/
if (!_fmpz_poly_divrem_divconquer_recursive(q1, d1q1, W1, p1, d1, n1, exact))
return 0;
/*
Compute d2q1 = d2 q1, of length lenB - 1
*/
d2q1 = W1;
_fmpz_poly_mul(d2q1, q1, n1, d2, n2);
/*
Compute dq1 = d1 q1 x^n2 + d2 q1, of length 2 n1 + n2 - 1
*/
_fmpz_vec_swap(dq1, d2q1, n2);
_fmpz_vec_add(dq1 + n2, dq1 + n2, d2q1 + n2, n1 - 1);
/*
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 = BQ;
_fmpz_vec_sub(t, A + n2 + (n1 - 1), dq1 + (n1 - 1), n2);
p2 = t - (n2 - 1);
/*
Compute q2 = t div d3, a 2 n2 - 1 by n2 division, so q2 will have
length n2; let d3q2 = d3 q2, of length 2 n2 - 1
*/
d3q2 = W1;
if (!_fmpz_poly_divrem_divconquer_recursive(q2, d3q2, W2, p2, d3, n2, exact))
return 0;
/*
Compute d4q2 = d4 q2, of length n1 + n2 - 1 = lenB - 1
*/
d4q2 = W2;
_fmpz_poly_mul(d4q2, d4, n1, q2, n2);
/*
Compute dq2 = d3q2 x^n1 + d4q2, of length n1 + 2 n2 - 1
*/
_fmpz_vec_swap(BQ, d4q2, n2);
_fmpz_vec_add(BQ + n2, BQ + n2, d4q2 + n2, n1 - 1);
_fmpz_vec_add(BQ + n1, BQ + n1, d3q2, 2 * n2 - 1);
/*
Note Q = q1 x^n2 + q2, and BQ = dq1 x^n2 + dq2
*/
}
return 1;
}