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/*
Copyright (C) 2008, 2009 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 "mpn_extras.h"
#include "fmpz.h"
#include "fmpz_vec.h"
#include "fmpz_poly.h"
static void
__fmpz_poly_pseudo_divrem_divconquer(fmpz * Q, fmpz * R,
ulong * d, const fmpz * A, slong lenA,
const fmpz * B, slong lenB, const fmpz_preinvn_t inv)
{
if (lenB <= 16 || (lenA > 2 * lenB - 1 && lenA < 128))
{
_fmpz_poly_pseudo_divrem_basecase(Q, R, d, A, lenA, B, lenB, inv);
}
else
{
const slong n2 = lenB / 2;
const slong n1 = lenB - n2;
const fmpz * d1 = B + n2;
const fmpz * d2 = B;
const fmpz * d3 = B + n1;
const fmpz * d4 = B;
if (lenA <= lenB + n2 - 1)
{
fmpz *p1, *r1, *d2q1;
fmpz *f;
/*
Shift A right by n1, zero the bottom n2 - 1 coeffs; call this p1
*/
p1 = (fmpz *) flint_malloc((lenA - n1) * sizeof(fmpz));
{
slong i;
flint_mpn_zero((nn_ptr) p1, n2 - 1);
for (i = n2 - 1; i < lenA - n1; i++)
p1[i] = (A + n1)[i];
}
/*
Compute p1 div d3, at most a 2 n2 - 1 by n2 division, leaving
lenA - lenB + 1 <= n2 terms in the quotient
*/
r1 = R + n1;
_fmpz_poly_pseudo_divrem_divconquer(Q, r1, d, p1, lenA - n1, d3, n2, inv);
flint_free(p1);
/*
Push the relevant {n2 - 1} terms of the remainder to the
top of {R, lenA}
*/
{
slong i;
for (i = n2 - 2; i >= 0; i--)
fmpz_swap(R + lenA - (n2 - 1) + i, r1 + i);
r1 = R + lenA - (n2 - 1);
}
/*
Compute d2q1 = Q d4 of length lenA - n2, which is
at most n1 + n2 - 1 terms
*/
d2q1 = R;
_fmpz_poly_mul(d2q1, d4, n1, Q, lenA - lenB + 1);
/*
Compute R = L^d R', where R' is the terms of A we have not dealt,
of which there are at most n1 + n2 - 1; that is,
Set R to {A, n1 + n2 - 1} * f + r1 x^n1 - d2q1
*/
_fmpz_vec_neg(R, R, lenA - n2);
_fmpz_vec_add(R + n1, R + n1, R + lenA - n2 + 1, lenA - lenB);
_fmpz_vec_swap(R + lenA - n2, R + 2 * lenA - lenB + 1 - n2, n2 - (lenA - lenB + 1));
f = R + lenB - 1;
fmpz_pow_ui(f, B + (lenB - 1), *d);
_fmpz_vec_scalar_addmul_fmpz(R, A, n1 + n2 - 1, f);
}
else if (lenA > 2 * lenB - 1)
{
/*
XXX: In this case, we expect A to be modifiable
*/
ulong s1, s2;
const slong shift = lenA - 2 * lenB + 1;
fmpz * q1 = Q + shift;
fmpz * q2 = Q;
fmpz * r1 = R;
fmpz *p1, *t;
fmpz_t f;
fmpz_init(f);
/*
Shift A right until it is of length 2 lenB - 1, call this p1;
zero the bottom lenB - 1 coeffs
*/
p1 = (fmpz *) flint_malloc((2 * lenB - 1) * sizeof(fmpz));
{
slong i;
flint_mpn_zero((nn_ptr) p1, lenB - 1);
for (i = lenB - 1; i < 2*lenB - 1; i++)
p1[i] = (A + shift)[i];
}
/*
Set q1 to p1 div B, a 2 lenB - 1 by lenB division, so q1 ends up
being at most length lenB; r1 is of length at most lenB - 1
*/
_fmpz_poly_pseudo_divrem_divconquer(q1, r1, &s1, p1, 2 * lenB - 1, B, lenB, inv);
flint_free(p1);
/*
Compute t = L^s1 a2 + r1 x^shift, of length at most lenA - lenB
since r1 is of length at most lenB - 1. Here a2 is what remains
of A after the first lenR coefficients are removed
*/
t = (fmpz *) A;
fmpz_pow_ui(f, B + (lenB - 1), s1);
_fmpz_vec_scalar_mul_fmpz(t, A, lenA - lenB, f);
_fmpz_vec_add(t + shift, t + shift, r1, lenB - 1);
/*
Compute q2 = t div B; it is a smaller division than the original
since len(t) <= lenA - lenB, and r2 has length at most lenB - 1
*/
_fmpz_poly_pseudo_divrem_divconquer(q2, R, &s2, t, lenA - lenB, B, lenB, inv);
/*
Write out Q = L^s2 q1 x^shift + q2, of length at most
lenB + shift. Note q2 has length at most shift since it is at
most an lenA - lenB by lenB division; q1 cannot have length zero
since we are doing pseudo division
*/
fmpz_pow_ui(f, B + (lenB - 1), s2);
_fmpz_vec_scalar_mul_fmpz(q1, q1, lenB, f);
*d = s1 + s2;
fmpz_clear(f);
}
else /* n1 + 2 n2 - 1 < lenA <= 2 lenB - 1 */
{
fmpz * q1 = Q + n2;
fmpz * q2 = Q;
fmpz * r1 = R;
fmpz * d2q1 = R + (n1 - 1);
fmpz *p1, *t;
fmpz_t f;
ulong s1, s2;
fmpz_init(f);
/*
Set p1 to the top lenA - 2 n2 coeffs of A, clearing the bottom
n1 - 1 coeffs
*/
p1 = (fmpz *) flint_malloc((lenA - 2 * n2) * sizeof(fmpz));
{
slong i;
flint_mpn_zero((nn_ptr) p1, n1 - 1);
for (i = n1 - 1; i < lenA - 2 * n2; i++)
p1[i] = (A + 2 * n2)[i];
}
/*
Set q1 to p1 div d1, at most a 2 n1 - 1 by n1 division, so q1 ends
up being of length at most n1; r1 is of length n1 - 1
*/
_fmpz_poly_pseudo_divrem_divconquer(q1, r1, &s1, p1, lenA - 2 * n2, d1, n1, inv);
flint_free(p1);
/*
Compute d2q1 = d2q1, of length lenA - lenB
Note lenA - lenB <= lenB - 1 <= 2 n2 and lenA - (n1 - 1) > 2 n2,
so we can store d2q1 in the top 2 n2 coeffs of R
*/
if (n2 >= lenA - n1 - 2 * n2 + 1)
_fmpz_poly_mul(d2q1, d2, n2, q1, lenA - (n1 + 2 * n2 - 1));
else
_fmpz_poly_mul(d2q1, q1, lenA - (n1 + 2 * n2 - 1), d2, n2);
/*
Compute
t = L^s1 * (a2 x^{n1 + n2 - 1} + a3)
+ r1 x^{2 n2} - d2q1 x^n2
of length at most lenB + n2 - 1, since r1 is of length at most
n1 - 1 and d2q1 is of length at most n1 + n2 - 1
*/
t = _fmpz_vec_init(n1 + 2 * n2 - 1);
fmpz_pow_ui(f, B + (lenB - 1), s1);
_fmpz_vec_scalar_mul_fmpz(t, A, n1 + 2 * n2 - 1, f);
_fmpz_vec_add(t + 2 * n2, t + 2 * n2, r1, n1 - 1);
_fmpz_vec_sub(t + n2, t + n2, d2q1, lenA - lenB);
/*
Compute q2 = t div B and set R to the remainder, at most a
lenB + n2 - 1 by lenB division, so q2 is of length at most n2
*/
_fmpz_poly_pseudo_divrem_divconquer(q2, R, &s2, t, lenB + n2 - 1, B, lenB, inv);
_fmpz_vec_clear(t, n1 + 2 * n2 - 1);
/*
Write Q = L^s2 q1 x^n2 + q2; note len(q1) is non-zero since
we are performing pseudo division
*/
fmpz_pow_ui(f, B + (lenB - 1), s2);
_fmpz_vec_scalar_mul_fmpz(q1, q1, lenA - lenB + 1 - n2, f);
*d = s1 + s2;
fmpz_clear(f);
}
}
}
void
_fmpz_poly_pseudo_divrem_divconquer(fmpz * Q, fmpz * R,
ulong * d, const fmpz * A, slong lenA,
const fmpz * B, slong lenB, const fmpz_preinvn_t inv)
{
if (lenA <= 2 * lenB - 1)
{
__fmpz_poly_pseudo_divrem_divconquer(Q, R, d, A, lenA, B, lenB, inv);
}
else /* lenA > 2 * lenB - 1 */
{
fmpz *S = _fmpz_vec_init(lenA);
_fmpz_vec_set(S, A, lenA);
__fmpz_poly_pseudo_divrem_divconquer(Q, R, d, S, lenA, B, lenB, inv);
_fmpz_vec_clear(S, lenA);
}
}
void
fmpz_poly_pseudo_divrem_divconquer(fmpz_poly_t Q, fmpz_poly_t R,
ulong * d, const fmpz_poly_t A,
const fmpz_poly_t B)
{
slong lenq, lenr;
fmpz *q, *r;
if (B->length == 0)
{
flint_throw(FLINT_DIVZERO, "(fmpz_poly_pseudo_divrem_divconquer): Division by zero.\n");
}
if (Q == R)
{
flint_throw(FLINT_ERROR, "(fmpz_poly_pseudo_divrem_divconquer): "
"Output arguments Q and R may not be aliased.\n");
}
if (A->length < B->length)
{
fmpz_poly_zero(Q);
fmpz_poly_set(R, A);
*d = 0;
return;
}
lenq = A->length - B->length + 1;
lenr = A->length;
if (Q == A || Q == B)
q = _fmpz_vec_init(lenq);
else
{
fmpz_poly_fit_length(Q, lenq);
q = Q->coeffs;
}
if (R == A || R == B)
r = _fmpz_vec_init(lenr);
else
{
fmpz_poly_fit_length(R, lenr);
r = R->coeffs;
}
_fmpz_poly_pseudo_divrem_divconquer(q, r, d, A->coeffs, A->length,
B->coeffs, B->length, NULL);
lenr = B->length - 1;
FMPZ_VEC_NORM(r, lenr);
if (Q == A || Q == B)
{
_fmpz_vec_clear(Q->coeffs, Q->alloc);
Q->coeffs = q;
Q->alloc = lenq;
Q->length = lenq;
}
else
_fmpz_poly_set_length(Q, lenq);
if (R == A || R == B)
{
_fmpz_vec_clear(R->coeffs, R->alloc);
R->coeffs = r;
R->alloc = A->length;
R->length = lenr;
}
else
_fmpz_poly_set_length(R, lenr);
}