215 lines
6.7 KiB
C
215 lines
6.7 KiB
C
/*=============================================================================
|
|
|
|
This file is part of FLINT.
|
|
|
|
FLINT is free software; you can redistribute it and/or modify
|
|
it under the terms of the GNU General Public License as published by
|
|
the Free Software Foundation; either version 2 of the License, or
|
|
(at your option) any later version.
|
|
|
|
FLINT is distributed in the hope that it will be useful,
|
|
but WITHOUT ANY WARRANTY; without even the implied warranty of
|
|
MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
|
|
GNU General Public License for more details.
|
|
|
|
You should have received a copy of the GNU General Public License
|
|
along with FLINT; if not, write to the Free Software
|
|
Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA
|
|
|
|
=============================================================================*/
|
|
/******************************************************************************
|
|
|
|
Copyright (C) 2008, 2009 William Hart
|
|
Copyright (C) 2010, 2011 Sebastian Pancratz
|
|
Copyright (C) 2013 Mike Hansen
|
|
|
|
******************************************************************************/
|
|
|
|
|
|
#ifdef T
|
|
|
|
#include "templates.h"
|
|
|
|
static void
|
|
__TEMPLATE(T, poly_divrem_divconquer) (TEMPLATE(T, struct) * Q,
|
|
TEMPLATE(T, struct) * R,
|
|
const TEMPLATE(T, struct) * A, slong lenA,
|
|
const TEMPLATE(T, struct) * B, slong lenB,
|
|
const TEMPLATE(T, t) invB,
|
|
const TEMPLATE(T, ctx_t) ctx)
|
|
{
|
|
if (lenA < 2 * lenB - 1)
|
|
{
|
|
/*
|
|
Convert unbalanced division into a 2 n1 - 1 by n1 division
|
|
*/
|
|
|
|
const slong n1 = lenA - lenB + 1;
|
|
const slong n2 = lenB - n1;
|
|
|
|
const TEMPLATE(T, struct) * p1 = A + n2;
|
|
const TEMPLATE(T, struct) * d1 = B + n2;
|
|
const TEMPLATE(T, struct) * d2 = B;
|
|
|
|
TEMPLATE(T, struct) * W =
|
|
_TEMPLATE(T, vec_init) ((2 * n1 - 1) + lenB - 1, ctx);
|
|
|
|
TEMPLATE(T, struct) * d1q1 = R + n2;
|
|
TEMPLATE(T, struct) * d2q1 = W + (2 * n1 - 1);
|
|
|
|
_TEMPLATE(T, poly_divrem_divconquer_recursive) (Q, d1q1, W, p1, d1, n1,
|
|
invB, ctx);
|
|
|
|
/*
|
|
Compute d2q1 = Q d2, of length lenB - 1
|
|
*/
|
|
|
|
if (n1 >= n2)
|
|
_TEMPLATE(T, poly_mul) (d2q1, Q, n1, d2, n2, ctx);
|
|
else
|
|
_TEMPLATE(T, poly_mul) (d2q1, d2, n2, Q, n1, ctx);
|
|
|
|
/*
|
|
Compute BQ = d1q1 * x^n1 + d2q1, of length lenB - 1;
|
|
then compute R = A - BQ
|
|
*/
|
|
|
|
_TEMPLATE(T, vec_swap) (R, d2q1, n2, ctx);
|
|
_TEMPLATE(T, poly_add) (R + n2, R + n2, n1 - 1, d2q1 + n2, n1 - 1,
|
|
ctx);
|
|
_TEMPLATE(T, poly_sub) (R, A, lenA, R, lenA, ctx);
|
|
|
|
_TEMPLATE(T, vec_clear) (W, (2 * n1 - 1) + lenB - 1, ctx);
|
|
}
|
|
else /* lenA = 2 * lenB - 1 */
|
|
{
|
|
TEMPLATE(T, struct) * W = _TEMPLATE(T, vec_init) (lenA, ctx);
|
|
|
|
_TEMPLATE(T, poly_divrem_divconquer_recursive) (Q, R, W, A, B, lenB,
|
|
invB, ctx);
|
|
|
|
_TEMPLATE(T, poly_sub) (R, A, lenB - 1, R, lenB - 1, ctx);
|
|
|
|
_TEMPLATE(T, vec_clear) (W, lenA, ctx);
|
|
}
|
|
}
|
|
|
|
void
|
|
_TEMPLATE(T, poly_divrem_divconquer) (TEMPLATE(T, struct) * Q,
|
|
TEMPLATE(T, struct) * R,
|
|
const TEMPLATE(T, struct) * A,
|
|
slong lenA, const TEMPLATE(T,
|
|
struct) * B,
|
|
slong lenB, const TEMPLATE(T, t) invB,
|
|
const TEMPLATE(T, ctx_t) ctx)
|
|
{
|
|
if (lenA <= 2 * lenB - 1)
|
|
{
|
|
__TEMPLATE(T, poly_divrem_divconquer) (Q, R, A, lenA, B, lenB, invB,
|
|
ctx);
|
|
}
|
|
else /* lenA > 2 * lenB - 1 */
|
|
{
|
|
slong shift, n = 2 * lenB - 1;
|
|
TEMPLATE(T, struct) * QB, *W;
|
|
|
|
_TEMPLATE(T, vec_set) (R, A, lenA, ctx);
|
|
W = _TEMPLATE(T, vec_init) (2 * n, ctx);
|
|
QB = W + n;
|
|
|
|
while (lenA >= n)
|
|
{
|
|
shift = lenA - n;
|
|
_TEMPLATE(T, poly_divrem_divconquer_recursive) (Q + shift, QB,
|
|
W, R + shift, B,
|
|
lenB, invB, ctx);
|
|
_TEMPLATE(T, poly_sub) (R + shift, R + shift, n, QB, n, ctx);
|
|
lenA -= lenB;
|
|
}
|
|
|
|
if (lenA >= lenB)
|
|
{
|
|
__TEMPLATE(T, poly_divrem_divconquer) (Q, W, R, lenA, B, lenB,
|
|
invB, ctx);
|
|
_TEMPLATE(T, vec_swap) (W, R, lenA, ctx);
|
|
}
|
|
|
|
_TEMPLATE(T, vec_clear) (W, 2 * n, ctx);
|
|
}
|
|
}
|
|
|
|
void
|
|
TEMPLATE(T, poly_divrem_divconquer) (TEMPLATE(T, poly_t) Q,
|
|
TEMPLATE(T, poly_t) R,
|
|
const TEMPLATE(T, poly_t) A,
|
|
const TEMPLATE(T, poly_t) B,
|
|
const TEMPLATE(T, ctx_t) ctx)
|
|
{
|
|
const slong lenA = A->length;
|
|
const slong lenB = B->length;
|
|
const slong lenQ = lenA - lenB + 1;
|
|
|
|
TEMPLATE(T, struct) * q, *r;
|
|
TEMPLATE(T, t) invB;
|
|
|
|
if (lenA < lenB)
|
|
{
|
|
TEMPLATE(T, poly_set) (R, A, ctx);
|
|
TEMPLATE(T, poly_zero) (Q, ctx);
|
|
return;
|
|
}
|
|
|
|
TEMPLATE(T, init) (invB, ctx);
|
|
TEMPLATE(T, inv) (invB, TEMPLATE(T, poly_lead) (B, ctx), ctx);
|
|
|
|
if (Q == A || Q == B)
|
|
{
|
|
q = _TEMPLATE(T, vec_init) (lenQ, ctx);
|
|
}
|
|
else
|
|
{
|
|
TEMPLATE(T, poly_fit_length) (Q, lenQ, ctx);
|
|
q = Q->coeffs;
|
|
}
|
|
|
|
if (R == A || R == B)
|
|
{
|
|
r = _TEMPLATE(T, vec_init) (lenA, ctx);
|
|
}
|
|
else
|
|
{
|
|
TEMPLATE(T, poly_fit_length) (R, lenA, ctx);
|
|
r = R->coeffs;
|
|
}
|
|
|
|
_TEMPLATE(T, poly_divrem_divconquer) (q, r, A->coeffs, lenA,
|
|
B->coeffs, lenB, invB, ctx);
|
|
|
|
if (Q == A || Q == B)
|
|
{
|
|
_TEMPLATE(T, vec_clear) (Q->coeffs, Q->alloc, ctx);
|
|
Q->coeffs = q;
|
|
Q->alloc = lenQ;
|
|
Q->length = lenQ;
|
|
}
|
|
else
|
|
{
|
|
_TEMPLATE(T, poly_set_length) (Q, lenQ, ctx);
|
|
}
|
|
|
|
if (R == A || R == B)
|
|
{
|
|
_TEMPLATE(T, vec_clear) (R->coeffs, R->alloc, ctx);
|
|
R->coeffs = r;
|
|
R->alloc = lenA;
|
|
R->length = lenA;
|
|
}
|
|
_TEMPLATE(T, poly_set_length) (R, lenB - 1, ctx);
|
|
_TEMPLATE(T, poly_normalise) (R, ctx);
|
|
|
|
TEMPLATE(T, clear) (invB, ctx);
|
|
}
|
|
|
|
|
|
#endif
|