152 lines
4.4 KiB
C
152 lines
4.4 KiB
C
/*=============================================================================
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This file is part of FLINT.
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FLINT is free software; you can redistribute it and/or modify
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it under the terms of the GNU General Public License as published by
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the Free Software Foundation; either version 2 of the License, or
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(at your option) any later version.
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FLINT is distributed in the hope that it will be useful,
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but WITHOUT ANY WARRANTY; without even the implied warranty of
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MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
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GNU General Public License for more details.
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You should have received a copy of the GNU General Public License
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along with FLINT; if not, write to the Free Software
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Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA
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=============================================================================*/
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/******************************************************************************
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Copyright (C) 2008, 2009 William Hart
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Copyright (C) 2010 Sebastian Pancratz
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******************************************************************************/
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#include <stdlib.h>
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#include <gmp.h>
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#include "flint.h"
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#include "fmpz.h"
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#include "fmpz_vec.h"
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#include "fmpz_poly.h"
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#define FLINT_DIVREMLOW_DIVCONQUER_CUTOFF 16
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void
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_fmpz_poly_divremlow_divconquer_recursive(fmpz * Q, fmpz * QB,
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const fmpz * A, const fmpz * B, slong lenB)
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{
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if (lenB <= FLINT_DIVREMLOW_DIVCONQUER_CUTOFF)
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{
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_fmpz_poly_divrem_basecase(Q, QB, A, 2 * lenB - 1, B, lenB);
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_fmpz_vec_sub(QB, A, QB, lenB - 1);
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}
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else
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{
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const slong n2 = lenB / 2;
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const slong n1 = lenB - n2;
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const fmpz * p1 = A + 2 * n2;
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const fmpz * p2;
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const fmpz * d1 = B + n2;
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const fmpz * d2 = B;
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fmpz * q1 = Q + n2;
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fmpz * q2 = Q;
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/*
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Think of the top lenB coefficients of QB as temporary space; this
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code will not depend on {QB, lenB - 1} and W being adjacent
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*/
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fmpz * W = QB + (lenB - 1);
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fmpz *d1q1, *d2q1, *t, *d3q2, *d4q2;
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/*
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Set q1 to p1 div d1, a 2 n1 - 1 by n1 division, so q1 has length
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at most n1; {W, n1 - 1} is d1 * q1 is truncated to length n1 - 1
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*/
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_fmpz_poly_divremlow_divconquer_recursive(q1, W, p1, d1, n1);
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/*
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W is of length lenB, but we only care about the bottom n1 - 1
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coeffs, which we push up by n2 + 1, to the very top; we do this
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manually here instead of via _fmpz_vec_swap() because the source
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and destination arrays overlap
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*/
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d1q1 = W + (n2 + 1);
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{
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slong i;
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for (i = 0; i < n1 - 1; i++)
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fmpz_swap(d1q1 + i, W + i);
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}
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/*
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Compute d2q1 = d2 * q1, of length at most lenB - 1; we'll need the
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top n2 coeffs for t and the bottom n1 - 1 coeffs for QB
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*/
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d2q1 = QB;
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_fmpz_poly_mul(d2q1, q1, n1, d2, n2);
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/*
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Compute {t - (n2 - 1), 2 n2 - 1} to be the top 2 n2 - 1 coeffs of
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A / x^n2 - (d1q1 x^n2 + d2q1).
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Note that actually the bottom n2 - 1 coeffs may be arbitrary
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*/
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t = W + n1;
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if (n1 == n2)
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fmpz_zero(t);
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_fmpz_vec_add(t, t, d2q1 + (n1 - 1), n2);
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_fmpz_vec_neg(t, t, n2);
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_fmpz_vec_add(t, t, A + (n1 + n2 - 1), n2);
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p2 = t - (n2 - 1);
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/*
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Move {QB, n1 - 1} into the bottom coefficients of W, so that
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we can use {QB, 2 n2 - 1} as space in the next division
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*/
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_fmpz_vec_swap(QB, W, n1 - 1);
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/*
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Compute q2 = t div {B + n1}, a 2 n2 - 1 by n2 division
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*/
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d3q2 = QB;
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_fmpz_poly_divremlow_divconquer_recursive(q2, d3q2, p2, B + n1, n2);
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_fmpz_vec_swap(QB + n1, d3q2, n2 - 1);
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if (lenB & WORD(1))
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fmpz_zero(QB + n2);
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_fmpz_vec_add(QB + n2, QB + n2, W, n1 - 1);
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/*
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Compute {d4q2, lenB - 1} as {B, n1} * {q2, n2}; then move the
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bottom n2 coeffs of this into {QB, n2}, and add the top n1 - 1
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coeffs to {QB + n2, n1 - 1}
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*/
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d4q2 = W;
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_fmpz_poly_mul(d4q2, B, n1, q2, n2);
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_fmpz_vec_swap(QB, d4q2, n2);
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_fmpz_vec_add(QB + n2, QB + n2, d4q2 + n2, n1 - 1);
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}
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}
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