142 lines
4.3 KiB
C
142 lines
4.3 KiB
C
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/*=============================================================================
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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, 2011 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 "nmod_vec.h"
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#include "nmod_poly.h"
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void
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_nmod_poly_divrem_divconquer_recursive(mp_ptr Q, mp_ptr BQ, mp_ptr W, mp_ptr V,
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mp_srcptr A, mp_srcptr B, slong lenB, nmod_t mod)
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{
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if (lenB <= NMOD_DIVREM_DIVCONQUER_CUTOFF)
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{
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mp_ptr t = V;
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mp_ptr w = t + 2*lenB - 1;
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flint_mpn_copyi(t + lenB - 1, A + lenB - 1, lenB);
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flint_mpn_zero(t, lenB - 1);
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_nmod_poly_divrem_basecase(Q, BQ, w, t, 2 * lenB - 1, B, lenB, mod);
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/* BQ = A - R */
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_nmod_vec_neg(BQ, BQ, lenB - 1, mod);
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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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mp_ptr W1 = W;
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mp_ptr W2 = W + n2;
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mp_srcptr p1 = A + 2 * n2;
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mp_srcptr p2;
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mp_srcptr d1 = B + n2;
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mp_srcptr d2 = B;
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mp_srcptr d3 = B + n1;
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mp_srcptr d4 = B;
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mp_ptr q1 = Q + n2;
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mp_ptr q2 = Q;
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mp_ptr dq1 = BQ + n2;
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mp_ptr d1q1 = BQ + n2 - (n1 - 1);
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mp_ptr d2q1, d3q2, d4q2, t;
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/*
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Set q1 to p1 div d1, a 2 n1 - 1 by n1 division so q1 ends up
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being of length n1; low(d1q1) = d1 q1 is of length n1 - 1
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*/
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_nmod_poly_divrem_divconquer_recursive(q1, d1q1, W1, V, p1, d1, n1, mod);
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/*
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Compute bottom n1 + n2 - 1 coeffs of d2q1 = d2 q1
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*/
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d2q1 = W1;
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_nmod_poly_mullow(d2q1, q1, n1, d2, n2, n1 + n2 - 1, mod);
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/*
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Compute dq1 = d1 q1 x^n2 + d2 q1, of length n1 + n2 - 1
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Split it into a segment of length n1 - 1 at dq1 and a piece
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of length n2 at BQ.
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*/
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flint_mpn_copyi(dq1, d2q1, n1 - 1);
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if (n2 > n1 - 1)
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BQ[0] = d2q1[n1 - 1];
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_nmod_vec_add(d1q1, d1q1, d2q1 + n2, n1 - 1, mod);
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/*
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Compute t = A/x^n2 - dq1, which has length 2 n1 + n2 - 1, but we
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are not interested in the top n1 coeffs as they will be zero, so
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this has effective length n1 + n2 - 1
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For the following division, we want to set {p2, 2 n2 - 1} to the
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top 2 n2 - 1 coeffs of this
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Since the bottom n2 - 1 coeffs of p2 are irrelevant for the
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division, we in fact set {t, n2} to the relevant coeffs
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*/
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t = W1;
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_nmod_vec_sub(t, A + n2 + (n1 - 1), BQ, n2, mod);
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p2 = t - (n2 - 1);
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/*
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Compute q2 = t div d3, a 2 n2 - 1 by n2 division, so q2 will have
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length n2; let low(d3q2) = d3 q2, of length n2 - 1
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*/
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d3q2 = BQ;
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_nmod_poly_divrem_divconquer_recursive(q2, d3q2, W2, V, p2, d3, n2, mod);
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/*
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Compute d4q2 = d4 q2, of length n1 + n2 - 1
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*/
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d4q2 = W1;
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_nmod_poly_mullow(d4q2, d4, n1, q2, n2, n1 + n2 - 1, mod);
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/*
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Compute dq2 = d3q2 x^n1 + d4q2, of length n1 + n2 - 1
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*/
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_nmod_vec_add(BQ + n1, BQ + n1, d3q2, n2 - 1, mod);
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flint_mpn_copyi(BQ, d4q2, n2);
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_nmod_vec_add(BQ + n2, BQ + n2, d4q2 + n2, n1 - 1, mod);
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/*
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Note Q = q1 x^n2 + q2, and BQ = dq1 x^n2 + dq2
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*/
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}
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}
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