362 lines
12 KiB
C
362 lines
12 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) 2011 William Hart
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Copyright (C) 2011 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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#include "nmod_poly_mat.h"
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#include "mpn_extras.h"
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/*
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We define a whole bunch of macros here which essentially provide
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the nmod_poly functionality as far as the setting of coefficient
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data and lengths is concerned, but which do not do any separate
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memory allocation. None of these macros support aliasing.
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*/
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#define __set(B, lenB, A, lenA) \
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do { \
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_nmod_vec_set((B), (A), (lenA)); \
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(lenB) = (lenA); \
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} while (0)
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#define __add(C, lenC, A, lenA, B, lenB) \
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do { \
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_nmod_poly_add((C), (A), (lenA), (B), (lenB), mod); \
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(lenC) = FLINT_MAX((lenA), (lenB)); \
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MPN_NORM((C), (lenC)); \
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} while (0)
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#define __sub(C, lenC, A, lenA, B, lenB) \
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do { \
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_nmod_poly_sub((C), (A), (lenA), (B), (lenB), mod); \
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(lenC) = FLINT_MAX((lenA), (lenB)); \
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MPN_NORM((C), (lenC)); \
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} while (0)
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#define __mul(C, lenC, A, lenA, B, lenB) \
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do { \
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if ((lenA) != 0 && (lenB) != 0) \
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{ \
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if ((lenA) >= (lenB)) \
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_nmod_poly_mul((C), (A), (lenA), (B), (lenB), mod); \
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else \
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_nmod_poly_mul((C), (B), (lenB), (A), (lenA), mod); \
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(lenC) = (lenA) + (lenB) - 1; \
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} \
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else \
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{ \
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(lenC) = 0; \
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} \
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} while (0)
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#define __divrem(Q, lenQ, R, lenR, A, lenA, B, lenB) \
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do { \
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if ((lenA) >= (lenB)) \
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{ \
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_nmod_poly_divrem((Q), (R), (A), (lenA), (B), (lenB), mod); \
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(lenQ) = (lenA) - (lenB) + 1; \
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(lenR) = (lenB) - 1; \
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MPN_NORM((R), (lenR)); \
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} \
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else \
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{ \
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_nmod_vec_set((R), (A), (lenA)); \
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(lenQ) = 0; \
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(lenR) = (lenA); \
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} \
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} while (0)
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#define __div(Q, lenQ, A, lenA, B, lenB) \
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do { \
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if ((lenA) >= (lenB)) \
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{ \
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_nmod_poly_div((Q), (A), (lenA), (B), (lenB), mod); \
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(lenQ) = (lenA) - (lenB) + 1; \
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} \
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else \
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{ \
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(lenQ) = 0; \
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} \
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} while (0)
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slong _nmod_poly_xgcd_hgcd(mp_ptr G, mp_ptr S, mp_ptr T,
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mp_srcptr A, slong lenA, mp_srcptr B, slong lenB,
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nmod_t mod)
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{
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const slong cutoff = FLINT_BIT_COUNT(mod.n) <= 8 ?
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NMOD_POLY_SMALL_GCD_CUTOFF : NMOD_POLY_GCD_CUTOFF;
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slong lenG, lenS, lenT;
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if (lenB == 1)
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{
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G[0] = B[0];
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T[0] = 1;
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lenG = 1;
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lenS = 0;
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lenT = 1;
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}
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else
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{
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mp_ptr q = _nmod_vec_init(lenA + lenB);
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mp_ptr r = q + lenA;
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slong lenq, lenr;
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__divrem(q, lenq, r, lenr, A, lenA, B, lenB);
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if (lenr == 0)
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{
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__set(G, lenG, B, lenB);
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T[0] = 1;
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lenS = 0;
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lenT = 1;
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}
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else
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{
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mp_ptr h, j, v, w, R[4], X;
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slong lenh, lenj, lenv, lenw, lenR[4];
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int sgnR;
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lenh = lenj = lenB;
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lenv = lenw = lenA + lenB - 2;
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lenR[0] = lenR[1] = lenR[2] = lenR[3] = (lenB + 1) / 2;
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X = _nmod_vec_init(2 * lenh + 2 * lenv + 4 * lenR[0]);
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h = X;
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j = h + lenh;
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v = j + lenj;
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w = v + lenv;
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R[0] = w + lenw;
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R[1] = R[0] + lenR[0];
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R[2] = R[1] + lenR[1];
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R[3] = R[2] + lenR[2];
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sgnR = _nmod_poly_hgcd(R, lenR, h, &lenh, j, &lenj, B, lenB, r, lenr, mod);
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if (sgnR > 0)
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{
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_nmod_vec_neg(S, R[1], lenR[1], mod);
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_nmod_vec_set(T, R[0], lenR[0]);
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}
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else
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{
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_nmod_vec_set(S, R[1], lenR[1]);
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_nmod_vec_neg(T, R[0], lenR[0], mod);
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}
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lenS = lenR[1];
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lenT = lenR[0];
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while (lenj != 0)
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{
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__divrem(q, lenq, r, lenr, h, lenh, j, lenj);
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__mul(v, lenv, q, lenq, T, lenT);
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{
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slong l;
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_nmod_vec_swap(S, T, FLINT_MAX(lenS, lenT));
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l = lenS; lenS = lenT; lenT = l;
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}
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__sub(T, lenT, T, lenT, v, lenv);
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if (lenr == 0)
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{
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__set(G, lenG, j, lenj);
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goto cofactor;
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}
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if (lenj < cutoff)
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{
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mp_ptr u0 = R[0], u1 = R[1];
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slong lenu0 = lenr - 1, lenu1 = lenj - 1;
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lenG = _nmod_poly_xgcd_euclidean(G, u0, u1, j, lenj, r, lenr, mod);
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MPN_NORM(u0, lenu0);
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MPN_NORM(u1, lenu1);
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__mul(v, lenv, S, lenS, u0, lenu0);
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__mul(w, lenw, T, lenT, u1, lenu1);
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__add(S, lenS, v, lenv, w, lenw);
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goto cofactor;
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}
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sgnR = _nmod_poly_hgcd(R, lenR, h, &lenh, j, &lenj, j,lenj, r, lenr, mod);
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__mul(v, lenv, R[1], lenR[1], T, lenT);
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__mul(w, lenw, R[2], lenR[2], S, lenS);
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__mul(q, lenq, S, lenS, R[3], lenR[3]);
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if (sgnR > 0)
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__sub(S, lenS, q, lenq, v, lenv);
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else
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__sub(S, lenS, v, lenv, q, lenq);
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__mul(q, lenq, T, lenT, R[0], lenR[0]);
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if (sgnR > WORD(0))
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__sub(T, lenT, q, lenq, w, lenw);
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else
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__sub(T, lenT, w, lenw, q, lenq);
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}
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__set(G, lenG, h, lenh);
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cofactor:
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__mul(v, lenv, S, lenS, A, lenA);
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__sub(w, lenw, G, lenG, v, lenv);
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__div(T, lenT, w, lenw, B, lenB);
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_nmod_vec_clear(X);
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}
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_nmod_vec_clear(q);
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}
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flint_mpn_zero(S + lenS, lenB - 1 - lenS);
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flint_mpn_zero(T + lenT, lenA - 1 - lenT);
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return lenG;
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}
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void
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nmod_poly_xgcd_hgcd(nmod_poly_t G, nmod_poly_t S, nmod_poly_t T,
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const nmod_poly_t A, const nmod_poly_t B)
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{
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if (A->length < B->length)
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{
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nmod_poly_xgcd_hgcd(G, T, S, B, A);
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}
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else /* lenA >= lenB >= 0 */
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{
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const slong lenA = A->length, lenB = B->length;
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mp_limb_t inv;
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if (lenA == 0) /* lenA = lenB = 0 */
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{
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nmod_poly_zero(G);
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nmod_poly_zero(S);
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nmod_poly_zero(T);
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}
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else if (lenB == 0) /* lenA > lenB = 0 */
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{
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inv = n_invmod(A->coeffs[lenA - 1], A->mod.n);
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nmod_poly_scalar_mul_nmod(G, A, inv);
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nmod_poly_zero(T);
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nmod_poly_set_coeff_ui(S, 0, inv);
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S->length = 1;
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}
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else if (lenB == 1) /* lenA >= lenB = 1 */
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{
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nmod_poly_fit_length(T, 1);
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T->length = 1;
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T->coeffs[0] = n_invmod(B->coeffs[0], A->mod.n);
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nmod_poly_one(G);
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nmod_poly_zero(S);
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}
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else /* lenA >= lenB >= 2 */
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{
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mp_ptr g, s, t;
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slong lenG;
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if (G == A || G == B)
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{
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g = _nmod_vec_init(FLINT_MIN(lenA, lenB));
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}
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else
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{
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nmod_poly_fit_length(G, FLINT_MIN(lenA, lenB));
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g = G->coeffs;
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}
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if (S == A || S == B)
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{
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s = _nmod_vec_init(FLINT_MAX(lenB - 1, 2));
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}
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else
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{
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nmod_poly_fit_length(S, FLINT_MAX(lenB - 1, 2));
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s = S->coeffs;
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}
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if (T == A || T == B)
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{
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t = _nmod_vec_init(FLINT_MAX(lenA - 1, 2));
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}
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else
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{
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nmod_poly_fit_length(T, FLINT_MAX(lenA - 1, 2));
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t = T->coeffs;
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}
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if (lenA >= lenB)
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lenG = _nmod_poly_xgcd_hgcd(g, s, t, A->coeffs, lenA,
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B->coeffs, lenB, A->mod);
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else
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lenG = _nmod_poly_xgcd_hgcd(g, t, s, B->coeffs, lenB,
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A->coeffs, lenA, A->mod);
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if (G == A || G == B)
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{
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flint_free(G->coeffs);
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G->coeffs = g;
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G->alloc = FLINT_MIN(lenA, lenB);
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}
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if (S == A || S == B)
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{
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flint_free(S->coeffs);
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S->coeffs = s;
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S->alloc = FLINT_MAX(lenB - 1, 2);
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}
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if (T == A || T == B)
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{
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flint_free(T->coeffs);
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T->coeffs = t;
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T->alloc = FLINT_MAX(lenA - 1, 2);
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}
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G->length = lenG;
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S->length = FLINT_MAX(lenB - lenG, 1);
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T->length = FLINT_MAX(lenA - lenG, 1);
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MPN_NORM(S->coeffs, S->length);
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MPN_NORM(T->coeffs, T->length);
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if (G->coeffs[lenG - 1] != 1)
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{
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inv = n_invmod(G->coeffs[lenG - 1], A->mod.n);
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nmod_poly_scalar_mul_nmod(G, G, inv);
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nmod_poly_scalar_mul_nmod(S, S, inv);
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nmod_poly_scalar_mul_nmod(T, T, inv);
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}
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}
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}
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}
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#undef __set
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#undef __add
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#undef __sub
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#undef __mul
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#undef __divrem
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#undef __div
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