/*============================================================================= 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) 2011 William Hart ******************************************************************************/ #include #include #include "flint.h" #include "nmod_vec.h" #include "nmod_poly.h" #include "ulong_extras.h" void _nmod_poly_div_basecase_1(mp_ptr Q, mp_ptr W, mp_srcptr A, slong A_len, mp_srcptr B, slong B_len, nmod_t mod) { mp_limb_t lead_inv = n_invmod(B[B_len - 1], mod.n); slong len, coeff = A_len - B_len; mp_ptr R1 = W; mp_srcptr Btop = B + B_len - 1; flint_mpn_copyi(R1, A + B_len - 1, A_len - B_len + 1); while (coeff >= 0) { R1[coeff] = n_mod2_preinv(R1[coeff], mod.n, mod.ninv); while (coeff >= 0 && R1[coeff] == WORD(0)) { Q[coeff--] = WORD(0); if (coeff >= 0) R1[coeff] = n_mod2_preinv(R1[coeff], mod.n, mod.ninv); } if (coeff >= 0) { mp_limb_t c, * R_sub; Q[coeff] = n_mulmod2_preinv(R1[coeff], lead_inv, mod.n, mod.ninv); c = n_negmod(Q[coeff], mod.n); len = FLINT_MIN(B_len - 1, coeff); R_sub = R1 + coeff - len; if (len > 0) mpn_addmul_1(R_sub, Btop - len, len, c); coeff--; } } } void _nmod_poly_div_basecase_2(mp_ptr Q, mp_ptr W, mp_srcptr A, slong A_len, mp_srcptr B, slong B_len, nmod_t mod) { slong coeff, i, len; mp_limb_t lead_inv = n_invmod(B[B_len - 1], mod.n); mp_ptr B2, R2; mp_srcptr Btop; B2 = W; for (i = 0; i < B_len - 1; i++) { B2[2 * i] = B[i]; B2[2 * i + 1] = 0; } Btop = B2 + 2*(B_len - 1); R2 = W + 2*(B_len - 1); for (i = 0; i < A_len - B_len + 1; i++) { R2[2 * i] = A[B_len + i - 1]; R2[2 * i + 1] = 0; } coeff = A_len - B_len; while (coeff >= 0) { mp_limb_t r_coeff; r_coeff = n_ll_mod_preinv(R2[2 * coeff + 1], R2[2 * coeff], mod.n, mod.ninv); while (coeff >= 0 && r_coeff == WORD(0)) { Q[coeff--] = WORD(0); if (coeff >= 0) r_coeff = n_ll_mod_preinv(R2[2 * coeff + 1], R2[2 * coeff], mod.n, mod.ninv); } if (coeff >= 0) { mp_limb_t c, * R_sub; Q[coeff] = n_mulmod2_preinv(r_coeff, lead_inv, mod.n, mod.ninv); c = n_negmod(Q[coeff], mod.n); len = FLINT_MIN(B_len - 1, coeff); R_sub = R2 + 2 * (coeff - len); if (len > 0) mpn_addmul_1(R_sub, Btop - 2*len, 2 * len, c); coeff--; } } } void _nmod_poly_div_basecase_3(mp_ptr Q, mp_ptr W, mp_srcptr A, slong A_len, mp_srcptr B, slong B_len, nmod_t mod) { slong coeff, i, len; mp_limb_t lead_inv = n_invmod(B[B_len - 1], mod.n); mp_limb_t r_coeff; mp_ptr B3, R3; mp_srcptr Btop; B3 = W; for (i = 0; i < B_len - 1; i++) { B3[3 * i] = B[i]; B3[3 * i + 1] = 0; B3[3 * i + 2] = 0; } Btop = B3 + 3*(B_len - 1); R3 = W + 3*(B_len - 1); for (i = 0; i < A_len - B_len + 1; i++) { R3[3 * i] = A[B_len + i - 1]; R3[3 * i + 1] = 0; R3[3 * i + 2] = 0; } coeff = A_len - B_len; while (coeff >= 0) { r_coeff = n_lll_mod_preinv(R3[3 * coeff + 2], R3[3 * coeff + 1], R3[3 * coeff], mod.n, mod.ninv); while (coeff >= 0 && r_coeff == WORD(0)) { Q[coeff--] = WORD(0); if (coeff >= 0) r_coeff = n_lll_mod_preinv(R3[3 * coeff + 2], R3[3 * coeff + 1], R3[3 * coeff], mod.n, mod.ninv); } if (coeff >= 0) { mp_limb_t c, * R_sub; Q[coeff] = n_mulmod2_preinv(r_coeff, lead_inv, mod.n, mod.ninv); c = n_negmod(Q[coeff], mod.n); len = FLINT_MIN(B_len - 1, coeff); R_sub = R3 + 3 * (coeff - len); if (len > 0) mpn_addmul_1(R_sub, Btop - 3*len, 3 * len, c); coeff--; } } } void _nmod_poly_div_basecase(mp_ptr Q, mp_ptr W, mp_srcptr A, slong A_len, mp_srcptr B, slong B_len, nmod_t mod) { slong bits = 2 * (FLINT_BITS - mod.norm) + FLINT_BIT_COUNT(A_len - B_len + 1); if (bits <= FLINT_BITS) _nmod_poly_div_basecase_1(Q, W, A, A_len, B, B_len, mod); else if (bits <= 2 * FLINT_BITS) _nmod_poly_div_basecase_2(Q, W, A, A_len, B, B_len, mod); else _nmod_poly_div_basecase_3(Q, W, A, A_len, B, B_len, mod); } void nmod_poly_div_basecase(nmod_poly_t Q, const nmod_poly_t A, const nmod_poly_t B) { mp_ptr Q_coeffs, W; nmod_poly_t t1; slong Alen, Blen; TMP_INIT; Blen = B->length; if (Blen == 0) { flint_printf("Exception (nmod_poly_div_base). Division by zero.\n"); abort(); } Alen = A->length; if (Alen < Blen) { nmod_poly_zero(Q); return; } if (Q == A || Q == B) { nmod_poly_init2_preinv(t1, B->mod.n, B->mod.ninv, Alen - Blen + 1); Q_coeffs = t1->coeffs; } else { nmod_poly_fit_length(Q, Alen - Blen + 1); Q_coeffs = Q->coeffs; } TMP_START; W = TMP_ALLOC(NMOD_DIV_BC_ITCH(Alen, Blen, A->mod)*sizeof(mp_limb_t)); _nmod_poly_div_basecase(Q_coeffs, W, A->coeffs, Alen, B->coeffs, Blen, B->mod); if (Q == A || Q == B) { nmod_poly_swap(Q, t1); nmod_poly_clear(t1); } Q->length = Alen - Blen + 1; TMP_END; _nmod_poly_normalise(Q); }