/*============================================================================= 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) 2010, 2011 William Hart Copyright (C) 2011 Sebastian Pancratz ******************************************************************************/ #include #include #include "flint.h" #include "nmod_vec.h" #include "nmod_poly.h" #include "ulong_extras.h" void _nmod_poly_rem_basecase_1(mp_ptr R, mp_ptr W, mp_srcptr A, slong lenA, mp_srcptr B, slong lenB, nmod_t mod) { if (lenB > 1) { const mp_limb_t invL = n_invmod(B[lenB - 1], mod.n); slong iR; mp_ptr R1 = W; flint_mpn_copyi(R1, A, lenA); for (iR = lenA - 1; iR >= lenB - 1; iR--) { if (R1[iR] != 0) { const mp_limb_t q = n_mulmod2_preinv(R1[iR], invL, mod.n, mod.ninv); const mp_limb_t c = n_negmod(q, mod.n); mpn_addmul_1(R1 + iR - lenB + 1, B, lenB - 1, c); } } _nmod_vec_reduce(R, R1, lenB - 1, mod); } } void _nmod_poly_rem_basecase_2(mp_ptr R, mp_ptr W, mp_srcptr A, slong lenA, mp_srcptr B, slong lenB, nmod_t mod) { if (lenB > 1) { const mp_limb_t invL = n_invmod(B[lenB - 1], mod.n); slong iR, i; mp_ptr B2 = W, R2 = W + 2*(lenB - 1); for (i = 0; i < lenB - 1; i++) { B2[2 * i] = B[i]; B2[2 * i + 1] = 0; } for (i = 0; i < lenA; i++) { R2[2 * i] = A[i]; R2[2 * i + 1] = 0; } for (iR = lenA - 1; iR >= lenB - 1; iR--) { const mp_limb_t r = n_ll_mod_preinv(R2[2 * iR + 1], R2[2 * iR], mod.n, mod.ninv); if (r != 0) { const mp_limb_t q = n_mulmod2_preinv(r, invL, mod.n, mod.ninv); const mp_limb_t c = n_negmod(q, mod.n); mpn_addmul_1(R2 + 2 * (iR - lenB + 1), B2, 2 * lenB - 2, c); } } for (iR = 0; iR < lenB - 1; iR++) R[iR] = n_ll_mod_preinv(R2[2*iR+1], R2[2*iR], mod.n, mod.ninv); } } void _nmod_poly_rem_basecase_3(mp_ptr R, mp_ptr W, mp_srcptr A, slong lenA, mp_srcptr B, slong lenB, nmod_t mod) { if (lenB > 1) { const mp_limb_t invL = n_invmod(B[lenB - 1], mod.n); slong iR, i; mp_ptr B3 = W, R3 = W + 3*(lenB - 1); for (i = 0; i < lenB - 1; i++) { B3[3 * i] = B[i]; B3[3 * i + 1] = 0; B3[3 * i + 2] = 0; } for (i = 0; i < lenA; i++) { R3[3 * i] = A[i]; R3[3 * i + 1] = 0; R3[3 * i + 2] = 0; } for (iR = lenA - 1; iR >= lenB - 1; iR--) { const mp_limb_t r = n_lll_mod_preinv(R3[3*iR + 2], R3[3*iR + 1], R3[3*iR], mod.n, mod.ninv); if (r != 0) { const mp_limb_t q = n_mulmod2_preinv(r, invL, mod.n, mod.ninv); const mp_limb_t c = n_negmod(q, mod.n); mpn_addmul_1(R3 + 3 * (iR - lenB + 1), B3, 3 * lenB - 3, c); } } for (iR = 0; iR < lenB - 1; iR++) R[iR] = n_lll_mod_preinv(R3[3 * iR + 2], R3[3 * iR + 1], R3[3 * iR], mod.n, mod.ninv); } } void _nmod_poly_rem_basecase(mp_ptr R, mp_ptr W, mp_srcptr A, slong lenA, mp_srcptr B, slong lenB, nmod_t mod) { const slong bits = 2 * (FLINT_BITS - mod.norm) + FLINT_BIT_COUNT(lenA - lenB + 1); if (bits <= FLINT_BITS) _nmod_poly_rem_basecase_1(R, W, A, lenA, B, lenB, mod); else if (bits <= 2 * FLINT_BITS) _nmod_poly_rem_basecase_2(R, W, A, lenA, B, lenB, mod); else _nmod_poly_rem_basecase_3(R, W, A, lenA, B, lenB, mod); } void nmod_poly_rem_basecase(nmod_poly_t R, const nmod_poly_t A, const nmod_poly_t B) { const slong lenA = A->length, lenB = B->length; mp_ptr r, W; nmod_poly_t t; TMP_INIT; if (lenB == 0) { flint_printf("Exception (nmod_poly_rem_basecase). Division by zero.\n"); abort(); } if (lenA < lenB) { nmod_poly_set(R, A); return; } if (R == A || R == B) { nmod_poly_init2_preinv(t, B->mod.n, B->mod.ninv, lenB - 1); r = t->coeffs; } else { nmod_poly_fit_length(R, lenB - 1); r = R->coeffs; } TMP_START; W = TMP_ALLOC(NMOD_DIVREM_BC_ITCH(lenA, lenB, A->mod)*sizeof(mp_limb_t)); _nmod_poly_rem_basecase(r, W, A->coeffs, lenA, B->coeffs, lenB, B->mod); if (R == A || R == B) { nmod_poly_swap(R, t); nmod_poly_clear(t); } R->length = lenB - 1; TMP_END; _nmod_poly_normalise(R); }