146 lines
3.8 KiB
C
146 lines
3.8 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) 2012 Fredrik Johansson
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******************************************************************************/
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#include <gmp.h>
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#include "flint.h"
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#include "ulong_extras.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_interpolation_weights(mp_ptr w, const mp_ptr * tree, slong len, nmod_t mod)
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{
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mp_ptr tmp;
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slong i, n, height;
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if (len == 0)
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return;
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if (len == 1)
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{
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w[0] = 1;
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return;
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}
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tmp = _nmod_vec_init(len + 1);
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height = FLINT_CLOG2(len);
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n = WORD(1) << (height - 1);
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_nmod_poly_mul(tmp, tree[height-1], n + 1,
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tree[height-1] + (n + 1), (len - n + 1), mod);
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_nmod_poly_derivative(tmp, tmp, len + 1, mod);
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_nmod_poly_evaluate_nmod_vec_fast_precomp(w, tmp, len, tree, len, mod);
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for (i = 0; i < len; i++)
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w[i] = n_invmod(w[i], mod.n);
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_nmod_vec_clear(tmp);
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}
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void
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_nmod_poly_interpolate_nmod_vec_fast_precomp(mp_ptr poly, mp_srcptr ys,
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const mp_ptr * tree, mp_srcptr weights, slong len, nmod_t mod)
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{
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mp_ptr t, u, pa, pb;
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slong i, pow, left;
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if (len == 0)
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return;
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t = _nmod_vec_init(len);
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u = _nmod_vec_init(len);
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for (i = 0; i < len; i++)
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poly[i] = nmod_mul(weights[i], ys[i], mod);
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for (i = 0; i < FLINT_CLOG2(len); i++)
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{
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pow = (WORD(1) << i);
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pa = tree[i];
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pb = poly;
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left = len;
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while (left >= 2 * pow)
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{
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_nmod_poly_mul(t, pa, pow + 1, pb + pow, pow, mod);
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_nmod_poly_mul(u, pa + pow + 1, pow + 1, pb, pow, mod);
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_nmod_vec_add(pb, t, u, 2 * pow, mod);
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left -= 2 * pow;
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pa += 2 * pow + 2;
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pb += 2 * pow;
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}
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if (left > pow)
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{
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_nmod_poly_mul(t, pa, pow + 1, pb + pow, left - pow, mod);
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_nmod_poly_mul(u, pb, pow, pa + pow + 1, left - pow + 1, mod);
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_nmod_vec_add(pb, t, u, left, mod);
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}
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}
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_nmod_vec_clear(t);
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_nmod_vec_clear(u);
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}
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void
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_nmod_poly_interpolate_nmod_vec_fast(mp_ptr poly,
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mp_srcptr xs, mp_srcptr ys, slong len, nmod_t mod)
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{
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mp_ptr * tree;
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mp_ptr w;
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tree = _nmod_poly_tree_alloc(len);
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_nmod_poly_tree_build(tree, xs, len, mod);
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w = _nmod_vec_init(len);
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_nmod_poly_interpolation_weights(w, tree, len, mod);
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_nmod_poly_interpolate_nmod_vec_fast_precomp(poly, ys, tree, w, len, mod);
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_nmod_vec_clear(w);
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_nmod_poly_tree_free(tree, len);
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}
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void
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nmod_poly_interpolate_nmod_vec_fast(nmod_poly_t poly,
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mp_srcptr xs, mp_srcptr ys, slong n)
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{
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if (n == 0)
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{
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nmod_poly_zero(poly);
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}
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else
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{
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nmod_poly_fit_length(poly, n);
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poly->length = n;
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_nmod_poly_interpolate_nmod_vec_fast(poly->coeffs,
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xs, ys, n, poly->mod);
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_nmod_poly_normalise(poly);
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}
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}
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