94 lines
2.5 KiB
C
94 lines
2.5 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 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_interpolate_nmod_vec_barycentric(mp_ptr poly,
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mp_srcptr xs, mp_srcptr ys, slong n, nmod_t mod)
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{
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mp_ptr P, Q, w;
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slong i, j;
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if (n == 1)
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{
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poly[0] = ys[0];
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return;
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}
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P = _nmod_vec_init(n + 1);
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Q = _nmod_vec_init(n);
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w = _nmod_vec_init(n);
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_nmod_poly_product_roots_nmod_vec(P, xs, n, mod);
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for (i = 0; i < n; i++)
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{
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w[i] = UWORD(1);
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for (j = 0; j < n; j++)
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{
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if (i != j)
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w[i] = nmod_mul(w[i], nmod_sub(xs[i], xs[j], mod), mod);
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}
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w[i] = n_invmod(w[i], mod.n);
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}
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_nmod_vec_zero(poly, n);
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for (i = 0; i < n; i++)
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{
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_nmod_poly_div_root(Q, P, n + 1, xs[i], mod);
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_nmod_vec_scalar_addmul_nmod(poly, Q, n,
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nmod_mul(w[i], ys[i], mod), mod);
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}
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_nmod_vec_clear(P);
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_nmod_vec_clear(Q);
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_nmod_vec_clear(w);
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}
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void
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nmod_poly_interpolate_nmod_vec_barycentric(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_barycentric(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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