112 lines
2.9 KiB
C
112 lines
2.9 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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static void
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_interpolate_newton(mp_ptr ys, mp_srcptr xs, slong n, nmod_t mod)
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{
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mp_limb_t p, q, t;
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slong i, j;
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for (i = 1; i < n; i++)
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{
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t = ys[i - 1];
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for (j = i; j < n; j++)
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{
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p = nmod_sub(ys[j], t, mod);
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q = nmod_sub(xs[j], xs[j - i], mod);
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t = ys[j];
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q = n_invmod(q, mod.n);
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ys[j] = n_mulmod2_preinv(p, q, mod.n, mod.ninv);
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}
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}
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}
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static void
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_newton_to_monomial(mp_ptr ys, mp_srcptr xs, slong n, nmod_t mod)
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{
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mp_limb_t t;
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slong i, j;
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for (i = n - 2; i >= 0; i--)
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{
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t = ys[i];
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ys[i] = ys[i + 1];
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for (j = i + 1; j < n - 1; j++)
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{
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ys[j] = nmod_sub(ys[j + 1],
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n_mulmod2_preinv(ys[j], xs[i], mod.n, mod.ninv), mod);
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}
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ys[n - 1] = nmod_sub(t,
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n_mulmod2_preinv(ys[n - 1], xs[i], mod.n, mod.ninv), mod);
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}
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_nmod_poly_reverse(ys, ys, n, n);
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}
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void
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_nmod_poly_interpolate_nmod_vec_newton(mp_ptr poly, mp_srcptr xs,
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mp_srcptr ys, slong n, nmod_t mod)
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{
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if (n == 1)
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{
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poly[0] = ys[0];
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}
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else
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{
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_nmod_vec_set(poly, ys, n);
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_interpolate_newton(poly, xs, n, mod);
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while (n > 0 && !poly[n-1]) n--;
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_newton_to_monomial(poly, xs, n, mod);
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}
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}
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void
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nmod_poly_interpolate_nmod_vec_newton(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_newton(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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