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/*=============================================================================
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 Fredrik Johansson
******************************************************************************/
#include <gmp.h>
#include "flint.h"
#include "ulong_extras.h"
#include "nmod_vec.h"
#include "nmod_poly.h"
void
_nmod_poly_interpolate_nmod_vec_barycentric(mp_ptr poly,
mp_srcptr xs, mp_srcptr ys, slong n, nmod_t mod)
{
mp_ptr P, Q, w;
slong i, j;
if (n == 1)
{
poly[0] = ys[0];
return;
}
P = _nmod_vec_init(n + 1);
Q = _nmod_vec_init(n);
w = _nmod_vec_init(n);
_nmod_poly_product_roots_nmod_vec(P, xs, n, mod);
for (i = 0; i < n; i++)
{
w[i] = UWORD(1);
for (j = 0; j < n; j++)
{
if (i != j)
w[i] = nmod_mul(w[i], nmod_sub(xs[i], xs[j], mod), mod);
}
w[i] = n_invmod(w[i], mod.n);
}
_nmod_vec_zero(poly, n);
for (i = 0; i < n; i++)
{
_nmod_poly_div_root(Q, P, n + 1, xs[i], mod);
_nmod_vec_scalar_addmul_nmod(poly, Q, n,
nmod_mul(w[i], ys[i], mod), mod);
}
_nmod_vec_clear(P);
_nmod_vec_clear(Q);
_nmod_vec_clear(w);
}
void
nmod_poly_interpolate_nmod_vec_barycentric(nmod_poly_t poly,
mp_srcptr xs, mp_srcptr ys, slong n)
{
if (n == 0)
{
nmod_poly_zero(poly);
}
else
{
nmod_poly_fit_length(poly, n);
poly->length = n;
_nmod_poly_interpolate_nmod_vec_barycentric(poly->coeffs,
xs, ys, n, poly->mod);
_nmod_poly_normalise(poly);
}
}
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