pqc/external/flint-2.4.3/nmod_poly/interpolate_nmod_vec_newton.c
2014-05-24 23:16:06 +02:00

112 lines
2.9 KiB
C

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