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