84 lines
2.2 KiB
C
84 lines
2.2 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 "fmpz.h"
|
||
|
|
#include "fmpz_poly.h"
|
||
|
|
|
||
|
|
|
||
|
|
static void
|
||
|
|
_fmpz_poly_interpolate_newton(fmpz * ys, const fmpz * xs, slong n)
|
||
|
|
{
|
||
|
|
fmpz_t p, q, t;
|
||
|
|
slong i, j;
|
||
|
|
|
||
|
|
fmpz_init(p);
|
||
|
|
fmpz_init(q);
|
||
|
|
fmpz_init(t);
|
||
|
|
|
||
|
|
for (i = 1; i < n; i++)
|
||
|
|
{
|
||
|
|
fmpz_set(t, ys + i - 1);
|
||
|
|
|
||
|
|
for (j = i; j < n; j++)
|
||
|
|
{
|
||
|
|
fmpz_sub(p, ys + j, t);
|
||
|
|
fmpz_sub(q, xs + j, xs + j - i);
|
||
|
|
fmpz_set(t, ys + j);
|
||
|
|
fmpz_divexact(ys + j, p, q);
|
||
|
|
}
|
||
|
|
}
|
||
|
|
|
||
|
|
fmpz_clear(p);
|
||
|
|
fmpz_clear(q);
|
||
|
|
fmpz_clear(t);
|
||
|
|
}
|
||
|
|
|
||
|
|
void
|
||
|
|
fmpz_poly_interpolate_fmpz_vec(fmpz_poly_t poly,
|
||
|
|
const fmpz * xs, const fmpz * ys, slong n)
|
||
|
|
{
|
||
|
|
if (n == 0)
|
||
|
|
{
|
||
|
|
fmpz_poly_zero(poly);
|
||
|
|
return;
|
||
|
|
}
|
||
|
|
else if (n == 1)
|
||
|
|
{
|
||
|
|
fmpz_poly_set_fmpz(poly, ys);
|
||
|
|
return;
|
||
|
|
}
|
||
|
|
else
|
||
|
|
{
|
||
|
|
fmpz_poly_fit_length(poly, n);
|
||
|
|
_fmpz_vec_set(poly->coeffs, ys, n);
|
||
|
|
_fmpz_poly_interpolate_newton(poly->coeffs, xs, n);
|
||
|
|
_fmpz_poly_set_length(poly, n);
|
||
|
|
_fmpz_poly_normalise(poly);
|
||
|
|
_fmpz_poly_newton_to_monomial(poly->coeffs, xs, poly->length);
|
||
|
|
}
|
||
|
|
}
|