pqc/external/flint-2.4.3/nmod_poly/revert_series_newton.c

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2014-05-18 22:03:37 +00:00
/*=============================================================================
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) 2010 Sebastian Pancratz
Copyright (C) 2011 Fredrik Johansson
******************************************************************************/
#include <gmp.h>
#include "flint.h"
#include "nmod_vec.h"
#include "nmod_poly.h"
#include "ulong_extras.h"
#define FLINT_REVERSE_NEWTON_CUTOFF 15
void
_nmod_poly_revert_series_newton(mp_ptr Qinv, mp_srcptr Q, slong n, nmod_t mod)
{
slong *a, i, k;
mp_ptr T, U, V;
if (n >= 1) Qinv[0] = UWORD(0);
if (n >= 2) Qinv[1] = n_invmod(Q[1], mod.n);
if (n <= 2)
return;
T = _nmod_vec_init(n);
U = _nmod_vec_init(n);
V = _nmod_vec_init(n);
k = n;
for (i = 1; (WORD(1) << i) < k; i++);
a = (slong *) flint_malloc(i * sizeof(slong));
a[i = 0] = k;
while (k >= FLINT_REVERSE_NEWTON_CUTOFF)
a[++i] = (k = (k + 1) / 2);
_nmod_poly_revert_series_lagrange(Qinv, Q, k, mod);
_nmod_vec_zero(Qinv + k, n - k);
for (i--; i >= 0; i--)
{
k = a[i];
_nmod_poly_compose_series(T, Q, k, Qinv, k, k, mod);
_nmod_poly_derivative(U, T, k, mod); U[k - 1] = UWORD(0);
T[1] = UWORD(0);
_nmod_poly_div_series(V, T, U, k, mod);
_nmod_poly_derivative(T, Qinv, k, mod);
_nmod_poly_mullow(U, V, k, T, k, k, mod);
_nmod_vec_sub(Qinv, Qinv, U, k, mod);
}
flint_free(a);
_nmod_vec_clear(T);
_nmod_vec_clear(U);
_nmod_vec_clear(V);
}
void
nmod_poly_revert_series_newton(nmod_poly_t Qinv,
const nmod_poly_t Q, slong n)
{
mp_ptr Qinv_coeffs, Q_coeffs;
nmod_poly_t t1;
slong Qlen;
Qlen = Q->length;
if (Qlen < 2 || Q->coeffs[0] != 0 || Q->coeffs[1] == 0)
{
flint_printf("Exception (nmod_poly_revert_series_newton). Input must have \n"
"zero constant and an invertible coefficient of x^1.\n");
abort();
}
if (Qlen < n)
{
Q_coeffs = _nmod_vec_init(n);
flint_mpn_copyi(Q_coeffs, Q->coeffs, Qlen);
flint_mpn_zero(Q_coeffs + Qlen, n - Qlen);
}
else
Q_coeffs = Q->coeffs;
if (Q == Qinv && Qlen >= n)
{
nmod_poly_init2(t1, Q->mod.n, n);
Qinv_coeffs = t1->coeffs;
}
else
{
nmod_poly_fit_length(Qinv, n);
Qinv_coeffs = Qinv->coeffs;
}
_nmod_poly_revert_series_newton(Qinv_coeffs, Q_coeffs, n, Q->mod);
if (Q == Qinv && Qlen >= n)
{
nmod_poly_swap(Qinv, t1);
nmod_poly_clear(t1);
}
Qinv->length = n;
if (Qlen < n)
_nmod_vec_clear(Q_coeffs);
_nmod_poly_normalise(Qinv);
}