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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) 2010 Sebastian Pancratz
Copyright (C) 2011 Fredrik Johansson
******************************************************************************/
#include <gmp.h>
#include "flint.h"
#include "fmpz.h"
#include "fmpz_poly.h"
#define FLINT_REVERSE_NEWTON_CUTOFF 10
void
_fmpz_poly_revert_series_newton(fmpz * Qinv, const fmpz * Q, slong n)
{
if (n <= 2)
{
_fmpz_vec_set(Qinv, Q, n);
return;
}
else
{
slong *a, i, k;
fmpz *T, *U, *V;
T = _fmpz_vec_init(n);
U = _fmpz_vec_init(n);
V = _fmpz_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);
_fmpz_poly_revert_series_lagrange(Qinv, Q, k);
_fmpz_vec_zero(Qinv + k, n - k);
for (i--; i >= 0; i--)
{
k = a[i];
_fmpz_poly_compose_series(T, Q, k, Qinv, k, k);
_fmpz_poly_derivative(U, T, k); fmpz_zero(U + k - 1);
fmpz_zero(T + 1);
_fmpz_poly_div_series(V, T, U, k);
_fmpz_poly_derivative(T, Qinv, k);
_fmpz_poly_mullow(U, V, k, T, k, k);
_fmpz_vec_sub(Qinv, Qinv, U, k);
}
flint_free(a);
_fmpz_vec_clear(T, n);
_fmpz_vec_clear(U, n);
_fmpz_vec_clear(V, n);
}
}
void
fmpz_poly_revert_series_newton(fmpz_poly_t Qinv, const fmpz_poly_t Q, slong n)
{
fmpz *Qcopy;
int Qalloc;
slong Qlen = Q->length;
if (Qlen < 2 || !fmpz_is_zero(Q->coeffs) || !fmpz_is_pm1(Q->coeffs + 1))
{
flint_printf("Exception (fmpz_poly_revert_series_newton). Input must have \n"
"zero constant term and +1 or -1 as coefficient of x^1.\n");
abort();
}
if (Qlen >= n)
{
Qcopy = Q->coeffs;
Qalloc = 0;
}
else
{
slong i;
Qcopy = (fmpz *) flint_malloc(n * sizeof(fmpz));
for (i = 0; i < Qlen; i++)
Qcopy[i] = Q->coeffs[i];
for ( ; i < n; i++)
Qcopy[i] = 0;
Qalloc = 1;
}
if (Qinv != Q)
{
fmpz_poly_fit_length(Qinv, n);
_fmpz_poly_revert_series_newton(Qinv->coeffs, Qcopy, n);
}
else
{
fmpz_poly_t t;
fmpz_poly_init2(t, n);
_fmpz_poly_revert_series_newton(t->coeffs, Qcopy, n);
fmpz_poly_swap(Qinv, t);
fmpz_poly_clear(t);
}
_fmpz_poly_set_length(Qinv, n);
_fmpz_poly_normalise(Qinv);
if (Qalloc)
flint_free(Qcopy);
}
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