132 lines
3.5 KiB
C
132 lines
3.5 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) 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);
|
|
}
|
|
|