144 lines
3.8 KiB
C
144 lines
3.8 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"
|
|
#include "ulong_extras.h"
|
|
|
|
|
|
/* pointer to (x/Q)^i */
|
|
#define Ri(ii) (R + (n-1)*((ii)-1))
|
|
|
|
void
|
|
_fmpz_poly_revert_series_lagrange_fast(fmpz * Qinv, const fmpz * Q, slong n)
|
|
{
|
|
slong i, j, k, m;
|
|
fmpz *R, *S, *T, *tmp;
|
|
fmpz_t t;
|
|
|
|
if (n <= 2)
|
|
{
|
|
_fmpz_vec_set(Qinv, Q, n);
|
|
return;
|
|
}
|
|
|
|
m = n_sqrt(n);
|
|
|
|
fmpz_init(t);
|
|
R = _fmpz_vec_init((n - 1) * m);
|
|
S = _fmpz_vec_init(n - 1);
|
|
T = _fmpz_vec_init(n - 1);
|
|
|
|
fmpz_zero(Qinv);
|
|
fmpz_set(Qinv + 1, Q + 1);
|
|
|
|
_fmpz_poly_inv_series(Ri(1), Q + 1, n - 1);
|
|
for (i = 2; i <= m; i++)
|
|
_fmpz_poly_mullow(Ri(i), Ri(i-1), n - 1, Ri(1), n - 1, n - 1);
|
|
for (i = 2; i < m; i++)
|
|
fmpz_divexact_ui(Qinv + i, Ri(i) + i - 1, i);
|
|
|
|
_fmpz_vec_set(S, Ri(m), n - 1);
|
|
|
|
for (i = m; i < n; i += m)
|
|
{
|
|
fmpz_divexact_ui(Qinv + i, S + i - 1, i);
|
|
|
|
for (j = 1; j < m && i + j < n; j++)
|
|
{
|
|
fmpz_mul(t, S + 0, Ri(j) + i + j - 1);
|
|
for (k = 1; k <= i + j - 1; k++)
|
|
fmpz_addmul(t, S + k, Ri(j) + i + j - 1 - k);
|
|
fmpz_divexact_ui(Qinv + i + j, t, i + j);
|
|
}
|
|
|
|
if (i + 1 < n)
|
|
{
|
|
_fmpz_poly_mullow(T, S, n - 1, Ri(m), n - 1, n - 1);
|
|
tmp = S; S = T; T = tmp;
|
|
}
|
|
}
|
|
|
|
fmpz_clear(t);
|
|
_fmpz_vec_clear(R, (n - 1) * m);
|
|
_fmpz_vec_clear(S, n - 1);
|
|
_fmpz_vec_clear(T, n - 1);
|
|
}
|
|
|
|
void
|
|
fmpz_poly_revert_series_lagrange_fast(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_lagrange_fast). Input must \n"
|
|
"have 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_lagrange_fast(Qinv->coeffs, Qcopy, n);
|
|
}
|
|
else
|
|
{
|
|
fmpz_poly_t t;
|
|
fmpz_poly_init2(t, n);
|
|
_fmpz_poly_revert_series_lagrange_fast(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);
|
|
}
|