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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) 2011-2014 Fredrik Johansson
******************************************************************************/
#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 Qlen, 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, FLINT_MIN(Qlen, n) - 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)
{
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 have \n"
"zero constant term and +1 or -1 as coefficient of x^1\n.");
abort();
}
if (Qinv != Q)
{
fmpz_poly_fit_length(Qinv, n);
_fmpz_poly_revert_series_lagrange_fast(Qinv->coeffs, Q->coeffs, Qlen, n);
}
else
{
fmpz_poly_t t;
fmpz_poly_init2(t, n);
_fmpz_poly_revert_series_lagrange_fast(t->coeffs, Q->coeffs, Qlen, n);
fmpz_poly_swap(Qinv, t);
fmpz_poly_clear(t);
}
_fmpz_poly_set_length(Qinv, n);
_fmpz_poly_normalise(Qinv);
}
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