mirror of
https://github.com/vale981/arb
synced 2025-03-05 09:21:38 -05:00
106 lines
2.7 KiB
C
106 lines
2.7 KiB
C
/*
|
|
Copyright (C) 2013 Fredrik Johansson
|
|
|
|
This file is part of Arb.
|
|
|
|
Arb is free software: you can redistribute it and/or modify it under
|
|
the terms of the GNU Lesser General Public License (LGPL) as published
|
|
by the Free Software Foundation; either version 2.1 of the License, or
|
|
(at your option) any later version. See <http://www.gnu.org/licenses/>.
|
|
*/
|
|
|
|
#include "acb_poly.h"
|
|
|
|
/* pointer to (x/Q)^i */
|
|
#define Ri(ii) (R + (n-1)*((ii)-1))
|
|
|
|
void
|
|
_acb_poly_revert_series_lagrange_fast(acb_ptr Qinv, acb_srcptr Q, slong Qlen, slong n, slong prec)
|
|
{
|
|
slong i, j, m;
|
|
acb_ptr R, S, T, tmp;
|
|
acb_t t;
|
|
|
|
if (n <= 2)
|
|
{
|
|
if (n >= 1)
|
|
acb_zero(Qinv);
|
|
if (n == 2)
|
|
acb_inv(Qinv + 1, Q + 1, prec);
|
|
return;
|
|
}
|
|
|
|
m = n_sqrt(n);
|
|
|
|
acb_init(t);
|
|
R = _acb_vec_init((n - 1) * m);
|
|
S = _acb_vec_init(n - 1);
|
|
T = _acb_vec_init(n - 1);
|
|
|
|
acb_zero(Qinv);
|
|
acb_inv(Qinv + 1, Q + 1, prec);
|
|
|
|
_acb_poly_inv_series(Ri(1), Q + 1, FLINT_MIN(Qlen, n) - 1, n - 1, prec);
|
|
for (i = 2; i <= m; i++)
|
|
_acb_poly_mullow(Ri(i), Ri((i + 1) / 2), n - 1, Ri(i / 2), n - 1, n - 1, prec);
|
|
|
|
for (i = 2; i < m; i++)
|
|
acb_div_ui(Qinv + i, Ri(i) + i - 1, i, prec);
|
|
|
|
_acb_vec_set(S, Ri(m), n - 1);
|
|
|
|
for (i = m; i < n; i += m)
|
|
{
|
|
acb_div_ui(Qinv + i, S + i - 1, i, prec);
|
|
|
|
for (j = 1; j < m && i + j < n; j++)
|
|
{
|
|
acb_dot(t, NULL, 0, S, 1, Ri(j) + i + j - 1, -1, i + j, prec);
|
|
acb_div_ui(Qinv + i + j, t, i + j, prec);
|
|
}
|
|
|
|
if (i + 1 < n)
|
|
{
|
|
_acb_poly_mullow(T, S, n - 1, Ri(m), n - 1, n - 1, prec);
|
|
tmp = S; S = T; T = tmp;
|
|
}
|
|
}
|
|
|
|
acb_clear(t);
|
|
_acb_vec_clear(R, (n - 1) * m);
|
|
_acb_vec_clear(S, n - 1);
|
|
_acb_vec_clear(T, n - 1);
|
|
}
|
|
|
|
void
|
|
acb_poly_revert_series_lagrange_fast(acb_poly_t Qinv,
|
|
const acb_poly_t Q, slong n, slong prec)
|
|
{
|
|
slong Qlen = Q->length;
|
|
|
|
if (Qlen < 2 || !acb_is_zero(Q->coeffs)
|
|
|| acb_contains_zero(Q->coeffs + 1))
|
|
{
|
|
flint_printf("Exception (acb_poly_revert_series_lagrange_fast). Input \n"
|
|
"must have zero constant term and nonzero coefficient of x^1.\n");
|
|
flint_abort();
|
|
}
|
|
|
|
if (Qinv != Q)
|
|
{
|
|
acb_poly_fit_length(Qinv, n);
|
|
_acb_poly_revert_series_lagrange_fast(Qinv->coeffs, Q->coeffs, Qlen, n, prec);
|
|
}
|
|
else
|
|
{
|
|
acb_poly_t t;
|
|
acb_poly_init2(t, n);
|
|
_acb_poly_revert_series_lagrange_fast(t->coeffs, Q->coeffs, Qlen, n, prec);
|
|
acb_poly_swap(Qinv, t);
|
|
acb_poly_clear(t);
|
|
}
|
|
|
|
_acb_poly_set_length(Qinv, n);
|
|
_acb_poly_normalise(Qinv);
|
|
}
|
|
|