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/*
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 "arb_poly.h"
#define CUTOFF 5
void
_arb_poly_revert_series_newton(arb_ptr Qinv, arb_srcptr Q, slong Qlen, slong n, slong prec)
{
slong i, k, a[FLINT_BITS];
arb_ptr T, U, V;
if (n <= 2)
{
if (n >= 1)
arb_zero(Qinv);
if (n == 2)
arb_inv(Qinv + 1, Q + 1, prec);
return;
}
T = _arb_vec_init(n);
U = _arb_vec_init(n);
V = _arb_vec_init(n);
k = n;
for (i = 1; (WORD(1) << i) < k; i++);
a[i = 0] = k;
while (k >= CUTOFF)
a[++i] = (k = (k + 1) / 2);
_arb_poly_revert_series_lagrange(Qinv, Q, Qlen, k, prec);
_arb_vec_zero(Qinv + k, n - k);
for (i--; i >= 0; i--)
{
k = a[i];
_arb_poly_compose_series(T, Q, FLINT_MIN(Qlen, k), Qinv, k, k, prec);
_arb_poly_derivative(U, T, k, prec); arb_zero(U + k - 1);
arb_zero(T + 1);
_arb_poly_div_series(V, T, k, U, k, k, prec);
_arb_poly_derivative(T, Qinv, k, prec);
_arb_poly_mullow(U, V, k, T, k, k, prec);
_arb_vec_sub(Qinv, Qinv, U, k, prec);
}
_arb_vec_clear(T, n);
_arb_vec_clear(U, n);
_arb_vec_clear(V, n);
}
void
arb_poly_revert_series_newton(arb_poly_t Qinv,
const arb_poly_t Q, slong n, slong prec)
{
slong Qlen = Q->length;
if (Qlen < 2 || !arb_is_zero(Q->coeffs)
|| arb_contains_zero(Q->coeffs + 1))
{
flint_printf("Exception (arb_poly_revert_series_newton). Input must \n"
"have zero constant term and nonzero coefficient of x^1.\n");
flint_abort();
}
if (Qinv != Q)
{
arb_poly_fit_length(Qinv, n);
_arb_poly_revert_series_newton(Qinv->coeffs, Q->coeffs, Qlen, n, prec);
}
else
{
arb_poly_t t;
arb_poly_init2(t, n);
_arb_poly_revert_series_newton(t->coeffs, Q->coeffs, Qlen, n, prec);
arb_poly_swap(Qinv, t);
arb_poly_clear(t);
}
_arb_poly_set_length(Qinv, n);
_arb_poly_normalise(Qinv);
}
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