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/*
Copyright (C) 2012 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"
static void
_arb_poly_exp_series_basecase_rec(arb_ptr f, arb_ptr a,
arb_srcptr h, slong hlen, slong n, slong prec)
{
slong k;
arb_t s;
arb_init(s);
arb_exp(f, h, prec);
for (k = 1; k < hlen; k++)
arb_mul_ui(a + k, h + k, k, prec);
for (k = 1; k < n; k++)
{
arb_dot(s, NULL, 0, a + 1, 1, f + k - 1, -1, FLINT_MIN(k, hlen - 1), prec);
arb_div_ui(f + k, s, k, prec);
}
arb_clear(s);
}
void
_arb_poly_exp_series_basecase(arb_ptr f,
arb_srcptr h, slong hlen, slong n, slong prec)
{
hlen = FLINT_MIN(n, hlen);
if (n < 20 || hlen < 0.9 * n || prec <= 2 * FLINT_BITS || n < 1000.0 / log(prec + 10) - 70)
{
arb_ptr t = _arb_vec_init(hlen);
_arb_poly_exp_series_basecase_rec(f, t, h, hlen, n, prec);
_arb_vec_clear(t, hlen);
}
else
{
slong m, v;
arb_ptr t, u;
m = (n + 2) / 3;
v = m * 2;
t = _arb_vec_init(n);
u = _arb_vec_init(n - m);
_arb_poly_mullow(t, h + m, hlen - m, h + m, hlen - m, n - v, prec);
_arb_vec_scalar_mul_2exp_si(t, t, n - v, -1);
_arb_vec_set(u, h + m, v - m);
_arb_poly_add(u + v - m, t, n - v, h + v, hlen - v, prec);
_arb_poly_exp_series_basecase_rec(f, t, h, m, n, prec);
_arb_poly_mullow(t, f, n, u, n - m, n - m, prec);
_arb_poly_add(f + m, f + m, n - m, t, n - m, prec);
_arb_vec_clear(t, n);
_arb_vec_clear(u, n - m);
}
}
void
arb_poly_exp_series_basecase(arb_poly_t f, const arb_poly_t h, slong n, slong prec)
{
slong hlen = h->length;
if (n == 0)
{
arb_poly_zero(f);
return;
}
if (hlen == 0)
{
arb_poly_one(f);
return;
}
arb_poly_fit_length(f, n);
_arb_poly_exp_series_basecase(f->coeffs, h->coeffs, hlen, n, prec);
_arb_poly_set_length(f, n);
_arb_poly_normalise(f);
}
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