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/*
Copyright (C) 2016 Fredrik Johansson
Copyright (C) 2019 D.H.J. Polymath
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"
void
_arb_poly_sinc_pi_series(arb_ptr g, arb_srcptr h, slong hlen, slong n, slong prec)
{
hlen = FLINT_MIN(hlen, n);
if (hlen == 1)
{
arb_sinc_pi(g, h, prec);
_arb_vec_zero(g + 1, n - 1);
}
else
{
arb_t pi;
arb_ptr t, u;
arb_init(pi);
t = _arb_vec_init(n + 1);
u = _arb_vec_init(hlen);
arb_const_pi(pi, prec);
_arb_vec_set(u, h, hlen);
if (arb_is_zero(h))
{
_arb_poly_sin_pi_series(t, u, hlen, n + 1, prec);
_arb_poly_div_series(g, t + 1, n, u + 1, hlen - 1, n, prec);
}
else
{
_arb_poly_sin_pi_series(t, u, hlen, n, prec);
_arb_poly_div_series(g, t, n, u, hlen, n, prec);
}
_arb_vec_scalar_div(g, g, n, pi, prec);
arb_clear(pi);
_arb_vec_clear(t, n + 1);
_arb_vec_clear(u, hlen);
}
}
void
arb_poly_sinc_pi_series(arb_poly_t g, const arb_poly_t h, slong n, slong prec)
{
slong hlen = h->length;
if (n == 0)
{
arb_poly_zero(g);
return;
}
if (hlen == 0)
{
arb_poly_one(g);
return;
}
if (hlen == 1)
n = 1;
arb_poly_fit_length(g, n);
_arb_poly_sinc_pi_series(g->coeffs, h->coeffs, hlen, n, prec);
_arb_poly_set_length(g, n);
_arb_poly_normalise(g);
}
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