mirror of
https://github.com/vale981/arb
synced 2025-03-05 09:21:38 -05:00
70 lines
1.5 KiB
C
70 lines
1.5 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"
|
|
|
|
|
|
void
|
|
_acb_poly_atan_series(acb_ptr g, acb_srcptr h, slong hlen, slong n, slong prec)
|
|
{
|
|
acb_t c;
|
|
acb_init(c);
|
|
|
|
acb_atan(c, h, prec);
|
|
|
|
hlen = FLINT_MIN(hlen, n);
|
|
|
|
if (hlen == 1)
|
|
{
|
|
_acb_vec_zero(g + 1, n - 1);
|
|
}
|
|
else
|
|
{
|
|
acb_ptr t, u;
|
|
slong ulen;
|
|
|
|
t = _acb_vec_init(n);
|
|
u = _acb_vec_init(n);
|
|
|
|
/* atan(h(x)) = integral(h'(x)/(1+h(x)^2)) */
|
|
ulen = FLINT_MIN(n, 2 * hlen - 1);
|
|
_acb_poly_mullow(u, h, hlen, h, hlen, ulen, prec);
|
|
acb_add_ui(u, u, 1, prec);
|
|
|
|
_acb_poly_derivative(t, h, hlen, prec);
|
|
_acb_poly_div_series(g, t, hlen - 1, u, ulen, n, prec);
|
|
_acb_poly_integral(g, g, n, prec);
|
|
|
|
_acb_vec_clear(t, n);
|
|
_acb_vec_clear(u, n);
|
|
}
|
|
|
|
acb_swap(g, c);
|
|
acb_clear(c);
|
|
}
|
|
|
|
void
|
|
acb_poly_atan_series(acb_poly_t g, const acb_poly_t h, slong n, slong prec)
|
|
{
|
|
slong hlen = h->length;
|
|
|
|
if (hlen == 0 || n == 0)
|
|
{
|
|
acb_poly_zero(g);
|
|
return;
|
|
}
|
|
|
|
acb_poly_fit_length(g, n);
|
|
_acb_poly_atan_series(g->coeffs, h->coeffs, hlen, n, prec);
|
|
_acb_poly_set_length(g, n);
|
|
_acb_poly_normalise(g);
|
|
}
|
|
|