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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 TAN_NEWTON_CUTOFF 20
void
_arb_poly_tan_series(arb_ptr g,
arb_srcptr h, slong hlen, slong len, slong prec)
{
hlen = FLINT_MIN(hlen, len);
if (hlen == 1)
{
arb_tan(g, h, prec);
_arb_vec_zero(g + 1, len - 1);
}
else if (len == 2)
{
arb_t t;
arb_init(t);
arb_tan(g, h, prec);
arb_mul(t, g, g, prec);
arb_add_ui(t, t, 1, prec);
arb_mul(g + 1, t, h + 1, prec); /* safe since hlen >= 2 */
arb_clear(t);
}
else
{
arb_ptr t, u;
t = _arb_vec_init(2 * len);
u = t + len;
NEWTON_INIT(TAN_NEWTON_CUTOFF, len)
NEWTON_BASECASE(n)
_arb_poly_sin_cos_series_basecase(t, u, h, hlen, n, prec, 0);
_arb_poly_div_series(g, t, n, u, n, n, prec);
NEWTON_END_BASECASE
NEWTON_LOOP(m, n)
_arb_poly_mullow(u, g, m, g, m, n, prec);
arb_add_ui(u, u, 1, prec);
_arb_poly_atan_series(t, g, m, n, prec);
_arb_poly_sub(t + m, h + m, FLINT_MAX(0, hlen - m), t + m, n - m, prec);
_arb_poly_mullow(g + m, u, n, t + m, n - m, n - m, prec);
NEWTON_END_LOOP
NEWTON_END
_arb_vec_clear(t, 2 * len);
}
}
void
arb_poly_tan_series(arb_poly_t g, const arb_poly_t h, slong n, slong prec)
{
if (h->length == 0 || n == 0)
{
arb_poly_zero(g);
return;
}
if (g == h)
{
arb_poly_t t;
arb_poly_init(t);
arb_poly_tan_series(t, h, n, prec);
arb_poly_swap(g, t);
arb_poly_clear(t);
return;
}
arb_poly_fit_length(g, n);
_arb_poly_tan_series(g->coeffs, h->coeffs, h->length, n, prec);
_arb_poly_set_length(g, n);
_arb_poly_normalise(g);
}
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