mirror of
https://github.com/vale981/arb
synced 2025-03-06 09:51:39 -05:00
93 lines
2.6 KiB
C
93 lines
2.6 KiB
C
/*=============================================================================
|
|
|
|
This file is part of ARB.
|
|
|
|
ARB is free software; you can redistribute it and/or modify
|
|
it under the terms of the GNU General Public License as published by
|
|
the Free Software Foundation; either version 2 of the License, or
|
|
(at your option) any later version.
|
|
|
|
ARB is distributed in the hope that it will be useful,
|
|
but WITHOUT ANY WARRANTY; without even the implied warranty of
|
|
MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
|
|
GNU General Public License for more details.
|
|
|
|
You should have received a copy of the GNU General Public License
|
|
along with ARB; if not, write to the Free Software
|
|
Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA
|
|
|
|
=============================================================================*/
|
|
/******************************************************************************
|
|
|
|
Copyright (C) 2013 Fredrik Johansson
|
|
|
|
******************************************************************************/
|
|
|
|
#include "fmprb_poly.h"
|
|
|
|
void
|
|
_fmprb_poly_acos_series(fmprb_struct * g, const fmprb_struct * h, long hlen, long n, long prec)
|
|
{
|
|
fmprb_t c;
|
|
fmprb_init(c);
|
|
|
|
fmprb_acos(c, h, prec);
|
|
|
|
hlen = FLINT_MIN(hlen, n);
|
|
|
|
if (hlen == 1)
|
|
{
|
|
_fmprb_vec_zero(g + 1, n - 1);
|
|
}
|
|
else
|
|
{
|
|
fmprb_struct *t, *u;
|
|
long ulen;
|
|
|
|
t = _fmprb_vec_init(n);
|
|
u = _fmprb_vec_init(n);
|
|
|
|
/* acos(h(x)) = integral(-h'(x)/sqrt(1-h(x)^2)) */
|
|
ulen = FLINT_MIN(n, 2 * hlen - 1);
|
|
_fmprb_poly_mullow(u, h, hlen, h, hlen, ulen, prec);
|
|
fmprb_sub_ui(u, u, 1, prec);
|
|
_fmprb_vec_neg(u, u, ulen);
|
|
_fmprb_poly_rsqrt_series(t, u, ulen, n, prec);
|
|
_fmprb_poly_derivative(u, h, hlen, prec);
|
|
_fmprb_poly_mullow(g, t, n, u, hlen - 1, n, prec);
|
|
_fmprb_poly_integral(g, g, n, prec);
|
|
_fmprb_vec_neg(g, g, n);
|
|
|
|
_fmprb_vec_clear(t, n);
|
|
_fmprb_vec_clear(u, n);
|
|
}
|
|
|
|
fmprb_swap(g, c);
|
|
fmprb_clear(c);
|
|
}
|
|
|
|
void
|
|
fmprb_poly_acos_series(fmprb_poly_t g, const fmprb_poly_t h, long n, long prec)
|
|
{
|
|
long hlen = h->length;
|
|
|
|
if (hlen == 0)
|
|
{
|
|
if (n == 0)
|
|
fmprb_poly_zero(g);
|
|
else
|
|
{
|
|
fmprb_poly_fit_length(g, 1);
|
|
fmprb_const_pi(g->coeffs, prec);
|
|
fmprb_mul_2exp_si(g->coeffs, g->coeffs, -1);
|
|
_fmprb_poly_set_length(g, 1);
|
|
}
|
|
return;
|
|
}
|
|
|
|
fmprb_poly_fit_length(g, n);
|
|
_fmprb_poly_acos_series(g->coeffs, h->coeffs, hlen, n, prec);
|
|
_fmprb_poly_set_length(g, n);
|
|
_fmprb_poly_normalise(g);
|
|
}
|
|
|