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/*=============================================================================
This file is part of FLINT.
FLINT 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.
FLINT 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 FLINT; if not, write to the Free Software
Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA
=============================================================================*/
/******************************************************************************
Copyright (C) 2011 Fredrik Johansson
******************************************************************************/
#include <gmp.h>
#include "flint.h"
#include "ulong_extras.h"
#include "nmod_vec.h"
#include "nmod_poly.h"
void
_nmod_poly_cos_series(mp_ptr g, mp_srcptr h, slong n, nmod_t mod)
{
mp_ptr t, u;
t = _nmod_vec_init(n);
u = _nmod_vec_init(n);
/* cos(x) = (1-tan(x/2)^2)/(1+tan(x/2)^2) */
_nmod_vec_scalar_mul_nmod(u, h, n, n_invmod(UWORD(2), mod.n), mod);
_nmod_poly_tan_series(t, u, n, mod);
_nmod_poly_mullow(u, t, n, t, n, n, mod);
_nmod_vec_neg(t, u, n, mod);
t[0] = u[0] = UWORD(1);
_nmod_poly_div_series(g, t, u, n, mod);
_nmod_vec_clear(t);
_nmod_vec_clear(u);
}
void
nmod_poly_cos_series(nmod_poly_t g, const nmod_poly_t h, slong n)
{
mp_ptr h_coeffs;
slong h_len = h->length;
if (h_len > 0 && h->coeffs[0] != UWORD(0))
{
flint_printf("Exception (nmod_poly_cos_series). Constant term != 0.\n");
abort();
}
if (h_len == 1 || n < 2)
{
nmod_poly_zero(g);
if (n > 0)
nmod_poly_set_coeff_ui(g, 0, UWORD(1));
return;
}
nmod_poly_fit_length(g, n);
if (h_len < n)
{
h_coeffs = _nmod_vec_init(n);
flint_mpn_copyi(h_coeffs, h->coeffs, h_len);
flint_mpn_zero(h_coeffs + h_len, n - h_len);
}
else
h_coeffs = h->coeffs;
_nmod_poly_cos_series(g->coeffs, h_coeffs, n, h->mod);
if (h_len < n)
_nmod_vec_clear(h_coeffs);
g->length = n;
_nmod_poly_normalise(g);
}
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