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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) 2012 Fredrik Johansson
******************************************************************************/
#include "flint.h"
#include "nmod_vec.h"
#include "nmod_poly.h"
#include "ulong_extras.h"
void
_nmod_poly_taylor_shift_convolution(mp_ptr p, mp_limb_t c, slong len, nmod_t mod)
{
slong i, n = len - 1;
mp_limb_t f, d;
mp_ptr t, u;
if (c == 0 || len <= 1)
return;
t = _nmod_vec_init(len);
u = _nmod_vec_init(len);
f = 1;
for (i = 2; i <= n; i++)
{
f = n_mulmod2_preinv(f, i, mod.n, mod.ninv);
p[i] = n_mulmod2_preinv(p[i], f, mod.n, mod.ninv);
}
_nmod_poly_reverse(p, p, len, len);
t[n] = 1;
for (i = n; i > 0; i--)
t[i - 1] = n_mulmod2_preinv(t[i], i, mod.n, mod.ninv);
if (c == mod.n - 1)
{
for (i = 1; i <= n; i += 2)
t[i] = nmod_neg(t[i], mod);
}
else if (c != 1)
{
d = c;
for (i = 1; i <= n; i++)
{
t[i] = n_mulmod2_preinv(t[i], d, mod.n, mod.ninv);
d = n_mulmod2_preinv(d, c, mod.n, mod.ninv);
}
}
_nmod_poly_mullow(u, p, len, t, len, len, mod);
f = n_mulmod2_preinv(f, f, mod.n, mod.ninv);
f = n_invmod(f, mod.n);
for (i = n; i >= 0; i--)
{
p[i] = n_mulmod2_preinv(u[n - i], f, mod.n, mod.ninv);
f = n_mulmod2_preinv(f, (i == 0) ? 1 : i, mod.n, mod.ninv);
}
_nmod_vec_clear(t);
_nmod_vec_clear(u);
}
void
nmod_poly_taylor_shift_convolution(nmod_poly_t g, const nmod_poly_t f,
mp_limb_t c)
{
if (f != g)
nmod_poly_set(g, f);
_nmod_poly_taylor_shift_convolution(g->coeffs, c, g->length, g->mod);
}
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