97 lines
2.6 KiB
C
97 lines
2.6 KiB
C
/*=============================================================================
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This file is part of FLINT.
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FLINT is free software; you can redistribute it and/or modify
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it under the terms of the GNU General Public License as published by
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the Free Software Foundation; either version 2 of the License, or
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(at your option) any later version.
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FLINT is distributed in the hope that it will be useful,
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but WITHOUT ANY WARRANTY; without even the implied warranty of
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MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
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GNU General Public License for more details.
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You should have received a copy of the GNU General Public License
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along with FLINT; if not, write to the Free Software
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Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA
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=============================================================================*/
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/******************************************************************************
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Copyright (C) 2012 Fredrik Johansson
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******************************************************************************/
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#include "flint.h"
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#include "nmod_vec.h"
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#include "nmod_poly.h"
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#include "ulong_extras.h"
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void
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_nmod_poly_taylor_shift_convolution(mp_ptr p, mp_limb_t c, slong len, nmod_t mod)
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{
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slong i, n = len - 1;
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mp_limb_t f, d;
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mp_ptr t, u;
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if (c == 0 || len <= 1)
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return;
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t = _nmod_vec_init(len);
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u = _nmod_vec_init(len);
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f = 1;
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for (i = 2; i <= n; i++)
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{
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f = n_mulmod2_preinv(f, i, mod.n, mod.ninv);
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p[i] = n_mulmod2_preinv(p[i], f, mod.n, mod.ninv);
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}
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_nmod_poly_reverse(p, p, len, len);
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t[n] = 1;
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for (i = n; i > 0; i--)
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t[i - 1] = n_mulmod2_preinv(t[i], i, mod.n, mod.ninv);
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if (c == mod.n - 1)
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{
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for (i = 1; i <= n; i += 2)
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t[i] = nmod_neg(t[i], mod);
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}
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else if (c != 1)
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{
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d = c;
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for (i = 1; i <= n; i++)
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{
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t[i] = n_mulmod2_preinv(t[i], d, mod.n, mod.ninv);
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d = n_mulmod2_preinv(d, c, mod.n, mod.ninv);
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}
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}
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_nmod_poly_mullow(u, p, len, t, len, len, mod);
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f = n_mulmod2_preinv(f, f, mod.n, mod.ninv);
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f = n_invmod(f, mod.n);
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for (i = n; i >= 0; i--)
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{
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p[i] = n_mulmod2_preinv(u[n - i], f, mod.n, mod.ninv);
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f = n_mulmod2_preinv(f, (i == 0) ? 1 : i, mod.n, mod.ninv);
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}
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_nmod_vec_clear(t);
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_nmod_vec_clear(u);
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}
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void
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nmod_poly_taylor_shift_convolution(nmod_poly_t g, const nmod_poly_t f,
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mp_limb_t c)
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{
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if (f != g)
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nmod_poly_set(g, f);
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_nmod_poly_taylor_shift_convolution(g->coeffs, c, g->length, g->mod);
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}
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