ALL: Add flint

external/flint-2.4.3/nmod_poly/taylor_shift_convolution.c

@@ -0,0 +1,96 @@
+/*=============================================================================
+
+    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);
+}