79 lines
2.1 KiB
C
79 lines
2.1 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 <gmp.h>
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#include "flint.h"
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#include "ulong_extras.h"
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#include "nmod_vec.h"
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#include "nmod_poly.h"
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mp_limb_t
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n_factorial_fast_mod2_preinv(ulong n, mp_limb_t p, mp_limb_t pinv)
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{
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slong i, m;
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nmod_t mod;
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mp_ptr t, u, v;
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mp_limb_t r, s;
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if (p == UWORD(1) || n >= p)
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return UWORD(0);
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if (n <= 1)
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return UWORD(1);
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nmod_init(&mod, p);
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m = n_sqrt(n);
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t = _nmod_vec_init(m + 1);
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u = _nmod_vec_init(m + 1);
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v = _nmod_vec_init(m + 1);
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t[0] = UWORD(0);
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for (i = 1; i < m; i++)
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t[i] = n_submod(t[i-1], UWORD(1), p);
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_nmod_poly_product_roots_nmod_vec(u, t, m, mod);
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for (i = 0; i < m; i++)
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t[i] = n_mod2_preinv(i * m + 1, p, pinv);
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_nmod_poly_evaluate_nmod_vec_fast(v, u, m + 1, t, m, mod);
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r = 1;
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for (i = 0; i < m; i++)
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r = n_mulmod2_preinv(r, v[i], mod.n, mod.ninv);
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for (s = m * m + 1; s <= n; s++)
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r = n_mulmod2_preinv(r, s, mod.n, mod.ninv);
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_nmod_vec_clear(t);
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_nmod_vec_clear(u);
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_nmod_vec_clear(v);
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return r;
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}
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