93 lines
2.4 KiB
C
93 lines
2.4 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) 2009 William Hart
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Copyright (C) 2011 Sebastian Pancratz
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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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mp_limb_t n_sqrtmod(mp_limb_t a, mp_limb_t p)
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{
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slong i, r, m;
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mp_limb_t p1, k, b, g, bpow, gpow, res;
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mp_limb_t pinv;
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if (a <= 1)
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{
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return a;
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}
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pinv = n_preinvert_limb(p);
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if (n_jacobi_unsigned(a, p) == -1)
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return 0;
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if ((p & UWORD(3)) == 3)
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{
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return n_powmod2_ui_preinv(a, (p + 1) / 4, p, pinv);
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}
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r = 0;
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p1 = p - 1;
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do {
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p1 >>= UWORD(1);
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r++;
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} while ((p1 & UWORD(1)) == 0);
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b = n_powmod2_ui_preinv(a, p1, p, pinv);
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for (k = 2; ; k++)
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{
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if (n_jacobi_unsigned(k, p) == -1) break;
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}
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g = n_powmod2_ui_preinv(k, p1, p, pinv);
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res = n_powmod2_ui_preinv(a, (p1 + 1) / 2, p, pinv);
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while (b != 1)
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{
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bpow = b;
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m = 0;
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do
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{
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bpow = n_mulmod2_preinv(bpow, bpow, p, pinv);
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m++;
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} while (m < r && bpow != 1);
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gpow = g;
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for (i = 1; i < r - m; i++)
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{
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gpow = n_mulmod2_preinv(gpow, gpow, p, pinv);
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}
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res = n_mulmod2_preinv(res, gpow, p, pinv);
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g = n_mulmod2_preinv(gpow, gpow, p, pinv);
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b = n_mulmod2_preinv(b, g, p, pinv);
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r = m;
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}
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return res;
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}
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