173 lines
4.2 KiB
C
173 lines
4.2 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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******************************************************************************/
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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
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n_xgcd(mp_limb_t * a, mp_limb_t * b, mp_limb_t x, mp_limb_t y)
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{
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mp_limb_signed_t u1 = UWORD(1);
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mp_limb_signed_t u2 = UWORD(0);
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mp_limb_signed_t v1 = UWORD(0);
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mp_limb_signed_t v2 = UWORD(1);
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mp_limb_signed_t t1, t2;
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mp_limb_t u3, v3;
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mp_limb_t quot, rem;
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u3 = x, v3 = y;
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if (v3 > u3)
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{
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rem = u3;
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t1 = u2;
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u2 = u1;
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u1 = t1;
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u3 = v3;
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t2 = v2;
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v2 = v1;
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v1 = t2;
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v3 = rem;
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}
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if ((mp_limb_signed_t) (x & y) < WORD(0)) /* x and y both have top bit set */
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{
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quot = u3 - v3;
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t2 = v2;
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t1 = u2;
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u2 = u1 - u2;
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u1 = t1;
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u3 = v3;
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v2 = v1 - v2;
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v1 = t2;
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v3 = quot;
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}
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while ((mp_limb_signed_t) (v3 << 1) < WORD(0)) /*second value has second msb set */
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{
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quot = u3 - v3;
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if (quot < v3)
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{
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t2 = v2;
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t1 = u2;
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u2 = u1 - u2;
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u1 = t1;
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u3 = v3;
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v2 = v1 - v2;
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v1 = t2;
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v3 = quot;
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}
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else if (quot < (v3 << 1))
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{
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t1 = u2;
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u2 = u1 - (u2 << 1);
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u1 = t1;
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u3 = v3;
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t2 = v2;
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v2 = v1 - (v2 << 1);
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v1 = t2;
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v3 = quot - u3;
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}
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else
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{
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t1 = u2;
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u2 = u1 - 3 * u2;
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u1 = t1;
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u3 = v3;
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t2 = v2;
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v2 = v1 - 3 * v2;
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v1 = t2;
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v3 = quot - (u3 << 1);
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}
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}
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while (v3)
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{
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quot = u3 - v3;
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if (u3 < (v3 << 2)) /* overflow not possible due to top 2 bits of v3 not being set */
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{
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if (quot < v3)
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{
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t2 = v2;
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t1 = u2;
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u2 = u1 - u2;
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u1 = t1;
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u3 = v3;
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v2 = v1 - v2;
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v1 = t2;
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v3 = quot;
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}
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else if (quot < (v3 << 1))
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{
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t1 = u2;
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u2 = u1 - (u2 << 1);
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u1 = t1;
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u3 = v3;
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t2 = v2;
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v2 = v1 - (v2 << 1);
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v1 = t2;
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v3 = quot - u3;
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}
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else
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{
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t1 = u2;
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u2 = u1 - 3 * u2;
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u1 = t1;
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u3 = v3;
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t2 = v2;
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v2 = v1 - 3 * v2;
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v1 = t2;
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v3 = quot - (u3 << 1);
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}
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}
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else
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{
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quot = u3 / v3;
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rem = u3 - v3 * quot;
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t1 = u2;
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u2 = u1 - quot * u2;
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u1 = t1;
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u3 = v3;
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t2 = v2;
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v2 = v1 - quot * v2;
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v1 = t2;
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v3 = rem;
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}
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}
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/* Quite remarkably, this always has |u1| < x/2 at this point, thus comparison with 0 is valid */
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if (u1 <= WORD(0))
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{
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u1 += y;
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v1 -= x;
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}
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*a = u1;
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*b = -v1;
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return u3;
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}
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