pqc/external/flint-2.4.3/ulong_extras/xgcd.c
2014-05-24 23:16:06 +02:00

173 lines
4.2 KiB
C

/*=============================================================================
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) 2009 William Hart
******************************************************************************/
#include <gmp.h>
#include "flint.h"
#include "ulong_extras.h"
mp_limb_t
n_xgcd(mp_limb_t * a, mp_limb_t * b, mp_limb_t x, mp_limb_t y)
{
mp_limb_signed_t u1 = UWORD(1);
mp_limb_signed_t u2 = UWORD(0);
mp_limb_signed_t v1 = UWORD(0);
mp_limb_signed_t v2 = UWORD(1);
mp_limb_signed_t t1, t2;
mp_limb_t u3, v3;
mp_limb_t quot, rem;
u3 = x, v3 = y;
if (v3 > u3)
{
rem = u3;
t1 = u2;
u2 = u1;
u1 = t1;
u3 = v3;
t2 = v2;
v2 = v1;
v1 = t2;
v3 = rem;
}
if ((mp_limb_signed_t) (x & y) < WORD(0)) /* x and y both have top bit set */
{
quot = u3 - v3;
t2 = v2;
t1 = u2;
u2 = u1 - u2;
u1 = t1;
u3 = v3;
v2 = v1 - v2;
v1 = t2;
v3 = quot;
}
while ((mp_limb_signed_t) (v3 << 1) < WORD(0)) /*second value has second msb set */
{
quot = u3 - v3;
if (quot < v3)
{
t2 = v2;
t1 = u2;
u2 = u1 - u2;
u1 = t1;
u3 = v3;
v2 = v1 - v2;
v1 = t2;
v3 = quot;
}
else if (quot < (v3 << 1))
{
t1 = u2;
u2 = u1 - (u2 << 1);
u1 = t1;
u3 = v3;
t2 = v2;
v2 = v1 - (v2 << 1);
v1 = t2;
v3 = quot - u3;
}
else
{
t1 = u2;
u2 = u1 - 3 * u2;
u1 = t1;
u3 = v3;
t2 = v2;
v2 = v1 - 3 * v2;
v1 = t2;
v3 = quot - (u3 << 1);
}
}
while (v3)
{
quot = u3 - v3;
if (u3 < (v3 << 2)) /* overflow not possible due to top 2 bits of v3 not being set */
{
if (quot < v3)
{
t2 = v2;
t1 = u2;
u2 = u1 - u2;
u1 = t1;
u3 = v3;
v2 = v1 - v2;
v1 = t2;
v3 = quot;
}
else if (quot < (v3 << 1))
{
t1 = u2;
u2 = u1 - (u2 << 1);
u1 = t1;
u3 = v3;
t2 = v2;
v2 = v1 - (v2 << 1);
v1 = t2;
v3 = quot - u3;
}
else
{
t1 = u2;
u2 = u1 - 3 * u2;
u1 = t1;
u3 = v3;
t2 = v2;
v2 = v1 - 3 * v2;
v1 = t2;
v3 = quot - (u3 << 1);
}
}
else
{
quot = u3 / v3;
rem = u3 - v3 * quot;
t1 = u2;
u2 = u1 - quot * u2;
u1 = t1;
u3 = v3;
t2 = v2;
v2 = v1 - quot * v2;
v1 = t2;
v3 = rem;
}
}
/* Quite remarkably, this always has |u1| < x/2 at this point, thus comparison with 0 is valid */
if (u1 <= WORD(0))
{
u1 += y;
v1 -= x;
}
*a = u1;
*b = -v1;
return u3;
}