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/*
Copyright (C) 2009, 2016 William Hart
This file is part of FLINT.
FLINT is free software: you can redistribute it and/or modify it under
the terms of the GNU Lesser General Public License (LGPL) as published
by the Free Software Foundation; either version 3 of the License, or
(at your option) any later version. See <https://www.gnu.org/licenses/>.
*/
#include "ulong_extras.h"
ulong
n_xgcd(ulong * a, ulong * b, ulong x, ulong y)
{
slong u1, u2, v1, v2, t1, t2;
ulong u3, v3, quot, rem, d;
FLINT_ASSERT(x >= y);
u1 = v2 = 1;
u2 = v1 = 0;
u3 = x;
v3 = y;
/* x and y both have top bit set */
if ((slong) (x & y) < WORD(0))
{
d = u3 - v3;
t2 = v2;
t1 = u2;
u2 = u1 - u2;
u1 = t1;
u3 = v3;
v2 = v1 - v2;
v1 = t2;
v3 = d;
}
/* second value has second msb set */
while ((slong) (v3 << 1) < WORD(0))
{
d = u3 - v3;
if (d < v3) /* quot = 1 */
{
t2 = v2;
t1 = u2;
u2 = u1 - u2;
u1 = t1;
u3 = v3;
v2 = v1 - v2;
v1 = t2;
v3 = d;
}
else if (d < (v3 << 1)) /* quot = 2 */
{
t1 = u2;
u2 = u1 - (u2 << 1);
u1 = t1;
u3 = v3;
t2 = v2;
v2 = v1 - ((ulong) v2 << 1);
v1 = t2;
v3 = d - u3;
}
else /* quot = 3 */
{
t1 = u2;
u2 = u1 - 3 * u2;
u1 = t1;
u3 = v3;
t2 = v2;
v2 = v1 - 3 * v2;
v1 = t2;
v3 = d - (u3 << 1);
}
}
while (v3)
{
d = u3 - v3;
/* overflow not possible, top 2 bits of v3 not set */
if (u3 < (v3 << 2))
{
if (d < v3) /* quot = 1 */
{
t2 = v2;
t1 = u2;
u2 = u1 - u2;
u1 = t1;
u3 = v3;
v2 = v1 - v2;
v1 = t2;
v3 = d;
}
else if (d < (v3 << 1)) /* quot = 2 */
{
t1 = u2;
u2 = u1 - ((ulong) u2 << 1);
u1 = t1;
u3 = v3;
t2 = v2;
v2 = v1 - ((ulong) v2 << 1);
v1 = t2;
v3 = d - u3;
}
else /* quot = 3 */
{
t1 = u2;
u2 = u1 - 3 * (ulong) u2;
u1 = t1;
u3 = v3;
t2 = v2;
v2 = v1 - 3 * (ulong) v2;
v1 = t2;
v3 = d - ((ulong) 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;
}
}
/* Remarkably, |u1| < x/2, thus comparison with 0 is valid */
if (u1 <= WORD(0))
{
u1 += y;
v1 -= x;
}
*a = u1;
*b = -(ulong) v1;
return u3;
}