/* -*-apcalc-*-
*
- * $Id: gfx.cal,v 1.1.4.1 2004/03/21 22:39:46 mdw Exp $
+ * $Id: gfx.cal,v 1.3 2004/04/08 01:36:15 mdw Exp $
*
* Testbed for %$\gf{2}$% poltnomial arithmetic
*
* MA 02111-1307, USA.
*/
-/*----- Revision history --------------------------------------------------*
- *
- * $Log: gfx.cal,v $
- * Revision 1.1.4.1 2004/03/21 22:39:46 mdw
- * Elliptic curves on binary fields work.
- *
- * Revision 1.1 2000/10/08 16:01:37 mdw
- * Prototypes of various bits of code.
- *
- */
-
/*----- Object types ------------------------------------------------------*/
obj gf { x };
return gf(l[[1]]);
}
-define gf_inv(a, b)
+define gf_gcd(a, b)
{
- local g, x, y, X, Y, u, v, t, q, r;
- x = gf(1); X = gf(0);
- y = gf(0); Y = gf(1);
-
- if (b == gf(0)) { g = a; } else if (a == gf(0)) { g = b; }
+ local swap = 0;
+ local g, x = 1, X = 0, y = 0, Y = 1, q, r, t;
+ if (a.x < b.x) {
+ t = a; a = b; b = t;
+ swap = 1;
+ }
+ if (b == gf(0))
+ g = a;
else {
while (b != gf(0)) {
- q = gf_div(b, a); r = gf_mod(b, a);
+ q = gf_div(a, b); r = gf_mod(a, b);
t = X * q + x; x = X; X = t;
t = Y * q + y; y = Y; Y = t;
- b = a; a = r;
+ a = b; b = r;
}
g = a;
}
- if (g != gf(1)) quit "not coprime in gf_inv";
- return Y;
+ if (swap) {
+ t = x; x = y; y = t;
+ }
+ return list(g, x, y);
+}
+
+define gf_inv(a, b)
+{
+ local l = gf_gcd(b, a);
+ if (l[[0]] != gf(1)) quit "not coprime in gf_inv";
+ return l[[2]];
}
/*----- That's all, folks -------------------------------------------------*/