/* -*-apcalc-*-
*
- * $Id: gfx.cal,v 1.1 2000/10/08 16:01:37 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 2000/10/08 16:01:37 mdw
- * Prototypes of various bits of code.
- *
- */
-
/*----- Object types ------------------------------------------------------*/
obj gf { x };
define gfx_div(rx, dx)
{
local r = gfint(rx), d = gfint(dx), i;
- local q = 0, dbits = highbit(d), rbits = highbit(r);
+ local q = 0, dbits, rbits;
+ dbits = highbit(d);
+ rbits = highbit(r);
for (i = rbits - dbits; i >= 0; i--) {
if (bit(r, i + dbits)) {
r = xor(r, d << i);
define gf_div(x, y)
{
- local l = gfx_div(x, y);
+ local l;
+ l = gfx_div(x, y);
return gf(l[[0]]);
}
define gf_mod(x, y)
{
- local l = gfx_div(x, y);
+ local l;
+ l = gfx_div(x, y);
return gf(l[[1]]);
}
+define gf_gcd(a, 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(a, b); r = gf_mod(a, b);
+ t = X * q + x; x = X; X = t;
+ t = Y * q + y; y = Y; Y = t;
+ a = b; b = r;
+ }
+ g = a;
+ }
+ 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 -------------------------------------------------*/