A small trick to Xor

An arithmetic way to perform exclusive-or – something that might have a small use somewhere.

Suppose you want the Xor of two booleans, but the language does not have Xor – like Scheme or Lua 5.1. The obvious thing to do is just implement it – it is very simple, e.g in Scheme: (define (xor a b) (and (not (and a b)) (or a b))).

But if you are dealing with numbers there might be a neat short cut. Instead of:

/* in C: check directions are on same side of surface (no transmission) */
const bool isSameSide = !( (inDot < 0.0f) ^ (outDot < 0.0f) );

do:

/* in C: check directions are on same side of surface (no transmission) */
const bool isSameSide = (inDot * outDot) > 0.0;

Because multiplication of signs has the same truth-function shape as Xor:

exclusive-or			sign-multiply
0	0	0	-	-	+
0	1	1	-	+	-
1	0	1	+	-	-
1	1	0	+	+	+

That is all.