I stand corrected and feel somewhat enlightened...but only somewhat, since I don't quite get all your math speak. Oh well, it makes sense. Do you happen to have a link to the C++ thread? I'd love to read it, but a search for "predetermined integers" gave me 2 irrelevant threads, and I don't quite feel like sifting through laserlight's and Elysia's combined 30,000+ posts. Thanks.