My goal was to create the fastest possible C program. If there's one thing computers are good at, it's math.
Simple operations take less time than complicated ones.
Also, I've looked at some past winning entries of your contest, and if you don't mind a little constructive criticsm, some of them are kind-of hard to figure out. I didn't want my program to fall into the same trap, so I went out of my way to write self-documenting code. Anyone who so much as glances at my program will immediately see that it adds two 16-bit unsigned integers by streaming their bits through a simulated cascade of hardware adders.