How can I safely average two unsigned ints in C++?
Your last approach seems promising. You can improve on that by manually considering the lowest bits of a and b:
unsigned int average = (a / 2) + (b / 2) + (a & b & 1);
This gives the correct results in case both a and b are odd.
If you know ahead of time which one is higher, a very efficient way is possible. Otherwise you're better off using one of the other strategies, instead of conditionally swapping to use this.
unsigned int average = low + ((high - low) / 2);
Here's a related article: http://googleresearch.blogspot.com/2006/06/extra-extra-read-all-about-it-nearly.html