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An interesting problem I ran into today: what is the fastest way to count the number of 1s in an n-bit integer? Is it possible to beat O(n)?
For example:
42 = 0b101010 => 3 ones
512 = 0b1000000000 => 1 one
Clearly, the naive algorithm is to simply count. But, are there any tricks to speed it up?
(This is merely an academic question; there is no expected performance gain by implementing such a strategy.)
See the fabulous Bit Twiddling Hacks article.