> Many, many, classes of problems turn into O(log n) problems, once you sort your input in some way. It might not be the most effective way of solving the problem, but it's often a fairly good one.

As a corollary, you can use binary search+linear interpolation as a fast way to approximate a strictly monotonic function, knowing its reciprocal, over a limited sets of outputs (e.g. n -> floor(255 * n^(1/2.2) + 0.5) for n in 0..255). You also get to work on bit_cast<s32>(...) as an optimization when the targeted FPU doesn't have conditional move instructions.