There are only four billion floats, so test them all (2014)

Many years ago now we built something that used a 60-bit truncated hash of URIs. So that's far too small to be comfortable that you won't run into collisions, but it's big enough that for modest sizes (hundreds of millions up to billions) a collision is unlikely. So you can have a slow path for the collision case, so long as that slow path is correct. For unit testing we needed at least one collision so we could see that…

On the topic of "test them all", I wrote this in my paper about error bounds and worst cases for complex multiplication (http://www.daemonology.net/papers/complexmultiply.pdf): [For finding worst-case inputs] the approach taken was to perform an exhaustive search, taking several hours on the second author’s laptop, of IEEE single-precision inputs, using only a few arguments from Theorem 1 to prune the search. Even though (2^32)^4 was far too large for it to be tractable to test all 4-tuples of single-precision…

Not often you can employ exhaustive testing, but it's useful in some cases. I did a project in college for a VLSI minor where we implemented a 16bit multiplier - after we got the chips back we were supposed to do scan testing, but I just wrote up a little program in an fpga, wired up my chip to test, and swept all the possible inputs verifying the output. I think I could only run this at 10MHz, and you…