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For testing purposes, I need to find two 64-bit integer values that exactly multiply to a 128-bit intermediate value with a specific bit pattern. Obviously, I can generate the desired intermediate value and divide by random values until I find a combination that works, but is there a more efficient way?
This problem sounds like integer factorisation. No fast algorithms are known unfortunately, but from glancing at that Wikipedia page it seems there are some (possibly tricky) algorithms that are faster than trial division.