FenderBender -- on MersenneForum.org "Determine Squares" -- came up with using Bloom filter to detect Quadratic non-residues modulo small primes in order to reject what inputs are certainly not square roots. This reduces, by > 99%, the amount of actual square root calc's done and therefore is more efficient and faster.
Search fur 32-bit vs 64-bit, hash values that make "perfect" Bloom filter. Variety of (simple) hash functions, requiring 2, 3, 4 or 5 hash values. Hideously vast search space...