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The simple XOR `commutative_eat()` implementation produces a lot of collisions. https://www.preprints.org/manuscript/201710.0192/v1/download is a useful reference on this topic. Running the included `hashTest.cc` without the hashlib changes, I get 49,580,349 collisions. The 49,995,000 (i,j) pairs (0 <= i < 10000, i < j < 10000) hash into only 414,651 unique hash values. We get simple collisions like (0,1) colliding with (2,3). With the hashlib changes, we get only 707,099 collisions and 49,287,901 unique hash values. Much better! The `commutative_hash` implementation corresponds to `Sum(4)` in the paper mentioned above. |
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