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mx3

Repo with non-cryptographic bit mixer, pseudo random number generator and a hash function. The functions were found semi-algorithmically as detailed in those posts:

• The construct of a bit mixer
• Tuning bit mixers
• The mx3 mix/prng/hash functions
• Improved mx3 and the RRC test

In short, first procedurally generated stack machines were used to find good mixer constructions. Then each construction was tuned to see how far it could be pushed and finally I decided to take the simplest most promising mixer and publish the result here.

Version 2

Version 2 greatly improves the quality of the mixer by adding an initial xor-shift and adjusting the xor-shift constants. The quality of hash stream mixer is also improved. Article here.

Version 3

Version 3 improves mx3::hash with better seeding and speed while maintaining the same good quality.

mx3::mix

Here is the mixer

inline uint64_t mix(uint64_t x) {
    x ^= x >> 32;
    x *= 0xbea225f9eb34556d;
    x ^= x >> 29;
    x *= 0xbea225f9eb34556d;
    x ^= x >> 32;
    x *= 0xbea225f9eb34556d;
    x ^= x >> 29;
    return x;
}

The name 'mx3' comes from this construction (version 1), multiply then xor-shift and repeat three times (referred to as 'mxmxmx' in posts).

mx3::random

The prng counter based and has a 64-bit state, hence it has a cycle of 2^64. Here is the implementation

class random {
public:
    explicit random(uint64_t seed) : _counter(mix(seed + C)) {}
    uint64_t operator()() { return mix(_counter++); }
private:
    uint64_t _counter;
};

mx3::hash

Uses the same construction, but to favor speed a lighter version mixes the stream before finalizing the hash with 'mix'.

Quality

• mx3::mix passes RRC-64-42-TF2-0.94, also see mx3 version 2
• mx3::random passes PractRand 2^45 (>32TB) without suspicion
• mx3::hash passes all SMHasher tests

Speed

A short preliminary note on speed (will update if I get around to do better tests)

• mx3::hash the speed is according to SMHasher for large keys 8000-9000 MiB/sec and for small keys about 40-50 cycles/hash.

Feedback

This work is to a large degree empirical without much theoretical attention. It would be interesting to know more of what properties and weaknesses mx3 has, so please don't hesitate to let me know!

License

The mx3 code is licensed under the CC0 license, but attribution is still appreciated!