LXM: better splittable pseudorandom number generators (and almost as fast)

In 2014, Steele, Lea, and Flood presented SplitMix, an object-oriented pseudorandom number generator (prng) that is quite fast (9 64-bit arithmetic/logical operations per 64 bits generated) also splittable . A conventional prng object provides a generate method returns one value updates the state of prng; has second operation, split , replaces original with two (seemingly) independent objects, by creating returning new such updating object. Splittable objects make it easy to organize use numbers in multithreaded programs structured using fork-join parallelism. This overall strategy still appears be sound, but specific arithmetic calculation used for SplitMix algorithm some detectable weaknesses, period any limited 2 Here we present LXM family algorithms. The idea old one: combine outputs algorithms, then (optionally) feed result mixing function. An uses linear congruential subgenerator F -linear subgenerator; examples studied this paper (LCG) 16 32 or 128 multipliers recommended L’Ecuyer Steele Vigna, xor-based (XBG) xoshiro xoroshiro as described Blackman Vigna. For functions study MurmurHash3 finalizer function; variants David Stafford, Doug degski; null (identity) Like both operation operation. Also like requires no locking other synchronization (other than usual memory fence after instance initialization), suitable simd instruction sets because branches loops. We analyze equidistribution properties generators, results thorough testing members family, TestU01 PractRand test suites, not only on single instances collections instances, parallel, ranging size from 24 Single include strong function appear have major significantly more robust against accidental correlation setting. believe LXM, “everyday” scientific machine-learning applications (but cryptographic applications), especially when concurrent threads distributed processes are involved.