LXM: Better Splittable Pseudorandom Number Generators (and Almost as Fast)
summary
LXM is a concrete PRNG design that sums an LCG and an F2-linear (xoroshiro/xoshiro) generator and then applies a mixer, claiming LCG+XBG+mix yields long periods (product of individual periods) and fixes low-bit failures. Implementations land in JDK17 deployed, pass TestU01 and PractRand, scale tested up to 2^24 parallel streams, and single instances with a strong mixer show no major weaknesses; timing results report LXM is almost as fast as SplitMix while being more robust against accidental correlation.
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chapters (14)
- 0:00Intro
- 0:25What Do We Want From a Pseudorandom Number Generator (PRNG)?
- 2:28Basic Structure of a Pseudorandom Number Generator (PRNG)
- 2:55Mathematical Description
- 3:38Slight Adjustment (Engineering Hack)
- 4:03Linear Congruential PRNG with Prime Modulus
- 6:12Parallel Streams?
- 6:35One Big State Cycle versus Many Smaller State Cycles
- 8:57Getting a Large Period without Quadratic Cost
- 10:08Compound PRNG Algorithm
- 10:58The LXM Algorithm (Ta-dal)
- 11:29Deployment
- 12:02Wait-What Makes LXM "Splittable"?
- 13:12Other Strengths of the LXM Algorithm
