Fast splittable pseudorandom number generators

Abstract

We describe a new algorithm SplitMix for an object-oriented and splittable pseudorandom number generator (PRNG) that is quite fast: 9 64-bit arithmetic/logical operations per 64 bits generated. A conventional linear PRNG object provides a generate method that returns one pseudorandom value and updates the state of the PRNG, but a splittable PRNG object also has a second operation, split , that replaces the original PRNG object with two (seemingly) independent PRNG objects, by creating and returning a new such object and updating the state of the original object. Splittable PRNG objects make it easy to organize the use of pseudorandom numbers in multithreaded programs structured using fork-join parallelism. No locking or synchronization is required (other than the usual memory fence immediately after object creation). Because the generate method has no loops or conditionals, it is suitable for SIMD or GPU implementation. We derive SplitMix from the DotMix algorithm of Leiserson, Schardl, and Sukha by making a series of program transformations and engineering improvements. The end result is an object-oriented version of the purely functional API used in the Haskell library for over a decade, but SplitMix is faster and produces pseudorandom sequences of higher quality; it is also far superior in quality and speed to java.util.Random, and has been included in Java JDK8 as the class java.util.SplittableRandom. We have tested the pseudorandom sequences produced by SplitMix using two standard statistical test suites (DieHarder and TestU01) and they appear to be adequate for "everyday" use, such as in Monte Carlo algorithms and randomized data structures where speed is important.