Summary

Provide new interface types and implementations for pseudorandom number generators (PRNGs), including jumpable PRNGs and an additional class of splittable PRNG algorithms (LXM).

Goals

• Make it easier to use various PRNG algorithms interchangeably in applications.
• Better support stream-based programming by providing streams of PRNG objects.
• Eliminate code duplication in existing PRNG classes.
• Carefully preserve existing behavior of class java.util.Random.

Non-Goals

It is not a goal to provide implementations of numerous other PRNG algorithms, only to provide a framework that can accommodate other PRNG algorithms. However, we have added three common algorithms that have already been widely deployed in other programming language environments.

Success Metrics

The output of the new LXM algorithms passes the existing well-known TestU01 and PractRand test suites.

• Pierre L'Ecuyer and Richard Simard. TestU01: A C Library for Empirical Testing of Random Number Generators. ACM Transactions on Mathematical Software 33, 4 (August 2007), article 22. ISSN 0098-3500. http://doi.acm.org/10.1145/1268776.1268777

• Richard Simard. TestU01 version 1.2.3 (August 2009). http://www.iro.umontreal.ca/~simardr/testu01/tu01.html

• Pierre L'Ecuyer and Richard Simard. TestU01: A Software Library in ANSI C for Empirical Testing of Random Number Generators: User's guide, compact version. Département d'Informatique et de Recherche Opérationnelle, Univerité de Montréal, May 2013. http://www.iro.umontreal.ca/~simardr/testu01/guideshorttestu01.pdf

• Chris Doty-Humphrey. PractRand version 0.90. July 2014. http://pracrand.sourceforge.net [That's not a typo. The name of the software is "PractRand"
  but the SourceForge project name is "pracrand".]

Jumpable and leapable PRNG algorithms pass tests that verify the commutativity of certain operations.

Motivation

We focus on five areas for improvement in the area of pseudorandom number generators in Java:

• With the legacy PRNG classes Random, ThreadLocalRandom, and SplittableRandom, it is difficult to replace any one of them in an application with some other algorithm, despite the fact that they all support pretty much the same set of methods. For example, if an application uses instances of class Random, it will necessarily declare variables of type Random, which cannot hold instances of class SplittableRandom; changing the application to use SplittableRandom would require changing the type of every variable (including method parameters) used to hold a PRNG object. The one exception is that ThreadLocalRandom is a subclass of Random, purely to allow variables of type Random to hold instances of ThreadLocalRandom, yet ThreadLocalRandom overrides nearly all the methods of Random. Interfaces can easily address this.

• Legacy classes Random, ThreadLocalRandom, and SplittableRandom all support such methods as nextDouble() and nextBoolean() as well as stream-producing methods such as ints() and longs(), but they have completely independent and nearly copy-and-paste identical implementations. Refactoring this code would made it easier to maintain and, moreover, documentation would makes it much easier for third parties to create new PRNG classes that also support the same complete suite of methods.

• In 2016, testing revealed two new weaknesses in the algorithm used by class SplittableRandom. On the one hand, a relatively minor revision can avoid those weaknesses. On the other hand, a new class of splittable PRNG algorithms (LXM) has also been discovered that are almost as fast, even easier to implement, and appear to completely avoid the three classes of weakness to which SplittableRandom is prone.

• Being able to obtain a stream of PRNG objects from a PRNG makes it much easier to express certain sorts of code using streaming methods.

• There are many PRNG algorithms in the literature that are not splittable but are jumpable (and perhaps also leapable, that is, capable of very long jumps as well as ordinary jumps), a property quite different from splitting that nevertheless also lends itself to supporting streams of PRNG objects. In the past, it has been difficult to take advantage of this property in Java. Examples of jumpable PRNG algorithms are Xoshiro256**, and Xoroshiro128+.

  • Xoshiro256** and Xoroshiro128+: http://xoshiro.di.unimi.it

Description

We provide a new interface, RandomGenerator, which supplies a uniform API for all existing and new PRNGs. RandomGenerators provide methods named ints, longs, doubles, nextBoolean, nextInt, nextLong, nextDouble, and nextFloat, with all their current parameter variations.

We provide four new specialized RandomGenerator interfaces:

• SplittableRandomGenerator extends RandomGenerator and also provides
  methods named split and splits. Splittability allows the user to spawn a new RandomGenerator from an existing RandomGenerator that will generally produce statistically independent results.

• JumpableRandomGenerator extendsRandomGenerator and also provides
  methods named jump and jumps. Jumpability allows a user to jump ahead a moderate number of draws.

• LeapableRandomGenerator extends RandomGenerator and also provides
  methods named leap and leaps. Leapability allows a user to jump ahead a large number of draws.

• ArbitrarilyJumpableRandomGenerator extends LeapableRandomGenerator and also provides additional variations of jump and jumps that allow an arbitrary jump distance to be specified.

We provide a new class RandomGeneratorFactory which is used to locate and construct instances of RandomGenerator implementations. The RandomGeneratorFactory uses the ServiceLoader.Provider API to register RandomGenerator implementations.

We have refactored Random, ThreadLocalRandom, and SplittableRandom so as to share most of their implementation code and, furthermore, make that code reusable by other algorithms as well. This refactoring creates underlying non-public abstract classes AbstractRandomGenerator, AbstractSplittableRandomGenerator, AbstractJumpableRandomGenerator, AbstractLeapableRandomGenerator, and AbstractArbitrarilyJumpableRandomGenerator, each provide only implementations for methods nextInt(), nextLong(), and (if relevant) either split(), or jump(), or jump() and leap(), or jump(distance). After this refactoring, Random, ThreadLocalRandom, and SplittableRandom inherit the RandomGenerator interface. Note that because SecureRandom is a subclass of Random, all instances of SecureRandom also automatically support the RandomGenerator interface, with no need to recode the SecureRandom class or any of its associated implementation engines.

We also added underlying non-public classes that extend AbstractSplittableRandomGenerator (and therefore implement SplittableRandomGenerator and RandomGenerator) to support six specific members of the LXM family of PRNG algorithms:

• L32X64MixRandom
• L32X64StarStarRandom
• L64X128MixRandom
• L64X128StarStarRandom
• L64X256MixRandom
• L64X1024MixRandom
• L128X128MixRandom
• L128X256MixRandom
• L128X1024MixRandom

The structure of the central nextLong (or nextInt) method of an LXM algorithm follows a suggestion in December 2017 by Sebastiano Vigna that using one LCG subgenerator and one xor-based subgenerator (rather than two LCG subgenerators) would provide a longer period, superior equidistribution, scalability, and better quality. Each of the specific implementations here combines one of the best currently known xor-based generators (xoroshiro or xoshiro, described by Blackman and Vigna in "Scrambled Linear Pseudorandom Number Generators", ACM Trans. Math. Softw., 2021) with an LCG that uses one of the best currently known multipliers (found by a search for better multipliers in 2019 by Steele and Vigna), and then applies a mixing function identified by Doug Lea. Testing has confirmed that the LXM algorithm is far superior in quality to the SplitMix algorithm (2014) used by SplittableRandom.

We also provide implementations of these widely-used PRNG algorithms:

• Xoshiro256PlusPlus
• Xoroshiro128PlusPlus

The non-public abstract implementations mentioned above may be supplied as part of a random number implementor SPI in the future.

This suite of algorithms provide Java programmers with a reasonable range of tradeoffs among space, time, quality, and compatibility with other languages.

Alternatives

We considered simply introducing new interfaces while leaving the implementations of Random, ThreadLocalRandom, and SplittableRandom as is. This would help to make PRNG objects more easily interchangeable but would not make it any easier to implement them.

We considered refactoring Random, ThreadLocalRandom, and SplittableRandom without changing their functionality or adding any new interfaces. We believe this would reduce their overall memory footprint, but do nothing to make future PRNG algorithms easier to implement or use.

Testing

• All existing tests for Random, ThreadLocalRandom, and SplittableRandom
  should continue to be used.

• New test, probably to be applied just once: The output of the refactored
  versions of Random, ThreadLocalRandom, and SplittableRandom (before
  repairing the two newly detected weaknesses) should be spot-checked against the existing (JDK 8) implementations to verify that their behavior remains
  unchanged.

• New test, probably to be applied just once: The output of the LXM algorithms
  should be spot-checked against the C-coded versions used for quality
  verification with TestU01 and PractRand.

• New test, to become a permanent part of the test suite: The jump() and
  leap() methods should be tested to verify that they do travel around the state cycle by the claimed distance. For example, starting from any specific initial state, the sequence of operations nextLong(); jump() ought to leave a
  generator in the same state as the sequence of operations jump(); nextLong().

Risks and Assumptions

We believe this is a medium project and the risks are minimal. Probably
the largest burden has been crafting the specification and the second-largest has been testing.

Care has been give to ensure the behaviour of legacy random number generators has not been affected.