Xoshiro
Xoshiro is a family of fast, space-efficient and high quality PRNGs. It is considered the state-of-the-art (SOTA) family of non-cryptographic pseudo random number generators (PRNGs). The Rust crate rand_xoshiro (which is part of the popular Rust crate rand) has implementations of Xoshiro256Plus and Xoshiro256PlusPlus . Xoshiro256PlusPlus is a very good PRNG for statistical simulation purpose. Specially, it supports jumping ahead which means that you can implement a fast and correct parallel PRNG based on it.
Mersenne Twister
Mersenne Twister was the state-of-the-art (SOTA) non-cryptographic pseudo random number generator (PRNG) before the Xoshiro faimily of PRNGs . It was implemented in many programming languages and was the default in many software and programming languages. Mersenne Twister has many different versions, among which the MT19937 is the most widely used one. The period of MT19937 is extreemly long (\(2^{19937}-1\)) and is equidistributed for generating vectors up to dimension 623. The MT19937 generate 32 bits random numbers. Combining two random blocks, one can generate 64 bits random numbers. This is often implemented together with the 32 bit version, and usually call MT19937_64. The MT19937_64 is equidistributed for generating vectors up to dimension 311.
WELL
A more modern family of random number generators than Mersenne Twister is the WELL random number generators, which have better equidistribution property and are better to escape the zeroland (initialization array contains many zero bits). However, the speed of the WELL generators is about 0.6 to 0.7 compared to the Mersenne Twister generators. Also the WELL random number generators has a large inner state (e.g., the WELL44497b uses about 33kb for its inner state while the MT19937 uses only about 2.5kb). This is usually not a problem on modern computers, but if you use lots of random number generators at the same time or if the code is run on a embedded device, it might worth considering the consume of memories of these generators. Among different versions of WELL generators, WELL19937c and WELL44497b are commonly used.
SFMT
SIMD-oriented Fast Mersenne Twister (SFMT) is an improved version of Mersenne Twister. It uses parallelism of modern CPUs and is about twice faster than mersenne Twister. SFMT also has better equidistribution property than Mersenne Twister, but not as good as WELL. SFMT recovers from 0-excess initial state faster than Mersenne Twister, but not faster than WELL. C++ implementations are available but I don't see a popular Java implementation so far.
PCG
PCG is a family of simple fast space-efficient statistically good algorithms for random number generation. Unlike many general-purpose RNGs, they are also hard to predict. C++ implementations are available, and the Rust crate rand_pcg (which is part of the popular Rust crate rand) has implementation of PCG32 and PCG64 . I don't see a popular Java implementation for PCG at this time.
Libraries for Random Number Generators
Java
- org.apache.commons.math3.random.RandomDataGenerator is a popular one. By default it uses a Well19937c generator. A customized RandomGenerator can be provided in the constructor.
Python
- Use the random model. It is based on a Mersenne Twister random number generator.