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Xorshift Family

Xorshift family is a class of PRNGs based on linear transformation that takes the exclusive or of a number with a bit-shifted version of itself1. They are extremely fast on mordern computer architectures, and are very suitable for non-cryptographically-secure use. The suffix -Star and -Plus in the RNG names denote to two classes of improved RNGs23, which make it to pass Big Crush in TestU01. -Star RNGs are obtained by scrambling the output of a normal Xorshift generator with a 64-bit invertible multiplier, while -Plus RNGs return the sum of two consecutive output of a Xorshift generator.

In this package there are four series of RNG types:

  • Xorshift64 and Xorshift64Star: They have a period of $2^{64}$, but not recommended because 64 bits of state are not enough for any serious purpose.
  • Xorshift128, Xorshift128Star and Xorshift128Plus: They have a period of $2^{128}$. Xorshift128Plus is presently used in the JavaScript engines of Chrome, Firefox and Safari.
  • Xorshift1024, Xorshift1024Star and Xorshift1024Plus: They have a long period of $2^{1024}$, and takes some more space for storing the state. If you are running large-scale parallel simulations, it's a good choice to use Xorshift1024Star.
  • Xoroshiro128, Xoroshiro128Star and Xoroshiro128Plus: The successor to Xorshift128 series. They make use of a carefully handcrafted shift/rotate-based linear transformation, resulting in a significant improvement in speed and in statistical quality. Therefore, Xoroshiro128Plus is the current best suggestion for replacing other low-quality generators.

All the RNG types produce UInt64 numbers, if you have need for other output type, see WrappedRNG.

Examples

The usage of Xorshift family is very simple and common:

julia> using RandomNumbers.Xorshifts

julia> r = Xoroshiro128Plus();  # create a RNG with truly random seed.

julia> r = Xoroshiro128Plus(0x1234567890abcdef)  # with a certain seed. Note that the seed must be non-zero.
Xoroshiro128Plus(0xe7eb72d97b4beac6, 0x9b86d56534ba1f9e)

julia> rand(r)
0.14263790854661185

julia> rand(r, UInt32)
0x0a0315b3

  1. Marsaglia G. Xorshift rngs[J]. Journal of Statistical Software, 2003, 8(14): 1-6. doi:10.18637/jss.v008.i14 ↩

  2. Vigna S. An experimental exploration of Marsaglia's xorshift generators, scrambled[J]. arXiv preprint arXiv:1402.6246, 2014. ↩

  3. Vigna S. Further scramblings of Marsaglia's xorshift generators[J]. arXiv preprint arXiv:1404.0390, 2014. ↩