Xoroshiroxorshift

Xoroshiroxorshift is a hybrid pseudorandom number generator that combines features of two well-known bitwise families, xoroshiro and xorshift. The aim is to blend their statistical properties by applying their state update rules in tandem or alternating rounds and then mixing the results to produce outputs. This approach is intended to provide a compact, fast generator with robust empirical performance across a range of test suites, while avoiding the pitfalls of relying on a single primitive.

A typical implementation maintains a pair of internal state words, often 64 bits each. The xoroshiro-style portion updates one component using a rotation and xorshift-style feedback, for example applying a sequence of shifts and a rotate operation. The xorshift portion updates the other component with its own sequence of xor and shift steps. The final output is formed by combining the two updated components, commonly by XORing their individual outputs or by adding them modulo the word size. Some variants may perform the two updates in alternating rounds and then cross-mix the results.

Seeding and period considerations are important. The generator generally requires non-zero seeds for both state components, or a single seed that is split into two parts. The implied period is very large, often approximating the product of the component periods, but exact guarantees depend on the chosen constants and implementation details. Proper seeding is essential to avoid degenerate states and correlation between the two parts.

Xoroshiroxorshift is intended for applications such as simulations and games where speed and reasonably good statistical properties are desirable. It is not designed for cryptographic use, and users should perform their own empirical testing to ensure suitability for their workloads. See also xoroshiro and xorshift for related principles.