xoroshiro

Xoroshiro is a family of pseudorandom number generators (PRNGs) designed for high performance and statistical quality. Developed by David Blackman and Sebastiano Vigna, the Xoroshiro generators emphasize speed, simplicity, and robustness, making them suitable for applications such as simulations, gaming, and scientific computing.

The core mechanism of Xoroshiro involves bitwise operations, primarily XOR and shifts, on internal state variables. Many variations exist within this family, with Xoroshiro128+ and Xoroshiro128++ being among the most commonly used. These variants differ mainly in their output transformations, which influence the statistical properties and period length.

Xoroshiro generators are known for their fast execution on modern hardware due to their simple arithmetic operations. They typically have long periods, often on the order of 2^128, ensuring a large cycle before repetition. While they excel in speed and generally pass many standard statistical tests, they are not cryptographically secure and should not be used for security-sensitive applications.

The design of Xoroshiro emphasizes linear operations to achieve high throughput, but it requires careful initialization to avoid poor sequences. Seeding is often performed using a more secure generator to ensure good initial states. The indicator for quality includes passing tests such as PractRand and DieHarder, with many implementations available as open-source libraries.

Overall, Xoroshiro is regarded as an efficient and reliable general-purpose PRNG, widely adopted in various software systems where speed and statistical quality are priorities. However, users should consider its limitations concerning cryptographic security and ensure proper seeding procedures.