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We introduce the Romu family of pseudo-random number generators (PRNGs) whichcombines the nonlinear operation of rotation with the linear operations ofmultiplication and (optionally) addition. Compared to conventional linear-onlyPRNGs, this mixture of linear and nonlinear operations achieves a greaterdegree of randomness using the same number of arithmetic operations. Orequivalently, it achieves the same randomness with fewer operations, resultingin higher speed. The statistical properties of these generators are strong, asthey pass BigCrush and PractRand -- the most stringent test suites available.In addition, Romu generators take maximum advantage of instruction-levelparallelism in modern superscalar processors, giving them an output latency ofzero clock-cycles when inlined, thus adding no delay to an application.Scaled-down versions of these generators can be created and tested, enablingone to estimate the maximum number of values the full-size generators cansupply before their randomness declines, ensuring the success of large jobs.Such capacity-estimates are rare for conventional PRNGs. A linear PRNG has asingle cycle of states of known length comprising almost all possible states.However, a Romu generator computes pseudo-random permutations of those states,creating multiple cycles with pseudo-random lengths which cannot be determinedby theory. But the ease of creating state-sizes of 128 or more bits allows (1)short cycles to be constrained to vanishingly low probabilities, and (2)thousands of parallel streams to be created having infinitesimal probabilitiesof overlap.

Romu: Fast Nonlinear Pseudo-Random Number Generators Providing High Quality