Further scramblings of Marsaglia's xorshift generators
This work addresses a specific issue in pseudorandom number generation for computational simulations, representing an incremental improvement over existing methods.
The paper tackled the weakness in lower bits of the XSadd pseudorandom number generator by introducing xorshift+, a variant using 64-bit operations, which resulted in extremely fast and high-quality generators in small dimensions.
xorshift* generators are a variant of Marsaglia's xorshift generators that eliminate linear artifacts typical of generators based on $\mathbf Z/2\mathbf Z$-linear operations using multiplication by a suitable constant. Shortly after high-dimensional xorshift* generators were introduced, Saito and Matsumoto suggested a different way to eliminate linear artifacts based on addition in $\mathbf Z/2^{32}\mathbf Z$, leading to the XSadd generator. Starting from the observation that the lower bits of XSadd are very weak, as its reverse fails systematically several statistical tests, we explore xorshift+, a variant of XSadd using 64-bit operations, which leads, in small dimension, to extremely fast high-quality generators.