# Further scramblings of Marsaglia's xorshift generators

arXiv: https://arxiv.org/abs/1404.0390 · HTML: https://mlsanity.com/paper/1404.0390/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 1 Apr 2014.

## Built on by (most cited first, 2 of 2)

- [QonFusion -- Quantum Approaches to Gaussian Random Variables: Applications in Stable Diffusion and Brownian Motion](https://mlsanity.com/paper/2309.16258/) (2023)
- [Memory-Efficient FPGA Implementation of Stochastic Simulated Annealing](https://mlsanity.com/paper/2601.18007/) (2026)

## Abstract (arXiv)

xorshift* generators are a variant of Marsaglia's xorshift generators that eliminate linear artifacts typical of generators based on mathbf Z/2mathbf 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/232mathbf 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.