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Lemire, Daniel, & O'Neill, Melissa (2019). Xorshift1024*, Xorshift1024+, Xorshift128+ and Xoroshiro128+ Fail Statistical Tests for Linearity. Computational and Applied Mathematics, 350, 139-142. https://doi.org/10.1016/j.cam.2018.10.019
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Content : Submitted Version License : Creative Commons Attribution. |
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| Item Type: | Journal Articles |
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| Refereed: | Yes |
| Status: | Published |
| Abstract: | L'Ecuyer & Simard's Big Crush statistical test suite has revealed statistical flaws in many popular random number generators including Marsaglia's XorShift generators. Vigna recently proposed some 64-bit variations on the Xorshift scheme that are further scrambled (i.e., Xorshift1024*, Xorshift1024+, Xorshift128+, Xoroshiro128+). Unlike their unscrambled counterparts, they pass Big Crush when interleaving blocks of 32 bits for each 64-bit word (most significant, least significant, most significant, least significant, etc.). We report that these scrambled generators systematically fail Big Crush---specifically the linear-complexity and matrix-rank tests that detect linearity---when taking the 32 lowest-order bits in reverse order from each 64-bit word. |
| Official URL: | https://www.sciencedirect.com/science/article/pii/... |
| Depositor: | Lemire, Daniel |
| Owner / Manager: | Daniel Lemire |
| Deposited: | 15 Oct 2018 13:58 |
| Last Modified: | 04 Jan 2019 18:24 |
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