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Xorshift1024*, xorshift1024+, xorshift128+ and xoroshiro128+ fail statistical tests for linearity. (English) Zbl 07006466
Summary: 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.
MSC:
65 Numerical analysis
62 Statistics
Software:
TestU01; XSadd
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References:
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