{"paper":{"title":"Xorshift1024*, Xorshift1024+, Xorshift128+ and Xoroshiro128+ Fail Statistical Tests for Linearity","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":[],"primary_cat":"cs.DS","authors_text":"Daniel Lemire, Melissa E. O'Neill","submitted_at":"2018-10-12T01:40:57Z","abstract_excerpt":"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 Crus"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1810.05313","kind":"arxiv","version":2},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}