{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,6,3]],"date-time":"2026-06-03T06:14:06Z","timestamp":1780467246308,"version":"3.54.1"},"reference-count":21,"publisher":"Association for Computing Machinery (ACM)","issue":"4","license":[{"start":{"date-parts":[[2005,10,1]],"date-time":"2005-10-01T00:00:00Z","timestamp":1128124800000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/www.acm.org\/publications\/policies\/copyright_policy#Background"}],"content-domain":{"domain":["dl.acm.org"],"crossmark-restriction":true},"short-container-title":["ACM Trans. Model. Comput. Simul."],"published-print":{"date-parts":[[2005,10]]},"abstract":"<jats:p>\n            G. Marsaglia recently introduced a class of very fast\n            <jats:italic>xorshift<\/jats:italic>\n            random number generators, whose implementation uses three \u201cxorshift\u201d operations. They belong to a large family of generators based on linear recurrences modulo 2, which also includes shift-register generators, the Mersenne twister, and several others. In this article, we analyze the theoretical properties of xorshift generators, search for the best ones with respect to the equidistribution criterion, and test them empirically. We find that the vast majority of xorshift generators with only three xorshift operations, including those having good equidistribution, fail several simple statistical tests. We also discuss generators with more than three xorshifts.\n          <\/jats:p>","DOI":"10.1145\/1113316.1113319","type":"journal-article","created":{"date-parts":[[2006,2,6]],"date-time":"2006-02-06T15:07:09Z","timestamp":1139238429000},"page":"346-361","update-policy":"https:\/\/doi.org\/10.1145\/crossmark-policy","source":"Crossref","is-referenced-by-count":69,"title":["On the xorshift random number generators"],"prefix":"10.1145","volume":"15","author":[{"given":"Fran\u00e7ois","family":"Panneton","sequence":"first","affiliation":[{"name":"Universit\u00e9 de Montr\u00e9al, Canada"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Pierre","family":"L'Ecuyer","sequence":"additional","affiliation":[{"name":"Universit\u00e9 de Montr\u00e9al, Canada"}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"320","published-online":{"date-parts":[[2005,10]]},"reference":[{"key":"e_1_2_1_1_1","doi-asserted-by":"crossref","first-page":"1","DOI":"10.18637\/jss.v011.i05","article-title":"Note on Marsaglia's xorshift random number generators","volume":"11","author":"Brent R. P.","year":"2004","unstructured":"Brent , R. P. 2004 a. Note on Marsaglia's xorshift random number generators . J. Stat. Soft. 11 , 5, 1 -- 4 . See http:\/\/www.jstatsoft.org\/v11\/i05\/brent.pdf. Brent, R. P. 2004a. Note on Marsaglia's xorshift random number generators. J. Stat. Soft. 11, 5, 1--4. See http:\/\/www.jstatsoft.org\/v11\/i05\/brent.pdf.","journal-title":"J. Stat. Soft."},{"key":"e_1_2_1_2_1","unstructured":"Brent R. P. 2004b. Some uniform and normal random number generators. http:\/\/web.comlab.ox.ac.uk\/oucl\/work\/richard.brent\/random.html.  Brent R. P. 2004b. Some uniform and normal random number generators. http:\/\/web.comlab.ox.ac.uk\/oucl\/work\/richard.brent\/random.html."},{"key":"e_1_2_1_3_1","doi-asserted-by":"publisher","DOI":"10.1145\/358150.358159"},{"key":"e_1_2_1_4_1","volume-title":"The Art of Computer Programming, Volume 2: Seminumerical Algorithms","author":"Knuth D. E.","unstructured":"Knuth , D. E. 1998. The Art of Computer Programming, Volume 2: Seminumerical Algorithms , Third ed. Addison-Wesley , Reading, Mass . Knuth, D. E. 1998. The Art of Computer Programming, Volume 2: Seminumerical Algorithms, Third ed. Addison-Wesley, Reading, Mass."},{"key":"e_1_2_1_5_1","doi-asserted-by":"crossref","unstructured":"L'Ecuyer P. 1996. Maximally equidistributed combined Tausworthe generators. Mathematics of Computation 65 213 203--213. 10.1090\/S0025-5718-96-00696-5   L'Ecuyer P. 1996. Maximally equidistributed combined Tausworthe generators. Mathematics of Computation 65 213 203--213. 10.1090\/S0025-5718-96-00696-5","DOI":"10.1090\/S0025-5718-96-00696-5"},{"key":"e_1_2_1_6_1","volume-title":"Handbook of Computational Statistics","author":"L'Ecuyer P.","unstructured":"L'Ecuyer , P. 2004. Random number generation . In Handbook of Computational Statistics , J. E. Gentle, W. Haerdle, and Y. Mori, Eds. Springer-Verlag , Berlin , 35--70. Chapter II.2. L'Ecuyer, P. 2004. Random number generation. In Handbook of Computational Statistics, J. E. Gentle, W. Haerdle, and Y. Mori, Eds. Springer-Verlag, Berlin, 35--70. Chapter II.2."},{"key":"e_1_2_1_7_1","doi-asserted-by":"publisher","DOI":"10.1016\/S0378-4754(02)00234-3"},{"key":"e_1_2_1_8_1","doi-asserted-by":"publisher","DOI":"10.1145\/326147.326156"},{"key":"e_1_2_1_9_1","doi-asserted-by":"publisher","DOI":"10.1016\/S0378-4754(00)00253-6"},{"key":"e_1_2_1_10_1","unstructured":"L'Ecuyer P. and Simard R. 2001b. TestU01: A software library in ANSI C for empirical testing of random number generators. Software User's Guide. Available at: http:\/\/www.iro.umontreal.ca\/~lecuyer.  L'Ecuyer P. and Simard R. 2001b. TestU01: A software library in ANSI C for empirical testing of random number generators. Software User's Guide. Available at: http:\/\/www.iro.umontreal.ca\/~lecuyer."},{"key":"e_1_2_1_11_1","doi-asserted-by":"crossref","unstructured":"Lidl R. and Niederreiter H. 1994. Introduction to Finite Fields and Their Applications Revised Ed. Cambridge University Press Cambridge.   Lidl R. and Niederreiter H. 1994. Introduction to Finite Fields and Their Applications Revised Ed. Cambridge University Press Cambridge.","DOI":"10.1017\/CBO9781139172769"},{"key":"e_1_2_1_12_1","volume-title":"Sixteenth Symposium on the Interface. Elsevier Science Publishers, North-Holland","author":"Marsaglia G.","year":"1985","unstructured":"Marsaglia , G. 1985 . A current view of random number generators. In Computer Science and Statistics , Sixteenth Symposium on the Interface. Elsevier Science Publishers, North-Holland , Amsterdam, 3--10. Marsaglia, G. 1985. A current view of random number generators. In Computer Science and Statistics, Sixteenth Symposium on the Interface. Elsevier Science Publishers, North-Holland, Amsterdam, 3--10."},{"key":"e_1_2_1_13_1","doi-asserted-by":"crossref","first-page":"1","DOI":"10.18637\/jss.v008.i14","article-title":"Xorshift RNGs","volume":"8","author":"Marsaglia G.","year":"2003","unstructured":"Marsaglia , G. 2003 . Xorshift RNGs . J. Stat. Soft. 8 , 14, 1 -- 6 . See http:\/\/www.jstatsoft.org\/v08\/i14\/xorshift.pdf. Marsaglia, G. 2003. Xorshift RNGs. J. Stat. Soft. 8, 14, 1--6. See http:\/\/www.jstatsoft.org\/v08\/i14\/xorshift.pdf.","journal-title":"J. Stat. 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