Efficient computer search of large-order multiple recursive pseudo-random number generators

Lih Yuan Deng, Jyh Jen Horng Shiau*, Henry Horng Shing Lu

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

6 Scopus citations


Utilizing some results in number theory, we propose an efficient method to speed up the computer search of large-order maximum-period Multiple Recursive Generators (MRGs). We conduct the computer search and identify many efficient and portable MRGs of order up to 25,013, which have the equi-distribution property in up to 25,013 dimensions and the period lengths up to 10 233,361 approximately. In addition, a theoretical test is adopted to further evaluate and compare these generators. An extensive empirical study shows that these generators behave well when tested with the stringent Crush battery of the test package TestU01.

Original languageEnglish
Pages (from-to)3228-3237
Number of pages10
JournalJournal of Computational and Applied Mathematics
Issue number13
StatePublished - 1 Jul 2012


  • DX/DL/DS generators
  • Empirical tests
  • Equi-distribution
  • Factorization
  • Portable and efficient generators
  • Primality testing


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