Efficient and portable multiple recursive generators of large order
Abstract
Deng and Xu [2003] proposed a system of multiple recursive generators of prime modulus p and order k, where all nonzero coefficients of the recurrence are equal. This type of generator is efficient because only a single multiplication is required. It is common to choose p -2 31 - 1 and some multipliers to further improve the speed of the generator. In this case, some fast implementations are available without using explicit division or multiplication. For such a p, Deng and Xu [2003] provided specific parameters, yielding the maximum period for recurrence of order k, up to 120. One problem of extending it to a larger k is the difficulty of finding a complete factorization of p k - 1. In this article, we apply an efficient technique to find k such that it is easy to factor p k - 1, with p = 2 31 - 1. The largest one found is k = 1597. To find multiple recursive generators of large order k, we introduce an efficient search algorithm with an early exit strategy in case of a failed search. For k = 1597, we constructed several efficient and portable generators with the period length approximately 10 1490301. © 2005 ACM.
Publication Title
ACM Transactions on Modeling and Computer Simulation
Recommended Citation
Deng, L. (2005). Efficient and portable multiple recursive generators of large order. ACM Transactions on Modeling and Computer Simulation, 15 (1), 1-13. https://doi.org/10.1145/1044322.1044323
