Efficient and portable multiple recursive generators of large order

摘要: Deng and Xu [2003] proposed a system of multiple recursive generators prime modulus p order k, where all nonzero coefficients the recurrence are equal. This type generator is efficient because only single multiplication required. It common to choose = 231−1 some multipliers further improve speed generator. In this case, fast implementations available without using explicit division or multiplication. For such p, provided specific parameters, yielding maximum period for up 120. One problem extending it larger k difficulty finding complete factorization pk−1. article, we apply an technique find that easy factor pk−1, with 231−1. The largest one found 1597. To large introduce search algorithm early exit strategy in case failed search. 1597, constructed several portable length approximately 1014903.1.