Introduction to finite fields and their applications
Introduction to finite fields and their applications
Efficient and portable combined random number generators
Communications of the ACM
A search for good multiple recursive random number generators
ACM Transactions on Modeling and Computer Simulation (TOMACS)
Multiplicative, congruential random-number generators with multiplier ± 2k1 ± 2k2 and modulus 2p - 1
ACM Transactions on Mathematical Software (TOMS)
The art of computer programming, volume 2 (3rd ed.): seminumerical algorithms
The art of computer programming, volume 2 (3rd ed.): seminumerical algorithms
Linear congruential generators of order K1
WSC '88 Proceedings of the 20th conference on Winter simulation
Beware of linear congruential generators with multipliers of the form a = ±2q ±2r
ACM Transactions on Mathematical Software (TOMS)
Coding the Lehmer pseudo-random number generator
Communications of the ACM
A system of high-dimensional, efficient, long-cycle and portable uniform random number generators
ACM Transactions on Modeling and Computer Simulation (TOMACS)
On the Deng-Lin random number generators and related methods
Statistics and Computing
TestU01: A C library for empirical testing of random number generators
ACM Transactions on Mathematical Software (TOMS)
Comparison of Point Sets and Sequences for Quasi-Monte Carlo and for Random Number Generation
SETA '08 Proceedings of the 5th international conference on Sequences and Their Applications
Scalable parallel multiple recursive generators of large order
Parallel Computing
Efficient computer search of large-order multiple recursive pseudo-random number generators
Journal of Computational and Applied Mathematics
Large-Order Multiple Recursive Generators with Modulus 231-1
INFORMS Journal on Computing
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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 = 231−1 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 pk−1. In this article, we apply an efficient technique to find k such that it is easy to factor pk−1, with p = 231−1. 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 1014903.1.