Introduction to finite fields and their applications
Introduction to finite fields and their applications
A search for good multiple recursive random number generators
ACM Transactions on Modeling and Computer Simulation (TOMACS)
The art of computer programming, volume 3: (2nd ed.) sorting and searching
The art of computer programming, volume 3: (2nd ed.) sorting and searching
Parallel linear congruential generators with prime moduli
Parallel Computing
Linear congruential generators of order K1
WSC '88 Proceedings of the 20th conference on Winter simulation
Algorithm 806: SPRNG: a scalable library for pseudorandom number generation
ACM Transactions on Mathematical Software (TOMS)
Shift Register Sequences
Testing parallel random number generators
Parallel Computing
An Object-Oriented Random-Number Package with Many Long Streams and Substreams
Operations Research
A system of high-dimensional, efficient, long-cycle and portable uniform random number generators
ACM Transactions on Modeling and Computer Simulation (TOMACS)
Efficient and portable multiple recursive generators of large order
ACM Transactions on Modeling and Computer Simulation (TOMACS)
Pseudo-random trees in Monte Carlo
Parallel Computing
Stochastic Relaxation, Gibbs Distributions, and the Bayesian Restoration of Images
IEEE Transactions on Pattern Analysis and Machine Intelligence
Large-Order Multiple Recursive Generators with Modulus 231-1
INFORMS Journal on Computing
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To speed up the process of performing a large statistical simulation study, it is natural and common to divide the large-scale simulation task into several relatively independent sub-tasks in a way that these sub-tasks can be handled by individual processors in parallel. To obtain a good overall simulation result by synthesizing results from these sub-tasks, it is crucial that good parallel random number generators are used. Thus, designing suitable and independent uniform random number generators for the sub-tasks has become a very important issue in large-scale parallel simulations. Two commonly used uniform random number generators, linear congruential generator (LCG) and multiple recursive generator (MRG), have served as backbone generators for some parallel random number generators constructed in the past. We will discuss some general construction methods. A systematic leapfrog method to automatically choose different multipliers for LCGs to have the maximum-period and a method to construct many maximum-period MRGs from a single MRG are available in the literature. In this paper, we propose to combine both approaches to generate different MRGs ''randomly'', quickly and automatically, while retaining the maximum-period property.