Lagged Fibonacci Random Number Generators for Distributed Memory Parallel Computers

To parallelize applications that require the use of random numbers, an efficient and good quality parallel random number generator is required. In this paper, we study the parallelization of lagged Fibonacci generators for distributed memory parallel computers. Two popular ways of generating a random sequence in parallel are studied: the contiguous subsequence technique and the leapfrog technique. We present a parallelization of the lagged Fibonacci plus/minus generators using the contiguous subsequence technique. For the leapfrog technique, we show that lagged Fibonacci generators with the exclusive or operator can be efficiently parallelized without any communication overhead when the number of processors is a power of 2. We also show that it is not possible to parallelize other lagged Fibonacci generators efficiently in a communication-free manner. We then present an efficient scalable parallelization of lagged Fibonacci plus/minus generators that uses communication. We discuss issues that arise in implementations of the proposed algorithms and comment on their practical efficiency. © 1997 Academic Press