Random number generators: good ones are hard to find
Communications of the ACM
On the periods of generalized Fibonacci recurrences
Mathematics of Computation
The art of computer programming, volume 2 (3rd ed.): seminumerical algorithms
The art of computer programming, volume 2 (3rd ed.): seminumerical algorithms
Shift Register Sequences
Parallel additive lagged Fibonacci random number generators
ICS '96 Proceedings of the 10th international conference on Supercomputing
Algorithm 806: SPRNG: a scalable library for pseudorandom number generation
ACM Transactions on Mathematical Software (TOMS)
Testing parallel random number generators
Parallel Computing
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We describe in detail the parallel implementation of a family of additive lagged-Fibonacci pseudorandom number generators. The theoretical structure of these generators is exploited to preserve their well-known randomness properties and to provide a parallel system of distinct cycles. The algorithm presented here solves the reproducibility problem for a far larger class of parallel Monte Carlo applications than has been previously possible. In particular, Monte Carlo applications that undergo "splitting" can be coded to be reproducible, independent both of the number of processors and the execution order of the parallel processes. A library of portable C routines (available from the authors) that implements these ideas is also described.