ACORN—A new method for generating sequences of uniformly distributed Pseudo-random numbers
Journal of Computational Physics
Communications of the ACM - Special issue on simulation
Random number generation and quasi-Monte Carlo methods
Random number generation and quasi-Monte Carlo methods
A search for good multiple recursive random number generators
ACM Transactions on Modeling and Computer Simulation (TOMACS)
The art of computer programming, volume 2 (3rd ed.): seminumerical algorithms
The art of computer programming, volume 2 (3rd ed.): seminumerical algorithms
Theoretical and empirical convergence results for additive congruential random number generators
Journal of Computational and Applied Mathematics
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This paper considers an approach to generating uniformly distributed pseudo-random numbers which works well in serial applications but which also appears particularly well-suited for application on parallel processing systems. Additive Congruential Random Number (ACORN) generators are straightforward to implement for arbitrarily large order and modulus; if implemented using integer arithmetic, it becomes possible to generate identical sequences on any machine. Previously published theoretical analysis has demonstrated that a kth order ACORN sequence approximates to being uniformly distributed in up to k dimensions, for any given k. ACORN generators can be constructed to give period lengths exceeding any given number (for example, with period length in excess of 2^3^0^p, for any given p). Results of empirical tests have demonstrated that, if p is greater than or equal to 2, then the ACORN generator can be used successfully for generating double precision uniform random variates. This paper demonstrates that an ACORN generator is a particular case of a multiple recursive generator (and, therefore, also a special case of a matrix generator). Both these latter approaches have been widely studied, and it is to be hoped that the results given in the present paper will lead to greater confidence in using the ACORN generators.