Pseudo-random number sequences for parallel computers

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Pseudo-Random number sequences are used in a variety of computer applications, such as Monte Carlo algorithms, Numerical analysis, program testing. The development of vector, array and multiprocessor supercomputer has necessitated the development of new techniques for parallel generation of pseudo-random number sequences. This work examines the randomness properties of three methods for generating parallel pseudo-random number sequences. A software package is written to examine the randomness characteristics of parallel pseudo-random number sequences. Parallel pseudo-random number sequences constructed from non-contiguous subsequences of single Linear Congruential sequences, a number of Pseudo-Random Tree sequences, and single and multiple Chebyshev Mixing Transformations sequences are extensively tested. The results from the conducted tests show that parallel sequences constructed from non-contiguous subsequences are the most suitable for multiprocessor implementation. Further, the consecutive numbers of alI Chebyshev mixing sequences are found to be related. It Is also found that there is a non-random pattern in tile distribution of consecutive pairs of tile Pseudo-Random Tree sequences.