We present a theoretical and empirical analysis of the quality of the CRAY-system random num ber generator RANF in parallel settings. Sub sequences of this generator are used to obtain parallel streams of random numbers for each pro cessor. We use the spectral test to analyze the quality of lagged subsequences of RANF with step sizes 21, l ≥ 1, appropriate for CRAY sys tems. Our results demonstrate that with increas ing l, the quality of lagged subsequences is strongly reduced in comparison to the original sequence. The results are supported by a numeri cal Monte Carlo integration study. We also use the spectral test to exhibit the well known long- range correlations between consecutive blocks of random numbers obtained from RANF.
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