A Comparison of the Correlational Behavior
of Random Number Generators for the IBM 360

Hutchinson states that the "new" (prime modulo)
multiplicative congruential pseudorandom generator, 
attributed to D. H. Lehmer, has passed the usual statistical
tests for random number generators.  It 
is here empirically shown that generators of this type
can produce sequences whose autocorrelation functions 
up to lag 50 exhibit evidence of nonrandomness for many
multiplicative constants.  An alternative generator 
proposed by Tausworthe, which uses irreducible polynomials
over the field of characteristic two, is shown 
to be free from this defect.  The applicability of these
two generators to the IBM 360 is then discussed. 
 Since computer word size can affect a generator's statistical
behavior the older mixed and simple congruential 
generators, although extensively tested on computers
having 36 or more bits per word, may not be optimum 
generators for the IBM 360.

CACM September, 1968

Whittlesey, J. R.

random numbers, pseudorandom number generators, autocorrelation
function, serial correlation, digital 
shift-register generators, linear recurrence modulo
two, irreducible polynomials, primitive trinomials 
modulo two, congruential generators, prime numbers,
statistical tests for randomness, IBM 360, 32-bit 
versus 36-bit word size

5.5

CA680910 JB February 21, 1978  4:44 PM

1674	4	1691
1691	4	1691
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2115	5	1691
2122	5	1691
1674	6	1691
1691	6	1691
1691	6	1691
1930	6	1691