A comparative analysis of two concepts in the generation of uniform pseudo-random numbers

In recent years, considerable attention has been given to find reliable methods capable of producing, within a digital computer, pseudo-random numbers obeying the uniform distribution on the unit interval. Apparently, the most popular method has been the congruence algorithm whose basic form Xi+1 = aX1 + b mod 2m (1) can be easily implemented on a binary computer with word size of m bits. Since its introduction, a number of papers1-3 have been written in which techniques, such as suggesting formulae1 to compute optimal values for a and b, have been presented to improve the statistical properties of the method. As a consequence, several versions with values for a and b to suit everybody's needs are now in existence. One must be aware that an analysis based on statistical testing cannot be entirely conclusive, especially if the power of some tests used is not known. Nevertheless, the comparative analysis of this study does indicate that a generator based on Tausworthe's concept exhibits a statistical behavior that is as good if not superior to that of the congruence algorithm. Therefore, the following advantage in its use are apparent: (1) Its functional form and statistical behavior are entirely machine independent. (2) It has been shown analytically that it generates values of a random variable uniformly distributed on the unit interval. (3) It can be easily programmed in FORTRAN without sacrificing any of its characteristics. (To the author's knowledge, none of these advantages can be claimed by any of the existing congruence algorithms.)