Generators of uniformly distributed random numbers are considered. Characteristics of congruential random number generators used in parallel simulation computation are discussed and the advantages of the shift register sequences are shown. An equivalence relation is given between shift register sequences and a field of polynomials that is very useful when random number generators are initialized.
The ideas of B. J. Collings and G. B. Hembree [J. Assoc. Comput. Mach. 33, 706-711 (1986; Zbl 0661.65003)] are used but with a different approach. The Connection Machine from Thinking Machine Corporation and the Floating Point Systems’ T Series are described. The implementation and initialization of the shift register sequences is described. The superiority of the generalized feedback shift register sequences over congruential generators is shown.