Linear Congruential Generators

Abstract

The linear congruential method is the most popular algorithm for random number generation in the field of computer simulations.The linear congruential generator (LCG) is defined by$$\begin{array}{*{20}{c}}{{X_n} = a{X_{n - 1}} + c(modM),} \\{{u_n} = \frac{{{X_n}}}{M},}\end{array}$$where a, c, and M are integers and Xn,n=1,2,...,is a sequence of integers with$$0 \leqslant {X_n} < M$$. The normalized sequence un, n =1,2,...,is a random number sequence in [0, 1). The following results tell us how to choose the parameters a, c, and M to obtain the maximal period lengths.