Bit-parallel random number generation for discrete uniform distributions

Abstract

When a die is cast, the outcome is one of the six sides, i.e. the outcome is discrete and uniformly distributed over the range R={1,2,3,4,5,6}. Generating random numbers with such a distribution is very easy: obtain a random number w∈ W, the domain of the random numbers, and take ( w mod |R|)+1 . However, many uniform discrete distributions have a rather short range, e.g., | R|=6 in a dice game, and | R|=3 for the walking directions of a 2-dimensional nonreversal random walk. The number w is typically a machine word, i.e. log 2(| W|)≈32 in a 32-bit computer, so generating a log 2(| R|)-bit random number has consumed about 32 random bits. When | W|⪢| R|, it is wasteful and hence inefficient. This paper presents an efficient algorithm for generating random numbers for the distributions with | R| discrete uniform outcomes. The algorithm uses parallel bit-wise operations on machine words. The performance results of the algorithm are presented. The statistical quality of the random numbers generated from this algorithm is also discussed.