Efficient multiply-with-carry random number generators with maximal period

Abstract

In this (largely expository) article, we propose a simple modification of the multiply-with-carry random number generators of Marsaglia [1994] and Couture and L'Écuyer [1997]. The resulting generators are both efficient (since they may be configured with a base b which is a power of 2) and exhibit maximal period. These generators are analyzed using a simple but powerful algebraic technique involving b -adic numbers.