Some long-period random number generators using shifts and xors

Marsaglia recently introduced a class of “xorshift” random number generators (RNGs) with periods 2n − 1 for n = 32, 64, etc. Here Marsaglia’s xorshift generators are generalised to obtain fast and highquality RNGs with extremely long periods. Whereas RNGs based on primitive trinomials may be unsatisfactory, because a trinomial has very small weight, these new generators can be chosen so that their minimal polynomials have a large number of non-zero terms and, hence, a large weight. A computer search using Magma has found good RNGs for n a power of two up to 4096. These RNGs have been implemented in a free software package xorgens.