Improved long-period generators based on linear recurrences modulo 2

Improved Long-Period Generators Based on Linear Recurrences

Fast uniform random number generators with extremely long periods have been defined and implemented based on linear recurrences modulo 2. The twisted GFSR and the Mersenne twister are famous recent examples. Besides the period length, the statistical quality of these generators is usually assessed via their equidistribution properties. The huge-period generators proposed so far are not quite op...

Construction of Equidistributed Generators based on linear recurrences modulo 2

Construction of Equidistributed Generators Based on Linear Recurrences Modulo 2

Random number generators based on linear recurrences modulo 2 are widely used and appear in different forms, such as the simple and combined Tausworthe generators, the GFSR, and the twisted GFSR generators. Low-discrepancy point sets for quasi-Monte Carlo integration can also be constructed based on these linear recurrences. The quality of these generators or point sets is usually measured by c...

On the Period of the Linear Congruential and Power Generators

This sequence was first considered as a pseudorandom number generator by D. H. Lehmer. For the power generator we are given integers e, n > 1 and a seed u = u0 > 1, and we compute the sequence ui+1 = u e i (mod n) so that ui = u ei (mod n). A popular case is e = 2, which is called the Blum–Blum–Shub (BBS) generator. Both of these generators are periodic sequences, and it is of interest to compu...

Optimizing linear maps modulo 2

This paper introduces and analyzes an algorithm to compile a series of exclusive-or operations. The compiled series is quite efficient, almost always beating the so-called “Four Russians” approach, and uses no temporary storage beyond its outputs. The algorithm is reasonably fast and surprisingly simple.