Twisted GFSR generators II

The twisted GFSR generators proposed in a previous article have a defect in k-distribution for k larger than the order of recurrence. In this follow up article, we introduce and analyze a new TGFSR variant having better k-distribution property. We provide an efficient algorithm to obtain the order of equidistribution, together with a tight upper bound on the order. We discuss a method to search for generators attaining this bound, and we list some of these such generators. The upper bound turns out to be (sometimes far) less than the maximum order of equidistribution for a generator of that period length, but far more than that for a GFSR with a working area of the same size

A Search for Good Pseudo-random Number Generators : Survey and Empirical Studies

In today's world, several applications demand numbers which appear random but are generated by a background algorithm; that is, pseudo-random numbers. Since late $19^{th}$ century, researchers have been working on pseudo-random number generators (PRNGs). Several PRNGs continue to develop, each one demanding to be better than the previous ones. In this scenario, this paper targets to verify the claim of so-called good generators and rank the existing generators based on strong empirical tests in same platforms. To do this, the genre of PRNGs developed so far has been explored and classified into three groups -- linear congruential generator based, linear feedback shift register based and cellular automata based. From each group, well-known generators have been chosen for empirical testing. Two types of empirical testing has been done on each PRNG -- blind statistical tests with Diehard battery of tests, TestU01 library and NIST statistical test-suite and graphical tests (lattice test and space-time diagram test). Finally, the selected $29$ PRNGs are divided into $24$ groups and are ranked according to their overall performance in all empirical tests

Hurst's Rescaled Range Statistical Analysis for Pseudorandom Number Generators used in Physical Simulations

The rescaled range statistical analysis (R/S) is proposed as a new method to detect correlations in pseudorandom number generators used in Monte Carlo simulations. In an extensive test it is demonstrated that the RS analysis provides a very sensitive method to reveal hidden long run and short run correlations. Several widely used and also some recently proposed pseudorandom number generators are subjected to this test. In many generators correlations are detected and quantified.Comment: 12 pages, 12 figures, 6 tables. Replaces previous version to correct citation [19

Twisted GFSR generators

The generalized feedback shift register(GFSR) algorithm suggested by Lewis and Payne is a widely used pseudorandom number generator, but has the following serious drawbacks: 1. Aninitialization scheme to assure higher order equidistribution is involved and is time-consuming. 2. Each bit of the generated words constitutes an m-sequence based on a primitive trinomial, which shows poor randomness with respect to weight distribution. 3. Large working area is necessary. 4. The period of sequence is far shorter than the theoretical upper bound. This paper presents the twisted GFSR(TGFSR) algorithm, as lightly but essentially modified version of the GFSR, which solves all the above problems without loss of merit. Some practical TGFSR generators were implemented and they passed strict empirical tests. These new generators are most suitable for simulation of a large distributive system, which requires a number of mutually independent pseudorandom number generators with compact size