Some comments on C. S. Wallace's random number generators

We outline some of Chris Wallace's contributions to pseudo-random number generation. In particular, we consider his idea for generating normally distributed variates without relying on a source of uniform random numbers, and compare it with more conventional methods for generating normal random numbers. Implementations of Wallace's idea can be very fast (approximately as fast as good uniform generators). We discuss the statistical quality of the output, and mention how certain pitfalls can be avoided.Comment: 13 pages. For further information, see http://wwwmaths.anu.edu.au/~brent/pub/pub213.htm

Pseudo Random Coins Show More Heads Than Tails

Tossing a coin is the most elementary Monte Carlo experiment. In a computer the coin is replaced by a pseudo random number generator. It can be shown analytically and by exact enumerations that popular random number generators are not capable of imitating a fair coin: pseudo random coins show more heads than tails. This bias explains the empirically observed failure of some random number generators in random walk experiments. It can be traced down to the special role of the value zero in the algebra of finite fields.Comment: 10 pages, 12 figure

Pseudorandom number generation based on controllable cellular automata

A novel Cellular Automata (CA) Controllable CA (CCA) is proposed in this paper. Further, CCA are applied in Pseudorandom Number Generation. Randomness test results on CCA Pseudorandom Number Generators (PRNGs) show that they are better than 1-d CA PRNGs and can be comparable to 2-d ones. But they do not lose the structure simplicity of 1-d CA. Further, we develop several different types of CCA PRNGs. Based on the comparison of the randomness of different CCA PRNGs, we find that their properties are decided by the actions of the controllable cells and their neighbors. These novel CCA may be applied in other applications where structure non-uniformity or asymmetry is desired

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