Simulated division with approximate factoring for the multiple recursive generator with both unrestricted multiplier and non-mersenne prime modulus

AbstractThis paper focuses on devising a general and efficient way of generating random numbers for the multiple recursive generator with both unrestricted multiplier and non-Mersenne prime modulus. We propose a new algorithm that embeds the technique of approximate factoring into the simulated division method. The proposed new algorithm improves the decomposition method in terms of both the suitability for various word-sizes of the computers and the efficiency characteristics, such as the number of arithmetic operations required and the computational time. Empirical simulations are conducted to compare and evaluate the computational time of this algorithm with the decomposition method for various computers

Efficient computer search of large-order multiple recursive pseudo-random number generators

AbstractUtilizing some results in number theory, we propose an efficient method to speed up the computer search of large-order maximum-period Multiple Recursive Generators (MRGs). We conduct the computer search and identify many efficient and portable MRGs of order up to 25,013, which have the equi-distribution property in up to 25,013 dimensions and the period lengths up to 10233,361 approximately. In addition, a theoretical test is adopted to further evaluate and compare these generators. An extensive empirical study shows that these generators behave well when tested with the stringent Crush battery of the test package TestU01

An Implementation of the Lattice and Spectral Tests for Multiple Recursive Linear Random Number Generators

this paper is to explain the implementation of a software package for analyzing the lattice structure of linear congruential or multiple recursive random number generators. Such generators are based on linear recurrences of the for