Maximally equidistributed combined Tausworthe generators
Mathematics of Computation
The art of computer programming, volume 2 (3rd ed.): seminumerical algorithms
The art of computer programming, volume 2 (3rd ed.): seminumerical algorithms
Tables of linear congruential generators of different sizes and good lattice structure
Mathematics of Computation
Tables of maximally equidistributed combined LFSR generators
Mathematics of Computation
An Asymptotically Random Tausworthe Sequence
Journal of the ACM (JACM)
On the performance of birthday spacings tests with certain families of random number generators
Mathematics and Computers in Simulation - IMACS sponsored Special issue on the second IMACS seminar on Monte Carlo methods
Sparse Serial Tests of Uniformity for Random Number Generators
SIAM Journal on Scientific Computing
Close-Point Spatial Tests and Their Application to Random Number Generators
Operations Research
Variance Reduction via Lattice Rules
Management Science
On the xorshift random number generators
ACM Transactions on Modeling and Computer Simulation (TOMACS)
Fast random number generators based on linear recurrences modulo 2: overview and comparison
WSC '05 Proceedings of the 37th conference on Winter simulation
TestU01: A C library for empirical testing of random number generators
ACM Transactions on Mathematical Software (TOMS)
A compact and accurate Gaussian variate generator
IEEE Transactions on Very Large Scale Integration (VLSI) Systems
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Most random number generators used in practice are based on linear recurrences, with linear output transformations. This gives long periods, fast implementations, and structures that are easy to analyze. But the points produced by these generators have very regular structures. Nonlinear generators can have less regular structures, but they are generally slower and much harder to analyze when their period is long.In this paper, combined generators with one large linear component, and a second component of a different type (nonlinear or linear), are proposed and studied. The structure of vectors of successive and non-successive output values produced by the combined generators is analyzed. Under mild conditions, these vector sets are proved to have at least as much uniformity than the corresponding sets for the linear component alone. In empirical statistical tests, these combined generators perform better than simple linear generator of comparable period lengths, because of their less regular structure. Efficient implementation methods are suggested.