About cookies on this site Our websites require some cookies to function properly (required). In addition, other cookies may be used with your consent to analyze site usage, improve the user experience and for advertising. For more information, please review your options. By visiting our website, you agree to our processing of information as described in IBM’sprivacy statement. To provide a smooth navigation, your cookie preferences will be shared across the IBM web domains listed here.
Publication
ACM Transactions on Modeling and Computer Simulation (TOMACS)
Paper
On the Lattice Structure of the Add-With-Carry and Subtract-With-Borrow Random Number Generators
Abstract
Marsaglia and Zaman recently proposed new classes of random number generators, called add-with-carry1993 and subtract-with-borrow(SWB), which are capable of quickly generating very long-period (pseudo)-random number sequences using very little memory. We show that these sequences are essentially equivalent to linear congruential sequences with very large prime moduli. So, the AWC/SWB generators can be viewed as efficient ways of implementing such large linear congruential generators. As a consequence, the theoretical properties of such generators can be studied in the same way as for linear congruential generators, namely, via the spectral and lattice tests. We also show how the equivalence can be exploited to implement efficient jumping-ahead facilities for the AWC and SWB sequences. Our numerical examples illustrate the fact that AWC/SWB generators have extremely bad lattice structure in high dimensions. © 1993, ACM. All rights reserved.