On the Lattice Structure of the Add-With-Carry and Subtract-With-Borrow Random Number Generators

Shu Tezuka, Pierre L'Ecuyer, Raymond Couture

Research output: Contribution to journalArticle

29 Citations (Scopus)

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.

Original languageEnglish
Pages (from-to)315-331
Number of pages17
JournalACM Transactions on Modeling and Computer Simulation (TOMACS)
Volume3
Issue number4
DOIs
Publication statusPublished - Jan 10 1993

All Science Journal Classification (ASJC) codes

  • Modelling and Simulation
  • Computer Science Applications

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