Random number generation and quasi-Monte Carlo methods
Random number generation and quasi-Monte Carlo methods
On the lattice structure of the add-with-carry and subtract-with-borrow random number generators
ACM Transactions on Modeling and Computer Simulation (TOMACS)
On the lattice structure of certain linear congruential sequences related to AWC/SWB 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
Uniform random number generators: a review
Proceedings of the 29th conference on Winter simulation
Uniform random number generators
Proceedings of the 30th conference on Winter simulation
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We study the multiply-with-carry family of generators proposed by G. Marsaglia (1994) as a generalisation of the previous add-with-carry and subtract-with-borrow families of G. Marsaglia and A. Zaman (1991). We define for them a general (infinite) state space and focus our attention on the (finite) subset of recurrent states. This subset will, in turn, split into possibly several subgenerators. We discuss the uniformity of the d-dimensional distribution of the output of these subgenerators over their full period. In order to improve this uniformity for higher dimensions, we propose a method for finding good parameters in terms of the spectral test.