A guide to simulation (2nd ed.)
A guide to simulation (2nd ed.)
Sphere-packings, lattices, and groups
Sphere-packings, lattices, and groups
Implementing a random number package with splitting facilities
ACM Transactions on Mathematical Software (TOMS)
Random number generation and quasi-Monte Carlo methods
Random number generation and quasi-Monte Carlo methods
A search for good multiple recursive random number generators
ACM Transactions on Modeling and Computer Simulation (TOMACS)
Multiplicative, congruential random-number generators with multiplier ± 2k1 ± 2k2 and modulus 2p - 1
ACM Transactions on Mathematical Software (TOMS)
Tables of linear congruential generators of different sizes and good lattice structure
Mathematics of Computation
Beware of linear congruential generators with multipliers of the form a = ±2q ±2r
ACM Transactions on Mathematical Software (TOMS)
The Art of Computer Programming Volumes 1-3 Boxed Set
The Art of Computer Programming Volumes 1-3 Boxed Set
Simulation Modeling and Analysis
Simulation Modeling and Analysis
Variance Reduction via Lattice Rules
Management Science
Software for uniform random number generation: distinguishing the good and the bad
Proceedings of the 33nd conference on Winter simulation
A new heavy-tailed discrete distribution for LRD M/G/∞ sample generation
Performance Evaluation
On the Deng-Lin random number generators and related methods
Statistics and Computing
AutoMod: simulating reality using AutoMod
Proceedings of the 34th conference on Winter simulation: exploring new frontiers
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)
The simulation power of automod
Proceedings of the 39th conference on Winter simulation: 40 years! The best is yet to come
A plug-in-based architecture for random number generation in simulation systems
Proceedings of the 40th Conference on Winter Simulation
Large-Order Multiple Recursive Generators with Modulus 231-1
INFORMS Journal on Computing
AutoMod™: providing simulation solutions for over 30 years
Proceedings of the Winter Simulation Conference
AutoMod™: providing simulation solutions for over 25 years
Proceedings of the Winter Simulation Conference
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We study a class of combined multiple recursive random number generators constructed in a way that each component runs fast and is easy to implement, while the combination enjoys excellent structural properties as measured by the spectral test. Each component is a linear recurrence of order k 1, modulo a large prime number, and the coefficients are either 0 or are of the form a = ±2q or a = ±2q ±2r. This allows a simple and very fast implementation, because each modular multiplication by a power of 2 can be implemented via a shift, plus a few additional operations for the modular reduction. We select the parameters in terms of the performance of the combined generator in the spectral test. We provide a specific implementation.