Random number generation and quasi-Monte Carlo methods
Random number generation and quasi-Monte Carlo methods
Multiplicative, congruential random-number generators with multiplier ± 2k1 ± 2k2 and modulus 2p - 1
ACM Transactions on Mathematical Software (TOMS)
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
Random number generation with primitive pentanomials
ACM Transactions on Modeling and Computer Simulation (TOMACS)
Fast combined multiple recursive generators with multipliers of the form a = ±2q ±2r
Proceedings of the 32nd conference on Winter simulation
Software for uniform random number generation: distinguishing the good and the bad
Proceedings of the 33nd conference on Winter simulation
A system of high-dimensional, efficient, long-cycle and portable uniform random number generators
ACM Transactions on Modeling and Computer Simulation (TOMACS)
Empirical evidence concerning AES
ACM Transactions on Modeling and Computer Simulation (TOMACS)
Efficient and portable multiple recursive generators of large order
ACM Transactions on Modeling and Computer Simulation (TOMACS)
On the xorshift random number generators
ACM Transactions on Modeling and Computer Simulation (TOMACS)
TestU01: A C library for empirical testing of random number generators
ACM Transactions on Mathematical Software (TOMS)
Large-Order Multiple Recursive Generators with Modulus 231-1
INFORMS Journal on Computing
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Linear congruential random-number generators with Mersenne prime modulus and multipliers of the form a = ±2q ±r have been proposed recently. Their main advantage is the availability of a simple and fast implementation algorithm for such multipliers. This note generalizes this algorithm, points out statistical weaknesses of these multipliers when used in a straightforward manner, and suggests in what context they could be used safely.