An exhaustive analysis of multiplicative congruential random number generators with modulus 231-1
SIAM Journal on Scientific and Statistical Computing
Efficient and portable combined random number generators
Communications of the ACM
Random number generators: good ones are hard to find
Communications of the ACM
Thoughts on pseudorandom number generators
Journal of Computational and Applied Mathematics - Random numbers and simulation
On the lattice structure of the add-with-carry and subtract-with-borrow random number generators
ACM Transactions on Modeling and Computer Simulation (TOMACS)
A search for good multiple recursive random number generators
ACM Transactions on Modeling and Computer Simulation (TOMACS)
Controlling correlations in parallel Monte Carlo
Parallel Computing
Inversive pseudorandom number generators: concepts, results and links
WSC '95 Proceedings of the 27th conference on Winter simulation
Orbits and lattices for linear random number generators with composite moduli
Mathematics of Computation
Distribution properties of multiply-with-carry random number generators
Mathematics of Computation
Inversive and linear congruential pseudorandom number generators in empirical tests
ACM Transactions on Modeling and Computer Simulation (TOMACS)
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
Fourier Analysis of Uniform Random Number Generators
Journal of the ACM (JACM)
Coding the Lehmer pseudo-random number generator
Communications of the ACM
Linear and inversive pseudorandom numbers for parallel and distributed simulation
PADS '98 Proceedings of the twelfth workshop on Parallel and distributed simulation
Uniform random number generators
Proceedings of the 30th conference on Winter simulation
Parallel streams of linear random numbers in the spectral test
ACM Transactions on Modeling and Computer Simulation (TOMACS)
Algorithm 806: SPRNG: a scalable library for pseudorandom number generation
ACM Transactions on Mathematical Software (TOMS)
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
Testing parallel random number generators
Parallel Computing
Towards the impact of the random sequence on genetic algorithms
AICI'10 Proceedings of the 2010 international conference on Artificial intelligence and computational intelligence: Part II
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We present a spectral test analysis of full-period subsequences with small step sizes generated by well-known linear congruential pseudorandom number generators. Subsequences may occur in certain simulation problems or as a method to get parallel streams of pseudorandom numbers. Applying the spectral test, it is possible to find bad subsequences with small step sizes for almost all linear pseudorandom number generators currently in use.