Parallelization of random number generators and long-range correlations
Numerische Mathematik
Computation of critical distances within multiplicative congruential pseudorandom number sequences
Journal of Computational and Applied Mathematics
Maximally equidistributed combined Tausworthe generators
Mathematics of Computation
Mersenne twister: a 623-dimensionally equidistributed uniform pseudo-random number generator
ACM Transactions on Modeling and Computer Simulation (TOMACS) - Special issue on uniform random number generation
Don't trust parallel Monte Carlo!
PADS '98 Proceedings of the twelfth workshop on Parallel and distributed simulation
Good random number generators are (not so) easy to find
Selected papers from the 2nd IMACS symposium on Mathematical modelling---2nd MATHMOD
TestU01: A C library for empirical testing of random number generators
ACM Transactions on Mathematical Software (TOMS)
Efficient Jump Ahead for F2-Linear Random Number Generators
INFORMS Journal on Computing
Programming Massively Parallel Processors: A Hands-on Approach
Programming Massively Parallel Processors: A Hands-on Approach
Variants of Mersenne Twister Suitable for Graphic Processors
ACM Transactions on Mathematical Software (TOMS)
Distribution of Random Streams in Stochastic Models in the Age of Multi-Core and Manycore Processors
PADS '11 Proceedings of the 2011 IEEE Workshop on Principles of Advanced and Distributed Simulation
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Random number generation is a key element of stochastic simulations. It has been widely studied for sequential applications purposes, enabling us to reliably use pseudo-random numbers in this case. Unfortunately, we cannot be so enthusiastic when dealing with parallel stochastic simulations. Many applications still neglect random stream parallelization, leading to potentially biased results. Particular parallel execution platforms, such as Graphics Processing Units (GPUs), add their constraints to those of Pseudo-Random Number Generators (PRNGs) used in parallel. It results in a situation where potential biases can be combined to performance drops when parallelization of random streams has not been carried out rigorously. Here, we propose criteria guiding the design of good GPU-enabled PRNGs. We enhance our comments with a study of the techniques aiming to correctly parallelize random streams, in the context of GPU-enabled stochastic simulations.