Random number generation and quasi-Monte Carlo methods
Random number generation and quasi-Monte Carlo methods
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
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
Generalized Feedback Shift Register Pseudorandom Number Algorithm
Journal of the ACM (JACM)
Tables of 64-bit Mersenne twisters
ACM Transactions on Modeling and Computer Simulation (TOMACS)
On the performance of birthday spacings tests with certain families of random number generators
Mathematics and Computers in Simulation - IMACS sponsored Special issue on the second IMACS seminar on Monte Carlo methods
Simulation Modeling and Analysis
Simulation Modeling and Analysis
Testing parallel random number generators
Parallel Computing
Improved long-period generators based on linear recurrences modulo 2
ACM Transactions on Mathematical Software (TOMS)
High Quality Uniform Random Number Generation Using LUT Optimised State-transition Matrices
Journal of VLSI Signal Processing Systems
Efficient Jump Ahead for F2-Linear Random Number Generators
INFORMS Journal on Computing
A Mersenne Twister Hardware Implementation for the Monte Carlo Localization Algorithm
Journal of Signal Processing Systems
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Stochastic simulations and other scientific applications that depend on random numbers are increasingly implemented in a parallelized manner in programmable logic. High-quality pseudo-random number generators (PRNG), such as the Mersenne Twister, are often based on binary linear recurrences and have extremely long periods (more than 21024. Many software implementations of such PRNGs exist, but hardware implementations are rare. We have developed an optimized, resource-efficient parallel framework for this class of random number generators that exploits the underlying algorithm as well as FPGA-specific architectural features. The framework also incorporates fast "jump-ahead" capability for these PRNGs, allowing simultaneous, independent sub-streams to be generated in parallel by partitioning one long-period pseudo-random sequence We demonstrate parallelized implementations of three types of PRNGs -- the 32-, 64- and 128-bit SIMD Mersenne Twister -- on Xilinx Virtex-II Pro FPGAs. Their area/throughput performance is impressive: for example, compared clock-for-clock with a previous FPGA implementation, a "two-parallelized" 32-bit Mersenne Twister uses 41% fewer resources. It can also scale to 350 MHz for a throughput of 22.4 Gbps, which is 5.5x faster than the older FPGA implementation and 7.1x faster than a dedicated software implementation. The quality of generated random numbers is verified with the standard statistical test batteries Diehard and TestU01. We also present two real-world application studies with multiple RNG streams: the Ziggurat method for generating normal random variables and a Monte Carlo photon-transport simulation.The availability of fast long-period random number generators with multiple streams accelerates hardware-based scientific simulations and allows them to scale to greater complexities