A Hardware Framework for the Fast Generation of Multiple Long-period Random Number Streams

Stochastic simulations and other scientific applications that depend on random numbers are increasingly implemented in a parallelized manner in programmable logic. High-quality pseudo-randoin 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 pseudorandom 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.