Random number generation is key to many applications in a wide variety of disciplines. Depending on the application, the quality of the random numbers from a particular generator can directly impact both computational performance and critically the outcome of the calculation.
High-energy physics applications use Monte Carlo simulations and machine learning widely, which both require high-quality random numbers. In recent years, to meet increasing performance requirements, many high-energy physics workloads leverage GPU acceleration. While on a CPU, there exist a wide variety of generators with different performance and quality characteristics, the same cannot be stated for GPU and FPGA accelerators.
On GPUs, the most common implementation is provided by cuRAND - an NVIDIA library that is not open source or peer reviewed by the scientific community. The highest-quality generator implemented in cuRAND is a version of the Mersenne Twister. Given the availability of better and faster random number generators, high-energy physics moved away from Mersenne Twister several years ago and nowadays MixMax is the standard generator in Geant4 via CLHEP.
The MixMax original design supports parallel streams with a seeding algorithm that makes it especially suited for GPU and FPGA where extreme parallelism is a key factor. In this study we implement the MixMax generator on both architectures and analyze its suitability and applicability for accelerator implementations. We evaluated the results against “Mersenne Twister for a Graphic Processor” (MTGP32) on GPUs which resulted in 5, 13 and 14 times higher throughput when a 240, 17 and 8 sized vector space was used respectively. The MixMax generator coded in VHDL and implemented on Xilinx Ultrascale+ FPGAs, requires 50% fewer total LUTs compared to a 32-bit Mersenne Twister (MT-19337), or ~75% fewer LUTs per output bit.
In summary, the state-of-the art MixMax pseudo random number generator has been implemented on GPU and FPGA platforms and the performance benchmarked.
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