This study introduces a methodology for forecasting accelerator performance in Particle Physics algorithms. Accelerating applications can require significant engineering effort, prototyping and measuring the speedup that might finally result in disappointing accelerator performance. The proposed methodology involves performance modelling and forecasting, enabling the prediction of potential speedup, identification of promising acceleration candidates, prior to any significant programming investment. By predicting worst-case scenarios, the methodology assists developers in deciding whether an application can benefit from acceleration, thus optimising effort. A Monte Carlo simulation example demonstrates the effectiveness of the proposed methodology. The result shows that the methodology provides a reasonable estimate for GPUs and, in the context of FPGAs, the predictions are extremely accurate, within 2% of the realised execution time.

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 Look Up Tables (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.