Programmable hardware, in particular Field Programmable Gate Arrays (FPGAs), promises a significant increase in computational performance for simulations in geophysical fluid dynamics compared with CPUs of similar power consumption. FPGAs allow adjusting the representation of floating-point numbers to specific application needs. We analyze the performance-precision trade-off on FPGA hardware for the two-scale Lorenz '95 model. We scale the size of this toy model to that of a high-performance computing application in order to make meaningful performance tests. We identify the minimal level of precision at which changes in model results are not significant compared with a maximal precision version of the model and find that this level is very similar for cases where the model is integrated for very short or long intervals. It is therefore a useful approach to investigate model errors due to rounding errors for very short simulations (e.g., 50 time steps) to obtain a range for the level of precision that can be used in expensive long-term simulations. We also show that an approach to reduce precision with increasing forecast time, when model errors are already accumulated, is very promising. We show that a speed-up of 1.9 times is possible in comparison to FPGA simulations in single precision if precision is reduced with no strong change in model error. The single-precision FPGA setup shows a speed-up of 2.8 times in comparison to our model implementation on two 6-core CPUs for large model setups.

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Reconfigurable architectures are becoming mainstream: Amazon, Microsoft and IBM are supporting such architectures in their data centres. The computationally intensive nature of atmospheric modelling is an attractive target for hardware acceleration using reconfigurable computing. Performance of hardware designs can be improved through the use of reduced-precision arithmetic, but maintaining appropriate accuracy is essential. We explore reduced-precision optimisation for simulating chaotic systems, targeting atmospheric modelling, in which even minor changes in arithmetic behaviour will cause simulations to diverge quickly. The possibility of equally valid simulations having differing outcomes means that standard techniques for comparing numerical accuracy are inappropriate. We use the Hellinger distance to compare statistical behaviour between reduced-precision CPU implementations to guide reconfigurable designs of a chaotic system, then analyse accuracy, performance and power efficiency of the resulting implementations. Our results show that with only a limited loss in accuracy corresponding to less than 10% uncertainty in input parameters, the throughput and energy efficiency of a single-precision chaotic system implemented on a Xilinx Virtex-6 SX475T Field Programmable Gate Array (FPGA) can be more than doubled

© 2015 IEEE.The computationally intensive nature of atmospheric modelling is an ideal target for hardware acceleration. Performance of hardware designs can be improved through the use of reduced precision arithmetic, but maintaining appropriate accuracy is essential. We explore reduced precision optimisation for simulating chaotic systems, targeting atmospheric modelling in which even minor changes in arithmetic behaviour can have a significant impact on system behaviour. Hence, standard techniques for comparing numerical accuracy are inappropriate. We use the Hellinger distance to compare statistical behaviour between reduced-precision CPU implementations to guide FPGA designs of a chaotic system, and analyse accuracy, performance and power efficiency of the resulting implementations. Our results show that with only a limited loss in accuracy corresponding to less than 10% uncertainly in input parameters, a single Xilinx Virtex 6 SXT475 FPGA can be 13 times faster and 23 times more power efficient than a 6-core Intel Xeon X5650 processor

Automated code generators for finite element local assembly have facilitated exploration of alternative implementation strategies within generated code. However, even for a theoretical performance indicator such as operation count, an optimal strategy for local assembly is unknown. We explore a code generation strategy based on symbolic integration and polynomial common sub-expression elimination (CSE). We present our implementation of a local assembly code generator using these techniques. We systematically evaluate the approach, measuring operation count, execution time and numerical error using a benchmark suite of synthetic variational forms, comparing against the FEniCS Form Compiler (FFC). Our benchmark forms span complexities chosen to expose the performance characteristics of different code generation approaches. We show that it is possible with additional computational cost, to consistently achieve much of, and sometimes substantially exceed, the performance of alternative approaches without compromising precision. Although the approach of using symbolic integration and CSE for optimizing local assembly is not new, we distinguish our work through our strategies for maintaining numerical precision and detecting common sub-expressions. We discuss the benefits of the symbolic approach for inferring numerical relationships, and analyze the relationship to other proposed techniques which also have greater computational complexity than those of FFC.