Implications of Reduced-Precision Computations in HPC: Performance, Energy and Error
Résumé
Error-tolerating applications are increasingly common in the emerging field of real-time HPC. Proposals have been made at the hardware level to take advantage of inherent perceptual limitations, redundant data, or reduced precision input [20], as well as to reduce system costs or improve power efficiency [19]. At the same time, works on floating-point to fixed-point conversion tools [9] allow us to trade-off the algorithm exactness for a more efficient implementation. In this work, we aim at leveraging existing, HPC-oriented hardware architectures, while including in the precision tuning an adaptive selection of floating-and fixed-point arithmetic. Our proposed solution takes advantage of the application domain knowledge of the programmers by involving them in the first step of the interaction chain. We rely on annotations written by the programmer on the input file to know which variables of a computational kernel should be converted to fixed-point. The second stage replaces the floating-point variables in the kernel with fixed-point equivalents. It also adds to the original source code the utility functions to perform data type conversions from floating-point to fixed-point, and vice versa. The output of the second stage is a new version of the kernel source code which exploits fixed-point computation instead of floating-point computation. As opposed to typical custom-width hardware designs, we only rely on the standard 16-bit, 32-bit and 64-bit types. We also explore the impact of the fixed-point representation on auto-vectorization. We discuss the effect of our solution in terms of time-to-solutions, error and energy-to-solution.
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