Architecture-aware Precision Tuning with Multiple Number Representation Systems

Precision tuning trades accuracy for speed and energy savings, usually by reducing the data width, or by switching from floating point to fixed point representations. However, comparing the precision across different representations is a difficult task. We present a metric that enables this comparison, and employ it to build a methodology based on Integer Linear Programming for tuning the data type selection. We apply the proposed metric and methodology to a range of processors, demonstrating an improvement in performance (up to $9 \times)$ with a very limited precision loss $(\lt 2.8$% for 90% of the benchmarks) on the PolyBench benchmark suite.