Exploiting community structure for floating-point precision tuning

Abstract

Floating-point types are notorious for their intricate representation. The effective use of mixed precision, i.e., using various precisions in different computations, is critical to achieve a good balance between accuracy and performance. Unfortunately, reasoning about mixed precision is difficult even for numerical experts. Techniques have been proposed to systematically search over floating-point variables and/or program instructions to find a faster, mixed-precision version of a given program. These techniques, however, are characterized by their black box nature, and face scalability limitations due to the large search space. In this paper, we exploit the community structure of floating-point variables to devise a scalable hierarchical search for precision tuning. Specifically, we perform dependence analysis and edge profiling to create a weighted dependence graph that presents a network of floating-point variables. We then formulate hierarchy construction on the network as a community detection problem, and present a hierarchical search algorithm that iteratively lowers precision with regard to communities. We implement our algorithm in the tool HiFPTuner, and show that it exhibits higher search efficiency over the state of the art for 75.9% of the experiments taking 59.6% less search time on average. Moreover, HiFPTuner finds more profitable configurations for 51.7% of the experiments, with one known to be as good as the global optimum found through exhaustive search.