Fine-Grained Global Search for Inputs Triggering Floating-Point Exceptions in Gpu Programs

Floating-point exceptions are hard to avoid and can cause disastrous consequences. However, testing methods for floating-point exceptions in GPU programs are currently quite limited due to their closed-source nature. Existing tools, even the state-of-the-art Xscope, still exhibit low search efficiency and poor input coverage. In this paper, we combine interval-wise random sampling and Markov Chain Monte Carlo (MCMC) sampling in a synergistic way to efficiently detect exception-inducing inputs in GPU programs. To improve the search efficiency, based on the bit patterns of exceptional floating-point values, we propose a floating-point format-aware input space partitioning method for random sampling and define a unified fitness function for MCMC sampling. We implement our approach in a tool DFEG and demonstrate it on 76 functions from the CUDA Math Library, HPC programs, and FPBench. DFEG outperforms Xscope in terms of both effectiveness and efficiency. DFEG finds $949 \times$ more exceptions than Xscope and detects new exceptions in 9 functions where Xscope fails. Moreover, compared to Xscope, DFEG achieves an average $34 \times$ speedup.