FPCC: Detecting Floating-Point Errors via Chain Conditions

Abstract

Floating-point arithmetic is notorious for its rounding errors, which can propagate and accumulate, leading to unacceptable results. Detecting inputs that can trigger significant floating-point errors is crucial for enhancing the reliability of numerical programs. Existing methods for generating error-triggering inputs often rely on costly shadow executions that involve high-precision computations or suffer from false positives. This paper introduces chain conditions to capture the propagation and accumulation of floating-point errors, using them to guide the search for error-triggering inputs. We have implemented a tool named FPCC and evaluated it on 88 functions from the GNU Scientific Library, as well as 21 functions with multiple inputs from previous research. The experimental results demonstrate the effectiveness and efficiency of our approach: (1) FPCC achieves 100% accuracy in detecting significant errors for the reported rank-1 inputs, while 72.69% rank-1 inputs from the state-of-the-art tool ATOMU can trigger significant errors. Overall, 99.64% (1049/1053) of the inputs reported by FPCC can trigger significant errors, whereas only 19.45% (141/723) of the inputs reported by ATOMU can trigger significant errors; (2) FPCC exhibits a 2.17x speedup over ATOMU in detecting significant errors; (3) FPCC also excels in supporting functions with multiple inputs, outperforming the state-of-the-art technique. To facilitate further research in the community, we have made FPCC available on GitHub at https://github.com/DataReportRe/FPCC.