Error detection of arithmetic expressions

Inspecting floating-point errors is essential to floating-point operations. In this paper, we present floating-point error detector (FPED), an inspector of floating-point errors for arithmetic expressions. FPED can pick a suitable benchmark generation approach by analyzing the distribution of the expression of a floating-point operation, thereby minimizing the possibilities of underreporting floating-point errors. FPED is also able to determine the significant sources of errors in a floating-point operation according to the frequencies of computation building blocks that contribute most to the floating-point errors, benefiting the follow-up optimizations of computation accuracies. We validate the correctness and functionalities of FPED by conducting experiments on the FPBench benchmark suite. The experimental results demonstrate that FPED can obtain more accurate detection results than the random detecting approach with respect to floating-point error detection. We also compare FPED with the existing dynamic error detection tools. The experimental results show that in most of the 33 test benchmarks, the maximum error results of FPED are greater than Herbgrind and the detection performance is higher than Herbgrind.