Detecting and Fixing Precision-Specific Operations for Measuring Floating-Point Errors

The accuracy of the floating-point calculation is critical to many applications and different methods have been proposed around floating-point accuracies, such as detecting the errors in the program, verifying the accuracy of the program, and optimizing the program to produce more accurate results. These approaches need a specification of the program to understand the ideal calculation performed by the program, which is usually approached by interpreting the program in a precision-unspecific way. However, many operations programmed in existing code are inherently precision-specific, which cannot be easily interpreted in a precision-unspecific way. In fact, the semantics used in existing approaches usually fail to interpret precision-specific operations correctly. In this paper, we present a systematic study on precision-specific operations. First, we propose a detection approach to detect precision-specific operations. Second, we propose a fixing approach to enable the tuning of precisions under the presence of precision-specific operations. Third, we studied the precision-specific operations in the GNU C standard math library based on our detection and fixing approaches. Our results show that (1) a significant number of code fragments in the standard C math library are precision-specific operations, and some large inaccuracies reported in existing studies are false positives or potential false positives due to precision-specific operations; (2) our detection approach has high precision and recall; (3) our fixing approach can lead to overall more accurate result.CPCI-S(ISTP)wangrancs@pku.edu.cn; zoudm@pku.edu.cn; hexinrui@pku.edu.cn; xiongyf@pku.edu.cn; zhanglucs@pku.edu.cn; hg@pku.edu.cn619-63