Empirical Research and Automatic Processing Method of Precision-specific Operation

Because of the digit limitation of floating point, significant inaccuracy often occurs during the process of mathematical calculation, which may lead to catastrophic loss. Normally, people believe that adjustment of floating-point precision is an effective way to solve this problem, since high-precision floating-point number has more digits to store information. Thus, it is a prevalent method to reduce the inaccuracy in much floating-point related research, that performing all the operations with higher precision. However, we discover that some operations may lead to larger error in higher precision. In this paper, we define this kind of operation that generates large error due to precision adjustment a precision-specific operation. Furthermore, we propose a lightweight searching algorithm for detecting precision-specific operations and figure out an automatic processing method to fixing them. In addition, we conducted an experiment on the scientific mathematic library of GLIBC. The result shows that there are many precision-specific operations, and our fixing approach can significantly reduce the inaccuracy.