Empirical Research and Automatic Processing Method of Precision-specific Operation

TL;DR

This paper investigates the issue of increased errors in floating-point calculations at higher precision, defines 'precision-specific operations', and proposes an automatic method to detect and fix these errors, improving accuracy in scientific computations.

Contribution

It introduces the concept of precision-specific operations, develops a lightweight detection algorithm, and presents an automatic fixing approach validated on GLIBC.

Findings

Many precision-specific operations exist in scientific libraries

The proposed method effectively reduces calculation inaccuracies

Higher precision can sometimes increase errors in certain operations

Abstract

Significant inaccuracy often occurs during the process of mathematical calculation due to the digit limitation of floating point, 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 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 light-weight 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 mathematical library of GLIBC. The result shows that there are many precision-specific operations, and our fixing approach can significantly reduce the inaccuracy.