Analyzing Math Library Functions via Summarization

Math library functions are widely used in embedded software to implement the complex computations. However, it is difficult for most abstract domains to analyze non-linear math library functions. This paper presents an approach to analyze commonly used math functions based on interval summarization, which abstracts a math library function to an interval based on its mathematical features. Furthermore, this paper studies soundness of interval summarization strategy based on floating-point number, and proposes a sound floating-point method to implement this strategy. Finally, we present a developed tool prototype named CFPAI for analyzing floating-point C programs based on abstract interpretation framework, and use sound floating-point interval summarization strategy to deal with the math library functions in the floating-point benchmarks. The experimental results show that the interval summarization strategy could reduce the number of false positives effectively for programs with math library functions.