Finding Round-Off Error Using Symbolic Execution.

Overflow and round-off error has been a research problem for decades. With the explosion of mobile and embedded devices, many software programs written for personal computer are now ported to run on embedded systems. The porting often requires changing floating-point numbers and operations to fixed-point ones and here round-off error between the two versions of the program occurs. We propose a novel approach that uses symbolic computation to produce a precise representation of the round-off error for a program. Then we can use solvers to find a global optimum of the round-off error symbolic expression as well as to generate test data that cause the worst round-off error. We implemented a tool based on the idea and our experimental results are better than recent related work.