Symbolic Round-O Error between Floating-Point and Fixed-Point

• Main Authors: Truong, Hoang Anh, Tran, Huy Vu, Nguyen, Bao Ngoc
• Format: Article
• Language: English
• Published: ĐHQGHN 2017
• Subjects: Round-Off Error; Symbolic Execution; Fixed-Point; Floating-Point
• Online Access: http://repository.vnu.edu.vn/handle/VNU_123/56690
• Institution: Vietnam National University, Hanoi

Overflow and round-off errors have been research problems for decades. With the explosion of mobile and embed-ded devices, many software programs written for personal computers are now ported to run on embedded systems.The porting often requires changing floating-point numbers and operations to fixed-point, and here round-off error between the two versions of the program often occurs. We propose a novel approach that uses symbolic compu-tation to produce a precise representation of the round-o error. From this representation, we can analyse various aspects of the error. For example we can use optimization tools like Mathematica to find the largest round-o error, or we can use SMT solvers to check if the error is always under a given bound. The representation can also be used to generate optimal test cases that produce the worst-case round-off error. We will show several experimental results demonstrating some applications of our symbolic round-off error.