Floating-point to Fixed-point Transformation Using Extreme Value Theory

Efficient hardware implementation of digital signal processing and communication algorithms requires using fixed-point arithmetic. However, most of these algorithms are developed in floating-point arithmetic. The automation of floating-point to fixed-point transformation is a key step for high-level synthesis. Based on Extreme Value Theory, this paper presents a novel approach to find both the optimal integer and fractional bit-widths for signals. Compared to traditional full simulation-based methods, this approach uses lightweight simulations to study the characteristics of extreme conditions. With theoretical probabilities to prevent overflows and meet the output error constraint, the proposed approach provides more practical solutions than those by analytical methods. Case studies and experimental results demonstrate its efficiency.