Digit-Recurrence Posit Division

Abstract: Posit arithmetic has emerged as a promising alternative to IEEE 754 floating-point representation, offering enhanced accuracy and dynamic range. However, division operations in posit systems remain challenging due to their inherent hardware complexity. In this work, we present posit division units based on the digit-recurrence algorithm, marking the first implementation of radix-4 digit-recurrence techniques within this context. Our approach incorporates hardware-centric optimizations including redundant arithmetic, on-the-fly quotient conversion, and operand scaling to streamline the division process while mitigating latency, area, and power overheads. Comprehensive synthesis evaluations across multiple posit configurations demonstrate significant performance improvements, including more than 80% energy reduction with small area overhead compared to existing methods, and a substantial decrease in the number of iterations. These results underscore the potential of our adapted algorithm to enhance the efficiency of posit-based arithmetic units.