SQRTLIB : Library of Hardware Square Root Designs

Abstract

Square-root is an elementary arithmetic function that is utilized not only for image and signal processing applications but also to extract vector functionalities. The square-root module demands high energy and hardware resources, apart from being a complex design to implement. In the past, many techniques, including Iterative, New Non-Restoring (New-NR), CORDIC, Piece-wise-linear (PWL) approximation, Look-Up-Tables (LUTs), Digit-by-digit based integer (Digit-Int) format and fixed-point (Digit-FP) format implementations were reported to realize square-root function. Cartesian genetic programming (CGP) is a type of evolutionary algorithm that is suggested to evolve circuits by exploring a large solution space. This paper attempts to develop a library of square-root circuits ranging from 2-bits to 8-bits and also benchmark the proposed CGP evolved square-root circuits with the other hardware implementations. All designs were analyzed using both FPGA and ASIC (130 nm Skywater node) flow to characterize hardware parameters and evaluated using various error metrics. Among all the implementations, CGP-derived square-root designs of fixed-point format offered the best trade-off between hardware and error characteristics. All novel designs of this work are made freely available in [1] for further research and development usage.