Modified restoring array-based power efficient approximate square root circuit and its application

In this paper, the authors present an investigation into the benefits of approximate computing in energy -efficient error-resilient applications. It proposes an approximate square root (SQR) circuit based on the modified restoring array square root (MRAS) architecture. The MRAS design incorporates strategic elimination, optimization, and simplification of restoring subtractor cells (SC) within a conventional restoring array SQR circuit. As a result, the proposed MRAS circuit efficiently computes the square root of a 2n-bit unsigned integer, offering a 27 percent reduction in area, 13 percent faster computation, and 50 percent lower power consumption compared to the exact SQR design. To introduce approximation, configurable SCs are integrated into the MRAS circuit, enabling dual operation modes for both accuracy and approximation. This feature allows the proposed approximate modified restoring array SQR (AMRAS) design to cater to both error-resilient and error-sensitive applications. The evaluation involves a thorough analysis of accuracy and design metrics for 16-bit unsigned exact, state-of-the-art, and proposed square rooters. The designs are implemented on Artix7 FPGA using Verilog-HDL and simulated in the Xilinx Vivado simulator. The results demonstrate that the proposed AMRAS achieves a good trade-off between accuracy and hardware, presenting an impressive 80 percent reduction in power consumption and a 36 percent faster computation. Additionally, the paper showcases the practical application of the proposed AMRAS square rooters in the Sobel edge detection for image processing.