Using Harmonized Parabolic Synthesis to Implement a Single-Precision Floating-Point Square Root Unit

Abstract

This paper proposes a novel method for performing square root operation on floating-point numbers represented in IEEE-754 single-precision (binary32) format. The method is implemented using Harmonized Parabolic Synthesis. It is implemented with and without pipeline stages individually and synthesized for two different Xilinx FPGA boards. The implementations show better resource usage and latency results when compared to other similar works including Xilinx intellectual property (IP) that uses the CORDIC method. Any method calculating the square root will make approximation errors. Unless these errors are distributed evenly around zero, they can accumulate and give a biased result. An attractive feature of the proposed method is the fact that it distributes the errors evenly around zero, in contrast to CORDIC for instance. Due to the small size, low latency, high throughput, and good error properties, the presented floating-point square root unit is suitable for high performance embedded systems. It can be integrated into a processor's floating point unit or be used as a stand-alone accelerator.