A Comparison of Radix-2 Square Root Algorithms Using Digit Recurrence
Staffan Ledin · KTH Publication Database DiVA (KTH Royal Institute of Technology) · 2015
When designing an electronic system, it might be desirable to implement a custom square root calculator unit to ensure quick calculations. The different questions when it comes to square root units are many. What algorithms are there? How are these algorithms implemented? What are the benefits and disadvantages of the different implementations? The goal of this thesis work is to try to answer these questions. In this paper, several different methods of calculating the radix-2 square root by digit recurrence are studied, designed and compared. The three main algorithms that are studied are the restoring square root algorithm, the non-restoring square root algorithm and the SRT (Sweeney, Robertson, Tocher) square root algorithm. They are all designed using the same technology and identical components where applicable. This is done in order to ensure that the comparisons give a fair assessment of the viability of the different algorithms. It is shown that the restoring and non-restoring square root algorithms perform similarly when using 65 nm technology, a 16 bit input, full data rate and 1.2 V power supply. The restoring square root algorithm have a slight edge when the systems are not pipelined, while the non-restoring algorithm performs slightly better when the systems are fully pipelined. The SRT square root algorithm perform worse than the other two in all cases.