A new non-restoring square root algorithm and its VLSI implementations

We present a new non-restoring square root algorithm that is very efficient to implement. The new algorithm presented here has the following features unlike other square root algorithms. First, the focus of the "non-restoring" is on the "partial remainder", not on "each bit of the square root", with each iteration. Second, it only requires one traditional adder/subtracter in each iteration, i.e., it does not require other hardware components, such as seed generators, multipliers, or even multiplexors. Third, it generates the correct resulting value even in the last bit position. Next, based on the resulting value of the last bit, a precise remainder can be obtained immediately without any correction or addition operation. And finally, it can be implemented at very fast clock rate because of the very simple operations at each iteration. We illustrate two VLSI implementations of the new algorithm. One is a fully pipelined high-performance implementation that can accept a new square-root instruction each clock cycle with each pipeline stage requiring a minimum number of gate counts. The other is a low-cost implementation that uses only a single adder/subtractor for iterative operation.