A simple pipelined squaring circuit for DSP

There are many digital signal processing applications where a shorter time delay of algorithms and efficient implementations are more important than accuracy. Since squaring is one of the fundamental operations widely used in digital signal processing algorithms, approximate squaring is proposed. We present a simple way of approximate squaring that allows achieving a desired accuracy. The proposed method uses the same simple combinational logic for the first approximation and correction terms. Performed analysis for various bit-length operands and level of approximation showed that maximum relative errors and average relative errors decrease significantly by adding more correction terms. The proposed squaring method can be implemented with a great level of parallelism. The pipelined implementation is also proposed in this paper. The proposed squarer achieved significant savings in area and power when compared to multiplier based squarer. As an example, an analysis of the impact of Euclidean distance calculation by approximate squaring on image retrieval is performed.