Fast Compensative Design Approach for the Approximate Squaring Function

In this paper, a systematic compensation approach is presented to efficiently design the approximate squaring function with a simple combinational logic circuit. Also, a set of recursive Boolean equations for general outputs is derived such that the logic circuit can be rapidly designed and reused for various bit-width inputs. In logic implementation, our design approach possesses less circuit cost and lower critical delay. Moreover, in error analysis, the maximum relative error (MRE) and average relative error (ARE) of squaring approximation are significantly improved by at least 26.95% and 61.59%, respectively, as compared with the existing approaches. Finally, a 7-bit approximate squaring function chip is accomplished to verify the circuit performance based on 0.6m CMOS technology. The chip layout occupies 127 135 m and the total number of transistors is 186.