Truncated squarers with constant and variable correction

This paper describes truncated squarers, which are specialized squarers with a portion of the squaring matrix eliminated. Rounding error and errors due to matrix reduction are quantified and analyzed. Constant and variable correction techniques are presented that minimize either the mean error or the maximum absolute error as required by the application. Area and delay estimates are presented for a number of designs, as well as error statistics obtained both analytically and numerically by exhaustive simulation. As an example, one design of a 16-bit truncated squarer using constant correction is 10.1 % faster and requires 27.9 % less area than a comparable standard squarer with true rounding. The range of error for this truncated squarer is - 0.892 to + 0.625 ulps, compared to ±0.5 ulps for the standard squarer.