Functional square root

Abstract: A new method for the high-speed computation of double-precision floating-point reciprocal, division, square root, and inverse square root operations is presented in this paper. This method employs a second-degree minimax polynomial approximation to obtain an accurate initial estimate of the reciprocal and the inverse square root values, and then performs a modified Goldschmidt iteration. The high accuracy of the initial approximation allows us to obtain double-precision results by computing a single Goldschmidt iteration, significantly reducing the latency of the algorithm. Two unfolded architectures are proposed: the first one computing only reciprocal and division operations, and the second one also including the computation of square root and inverse square root. The execution times and area costs for both architectures are estimated, and a comparison with other multiplicative-based methods is presented. The results of this comparison show the achievement of a lower latency than these methods, with similar hardware requirements.

Abstract: An apparatus and method for demodulating a square root of the sum of squares of two inputs I and Q in a digital signal processing are provided. The square root {square root over (I 2 +Q 2 )} is approximated by an equation aX +bY, wherein coefficients a and b are special binary numbers. Due to the numbers, the square root {square root over (I 2 +Q 2 )} can be quickly computed by the operation of shifting and addition. A plurality of possible approximation values for the coefficients a and b are provided, as well as the use of a comparator to select the maximal one among the possible approximation values.