Floating-Point Inverse Square Root Algorithm Based on Taylor-Series Expansion

Abstract

This brief describes a segmented structure to deal with inverse square root in floating-point digital calculation arithmetic, based on Taylor-Series expansion; it uses only the small number of their expansion terms to achieve a fast evaluation of these functions in high precision. Taylor-series expansions of the inverse square root are examined for several center points with their convergence ranges, and the inverse square root calculation algorithm trade-offs among accuracy, numbers of multiplications/additions/subtractions and LUT sizes are shown; the designer can choose the optimal algorithm for his digital inverse square root calculation, and build its conceptual dedicated hardware architecture design with the contents described here.