Correctly rounded reciprocal square-root by digit recurrence and radix-4 implementation

In this work we present a reciprocal square-root algorithm by digit recurrence and selection by a staircase function, and the radix-4 implementation. As similar algorithms for division and square-root, the results are obtained correctly rounded in a straightforward manner (in contrast to existing methods to compute the reciprocal square-root). Although apparently a single selection function can only be used for j greater than or equal to 2 (the selection constants are different for j = 0, j = 1 and j greater than or equal to 2), we show that it is possible to use a single selection function for all iterations. We perform a rough comparison with existing methods and we conclude that our implementation is a low hardware complexity solution with moderate latency, specially for exactly rounded results.