On the efficient implementation of higher radix square root algorithms

Abstract

Square root nonrestoring algorithms operating with a radix higher than two (but power of 2) are discussed. Formulas are derived delimiting the feasibility space of the class of algorithms considered as a function of the different parameters. This definition leads to the determination of some of these parameters; in particular, it is possible to compute the number of partial reminder bits to be inspected for digit selection and the number of operand bits to be inspected to generate the first radicand value, as both parameters have a relevant impact on the implementation. The specific case of radix 4, digit set (-2, -1, 0, +1, +2) and partial remainder represented by the sum of two numbers is considered.<>