Algorithm for high speed shared radix 4 division and radix 4 square-root

Abstract

An algorithm to implement radix four division and radix four square-root in a shared hardware for IEEE standard for binary floating point format will be described. The algorithm is best suited to be implemented in either off-the-shelf components or being a portion of a VLSI floating-point chip. Division and square-root bits are generated by a non-restoring method while keeping the partial remainder, partial radicand, quotient and root all in redundant forms. The core iteration involves a 8-bit carry look-ahead adder, a multiplexer to convert two's complement to sign magnitude, a 19-term next quotient/root prediction PLA, a divisor/root multiple selector, and a carry save adder. At the end, two iterations of carry look-ahead adder across the length of the mantissa are required to generate the quotient/root in a correctly rounded form. Despite its simplicity in the hardware requirement, the algorithm takes only about 30 cycles to compute double precision division or square-root. Finally, extending the algorithm to radix eight or higher division/square-root will be discussed.