An Efficient Hardware Implementation for a Reciprocal Unit

Abstract

The computation of the reciprocal of a numerical value is an important ingredient of many algorithms. We present a compact hardware architecture to compute reciprocals by two or three Newton-Raphson iterations to obtain the accuracy of IEEE 754 single- and double-precision standard, respectively. We estimate the initialization value by a specially designed second-order polynomial approximating the reciprocal. By using a second-order polynomial, we succeed in using one single hardware architecture for both, the polynomial approximation computations as well as the Newton-Raphson iterations. Therefore, we obtain a most compact hardware implementation for the complete reciprocal computation.