Novel floating-point online division algorithm

Abstract

A description is given of an online division (reciprocal) algorithm for (maximally) redundant floating-point numbers of arbitrary radix. The algorithm works for normalized, quasi-normalized, and pseudonormalized numbers, and can therefore be applied in chained online computations. The online delay of the proposed algorithm is reported. The algorithm consists of two steps: the first m digits of the result are generated by a simple table lookup method: the remaining n-m digits are generated by using an adapted Newton-Raphson iteration method. In the second step, the online digits are created by using a fast and simple selection mechanism.