Rounding for quadratically converging algorithms for division and square root

Abstract

Exactly rounded results are necessary for many architectures such as IEEE 754 standard. For division and square root, rounding is easy to perform if a remainder is available. But for quadratically converging algorithms, the remainder is not typically calculated. Past implementations have required the additional delay to calculate the remainder, or calculate the approximate solution to twice the accuracy, or have resulted in a close but not exact solution. This paper shows how the additional delay of calculating the remainder can be reduced if extra precision is available.