On the normalization requirement of divisor in divide-and-correct methods

Abstract

This paper presents an analysis on the normalization requirement of the divisor in a divide-and-correct method. This analysis is made subject to the condition that not more than one correction is required to obtain the true quotient character, from the trial estimate got from the division of a two-precision segment of every partial remainder by a suitably rounded single-precision divisor. (This segmented division is denoted here as a (2, 1) precision basic division.) It is found that the normalization requirement could be narrowed down to a smaller range of divisors, provided the magnitude of the character next to the leading character of the divisor is known. If, however, the normalization is to be eliminated one has to choose proper higher precision segments of operands for the basic division. Also considered is the possibility of eliminating the normalization by an increase on the number of corrections on the quotient estimate got from a (2, 1) precision basic division. It is shown that such a scheme is economical only for small radices.