On the Normalization Requirement of
Divisor in Divide- and- Correct Methods

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.

CACM December, 1967

Krishnamurthy, E. V.
Nandi, S. K.

CA671210 JB February 26, 1978  2:15 PM

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