A Note on Division Algorithms Based on Multiplication

The algorithm of division based on multiplication is well known [1]-[5]. It permits utilization of fast multiply hardware in the implementation of division. The algorithm defines an iterative process in which numerator and denominator are both multiplied by the same factor m
i
such that the denominator converges to 1 and the numerator to the quotient. Convergence can be speeded up by finding a good value for m
0
, the first multiplier, by means of table lookup. The first two bits of the denominator D are 0.1 (assuming a normalized denominator). The next n bits are used to enter the table, yielding m
0
and D
1
=m
0
*D, where D
1
has a bits of convergence and as shown in [6].