CONSTANT-DIVISION ALGORITHMS

There exist many types of special-purpose systems that require rapid a nd repeated division by a set of known constant divisors. Numerous sol utions have been proposed in response to the deficiencies of the conve ntional division algorithms for applications which involve repeated di visions by known constants. Six approaches are reviewed in detail and their relationships are shown by reducing them to equivalent forms. Pr oving the equivalence of these algorithms allows them to be considered as alternative implementations of the same basic function. Proof of c orrectness of one form serves to verify all the methods. The analytica l process has led to an improved understanding of constant division an d of the division operation in general. It has provided a foundation f or further analysis and algorithm development, including the establish ment of the theoretical basis of quotient and remainder generation, a generalised implementation of division by divisors 2(n) +/- 1, and ext ension of this method to divide by small integers by generating the va lue of the B-sequence, the value in one period, of the integer recipro cal.