Constant-division algorithms

There exist many types of special-purpose systems that require rapid and repeated division by a set of known constant divisors. Numerous solutions have been proposed in response to the deficiencies of the conventional division algorithms for applications which involve repeated divisions by known constants. Six approaches are reviewed in detail and their relationships are shown by reducing them to equivalent forms. Proving the equivalence of these algorithms allows them to be considered as alternative implementations of the same basic function. Proof of correctness of one form serves to verify all the methods. The analytical process has led to an improved understanding of constant division and of the division operation in general. It has provided a foundation for further analysis and algorithm development, including the establishment of the theoretical basis of quotient and remainder generation, a generalised implementation of division by divisors 2ⁿ ±1, and extension of this method to divide by small integers by generating the value of the B-sequence, the value in one period, of the integer reciprocal