Multiplicative Division Employing Independent Factors

We introduce a division procedure where a normalized quotient approximation is derived as a product of four independent closed form factors. Specific derivations of the method for IEEE-754 standard binary single and double precision division are developed in detail. Theoretical error bounds are derived to prove correctness for obtaining properly rounded single precision quotients by rounding the product of these four factors. The proofs include exhaustive verification for the single precision extremal cases. For double precision quotient approximations, the error bounds verify suitable accuracy so that further determination of the remainder sign is sufficient to obtain precisely rounded double precision quotients. Selected experimental results are provided to illustrate the double precision level quotient approximations. A prescaling process is introduced to reduce the table size requirements for these double precision approximations to less than 5-Kbytes.