Error-free parallel rational arithmetic for optical and VLSI computing.

An error-free carry-free (parallel) rational arithmetic system based on residue and p-adic representation is introduced. In this system, Farey rational numbers, whose numerators and denominators are bounded, are encoded into Para-Hensel codes (parallel rational Hensel code), and the parallel element-wise arithmetic is performed using these codes. The algorithms for encoding into and decoding from the Para-Hensel code and the arithmetic algorithms are described. This system will have extensive applications in massively parallel processors.