Matrix processors using p-ADIC arithmetic for exact linear computations

Abstract

A unique code (called Hensel's code) is derived for a rational number, by truncating its infinite padic expansion. The four basic arithmetic algorithms for these codes are described and their application to rational matrix computations is demonstrated by solving a system of linear equations exactly, using the Gaussian elimination procedure. A comparative study of the computational complexity involved in this arithmetic and the multiple prime module arithmetic is made with reference to matrix computations. On this basis, a multiple padic scheme is suggested for the design of a highly parallel matrix processor.