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IASI Research Report n. 223 (Previous Next) Colagrossi A.,

Limongelli C.Big numbers p-adic arithmetic: a parallel approach.ABSTRACT Approximated p-adic arithmetic in the form of Hensel codes, has received a great attention in the past years. Several contributions made really effective this p-adic arithmetic. However it has been shown that the appliability of p-adic arithmetic is strongly constrained by the size of rational numbers which constitutes the output of the given computation.
The key idea, that we like to present here, is to completely take the advantage of varying the prime p, by choosing it as a very large number. This choise will suggest a definition of a new algorithm which will benefit from a parallel execution.
Our aim is to perform "big" rational numbers arithmetic applying the so called g-adic approach, based on the theory of g-adic numbers.
This paper describes a general schema of g-adic computation and then presents two algorithms to perform the inverse mapping together with the related complexity analysis.