A method for Hensel code overflow detection

Authors:
Xinkai Li;Chao Lu;Jon A. Sjogren
Affiliations:
Towson University, Towson, MD;Towson University, Towson, MD;Air Force Office of Scientific Research, Arlington, VA
Venue:
ACM SIGAPP Applied Computing Review
Year:
2012

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Abstract

Hensel code was originally defined by Krishnamurthy, Rao and Subramanian [1], which was developed from the P--adic number system first proposed by Hensel in 1900s. The purpose was to realize exact computation for rational numbers. The Hensel code arithmetic has been well developed [1, 2, 3], but the problem of detecting Hensel code overflow and underflow has not been properly addressed [3]. In this paper, we proposed a method for Hensel code overflow detection. The method can realize overflow detection by the prime p and the Hensel code itself. Using this method, a few digits of the Hensel code will be sacrificed.