he Basisfor Implementation of Ad itive Operations intheResidue Number System
Akio Sasaki · 1968
A newresidue nunmber system algebra hasbeenprevi- ously proposed bytheauthor. Thealgebra hassolved anessential theoretical barrier intheresidue numbersystem andhasenabled onetopursue additive operations intheresidue numbersystem to their full extent, overcoming suchdifficulties asrestrictions onthe signormagnitude ofnumbersinthesystem. Inthis paper, basic theorems inthealgebra areintroduced first, andthen, basedonthe theorems, table look-up oriented solutions forhardware overflow checking, signdetection, andfloating-point additive operations are given. Thetheorems expound thebehavior ofaquantity treated as aveiled mysterious function intheliterature. Tothebestknowledge oftheauthor, hardware overflow-checking schemes andfloating- point additive operations intheresidue numbersystem havenever beenreported elsewhere. Sofar, theupper limit ofthemagnitude of numbersinthesystemeverdiscussed hasbeentheonethatis theory-limited, andfloating-point operations intheresidue number system haveneverbeendiscussed. IndexTerms-Addition andsubtraction, addition andsubtraction intheresidue numbersystem, computer arithmetics, floating-point addition andsubtraction, magnitude comparison intheresidue num- bersystem, overflow checking intheresidue numbersystem, residue numbersystem, residue numbersystemfloating-point additive operations, sign detection intheresidue numbersystem, theorems intheresidue numbersystem. NOMENCLATURE mi,i=1,2,** ,k:moduli orthebases oftheresidue numbersystem. Themoduliare assumed toberelatively prime so thatthesystemisnonredundant andtheChinese Remainder Theo- remholds M: product ofthemodulimithrough