Floating-Point Arithmetic Algorithms in the Symmetric Residue Number System

Abstract

The residue number system is an integer number system and is inconvenient to represent numbers with fractional parts. In the symmetric residue system, a new representation of floating-point numbers and arithmetic algorithms for its addition, subtraction, multiplication, and division are proposed. A floating-point number is expressed as an integer multiplied by a product of the moduli. The proposed system assumes existence of necessary conversion procedures before and after the computation.