DESIGN AND ANALYSIS OF NONBINARY RADIX FLOATING-POINT REPRESENTATIONS

This paper examines the feasibility of higher radix floating point representations and in particular decimal based representations. Traditional analyses of such representations have assumed the format of a floating point datum to be roughly identical to that of traditional binary floating point encodings such as the IEEE P754 task group standard representations. We relax this restriction and proposed a method of encoding higher radix floating point data with range, precision and storage requirements comparable to those exhibited by traditional binary representations. Results from McKeeman's Maximum and Average Relative Representational Error (MRRE and ARRE) analyses, Brent's RMS error evaluation, Matula's ratio of significance space and gap functions, and Brown and Richman's exponent range estimates are extended to accommodate the proposed representation. A decimal alternative to traditional binary representations is proposed and the behavior of such a system is contrasted with that of a comparable binary system.