Decimal floating point representation
Description
This study considers the contemporary use of decimal based floating point representations. Because decimal representations do not require conversion of values between decimal and binary based systems, they are preferred over traditional binary systems. Floating point base conversions require considerable computational effort and frequently result in values that cannot be represented finitely within the target representation. The causes of base conversion error between decimal and binary systems are examined and the superiority of the decimal system for modeling arbitrary rational numbers is demonstrated Decimal based systems have, unfortunately, long been considered as deficient in their representational error behavior when compared with binary systems of similar storage size and range. This study proposes an alternative format to the traditional encodings assumed for a base ten floating point implementation. This encoding is termed the Decimal Floating Point (DFP) format. The DFP format is evaluated with the traditional measures of floating point accuracy and compared to a binary system of comparable size and range. 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 DFP format. The error performance of the DFP format is shown to be equal or superior to that of a comparable binary representation while exponent range achieves 83% that of the binary case Implementation of the DFP system is demonstrated and the impact shown to be confined to the Arithmetic and Logic Unit of a computer CPU