A feasibility analysis of binary fixed-slash and floating-slash number systems

Author

Matula, David W. ; Kornerup, Peter

Author_Institution

Comput. Sci. Dept., Southern Methodist Univ., Dallas, TX, USA

fYear

1978

fDate

25-27 Oct. 1978

Firstpage

29

Lastpage

38

Abstract

Design and analysis of finite precision rational number systems based on fixed-slash and floating-slash representation is pursued. Natural formats for binary fixed-slash and binary floating-slash number representation in computer words are described. Compatibility with standard integer representation is obtained. Redundancy in the´ representation is shown to be minimal. Arithmetic register requirements are considered. Worst case and average case rounding errors are determined, and the concept of adaptive variable precision in the rounding is developed.

Keywords

fixed point arithmetic; floating point arithmetic; number theory; redundancy; adaptive variable precision; arithmetic register requirement; average case rounding errors; binary fixed-slash number representation; binary floating-slash number representation; computer words; feasibility analysis; finite precision rational number system; redundancy; standard integer representation; worst case rounding error; Accuracy; Adaptive systems; Additives; Computers; Lead; Loss measurement; Redundancy; Adaptive variable precision; Adjacent fractions; Binary numeric word format; Farey fractions; Finite precision; Fixed-slash numbers; Floating-slash numbers; Integer compatibility; Mediant roundings; Range of number system; Rational arithmetic; Redundancy; Worst case and average case rounding error;

fLanguage

English

Publisher

ieee

Conference_Titel

Computer Arithmetic (ARITH), 1978 IEEE 4th Symposium on

Conference_Location

Santa Monica, CA

Type

conf

DOI

10.1109/ARITH.1978.6155752

Filename

6155752