What every computer scientist should know about floating-point arithmetic

1991/03/01 by David Theo Goldberg · 23 citations
Computer Science · Mathematics · #Arithmetic #Compiler #Computational Physics and Python Applications #Computer science #Digital Filter Design and Implementation #Double-precision floating-point format #Floating point #Floating-point unit #IEEE floating point #Mathematics #Numerical Methods and Algorithms #Operating system #Parallel computing #Point (geometry) #Programming language #Rounding

paper · doi:10.1145/103162.103163

openalex publication_date 1991/03/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/31

Abstract

Floating-point arithmetic is considered as esoteric subject by many people. This is rather surprising, because floating-point is ubiquitous in computer systems: Almost every language has a floating-point datatype; computers from PCs to supercomputers have floating-point accelerators; most compilers will be called upon to compile floating-point algorithms from time to time; and virtually every operating system must respond to floating-point exceptions such as overflow. This paper presents a tutorial on the aspects of floating-point that have a direct impact on designers of computer systems. It begins with background on floating-point representation and rounding error, continues with a discussion of the IEEE floating point standard, and concludes with examples of how computer system builders can better support floating point.

Citations

• IEEE Standard for Binary Floating-Point Arithmetic

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