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What Every Computer Scientist Should Know About Floating-Point Arithmetic
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" Numerical Computation Guide
Appendix D
What Every Computer Scientist Should Know About Floating-Point Arithmetic
Note – This appendix is an edited reprint of the paper What Every Computer Scientist Should Know About Floating-Point Arithmetic , by David Goldberg, published in the March, 1991 issue of Computing Surveys. Copyright 1991, Association for Computing Machinery, Inc., reprinted by permission.
Abstract
Floating-point arithmetic is considered an 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 those 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 numerous examples of how computer builders can better support floating-point.
Categories and Subject Descriptors: (Primary) C.0 [Computer Systems Organization]: General -- instruction set design ; D.3.4 [Programming Languages]: Processors -- compilers, optimization ; G.1.0 [Numerical Analysis]: General -- computer arithmetic, error analysis, numerical algorithms (Secondary)
D.2.1 [Software Engineering]: Requirements/Specifications -- languages ; D.3.4 Programming Languages]: Formal Definitions and Theory -- semantics ; D.4.1 Operating Systems]: Process Management -- synchronization .
General Terms: Algorithms, Design, Languages
Additional Key Words and Phras"
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