One of the few books on the subject, Floating-Point Computation by Pat Sterbenz, is long out of print. There are, however, remarkably few sources of detailed information about it. Introductionīuilders of computer systems often need information about floating-point arithmetic.

General Terms: Algorithms, Design, LanguagesĪdditional Key Words and Phrases: Denormalized number, exception, floating-point, floating-point standard, gradual underflow, guard digit, NaN, overflow, relative error, rounding error, rounding mode, ulp, underflow. 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.Ĭategories and Subject Descriptors: (Primary) C.0 : General - instruction set design D.3.4 : Processors - compilers, optimization G.1.0 : General - computer arithmetic, error analysis, numerical algorithms (Secondary)ĭ.2.1 : Requirements/Specifications - languages D.3.4 Programming Languages]: Formal Definitions and Theory - semantics D.4.1 Operating Systems]: Process Management - synchronization. This paper presents a tutorial on those aspects of floating-point that have a direct impact on designers of 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 is rather surprising because floating-point is ubiquitous in computer systems.

Copyright 1991, Association for Computing Machinery, Inc., reprinted by permission.įloating-point arithmetic is considered an esoteric subject by many people. 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. Appendix D What Every Computer Scientist Should Know About Floating-Point Arithmetic

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