Abstract

page 154 Introduction page 154 Rounding Err or page 155 The IEEE Standard page 171 Systems Aspects page 193 The Details page 207 Summary page 221 Acknowledgments page 222 References page 222 Theorem 14 and Theorem 8 page 225 154 Numerical Computation Guide E Abstract Floating-point arithmetic is consider ed 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 fr om PC's to supercomputers have floating-point accelerators; most compilers will be called upon to compile floating-point algorithms fr om time to time; and virtually every operating system must r espond to floating-point exceptions such as overflow. This paper pr esents a tutorial on those aspects of floatingpoint that have a dir ect impact on designers of computer systems. It begins with background on floating-point r epresentation and r ounding error, continues with a discussion of the IEEE fl...

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