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

1813	The Art of Computer Programming - Knuth - 1968
1128	The C Programming Language - Kernighan, Ritchie - 1988
145	The Art of Computer - Knuth - 1998
79	A floating-point technique for extending the available precision - Dekker - 1971
41	The Sign/Logarithm Number System - Swartzlander, Alexopoulos - 1975
33	Underflow and the reliability of numerical software - Demmel - 1984
29	Cuts for Complex Elementary Functions. The State of Art in Numerical Analysis - Kahan, Branch - 1987
29	Floating-Point Computation - Sterbenz - 1974
24	A simple but realistic model of floating-point computation,ACM - Brown - 1981
24	A proposed radix- and word-lengthindependent standard for floating-point arithmetic - Cody, Coonen, et al. - 1984
24	Contributions to a Proposed Standard for Binary FloatingPoint Arithmetic - Coonen - 1984
21	Standard 754-1985 for Binary FloatingPoint Arithmetic - IEEE - 1987
21	The Arithmetic of the Digital Computer: A New Approach - Kulisch, Miranker - 1986
18	A Survey Of Error Analysis - Kahan - 1972
13	The C Programming Language. Prentice-Hall, Englewood Cli s - Kernighan, Ritchie - 1988
12	27 Bits Are Not Enough for 8-Digit Accuracy - Goldberg - 1967
12	Finite precision rational arithmetic: Slash number systems - Matula, Kornerup - 1985
9	American National Standard Programming Language FORTRAN - ANSI - 1978
9	Compiler Support for Floating-point Computation - Farnum - 1988
8	Computer arithmetic. In Computer Architecture: A Quantitative Approach - Goldberg - 2002
8	The Near Orthogonality of Syntax - Kahan, Coonen - 1982
7	Arithmetic for vector processors - Kirchner, Kulisch - 1988
4	The Arithmetic of the Digital Computer: A New Approach - Kulish, Miranker - 1986
4	A Portable Floating-Point Environment, unpublished manuscript. What Every Computer Scientist Should Know About Floating Point Arithmetic 223 - Barnett - 1987
4	Floating-Point Standards --- Theory and Practice, in "Reliability in Computing: the role of interval methods in scientific computing - Cody - 1988
4	Unpublished lectures given at Sun Microsystems - Kahan - 1988
4	Arithmetic for Vector - Kirchner, Kulisch - 1987
4	Evading the Drift - Reiser, Knuth - 1975
3	Anomalies in the IBM ACRITH package - Kahan, LeBlanc - 1985
2	Calculating Area and Angle of a Needle-like Triangle, unpublished manuscript - Kahan - 1986
2	Evading the drift in floating-point addition Inf. Process - REISER, KNUTH - 1975
2	Numerical Computation Guide - unknown authors - 1986
2	Numerical Computation Guide - unknown authors - 1986
1	A portable floating-point environment. Unpubhshed manuscript - 13ARNETT - 1987
1	Floating-point standards–Theory and practice - CODY - 1988
1	Computer Solut~on of Linear Algebraic Systems - FORSYTHE, MOLER - 1967
1	Unpublished lectures given at - KAHAN - 1988
1	The near orthogonality of syntax, semantics, and diagnostics in numerical programming environments - KAHAN, COONEN - 1982
1	A Proposed Radix- and Word-length-independent Standard for Floating-point Arithmetic - al - 1984
1	27 Bits Ar e Not Enough for 8-Digit Accuracy - Goldberg - 1967
1	Computer Arithmetic, in "Computer Architecture: A Quantitative Approach", by David - Goldberg - 1990
1	1982.HP-15C Advanced Functions Handbook - Packard
1	1972.A Survey Of Err or Analysis, in Information Pr ocessing 71 - Kahan
1	Unpublished lectur es given at Sun Micr osystems - Kahan - 1988
1	ome T. 1982.The Near Orthogonality of Syntax - Kahan, Coonen
1	Arithmetic for V ector - Kirchner, Kulisch - 1987