A Simple but Realistic Model of Floating-Point Computation

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A Simple but Realistic Model of Floating-Point Computation

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ACM Transactions on Mathematical Software (TOMS) archive
Volume 7 , Issue 4 (December 1981) table of contents

Pages: 445 - 480

Year of Publication: 1981

ISSN:0098-3500

Author

W. S. Brown

Bell Laboratories, 600 Mountain Avenue, Murray Hill, NJ

Publisher

ACM New York, NY, USA

Bibliometrics

Downloads (6 Weeks): 4, Downloads (12 Months): 33, Citation Count: 12

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references cited by index terms collaborative colleagues

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REFERENCES

Note: OCR errors may be found in this Reference List extracted from the full text article. ACM has opted to expose the complete List rather than only correct and linked references.

	1	James L. Blue, A Portable Fortran Program to Find the Euclidean Norm of a Vector, ACM Transactions on Mathematical Software (TOMS), v.4 n.1, p.15-23, March 1978 [doi>10.1145/355769.355771]
	2	BROWN, W.S. Some fundamentals of performance evaluation for numerical software. In Performance Evaluation of Numerical Software, L.D. Fosdick (Ed.), North-Holland, Amsterdam, 1979, pp. 17-30.
	3	BROWN, W.S. Altran User's Manual, 4th ed. Bell Laboratories, Murray Hill, N.J., 1977.
	4	BROWN, W.S. A realistic model of floating-point computation. In Mathematical Software III, John R. Rice (Ed.), Academic Press, New York, 1977, pp. 343-360.
	5	W. S. Brown , S. I. Feldman, Environment Parameters and Basic Functions for Floating-Point Computation, ACM Transactions on Mathematical Software (TOMS), v.6 n.4, p.510-523, Dec. 1980 [doi>10.1145/355921.355924]
	6	BURKS, A.W., GOLDSTINE, H.H., AND VON NEUMANN, J. Preliminary discussion of the logical design of an electronic computing instrument. In Collected Works of John Von Neumann, A.H. Taub (Ed.), vol. 5, Pergamon Press, New York, 1963, pp. 34-79. (See especially p. 57.)
	7	Jerome Coonen , William Kahan , John Palmer , Tom Pittman , David Stevenson, A proposed standard for binary floating point arthmetic, ACM SIGNUM Newsletter, v.14 n.si-2, p.4-12, October 1979 [doi>10.1145/1057520.1057521]
	8	W. Crowell, Portability of Numerical Software: Proceedings, Springer-Verlag New York, Inc., Secaucus, NJ, 1977
	9	DEKKER, T.J. Correctness proof and machine arithmetic. In Performance Evaluation of Numerical Software, L.D. Fosdick (Ed.), North-Holland, Amsterdam, 1979, pp. 31-44.
	10	Brian Ford, Parameterization of the Environment for Transportable Numerical Software, ACM Transactions on Mathematical Software (TOMS), v.4 n.2, p.100-103, June 1978 [doi>10.1145/355780.355782]
	11	FORSYTHE, G.E., AND MOLER, C.B. Computer Solution of Linear Algebraic Systems. Prentice- Hall, Englewood Cliffs, N.J., 1967. (See especially p. 87.)
	12	P. A. Fox , A. P. Hall , N. L. Schryer, The PORT Mathematical Subroutine Library, ACM Transactions on Mathematical Software (TOMS), v.4 n.2, p.104-126, June 1978 [doi>10.1145/355780.355783]
	13	Bob Fraley , Steve Walther, Proposal to eliminate denormalized numbers, ACM SIGNUM Newsletter, v.14 n.si-2, p.22-23, October 1979 [doi>10.1145/1057520.1057523]
	14	W. Morven Gentleman , Scott B. Marovich, More on algorithms that reveal properties of floating point arithmetic units, Communications of the ACM, v.17 n.5, p.276-277, May 1974 [doi>10.1145/360980.361003]
	15	KAHAN, W. Private c~)mmunication.
	16	KNUTH, D.E. Accuracy of floating-point arithmetic. In Seminumerical Algorithms, vol. 2 of The Art of Computer Programming, Addison-Wesley, Reading, Mass., 1969, pp. 195-210.
	17	C. L. Lawson , R. J. Hanson , F. T. Krogh , D. R. Kincaid, Algorithm 539: Basic Linear Algebra Subprograms for Fortran Usage [F1], ACM Transactions on Mathematical Software (TOMS), v.5 n.3, p.324-325, Sept. 1979 [doi>10.1145/355841.355848]
	18	Michael A. Malcolm, Algorithms to reveal properties of floating-point arithmetic, Communications of the ACM, v.15 n.11, p.949-951, Nov. 1972 [doi>10.1145/355606.361870]
	19	MOORE, R.E. Interval Analysis. Prentice-Hall, Englewood Cliffs, N.J., 1966.
	20	Mary Payne , William Strecker, Draft proposal for a binary normalized floating point standard, ACM SIGNUM Newsletter, v.14 n.si-2, p.24-28, October 1979 [doi>10.1145/1057520.1057524]
	21	Christian H. Reinsch, Principles and preferences for computer arithmetic, ACM SIGNUM Newsletter, v.14 n.1, p.12-27, March 1979 [doi>10.1145/1053417.1053418]
	22	SCHRYER, N.L. A test of a computer's floating-point arithmetic unit. Computing Science Tech. Rep. No. 89, Bell Laboratories, Murray Hill, N. J., Feb. 1981.
	23	J. H. Wilkinson, The algebraic eigenvalue problem, Oxford University Press, Inc., New York, NY, 1988
	24	James H. Wilkinson, Rounding Errors in Algebraic Processes, Dover Publications, Incorporated, 1994

CITED BY 12

	Mark P. W. Mutrie , Richard H. Bartels , Bruce W. Char, An approach for floating-point error analysis using computer algebra, Papers from the international symposium on Symbolic and algebraic computation, p.284-293, July 27-29, 1992, Berkeley, California, United States
	David Goldberg, The design of floating-point data types, ACM Letters on Programming Languages and Systems (LOPLAS), v.1 n.2, p.138-151, June 1992
	David M. Gay , Eric Grosse, Self-adapting Fortran 77 machine constants: comment on Algorithm 528, ACM Transactions on Mathematical Software (TOMS), v.25 n.1, p.123-126, March 1999
	David Goldberg, What every computer scientist should know about floating-point arithmetic, ACM Computing Surveys (CSUR), v.23 n.1, p.5-48, March 1991
	John R. Hauser, Handling floating-point exceptions in numeric programs, ACM Transactions on Programming Languages and Systems (TOPLAS), v.18 n.2, p.139-174, March 1996
	Geoff Barrett, Formal Methods Applied to a Floating-Point Number System, IEEE Transactions on Software Engineering, v.15 n.5, p.611-621, May 1989
	W. J. Cody , J. T. Coonen , D. M. Gay , K. Hanson , D. Hough , W. Kahan , R. Karpinski , J. Palmer , F. N. Ris , D. Stevenson, A proposed radix- and word-length-independent standard for floating-point arithmetic, ACM SIGNUM Newsletter, v.20 n.1, p.37-51, January 1985
	Mary Payne , Craig Schaffert , Brian Wichmann, Proposal for a language compatible arithmetic standard, ACM SIGNUM Newsletter, v.25 n.1, p.2-43, January 1990
	Kenneth W. Dritz, Rationale for the proposed standard for a generic package of elementary functions for Ada, ACM SIGAda Ada Letters, v.XI n.7, p.47-65, Fall 1991
	CORPORATE ISO-IEC/JTC1/SC22/WG9 (Ada) Numerics Rapporteur Group, Proposed standard for a generic package of primitive functions for Ada, ACM SIGAda Ada Letters, v.XI n.7, p.66-82, Fall 1991
	Graham S. Hodgson, Rationale for the proposed standard for package of real and complex type declarations and basic operations for Ada (including vector and matrix types), ACM SIGAda Ada Letters, v.XI n.7, p.131-139, Fall 1991
	Donald A. Celarier , Donald W. Sando, An Ada math library for real-time avionics, ACM SIGAda Ada Letters, v.XI n.7, p.274-284, Fall 1991

INDEX TERMS

Primary Classification:
G. Mathematics of Computing

Additional Classification:
G. Mathematics of Computing
G.1 NUMERICAL ANALYSIS
G.1.0 General
Subjects: Error analysis; Computer arithmetic

General Terms:
Performance, Reliability, Theory

Collaborative Colleagues:

W. S. Brown: colleagues

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