Computer Interval Arithmetic: Definition and Proof of Correct Implementation

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Computer Interval Arithmetic: Definition and Proof of Correct Implementation

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Journal of the ACM (JACM) archive
Volume 17 , Issue 4 (October 1970) table of contents

Pages: 603 - 612

Year of Publication: 1970

ISSN:0004-5411

Authors

Donald I. Good	Department of Computer Sciences, University of Texas at Austin, Austin, Texas and University of Wisconsin, Computer Sciences Department and Computing Center, Madison, Wisconsin
Ralph L. London	University of Wisconsin, Computer Sciences Department and Computing Center, Madison, Wisconsin

Publisher

ACM New York, NY, USA

Bibliometrics

Downloads (6 Weeks): 6, Downloads (12 Months): 36, Citation Count: 8

Additional Information:

abstract references cited by index terms collaborative colleagues

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ABSTRACT

A definition is given of computer interval arithmetic suitable for implementation on a digital computer. Some computational properties and simplifications are derived. An ALGOL code segment is proved to be a correct implementation of the definition on a specified machine environment.

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	BURROUGHS CORPORATION. Burroughs B5500 information processing systems Extended Algol reference manual. Detroit, Mich., 1966.
	2	COLLINS, G.E. Interval arithmetic for the IBM 704. IBM Corp., 1960.
	3	FLOYD, R.W. Assigning meanings to programs. Proc. Symposia in Appl. Math., Vol. 19- Mathematical Aspects of Computer Science (1966). Amer. Math. Soc., Providence. R.I., 1967, pp. 19-32.
	4	GOOD, D. I ., AND LONDON, R. L. Interval arithmetic for the Burroughs B5500: Four Algol procedures and proofs of their correctness. Computer Sciences Tech. Rep. No. 26, U. of Wisconsin, Madison, Wis., June 1968.
	5	Donald E. Knuth, The art of computer programming, volume 1 (3rd ed.): fundamental algorithms, Addison Wesley Longman Publishing Co., Inc., Redwood City, CA, 1997
	6	LONDON, R.L. Computer programs can be proved correct. In Banerji, R. B, and Mesarovic, M. D. (Eds.), Theoretical Approaches to Nonrnumerical Problem Solving--Proc. Systems Symposium at Case Western Reserve University, Springer-Verlag, New York, 1970, pp. 281-302.
	7	Ralph L. London, Certification of algorithm 245 [M1]:treesort 3:proof of algorithms—a new kind of certification, Communications of the ACM, v.13 n.6, p.371-373, June 1970 [doi>10.1145/362384.362507]
	8	MOORE, R.E. Interval Analysis. Prentice-Hall, Englewood Cliffs, N.J., 1966:
	9	LADNER, T. D., ANn YOHE, J.M. An interval arithmetic package for the Univac 1108. Tech. Summary Rep. No. 1055, Math. Res. Center, U. of Wisconsin, Madison, Wis., May 1970.
	10	YoHE, J. M. Best possible floating-point arithmetic: Tech. Summary Rep. No. 1054 Math. Res. Center, U. of Wisconsin, Madison, Wis., March 1970.

CITED BY 8

	Ralph L. London, A view of program verification, ACM SIGPLAN Notices, v.10 n.6, p.534-545, June 1975
	C. V. Ramamoorthy , S. F. Ho, Testing large software with automated software evaluation systems, ACM SIGPLAN Notices, v.10 n.6, p.382-394, June 1975
	K. A. Redish, Comment on London's certification of algorithms 245, Communications of the ACM, v.14 n.1, p.50-51, Jan. 1971
	J. M. Yohe, Software for Interval Arithmetic: A Reasonably Portable Package, ACM Transactions on Mathematical Software (TOMS), v.5 n.1, p.50-63, March 1979
	Ralph L. London, The current state of proving programs correct, Proceedings of the ACM annual conference, p.39-46, August 01-01, 1972, Boston, Massachusetts, United States
	Alan Bundy, A generalized interval package and its use for semantic checking, ACM Transactions on Mathematical Software (TOMS), v.10 n.4, p.397-409, Dec. 1984
	Herbert Fischer , Alvin J. Surkan, Implementation of interval arithmetic using APL, ACM SIGAPL APL Quote Quad, v.6 n.1, Spring 1975
	T. A. Linden, A summary of progress toward proving program correctness, Proceedings of the December 5-7, 1972, fall joint computer conference, part I, December 05-07, 1972, Anaheim, California