Monte carlo arithmetic: How to gamble with floating point and win

Computing in Science and Engineering

Volumn 2, Issue 4, 2000, Pages 58-68

  Parker, D Stott ^a   Pierce, Brad ^b   Eggert, Paul R ^c  

^a UNIVERSITY OF CALIFORNIA   (United States)

^b CADENCE DESIGN SYSTEMS   (United States)

^c Twin Sun Inc   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 85008050388     PISSN: 15219615     EISSN: None     Source Type: Journal    
DOI: 10.1109/5992.852391     Document Type: Article

References (12)

1. D.E. Knuth, The Art of Computer Programming, Vol. II: Seminumerical Algorithms, Addison-Wesley, New York, 1969.
2. D.S. Parker, Monte Carlo Arithmetic: Systematic Random Improvements upon Floating-Point Arithmetic, Tech. Report CSD-970002, Computer Science Dept., Univ. of California, Los Angeles, 1997.
3. D. Goldberg, “What Every Computer Scientist Should Know about Floating-Point Arithmetic,” ACM Computing Surveys, Vol. 23, No. 1, Mar. 1991, pp. 5-48; www.validgh.com/goldberg/ paper.ps (current June 2000).
4. N.J. Higham, Accuracy and Stability of Numerical Algorithms, SIAM Press, Philadelphia, 1996.
5. ANSI/IEEE Std 754-1985: IEEE Standard for Binary Floating-Point Arithmetic, American Nat'l Standards Inst., New York, 1985.
6. B.A. Pierce, Applications of Randomization to Floating-Point Arithmetic and to Linear Systems Solution, PhD diss., Computer Science Dept., Univ. of California, Los Angeles, 1997.
7. W. Kahan, “The Programming Environment's Contribution to Program Robustness,” SIGNUM Newsletter, Vol. 16, No. 4, Oct. 1981, p.10.
8. J.R. Taylor, An Introduction to Error Analysis: The Study of Uncertainties in Physical Measurements, 2nd Ed., Univ. Science Books, Mill Valley, Calif., 2000.
9. J.-C. Bajard et al., Introduction to the Special Issue on Real Numbers and Computers, J. Universal Computer Science, Vol. 1, No. 7, July 1995, p. 438.
10. G.H. Golub and C.F. Van Loan, Matrix Computations: 2nd Ed., Johns Hopkins Univ. Press, Baltimore, 1989.
11. W. Kahan, “The Improbability of Probabilistic Error Analyses for Numerical Computations,” UC Berkeley Statistics Colloquium, 28 Feb. 1996; www.cs.berkeley.edu/~wkahan/improber.ps (current May 2000).
12. G.E. Forsythe, “Round-Off Errors in Numerical Integration on Automatic Machinery: Preliminary Report,” Bull. AMS, Vol. 56, 1950, p. 61.