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The distribution of l.s.d. and its implications for computer design

Published online by Cambridge University Press:  01 August 2016

Peter R. Turner
Peter R. Turner*
Affiliation:
Department of Mathematics, University of Lancaster, Lancaster LA1 4YL
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Extract

I was interested to see in a recent issue of the Gazette a note from Hoare and Wright [1] about the distribution of leading significant digits, l.s.d., and “Benford’s Law” that this distribution is logarithmic. This distribution has fascinated many people since Benford’s original observation [2] in 1938 of the dirty pages at the beginning of a book of log tables.

Type
Research Article
Information
The Mathematical Gazette , Volume 71 , Issue 455 , March 1987 , pp. 26 - 31
Copyright
Copyright © Mathematical Association 1987

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References

1. Hoare, G.T. and Wright, E.E., The distribution of first significant digits, Math. Gaz. 70, 34–37 (1986).Google Scholar
2. Benford, F., The law of anomalous numbers, Proc. Am. Phil. Soc. 78, 551–572 (1938).Google Scholar
3. Knuth, D.E., The art of computer programming, Vol. 2; Seminumerical algorithms, Addison-Wesley. (1969).Google Scholar
4. Turner, P.R., Further revelations on l.s.d., IMA J. on Num. Anal. 4, 225–231 (1984).Google Scholar
5. Turner, P.R., The distribution of leading significant digits, IMA J. on Num. Anal. 2, 407–412 (1982).Google Scholar
6. Bustoz, J., Feldstein, A., Goodman, R. and Linnainmaa, S., Improved trailing digits estimates applied to optimal computer arithmetic, J. Assoc. of Comp. Mach. 26, 716–730 (1979).Google Scholar
7. Feldstein, A. and Turner, P.R., Overflow, underflow and severe loss of significance in floating-point addition and subtraction, IMA J. on Num. Anal. 6, 241–251 (1986).Google Scholar
8. Clenshaw, C.W. and Olver, F.W.J., Beyond Floating Point, J. Assoc. of Comp. Mach. 31, 319–328 (1984).Google Scholar