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Home/Magazine Archive/May 1974 (Vol. 17, No. 5)/On the distributions of significant digits and roundoff.../Abstract

On the distributions of significant digits and roundoff errors

By Nai-Kuan Tsao
Communications of the ACM, May 1974, Vol. 17 No. 5, Pages 269-271
10.1145/360980.360998
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Generalized logarithmic law is derived for the distribution of the first t significant digits of a random digital integer. This result is then used to determine the distribution of the roundoff errors in floating-point operations, which is a mixture of uniform and reciprocal distributions.

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