On the distributions of significant digits and roundoff errors

ABSTRACT

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.

REFERENCES

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• 8: Toyohisa Kaneko , Bede Liu, On Local Roundoff Errors in Floating-Point Arithmetic, Journal of the ACM (JACM), v.20 n.3, p.391-398, July 1973 [doi>10.1145/321765.321771]

INDEX TERMS

Primary Classification:
  G. Mathematics of Computing
  G.1 NUMERICAL ANALYSIS
      G.1.0 General
          Subjects: Computer arithmetic

General Terms:
Performance

Keywords:
floating-point operations, mean value, reciprocal distribution, roundoff errors, significant digits, uniform distribution, variance