On the distributions of significant digits and roundoff errors

Authors:
Nai-Kuan Tsao
Affiliations:
Dept. of Air Force, Wright-Patterson Air Force Base, OH
Venue:
Communications of the ACM
Year:
1974

Citing 2
Cited 4

On Local Roundoff Errors in Floating-Point Arithmetic

Journal of the ACM (JACM)
Rounding Errors in Algebraic Processes

Rounding Errors in Algebraic Processes

Best “ordering” for floating-point addition

ACM Transactions on Mathematical Software (TOMS)
Convergence Estimates for the Distribution of Trailing Digits

Journal of the ACM (JACM)
Improved Trailing Digits Estimates Applied to Optimal Computer Arithmetic

Journal of the ACM (JACM)
Analysis of Rounding Methods in Floating-Point Arithmetic

IEEE Transactions on Computers

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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.