On roundoff error distributions in floating point and logarithmic arithmetic

Probabilistic models of floating point and logarithmic arithmetic are constructed using assumptions with both theoretical and empirical justification. The justification of these assumptions resolves open questions in Hamming (1970) and Bustoz et al. (1979). These models are applied to errors from sums and inner products. A comparison is made between the error analysis properties of floating point and logarithmic computers. We conclude that the logarithmic computer has smaller error confidence intervals for roundoff errors than a floating point computer with the same computer word size and approximately the same number range.