A simulative study of correlated error propagation in various finite arithmetics

The accumulated round-off error incurred in long arithmetic computations involving a randomized mixture of addition, subtraction, multiplication and division operations applied to an initial randomly generated data base is studied via simulation. Truncated and rounded floating-point arithmetic and truncated and rounded logarithmic arithmetic are simultaneously utilized for each of the computation sequences and the resulting round-off error accumulations for these four systems are compared. Fundamental results related to the nature of the correlated errors incurred under various arithmetic operator mixes are discussed.