A Simulative Study of Correlated Error Propagation in Various Finite-Precision Arithmetics

The accumulated roundoff 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 roundoff error accumulations for these four systems are compared. The nature of the correlated errors incurred under various arithmetic operator mixes are discussed.