Abstract
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.
Zusammenfassung
Unter Zugrundelegung von sowohl theoretisch als auch empirisch gerechtfertigter Annahmen wird ein stochastisches Modell der Gleitkomma- und der logarithmischen Arithmetik konstruiert. Die Rechtfertigung dieser Annahmen löst offene Fragen bei Hamming (1970) und Bustoz et al. (1979).
Diese Modelle werden auf die Fehler von Summen und inneren Produkten angewendet.
Es wird ein Vergleich zwischen den Eigenschaften von Gleitkomma- und logarithmischen Rechnern hinsichtlich ihrer Fehleranalyse angestellt. Wir kommen zu dem Schluß, daß der logarithmische Rechner kleinere Fehlerkonfidenzintervalle für die Rundungsfehler aufweist als ein Gleitkommarechner mit der gleichen Wortlänge und dem annähernd gleichen Zahlenbereich.
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Work sponsored by the National Science Foundation under contract No. MCS-790150 and under contract No. MCS-8201065. This paper is based upon the first author's Ph. D. dissertation.
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Barlow, J.L., Bareiss, E.H. On roundoff error distributions in floating point and logarithmic arithmetic. Computing 34, 325–347 (1985). https://doi.org/10.1007/BF02251833
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DOI: https://doi.org/10.1007/BF02251833