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Distributions of floating point numbers

Verteilungen von Gleitpunktzahlen

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Abstract

The logarithmic distribution is commonly used to model mantissae of floating point numbers. It is known that floating point products of logarithmically distributed mantissae are logarithmically distributed, while floating point sums are not. In this paper a distribution for floating point sums is derived, and for a special case of logarithmically distributed mantissae the deviation of this distribution from the logarithmic distribution is determined.

Zusammenfassung

Zur Modellierung der Mantissen von Gleitpunktzahlen wird im allgemeinen eine logarithmische Verteilung verwendet. Dabei sind Gleitpunkt-Produkte von logarithmisch verteilten Mantissen wieder logarithmisch verteilt, nicht jedoch Gleitpunkt-Summen. In dieser Arbeit wird eine Verteilung für Gleitpunkt-Summen hergeleitet; für einen Spezialfall wird die Abweichung dieser Verteilung von der logarithmischen Verteilung bestimmt.

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Authors and Affiliations

  1. Department of Mathematics, University of Wisconsin-La Crosse, 54601, La Crosse, WI, USA

    J. K. Scheidt & C. W. Schelin

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  1. J. K. Scheidt
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  2. C. W. Schelin
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Scheidt, J.K., Schelin, C.W. Distributions of floating point numbers. Computing 38, 315–324 (1987). https://doi.org/10.1007/BF02278709

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  • DOI: https://doi.org/10.1007/BF02278709

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