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Karlsruhe Accurate Arithmetic (KAA), or Karlsruhe Accurate Arithmetic Approach (KAAA), augments conventional floating-point arithmetic with good error behaviour with new operations to calculate scalar products with a single rounding error.^[1]

The foundations for KAA were developed at the University of Karlsruhe starting in the late 1960s.^[2]^[3]^[4]

References

^ McDermid, John A. (1993) [1991]. "Chapter 8.5.2". Software Engineer's Reference Book (revised ed.). Butterworth-Heinemann Ltd. / Elsevier. p. 187. ISBN 0-7506-0813-7. ISBN 1483105083 / ISBN 9781483105086. Retrieved 2016-05-30.
^ CW (1985-12-20). "Rechner liefern keine korrekten Ergebnisse - Neue Arithmetik der Karlsruher Forschungsgruppe Kulisch in der 4361 realisiert" [Computers don't deliver exact results - Karlsruhe research team Kulisch implements new computer arithmetic for the IBM 4361]. Computerwoche (in German). Karlsruhe, Germany: IDG Business Media GmbH. Archived from the original on 2016-05-30. Retrieved 2016-05-30.
^ Lortz, Bruno (1971). Eine Langzahlarithmetik mit optimaler einseitiger Rundung [A large-number arithmetic with optimal one-side rounding] (Ph.D. thesis) (in German). Universität Karlsruhe.
^ Kulisch, Ulrich W. (1976). Grundlagen des Numerischen Rechnens. Mathematische Begründung der Rechnerarithmetik (in German). Mannheim, Germany: Bibliographisches Institut. ISBN 3-411-01517-9. ISBN 978-3-411-01517-7.

Kulisch, Ulrich W.; Miranker, Willard L. (1981). Rheinboldt, Werner (ed.). Computer arithmetic in theory and practice. Computer Science and Applied Mathematics (1 ed.). New York, USA: Academic Press, Inc. ISBN 0-12-428650-X.
PI (1986-08-29). "Cadmus jetzt mit Kulisch-Arithmetik - Uni Karlsruhe gibt Pascal-Compiler nach München" [Cadmus now comes with Kulisch arithmetic - University Karlsruhe delivers Pascal compiler to Munich]. Computerwoche (in German). Munich / Karlsruhe, Germany: IDG Business Media GmbH. Archived from the original on 2016-05-30. Retrieved 2016-05-30.
Bamberger, Lothar; Davenport, James H.; Fischer, Hans-Christoph; Kok, Jan; Schumacher, Günter; Ullrich, Christian; Wallis, Peter J. L.; Winter, Dik T.; Wolff von Gudenberg, Jürgen (1990). Wallis, Peter J. L. (ed.). Improving Floating-Point Programming (1st ed.). Bath, United Kingdom: John Wiley & Sons Ltd. ISBN 0-471-92437-7. ISBN 978-0-471-92437-1.
"Professoren-Porträt: Prof. Dr. Ulrich Kulisch". Eulenspiegel (in German). WS97/98 (1). Karlsruher Institut für Technologie, Fachschaft Mathematik Informatik. 2013-07-19 [October 1997]. Archived from the original on 2016-05-30. Retrieved 2016-05-30.
Balagurusamy, E. (1999). Numerical Methods (25th reprint (2008) ed.). New Delhi, India: Tata McGraw-Hill Publishing Company Limited. p. 52. ISBN 0-07-463311-2. ISBN 978-0-07-463311-3. Retrieved 2016-05-30.
Pöppe, Christoph (2000-09-01). "Numerische Mathematik: Rechnen mit garantierter Genauigkeit" [Numerical mathematics: Calculating with guaranteed accuracy]. Spektrum der Wissenschaft (in German). 2000 (9). Spektrum der Wissenschaft Verlagsgesellschaft mbH: 54–. Archived from the original on 2016-05-30. Retrieved 2016-05-30.
IBM System/370 RPQ High Accuracy Arithmetic (PDF) (1 ed.). IBM. January 1984. Retrieved 2024-04-24.

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[McDermid_1991-1] McDermid, John A. (1993) [1991]. "Chapter 8.5.2". Software Engineer's Reference Book (revised ed.). Butterworth-Heinemann Ltd. / Elsevier. p. 187. ISBN 0-7506-0813-7. ISBN 1483105083 / ISBN 9781483105086. Retrieved 2016-05-30.

[IBM_4361_1985-2] CW (1985-12-20). "Rechner liefern keine korrekten Ergebnisse - Neue Arithmetik der Karlsruher Forschungsgruppe Kulisch in der 4361 realisiert" [Computers don't deliver exact results - Karlsruhe research team Kulisch implements new computer arithmetic for the IBM 4361]. Computerwoche (in German). Karlsruhe, Germany: IDG Business Media GmbH. Archived from the original on 2016-05-30. Retrieved 2016-05-30.

[Lortz_1971-3] Lortz, Bruno (1971). Eine Langzahlarithmetik mit optimaler einseitiger Rundung [A large-number arithmetic with optimal one-side rounding] (Ph.D. thesis) (in German). Universität Karlsruhe.

[Kulisch_1976-4] Kulisch, Ulrich W. (1976). Grundlagen des Numerischen Rechnens. Mathematische Begründung der Rechnerarithmetik (in German). Mannheim, Germany: Bibliographisches Institut. ISBN 3-411-01517-9. ISBN 978-3-411-01517-7.

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Karlsruhe Accurate Arithmetic

See also

References

Further reading