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A Modified Staggered Correction Arithmetic with Enhanced Accuracy and Very Wide Exponent Range

Authors: Frithjof Blomquist, Werner Hofschuster, and Walter Krämer

Published in: Dagstuhl Seminar Proceedings, Volume 8021, Numerical Validation in Current Hardware Architectures (2008)

Abstract

A so called staggered precision arithmetic is a special kind of a multiple precision arithmetic based on the underlying floating point data format (typically IEEE double format) and fast floating point operations as well as exact dot product computations. Due to floating point limitations it is not an arbitrary precision arithmetic. However, it typically allows computations using several hundred mantissa digits. A set of new modified staggered arithmetics for real and complex data as well as for real interval and complex interval data with very wide exponent range is presented. Some applications show the increased accuracy of computed results compared to ordinary staggered interval computations. The very wide exponent range of the new arithmetic operations allows computations far beyond the IEEE data formats. The new arithmetics would be extremly fast, if an exact dot product was available in hardware (the fused accumulate and add instruction is only one step in this direction).

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Frithjof Blomquist, Werner Hofschuster, and Walter Krämer. A Modified Staggered Correction Arithmetic with Enhanced Accuracy and Very Wide Exponent Range. In Numerical Validation in Current Hardware Architectures. Dagstuhl Seminar Proceedings, Volume 8021, pp. 1-23, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2008)

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@InProceedings{blomquist_et_al:DagSemProc.08021.3,
  author =	{Blomquist, Frithjof and Hofschuster, Werner and Kr\"{a}mer, Walter},
  title =	{{A Modified Staggered Correction Arithmetic  with Enhanced Accuracy and Very Wide Exponent Range}},
  booktitle =	{Numerical Validation in Current Hardware Architectures},
  pages =	{1--23},
  series =	{Dagstuhl Seminar Proceedings (DagSemProc)},
  ISSN =	{1862-4405},
  year =	{2008},
  volume =	{8021},
  editor =	{Annie Cuyt and Walter Kr\"{a}mer and Wolfram Luther and Peter Markstein},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/DagSemProc.08021.3},
  URN =		{urn:nbn:de:0030-drops-14454},
  doi =		{10.4230/DagSemProc.08021.3},
  annote =	{Keywords: Staggered correction, multiple precision, C-XSC, interval computation, wide exponent range, reliable numerical computations, complex interval funct}
}

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A Modified Staggered Correction Arithmetic with Enhanced Accuracy and Very Wide Exponent Range

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