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URN: urn:nbn:de:0030-drops-14454
URL: http://drops.dagstuhl.de/opus/volltexte/2008/1445/
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Blomquist, Frithjof ; Hofschuster, Werner ; Krämer, Walter

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

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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).

BibTeX - Entry

@InProceedings{blomquist_et_al:DSP:2008:1445,
  author =	{Frithjof Blomquist and Werner Hofschuster and Walter Kr{\"a}mer},
  title =	{A Modified Staggered Correction Arithmetic  with Enhanced Accuracy and Very Wide Exponent Range},
  booktitle =	{Numerical Validation in Current Hardware Architectures},
  year =	{2008},
  editor =	{Annie Cuyt and Walter Kr{\"a}mer and Wolfram Luther and Peter Markstein},
  number =	{08021},
  series =	{Dagstuhl Seminar Proceedings},
  ISSN =	{1862-4405},
  publisher =	{Internationales Begegnungs- und Forschungszentrum f{\"u}r Informatik (IBFI), Schloss Dagstuhl, Germany},
  address =	{Dagstuhl, Germany},
  URL =		{http://drops.dagstuhl.de/opus/volltexte/2008/1445},
  annote =	{Keywords: Staggered correction, multiple precision, C-XSC,    interval computation, wide exponent range, reliable numerical computations, complex interval funct}
}

Keywords: Staggered correction, multiple precision, C-XSC, interval computation, wide exponent range, reliable numerical computations, complex interval funct
Seminar: 08021 - Numerical Validation in Current Hardware Architectures
Issue Date: 2008
Date of publication: 22.04.2008


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