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Second Note on Basic Interval Arithmetic for IEEE754R

Authors: John D. Pryce, George C. Corliss, R. Baker Kearfott, Ned S. Nedialkov, and Spencer Smith

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

Abstract

The IFIP Working Group 2.5 on Numerical Software (IFIPWG2.5) wrote on 5th Septem- ber 2007 to the IEEE Standards Committee concerned with revising the IEEE Floating- Point Arithmetic Standards 754 and 854 (IEEE754R), expressing the unanimous request of IFIPWG2.5 that the following requirement be included in the future computer arithmetic standard: For the data format double precision, interval arithmetic should be made available at the speed of simple floating-point arithmetic. IEEE754R (we believe) welcomed this development. They had before them a document defining interval arithmetic operations but, to be the basis of a standards document, it needed more detail. Members of the Interval Subroutine Library (ISL) team were asked to comment, in an email from Ulrich Kulisch that enclosed one from Jim Demmel to Van Snyder raising the issue. This paper provides ISL's comments.

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John D. Pryce, George C. Corliss, R. Baker Kearfott, Ned S. Nedialkov, and Spencer Smith. Second Note on Basic Interval Arithmetic for IEEE754R. In Numerical Validation in Current Hardware Architectures. Dagstuhl Seminar Proceedings, Volume 8021, pp. 1-8, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2008)

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@InProceedings{pryce_et_al:DagSemProc.08021.18,
  author =	{Pryce, John D. and Corliss, George C. and Kearfott, R. Baker and Nedialkov, Ned S. and Smith, Spencer},
  title =	{{Second Note on Basic Interval Arithmetic for IEEE754R}},
  booktitle =	{Numerical Validation in Current Hardware Architectures},
  pages =	{1--8},
  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.08021.18},
  URN =		{urn:nbn:de:0030-drops-14517},
  doi =		{10.4230/DagSemProc.08021.18},
  annote =	{Keywords: Interval arithmetic, validated computation, floating point, standards, exceptions, not an interval}
}

Document

DOI: 10.4230/DagSemProc.06021.7

Interval Subroutine Library Mission

Authors: George F. Corliss, R. Baker Kearfott, Ned Nedialkov, John D. Pryce, and Spencer Smith

Published in: Dagstuhl Seminar Proceedings, Volume 6021, Reliable Implementation of Real Number Algorithms: Theory and Practice (2006)

Abstract

We propose the collection, standardization, and distribution of a full-featured production quality library for reliable scientific computing with routines using interval techniques for use by the wide community of applications developers.

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George F. Corliss, R. Baker Kearfott, Ned Nedialkov, John D. Pryce, and Spencer Smith. Interval Subroutine Library Mission. In Reliable Implementation of Real Number Algorithms: Theory and Practice. Dagstuhl Seminar Proceedings, Volume 6021, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2006)

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@InProceedings{corliss_et_al:DagSemProc.06021.7,
  author =	{Corliss, George F. and Kearfott, R. Baker and Nedialkov, Ned and Pryce, John D. and Smith, Spencer},
  title =	{{Interval Subroutine Library Mission}},
  booktitle =	{Reliable Implementation of Real Number Algorithms: Theory and Practice},
  series =	{Dagstuhl Seminar Proceedings (DagSemProc)},
  ISSN =	{1862-4405},
  year =	{2006},
  volume =	{6021},
  editor =	{Peter Hertling and Christoph M. Hoffmann and Wolfram Luther and Nathalie Revol},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/DagSemProc.06021.7},
  URN =		{urn:nbn:de:0030-drops-7122},
  doi =		{10.4230/DagSemProc.06021.7},
  annote =	{Keywords: Subroutine library, problem-solving library, C++ interval standard}
}

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Second Note on Basic Interval Arithmetic for IEEE754R

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Interval Subroutine Library Mission

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