Skip to main content

Interval Arithmetic Using SSE-2

  • Conference paper

Part of the Lecture Notes in Computer Science book series (LNTCS,volume 5045)

Abstract

We present an implementation of double precision interval arithmetic using the single-instruction-multiple-data SSE-2 instruction and register set extensions. The implementation is part of a package for exact real arithmetic, which defines the interval arithmetic variation that must be used: incorrect operations such as division by zero cause exceptions and loose evaluation of the operations is in effect. The SSE-2 extensions are suitable for the job, because they can be used to operate on a pair of double precision numbers and include separate rounding mode control and detection of the exceptional conditions. The paper describes the ideas we use to fit interval arithmetic to this set of instructions, shows a performance comparison with other freely available interval arithmetic packages, and discusses possible very simple hardware extensions that can significantly increase the performance of interval arithmetic.

Keywords

  • Hardware Implementation
  • Double Precision
  • Interval Arithmetic
  • Execution Path
  • Intel Corp

These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

This is a preview of subscription content, access via your institution.

Buying options

Chapter
USD   29.95
Price excludes VAT (Canada)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD   39.99
Price excludes VAT (Canada)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD   54.99
Price excludes VAT (Canada)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Learn about institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. von Gudenberg, J.W.: Interval Arithmetic on Multimedia Architectures. Reliable Computing 8(4) (2002)

    Google Scholar 

  2. Hofschuster, W., Krämer, W., Lerch, M., Tischler G., von Gudenberg, J.W.: The Interval Library fi_lib++ 2.0 Design, Features and Sample Programs. Preprint 2001/4,Universität Wuppertal (2001), http://www.math.uni-wuppertal.de/wrswt/preprints/prep_01_4.pdf

  3. Kolla, R., Vodopivec, A., von Gudenberg, J.W.: The IAX Architecture – Interval Arithmetic Extension. Universität Würzburg, Institut für Informatik, Techn. Report TR225 (1999), http://www2.informatik.uni-wuerzburg.de/mitarbeiter/wvg/Public/iax.ps.gz

  4. Kearfott, R.B.: Interval Computations: Introduction, Uses, and Resources. Euromath Bulletin 2(1), 95–112 (1996)

    MathSciNet  Google Scholar 

  5. Lambov, B.: RealLib: An Efficient Implementation Exact Real Arithmetic. Mathematical Structures in Computer Science (to appear), http://www.brics.dk/~barnie/RealLib/

  6. Boost Interval Arithmetic Library, http://www.boost.org/libs/numeric/interval/doc/interval.htm

  7. IEEE Standards Committee 754, IEEE Standard for Binary Floating-Point Arithmetic, ANSI/IEEE Standard 754-1985. Institute of Electrical and Electronics Engineers, New York (1985); reprinted in SIGPLAN Notices, 22(2), 9–25 (1987)

    Google Scholar 

  8. Intel Corp. IA-32 Intel® Architecture Software Developer’s Manual, Volumes 1-3, http://developer.intel.com/design/pentium4/manuals/index_new.htm

  9. Intel Corp. Using SSE3 Technology in Algorithms with Complex Arithmetic, http://www.intel.com/cd/ids/developer/asmo-na/eng/dc/pentium4/optimization/66717.htm

  10. Intel Corp. Next Generation Intel Processor: Software Developers Guide, http://www.intel.com/cd/ids/developer/asmo-na/eng/dc/pentium4/optimization/66756.htm

Download references

Author information

Authors and Affiliations

Authors

Editor information

Editors and Affiliations

Rights and permissions

Reprints and Permissions

Copyright information

© 2008 Springer-Verlag Berlin Heidelberg

About this paper

Cite this paper

Lambov, B. (2008). Interval Arithmetic Using SSE-2. In: Hertling, P., Hoffmann, C.M., Luther, W., Revol, N. (eds) Reliable Implementation of Real Number Algorithms: Theory and Practice. Lecture Notes in Computer Science, vol 5045. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-85521-7_6

Download citation

  • DOI: https://doi.org/10.1007/978-3-540-85521-7_6

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-85520-0

  • Online ISBN: 978-3-540-85521-7

  • eBook Packages: Computer ScienceComputer Science (R0)