The Mainstreaming of Interval Arithmetic

  • John L. Gustafson


Interval arithmetic and validated arithmetic methods are almost unknown in the United States, and are absent in the federally funded High Performance Computing efforts of the last twenty years. The focus has been on ßoatingpoint operations per second (FLOPS) to the exclusion of any concern for the correctness of the result. However, the treaty-mandated need to validate nuclear weapons without physical experiments (the ASCI program) may prove to be the key to changing this. Radiation transport provides an example where bounded intervals can provide much more useful answers than existing point methods, whether they are used for modeling nuclear reactions or for computer-generated graphics. This example, and others, can be used to illustrate a general strategy that will allow us to move interval arithmetic into the mainstream of high-speed computing.


Interval Arithmetic Physical Simulation Answer Quality Twiddle Factor Interval Physic 
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  1. 1.
    Boyce, W.E., and DePrima, R.C., Elementary Differential Equations and Boundary Value Problems, Second Edition. New York: John Wiley & Sons, 1969.MATHGoogle Scholar
  2. 2.
    Greengard, L. and Rokhlin, V., A fast algorithm for particle simulations. Journal of Computational Physics, 73, 1988.Google Scholar
  3. 3.
    Hanrahan, P., Salzman, D., and Aupperle, L. A rapid hierarchical radiosity algorithm. Computer Graphics 25, 1991; 4:197–206.MATHGoogle Scholar
  4. 4.
    Rojas, R., and Hashagen, V., editors, The First Computers: History and Architectures. Cambridge: MIT Press, 2000.Google Scholar
  5. 5.
    Sillion, F. and Puech, C. Radiosity and Global Illumination. San Francisco: Morgan Kaufmann Publishers, Inc., 1994.Google Scholar
  6. 6.
    U.S. Department of Senate, Daily Press Briefing, DOT #147, Sept. 11, 1999.Google Scholar

Copyright information

© Springer-Verlag Wien 2001

Authors and Affiliations

  • John L. Gustafson
    • 1
  1. 1.Sun Microsystems, Inc.Palo AltoUSA

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