Efficient and reliable methods for rounded-interval arithmetic

S. L. Abrams, W. Cho, C. Y. Hu, Takashi Maekawa, N. M. Patrikalakis, E. C. Sherbrooke, X. Ye

Research output: Contribution to journalArticle

29 Citations (Scopus)

Abstract

We present an efficient and reliable method for computing the unitin-the-last-place (ulp) of a double-precision floating-point number, taking advantage of the standard binary representation for floatingpoint numbers defined by IEEE Std 754-1985. The ulp is necessary to perform software rounding for robust rounded-interval arithmetic (RIA) operations. Hardware rounding, using two of the standard rounding modes defined by IEEE-754, may be more efficient. RIA has been used to produce robust software systems for the solution of systems of nonlinear equations, interrogation of geometric and differential properties of curves and surfaces, curve and surface intersections, and solid modeling.

Original languageEnglish
Pages (from-to)657-665
Number of pages9
JournalCAD Computer Aided Design
Volume30
Issue number8
DOIs
Publication statusPublished - 1998 Jan 1
Externally publishedYes

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Nonlinear equations
Hardware

Keywords

  • Binary representation
  • Denormalized number
  • IEEE Std 754-1985
  • Rounded-interval arithmetic
  • Unit-in-the-last-place

ASJC Scopus subject areas

  • Computer Science Applications
  • Computer Graphics and Computer-Aided Design
  • Industrial and Manufacturing Engineering

Cite this

Abrams, S. L., Cho, W., Hu, C. Y., Maekawa, T., Patrikalakis, N. M., Sherbrooke, E. C., & Ye, X. (1998). Efficient and reliable methods for rounded-interval arithmetic. CAD Computer Aided Design, 30(8), 657-665. https://doi.org/10.1016/S0010-4485(97)00086-9

Efficient and reliable methods for rounded-interval arithmetic. / Abrams, S. L.; Cho, W.; Hu, C. Y.; Maekawa, Takashi; Patrikalakis, N. M.; Sherbrooke, E. C.; Ye, X.

In: CAD Computer Aided Design, Vol. 30, No. 8, 01.01.1998, p. 657-665.

Research output: Contribution to journalArticle

Abrams, SL, Cho, W, Hu, CY, Maekawa, T, Patrikalakis, NM, Sherbrooke, EC & Ye, X 1998, 'Efficient and reliable methods for rounded-interval arithmetic', CAD Computer Aided Design, vol. 30, no. 8, pp. 657-665. https://doi.org/10.1016/S0010-4485(97)00086-9
Abrams, S. L. ; Cho, W. ; Hu, C. Y. ; Maekawa, Takashi ; Patrikalakis, N. M. ; Sherbrooke, E. C. ; Ye, X. / Efficient and reliable methods for rounded-interval arithmetic. In: CAD Computer Aided Design. 1998 ; Vol. 30, No. 8. pp. 657-665.
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