Efficient and reliable methods for rounded-interval arithmetic

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

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

30 Citations (Scopus)


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
Issue number8
Publication statusPublished - 1998
Externally publishedYes


  • 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


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