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

doi:10.1016/S0010-4485(97)00086-9

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 journal › Article › peer-review

30 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 language	English
Pages (from-to)	657-665
Number of pages	9
Journal	CAD Computer Aided Design
Volume	30
Issue number	8
DOIs	https://doi.org/10.1016/S0010-4485(97)00086-9
Publication status	Published - 1998
Externally published	Yes

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

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10.1016/S0010-4485(97)00086-9

Cite this

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title = "Efficient and reliable methods for rounded-interval arithmetic",

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.",

keywords = "Binary representation, Denormalized number, IEEE Std 754-1985, Rounded-interval arithmetic, Unit-in-the-last-place",

author = "Abrams, {S. L.} and W. Cho and Hu, {C. Y.} and T. Maekawa and Patrikalakis, {N. M.} and Sherbrooke, {E. C.} and X. Ye",

note = "Funding Information: The authorsw ould like to thank Dr F. Pettinati of VSIS, Inc., for his input, which lead to this short communication. Funding for this work was obtained from ONR and NSF under grants NO001 4-96-l -0857 and DMI-9500394.",

year = "1998",

doi = "10.1016/S0010-4485(97)00086-9",

language = "English",

volume = "30",

pages = "657--665",

journal = "CAD Computer Aided Design",

issn = "0010-4485",

publisher = "Elsevier Limited",

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T1 - Efficient and reliable methods for rounded-interval arithmetic

AU - Abrams, S. L.

AU - Cho, W.

AU - Hu, C. Y.

AU - Maekawa, T.

AU - Patrikalakis, N. M.

AU - Sherbrooke, E. C.

AU - Ye, X.

N1 - Funding Information: The authorsw ould like to thank Dr F. Pettinati of VSIS, Inc., for his input, which lead to this short communication. Funding for this work was obtained from ONR and NSF under grants NO001 4-96-l -0857 and DMI-9500394.

PY - 1998

Y1 - 1998

N2 - 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.

AB - 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.

KW - Binary representation

KW - Denormalized number

KW - IEEE Std 754-1985

KW - Rounded-interval arithmetic

KW - Unit-in-the-last-place

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Efficient and reliable methods for rounded-interval arithmetic

Abstract

Keywords

ASJC Scopus subject areas

Access to Document

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