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Computation of the unit in the first place (ufp) and the unit in the last place (ulp) in precision-p base β
Citation Link: https://doi.org/10.15480/882.5169
Publikationstyp
Journal Article
Date Issued
2023-06
Sprache
English
Author(s)
Institut
TORE-DOI
Journal
Volume
63
Issue
2
Article Number
28
Citation
BIT Numerical Mathematics 63 (2): 28 (2023-06)
Publisher DOI
Scopus ID
Publisher
Springer Science + Business Media B.V.
There are simple algorithms to compute the predecessor, successor, unit in the first place, unit in the last place etc. in binary arithmetic. In this note equally simple algorithms for computing the unit in the first place and the unit in the last place in precision-p base- β arithmetic with p⩾ 1 and with β⩾ 2 are presented. The algorithms work in the underflow range, and numbers close to overflow are treated by scaling. The algorithms use only the basic operations with directed rounding. If the successor (or predecessor) of a floating-point number is available, an algorithm in rounding to nearest is presented as well.
Subjects
Base-β
Floating-point arithmetic
INTLAB
Precision-p
Predecessor
Successor
Unit in the first place
Unit in the last place
DDC Class
510: Mathematik
Publication version
acceptedVersion
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s10543-023-00970-2-1.pdf
Size
546.15 KB
Format
Adobe PDF