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IEEE754 precision-kbase-β arithmetic inherited by precision-m base-β arithmetic for k<m
Publikationstyp
Journal Article
Date Issued
2016-12-01
Sprache
English
Author(s)
Institut
TORE-URI
Volume
43
Issue
3
Article Number
20
Citation
ACM Transactions on Mathematical Software 3 (43): Art.-Nr.: 20 (2016-12-01)
Publisher DOI
Scopus ID
Suppose an m-digit floating-point arithmetic in base β ≥ 2 following the IEEE754 arithmetic standard is available. We show how a k-digit arithmetic with k < mcan be inherited solely using m-digit operations. This includes the rounding into kdigits, the four basic operations and the square root, all for even or odd base β. In particular, we characterize the relation between k and mso that no double rounding occurs when computing in mdigits and rounding the result into k digits. We discuss rounding to nearest as well as directed rounding, and our approach covers exceptional values including signed zero. For binary arithmetic, a Matlab toolbox based on binary64 including k-bit scalar, vector and matrix operations as well as k-bit interval arithmetic is part of Version 8 of INTLAB, the Matlab toolbox for reliable computing.
Subjects
Base-β
Double rounding
Floating-point arithmetic
IEEE754
Interval arithmetic
INTLAB
Unit in the first place (UFP)
DDC Class
510: Mathematik