Rump, Siegfried M.Siegfried M.Rump2020-03-052020-03-052016-12-01ACM Transactions on Mathematical Software 3 (43): Art.-Nr.: 20 (2016-12-01)http://hdl.handle.net/11420/5207Suppose 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.en0098-350020163Base-βDouble roundingFloating-point arithmeticIEEE754Interval arithmeticINTLABUnit in the first place (UFP)MathematikJournal Article10.1145/2785965Other