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.
IEEE754 precision-kbase-β arithmetic inherited by precision-m base-β arithmetic for k
2016-12-01
Article (Journal)
Electronic Resource
English
ARITHMETIC DEVICE, ARITHMETIC METHOD, ARITHMETIC SYSTEM, AND PROGRAM
European Patent Office | 2018
|