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.


    Access

    Download


    Export, share and cite



    Title :

    IEEE754 precision-kbase-β arithmetic inherited by precision-m base-β arithmetic for k


    Contributors:

    Publication date :

    2016-12-01


    Type of media :

    Article (Journal)


    Type of material :

    Electronic Resource


    Language :

    English



    Classification :

    DDC:    510 / 629



    ARITHMETIC DEVICE, ARITHMETIC METHOD, ARITHMETIC SYSTEM, AND PROGRAM

    NISHIDA NOBUYUKI / TERASHIMA YASUO | European Patent Office | 2018

    Free access


    ARITHMETIC SYSTEM, AND ARITHMETIC UNIT

    MORISHIMA KENTA | European Patent Office | 2020

    Free access

    ARITHMETIC UNIT AND ARITHMETIC METHOD

    UJITOKO YUSUKE / HOTTA YUUKI | European Patent Office | 2020

    Free access

    ARITHMETIC DEVICE AND ARITHMETIC METHOD

    HAYASE SHIGENORI / IKEDA MICHIHIKO / MONJI TATSUHIKO | European Patent Office | 2021

    Free access