Efficient calculations of faithfully rounded l2-norms of n-vectors

Stef Graillat, Christoph Lauter, Ping Tak Peter Tang, Naoya Yamanaka, Shinichi Oishi

    Research output: Contribution to journalArticle

    4 Citations (Scopus)

    Abstract

    In this article, we present an efficient algorithm to compute the faithful rounding of the l2-norm of a floatingpoint vector. This means that the result is accurate to within 1 bit of the underlying floating-point type. This algorithm does not generate overflows or underflows spuriously, but does so when the final result calls for such a numerical exception to be raised. Moreover, the algorithm is well suited for parallel implementation and vectorization. The implementation runs up to 3 times faster than the netlib version on current processors.

    Original languageEnglish
    Article number24
    JournalACM Transactions on Mathematical Software
    Volume41
    Issue number4
    DOIs
    Publication statusPublished - 2015 Oct 1

    Fingerprint

    Norm
    Vectorization
    Overflow
    Rounding
    Floating point
    Faithful
    Parallel Implementation
    Exception
    Efficient Algorithms

    Keywords

    • 2-norm
    • Error-free transformations
    • Faithful rounding
    • Floating-point arithmetic
    • Overflow
    • Underflow

    ASJC Scopus subject areas

    • Software
    • Applied Mathematics

    Cite this

    Efficient calculations of faithfully rounded l2-norms of n-vectors. / Graillat, Stef; Lauter, Christoph; Tang, Ping Tak Peter; Yamanaka, Naoya; Oishi, Shinichi.

    In: ACM Transactions on Mathematical Software, Vol. 41, No. 4, 24, 01.10.2015.

    Research output: Contribution to journalArticle

    Graillat, Stef ; Lauter, Christoph ; Tang, Ping Tak Peter ; Yamanaka, Naoya ; Oishi, Shinichi. / Efficient calculations of faithfully rounded l2-norms of n-vectors. In: ACM Transactions on Mathematical Software. 2015 ; Vol. 41, No. 4.
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