Accurate sum and dot product

Takeshi Ogita, Siegfried M. Rump, Shinichi Oishi

    Research output: Contribution to journalArticle

    178 Citations (Scopus)

    Abstract

    Algorithms for summation and dot product of floating-point numbers are presented which are fast in terms of measured computing time. We show that the computed results are as accurate as if computed in twice or AT-fold working precision, K ≥ 3. For twice the working precision our algorithms for summation and dot product are some 40% faster than the corresponding XBLAS routines while sharing similar error estimates. Our algorithms are widely applicable because they require only addition, subtraction, and multiplication of floating-point numbers in the same working precision as the given data. Higher precision is unnecessary, algorithms are straight loops without branch, and no access to mantissa or exponent is necessary.

    Original languageEnglish
    Pages (from-to)1955-1988
    Number of pages34
    JournalSIAM Journal on Scientific Computing
    Volume26
    Issue number6
    DOIs
    Publication statusPublished - 2005

    Fingerprint

    Scalar, inner or dot product
    Floating point
    Summation
    Mantissa
    Subtraction
    Straight
    Error Estimates
    Multiplication
    Sharing
    Branch
    Fold
    Exponent
    Necessary
    Computing

    Keywords

    • Accurate dot product
    • Accurate summation
    • Fast algorithms
    • High precision
    • Verified error bounds

    ASJC Scopus subject areas

    • Mathematics(all)
    • Applied Mathematics

    Cite this

    Accurate sum and dot product. / Ogita, Takeshi; Rump, Siegfried M.; Oishi, Shinichi.

    In: SIAM Journal on Scientific Computing, Vol. 26, No. 6, 2005, p. 1955-1988.

    Research output: Contribution to journalArticle

    Ogita, Takeshi ; Rump, Siegfried M. ; Oishi, Shinichi. / Accurate sum and dot product. In: SIAM Journal on Scientific Computing. 2005 ; Vol. 26, No. 6. pp. 1955-1988.
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