Accurate sum and dot product

Takeshi Ogita*, Siegfried M. Rump, Shin'ichi Oishi

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

193 Citations (Scopus)


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 of Scientific Computing
Issue number6
Publication statusPublished - 2005


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

ASJC Scopus subject areas

  • Computational Mathematics
  • Applied Mathematics


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