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 journalArticlepeer-review

11 Citations (Scopus)


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
Issue number4
Publication statusPublished - 2015 Oct


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

ASJC Scopus subject areas

  • Software
  • Applied Mathematics


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