@Article{Graillat:2015:ECF,
  author =       "Stef Graillat and Christoph Lauter and
                  Ping Tak Peter Tang and Naoya Yamanaka and 
                  Shin'ichi Oishi",
  title =        "Efficient calculations of faithfully rounded $l_2$-norms
                  of $n$-vectors",
  journal =      "{ACM} Transactions on Mathematical Software",
  volume =       "41",
  number =       "4",
  accepted =     "1 November 2014",
  upcoming =     "true", 
  abstract =     "
                  In this paper, we present an efficient algorithm to
                  compute the faithful rounding of the $l_2$-norm of
                  a floating-point vector. This means that the result
                  is accurate to within one bit of the underlying
                  floating-point type.
                  This algorithm does not generate overflows or underflows
                  spuriously, but does so when the final result indeed 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 rocessors.",
}