@Article{Goualard:2014:HDY,
  author =       "Fr\'{e}d\'{e}ric Goualard",
  title =        "How do you Compute the Midpoint of an Interval?",
  journal =      "{ACM} Transactions on Mathematical Software",
  volume  =      40,
  number  =      2,
  year    =      2014,
  month   =      feb,
  pages =        "11:1--11:25",
  url =          "http://doi.acm.org/10.1145/2493882",
  accepted =     "1 May 2013",
  abstract =     "
                  The algorithm that computes the midpoint of an interval
                  with floating-point bounds requires some careful
                  devising to handle all possible inputs correctly. We
                  review several implementations from prominent C/C++
                  interval arithmetic packages and analyze their potential
                  failure to deliver the expected results. We then show
                  how to amend them to avoid common pitfalls.  The results
                  presented are also relevant to non-interval arithmetic
                  computation such as the implementation of bisection
                  methods.  Enough background on IEEE 754 floating-point
                  arithmetic is provided for this paper to serve as a
                  practical introduction to the analysis of floating-point
                  computation.",
}