Consider an interval $[x-2^n,x+2^n]$ defined by a binary float $x$ and a power of two $2^n$ typically much smaller than $x$. I would like to know whether an efficient algorithm exists to determine the shortest decimal expansion within the interval. What is the basic idea of such an algorithm? Perhaps such an algorithm has already been published?

In my own search, I have come across the work of [Steele & White “How to print floating-point numbers accurately”][1], but it is not clear to me whether it applies in the sense that their results can be adapted to this particular case.

  [1]: https://doi.org/10.1145/93548.93559