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    $\begingroup$ Can you explain me why the range difference determines everything? $\endgroup$ Commented Mar 12, 2016 at 11:40
  • $\begingroup$ The result must fit in a fixed number of bits, 52 for doubles and 23 for singles. You can try doing the addition manually (with singles, it is easier). $\endgroup$ Commented Mar 12, 2016 at 13:34