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How do you assess code for problems handling leap seconds (particularly Java)?

We recently got notice that there may be a negative leap second at the end of the year and we need to determine how it will affect our programs (we write mostly java programs). I’ve done some searching on this site and around the web and I see some discussions about leap seconds, but they all seem to be about “does this block of code have a problem with leap seconds?” or “how does java handle leap seconds?” And even then, the answers are hard to wrap my mind around. It’s hard to figure out what it means for time to change out from under you.