The problem with most answers so far is that you have an unusual "equality". If A and B are similar but not identical, you want to treat them as equal. Basically, A and A+epsilon still compare as equal, but A+2*epsilon does not (for some unspecified epsilon). Or, depending on your algorithm, A*(1+epsilon) does and A*(1+2*epsilon) does not.
That does mean that A+epsilon compares equal to A+2*epsilon. Thus A = B and B = C does not imply A = C. This breaks common assumptions in <algorithm>
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You can still sort the values, that is a sane thing to do. But you have to consider what to do with a long range of similar values in the result. If the range is long enough, the difference between the first and last can still be large. There's no simple answer.