But 13 is also equivalent to -2 and 1, mod 3. Why are you doing the modulo operation in the first place?

From a mathematical standpoint, I've never seen a use for returning -2 here. I want something unique for the group, so I can ask e.g. `x mod 3 == y mod 3` and have it work regardless of whether x or/and y are negative.

Sure, but then why if:

  -13 \equiv 5 \pmod 3

it is the case that:

  > -13 % 3 === 5 % 3
  false

I think it's better to use a convention where for all a, b, m, if a and b are congruent mod m, then a%m === b%m