[marko_oktabyr]

> That's not how modulo arithmetic works.

We should be a bit careful with what one means by "modulo arithmetic" here. If we are talking about arithmetic in Z/nZ (read "integers modulo n"), then the objects being acted upon are no longer integers, but equivalence classes of integers. That is, the set of all integers that satisfy the equivalence relation "~" where "a ~ b" means a - b = k*n for some integer k. For example, one of the equivalence classes in Z/3Z would be the set {..., -4, -1, 2, 5, ...}.

Since every element of the set is equivalent under that relation, we typically will choose a representative of that equivalence class, e.g., [2] for the previous class. If we view the "mod" or "modulo" operator to be a mapping from the integers to a particular representative of its equivalence class, there's no reason that negative values should be excluded. [-1] refers to the same equivalence class as [2], [32], and [-7]. The details of how integers are mapped to a chosen representative seem to vary from language to language, but modular arithmetic works all the same between them.

[shikon7]

But 2 mod 3 should still give the same as -1 mod 3. If the representative for the same equivalence class is allowed to be different depending on the input, you could just as well use the number itself.

[marko_oktabyr]

At the risk of being snarky, I should certainly hope the output depends on the input.

On a more serious note, there are quite reasonable properties that are satisfied by keeping the sign of the first argument as the chosen representative. In particular, for any two nonzero integers a and b, we have that:

a = (a / b) * b + (a mod b)

Where division should be interpreted as integer division that rounds towards zero. If a=-1 and b=3, then (a/b) would be zero which would require (a mod b) to be -1 if we want the above to hold. Also note that other rounding choices (e.g., rounding towards negative infinity) could impose (a mod b) = 2.

So choosing a particular representative comes down to choosing what properties you want your function to have in relation to other arithmetic.

[oasisaimlessly]

There is no "particular representative"; every equivalence class (except 0) has two possible representatives.

... and that's exactly why the C modulo operator sucks.