It's hard to tell about APIs, since there's no caselaw, but the rule for texts is that the smaller they are, the more original they have to be to qualify for copyright protection - so conversely, the sheer length of a work makes it more likely to be protected even if it's not that original.

So "add(a, b) returning the sum of the two" is probably not copyrightable by itself, but a whole namespace full of functions might be.