I mean, cosine is pretty common... The next level solution is to apply generators so that either the decimal stream or the continued fraction is allowed to be

I mean, cosine is pretty common... The next level solution is to apply generators so that either the decimal stream or the continued fraction is allowed to be infinitely precise, but I think this can have dangerous effects where checking whether a number is equal to 0 or maybe 1 can involve infinite computation? So that's where you really understand “oh, I do really need that epsilon, for comparisons’ sake.” For continued fractions I think you can also just have your library bound the size of the integers involved? So “it’s an array of signed int32s, but if your continued fraction generates a number that would overflow that, we just truncate the stream at that point.” Then the library is able to say that these two things are equal because their difference is [0; int_overflow] which becomes just [0]. Something like that.