I think you're right, but it depends on what's your computational model. In word-RAM you usually assume that log n < w where w is the machine word, and you can

I think you're right, but it depends on what's your computational model. In word-RAM you usually assume that log n < w where w is the machine word, and you can do arithmetical operations on words in O(1), so if your coefficients fit in w bits the complexity is O(n log n). You could say it's a trick but it's a convenient trick, since on a real-world machines w is much larger than you need (64). I don't know if you can make the same argument about floating point computations.