It generally changes the analysis very little but makes it more annoying, which is why arithmetic is usually taken to be O(1). Formally speaking you'd have to specify a computational model to be able to talk about complexity (there is no such thing as 'complexity' but only 'complexity respective to a model'; e.g. you can change the big-O complexity on Turing machines by using more tapes).
The computational model of a book like CLRS is "arithmetic is O(1), but we're not going to abuse that bug".
The computational model of a book like CLRS is "arithmetic is O(1), but we're not going to abuse that bug".