If we don't treat almost all integers in an algorithm as fixed size then the analysis gets really messy and annoying in a way that has nothing to do with real computers.

And if the algorithm actually did anything with the value that made it grow or shrink with the recursion, the TCO version would stop being O(n) under such a framework. This only works because it's passing 0 around every iteration. And this probably applies to the TCO version too depending on how you expect to run it.

I was going to write something similar.

Regardless, the comment I replied to is fundamentally confused (presented a tail recursive algorithm and said it didn't have tail calls, presented a linear algorithm that uses a linear amount of memory and claims it's O(n log n) for some reason but no clarification if it's in time or space). I'd rather hear from the person I responded to than whatever guesses the rest of us can come up with because it needs several points of clarification to be understood.

> If we don't treat almost all integers in an algorithm as fixed size then the analysis gets really messy and annoying in a way that has nothing to do with real computers.

I guess nobody does numerical computing or distributed systems with real computers anymore, huh.

Wrong way around. Almost all the numbers in those systems are fixed-size. There's a few types of variable width payload, but all the little ancillary types are 64 bits or whatever.