> If n is bounded, then log(n) is bounded, yes. But so is n^n.
Yes, but in _practice_ the difference in the bounds is gigantic. log(n) is not just bounded for all practical purposes, it's bounded by a constant that's just not that big. That is simply not true for n^n, or even just n.
> In practice, log(n) is no guarantee for an algorithm being quick.
Sure, the constant matters.
> cause thousands of really slow page faults.
Which means the constant is huge. I agree that this is a problem, sure.
> for strict enough real time guarantees and for large enough values of n, log(n) is too slow.
It really depends on what the operations are. log(n) randomly-distributed memory accesses are a problem, I agree. If you have to touch that much memory and have a paged memory system, you lose no matter whether your memory is dynamically or statically allocated. You're right that dynamic allocation can make it more necessary to touch that much memory.
By the way, I fully agree that if you want to do hard realtime and have any hope of actually shipping, sticking to no dynamic allocation is probably simpler than doing the analysis to prove that your dynamic allocations are OK.