Unclear problem in 'Reusable barrier problem #1'

[viralmutant]

The problem described in the Section 3.7.2 for the non-solution in 3.7.1 is

If the n − 1th thread is interrupted at this point, and then the nth thread
comes through the mutex, both threads will find that count==n and both
threads will signal the turnstile. In fact, it is even possible that all the threads
will signal the turnstile.

Isn't this also true for the working solution described in 3.6.4 ? The text under that head says

It might seem dangerous to read the value of count outside the mutex. In
this case it is not a problem
Isn't that the same problem described in section 3.7.2 ?
What would be the problem if all the threads signal but none of them is in wait yet ?

[Spoonbender]

The fact that two threads will see that count == n and both will call barrier.signal() doesn't change the functionality of the one-time barrier discussed in 3.6.x., since the code doesn't reuse this barrier - so its final state doesn't matter, since the guarantees made by the barrier are held.
It matters in 3.7.1 because if the turnstile is over-signaled then its internal counter will not be zero when we re-use the barrier and hit line 9 again, which means the barrier will be opened before all N threads reached it.

[viralmutant]

The fact that two threads will see that count == n and both will call barrier.signal() doesn't change the functionality of the one-time barrier discussed in 3.6.x., since the code doesn't reuse this barrier - so its final state doesn't matter, since the guarantees made by the barrier are held. It matters in 3.7.1 because if the turnstile is over-signaled then its internal counter will not be zero when we re-use the barrier and hit line 9 again, which means the barrier will be opened before all N threads reached it.

Yup !! Got it. Thanks
But I have 1 more doubt in 'Preloaded Turnstile' solution. Since we have signal(n) construct, we can very well re-use a single turnstile, right ? Instead of having turnstile and turnstile2 ?
Or is it that they are explaining how to re-use Barrier in general and what goes inside the python Barrier class(as explained in the next section), b'coz re-usable barrier object in python is from where my confusion stemmed.