Looking further in this context, number of active parallel workers is:
    parallel_register_count - parallel_terminate_count

Can active workers ever be greater than max_parallel_workers, I think no.
Then why should there be greater than check in the following condition:

    if (parallel && (BackgroundWorkerData->parallel_register_count -
BackgroundWorkerData->parallel_terminate_count) >= max_parallel_workers)

I feel there should be an assert if
    (BackgroundWorkerData->parallel_register_count
- BackgroundWorkerData->parallel_terminate_count) > max_parallel_workers)

And the check could be
    if (parallel && (active_parallel_workers == max_parallel_workers))
        then do not register new parallel wokers and return.

There should be no tolerance for the case when active_parallel_workers >
max_parallel_workers. After all that is the purpose of max_parallel_workers.

Is it like multiple backends trying to register parallel workers at the
same time, for which the greater than check should be present?

Thoughts?

Regards,
Neha

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