Hi, I have a question about the following code in `Executor::_invoke`:

```cpp
// Reset the join counter with strong dependencies to support cycles.
// + We must do this before scheduling the successors to avoid race
//   condition on _predecessors.
// + We must use fetch_add instead of direct assigning
//   because the user-level call on "invoke" may explicitly schedule
//   this task again (e.g., pipeline) which can access the join_counter.
node->_join_counter.fetch_add(
  node->_nstate & NSTATE::STRONG_DEPENDENCIES_MASK,
  std::memory_order_relaxed
);

I understand why the join counter needs to be restored before scheduling successors.

For example, in a cycle:

A -> B -> A

after A becomes ready, its join counter is 0. Before B is allowed to run and potentially decrement A again, A needs to restore its strong dependency count for the next iteration.

However, for this purpose alone, it seems that:

node->_join_counter.store(
  node->_nstate & NSTATE::STRONG_DEPENDENCIES_MASK,
  std::memory_order_relaxed
);

would also work, assuming the current invocation exclusively owns the node's join-counter state.

So I am trying to understand the exact concurrency scenario that requires fetch_add.

My current understanding is that the important case may be something like this:

A ----\
       -> D
B ----/

where D has two strong dependencies:

D.join_counter = 2

Then another runtime task explicitly schedules D:

rt.schedule(D);

and Runtime::schedule resets the target counter to zero before scheduling it:

node->_join_counter.store(0, std::memory_order_relaxed);

Suppose D is executing while one of its normal strong predecessors finishes:

Runtime::schedule(D):
2 -> 0

A finishes:
0 -> size_t(-1)

Then when the explicitly scheduled invocation of D completes:

D.join_counter.fetch_add(2);

the counter becomes logically:

-1 + 2 = 1

which preserves the fact that A has already finished.

If this were instead:

D.join_counter.store(2);

then the decrement caused by A would be overwritten, and the counter would incorrectly become 2.

Is this the main reason fetch_add is required here?

I also have a related question about activation semantics.

Continuing the example above, after the explicitly scheduled invocation of D finishes, the counter becomes 1. When B later finishes:

1 -> 0

the normal dependency path may schedule D again.

So D may execute once because of Runtime::schedule(D) and later execute again because its normal strong dependencies become satisfied.

Is this intentional semantics of Runtime::schedule?

In other words, is the intended model:

1. Runtime::schedule(task) creates an additional execution of an active task, independently of its normal dependency-triggered execution;
2. fetch_add(strong_dependencies) preserves concurrent dependency-counter updates that occurred while that explicit execution was running;
3. fetch_add is not intended to prevent duplicate/overlapping activations of the same node.

The comment mentions pipeline as an example:

// user-level call on "invoke" may explicitly schedule
// this task again (e.g., pipeline)

I noticed that Pipeline also maintains its own per-cell counters:

_lines[line][pipe].join_counter

while its line tasks are scheduled through NonpreemptiveRuntime::schedule.

So I am also wondering whether pipeline is only an example showing that invoke() may modify task scheduling state, rather than a direct example where a non-zero Node::_join_counter specifically requires this fetch_add.

Could you clarify the intended invariant of Node::_join_counter around:

normal dependency scheduling
Runtime::schedule
task invocation
join-counter restoration

and the exact race that fetch_add is designed to handle?

Thanks!