Ordering finalizers in the SemiSpace GC
After a collection, the SemiSpace GC should call the finalizers on some of the objects that have one and that have become unreachable. Basically, if there is a reference chain from an object a to an object b then it should not call the finalizer for b immediately, but just keep b alive and try again to call its finalizer after the next collection.
This basic idea fails when there are cycles. It's not a good idea to keep the objects alive forever or to never call any of the finalizers. The model we came up with is that in this case, we could just call the finalizer of one of the objects in the cycle -- but only, of course, if there are no other objects outside the cycle that has a finalizer and a reference to the cycle.
More precisely, given the graph of references between objects:
for each strongly connected component C of the graph: if C has at least one object with a finalizer: if there is no object outside C which has a finalizer and indirectly references the objects in C: mark one of the objects of C that has a finalizer copy C and all objects it references to the new space for each marked object: detach the finalizer (so that it's not called more than once) call the finalizer
During deal_with_objects_with_finalizers(), each object x can be in 4 possible states:
state[x] == 0: unreachable state[x] == 1: (temporary state, see below) state[x] == 2: reachable from any finalizer state[x] == 3: alive
Initially, objects are in state 0 or 3 depending on whether they have been copied or not by the regular sweep done just before. The invariant is that if there is a reference from x to y, then state[y] >= state[x].
The state 2 is used for objects that are reachable from a finalizer but that may be in the same strongly connected component than the finalizer. The state of these objects goes to 3 when we prove that they can be reached from a finalizer which is definitely not in the same strongly connected component. Finalizers on objects with state 3 must not be called.
Let closure(x) be the list of objects reachable from x, including x itself. Pseudo-code (high-level) to get the list of marked objects:
marked =  for x in objects_with_finalizers: if state[x] != 0: continue marked.append(x) for y in closure(x): if state[y] == 0: state[y] = 2 elif state[y] == 2: state[y] = 3 for x in marked: assert state[x] >= 2 if state[x] != 2: marked.remove(x)
This does the right thing independently on the order in which the objects_with_finalizers are enumerated. First assume that [x1, .., xn] are all in the same unreachable strongly connected component; no object with finalizer references this strongly connected component from outside. Then:
- when x1 is processed, state[x1] == .. == state[xn] == 0 independently of whatever else we did before. So x1 gets marked and we set state[x1] = .. = state[xn] = 2.
- when x2, ... xn are processed, their state is != 0 so we do nothing.
- in the final loop, only x1 is marked and state[x1] == 2 so it stays marked.
Now, let's assume that x1 and x2 are not in the same strongly connected component and there is a reference path from x1 to x2. Then:
- if x1 is enumerated before x2, then x2 is in closure(x1) and so its state gets at least >= 2 when we process x1. When we process x2 later we just skip it ("continue" line) and so it doesn't get marked.
- if x2 is enumerated before x1, then when we process x2 we mark it and set its state to >= 2 (before x2 is in closure(x2)), and then when we process x1 we set state[x2] == 3. So in the final loop x2 gets removed from the "marked" list.
I think that it proves that the algorithm is doing what we want.
The next step is to remove the use of closure() in the algorithm in such a way that the new algorithm has a reasonable performance -- linear in the number of objects whose state it manipulates:
marked =  for x in objects_with_finalizers: if state[x] != 0: continue marked.append(x) recursing on the objects y starting from x: if state[y] == 0: state[y] = 1 follow y's children recursively elif state[y] == 2: state[y] = 3 follow y's children recursively else: don't need to recurse inside y recursing on the objects y starting from x: if state[y] == 1: state[y] = 2 follow y's children recursively else: don't need to recurse inside y for x in marked: assert state[x] >= 2 if state[x] != 2: marked.remove(x)
In this algorithm we follow the children of each object at most 3 times, when the state of the object changes from 0 to 1 to 2 to 3. In a visit that doesn't change the state of an object, we don't follow its children recursively.
In practice, in the SemiSpace, Generation and Hybrid GCs, we can encode the 4 states with a single extra bit in the header:
state is_forwarded? bit set? bit set in the copy? 0 no no n/a 1 no yes n/a 2 yes yes yes 3 yes whatever no
So the loop above that does the transition from state 1 to state 2 is really just a copy(x) followed by scan_copied(). We must also clear the bit in the copy at the end, to clean up before the next collection (which means recursively bumping the state from 2 to 3 in the final loop).
In the MiniMark GC, the objects don't move (apart from when they are copied out of the nursery), but we use the flag GCFLAG_VISITED to mark objects that survive, so we can also have a single extra bit for finalizers:
state GCFLAG_VISITED GCFLAG_FINALIZATION_ORDERING 0 no no 1 no yes 2 yes yes 3 yes no