[REVISED DOCUMENT] lockdep: Crossrelease feature documentation

[Byungchul Park]

This document describes the concept of crossrelease feature.

Signed-off-by: Byungchul Park <byungchul.park@xxxxxxx>
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+Crossrelease
+============
+
+Started by Byungchul Park <byungchul.park@xxxxxxx>
+
+Contents:
+
+ (*) Background
+
+     - What causes deadlock
+     - How lockdep works
+
+ (*) Limitation
+
+     - Limit lockdep
+     - Pros from the limitation
+     - Cons from the limitation
+     - Relax the limitation
+
+ (*) Crossrelease
+
+     - Introduce crossrelease
+     - Introduce commit
+
+ (*) Implementation
+
+     - Data structures
+     - How crossrelease works
+
+ (*) Optimizations
+
+     - Avoid duplication
+     - Lockless for hot paths
+
+ (*) APPENDIX A: What lockdep does to work aggresively
+
+ (*) APPENDIX B: How to avoid adding false dependencies
+
+
+==========
+Background
+==========
+
+What causes deadlock
+--------------------
+
+A deadlock occurs when a context is waiting for an event to happen,
+which is impossible because another (or the) context who can trigger the
+event is also waiting for another (or the) event to happen, which is
+also impossible due to the same reason.
+
+For example:
+
+   A context going to trigger event C is waiting for event A to happen.
+   A context going to trigger event A is waiting for event B to happen.
+   A context going to trigger event B is waiting for event C to happen.
+
+A deadlock occurs when these three wait operations run at the same time,
+because event C cannot be triggered if event A does not happen, which in
+turn cannot be triggered if event B does not happen, which in turn
+cannot be triggered if event C does not happen. After all, no event can
+be triggered since any of them never meets its condition to wake up.
+
+A dependency might exist between two waiters and a deadlock might happen
+due to an incorrect releationship between dependencies. Thus, we must
+define what a dependency is first. A dependency exists between them if:
+
+   1. There are two waiters waiting for each event at a given time.
+   2. The only way to wake up each waiter is to trigger its event.
+   3. Whether one can be woken up depends on whether the other can.
+
+Each wait in the example creates its dependency like:
+
+   Event C depends on event A.
+   Event A depends on event B.
+   Event B depends on event C.
+
+   NOTE: Precisely speaking, a dependency is one between whether a
+   waiter for an event can be woken up and whether another waiter for
+   another event can be woken up. However from now on, we will describe
+   a dependency as if it's one between an event and another event for
+   simplicity.
+
+And they form circular dependencies like:
+
+    -> C -> A -> B -
+   /                \
+   \                /
+    ----------------
+
+   where 'A -> B' means that event A depends on event B.
+
+Such circular dependencies lead to a deadlock since no waiter can meet
+its condition to wake up as described.
+
+CONCLUSION
+
+Circular dependencies cause a deadlock.
+
+
+How lockdep works
+-----------------
+
+Lockdep tries to detect a deadlock by checking dependencies created by
+lock operations, acquire and release. Waiting for a lock corresponds to
+waiting for an event, and releasing a lock corresponds to triggering an
+event in the previous section.
+
+In short, lockdep does:
+
+   1. Detect a new dependency.
+   2. Add the dependency into a global graph.
+   3. Check if that makes dependencies circular.
+   4. Report a deadlock or its possibility if so.
+
+For example, consider a graph built by lockdep that looks like:
+
+   A -> B -
+           \
+            -> E
+           /
+   C -> D -
+
+   where A, B,..., E are different lock classes.
+
+Lockdep will add a dependency into the graph on detection of a new
+dependency. For example, it will add a dependency 'E -> C' when a new
+dependency between lock E and lock C is detected. Then the graph will be:
+
+       A -> B -
+               \
+                -> E -
+               /      \
+    -> C -> D -        \
+   /                   /
+   \                  /
+    ------------------
+
+   where A, B,..., E are different lock classes.
+
+This graph contains a subgraph which demonstrates circular dependencies:
+
+                -> E -
+               /      \
+    -> C -> D -        \
+   /                   /
+   \                  /
+    ------------------
+
+   where C, D and E are different lock classes.
+
+This is the condition under which a deadlock might occur. Lockdep
+reports it on detection after adding a new dependency. This is the way
+how lockdep works.
+
+CONCLUSION
+
+Lockdep detects a deadlock or its possibility by checking if circular
+dependencies were created after adding each new dependency.
+
+
+==========
+Limitation
+==========
+
+Limit lockdep
+-------------
+
+Limiting lockdep to work on only typical locks e.g. spin locks and
+mutexes, which are released within the acquire context, the
+implementation becomes simple but its capacity for detection becomes
+limited. Let's check pros and cons in next section.
+
+
+Pros from the limitation
+------------------------
+
+Given the limitation, when acquiring a lock, locks in a held_locks
+cannot be released if the context cannot acquire it so has to wait to
+acquire it, which means all waiters for the locks in the held_locks are
+stuck. It's an exact case to create dependencies between each lock in
+the held_locks and the lock to acquire.
+
+For example:
+
+   CONTEXT X
+   ---------
+   acquire A
+   acquire B /* Add a dependency 'A -> B' */
+   release B
+   release A
+
+   where A and B are different lock classes.
+
+When acquiring lock A, the held_locks of CONTEXT X is empty thus no
+dependency is added. But when acquiring lock B, lockdep detects and adds
+a new dependency 'A -> B' between lock A in the held_locks and lock B.
+They can be simply added whenever acquiring each lock.
+
+And data required by lockdep exists in a local structure, held_locks
+embedded in task_struct. Forcing to access the data within the context,
+lockdep can avoid racy problems without explicit locks while handling
+the local data.
+
+Lastly, lockdep only needs to keep locks currently being held, to build
+a dependency graph. However, relaxing the limitation, it needs to keep
+even locks already released, because a decision whether they created
+dependencies might be long-deferred.
+
+To sum up, we can expect several advantages from the limitation:
+
+   1. Lockdep can easily identify a dependency when acquiring a lock.
+   2. Races are avoidable while accessing local locks in a held_locks.
+   3. Lockdep only needs to keep locks currently being held.
+
+CONCLUSION
+
+Given the limitation, the implementation becomes simple and efficient.
+
+
+Cons from the limitation
+------------------------
+
+Given the limitation, lockdep is applicable only to typical locks. For
+example, page locks for page access or completions for synchronization
+cannot work with lockdep.
+
+Can we detect deadlocks below, under the limitation?
+
+Example 1:
+
+   CONTEXT X	   CONTEXT Y	   CONTEXT Z
+   ---------	   ---------	   ----------
+		   mutex_lock A
+   lock_page B
+		   lock_page B
+				   mutex_lock A /* DEADLOCK */
+				   unlock_page B held by X
+		   unlock_page B
+		   mutex_unlock A
+				   mutex_unlock A
+
+   where A and B are different lock classes.
+
+No, we cannot.
+
+Example 2:
+
+   CONTEXT X		   CONTEXT Y
+   ---------		   ---------
+			   mutex_lock A
+   mutex_lock A
+			   wait_for_complete B /* DEADLOCK */
+   complete B
+			   mutex_unlock A
+   mutex_unlock A
+
+   where A is a lock class and B is a completion variable.
+
+No, we cannot.
+
+CONCLUSION
+
+Given the limitation, lockdep cannot detect a deadlock or its
+possibility caused by page locks or completions.
+
+
+Relax the limitation
+--------------------
+
+Under the limitation, things to create dependencies are limited to
+typical locks. However, synchronization primitives like page locks and
+completions, which are allowed to be released in any context, also
+create dependencies and can cause a deadlock. So lockdep should track
+these locks to do a better job. We have to relax the limitation for
+these locks to work with lockdep.
+
+Detecting dependencies is very important for lockdep to work because
+adding a dependency means adding an opportunity to check whether it
+causes a deadlock. The more lockdep adds dependencies, the more it
+thoroughly works. Thus Lockdep has to do its best to detect and add as
+many true dependencies into a graph as possible.
+
+For example, considering only typical locks, lockdep builds a graph like:
+
+   A -> B -
+           \
+            -> E
+           /
+   C -> D -
+
+   where A, B,..., E are different lock classes.
+
+On the other hand, under the relaxation, additional dependencies might
+be created and added. Assuming additional 'FX -> C' and 'E -> GX' are
+added thanks to the relaxation, the graph will be:
+
+         A -> B -
+                 \
+                  -> E -> GX
+                 /
+   FX -> C -> D -
+
+   where A, B,..., E, FX and GX are different lock classes, and a suffix
+   'X' is added on non-typical locks.
+
+The latter graph gives us more chances to check circular dependencies
+than the former. However, it might suffer performance degradation since
+relaxing the limitation, with which design and implementation of lockdep
+can be efficient, might introduce inefficiency inevitably. So lockdep
+should provide two options, strong detection and efficient detection.
+
+Choosing efficient detection:
+
+   Lockdep works with only locks restricted to be released within the
+   acquire context. However, lockdep works efficiently.
+
+Choosing strong detection:
+
+   Lockdep works with all synchronization primitives. However, lockdep
+   suffers performance degradation.
+
+CONCLUSION
+
+Relaxing the limitation, lockdep can add additional dependencies giving
+additional opportunities to check circular dependencies.
+
+
+============
+Crossrelease
+============
+
+Introduce crossrelease
+----------------------
+
+In order to allow lockdep to handle additional dependencies by what
+might be released in any context, namely 'crosslock', we have to be able
+to identify those created by crosslocks. The proposed 'crossrelease'
+feature provoides a way to do that.
+
+Crossrelease feature has to do:
+
+   1. Identify dependencies created by crosslocks.
+   2. Add the dependencies into a dependency graph.
+
+That's all. Once a meaningful dependency is added into graph, then
+lockdep would work with the graph as it did. The most important thing
+crossrelease feature has to do is to correctly identify and add true
+dependencies into the global graph.
+
+A dependency e.g. 'A -> B' can be identified only in the A's release
+context because a decision required to identify the dependency can be
+made only in the release context. That is to decide whether A can be
+released so that a waiter for A can be woken up. It cannot be made in
+other than the A's release context.
+
+It's no matter for typical locks because each acquire context is same as
+its release context, thus lockdep can decide whether a lock can be
+released in the acquire context. However for crosslocks, lockdep cannot
+make the decision in the acquire context but has to wait until the
+release context is identified.
+
+Therefore, deadlocks by crosslocks cannot be detected just when it
+happens, because those cannot be identified until the crosslocks are
+released. However, deadlock possibilities can be detected and it's very
+worth. See 'APPENDIX A' section to check why.
+
+CONCLUSION
+
+Using crossrelease feature, lockdep can work with what might be released
+in any context, namely crosslock.
+
+
+Introduce commit
+----------------
+
+Since crossrelease defers the work adding true dependencies of
+crosslocks until they are actually released, crossrelease has to queue
+all acquisitions which might create dependencies with the crosslocks.
+Then it identifies dependencies using the queued data in batches at a
+proper time. We call it 'commit'.
+
+There are four types of dependencies:
+
+1. TT type: 'typical lock A -> typical lock B'
+
+   Just when acquiring B, lockdep can see it's in the A's release
+   context. So the dependency between A and B can be identified
+   immediately. Commit is unnecessary.
+
+2. TC type: 'typical lock A -> crosslock BX'
+
+   Just when acquiring BX, lockdep can see it's in the A's release
+   context. So the dependency between A and BX can be identified
+   immediately. Commit is unnecessary, too.
+
+3. CT type: 'crosslock AX -> typical lock B'
+
+   When acquiring B, lockdep cannot identify the dependency because
+   there's no way to know if it's in the AX's release context. It has
+   to wait until the decision can be made. Commit is necessary.
+
+4. CC type: 'crosslock AX -> crosslock BX'
+
+   When acquiring BX, lockdep cannot identify the dependency because
+   there's no way to know if it's in the AX's release context. It has
+   to wait until the decision can be made. Commit is necessary.
+   But, handling CC type is not implemented yet. It's a future work.
+
+Lockdep can work without commit for typical locks, but commit step is
+necessary once crosslocks are involved. Introducing commit, lockdep
+performs three steps. What lockdep does in each step is:
+
+1. Acquisition: For typical locks, lockdep does what it originally did
+   and queues the lock so that CT type dependencies can be checked using
+   it at the commit step. For crosslocks, it saves data which will be
+   used at the commit step and increases a reference count for it.
+
+2. Commit: No action is reauired for typical locks. For crosslocks,
+   lockdep adds CT type dependencies using the data saved at the
+   acquisition step.
+
+3. Release: No changes are required for typical locks. When a crosslock
+   is released, it decreases a reference count for it.
+
+CONCLUSION
+
+Crossrelease introduces commit step to handle dependencies of crosslocks
+in batches at a proper time.
+
+
+==============
+Implementation
+==============
+
+Data structures
+---------------
+
+Crossrelease introduces two main data structures.
+
+1. hist_lock
+
+   This is an array embedded in task_struct, for keeping lock history so
+   that dependencies can be added using them at the commit step. Since
+   it's local data, it can be accessed locklessly in the owner context.
+   The array is filled at the acquisition step and consumed at the
+   commit step. And it's managed in circular manner.
+
+2. cross_lock
+
+   One per lockdep_map exists. This is for keeping data of crosslocks
+   and used at the commit step.
+
+
+How crossrelease works
+----------------------
+
+It's the key of how crossrelease works, to defer necessary works to an
+appropriate point in time and perform in at once at the commit step.
+Let's take a look with examples step by step, starting from how lockdep
+works without crossrelease for typical locks.
+
+   acquire A /* Push A onto held_locks */
+   acquire B /* Push B onto held_locks and add 'A -> B' */
+   acquire C /* Push C onto held_locks and add 'B -> C' */
+   release C /* Pop C from held_locks */
+   release B /* Pop B from held_locks */
+   release A /* Pop A from held_locks */
+
+   where A, B and C are different lock classes.
+
+   NOTE: This document assumes that readers already understand how
+   lockdep works without crossrelease thus omits details. But there's
+   one thing to note. Lockdep pretends to pop a lock from held_locks
+   when releasing it. But it's subtly different from the original pop
+   operation because lockdep allows other than the top to be poped.
+
+In this case, lockdep adds 'the top of held_locks -> the lock to acquire'
+dependency every time acquiring a lock.
+
+After adding 'A -> B', a dependency graph will be:
+
+   A -> B
+
+   where A and B are different lock classes.
+
+And after adding 'B -> C', the graph will be:
+
+   A -> B -> C
+
+   where A, B and C are different lock classes.
+
+Let's performs commit step even for typical locks to add dependencies.
+Of course, commit step is not necessary for them, however, it would work
+well because this is a more general way.
+
+   acquire A
+   /*
+    * Queue A into hist_locks
+    *
+    * In hist_locks: A
+    * In graph: Empty
+    */
+
+   acquire B
+   /*
+    * Queue B into hist_locks
+    *
+    * In hist_locks: A, B
+    * In graph: Empty
+    */
+
+   acquire C
+   /*
+    * Queue C into hist_locks
+    *
+    * In hist_locks: A, B, C
+    * In graph: Empty
+    */
+
+   commit C
+   /*
+    * Add 'C -> ?'
+    * Answer the following to decide '?'
+    * What has been queued since acquire C: Nothing
+    *
+    * In hist_locks: A, B, C
+    * In graph: Empty
+    */
+
+   release C
+
+   commit B
+   /*
+    * Add 'B -> ?'
+    * Answer the following to decide '?'
+    * What has been queued since acquire B: C
+    *
+    * In hist_locks: A, B, C
+    * In graph: 'B -> C'
+    */
+
+   release B
+
+   commit A
+   /*
+    * Add 'A -> ?'
+    * Answer the following to decide '?'
+    * What has been queued since acquire A: B, C
+    *
+    * In hist_locks: A, B, C
+    * In graph: 'B -> C', 'A -> B', 'A -> C'
+    */
+
+   release A
+
+   where A, B and C are different lock classes.
+
+In this case, dependencies are added at the commit step as described.
+
+After commits for A, B and C, the graph will be:
+
+   A -> B -> C
+
+   where A, B and C are different lock classes.
+
+   NOTE: A dependency 'A -> C' is optimized out.
+
+We can see the former graph built without commit step is same as the
+latter graph built using commit steps. Of course the former way leads to
+earlier finish for building the graph, which means we can detect a
+deadlock or its possibility sooner. So the former way would be prefered
+when possible. But we cannot avoid using the latter way for crosslocks.
+
+Let's look at how commit steps work for crosslocks. In this case, the
+commit step is performed only on crosslock AX as real. And it assumes
+that the AX release context is different from the AX acquire context.
+
+   BX RELEASE CONTEXT		   BX ACQUIRE CONTEXT
+   ------------------		   ------------------
+				   acquire A
+				   /*
+				    * Push A onto held_locks
+				    * Queue A into hist_locks
+				    *
+				    * In held_locks: A
+				    * In hist_locks: A
+				    * In graph: Empty
+				    */
+
+				   acquire BX
+				   /*
+				    * Add 'the top of held_locks -> BX'
+				    *
+				    * In held_locks: A
+				    * In hist_locks: A
+				    * In graph: 'A -> BX'
+				    */
+
+   ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
+   It must be guaranteed that the following operations are seen after
+   acquiring BX globally. It can be done by things like barrier.
+   ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
+
+   acquire C
+   /*
+    * Push C onto held_locks
+    * Queue C into hist_locks
+    *
+    * In held_locks: C
+    * In hist_locks: C
+    * In graph: 'A -> BX'
+    */
+
+   release C
+   /*
+    * Pop C from held_locks
+    *
+    * In held_locks: Empty
+    * In hist_locks: C
+    * In graph: 'A -> BX'
+    */
+				   acquire D
+				   /*
+				    * Push D onto held_locks
+				    * Queue D into hist_locks
+				    * Add 'the top of held_locks -> D'
+				    *
+				    * In held_locks: A, D
+				    * In hist_locks: A, D
+				    * In graph: 'A -> BX', 'A -> D'
+				    */
+   acquire E
+   /*
+    * Push E onto held_locks
+    * Queue E into hist_locks
+    *
+    * In held_locks: E
+    * In hist_locks: C, E
+    * In graph: 'A -> BX', 'A -> D'
+    */
+
+   release E
+   /*
+    * Pop E from held_locks
+    *
+    * In held_locks: Empty
+    * In hist_locks: D, E
+    * In graph: 'A -> BX', 'A -> D'
+    */
+				   release D
+				   /*
+				    * Pop D from held_locks
+				    *
+				    * In held_locks: A
+				    * In hist_locks: A, D
+				    * In graph: 'A -> BX', 'A -> D'
+				    */
+   commit BX
+   /*
+    * Add 'BX -> ?'
+    * What has been queued since acquire BX: C, E
+    *
+    * In held_locks: Empty
+    * In hist_locks: D, E
+    * In graph: 'A -> BX', 'A -> D',
+    *           'BX -> C', 'BX -> E'
+    */
+
+   release BX
+   /*
+    * In held_locks: Empty
+    * In hist_locks: D, E
+    * In graph: 'A -> BX', 'A -> D',
+    *           'BX -> C', 'BX -> E'
+    */
+				   release A
+				   /*
+				    * Pop A from held_locks
+				    *
+				    * In held_locks: Empty
+				    * In hist_locks: A, D
+				    * In graph: 'A -> BX', 'A -> D',
+				    *           'BX -> C', 'BX -> E'
+				    */
+
+   where A, BX, C,..., E are different lock classes, and a suffix 'X' is
+   added on crosslocks.
+
+Crossrelease considers all acquisitions after acqiuring BX are
+candidates which might create dependencies with BX. True dependencies
+will be determined when identifying the release context of BX. Meanwhile,
+all typical locks are queued so that they can be used at the commit step.
+And then two dependencies 'BX -> C' and 'BX -> E' are added at the
+commit step when identifying the release context.
+
+The final graph will be, with crossrelease:
+
+               -> C
+              /
+       -> BX -
+      /       \
+   A -         -> E
+      \
+       -> D
+
+   where A, BX, C,..., E are different lock classes, and a suffix 'X' is
+   added on crosslocks.
+
+However, the final graph will be, without crossrelease:
+
+   A -> D
+
+   where A and D are different lock classes.
+
+The former graph has three more dependencies, 'A -> BX', 'BX -> C' and
+'BX -> E' giving additional opportunities to check if they cause
+deadlocks. This way lockdep can detect a deadlock or its possibility
+caused by crosslocks.
+
+CONCLUSION
+
+We checked how crossrelease works with several examples.
+
+
+=============
+Optimizations
+=============
+
+Avoid duplication
+-----------------
+
+Crossrelease feature uses a cache like what lockdep already uses for
+dependency chains, but this time it's for caching CT type dependencies.
+Once that dependency is cached, the same will never be added again.
+
+
+Lockless for hot paths
+----------------------
+
+To keep all locks for later use at the commit step, crossrelease adopts
+a local array embedded in task_struct, which makes access to the data
+lockless by forcing it to happen only within the owner context. It's
+like how lockdep handles held_locks. Lockless implmentation is important
+since typical locks are very frequently acquired and released.
+
+
+=================================================
+APPENDIX A: What lockdep does to work aggresively
+=================================================
+
+A deadlock actually occurs when all wait operations creating circular
+dependencies run at the same time. Even though they don't, a potential
+deadlock exists if the problematic dependencies exist. Thus it's
+meaningful to detect not only an actual deadlock but also its potential
+possibility. The latter is rather valuable. When a deadlock occurs
+actually, we can identify what happens in the system by some means or
+other even without lockdep. However, there's no way to detect possiblity
+without lockdep unless the whole code is parsed in head. It's terrible.
+Lockdep does the both, and crossrelease only focuses on the latter.
+
+Whether or not a deadlock actually occurs depends on several factors.
+For example, what order contexts are switched in is a factor. Assuming
+circular dependencies exist, a deadlock would occur when contexts are
+switched so that all wait operations creating the dependencies run
+simultaneously. Thus to detect a deadlock possibility even in the case
+that it has not occured yet, lockdep should consider all possible
+combinations of dependencies, trying to:
+
+1. Use a global dependency graph.
+
+   Lockdep combines all dependencies into one global graph and uses them,
+   regardless of which context generates them or what order contexts are
+   switched in. Aggregated dependencies are only considered so they are
+   prone to be circular if a problem exists.
+
+2. Check dependencies between classes instead of instances.
+
+   What actually causes a deadlock are instances of lock. However,
+   lockdep checks dependencies between classes instead of instances.
+   This way lockdep can detect a deadlock which has not happened but
+   might happen in future by others but the same class.
+
+3. Assume all acquisitions lead to waiting.
+
+   Although locks might be acquired without waiting which is essential
+   to create dependencies, lockdep assumes all acquisitions lead to
+   waiting since it might be true some time or another.
+
+CONCLUSION
+
+Lockdep detects not only an actual deadlock but also its possibility,
+and the latter is more valuable.
+
+
+==================================================
+APPENDIX B: How to avoid adding false dependencies
+==================================================
+
+Remind what a dependency is. A dependency exists if:
+
+   1. There are two waiters waiting for each event at a given time.
+   2. The only way to wake up each waiter is to trigger its event.
+   3. Whether one can be woken up depends on whether the other can.
+
+For example:
+
+   acquire A
+   acquire B /* A dependency 'A -> B' exists */
+   release B
+   release A
+
+   where A and B are different lock classes.
+
+A depedency 'A -> B' exists since:
+
+   1. A waiter for A and a waiter for B might exist when acquiring B.
+   2. Only way to wake up each is to release what it waits for.
+   3. Whether the waiter for A can be woken up depends on whether the
+      other can. IOW, TASK X cannot release A if it fails to acquire B.
+
+For another example:
+
+   TASK X			   TASK Y
+   ------			   ------
+				   acquire AX
+   acquire B /* A dependency 'AX -> B' exists */
+   release B
+   release AX held by Y
+
+   where AX and B are different lock classes, and a suffix 'X' is added
+   on crosslocks.
+
+Even in this case involving crosslocks, the same rule can be applied. A
+depedency 'AX -> B' exists since:
+
+   1. A waiter for AX and a waiter for B might exist when acquiring B.
+   2. Only way to wake up each is to release what it waits for.
+   3. Whether the waiter for AX can be woken up depends on whether the
+      other can. IOW, TASK X cannot release AX if it fails to acquire B.
+
+Let's take a look at more complicated example:
+
+   TASK X			   TASK Y
+   ------			   ------
+   acquire B
+   release B
+   fork Y
+				   acquire AX
+   acquire C /* A dependency 'AX -> C' exists */
+   release C
+   release AX held by Y
+
+   where AX, B and C are different lock classes, and a suffix 'X' is
+   added on crosslocks.
+
+Does a dependency 'AX -> B' exist? Nope.
+
+Two waiters are essential to create a dependency. However, waiters for
+AX and B to create 'AX -> B' cannot exist at the same time in this
+example. Thus the dependency 'AX -> B' cannot be created.
+
+It would be ideal if the full set of true ones can be considered. But
+we can ensure nothing but what actually happened. Relying on what
+actually happens at runtime, we can anyway add only true ones, though
+they might be a subset of true ones. It's similar to how lockdep works
+for typical locks. There might be more true dependencies than what
+lockdep has detected in runtime. Lockdep has no choice but to rely on
+what actually happens. Crossrelease also relies on it.
+
+CONCLUSION
+
+Relying on what actually happens, lockdep can avoid adding false
+dependencies.
-- 
1.9.1