[RFC tip/locking/lockdep v6 01/20] lockdep/Documention: Recursive read lock detection reasoning

[Boqun Feng <boqun.feng@gmail.com>]

This patch add the documentation piece for the reasoning of deadlock
detection related to recursive read lock. The following sections are
added:

*	Explain what is a recursive read lock, and what deadlock cases
	they could introduce.

*	Introduce the notations for different types of dependencies, and
	the definition of strong paths.

*	Proof for a closed strong path is both sufficient and necessary
	for deadlock detections with recursive read locks involved. The
	proof could also explain why we call the path "strong"

Signed-off-by: Boqun Feng <boqun.feng@gmail.com>
---
 Documentation/locking/lockdep-design.txt | 178 +++++++++++++++++++++++++++++++
 1 file changed, 178 insertions(+)

diff --git a/Documentation/locking/lockdep-design.txt b/Documentation/locking/lockdep-design.txt
index 9de1c158d44c..6bb9e90e2c4f 100644
--- a/Documentation/locking/lockdep-design.txt
+++ b/Documentation/locking/lockdep-design.txt
@@ -284,3 +284,181 @@ Run the command and save the output, then compare against the output from
 a later run of this command to identify the leakers.  This same output
 can also help you find situations where runtime lock initialization has
 been omitted.
+
+Recursive read locks:
+---------------------
+
+Lockdep now is equipped with deadlock detection for recursive read locks.
+
+Recursive read locks, as their name indicates, are the locks able to be
+acquired recursively. Unlike non-recursive read locks, recursive read locks
+only get blocked by current write lock *holders* other than write lock
+*waiters*, for example:
+
+	TASK A:			TASK B:
+
+	read_lock(X);
+
+				write_lock(X);
+
+	read_lock(X);
+
+is not a deadlock for recursive read locks, as while the task B is waiting for
+the lock X, the second read_lock() doesn't need to wait because it's a recursive
+read lock. However if the read_lock() is non-recursive read lock, then the above
+case is a deadlock, because even if the write_lock() in TASK B can not get the
+lock, but it can block the second read_lock() in TASK A.
+
+Note that a lock can be a write lock (exclusive lock), a non-recursive read
+lock (non-recursive shared lock) or a recursive read lock (recursive shared
+lock), depending on the lock operations used to acquire it (more specifically,
+the value of the 'read' parameter for lock_acquire()). In other words, a single
+lock instance has three types of acquisition depending on the acquisition
+functions: exclusive, non-recursive read, and recursive read.
+
+To be concise, we call that write locks and non-recursive read locks as
+"non-recursive" locks and recursive read locks as "recursive" locks.
+
+Recursive locks don't block each other, while non-recursive locks do (this is
+even true for two non-recursive read locks). A non-recursive lock can block the
+corresponding recursive lock, and vice versa.
+
+A deadlock case with recursive locks involved is as follow:
+
+	TASK A:			TASK B:
+
+	read_lock(X);
+				read_lock(Y);
+	write_lock(Y);
+				write_lock(X);
+
+Task A is waiting for task B to read_unlock() Y and task B is waiting for task
+A to read_unlock() X.
+
+Dependency types and strong dependency paths:
+---------------------------------------------
+In order to detect deadlocks as above, lockdep needs to track different dependencies.
+There are 4 categories for dependency edges in the lockdep graph:
+
+1) -(NN)->: non-recursive to non-recursive dependency. "X -(NN)-> Y" means
+            X -> Y and both X and Y are non-recursive locks.
+
+2) -(RN)->: recursive to non-recursive dependency. "X -(RN)-> Y" means
+            X -> Y and X is recursive read lock and Y is non-recursive lock.
+
+3) -(NR)->: non-recursive to recursive dependency, "X -(NR)-> Y" means
+            X -> Y and X is non-recursive lock and Y is recursive lock.
+
+4) -(RR)->: recursive to recursive dependency, "X -(RR)-> Y" means
+            X -> Y and both X and Y are recursive locks.
+
+Note that given two locks, they may have multiple dependencies between them, for example:
+
+	TASK A:
+
+	read_lock(X);
+	write_lock(Y);
+	...
+
+	TASK B:
+
+	write_lock(X);
+	write_lock(Y);
+
+, we have both X -(RN)-> Y and X -(NN)-> Y in the dependency graph.
+
+We use -(*N)-> for edges that is either -(RN)-> or -(NN)->, the similar for -(N*)->,
+-(*R)-> and -(R*)->
+
+A "path" is a series of conjunct dependency edges in the graph. And we define a
+"strong" path, which indicates the strong dependency throughout each dependency
+in the path, as the path that doesn't have two conjunct edges (dependencies) as
+-(*R)-> and -(R*)->. In other words, a "strong" path is a path from a lock
+walking to another through the lock dependencies, and if X -> Y -> Z in the
+path (where X, Y, Z are locks), if the walk from X to Y is through a -(NR)-> or
+-(RR)-> dependency, the walk from Y to Z must not be through a -(RN)-> or
+-(RR)-> dependency, otherwise it's not a strong path.
+
+We will see why the path is called "strong" in next section.
+
+Recursive Read Deadlock Detection:
+----------------------------------
+
+We now prove two things:
+
+Lemma 1:
+
+If there is a closed strong path (i.e. a strong cirle), then there is a
+combination of locking sequences that causes deadlock. I.e. a strong circle is
+sufficient for deadlock detection.
+
+Lemma 2:
+
+If there is no closed strong path (i.e. strong cirle), then there is no
+combination of locking sequences that could cause deadlock. I.e.  strong
+circles are necessary for deadlock detection.
+
+With these two Lemmas, we can easily say a closed strong path is both sufficient
+and necessary for deadlocks, therefore a closed strong path is equivalent to
+deadlock possibility. As a closed strong path stands for a dependency chain that
+could cause deadlocks, so we call it "strong", considering there are dependency
+circles that won't cause deadlocks.
+
+Proof for sufficiency (Lemma 1):
+
+Let's say we have a strong cirlce:
+
+	L1 -> L2 ... -> Ln -> L1
+
+, which means we have dependencies:
+
+	L1 -> L2
+	L2 -> L3
+	...
+	Ln-1 -> Ln
+	Ln -> L1
+
+We now can construct a combination of locking sequences that cause deadlock:
+
+Firstly let's make one CPU/task get the L1 in L1 -> L2, and then another get
+the L2 in L2 -> L3, and so on. After this, all of the Lx in Lx -> Lx+1 are
+held by different CPU/tasks.
+
+And then because we have L1 -> L2, so the holder of L1 is going to acquire L2
+in L1 -> L2, however since L2 is already held by another CPU/task, plus L1 ->
+L2 and L2 -> L3 are not *R and R* (the definition of strong), therefore the
+holder of L1 can not get L2, it has to wait L2's holder to release.
+
+Moreover, we can have a similar conclusion for L2's holder: it has to wait L3's
+holder to release, and so on. We now can proof that Lx's holder has to wait for
+Lx+1's holder to release, and note that Ln+1 is L1, so we have a circular
+waiting scenario and nobody can get progress, therefore a deadlock.
+
+Proof for necessary (Lemma 2):
+
+Lemma 2 is equivalent to: If there is a deadlock scenario, then there must be a
+strong circle in the dependency graph.
+
+According to Wikipedia[1], if there is a deadlock, then there must be a circular
+waiting scenario, means there are N CPU/tasks, where CPU/task P1 is waiting for
+a lock held by P2, and P2 is waiting for a lock held by P3, ... and Pn is waiting
+for a lock held by P1. Let's name the lock Px is waiting as Lx, so since P1 is waiting
+for L1 and holding Ln, so we will have Ln -> L1 in the dependency graph. Similarly,
+we have L1 -> L2, L2 -> L3, ..., Ln-1 -> Ln in the dependency graph, which means we
+have a circle:
+
+	Ln -> L1 -> L2 -> ... -> Ln
+
+, and now let's prove the circle is strong:
+
+For a lock Lx, Px contributes the dependency Lx-1 -> Lx and Px+1 contributes
+the dependency Lx -> Lx+1, and since Px is waiting for Px+1 to release Lx,
+so Lx can not be both recursive in Lx -> Lx+1 and Lx-1 -> Lx, because recursive
+locks don't block each other, therefore Lx-1 -> Lx and Lx -> Lx+1 can not be a
+-(*R)-> -(R*)-> pair, and this is true for any lock in the circle, therefore,
+the circle is strong.
+
+References:
+-----------
+[1]: https://en.wikipedia.org/wiki/Deadlock
+[2]: Shibu, K. (2009). Intro To Embedded Systems (1st ed.). Tata McGraw-Hill
-- 
2.16.2