[PATCH 10/17] locking/lockdep: Support read-write lock's deadlock detection

[Yuyang Du]

A read-write lock is different from an exclusive lock only in that there
can be concurrent read locks, while a write lock is essentially the same
as an exclusive lock.

Read-write lock has not been well supported for deadlock detection so
far. This patch series designs and implements an algorithm to add this
important missing feature to lockdep.

To articulate the algorithm plainly, lets first give an abstract of the
problem statement. And, to make the problem simple and easy to
describe, recursive-read locks are not considered; they will be covered
later, and actually recursive-read lock is very easy if the read-lock
problem is solved.

Waiting relations in a circular fashion are at the heart of a deadlock:
a circle is universally *necessary* for any deadlock, albeit not
*sufficient* with read-write locks. A deadlock circle can be arbitrarily
long with many tasks contributing some arcs. But no matter how long the
circle is, it has to complete with a final arc, so the problem to solve
can be stated as:

Lemma #1
--------

  Detecing deadlock is to find when such a circle is going to complete
  at the *final* arc.

Assume there are n tasks contribute to that circle, denoted as T_1, T_2,
..., T_n, these tasks can be grouped as (T_1, ..., T_n-1) and T_n. And
by combining the former virtually, we get a big T1 and T2 (with task
numbers adjusted). This essentially means:

Lemma #2
--------

  Two tasks can virtually represent any situation with any number of
  tasks to check for deadlock.

Actually, how long the circle is does not really matter since the
problem as stated is what a difference the final missing arc can make:
deadlock or not; therefore, we need a just few locks that are enough to
represent all the possibilities. And this leads to:

Lemma #3
--------

  Any deadlock scenario can be converted to an ABBA deadlock.

where AB comes from T1 and BA from T2 (T1 and T2 are made by Lemma #2),
which says any other associated locks in the graph are not critical or
necessary and thus may be ignored. For example:

    T1        T2
    --        --

    L1        L7
    L2        L2

    A         B
    L3        L3
    L4        L8
    B         A    [Deadlock]

    L5
    L6

from deadlock perspective is equivalent to an ABBA:

    T1        T2
    --        --

    A         B
    B         A    [Deadlock]

Despite the lemmas, three facts are relevant to the problem: (a) with a
new arc, determining whether it completes a circle is an easy task, (b)
a new direct arc (a direct dependency) can introduce a number of
indirect arcs (indirect dependencies), and (c) checking all the
additional arcs (direct and indirect) efficiently is not so easy since
lock operations are frequent and lock graph can be gigantic. Actually,
if it is free to check any number of arcs, deadlock detection even with
read-write locks is fairly easy. That said performance is what the real
difficulty is, so a good algorithm should not only be self-evident that
it does solve the problem but also do so at low cost.

Here we try a start to solve it!

Having grasped the problem statement, we are good to proceed to a
divide-and-conquer approach to the solution: the entire problem is
broken down into a comprehensive list of simple and abstract problem
cases to solve, and if each and every one of them is solved, the entire
problem is solved.

The division is based on the type of the final arc or dependency in T2.
Based on Lemma #2, we use only two tasks in the following discussion.
And based on Lemma #3, these cases are all ABBAs. To be concise, the
following symbol R stands for read lock, W stands for write lock or
exclusive lock, and X stands for either R or W.

---------------------------------------------------------------
When the final dependency is ended with read lock and read lock
---------------------------------------------------------------

Case #1:

    T1        T2
    --        --

    W1        R2
    W2        R1   [Deadlock]

Case #2:

    T1        T2

    X1        R2
    R2        R1   [No deadlock]

------------------------------------------------------
When the final dependency is write lock and write lock
------------------------------------------------------

Case #3:

    T1        T2
    --        --

    X1        W2
    X2        W1   [Deadlock]

-----------------------------------------------------
When the final dependency is read lock and write lock
-----------------------------------------------------

Note that the final dependency is ended with write lock and read lock is
essentially the same as this one so that case is omitted.

Case #4:

    T1        T2
    --        --

    X1        R2
    W2        W1   [Deadlock]

Case #5:

    T1        T2
    --        --

    X1        R2
    R2        W1   [No deadlock]

Solving the above cases (no false positive or false negative) is
actually fairly easy to do; we therefore have our first *Simple
Algorithm*:

----------------
Simple Algorithm
----------------

Step 1
------

Keep track of each dependency's read or write ends. There is a
combination of four types:

   - read -> read
   - read -> write
   - write -> read
   - write -> write

Step 2
------

Redundancy check (as to whether adding a dependency into graph) for a
direct dependency needs to be beefed up considering dependency's read-
or write-ended types: a direct dependency is redundant to an indirect
dependency only if their ends have the same types. However, for
simplicity, direct dependencies can be added right away and if the
dependency to add already exists, the dependency can simply be
"upgraded" update the end type towards more exclusive (the exlusiveness
increases from recursive read -> read -> write).

Step 3
------

Traverse the dependency graph to find whether a deadlock circle can be
formed by adding a new direct dependency. There can be circles that are
not deadlock. In order to find a deadlock circle efficiently, the new
dependency's read lock or read locks if existent can *start* from or/and
*end* to write-ended dependences correspondingly. As a result, Step 3
can avoid the following false negative case easily for example:

Case #6:

    T1        T2
    --        --

    R1
    R2

   (R1 R2 released)

    W1        R2
    W2        R1   [Deadlock]

*Simple Algorithm* done loosely described.

I wish we lived in a fairy-tale world that the problem has been solved
so easily, but the reality is not. Huge false negatives owing to
indirect dependencies could appear, which is illustrated as the
following case to further solve:

Case #7:

    T1        T2
    --        --

    X1        X3
    R2        R2
    X3        X1   [Deadlock]

where X1's and X3's in the two tasks create a deadlock scenario (each may
be one of the the deadlock cases above). When checking direct dependency
R2 -> X1, there is no obvious deadlock using our *Simple Algorithm*,
however, under the hood the actual deadlock is formed after R2
introduces an indirect dependency X3 -> X1, which could comfortably be
missed.

To detect deadlock scenario like Case #7, a naive option is to check all
additional indirect dependencies, but this option would be so
inefficient to do and thus is simply passed. To find an efficient
solution instead, lets first contrive a no-deadlock Case #8 for
comparison (which is essentially rewritten from Case #5).

Case #8:

    T1        T2
    --        --

    X1
    X3        R2
    R2        X1   [No deadlock]

Having considered Case #7 and Case #8, a final working algorithm can be
formulated:

---------------
Final Algorithm
---------------

This *Final Algorithm* is beefed up from Simple Algorithm using the
following lemmas:

Lemma #4
--------

  The direct dependency R2 -> X1 that serves in the path from X3 -> X1 is
  *critical*.

Although the actual deadlock in Case #7 cannot be easily found by our
Simple Algorithm, however, by strengthening the algorithm somehow the
deadlock *definitely* can be found from the direct dependency (i.e., R2
-> X1 in Case #7). In other words, the critical direct dependency (a
final arc) suffices to find any deadlock if there is a deadlock,
otherwise there is no deadlock. As a matter of fact, after a false
deadlock (R2 -> X1 -> R2), if the search continues the true deadlock (R2
-> X1 -> R2 -> X3 -> R2) will eventually be taken out of the hood.

Lemma #5
--------

  Missed in Case #8, the game changer to Case #7 is that it has X3 in T2
  whereas Case #8 does not.

Having considered this, our *Final Algorithm* can be adjusted from
*Simple Algorithm* by adding:

(a). Continue searching the graph to find a new circle.

(b). In the new circle, if previous locks in T2's stack (or chain) are in
     it and then check whether the circle is indeed a deadlock. This is
     done by checking each newly introduced indirect dependency (such as
     X3 -> X1 in Case #7) according to our Simple Algorithm as before.

(c). If a deadlock is found then the algorithm is done, otherwise go to
     (a) unless the entire graph is traversed.

Lemma #6
--------

  Lemma #5 nicely raises a question whether a previous lock involved
  indirect dependency in T2 is *necessary*. The answer is yes, otherwise
  our *Simple Algorithm* has already solved the problem.

Lemma #7
--------

  It is also natual to ask whether the indirect dependencies in T2 only
  is *sufficient*: what if the indirect dependency (partly) has
  dependencies from T1. The answer is yes too.

Because Lemma #2 and Lemma #3 say that any deadlock is an ABBA so that
T1 can only contribute an AB and T2 must have a BA. Since we assumed T1
has no deadlock and Lemma #4 says the new dependency is *critical*, then
any deadlock formed by new direct or indirect dependencies introduced in
T2 (which is the BA part) will definitely be found with *Simple
Algorithm* or *Final Algorithm* respectively.

This is perhaps the most subtle and difficult part of this algorithm. To
test Lemma #7 holds true, one may try to contrive a case based on the
Case #8 or freely to generate a deadlock case if possible.

Anyway, any new cases are welcome. Cases matter in this algorithm
because as stated before, this algorithm solves the read-write lock
deadlock detection problem by having solved all the contrived cases (be
it deadlock or no deadlock). And if a case is not covered here, it
likely will defeat this algorithm, but if otherwise this algorithm just
works sound and complete.

*Final Algorithm* done loosely described.

Signed-off-by: Yuyang Du <duyuyang@xxxxxxxxx>
---
 kernel/locking/lockdep.c | 133 ++++++++++++++++++++++++++++++++++++++++++-----
 1 file changed, 120 insertions(+), 13 deletions(-)

diff --git a/kernel/locking/lockdep.c b/kernel/locking/lockdep.c
index fed5d11..26690f88 100644
--- a/kernel/locking/lockdep.c
+++ b/kernel/locking/lockdep.c
@@ -85,6 +85,7 @@
  */
 static arch_spinlock_t lockdep_lock = (arch_spinlock_t)__ARCH_SPIN_LOCK_UNLOCKED;
 static struct task_struct *lockdep_selftest_task_struct;
+static bool inside_selftest(void);
 
 static int graph_lock(void)
 {
@@ -1788,13 +1789,16 @@ static inline void set_lock_type2(struct lock_list *lock, int read)
  * lead to <target>. If it can, there is a circle when adding
  * <target> -> <src> dependency.
  *
+ * If there is a circle, there may be a deadlock.
+ *
  * Print an error and return 0 if it does.
  */
 static noinline int
-check_deadlock_graph(struct held_lock *src, struct held_lock *target,
-		     struct lock_trace *trace)
+check_deadlock_graph(struct task_struct *curr, struct held_lock *src,
+		     struct held_lock *target, struct lock_trace *trace)
 {
-	int ret;
+	int ret, i;
+	bool init = true;
 	struct lock_list *uninitialized_var(target_entry);
 	struct lock_list src_entry = {
 		.class = hlock_class(src),
@@ -1803,19 +1807,122 @@ static inline void set_lock_type2(struct lock_list *lock, int read)
 
 	debug_atomic_inc(nr_cyclic_checks);
 
-	ret = check_path(hlock_class(target), &src_entry, &target_entry, true);
+	while (true) {
+		ret = check_path(hlock_class(target), &src_entry,
+				 &target_entry, init);
+		init = false;
+
+		/* Found a circle, is it deadlock? */
+		if (unlikely(!ret)) {
+			struct lock_list *parent;
 
-	if (unlikely(!ret)) {
-		if (!trace->nr_entries) {
 			/*
-			 * If save_trace fails here, the printing might
-			 * trigger a WARN but because of the !nr_entries it
-			 * should not do bad things.
+			 * Note that we have an assumption that no lock
+			 * class can be both read and recursive-read.
+			 *
+			 * Check this direct dependency.
+			 *
+			 * Step 1: next's lock type and source dependency's
+			 * lock type are exclusive, no?
+			 *
+			 * Find the first dependency after source dependency.
 			 */
-			save_trace(trace);
-		}
+			parent = find_next_dep_in_path(&src_entry, target_entry);
+			if (!parent) {
+				DEBUG_LOCKS_WARN_ON(1);
+				return -3;
+			}
+
+			if (src->read & get_lock_type1(parent))
+				goto cont;
+
+			/*
+			 * Step 2: prev's lock type and target dependency's
+			 * lock type are exclusive, yes?
+			 */
+			if (!(target->read & get_lock_type2(target_entry)))
+				goto print;
+
+			/*
+			 * Check indirect dependency from even further
+			 * previous lock.
+			 */
+			for (i = 0; i < curr->lockdep_depth; i++) {
+				struct held_lock *prev = curr->held_locks + i;
+
+				if (prev->irq_context != src->irq_context)
+					continue;
 
-		print_circular_bug(&src_entry, target_entry, src, target);
+				/*
+				 * We arrived at the same prev lock in this
+				 * direct dependency checking.
+				 */
+				if (prev == target)
+					break;
+
+				/*
+				 * Since the src lock (the next lock to
+				 * acquire) is neither recursive nor nested
+				 * lock, so this prev class cannot be src
+				 * class, then does the path have this
+				 * previous lock?
+				 *
+				 * With read locks it would be possible a
+				 * lock can reoccur in a path. For example:
+				 *
+				 * -> RL1 -> RL2 -> RL3 -> RL1 -> ...
+				 *
+				 * and for another three examples:
+				 *
+				 * Ex1: -> RL1 -> WL2 -> RL3 -> RL1
+				 * Ex2; -> WL1 -> RL2 -> RL3 -> WL1
+				 * Ex3: -> RL1 -> RL2 -> RL3 -> WL1
+				 *
+				 * This can result in that a path may
+				 * encounter a lock twice or more, but we
+				 * used the breadth-first search algorithm
+				 * that will find the shortest path,
+				 * which means that this path can not have
+				 * the same (middle) lock multiple times.
+				 * However, is Ex3 a problem?
+				 */
+				parent = find_lock_in_path(hlock_class(prev),
+							   target_entry);
+				if (parent) {
+					/*
+					 * Yes, we have a candidiate indirect
+					 * dependency to check.
+					 *
+					 * Again step 2: new prev's lock
+					 * type and its dependency in graph
+					 * are exclusive, yes?
+					 *
+					 * Note that we don't need step 1
+					 * again.
+					 */
+					if (!(prev->read & get_lock_type2(parent)))
+						goto print;
+				}
+			}
+cont:
+			mark_lock_unaccessed(target_entry);
+			continue;
+print:
+			if (!trace->nr_entries) {
+				/*
+				 * If save_trace fails here, the printing
+				 * might trigger a WARN but because of the
+				 * !nr_entries it should not do bad things.
+				 */
+				save_trace(trace);
+			}
+
+			print_circular_bug(&src_entry, target_entry,
+					   src, target);
+			break;
+		} else
+			/* The graph is all traversed or an error occurred */
+			break;
 	}
 
 	return ret;
@@ -2510,7 +2617,7 @@ static inline void inc_chains(void)
 	 * MAX_CIRCULAR_QUEUE_SIZE) which keeps track of a breadth of nodes
 	 * in the graph whose neighbours are to be checked.
 	 */
-	ret = check_deadlock_graph(next, prev, trace);
+	ret = check_deadlock_graph(curr, next, prev, trace);
 	if (unlikely(ret <= 0))
 		return 0;
 
-- 
1.8.3.1