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+ Locking scheme used for directory operations is based on two
+kinds of locks - per-inode (->i_mutex) and per-filesystem
+ For our purposes all operations fall in 5 classes:
+1) read access. Locking rules: caller locks directory we are accessing.
+2) object creation. Locking rules: same as above.
+3) object removal. Locking rules: caller locks parent, finds victim,
+locks victim and calls the method.
+4) rename() that is _not_ cross-directory. Locking rules: caller locks
+the parent, finds source and target, if target already exists - locks it
+and then calls the method.
+5) link creation. Locking rules:
+ * lock parent
+ * check that source is not a directory
+ * lock source
+ * call the method.
+6) cross-directory rename. The trickiest in the whole bunch. Locking
+ * lock the filesystem
+ * lock parents in "ancestors first" order.
+ * find source and target.
+ * if old parent is equal to or is a descendent of target
+ fail with -ENOTEMPTY
+ * if new parent is equal to or is a descendent of source
+ fail with -ELOOP
+ * if target exists - lock it.
+ * call the method.
+The rules above obviously guarantee that all directories that are going to be
+read, modified or removed by method will be locked by caller.
+If no directory is its own ancestor, the scheme above is deadlock-free.
+ First of all, at any moment we have a partial ordering of the
+objects - A < B iff A is an ancestor of B.
+ That ordering can change. However, the following is true:
+(1) if object removal or non-cross-directory rename holds lock on A and
+ attempts to acquire lock on B, A will remain the parent of B until we
+ acquire the lock on B. (Proof: only cross-directory rename can change
+ the parent of object and it would have to lock the parent).
+(2) if cross-directory rename holds the lock on filesystem, order will not
+ change until rename acquires all locks. (Proof: other cross-directory
+ renames will be blocked on filesystem lock and we don't start changing
+ the order until we had acquired all locks).
+(3) any operation holds at most one lock on non-directory object and
+ that lock is acquired after all other locks. (Proof: see descriptions
+ of operations).
+ Now consider the minimal deadlock. Each process is blocked on
+attempt to acquire some lock and already holds at least one lock. Let's
+consider the set of contended locks. First of all, filesystem lock is
+not contended, since any process blocked on it is not holding any locks.
+Thus all processes are blocked on ->i_mutex.
+ Non-directory objects are not contended due to (3). Thus link
+creation can't be a part of deadlock - it can't be blocked on source
+and it means that it doesn't hold any locks.
+ Any contended object is either held by cross-directory rename or
+has a child that is also contended. Indeed, suppose that it is held by
+operation other than cross-directory rename. Then the lock this operation
+is blocked on belongs to child of that object due to (1).
+ It means that one of the operations is cross-directory rename.
+Otherwise the set of contended objects would be infinite - each of them
+would have a contended child and we had assumed that no object is its
+own descendent. Moreover, there is exactly one cross-directory rename
+ Consider the object blocking the cross-directory rename. One
+of its descendents is locked by cross-directory rename (otherwise we
+would again have an infinite set of contended objects). But that
+means that cross-directory rename is taking locks out of order. Due
+to (2) the order hadn't changed since we had acquired filesystem lock.
+But locking rules for cross-directory rename guarantee that we do not
+try to acquire lock on descendent before the lock on ancestor.
+Contradiction. I.e. deadlock is impossible. Q.E.D.
+ These operations are guaranteed to avoid loop creation. Indeed,
+the only operation that could introduce loops is cross-directory rename.
+Since the only new (parent, child) pair added by rename() is (new parent,
+source), such loop would have to contain these objects and the rest of it
+would have to exist before rename(). I.e. at the moment of loop creation
+rename() responsible for that would be holding filesystem lock and new parent
+would have to be equal to or a descendent of source. But that means that
+new parent had been equal to or a descendent of source since the moment when
+we had acquired filesystem lock and rename() would fail with -ELOOP in that
+ While this locking scheme works for arbitrary DAGs, it relies on
+ability to check that directory is a descendent of another object. Current
+implementation assumes that directory graph is a tree. This assumption is
+also preserved by all operations (cross-directory rename on a tree that would
+not introduce a cycle will leave it a tree and link() fails for directories).
+ Notice that "directory" in the above == "anything that might have
+children", so if we are going to introduce hybrid objects we will need
+either to make sure that link(2) doesn't work for them or to make changes
+in is_subdir() that would make it work even in presence of such beasts.