| 	Locking scheme used for directory operations is based on two | 
 | kinds of locks - per-inode (->i_mutex) and per-filesystem | 
 | (->s_vfs_rename_mutex). | 
 |  | 
 | 	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 | 
 | rules: | 
 | 	* 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. | 
 | Proof: | 
 |  | 
 | 	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 | 
 | (see above). | 
 |  | 
 | 	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 | 
 | case. | 
 |  | 
 | 	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. |