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The augmented rbtree helper functions are not exported to modules right
now.

(We have started using augmented rbtrees in the upcoming version of
drbd.)
Signed-off-by: Andreas Gruenbacher <agruen@linbit.com>
Signed-off-by: Linus Torvalds <torvalds@linux-foundation.org>

Reimplement augmented RB-trees without sprinkling extra branches
all over the RB-tree code (which lives in the scheduler hot path).

This approach is 'borrowed' from Fabio's BFQ implementation and
relies on traversing the rebalance path after the RB-tree-op to
correct the heap property for insertion/removal and make up for
the damage done by the tree rotations.

For insertion the rebalance path is trivially that from the new
node upwards to the root, for removal it is that from the deepest
node in the path from the to be removed node that will still
be around after the removal.

[ This patch also fixes a video driver regression reported by
  Ali Gholami Rudi - the memtype->subtree_max_end was updated
  incorrectly. ]
Acked-by: Suresh Siddha <suresh.b.siddha@intel.com>
Acked-by: Venkatesh Pallipadi <venki@google.com>
Signed-off-by: Peter Zijlstra <a.p.zijlstra@chello.nl>
Tested-by: Ali Gholami Rudi <ali@rudi.ir>
Cc: Fabio Checconi <fabio@gandalf.sssup.it>
Cc: "H. Peter Anvin" <hpa@zytor.com>
Cc: Andrew Morton <akpm@linux-foundation.org>
Cc: Linus Torvalds <torvalds@linux-foundation.org>
LKML-Reference: <1275414172.27810.27961.camel@twins>
Signed-off-by: Ingo Molnar <mingo@elte.hu>

Add support for augmented rbtrees in core rbtree code.

This will be used in subsequent patches, in x86 PAT code, which needs
interval trees to efficiently keep track of PAT ranges.
Signed-off-by: Venkatesh Pallipadi <venkatesh.pallipadi@intel.com>
LKML-Reference: <20100210232343.GA11465@linux-os.sc.intel.com>
Signed-off-by: Suresh Siddha <suresh.b.siddha@intel.com>
Signed-off-by: H. Peter Anvin <hpa@zytor.com>

Furthermore, notice that the initial checks:

	if (!node->rb_left)
		child = node->rb_right;
	else if (!node->rb_right)
		child = node->rb_left;
	else
	{
		...
	}
guarantee that old->rb_right is set in the final else branch, therefore
we can omit checking that again.
Signed-off-by: Wolfram Strepp <wstrepp@gmx.de>
Signed-off-by: Peter Zijlstra <a.p.zijlstra@chello.nl>
Signed-off-by: Andrew Morton <akpm@linux-foundation.org>
Signed-off-by: Linus Torvalds <torvalds@linux-foundation.org>

There are two cases when a node, having 2 childs, is erased:
'normal case': the successor is not the right-hand-child of the node to be erased
'special case': the successor is the right-hand child of the node to be erased

Here some ascii-art, with following symbols (referring to the code):
O: node to be deleted
N: the successor of O
P: parent of N
C: child of N
L: some other node

normal case:

               O                         N
              / \                       / \
             /   \                     /   \
            L     \                   L     \
           / \     P      ---->      / \     P
                  / \                       / \
                 /                         /
                N                         C
                 \                       / \
                  \
                   C
                  / \

special case:
              O|P                        N
              / \                       / \
             /   \                     /   \
            L     \                   L     \
           / \     N      ---->      /       C
                    \                       / \
                     \
                      C
                     / \

Notice that for the special case we don't have to reconnect C to N.
Signed-off-by: Wolfram Strepp <wstrepp@gmx.de>
Signed-off-by: Peter Zijlstra <a.p.zijlstra@chello.nl>
Signed-off-by: Andrew Morton <akpm@linux-foundation.org>
Signed-off-by: Linus Torvalds <torvalds@linux-foundation.org>

First, move some code around in order to make the next change more obvious.

[akpm@linux-foundation.org: coding-style fixes]
Signed-off-by: Peter Zijlstra <a.p.zijlstra@chello.nl>
Signed-off-by: Wolfram Strepp <wstrepp@gmx.de>
Signed-off-by: Andrew Morton <akpm@linux-foundation.org>
Signed-off-by: Linus Torvalds <torvalds@linux-foundation.org>

Tfour 4 redundant if-conditions in function __rb_erase_color() in
lib/rbtree.c are removed.

In pseudo-source-code, the structure of the code is as follows:

if ((!A || B) && (!C || D)) {
	.
	.
	.
} else {
	if (!C || D) {//if this is true, it implies: (A == true) && (B == false)
		if (A) {//hence this always evaluates to 'true'...
			.
		}
		.
		//at this point, C always becomes true, because of:
		__rb_rotate_right/left();
		//and:
		other = parent->rb_right/left;
	}
	.
	.
	if (C) {//...and this too !
		.
	}
}
Signed-off-by: Wolfram Strepp <wstrepp@gmx.de>
Acked-by: Peter Zijlstra <a.p.zijlstra@chello.nl>
Cc: Andrea Arcangeli <andrea@qumranet.com>
Signed-off-by: Andrew Morton <akpm@linux-foundation.org>
Signed-off-by: Linus Torvalds <torvalds@linux-foundation.org>

The 'rb_first()', 'rb_last()', 'rb_next()' and 'rb_prev()' calls
take a pointer to an RB node or RB root. They do not change the
pointed objects, so add a 'const' qualifier in order to make life
of the users of these functions easier.

Indeed, if I have my own constant pointer &const struct my_type *p,
and I call 'rb_next(&p->rb)', I get a GCC warning:

warning: passing argument 1 of ‘rb_next’ discards qualifiers from pointer target type
Signed-off-by: Artem Bityutskiy <Artem.Bityutskiy@nokia.com>
Signed-off-by: David Woodhouse <David.Woodhouse@intel.com>
Signed-off-by: Linus Torvalds <torvalds@linux-foundation.org>

The conditions got reserved. Also make rb_next() and rb_prev() check
for the empty condition.
Signed-off-by: Jens Axboe <axboe@suse.de>

Since rb_insert_color() is part of the _public_ API, while the others are
purely internal, switch to be consistent with that.
Signed-off-by: David Woodhouse <dwmw2@infradead.org>

We only used a single bit for colour information, so having a whole
machine word of space allocated for it was a bit wasteful. Instead,
store it in the lowest bit of the 'parent' pointer, since that was
always going to be aligned anyway.
Signed-off-by: David Woodhouse <dwmw2@infradead.org>

Observe rb_erase(), when the victim node 'old' has two children so
neither of the simple cases at the beginning are taken.

Observe that it effectively does an 'rb_next()' operation to find the
next (by value) node in the tree. That is; we go to the victim's
right-hand child and then follow left-hand pointers all the way
down the tree as far as we can until we find the next node 'node'. We
end up with 'node' being either the same immediate right-hand child of
'old', or one of its descendants on the far left-hand side.

For a start, we _know_ that 'node' has a parent. We can drop that check.

We also know that if 'node's parent is 'old', then 'node' is the
right-hand child of its parent. And that if 'node's parent is _not_
'old', then 'node' is the left-hand child of its parent.

So instead of checking for 'node->rb_parent == old' in one place and
also checking 'node's heritage separately when we're trying to change
its link from its parent, we can shuffle things around a bit and do
it like this...
Signed-off-by: David Woodhouse <dwmw2@infradead.org>

Initial git repository build. I'm not bothering with the full history,
even though we have it. We can create a separate "historical" git
archive of that later if we want to, and in the meantime it's about
3.2GB when imported into git - space that would just make the early
git days unnecessarily complicated, when we don't have a lot of good
infrastructure for it.

Let it rip!