rbtree: empty nodes have no color

Empty nodes have no color.  We can make use of this property to simplify
the code emitted by the RB_EMPTY_NODE and RB_CLEAR_NODE macros.  Also,
we can get rid of the rb_init_node function which had been introduced by
commit 88d19cf37952 ("timers: Add rb_init_node() to allow for stack
allocated rb nodes") to avoid some issue with the empty node's color not
being initialized.

I'm not sure what the RB_EMPTY_NODE checks in rb_prev() / rb_next() are
doing there, though.  axboe introduced them in commit
("rbtree: fixed reversed RB_EMPTY_NODE and rb_next/prev").  The way I
see it, the 'empty node' abstraction is only used by rbtree users to
flag nodes that they haven't inserted in any rbtree, so asking the
predecessor or successor of such nodes doesn't make any sense.

One final rb_init_node() caller was recently added in sysctl code to
implement faster sysctl name lookups.  This code doesn't make use of
RB_EMPTY_NODE at all, and from what I could see it only called
rb_init_node() under the mistaken assumption that such initialization was
required before node insertion.

[sfr@canb.auug.org.au: fix net/ceph/osd_client.c build]
Signed-off-by: Michel Lespinasse <walken@google.com>
Cc: Andrea Arcangeli <aarcange@redhat.com>
Acked-by: David Woodhouse <David.Woodhouse@intel.com>
Cc: Rik van Riel <riel@redhat.com>
Cc: Peter Zijlstra <a.p.zijlstra@chello.nl>
Cc: Daniel Santos <daniel.santos@pobox.com>
Cc: Jens Axboe <axboe@kernel.dk>
Cc: "Eric W. Biederman" <ebiederm@xmission.com>
Cc: John Stultz <john.stultz@linaro.org>
Signed-off-by: Stephen Rothwell <sfr@canb.auug.org.au>
Signed-off-by: Andrew Morton <akpm@linux-foundation.org>
Signed-off-by: Linus Torvalds <torvalds@linux-foundation.org>
Signed-off-by: Pranav Vashi <neobuddy89@gmail.com>
rbtree: move some implementation details from rbtree.h to rbtree.c

rbtree users must use the documented APIs to manipulate the tree
structure.  Low-level helpers to manipulate node colors and parenthood are
not part of that API, so move them to lib/rbtree.c

[dwmw2@infradead.org: fix jffs2 build issue due to renamed __rb_parent_color field]
Signed-off-by: Michel Lespinasse <walken@google.com>
Cc: Andrea Arcangeli <aarcange@redhat.com>
Acked-by: David Woodhouse <David.Woodhouse@intel.com>
Cc: Rik van Riel <riel@redhat.com>
Cc: Peter Zijlstra <a.p.zijlstra@chello.nl>
Cc: Daniel Santos <daniel.santos@pobox.com>
Cc: Jens Axboe <axboe@kernel.dk>
Cc: "Eric W. Biederman" <ebiederm@xmission.com>
Signed-off-by: David Woodhouse <David.Woodhouse@intel.com>
Signed-off-by: Andrew Morton <akpm@linux-foundation.org>
Signed-off-by: Linus Torvalds <torvalds@linux-foundation.org>
Signed-off-by: Pranav Vashi <neobuddy89@gmail.com>
rbtree: reference Documentation/rbtree.txt for usage instructions

I recently started looking at the rbtree code (with an eye towards
improving the augmented rbtree support, but I haven't gotten there yet).
I noticed a lot of possible speed improvements, which I am now proposing
in this patch set.

Patches 1-4 are preparatory: remove internal functions from rbtree.h so
that users won't be tempted to use them instead of the documented APIs,
clean up some incorrect usages I've noticed (in particular, with the
recently added fs/proc/proc_sysctl.c rbtree usage), reference the
documentation so that people have one less excuse to miss it, etc.

Patch 5 is a small module I wrote to check the rbtree performance.  It
creates 100 nodes with random keys and repeatedly inserts and erases them
from an rbtree.  Additionally, it has code to check for rbtree invariants
after each insert or erase operation.

Patches 6-12 is where the rbtree optimizations are done, and they touch
only that one file, lib/rbtree.c .  I am getting good results out of these
- in my small benchmark doing rbtree insertion (including search) and
erase, I'm seeing a 30% runtime reduction on Sandybridge E5, which is more
than I initially thought would be possible.  (the results aren't as
impressive on my two other test hosts though, AMD barcelona and Intel
Westmere, where I am seeing 14% runtime reduction only).  The code size -
both source (ommiting comments) and compiled - is also shorter after these
changes.  However, I do admit that the updated code is more arduous to
read - one big reason for that is the removal of the tree rotation
helpers, which added some overhead but also made it easier to reason about
things locally.  Overall, I believe this is an acceptable compromise,
given that this code doesn't get modified very often, and that I have good
tests for it.

Upon Peter's suggestion, I added comments showing the rtree configuration
before every rotation.  I think they help; however it's still best to have
a copy of the cormen/leiserson/rivest book when digging into this code.

This patch: reference Documentation/rbtree.txt for usage instructions

include/linux/rbtree.h included some basic usage instructions, while
Documentation/rbtree.txt had some more complete and easier to follow
instructions.  Replacing the former with a reference to the latter.

Signed-off-by: Michel Lespinasse <walken@google.com>
Cc: Andrea Arcangeli <aarcange@redhat.com>
Acked-by: David Woodhouse <David.Woodhouse@intel.com>
Cc: Rik van Riel <riel@redhat.com>
Cc: Peter Zijlstra <a.p.zijlstra@chello.nl>
Cc: Daniel Santos <daniel.santos@pobox.com>
Cc: Jens Axboe <axboe@kernel.dk>
Cc: "Eric W. Biederman" <ebiederm@xmission.com>
Signed-off-by: Andrew Morton <akpm@linux-foundation.org>
Signed-off-by: Linus Torvalds <torvalds@linux-foundation.org>
Signed-off-by: Pranav Vashi <neobuddy89@gmail.com>
rbtree: faster augmented rbtree manipulation & fs tune code