rbtree: cache leftmost node internally

rbtree: cache leftmost node internally

Patch series "rbtree: Cache leftmost node internally", v4.

A series to extending rbtrees to internally cache the leftmost node such
that we can have fast overlap check optimization for all interval tree
users[1].  The benefits of this series are that:

(i)   Unify users that do internal leftmost node caching.
(ii)  Optimize all interval tree users.
(iii) Convert at least two new users (epoll and procfs) to the new interface.

This patch (of 16):

Red-black tree semantics imply that nodes with smaller or greater (or
equal for duplicates) keys always be to the left and right,
respectively.  For the kernel this is extremely evident when considering
our rb_first() semantics.  Enabling lookups for the smallest node in the
tree in O(1) can save a good chunk of cycles in not having to walk down
the tree each time.  To this end there are a few core users that
explicitly do this, such as the scheduler and rtmutexes.  There is also
the desire for interval trees to have this optimization allowing faster
overlap checking.

This patch introduces a new 'struct rb_root_cached' which is just the
root with a cached pointer to the leftmost node.  The reason why the
regular rb_root was not extended instead of adding a new structure was
that this allows the user to have the choice between memory footprint
and actual tree performance.  The new wrappers on top of the regular
rb_root calls are:

 - rb_first_cached(cached_root) -- which is a fast replacement
     for rb_first.

 - rb_insert_color_cached(node, cached_root, new)

 - rb_erase_cached(node, cached_root)

In addition, augmented cached interfaces are also added for basic
insertion and deletion operations; which becomes important for the
interval tree changes.

With the exception of the inserts, which adds a bool for updating the
new leftmost, the interfaces are kept the same.  To this end, porting rb
users to the cached version becomes really trivial, and keeping current
rbtree semantics for users that don't care about the optimization
requires zero overhead.

Link: http://lkml.kernel.org/r/20170719014603.19029-2-dave@stgolabs.net
Signed-off-by: Davidlohr Bueso <dbueso@suse.de>
Reviewed-by: Jan Kara <jack@suse.cz>
Acked-by: Peter Zijlstra (Intel) <peterz@infradead.org>
Signed-off-by: Andrew Morton <akpm@linux-foundation.org>
Signed-off-by: Linus Torvalds <torvalds@linux-foundation.org>