rbtree: add prio tree and interval tree tests

Patch 1 implements support for interval trees, on top of the augmented
rbtree API. It also adds synthetic tests to compare the performance of
interval trees vs prio trees. Short answers is that interval trees are
slightly faster (~25%) on insert/erase, and much faster (~2.4 - 3x)
on search. It is debatable how realistic the synthetic test is, and I have
not made such measurements yet, but my impression is that interval trees
would still come out faster.

Patch 2 uses a preprocessor template to make the interval tree generic,
and uses it as a replacement for the vma prio_tree.

Patch 3 takes the other prio_tree user, kmemleak, and converts it to use
a basic rbtree. We don't actually need the augmented rbtree support here
because the intervals are always non-overlapping.

Patch 4 removes the now-unused prio tree library.

Patch 5 proposes an additional optimization to rb_erase_augmented, now
providing it as an inline function so that the augmented callbacks can be
inlined in. This provides an additional 5-10% performance improvement
for the interval tree insert/erase benchmark. There is a maintainance cost
as it exposes augmented rbtree users to some of the rbtree library internals;
however I think this cost shouldn't be too high as I expect the augmented
rbtree will always have much less users than the base rbtree.

I should probably add a quick summary of why I think it makes sense to
replace prio trees with augmented rbtree based interval trees now.  One of
the drivers is that we need augmented rbtrees for Rik's vma gap finding
code, and once you have them, it just makes sense to use them for interval
trees as well, as this is the simpler and more well known algorithm.  prio
trees, in comparison, seem *too* clever: they impose an additional 'heap'
constraint on the tree, which they use to guarantee a faster worst-case
complexity of O(k+log N) for stabbing queries in a well-balanced prio
tree, vs O(k*log N) for interval trees (where k=number of matches,
N=number of intervals).  Now this sounds great, but in practice prio trees
don't realize this theorical benefit.  First, the additional constraint
makes them harder to update, so that the kernel implementation has to
simplify things by balancing them like a radix tree, which is not always
ideal.  Second, the fact that there are both index and heap properties
makes both tree manipulation and search more complex, which results in a
higher multiplicative time constant.  As it turns out, the simple interval
tree algorithm ends up running faster than the more clever prio tree.

This patch:

Add two test modules:

- prio_tree_test measures the performance of lib/prio_tree.c, both for
  insertion/removal and for stabbing searches

- interval_tree_test measures the performance of a library of equivalent
  functionality, built using the augmented rbtree support.

In order to support the second test module, lib/interval_tree.c is
introduced. It is kept separate from the interval_tree_test main file
for two reasons: first we don't want to provide an unfair advantage
over prio_tree_test by having everything in a single compilation unit,
and second there is the possibility that the interval tree functionality
could get some non-test users in kernel over time.

Signed-off-by: Michel Lespinasse <walken@google.com>
Cc: Rik van Riel <riel@redhat.com>
Cc: Hillf Danton <dhillf@gmail.com>
Cc: Peter Zijlstra <a.p.zijlstra@chello.nl>
Cc: Catalin Marinas <catalin.marinas@arm.com>
Cc: Andrea Arcangeli <aarcange@redhat.com>
Cc: David Woodhouse <dwmw2@infradead.org>
Signed-off-by: Andrew Morton <akpm@linux-foundation.org>
Signed-off-by: Linus Torvalds <torvalds@linux-foundation.org>

Conflicts:

	lib/Kconfig.debug
	lib/Makefile
mm: replace vma prio_tree with an interval tree

Implement an interval tree as a replacement for the VMA prio_tree.  The
algorithms are similar to lib/interval_tree.c; however that code can't be
directly reused as the interval endpoints are not explicitly stored in the
VMA.  So instead, the common algorithm is moved into a template and the
details (node type, how to get interval endpoints from the node, etc) are
filled in using the C preprocessor.

Once the interval tree functions are available, using them as a
replacement to the VMA prio tree is a relatively simple, mechanical job.

Signed-off-by: Michel Lespinasse <walken@google.com>
Cc: Rik van Riel <riel@redhat.com>
Cc: Hillf Danton <dhillf@gmail.com>
Cc: Peter Zijlstra <a.p.zijlstra@chello.nl>
Cc: Catalin Marinas <catalin.marinas@arm.com>
Cc: Andrea Arcangeli <aarcange@redhat.com>
Cc: David Woodhouse <dwmw2@infradead.org>
Signed-off-by: Andrew Morton <akpm@linux-foundation.org>
Signed-off-by: Linus Torvalds <torvalds@linux-foundation.org>

Conflicts:

	arch/parisc/kernel/cache.c
	arch/x86/mm/hugetlbpage.c
	include/linux/mm.h
	kernel/events/uprobes.c
	mm/Makefile
	mm/mmap.c
mm: interval tree updates

Update the generic interval tree code that was introduced in "mm: replace
vma prio_tree with an interval tree".

Changes:

- fixed 'endpoing' typo noticed by Andrew Morton

- replaced include/linux/interval_tree_tmpl.h, which was used as a
  template (including it automatically defined the interval tree
  functions) with include/linux/interval_tree_generic.h, which only
  defines a preprocessor macro INTERVAL_TREE_DEFINE(), which itself
  defines the interval tree functions when invoked. Now that is a very
  long macro which is unfortunate, but it does make the usage sites
  (lib/interval_tree.c and mm/interval_tree.c) a bit nicer than previously.

- make use of RB_DECLARE_CALLBACKS() in the INTERVAL_TREE_DEFINE() macro,
  instead of duplicating that code in the interval tree template.

- replaced vma_interval_tree_add(), which was actually handling the
  nonlinear and interval tree cases, with vma_interval_tree_insert_after()
  which handles only the interval tree case and has an API that is more
  consistent with the other interval tree handling functions.
  The nonlinear case is now handled explicitly in kernel/fork.c dup_mmap().

Signed-off-by: Michel Lespinasse <walken@google.com>
Cc: Andrea Arcangeli <aarcange@redhat.com>
Cc: Rik van Riel <riel@redhat.com>
Cc: Peter Zijlstra <a.p.zijlstra@chello.nl>
Cc: Daniel Santos <daniel.santos@pobox.com>
Cc: Hugh Dickins <hughd@google.com>
Signed-off-by: Andrew Morton <akpm@linux-foundation.org>
Signed-off-by: Linus Torvalds <torvalds@linux-foundation.org>

Conflicts:

	include/linux/interval_tree_tmpl.h
mm anon rmap: replace same_anon_vma linked list with an interval tree.

When a large VMA (anon or private file mapping) is first touched, which
will populate its anon_vma field, and then split into many regions through
the use of mprotect(), the original anon_vma ends up linking all of the
vmas on a linked list.  This can cause rmap to become inefficient, as we
have to walk potentially thousands of irrelevent vmas before finding the
one a given anon page might fall into.

By replacing the same_anon_vma linked list with an interval tree (where
each avc's interval is determined by its vma's start and last pgoffs), we
can make rmap efficient for this use case again.

While the change is large, all of its pieces are fairly simple.

Most places that were walking the same_anon_vma list were looking for a
known pgoff, so they can just use the anon_vma_interval_tree_foreach()
interval tree iterator instead.  The exception here is ksm, where the
page's index is not known.  It would probably be possible to rework ksm so
that the index would be known, but for now I have decided to keep things
simple and just walk the entirety of the interval tree there.

When updating vma's that already have an anon_vma assigned, we must take
care to re-index the corresponding avc's on their interval tree.  This is
done through the use of anon_vma_interval_tree_pre_update_vma() and
anon_vma_interval_tree_post_update_vma(), which remove the avc's from
their interval tree before the update and re-insert them after the update.
 The anon_vma stays locked during the update, so there is no chance that
rmap would miss the vmas that are being updated.

Signed-off-by: Michel Lespinasse <walken@google.com>
Cc: Andrea Arcangeli <aarcange@redhat.com>
Cc: Rik van Riel <riel@redhat.com>
Cc: Peter Zijlstra <a.p.zijlstra@chello.nl>
Cc: Daniel Santos <daniel.santos@pobox.com>
Cc: Hugh Dickins <hughd@google.com>
Signed-off-by: Andrew Morton <akpm@linux-foundation.org>
Signed-off-by: Linus Torvalds <torvalds@linux-foundation.org>

Conflicts:

	include/linux/mm.h
	include/linux/rmap.h
	mm/mmap.c
	mm/rmap.c
mm: add CONFIG_DEBUG_VM_RB build option

Add a CONFIG_DEBUG_VM_RB build option for the previously existing
DEBUG_MM_RB code.  Now that Andi Kleen modified it to avoid using
recursive algorithms, we can expose it a bit more.

Also extend this code to validate_mm() after stack expansion, and to check
that the vma's start and last pgoffs have not changed since the nodes were
inserted on the anon vma interval tree (as it is important that the nodes
be reindexed after each such update).

Signed-off-by: Michel Lespinasse <walken@google.com>
Cc: Andrea Arcangeli <aarcange@redhat.com>
Cc: Rik van Riel <riel@redhat.com>
Cc: Peter Zijlstra <a.p.zijlstra@chello.nl>
Cc: Daniel Santos <daniel.santos@pobox.com>
Cc: Hugh Dickins <hughd@google.com>
Signed-off-by: Andrew Morton <akpm@linux-foundation.org>
Signed-off-by: Linus Torvalds <torvalds@linux-foundation.org>
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>
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 10fd48f2376d
("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>

Conflicts:

	fs/proc/proc_sysctl.c
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>
rbtree: faster augmented rbtree manipulation

Introduce new augmented rbtree APIs that allow minimal recalculation of
augmented node information.

A new callback is added to the rbtree insertion and erase rebalancing
functions, to be called on each tree rotations. Such rotations preserve
the subtree's root augmented value, but require recalculation of the one
child that was previously located at the subtree root.

In the insertion case, the handcoded search phase must be updated to
maintain the augmented information on insertion, and then the rbtree
coloring/rebalancing algorithms keep it up to date.

In the erase case, things are more complicated since it is library
code that manipulates the rbtree in order to remove internal nodes.
This requires a couple additional callbacks to copy a subtree's
augmented value when a new root is stitched in, and to recompute
augmented values down the ancestry path when a node is removed from
the tree.

In order to preserve maximum speed for the non-augmented case,
we provide two versions of each tree manipulation function.
rb_insert_augmented() is the augmented equivalent of rb_insert_color(),
and rb_erase_augmented() is the augmented equivalent of rb_erase().

Signed-off-by: Michel Lespinasse <walken@google.com>
Acked-by: Rik van Riel <riel@redhat.com>
Cc: Peter Zijlstra <a.p.zijlstra@chello.nl>
Cc: Andrea Arcangeli <aarcange@redhat.com>
Cc: David Woodhouse <dwmw2@infradead.org>
Signed-off-by: Andrew Morton <akpm@linux-foundation.org>
Signed-off-by: Linus Torvalds <torvalds@linux-foundation.org>

Conflicts:

	Documentation/rbtree.txt
	lib/rbtree.c
	lib/rbtree_test.c