interval-tree: Add a utility to iterate over spans in an interval tree

The span iterator travels over the indexes of the interval_tree, not the
nodes, and classifies spans of indexes as either 'used' or 'hole'.

'used' spans are fully covered by nodes in the tree and 'hole' spans have
no node intersecting the span.

This is done greedily such that spans are maximally sized and every
iteration step switches between used/hole.

As an example a trivial allocator can be written as:

for (interval_tree_span_iter_first(&span, itree, 0, ULONG_MAX);
!interval_tree_span_iter_done(&span);
interval_tree_span_iter_next(&span))
if (span.is_hole &&
span.last_hole - span.start_hole >= allocation_size - 1)
return span.start_hole;

With all the tricky boundary conditions handled by the library code.

The following iommufd patches have several algorithms for its overlapping
node interval trees that are significantly simplified with this kind of
iteration primitive. As it seems generally useful, put it into lib/.

Link: https://lore.kernel.org/r/3-v6-a196d26f289e+11787-iommufd_jgg@nvidia.com
Reviewed-by: Kevin Tian <kevin.tian@intel.com>
Reviewed-by: Eric Auger <eric.auger@redhat.com>
Tested-by: Nicolin Chen <nicolinc@nvidia.com>
Tested-by: Yi Liu <yi.l.liu@intel.com>
Tested-by: Lixiao Yang <lixiao.yang@intel.com>
Tested-by: Matthew Rosato <mjrosato@linux.ibm.com>
Signed-off-by: Jason Gunthorpe <jgg@nvidia.com>

treewide: Add SPDX license identifier for missed files

Add SPDX license identifiers to all files which:

- Have no license information of any form

- Have EXPORT_.*_SYMBOL_GPL inside which was used in the
initial scan/conversion to ignore the file

These files fall under the project license, GPL v2 only. The resulting SPDX
license identifier is:

GPL-2.0-only

Signed-off-by: Thomas Gleixner <tglx@linutronix.de>
Signed-off-by: Greg Kroah-Hartman <gregkh@linuxfoundation.org>

lib/interval_tree.c: simplify includes

The file uses nothing from init.h, and also doesn't need the full module.h
machinery; export.h is sufficient. The latter requires the user to ensure
compiler.h is included, so do that explicitly instead of relying on some
other header pulling it in.

Signed-off-by: Rasmus Villemoes <linux@rasmusvillemoes.dk>
Signed-off-by: Andrew Morton <akpm@linux-foundation.org>
Signed-off-by: Linus Torvalds <torvalds@linux-foundation.org>

lib: Export interval_tree

lib/interval_tree.c provides a simple interface for an interval-tree
(an augmented red-black tree) but is only built when testing the generic
macros for building interval-trees. For drivers with modest needs,
export the simple interval-tree library as is.

v2: Lots of help from Michel Lespinasse to only compile the code
as required:
- make INTERVAL_TREE a config option
- make INTERVAL_TREE_TEST select the library functions
and sanitize the filenames & Makefile
- prepare interval_tree for being built as a module if required

Signed-off-by: Chris Wilson <chris@chris-wilson.co.uk>
Cc: Michel Lespinasse <walken@google.com>
Cc: 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>
Cc: Andrew Morton <akpm@linux-foundation.org>
Reviewed-by: Michel Lespinasse <walken@google.com>
[Acked for inclusion via drm/i915 by Andrew Morton.]
[danvet: switch to _GPL as per the mailing list discussion.]
Signed-off-by: Daniel Vetter <daniel.vetter@ffwll.ch>

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>

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>

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>