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:
