In dup_mmap(), using __mt_dup() to duplicate the old maple tree and then
directly replacing the entries of VMAs in the new maple tree can result in
better performance.  __mt_dup() uses DFS pre-order to duplicate the maple
tree, so it is efficient.

The average time complexity of __mt_dup() is O(n), where n is the number
of VMAs.  The proof of the time complexity is provided in the commit log
that introduces __mt_dup().  After duplicating the maple tree, each
element is traversed and replaced (ignoring the cases of deletion, which
are rare).  Since it is only a replacement operation for each element,
this process is also O(n).

Analyzing the exact time complexity of the previous algorithm is
challenging because each insertion can involve appending to a node,
pushing data to adjacent nodes, or even splitting nodes.  The frequency of
each action is difficult to calculate.  The worst-case scenario for a
single insertion is when the tree undergoes splitting at every level.  If
we consider each insertion as the worst-case scenario, we can determine
that the upper bound of the time complexity is O(n*log(n)), although this
is a loose upper bound.  However, based on the test data, it appears that
the actual time complexity is likely to be O(n).

As the entire maple tree is duplicated using __mt_dup(), if dup_mmap()
fails, there will be a portion of VMAs that have not been duplicated in
the maple tree.  To handle this, we mark the failure point with
XA_ZERO_ENTRY.  In exit_mmap(), if this marker is encountered, stop
releasing VMAs that have not been duplicated after this point.

There is a "spawn" in byte-unixbench[1], which can be used to test the
performance of fork().  I modified it slightly to make it work with
different number of VMAs.

Below are the test results.  The first row shows the number of VMAs.  The
second and third rows show the number of fork() calls per ten seconds,
corresponding to next-20231006 and the this patchset, respectively.  The
test results were obtained with CPU binding to avoid scheduler load
balancing that could cause unstable results.  There are still some
fluctuations in the test results, but at least they are better than the
original performance.

21     121   221    421    821    1621   3221   6421   12821  25621  51221
112100 76261 54227  34035  20195  11112  6017   3161   1606   802    393
114558 83067 65008  45824  28751  16072  8922   4747   2436   1233   599
2.19%  8.92% 19.88% 34.64% 42.37% 44.64% 48.28% 50.17% 51.68% 53.74% 52.42%

[1] https://github.com/kdlucas/byte-unixbench/tree/master

Link: https://lkml.kernel.org/r/20231027033845.90608-11-zhangpeng.00@bytedance.comSigned-off-by: Peng Zhang <zhangpeng.00@bytedance.com>
Suggested-by: Liam R. Howlett <Liam.Howlett@oracle.com>
Reviewed-by: Liam R. Howlett <Liam.Howlett@oracle.com>
Cc: Christian Brauner <brauner@kernel.org>
Cc: Jonathan Corbet <corbet@lwn.net>
Cc: Mateusz Guzik <mjguzik@gmail.com>
Cc: Mathieu Desnoyers <mathieu.desnoyers@efficios.com>
Cc: Matthew Wilcox <willy@infradead.org>
Cc: Michael S. Tsirkin <mst@redhat.com>
Cc: Mike Christie <michael.christie@oracle.com>
Cc: Nicholas Piggin <npiggin@gmail.com>
Cc: Peter Zijlstra <peterz@infradead.org>
Cc: Suren Baghdasaryan <surenb@google.com>
Signed-off-by: Andrew Morton <akpm@linux-foundation.org>