Re: [RFC PATCH v2] Introduce Hierarchical Per-CPU Counters

["Liam R. Howlett" <Liam.Howlett@oracle.com>]

* Matthew Wilcox <willy@infradead.org> [250408 13:03]:
> On Tue, Apr 08, 2025 at 09:37:18AM -0700, Christoph Lameter (Ampere) wrote:
> > > The hierarchical per-CPU counters propagate a sum approximation through
> > > a binary tree. When reaching the batch size, the carry is propagated
> > > through a binary tree which consists of log2(nr_cpu_ids) levels. The
> > > batch size for each level is twice the batch size of the prior level.
> > 
> > A binary tree? Could we do this N-way? Otherwise the tree will be 8 levels
> > on a 512 cpu machine. Given the inflation of the number of cpus this
> > scheme better work up to 8K cpus.
> 
> I find that a fan-out somewhere between 8 and 16 works well in practice.
> log16(512) gives a 3 level tree as does a log8 tree.  log16(8192) is a 4
> level tree whereas log8(8192) is a 5 level tree.  Not a big difference
> either way.
> 
> Somebody was trying to persuade me that a new tree type that maintained
> additional information at each level of the tree to make some operations
> log(log(N)) would be a better idea than a B-tree that is log(N).  I
> countered that a wider tree made the argument unsound at any size tree
> up to 100k.  And we don't tend to have _that_ many objects in a
> data structure inside the kernel.

I still maintain vEB trees are super cool, but I am glad we didn't try
to implement an RCU safe version.

> 
> ceil(log14(100,000)) = 5
> ceil(log2(log2(100,000))) = 5
> 
> at a million, there's actually a gap, 6 vs 5.  But constant factors
> become a much larger factor than scalability arguments at that point.

In retrospect, it seems more of a math win than a practical win - and
only really the O(n) bounds.  Beyond what willy points out, writes
rippling up the tree should be a concern for most users since it will
impact the restart of readers and negatively affect the writer speed -
but probably not here (hot plug?).

Working in (multiples of) cacheline sized b-tree nodes makes the most
sense, in my experience.

Thanks,
Liam