linux-kernel - Re: [PATCH 11/39] autonuma: CPU follow memory algorithm

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Date:	Tue, 27 Mar 2012 16:37:37 +0200
From:	Andrea Arcangeli <aarcange@...hat.com>
To:	Peter Zijlstra <a.p.zijlstra@...llo.nl>
Cc:	Linus Torvalds <torvalds@...ux-foundation.org>,
	Hillf Danton <dhillf@...il.com>,
	"Paul E. McKenney" <paulmck@...ux.vnet.ibm.com>,
	Dan Smith <danms@...ibm.com>, Paul Turner <pjt@...gle.com>,
	Lai Jiangshan <laijs@...fujitsu.com>,
	Rik van Riel <riel@...hat.com>, Ingo Molnar <mingo@...e.hu>,
	Andrew Morton <akpm@...ux-foundation.org>,
	Lee Schermerhorn <Lee.Schermerhorn@...com>, linux-mm@...ck.org,
	Suresh Siddha <suresh.b.siddha@...el.com>,
	Mike Galbraith <efault@....de>,
	Bharata B Rao <bharata.rao@...il.com>,
	Thomas Gleixner <tglx@...utronix.de>,
	Johannes Weiner <hannes@...xchg.org>,
	linux-kernel@...r.kernel.org
Subject: Re: [PATCH 11/39] autonuma: CPU follow memory algorithm

On Tue, Mar 27, 2012 at 10:39:55AM +0200, Peter Zijlstra wrote:
> You can talk pretty much anything down to O(1) that way. Take an
> algorithm that is O(n) in the number of tasks, since you know you have a
> pid-space constraint of 30bits you can never have more than 2^30 (aka
> 1Gi) tasks, hence your algorithm is O(2^30) aka O(1).

Still this O notation thingy... This is not about the max value but
about the fact the number is _variable_ or _fixed_.

If you have a variable amount of entries (and variable amount of
memory) in a list it's O(N) where N is the number of entries (even if
we know the max ram is maybe 4TB?). If you've a _fixed_ number of them
it's O(1). Even if the fixed number is very large.

It basically shows it won't degraded depending on load, and the cost
per-schedule remains exactly fixed at all times (non liner cacheline
and out-of-order CPU execution/HT effects aside).

If it was O(N) the time this would take to run for each schedule shall
have to vary at runtime depending on a some variable factor N and
that's not the case here.

You can argue about CPU hotplug though.

But this is just math nitpicking because I already pointed out I agree
the cacheline hits on a 1024 way would be measurable and needs fixing.

I'm not sure how useful it is to keep arguing on the O notation when
we agree on what shall be optimized in practice.
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