Date: Wed, 19 Jul 2017 15:43:37 +0200
From: Peter Zijlstra <peterz@infradead.org>
To: "Li, Aubrey" <aubrey.li@linux.intel.com>
Cc: Andi Kleen <ak@linux.intel.com>,
        Frederic Weisbecker <fweisbec@gmail.com>,
        Christoph Lameter <cl@linux.com>, Aubrey Li <aubrey.li@intel.com>,
        tglx@linutronix.de, len.brown@intel.com, rjw@rjwysocki.net,
        tim.c.chen@linux.intel.com, arjan@linux.intel.com,
        paulmck@linux.vnet.ibm.com, yang.zhang.wz@gmail.com, x86@kernel.org,
        linux-kernel@vger.kernel.org, daniel.lezcano@linaro.org
Subject: Re: [RFC PATCH v1 00/11] Create fast idle path for short idle periods
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On Tue, Jul 18, 2017 at 11:14:57AM +0800, Li, Aubrey wrote:
> On 2017/7/18 3:23, Peter Zijlstra wrote:
> > On Fri, Jul 14, 2017 at 09:26:19AM -0700, Andi Kleen wrote:
> >>> And as said; Daniel has been working on a better predictor -- now he's
> >>> probably not used it on the network workload you're looking at, so that
> >>> might be something to consider.
> >>
> >> Deriving a better idle predictor is a bit orthogonal to fast idle.
> > 
> > No. If you want a different C state selected we need to fix the current
> > C state selector. We're not going to tinker.
> > 
> > And the predictor is probably the most fundamental part of the whole C
> > state selection logic.
> > 
> > Now I think the problem is that the current predictor goes for an
> > average idle duration. This means that we, on average, get it wrong 50%
> > of the time. For performance that's bad.
> > 
> > If you want to improve the worst case, we need to consider a cumulative
> > distribution function, and staying with the Gaussian assumption already
> > present, that would mean using:
> > 
> > 	 1              x - mu
> > CDF(x) = - [ 1 + erf(-------------) ]
> > 	 2           sigma sqrt(2)
> > 
> > Where, per the normal convention mu is the average and sigma^2 the
> > variance. See also:
> > 
> >   https://en.wikipedia.org/wiki/Normal_distribution
> > 
> > We then solve CDF(x) = n% to find the x for which we get it wrong n% of
> > the time (IIRC something like: 'mu - 2sigma' ends up being 5% or so).
> > 
> > This conceptually gets us better exit latency for the cases where we got
> > it wrong before, and practically pushes down the estimate which gets us
> > C1 longer.
> > 
> > Of course, this all assumes a Gaussian distribution to begin with, if we
> > get bimodal (or worse) distributions we can still get it wrong. To fix
> > that, we'd need to do something better than what we currently have.
> > 
> Maybe you are talking about applying some machine learning algorithm online
> to fit a multivariate normal distribution, :)

See here for an implementation of what I spoke about above:

  https://lkml.kernel.org/r/20170719133940.uytsixvfgpmo3ane@hirez.programming.kicks-ass.net

Very much statistics 101.