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From: Peter Zijlstra <pet...@infradead.org>
Newsgroups: linux.kernel
Subject: Re: High CPU load when machine is idle (related to PROBLEM:  Unusually high load average when idle in 2.6.35, 2.6.35.1 and later)
Date: Tue, 26 Oct 2010 16:10:02 +0200
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On Tue, 2010-10-26 at 14:44 +0200, Peter Zijlstra wrote:
> a smarter patch will try and avoid that loop. 

 a1 = a0 * e + a * (1 - e)

 a2 = a1 * e + a * (1 - e)
    = (a0 * e + a * (1 - e)) * e + a * (1 - e)
    = a0 * e^2 + a * (1 - e) * (1 + e)

 a3 = a2 * e + a * (1 - e)
    = (a0 * e^2 + a * (1 - e) * (1 + e)) * e + a * (1 - e)
    = a0 * e^3 + a * (1 - e) * (1 + e + e^2)

 an = a0 * e^n + a * (1 - e) * (1 + e + ... + e^n-1)
    = a0 * e^n + a * (1 - e) * (1 - e^n)/(1 - e)
    = a0 * e^n + a * (1 - e^n)


the trouble seems to be that that is a rather slow function, stuffing
that in a table will either give us very large tables or very coarse
decay.

   n: an         an * 2048

   1: 0.99446    2037
   2: 0.98895    2025
   4: 0.978023   2003
   8: 0.956529   1959
  16: 0.914947   1874
  32: 0.837128   1714
  64: 0.700784   1435
 128: 0.491098   1006
 256: 0.241177    494
 512: 0.0581666   119
1024: 0.00338335    7
2048: 1.14471e-05   0



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