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    SubjectRe: 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)
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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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