Collecting entropy from device_attach() times.

[Mariusz Gromada]

> On Wed, Sep 19, 2012 at 09:29:23PM +0200, Pawel Jakub Dawidek wrote:
> Here's how the distribution looks like for device_attach() times of my 
> sound card. The times were 26bit numbers, so this is after discarding 
> top ten bits, which leave us with 16 lower bits of pure entropy:) 
> http://people.freebsd.org/~pjd/misc/harvest_device_attach.png Kudos to 
> my friend Mariusz (CCed) who is mathematician and who helped me with 
> visualization and also promissed to prepare formal proof:) 

Hi All,

I am not a mathematician :-) Below you will find some initial formal proof.

Problem definition: checking if data sample comes from uniform distribution.
Data sample: 2081 empirical observations (after discarding top ten bits)
One-sample Kolmogorv-Smirnov test
Hypothesis (based on the Cumulative Distribution Functions)
H0: Empirical CDF given by 2081 obs. = theoretical uniform CDF
H1: (alternatively) Empirical CDF is different than theoretical uniform CDF
K-S Statistic: D = 0.017405527
p-value = 0.535

Interpretation: if p-value is much higher than significance level 
(alpha) then there is no reason to reject H0 hypothesis, if p-value is 
much smaller than significance level (alpha) then we strongly reject H0 
hypothesis.

So take any reasonable significance level (i.e. alpha = 0.05 which is 
far less than 0.535) and you have a proof that empirical observations 
are in fact given by random uniform numbers.

Additionally please take a look on the linked chart
http://bamper.vot.pl/ks.jpg

It shows:
Good fit in general
Best fit for the range 0 - c.a 3000
Worse fit for the range c.a. 3000 - 65536

It means that numbers between 0 - 3000 are more random than numbers 
between 3000 - 6536

Best regards,
Mariusz