[LTP] [PATCH] getrandom02: relax check for returned data

[Cyril Hrubis <chrubis@suse.cz>]

Hi!
> > gnuplot> comb(n,k) = gamma(n+1)/(gamma(k+1) * gamma(n - k + 1))
> > gnuplot> plot [6:30] 256 * comb(x, int(6 + x * 0.2)) / (256 ** int(6 + x * 0.2))
> 
> This does not look correct to me. Try it with old formula, it goes above 1:
> gnuplot> comb(n,k) = gamma(n+1)/(gamma(k+1) * gamma(n - k + 1))
> gnuplot> plot [6:30] 256 * comb(x, int(x * 0.1)) / (256 ** int(x * 0.1))

You are right, this would be for if we fail the test test when
table[i] >= max, which would fail with 100% probability for most of the smaller
buffers, hence we get results that does not make much sense. We have to
add 1 to the int(x * 0.1) in the formula.

Try plotting this:

plot [10:60] 256 * comb(x, int(x * 0.1) + 1) / (256 ** (int(x * 0.1) + 1))

which pretty much shows the same you are saying for N=19 the old formula
has about 70% chance of failing. Well your script with poisson
aproximation gets close to 50% but the order of magnitude seems to be
the same for both formulae.

> ---
> 
> With old formula, for N<20 (and max=1), this is pretty much birthday
> problem [1] with smaller pool - we don't have 365 days, we have 256 bytes.
> 
> With birthday problem you get 50% chance of having 2 people with same
> birthday if number of people is 23. Since we have smaller pool, I'd expect
> we reach 50% chance sooner.
> 
> With N>=20, max increases and it gets a lot more complicated. Best advice
> I've found online was to use Poisson approximation [2].
> 
> Based on that (see attached python snippet) I'm getting that:
> "x*0.1" is quite bad, specially for N=19
> "6+x*0.2" is a lot better, with chance ~10^-16

I'm getting the same with the fixed formula in gnuplot:

plot [10:60] 256 * comb(x, int(6 + x * 0.2) + 1) / (256 ** (int(6 + x * 0.2) + 1))

This shows a peak for 15 which is about ~10^-16.

> I'll send v2, with "6+x*0.2".

Agreed.

-- 
Cyril Hrubis
chrubis@suse.cz