On Apr 22, 2015, at 11:56 AM, Hugh E Cruickshank <hugh at forsoft.com>
wrote:>
> I have done some "what if" testing.
Using which tool? My simulator, or something you cooked up yourself? If the
latter, would you care to share?
I?ve updated mine to break out the stats for 3+ volumes instead of just
reporting all multi-volume fscks together:
https://gist.github.com/wyoung/7c94967bb635de48d058
Then I rewrote that in C++, since these 8-volume simulations were literally
going to take days with the Perl version:
https://gist.github.com/wyoung/966383b4efbb63aafc71
(The Perl version is about 1/5 the speed of the C++ one. This actually isn?t
all that bad, considering that it?s an interpreted dynamically-typed language
going up against a statically-typed native-code compiled language.)
> Using the prime numbers 7, 11, 13, 17, 19, 23, 29 and 31 the is a
> maximum of 7 incidents per year of 2 fscks per week and none for 3 or
> more.
This is why I pointed out that you only need *relatively* prime numbers: so that
if you decide the largest max-mount-count can?t be over 31, you don?t have to go
clear down to 7 in order to find the last prime for 8 volumes.
Using relatively-prime numbers, you can skew the set upwards quite a bit without
increasing the largest value. The most efficient set I?ve been able to come up
with is:
17, 19, 23, 25, 27, 28, 29, 31
The three composite values (25, 27, and 28) do not share any common factors: 25
uses 5 twice, 27 uses 3 thrice, and 28 uses 7 plus twice 2.
My newer simulators give these results for the chances of a multi-volume fsck
with your prime set:
period: ~6.7 billion
2-volume: 8.12%
3-volume: 1.08%
4-volume: 0.09%
>5: < 0.01% chance
total: 9.3%
My relatively prime improved set gives these results because the set?s median is
higher while keeping the same maximum, while also avoiding any reuse of prime
factors:
period: ~126.2 billion
2-volume: 0.37%
3-volume: 0.33%
4-volume: 0.02%
>5: < 0.01% chance
total: 0.7%
See? Number theory *is* useful in real life. :)