Re: Adding compression/checksum support for bluestore.

[Chris Dunlop <chris@onthe.net.au>]

On Wed, Apr 06, 2016 at 06:06:25PM +0000, Allen Samuels wrote:
>>>> On the bright side, if the 10^-9 formula (Chris #1, Chris #2, Sage)
>>>> are anywhere near correct, they indicate with a block size of 4K and
>>>> 32-bit checksum, you'd need to read 5 * 10^21 bits, or 0.5 ZB, to get
>>>> to a 1% chance of seeing unflagged bad data, e.g.:
>> 
>> P(bad data) @ U=10^-15, C=32, D=(4 * 8 * 1024), N=(5 * 8 * 10^21)
>>   = 1 - (2^-C * (1-U)^D - 2^-C + 1) ^ (N / D)
>>   = 1 - (2^-32 * (1-(10^-15))^(4 * 8 * 1024) - 2^-32 + 1) ^ ((5 * 8 * 10^21) / (4 * 8 * 1024))
>>   = 0.009269991978483162962573463579660791470065102520727107106
>>   = 0.92%
> 
> Where does 10^21 come into the equation? I thought we were dealing with 5PB. 

ZB rather than PB. But I see my explanatory text still doesn't match the
numbers actually being plugged into the formula. Sigh.

Corrected explanatory text: with a 4KB block size, 32 bit checksum and BER 1
x 10^-15, 5 ZB of data gets you close to a 1% chance of seeing unflagged bad
data.