RE: Adding compression/checksum support for bluestore.

From: Allen Samuels <Allen.Samuels@sandisk.com>
To: Sage Weil <sage@newdream.net>
Cc: Chris Dunlop <chris@onthe.net.au>,
	Igor Fedotov <ifedotov@mirantis.com>,
	ceph-devel <ceph-devel@vger.kernel.org>
Subject: RE: Adding compression/checksum support for bluestore.
Date: Tue, 5 Apr 2016 20:41:47 +0000	[thread overview]
Message-ID: <CY1PR0201MB1897F3E8DD10367C398F6E95E89E0@CY1PR0201MB1897.namprd02.prod.outlook.com> (raw)
In-Reply-To: <alpine.DEB.2.11.1604050828340.19675@cpach.fuggernut.com>

> -----Original Message-----
> From: Sage Weil [mailto:sage@newdream.net]
> Sent: Tuesday, April 05, 2016 5:36 AM
> To: Allen Samuels <Allen.Samuels@sandisk.com>
> Cc: Chris Dunlop <chris@onthe.net.au>; Igor Fedotov
> <ifedotov@mirantis.com>; ceph-devel <ceph-devel@vger.kernel.org>
> Subject: RE: Adding compression/checksum support for bluestore.
> 
> On Mon, 4 Apr 2016, Allen Samuels wrote:
> > But there's an approximation that gets the job done for us.
> >
> > When U is VERY SMALL (this will always be true for us :)).
> >
> > The you can approximate 1-(1-U)^D as D * U.  (for even modest values
> > of U (say 10-5), this is a very good approximation).
> >
> > Now the math is easy.
> >
> > The odds of failure for reading a block of size D is now D * U, with
> > checksum correction it becomes (D * U) / (2^C).
> >
> > It's now clear that if you double the data size, you need to add one
> > bit to your checksum to compensate.
> >
> > (Again, the actual math is less than 1 bit, but in the range we care
> > about 1 bit will always do it).
> >
> > Anyways, that's what we worked out.
> 
> D = block size, U = hw UBER, C = checksum.  Let's add N = number of bits you
> actually want to read.  In that case, we have to read (N / D) blocks of D bits,
> and we get
> 
> P(reading N bits and getting some bad data and not knowing it)
> 	= (D * U) / (2^C) * (N / D)
> 	= U * N / 2^C
> 
> and the D term (block size) disappears.  IIUC this is what Chris was originally
> getting at.  The block size affects the probability I get an error on one block,
> but if I am a user reading something, you don't care about block size--you
> care about how much data you want to read.  I think in that case it doesn't
> really matter (modulo rounding error, minimum read size, how precisely we
> can locate the error, etc.).
> 
> Is that right?

It's a "Bit Error Rate", not an "I/O error rate" -- it doesn't matter how you chunk of the bits into blocks and I/O operations.

> 
> sage