On Tue, 5 Apr 2016, Allen Samuels wrote: > > -----Original Message----- > > From: Sage Weil [mailto:sage@xxxxxxxxxxxx] > > Sent: Tuesday, April 05, 2016 5:36 AM > > To: Allen Samuels <Allen.Samuels@xxxxxxxxxxx> > > Cc: Chris Dunlop <chris@xxxxxxxxxxxx>; Igor Fedotov > > <ifedotov@xxxxxxxxxxxx>; ceph-devel <ceph-devel@xxxxxxxxxxxxxxx> > > 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. Right. And you use it to calculate "The odds of failure for reading a block of size D", but I'm saying that the user doesn't care about D (which is an implementation detail). They care about N, the amoutn of data they want to read. And when you calculate the probability of getting bad data after reading *N* bits, it has nothing to do with D. Does that make sense? sage -- To unsubscribe from this list: send the line "unsubscribe ceph-devel" in the body of a message to majordomo@xxxxxxxxxxxxxxx More majordomo info at http://vger.kernel.org/majordomo-info.html
