From mboxrd@z Thu Jan 1 00:00:00 1970 From: Allen Samuels Subject: RE: Adding compression/checksum support for bluestore. Date: Fri, 1 Apr 2016 23:08:35 +0000 Message-ID: References: <20160401035610.GA5671@onthe.net.au> <20160401052838.GA8044@onthe.net.au> <20160401194912.GA18636@onthe.net.au> Mime-Version: 1.0 Content-Type: text/plain; charset="us-ascii" Content-Transfer-Encoding: 8BIT Return-path: Received: from mail-bn1bon0081.outbound.protection.outlook.com ([157.56.111.81]:39088 "EHLO na01-bn1-obe.outbound.protection.outlook.com" rhost-flags-OK-OK-OK-FAIL) by vger.kernel.org with ESMTP id S1753252AbcDAXIj convert rfc822-to-8bit (ORCPT ); Fri, 1 Apr 2016 19:08:39 -0400 In-Reply-To: <20160401194912.GA18636@onthe.net.au> Content-Language: en-US Sender: ceph-devel-owner@vger.kernel.org List-ID: To: Chris Dunlop , Sage Weil Cc: Igor Fedotov , ceph-devel > -----Original Message----- > From: Chris Dunlop [mailto:chris@onthe.net.au] > Sent: Friday, April 01, 2016 12:49 PM > To: Sage Weil > Cc: Allen Samuels ; Igor Fedotov > ; ceph-devel > Subject: Re: Adding compression/checksum support for bluestore. > > On Fri, Apr 01, 2016 at 10:58:17AM -0400, Sage Weil wrote: > > On Fri, 1 Apr 2016, Chris Dunlop wrote: > >> On Fri, Apr 01, 2016 at 12:56:48AM -0400, Sage Weil wrote: > >>> On Fri, 1 Apr 2016, Chris Dunlop wrote: > >>>> On Wed, Mar 30, 2016 at 10:52:37PM +0000, Allen Samuels wrote: > >>>>> One thing to also factor in is that if you increase the span of a > >>>>> checksum, you degrade the quality of the checksum. So if you go > >>>>> with 128K chunks of data you'll likely want to increase the > >>>>> checksum itself from something beyond a CRC-32. Maybe somebody > out > >>>>> there has a good way of describing this quanitatively. > >>>> > >>>> I would have thought the "quality" of a checksum would be a > >>>> function of how many bits it is, and how evenly and randomly it's > >>>> distributed, and unrelated to the amount of data being checksummed. > >>>> > >>>> I.e. if you have any amount of data covered by an N-bit evenly > >>>> randomly distributed checksum, and "something" goes wrong with the > >>>> data (or the checksum), the chance of the checksum still matching the > data is 1 in 2^n. > >>> > >>> Say there is some bit error rate per bit. If you double the amount > >>> of data you're checksumming, then you'll see twice as many errors. > >>> That means that even though your 32-bit checksum is right 2^32-1 > >>> times out of 2^32, you're twice as likely to hit that 1 in 2^32 > >>> chance of getting a correct checksum on wrong data. > >> > >> It seems to me, if we're talking about a single block of data > >> protected by a 32-bit checksum, it doesn't matter how many errors > >> there are within the block, the chance of a false checksum match is still > only 1 in 2^32. > > > > It's not a question of how many errors are in the block, it's a > > question of whether there are more than 0 errors. If the bit error > > rate is so low it's 0, our probability of a false positive is 0, no > > matter how many blocks there are. So for a bit error rate of 10e-15, > > then it's 10e-15 * 1^-32. But if there are 1000 bits in a block, it becomes > 10e-12 * 1^-32. > > > > In other words, we're only rolling the checksum dice when there is > > actually an error, and larger blocks are more likely to have errors. > > If your blocks were so large you were effectively guaranteed to have > > an error in every one, then the effective false positive rate would be > > exactly the checksum false positive rate (2^-32). > > Good point, I hadn't thought about it like that. But that's the "single block" > case. On the other hand, a large storage system is the same case as the > stream of blocks: for a given storage (stream) size, your chance of hitting an > error is constant, regardless of the size of the individual blocks within the > storage. Then, if/when you hit an error, the chance of getting a false positive > on the checksum is a function of the checksum bits and independent of the > block size. I think we're getting confused about terminology. What matters isn't "blocks" but the ratio of bits of checksum to bits of data covered by that checksum. That ratio determines the BER of reading that data and hence the overall system. If you double the amount of data you need to add 1 bit of checksum to maintain the same BER. I started this discussion in reaction to Sage's observation that we could reduce the checksum storage overhead by checksuming larger blocks. My point is that this will degrade the BER of system accordingly. That's neither good nor bad, but it's something that will matter to people. If you go from a 4K chunk of data with, say a 32-bit checksum to a 128K chunk of data with the same 32-bit checksum, then you simply have to accept that the BER is reduced by that ratio (4K / 128K) OR you have to move to checksum value that has 32 more bits in it (128K/4K). Whether that's acceptable is a user choice. I think it's good to parameterize the checksum algorithms and checksumming block size. All we need to do is to document the system level effects, etc., and give people guidance on how to connect these settings with the magnitude of data under management (which matters) and the HW UBER (which may vary A LOT from device to device). > > >> If we're talking about a stream of checksummed blocks, where the > >> stream is subject to some BER, then, yes, your chances of getting a false > match go up. > >> But that's still independent of the block size, rather it's a > >> function of the number of possibly corrupt blocks. > >> > >> In fact, if you have a stream of data subject to some BER and split > >> into checksummed blocks, the larger the blocks and thereby the lower > >> the number of blocks, the lower the chance of a false match. > > > > > > sage > > Chris