Tuesday Jul 21, 2009

Triple-Parity RAID-Z

Double-parity RAID, or RAID-6, is the de facto industry standard for storage; when I started talking about triple-parity RAID for ZFS earlier this year, the need wasn't always immediately obvious. Double-parity RAID, of course, provides protection from up to two failures (data corruption or the whole drive) within a RAID stripe. The necessity of triple-parity RAID arises from the observation that while hard drive capacity has roughly followed Kryder's law, doubling annually, hard drive throughput has improved far more modestly. Accordingly, the time to populate a replacement drive in a RAID stripe is increasing rapidly. Today, a 1TB SAS drive takes about 4 hours to fill at its theoretical peak throughput; in a real-world environment that number can easily double, and 2TB and 3TB drives expected this year and next won't move data much faster. Those long periods spent in a degraded state increase the exposure to the bit errors and other drive failures that would in turn lead to data loss. The industry moved to double-parity RAID because one parity disk was insufficient; longer resilver times mean that we're spending more and more time back at single-parity. From that it was obvious that double-parity will soon become insufficient. (I'm working on an article that examines these phenomena quantitatively so stay tuned... update Dec 21, 2009: you can find the article here)

Last week I integrated triple-parity RAID into ZFS. You can take a look at the implementation and the details of the algorithm here, but rather than describing the specifics, I wanted to describe its genesis. For double-parity RAID-Z, we drew on the work of Peter Anvin which was also the basis of RAID-6 in Linux. This work was more or less a tutorial for systems programers, simplifying some of the more subtle underlying mathematics with an eye towards optimization. While a systems programmer by trade, I have a background in mathematics so was interested to understand the foundational work. James S. Plank's paper A Tutorial on Reed-Solomon Coding for Fault-Tolerance in RAID-like Systems describes a technique for generalized N+M RAID. Not only was it simple to implement, but it could easily be made to perform well. I struggled for far too long trying to make the code work before discovering trivial flaws with the math itself. A bit more digging revealed that the author himself had published Note: Correction to the 1997 Tutorial on Reed-Solomon Coding 8 years later addressing those same flaws.

Predictably, the mathematically accurate version was far harder to optimize, stifling my enthusiasm for the generalized case. My more serious concern was that the double-parity RAID-Z code suffered some similar systemic flaw. This fear was quickly assuaged as I verified that the RAID-6 algorithm was sound. Further, from this investigation I was able to find a related method for doing triple-parity RAID-Z that was nearly as simple as its double-parity cousin. The math is a bit dense; but the key observation was that given that 3 is the smallest factor of 255 (the largest value representable by an unsigned byte) it was possible to find exactly of 3 different seed or generator values after which there were collections of failures that formed uncorrectable singularities. Using that technique I was able to implement a triple-parity RAID-Z scheme that performed nearly as well as the double-parity version.

As far as generic N-way RAID-Z goes, it's still something I'd like to add to ZFS. Triple-parity will suffice for quite a while, but we may want more parity sooner for a variety of reasons. Plank's revised algorithm is an excellent start. The test will be if it can be made to perform well enough or if some new clever algorithm will need to be devised. Now, as for what to call these additional RAID levels, I'm not sure. RAID-7 or RAID-8 seem a bit ridiculous and RAID-TP and RAID-QP aren't any better. Fortunately, in ZFS triple-parity RAID is just raidz3.

A little over three years ago, I integrated double-parity RAID-Z into ZFS, a feature expected of enterprise class storage. This was in the early days of Fishworks when much of our focus was on addressing functional gaps. The move to triple-parity RAID-Z comes in the wake of a number of our unique advancements to the state of the art such as DTrace-powered Analytics and the Hybrid Storage Pool as the Sun Storage 7000 series products meet and exceed the standards set by the industry. Triple-parity RAID-Z will, of course, be a feature included in the next major software update for the 7000 series (2009.Q3).

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Adam Leventhal, Fishworks engineer

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