On 11/18/2013 02:08 PM, Andrea Mazzoleni wrote: > Hi, > > I want to report that I recently implemented a support for > arbitrary number of parities that could be useful also for Linux > RAID and Btrfs, both currently limited to double parity. > > In short, to generate the parity I use a Cauchy matrix specifically > built to be compatible with the existing Linux parity computation, > and extensible to an arbitrary number of parities. This without > limitations on the number of data disks. > > The Cauchy matrix for six parities is: > > 01 01 01 01 01 01 01 01 01 01 01 01 01 01 01 01 01 01 01 01 01 01... > 01 02 04 08 10 20 40 80 1d 3a 74 e8 cd 87 13 26 4c 98 2d 5a b4 75... > 01 f5 d2 c4 9a 71 f1 7f fc 87 c1 c6 19 2f 40 55 3d ba 53 04 9c 61... > 01 bb a6 d7 c7 07 ce 82 4a 2f a5 9b b6 60 f1 ad e7 f4 06 d2 df 2e... > 01 97 7f 9c 7c 18 bd a2 58 1a da 74 70 a3 e5 47 29 07 f5 80 23 e9... > 01 2b 3f cf 73 2c d6 ed cb 74 15 78 8a c1 17 c9 89 68 21 ab 76 3b... > > You can easily recognize the first row as RAID5 based on a simple > XOR, and the second row as RAID6 based on multiplications by powers > of 2. The other rows are for additional parity levels and they > require multiplications by arbitrary values that can be implemented > using the PSHUFB instruction. > Hello, This looks very interesting indeed. Could you perhaps describe how the Cauchy matrix is derived, and under what conditions it would become singular? -hpa -- To unsubscribe from this list: send the line "unsubscribe linux-raid" in the body of a message to majordomo@xxxxxxxxxxxxxxx More majordomo info at http://vger.kernel.org/majordomo-info.html
