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Reviews the RAID comments.

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Andrea Mazzoleni 2013-10-15 19:14:08 +02:00
parent ea039306ce
commit 39d18280bb
1 changed files with 26 additions and 13 deletions
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raid.c
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@ -1684,7 +1684,7 @@ void raid_gen(unsigned level, unsigned char** vbuf, unsigned data, unsigned size
* Q = sum(2^i * Di) 0<=i<n
*
* To support RAIDTP (Triple Parity), we use an extension of the same approach,
* also described in the paper "Multiple-parity RAID" [2], with the additional
* described in the paper "Multiple-parity RAID" [2], with the additional
* parity coefficient "4".
* This method is also the same used by ZFS to implement its RAIDTP support.
*
@ -1699,12 +1699,19 @@ void raid_gen(unsigned level, unsigned char** vbuf, unsigned data, unsigned size
* R = sum(4^i * Di) 0<=i<n
* S = sum(8^i * Di) 0<=i<n
*
* Note that for RAIDQP we don't have the guarantee to always have a system of
* independent linear equations, and in some cases the equations are no not solvable.
* For RAIDQP we don't have the guarantee to always have a system of independent linear
* equations, and in some cases the equations are not solvable.
*
* This is expected because the Vandermonde matrix we use to compute the parity
* This is expected because the Vandermonde matrix used to compute the parity
* has no guarantee to have all its submatrixes not singular [3, Chap 11, Problem 7]
* and this is a requirement to have a working MDS code [3, Chap 11, Theorem 8].
* and this is a requirement to have a MDS code [3, Chap 11, Theorem 8].
*
* If it surprises that even using a Vandermonde matrix we don't have a MDS code,
* consider that the matrix A we use to compute the parity, is not the MDS generator
* matrix G, but only a submatrix of it. The generator matrix G is the concatenation
* of I and A, as G = [I | A], where I is the identity matrix.
* Setting the matrix G as Vandermonde matrix would have guaranteed to have a MDS code,
* but setting only A as a Vandermonde matrix doesn't give this guarantee.
*
* Using the primitive polynomial 285, RAIDQP works for up to 21 data disks
* with parity coefficients "1,2,4,8". Changing polynomial to one of 391/451/463/487,
@ -1716,15 +1723,20 @@ void raid_gen(unsigned level, unsigned char** vbuf, unsigned data, unsigned size
* primitive polynomial 100087 or 122563 that supports Hexa (6) Parity with
* parity coefficients 1,2,4,8,16,32 for up to 89 disks.
*
* A general method working for any number of disks, is to use a a Cauchy matrix [4],
* instead of a Vandermonde matrix to setup the matrix used to compute the parity.
* A general method working for any number of disks is to setup the matrix
* used to compute the parity as a Cauchy matrix [4], or set the MDS generator
* matrix as Vandermonde matrix, and do some transformations to it until it
* can be expressed as the concatenation of the identify matrix and the
* submatrix used to generate the parity [5].
*
* But with a such matrix, we would obtain a slower performance, because the
* coefficients of the equations are arbitrarily chosen, and not powers of
* the same coefficient.
* This means that you need to use multiplication tables to implement the
* coefficients of the equations are arbitrarily chosen, and not powers of
* the same value.
* This means that we would need to use multiplication tables to implement the
* parity computation, instead of the fast approach described in [1].
* Note anyway, that there is also a way to implement multiplication tables
* in a very fast way with SSE instructions [5].
* Note anyway, that there is also a method to implement very fast multiplication
* tables with SSE instructions [6] that it's already competitive with the RAIDQP
* parity computation.
*
* In details, RAIDTP is implemented for n disks Di, computing the parities
* P,Q,R with:
@ -1782,7 +1794,8 @@ void raid_gen(unsigned level, unsigned char** vbuf, unsigned data, unsigned size
* [2] Brown, "Multiple-parity RAID", 2011
* [3] MacWilliams, Sloane, "The Theory of Error-Correcting Codes", 1977
* [4] Blömer, "An XOR-Based Erasure-Resilient Coding Scheme", 1995
* [5] Plank, "Screaming Fast Galois Field Arithmetic Using Intel SIMD Instructions", 2013
* [5] Plank, "Note: Correction to the 1997 Tutorial on Reed-Solomon Coding", 2003
* [6] Plank, "Screaming Fast Galois Field Arithmetic Using Intel SIMD Instructions", 2013
*/
/**