Patent Grant
7343546
Embodiments of the invention relate to syndrome generation and data recovery, and more specifically to RAID syndrome generation and data recovery.
With the increase in use of large-scale storage systems, such as with Fiber Channel and Gigabit Ethernet systems, there is an increase in the susceptibility of these systems to multiple disk failures. The rapid growth of disk capacity also prolongs the disk recovery time in the event of disk failures. This prolonged recovery time increases the probability of subsequent disk failures during the reconstruction of user data and parity information stored in a faulty disk. In addition, latent sector failures caused by data that was left unread for a long period of time may prevent data recovery after a disk failure that results in loss of data. The use of less expensive disks, such as ATA (Advanced Technology Attachment) disks, in arrays where high data integrity is required also increases the probability of such disk failures.
RAID (Redundant Array of Independent Disks) architectures have been developed to allow recovery from disk failures. Typically, the XOR (Exclusive-OR) of data from a number of disks is maintained on a redundant disk. In the event of a disk failure, the data on the failed disk is reconstructed by XORing the data on the surviving disks. The reconstructed data is written to a spare disk. However, data will be lost if the second disk fails before the reconstruction is complete. Traditional disk arrays that protect the loss of no more than one disk are inadequate for data recovery, especially for large-scale storage systems.
The invention is illustrated by way of example, and not by way of limitation, in the figures of the accompanying drawings in which like reference numerals refer to similar elements.
Embodiments of a system and method for syndrome generation and data recovery are described. In the following description, numerous specific details are set forth. However, it is understood that embodiments of the invention may be practiced without these specific details. In other instances, well-known circuits, structures and techniques have not been shown in detail in order not to obscure the understanding of this description.
Reference throughout this specification to “one embodiment” or “an embodiment” means that a particular feature, structure, or characteristic described in connection with the embodiment is included in at least one embodiment of the invention. Thus, the appearances of the phrases “in one embodiment” or “in an embodiment” in various places throughout this specification are not necessarily all referring to the same embodiment. Furthermore, the particular features, structures, or characteristics may be combined in any suitable manner in one or more embodiments.
Referring to
The following are the equations for generating P and Q for a storage array with n data disks and two check disks:
P=D0⊕D1⊕D2 . . . ⊕Dn−1 (Equation 1)
Q=g0*D0⊕g1*D1⊕g2*D2 . . . gn−1*Dn−1 (Equation 2)
P is the simple parity of data (D) computed across a stripe using ⊕ (XOR) operations. Q requires multiplication (*) using a Galois Field multiplier (g).
The following equations show the generation of P and Q when updating a data block Da:
P(new)=P(old)⊕Da(old)⊕Da(new)
Q(new)=Q(old)⊕ga*Da(old)⊕ga*Da(new).
There are four cases of multiple disk failure that require recovery. In case one, P and Q fail. In this case, P and Q may be regenerated using Equations 1 and 2 shown above.
In case two, Q and a data disk (Da) fail. In this case, Da may be regenerated using P and the remaining data disks via Equation 1. Q may then be regenerated using Equation 2.
In case three, P and a data disk (Da) fail. In this case, Da may be regenerated using Q, the remaining data disks, and the following equation:
Da=(Q⊕Qa)*g−a=(Q⊕Qa)*g255−a, where
Qa=g0D0⊕g1D1⊕ . . . ⊕ga−1Da−1⊕ga+aDa+1 . . . ⊕gn−1Dn−1.
After Da is regenerated, P may be regenerated using Equation 1.
In case four, two data disks (Da and Db) fail. In this case, Da and Db may be regenerated using P and Q, the remaining data disks, and the following equations:
Da=(g−a*(Q⊕Qab)⊕gb−a*(P⊕Pab))/(gb−a⊕0000 0001)
Db=Da⊕(P⊕Pab), where
Pab=D0⊕D1⊕ . . . ⊕Da−1⊕Da+1 . . . ⊕Db−1⊕Db+1 . . . ⊕Dn−1
Qab=g0D0⊕g1D1⊕ . . . ⊕ga−1Da−1⊕ga+1Da+1 . . . ⊕gb−1Db−1⊕gb−1Db+1 . . . ⊕gn−1Dn−1.
The following are examples of recovery from disk failures in the cases described above. In the following examples, the datapath is assumed to be one byte or 8 bits wide. Therefore, a Galois Field, GF (28) is used. The invention may be implemented for datapaths that are more or less than one byte wide, and larger or smaller Galois fields may be used.
The following equations may be used for multiplying two 8-bit elements (b and c) to yield an 8-bit product (a).
b=[b7b6b5b4b3b2b1b0] and c=[c7c6c5c4c3c2c1c0].
g−a=g255−a.
The following example shows how to generate P and Q parity for a disk array with four data disks and two parity disks. Assume that each data block contains one data byte. Let Di be the data contain in disk I (i=0, 1, 2, 3). Consider the following data stripe: D0=1011 0100, D1=0010 1100, D2=1100 0110 and D3=101 0101. Then, P may be generated using Equation 1 as follows:
Q may be generated using Equation 2 as follows:
Q=g0D0⊕g1D1⊕g2D2⊕g3D3.
From the table in
Therefore,
The following example shows how to recover from two disk failures using the array generated above. In the first case, P and Q fail. In this case, P and Q are regenerated using Equations 1 and 2 as shown above. In the second case, Q and a data disk (Da) fail. In this case, Da may be regenerated using P and the remaining data disks via Equation 1. Q may then be regenerated using Equation 2. In the third case, P and a data disk (Da) fail. In this case, Da may be regenerated using Q, the remaining data disks, and the following equation:
Da=(Q⊕Qa)*g−a=(Q⊕Qa)*g255−a, where
Qa=g0D0⊕g1D1⊕ . . . ⊕ga−1Da−1⊕ga+1Da+1 . . . ⊕gn−1Dn−1.
For example, suppose disk 2 fails. Then,
Using the table in
P may then be regenerated using Equation 1, since all data blocks are now available.
In the fourth case, two data disks (Da and Db) fail. In this case, Da and Db may be regenerated using P and Q, the remaining data disks, and the following equations:
Da=(g−a*(Q⊕Qab)⊕gb−a*(P⊕Pab))/(gb−a⊕0000 0001)
Db=Da⊕(P⊕Pab), where
Pab=D0⊕ . . . ⊕Da−1⊕Da+1 . . . ⊕Db−1⊕Db+1 . . . ⊕Dn−1
Qab=g0D0⊕g1D1⊕ . . . ⊕ga−1Da−1⊕ga+1Da+1 . . . ⊕gb−1Db−1⊕gb+1Db+1 . . . ⊕gn−1Dn−1.
For example, assume that disks 1 and 3 failed. Then,
From the table in
The multiplier 302 multiplies the multiplicand 330 with the data 320 read from the storage blocks shown in
System 300 may also include a divider 314 to be used to perform the division operations for the equations described above with respect to the four cases in which multiple disks fail. For example, in case four, the computation for regeneration of Da has a division operation, which may be performed by divider 314. Data may be allowed to pass through the divider 314 by setting the divisor 340 equal to one. This may be desired when no division operation is required to be performed.
As shown in
While the invention has been described in terms of several embodiments, those of ordinary skill in the art will recognize that the invention is not limited to the embodiments described, but can be practiced with modification and alteration within the spirit and scope of the appended claims. The description is thus to be regarded as illustrative instead of limiting.
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