JP5131379B2 - RAID device and Galois field product operation processing method - Google Patents

Description

  The present invention relates to a RAID apparatus for calculating data parity by Galois field arithmetic and a Galois field product calculation method, and more particularly to a RAID apparatus and Galois field product calculation method suitable for restoring a double failure of a disk group. About.

  RAID (Redundant Array of Independent Disks) 6 is known as a method that can restore a double disk failure. As this RAID 6 method, a one-dimensional redundancy method has been proposed (for example, see Patent Document 1).

  In the configuration of RAID 6 in FIG. 14, three data disk devices (hard disk drives) 101, 102, 103 and two parity disk devices (hard disk drives) 104, 105 are connected to the RAID controller 110. The

  The one-dimensional redundancy method generates two types of parity from data. As shown in FIG. 15, the first parity P is the parity obtained by adding (XOR) the data D1, D2, and D3, as in the conventional RAID5. The parity P is stored in the first disk device 104. Hereinafter, the symbol “+” indicates XOR (exclusive OR).

  The second parity Q is obtained by weighting each data D1, D2, D3 by Galois field product operation and adding them together (XOR) as a parity. This parity Q is stored in the second disk device 105.

  One Galois field is determined for each data disk device 101, 102, 103, and it is necessary for each data disk device 101, 102, 103 to be different in order to restore a double failure. . For example, as shown in FIG. 15, if the number of data bits is 16 bits, the Galois field GF (2 ^ 16) can take 2 16 finite points. In addition, four arithmetic operations of Galois fields can be performed with a predetermined law. The one-dimensional redundancy method enables parity distribution and is effective in detecting and restoring double faults.

  As shown in FIG. 15, in parity generation using a Galois field, it is necessary to perform an operation using two variables of data and a Galois field as a product operation of the Galois field. For this reason, processing time is required to generate parity for the XOR operation (parity P operation) of RAID 5, and the performance deteriorates.

  In order to simplify the product operation of the Galois field, an α-times weighting (product operation) algorithm using shift, AND, and XOR is proposed for a plurality of data (for example, see Non-Patent Document 1). In this proposed paper, pages 4 to 5 explain the parity generation and data recovery equations when the data is 8 bits. Is disclosed.

  The algorithm described in the C language will be described with reference to FIG. 16 and FIG. “V” in FIG. 16 indicates 8-bit, 4-symbol (32-bit) target data.

  First, 8-bit data of the disk device is loaded into four 32-bit registers (S100). The entire target data v (32 bits) is shifted to the left by 1 bit (upper direction) (S101). The data v << 1 shifted to the left by 1 bit has a value twice as large as the target data v in units of 32 bits.

  Next, in the shifted data v << 1, the bits that affected other symbols due to the shift of the data v are masked. Therefore, a mask value “0xfefefe” is prepared, and an AND operation is performed on the shifted data v << 1 and the mask value to obtain masked data vv (S102). By this operation, the value at the right end of the 8-bit interval (bits affected by the shift) is set to “0”. That is, since the entire 32 bits are shifted, the rightmost bit of the target symbol is prevented from being affected by the most significant bit of the symbol right next to the target symbol.

  Next, a mask (v) function is created from the target data v as shown in FIG. 17 (S103). As shown in FIG. 17, when the left end of the 8-bit interval of the 32-bit target data v is “1”, the mask (v) function indicates “11111111” of 8 bits and “0” at the left end. ”Represents 8-bit“ 00000000 ”. That is, a mask (v) function is created that applies 8-bit all “1” to symbols carried by shift, and applies 8-bit all “0” to symbols not carried.

  For this reason, the mask value “0x80808080”, that is, “1” appears at an interval of 8 bits, and the others take the logical product (AND) of the value “0” and the target data v (S110). This mask value extracts the first bit of each symbol.

  Next, the 32-bit data v << 1 (double data) obtained by shifting the logical product value by 1 bit to the left is calculated, and the 32-bit data v >> 7 (7-bit data shifted by 7 bits to the right) Subtract 32-bit data v >> 7 shifted 7 bits to the right from 32-bit data v << 1 (double data) shifted by 1 bit to the left, and mask (v) function MASK (v) is obtained (S112). This function has a role of distinguishing a symbol whose first bit is “1” from the other symbols.

  Returning to FIG. 16, the logic of the coefficient value “0x1d1d1d1d” corresponding to the generator polynomial (= x ^ 8 + x ^ 2 + 1) of the 8-bit Galois field GF (2 to the 8th power) and the mask (v) function MASK (v) The product (AND) is calculated (S104). That is, of the four symbols, only the symbol having the leading bit “1” is replaced with “00011101” of the coefficient value “0x1d1d1d1d”.

  XOR of the logical product result and the masked target data vv calculated in step S102 is obtained to obtain target data α · v multiplied by α (S105). If these steps are repeated for the α-folded target data α · v, data of the square of α of the target data v is obtained. Similarly, it is possible to calculate data that is a multiple of α of the target data v.

  Thus, in the prior art, in step S100, substitution, shift, AND in step S101, AND, in step S103 (FIG. 17), AND, double shift, subtraction, in step S104, AND, in step S105, the XOR of By nine operations, parallel processing of Galois volume calculation of several symbols (here, 4 symbols) can be realized.

Japanese Unexamined Patent Publication No. 2000-259359 (FIGS. 5 and 6)

Thesis “The mathematics of RAID-6” (author H. Peter Anvin, online paper, http://kernel.org/pub/linux/kernel/people/hpa/raid6.pdf, accessed October 26, 2006)

  In this conventional Galois field product operation processing, parallel processing of a plurality of symbols (4 symbols in the above example) can be realized. However, in order to multiply by α, 9 steps of operation are required. Therefore, in order to calculate α times the power of n, 9 · n steps are required.

  In particular, with the recent increase in storage capacity, the number of symbols of target data (the number of data disk devices) also tends to increase. For example, 14 data disk devices are provided for two parity disk devices. In the case of configuring RAID 6, it is necessary to calculate the 13th power of α, and 9 · 13 = 117 steps are required, and further reduction of the number of steps is desired.

  In addition, in the case of calculating by repetition, it is desired for speeding up that the number of repetitions or the number of repetitions (the number of loops of the product operation algorithm) is small.

  Further, not only in the generation process but also in the restoration process, it is desired that the number of iterations is small in the Galois field product calculation process from the viewpoint of shortening the processing time.

  Accordingly, an object of the present invention is to provide a RAID device and a Galois field product operation processing method for shortening the processing time of Galois volume operation.

  Another object of the present invention is to provide a RAID apparatus and a Galois field product operation processing method for reducing the number of steps of parallel processing of Galois volume operation.

  It is another object of the present invention to provide a RAID apparatus and Galois field product operation processing method for reducing the number of repetitions of parallel processing of Galois volume operations.

  In order to achieve this object, the RAID device according to the present invention divides data into n parts, n data storage units each storing the divided data, and a first Paris obtained from the combination of the divided data. Stores the tee data and second parity data obtained by multiplying the divided data with a Galois field element in the parity generation equation and calculating the generation equation using the product operation result. A parity storage unit, the data is divided into n, the first parity data and the second parity data are calculated, and the first parity data and the second parity data are And a control unit that stores data in a storage unit, and the control unit sets a minimum integer larger than (n−1) / 2 among the n data storage units to s Then, let α ^ (i−1) be the element of the Galois field of the data of the i = 1 to s + 1th data storage unit, and let the element of the Galois field of the data of the i = s + 2 to the nth data storage unit be The product operation is executed with α ^ (− i + s + 1) as a weight.

  Further, the Galois field product operation processing method of the present invention is for dividing data into n parts and generating parity data of data of n data storage units each storing the divided data by using a Galois field. In the Galois volume calculation processing method, when the smallest integer larger than (n−1) / 2 among the n data storage units is s, the Galois field of data of i = 1 to s + 1th data storage unit Performing a product operation with α ^ (i−1) as the element of i = s + 2 to the Galois field element of the data in the n-th data storage unit and α ^ (− i + s + 1) as a weight. And calculating a generation equation using the parity Galois field with the product operation result.

  In the present invention, it is preferable that the control unit shifts the n-divided data, extracts carry data by shift, creates a mask of carry data, and uses the mask to shift the shifted data. And the correction value are calculated, and the product operation result multiplied by α is calculated.

  In the present invention, it is preferable that the control unit repeats the product operation m times and calculates a product operation result of α ^ m times.

  In the present invention, it is preferable that the control unit sets the data of the data storage unit in which the failure has occurred as unknown data when a failure occurs in any data storage unit of the data storage unit, and the first parity data and The unknown data is restored from the simultaneous equations of the Galois field using second parity data and data of the data storage unit other than the failed data storage unit.

  Assuming that the smallest integer greater than (n−1) / 2 among n data storage units is s, i ^ (i) as the element of the Galois field of data of i = 1 to s + 1th data storage unit -1), i = s + 2 to the nth data storage unit data Galois field element, α ^ (− i + s + 1) is used as a weighting, and the product operation is executed. Galois field product operation is possible.

It is a block diagram of the RAID apparatus of one Embodiment of this invention. It is explanatory drawing of the parity production | generation method of one Embodiment of this invention. It is a Galois volume calculation processing flowchart of the parity Q of FIG. FIG. 3 is a detailed process flow diagram of FIG. It is explanatory drawing of the specific example of the product calculation process of FIG. It is explanatory drawing of the mask creation process of FIG. It is explanatory drawing of the Galois volume calculation process of other embodiment of this invention. It is explanatory drawing of the product calculation process of FIG. It is a Galois volume calculation process flowchart of the parity Q of FIG. FIG. 10 is an operation processing flowchart of FIG. FIG. 10 is a detailed process flow diagram of FIG. It is a Galois volume calculation processing flow figure of another embodiment of this invention. It is explanatory drawing of the product calculation process of FIG. It is a block diagram of conventional RAID6. It is explanatory drawing of the parity data of the conventional RAID6. It is explanatory drawing of the product calculation of the conventional Galois field, It is explanatory drawing of the conventional mask creation processing.

  Hereinafter, embodiments of the present invention will be described in the order of a RAID device, a Galois volume calculation process, another Galois volume calculation process, another Galois volume calculation process, and another embodiment. It is not limited to the embodiment.

(RAID device)
FIG. 1 is a configuration diagram of a RAID device according to an embodiment of the present invention, and FIG. 2 is an explanatory diagram of parity calculation using the Galois field. As shown in FIG. 1, the RAID device includes a RAID controller 12 connected to the host computer 16 and a plurality (14 units in this case) connected to the RAID controller 12 by an FC (Fibre Channel) loop 14 and the like. ) Data disk devices (hard disk drives) 10-1 to 10-14 and two parity disk devices (hard disk drives) 10-15 and 10-16. That is, this is a RAID 6 configuration with double parity.

  As shown in FIG. 2, the first parity P is generated by XOR of the data D1 to D14 in the column direction of the data disk devices 10-1 to 10-14, and the correspondence of the first parity disk device 10-15. Stored in the address. The second parity Q is generated by XORing the data D1 to D14 in the column direction of the data disk devices 10-1 to 10-14 by weighting by product operation of Galois field, and the second parity disk device 10 Stored in the corresponding address of -16. That is, the parity Q is calculated by the following equation (1).

  The symbol “+” indicates an XOR operation. These parity calculations are executed by the RAID controller 12. Here, if one symbol is 16 bits, the Galois field is GF (2 to the 16th power), and its primitive polynomial (generator polynomial) is expressed by the following equation (2).

  In this embodiment, the mask value used for Galois volume calculation is “32768”, and only the most significant bit of 16-bit data is “1” data. Also, the value “4107” is a value obtained by substituting “2” into x, excluding the x16 power of the primitive polynomial in equation (2).

  When the RAID controller 12 writes data to the disk devices 10-1 to 10-4, it calculates the parity P by XOR operation and stores it in the first parity disk device 10-15, which will be described below. The product operation processing and XOR operation of the Galois field to be performed are performed, and the parity Q is calculated and stored in the second parity disk device 10-16.

(Galois volume calculation)
FIG. 3 is a Galois volume calculation processing flow diagram of one embodiment of the present invention, FIG. 4 is a detailed processing flow diagram of FIG. 3, FIG. 5 is an explanatory diagram of specific examples of FIGS. 3 and 4, and FIG. FIG. 10 is an explanatory diagram of a product operation of carry symbols.

  In FIG. 3 and below, an example in which one symbol is 16 bits and 8 symbols are processed in parallel will be described. For example, an Intel (registered trademark) CPU has an MMX instruction set. The MMX instruction set uses xmm registers. Parallel processing is performed using this xmm register. The xmm register length is 16 bytes. When one symbol is 16 bits at a time, parallel processing of weighting of data of 8 symbols can be performed.

  The basic processing of Galois volume calculation will be described with reference to FIG.

  (S10) First, 8 symbols are loaded into the xmm1 register.

  (S12) Next, each symbol in the xmm1 register is shifted to the left by 1 bit, and the value of each symbol is doubled.

  (S14) Using the mask value, a symbol whose value is reduced by the shift (that is, a symbol in which a carry of the most significant bit occurs) is detected.

  (S16) XOR a predetermined value (“4107”) to the symbol having a smaller value among the shifted symbols.

Next, the weighting process using MMX will be described in detail with reference to FIG. In addition, a specific explanation will be given by taking, as an example, weighting of Galois field (product calculation of Galois field) of data disk number i = 2 with reference to FIGS. In the case of the data disk number i = 2, the data D _{i = 2} is weighted by α times from the parity Q generator polynomial of equation (1).

  (S20) Data is substituted into the xmm register, and the number of repetitions MAX to be processed is set. For example, when the disk number i = 2, MAX = 1. Also, the repeat count pointer i is initialized to “0”. Further, when MAX = 0, the contents of the xmm register are output and the following steps are not executed. For example, as shown in FIG. 5, 8 symbols (1 symbol, 16 bits) of data to be weighted (Di = 2 data) are picked up from the disk of data disk number i = 2, and this is substituted into the xmm1 register. (Xmm1 in FIG. 5).

  Also, 8-symbol data v32768 and v4107 into which the values “32768” and “4107” are input are prepared. The value “32768” indicates that there is a value of “1” only in the 16th bit, and is data for detecting a symbol that causes a carry by a shift. The value “4107” is (x ^ 12 + x ^ 3 + x + 1) of the primitive polynomial (x ^ 16 + x ^ 12 + x ^ 3 + x + 1) of the 16-bit Galois field GF (2 ^ 16) ) Is substituted by x = 2. That is, 4096 + 8 + 2 + 1 = 4107.

  (S22) Next, the value assigned to the xmm1 register is moved to the xmm2 register in accordance with the move command (MOVQ). In response to the shift instruction (PSLLW), each symbol of the xmm2 register is shifted to the left (upward) by 1 bit (xmm2 in FIG. 5). Thereby, each symbol is doubled (= α times), but since one symbol is 16 bits, the carried bit portion overflows. For this reason, as shown by xmm2 in FIG. 5, there are a place where the value doubles (single underline) and a place where the value becomes smaller than before the shift (double underline). The place where the value is smaller than before the shift is the place where overflow has occurred.

  (S24) XOR of the value “4107” is performed only on the portion (symbol) where this value becomes small. For this reason, first, a symbol having a smaller value is extracted, and the value of the extracted symbol is all “1” (ie, 65535). This will be described with reference to FIG. In accordance with the AND instruction (PAND), the logical product (AND) of each symbol value of the xmm1 register of FIG. 5 and the value “32768” of the v32768 is obtained, and the xmm1 register is updated. As shown in (xmm1 & v32768) in FIGS. 4 and 5, only the overflowed symbol (the symbol whose value has decreased) among the 8 symbols is replaced with the value “32768”, and the symbol that does not overflow has the value “0”. Is replaced by

  Next, the value determination of 8 symbols is performed, and the value of the symbol is replaced with the value “65535” or the value “0”. That is, according to the comparison and maximum value setting command (PCMPEQW), the value of each symbol of (xmm1 & v32768) is compared with the value “32768”, and if both match, the 16 bits of the symbol are all “1”. If the two do not match, the 16 bits of the symbol are replaced with all “0” (= 0). As a result, a mask of value “4107” is created.

  (S26) Then, in accordance with the AND instruction (PAND), the logical product (AND) of the value of each symbol in the xmm1 register and the value “4107” of v4107 is obtained, and the xmm1 register is updated. Thus, only the symbol having a smaller value in the xmm1 register of 8 symbols is replaced with the value “4107”, and the symbol whose value is not decreased is replaced with the value “0”.

  (S28) In response to the XOR instruction (PXOR), the XOR (exclusive logical ring) between the updated value of each symbol in the xmm1 register and the value of each symbol in the xmm2 register obtained in step S22 is obtained. The result of double weighting is obtained.

  (S30) When “break” is detected, the process is stopped and the value of xmm1 is determined. Otherwise, the process returns to step S24.

  (S32) At the start of the α-fold calculation process, the repetition number pointer i is incremented by “1”. Then, it is determined whether the repetition number pointer i is equal to or larger than the set repetition number MAX. If the repeat count pointer i is not equal to or greater than the set repeat count MAX, the process proceeds to step S24.

  (S34) On the other hand, when the repetition count pointer i is equal to or larger than the set repetition count MAX, the set repetition count is completed, so “break” is notified and xmm1 is output as a result.

  For example, in FIG. 5, when the value “36934” of the second symbol is simply doubled, it becomes “73868”, but since one symbol is limited to 16 bits, overflow occurs, and the value of the symbol is Since it overflows by 1 bit, it is 8332 (= 73868-65536) in 16-bit display. However, the significant value of the double value of the second symbol is 16 bits from the 17th bit to the second bit. In order to correct this significant bit, the correction value “4107” is used and converted to the value “12423”.

  The processing in steps S22 to S28 can be realized by an instruction having a low latency (latency = 2), and the processing time can be shortened. In the weighting of α ^ j times, the processing of steps S22 to S28 is repeated j times.

  Here, the mask processing of this embodiment will be described with reference to FIG. FIG. 6 shows mask processing for extracting a symbol whose value has been reduced by shifting. First, an overflow symbol and a symbol that does not overflow are identified by the value of the xmm1 register and the AND of v32768. Next, these symbols are compared with the value “32768”, and a symbol that matches both is replaced with all “1” (= 65535) to create a mask. Then, AND with the value v4107 is obtained to obtain the desired xmm1.

  On the other hand, as shown in FIG. 17, in the prior art, the value “0x80808080” is added to the original symbol v, and an overflow symbol and a symbol that does not overflow are identified. Next, in order to create a mask from this result, a result obtained by shifting the result by 1 bit to the left and a value shifted by 7 bits to the right are created, and these shift results are subtracted.

  In other words, in the present embodiment, the mask processing of FIG. 6 is performed with two instructions of AND and a comparison instruction for mask creation, but conventionally with four instructions of AND, shift twice, and subtraction instruction. Running.

  Furthermore, in this embodiment, as shown in FIG. 5, the left shift is performed independently for each symbol, whereas in the prior art, as shown in FIG. Done in units. For this reason, the prior art requires an extra process for forcibly replacing the right end of the symbol with “0” after the shift so that the right end of the symbol is not affected by the most significant bit of the right adjacent symbol. .

  Therefore, what was conventionally executed with 9 instructions can be executed with 6 instructions in this embodiment. That is, it takes only 2/3 processing time to multiply by α, and Galois field product operation can be executed at high speed. For example, in the product operation of α to the 13th power, conventionally, 9 × 13 = 117 instructions (steps) are required, but in the present embodiment, 6 × 13 = 78 instructions (steps) are sufficient. Furthermore, in the product operation of Expression (1), conventionally, execution of 9 × (1 + 2 + 3 + 4 + 5 + 6 + 7 + 8 + 9 + 10 + 11 + 12 + 13 = 91) = 819 instructions is required, but in this embodiment, execution of 6 × (1 + 2 + 3 + 4 + 5 + 6 + 7 + 8 + 9 + 10 + 11 + 12 + 13 = 91) = 546 Galois volume calculation can be executed at high speed.

  Furthermore, in this embodiment, since 8 symbols can be processed in parallel, the processing speed can be doubled compared to the conventional 4-symbol parallel processing. As a result, the Galois volume can be obtained in 1/3 processing time. Calculation can be realized.

(Other Galois volume calculation processing)
7 is a process flow diagram of another embodiment of the Galois volume calculation process of the present invention, FIG. 8 is an explanatory diagram of the weighting process of FIG. 7, and FIG. 9 is the product calculation process of α ⁻¹ times of FIG. FIG. 10 is an explanatory diagram of the operation, and FIG. 11 is a detailed processing flowchart of FIG.

  In the above-described embodiment, the processing time for one Galois field product operation process is shortened. However, in this embodiment, the number of loops of the parallel processing algorithm of the product operation process is reduced. The element of the Galois field is determined and the product operation processing time of the Galois field is shortened.

As shown in FIG. 7, similarly to FIGS. 1 and 2, assuming that the data disk device is composed of 14 units, when i = 1 to 8 for data disk number i (= 1 to 14), , Α ⁱ⁻¹ times weighting, weighting calculation processing of FIGS. 4 to 6 is performed, and when i = 9 to 14, weighting by α− ^{i + 8} times is performed, and α ⁻¹ described in FIG. Use a double weighting algorithm.

When this weighting allocation is generalized, an example in which the data disk device is composed of n units, the case where the data disk number i = 1 to s + 1, where s is the smallest integer greater than (n−1) / 2. Performs weighting by α ^ (i−1) times, performs the weighting calculation processing of FIGS. 4 to 6, and when i = s + 2 to n, performs weighting by α− ^{i + s + 1} times.

Since the α-times weighting processing has been described with reference to FIGS. 4 to 6, the description thereof is omitted here, and the α- ¹ times weighting processing is described with reference to FIGS. 8 to 11.

  As shown in FIG. 8, the first parity P is generated by XOR of the data D1 to D14 in the column direction of the data disk devices 10-1 to 10-14, and the correspondence of the first parity disk device 10-15. Stored in the address. The second parity Q is generated by XORing the data D1 to D14 in the column direction of the data disk devices 10-1 to 10-14 by weighting by product operation of Galois field, and the second parity disk device 10 Stored in the corresponding address of -16. That is, the parity Q is calculated by the following equation (3).

  The symbol “+” indicates an XOR operation. These parity calculations are executed by the RAID controller 12. Here, if one symbol is 16 bits, the Galois field is GF (2 to the 16th power), and its primitive polynomial (generator polynomial) is expressed by the above equation (2).

In this embodiment, the mask value used for α- ¹ times Galois volume calculation is “1”, and only the least significant bit of 16-bit data is “1” data. Further, the value “34821” is a value obtained by dividing the primitive polynomial of Expression (2) by x and substituting “2” for x of the divided expression.

  When the RAID controller 12 writes data to the disk devices 10-1 to 10-14, it calculates the parity P by XOR operation and stores it in the first parity disk device 10-15, which will be described below. The product operation processing and XOR operation of the Galois field to be performed are performed, and the parity Q is calculated and stored in the second parity disk device 10-16.

  Even in FIG. 9 and below, an example will be described in which one symbol is 16 bits and eight symbols are processed in parallel. For example, an Intel (registered trademark) CPU has an MMX instruction set. The MMX instruction set uses xmm registers. Parallel processing is performed using this xmm register. The xmm register length is 16 bytes. When one symbol is 16 bits at a time, parallel processing of weighting of data of 8 symbols can be performed.

With reference to FIG. 9, basic processing of α- ¹ times Galois volume calculation will be described.

  (S40) First, 8 symbols are loaded into the xmm1 register.

  (S42) Next, each symbol in the xmm1 register is shifted by one bit to the right (the least significant bit direction), and the value of each symbol is halved.

  (S44) Using the mask value, a symbol whose value is lost due to the shift (that is, a symbol in which the least significant bit “1” of the target symbol disappears) is detected.

  (S46) XOR the predetermined value (“34821”) to the missing symbol among the shifted symbols.

Next, the weighting process using MMX will be described in detail with reference to FIG. Further, a specific explanation will be given with reference to FIG. 10, taking as an example weighting of Galois field (product calculation of Galois field) of α- ¹ times the data disk number i = 9. In the case of the data disk number i = 9, the data D _{i = 9} is weighted by α ⁻¹ times from the parity Q generator polynomial in equation (3).

  (S50) Data is substituted into the xmm register, and the number of repetitions MAX to be processed is set. For example, when the disk number i = 9, MAX = 1. Also, the repeat count pointer i is initialized to “0”. For example, as in FIG. 5, 8 symbols (1 symbol, 16 bits) of data (Di = 9 data) to be weighted are picked up from the disk of data disk number i = 9, and this is substituted into the xmm1 register ( (1) of FIG.

  Also, 8-symbol data v1 and v34821 to which the values “1” and “34821” are input are prepared. The value “1” indicates that only the lowest bit of the first bit has a value of “1”, and is data for detecting a symbol in which a digit is lost due to a left shift.

  The value “34281” is obtained by subtracting “1” from the primitive polynomial (x ^ 16 + x ^ 12 + x ^ 3 + x + 1) of the 16-bit Galois field GF (2 ^ 16) and the result is x This is the value obtained by substituting x = 2 into the divided polynomial (x ^ 15 + x ^ 11 + x ^ 2 + 1). This means (α ^ 16 + α ^ 12 + based on the principle that the primitive polynomial (α ^ 16 + α ^ 12 + α ^ 3 + α + 1) = 0 of the 16-bit Galois field GF (2 ^ 16) α ^ 3 + α) = 1 holds. If “2” is substituted for α, 69642 = 1 is obtained. If both sides are shifted by one bit in the right (least significant) direction, 34821 = value disappears. If “1” is present on the right side of 16-bit data and the right shift is performed, “1” on the right side disappears. Therefore, the value is corrected by XORing “34821”.

(S52) Next, the value assigned to the xmm1 register is moved to the xmm2 register in accordance with the move command (MOVQ). In response to the shift instruction (PSRLW), each symbol of the xmm2 register is shifted to the right (lower direction) by 1 bit (xmm2 in (2) of FIG. 10). As a result, each symbol is halved (= α ⁻¹ ), but since one symbol is 16 bits, the dropped bit portion underflows. For this reason, as in FIG. 5, a place where the value is doubled as it is and a place where a digit is dropped (underflowed place) are mixed.

  (S54) XOR of the value “34821” is performed only on the place (symbol) where the digits are dropped. For this reason, first, a missing symbol is extracted, and the value of the extracted symbol is all “1” (ie, 65535). That is, in accordance with the AND instruction (PAND), the logical product (AND) of the value of each symbol in the xmm1 register of FIG. 10 and the value “1” of v1 is calculated, and the xmm1 register is updated. In (xmm1 & v1), only the symbol having the lowest digit “1” among the 8 symbols is replaced with the value “1”, and the others are replaced with the value “0”.

  Next, the value determination of 8 symbols is performed, and the value of the symbol is replaced with the value “65535” or the value “0”. That is, according to the comparison and maximum value setting command (PCMPEQW), the value of each symbol of (xmm1 & v1) is compared with the value “1”, and if both match, the 16 bits of the symbol are all set to “1”. If the two do not match, the 16 bits of the symbol are replaced with all “0” (= 0). As a result, a mask having a value “34821” is created.

  (S56) Then, in response to the AND instruction (PAND), the logical product (AND) of the value of each symbol in the xmm1 register and the value “34821” of v34821 is calculated, and the xmm1 register is updated. As a result, only the symbol having the lowest digit “1” in the xmm1 register of 8 symbols is replaced with the value “34821”, and the other symbols are replaced with the value “0”.

(S58) In response to the XOR instruction (PXOR), the XOR (exclusive logical ring) between the updated value of each symbol in the xmm1 register and the value of each symbol in the xmm2 register obtained in step S52 is obtained. ^The result of weighting by ^-1 is obtained.

  (S60) When “break” is detected, the process is stopped and the value of xmm1 is determined. Otherwise, the process returns to step S54.

  (S62) At the start of the α ^ −1 times calculation process, the iteration number pointer i is incremented by “1”. Then, it is determined whether the repetition number pointer i is equal to or larger than the set repetition number MAX. If the repeat count pointer i is not equal to or greater than the set repeat count MAX, the process proceeds to step S54.

  (S64) On the other hand, when the repetition count pointer i is equal to or larger than the set repetition count MAX, the set repetition count is completed, so “break” is notified and xmm1 is output as a result.

Thus, the feature of this α- ¹ times weighting algorithm is that the value assigned to the xmm register is shifted by 1 bit to the right, and the basic idea is the same as the α times weighting algorithm. The output is a weighted result of α ^ − (i−8) times for the disk numbers i = 9 to 14.

In this way, the elements of the Galois field need only be different for each disk, and it is not always necessary to use the elements of the Galois field having a multiplier proportional to the disk number i as shown in equation (1). Using this, the Galois field to be used is α ⁱ⁻¹ times and α ^{−i + 8} times with the disk number i that uses the weighting process of α times and α ⁻¹ times and minimizes the number of repetitions. Allocate weights. Thereby, in FIGS. 7 and 8, the maximum number of loops is seven.

  If only the method of FIG. 4 is used, the number of loops is 13 at maximum, and the effect of reducing the number of loops according to this embodiment is great.

In this embodiment, the weighting processing of α times and α ⁻¹ times has been described in the example of FIG. 4. However, α times by another iteration and α ⁿ times by ⁿ iterations. Other methods that can perform product operations are also applicable.

  Of course, if the product operation processing of the embodiment of FIG. 4 is used, even in this embodiment, it can be executed with 6 instructions, and it takes 2/3 processing time to multiply by α. Can perform product operations. Similarly, since 8 symbols can be processed in parallel, the processing can be performed twice as fast as the conventional 4-symbol parallel processing. As a result, Galois volume calculation can be realized in 1/3 processing time.

(Still another Galois volume calculation process)
FIG. 12 is a process flow diagram of still another embodiment of the Galois volume calculation process of the present invention, and FIG. 13 is an explanatory diagram of the process of FIG. This embodiment shows a weighting process of an element α ^ k times of an arbitrary Galois field using the α times arithmetic processing of the embodiments of FIGS. 4 to 6, and has a merit that the maximum number of iterations is 15 times. There is. This product operation processing is effective particularly when k times k is large, and it is preferable to use it when restoring a double disk failure.

  As shown in FIG. 13, for example, when weighting the element α ^ 33653 times (α raised to 33653) of the largest Galois field of the 16-bit Galois field GF (2 ^ 16), α times that in FIG. When the weighting algorithm is used, the number of iterations is 33653, and when the weighting algorithm of α ^ (-1) times in FIG. 7 is used, the number of iterations is 31882, which is not efficient. .

  Therefore, in such a case, an arbitrary Galois field weighting algorithm is used. This algorithm is characterized by the use of a Galois field vector representation. The element of an arbitrary Galois field has the relationship of the following formula (4).

  However, gfw (i) is either “0” or “1”. That is, an arbitrary Galois field can be represented by a binary vector representation (gfw (0), gfw (1),..., Gfw (15)).

  For the weighting of 1 symbol D by α ^ k, the distribution law is established as shown in the following equation (5).

  The weighting process of FIGS. 12 and 13 performs weighting using this distribution law. For example, when weighting α ^ 33653 times, there is a relationship of the following equation (6) from the Galois field law.

  Therefore, in the above-described vector expression, (gfw (0), gfw (1),..., Gfw (15)) = (1, 0, 1, 0,..., 0).

  The number of iterations is set to be the number of iterations MAX = 2 because the maximum i that satisfies gfw (i) = 1 is used as the setting value. The reason for this is that α ^ 3 · D, α ^ 4 · D, ... do not require weighting, so it is possible to reduce the number of extra iterations by specifying “2” as the number of iterations MAX. Thus, the processing time can be shortened.

  FIG. 13 shows an example of weighting α ^ 33653 times of 8-symbol data (D1, D2, D3, D4, D5, D6, D7, D8). When MAX = 2 iterations are repeated, weighted data of α ^ 0 = 1 time, α ^ 1 time, and α ^ 2 times are created. Of these, the i-th α ^ i-fold weighted data satisfying gfw (i) = 1 is added (XOR). In this example, the zeroth and second weighting data are added (XOR).

  Accordingly, the target weighting data α ^ 33653 · Dj (j = 1, 2,..., 8) can be obtained by (α ＾ 0 · Dj + α ^ 2 · Dj).

  The processing will be described with reference to FIG.

  (S70) Data is substituted into the xmm1 register, and the number of repetitions MAX to be processed is set. The xmm2 register is initialized to v0 (all “0”). Also, the repeat count pointer i is initialized to “0”. Further, when MAX = 0, the contents of the xmm register 1 are output and the following steps are not executed. Then, the vector gfw is set.

  Similarly to FIG. 4, 8-symbol data v32768 and v4107 into which the values “32768” and “4107” are input are prepared. The value “32768” indicates that there is a value of “1” only in the 16th bit, and is data for detecting a symbol that causes a carry by a shift. The value “4107” is (x ^ 12 + x ^ 3 + x + 1) of the primitive polynomial (x ^ 16 + x ^ 12 + x ^ 3 + x + 1) of the 16-bit Galois field GF (2 ^ 16) ) Is substituted by x = 2. That is, 4096 + 8 + 2 + 1 = 4107.

  (S72) Next, according to the move command (MOVQ), the value assigned to the xmm1 register is moved to the xmm3 register. In response to the shift instruction (PSLLW), each symbol in the xmm3 register is shifted to the left (upward) by 1 bit. Thereby, each symbol is doubled (= α times), but since one symbol is 16 bits, the carried bit portion overflows. For this reason, there are locations where the value is doubled and locations where the value is smaller than before the shift. The place where the value is smaller than before the shift is the place where overflow has occurred.

  (S74) XOR of the value “4107” is performed only on the portion (symbol) where the value becomes small. For this reason, first, a symbol having a smaller value is extracted, and the value of the extracted symbol is all “1” (ie, 65535). That is, in accordance with the AND instruction (PAND), the logical product (AND) of the value of each symbol of the xmm1 register and the value “32768” of the v32768 is calculated, and the xmm1 register is updated. Of the 8 symbols, only the overflowed symbol (the symbol whose value has decreased) is replaced with the value “32768”, and the non-overflowed symbol is replaced with the value “0”.

  Next, the value determination of 8 symbols is performed, and the value of the symbol is replaced with the value “65535” or the value “0”. That is, according to the comparison and maximum value setting command (PCMPEQW), the value of each symbol of (xmm1 & v32768) is compared with the value “32768”, and if both match, the 16 bits of the symbol are all “1”. If the two do not match, the 16 bits of the symbol are replaced with all “0” (= 0). As a result, a mask of value “4107” is created.

  (S76) Then, in response to the AND instruction (PAND), the logical product (AND) of the value of each symbol in the xmm1 register and the value “4107” of v4107 is obtained, and the xmm1 register is updated. Thus, only the symbol having a smaller value in the xmm1 register of 8 symbols is replaced with the value “4107”, and the symbol whose value is not decreased is replaced with the value “0”.

  (S78) In response to the XOR instruction (PXOR), the XOR (exclusive logical ring) between the updated value of each symbol in the xmm1 register and the value of each symbol in the xmm3 register obtained in step S72 is obtained, and α The result of double weighting is obtained.

  (S80) When “break” is detected, the process is stopped and the value of xmm1 is determined. Otherwise, the process returns to step S74.

  (S82) The XOR calculation unit moves the processing result of the xmm1 register to the xmm4 register in accordance with the move command (MOVQ).

  (S84) It is determined whether gfw (i) at the time of the process is “1”.

  (S86) When gfw (i) is “1”, as described above, since it is an XOR target, the XOR between the contents of the xmm2 register and the contents of the xmm4 register is calculated, Update the xmm2 register.

  (S88) The repeat count pointer i is incremented by “1”.

  (S90) Then, it is determined whether the repetition number pointer i is equal to or larger than the set repetition number MAX. If the repeat count pointer i is not equal to or greater than the set repeat count MAX, the process proceeds to step S74.

  (S92) On the other hand, when the repetition count pointer i is equal to or larger than the set repetition count MAX, the set repetition count is completed, so “break” is notified to the loop of the α-fold calculation unit, and xmm2 is obtained as a result. ,Output.

  In this way, the maximum number of repetitions of the weighting process of α ^ k times can be reduced, which is effective when k is large, and can be restored at high speed when used to restore a double disk failure.

(Other embodiments)
In the above-described embodiment, the description has been given of the RAID 6 storage apparatus including 14 data disk apparatuses and two parity disk apparatuses. However, the present invention can be applied to other configurations.

  Further, the generation of parity Q uses the Galois volume calculation processing of the embodiment of FIG. 4 or the other embodiment of FIG. 11, and the restoration of a double failure using the parity P, Q is shown in FIG. Furthermore, using the Galois volume calculation process of another embodiment can perform both parity generation and restoration at high speed. However, the generation of the parity Q uses the Galois volume calculation processing of the embodiment of FIG. 4 or the other embodiment of FIG. 11, and the restoration of the double fault by the parity P and Q is also the same as the embodiment of FIG. Alternatively, the Galois volume calculation process of another embodiment of FIG. 11 can be used. Further, the Galois volume calculation processing of still another embodiment of FIG. 12 including the embodiment of FIG. 4 can also be used for generation of parity Q and restoration of double failure by parity P, Q.

  As mentioned above, although this invention was demonstrated by embodiment, this invention can be variously deformed within the range of the meaning, and this is not excluded from the scope of the present invention.

  (Supplementary note 1) A plurality of data storage units for dividing data and storing each of the divided data, first parity data obtained from a combination of the divided data, and a Galois field in a parity generation method formula A parity storage unit for storing the second parity data obtained by performing a product operation on the divided data and calculating the generation equation using a product operation result; and dividing the data A control unit that calculates the first parity data and the second parity data, and stores the first parity data and the second parity data in the parity storage unit. The control unit loads each of the divided data into a register, and bit-shifts each data of the register in the upper digit direction to load the loaded data. Data and a fixed value for detecting a carry bit by the shift, and comparing the result of the logical product with the fixed value to obtain the data having the carry bit as the data To create a mask, calculate a logical product of the maximum value of the mask and the correction value for correcting the carry, and perform an exclusive OR (XOR) of the operation result and the shifted data ) To obtain the result of product operation of the data under the Galois field.

  (Supplementary Note 2) When a failure occurs in any data storage unit of the data storage unit, the control unit sets the data in the failed data storage unit as unknown data, and the first parity data and the second parity data. The RAID apparatus according to claim 1, wherein the unknown data is restored from the simultaneous equations of the Galois field using data and data of the data storage unit other than the failed data storage unit.

  (Supplementary note 3) The RAID device according to Supplementary note 1, wherein the control unit uses the fixed value having the same number of bits as the number of bits of the data in which only the most significant bit is "1".

  (Supplementary note 4) The RAID device according to supplementary note 1, wherein the control unit loads a plurality of data into the register and executes the product operation processing on the plurality of data in parallel.

  (Additional remark 5) The said control unit uses the said correction value obtained from the primitive polynomial of the said Galois field, The RAID apparatus of Additional remark 1 characterized by the above-mentioned.

  (Supplementary note 6) The RAID device according to Supplementary note 1, wherein the control unit repeats the product operation for the original degree of the Galois field.

  (Additional remark 7) The said control unit performs the vector operation of the element of the said Galois field, distributes a weight value using a distribution law, and performs the product operation of the element of the said Galois field, It is characterized by the above-mentioned. Appendix 1 RAID device.

  (Supplementary note 8) The control unit executes the product operation of the distributed first weight values for the number of times of the first weight value, and then uses the execution result to execute the product operation of the second weight value. And the product operation result of the first weight value and the product operation result of the second weight value are exclusive-ORed to obtain the original product operation result of the Galois field. The RAID device of appendix 7.

  (Supplementary note 9) n data storage units that divide data into n and store the divided data, first parity data obtained from a combination of the divided data, and Galois in the parity generation equation A parity storage unit that stores a second parity data obtained by performing a product operation on the divided data and calculating the generation equation using a product operation result; and n A control unit that divides, calculates the first parity data and the second parity data, and stores the first parity data and the second parity data in the parity storage unit; The control unit has i = 1 to s + 1th data, where s is the smallest integer greater than (n−1) / 2 among the n data storage units. As a Galois field element of the storage unit data, α ^ (i−1), i = s + 2 to n-th data storage unit data Galois field element, α ^ (− i + s + 1) as a weight, A RAID apparatus that performs the product operation.

  (Supplementary Note 10) The control unit shifts the n-divided data, extracts carry data by the shift, creates a mask of carry data, and uses the mask to convert the shifted data and the correction value. The RAID device according to appendix 9, wherein an XOR operation is performed and a product operation result of α times is calculated.

  (Supplementary note 11) The RAID device according to Supplementary note 10, wherein the control unit repeats the product computation m times and computes a product computation result of α ^ m times.

  (Additional remark 12) When the failure of any data storage unit of the data storage unit, the control unit sets the data of the data storage unit in which the failure has occurred as unknown data, and the first parity data and the second parity data The RAID device according to appendix 9, wherein the unknown data is restored from the simultaneous equations of the Galois field using data and data of the data storage unit other than the failed data storage unit.

  (Supplementary Note 13) A step of loading each of the distributed data into a register, a step of bit-shifting each data of the register in the upper digit direction, and detecting a carry bit by the loaded data and the shift Taking a logical product with a fixed value of the data, comparing the result of the logical product with the fixed value, replacing the data having the carry bits with the maximum value of the data, and creating a mask; and Calculating a logical product of the maximum value of the mask and a correction value for correcting the carry, and calculating an exclusive OR (XOR) of the calculation result and the shifted data, A Galois volume arithmetic processing method, comprising: obtaining a result of product operation of an element of the Galois field.

  (Supplementary Note 14) The logical product step with the fixed value includes a step of using the fixed value having the same number of bits as the number of bits of the data in which only the most significant bit is “1”. The Galois volume calculation processing method according to attachment 13.

  (Supplementary Note 15) The load step includes a step of loading a plurality of data into the register, and the shift step, a logical product step, a creation step, a logical product step, and an exclusive logical sum step are performed on the plurality of data. The Galois volume arithmetic processing method according to appendix 13, which is executed in parallel.

  (Supplementary note 16) The Galois volume arithmetic processing method according to supplementary note 13, wherein the logical product step with the correction value includes a step of using the correction value obtained from the primitive polynomial of the Galois field.

  (Additional remark 17) The Galois volume arithmetic processing method of Additional remark 13 which further has the step which repeats the said product calculation by the original order of the said Galois field.

  (Supplementary note 18) The method further includes the step of performing vector operation on the Galois field element and distributing the weighting value using a distribution law to perform a product operation of the Galois field element. The Galois volume calculation processing method according to Supplementary Note 13.

  (Supplementary Note 19) The execution step includes a step of executing a product operation of the distributed first weight values for the number of times of the first weight value, and a second weight value using the execution result. And the step of obtaining the original product operation result of the Galois field by taking the exclusive OR of the product operation result of the first weight value and the product operation result of the second weight value. The Galois volume calculation processing method according to appendix 18, characterized by comprising:

  (Supplementary note 20) In a Galois volume arithmetic processing method for generating parity data of data of n data storage units each storing divided data by using a Galois field, the n data Assuming that the smallest integer greater than (n−1) / 2 among the data storage units is s, α ^ (i−1) as the element of the Galois field of the data of i = 1 to s + 1th data storage unit. I = s + 2 to the nth data storage unit, the step of executing a product operation using α ^ (− i + s + 1) as the weight of the Galois field element of the data, and the product operation result, A Galois volume calculation processing method comprising a step of calculating a generation equation using a body.

  (Supplementary Note 21) The product calculation step includes shifting the n-divided data, extracting carry data by the shift, creating a mask of carry data, and using the mask, the shifted data and the correction value The Galois volume arithmetic processing method according to appendix 20, characterized by comprising the step of performing an XOR operation of the above and calculating a product operation result of α times.

  (Supplementary note 22) The Galois volume arithmetic processing method according to supplementary note 21, further comprising a step of repeating the product computation m times and computing a product computation result of α ^ m times.

  Assuming that the smallest integer greater than (n−1) / 2 among n data storage units is s, i ^ (i) as the element of the Galois field of data of i = 1 to s + 1th data storage unit -1), i = s + 2 to the nth data storage unit data Galois field element, α ^ (− i + s + 1) is used as a weighting, and the product operation is executed. Galois field product operation is possible.

10-1 to 10-14 Data disk device 10-15 to 10-16 Parity disk device 12 RAID controller 14 Connection bus 16 Host

Claims (2)

N data storage units that divide the data into n and store the divided data respectively;
The first parity data obtained from the combination of the divided data and the Galois field element in the parity generation equation are multiplied with the divided data, and the generation equation is calculated using the product calculation result. A parity storage unit for storing the second parity data obtained by
The data is divided into n, the first parity data and the second parity data are calculated, and the first parity data and the second parity data are stored in the parity storage unit. A control unit,
The control unit is a Galois field element of data of i = 1 to s + 1th data storage unit, where s is the smallest integer greater than (n−1) / 2 among the n data storage units. The product operation is executed by using α ^ (i-1) as the Galois field element of data of i = s + 2 to nth data storage unit and α ^ (-i + s + 1) as a weight. RAID device. In a Galois volume arithmetic processing method for generating parity data of data of n data storage units each storing divided data by using n Galois fields.
Assuming that the smallest integer greater than (n−1) / 2 among the n data storage units is s, as the element of the Galois field of data of i = 1 to s + 1th data storage unit, α ^ ( performing a product operation using i-1) as a weighting element of a Galois field of data of i = s + 2 to n-th data storage unit, α ^ (− i + s + 1),
A Galois volume calculation processing method comprising: calculating a generation equation using the parity Galois field based on the product calculation result.

Images