snapraid/cov/raid/raid.c.gcov.html
2015-12-28 16:31:46 +01:00

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<td class="headerValue">2015-05-12</td>
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<td class="headerCovTableEntry">9</td>
<td class="headerCovTableEntry">9</td>
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<pre class="sourceHeading"> Line data Source code</pre>
<pre class="source">
<a name="1"><span class="lineNum"> 1 </span> : /*</a>
<span class="lineNum"> 2 </span> : * Copyright (C) 2013 Andrea Mazzoleni
<span class="lineNum"> 3 </span> : *
<span class="lineNum"> 4 </span> : * This program is free software: you can redistribute it and/or modify
<span class="lineNum"> 5 </span> : * it under the terms of the GNU General Public License as published by
<span class="lineNum"> 6 </span> : * the Free Software Foundation, either version 2 of the License, or
<span class="lineNum"> 7 </span> : * (at your option) any later version.
<span class="lineNum"> 8 </span> : *
<span class="lineNum"> 9 </span> : * This program is distributed in the hope that it will be useful,
<span class="lineNum"> 10 </span> : * but WITHOUT ANY WARRANTY; without even the implied warranty of
<span class="lineNum"> 11 </span> : * MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
<span class="lineNum"> 12 </span> : * GNU General Public License for more details.
<span class="lineNum"> 13 </span> : */
<span class="lineNum"> 14 </span> :
<span class="lineNum"> 15 </span> : #include &quot;internal.h&quot;
<span class="lineNum"> 16 </span> : #include &quot;gf.h&quot;
<span class="lineNum"> 17 </span> :
<span class="lineNum"> 18 </span> : /*
<span class="lineNum"> 19 </span> : * This is a RAID implementation working in the Galois Field GF(2^8) with
<span class="lineNum"> 20 </span> : * the primitive polynomial x^8 + x^4 + x^3 + x^2 + 1 (285 decimal), and
<span class="lineNum"> 21 </span> : * supporting up to six parity levels.
<span class="lineNum"> 22 </span> : *
<span class="lineNum"> 23 </span> : * For RAID5 and RAID6 it works as as described in the H. Peter Anvin's
<span class="lineNum"> 24 </span> : * paper &quot;The mathematics of RAID-6&quot; [1]. Please refer to this paper for a
<span class="lineNum"> 25 </span> : * complete explanation.
<span class="lineNum"> 26 </span> : *
<span class="lineNum"> 27 </span> : * To support triple parity, it was first evaluated and then dropped, an
<span class="lineNum"> 28 </span> : * extension of the same approach, with additional parity coefficients set
<span class="lineNum"> 29 </span> : * as powers of 2^-1, with equations:
<span class="lineNum"> 30 </span> : *
<span class="lineNum"> 31 </span> : * P = sum(Di)
<span class="lineNum"> 32 </span> : * Q = sum(2^i * Di)
<span class="lineNum"> 33 </span> : * R = sum(2^-i * Di) with 0&lt;=i&lt;N
<span class="lineNum"> 34 </span> : *
<span class="lineNum"> 35 </span> : * This approach works well for triple parity and it's very efficient,
<span class="lineNum"> 36 </span> : * because we can implement very fast parallel multiplications and
<span class="lineNum"> 37 </span> : * divisions by 2 in GF(2^8).
<span class="lineNum"> 38 </span> : *
<span class="lineNum"> 39 </span> : * It's also similar at the approach used by ZFS RAIDZ3, with the
<span class="lineNum"> 40 </span> : * difference that ZFS uses powers of 4 instead of 2^-1.
<span class="lineNum"> 41 </span> : *
<span class="lineNum"> 42 </span> : * Unfortunately it doesn't work beyond triple parity, because whatever
<span class="lineNum"> 43 </span> : * value we choose to generate the power coefficients to compute other
<span class="lineNum"> 44 </span> : * parities, the resulting equations are not solvable for some
<span class="lineNum"> 45 </span> : * combinations of missing disks.
<span class="lineNum"> 46 </span> : *
<span class="lineNum"> 47 </span> : * This is expected, because the Vandermonde matrix used to compute the
<span class="lineNum"> 48 </span> : * parity has no guarantee to have all submatrices not singular
<span class="lineNum"> 49 </span> : * [2, Chap 11, Problem 7] and this is a requirement to have
<span class="lineNum"> 50 </span> : * a MDS (Maximum Distance Separable) code [2, Chap 11, Theorem 8].
<span class="lineNum"> 51 </span> : *
<span class="lineNum"> 52 </span> : * To overcome this limitation, we use a Cauchy matrix [3][4] to compute
<span class="lineNum"> 53 </span> : * the parity. A Cauchy matrix has the property to have all the square
<span class="lineNum"> 54 </span> : * submatrices not singular, resulting in always solvable equations,
<span class="lineNum"> 55 </span> : * for any combination of missing disks.
<span class="lineNum"> 56 </span> : *
<span class="lineNum"> 57 </span> : * The problem of this approach is that it requires the use of
<span class="lineNum"> 58 </span> : * generic multiplications, and not only by 2 or 2^-1, potentially
<span class="lineNum"> 59 </span> : * affecting badly the performance.
<span class="lineNum"> 60 </span> : *
<span class="lineNum"> 61 </span> : * Hopefully there is a method to implement parallel multiplications
<span class="lineNum"> 62 </span> : * using SSSE3 or AVX2 instructions [1][5]. Method competitive with the
<span class="lineNum"> 63 </span> : * computation of triple parity using power coefficients.
<span class="lineNum"> 64 </span> : *
<span class="lineNum"> 65 </span> : * Another important property of the Cauchy matrix is that we can setup
<span class="lineNum"> 66 </span> : * the first two rows with coeffients equal at the RAID5 and RAID6 approach
<span class="lineNum"> 67 </span> : * decribed, resulting in a compatible extension, and requiring SSSE3
<span class="lineNum"> 68 </span> : * or AVX2 instructions only if triple parity or beyond is used.
<span class="lineNum"> 69 </span> : *
<span class="lineNum"> 70 </span> : * The matrix is also adjusted, multipling each row by a constant factor
<span class="lineNum"> 71 </span> : * to make the first column of all 1, to optimize the computation for
<span class="lineNum"> 72 </span> : * the first disk.
<span class="lineNum"> 73 </span> : *
<span class="lineNum"> 74 </span> : * This results in the matrix A[row,col] defined as:
<span class="lineNum"> 75 </span> : *
<span class="lineNum"> 76 </span> : * 01 01 01 01 01 01 01 01 01 01 01 01 01 01 01 01 01 01 01 01 01 01...
<span class="lineNum"> 77 </span> : * 01 02 04 08 10 20 40 80 1d 3a 74 e8 cd 87 13 26 4c 98 2d 5a b4 75...
<span class="lineNum"> 78 </span> : * 01 f5 d2 c4 9a 71 f1 7f fc 87 c1 c6 19 2f 40 55 3d ba 53 04 9c 61...
<span class="lineNum"> 79 </span> : * 01 bb a6 d7 c7 07 ce 82 4a 2f a5 9b b6 60 f1 ad e7 f4 06 d2 df 2e...
<span class="lineNum"> 80 </span> : * 01 97 7f 9c 7c 18 bd a2 58 1a da 74 70 a3 e5 47 29 07 f5 80 23 e9...
<span class="lineNum"> 81 </span> : * 01 2b 3f cf 73 2c d6 ed cb 74 15 78 8a c1 17 c9 89 68 21 ab 76 3b...
<span class="lineNum"> 82 </span> : *
<span class="lineNum"> 83 </span> : * This matrix supports 6 level of parity, one for each row, for up to 251
<span class="lineNum"> 84 </span> : * data disks, one for each column, with all the 377,342,351,231 square
<span class="lineNum"> 85 </span> : * submatrices not singular, verified also with brute-force.
<span class="lineNum"> 86 </span> : *
<span class="lineNum"> 87 </span> : * This matrix can be extended to support any number of parities, just
<span class="lineNum"> 88 </span> : * adding additional rows, and removing one column for each new row.
<span class="lineNum"> 89 </span> : * (see mktables.c for more details in how the matrix is generated)
<span class="lineNum"> 90 </span> : *
<span class="lineNum"> 91 </span> : * In details, parity is computed as:
<span class="lineNum"> 92 </span> : *
<span class="lineNum"> 93 </span> : * P = sum(Di)
<span class="lineNum"> 94 </span> : * Q = sum(2^i * Di)
<span class="lineNum"> 95 </span> : * R = sum(A[2,i] * Di)
<span class="lineNum"> 96 </span> : * S = sum(A[3,i] * Di)
<span class="lineNum"> 97 </span> : * T = sum(A[4,i] * Di)
<span class="lineNum"> 98 </span> : * U = sum(A[5,i] * Di) with 0&lt;=i&lt;N
<span class="lineNum"> 99 </span> : *
<span class="lineNum"> 100 </span> : * To recover from a failure of six disks at indexes x,y,z,h,v,w,
<span class="lineNum"> 101 </span> : * with 0&lt;=x&lt;y&lt;z&lt;h&lt;v&lt;w&lt;N, we compute the parity of the available N-6
<span class="lineNum"> 102 </span> : * disks as:
<span class="lineNum"> 103 </span> : *
<span class="lineNum"> 104 </span> : * Pa = sum(Di)
<span class="lineNum"> 105 </span> : * Qa = sum(2^i * Di)
<span class="lineNum"> 106 </span> : * Ra = sum(A[2,i] * Di)
<span class="lineNum"> 107 </span> : * Sa = sum(A[3,i] * Di)
<span class="lineNum"> 108 </span> : * Ta = sum(A[4,i] * Di)
<span class="lineNum"> 109 </span> : * Ua = sum(A[5,i] * Di) with 0&lt;=i&lt;N,i!=x,i!=y,i!=z,i!=h,i!=v,i!=w.
<span class="lineNum"> 110 </span> : *
<span class="lineNum"> 111 </span> : * And if we define:
<span class="lineNum"> 112 </span> : *
<span class="lineNum"> 113 </span> : * Pd = Pa + P
<span class="lineNum"> 114 </span> : * Qd = Qa + Q
<span class="lineNum"> 115 </span> : * Rd = Ra + R
<span class="lineNum"> 116 </span> : * Sd = Sa + S
<span class="lineNum"> 117 </span> : * Td = Ta + T
<span class="lineNum"> 118 </span> : * Ud = Ua + U
<span class="lineNum"> 119 </span> : *
<span class="lineNum"> 120 </span> : * we can sum these two sets of equations, obtaining:
<span class="lineNum"> 121 </span> : *
<span class="lineNum"> 122 </span> : * Pd = Dx + Dy + Dz + Dh + Dv + Dw
<span class="lineNum"> 123 </span> : * Qd = 2^x * Dx + 2^y * Dy + 2^z * Dz + 2^h * Dh + 2^v * Dv + 2^w * Dw
<span class="lineNum"> 124 </span> : * Rd = A[2,x] * Dx + A[2,y] * Dy + A[2,z] * Dz + A[2,h] * Dh + A[2,v] * Dv + A[2,w] * Dw
<span class="lineNum"> 125 </span> : * Sd = A[3,x] * Dx + A[3,y] * Dy + A[3,z] * Dz + A[3,h] * Dh + A[3,v] * Dv + A[3,w] * Dw
<span class="lineNum"> 126 </span> : * Td = A[4,x] * Dx + A[4,y] * Dy + A[4,z] * Dz + A[4,h] * Dh + A[4,v] * Dv + A[4,w] * Dw
<span class="lineNum"> 127 </span> : * Ud = A[5,x] * Dx + A[5,y] * Dy + A[5,z] * Dz + A[5,h] * Dh + A[5,v] * Dv + A[5,w] * Dw
<span class="lineNum"> 128 </span> : *
<span class="lineNum"> 129 </span> : * A linear system always solvable because the coefficients matrix is
<span class="lineNum"> 130 </span> : * always not singular due the properties of the matrix A[].
<span class="lineNum"> 131 </span> : *
<span class="lineNum"> 132 </span> : * Resulting speed in x64, with 8 data disks, using a stripe of 256 KiB,
<span class="lineNum"> 133 </span> : * for a Core i5-4670K Haswell Quad-Core 3.4GHz is:
<span class="lineNum"> 134 </span> : *
<span class="lineNum"> 135 </span> : * int8 int32 int64 sse2 ssse3 avx2
<span class="lineNum"> 136 </span> : * gen1 13339 25438 45438 50588
<span class="lineNum"> 137 </span> : * gen2 4115 6514 21840 32201
<span class="lineNum"> 138 </span> : * gen3 814 10154 18613
<span class="lineNum"> 139 </span> : * gen4 620 7569 14229
<span class="lineNum"> 140 </span> : * gen5 496 5149 10051
<span class="lineNum"> 141 </span> : * gen6 413 4239 8190
<span class="lineNum"> 142 </span> : *
<span class="lineNum"> 143 </span> : * Values are in MiB/s of data processed by a single thread, not counting
<span class="lineNum"> 144 </span> : * generated parity.
<span class="lineNum"> 145 </span> : *
<span class="lineNum"> 146 </span> : * You can replicate these results in your machine using the
<span class="lineNum"> 147 </span> : * &quot;raid/test/speedtest.c&quot; program.
<span class="lineNum"> 148 </span> : *
<span class="lineNum"> 149 </span> : * For comparison, the triple parity computation using the power
<span class="lineNum"> 150 </span> : * coeffients &quot;1,2,2^-1&quot; is only a little faster than the one based on
<span class="lineNum"> 151 </span> : * the Cauchy matrix if SSSE3 or AVX2 is present.
<span class="lineNum"> 152 </span> : *
<span class="lineNum"> 153 </span> : * int8 int32 int64 sse2 ssse3 avx2
<span class="lineNum"> 154 </span> : * genz 2337 2874 10920 18944
<span class="lineNum"> 155 </span> : *
<span class="lineNum"> 156 </span> : * In conclusion, the use of power coefficients, and specifically powers
<span class="lineNum"> 157 </span> : * of 1,2,2^-1, is the best option to implement triple parity in CPUs
<span class="lineNum"> 158 </span> : * without SSSE3 and AVX2.
<span class="lineNum"> 159 </span> : * But if a modern CPU with SSSE3 or AVX2 is available, the Cauchy
<span class="lineNum"> 160 </span> : * matrix is the best option because it provides a fast and general
<span class="lineNum"> 161 </span> : * approach working for any number of parities.
<span class="lineNum"> 162 </span> : *
<span class="lineNum"> 163 </span> : * References:
<span class="lineNum"> 164 </span> : * [1] Anvin, &quot;The mathematics of RAID-6&quot;, 2004
<span class="lineNum"> 165 </span> : * [2] MacWilliams, Sloane, &quot;The Theory of Error-Correcting Codes&quot;, 1977
<span class="lineNum"> 166 </span> : * [3] Blomer, &quot;An XOR-Based Erasure-Resilient Coding Scheme&quot;, 1995
<span class="lineNum"> 167 </span> : * [4] Roth, &quot;Introduction to Coding Theory&quot;, 2006
<span class="lineNum"> 168 </span> : * [5] Plank, &quot;Screaming Fast Galois Field Arithmetic Using Intel SIMD Instructions&quot;, 2013
<span class="lineNum"> 169 </span> : */
<span class="lineNum"> 170 </span> :
<span class="lineNum"> 171 </span> : /**
<span class="lineNum"> 172 </span> : * Generator matrix currently used.
<span class="lineNum"> 173 </span> : */
<a name="174"><span class="lineNum"> 174 </span> : const uint8_t (*raid_gfgen)[256];</a>
<span class="lineNum"> 175 </span> :
<span class="lineNum"> 176 </span><span class="lineCov"> 480 : void raid_mode(int mode)</span>
<span class="lineNum"> 177 </span> : {
<span class="lineNum"> 178 </span><span class="lineCov"> 480 : if (mode == RAID_MODE_VANDERMONDE) {</span>
<span class="lineNum"> 179 </span><span class="lineCov"> 2 : raid_gen_ptr[2] = raid_genz_ptr;</span>
<span class="lineNum"> 180 </span><span class="lineCov"> 2 : raid_gfgen = gfvandermonde;</span>
<span class="lineNum"> 181 </span> : } else {
<span class="lineNum"> 182 </span><span class="lineCov"> 478 : raid_gen_ptr[2] = raid_gen3_ptr;</span>
<span class="lineNum"> 183 </span><span class="lineCov"> 478 : raid_gfgen = gfcauchy;</span>
<span class="lineNum"> 184 </span> : }
<span class="lineNum"> 185 </span><span class="lineCov"> 480 : }</span>
<span class="lineNum"> 186 </span> :
<span class="lineNum"> 187 </span> : /**
<span class="lineNum"> 188 </span> : * Buffer filled with 0 used in recovering.
<span class="lineNum"> 189 </span> : */
<a name="190"><span class="lineNum"> 190 </span> : static void *raid_zero_block;</a>
<span class="lineNum"> 191 </span> :
<span class="lineNum"> 192 </span><span class="lineCov"> 187 : void raid_zero(void *zero)</span>
<span class="lineNum"> 193 </span> : {
<span class="lineNum"> 194 </span><span class="lineCov"> 187 : raid_zero_block = zero;</span>
<span class="lineNum"> 195 </span><span class="lineCov"> 187 : }</span>
<span class="lineNum"> 196 </span> :
<span class="lineNum"> 197 </span> : /*
<span class="lineNum"> 198 </span> : * Forwarders for parity computation.
<span class="lineNum"> 199 </span> : *
<span class="lineNum"> 200 </span> : * These functions compute the parity blocks from the provided data.
<span class="lineNum"> 201 </span> : *
<span class="lineNum"> 202 </span> : * The number of parities to compute is implicit in the position in the
<span class="lineNum"> 203 </span> : * forwarder vector. Position at index #i, computes (#i+1) parities.
<span class="lineNum"> 204 </span> : *
<span class="lineNum"> 205 </span> : * All these functions give the guarantee that parities are written
<span class="lineNum"> 206 </span> : * in order. First parity P, then parity Q, and so on.
<span class="lineNum"> 207 </span> : * This allows to specify the same memory buffer for multiple parities
<span class="lineNum"> 208 </span> : * knowning that you'll get the latest written one.
<span class="lineNum"> 209 </span> : * This characteristic is used by the raid_delta_gen() function to
<span class="lineNum"> 210 </span> : * avoid to damage unused parities in recovering.
<span class="lineNum"> 211 </span> : *
<span class="lineNum"> 212 </span> : * @nd Number of data blocks
<span class="lineNum"> 213 </span> : * @size Size of the blocks pointed by @v. It must be a multipler of 64.
<span class="lineNum"> 214 </span> : * @v Vector of pointers to the blocks of data and parity.
<span class="lineNum"> 215 </span> : * It has (@nd + #parities) elements. The starting elements are the blocks
<span class="lineNum"> 216 </span> : * for data, following with the parity blocks.
<span class="lineNum"> 217 </span> : * Each block has @size bytes.
<span class="lineNum"> 218 </span> : */
<span class="lineNum"> 219 </span> : void (*raid_gen_ptr[RAID_PARITY_MAX])(int nd, size_t size, void **vv);
<span class="lineNum"> 220 </span> : void (*raid_gen3_ptr)(int nd, size_t size, void **vv);
<a name="221"><span class="lineNum"> 221 </span> : void (*raid_genz_ptr)(int nd, size_t size, void **vv);</a>
<span class="lineNum"> 222 </span> :
<span class="lineNum"> 223 </span><span class="lineCov"> 1196804 : void raid_gen(int nd, int np, size_t size, void **v)</span>
<span class="lineNum"> 224 </span> : {
<span class="lineNum"> 225 </span> : /* enforce limit on size */
<span class="lineNum"> 226 </span><span class="lineCov"> 1196804 : BUG_ON(size % 64 != 0);</span>
<span class="lineNum"> 227 </span> :
<span class="lineNum"> 228 </span> : /* enforce limit on number of failures */
<span class="lineNum"> 229 </span><span class="lineCov"> 1196804 : BUG_ON(np &lt; 1);</span>
<span class="lineNum"> 230 </span><span class="lineCov"> 1196804 : BUG_ON(np &gt; RAID_PARITY_MAX);</span>
<span class="lineNum"> 231 </span> :
<span class="lineNum"> 232 </span><span class="lineCov"> 1196804 : raid_gen_ptr[np - 1](nd, size, v);</span>
<span class="lineNum"> 233 </span><span class="lineCov"> 1196804 : }</span>
<span class="lineNum"> 234 </span> :
<span class="lineNum"> 235 </span> : /**
<span class="lineNum"> 236 </span> : * Inverts the square matrix M of size nxn into V.
<span class="lineNum"> 237 </span> : *
<span class="lineNum"> 238 </span> : * This is not a general matrix inversion because we assume the matrix M
<span class="lineNum"> 239 </span> : * to have all the square submatrix not singular.
<span class="lineNum"> 240 </span> : * We use Gauss elimination to invert.
<span class="lineNum"> 241 </span> : *
<span class="lineNum"> 242 </span> : * @M Matrix to invert with @n rows and @n columns.
<span class="lineNum"> 243 </span> : * @V Destination matrix where the result is put.
<a name="244"><span class="lineNum"> 244 </span> : * @n Number of rows and columns of the matrix.</a>
<span class="lineNum"> 245 </span> : */
<span class="lineNum"> 246 </span><span class="lineCov"> 172492 : void raid_invert(uint8_t *M, uint8_t *V, int n)</span>
<span class="lineNum"> 247 </span> : {
<span class="lineNum"> 248 </span> : int i, j, k;
<span class="lineNum"> 249 </span> :
<span class="lineNum"> 250 </span> : /* set the identity matrix in V */
<span class="lineNum"> 251 </span><span class="lineCov"> 797645 : for (i = 0; i &lt; n; ++i)</span>
<span class="lineNum"> 252 </span><span class="lineCov"> 3220636 : for (j = 0; j &lt; n; ++j)</span>
<span class="lineNum"> 253 </span><span class="lineCov"> 2595483 : V[i * n + j] = i == j;</span>
<span class="lineNum"> 254 </span> :
<span class="lineNum"> 255 </span> : /* for each element in the diagonal */
<span class="lineNum"> 256 </span><span class="lineCov"> 797645 : for (k = 0; k &lt; n; ++k) {</span>
<span class="lineNum"> 257 </span> : uint8_t f;
<span class="lineNum"> 258 </span> :
<span class="lineNum"> 259 </span> : /* the diagonal element cannot be 0 because */
<span class="lineNum"> 260 </span> : /* we are inverting matrices with all the square */
<span class="lineNum"> 261 </span> : /* submatrices not singular */
<span class="lineNum"> 262 </span><span class="lineCov"> 625153 : BUG_ON(M[k * n + k] == 0);</span>
<span class="lineNum"> 263 </span> :
<span class="lineNum"> 264 </span> : /* make the diagonal element to be 1 */
<span class="lineNum"> 265 </span><span class="lineCov"> 1250306 : f = inv(M[k * n + k]);</span>
<span class="lineNum"> 266 </span><span class="lineCov"> 3220636 : for (j = 0; j &lt; n; ++j) {</span>
<span class="lineNum"> 267 </span><span class="lineCov"> 5190966 : M[k * n + j] = mul(f, M[k * n + j]);</span>
<span class="lineNum"> 268 </span><span class="lineCov"> 5190966 : V[k * n + j] = mul(f, V[k * n + j]);</span>
<span class="lineNum"> 269 </span> : }
<span class="lineNum"> 270 </span> :
<span class="lineNum"> 271 </span> : /* make all the elements over and under the diagonal */
<span class="lineNum"> 272 </span> : /* to be zero */
<span class="lineNum"> 273 </span><span class="lineCov"> 3220636 : for (i = 0; i &lt; n; ++i) {</span>
<span class="lineNum"> 274 </span><span class="lineCov"> 2595483 : if (i == k)</span>
<span class="lineNum"> 275 </span><span class="lineCov"> 625153 : continue;</span>
<span class="lineNum"> 276 </span><span class="lineCov"> 1970330 : f = M[i * n + k];</span>
<span class="lineNum"> 277 </span><span class="lineCov"> 11280588 : for (j = 0; j &lt; n; ++j) {</span>
<span class="lineNum"> 278 </span><span class="lineCov"> 18620516 : M[i * n + j] ^= mul(f, M[k * n + j]);</span>
<span class="lineNum"> 279 </span><span class="lineCov"> 18620516 : V[i * n + j] ^= mul(f, V[k * n + j]);</span>
<span class="lineNum"> 280 </span> : }
<span class="lineNum"> 281 </span> : }
<span class="lineNum"> 282 </span> : }
<span class="lineNum"> 283 </span><span class="lineCov"> 172492 : }</span>
<span class="lineNum"> 284 </span> :
<span class="lineNum"> 285 </span> : /**
<span class="lineNum"> 286 </span> : * Computes the parity without the missing data blocks
<span class="lineNum"> 287 </span> : * and store it in the buffers of such data blocks.
<span class="lineNum"> 288 </span> : *
<a name="289"><span class="lineNum"> 289 </span> : * This is the parity expressed as Pa,Qa,Ra,Sa,Ta,Ua in the equations.</a>
<span class="lineNum"> 290 </span> : */
<span class="lineNum"> 291 </span><span class="lineCov"> 171154 : void raid_delta_gen(int nr, int *id, int *ip, int nd, size_t size, void **v)</span>
<span class="lineNum"> 292 </span> : {
<span class="lineNum"> 293 </span> : void *p[RAID_PARITY_MAX];
<span class="lineNum"> 294 </span> : void *pa[RAID_PARITY_MAX];
<span class="lineNum"> 295 </span> : int i, j;
<span class="lineNum"> 296 </span> : int np;
<span class="lineNum"> 297 </span> : void *latest;
<span class="lineNum"> 298 </span> :
<span class="lineNum"> 299 </span> : /* total number of parities we are going to process */
<span class="lineNum"> 300 </span> : /* they are both the used and the unused ones */
<span class="lineNum"> 301 </span><span class="lineCov"> 171154 : np = ip[nr - 1] + 1;</span>
<span class="lineNum"> 302 </span> :
<span class="lineNum"> 303 </span> : /* latest missing data block */
<span class="lineNum"> 304 </span><span class="lineCov"> 171154 : latest = v[id[nr - 1]];</span>
<span class="lineNum"> 305 </span> :
<span class="lineNum"> 306 </span> : /* setup pointers for delta computation */
<span class="lineNum"> 307 </span><span class="lineCov"> 872118 : for (i = 0, j = 0; i &lt; np; ++i) {</span>
<span class="lineNum"> 308 </span> : /* keep a copy of the original parity vector */
<span class="lineNum"> 309 </span><span class="lineCov"> 700964 : p[i] = v[nd + i];</span>
<span class="lineNum"> 310 </span> :
<span class="lineNum"> 311 </span><span class="lineCov"> 700964 : if (ip[j] == i) {</span>
<span class="lineNum"> 312 </span> : /*
<span class="lineNum"> 313 </span> : * Set used parities to point to the missing
<span class="lineNum"> 314 </span> : * data blocks.
<span class="lineNum"> 315 </span> : *
<span class="lineNum"> 316 </span> : * The related data blocks are instead set
<span class="lineNum"> 317 </span> : * to point to the &quot;zero&quot; buffer.
<span class="lineNum"> 318 </span> : */
<span class="lineNum"> 319 </span> :
<span class="lineNum"> 320 </span> : /* the latest parity to use ends the for loop and */
<span class="lineNum"> 321 </span> : /* then it cannot happen to process more of them */
<span class="lineNum"> 322 </span><span class="lineCov"> 605141 : BUG_ON(j &gt;= nr);</span>
<span class="lineNum"> 323 </span> :
<span class="lineNum"> 324 </span> : /* buffer for missing data blocks */
<span class="lineNum"> 325 </span><span class="lineCov"> 605141 : pa[j] = v[id[j]];</span>
<span class="lineNum"> 326 </span> :
<span class="lineNum"> 327 </span> : /* set at zero the missing data blocks */
<span class="lineNum"> 328 </span><span class="lineCov"> 605141 : v[id[j]] = raid_zero_block;</span>
<span class="lineNum"> 329 </span> :
<span class="lineNum"> 330 </span> : /* compute the parity over the missing data blocks */
<span class="lineNum"> 331 </span><span class="lineCov"> 605141 : v[nd + i] = pa[j];</span>
<span class="lineNum"> 332 </span> :
<span class="lineNum"> 333 </span> : /* check for the next used entry */
<span class="lineNum"> 334 </span><span class="lineCov"> 605141 : ++j;</span>
<span class="lineNum"> 335 </span> : } else {
<span class="lineNum"> 336 </span> : /*
<span class="lineNum"> 337 </span> : * Unused parities are going to be rewritten with
<span class="lineNum"> 338 </span> : * not significative data, becase we don't have
<span class="lineNum"> 339 </span> : * functions able to compute only a subset of
<span class="lineNum"> 340 </span> : * parities.
<span class="lineNum"> 341 </span> : *
<span class="lineNum"> 342 </span> : * To avoid this, we reuse parity buffers,
<span class="lineNum"> 343 </span> : * assuming that all the parity functions write
<span class="lineNum"> 344 </span> : * parities in order.
<span class="lineNum"> 345 </span> : *
<span class="lineNum"> 346 </span> : * We assign the unused parity block to the same
<span class="lineNum"> 347 </span> : * block of the latest used parity that we know it
<span class="lineNum"> 348 </span> : * will be written.
<span class="lineNum"> 349 </span> : *
<span class="lineNum"> 350 </span> : * This means that this block will be written
<span class="lineNum"> 351 </span> : * multiple times and only the latest write will
<span class="lineNum"> 352 </span> : * contain the correct data.
<span class="lineNum"> 353 </span> : */
<span class="lineNum"> 354 </span><span class="lineCov"> 95823 : v[nd + i] = latest;</span>
<span class="lineNum"> 355 </span> : }
<span class="lineNum"> 356 </span> : }
<span class="lineNum"> 357 </span> :
<span class="lineNum"> 358 </span> : /* all the parities have to be processed */
<span class="lineNum"> 359 </span><span class="lineCov"> 171154 : BUG_ON(j != nr);</span>
<span class="lineNum"> 360 </span> :
<span class="lineNum"> 361 </span> : /* recompute the parity, note that np may be smaller than the */
<span class="lineNum"> 362 </span> : /* total number of parities available */
<span class="lineNum"> 363 </span><span class="lineCov"> 171154 : raid_gen(nd, np, size, v);</span>
<span class="lineNum"> 364 </span> :
<span class="lineNum"> 365 </span> : /* restore data buffers as before */
<span class="lineNum"> 366 </span><span class="lineCov"> 776295 : for (j = 0; j &lt; nr; ++j)</span>
<span class="lineNum"> 367 </span><span class="lineCov"> 605141 : v[id[j]] = pa[j];</span>
<span class="lineNum"> 368 </span> :
<span class="lineNum"> 369 </span> : /* restore parity buffers as before */
<span class="lineNum"> 370 </span><span class="lineCov"> 872118 : for (i = 0; i &lt; np; ++i)</span>
<span class="lineNum"> 371 </span><span class="lineCov"> 700964 : v[nd + i] = p[i];</span>
<span class="lineNum"> 372 </span><span class="lineCov"> 171154 : }</span>
<span class="lineNum"> 373 </span> :
<span class="lineNum"> 374 </span> : /**
<span class="lineNum"> 375 </span> : * Recover failure of one data block for PAR1.
<span class="lineNum"> 376 </span> : *
<span class="lineNum"> 377 </span> : * Starting from the equation:
<span class="lineNum"> 378 </span> : *
<span class="lineNum"> 379 </span> : * Pd = Dx
<span class="lineNum"> 380 </span> : *
<span class="lineNum"> 381 </span> : * and solving we get:
<span class="lineNum"> 382 </span> : *
<a name="383"><span class="lineNum"> 383 </span> : * Dx = Pd</a>
<span class="lineNum"> 384 </span> : */
<span class="lineNum"> 385 </span><span class="lineCov"> 100552 : void raid_rec1of1(int *id, int nd, size_t size, void **v)</span>
<span class="lineNum"> 386 </span> : {
<span class="lineNum"> 387 </span> : void *p;
<span class="lineNum"> 388 </span> : void *pa;
<span class="lineNum"> 389 </span> :
<span class="lineNum"> 390 </span> : /* for PAR1 we can directly compute the missing block */
<span class="lineNum"> 391 </span> : /* and we don't need to use the zero buffer */
<span class="lineNum"> 392 </span><span class="lineCov"> 100552 : p = v[nd];</span>
<span class="lineNum"> 393 </span><span class="lineCov"> 100552 : pa = v[id[0]];</span>
<span class="lineNum"> 394 </span> :
<span class="lineNum"> 395 </span> : /* use the parity as missing data block */
<span class="lineNum"> 396 </span><span class="lineCov"> 100552 : v[id[0]] = p;</span>
<span class="lineNum"> 397 </span> :
<span class="lineNum"> 398 </span> : /* compute the parity over the missing data block */
<span class="lineNum"> 399 </span><span class="lineCov"> 100552 : v[nd] = pa;</span>
<span class="lineNum"> 400 </span> :
<span class="lineNum"> 401 </span> : /* compute */
<span class="lineNum"> 402 </span><span class="lineCov"> 100552 : raid_gen(nd, 1, size, v);</span>
<span class="lineNum"> 403 </span> :
<span class="lineNum"> 404 </span> : /* restore as before */
<span class="lineNum"> 405 </span><span class="lineCov"> 100552 : v[id[0]] = pa;</span>
<span class="lineNum"> 406 </span><span class="lineCov"> 100552 : v[nd] = p;</span>
<span class="lineNum"> 407 </span><span class="lineCov"> 100552 : }</span>
<span class="lineNum"> 408 </span> :
<span class="lineNum"> 409 </span> : /**
<span class="lineNum"> 410 </span> : * Recover failure of two data blocks for PAR2.
<span class="lineNum"> 411 </span> : *
<span class="lineNum"> 412 </span> : * Starting from the equations:
<span class="lineNum"> 413 </span> : *
<span class="lineNum"> 414 </span> : * Pd = Dx + Dy
<span class="lineNum"> 415 </span> : * Qd = 2^id[0] * Dx + 2^id[1] * Dy
<span class="lineNum"> 416 </span> : *
<span class="lineNum"> 417 </span> : * and solving we get:
<span class="lineNum"> 418 </span> : *
<span class="lineNum"> 419 </span> : * 1 2^(-id[0])
<span class="lineNum"> 420 </span> : * Dy = ------------------- * Pd + ------------------- * Qd
<span class="lineNum"> 421 </span> : * 2^(id[1]-id[0]) + 1 2^(id[1]-id[0]) + 1
<span class="lineNum"> 422 </span> : *
<span class="lineNum"> 423 </span> : * Dx = Dy + Pd
<span class="lineNum"> 424 </span> : *
<span class="lineNum"> 425 </span> : * with conditions:
<span class="lineNum"> 426 </span> : *
<span class="lineNum"> 427 </span> : * 2^id[0] != 0
<span class="lineNum"> 428 </span> : * 2^(id[1]-id[0]) + 1 != 0
<span class="lineNum"> 429 </span> : *
<a name="430"><span class="lineNum"> 430 </span> : * That are always satisfied for any 0&lt;=id[0]&lt;id[1]&lt;255.</a>
<span class="lineNum"> 431 </span> : */
<span class="lineNum"> 432 </span><span class="lineCov"> 132 : void raid_rec2of2_int8(int *id, int *ip, int nd, size_t size, void **vv)</span>
<span class="lineNum"> 433 </span> : {
<span class="lineNum"> 434 </span><span class="lineCov"> 132 : uint8_t **v = (uint8_t **)vv;</span>
<span class="lineNum"> 435 </span> : size_t i;
<span class="lineNum"> 436 </span> : uint8_t *p;
<span class="lineNum"> 437 </span> : uint8_t *pa;
<span class="lineNum"> 438 </span> : uint8_t *q;
<span class="lineNum"> 439 </span> : uint8_t *qa;
<span class="lineNum"> 440 </span> : const uint8_t *T[2];
<span class="lineNum"> 441 </span> :
<span class="lineNum"> 442 </span> : /* get multiplication tables */
<span class="lineNum"> 443 </span><span class="lineCov"> 528 : T[0] = table(inv(pow2(id[1] - id[0]) ^ 1));</span>
<span class="lineNum"> 444 </span><span class="lineCov"> 660 : T[1] = table(inv(pow2(id[0]) ^ pow2(id[1])));</span>
<span class="lineNum"> 445 </span> :
<span class="lineNum"> 446 </span> : /* compute delta parity */
<span class="lineNum"> 447 </span><span class="lineCov"> 132 : raid_delta_gen(2, id, ip, nd, size, vv);</span>
<span class="lineNum"> 448 </span> :
<span class="lineNum"> 449 </span><span class="lineCov"> 132 : p = v[nd];</span>
<span class="lineNum"> 450 </span><span class="lineCov"> 132 : q = v[nd + 1];</span>
<span class="lineNum"> 451 </span><span class="lineCov"> 132 : pa = v[id[0]];</span>
<span class="lineNum"> 452 </span><span class="lineCov"> 132 : qa = v[id[1]];</span>
<span class="lineNum"> 453 </span> :
<span class="lineNum"> 454 </span><span class="lineCov"> 33924 : for (i = 0; i &lt; size; ++i) {</span>
<span class="lineNum"> 455 </span> : /* delta */
<span class="lineNum"> 456 </span><span class="lineCov"> 33792 : uint8_t Pd = p[i] ^ pa[i];</span>
<span class="lineNum"> 457 </span><span class="lineCov"> 33792 : uint8_t Qd = q[i] ^ qa[i];</span>
<span class="lineNum"> 458 </span> :
<span class="lineNum"> 459 </span> : /* reconstruct */
<span class="lineNum"> 460 </span><span class="lineCov"> 33792 : uint8_t Dy = T[0][Pd] ^ T[1][Qd];</span>
<span class="lineNum"> 461 </span><span class="lineCov"> 33792 : uint8_t Dx = Pd ^ Dy;</span>
<span class="lineNum"> 462 </span> :
<span class="lineNum"> 463 </span> : /* set */
<span class="lineNum"> 464 </span><span class="lineCov"> 33792 : pa[i] = Dx;</span>
<span class="lineNum"> 465 </span><span class="lineCov"> 33792 : qa[i] = Dy;</span>
<span class="lineNum"> 466 </span> : }
<span class="lineNum"> 467 </span><span class="lineCov"> 132 : }</span>
<span class="lineNum"> 468 </span> :
<span class="lineNum"> 469 </span> : /*
<span class="lineNum"> 470 </span> : * Forwarders for data recovery.
<span class="lineNum"> 471 </span> : *
<span class="lineNum"> 472 </span> : * These functions recover data blocks using the specified parity
<span class="lineNum"> 473 </span> : * to recompute the missing data.
<span class="lineNum"> 474 </span> : *
<span class="lineNum"> 475 </span> : * Note that the format of vectors @id/@ip is different than raid_rec().
<span class="lineNum"> 476 </span> : * For example, in the vector @ip the first parity is represented with the
<span class="lineNum"> 477 </span> : * value 0 and not @nd.
<span class="lineNum"> 478 </span> : *
<span class="lineNum"> 479 </span> : * @nr Number of failed data blocks to recover.
<span class="lineNum"> 480 </span> : * @id[] Vector of @nr indexes of the data blocks to recover.
<span class="lineNum"> 481 </span> : * The indexes start from 0. They must be in order.
<span class="lineNum"> 482 </span> : * @ip[] Vector of @nr indexes of the parity blocks to use in the recovering.
<span class="lineNum"> 483 </span> : * The indexes start from 0. They must be in order.
<span class="lineNum"> 484 </span> : * @nd Number of data blocks.
<span class="lineNum"> 485 </span> : * @np Number of parity blocks.
<span class="lineNum"> 486 </span> : * @size Size of the blocks pointed by @v. It must be a multipler of 64.
<span class="lineNum"> 487 </span> : * @v Vector of pointers to the blocks of data and parity.
<span class="lineNum"> 488 </span> : * It has (@nd + @np) elements. The starting elements are the blocks
<span class="lineNum"> 489 </span> : * for data, following with the parity blocks.
<span class="lineNum"> 490 </span> : * Each block has @size bytes.
<span class="lineNum"> 491 </span> : */
<span class="lineNum"> 492 </span> : void (*raid_rec_ptr[RAID_PARITY_MAX])(
<a name="493"><span class="lineNum"> 493 </span> : int nr, int *id, int *ip, int nd, size_t size, void **vv);</a>
<span class="lineNum"> 494 </span> :
<span class="lineNum"> 495 </span><span class="lineCov"> 901 : void raid_rec(int nr, int *ir, int nd, int np, size_t size, void **v)</span>
<span class="lineNum"> 496 </span> : {
<span class="lineNum"> 497 </span> : int nrd; /* number of data blocks to recover */
<span class="lineNum"> 498 </span> : int nrp; /* number of parity blocks to recover */
<span class="lineNum"> 499 </span> :
<span class="lineNum"> 500 </span> : /* enforce limit on size */
<span class="lineNum"> 501 </span><span class="lineCov"> 901 : BUG_ON(size % 64 != 0);</span>
<span class="lineNum"> 502 </span> :
<span class="lineNum"> 503 </span> : /* enforce limit on number of failures */
<span class="lineNum"> 504 </span><span class="lineCov"> 901 : BUG_ON(nr &gt; np);</span>
<span class="lineNum"> 505 </span><span class="lineCov"> 901 : BUG_ON(np &gt; RAID_PARITY_MAX);</span>
<span class="lineNum"> 506 </span> :
<span class="lineNum"> 507 </span> : /* enforce order in index vector */
<span class="lineNum"> 508 </span><span class="lineCov"> 901 : BUG_ON(nr &gt;= 2 &amp;&amp; ir[0] &gt;= ir[1]);</span>
<span class="lineNum"> 509 </span><span class="lineCov"> 901 : BUG_ON(nr &gt;= 3 &amp;&amp; ir[1] &gt;= ir[2]);</span>
<span class="lineNum"> 510 </span><span class="lineCov"> 901 : BUG_ON(nr &gt;= 4 &amp;&amp; ir[2] &gt;= ir[3]);</span>
<span class="lineNum"> 511 </span><span class="lineCov"> 901 : BUG_ON(nr &gt;= 5 &amp;&amp; ir[3] &gt;= ir[4]);</span>
<span class="lineNum"> 512 </span><span class="lineCov"> 901 : BUG_ON(nr &gt;= 6 &amp;&amp; ir[4] &gt;= ir[5]);</span>
<span class="lineNum"> 513 </span> :
<span class="lineNum"> 514 </span> : /* enforce limit on index vector */
<span class="lineNum"> 515 </span><span class="lineCov"> 901 : BUG_ON(nr &gt; 0 &amp;&amp; ir[nr-1] &gt;= nd + np);</span>
<span class="lineNum"> 516 </span> :
<span class="lineNum"> 517 </span> : /* count the number of data blocks to recover */
<span class="lineNum"> 518 </span><span class="lineCov"> 901 : nrd = 0;</span>
<span class="lineNum"> 519 </span><span class="lineCov"> 3607 : while (nrd &lt; nr &amp;&amp; ir[nrd] &lt; nd)</span>
<span class="lineNum"> 520 </span><span class="lineCov"> 1805 : ++nrd;</span>
<span class="lineNum"> 521 </span> :
<span class="lineNum"> 522 </span> : /* all the remaining are parity */
<span class="lineNum"> 523 </span><span class="lineCov"> 901 : nrp = nr - nrd;</span>
<span class="lineNum"> 524 </span> :
<span class="lineNum"> 525 </span> : /* enforce limit on number of failures */
<span class="lineNum"> 526 </span><span class="lineCov"> 901 : BUG_ON(nrd &gt; nd);</span>
<span class="lineNum"> 527 </span><span class="lineCov"> 901 : BUG_ON(nrp &gt; np);</span>
<span class="lineNum"> 528 </span> :
<span class="lineNum"> 529 </span> : /* if failed data is present */
<span class="lineNum"> 530 </span><span class="lineCov"> 901 : if (nrd != 0) {</span>
<span class="lineNum"> 531 </span> : int ip[RAID_PARITY_MAX];
<span class="lineNum"> 532 </span> : int i, j, k;
<span class="lineNum"> 533 </span> :
<span class="lineNum"> 534 </span> : /* setup the vector of parities to use */
<span class="lineNum"> 535 </span><span class="lineCov"> 6258 : for (i = 0, j = 0, k = 0; i &lt; np; ++i) {</span>
<span class="lineNum"> 536 </span><span class="lineCov"> 5359 : if (j &lt; nrp &amp;&amp; ir[nrd + j] == nd + i) {</span>
<span class="lineNum"> 537 </span> : /* this parity has to be recovered */
<span class="lineNum"> 538 </span><span class="lineCov"> 22 : ++j;</span>
<span class="lineNum"> 539 </span> : } else {
<span class="lineNum"> 540 </span> : /* this parity is used for recovering */
<span class="lineNum"> 541 </span><span class="lineCov"> 5337 : ip[k] = i;</span>
<span class="lineNum"> 542 </span><span class="lineCov"> 5337 : ++k;</span>
<span class="lineNum"> 543 </span> : }
<span class="lineNum"> 544 </span> : }
<span class="lineNum"> 545 </span> :
<span class="lineNum"> 546 </span> : /* recover the nrd data blocks specified in ir[], */
<span class="lineNum"> 547 </span> : /* using the first nrd parity in ip[] for recovering */
<span class="lineNum"> 548 </span><span class="lineCov"> 899 : raid_rec_ptr[nrd - 1](nrd, ir, ip, nd, size, v);</span>
<span class="lineNum"> 549 </span> : }
<span class="lineNum"> 550 </span> :
<span class="lineNum"> 551 </span> : /* recompute all the parities up to the last bad one */
<span class="lineNum"> 552 </span><span class="lineCov"> 901 : if (nrp != 0)</span>
<span class="lineNum"> 553 </span><span class="lineCov"> 12 : raid_gen(nd, ir[nr - 1] - nd + 1, size, v);</span>
<a name="554"><span class="lineNum"> 554 </span><span class="lineCov"> 901 : }</span></a>
<span class="lineNum"> 555 </span> :
<span class="lineNum"> 556 </span><span class="lineCov"> 213294 : void raid_data(int nr, int *id, int *ip, int nd, size_t size, void **v)</span>
<span class="lineNum"> 557 </span> : {
<span class="lineNum"> 558 </span> : /* enforce limit on size */
<span class="lineNum"> 559 </span><span class="lineCov"> 213294 : BUG_ON(size % 64 != 0);</span>
<span class="lineNum"> 560 </span> :
<span class="lineNum"> 561 </span> : /* enforce limit on number of failures */
<span class="lineNum"> 562 </span><span class="lineCov"> 213294 : BUG_ON(nr &gt; nd);</span>
<span class="lineNum"> 563 </span><span class="lineCov"> 213294 : BUG_ON(nr &gt; RAID_PARITY_MAX);</span>
<span class="lineNum"> 564 </span> :
<span class="lineNum"> 565 </span> : /* enforce order in index vector for data */
<span class="lineNum"> 566 </span><span class="lineCov"> 213294 : BUG_ON(nr &gt;= 2 &amp;&amp; id[0] &gt;= id[1]);</span>
<span class="lineNum"> 567 </span><span class="lineCov"> 213294 : BUG_ON(nr &gt;= 3 &amp;&amp; id[1] &gt;= id[2]);</span>
<span class="lineNum"> 568 </span><span class="lineCov"> 213294 : BUG_ON(nr &gt;= 4 &amp;&amp; id[2] &gt;= id[3]);</span>
<span class="lineNum"> 569 </span><span class="lineCov"> 213294 : BUG_ON(nr &gt;= 5 &amp;&amp; id[3] &gt;= id[4]);</span>
<span class="lineNum"> 570 </span><span class="lineCov"> 213294 : BUG_ON(nr &gt;= 6 &amp;&amp; id[4] &gt;= id[5]);</span>
<span class="lineNum"> 571 </span> :
<span class="lineNum"> 572 </span> : /* enforce limit on index vector for data */
<span class="lineNum"> 573 </span><span class="lineCov"> 213294 : BUG_ON(nr &gt; 0 &amp;&amp; id[nr-1] &gt;= nd);</span>
<span class="lineNum"> 574 </span> :
<span class="lineNum"> 575 </span> : /* enforce order in index vector for parity */
<span class="lineNum"> 576 </span><span class="lineCov"> 213294 : BUG_ON(nr &gt;= 2 &amp;&amp; ip[0] &gt;= ip[1]);</span>
<span class="lineNum"> 577 </span><span class="lineCov"> 213294 : BUG_ON(nr &gt;= 3 &amp;&amp; ip[1] &gt;= ip[2]);</span>
<span class="lineNum"> 578 </span><span class="lineCov"> 213294 : BUG_ON(nr &gt;= 4 &amp;&amp; ip[2] &gt;= ip[3]);</span>
<span class="lineNum"> 579 </span><span class="lineCov"> 213294 : BUG_ON(nr &gt;= 5 &amp;&amp; ip[3] &gt;= ip[4]);</span>
<span class="lineNum"> 580 </span><span class="lineCov"> 213294 : BUG_ON(nr &gt;= 6 &amp;&amp; ip[4] &gt;= ip[5]);</span>
<span class="lineNum"> 581 </span> :
<span class="lineNum"> 582 </span> : /* if failed data is present */
<span class="lineNum"> 583 </span><span class="lineCov"> 213294 : if (nr != 0)</span>
<span class="lineNum"> 584 </span><span class="lineCov"> 213292 : raid_rec_ptr[nr - 1](nr, id, ip, nd, size, v);</span>
<span class="lineNum"> 585 </span><span class="lineCov"> 213294 : }</span>
<span class="lineNum"> 586 </span> :
</pre>
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