1 /*
   2  * CDDL HEADER START
   3  *
   4  * The contents of this file are subject to the terms of the
   5  * Common Development and Distribution License (the "License").
   6  * You may not use this file except in compliance with the License.
   7  *
   8  * You can obtain a copy of the license at usr/src/OPENSOLARIS.LICENSE
   9  * or http://www.opensolaris.org/os/licensing.
  10  * See the License for the specific language governing permissions
  11  * and limitations under the License.
  12  *
  13  * When distributing Covered Code, include this CDDL HEADER in each
  14  * file and include the License file at usr/src/OPENSOLARIS.LICENSE.
  15  * If applicable, add the following below this CDDL HEADER, with the
  16  * fields enclosed by brackets "[]" replaced with your own identifying
  17  * information: Portions Copyright [yyyy] [name of copyright owner]
  18  *
  19  * CDDL HEADER END
  20  */
  21 
  22 /*
  23  * Copyright (c) 2005, 2010, Oracle and/or its affiliates. All rights reserved.
  24  * Copyright (c) 2012 by Delphix. All rights reserved.
  25  */
  26 
  27 #include <sys/zfs_context.h>
  28 #include <sys/spa.h>
  29 #include <sys/vdev_impl.h>
  30 #include <sys/zio.h>
  31 #include <sys/zio_checksum.h>
  32 #include <sys/fs/zfs.h>
  33 #include <sys/fm/fs/zfs.h>
  34 
  35 /*
  36  * Virtual device vector for RAID-Z.
  37  *
  38  * This vdev supports single, double, and triple parity. For single parity,
  39  * we use a simple XOR of all the data columns. For double or triple parity,
  40  * we use a special case of Reed-Solomon coding. This extends the
  41  * technique described in "The mathematics of RAID-6" by H. Peter Anvin by
  42  * drawing on the system described in "A Tutorial on Reed-Solomon Coding for
  43  * Fault-Tolerance in RAID-like Systems" by James S. Plank on which the
  44  * former is also based. The latter is designed to provide higher performance
  45  * for writes.
  46  *
  47  * Note that the Plank paper claimed to support arbitrary N+M, but was then
  48  * amended six years later identifying a critical flaw that invalidates its
  49  * claims. Nevertheless, the technique can be adapted to work for up to
  50  * triple parity. For additional parity, the amendment "Note: Correction to
  51  * the 1997 Tutorial on Reed-Solomon Coding" by James S. Plank and Ying Ding
  52  * is viable, but the additional complexity means that write performance will
  53  * suffer.
  54  *
  55  * All of the methods above operate on a Galois field, defined over the
  56  * integers mod 2^N. In our case we choose N=8 for GF(8) so that all elements
  57  * can be expressed with a single byte. Briefly, the operations on the
  58  * field are defined as follows:
  59  *
  60  *   o addition (+) is represented by a bitwise XOR
  61  *   o subtraction (-) is therefore identical to addition: A + B = A - B
  62  *   o multiplication of A by 2 is defined by the following bitwise expression:
  63  *      (A * 2)_7 = A_6
  64  *      (A * 2)_6 = A_5
  65  *      (A * 2)_5 = A_4
  66  *      (A * 2)_4 = A_3 + A_7
  67  *      (A * 2)_3 = A_2 + A_7
  68  *      (A * 2)_2 = A_1 + A_7
  69  *      (A * 2)_1 = A_0
  70  *      (A * 2)_0 = A_7
  71  *
  72  * In C, multiplying by 2 is therefore ((a << 1) ^ ((a & 0x80) ? 0x1d : 0)).
  73  * As an aside, this multiplication is derived from the error correcting
  74  * primitive polynomial x^8 + x^4 + x^3 + x^2 + 1.
  75  *
  76  * Observe that any number in the field (except for 0) can be expressed as a
  77  * power of 2 -- a generator for the field. We store a table of the powers of
  78  * 2 and logs base 2 for quick look ups, and exploit the fact that A * B can
  79  * be rewritten as 2^(log_2(A) + log_2(B)) (where '+' is normal addition rather
  80  * than field addition). The inverse of a field element A (A^-1) is therefore
  81  * A ^ (255 - 1) = A^254.
  82  *
  83  * The up-to-three parity columns, P, Q, R over several data columns,
  84  * D_0, ... D_n-1, can be expressed by field operations:
  85  *
  86  *      P = D_0 + D_1 + ... + D_n-2 + D_n-1
  87  *      Q = 2^n-1 * D_0 + 2^n-2 * D_1 + ... + 2^1 * D_n-2 + 2^0 * D_n-1
  88  *        = ((...((D_0) * 2 + D_1) * 2 + ...) * 2 + D_n-2) * 2 + D_n-1
  89  *      R = 4^n-1 * D_0 + 4^n-2 * D_1 + ... + 4^1 * D_n-2 + 4^0 * D_n-1
  90  *        = ((...((D_0) * 4 + D_1) * 4 + ...) * 4 + D_n-2) * 4 + D_n-1
  91  *
  92  * We chose 1, 2, and 4 as our generators because 1 corresponds to the trival
  93  * XOR operation, and 2 and 4 can be computed quickly and generate linearly-
  94  * independent coefficients. (There are no additional coefficients that have
  95  * this property which is why the uncorrected Plank method breaks down.)
  96  *
  97  * See the reconstruction code below for how P, Q and R can used individually
  98  * or in concert to recover missing data columns.
  99  */
 100 
 101 typedef struct raidz_col {
 102         uint64_t rc_devidx;             /* child device index for I/O */
 103         uint64_t rc_offset;             /* device offset */
 104         uint64_t rc_size;               /* I/O size */
 105         void *rc_data;                  /* I/O data */
 106         void *rc_gdata;                 /* used to store the "good" version */
 107         int rc_error;                   /* I/O error for this device */
 108         uint8_t rc_tried;               /* Did we attempt this I/O column? */
 109         uint8_t rc_skipped;             /* Did we skip this I/O column? */
 110 } raidz_col_t;
 111 
 112 typedef struct raidz_map {
 113         uint64_t rm_cols;               /* Regular column count */
 114         uint64_t rm_scols;              /* Count including skipped columns */
 115         uint64_t rm_bigcols;            /* Number of oversized columns */
 116         uint64_t rm_asize;              /* Actual total I/O size */
 117         uint64_t rm_missingdata;        /* Count of missing data devices */
 118         uint64_t rm_missingparity;      /* Count of missing parity devices */
 119         uint64_t rm_firstdatacol;       /* First data column/parity count */
 120         uint64_t rm_nskip;              /* Skipped sectors for padding */
 121         uint64_t rm_skipstart;  /* Column index of padding start */
 122         void *rm_datacopy;              /* rm_asize-buffer of copied data */
 123         uintptr_t rm_reports;           /* # of referencing checksum reports */
 124         uint8_t rm_freed;               /* map no longer has referencing ZIO */
 125         uint8_t rm_ecksuminjected;      /* checksum error was injected */
 126         raidz_col_t rm_col[1];          /* Flexible array of I/O columns */
 127 } raidz_map_t;
 128 
 129 #define VDEV_RAIDZ_P            0
 130 #define VDEV_RAIDZ_Q            1
 131 #define VDEV_RAIDZ_R            2
 132 
 133 #define VDEV_RAIDZ_MUL_2(x)     (((x) << 1) ^ (((x) & 0x80) ? 0x1d : 0))
 134 #define VDEV_RAIDZ_MUL_4(x)     (VDEV_RAIDZ_MUL_2(VDEV_RAIDZ_MUL_2(x)))
 135 
 136 /*
 137  * We provide a mechanism to perform the field multiplication operation on a
 138  * 64-bit value all at once rather than a byte at a time. This works by
 139  * creating a mask from the top bit in each byte and using that to
 140  * conditionally apply the XOR of 0x1d.
 141  */
 142 #define VDEV_RAIDZ_64MUL_2(x, mask) \
 143 { \
 144         (mask) = (x) & 0x8080808080808080ULL; \
 145         (mask) = ((mask) << 1) - ((mask) >> 7); \
 146         (x) = (((x) << 1) & 0xfefefefefefefefeULL) ^ \
 147             ((mask) & 0x1d1d1d1d1d1d1d1d); \
 148 }
 149 
 150 #define VDEV_RAIDZ_64MUL_4(x, mask) \
 151 { \
 152         VDEV_RAIDZ_64MUL_2((x), mask); \
 153         VDEV_RAIDZ_64MUL_2((x), mask); \
 154 }
 155 
 156 /*
 157  * Force reconstruction to use the general purpose method.
 158  */
 159 int vdev_raidz_default_to_general;
 160 
 161 /*
 162  * These two tables represent powers and logs of 2 in the Galois field defined
 163  * above. These values were computed by repeatedly multiplying by 2 as above.
 164  */
 165 static const uint8_t vdev_raidz_pow2[256] = {
 166         0x01, 0x02, 0x04, 0x08, 0x10, 0x20, 0x40, 0x80,
 167         0x1d, 0x3a, 0x74, 0xe8, 0xcd, 0x87, 0x13, 0x26,
 168         0x4c, 0x98, 0x2d, 0x5a, 0xb4, 0x75, 0xea, 0xc9,
 169         0x8f, 0x03, 0x06, 0x0c, 0x18, 0x30, 0x60, 0xc0,
 170         0x9d, 0x27, 0x4e, 0x9c, 0x25, 0x4a, 0x94, 0x35,
 171         0x6a, 0xd4, 0xb5, 0x77, 0xee, 0xc1, 0x9f, 0x23,
 172         0x46, 0x8c, 0x05, 0x0a, 0x14, 0x28, 0x50, 0xa0,
 173         0x5d, 0xba, 0x69, 0xd2, 0xb9, 0x6f, 0xde, 0xa1,
 174         0x5f, 0xbe, 0x61, 0xc2, 0x99, 0x2f, 0x5e, 0xbc,
 175         0x65, 0xca, 0x89, 0x0f, 0x1e, 0x3c, 0x78, 0xf0,
 176         0xfd, 0xe7, 0xd3, 0xbb, 0x6b, 0xd6, 0xb1, 0x7f,
 177         0xfe, 0xe1, 0xdf, 0xa3, 0x5b, 0xb6, 0x71, 0xe2,
 178         0xd9, 0xaf, 0x43, 0x86, 0x11, 0x22, 0x44, 0x88,
 179         0x0d, 0x1a, 0x34, 0x68, 0xd0, 0xbd, 0x67, 0xce,
 180         0x81, 0x1f, 0x3e, 0x7c, 0xf8, 0xed, 0xc7, 0x93,
 181         0x3b, 0x76, 0xec, 0xc5, 0x97, 0x33, 0x66, 0xcc,
 182         0x85, 0x17, 0x2e, 0x5c, 0xb8, 0x6d, 0xda, 0xa9,
 183         0x4f, 0x9e, 0x21, 0x42, 0x84, 0x15, 0x2a, 0x54,
 184         0xa8, 0x4d, 0x9a, 0x29, 0x52, 0xa4, 0x55, 0xaa,
 185         0x49, 0x92, 0x39, 0x72, 0xe4, 0xd5, 0xb7, 0x73,
 186         0xe6, 0xd1, 0xbf, 0x63, 0xc6, 0x91, 0x3f, 0x7e,
 187         0xfc, 0xe5, 0xd7, 0xb3, 0x7b, 0xf6, 0xf1, 0xff,
 188         0xe3, 0xdb, 0xab, 0x4b, 0x96, 0x31, 0x62, 0xc4,
 189         0x95, 0x37, 0x6e, 0xdc, 0xa5, 0x57, 0xae, 0x41,
 190         0x82, 0x19, 0x32, 0x64, 0xc8, 0x8d, 0x07, 0x0e,
 191         0x1c, 0x38, 0x70, 0xe0, 0xdd, 0xa7, 0x53, 0xa6,
 192         0x51, 0xa2, 0x59, 0xb2, 0x79, 0xf2, 0xf9, 0xef,
 193         0xc3, 0x9b, 0x2b, 0x56, 0xac, 0x45, 0x8a, 0x09,
 194         0x12, 0x24, 0x48, 0x90, 0x3d, 0x7a, 0xf4, 0xf5,
 195         0xf7, 0xf3, 0xfb, 0xeb, 0xcb, 0x8b, 0x0b, 0x16,
 196         0x2c, 0x58, 0xb0, 0x7d, 0xfa, 0xe9, 0xcf, 0x83,
 197         0x1b, 0x36, 0x6c, 0xd8, 0xad, 0x47, 0x8e, 0x01
 198 };
 199 static const uint8_t vdev_raidz_log2[256] = {
 200         0x00, 0x00, 0x01, 0x19, 0x02, 0x32, 0x1a, 0xc6,
 201         0x03, 0xdf, 0x33, 0xee, 0x1b, 0x68, 0xc7, 0x4b,
 202         0x04, 0x64, 0xe0, 0x0e, 0x34, 0x8d, 0xef, 0x81,
 203         0x1c, 0xc1, 0x69, 0xf8, 0xc8, 0x08, 0x4c, 0x71,
 204         0x05, 0x8a, 0x65, 0x2f, 0xe1, 0x24, 0x0f, 0x21,
 205         0x35, 0x93, 0x8e, 0xda, 0xf0, 0x12, 0x82, 0x45,
 206         0x1d, 0xb5, 0xc2, 0x7d, 0x6a, 0x27, 0xf9, 0xb9,
 207         0xc9, 0x9a, 0x09, 0x78, 0x4d, 0xe4, 0x72, 0xa6,
 208         0x06, 0xbf, 0x8b, 0x62, 0x66, 0xdd, 0x30, 0xfd,
 209         0xe2, 0x98, 0x25, 0xb3, 0x10, 0x91, 0x22, 0x88,
 210         0x36, 0xd0, 0x94, 0xce, 0x8f, 0x96, 0xdb, 0xbd,
 211         0xf1, 0xd2, 0x13, 0x5c, 0x83, 0x38, 0x46, 0x40,
 212         0x1e, 0x42, 0xb6, 0xa3, 0xc3, 0x48, 0x7e, 0x6e,
 213         0x6b, 0x3a, 0x28, 0x54, 0xfa, 0x85, 0xba, 0x3d,
 214         0xca, 0x5e, 0x9b, 0x9f, 0x0a, 0x15, 0x79, 0x2b,
 215         0x4e, 0xd4, 0xe5, 0xac, 0x73, 0xf3, 0xa7, 0x57,
 216         0x07, 0x70, 0xc0, 0xf7, 0x8c, 0x80, 0x63, 0x0d,
 217         0x67, 0x4a, 0xde, 0xed, 0x31, 0xc5, 0xfe, 0x18,
 218         0xe3, 0xa5, 0x99, 0x77, 0x26, 0xb8, 0xb4, 0x7c,
 219         0x11, 0x44, 0x92, 0xd9, 0x23, 0x20, 0x89, 0x2e,
 220         0x37, 0x3f, 0xd1, 0x5b, 0x95, 0xbc, 0xcf, 0xcd,
 221         0x90, 0x87, 0x97, 0xb2, 0xdc, 0xfc, 0xbe, 0x61,
 222         0xf2, 0x56, 0xd3, 0xab, 0x14, 0x2a, 0x5d, 0x9e,
 223         0x84, 0x3c, 0x39, 0x53, 0x47, 0x6d, 0x41, 0xa2,
 224         0x1f, 0x2d, 0x43, 0xd8, 0xb7, 0x7b, 0xa4, 0x76,
 225         0xc4, 0x17, 0x49, 0xec, 0x7f, 0x0c, 0x6f, 0xf6,
 226         0x6c, 0xa1, 0x3b, 0x52, 0x29, 0x9d, 0x55, 0xaa,
 227         0xfb, 0x60, 0x86, 0xb1, 0xbb, 0xcc, 0x3e, 0x5a,
 228         0xcb, 0x59, 0x5f, 0xb0, 0x9c, 0xa9, 0xa0, 0x51,
 229         0x0b, 0xf5, 0x16, 0xeb, 0x7a, 0x75, 0x2c, 0xd7,
 230         0x4f, 0xae, 0xd5, 0xe9, 0xe6, 0xe7, 0xad, 0xe8,
 231         0x74, 0xd6, 0xf4, 0xea, 0xa8, 0x50, 0x58, 0xaf,
 232 };
 233 
 234 static void vdev_raidz_generate_parity(raidz_map_t *rm);
 235 
 236 /*
 237  * Multiply a given number by 2 raised to the given power.
 238  */
 239 static uint8_t
 240 vdev_raidz_exp2(uint_t a, int exp)
 241 {
 242         if (a == 0)
 243                 return (0);
 244 
 245         ASSERT(exp >= 0);
 246         ASSERT(vdev_raidz_log2[a] > 0 || a == 1);
 247 
 248         exp += vdev_raidz_log2[a];
 249         if (exp > 255)
 250                 exp -= 255;
 251 
 252         return (vdev_raidz_pow2[exp]);
 253 }
 254 
 255 static void
 256 vdev_raidz_map_free(raidz_map_t *rm)
 257 {
 258         int c;
 259         size_t size;
 260 
 261         for (c = 0; c < rm->rm_firstdatacol; c++) {
 262                 zio_buf_free(rm->rm_col[c].rc_data, rm->rm_col[c].rc_size);
 263 
 264                 if (rm->rm_col[c].rc_gdata != NULL)
 265                         zio_buf_free(rm->rm_col[c].rc_gdata,
 266                             rm->rm_col[c].rc_size);
 267         }
 268 
 269         size = 0;
 270         for (c = rm->rm_firstdatacol; c < rm->rm_cols; c++)
 271                 size += rm->rm_col[c].rc_size;
 272 
 273         if (rm->rm_datacopy != NULL)
 274                 zio_buf_free(rm->rm_datacopy, size);
 275 
 276         kmem_free(rm, offsetof(raidz_map_t, rm_col[rm->rm_scols]));
 277 }
 278 
 279 static void
 280 vdev_raidz_map_free_vsd(zio_t *zio)
 281 {
 282         raidz_map_t *rm = zio->io_vsd;
 283 
 284         ASSERT0(rm->rm_freed);
 285         rm->rm_freed = 1;
 286 
 287         if (rm->rm_reports == 0)
 288                 vdev_raidz_map_free(rm);
 289 }
 290 
 291 /*ARGSUSED*/
 292 static void
 293 vdev_raidz_cksum_free(void *arg, size_t ignored)
 294 {
 295         raidz_map_t *rm = arg;
 296 
 297         ASSERT3U(rm->rm_reports, >, 0);
 298 
 299         if (--rm->rm_reports == 0 && rm->rm_freed != 0)
 300                 vdev_raidz_map_free(rm);
 301 }
 302 
 303 static void
 304 vdev_raidz_cksum_finish(zio_cksum_report_t *zcr, const void *good_data)
 305 {
 306         raidz_map_t *rm = zcr->zcr_cbdata;
 307         size_t c = zcr->zcr_cbinfo;
 308         size_t x;
 309 
 310         const char *good = NULL;
 311         const char *bad = rm->rm_col[c].rc_data;
 312 
 313         if (good_data == NULL) {
 314                 zfs_ereport_finish_checksum(zcr, NULL, NULL, B_FALSE);
 315                 return;
 316         }
 317 
 318         if (c < rm->rm_firstdatacol) {
 319                 /*
 320                  * The first time through, calculate the parity blocks for
 321                  * the good data (this relies on the fact that the good
 322                  * data never changes for a given logical ZIO)
 323                  */
 324                 if (rm->rm_col[0].rc_gdata == NULL) {
 325                         char *bad_parity[VDEV_RAIDZ_MAXPARITY];
 326                         char *buf;
 327 
 328                         /*
 329                          * Set up the rm_col[]s to generate the parity for
 330                          * good_data, first saving the parity bufs and
 331                          * replacing them with buffers to hold the result.
 332                          */
 333                         for (x = 0; x < rm->rm_firstdatacol; x++) {
 334                                 bad_parity[x] = rm->rm_col[x].rc_data;
 335                                 rm->rm_col[x].rc_data = rm->rm_col[x].rc_gdata =
 336                                     zio_buf_alloc(rm->rm_col[x].rc_size);
 337                         }
 338 
 339                         /* fill in the data columns from good_data */
 340                         buf = (char *)good_data;
 341                         for (; x < rm->rm_cols; x++) {
 342                                 rm->rm_col[x].rc_data = buf;
 343                                 buf += rm->rm_col[x].rc_size;
 344                         }
 345 
 346                         /*
 347                          * Construct the parity from the good data.
 348                          */
 349                         vdev_raidz_generate_parity(rm);
 350 
 351                         /* restore everything back to its original state */
 352                         for (x = 0; x < rm->rm_firstdatacol; x++)
 353                                 rm->rm_col[x].rc_data = bad_parity[x];
 354 
 355                         buf = rm->rm_datacopy;
 356                         for (x = rm->rm_firstdatacol; x < rm->rm_cols; x++) {
 357                                 rm->rm_col[x].rc_data = buf;
 358                                 buf += rm->rm_col[x].rc_size;
 359                         }
 360                 }
 361 
 362                 ASSERT3P(rm->rm_col[c].rc_gdata, !=, NULL);
 363                 good = rm->rm_col[c].rc_gdata;
 364         } else {
 365                 /* adjust good_data to point at the start of our column */
 366                 good = good_data;
 367 
 368                 for (x = rm->rm_firstdatacol; x < c; x++)
 369                         good += rm->rm_col[x].rc_size;
 370         }
 371 
 372         /* we drop the ereport if it ends up that the data was good */
 373         zfs_ereport_finish_checksum(zcr, good, bad, B_TRUE);
 374 }
 375 
 376 /*
 377  * Invoked indirectly by zfs_ereport_start_checksum(), called
 378  * below when our read operation fails completely.  The main point
 379  * is to keep a copy of everything we read from disk, so that at
 380  * vdev_raidz_cksum_finish() time we can compare it with the good data.
 381  */
 382 static void
 383 vdev_raidz_cksum_report(zio_t *zio, zio_cksum_report_t *zcr, void *arg)
 384 {
 385         size_t c = (size_t)(uintptr_t)arg;
 386         caddr_t buf;
 387 
 388         raidz_map_t *rm = zio->io_vsd;
 389         size_t size;
 390 
 391         /* set up the report and bump the refcount  */
 392         zcr->zcr_cbdata = rm;
 393         zcr->zcr_cbinfo = c;
 394         zcr->zcr_finish = vdev_raidz_cksum_finish;
 395         zcr->zcr_free = vdev_raidz_cksum_free;
 396 
 397         rm->rm_reports++;
 398         ASSERT3U(rm->rm_reports, >, 0);
 399 
 400         if (rm->rm_datacopy != NULL)
 401                 return;
 402 
 403         /*
 404          * It's the first time we're called for this raidz_map_t, so we need
 405          * to copy the data aside; there's no guarantee that our zio's buffer
 406          * won't be re-used for something else.
 407          *
 408          * Our parity data is already in separate buffers, so there's no need
 409          * to copy them.
 410          */
 411 
 412         size = 0;
 413         for (c = rm->rm_firstdatacol; c < rm->rm_cols; c++)
 414                 size += rm->rm_col[c].rc_size;
 415 
 416         buf = rm->rm_datacopy = zio_buf_alloc(size);
 417 
 418         for (c = rm->rm_firstdatacol; c < rm->rm_cols; c++) {
 419                 raidz_col_t *col = &rm->rm_col[c];
 420 
 421                 bcopy(col->rc_data, buf, col->rc_size);
 422                 col->rc_data = buf;
 423 
 424                 buf += col->rc_size;
 425         }
 426         ASSERT3P(buf - (caddr_t)rm->rm_datacopy, ==, size);
 427 }
 428 
 429 static const zio_vsd_ops_t vdev_raidz_vsd_ops = {
 430         vdev_raidz_map_free_vsd,
 431         vdev_raidz_cksum_report
 432 };
 433 
 434 static raidz_map_t *
 435 vdev_raidz_map_alloc(zio_t *zio, uint64_t unit_shift, uint64_t dcols,
 436     uint64_t nparity)
 437 {
 438         raidz_map_t *rm;
 439         uint64_t b = zio->io_offset >> unit_shift;
 440         uint64_t s = zio->io_size >> unit_shift;
 441         uint64_t f = b % dcols;
 442         uint64_t o = (b / dcols) << unit_shift;
 443         uint64_t q, r, c, bc, col, acols, scols, coff, devidx, asize, tot;
 444 
 445         q = s / (dcols - nparity);
 446         r = s - q * (dcols - nparity);
 447         bc = (r == 0 ? 0 : r + nparity);
 448         tot = s + nparity * (q + (r == 0 ? 0 : 1));
 449 
 450         if (q == 0) {
 451                 acols = bc;
 452                 scols = MIN(dcols, roundup(bc, nparity + 1));
 453         } else {
 454                 acols = dcols;
 455                 scols = dcols;
 456         }
 457 
 458         ASSERT3U(acols, <=, scols);
 459 
 460         rm = kmem_alloc(offsetof(raidz_map_t, rm_col[scols]), KM_SLEEP);
 461 
 462         rm->rm_cols = acols;
 463         rm->rm_scols = scols;
 464         rm->rm_bigcols = bc;
 465         rm->rm_skipstart = bc;
 466         rm->rm_missingdata = 0;
 467         rm->rm_missingparity = 0;
 468         rm->rm_firstdatacol = nparity;
 469         rm->rm_datacopy = NULL;
 470         rm->rm_reports = 0;
 471         rm->rm_freed = 0;
 472         rm->rm_ecksuminjected = 0;
 473 
 474         asize = 0;
 475 
 476         for (c = 0; c < scols; c++) {
 477                 col = f + c;
 478                 coff = o;
 479                 if (col >= dcols) {
 480                         col -= dcols;
 481                         coff += 1ULL << unit_shift;
 482                 }
 483                 rm->rm_col[c].rc_devidx = col;
 484                 rm->rm_col[c].rc_offset = coff;
 485                 rm->rm_col[c].rc_data = NULL;
 486                 rm->rm_col[c].rc_gdata = NULL;
 487                 rm->rm_col[c].rc_error = 0;
 488                 rm->rm_col[c].rc_tried = 0;
 489                 rm->rm_col[c].rc_skipped = 0;
 490 
 491                 if (c >= acols)
 492                         rm->rm_col[c].rc_size = 0;
 493                 else if (c < bc)
 494                         rm->rm_col[c].rc_size = (q + 1) << unit_shift;
 495                 else
 496                         rm->rm_col[c].rc_size = q << unit_shift;
 497 
 498                 asize += rm->rm_col[c].rc_size;
 499         }
 500 
 501         ASSERT3U(asize, ==, tot << unit_shift);
 502         rm->rm_asize = roundup(asize, (nparity + 1) << unit_shift);
 503         rm->rm_nskip = roundup(tot, nparity + 1) - tot;
 504         ASSERT3U(rm->rm_asize - asize, ==, rm->rm_nskip << unit_shift);
 505         ASSERT3U(rm->rm_nskip, <=, nparity);
 506 
 507         for (c = 0; c < rm->rm_firstdatacol; c++)
 508                 rm->rm_col[c].rc_data = zio_buf_alloc(rm->rm_col[c].rc_size);
 509 
 510         rm->rm_col[c].rc_data = zio->io_data;
 511 
 512         for (c = c + 1; c < acols; c++)
 513                 rm->rm_col[c].rc_data = (char *)rm->rm_col[c - 1].rc_data +
 514                     rm->rm_col[c - 1].rc_size;
 515 
 516         /*
 517          * If all data stored spans all columns, there's a danger that parity
 518          * will always be on the same device and, since parity isn't read
 519          * during normal operation, that that device's I/O bandwidth won't be
 520          * used effectively. We therefore switch the parity every 1MB.
 521          *
 522          * ... at least that was, ostensibly, the theory. As a practical
 523          * matter unless we juggle the parity between all devices evenly, we
 524          * won't see any benefit. Further, occasional writes that aren't a
 525          * multiple of the LCM of the number of children and the minimum
 526          * stripe width are sufficient to avoid pessimal behavior.
 527          * Unfortunately, this decision created an implicit on-disk format
 528          * requirement that we need to support for all eternity, but only
 529          * for single-parity RAID-Z.
 530          *
 531          * If we intend to skip a sector in the zeroth column for padding
 532          * we must make sure to note this swap. We will never intend to
 533          * skip the first column since at least one data and one parity
 534          * column must appear in each row.
 535          */
 536         ASSERT(rm->rm_cols >= 2);
 537         ASSERT(rm->rm_col[0].rc_size == rm->rm_col[1].rc_size);
 538 
 539         if (rm->rm_firstdatacol == 1 && (zio->io_offset & (1ULL << 20))) {
 540                 devidx = rm->rm_col[0].rc_devidx;
 541                 o = rm->rm_col[0].rc_offset;
 542                 rm->rm_col[0].rc_devidx = rm->rm_col[1].rc_devidx;
 543                 rm->rm_col[0].rc_offset = rm->rm_col[1].rc_offset;
 544                 rm->rm_col[1].rc_devidx = devidx;
 545                 rm->rm_col[1].rc_offset = o;
 546 
 547                 if (rm->rm_skipstart == 0)
 548                         rm->rm_skipstart = 1;
 549         }
 550 
 551         zio->io_vsd = rm;
 552         zio->io_vsd_ops = &vdev_raidz_vsd_ops;
 553         return (rm);
 554 }
 555 
 556 static void
 557 vdev_raidz_generate_parity_p(raidz_map_t *rm)
 558 {
 559         uint64_t *p, *src, pcount, ccount, i;
 560         int c;
 561 
 562         pcount = rm->rm_col[VDEV_RAIDZ_P].rc_size / sizeof (src[0]);
 563 
 564         for (c = rm->rm_firstdatacol; c < rm->rm_cols; c++) {
 565                 src = rm->rm_col[c].rc_data;
 566                 p = rm->rm_col[VDEV_RAIDZ_P].rc_data;
 567                 ccount = rm->rm_col[c].rc_size / sizeof (src[0]);
 568 
 569                 if (c == rm->rm_firstdatacol) {
 570                         ASSERT(ccount == pcount);
 571                         for (i = 0; i < ccount; i++, src++, p++) {
 572                                 *p = *src;
 573                         }
 574                 } else {
 575                         ASSERT(ccount <= pcount);
 576                         for (i = 0; i < ccount; i++, src++, p++) {
 577                                 *p ^= *src;
 578                         }
 579                 }
 580         }
 581 }
 582 
 583 static void
 584 vdev_raidz_generate_parity_pq(raidz_map_t *rm)
 585 {
 586         uint64_t *p, *q, *src, pcnt, ccnt, mask, i;
 587         int c;
 588 
 589         pcnt = rm->rm_col[VDEV_RAIDZ_P].rc_size / sizeof (src[0]);
 590         ASSERT(rm->rm_col[VDEV_RAIDZ_P].rc_size ==
 591             rm->rm_col[VDEV_RAIDZ_Q].rc_size);
 592 
 593         for (c = rm->rm_firstdatacol; c < rm->rm_cols; c++) {
 594                 src = rm->rm_col[c].rc_data;
 595                 p = rm->rm_col[VDEV_RAIDZ_P].rc_data;
 596                 q = rm->rm_col[VDEV_RAIDZ_Q].rc_data;
 597 
 598                 ccnt = rm->rm_col[c].rc_size / sizeof (src[0]);
 599 
 600                 if (c == rm->rm_firstdatacol) {
 601                         ASSERT(ccnt == pcnt || ccnt == 0);
 602                         for (i = 0; i < ccnt; i++, src++, p++, q++) {
 603                                 *p = *src;
 604                                 *q = *src;
 605                         }
 606                         for (; i < pcnt; i++, src++, p++, q++) {
 607                                 *p = 0;
 608                                 *q = 0;
 609                         }
 610                 } else {
 611                         ASSERT(ccnt <= pcnt);
 612 
 613                         /*
 614                          * Apply the algorithm described above by multiplying
 615                          * the previous result and adding in the new value.
 616                          */
 617                         for (i = 0; i < ccnt; i++, src++, p++, q++) {
 618                                 *p ^= *src;
 619 
 620                                 VDEV_RAIDZ_64MUL_2(*q, mask);
 621                                 *q ^= *src;
 622                         }
 623 
 624                         /*
 625                          * Treat short columns as though they are full of 0s.
 626                          * Note that there's therefore nothing needed for P.
 627                          */
 628                         for (; i < pcnt; i++, q++) {
 629                                 VDEV_RAIDZ_64MUL_2(*q, mask);
 630                         }
 631                 }
 632         }
 633 }
 634 
 635 static void
 636 vdev_raidz_generate_parity_pqr(raidz_map_t *rm)
 637 {
 638         uint64_t *p, *q, *r, *src, pcnt, ccnt, mask, i;
 639         int c;
 640 
 641         pcnt = rm->rm_col[VDEV_RAIDZ_P].rc_size / sizeof (src[0]);
 642         ASSERT(rm->rm_col[VDEV_RAIDZ_P].rc_size ==
 643             rm->rm_col[VDEV_RAIDZ_Q].rc_size);
 644         ASSERT(rm->rm_col[VDEV_RAIDZ_P].rc_size ==
 645             rm->rm_col[VDEV_RAIDZ_R].rc_size);
 646 
 647         for (c = rm->rm_firstdatacol; c < rm->rm_cols; c++) {
 648                 src = rm->rm_col[c].rc_data;
 649                 p = rm->rm_col[VDEV_RAIDZ_P].rc_data;
 650                 q = rm->rm_col[VDEV_RAIDZ_Q].rc_data;
 651                 r = rm->rm_col[VDEV_RAIDZ_R].rc_data;
 652 
 653                 ccnt = rm->rm_col[c].rc_size / sizeof (src[0]);
 654 
 655                 if (c == rm->rm_firstdatacol) {
 656                         ASSERT(ccnt == pcnt || ccnt == 0);
 657                         for (i = 0; i < ccnt; i++, src++, p++, q++, r++) {
 658                                 *p = *src;
 659                                 *q = *src;
 660                                 *r = *src;
 661                         }
 662                         for (; i < pcnt; i++, src++, p++, q++, r++) {
 663                                 *p = 0;
 664                                 *q = 0;
 665                                 *r = 0;
 666                         }
 667                 } else {
 668                         ASSERT(ccnt <= pcnt);
 669 
 670                         /*
 671                          * Apply the algorithm described above by multiplying
 672                          * the previous result and adding in the new value.
 673                          */
 674                         for (i = 0; i < ccnt; i++, src++, p++, q++, r++) {
 675                                 *p ^= *src;
 676 
 677                                 VDEV_RAIDZ_64MUL_2(*q, mask);
 678                                 *q ^= *src;
 679 
 680                                 VDEV_RAIDZ_64MUL_4(*r, mask);
 681                                 *r ^= *src;
 682                         }
 683 
 684                         /*
 685                          * Treat short columns as though they are full of 0s.
 686                          * Note that there's therefore nothing needed for P.
 687                          */
 688                         for (; i < pcnt; i++, q++, r++) {
 689                                 VDEV_RAIDZ_64MUL_2(*q, mask);
 690                                 VDEV_RAIDZ_64MUL_4(*r, mask);
 691                         }
 692                 }
 693         }
 694 }
 695 
 696 /*
 697  * Generate RAID parity in the first virtual columns according to the number of
 698  * parity columns available.
 699  */
 700 static void
 701 vdev_raidz_generate_parity(raidz_map_t *rm)
 702 {
 703         switch (rm->rm_firstdatacol) {
 704         case 1:
 705                 vdev_raidz_generate_parity_p(rm);
 706                 break;
 707         case 2:
 708                 vdev_raidz_generate_parity_pq(rm);
 709                 break;
 710         case 3:
 711                 vdev_raidz_generate_parity_pqr(rm);
 712                 break;
 713         default:
 714                 cmn_err(CE_PANIC, "invalid RAID-Z configuration");
 715         }
 716 }
 717 
 718 static int
 719 vdev_raidz_reconstruct_p(raidz_map_t *rm, int *tgts, int ntgts)
 720 {
 721         uint64_t *dst, *src, xcount, ccount, count, i;
 722         int x = tgts[0];
 723         int c;
 724 
 725         ASSERT(ntgts == 1);
 726         ASSERT(x >= rm->rm_firstdatacol);
 727         ASSERT(x < rm->rm_cols);
 728 
 729         xcount = rm->rm_col[x].rc_size / sizeof (src[0]);
 730         ASSERT(xcount <= rm->rm_col[VDEV_RAIDZ_P].rc_size / sizeof (src[0]));
 731         ASSERT(xcount > 0);
 732 
 733         src = rm->rm_col[VDEV_RAIDZ_P].rc_data;
 734         dst = rm->rm_col[x].rc_data;
 735         for (i = 0; i < xcount; i++, dst++, src++) {
 736                 *dst = *src;
 737         }
 738 
 739         for (c = rm->rm_firstdatacol; c < rm->rm_cols; c++) {
 740                 src = rm->rm_col[c].rc_data;
 741                 dst = rm->rm_col[x].rc_data;
 742 
 743                 if (c == x)
 744                         continue;
 745 
 746                 ccount = rm->rm_col[c].rc_size / sizeof (src[0]);
 747                 count = MIN(ccount, xcount);
 748 
 749                 for (i = 0; i < count; i++, dst++, src++) {
 750                         *dst ^= *src;
 751                 }
 752         }
 753 
 754         return (1 << VDEV_RAIDZ_P);
 755 }
 756 
 757 static int
 758 vdev_raidz_reconstruct_q(raidz_map_t *rm, int *tgts, int ntgts)
 759 {
 760         uint64_t *dst, *src, xcount, ccount, count, mask, i;
 761         uint8_t *b;
 762         int x = tgts[0];
 763         int c, j, exp;
 764 
 765         ASSERT(ntgts == 1);
 766 
 767         xcount = rm->rm_col[x].rc_size / sizeof (src[0]);
 768         ASSERT(xcount <= rm->rm_col[VDEV_RAIDZ_Q].rc_size / sizeof (src[0]));
 769 
 770         for (c = rm->rm_firstdatacol; c < rm->rm_cols; c++) {
 771                 src = rm->rm_col[c].rc_data;
 772                 dst = rm->rm_col[x].rc_data;
 773 
 774                 if (c == x)
 775                         ccount = 0;
 776                 else
 777                         ccount = rm->rm_col[c].rc_size / sizeof (src[0]);
 778 
 779                 count = MIN(ccount, xcount);
 780 
 781                 if (c == rm->rm_firstdatacol) {
 782                         for (i = 0; i < count; i++, dst++, src++) {
 783                                 *dst = *src;
 784                         }
 785                         for (; i < xcount; i++, dst++) {
 786                                 *dst = 0;
 787                         }
 788 
 789                 } else {
 790                         for (i = 0; i < count; i++, dst++, src++) {
 791                                 VDEV_RAIDZ_64MUL_2(*dst, mask);
 792                                 *dst ^= *src;
 793                         }
 794 
 795                         for (; i < xcount; i++, dst++) {
 796                                 VDEV_RAIDZ_64MUL_2(*dst, mask);
 797                         }
 798                 }
 799         }
 800 
 801         src = rm->rm_col[VDEV_RAIDZ_Q].rc_data;
 802         dst = rm->rm_col[x].rc_data;
 803         exp = 255 - (rm->rm_cols - 1 - x);
 804 
 805         for (i = 0; i < xcount; i++, dst++, src++) {
 806                 *dst ^= *src;
 807                 for (j = 0, b = (uint8_t *)dst; j < 8; j++, b++) {
 808                         *b = vdev_raidz_exp2(*b, exp);
 809                 }
 810         }
 811 
 812         return (1 << VDEV_RAIDZ_Q);
 813 }
 814 
 815 static int
 816 vdev_raidz_reconstruct_pq(raidz_map_t *rm, int *tgts, int ntgts)
 817 {
 818         uint8_t *p, *q, *pxy, *qxy, *xd, *yd, tmp, a, b, aexp, bexp;
 819         void *pdata, *qdata;
 820         uint64_t xsize, ysize, i;
 821         int x = tgts[0];
 822         int y = tgts[1];
 823 
 824         ASSERT(ntgts == 2);
 825         ASSERT(x < y);
 826         ASSERT(x >= rm->rm_firstdatacol);
 827         ASSERT(y < rm->rm_cols);
 828 
 829         ASSERT(rm->rm_col[x].rc_size >= rm->rm_col[y].rc_size);
 830 
 831         /*
 832          * Move the parity data aside -- we're going to compute parity as
 833          * though columns x and y were full of zeros -- Pxy and Qxy. We want to
 834          * reuse the parity generation mechanism without trashing the actual
 835          * parity so we make those columns appear to be full of zeros by
 836          * setting their lengths to zero.
 837          */
 838         pdata = rm->rm_col[VDEV_RAIDZ_P].rc_data;
 839         qdata = rm->rm_col[VDEV_RAIDZ_Q].rc_data;
 840         xsize = rm->rm_col[x].rc_size;
 841         ysize = rm->rm_col[y].rc_size;
 842 
 843         rm->rm_col[VDEV_RAIDZ_P].rc_data =
 844             zio_buf_alloc(rm->rm_col[VDEV_RAIDZ_P].rc_size);
 845         rm->rm_col[VDEV_RAIDZ_Q].rc_data =
 846             zio_buf_alloc(rm->rm_col[VDEV_RAIDZ_Q].rc_size);
 847         rm->rm_col[x].rc_size = 0;
 848         rm->rm_col[y].rc_size = 0;
 849 
 850         vdev_raidz_generate_parity_pq(rm);
 851 
 852         rm->rm_col[x].rc_size = xsize;
 853         rm->rm_col[y].rc_size = ysize;
 854 
 855         p = pdata;
 856         q = qdata;
 857         pxy = rm->rm_col[VDEV_RAIDZ_P].rc_data;
 858         qxy = rm->rm_col[VDEV_RAIDZ_Q].rc_data;
 859         xd = rm->rm_col[x].rc_data;
 860         yd = rm->rm_col[y].rc_data;
 861 
 862         /*
 863          * We now have:
 864          *      Pxy = P + D_x + D_y
 865          *      Qxy = Q + 2^(ndevs - 1 - x) * D_x + 2^(ndevs - 1 - y) * D_y
 866          *
 867          * We can then solve for D_x:
 868          *      D_x = A * (P + Pxy) + B * (Q + Qxy)
 869          * where
 870          *      A = 2^(x - y) * (2^(x - y) + 1)^-1
 871          *      B = 2^(ndevs - 1 - x) * (2^(x - y) + 1)^-1
 872          *
 873          * With D_x in hand, we can easily solve for D_y:
 874          *      D_y = P + Pxy + D_x
 875          */
 876 
 877         a = vdev_raidz_pow2[255 + x - y];
 878         b = vdev_raidz_pow2[255 - (rm->rm_cols - 1 - x)];
 879         tmp = 255 - vdev_raidz_log2[a ^ 1];
 880 
 881         aexp = vdev_raidz_log2[vdev_raidz_exp2(a, tmp)];
 882         bexp = vdev_raidz_log2[vdev_raidz_exp2(b, tmp)];
 883 
 884         for (i = 0; i < xsize; i++, p++, q++, pxy++, qxy++, xd++, yd++) {
 885                 *xd = vdev_raidz_exp2(*p ^ *pxy, aexp) ^
 886                     vdev_raidz_exp2(*q ^ *qxy, bexp);
 887 
 888                 if (i < ysize)
 889                         *yd = *p ^ *pxy ^ *xd;
 890         }
 891 
 892         zio_buf_free(rm->rm_col[VDEV_RAIDZ_P].rc_data,
 893             rm->rm_col[VDEV_RAIDZ_P].rc_size);
 894         zio_buf_free(rm->rm_col[VDEV_RAIDZ_Q].rc_data,
 895             rm->rm_col[VDEV_RAIDZ_Q].rc_size);
 896 
 897         /*
 898          * Restore the saved parity data.
 899          */
 900         rm->rm_col[VDEV_RAIDZ_P].rc_data = pdata;
 901         rm->rm_col[VDEV_RAIDZ_Q].rc_data = qdata;
 902 
 903         return ((1 << VDEV_RAIDZ_P) | (1 << VDEV_RAIDZ_Q));
 904 }
 905 
 906 /* BEGIN CSTYLED */
 907 /*
 908  * In the general case of reconstruction, we must solve the system of linear
 909  * equations defined by the coeffecients used to generate parity as well as
 910  * the contents of the data and parity disks. This can be expressed with
 911  * vectors for the original data (D) and the actual data (d) and parity (p)
 912  * and a matrix composed of the identity matrix (I) and a dispersal matrix (V):
 913  *
 914  *            __   __                     __     __
 915  *            |     |         __     __   |  p_0  |
 916  *            |  V  |         |  D_0  |   | p_m-1 |
 917  *            |     |    x    |   :   | = |  d_0  |
 918  *            |  I  |         | D_n-1 |   |   :   |
 919  *            |     |         ~~     ~~   | d_n-1 |
 920  *            ~~   ~~                     ~~     ~~
 921  *
 922  * I is simply a square identity matrix of size n, and V is a vandermonde
 923  * matrix defined by the coeffecients we chose for the various parity columns
 924  * (1, 2, 4). Note that these values were chosen both for simplicity, speedy
 925  * computation as well as linear separability.
 926  *
 927  *      __               __               __     __
 928  *      |   1   ..  1 1 1 |               |  p_0  |
 929  *      | 2^n-1 ..  4 2 1 |   __     __   |   :   |
 930  *      | 4^n-1 .. 16 4 1 |   |  D_0  |   | p_m-1 |
 931  *      |   1   ..  0 0 0 |   |  D_1  |   |  d_0  |
 932  *      |   0   ..  0 0 0 | x |  D_2  | = |  d_1  |
 933  *      |   :       : : : |   |   :   |   |  d_2  |
 934  *      |   0   ..  1 0 0 |   | D_n-1 |   |   :   |
 935  *      |   0   ..  0 1 0 |   ~~     ~~   |   :   |
 936  *      |   0   ..  0 0 1 |               | d_n-1 |
 937  *      ~~               ~~               ~~     ~~
 938  *
 939  * Note that I, V, d, and p are known. To compute D, we must invert the
 940  * matrix and use the known data and parity values to reconstruct the unknown
 941  * data values. We begin by removing the rows in V|I and d|p that correspond
 942  * to failed or missing columns; we then make V|I square (n x n) and d|p
 943  * sized n by removing rows corresponding to unused parity from the bottom up
 944  * to generate (V|I)' and (d|p)'. We can then generate the inverse of (V|I)'
 945  * using Gauss-Jordan elimination. In the example below we use m=3 parity
 946  * columns, n=8 data columns, with errors in d_1, d_2, and p_1:
 947  *           __                               __
 948  *           |  1   1   1   1   1   1   1   1  |
 949  *           | 128  64  32  16  8   4   2   1  | <-----+-+-- missing disks
 950  *           |  19 205 116  29  64  16  4   1  |      / /
 951  *           |  1   0   0   0   0   0   0   0  |     / /
 952  *           |  0   1   0   0   0   0   0   0  | <--' /
 953  *  (V|I)  = |  0   0   1   0   0   0   0   0  | <---'
 954  *           |  0   0   0   1   0   0   0   0  |
 955  *           |  0   0   0   0   1   0   0   0  |
 956  *           |  0   0   0   0   0   1   0   0  |
 957  *           |  0   0   0   0   0   0   1   0  |
 958  *           |  0   0   0   0   0   0   0   1  |
 959  *           ~~                               ~~
 960  *           __                               __
 961  *           |  1   1   1   1   1   1   1   1  |
 962  *           | 128  64  32  16  8   4   2   1  |
 963  *           |  19 205 116  29  64  16  4   1  |
 964  *           |  1   0   0   0   0   0   0   0  |
 965  *           |  0   1   0   0   0   0   0   0  |
 966  *  (V|I)' = |  0   0   1   0   0   0   0   0  |
 967  *           |  0   0   0   1   0   0   0   0  |
 968  *           |  0   0   0   0   1   0   0   0  |
 969  *           |  0   0   0   0   0   1   0   0  |
 970  *           |  0   0   0   0   0   0   1   0  |
 971  *           |  0   0   0   0   0   0   0   1  |
 972  *           ~~                               ~~
 973  *
 974  * Here we employ Gauss-Jordan elimination to find the inverse of (V|I)'. We
 975  * have carefully chosen the seed values 1, 2, and 4 to ensure that this
 976  * matrix is not singular.
 977  * __                                                                 __
 978  * |  1   1   1   1   1   1   1   1     1   0   0   0   0   0   0   0  |
 979  * |  19 205 116  29  64  16  4   1     0   1   0   0   0   0   0   0  |
 980  * |  1   0   0   0   0   0   0   0     0   0   1   0   0   0   0   0  |
 981  * |  0   0   0   1   0   0   0   0     0   0   0   1   0   0   0   0  |
 982  * |  0   0   0   0   1   0   0   0     0   0   0   0   1   0   0   0  |
 983  * |  0   0   0   0   0   1   0   0     0   0   0   0   0   1   0   0  |
 984  * |  0   0   0   0   0   0   1   0     0   0   0   0   0   0   1   0  |
 985  * |  0   0   0   0   0   0   0   1     0   0   0   0   0   0   0   1  |
 986  * ~~                                                                 ~~
 987  * __                                                                 __
 988  * |  1   0   0   0   0   0   0   0     0   0   1   0   0   0   0   0  |
 989  * |  1   1   1   1   1   1   1   1     1   0   0   0   0   0   0   0  |
 990  * |  19 205 116  29  64  16  4   1     0   1   0   0   0   0   0   0  |
 991  * |  0   0   0   1   0   0   0   0     0   0   0   1   0   0   0   0  |
 992  * |  0   0   0   0   1   0   0   0     0   0   0   0   1   0   0   0  |
 993  * |  0   0   0   0   0   1   0   0     0   0   0   0   0   1   0   0  |
 994  * |  0   0   0   0   0   0   1   0     0   0   0   0   0   0   1   0  |
 995  * |  0   0   0   0   0   0   0   1     0   0   0   0   0   0   0   1  |
 996  * ~~                                                                 ~~
 997  * __                                                                 __
 998  * |  1   0   0   0   0   0   0   0     0   0   1   0   0   0   0   0  |
 999  * |  0   1   1   0   0   0   0   0     1   0   1   1   1   1   1   1  |
1000  * |  0  205 116  0   0   0   0   0     0   1   19  29  64  16  4   1  |
1001  * |  0   0   0   1   0   0   0   0     0   0   0   1   0   0   0   0  |
1002  * |  0   0   0   0   1   0   0   0     0   0   0   0   1   0   0   0  |
1003  * |  0   0   0   0   0   1   0   0     0   0   0   0   0   1   0   0  |
1004  * |  0   0   0   0   0   0   1   0     0   0   0   0   0   0   1   0  |
1005  * |  0   0   0   0   0   0   0   1     0   0   0   0   0   0   0   1  |
1006  * ~~                                                                 ~~
1007  * __                                                                 __
1008  * |  1   0   0   0   0   0   0   0     0   0   1   0   0   0   0   0  |
1009  * |  0   1   1   0   0   0   0   0     1   0   1   1   1   1   1   1  |
1010  * |  0   0  185  0   0   0   0   0    205  1  222 208 141 221 201 204 |
1011  * |  0   0   0   1   0   0   0   0     0   0   0   1   0   0   0   0  |
1012  * |  0   0   0   0   1   0   0   0     0   0   0   0   1   0   0   0  |
1013  * |  0   0   0   0   0   1   0   0     0   0   0   0   0   1   0   0  |
1014  * |  0   0   0   0   0   0   1   0     0   0   0   0   0   0   1   0  |
1015  * |  0   0   0   0   0   0   0   1     0   0   0   0   0   0   0   1  |
1016  * ~~                                                                 ~~
1017  * __                                                                 __
1018  * |  1   0   0   0   0   0   0   0     0   0   1   0   0   0   0   0  |
1019  * |  0   1   1   0   0   0   0   0     1   0   1   1   1   1   1   1  |
1020  * |  0   0   1   0   0   0   0   0    166 100  4   40 158 168 216 209 |
1021  * |  0   0   0   1   0   0   0   0     0   0   0   1   0   0   0   0  |
1022  * |  0   0   0   0   1   0   0   0     0   0   0   0   1   0   0   0  |
1023  * |  0   0   0   0   0   1   0   0     0   0   0   0   0   1   0   0  |
1024  * |  0   0   0   0   0   0   1   0     0   0   0   0   0   0   1   0  |
1025  * |  0   0   0   0   0   0   0   1     0   0   0   0   0   0   0   1  |
1026  * ~~                                                                 ~~
1027  * __                                                                 __
1028  * |  1   0   0   0   0   0   0   0     0   0   1   0   0   0   0   0  |
1029  * |  0   1   0   0   0   0   0   0    167 100  5   41 159 169 217 208 |
1030  * |  0   0   1   0   0   0   0   0    166 100  4   40 158 168 216 209 |
1031  * |  0   0   0   1   0   0   0   0     0   0   0   1   0   0   0   0  |
1032  * |  0   0   0   0   1   0   0   0     0   0   0   0   1   0   0   0  |
1033  * |  0   0   0   0   0   1   0   0     0   0   0   0   0   1   0   0  |
1034  * |  0   0   0   0   0   0   1   0     0   0   0   0   0   0   1   0  |
1035  * |  0   0   0   0   0   0   0   1     0   0   0   0   0   0   0   1  |
1036  * ~~                                                                 ~~
1037  *                   __                               __
1038  *                   |  0   0   1   0   0   0   0   0  |
1039  *                   | 167 100  5   41 159 169 217 208 |
1040  *                   | 166 100  4   40 158 168 216 209 |
1041  *       (V|I)'^-1 = |  0   0   0   1   0   0   0   0  |
1042  *                   |  0   0   0   0   1   0   0   0  |
1043  *                   |  0   0   0   0   0   1   0   0  |
1044  *                   |  0   0   0   0   0   0   1   0  |
1045  *                   |  0   0   0   0   0   0   0   1  |
1046  *                   ~~                               ~~
1047  *
1048  * We can then simply compute D = (V|I)'^-1 x (d|p)' to discover the values
1049  * of the missing data.
1050  *
1051  * As is apparent from the example above, the only non-trivial rows in the
1052  * inverse matrix correspond to the data disks that we're trying to
1053  * reconstruct. Indeed, those are the only rows we need as the others would
1054  * only be useful for reconstructing data known or assumed to be valid. For
1055  * that reason, we only build the coefficients in the rows that correspond to
1056  * targeted columns.
1057  */
1058 /* END CSTYLED */
1059 
1060 static void
1061 vdev_raidz_matrix_init(raidz_map_t *rm, int n, int nmap, int *map,
1062     uint8_t **rows)
1063 {
1064         int i, j;
1065         int pow;
1066 
1067         ASSERT(n == rm->rm_cols - rm->rm_firstdatacol);
1068 
1069         /*
1070          * Fill in the missing rows of interest.
1071          */
1072         for (i = 0; i < nmap; i++) {
1073                 ASSERT3S(0, <=, map[i]);
1074                 ASSERT3S(map[i], <=, 2);
1075 
1076                 pow = map[i] * n;
1077                 if (pow > 255)
1078                         pow -= 255;
1079                 ASSERT(pow <= 255);
1080 
1081                 for (j = 0; j < n; j++) {
1082                         pow -= map[i];
1083                         if (pow < 0)
1084                                 pow += 255;
1085                         rows[i][j] = vdev_raidz_pow2[pow];
1086                 }
1087         }
1088 }
1089 
1090 static void
1091 vdev_raidz_matrix_invert(raidz_map_t *rm, int n, int nmissing, int *missing,
1092     uint8_t **rows, uint8_t **invrows, const uint8_t *used)
1093 {
1094         int i, j, ii, jj;
1095         uint8_t log;
1096 
1097         /*
1098          * Assert that the first nmissing entries from the array of used
1099          * columns correspond to parity columns and that subsequent entries
1100          * correspond to data columns.
1101          */
1102         for (i = 0; i < nmissing; i++) {
1103                 ASSERT3S(used[i], <, rm->rm_firstdatacol);
1104         }
1105         for (; i < n; i++) {
1106                 ASSERT3S(used[i], >=, rm->rm_firstdatacol);
1107         }
1108 
1109         /*
1110          * First initialize the storage where we'll compute the inverse rows.
1111          */
1112         for (i = 0; i < nmissing; i++) {
1113                 for (j = 0; j < n; j++) {
1114                         invrows[i][j] = (i == j) ? 1 : 0;
1115                 }
1116         }
1117 
1118         /*
1119          * Subtract all trivial rows from the rows of consequence.
1120          */
1121         for (i = 0; i < nmissing; i++) {
1122                 for (j = nmissing; j < n; j++) {
1123                         ASSERT3U(used[j], >=, rm->rm_firstdatacol);
1124                         jj = used[j] - rm->rm_firstdatacol;
1125                         ASSERT3S(jj, <, n);
1126                         invrows[i][j] = rows[i][jj];
1127                         rows[i][jj] = 0;
1128                 }
1129         }
1130 
1131         /*
1132          * For each of the rows of interest, we must normalize it and subtract
1133          * a multiple of it from the other rows.
1134          */
1135         for (i = 0; i < nmissing; i++) {
1136                 for (j = 0; j < missing[i]; j++) {
1137                         ASSERT0(rows[i][j]);
1138                 }
1139                 ASSERT3U(rows[i][missing[i]], !=, 0);
1140 
1141                 /*
1142                  * Compute the inverse of the first element and multiply each
1143                  * element in the row by that value.
1144                  */
1145                 log = 255 - vdev_raidz_log2[rows[i][missing[i]]];
1146 
1147                 for (j = 0; j < n; j++) {
1148                         rows[i][j] = vdev_raidz_exp2(rows[i][j], log);
1149                         invrows[i][j] = vdev_raidz_exp2(invrows[i][j], log);
1150                 }
1151 
1152                 for (ii = 0; ii < nmissing; ii++) {
1153                         if (i == ii)
1154                                 continue;
1155 
1156                         ASSERT3U(rows[ii][missing[i]], !=, 0);
1157 
1158                         log = vdev_raidz_log2[rows[ii][missing[i]]];
1159 
1160                         for (j = 0; j < n; j++) {
1161                                 rows[ii][j] ^=
1162                                     vdev_raidz_exp2(rows[i][j], log);
1163                                 invrows[ii][j] ^=
1164                                     vdev_raidz_exp2(invrows[i][j], log);
1165                         }
1166                 }
1167         }
1168 
1169         /*
1170          * Verify that the data that is left in the rows are properly part of
1171          * an identity matrix.
1172          */
1173         for (i = 0; i < nmissing; i++) {
1174                 for (j = 0; j < n; j++) {
1175                         if (j == missing[i]) {
1176                                 ASSERT3U(rows[i][j], ==, 1);
1177                         } else {
1178                                 ASSERT0(rows[i][j]);
1179                         }
1180                 }
1181         }
1182 }
1183 
1184 static void
1185 vdev_raidz_matrix_reconstruct(raidz_map_t *rm, int n, int nmissing,
1186     int *missing, uint8_t **invrows, const uint8_t *used)
1187 {
1188         int i, j, x, cc, c;
1189         uint8_t *src;
1190         uint64_t ccount;
1191         uint8_t *dst[VDEV_RAIDZ_MAXPARITY];
1192         uint64_t dcount[VDEV_RAIDZ_MAXPARITY];
1193         uint8_t log, val;
1194         int ll;
1195         uint8_t *invlog[VDEV_RAIDZ_MAXPARITY];
1196         uint8_t *p, *pp;
1197         size_t psize;
1198 
1199         psize = sizeof (invlog[0][0]) * n * nmissing;
1200         p = kmem_alloc(psize, KM_SLEEP);
1201 
1202         for (pp = p, i = 0; i < nmissing; i++) {
1203                 invlog[i] = pp;
1204                 pp += n;
1205         }
1206 
1207         for (i = 0; i < nmissing; i++) {
1208                 for (j = 0; j < n; j++) {
1209                         ASSERT3U(invrows[i][j], !=, 0);
1210                         invlog[i][j] = vdev_raidz_log2[invrows[i][j]];
1211                 }
1212         }
1213 
1214         for (i = 0; i < n; i++) {
1215                 c = used[i];
1216                 ASSERT3U(c, <, rm->rm_cols);
1217 
1218                 src = rm->rm_col[c].rc_data;
1219                 ccount = rm->rm_col[c].rc_size;
1220                 for (j = 0; j < nmissing; j++) {
1221                         cc = missing[j] + rm->rm_firstdatacol;
1222                         ASSERT3U(cc, >=, rm->rm_firstdatacol);
1223                         ASSERT3U(cc, <, rm->rm_cols);
1224                         ASSERT3U(cc, !=, c);
1225 
1226                         dst[j] = rm->rm_col[cc].rc_data;
1227                         dcount[j] = rm->rm_col[cc].rc_size;
1228                 }
1229 
1230                 ASSERT(ccount >= rm->rm_col[missing[0]].rc_size || i > 0);
1231 
1232                 for (x = 0; x < ccount; x++, src++) {
1233                         if (*src != 0)
1234                                 log = vdev_raidz_log2[*src];
1235 
1236                         for (cc = 0; cc < nmissing; cc++) {
1237                                 if (x >= dcount[cc])
1238                                         continue;
1239 
1240                                 if (*src == 0) {
1241                                         val = 0;
1242                                 } else {
1243                                         if ((ll = log + invlog[cc][i]) >= 255)
1244                                                 ll -= 255;
1245                                         val = vdev_raidz_pow2[ll];
1246                                 }
1247 
1248                                 if (i == 0)
1249                                         dst[cc][x] = val;
1250                                 else
1251                                         dst[cc][x] ^= val;
1252                         }
1253                 }
1254         }
1255 
1256         kmem_free(p, psize);
1257 }
1258 
1259 static int
1260 vdev_raidz_reconstruct_general(raidz_map_t *rm, int *tgts, int ntgts)
1261 {
1262         int n, i, c, t, tt;
1263         int nmissing_rows;
1264         int missing_rows[VDEV_RAIDZ_MAXPARITY];
1265         int parity_map[VDEV_RAIDZ_MAXPARITY];
1266 
1267         uint8_t *p, *pp;
1268         size_t psize;
1269 
1270         uint8_t *rows[VDEV_RAIDZ_MAXPARITY];
1271         uint8_t *invrows[VDEV_RAIDZ_MAXPARITY];
1272         uint8_t *used;
1273 
1274         int code = 0;
1275 
1276 
1277         n = rm->rm_cols - rm->rm_firstdatacol;
1278 
1279         /*
1280          * Figure out which data columns are missing.
1281          */
1282         nmissing_rows = 0;
1283         for (t = 0; t < ntgts; t++) {
1284                 if (tgts[t] >= rm->rm_firstdatacol) {
1285                         missing_rows[nmissing_rows++] =
1286                             tgts[t] - rm->rm_firstdatacol;
1287                 }
1288         }
1289 
1290         /*
1291          * Figure out which parity columns to use to help generate the missing
1292          * data columns.
1293          */
1294         for (tt = 0, c = 0, i = 0; i < nmissing_rows; c++) {
1295                 ASSERT(tt < ntgts);
1296                 ASSERT(c < rm->rm_firstdatacol);
1297 
1298                 /*
1299                  * Skip any targeted parity columns.
1300                  */
1301                 if (c == tgts[tt]) {
1302                         tt++;
1303                         continue;
1304                 }
1305 
1306                 code |= 1 << c;
1307 
1308                 parity_map[i] = c;
1309                 i++;
1310         }
1311 
1312         ASSERT(code != 0);
1313         ASSERT3U(code, <, 1 << VDEV_RAIDZ_MAXPARITY);
1314 
1315         psize = (sizeof (rows[0][0]) + sizeof (invrows[0][0])) *
1316             nmissing_rows * n + sizeof (used[0]) * n;
1317         p = kmem_alloc(psize, KM_SLEEP);
1318 
1319         for (pp = p, i = 0; i < nmissing_rows; i++) {
1320                 rows[i] = pp;
1321                 pp += n;
1322                 invrows[i] = pp;
1323                 pp += n;
1324         }
1325         used = pp;
1326 
1327         for (i = 0; i < nmissing_rows; i++) {
1328                 used[i] = parity_map[i];
1329         }
1330 
1331         for (tt = 0, c = rm->rm_firstdatacol; c < rm->rm_cols; c++) {
1332                 if (tt < nmissing_rows &&
1333                     c == missing_rows[tt] + rm->rm_firstdatacol) {
1334                         tt++;
1335                         continue;
1336                 }
1337 
1338                 ASSERT3S(i, <, n);
1339                 used[i] = c;
1340                 i++;
1341         }
1342 
1343         /*
1344          * Initialize the interesting rows of the matrix.
1345          */
1346         vdev_raidz_matrix_init(rm, n, nmissing_rows, parity_map, rows);
1347 
1348         /*
1349          * Invert the matrix.
1350          */
1351         vdev_raidz_matrix_invert(rm, n, nmissing_rows, missing_rows, rows,
1352             invrows, used);
1353 
1354         /*
1355          * Reconstruct the missing data using the generated matrix.
1356          */
1357         vdev_raidz_matrix_reconstruct(rm, n, nmissing_rows, missing_rows,
1358             invrows, used);
1359 
1360         kmem_free(p, psize);
1361 
1362         return (code);
1363 }
1364 
1365 static int
1366 vdev_raidz_reconstruct(raidz_map_t *rm, int *t, int nt)
1367 {
1368         int tgts[VDEV_RAIDZ_MAXPARITY], *dt;
1369         int ntgts;
1370         int i, c;
1371         int code;
1372         int nbadparity, nbaddata;
1373         int parity_valid[VDEV_RAIDZ_MAXPARITY];
1374 
1375         /*
1376          * The tgts list must already be sorted.
1377          */
1378         for (i = 1; i < nt; i++) {
1379                 ASSERT(t[i] > t[i - 1]);
1380         }
1381 
1382         nbadparity = rm->rm_firstdatacol;
1383         nbaddata = rm->rm_cols - nbadparity;
1384         ntgts = 0;
1385         for (i = 0, c = 0; c < rm->rm_cols; c++) {
1386                 if (c < rm->rm_firstdatacol)
1387                         parity_valid[c] = B_FALSE;
1388 
1389                 if (i < nt && c == t[i]) {
1390                         tgts[ntgts++] = c;
1391                         i++;
1392                 } else if (rm->rm_col[c].rc_error != 0) {
1393                         tgts[ntgts++] = c;
1394                 } else if (c >= rm->rm_firstdatacol) {
1395                         nbaddata--;
1396                 } else {
1397                         parity_valid[c] = B_TRUE;
1398                         nbadparity--;
1399                 }
1400         }
1401 
1402         ASSERT(ntgts >= nt);
1403         ASSERT(nbaddata >= 0);
1404         ASSERT(nbaddata + nbadparity == ntgts);
1405 
1406         dt = &tgts[nbadparity];
1407 
1408         /*
1409          * See if we can use any of our optimized reconstruction routines.
1410          */
1411         if (!vdev_raidz_default_to_general) {
1412                 switch (nbaddata) {
1413                 case 1:
1414                         if (parity_valid[VDEV_RAIDZ_P])
1415                                 return (vdev_raidz_reconstruct_p(rm, dt, 1));
1416 
1417                         ASSERT(rm->rm_firstdatacol > 1);
1418 
1419                         if (parity_valid[VDEV_RAIDZ_Q])
1420                                 return (vdev_raidz_reconstruct_q(rm, dt, 1));
1421 
1422                         ASSERT(rm->rm_firstdatacol > 2);
1423                         break;
1424 
1425                 case 2:
1426                         ASSERT(rm->rm_firstdatacol > 1);
1427 
1428                         if (parity_valid[VDEV_RAIDZ_P] &&
1429                             parity_valid[VDEV_RAIDZ_Q])
1430                                 return (vdev_raidz_reconstruct_pq(rm, dt, 2));
1431 
1432                         ASSERT(rm->rm_firstdatacol > 2);
1433 
1434                         break;
1435                 }
1436         }
1437 
1438         code = vdev_raidz_reconstruct_general(rm, tgts, ntgts);
1439         ASSERT(code < (1 << VDEV_RAIDZ_MAXPARITY));
1440         ASSERT(code > 0);
1441         return (code);
1442 }
1443 
1444 static int
1445 vdev_raidz_open(vdev_t *vd, uint64_t *asize, uint64_t *max_asize,
1446     uint64_t *ashift)
1447 {
1448         vdev_t *cvd;
1449         uint64_t nparity = vd->vdev_nparity;
1450         int c;
1451         int lasterror = 0;
1452         int numerrors = 0;
1453 
1454         ASSERT(nparity > 0);
1455 
1456         if (nparity > VDEV_RAIDZ_MAXPARITY ||
1457             vd->vdev_children < nparity + 1) {
1458                 vd->vdev_stat.vs_aux = VDEV_AUX_BAD_LABEL;
1459                 return (EINVAL);
1460         }
1461 
1462         vdev_open_children(vd);
1463 
1464         for (c = 0; c < vd->vdev_children; c++) {
1465                 cvd = vd->vdev_child[c];
1466 
1467                 if (cvd->vdev_open_error != 0) {
1468                         lasterror = cvd->vdev_open_error;
1469                         numerrors++;
1470                         continue;
1471                 }
1472 
1473                 *asize = MIN(*asize - 1, cvd->vdev_asize - 1) + 1;
1474                 *max_asize = MIN(*max_asize - 1, cvd->vdev_max_asize - 1) + 1;
1475                 *ashift = MAX(*ashift, cvd->vdev_ashift);
1476         }
1477 
1478         *asize *= vd->vdev_children;
1479         *max_asize *= vd->vdev_children;
1480 
1481         if (numerrors > nparity) {
1482                 vd->vdev_stat.vs_aux = VDEV_AUX_NO_REPLICAS;
1483                 return (lasterror);
1484         }
1485 
1486         return (0);
1487 }
1488 
1489 static void
1490 vdev_raidz_close(vdev_t *vd)
1491 {
1492         int c;
1493 
1494         for (c = 0; c < vd->vdev_children; c++)
1495                 vdev_close(vd->vdev_child[c]);
1496 }
1497 
1498 static uint64_t
1499 vdev_raidz_asize(vdev_t *vd, uint64_t psize)
1500 {
1501         uint64_t asize;
1502         uint64_t ashift = vd->vdev_top->vdev_ashift;
1503         uint64_t cols = vd->vdev_children;
1504         uint64_t nparity = vd->vdev_nparity;
1505 
1506         asize = ((psize - 1) >> ashift) + 1;
1507         asize += nparity * ((asize + cols - nparity - 1) / (cols - nparity));
1508         asize = roundup(asize, nparity + 1) << ashift;
1509 
1510         return (asize);
1511 }
1512 
1513 static void
1514 vdev_raidz_child_done(zio_t *zio)
1515 {
1516         raidz_col_t *rc = zio->io_private;
1517 
1518         rc->rc_error = zio->io_error;
1519         rc->rc_tried = 1;
1520         rc->rc_skipped = 0;
1521 }
1522 
1523 static int
1524 vdev_raidz_io_start(zio_t *zio)
1525 {
1526         vdev_t *vd = zio->io_vd;
1527         vdev_t *tvd = vd->vdev_top;
1528         vdev_t *cvd;
1529         raidz_map_t *rm;
1530         raidz_col_t *rc;
1531         int c, i;
1532 
1533         rm = vdev_raidz_map_alloc(zio, tvd->vdev_ashift, vd->vdev_children,
1534             vd->vdev_nparity);
1535 
1536         ASSERT3U(rm->rm_asize, ==, vdev_psize_to_asize(vd, zio->io_size));
1537 
1538         if (zio->io_type == ZIO_TYPE_WRITE) {
1539                 vdev_raidz_generate_parity(rm);
1540 
1541                 for (c = 0; c < rm->rm_cols; c++) {
1542                         rc = &rm->rm_col[c];
1543                         cvd = vd->vdev_child[rc->rc_devidx];
1544                         zio_nowait(zio_vdev_child_io(zio, NULL, cvd,
1545                             rc->rc_offset, rc->rc_data, rc->rc_size,
1546                             zio->io_type, zio->io_priority, 0,
1547                             vdev_raidz_child_done, rc));
1548                 }
1549 
1550                 /*
1551                  * Generate optional I/Os for any skipped sectors to improve
1552                  * aggregation contiguity.
1553                  */
1554                 for (c = rm->rm_skipstart, i = 0; i < rm->rm_nskip; c++, i++) {
1555                         ASSERT(c <= rm->rm_scols);
1556                         if (c == rm->rm_scols)
1557                                 c = 0;
1558                         rc = &rm->rm_col[c];
1559                         cvd = vd->vdev_child[rc->rc_devidx];
1560                         zio_nowait(zio_vdev_child_io(zio, NULL, cvd,
1561                             rc->rc_offset + rc->rc_size, NULL,
1562                             1 << tvd->vdev_ashift,
1563                             zio->io_type, zio->io_priority,
1564                             ZIO_FLAG_NODATA | ZIO_FLAG_OPTIONAL, NULL, NULL));
1565                 }
1566 
1567                 return (ZIO_PIPELINE_CONTINUE);
1568         }
1569 
1570         ASSERT(zio->io_type == ZIO_TYPE_READ);
1571 
1572         /*
1573          * Iterate over the columns in reverse order so that we hit the parity
1574          * last -- any errors along the way will force us to read the parity.
1575          */
1576         for (c = rm->rm_cols - 1; c >= 0; c--) {
1577                 rc = &rm->rm_col[c];
1578                 cvd = vd->vdev_child[rc->rc_devidx];
1579                 if (!vdev_readable(cvd)) {
1580                         if (c >= rm->rm_firstdatacol)
1581                                 rm->rm_missingdata++;
1582                         else
1583                                 rm->rm_missingparity++;
1584                         rc->rc_error = ENXIO;
1585                         rc->rc_tried = 1;    /* don't even try */
1586                         rc->rc_skipped = 1;
1587                         continue;
1588                 }
1589                 if (vdev_dtl_contains(cvd, DTL_MISSING, zio->io_txg, 1)) {
1590                         if (c >= rm->rm_firstdatacol)
1591                                 rm->rm_missingdata++;
1592                         else
1593                                 rm->rm_missingparity++;
1594                         rc->rc_error = ESTALE;
1595                         rc->rc_skipped = 1;
1596                         continue;
1597                 }
1598                 if (c >= rm->rm_firstdatacol || rm->rm_missingdata > 0 ||
1599                     (zio->io_flags & (ZIO_FLAG_SCRUB | ZIO_FLAG_RESILVER))) {
1600                         zio_nowait(zio_vdev_child_io(zio, NULL, cvd,
1601                             rc->rc_offset, rc->rc_data, rc->rc_size,
1602                             zio->io_type, zio->io_priority, 0,
1603                             vdev_raidz_child_done, rc));
1604                 }
1605         }
1606 
1607         return (ZIO_PIPELINE_CONTINUE);
1608 }
1609 
1610 
1611 /*
1612  * Report a checksum error for a child of a RAID-Z device.
1613  */
1614 static void
1615 raidz_checksum_error(zio_t *zio, raidz_col_t *rc, void *bad_data)
1616 {
1617         vdev_t *vd = zio->io_vd->vdev_child[rc->rc_devidx];
1618 
1619         if (!(zio->io_flags & ZIO_FLAG_SPECULATIVE)) {
1620                 zio_bad_cksum_t zbc;
1621                 raidz_map_t *rm = zio->io_vsd;
1622 
1623                 mutex_enter(&vd->vdev_stat_lock);
1624                 vd->vdev_stat.vs_checksum_errors++;
1625                 mutex_exit(&vd->vdev_stat_lock);
1626 
1627                 zbc.zbc_has_cksum = 0;
1628                 zbc.zbc_injected = rm->rm_ecksuminjected;
1629 
1630                 zfs_ereport_post_checksum(zio->io_spa, vd, zio,
1631                     rc->rc_offset, rc->rc_size, rc->rc_data, bad_data,
1632                     &zbc);
1633         }
1634 }
1635 
1636 /*
1637  * We keep track of whether or not there were any injected errors, so that
1638  * any ereports we generate can note it.
1639  */
1640 static int
1641 raidz_checksum_verify(zio_t *zio)
1642 {
1643         zio_bad_cksum_t zbc;
1644         raidz_map_t *rm = zio->io_vsd;
1645 
1646         int ret = zio_checksum_error(zio, &zbc);
1647         if (ret != 0 && zbc.zbc_injected != 0)
1648                 rm->rm_ecksuminjected = 1;
1649 
1650         return (ret);
1651 }
1652 
1653 /*
1654  * Generate the parity from the data columns. If we tried and were able to
1655  * read the parity without error, verify that the generated parity matches the
1656  * data we read. If it doesn't, we fire off a checksum error. Return the
1657  * number such failures.
1658  */
1659 static int
1660 raidz_parity_verify(zio_t *zio, raidz_map_t *rm)
1661 {
1662         void *orig[VDEV_RAIDZ_MAXPARITY];
1663         int c, ret = 0;
1664         raidz_col_t *rc;
1665 
1666         for (c = 0; c < rm->rm_firstdatacol; c++) {
1667                 rc = &rm->rm_col[c];
1668                 if (!rc->rc_tried || rc->rc_error != 0)
1669                         continue;
1670                 orig[c] = zio_buf_alloc(rc->rc_size);
1671                 bcopy(rc->rc_data, orig[c], rc->rc_size);
1672         }
1673 
1674         vdev_raidz_generate_parity(rm);
1675 
1676         for (c = 0; c < rm->rm_firstdatacol; c++) {
1677                 rc = &rm->rm_col[c];
1678                 if (!rc->rc_tried || rc->rc_error != 0)
1679                         continue;
1680                 if (bcmp(orig[c], rc->rc_data, rc->rc_size) != 0) {
1681                         raidz_checksum_error(zio, rc, orig[c]);
1682                         rc->rc_error = ECKSUM;
1683                         ret++;
1684                 }
1685                 zio_buf_free(orig[c], rc->rc_size);
1686         }
1687 
1688         return (ret);
1689 }
1690 
1691 /*
1692  * Keep statistics on all the ways that we used parity to correct data.
1693  */
1694 static uint64_t raidz_corrected[1 << VDEV_RAIDZ_MAXPARITY];
1695 
1696 static int
1697 vdev_raidz_worst_error(raidz_map_t *rm)
1698 {
1699         int error = 0;
1700 
1701         for (int c = 0; c < rm->rm_cols; c++)
1702                 error = zio_worst_error(error, rm->rm_col[c].rc_error);
1703 
1704         return (error);
1705 }
1706 
1707 /*
1708  * Iterate over all combinations of bad data and attempt a reconstruction.
1709  * Note that the algorithm below is non-optimal because it doesn't take into
1710  * account how reconstruction is actually performed. For example, with
1711  * triple-parity RAID-Z the reconstruction procedure is the same if column 4
1712  * is targeted as invalid as if columns 1 and 4 are targeted since in both
1713  * cases we'd only use parity information in column 0.
1714  */
1715 static int
1716 vdev_raidz_combrec(zio_t *zio, int total_errors, int data_errors)
1717 {
1718         raidz_map_t *rm = zio->io_vsd;
1719         raidz_col_t *rc;
1720         void *orig[VDEV_RAIDZ_MAXPARITY];
1721         int tstore[VDEV_RAIDZ_MAXPARITY + 2];
1722         int *tgts = &tstore[1];
1723         int current, next, i, c, n;
1724         int code, ret = 0;
1725 
1726         ASSERT(total_errors < rm->rm_firstdatacol);
1727 
1728         /*
1729          * This simplifies one edge condition.
1730          */
1731         tgts[-1] = -1;
1732 
1733         for (n = 1; n <= rm->rm_firstdatacol - total_errors; n++) {
1734                 /*
1735                  * Initialize the targets array by finding the first n columns
1736                  * that contain no error.
1737                  *
1738                  * If there were no data errors, we need to ensure that we're
1739                  * always explicitly attempting to reconstruct at least one
1740                  * data column. To do this, we simply push the highest target
1741                  * up into the data columns.
1742                  */
1743                 for (c = 0, i = 0; i < n; i++) {
1744                         if (i == n - 1 && data_errors == 0 &&
1745                             c < rm->rm_firstdatacol) {
1746                                 c = rm->rm_firstdatacol;
1747                         }
1748 
1749                         while (rm->rm_col[c].rc_error != 0) {
1750                                 c++;
1751                                 ASSERT3S(c, <, rm->rm_cols);
1752                         }
1753 
1754                         tgts[i] = c++;
1755                 }
1756 
1757                 /*
1758                  * Setting tgts[n] simplifies the other edge condition.
1759                  */
1760                 tgts[n] = rm->rm_cols;
1761 
1762                 /*
1763                  * These buffers were allocated in previous iterations.
1764                  */
1765                 for (i = 0; i < n - 1; i++) {
1766                         ASSERT(orig[i] != NULL);
1767                 }
1768 
1769                 orig[n - 1] = zio_buf_alloc(rm->rm_col[0].rc_size);
1770 
1771                 current = 0;
1772                 next = tgts[current];
1773 
1774                 while (current != n) {
1775                         tgts[current] = next;
1776                         current = 0;
1777 
1778                         /*
1779                          * Save off the original data that we're going to
1780                          * attempt to reconstruct.
1781                          */
1782                         for (i = 0; i < n; i++) {
1783                                 ASSERT(orig[i] != NULL);
1784                                 c = tgts[i];
1785                                 ASSERT3S(c, >=, 0);
1786                                 ASSERT3S(c, <, rm->rm_cols);
1787                                 rc = &rm->rm_col[c];
1788                                 bcopy(rc->rc_data, orig[i], rc->rc_size);
1789                         }
1790 
1791                         /*
1792                          * Attempt a reconstruction and exit the outer loop on
1793                          * success.
1794                          */
1795                         code = vdev_raidz_reconstruct(rm, tgts, n);
1796                         if (raidz_checksum_verify(zio) == 0) {
1797                                 atomic_inc_64(&raidz_corrected[code]);
1798 
1799                                 for (i = 0; i < n; i++) {
1800                                         c = tgts[i];
1801                                         rc = &rm->rm_col[c];
1802                                         ASSERT(rc->rc_error == 0);
1803                                         if (rc->rc_tried)
1804                                                 raidz_checksum_error(zio, rc,
1805                                                     orig[i]);
1806                                         rc->rc_error = ECKSUM;
1807                                 }
1808 
1809                                 ret = code;
1810                                 goto done;
1811                         }
1812 
1813                         /*
1814                          * Restore the original data.
1815                          */
1816                         for (i = 0; i < n; i++) {
1817                                 c = tgts[i];
1818                                 rc = &rm->rm_col[c];
1819                                 bcopy(orig[i], rc->rc_data, rc->rc_size);
1820                         }
1821 
1822                         do {
1823                                 /*
1824                                  * Find the next valid column after the current
1825                                  * position..
1826                                  */
1827                                 for (next = tgts[current] + 1;
1828                                     next < rm->rm_cols &&
1829                                     rm->rm_col[next].rc_error != 0; next++)
1830                                         continue;
1831 
1832                                 ASSERT(next <= tgts[current + 1]);
1833 
1834                                 /*
1835                                  * If that spot is available, we're done here.
1836                                  */
1837                                 if (next != tgts[current + 1])
1838                                         break;
1839 
1840                                 /*
1841                                  * Otherwise, find the next valid column after
1842                                  * the previous position.
1843                                  */
1844                                 for (c = tgts[current - 1] + 1;
1845                                     rm->rm_col[c].rc_error != 0; c++)
1846                                         continue;
1847 
1848                                 tgts[current] = c;
1849                                 current++;
1850 
1851                         } while (current != n);
1852                 }
1853         }
1854         n--;
1855 done:
1856         for (i = 0; i < n; i++) {
1857                 zio_buf_free(orig[i], rm->rm_col[0].rc_size);
1858         }
1859 
1860         return (ret);
1861 }
1862 
1863 static void
1864 vdev_raidz_io_done(zio_t *zio)
1865 {
1866         vdev_t *vd = zio->io_vd;
1867         vdev_t *cvd;
1868         raidz_map_t *rm = zio->io_vsd;
1869         raidz_col_t *rc;
1870         int unexpected_errors = 0;
1871         int parity_errors = 0;
1872         int parity_untried = 0;
1873         int data_errors = 0;
1874         int total_errors = 0;
1875         int n, c;
1876         int tgts[VDEV_RAIDZ_MAXPARITY];
1877         int code;
1878 
1879         ASSERT(zio->io_bp != NULL);  /* XXX need to add code to enforce this */
1880 
1881         ASSERT(rm->rm_missingparity <= rm->rm_firstdatacol);
1882         ASSERT(rm->rm_missingdata <= rm->rm_cols - rm->rm_firstdatacol);
1883 
1884         for (c = 0; c < rm->rm_cols; c++) {
1885                 rc = &rm->rm_col[c];
1886 
1887                 if (rc->rc_error) {
1888                         ASSERT(rc->rc_error != ECKSUM);      /* child has no bp */
1889 
1890                         if (c < rm->rm_firstdatacol)
1891                                 parity_errors++;
1892                         else
1893                                 data_errors++;
1894 
1895                         if (!rc->rc_skipped)
1896                                 unexpected_errors++;
1897 
1898                         total_errors++;
1899                 } else if (c < rm->rm_firstdatacol && !rc->rc_tried) {
1900                         parity_untried++;
1901                 }
1902         }
1903 
1904         if (zio->io_type == ZIO_TYPE_WRITE) {
1905                 /*
1906                  * XXX -- for now, treat partial writes as a success.
1907                  * (If we couldn't write enough columns to reconstruct
1908                  * the data, the I/O failed.  Otherwise, good enough.)
1909                  *
1910                  * Now that we support write reallocation, it would be better
1911                  * to treat partial failure as real failure unless there are
1912                  * no non-degraded top-level vdevs left, and not update DTLs
1913                  * if we intend to reallocate.
1914                  */
1915                 /* XXPOLICY */
1916                 if (total_errors > rm->rm_firstdatacol)
1917                         zio->io_error = vdev_raidz_worst_error(rm);
1918 
1919                 return;
1920         }
1921 
1922         ASSERT(zio->io_type == ZIO_TYPE_READ);
1923         /*
1924          * There are three potential phases for a read:
1925          *      1. produce valid data from the columns read
1926          *      2. read all disks and try again
1927          *      3. perform combinatorial reconstruction
1928          *
1929          * Each phase is progressively both more expensive and less likely to
1930          * occur. If we encounter more errors than we can repair or all phases
1931          * fail, we have no choice but to return an error.
1932          */
1933 
1934         /*
1935          * If the number of errors we saw was correctable -- less than or equal
1936          * to the number of parity disks read -- attempt to produce data that
1937          * has a valid checksum. Naturally, this case applies in the absence of
1938          * any errors.
1939          */
1940         if (total_errors <= rm->rm_firstdatacol - parity_untried) {
1941                 if (data_errors == 0) {
1942                         if (raidz_checksum_verify(zio) == 0) {
1943                                 /*
1944                                  * If we read parity information (unnecessarily
1945                                  * as it happens since no reconstruction was
1946                                  * needed) regenerate and verify the parity.
1947                                  * We also regenerate parity when resilvering
1948                                  * so we can write it out to the failed device
1949                                  * later.
1950                                  */
1951                                 if (parity_errors + parity_untried <
1952                                     rm->rm_firstdatacol ||
1953                                     (zio->io_flags & ZIO_FLAG_RESILVER)) {
1954                                         n = raidz_parity_verify(zio, rm);
1955                                         unexpected_errors += n;
1956                                         ASSERT(parity_errors + n <=
1957                                             rm->rm_firstdatacol);
1958                                 }
1959                                 goto done;
1960                         }
1961                 } else {
1962                         /*
1963                          * We either attempt to read all the parity columns or
1964                          * none of them. If we didn't try to read parity, we
1965                          * wouldn't be here in the correctable case. There must
1966                          * also have been fewer parity errors than parity
1967                          * columns or, again, we wouldn't be in this code path.
1968                          */
1969                         ASSERT(parity_untried == 0);
1970                         ASSERT(parity_errors < rm->rm_firstdatacol);
1971 
1972                         /*
1973                          * Identify the data columns that reported an error.
1974                          */
1975                         n = 0;
1976                         for (c = rm->rm_firstdatacol; c < rm->rm_cols; c++) {
1977                                 rc = &rm->rm_col[c];
1978                                 if (rc->rc_error != 0) {
1979                                         ASSERT(n < VDEV_RAIDZ_MAXPARITY);
1980                                         tgts[n++] = c;
1981                                 }
1982                         }
1983 
1984                         ASSERT(rm->rm_firstdatacol >= n);
1985 
1986                         code = vdev_raidz_reconstruct(rm, tgts, n);
1987 
1988                         if (raidz_checksum_verify(zio) == 0) {
1989                                 atomic_inc_64(&raidz_corrected[code]);
1990 
1991                                 /*
1992                                  * If we read more parity disks than were used
1993                                  * for reconstruction, confirm that the other
1994                                  * parity disks produced correct data. This
1995                                  * routine is suboptimal in that it regenerates
1996                                  * the parity that we already used in addition
1997                                  * to the parity that we're attempting to
1998                                  * verify, but this should be a relatively
1999                                  * uncommon case, and can be optimized if it
2000                                  * becomes a problem. Note that we regenerate
2001                                  * parity when resilvering so we can write it
2002                                  * out to failed devices later.
2003                                  */
2004                                 if (parity_errors < rm->rm_firstdatacol - n ||
2005                                     (zio->io_flags & ZIO_FLAG_RESILVER)) {
2006                                         n = raidz_parity_verify(zio, rm);
2007                                         unexpected_errors += n;
2008                                         ASSERT(parity_errors + n <=
2009                                             rm->rm_firstdatacol);
2010                                 }
2011 
2012                                 goto done;
2013                         }
2014                 }
2015         }
2016 
2017         /*
2018          * This isn't a typical situation -- either we got a read error or
2019          * a child silently returned bad data. Read every block so we can
2020          * try again with as much data and parity as we can track down. If
2021          * we've already been through once before, all children will be marked
2022          * as tried so we'll proceed to combinatorial reconstruction.
2023          */
2024         unexpected_errors = 1;
2025         rm->rm_missingdata = 0;
2026         rm->rm_missingparity = 0;
2027 
2028         for (c = 0; c < rm->rm_cols; c++) {
2029                 if (rm->rm_col[c].rc_tried)
2030                         continue;
2031 
2032                 zio_vdev_io_redone(zio);
2033                 do {
2034                         rc = &rm->rm_col[c];
2035                         if (rc->rc_tried)
2036                                 continue;
2037                         zio_nowait(zio_vdev_child_io(zio, NULL,
2038                             vd->vdev_child[rc->rc_devidx],
2039                             rc->rc_offset, rc->rc_data, rc->rc_size,
2040                             zio->io_type, zio->io_priority, 0,
2041                             vdev_raidz_child_done, rc));
2042                 } while (++c < rm->rm_cols);
2043 
2044                 return;
2045         }
2046 
2047         /*
2048          * At this point we've attempted to reconstruct the data given the
2049          * errors we detected, and we've attempted to read all columns. There
2050          * must, therefore, be one or more additional problems -- silent errors
2051          * resulting in invalid data rather than explicit I/O errors resulting
2052          * in absent data. We check if there is enough additional data to
2053          * possibly reconstruct the data and then perform combinatorial
2054          * reconstruction over all possible combinations. If that fails,
2055          * we're cooked.
2056          */
2057         if (total_errors > rm->rm_firstdatacol) {
2058                 zio->io_error = vdev_raidz_worst_error(rm);
2059 
2060         } else if (total_errors < rm->rm_firstdatacol &&
2061             (code = vdev_raidz_combrec(zio, total_errors, data_errors)) != 0) {
2062                 /*
2063                  * If we didn't use all the available parity for the
2064                  * combinatorial reconstruction, verify that the remaining
2065                  * parity is correct.
2066                  */
2067                 if (code != (1 << rm->rm_firstdatacol) - 1)
2068                         (void) raidz_parity_verify(zio, rm);
2069         } else {
2070                 /*
2071                  * We're here because either:
2072                  *
2073                  *      total_errors == rm_first_datacol, or
2074                  *      vdev_raidz_combrec() failed
2075                  *
2076                  * In either case, there is enough bad data to prevent
2077                  * reconstruction.
2078                  *
2079                  * Start checksum ereports for all children which haven't
2080                  * failed, and the IO wasn't speculative.
2081                  */
2082                 zio->io_error = ECKSUM;
2083 
2084                 if (!(zio->io_flags & ZIO_FLAG_SPECULATIVE)) {
2085                         for (c = 0; c < rm->rm_cols; c++) {
2086                                 rc = &rm->rm_col[c];
2087                                 if (rc->rc_error == 0) {
2088                                         zio_bad_cksum_t zbc;
2089                                         zbc.zbc_has_cksum = 0;
2090                                         zbc.zbc_injected =
2091                                             rm->rm_ecksuminjected;
2092 
2093                                         zfs_ereport_start_checksum(
2094                                             zio->io_spa,
2095                                             vd->vdev_child[rc->rc_devidx],
2096                                             zio, rc->rc_offset, rc->rc_size,
2097                                             (void *)(uintptr_t)c, &zbc);
2098                                 }
2099                         }
2100                 }
2101         }
2102 
2103 done:
2104         zio_checksum_verified(zio);
2105 
2106         if (zio->io_error == 0 && spa_writeable(zio->io_spa) &&
2107             (unexpected_errors || (zio->io_flags & ZIO_FLAG_RESILVER))) {
2108                 /*
2109                  * Use the good data we have in hand to repair damaged children.
2110                  */
2111                 for (c = 0; c < rm->rm_cols; c++) {
2112                         rc = &rm->rm_col[c];
2113                         cvd = vd->vdev_child[rc->rc_devidx];
2114 
2115                         if (rc->rc_error == 0)
2116                                 continue;
2117 
2118                         zio_nowait(zio_vdev_child_io(zio, NULL, cvd,
2119                             rc->rc_offset, rc->rc_data, rc->rc_size,
2120                             ZIO_TYPE_WRITE, zio->io_priority,
2121                             ZIO_FLAG_IO_REPAIR | (unexpected_errors ?
2122                             ZIO_FLAG_SELF_HEAL : 0), NULL, NULL));
2123                 }
2124         }
2125 }
2126 
2127 static void
2128 vdev_raidz_state_change(vdev_t *vd, int faulted, int degraded)
2129 {
2130         if (faulted > vd->vdev_nparity)
2131                 vdev_set_state(vd, B_FALSE, VDEV_STATE_CANT_OPEN,
2132                     VDEV_AUX_NO_REPLICAS);
2133         else if (degraded + faulted != 0)
2134                 vdev_set_state(vd, B_FALSE, VDEV_STATE_DEGRADED, VDEV_AUX_NONE);
2135         else
2136                 vdev_set_state(vd, B_FALSE, VDEV_STATE_HEALTHY, VDEV_AUX_NONE);
2137 }
2138 
2139 vdev_ops_t vdev_raidz_ops = {
2140         vdev_raidz_open,
2141         vdev_raidz_close,
2142         vdev_raidz_asize,
2143         vdev_raidz_io_start,
2144         vdev_raidz_io_done,
2145         vdev_raidz_state_change,
2146         NULL,
2147         NULL,
2148         VDEV_TYPE_RAIDZ,        /* name of this vdev type */
2149         B_FALSE                 /* not a leaf vdev */
2150 };