/* * CDDL HEADER START * * The contents of this file are subject to the terms of the * Common Development and Distribution License (the "License"). * You may not use this file except in compliance with the License. * * You can obtain a copy of the license at usr/src/OPENSOLARIS.LICENSE * or http://www.opensolaris.org/os/licensing. * See the License for the specific language governing permissions * and limitations under the License. * * When distributing Covered Code, include this CDDL HEADER in each * file and include the License file at usr/src/OPENSOLARIS.LICENSE. * If applicable, add the following below this CDDL HEADER, with the * fields enclosed by brackets "[]" replaced with your own identifying * information: Portions Copyright [yyyy] [name of copyright owner] * * CDDL HEADER END */ /* * Copyright 2010 Sun Microsystems, Inc. All rights reserved. * Use is subject to license terms. */ #include #include #include #include #include #include #include /* * Virtual device vector for RAID-Z. * * This vdev supports single, double, and triple parity. For single parity, * we use a simple XOR of all the data columns. For double or triple parity, * we use a special case of Reed-Solomon coding. This extends the * technique described in "The mathematics of RAID-6" by H. Peter Anvin by * drawing on the system described in "A Tutorial on Reed-Solomon Coding for * Fault-Tolerance in RAID-like Systems" by James S. Plank on which the * former is also based. The latter is designed to provide higher performance * for writes. * * Note that the Plank paper claimed to support arbitrary N+M, but was then * amended six years later identifying a critical flaw that invalidates its * claims. Nevertheless, the technique can be adapted to work for up to * triple parity. For additional parity, the amendment "Note: Correction to * the 1997 Tutorial on Reed-Solomon Coding" by James S. Plank and Ying Ding * is viable, but the additional complexity means that write performance will * suffer. * * All of the methods above operate on a Galois field, defined over the * integers mod 2^N. In our case we choose N=8 for GF(8) so that all elements * can be expressed with a single byte. Briefly, the operations on the * field are defined as follows: * * o addition (+) is represented by a bitwise XOR * o subtraction (-) is therefore identical to addition: A + B = A - B * o multiplication of A by 2 is defined by the following bitwise expression: * (A * 2)_7 = A_6 * (A * 2)_6 = A_5 * (A * 2)_5 = A_4 * (A * 2)_4 = A_3 + A_7 * (A * 2)_3 = A_2 + A_7 * (A * 2)_2 = A_1 + A_7 * (A * 2)_1 = A_0 * (A * 2)_0 = A_7 * * In C, multiplying by 2 is therefore ((a << 1) ^ ((a & 0x80) ? 0x1d : 0)). * As an aside, this multiplication is derived from the error correcting * primitive polynomial x^8 + x^4 + x^3 + x^2 + 1. * * Observe that any number in the field (except for 0) can be expressed as a * power of 2 -- a generator for the field. We store a table of the powers of * 2 and logs base 2 for quick look ups, and exploit the fact that A * B can * be rewritten as 2^(log_2(A) + log_2(B)) (where '+' is normal addition rather * than field addition). The inverse of a field element A (A^-1) is therefore * A ^ (255 - 1) = A^254. * * The up-to-three parity columns, P, Q, R over several data columns, * D_0, ... D_n-1, can be expressed by field operations: * * P = D_0 + D_1 + ... + D_n-2 + D_n-1 * Q = 2^n-1 * D_0 + 2^n-2 * D_1 + ... + 2^1 * D_n-2 + 2^0 * D_n-1 * = ((...((D_0) * 2 + D_1) * 2 + ...) * 2 + D_n-2) * 2 + D_n-1 * R = 4^n-1 * D_0 + 4^n-2 * D_1 + ... + 4^1 * D_n-2 + 4^0 * D_n-1 * = ((...((D_0) * 4 + D_1) * 4 + ...) * 4 + D_n-2) * 4 + D_n-1 * * We chose 1, 2, and 4 as our generators because 1 corresponds to the trival * XOR operation, and 2 and 4 can be computed quickly and generate linearly- * independent coefficients. (There are no additional coefficients that have * this property which is why the uncorrected Plank method breaks down.) * * See the reconstruction code below for how P, Q and R can used individually * or in concert to recover missing data columns. */ typedef struct raidz_col { uint64_t rc_devidx; /* child device index for I/O */ uint64_t rc_offset; /* device offset */ uint64_t rc_size; /* I/O size */ void *rc_data; /* I/O data */ void *rc_gdata; /* used to store the "good" version */ int rc_error; /* I/O error for this device */ uint8_t rc_tried; /* Did we attempt this I/O column? */ uint8_t rc_skipped; /* Did we skip this I/O column? */ } raidz_col_t; typedef struct raidz_map { uint64_t rm_cols; /* Regular column count */ uint64_t rm_scols; /* Count including skipped columns */ uint64_t rm_bigcols; /* Number of oversized columns */ uint64_t rm_asize; /* Actual total I/O size */ uint64_t rm_missingdata; /* Count of missing data devices */ uint64_t rm_missingparity; /* Count of missing parity devices */ uint64_t rm_firstdatacol; /* First data column/parity count */ uint64_t rm_nskip; /* Skipped sectors for padding */ uint64_t rm_skipstart; /* Column index of padding start */ void *rm_datacopy; /* rm_asize-buffer of copied data */ uintptr_t rm_reports; /* # of referencing checksum reports */ uint8_t rm_freed; /* map no longer has referencing ZIO */ uint8_t rm_ecksuminjected; /* checksum error was injected */ raidz_col_t rm_col[1]; /* Flexible array of I/O columns */ } raidz_map_t; #define VDEV_RAIDZ_P 0 #define VDEV_RAIDZ_Q 1 #define VDEV_RAIDZ_R 2 #define VDEV_RAIDZ_MUL_2(x) (((x) << 1) ^ (((x) & 0x80) ? 0x1d : 0)) #define VDEV_RAIDZ_MUL_4(x) (VDEV_RAIDZ_MUL_2(VDEV_RAIDZ_MUL_2(x))) /* * We provide a mechanism to perform the field multiplication operation on a * 64-bit value all at once rather than a byte at a time. This works by * creating a mask from the top bit in each byte and using that to * conditionally apply the XOR of 0x1d. */ #define VDEV_RAIDZ_64MUL_2(x, mask) \ { \ (mask) = (x) & 0x8080808080808080ULL; \ (mask) = ((mask) << 1) - ((mask) >> 7); \ (x) = (((x) << 1) & 0xfefefefefefefefeULL) ^ \ ((mask) & 0x1d1d1d1d1d1d1d1d); \ } #define VDEV_RAIDZ_64MUL_4(x, mask) \ { \ VDEV_RAIDZ_64MUL_2((x), mask); \ VDEV_RAIDZ_64MUL_2((x), mask); \ } /* * Force reconstruction to use the general purpose method. */ int vdev_raidz_default_to_general; /* * These two tables represent powers and logs of 2 in the Galois field defined * above. These values were computed by repeatedly multiplying by 2 as above. */ static const uint8_t vdev_raidz_pow2[256] = { 0x01, 0x02, 0x04, 0x08, 0x10, 0x20, 0x40, 0x80, 0x1d, 0x3a, 0x74, 0xe8, 0xcd, 0x87, 0x13, 0x26, 0x4c, 0x98, 0x2d, 0x5a, 0xb4, 0x75, 0xea, 0xc9, 0x8f, 0x03, 0x06, 0x0c, 0x18, 0x30, 0x60, 0xc0, 0x9d, 0x27, 0x4e, 0x9c, 0x25, 0x4a, 0x94, 0x35, 0x6a, 0xd4, 0xb5, 0x77, 0xee, 0xc1, 0x9f, 0x23, 0x46, 0x8c, 0x05, 0x0a, 0x14, 0x28, 0x50, 0xa0, 0x5d, 0xba, 0x69, 0xd2, 0xb9, 0x6f, 0xde, 0xa1, 0x5f, 0xbe, 0x61, 0xc2, 0x99, 0x2f, 0x5e, 0xbc, 0x65, 0xca, 0x89, 0x0f, 0x1e, 0x3c, 0x78, 0xf0, 0xfd, 0xe7, 0xd3, 0xbb, 0x6b, 0xd6, 0xb1, 0x7f, 0xfe, 0xe1, 0xdf, 0xa3, 0x5b, 0xb6, 0x71, 0xe2, 0xd9, 0xaf, 0x43, 0x86, 0x11, 0x22, 0x44, 0x88, 0x0d, 0x1a, 0x34, 0x68, 0xd0, 0xbd, 0x67, 0xce, 0x81, 0x1f, 0x3e, 0x7c, 0xf8, 0xed, 0xc7, 0x93, 0x3b, 0x76, 0xec, 0xc5, 0x97, 0x33, 0x66, 0xcc, 0x85, 0x17, 0x2e, 0x5c, 0xb8, 0x6d, 0xda, 0xa9, 0x4f, 0x9e, 0x21, 0x42, 0x84, 0x15, 0x2a, 0x54, 0xa8, 0x4d, 0x9a, 0x29, 0x52, 0xa4, 0x55, 0xaa, 0x49, 0x92, 0x39, 0x72, 0xe4, 0xd5, 0xb7, 0x73, 0xe6, 0xd1, 0xbf, 0x63, 0xc6, 0x91, 0x3f, 0x7e, 0xfc, 0xe5, 0xd7, 0xb3, 0x7b, 0xf6, 0xf1, 0xff, 0xe3, 0xdb, 0xab, 0x4b, 0x96, 0x31, 0x62, 0xc4, 0x95, 0x37, 0x6e, 0xdc, 0xa5, 0x57, 0xae, 0x41, 0x82, 0x19, 0x32, 0x64, 0xc8, 0x8d, 0x07, 0x0e, 0x1c, 0x38, 0x70, 0xe0, 0xdd, 0xa7, 0x53, 0xa6, 0x51, 0xa2, 0x59, 0xb2, 0x79, 0xf2, 0xf9, 0xef, 0xc3, 0x9b, 0x2b, 0x56, 0xac, 0x45, 0x8a, 0x09, 0x12, 0x24, 0x48, 0x90, 0x3d, 0x7a, 0xf4, 0xf5, 0xf7, 0xf3, 0xfb, 0xeb, 0xcb, 0x8b, 0x0b, 0x16, 0x2c, 0x58, 0xb0, 0x7d, 0xfa, 0xe9, 0xcf, 0x83, 0x1b, 0x36, 0x6c, 0xd8, 0xad, 0x47, 0x8e, 0x01 }; static const uint8_t vdev_raidz_log2[256] = { 0x00, 0x00, 0x01, 0x19, 0x02, 0x32, 0x1a, 0xc6, 0x03, 0xdf, 0x33, 0xee, 0x1b, 0x68, 0xc7, 0x4b, 0x04, 0x64, 0xe0, 0x0e, 0x34, 0x8d, 0xef, 0x81, 0x1c, 0xc1, 0x69, 0xf8, 0xc8, 0x08, 0x4c, 0x71, 0x05, 0x8a, 0x65, 0x2f, 0xe1, 0x24, 0x0f, 0x21, 0x35, 0x93, 0x8e, 0xda, 0xf0, 0x12, 0x82, 0x45, 0x1d, 0xb5, 0xc2, 0x7d, 0x6a, 0x27, 0xf9, 0xb9, 0xc9, 0x9a, 0x09, 0x78, 0x4d, 0xe4, 0x72, 0xa6, 0x06, 0xbf, 0x8b, 0x62, 0x66, 0xdd, 0x30, 0xfd, 0xe2, 0x98, 0x25, 0xb3, 0x10, 0x91, 0x22, 0x88, 0x36, 0xd0, 0x94, 0xce, 0x8f, 0x96, 0xdb, 0xbd, 0xf1, 0xd2, 0x13, 0x5c, 0x83, 0x38, 0x46, 0x40, 0x1e, 0x42, 0xb6, 0xa3, 0xc3, 0x48, 0x7e, 0x6e, 0x6b, 0x3a, 0x28, 0x54, 0xfa, 0x85, 0xba, 0x3d, 0xca, 0x5e, 0x9b, 0x9f, 0x0a, 0x15, 0x79, 0x2b, 0x4e, 0xd4, 0xe5, 0xac, 0x73, 0xf3, 0xa7, 0x57, 0x07, 0x70, 0xc0, 0xf7, 0x8c, 0x80, 0x63, 0x0d, 0x67, 0x4a, 0xde, 0xed, 0x31, 0xc5, 0xfe, 0x18, 0xe3, 0xa5, 0x99, 0x77, 0x26, 0xb8, 0xb4, 0x7c, 0x11, 0x44, 0x92, 0xd9, 0x23, 0x20, 0x89, 0x2e, 0x37, 0x3f, 0xd1, 0x5b, 0x95, 0xbc, 0xcf, 0xcd, 0x90, 0x87, 0x97, 0xb2, 0xdc, 0xfc, 0xbe, 0x61, 0xf2, 0x56, 0xd3, 0xab, 0x14, 0x2a, 0x5d, 0x9e, 0x84, 0x3c, 0x39, 0x53, 0x47, 0x6d, 0x41, 0xa2, 0x1f, 0x2d, 0x43, 0xd8, 0xb7, 0x7b, 0xa4, 0x76, 0xc4, 0x17, 0x49, 0xec, 0x7f, 0x0c, 0x6f, 0xf6, 0x6c, 0xa1, 0x3b, 0x52, 0x29, 0x9d, 0x55, 0xaa, 0xfb, 0x60, 0x86, 0xb1, 0xbb, 0xcc, 0x3e, 0x5a, 0xcb, 0x59, 0x5f, 0xb0, 0x9c, 0xa9, 0xa0, 0x51, 0x0b, 0xf5, 0x16, 0xeb, 0x7a, 0x75, 0x2c, 0xd7, 0x4f, 0xae, 0xd5, 0xe9, 0xe6, 0xe7, 0xad, 0xe8, 0x74, 0xd6, 0xf4, 0xea, 0xa8, 0x50, 0x58, 0xaf, }; static void vdev_raidz_generate_parity(raidz_map_t *rm); /* * Multiply a given number by 2 raised to the given power. */ static uint8_t vdev_raidz_exp2(uint_t a, int exp) { if (a == 0) return (0); ASSERT(exp >= 0); ASSERT(vdev_raidz_log2[a] > 0 || a == 1); exp += vdev_raidz_log2[a]; if (exp > 255) exp -= 255; return (vdev_raidz_pow2[exp]); } static void vdev_raidz_map_free(raidz_map_t *rm) { int c; size_t size; for (c = 0; c < rm->rm_firstdatacol; c++) { zio_buf_free(rm->rm_col[c].rc_data, rm->rm_col[c].rc_size); if (rm->rm_col[c].rc_gdata != NULL) zio_buf_free(rm->rm_col[c].rc_gdata, rm->rm_col[c].rc_size); } size = 0; for (c = rm->rm_firstdatacol; c < rm->rm_cols; c++) size += rm->rm_col[c].rc_size; if (rm->rm_datacopy != NULL) zio_buf_free(rm->rm_datacopy, size); kmem_free(rm, offsetof(raidz_map_t, rm_col[rm->rm_scols])); } static void vdev_raidz_map_free_vsd(zio_t *zio) { raidz_map_t *rm = zio->io_vsd; ASSERT3U(rm->rm_freed, ==, 0); rm->rm_freed = 1; if (rm->rm_reports == 0) vdev_raidz_map_free(rm); } /*ARGSUSED*/ static void vdev_raidz_cksum_free(void *arg, size_t ignored) { raidz_map_t *rm = arg; ASSERT3U(rm->rm_reports, >, 0); if (--rm->rm_reports == 0 && rm->rm_freed != 0) vdev_raidz_map_free(rm); } static void vdev_raidz_cksum_finish(zio_cksum_report_t *zcr, const void *good_data) { raidz_map_t *rm = zcr->zcr_cbdata; size_t c = zcr->zcr_cbinfo; size_t x; const char *good = NULL; const char *bad = rm->rm_col[c].rc_data; if (good_data == NULL) { zfs_ereport_finish_checksum(zcr, NULL, NULL, B_FALSE); return; } if (c < rm->rm_firstdatacol) { /* * The first time through, calculate the parity blocks for * the good data (this relies on the fact that the good * data never changes for a given logical ZIO) */ if (rm->rm_col[0].rc_gdata == NULL) { char *bad_parity[VDEV_RAIDZ_MAXPARITY]; char *buf; /* * Set up the rm_col[]s to generate the parity for * good_data, first saving the parity bufs and * replacing them with buffers to hold the result. */ for (x = 0; x < rm->rm_firstdatacol; x++) { bad_parity[x] = rm->rm_col[x].rc_data; rm->rm_col[x].rc_data = rm->rm_col[x].rc_gdata = zio_buf_alloc(rm->rm_col[x].rc_size); } /* fill in the data columns from good_data */ buf = (char *)good_data; for (; x < rm->rm_cols; x++) { rm->rm_col[x].rc_data = buf; buf += rm->rm_col[x].rc_size; } /* * Construct the parity from the good data. */ vdev_raidz_generate_parity(rm); /* restore everything back to its original state */ for (x = 0; x < rm->rm_firstdatacol; x++) rm->rm_col[x].rc_data = bad_parity[x]; buf = rm->rm_datacopy; for (x = rm->rm_firstdatacol; x < rm->rm_cols; x++) { rm->rm_col[x].rc_data = buf; buf += rm->rm_col[x].rc_size; } } ASSERT3P(rm->rm_col[c].rc_gdata, !=, NULL); good = rm->rm_col[c].rc_gdata; } else { /* adjust good_data to point at the start of our column */ good = good_data; for (x = rm->rm_firstdatacol; x < c; x++) good += rm->rm_col[x].rc_size; } /* we drop the ereport if it ends up that the data was good */ zfs_ereport_finish_checksum(zcr, good, bad, B_TRUE); } /* * Invoked indirectly by zfs_ereport_start_checksum(), called * below when our read operation fails completely. The main point * is to keep a copy of everything we read from disk, so that at * vdev_raidz_cksum_finish() time we can compare it with the good data. */ static void vdev_raidz_cksum_report(zio_t *zio, zio_cksum_report_t *zcr, void *arg) { size_t c = (size_t)(uintptr_t)arg; caddr_t buf; raidz_map_t *rm = zio->io_vsd; size_t size; /* set up the report and bump the refcount */ zcr->zcr_cbdata = rm; zcr->zcr_cbinfo = c; zcr->zcr_finish = vdev_raidz_cksum_finish; zcr->zcr_free = vdev_raidz_cksum_free; rm->rm_reports++; ASSERT3U(rm->rm_reports, >, 0); if (rm->rm_datacopy != NULL) return; /* * It's the first time we're called for this raidz_map_t, so we need * to copy the data aside; there's no guarantee that our zio's buffer * won't be re-used for something else. * * Our parity data is already in separate buffers, so there's no need * to copy them. */ size = 0; for (c = rm->rm_firstdatacol; c < rm->rm_cols; c++) size += rm->rm_col[c].rc_size; buf = rm->rm_datacopy = zio_buf_alloc(size); for (c = rm->rm_firstdatacol; c < rm->rm_cols; c++) { raidz_col_t *col = &rm->rm_col[c]; bcopy(col->rc_data, buf, col->rc_size); col->rc_data = buf; buf += col->rc_size; } ASSERT3P(buf - (caddr_t)rm->rm_datacopy, ==, size); } static const zio_vsd_ops_t vdev_raidz_vsd_ops = { vdev_raidz_map_free_vsd, vdev_raidz_cksum_report }; static raidz_map_t * vdev_raidz_map_alloc(zio_t *zio, uint64_t unit_shift, uint64_t dcols, uint64_t nparity) { raidz_map_t *rm; uint64_t b = zio->io_offset >> unit_shift; uint64_t s = zio->io_size >> unit_shift; uint64_t f = b % dcols; uint64_t o = (b / dcols) << unit_shift; uint64_t q, r, c, bc, col, acols, scols, coff, devidx, asize, tot; q = s / (dcols - nparity); r = s - q * (dcols - nparity); bc = (r == 0 ? 0 : r + nparity); tot = s + nparity * (q + (r == 0 ? 0 : 1)); if (q == 0) { acols = bc; scols = MIN(dcols, roundup(bc, nparity + 1)); } else { acols = dcols; scols = dcols; } ASSERT3U(acols, <=, scols); rm = kmem_alloc(offsetof(raidz_map_t, rm_col[scols]), KM_SLEEP); rm->rm_cols = acols; rm->rm_scols = scols; rm->rm_bigcols = bc; rm->rm_skipstart = bc; rm->rm_missingdata = 0; rm->rm_missingparity = 0; rm->rm_firstdatacol = nparity; rm->rm_datacopy = NULL; rm->rm_reports = 0; rm->rm_freed = 0; rm->rm_ecksuminjected = 0; asize = 0; for (c = 0; c < scols; c++) { col = f + c; coff = o; if (col >= dcols) { col -= dcols; coff += 1ULL << unit_shift; } rm->rm_col[c].rc_devidx = col; rm->rm_col[c].rc_offset = coff; rm->rm_col[c].rc_data = NULL; rm->rm_col[c].rc_gdata = NULL; rm->rm_col[c].rc_error = 0; rm->rm_col[c].rc_tried = 0; rm->rm_col[c].rc_skipped = 0; if (c >= acols) rm->rm_col[c].rc_size = 0; else if (c < bc) rm->rm_col[c].rc_size = (q + 1) << unit_shift; else rm->rm_col[c].rc_size = q << unit_shift; asize += rm->rm_col[c].rc_size; } ASSERT3U(asize, ==, tot << unit_shift); rm->rm_asize = roundup(asize, (nparity + 1) << unit_shift); rm->rm_nskip = roundup(tot, nparity + 1) - tot; ASSERT3U(rm->rm_asize - asize, ==, rm->rm_nskip << unit_shift); ASSERT3U(rm->rm_nskip, <=, nparity); for (c = 0; c < rm->rm_firstdatacol; c++) rm->rm_col[c].rc_data = zio_buf_alloc(rm->rm_col[c].rc_size); rm->rm_col[c].rc_data = zio->io_data; for (c = c + 1; c < acols; c++) rm->rm_col[c].rc_data = (char *)rm->rm_col[c - 1].rc_data + rm->rm_col[c - 1].rc_size; /* * If all data stored spans all columns, there's a danger that parity * will always be on the same device and, since parity isn't read * during normal operation, that that device's I/O bandwidth won't be * used effectively. We therefore switch the parity every 1MB. * * ... at least that was, ostensibly, the theory. As a practical * matter unless we juggle the parity between all devices evenly, we * won't see any benefit. Further, occasional writes that aren't a * multiple of the LCM of the number of children and the minimum * stripe width are sufficient to avoid pessimal behavior. * Unfortunately, this decision created an implicit on-disk format * requirement that we need to support for all eternity, but only * for single-parity RAID-Z. * * If we intend to skip a sector in the zeroth column for padding * we must make sure to note this swap. We will never intend to * skip the first column since at least one data and one parity * column must appear in each row. */ ASSERT(rm->rm_cols >= 2); ASSERT(rm->rm_col[0].rc_size == rm->rm_col[1].rc_size); if (rm->rm_firstdatacol == 1 && (zio->io_offset & (1ULL << 20))) { devidx = rm->rm_col[0].rc_devidx; o = rm->rm_col[0].rc_offset; rm->rm_col[0].rc_devidx = rm->rm_col[1].rc_devidx; rm->rm_col[0].rc_offset = rm->rm_col[1].rc_offset; rm->rm_col[1].rc_devidx = devidx; rm->rm_col[1].rc_offset = o; if (rm->rm_skipstart == 0) rm->rm_skipstart = 1; } zio->io_vsd = rm; zio->io_vsd_ops = &vdev_raidz_vsd_ops; return (rm); } static void vdev_raidz_generate_parity_p(raidz_map_t *rm) { uint64_t *p, *src, pcount, ccount, i; int c; pcount = rm->rm_col[VDEV_RAIDZ_P].rc_size / sizeof (src[0]); for (c = rm->rm_firstdatacol; c < rm->rm_cols; c++) { src = rm->rm_col[c].rc_data; p = rm->rm_col[VDEV_RAIDZ_P].rc_data; ccount = rm->rm_col[c].rc_size / sizeof (src[0]); if (c == rm->rm_firstdatacol) { ASSERT(ccount == pcount); for (i = 0; i < ccount; i++, src++, p++) { *p = *src; } } else { ASSERT(ccount <= pcount); for (i = 0; i < ccount; i++, src++, p++) { *p ^= *src; } } } } static void vdev_raidz_generate_parity_pq(raidz_map_t *rm) { uint64_t *p, *q, *src, pcnt, ccnt, mask, i; int c; pcnt = rm->rm_col[VDEV_RAIDZ_P].rc_size / sizeof (src[0]); ASSERT(rm->rm_col[VDEV_RAIDZ_P].rc_size == rm->rm_col[VDEV_RAIDZ_Q].rc_size); for (c = rm->rm_firstdatacol; c < rm->rm_cols; c++) { src = rm->rm_col[c].rc_data; p = rm->rm_col[VDEV_RAIDZ_P].rc_data; q = rm->rm_col[VDEV_RAIDZ_Q].rc_data; ccnt = rm->rm_col[c].rc_size / sizeof (src[0]); if (c == rm->rm_firstdatacol) { ASSERT(ccnt == pcnt || ccnt == 0); for (i = 0; i < ccnt; i++, src++, p++, q++) { *p = *src; *q = *src; } for (; i < pcnt; i++, src++, p++, q++) { *p = 0; *q = 0; } } else { ASSERT(ccnt <= pcnt); /* * Apply the algorithm described above by multiplying * the previous result and adding in the new value. */ for (i = 0; i < ccnt; i++, src++, p++, q++) { *p ^= *src; VDEV_RAIDZ_64MUL_2(*q, mask); *q ^= *src; } /* * Treat short columns as though they are full of 0s. * Note that there's therefore nothing needed for P. */ for (; i < pcnt; i++, q++) { VDEV_RAIDZ_64MUL_2(*q, mask); } } } } static void vdev_raidz_generate_parity_pqr(raidz_map_t *rm) { uint64_t *p, *q, *r, *src, pcnt, ccnt, mask, i; int c; pcnt = rm->rm_col[VDEV_RAIDZ_P].rc_size / sizeof (src[0]); ASSERT(rm->rm_col[VDEV_RAIDZ_P].rc_size == rm->rm_col[VDEV_RAIDZ_Q].rc_size); ASSERT(rm->rm_col[VDEV_RAIDZ_P].rc_size == rm->rm_col[VDEV_RAIDZ_R].rc_size); for (c = rm->rm_firstdatacol; c < rm->rm_cols; c++) { src = rm->rm_col[c].rc_data; p = rm->rm_col[VDEV_RAIDZ_P].rc_data; q = rm->rm_col[VDEV_RAIDZ_Q].rc_data; r = rm->rm_col[VDEV_RAIDZ_R].rc_data; ccnt = rm->rm_col[c].rc_size / sizeof (src[0]); if (c == rm->rm_firstdatacol) { ASSERT(ccnt == pcnt || ccnt == 0); for (i = 0; i < ccnt; i++, src++, p++, q++, r++) { *p = *src; *q = *src; *r = *src; } for (; i < pcnt; i++, src++, p++, q++, r++) { *p = 0; *q = 0; *r = 0; } } else { ASSERT(ccnt <= pcnt); /* * Apply the algorithm described above by multiplying * the previous result and adding in the new value. */ for (i = 0; i < ccnt; i++, src++, p++, q++, r++) { *p ^= *src; VDEV_RAIDZ_64MUL_2(*q, mask); *q ^= *src; VDEV_RAIDZ_64MUL_4(*r, mask); *r ^= *src; } /* * Treat short columns as though they are full of 0s. * Note that there's therefore nothing needed for P. */ for (; i < pcnt; i++, q++, r++) { VDEV_RAIDZ_64MUL_2(*q, mask); VDEV_RAIDZ_64MUL_4(*r, mask); } } } } /* * Generate RAID parity in the first virtual columns according to the number of * parity columns available. */ static void vdev_raidz_generate_parity(raidz_map_t *rm) { switch (rm->rm_firstdatacol) { case 1: vdev_raidz_generate_parity_p(rm); break; case 2: vdev_raidz_generate_parity_pq(rm); break; case 3: vdev_raidz_generate_parity_pqr(rm); break; default: cmn_err(CE_PANIC, "invalid RAID-Z configuration"); } } static int vdev_raidz_reconstruct_p(raidz_map_t *rm, int *tgts, int ntgts) { uint64_t *dst, *src, xcount, ccount, count, i; int x = tgts[0]; int c; ASSERT(ntgts == 1); ASSERT(x >= rm->rm_firstdatacol); ASSERT(x < rm->rm_cols); xcount = rm->rm_col[x].rc_size / sizeof (src[0]); ASSERT(xcount <= rm->rm_col[VDEV_RAIDZ_P].rc_size / sizeof (src[0])); ASSERT(xcount > 0); src = rm->rm_col[VDEV_RAIDZ_P].rc_data; dst = rm->rm_col[x].rc_data; for (i = 0; i < xcount; i++, dst++, src++) { *dst = *src; } for (c = rm->rm_firstdatacol; c < rm->rm_cols; c++) { src = rm->rm_col[c].rc_data; dst = rm->rm_col[x].rc_data; if (c == x) continue; ccount = rm->rm_col[c].rc_size / sizeof (src[0]); count = MIN(ccount, xcount); for (i = 0; i < count; i++, dst++, src++) { *dst ^= *src; } } return (1 << VDEV_RAIDZ_P); } static int vdev_raidz_reconstruct_q(raidz_map_t *rm, int *tgts, int ntgts) { uint64_t *dst, *src, xcount, ccount, count, mask, i; uint8_t *b; int x = tgts[0]; int c, j, exp; ASSERT(ntgts == 1); xcount = rm->rm_col[x].rc_size / sizeof (src[0]); ASSERT(xcount <= rm->rm_col[VDEV_RAIDZ_Q].rc_size / sizeof (src[0])); for (c = rm->rm_firstdatacol; c < rm->rm_cols; c++) { src = rm->rm_col[c].rc_data; dst = rm->rm_col[x].rc_data; if (c == x) ccount = 0; else ccount = rm->rm_col[c].rc_size / sizeof (src[0]); count = MIN(ccount, xcount); if (c == rm->rm_firstdatacol) { for (i = 0; i < count; i++, dst++, src++) { *dst = *src; } for (; i < xcount; i++, dst++) { *dst = 0; } } else { for (i = 0; i < count; i++, dst++, src++) { VDEV_RAIDZ_64MUL_2(*dst, mask); *dst ^= *src; } for (; i < xcount; i++, dst++) { VDEV_RAIDZ_64MUL_2(*dst, mask); } } } src = rm->rm_col[VDEV_RAIDZ_Q].rc_data; dst = rm->rm_col[x].rc_data; exp = 255 - (rm->rm_cols - 1 - x); for (i = 0; i < xcount; i++, dst++, src++) { *dst ^= *src; for (j = 0, b = (uint8_t *)dst; j < 8; j++, b++) { *b = vdev_raidz_exp2(*b, exp); } } return (1 << VDEV_RAIDZ_Q); } static int vdev_raidz_reconstruct_pq(raidz_map_t *rm, int *tgts, int ntgts) { uint8_t *p, *q, *pxy, *qxy, *xd, *yd, tmp, a, b, aexp, bexp; void *pdata, *qdata; uint64_t xsize, ysize, i; int x = tgts[0]; int y = tgts[1]; ASSERT(ntgts == 2); ASSERT(x < y); ASSERT(x >= rm->rm_firstdatacol); ASSERT(y < rm->rm_cols); ASSERT(rm->rm_col[x].rc_size >= rm->rm_col[y].rc_size); /* * Move the parity data aside -- we're going to compute parity as * though columns x and y were full of zeros -- Pxy and Qxy. We want to * reuse the parity generation mechanism without trashing the actual * parity so we make those columns appear to be full of zeros by * setting their lengths to zero. */ pdata = rm->rm_col[VDEV_RAIDZ_P].rc_data; qdata = rm->rm_col[VDEV_RAIDZ_Q].rc_data; xsize = rm->rm_col[x].rc_size; ysize = rm->rm_col[y].rc_size; rm->rm_col[VDEV_RAIDZ_P].rc_data = zio_buf_alloc(rm->rm_col[VDEV_RAIDZ_P].rc_size); rm->rm_col[VDEV_RAIDZ_Q].rc_data = zio_buf_alloc(rm->rm_col[VDEV_RAIDZ_Q].rc_size); rm->rm_col[x].rc_size = 0; rm->rm_col[y].rc_size = 0; vdev_raidz_generate_parity_pq(rm); rm->rm_col[x].rc_size = xsize; rm->rm_col[y].rc_size = ysize; p = pdata; q = qdata; pxy = rm->rm_col[VDEV_RAIDZ_P].rc_data; qxy = rm->rm_col[VDEV_RAIDZ_Q].rc_data; xd = rm->rm_col[x].rc_data; yd = rm->rm_col[y].rc_data; /* * We now have: * Pxy = P + D_x + D_y * Qxy = Q + 2^(ndevs - 1 - x) * D_x + 2^(ndevs - 1 - y) * D_y * * We can then solve for D_x: * D_x = A * (P + Pxy) + B * (Q + Qxy) * where * A = 2^(x - y) * (2^(x - y) + 1)^-1 * B = 2^(ndevs - 1 - x) * (2^(x - y) + 1)^-1 * * With D_x in hand, we can easily solve for D_y: * D_y = P + Pxy + D_x */ a = vdev_raidz_pow2[255 + x - y]; b = vdev_raidz_pow2[255 - (rm->rm_cols - 1 - x)]; tmp = 255 - vdev_raidz_log2[a ^ 1]; aexp = vdev_raidz_log2[vdev_raidz_exp2(a, tmp)]; bexp = vdev_raidz_log2[vdev_raidz_exp2(b, tmp)]; for (i = 0; i < xsize; i++, p++, q++, pxy++, qxy++, xd++, yd++) { *xd = vdev_raidz_exp2(*p ^ *pxy, aexp) ^ vdev_raidz_exp2(*q ^ *qxy, bexp); if (i < ysize) *yd = *p ^ *pxy ^ *xd; } zio_buf_free(rm->rm_col[VDEV_RAIDZ_P].rc_data, rm->rm_col[VDEV_RAIDZ_P].rc_size); zio_buf_free(rm->rm_col[VDEV_RAIDZ_Q].rc_data, rm->rm_col[VDEV_RAIDZ_Q].rc_size); /* * Restore the saved parity data. */ rm->rm_col[VDEV_RAIDZ_P].rc_data = pdata; rm->rm_col[VDEV_RAIDZ_Q].rc_data = qdata; return ((1 << VDEV_RAIDZ_P) | (1 << VDEV_RAIDZ_Q)); } /* BEGIN CSTYLED */ /* * In the general case of reconstruction, we must solve the system of linear * equations defined by the coeffecients used to generate parity as well as * the contents of the data and parity disks. This can be expressed with * vectors for the original data (D) and the actual data (d) and parity (p) * and a matrix composed of the identity matrix (I) and a dispersal matrix (V): * * __ __ __ __ * | | __ __ | p_0 | * | V | | D_0 | | p_m-1 | * | | x | : | = | d_0 | * | I | | D_n-1 | | : | * | | ~~ ~~ | d_n-1 | * ~~ ~~ ~~ ~~ * * I is simply a square identity matrix of size n, and V is a vandermonde * matrix defined by the coeffecients we chose for the various parity columns * (1, 2, 4). Note that these values were chosen both for simplicity, speedy * computation as well as linear separability. * * __ __ __ __ * | 1 .. 1 1 1 | | p_0 | * | 2^n-1 .. 4 2 1 | __ __ | : | * | 4^n-1 .. 16 4 1 | | D_0 | | p_m-1 | * | 1 .. 0 0 0 | | D_1 | | d_0 | * | 0 .. 0 0 0 | x | D_2 | = | d_1 | * | : : : : | | : | | d_2 | * | 0 .. 1 0 0 | | D_n-1 | | : | * | 0 .. 0 1 0 | ~~ ~~ | : | * | 0 .. 0 0 1 | | d_n-1 | * ~~ ~~ ~~ ~~ * * Note that I, V, d, and p are known. To compute D, we must invert the * matrix and use the known data and parity values to reconstruct the unknown * data values. We begin by removing the rows in V|I and d|p that correspond * to failed or missing columns; we then make V|I square (n x n) and d|p * sized n by removing rows corresponding to unused parity from the bottom up * to generate (V|I)' and (d|p)'. We can then generate the inverse of (V|I)' * using Gauss-Jordan elimination. In the example below we use m=3 parity * columns, n=8 data columns, with errors in d_1, d_2, and p_1: * __ __ * | 1 1 1 1 1 1 1 1 | * | 128 64 32 16 8 4 2 1 | <-----+-+-- missing disks * | 19 205 116 29 64 16 4 1 | / / * | 1 0 0 0 0 0 0 0 | / / * | 0 1 0 0 0 0 0 0 | <--' / * (V|I) = | 0 0 1 0 0 0 0 0 | <---' * | 0 0 0 1 0 0 0 0 | * | 0 0 0 0 1 0 0 0 | * | 0 0 0 0 0 1 0 0 | * | 0 0 0 0 0 0 1 0 | * | 0 0 0 0 0 0 0 1 | * ~~ ~~ * __ __ * | 1 1 1 1 1 1 1 1 | * | 128 64 32 16 8 4 2 1 | * | 19 205 116 29 64 16 4 1 | * | 1 0 0 0 0 0 0 0 | * | 0 1 0 0 0 0 0 0 | * (V|I)' = | 0 0 1 0 0 0 0 0 | * | 0 0 0 1 0 0 0 0 | * | 0 0 0 0 1 0 0 0 | * | 0 0 0 0 0 1 0 0 | * | 0 0 0 0 0 0 1 0 | * | 0 0 0 0 0 0 0 1 | * ~~ ~~ * * Here we employ Gauss-Jordan elimination to find the inverse of (V|I)'. We * have carefully chosen the seed values 1, 2, and 4 to ensure that this * matrix is not singular. * __ __ * | 1 1 1 1 1 1 1 1 1 0 0 0 0 0 0 0 | * | 19 205 116 29 64 16 4 1 0 1 0 0 0 0 0 0 | * | 1 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 | * | 0 0 0 1 0 0 0 0 0 0 0 1 0 0 0 0 | * | 0 0 0 0 1 0 0 0 0 0 0 0 1 0 0 0 | * | 0 0 0 0 0 1 0 0 0 0 0 0 0 1 0 0 | * | 0 0 0 0 0 0 1 0 0 0 0 0 0 0 1 0 | * | 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 1 | * ~~ ~~ * __ __ * | 1 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 | * | 1 1 1 1 1 1 1 1 1 0 0 0 0 0 0 0 | * | 19 205 116 29 64 16 4 1 0 1 0 0 0 0 0 0 | * | 0 0 0 1 0 0 0 0 0 0 0 1 0 0 0 0 | * | 0 0 0 0 1 0 0 0 0 0 0 0 1 0 0 0 | * | 0 0 0 0 0 1 0 0 0 0 0 0 0 1 0 0 | * | 0 0 0 0 0 0 1 0 0 0 0 0 0 0 1 0 | * | 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 1 | * ~~ ~~ * __ __ * | 1 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 | * | 0 1 1 0 0 0 0 0 1 0 1 1 1 1 1 1 | * | 0 205 116 0 0 0 0 0 0 1 19 29 64 16 4 1 | * | 0 0 0 1 0 0 0 0 0 0 0 1 0 0 0 0 | * | 0 0 0 0 1 0 0 0 0 0 0 0 1 0 0 0 | * | 0 0 0 0 0 1 0 0 0 0 0 0 0 1 0 0 | * | 0 0 0 0 0 0 1 0 0 0 0 0 0 0 1 0 | * | 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 1 | * ~~ ~~ * __ __ * | 1 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 | * | 0 1 1 0 0 0 0 0 1 0 1 1 1 1 1 1 | * | 0 0 185 0 0 0 0 0 205 1 222 208 141 221 201 204 | * | 0 0 0 1 0 0 0 0 0 0 0 1 0 0 0 0 | * | 0 0 0 0 1 0 0 0 0 0 0 0 1 0 0 0 | * | 0 0 0 0 0 1 0 0 0 0 0 0 0 1 0 0 | * | 0 0 0 0 0 0 1 0 0 0 0 0 0 0 1 0 | * | 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 1 | * ~~ ~~ * __ __ * | 1 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 | * | 0 1 1 0 0 0 0 0 1 0 1 1 1 1 1 1 | * | 0 0 1 0 0 0 0 0 166 100 4 40 158 168 216 209 | * | 0 0 0 1 0 0 0 0 0 0 0 1 0 0 0 0 | * | 0 0 0 0 1 0 0 0 0 0 0 0 1 0 0 0 | * | 0 0 0 0 0 1 0 0 0 0 0 0 0 1 0 0 | * | 0 0 0 0 0 0 1 0 0 0 0 0 0 0 1 0 | * | 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 1 | * ~~ ~~ * __ __ * | 1 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 | * | 0 1 0 0 0 0 0 0 167 100 5 41 159 169 217 208 | * | 0 0 1 0 0 0 0 0 166 100 4 40 158 168 216 209 | * | 0 0 0 1 0 0 0 0 0 0 0 1 0 0 0 0 | * | 0 0 0 0 1 0 0 0 0 0 0 0 1 0 0 0 | * | 0 0 0 0 0 1 0 0 0 0 0 0 0 1 0 0 | * | 0 0 0 0 0 0 1 0 0 0 0 0 0 0 1 0 | * | 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 1 | * ~~ ~~ * __ __ * | 0 0 1 0 0 0 0 0 | * | 167 100 5 41 159 169 217 208 | * | 166 100 4 40 158 168 216 209 | * (V|I)'^-1 = | 0 0 0 1 0 0 0 0 | * | 0 0 0 0 1 0 0 0 | * | 0 0 0 0 0 1 0 0 | * | 0 0 0 0 0 0 1 0 | * | 0 0 0 0 0 0 0 1 | * ~~ ~~ * * We can then simply compute D = (V|I)'^-1 x (d|p)' to discover the values * of the missing data. * * As is apparent from the example above, the only non-trivial rows in the * inverse matrix correspond to the data disks that we're trying to * reconstruct. Indeed, those are the only rows we need as the others would * only be useful for reconstructing data known or assumed to be valid. For * that reason, we only build the coefficients in the rows that correspond to * targeted columns. */ /* END CSTYLED */ static void vdev_raidz_matrix_init(raidz_map_t *rm, int n, int nmap, int *map, uint8_t **rows) { int i, j; int pow; ASSERT(n == rm->rm_cols - rm->rm_firstdatacol); /* * Fill in the missing rows of interest. */ for (i = 0; i < nmap; i++) { ASSERT3S(0, <=, map[i]); ASSERT3S(map[i], <=, 2); pow = map[i] * n; if (pow > 255) pow -= 255; ASSERT(pow <= 255); for (j = 0; j < n; j++) { pow -= map[i]; if (pow < 0) pow += 255; rows[i][j] = vdev_raidz_pow2[pow]; } } } static void vdev_raidz_matrix_invert(raidz_map_t *rm, int n, int nmissing, int *missing, uint8_t **rows, uint8_t **invrows, const uint8_t *used) { int i, j, ii, jj; uint8_t log; /* * Assert that the first nmissing entries from the array of used * columns correspond to parity columns and that subsequent entries * correspond to data columns. */ for (i = 0; i < nmissing; i++) { ASSERT3S(used[i], <, rm->rm_firstdatacol); } for (; i < n; i++) { ASSERT3S(used[i], >=, rm->rm_firstdatacol); } /* * First initialize the storage where we'll compute the inverse rows. */ for (i = 0; i < nmissing; i++) { for (j = 0; j < n; j++) { invrows[i][j] = (i == j) ? 1 : 0; } } /* * Subtract all trivial rows from the rows of consequence. */ for (i = 0; i < nmissing; i++) { for (j = nmissing; j < n; j++) { ASSERT3U(used[j], >=, rm->rm_firstdatacol); jj = used[j] - rm->rm_firstdatacol; ASSERT3S(jj, <, n); invrows[i][j] = rows[i][jj]; rows[i][jj] = 0; } } /* * For each of the rows of interest, we must normalize it and subtract * a multiple of it from the other rows. */ for (i = 0; i < nmissing; i++) { for (j = 0; j < missing[i]; j++) { ASSERT3U(rows[i][j], ==, 0); } ASSERT3U(rows[i][missing[i]], !=, 0); /* * Compute the inverse of the first element and multiply each * element in the row by that value. */ log = 255 - vdev_raidz_log2[rows[i][missing[i]]]; for (j = 0; j < n; j++) { rows[i][j] = vdev_raidz_exp2(rows[i][j], log); invrows[i][j] = vdev_raidz_exp2(invrows[i][j], log); } for (ii = 0; ii < nmissing; ii++) { if (i == ii) continue; ASSERT3U(rows[ii][missing[i]], !=, 0); log = vdev_raidz_log2[rows[ii][missing[i]]]; for (j = 0; j < n; j++) { rows[ii][j] ^= vdev_raidz_exp2(rows[i][j], log); invrows[ii][j] ^= vdev_raidz_exp2(invrows[i][j], log); } } } /* * Verify that the data that is left in the rows are properly part of * an identity matrix. */ for (i = 0; i < nmissing; i++) { for (j = 0; j < n; j++) { if (j == missing[i]) { ASSERT3U(rows[i][j], ==, 1); } else { ASSERT3U(rows[i][j], ==, 0); } } } } static void vdev_raidz_matrix_reconstruct(raidz_map_t *rm, int n, int nmissing, int *missing, uint8_t **invrows, const uint8_t *used) { int i, j, x, cc, c; uint8_t *src; uint64_t ccount; uint8_t *dst[VDEV_RAIDZ_MAXPARITY]; uint64_t dcount[VDEV_RAIDZ_MAXPARITY]; uint8_t log, val; int ll; uint8_t *invlog[VDEV_RAIDZ_MAXPARITY]; uint8_t *p, *pp; size_t psize; psize = sizeof (invlog[0][0]) * n * nmissing; p = kmem_alloc(psize, KM_SLEEP); for (pp = p, i = 0; i < nmissing; i++) { invlog[i] = pp; pp += n; } for (i = 0; i < nmissing; i++) { for (j = 0; j < n; j++) { ASSERT3U(invrows[i][j], !=, 0); invlog[i][j] = vdev_raidz_log2[invrows[i][j]]; } } for (i = 0; i < n; i++) { c = used[i]; ASSERT3U(c, <, rm->rm_cols); src = rm->rm_col[c].rc_data; ccount = rm->rm_col[c].rc_size; for (j = 0; j < nmissing; j++) { cc = missing[j] + rm->rm_firstdatacol; ASSERT3U(cc, >=, rm->rm_firstdatacol); ASSERT3U(cc, <, rm->rm_cols); ASSERT3U(cc, !=, c); dst[j] = rm->rm_col[cc].rc_data; dcount[j] = rm->rm_col[cc].rc_size; } ASSERT(ccount >= rm->rm_col[missing[0]].rc_size || i > 0); for (x = 0; x < ccount; x++, src++) { if (*src != 0) log = vdev_raidz_log2[*src]; for (cc = 0; cc < nmissing; cc++) { if (x >= dcount[cc]) continue; if (*src == 0) { val = 0; } else { if ((ll = log + invlog[cc][i]) >= 255) ll -= 255; val = vdev_raidz_pow2[ll]; } if (i == 0) dst[cc][x] = val; else dst[cc][x] ^= val; } } } kmem_free(p, psize); } static int vdev_raidz_reconstruct_general(raidz_map_t *rm, int *tgts, int ntgts) { int n, i, c, t, tt; int nmissing_rows; int missing_rows[VDEV_RAIDZ_MAXPARITY]; int parity_map[VDEV_RAIDZ_MAXPARITY]; uint8_t *p, *pp; size_t psize; uint8_t *rows[VDEV_RAIDZ_MAXPARITY]; uint8_t *invrows[VDEV_RAIDZ_MAXPARITY]; uint8_t *used; int code = 0; n = rm->rm_cols - rm->rm_firstdatacol; /* * Figure out which data columns are missing. */ nmissing_rows = 0; for (t = 0; t < ntgts; t++) { if (tgts[t] >= rm->rm_firstdatacol) { missing_rows[nmissing_rows++] = tgts[t] - rm->rm_firstdatacol; } } /* * Figure out which parity columns to use to help generate the missing * data columns. */ for (tt = 0, c = 0, i = 0; i < nmissing_rows; c++) { ASSERT(tt < ntgts); ASSERT(c < rm->rm_firstdatacol); /* * Skip any targeted parity columns. */ if (c == tgts[tt]) { tt++; continue; } code |= 1 << c; parity_map[i] = c; i++; } ASSERT(code != 0); ASSERT3U(code, <, 1 << VDEV_RAIDZ_MAXPARITY); psize = (sizeof (rows[0][0]) + sizeof (invrows[0][0])) * nmissing_rows * n + sizeof (used[0]) * n; p = kmem_alloc(psize, KM_SLEEP); for (pp = p, i = 0; i < nmissing_rows; i++) { rows[i] = pp; pp += n; invrows[i] = pp; pp += n; } used = pp; for (i = 0; i < nmissing_rows; i++) { used[i] = parity_map[i]; } for (tt = 0, c = rm->rm_firstdatacol; c < rm->rm_cols; c++) { if (tt < nmissing_rows && c == missing_rows[tt] + rm->rm_firstdatacol) { tt++; continue; } ASSERT3S(i, <, n); used[i] = c; i++; } /* * Initialize the interesting rows of the matrix. */ vdev_raidz_matrix_init(rm, n, nmissing_rows, parity_map, rows); /* * Invert the matrix. */ vdev_raidz_matrix_invert(rm, n, nmissing_rows, missing_rows, rows, invrows, used); /* * Reconstruct the missing data using the generated matrix. */ vdev_raidz_matrix_reconstruct(rm, n, nmissing_rows, missing_rows, invrows, used); kmem_free(p, psize); return (code); } static int vdev_raidz_reconstruct(raidz_map_t *rm, int *t, int nt) { int tgts[VDEV_RAIDZ_MAXPARITY], *dt; int ntgts; int i, c; int code; int nbadparity, nbaddata; int parity_valid[VDEV_RAIDZ_MAXPARITY]; /* * The tgts list must already be sorted. */ for (i = 1; i < nt; i++) { ASSERT(t[i] > t[i - 1]); } nbadparity = rm->rm_firstdatacol; nbaddata = rm->rm_cols - nbadparity; ntgts = 0; for (i = 0, c = 0; c < rm->rm_cols; c++) { if (c < rm->rm_firstdatacol) parity_valid[c] = B_FALSE; if (i < nt && c == t[i]) { tgts[ntgts++] = c; i++; } else if (rm->rm_col[c].rc_error != 0) { tgts[ntgts++] = c; } else if (c >= rm->rm_firstdatacol) { nbaddata--; } else { parity_valid[c] = B_TRUE; nbadparity--; } } ASSERT(ntgts >= nt); ASSERT(nbaddata >= 0); ASSERT(nbaddata + nbadparity == ntgts); dt = &tgts[nbadparity]; /* * See if we can use any of our optimized reconstruction routines. */ if (!vdev_raidz_default_to_general) { switch (nbaddata) { case 1: if (parity_valid[VDEV_RAIDZ_P]) return (vdev_raidz_reconstruct_p(rm, dt, 1)); ASSERT(rm->rm_firstdatacol > 1); if (parity_valid[VDEV_RAIDZ_Q]) return (vdev_raidz_reconstruct_q(rm, dt, 1)); ASSERT(rm->rm_firstdatacol > 2); break; case 2: ASSERT(rm->rm_firstdatacol > 1); if (parity_valid[VDEV_RAIDZ_P] && parity_valid[VDEV_RAIDZ_Q]) return (vdev_raidz_reconstruct_pq(rm, dt, 2)); ASSERT(rm->rm_firstdatacol > 2); break; } } code = vdev_raidz_reconstruct_general(rm, tgts, ntgts); ASSERT(code < (1 << VDEV_RAIDZ_MAXPARITY)); ASSERT(code > 0); return (code); } static int vdev_raidz_open(vdev_t *vd, uint64_t *asize, uint64_t *ashift) { vdev_t *cvd; uint64_t nparity = vd->vdev_nparity; int c; int lasterror = 0; int numerrors = 0; ASSERT(nparity > 0); if (nparity > VDEV_RAIDZ_MAXPARITY || vd->vdev_children < nparity + 1) { vd->vdev_stat.vs_aux = VDEV_AUX_BAD_LABEL; return (EINVAL); } vdev_open_children(vd); for (c = 0; c < vd->vdev_children; c++) { cvd = vd->vdev_child[c]; if (cvd->vdev_open_error != 0) { lasterror = cvd->vdev_open_error; numerrors++; continue; } *asize = MIN(*asize - 1, cvd->vdev_asize - 1) + 1; *ashift = MAX(*ashift, cvd->vdev_ashift); } *asize *= vd->vdev_children; if (numerrors > nparity) { vd->vdev_stat.vs_aux = VDEV_AUX_NO_REPLICAS; return (lasterror); } return (0); } static void vdev_raidz_close(vdev_t *vd) { int c; for (c = 0; c < vd->vdev_children; c++) vdev_close(vd->vdev_child[c]); } static uint64_t vdev_raidz_asize(vdev_t *vd, uint64_t psize) { uint64_t asize; uint64_t ashift = vd->vdev_top->vdev_ashift; uint64_t cols = vd->vdev_children; uint64_t nparity = vd->vdev_nparity; asize = ((psize - 1) >> ashift) + 1; asize += nparity * ((asize + cols - nparity - 1) / (cols - nparity)); asize = roundup(asize, nparity + 1) << ashift; return (asize); } static void vdev_raidz_child_done(zio_t *zio) { raidz_col_t *rc = zio->io_private; rc->rc_error = zio->io_error; rc->rc_tried = 1; rc->rc_skipped = 0; } static int vdev_raidz_io_start(zio_t *zio) { vdev_t *vd = zio->io_vd; vdev_t *tvd = vd->vdev_top; vdev_t *cvd; raidz_map_t *rm; raidz_col_t *rc; int c, i; rm = vdev_raidz_map_alloc(zio, tvd->vdev_ashift, vd->vdev_children, vd->vdev_nparity); ASSERT3U(rm->rm_asize, ==, vdev_psize_to_asize(vd, zio->io_size)); if (zio->io_type == ZIO_TYPE_WRITE) { vdev_raidz_generate_parity(rm); for (c = 0; c < rm->rm_cols; c++) { rc = &rm->rm_col[c]; cvd = vd->vdev_child[rc->rc_devidx]; zio_nowait(zio_vdev_child_io(zio, NULL, cvd, rc->rc_offset, rc->rc_data, rc->rc_size, zio->io_type, zio->io_priority, 0, vdev_raidz_child_done, rc)); } /* * Generate optional I/Os for any skipped sectors to improve * aggregation contiguity. */ for (c = rm->rm_skipstart, i = 0; i < rm->rm_nskip; c++, i++) { ASSERT(c <= rm->rm_scols); if (c == rm->rm_scols) c = 0; rc = &rm->rm_col[c]; cvd = vd->vdev_child[rc->rc_devidx]; zio_nowait(zio_vdev_child_io(zio, NULL, cvd, rc->rc_offset + rc->rc_size, NULL, 1 << tvd->vdev_ashift, zio->io_type, zio->io_priority, ZIO_FLAG_NODATA | ZIO_FLAG_OPTIONAL, NULL, NULL)); } return (ZIO_PIPELINE_CONTINUE); } ASSERT(zio->io_type == ZIO_TYPE_READ); /* * Iterate over the columns in reverse order so that we hit the parity * last -- any errors along the way will force us to read the parity. */ for (c = rm->rm_cols - 1; c >= 0; c--) { rc = &rm->rm_col[c]; cvd = vd->vdev_child[rc->rc_devidx]; if (!vdev_readable(cvd)) { if (c >= rm->rm_firstdatacol) rm->rm_missingdata++; else rm->rm_missingparity++; rc->rc_error = ENXIO; rc->rc_tried = 1; /* don't even try */ rc->rc_skipped = 1; continue; } if (vdev_dtl_contains(cvd, DTL_MISSING, zio->io_txg, 1)) { if (c >= rm->rm_firstdatacol) rm->rm_missingdata++; else rm->rm_missingparity++; rc->rc_error = ESTALE; rc->rc_skipped = 1; continue; } if (c >= rm->rm_firstdatacol || rm->rm_missingdata > 0 || (zio->io_flags & (ZIO_FLAG_SCRUB | ZIO_FLAG_RESILVER))) { zio_nowait(zio_vdev_child_io(zio, NULL, cvd, rc->rc_offset, rc->rc_data, rc->rc_size, zio->io_type, zio->io_priority, 0, vdev_raidz_child_done, rc)); } } return (ZIO_PIPELINE_CONTINUE); } /* * Report a checksum error for a child of a RAID-Z device. */ static void raidz_checksum_error(zio_t *zio, raidz_col_t *rc, void *bad_data) { vdev_t *vd = zio->io_vd->vdev_child[rc->rc_devidx]; if (!(zio->io_flags & ZIO_FLAG_SPECULATIVE)) { zio_bad_cksum_t zbc; raidz_map_t *rm = zio->io_vsd; mutex_enter(&vd->vdev_stat_lock); vd->vdev_stat.vs_checksum_errors++; mutex_exit(&vd->vdev_stat_lock); zbc.zbc_has_cksum = 0; zbc.zbc_injected = rm->rm_ecksuminjected; zfs_ereport_post_checksum(zio->io_spa, vd, zio, rc->rc_offset, rc->rc_size, rc->rc_data, bad_data, &zbc); } } /* * We keep track of whether or not there were any injected errors, so that * any ereports we generate can note it. */ static int raidz_checksum_verify(zio_t *zio) { zio_bad_cksum_t zbc; raidz_map_t *rm = zio->io_vsd; int ret = zio_checksum_error(zio, &zbc); if (ret != 0 && zbc.zbc_injected != 0) rm->rm_ecksuminjected = 1; return (ret); } /* * Generate the parity from the data columns. If we tried and were able to * read the parity without error, verify that the generated parity matches the * data we read. If it doesn't, we fire off a checksum error. Return the * number such failures. */ static int raidz_parity_verify(zio_t *zio, raidz_map_t *rm) { void *orig[VDEV_RAIDZ_MAXPARITY]; int c, ret = 0; raidz_col_t *rc; for (c = 0; c < rm->rm_firstdatacol; c++) { rc = &rm->rm_col[c]; if (!rc->rc_tried || rc->rc_error != 0) continue; orig[c] = zio_buf_alloc(rc->rc_size); bcopy(rc->rc_data, orig[c], rc->rc_size); } vdev_raidz_generate_parity(rm); for (c = 0; c < rm->rm_firstdatacol; c++) { rc = &rm->rm_col[c]; if (!rc->rc_tried || rc->rc_error != 0) continue; if (bcmp(orig[c], rc->rc_data, rc->rc_size) != 0) { raidz_checksum_error(zio, rc, orig[c]); rc->rc_error = ECKSUM; ret++; } zio_buf_free(orig[c], rc->rc_size); } return (ret); } /* * Keep statistics on all the ways that we used parity to correct data. */ static uint64_t raidz_corrected[1 << VDEV_RAIDZ_MAXPARITY]; static int vdev_raidz_worst_error(raidz_map_t *rm) { int error = 0; for (int c = 0; c < rm->rm_cols; c++) error = zio_worst_error(error, rm->rm_col[c].rc_error); return (error); } /* * Iterate over all combinations of bad data and attempt a reconstruction. * Note that the algorithm below is non-optimal because it doesn't take into * account how reconstruction is actually performed. For example, with * triple-parity RAID-Z the reconstruction procedure is the same if column 4 * is targeted as invalid as if columns 1 and 4 are targeted since in both * cases we'd only use parity information in column 0. */ static int vdev_raidz_combrec(zio_t *zio, int total_errors, int data_errors) { raidz_map_t *rm = zio->io_vsd; raidz_col_t *rc; void *orig[VDEV_RAIDZ_MAXPARITY]; int tstore[VDEV_RAIDZ_MAXPARITY + 2]; int *tgts = &tstore[1]; int current, next, i, c, n; int code, ret = 0; ASSERT(total_errors < rm->rm_firstdatacol); /* * This simplifies one edge condition. */ tgts[-1] = -1; for (n = 1; n <= rm->rm_firstdatacol - total_errors; n++) { /* * Initialize the targets array by finding the first n columns * that contain no error. * * If there were no data errors, we need to ensure that we're * always explicitly attempting to reconstruct at least one * data column. To do this, we simply push the highest target * up into the data columns. */ for (c = 0, i = 0; i < n; i++) { if (i == n - 1 && data_errors == 0 && c < rm->rm_firstdatacol) { c = rm->rm_firstdatacol; } while (rm->rm_col[c].rc_error != 0) { c++; ASSERT3S(c, <, rm->rm_cols); } tgts[i] = c++; } /* * Setting tgts[n] simplifies the other edge condition. */ tgts[n] = rm->rm_cols; /* * These buffers were allocated in previous iterations. */ for (i = 0; i < n - 1; i++) { ASSERT(orig[i] != NULL); } orig[n - 1] = zio_buf_alloc(rm->rm_col[0].rc_size); current = 0; next = tgts[current]; while (current != n) { tgts[current] = next; current = 0; /* * Save off the original data that we're going to * attempt to reconstruct. */ for (i = 0; i < n; i++) { ASSERT(orig[i] != NULL); c = tgts[i]; ASSERT3S(c, >=, 0); ASSERT3S(c, <, rm->rm_cols); rc = &rm->rm_col[c]; bcopy(rc->rc_data, orig[i], rc->rc_size); } /* * Attempt a reconstruction and exit the outer loop on * success. */ code = vdev_raidz_reconstruct(rm, tgts, n); if (raidz_checksum_verify(zio) == 0) { atomic_inc_64(&raidz_corrected[code]); for (i = 0; i < n; i++) { c = tgts[i]; rc = &rm->rm_col[c]; ASSERT(rc->rc_error == 0); if (rc->rc_tried) raidz_checksum_error(zio, rc, orig[i]); rc->rc_error = ECKSUM; } ret = code; goto done; } /* * Restore the original data. */ for (i = 0; i < n; i++) { c = tgts[i]; rc = &rm->rm_col[c]; bcopy(orig[i], rc->rc_data, rc->rc_size); } do { /* * Find the next valid column after the current * position.. */ for (next = tgts[current] + 1; next < rm->rm_cols && rm->rm_col[next].rc_error != 0; next++) continue; ASSERT(next <= tgts[current + 1]); /* * If that spot is available, we're done here. */ if (next != tgts[current + 1]) break; /* * Otherwise, find the next valid column after * the previous position. */ for (c = tgts[current - 1] + 1; rm->rm_col[c].rc_error != 0; c++) continue; tgts[current] = c; current++; } while (current != n); } } n--; done: for (i = 0; i < n; i++) { zio_buf_free(orig[i], rm->rm_col[0].rc_size); } return (ret); } static void vdev_raidz_io_done(zio_t *zio) { vdev_t *vd = zio->io_vd; vdev_t *cvd; raidz_map_t *rm = zio->io_vsd; raidz_col_t *rc; int unexpected_errors = 0; int parity_errors = 0; int parity_untried = 0; int data_errors = 0; int total_errors = 0; int n, c; int tgts[VDEV_RAIDZ_MAXPARITY]; int code; ASSERT(zio->io_bp != NULL); /* XXX need to add code to enforce this */ ASSERT(rm->rm_missingparity <= rm->rm_firstdatacol); ASSERT(rm->rm_missingdata <= rm->rm_cols - rm->rm_firstdatacol); for (c = 0; c < rm->rm_cols; c++) { rc = &rm->rm_col[c]; if (rc->rc_error) { ASSERT(rc->rc_error != ECKSUM); /* child has no bp */ if (c < rm->rm_firstdatacol) parity_errors++; else data_errors++; if (!rc->rc_skipped) unexpected_errors++; total_errors++; } else if (c < rm->rm_firstdatacol && !rc->rc_tried) { parity_untried++; } } if (zio->io_type == ZIO_TYPE_WRITE) { /* * XXX -- for now, treat partial writes as a success. * (If we couldn't write enough columns to reconstruct * the data, the I/O failed. Otherwise, good enough.) * * Now that we support write reallocation, it would be better * to treat partial failure as real failure unless there are * no non-degraded top-level vdevs left, and not update DTLs * if we intend to reallocate. */ /* XXPOLICY */ if (total_errors > rm->rm_firstdatacol) zio->io_error = vdev_raidz_worst_error(rm); return; } ASSERT(zio->io_type == ZIO_TYPE_READ); /* * There are three potential phases for a read: * 1. produce valid data from the columns read * 2. read all disks and try again * 3. perform combinatorial reconstruction * * Each phase is progressively both more expensive and less likely to * occur. If we encounter more errors than we can repair or all phases * fail, we have no choice but to return an error. */ /* * If the number of errors we saw was correctable -- less than or equal * to the number of parity disks read -- attempt to produce data that * has a valid checksum. Naturally, this case applies in the absence of * any errors. */ if (total_errors <= rm->rm_firstdatacol - parity_untried) { if (data_errors == 0) { if (raidz_checksum_verify(zio) == 0) { /* * If we read parity information (unnecessarily * as it happens since no reconstruction was * needed) regenerate and verify the parity. * We also regenerate parity when resilvering * so we can write it out to the failed device * later. */ if (parity_errors + parity_untried < rm->rm_firstdatacol || (zio->io_flags & ZIO_FLAG_RESILVER)) { n = raidz_parity_verify(zio, rm); unexpected_errors += n; ASSERT(parity_errors + n <= rm->rm_firstdatacol); } goto done; } } else { /* * We either attempt to read all the parity columns or * none of them. If we didn't try to read parity, we * wouldn't be here in the correctable case. There must * also have been fewer parity errors than parity * columns or, again, we wouldn't be in this code path. */ ASSERT(parity_untried == 0); ASSERT(parity_errors < rm->rm_firstdatacol); /* * Identify the data columns that reported an error. */ n = 0; for (c = rm->rm_firstdatacol; c < rm->rm_cols; c++) { rc = &rm->rm_col[c]; if (rc->rc_error != 0) { ASSERT(n < VDEV_RAIDZ_MAXPARITY); tgts[n++] = c; } } ASSERT(rm->rm_firstdatacol >= n); code = vdev_raidz_reconstruct(rm, tgts, n); if (raidz_checksum_verify(zio) == 0) { atomic_inc_64(&raidz_corrected[code]); /* * If we read more parity disks than were used * for reconstruction, confirm that the other * parity disks produced correct data. This * routine is suboptimal in that it regenerates * the parity that we already used in addition * to the parity that we're attempting to * verify, but this should be a relatively * uncommon case, and can be optimized if it * becomes a problem. Note that we regenerate * parity when resilvering so we can write it * out to failed devices later. */ if (parity_errors < rm->rm_firstdatacol - n || (zio->io_flags & ZIO_FLAG_RESILVER)) { n = raidz_parity_verify(zio, rm); unexpected_errors += n; ASSERT(parity_errors + n <= rm->rm_firstdatacol); } goto done; } } } /* * This isn't a typical situation -- either we got a read error or * a child silently returned bad data. Read every block so we can * try again with as much data and parity as we can track down. If * we've already been through once before, all children will be marked * as tried so we'll proceed to combinatorial reconstruction. */ unexpected_errors = 1; rm->rm_missingdata = 0; rm->rm_missingparity = 0; for (c = 0; c < rm->rm_cols; c++) { if (rm->rm_col[c].rc_tried) continue; zio_vdev_io_redone(zio); do { rc = &rm->rm_col[c]; if (rc->rc_tried) continue; zio_nowait(zio_vdev_child_io(zio, NULL, vd->vdev_child[rc->rc_devidx], rc->rc_offset, rc->rc_data, rc->rc_size, zio->io_type, zio->io_priority, 0, vdev_raidz_child_done, rc)); } while (++c < rm->rm_cols); return; } /* * At this point we've attempted to reconstruct the data given the * errors we detected, and we've attempted to read all columns. There * must, therefore, be one or more additional problems -- silent errors * resulting in invalid data rather than explicit I/O errors resulting * in absent data. We check if there is enough additional data to * possibly reconstruct the data and then perform combinatorial * reconstruction over all possible combinations. If that fails, * we're cooked. */ if (total_errors > rm->rm_firstdatacol) { zio->io_error = vdev_raidz_worst_error(rm); } else if (total_errors < rm->rm_firstdatacol && (code = vdev_raidz_combrec(zio, total_errors, data_errors)) != 0) { /* * If we didn't use all the available parity for the * combinatorial reconstruction, verify that the remaining * parity is correct. */ if (code != (1 << rm->rm_firstdatacol) - 1) (void) raidz_parity_verify(zio, rm); } else { /* * We're here because either: * * total_errors == rm_first_datacol, or * vdev_raidz_combrec() failed * * In either case, there is enough bad data to prevent * reconstruction. * * Start checksum ereports for all children which haven't * failed, and the IO wasn't speculative. */ zio->io_error = ECKSUM; if (!(zio->io_flags & ZIO_FLAG_SPECULATIVE)) { for (c = 0; c < rm->rm_cols; c++) { rc = &rm->rm_col[c]; if (rc->rc_error == 0) { zio_bad_cksum_t zbc; zbc.zbc_has_cksum = 0; zbc.zbc_injected = rm->rm_ecksuminjected; zfs_ereport_start_checksum( zio->io_spa, vd->vdev_child[rc->rc_devidx], zio, rc->rc_offset, rc->rc_size, (void *)(uintptr_t)c, &zbc); } } } } done: zio_checksum_verified(zio); if (zio->io_error == 0 && spa_writeable(zio->io_spa) && (unexpected_errors || (zio->io_flags & ZIO_FLAG_RESILVER))) { /* * Use the good data we have in hand to repair damaged children. */ for (c = 0; c < rm->rm_cols; c++) { rc = &rm->rm_col[c]; cvd = vd->vdev_child[rc->rc_devidx]; if (rc->rc_error == 0) continue; zio_nowait(zio_vdev_child_io(zio, NULL, cvd, rc->rc_offset, rc->rc_data, rc->rc_size, ZIO_TYPE_WRITE, zio->io_priority, ZIO_FLAG_IO_REPAIR | (unexpected_errors ? ZIO_FLAG_SELF_HEAL : 0), NULL, NULL)); } } } static void vdev_raidz_state_change(vdev_t *vd, int faulted, int degraded) { if (faulted > vd->vdev_nparity) vdev_set_state(vd, B_FALSE, VDEV_STATE_CANT_OPEN, VDEV_AUX_NO_REPLICAS); else if (degraded + faulted != 0) vdev_set_state(vd, B_FALSE, VDEV_STATE_DEGRADED, VDEV_AUX_NONE); else vdev_set_state(vd, B_FALSE, VDEV_STATE_HEALTHY, VDEV_AUX_NONE); } vdev_ops_t vdev_raidz_ops = { vdev_raidz_open, vdev_raidz_close, vdev_raidz_asize, vdev_raidz_io_start, vdev_raidz_io_done, vdev_raidz_state_change, NULL, NULL, VDEV_TYPE_RAIDZ, /* name of this vdev type */ B_FALSE /* not a leaf vdev */ };