MFC r226549,r226550,r226551,r226552,r226553,r226554,r226568,r226569,r226611,

[FreeBSD/releng/9.0.git] / sys / cddl / boot / zfs / zfssubr.c

/*
 * 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 2007 Sun Microsystems, Inc.  All rights reserved.
 * Use is subject to license terms.
 */

#include <sys/cdefs.h>
__FBSDID("$FreeBSD$");

static uint64_t zfs_crc64_table[256];

#define ECKSUM  666

#define ASSERT(...)     do { } while (0)
#define ASSERT3U(...)   do { } while (0)
#define ASSERT3S(...)   do { } while (0)

#define panic(...)      do {                                            \
        printf(__VA_ARGS__);                                            \
        for (;;) ;                                                      \
} while (0)

#define kmem_alloc(size, flag)  zfs_alloc((size))
#define kmem_free(ptr, size)    zfs_free((ptr), (size))

static void
zfs_init_crc(void)
{
        int i, j;
        uint64_t *ct;

        /*
         * Calculate the crc64 table (used for the zap hash
         * function).
         */
        if (zfs_crc64_table[128] != ZFS_CRC64_POLY) {
                memset(zfs_crc64_table, 0, sizeof(zfs_crc64_table));
                for (i = 0; i < 256; i++)
                        for (ct = zfs_crc64_table + i, *ct = i, j = 8; j > 0; j--)
                                *ct = (*ct >> 1) ^ (-(*ct & 1) & ZFS_CRC64_POLY);
        }
}

static void
zio_checksum_off(const void *buf, uint64_t size, zio_cksum_t *zcp)
{
        ZIO_SET_CHECKSUM(zcp, 0, 0, 0, 0);
}

/*
 * Signature for checksum functions.
 */
typedef void zio_checksum_t(const void *data, uint64_t size, zio_cksum_t *zcp);

/*
 * Information about each checksum function.
 */
typedef struct zio_checksum_info {
        zio_checksum_t  *ci_func[2]; /* checksum function for each byteorder */
        int             ci_correctable; /* number of correctable bits   */
        int             ci_eck;         /* uses zio embedded checksum? */
        int             ci_dedup;       /* strong enough for dedup? */
        const char      *ci_name;       /* descriptive name */
} zio_checksum_info_t;

#include "fletcher.c"
#include "sha256.c"

static zio_checksum_info_t zio_checksum_table[ZIO_CHECKSUM_FUNCTIONS] = {
        {{NULL,                 NULL},                  0, 0, 0, "inherit"},
        {{NULL,                 NULL},                  0, 0, 0, "on"},
        {{zio_checksum_off,     zio_checksum_off},      0, 0, 0, "off"},
        {{zio_checksum_SHA256,  zio_checksum_SHA256},   1, 1, 0, "label"},
        {{zio_checksum_SHA256,  zio_checksum_SHA256},   1, 1, 0, "gang_header"},
        {{fletcher_2_native,    fletcher_2_byteswap},   0, 1, 0, "zilog"},
        {{fletcher_2_native,    fletcher_2_byteswap},   0, 0, 0, "fletcher2"},
        {{fletcher_4_native,    fletcher_4_byteswap},   1, 0, 0, "fletcher4"},
        {{zio_checksum_SHA256,  zio_checksum_SHA256},   1, 0, 1, "SHA256"},
        {{fletcher_4_native,    fletcher_4_byteswap},   0, 1, 0, "zillog2"},
};


/*
 * Common signature for all zio compress/decompress functions.
 */
typedef size_t zio_compress_func_t(void *src, void *dst,
    size_t s_len, size_t d_len, int);
typedef int zio_decompress_func_t(void *src, void *dst,
    size_t s_len, size_t d_len, int);

/*
 * Information about each compression function.
 */
typedef struct zio_compress_info {
        zio_compress_func_t     *ci_compress;   /* compression function */
        zio_decompress_func_t   *ci_decompress; /* decompression function */
        int                     ci_level;       /* level parameter */
        const char              *ci_name;       /* algorithm name */
} zio_compress_info_t;

#include "lzjb.c"
#include "zle.c"

/*
 * Compression vectors.
 */
static zio_compress_info_t zio_compress_table[ZIO_COMPRESS_FUNCTIONS] = {
        {NULL,                  NULL,                   0,      "inherit"},
        {NULL,                  NULL,                   0,      "on"},
        {NULL,                  NULL,                   0,      "uncompressed"},
        {NULL,                  lzjb_decompress,        0,      "lzjb"},
        {NULL,                  NULL,                   0,      "empty"},
        {NULL,                  NULL,                   1,      "gzip-1"},
        {NULL,                  NULL,                   2,      "gzip-2"},
        {NULL,                  NULL,                   3,      "gzip-3"},
        {NULL,                  NULL,                   4,      "gzip-4"},
        {NULL,                  NULL,                   5,      "gzip-5"},
        {NULL,                  NULL,                   6,      "gzip-6"},
        {NULL,                  NULL,                   7,      "gzip-7"},
        {NULL,                  NULL,                   8,      "gzip-8"},
        {NULL,                  NULL,                   9,      "gzip-9"},
        {NULL,                  zle_decompress,         64,     "zle"},
};

static void
byteswap_uint64_array(void *vbuf, size_t size)
{
        uint64_t *buf = vbuf;
        size_t count = size >> 3;
        int i;

        ASSERT((size & 7) == 0);

        for (i = 0; i < count; i++)
                buf[i] = BSWAP_64(buf[i]);
}

/*
 * Set the external verifier for a gang block based on <vdev, offset, txg>,
 * a tuple which is guaranteed to be unique for the life of the pool.
 */
static void
zio_checksum_gang_verifier(zio_cksum_t *zcp, const blkptr_t *bp)
{
        const dva_t *dva = BP_IDENTITY(bp);
        uint64_t txg = BP_PHYSICAL_BIRTH(bp);

        ASSERT(BP_IS_GANG(bp));

        ZIO_SET_CHECKSUM(zcp, DVA_GET_VDEV(dva), DVA_GET_OFFSET(dva), txg, 0);
}

/*
 * Set the external verifier for a label block based on its offset.
 * The vdev is implicit, and the txg is unknowable at pool open time --
 * hence the logic in vdev_uberblock_load() to find the most recent copy.
 */
static void
zio_checksum_label_verifier(zio_cksum_t *zcp, uint64_t offset)
{
        ZIO_SET_CHECKSUM(zcp, offset, 0, 0, 0);
}

static int
zio_checksum_verify(const blkptr_t *bp, void *data)
{
        uint64_t size;
        unsigned int checksum;
        zio_checksum_info_t *ci;
        zio_cksum_t actual_cksum, expected_cksum, verifier;
        int byteswap;

        checksum = BP_GET_CHECKSUM(bp);
        size = BP_GET_PSIZE(bp);

        if (checksum >= ZIO_CHECKSUM_FUNCTIONS)
                return (EINVAL);
        ci = &zio_checksum_table[checksum];
        if (ci->ci_func[0] == NULL || ci->ci_func[1] == NULL)
                return (EINVAL);

        if (ci->ci_eck) {
                zio_eck_t *eck;

                ASSERT(checksum == ZIO_CHECKSUM_GANG_HEADER ||
                    checksum == ZIO_CHECKSUM_LABEL);

                eck = (zio_eck_t *)((char *)data + size) - 1;

                if (checksum == ZIO_CHECKSUM_GANG_HEADER)
                        zio_checksum_gang_verifier(&verifier, bp);
                else if (checksum == ZIO_CHECKSUM_LABEL)
                        zio_checksum_label_verifier(&verifier,
                            DVA_GET_OFFSET(BP_IDENTITY(bp)));
                else
                        verifier = bp->blk_cksum;

                byteswap = (eck->zec_magic == BSWAP_64(ZEC_MAGIC));

                if (byteswap)
                        byteswap_uint64_array(&verifier, sizeof (zio_cksum_t));

                expected_cksum = eck->zec_cksum;
                eck->zec_cksum = verifier;
                ci->ci_func[byteswap](data, size, &actual_cksum);
                eck->zec_cksum = expected_cksum;

                if (byteswap)
                        byteswap_uint64_array(&expected_cksum,
                            sizeof (zio_cksum_t));
        } else {
                expected_cksum = bp->blk_cksum;
                ci->ci_func[0](data, size, &actual_cksum);
        }

        if (!ZIO_CHECKSUM_EQUAL(actual_cksum, expected_cksum)) {
                /*printf("ZFS: read checksum failed\n");*/
                return (EIO);
        }

        return (0);
}

static int
zio_decompress_data(int cpfunc, void *src, uint64_t srcsize,
        void *dest, uint64_t destsize)
{
        zio_compress_info_t *ci;

        if (cpfunc >= ZIO_COMPRESS_FUNCTIONS) {
                printf("ZFS: unsupported compression algorithm %u\n", cpfunc);
                return (EIO);
        }

        ci = &zio_compress_table[cpfunc];
        if (!ci->ci_decompress) {
                printf("ZFS: unsupported compression algorithm %s\n",
                    ci->ci_name);
                return (EIO);
        }

        return (ci->ci_decompress(src, dest, srcsize, destsize, ci->ci_level));
}

static uint64_t
zap_hash(uint64_t salt, const char *name)
{
        const uint8_t *cp;
        uint8_t c;
        uint64_t crc = salt;

        ASSERT(crc != 0);
        ASSERT(zfs_crc64_table[128] == ZFS_CRC64_POLY);
        for (cp = (const uint8_t *)name; (c = *cp) != '\0'; cp++)
                crc = (crc >> 8) ^ zfs_crc64_table[(crc ^ c) & 0xFF];

        /*
         * Only use 28 bits, since we need 4 bits in the cookie for the
         * collision differentiator.  We MUST use the high bits, since
         * those are the onces that we first pay attention to when
         * chosing the bucket.
         */
        crc &= ~((1ULL << (64 - ZAP_HASHBITS)) - 1);

        return (crc);
}

static void *zfs_alloc(size_t size);
static void zfs_free(void *ptr, size_t size);

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 */
        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 */
        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) & 0x1d1d1d1d1d1d1d1dULL); \
}

#define VDEV_RAIDZ_64MUL_4(x, mask) \
{ \
        VDEV_RAIDZ_64MUL_2((x), mask); \
        VDEV_RAIDZ_64MUL_2((x), mask); \
}

/*
 * 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,
};

/*
 * Multiply a given number by 2 raised to the given power.
 */
static uint8_t
vdev_raidz_exp2(uint8_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_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:
                panic("invalid RAID-Z configuration");
        }
}

/* 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;

        log = 0;        /* gcc */
        psize = sizeof (invlog[0][0]) * n * nmissing;
        p = zfs_alloc(psize);

        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;
                        }
                }
        }

        zfs_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];
        int ntgts;
        int i, c;
        int code;
        int nbadparity, nbaddata;

        /*
         * 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 (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 {
                        nbadparity--;
                }
        }

        ASSERT(ntgts >= nt);
        ASSERT(nbaddata >= 0);
        ASSERT(nbaddata + nbadparity == ntgts);

        code = vdev_raidz_reconstruct_general(rm, tgts, ntgts);
        ASSERT(code < (1 << VDEV_RAIDZ_MAXPARITY));
        ASSERT(code > 0);
        return (code);
}

static raidz_map_t *
vdev_raidz_map_alloc(void *data, off_t offset, size_t size, uint64_t unit_shift,
    uint64_t dcols, uint64_t nparity)
{
        raidz_map_t *rm;
        uint64_t b = offset >> unit_shift;
        uint64_t s = 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 = zfs_alloc(offsetof(raidz_map_t, rm_col[scols]));

        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_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_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 = zfs_alloc(rm->rm_col[c].rc_size);

        rm->rm_col[c].rc_data = 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 && (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;
        }

        return (rm);
}

static void
vdev_raidz_map_free(raidz_map_t *rm)
{
        int c;

        for (c = rm->rm_firstdatacol - 1; c >= 0; c--)
                zfs_free(rm->rm_col[c].rc_data, rm->rm_col[c].rc_size);

        zfs_free(rm, offsetof(raidz_map_t, rm_col[rm->rm_scols]));
}

static vdev_t *
vdev_child(vdev_t *pvd, uint64_t devidx)
{
        vdev_t *cvd;

        STAILQ_FOREACH(cvd, &pvd->v_children, v_childlink) {
                if (cvd->v_id == devidx)
                        break;
        }

        return (cvd);
}

/*
 * 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(const blkptr_t *bp, void *data, uint64_t size)
{

        return (zio_checksum_verify(bp, data));
}

/*
 * 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(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] = zfs_alloc(rc->rc_size);
                bcopy(rc->rc_data, orig[c], rc->rc_size);
        }

        vdev_raidz_generate_parity(rm);

        for (c = rm->rm_firstdatacol - 1; c >= 0; 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) {
                        rc->rc_error = ECKSUM;
                        ret++;
                }
                zfs_free(orig[c], rc->rc_size);
        }

        return (ret);
}

/*
 * 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(raidz_map_t *rm, const blkptr_t *bp, void *data,
    off_t offset, uint64_t bytes, int total_errors, int data_errors)
{
        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] = zfs_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(bp, data, bytes) == 0) {
                                for (i = 0; i < n; i++) {
                                        c = tgts[i];
                                        rc = &rm->rm_col[c];
                                        ASSERT(rc->rc_error == 0);
                                        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 = n - 1; i >= 0; i--) {
                zfs_free(orig[i], rm->rm_col[0].rc_size);
        }

        return (ret);
}

static int
vdev_raidz_read(vdev_t *vd, const blkptr_t *bp, void *data,
    off_t offset, size_t bytes)
{
        vdev_t *tvd = vd->v_top;
        vdev_t *cvd;
        raidz_map_t *rm;
        raidz_col_t *rc;
        int c, error;
        int unexpected_errors;
        int parity_errors;
        int parity_untried;
        int data_errors;
        int total_errors;
        int n;
        int tgts[VDEV_RAIDZ_MAXPARITY];
        int code;

        rc = NULL;      /* gcc */
        error = 0;

        rm = vdev_raidz_map_alloc(data, offset, bytes, tvd->v_ashift,
            vd->v_nchildren, vd->v_nparity);

        /*
         * 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 = vdev_child(vd, rc->rc_devidx);
                if (cvd == NULL || cvd->v_state != VDEV_STATE_HEALTHY) {
                        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 0           /* XXX: Too hard for the boot code. */
                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;
                }
#endif
                if (c >= rm->rm_firstdatacol || rm->rm_missingdata > 0) {
                        rc->rc_error = cvd->v_read(cvd, NULL, rc->rc_data,
                            rc->rc_offset, rc->rc_size);
                        rc->rc_tried = 1;
                        rc->rc_skipped = 0;
                }
        }

reconstruct:
        unexpected_errors = 0;
        parity_errors = 0;
        parity_untried = 0;
        data_errors = 0;
        total_errors = 0;

        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++;
                }
        }

        /*
         * 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(bp, data, bytes) == 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) {
                                        n = raidz_parity_verify(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(bp, data, bytes) == 0) {
                                /*
                                 * 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) {
                                        n = raidz_parity_verify(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;

        n = 0;
        for (c = 0; c < rm->rm_cols; c++) {
                rc = &rm->rm_col[c];

                if (rc->rc_tried)
                        continue;

                cvd = vdev_child(vd, rc->rc_devidx);
                ASSERT(cvd != NULL);
                rc->rc_error = cvd->v_read(cvd, NULL,
                    rc->rc_data, rc->rc_offset, rc->rc_size);
                if (rc->rc_error == 0)
                        n++;
                rc->rc_tried = 1;
                rc->rc_skipped = 0;
        }
        /*
         * If we managed to read anything more, retry the
         * reconstruction.
         */
        if (n > 0)
                goto reconstruct;

        /*
         * 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) {
                error = EIO;
        } else if (total_errors < rm->rm_firstdatacol &&
            (code = vdev_raidz_combrec(rm, bp, data, offset, bytes,
             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(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.
                 */
                error = ECKSUM;
        }

done:
        vdev_raidz_map_free(rm);

        return (error);
}