/*

 * 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.

 */

#pragma ident	"%Z%%M%	%I%	%E% SMI"

#include <sys/zfs_context.h>

#include <sys/spa.h>

#include <sys/vdev_impl.h>

#include <sys/zio.h>

#include <sys/zio_checksum.h>

#include <sys/fs/zfs.h>

#include <sys/fm/fs/zfs.h>

/*

 * Virtual device vector for RAID-Z.

 *

 * This vdev supports both single and double parity. For single parity, we

 * use a simple XOR of all the data columns. For double parity, we use both

 * the simple XOR as well as a technique described in "The mathematics of

 * RAID-6" by H. Peter Anvin. This technique defines a Galois field, GF(2^8),

 * over the integers expressable in 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)).

 *

 * 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 A^254.

 *

 * The two parity columns, P and Q, 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

 *

 * See the reconstruction code below for how P and Q 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 */

	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;		/* Column count */

	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 */

	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_MAXPARITY	2

#define	VDEV_RAIDZ_MUL_2(a)	(((a) << 1) ^ (((a) & 0x80) ? 0x1d : 0))

/*

 * 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(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 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, coff, devidx;

	q = s / (dcols - nparity);

	r = s - q * (dcols - nparity);

	bc = (r == 0 ? 0 : r + nparity);

	acols = (q == 0 ? bc : dcols);

	rm = kmem_alloc(offsetof(raidz_map_t, rm_col[acols]), KM_SLEEP);

	rm->rm_cols = acols;

	rm->rm_bigcols = bc;

	rm->rm_asize = 0;

	rm->rm_missingdata = 0;

	rm->rm_missingparity = 0;

	rm->rm_firstdatacol = nparity;

	for (c = 0; c < acols; 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_size = (q + (c < bc)) << unit_shift;

		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;

		rm->rm_asize += rm->rm_col[c].rc_size;

	}

	rm->rm_asize = roundup(rm->rm_asize, (nparity + 1) << unit_shift);

	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.

	 */

	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;

	}

	zio->io_vsd = rm;

	return (rm);

}

static void

vdev_raidz_map_free(zio_t *zio)

{

	raidz_map_t *rm = zio->io_vsd;

	int c;

	for (c = 0; c < rm->rm_firstdatacol; c++)

		zio_buf_free(rm->rm_col[c].rc_data, rm->rm_col[c].rc_size);

	kmem_free(rm, offsetof(raidz_map_t, rm_col[rm->rm_cols]));

	zio->io_vsd = NULL;

}

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++, p++, src++) {

				*p = *src;

			}

		} else {

			ASSERT(ccount <= pcount);

			for (i = 0; i < ccount; i++, p++, src++) {

				*p ^= *src;

			}

		}

	}

}

static void

vdev_raidz_generate_parity_pq(raidz_map_t *rm)

{

	uint64_t *q, *p, *src, pcount, ccount, mask, i;

	int c;

	pcount = 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;

		ccount = rm->rm_col[c].rc_size / sizeof (src[0]);

		if (c == rm->rm_firstdatacol) {

			ASSERT(ccount == pcount || ccount == 0);

			for (i = 0; i < ccount; i++, p++, q++, src++) {

				*q = *src;

				*p = *src;

			}

			for (; i < pcount; i++, p++, q++, src++) {

				*q = 0;

				*p = 0;

			}

		} else {

			ASSERT(ccount <= pcount);

			/*

			 * Rather than multiplying each byte individually (as

			 * described above), we are able to handle 8 at once

			 * by generating a mask based on the high bit in each

			 * byte and using that to conditionally XOR in 0x1d.

			 */

			for (i = 0; i < ccount; i++, p++, q++, src++) {

				mask = *q & 0x8080808080808080ULL;

				mask = (mask << 1) - (mask >> 7);

				*q = ((*q << 1) & 0xfefefefefefefefeULL) ^

				    (mask & 0x1d1d1d1d1d1d1d1dULL);

				*q ^= *src;

				*p ^= *src;

			}

			/*

			 * Treat short columns as though they are full of 0s.

			 */

			for (; i < pcount; i++, q++) {

				mask = *q & 0x8080808080808080ULL;

				mask = (mask << 1) - (mask >> 7);

				*q = ((*q << 1) & 0xfefefefefefefefeULL) ^

				    (mask & 0x1d1d1d1d1d1d1d1dULL);

			}

		}

	}

}

static void

vdev_raidz_reconstruct_p(raidz_map_t *rm, int x)

{

	uint64_t *dst, *src, xcount, ccount, count, i;

	int c;

	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;

		}

	}

}

static void

vdev_raidz_reconstruct_q(raidz_map_t *rm, int x)

{

	uint64_t *dst, *src, xcount, ccount, count, mask, i;

	uint8_t *b;

	int c, j, exp;

	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 an explanation of this, see the comment in

			 * vdev_raidz_generate_parity_pq() above.

			 */

			for (i = 0; i < count; i++, dst++, src++) {

				mask = *dst & 0x8080808080808080ULL;

				mask = (mask << 1) - (mask >> 7);

				*dst = ((*dst << 1) & 0xfefefefefefefefeULL) ^

				    (mask & 0x1d1d1d1d1d1d1d1dULL);

				*dst ^= *src;

			}

			for (; i < xcount; i++, dst++) {

				mask = *dst & 0x8080808080808080ULL;

				mask = (mask << 1) - (mask >> 7);

				*dst = ((*dst << 1) & 0xfefefefefefefefeULL) ^

				    (mask & 0x1d1d1d1d1d1d1d1dULL);

			}

		}

	}

	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);

		}

	}

}

static void

vdev_raidz_reconstruct_pq(raidz_map_t *rm, int x, int y)

{

	uint8_t *p, *q, *pxy, *qxy, *xd, *yd, tmp, a, b, aexp, bexp;

	void *pdata, *qdata;

	uint64_t xsize, ysize, i;

	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 =