zfs-builds-mm/zfs-0.8.1/module/zfs/vdev_raidz_math_impl.h

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2019-07-06 23:40:11 +02:00
/*
* 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 (C) 2016 Gvozden Nešković. All rights reserved.
*/
#ifndef _VDEV_RAIDZ_MATH_IMPL_H
#define _VDEV_RAIDZ_MATH_IMPL_H
#include <sys/types.h>
#define raidz_inline inline __attribute__((always_inline))
#ifndef noinline
#define noinline __attribute__((noinline))
#endif
/*
* Functions calculate multiplication constants for data reconstruction.
* Coefficients depend on RAIDZ geometry, indexes of failed child vdevs, and
* used parity columns for reconstruction.
* @rm RAIDZ map
* @tgtidx array of missing data indexes
* @coeff output array of coefficients. Array must be provided by
* user and must hold minimum MUL_CNT values.
*/
static noinline void
raidz_rec_q_coeff(const raidz_map_t *rm, const int *tgtidx, unsigned *coeff)
{
const unsigned ncols = raidz_ncols(rm);
const unsigned x = tgtidx[TARGET_X];
coeff[MUL_Q_X] = gf_exp2(255 - (ncols - x - 1));
}
static noinline void
raidz_rec_r_coeff(const raidz_map_t *rm, const int *tgtidx, unsigned *coeff)
{
const unsigned ncols = raidz_ncols(rm);
const unsigned x = tgtidx[TARGET_X];
coeff[MUL_R_X] = gf_exp4(255 - (ncols - x - 1));
}
static noinline void
raidz_rec_pq_coeff(const raidz_map_t *rm, const int *tgtidx, unsigned *coeff)
{
const unsigned ncols = raidz_ncols(rm);
const unsigned x = tgtidx[TARGET_X];
const unsigned y = tgtidx[TARGET_Y];
gf_t a, b, e;
a = gf_exp2(x + 255 - y);
b = gf_exp2(255 - (ncols - x - 1));
e = a ^ 0x01;
coeff[MUL_PQ_X] = gf_div(a, e);
coeff[MUL_PQ_Y] = gf_div(b, e);
}
static noinline void
raidz_rec_pr_coeff(const raidz_map_t *rm, const int *tgtidx, unsigned *coeff)
{
const unsigned ncols = raidz_ncols(rm);
const unsigned x = tgtidx[TARGET_X];
const unsigned y = tgtidx[TARGET_Y];
gf_t a, b, e;
a = gf_exp4(x + 255 - y);
b = gf_exp4(255 - (ncols - x - 1));
e = a ^ 0x01;
coeff[MUL_PR_X] = gf_div(a, e);
coeff[MUL_PR_Y] = gf_div(b, e);
}
static noinline void
raidz_rec_qr_coeff(const raidz_map_t *rm, const int *tgtidx, unsigned *coeff)
{
const unsigned ncols = raidz_ncols(rm);
const unsigned x = tgtidx[TARGET_X];
const unsigned y = tgtidx[TARGET_Y];
gf_t nx, ny, nxxy, nxyy, d;
nx = gf_exp2(ncols - x - 1);
ny = gf_exp2(ncols - y - 1);
nxxy = gf_mul(gf_mul(nx, nx), ny);
nxyy = gf_mul(gf_mul(nx, ny), ny);
d = nxxy ^ nxyy;
coeff[MUL_QR_XQ] = ny;
coeff[MUL_QR_X] = gf_div(ny, d);
coeff[MUL_QR_YQ] = nx;
coeff[MUL_QR_Y] = gf_div(nx, d);
}
static noinline void
raidz_rec_pqr_coeff(const raidz_map_t *rm, const int *tgtidx, unsigned *coeff)
{
const unsigned ncols = raidz_ncols(rm);
const unsigned x = tgtidx[TARGET_X];
const unsigned y = tgtidx[TARGET_Y];
const unsigned z = tgtidx[TARGET_Z];
gf_t nx, ny, nz, nxx, nyy, nzz, nyyz, nyzz, xd, yd;
nx = gf_exp2(ncols - x - 1);
ny = gf_exp2(ncols - y - 1);
nz = gf_exp2(ncols - z - 1);
nxx = gf_exp4(ncols - x - 1);
nyy = gf_exp4(ncols - y - 1);
nzz = gf_exp4(ncols - z - 1);
nyyz = gf_mul(gf_mul(ny, nz), ny);
nyzz = gf_mul(nzz, ny);
xd = gf_mul(nxx, ny) ^ gf_mul(nx, nyy) ^ nyyz ^
gf_mul(nxx, nz) ^ gf_mul(nzz, nx) ^ nyzz;
yd = gf_inv(ny ^ nz);
coeff[MUL_PQR_XP] = gf_div(nyyz ^ nyzz, xd);
coeff[MUL_PQR_XQ] = gf_div(nyy ^ nzz, xd);
coeff[MUL_PQR_XR] = gf_div(ny ^ nz, xd);
coeff[MUL_PQR_YU] = nx;
coeff[MUL_PQR_YP] = gf_mul(nz, yd);
coeff[MUL_PQR_YQ] = yd;
}
/*
* Method for zeroing a buffer (can be implemented using SIMD).
* This method is used by multiple for gen/rec functions.
*
* @dc Destination buffer
* @dsize Destination buffer size
* @private Unused
*/
static int
raidz_zero_abd_cb(void *dc, size_t dsize, void *private)
{
v_t *dst = (v_t *)dc;
size_t i;
ZERO_DEFINE();
(void) private; /* unused */
ZERO(ZERO_D);
for (i = 0; i < dsize / sizeof (v_t); i += (2 * ZERO_STRIDE)) {
STORE(dst + i, ZERO_D);
STORE(dst + i + ZERO_STRIDE, ZERO_D);
}
return (0);
}
#define raidz_zero(dabd, size) \
{ \
abd_iterate_func(dabd, 0, size, raidz_zero_abd_cb, NULL); \
}
/*
* Method for copying two buffers (can be implemented using SIMD).
* This method is used by multiple for gen/rec functions.
*
* @dc Destination buffer
* @sc Source buffer
* @dsize Destination buffer size
* @ssize Source buffer size
* @private Unused
*/
static int
raidz_copy_abd_cb(void *dc, void *sc, size_t size, void *private)
{
v_t *dst = (v_t *)dc;
const v_t *src = (v_t *)sc;
size_t i;
COPY_DEFINE();
(void) private; /* unused */
for (i = 0; i < size / sizeof (v_t); i += (2 * COPY_STRIDE)) {
LOAD(src + i, COPY_D);
STORE(dst + i, COPY_D);
LOAD(src + i + COPY_STRIDE, COPY_D);
STORE(dst + i + COPY_STRIDE, COPY_D);
}
return (0);
}
#define raidz_copy(dabd, sabd, size) \
{ \
abd_iterate_func2(dabd, sabd, 0, 0, size, raidz_copy_abd_cb, NULL);\
}
/*
* Method for adding (XORing) two buffers.
* Source and destination are XORed together and result is stored in
* destination buffer. This method is used by multiple for gen/rec functions.
*
* @dc Destination buffer
* @sc Source buffer
* @dsize Destination buffer size
* @ssize Source buffer size
* @private Unused
*/
static int
raidz_add_abd_cb(void *dc, void *sc, size_t size, void *private)
{
v_t *dst = (v_t *)dc;
const v_t *src = (v_t *)sc;
size_t i;
ADD_DEFINE();
(void) private; /* unused */
for (i = 0; i < size / sizeof (v_t); i += (2 * ADD_STRIDE)) {
LOAD(dst + i, ADD_D);
XOR_ACC(src + i, ADD_D);
STORE(dst + i, ADD_D);
LOAD(dst + i + ADD_STRIDE, ADD_D);
XOR_ACC(src + i + ADD_STRIDE, ADD_D);
STORE(dst + i + ADD_STRIDE, ADD_D);
}
return (0);
}
#define raidz_add(dabd, sabd, size) \
{ \
abd_iterate_func2(dabd, sabd, 0, 0, size, raidz_add_abd_cb, NULL);\
}
/*
* Method for multiplying a buffer with a constant in GF(2^8).
* Symbols from buffer are multiplied by a constant and result is stored
* back in the same buffer.
*
* @dc In/Out data buffer.
* @size Size of the buffer
* @private pointer to the multiplication constant (unsigned)
*/
static int
raidz_mul_abd_cb(void *dc, size_t size, void *private)
{
const unsigned mul = *((unsigned *)private);
v_t *d = (v_t *)dc;
size_t i;
MUL_DEFINE();
for (i = 0; i < size / sizeof (v_t); i += (2 * MUL_STRIDE)) {
LOAD(d + i, MUL_D);
MUL(mul, MUL_D);
STORE(d + i, MUL_D);
LOAD(d + i + MUL_STRIDE, MUL_D);
MUL(mul, MUL_D);
STORE(d + i + MUL_STRIDE, MUL_D);
}
return (0);
}
/*
* Syndrome generation/update macros
*
* Require LOAD(), XOR(), STORE(), MUL2(), and MUL4() macros
*/
#define P_D_SYNDROME(D, T, t) \
{ \
LOAD((t), T); \
XOR(D, T); \
STORE((t), T); \
}
#define Q_D_SYNDROME(D, T, t) \
{ \
LOAD((t), T); \
MUL2(T); \
XOR(D, T); \
STORE((t), T); \
}
#define Q_SYNDROME(T, t) \
{ \
LOAD((t), T); \
MUL2(T); \
STORE((t), T); \
}
#define R_D_SYNDROME(D, T, t) \
{ \
LOAD((t), T); \
MUL4(T); \
XOR(D, T); \
STORE((t), T); \
}
#define R_SYNDROME(T, t) \
{ \
LOAD((t), T); \
MUL4(T); \
STORE((t), T); \
}
/*
* PARITY CALCULATION
*
* Macros *_SYNDROME are used for parity/syndrome calculation.
* *_D_SYNDROME() macros are used to calculate syndrome between 0 and
* length of data column, and *_SYNDROME() macros are only for updating
* the parity/syndrome if data column is shorter.
*
* P parity is calculated using raidz_add_abd().
*/
/*
* Generate P parity (RAIDZ1)
*
* @rm RAIDZ map
*/
static raidz_inline void
raidz_generate_p_impl(raidz_map_t * const rm)
{
size_t c;
const size_t ncols = raidz_ncols(rm);
const size_t psize = rm->rm_col[CODE_P].rc_size;
abd_t *pabd = rm->rm_col[CODE_P].rc_abd;
size_t size;
abd_t *dabd;
raidz_math_begin();
/* start with first data column */
raidz_copy(pabd, rm->rm_col[1].rc_abd, psize);
for (c = 2; c < ncols; c++) {
dabd = rm->rm_col[c].rc_abd;
size = rm->rm_col[c].rc_size;
/* add data column */
raidz_add(pabd, dabd, size);
}
raidz_math_end();
}
/*
* Generate PQ parity (RAIDZ2)
* The function is called per data column.
*
* @c array of pointers to parity (code) columns
* @dc pointer to data column
* @csize size of parity columns
* @dsize size of data column
*/
static void
raidz_gen_pq_add(void **c, const void *dc, const size_t csize,
const size_t dsize)
{
v_t *p = (v_t *)c[0];
v_t *q = (v_t *)c[1];
const v_t *d = (v_t *)dc;
const v_t * const dend = d + (dsize / sizeof (v_t));
const v_t * const qend = q + (csize / sizeof (v_t));
GEN_PQ_DEFINE();
MUL2_SETUP();
for (; d < dend; d += GEN_PQ_STRIDE, p += GEN_PQ_STRIDE,
q += GEN_PQ_STRIDE) {
LOAD(d, GEN_PQ_D);
P_D_SYNDROME(GEN_PQ_D, GEN_PQ_C, p);
Q_D_SYNDROME(GEN_PQ_D, GEN_PQ_C, q);
}
for (; q < qend; q += GEN_PQ_STRIDE) {
Q_SYNDROME(GEN_PQ_C, q);
}
}
/*
* Generate PQ parity (RAIDZ2)
*
* @rm RAIDZ map
*/
static raidz_inline void
raidz_generate_pq_impl(raidz_map_t * const rm)
{
size_t c;
const size_t ncols = raidz_ncols(rm);
const size_t csize = rm->rm_col[CODE_P].rc_size;
size_t dsize;
abd_t *dabd;
abd_t *cabds[] = {
rm->rm_col[CODE_P].rc_abd,
rm->rm_col[CODE_Q].rc_abd
};
raidz_math_begin();
raidz_copy(cabds[CODE_P], rm->rm_col[2].rc_abd, csize);
raidz_copy(cabds[CODE_Q], rm->rm_col[2].rc_abd, csize);
for (c = 3; c < ncols; c++) {
dabd = rm->rm_col[c].rc_abd;
dsize = rm->rm_col[c].rc_size;
abd_raidz_gen_iterate(cabds, dabd, csize, dsize, 2,
raidz_gen_pq_add);
}
raidz_math_end();
}
/*
* Generate PQR parity (RAIDZ3)
* The function is called per data column.
*
* @c array of pointers to parity (code) columns
* @dc pointer to data column
* @csize size of parity columns
* @dsize size of data column
*/
static void
raidz_gen_pqr_add(void **c, const void *dc, const size_t csize,
const size_t dsize)
{
v_t *p = (v_t *)c[0];
v_t *q = (v_t *)c[1];
v_t *r = (v_t *)c[CODE_R];
const v_t *d = (v_t *)dc;
const v_t * const dend = d + (dsize / sizeof (v_t));
const v_t * const qend = q + (csize / sizeof (v_t));
GEN_PQR_DEFINE();
MUL2_SETUP();
for (; d < dend; d += GEN_PQR_STRIDE, p += GEN_PQR_STRIDE,
q += GEN_PQR_STRIDE, r += GEN_PQR_STRIDE) {
LOAD(d, GEN_PQR_D);
P_D_SYNDROME(GEN_PQR_D, GEN_PQR_C, p);
Q_D_SYNDROME(GEN_PQR_D, GEN_PQR_C, q);
R_D_SYNDROME(GEN_PQR_D, GEN_PQR_C, r);
}
for (; q < qend; q += GEN_PQR_STRIDE, r += GEN_PQR_STRIDE) {
Q_SYNDROME(GEN_PQR_C, q);
R_SYNDROME(GEN_PQR_C, r);
}
}
/*
* Generate PQR parity (RAIDZ2)
*
* @rm RAIDZ map
*/
static raidz_inline void
raidz_generate_pqr_impl(raidz_map_t * const rm)
{
size_t c;
const size_t ncols = raidz_ncols(rm);
const size_t csize = rm->rm_col[CODE_P].rc_size;
size_t dsize;
abd_t *dabd;
abd_t *cabds[] = {
rm->rm_col[CODE_P].rc_abd,
rm->rm_col[CODE_Q].rc_abd,
rm->rm_col[CODE_R].rc_abd
};
raidz_math_begin();
raidz_copy(cabds[CODE_P], rm->rm_col[3].rc_abd, csize);
raidz_copy(cabds[CODE_Q], rm->rm_col[3].rc_abd, csize);
raidz_copy(cabds[CODE_R], rm->rm_col[3].rc_abd, csize);
for (c = 4; c < ncols; c++) {
dabd = rm->rm_col[c].rc_abd;
dsize = rm->rm_col[c].rc_size;
abd_raidz_gen_iterate(cabds, dabd, csize, dsize, 3,
raidz_gen_pqr_add);
}
raidz_math_end();
}
/*
* DATA RECONSTRUCTION
*
* Data reconstruction process consists of two phases:
* - Syndrome calculation
* - Data reconstruction
*
* Syndrome is calculated by generating parity using available data columns
* and zeros in places of erasure. Existing parity is added to corresponding
* syndrome value to obtain the [P|Q|R]syn values from equation:
* P = Psyn + Dx + Dy + Dz
* Q = Qsyn + 2^x * Dx + 2^y * Dy + 2^z * Dz
* R = Rsyn + 4^x * Dx + 4^y * Dy + 4^z * Dz
*
* For data reconstruction phase, the corresponding equations are solved
* for missing data (Dx, Dy, Dz). This generally involves multiplying known
* symbols by an coefficient and adding them together. The multiplication
* constant coefficients are calculated ahead of the operation in
* raidz_rec_[q|r|pq|pq|qr|pqr]_coeff() functions.
*
* IMPLEMENTATION NOTE: RAID-Z block can have complex geometry, with "big"
* and "short" columns.
* For this reason, reconstruction is performed in minimum of
* two steps. First, from offset 0 to short_size, then from short_size to
* short_size. Calculation functions REC_[*]_BLOCK() are implemented to work
* over both ranges. The split also enables removal of conditional expressions
* from loop bodies, improving throughput of SIMD implementations.
* For the best performance, all functions marked with raidz_inline attribute
* must be inlined by compiler.
*
* parity data
* columns columns
* <----------> <------------------>
* x y <----+ missing columns (x, y)
* | |
* +---+---+---+---+-v-+---+-v-+---+ ^ 0
* | | | | | | | | | |
* | | | | | | | | | |
* | P | Q | R | D | D | D | D | D | |
* | | | | 0 | 1 | 2 | 3 | 4 | |
* | | | | | | | | | v
* | | | | | +---+---+---+ ^ short_size
* | | | | | | |
* +---+---+---+---+---+ v big_size
* <------------------> <---------->
* big columns short columns
*
*/
/*
* Reconstruct single data column using P parity
*
* @syn_method raidz_add_abd()
* @rec_method not applicable
*
* @rm RAIDZ map
* @tgtidx array of missing data indexes
*/
static raidz_inline int
raidz_reconstruct_p_impl(raidz_map_t *rm, const int *tgtidx)
{
size_t c;
const size_t firstdc = raidz_parity(rm);
const size_t ncols = raidz_ncols(rm);
const size_t x = tgtidx[TARGET_X];
const size_t xsize = rm->rm_col[x].rc_size;
abd_t *xabd = rm->rm_col[x].rc_abd;
size_t size;
abd_t *dabd;
raidz_math_begin();
/* copy P into target */
raidz_copy(xabd, rm->rm_col[CODE_P].rc_abd, xsize);
/* generate p_syndrome */
for (c = firstdc; c < ncols; c++) {
if (c == x)
continue;
dabd = rm->rm_col[c].rc_abd;
size = MIN(rm->rm_col[c].rc_size, xsize);
raidz_add(xabd, dabd, size);
}
raidz_math_end();
return (1 << CODE_P);
}
/*
* Generate Q syndrome (Qsyn)
*
* @xc array of pointers to syndrome columns
* @dc data column (NULL if missing)
* @xsize size of syndrome columns
* @dsize size of data column (0 if missing)
*/
static void
raidz_syn_q_abd(void **xc, const void *dc, const size_t xsize,
const size_t dsize)
{
v_t *x = (v_t *)xc[TARGET_X];
const v_t *d = (v_t *)dc;
const v_t * const dend = d + (dsize / sizeof (v_t));
const v_t * const xend = x + (xsize / sizeof (v_t));
SYN_Q_DEFINE();
MUL2_SETUP();
for (; d < dend; d += SYN_STRIDE, x += SYN_STRIDE) {
LOAD(d, SYN_Q_D);
Q_D_SYNDROME(SYN_Q_D, SYN_Q_X, x);
}
for (; x < xend; x += SYN_STRIDE) {
Q_SYNDROME(SYN_Q_X, x);
}
}
/*
* Reconstruct single data column using Q parity
*
* @syn_method raidz_add_abd()
* @rec_method raidz_mul_abd_cb()
*
* @rm RAIDZ map
* @tgtidx array of missing data indexes
*/
static raidz_inline int
raidz_reconstruct_q_impl(raidz_map_t *rm, const int *tgtidx)
{
size_t c;
size_t dsize;
abd_t *dabd;
const size_t firstdc = raidz_parity(rm);
const size_t ncols = raidz_ncols(rm);
const size_t x = tgtidx[TARGET_X];
abd_t *xabd = rm->rm_col[x].rc_abd;
const size_t xsize = rm->rm_col[x].rc_size;
abd_t *tabds[] = { xabd };
unsigned coeff[MUL_CNT];
raidz_rec_q_coeff(rm, tgtidx, coeff);
raidz_math_begin();
/* Start with first data column if present */
if (firstdc != x) {
raidz_copy(xabd, rm->rm_col[firstdc].rc_abd, xsize);
} else {
raidz_zero(xabd, xsize);
}
/* generate q_syndrome */
for (c = firstdc+1; c < ncols; c++) {
if (c == x) {
dabd = NULL;
dsize = 0;
} else {
dabd = rm->rm_col[c].rc_abd;
dsize = rm->rm_col[c].rc_size;
}
abd_raidz_gen_iterate(tabds, dabd, xsize, dsize, 1,
raidz_syn_q_abd);
}
/* add Q to the syndrome */
raidz_add(xabd, rm->rm_col[CODE_Q].rc_abd, xsize);
/* transform the syndrome */
abd_iterate_func(xabd, 0, xsize, raidz_mul_abd_cb, (void*) coeff);
raidz_math_end();
return (1 << CODE_Q);
}
/*
* Generate R syndrome (Rsyn)
*
* @xc array of pointers to syndrome columns
* @dc data column (NULL if missing)
* @tsize size of syndrome columns
* @dsize size of data column (0 if missing)
*/
static void
raidz_syn_r_abd(void **xc, const void *dc, const size_t tsize,
const size_t dsize)
{
v_t *x = (v_t *)xc[TARGET_X];
const v_t *d = (v_t *)dc;
const v_t * const dend = d + (dsize / sizeof (v_t));
const v_t * const xend = x + (tsize / sizeof (v_t));
SYN_R_DEFINE();
MUL2_SETUP();
for (; d < dend; d += SYN_STRIDE, x += SYN_STRIDE) {
LOAD(d, SYN_R_D);
R_D_SYNDROME(SYN_R_D, SYN_R_X, x);
}
for (; x < xend; x += SYN_STRIDE) {
R_SYNDROME(SYN_R_X, x);
}
}
/*
* Reconstruct single data column using R parity
*
* @syn_method raidz_add_abd()
* @rec_method raidz_mul_abd_cb()
*
* @rm RAIDZ map
* @tgtidx array of missing data indexes
*/
static raidz_inline int
raidz_reconstruct_r_impl(raidz_map_t *rm, const int *tgtidx)
{
size_t c;
size_t dsize;
abd_t *dabd;
const size_t firstdc = raidz_parity(rm);
const size_t ncols = raidz_ncols(rm);
const size_t x = tgtidx[TARGET_X];
const size_t xsize = rm->rm_col[x].rc_size;
abd_t *xabd = rm->rm_col[x].rc_abd;
abd_t *tabds[] = { xabd };
unsigned coeff[MUL_CNT];
raidz_rec_r_coeff(rm, tgtidx, coeff);
raidz_math_begin();
/* Start with first data column if present */
if (firstdc != x) {
raidz_copy(xabd, rm->rm_col[firstdc].rc_abd, xsize);
} else {
raidz_zero(xabd, xsize);
}
/* generate q_syndrome */
for (c = firstdc+1; c < ncols; c++) {
if (c == x) {
dabd = NULL;
dsize = 0;
} else {
dabd = rm->rm_col[c].rc_abd;
dsize = rm->rm_col[c].rc_size;
}
abd_raidz_gen_iterate(tabds, dabd, xsize, dsize, 1,
raidz_syn_r_abd);
}
/* add R to the syndrome */
raidz_add(xabd, rm->rm_col[CODE_R].rc_abd, xsize);
/* transform the syndrome */
abd_iterate_func(xabd, 0, xsize, raidz_mul_abd_cb, (void *)coeff);
raidz_math_end();
return (1 << CODE_R);
}
/*
* Generate P and Q syndromes
*
* @xc array of pointers to syndrome columns
* @dc data column (NULL if missing)
* @tsize size of syndrome columns
* @dsize size of data column (0 if missing)
*/
static void
raidz_syn_pq_abd(void **tc, const void *dc, const size_t tsize,
const size_t dsize)
{
v_t *x = (v_t *)tc[TARGET_X];
v_t *y = (v_t *)tc[TARGET_Y];
const v_t *d = (v_t *)dc;
const v_t * const dend = d + (dsize / sizeof (v_t));
const v_t * const yend = y + (tsize / sizeof (v_t));
SYN_PQ_DEFINE();
MUL2_SETUP();
for (; d < dend; d += SYN_STRIDE, x += SYN_STRIDE, y += SYN_STRIDE) {
LOAD(d, SYN_PQ_D);
P_D_SYNDROME(SYN_PQ_D, SYN_PQ_X, x);
Q_D_SYNDROME(SYN_PQ_D, SYN_PQ_X, y);
}
for (; y < yend; y += SYN_STRIDE) {
Q_SYNDROME(SYN_PQ_X, y);
}
}
/*
* Reconstruct data using PQ parity and PQ syndromes
*
* @tc syndrome/result columns
* @tsize size of syndrome/result columns
* @c parity columns
* @mul array of multiplication constants
*/
static void
raidz_rec_pq_abd(void **tc, const size_t tsize, void **c,
const unsigned *mul)
{
v_t *x = (v_t *)tc[TARGET_X];
v_t *y = (v_t *)tc[TARGET_Y];
const v_t * const xend = x + (tsize / sizeof (v_t));
const v_t *p = (v_t *)c[CODE_P];
const v_t *q = (v_t *)c[CODE_Q];
REC_PQ_DEFINE();
for (; x < xend; x += REC_PQ_STRIDE, y += REC_PQ_STRIDE,
p += REC_PQ_STRIDE, q += REC_PQ_STRIDE) {
LOAD(x, REC_PQ_X);
LOAD(y, REC_PQ_Y);
XOR_ACC(p, REC_PQ_X);
XOR_ACC(q, REC_PQ_Y);
/* Save Pxy */
COPY(REC_PQ_X, REC_PQ_T);
/* Calc X */
MUL(mul[MUL_PQ_X], REC_PQ_X);
MUL(mul[MUL_PQ_Y], REC_PQ_Y);
XOR(REC_PQ_Y, REC_PQ_X);
STORE(x, REC_PQ_X);
/* Calc Y */
XOR(REC_PQ_T, REC_PQ_X);
STORE(y, REC_PQ_X);
}
}
/*
* Reconstruct two data columns using PQ parity
*
* @syn_method raidz_syn_pq_abd()
* @rec_method raidz_rec_pq_abd()
*
* @rm RAIDZ map
* @tgtidx array of missing data indexes
*/
static raidz_inline int
raidz_reconstruct_pq_impl(raidz_map_t *rm, const int *tgtidx)
{
size_t c;
size_t dsize;
abd_t *dabd;
const size_t firstdc = raidz_parity(rm);
const size_t ncols = raidz_ncols(rm);
const size_t x = tgtidx[TARGET_X];
const size_t y = tgtidx[TARGET_Y];
const size_t xsize = rm->rm_col[x].rc_size;
const size_t ysize = rm->rm_col[y].rc_size;
abd_t *xabd = rm->rm_col[x].rc_abd;
abd_t *yabd = rm->rm_col[y].rc_abd;
abd_t *tabds[2] = { xabd, yabd };
abd_t *cabds[] = {
rm->rm_col[CODE_P].rc_abd,
rm->rm_col[CODE_Q].rc_abd
};
unsigned coeff[MUL_CNT];
raidz_rec_pq_coeff(rm, tgtidx, coeff);
/*
* Check if some of targets is shorter then others
* In this case, shorter target needs to be replaced with
* new buffer so that syndrome can be calculated.
*/
if (ysize < xsize) {
yabd = abd_alloc(xsize, B_FALSE);
tabds[1] = yabd;
}
raidz_math_begin();
/* Start with first data column if present */
if (firstdc != x) {
raidz_copy(xabd, rm->rm_col[firstdc].rc_abd, xsize);
raidz_copy(yabd, rm->rm_col[firstdc].rc_abd, xsize);
} else {
raidz_zero(xabd, xsize);
raidz_zero(yabd, xsize);
}
/* generate q_syndrome */
for (c = firstdc+1; c < ncols; c++) {
if (c == x || c == y) {
dabd = NULL;
dsize = 0;
} else {
dabd = rm->rm_col[c].rc_abd;
dsize = rm->rm_col[c].rc_size;
}
abd_raidz_gen_iterate(tabds, dabd, xsize, dsize, 2,
raidz_syn_pq_abd);
}
abd_raidz_rec_iterate(cabds, tabds, xsize, 2, raidz_rec_pq_abd, coeff);
/* Copy shorter targets back to the original abd buffer */
if (ysize < xsize)
raidz_copy(rm->rm_col[y].rc_abd, yabd, ysize);
raidz_math_end();
if (ysize < xsize)
abd_free(yabd);
return ((1 << CODE_P) | (1 << CODE_Q));
}
/*
* Generate P and R syndromes
*
* @xc array of pointers to syndrome columns
* @dc data column (NULL if missing)
* @tsize size of syndrome columns
* @dsize size of data column (0 if missing)
*/
static void
raidz_syn_pr_abd(void **c, const void *dc, const size_t tsize,
const size_t dsize)
{
v_t *x = (v_t *)c[TARGET_X];
v_t *y = (v_t *)c[TARGET_Y];
const v_t *d = (v_t *)dc;
const v_t * const dend = d + (dsize / sizeof (v_t));
const v_t * const yend = y + (tsize / sizeof (v_t));
SYN_PR_DEFINE();
MUL2_SETUP();
for (; d < dend; d += SYN_STRIDE, x += SYN_STRIDE, y += SYN_STRIDE) {
LOAD(d, SYN_PR_D);
P_D_SYNDROME(SYN_PR_D, SYN_PR_X, x);
R_D_SYNDROME(SYN_PR_D, SYN_PR_X, y);
}
for (; y < yend; y += SYN_STRIDE) {
R_SYNDROME(SYN_PR_X, y);
}
}
/*
* Reconstruct data using PR parity and PR syndromes
*
* @tc syndrome/result columns
* @tsize size of syndrome/result columns
* @c parity columns
* @mul array of multiplication constants
*/
static void
raidz_rec_pr_abd(void **t, const size_t tsize, void **c,
const unsigned *mul)
{
v_t *x = (v_t *)t[TARGET_X];
v_t *y = (v_t *)t[TARGET_Y];
const v_t * const xend = x + (tsize / sizeof (v_t));
const v_t *p = (v_t *)c[CODE_P];
const v_t *q = (v_t *)c[CODE_Q];
REC_PR_DEFINE();
for (; x < xend; x += REC_PR_STRIDE, y += REC_PR_STRIDE,
p += REC_PR_STRIDE, q += REC_PR_STRIDE) {
LOAD(x, REC_PR_X);
LOAD(y, REC_PR_Y);
XOR_ACC(p, REC_PR_X);
XOR_ACC(q, REC_PR_Y);
/* Save Pxy */
COPY(REC_PR_X, REC_PR_T);
/* Calc X */
MUL(mul[MUL_PR_X], REC_PR_X);
MUL(mul[MUL_PR_Y], REC_PR_Y);
XOR(REC_PR_Y, REC_PR_X);
STORE(x, REC_PR_X);
/* Calc Y */
XOR(REC_PR_T, REC_PR_X);
STORE(y, REC_PR_X);
}
}
/*
* Reconstruct two data columns using PR parity
*
* @syn_method raidz_syn_pr_abd()
* @rec_method raidz_rec_pr_abd()
*
* @rm RAIDZ map
* @tgtidx array of missing data indexes
*/
static raidz_inline int
raidz_reconstruct_pr_impl(raidz_map_t *rm, const int *tgtidx)
{
size_t c;
size_t dsize;
abd_t *dabd;
const size_t firstdc = raidz_parity(rm);
const size_t ncols = raidz_ncols(rm);
const size_t x = tgtidx[0];
const size_t y = tgtidx[1];
const size_t xsize = rm->rm_col[x].rc_size;
const size_t ysize = rm->rm_col[y].rc_size;
abd_t *xabd = rm->rm_col[x].rc_abd;
abd_t *yabd = rm->rm_col[y].rc_abd;
abd_t *tabds[2] = { xabd, yabd };
abd_t *cabds[] = {
rm->rm_col[CODE_P].rc_abd,
rm->rm_col[CODE_R].rc_abd
};
unsigned coeff[MUL_CNT];
raidz_rec_pr_coeff(rm, tgtidx, coeff);
/*
* Check if some of targets are shorter then others.
* They need to be replaced with a new buffer so that syndrome can
* be calculated on full length.
*/
if (ysize < xsize) {
yabd = abd_alloc(xsize, B_FALSE);
tabds[1] = yabd;
}
raidz_math_begin();
/* Start with first data column if present */
if (firstdc != x) {
raidz_copy(xabd, rm->rm_col[firstdc].rc_abd, xsize);
raidz_copy(yabd, rm->rm_col[firstdc].rc_abd, xsize);
} else {
raidz_zero(xabd, xsize);
raidz_zero(yabd, xsize);
}
/* generate q_syndrome */
for (c = firstdc+1; c < ncols; c++) {
if (c == x || c == y) {
dabd = NULL;
dsize = 0;
} else {
dabd = rm->rm_col[c].rc_abd;
dsize = rm->rm_col[c].rc_size;
}
abd_raidz_gen_iterate(tabds, dabd, xsize, dsize, 2,
raidz_syn_pr_abd);
}
abd_raidz_rec_iterate(cabds, tabds, xsize, 2, raidz_rec_pr_abd, coeff);
/*
* Copy shorter targets back to the original abd buffer
*/
if (ysize < xsize)
raidz_copy(rm->rm_col[y].rc_abd, yabd, ysize);
raidz_math_end();
if (ysize < xsize)
abd_free(yabd);
return ((1 << CODE_P) | (1 << CODE_Q));
}
/*
* Generate Q and R syndromes
*
* @xc array of pointers to syndrome columns
* @dc data column (NULL if missing)
* @tsize size of syndrome columns
* @dsize size of data column (0 if missing)
*/
static void
raidz_syn_qr_abd(void **c, const void *dc, const size_t tsize,
const size_t dsize)
{
v_t *x = (v_t *)c[TARGET_X];
v_t *y = (v_t *)c[TARGET_Y];
const v_t * const xend = x + (tsize / sizeof (v_t));
const v_t *d = (v_t *)dc;
const v_t * const dend = d + (dsize / sizeof (v_t));
SYN_QR_DEFINE();
MUL2_SETUP();
for (; d < dend; d += SYN_STRIDE, x += SYN_STRIDE, y += SYN_STRIDE) {
LOAD(d, SYN_PQ_D);
Q_D_SYNDROME(SYN_QR_D, SYN_QR_X, x);
R_D_SYNDROME(SYN_QR_D, SYN_QR_X, y);
}
for (; x < xend; x += SYN_STRIDE, y += SYN_STRIDE) {
Q_SYNDROME(SYN_QR_X, x);
R_SYNDROME(SYN_QR_X, y);
}
}
/*
* Reconstruct data using QR parity and QR syndromes
*
* @tc syndrome/result columns
* @tsize size of syndrome/result columns
* @c parity columns
* @mul array of multiplication constants
*/
static void
raidz_rec_qr_abd(void **t, const size_t tsize, void **c,
const unsigned *mul)
{
v_t *x = (v_t *)t[TARGET_X];
v_t *y = (v_t *)t[TARGET_Y];
const v_t * const xend = x + (tsize / sizeof (v_t));
const v_t *p = (v_t *)c[CODE_P];
const v_t *q = (v_t *)c[CODE_Q];
REC_QR_DEFINE();
for (; x < xend; x += REC_QR_STRIDE, y += REC_QR_STRIDE,
p += REC_QR_STRIDE, q += REC_QR_STRIDE) {
LOAD(x, REC_QR_X);
LOAD(y, REC_QR_Y);
XOR_ACC(p, REC_QR_X);
XOR_ACC(q, REC_QR_Y);
/* Save Pxy */
COPY(REC_QR_X, REC_QR_T);
/* Calc X */
MUL(mul[MUL_QR_XQ], REC_QR_X); /* X = Q * xqm */
XOR(REC_QR_Y, REC_QR_X); /* X = R ^ X */
MUL(mul[MUL_QR_X], REC_QR_X); /* X = X * xm */
STORE(x, REC_QR_X);
/* Calc Y */
MUL(mul[MUL_QR_YQ], REC_QR_T); /* X = Q * xqm */
XOR(REC_QR_Y, REC_QR_T); /* X = R ^ X */
MUL(mul[MUL_QR_Y], REC_QR_T); /* X = X * xm */
STORE(y, REC_QR_T);
}
}
/*
* Reconstruct two data columns using QR parity
*
* @syn_method raidz_syn_qr_abd()
* @rec_method raidz_rec_qr_abd()
*
* @rm RAIDZ map
* @tgtidx array of missing data indexes
*/
static raidz_inline int
raidz_reconstruct_qr_impl(raidz_map_t *rm, const int *tgtidx)
{
size_t c;
size_t dsize;
abd_t *dabd;
const size_t firstdc = raidz_parity(rm);
const size_t ncols = raidz_ncols(rm);
const size_t x = tgtidx[TARGET_X];
const size_t y = tgtidx[TARGET_Y];
const size_t xsize = rm->rm_col[x].rc_size;
const size_t ysize = rm->rm_col[y].rc_size;
abd_t *xabd = rm->rm_col[x].rc_abd;
abd_t *yabd = rm->rm_col[y].rc_abd;
abd_t *tabds[2] = { xabd, yabd };
abd_t *cabds[] = {
rm->rm_col[CODE_Q].rc_abd,
rm->rm_col[CODE_R].rc_abd
};
unsigned coeff[MUL_CNT];
raidz_rec_qr_coeff(rm, tgtidx, coeff);
/*
* Check if some of targets is shorter then others
* In this case, shorter target needs to be replaced with
* new buffer so that syndrome can be calculated.
*/
if (ysize < xsize) {
yabd = abd_alloc(xsize, B_FALSE);
tabds[1] = yabd;
}
raidz_math_begin();
/* Start with first data column if present */
if (firstdc != x) {
raidz_copy(xabd, rm->rm_col[firstdc].rc_abd, xsize);
raidz_copy(yabd, rm->rm_col[firstdc].rc_abd, xsize);
} else {
raidz_zero(xabd, xsize);
raidz_zero(yabd, xsize);
}
/* generate q_syndrome */
for (c = firstdc+1; c < ncols; c++) {
if (c == x || c == y) {
dabd = NULL;
dsize = 0;
} else {
dabd = rm->rm_col[c].rc_abd;
dsize = rm->rm_col[c].rc_size;
}
abd_raidz_gen_iterate(tabds, dabd, xsize, dsize, 2,
raidz_syn_qr_abd);
}
abd_raidz_rec_iterate(cabds, tabds, xsize, 2, raidz_rec_qr_abd, coeff);
/*
* Copy shorter targets back to the original abd buffer
*/
if (ysize < xsize)
raidz_copy(rm->rm_col[y].rc_abd, yabd, ysize);
raidz_math_end();
if (ysize < xsize)
abd_free(yabd);
return ((1 << CODE_Q) | (1 << CODE_R));
}
/*
* Generate P, Q, and R syndromes
*
* @xc array of pointers to syndrome columns
* @dc data column (NULL if missing)
* @tsize size of syndrome columns
* @dsize size of data column (0 if missing)
*/
static void
raidz_syn_pqr_abd(void **c, const void *dc, const size_t tsize,
const size_t dsize)
{
v_t *x = (v_t *)c[TARGET_X];
v_t *y = (v_t *)c[TARGET_Y];
v_t *z = (v_t *)c[TARGET_Z];
const v_t * const yend = y + (tsize / sizeof (v_t));
const v_t *d = (v_t *)dc;
const v_t * const dend = d + (dsize / sizeof (v_t));
SYN_PQR_DEFINE();
MUL2_SETUP();
for (; d < dend; d += SYN_STRIDE, x += SYN_STRIDE, y += SYN_STRIDE,
z += SYN_STRIDE) {
LOAD(d, SYN_PQR_D);
P_D_SYNDROME(SYN_PQR_D, SYN_PQR_X, x)
Q_D_SYNDROME(SYN_PQR_D, SYN_PQR_X, y);
R_D_SYNDROME(SYN_PQR_D, SYN_PQR_X, z);
}
for (; y < yend; y += SYN_STRIDE, z += SYN_STRIDE) {
Q_SYNDROME(SYN_PQR_X, y);
R_SYNDROME(SYN_PQR_X, z);
}
}
/*
* Reconstruct data using PRQ parity and PQR syndromes
*
* @tc syndrome/result columns
* @tsize size of syndrome/result columns
* @c parity columns
* @mul array of multiplication constants
*/
static void
raidz_rec_pqr_abd(void **t, const size_t tsize, void **c,
const unsigned * const mul)
{
v_t *x = (v_t *)t[TARGET_X];
v_t *y = (v_t *)t[TARGET_Y];
v_t *z = (v_t *)t[TARGET_Z];
const v_t * const xend = x + (tsize / sizeof (v_t));
const v_t *p = (v_t *)c[CODE_P];
const v_t *q = (v_t *)c[CODE_Q];
const v_t *r = (v_t *)c[CODE_R];
REC_PQR_DEFINE();
for (; x < xend; x += REC_PQR_STRIDE, y += REC_PQR_STRIDE,
z += REC_PQR_STRIDE, p += REC_PQR_STRIDE, q += REC_PQR_STRIDE,
r += REC_PQR_STRIDE) {
LOAD(x, REC_PQR_X);
LOAD(y, REC_PQR_Y);
LOAD(z, REC_PQR_Z);
XOR_ACC(p, REC_PQR_X);
XOR_ACC(q, REC_PQR_Y);
XOR_ACC(r, REC_PQR_Z);
/* Save Pxyz and Qxyz */
COPY(REC_PQR_X, REC_PQR_XS);
COPY(REC_PQR_Y, REC_PQR_YS);
/* Calc X */
MUL(mul[MUL_PQR_XP], REC_PQR_X); /* Xp = Pxyz * xp */
MUL(mul[MUL_PQR_XQ], REC_PQR_Y); /* Xq = Qxyz * xq */
XOR(REC_PQR_Y, REC_PQR_X);
MUL(mul[MUL_PQR_XR], REC_PQR_Z); /* Xr = Rxyz * xr */
XOR(REC_PQR_Z, REC_PQR_X); /* X = Xp + Xq + Xr */
STORE(x, REC_PQR_X);
/* Calc Y */
XOR(REC_PQR_X, REC_PQR_XS); /* Pyz = Pxyz + X */
MUL(mul[MUL_PQR_YU], REC_PQR_X); /* Xq = X * upd_q */
XOR(REC_PQR_X, REC_PQR_YS); /* Qyz = Qxyz + Xq */
COPY(REC_PQR_XS, REC_PQR_X); /* restore Pyz */
MUL(mul[MUL_PQR_YP], REC_PQR_X); /* Yp = Pyz * yp */
MUL(mul[MUL_PQR_YQ], REC_PQR_YS); /* Yq = Qyz * yq */
XOR(REC_PQR_X, REC_PQR_YS); /* Y = Yp + Yq */
STORE(y, REC_PQR_YS);
/* Calc Z */
XOR(REC_PQR_XS, REC_PQR_YS); /* Z = Pz = Pyz + Y */
STORE(z, REC_PQR_YS);
}
}
/*
* Reconstruct three data columns using PQR parity
*
* @syn_method raidz_syn_pqr_abd()
* @rec_method raidz_rec_pqr_abd()
*
* @rm RAIDZ map
* @tgtidx array of missing data indexes
*/
static raidz_inline int
raidz_reconstruct_pqr_impl(raidz_map_t *rm, const int *tgtidx)
{
size_t c;
size_t dsize;
abd_t *dabd;
const size_t firstdc = raidz_parity(rm);
const size_t ncols = raidz_ncols(rm);
const size_t x = tgtidx[TARGET_X];
const size_t y = tgtidx[TARGET_Y];
const size_t z = tgtidx[TARGET_Z];
const size_t xsize = rm->rm_col[x].rc_size;
const size_t ysize = rm->rm_col[y].rc_size;
const size_t zsize = rm->rm_col[z].rc_size;
abd_t *xabd = rm->rm_col[x].rc_abd;
abd_t *yabd = rm->rm_col[y].rc_abd;
abd_t *zabd = rm->rm_col[z].rc_abd;
abd_t *tabds[] = { xabd, yabd, zabd };
abd_t *cabds[] = {
rm->rm_col[CODE_P].rc_abd,
rm->rm_col[CODE_Q].rc_abd,
rm->rm_col[CODE_R].rc_abd
};
unsigned coeff[MUL_CNT];
raidz_rec_pqr_coeff(rm, tgtidx, coeff);
/*
* Check if some of targets is shorter then others
* In this case, shorter target needs to be replaced with
* new buffer so that syndrome can be calculated.
*/
if (ysize < xsize) {
yabd = abd_alloc(xsize, B_FALSE);
tabds[1] = yabd;
}
if (zsize < xsize) {
zabd = abd_alloc(xsize, B_FALSE);
tabds[2] = zabd;
}
raidz_math_begin();
/* Start with first data column if present */
if (firstdc != x) {
raidz_copy(xabd, rm->rm_col[firstdc].rc_abd, xsize);
raidz_copy(yabd, rm->rm_col[firstdc].rc_abd, xsize);
raidz_copy(zabd, rm->rm_col[firstdc].rc_abd, xsize);
} else {
raidz_zero(xabd, xsize);
raidz_zero(yabd, xsize);
raidz_zero(zabd, xsize);
}
/* generate q_syndrome */
for (c = firstdc+1; c < ncols; c++) {
if (c == x || c == y || c == z) {
dabd = NULL;
dsize = 0;
} else {
dabd = rm->rm_col[c].rc_abd;
dsize = rm->rm_col[c].rc_size;
}
abd_raidz_gen_iterate(tabds, dabd, xsize, dsize, 3,
raidz_syn_pqr_abd);
}
abd_raidz_rec_iterate(cabds, tabds, xsize, 3, raidz_rec_pqr_abd, coeff);
/*
* Copy shorter targets back to the original abd buffer
*/
if (ysize < xsize)
raidz_copy(rm->rm_col[y].rc_abd, yabd, ysize);
if (zsize < xsize)
raidz_copy(rm->rm_col[z].rc_abd, zabd, zsize);
raidz_math_end();
if (ysize < xsize)
abd_free(yabd);
if (zsize < xsize)
abd_free(zabd);
return ((1 << CODE_P) | (1 << CODE_Q) | (1 << CODE_R));
}
#endif /* _VDEV_RAIDZ_MATH_IMPL_H */