/* * 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 #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 */