snapraid/raid/int.c

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2019-01-07 14:06:15 +01:00
/*
* Copyright (C) 2013 Andrea Mazzoleni
*
* This program is free software: you can redistribute it and/or modify
* it under the terms of the GNU General Public License as published by
* the Free Software Foundation, either version 2 of the License, or
* (at your option) any later version.
*
* This program is distributed in the hope that it will be useful,
* but WITHOUT ANY WARRANTY; without even the implied warranty of
* MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
* GNU General Public License for more details.
*/
#include "internal.h"
#include "gf.h"
/*
* GEN1 (RAID5 with xor) 32bit C implementation
*/
void raid_gen1_int32(int nd, size_t size, void **vv)
{
uint8_t **v = (uint8_t **)vv;
uint8_t *p;
int d, l;
size_t i;
uint32_t p0;
uint32_t p1;
l = nd - 1;
p = v[nd];
for (i = 0; i < size; i += 8) {
p0 = v_32(v[l][i]);
p1 = v_32(v[l][i + 4]);
for (d = l - 1; d >= 0; --d) {
p0 ^= v_32(v[d][i]);
p1 ^= v_32(v[d][i + 4]);
}
v_32(p[i]) = p0;
v_32(p[i + 4]) = p1;
}
}
/*
* GEN1 (RAID5 with xor) 64bit C implementation
*/
void raid_gen1_int64(int nd, size_t size, void **vv)
{
uint8_t **v = (uint8_t **)vv;
uint8_t *p;
int d, l;
size_t i;
uint64_t p0;
uint64_t p1;
l = nd - 1;
p = v[nd];
for (i = 0; i < size; i += 16) {
p0 = v_64(v[l][i]);
p1 = v_64(v[l][i + 8]);
for (d = l - 1; d >= 0; --d) {
p0 ^= v_64(v[d][i]);
p1 ^= v_64(v[d][i + 8]);
}
v_64(p[i]) = p0;
v_64(p[i + 8]) = p1;
}
}
/*
* GEN2 (RAID6 with powers of 2) 32bit C implementation
*/
void raid_gen2_int32(int nd, size_t size, void **vv)
{
uint8_t **v = (uint8_t **)vv;
uint8_t *p;
uint8_t *q;
int d, l;
size_t i;
uint32_t d0, q0, p0;
uint32_t d1, q1, p1;
l = nd - 1;
p = v[nd];
q = v[nd + 1];
for (i = 0; i < size; i += 8) {
q0 = p0 = v_32(v[l][i]);
q1 = p1 = v_32(v[l][i + 4]);
for (d = l - 1; d >= 0; --d) {
d0 = v_32(v[d][i]);
d1 = v_32(v[d][i + 4]);
p0 ^= d0;
p1 ^= d1;
q0 = x2_32(q0);
q1 = x2_32(q1);
q0 ^= d0;
q1 ^= d1;
}
v_32(p[i]) = p0;
v_32(p[i + 4]) = p1;
v_32(q[i]) = q0;
v_32(q[i + 4]) = q1;
}
}
/*
* GEN2 (RAID6 with powers of 2) 64bit C implementation
*/
void raid_gen2_int64(int nd, size_t size, void **vv)
{
uint8_t **v = (uint8_t **)vv;
uint8_t *p;
uint8_t *q;
int d, l;
size_t i;
uint64_t d0, q0, p0;
uint64_t d1, q1, p1;
l = nd - 1;
p = v[nd];
q = v[nd + 1];
for (i = 0; i < size; i += 16) {
q0 = p0 = v_64(v[l][i]);
q1 = p1 = v_64(v[l][i + 8]);
for (d = l - 1; d >= 0; --d) {
d0 = v_64(v[d][i]);
d1 = v_64(v[d][i + 8]);
p0 ^= d0;
p1 ^= d1;
q0 = x2_64(q0);
q1 = x2_64(q1);
q0 ^= d0;
q1 ^= d1;
}
v_64(p[i]) = p0;
v_64(p[i + 8]) = p1;
v_64(q[i]) = q0;
v_64(q[i + 8]) = q1;
}
}
/*
* GEN3 (triple parity with Cauchy matrix) 8bit C implementation
*
* Note that instead of a generic multiplication table, likely resulting
* in multiple cache misses, a precomputed table could be used.
* But this is only a kind of reference function, and we are not really
* interested in speed.
*/
void raid_gen3_int8(int nd, size_t size, void **vv)
{
uint8_t **v = (uint8_t **)vv;
uint8_t *p;
uint8_t *q;
uint8_t *r;
int d, l;
size_t i;
uint8_t d0, r0, q0, p0;
l = nd - 1;
p = v[nd];
q = v[nd + 1];
r = v[nd + 2];
for (i = 0; i < size; i += 1) {
p0 = q0 = r0 = 0;
for (d = l; d > 0; --d) {
d0 = v_8(v[d][i]);
p0 ^= d0;
q0 ^= gfmul[d0][gfgen[1][d]];
r0 ^= gfmul[d0][gfgen[2][d]];
}
/* first disk with all coefficients at 1 */
d0 = v_8(v[0][i]);
p0 ^= d0;
q0 ^= d0;
r0 ^= d0;
v_8(p[i]) = p0;
v_8(q[i]) = q0;
v_8(r[i]) = r0;
}
}
/*
* GEN4 (quad parity with Cauchy matrix) 8bit C implementation
*
* Note that instead of a generic multiplication table, likely resulting
* in multiple cache misses, a precomputed table could be used.
* But this is only a kind of reference function, and we are not really
* interested in speed.
*/
void raid_gen4_int8(int nd, size_t size, void **vv)
{
uint8_t **v = (uint8_t **)vv;
uint8_t *p;
uint8_t *q;
uint8_t *r;
uint8_t *s;
int d, l;
size_t i;
uint8_t d0, s0, r0, q0, p0;
l = nd - 1;
p = v[nd];
q = v[nd + 1];
r = v[nd + 2];
s = v[nd + 3];
for (i = 0; i < size; i += 1) {
p0 = q0 = r0 = s0 = 0;
for (d = l; d > 0; --d) {
d0 = v_8(v[d][i]);
p0 ^= d0;
q0 ^= gfmul[d0][gfgen[1][d]];
r0 ^= gfmul[d0][gfgen[2][d]];
s0 ^= gfmul[d0][gfgen[3][d]];
}
/* first disk with all coefficients at 1 */
d0 = v_8(v[0][i]);
p0 ^= d0;
q0 ^= d0;
r0 ^= d0;
s0 ^= d0;
v_8(p[i]) = p0;
v_8(q[i]) = q0;
v_8(r[i]) = r0;
v_8(s[i]) = s0;
}
}
/*
* GEN5 (penta parity with Cauchy matrix) 8bit C implementation
*
* Note that instead of a generic multiplication table, likely resulting
* in multiple cache misses, a precomputed table could be used.
* But this is only a kind of reference function, and we are not really
* interested in speed.
*/
void raid_gen5_int8(int nd, size_t size, void **vv)
{
uint8_t **v = (uint8_t **)vv;
uint8_t *p;
uint8_t *q;
uint8_t *r;
uint8_t *s;
uint8_t *t;
int d, l;
size_t i;
uint8_t d0, t0, s0, r0, q0, p0;
l = nd - 1;
p = v[nd];
q = v[nd + 1];
r = v[nd + 2];
s = v[nd + 3];
t = v[nd + 4];
for (i = 0; i < size; i += 1) {
p0 = q0 = r0 = s0 = t0 = 0;
for (d = l; d > 0; --d) {
d0 = v_8(v[d][i]);
p0 ^= d0;
q0 ^= gfmul[d0][gfgen[1][d]];
r0 ^= gfmul[d0][gfgen[2][d]];
s0 ^= gfmul[d0][gfgen[3][d]];
t0 ^= gfmul[d0][gfgen[4][d]];
}
/* first disk with all coefficients at 1 */
d0 = v_8(v[0][i]);
p0 ^= d0;
q0 ^= d0;
r0 ^= d0;
s0 ^= d0;
t0 ^= d0;
v_8(p[i]) = p0;
v_8(q[i]) = q0;
v_8(r[i]) = r0;
v_8(s[i]) = s0;
v_8(t[i]) = t0;
}
}
/*
* GEN6 (hexa parity with Cauchy matrix) 8bit C implementation
*
* Note that instead of a generic multiplication table, likely resulting
* in multiple cache misses, a precomputed table could be used.
* But this is only a kind of reference function, and we are not really
* interested in speed.
*/
void raid_gen6_int8(int nd, size_t size, void **vv)
{
uint8_t **v = (uint8_t **)vv;
uint8_t *p;
uint8_t *q;
uint8_t *r;
uint8_t *s;
uint8_t *t;
uint8_t *u;
int d, l;
size_t i;
uint8_t d0, u0, t0, s0, r0, q0, p0;
l = nd - 1;
p = v[nd];
q = v[nd + 1];
r = v[nd + 2];
s = v[nd + 3];
t = v[nd + 4];
u = v[nd + 5];
for (i = 0; i < size; i += 1) {
p0 = q0 = r0 = s0 = t0 = u0 = 0;
for (d = l; d > 0; --d) {
d0 = v_8(v[d][i]);
p0 ^= d0;
q0 ^= gfmul[d0][gfgen[1][d]];
r0 ^= gfmul[d0][gfgen[2][d]];
s0 ^= gfmul[d0][gfgen[3][d]];
t0 ^= gfmul[d0][gfgen[4][d]];
u0 ^= gfmul[d0][gfgen[5][d]];
}
/* first disk with all coefficients at 1 */
d0 = v_8(v[0][i]);
p0 ^= d0;
q0 ^= d0;
r0 ^= d0;
s0 ^= d0;
t0 ^= d0;
u0 ^= d0;
v_8(p[i]) = p0;
v_8(q[i]) = q0;
v_8(r[i]) = r0;
v_8(s[i]) = s0;
v_8(t[i]) = t0;
v_8(u[i]) = u0;
}
}
/*
* Recover failure of one data block at index id[0] using parity at index
* ip[0] for any RAID level.
*
* Starting from the equation:
*
* Pd = A[ip[0],id[0]] * Dx
*
* and solving we get:
*
* Dx = A[ip[0],id[0]]^-1 * Pd
*/
void raid_rec1_int8(int nr, int *id, int *ip, int nd, size_t size, void **vv)
{
uint8_t **v = (uint8_t **)vv;
uint8_t *p;
uint8_t *pa;
const uint8_t *T;
uint8_t G;
uint8_t V;
size_t i;
(void)nr; /* unused, it's always 1 */
/* if it's RAID5 uses the faster function */
if (ip[0] == 0) {
raid_rec1of1(id, nd, size, vv);
return;
}
/* setup the coefficients matrix */
G = A(ip[0], id[0]);
/* invert it to solve the system of linear equations */
V = inv(G);
/* get multiplication tables */
T = table(V);
/* compute delta parity */
raid_delta_gen(1, id, ip, nd, size, vv);
p = v[nd + ip[0]];
pa = v[id[0]];
for (i = 0; i < size; ++i) {
/* delta */
uint8_t Pd = p[i] ^ pa[i];
/* reconstruct */
pa[i] = T[Pd];
}
}
/*
* Recover failure of two data blocks at indexes id[0],id[1] using parity at
* indexes ip[0],ip[1] for any RAID level.
*
* Starting from the equations:
*
* Pd = A[ip[0],id[0]] * Dx + A[ip[0],id[1]] * Dy
* Qd = A[ip[1],id[0]] * Dx + A[ip[1],id[1]] * Dy
*
* we solve inverting the coefficients matrix.
*/
void raid_rec2_int8(int nr, int *id, int *ip, int nd, size_t size, void **vv)
{
uint8_t **v = (uint8_t **)vv;
uint8_t *p;
uint8_t *pa;
uint8_t *q;
uint8_t *qa;
const int N = 2;
const uint8_t *T[N][N];
uint8_t G[N * N];
uint8_t V[N * N];
size_t i;
int j, k;
(void)nr; /* unused, it's always 2 */
/* if it's RAID6 recovering with P and Q uses the faster function */
if (ip[0] == 0 && ip[1] == 1) {
raid_rec2of2_int8(id, ip, nd, size, vv);
return;
}
/* setup the coefficients matrix */
for (j = 0; j < N; ++j)
for (k = 0; k < N; ++k)
G[j * N + k] = A(ip[j], id[k]);
/* invert it to solve the system of linear equations */
raid_invert(G, V, N);
/* get multiplication tables */
for (j = 0; j < N; ++j)
for (k = 0; k < N; ++k)
T[j][k] = table(V[j * N + k]);
/* compute delta parity */
raid_delta_gen(2, id, ip, nd, size, vv);
p = v[nd + ip[0]];
q = v[nd + ip[1]];
pa = v[id[0]];
qa = v[id[1]];
for (i = 0; i < size; ++i) {
/* delta */
uint8_t Pd = p[i] ^ pa[i];
uint8_t Qd = q[i] ^ qa[i];
/* reconstruct */
pa[i] = T[0][0][Pd] ^ T[0][1][Qd];
qa[i] = T[1][0][Pd] ^ T[1][1][Qd];
}
}
/*
* Recover failure of N data blocks at indexes id[N] using parity at indexes
* ip[N] for any RAID level.
*
* Starting from the N equations, with 0<=i<N :
*
* PD[i] = sum(A[ip[i],id[j]] * D[i]) 0<=j<N
*
* we solve inverting the coefficients matrix.
*
* Note that referring at previous equations you have:
* PD[0] = Pd, PD[1] = Qd, PD[2] = Rd, ...
* D[0] = Dx, D[1] = Dy, D[2] = Dz, ...
*/
void raid_recX_int8(int nr, int *id, int *ip, int nd, size_t size, void **vv)
{
uint8_t **v = (uint8_t **)vv;
uint8_t *p[RAID_PARITY_MAX];
uint8_t *pa[RAID_PARITY_MAX];
const uint8_t *T[RAID_PARITY_MAX][RAID_PARITY_MAX];
uint8_t G[RAID_PARITY_MAX * RAID_PARITY_MAX];
uint8_t V[RAID_PARITY_MAX * RAID_PARITY_MAX];
size_t i;
int j, k;
/* setup the coefficients matrix */
for (j = 0; j < nr; ++j)
for (k = 0; k < nr; ++k)
G[j * nr + k] = A(ip[j], id[k]);
/* invert it to solve the system of linear equations */
raid_invert(G, V, nr);
/* get multiplication tables */
for (j = 0; j < nr; ++j)
for (k = 0; k < nr; ++k)
T[j][k] = table(V[j * nr + k]);
/* compute delta parity */
raid_delta_gen(nr, id, ip, nd, size, vv);
for (j = 0; j < nr; ++j) {
p[j] = v[nd + ip[j]];
pa[j] = v[id[j]];
}
for (i = 0; i < size; ++i) {
uint8_t PD[RAID_PARITY_MAX];
/* delta */
for (j = 0; j < nr; ++j)
PD[j] = p[j][i] ^ pa[j][i];
/* reconstruct */
for (j = 0; j < nr; ++j) {
uint8_t b = 0;
for (k = 0; k < nr; ++k)
b ^= T[j][k][PD[k]];
pa[j][i] = b;
}
}
}