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snapraid/raid/int.c

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// SPDX-License-Identifier: GPL-2.0-or-later
// Copyright (C) 2013 Andrea Mazzoleni
#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_read32(&v[l][i]);
p1 = v_read32(&v[l][i + 4]);
for (d = l - 1; d >= 0; --d) {
p0 ^= v_read32(&v[d][i]);
p1 ^= v_read32(&v[d][i + 4]);
}
v_write32(&p[i], p0);
v_write32(&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_read64(&v[l][i]);
p1 = v_read64(&v[l][i + 8]);
for (d = l - 1; d >= 0; --d) {
p0 ^= v_read64(&v[d][i]);
p1 ^= v_read64(&v[d][i + 8]);
}
v_write64(&p[i], p0);
v_write64(&p[i + 8], p1);
}
}
/*
* GEN2 (double parity) 32bit C implementation using only Q *= 2.
*/
static __always_inline void raid_gen2_int32_x2(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;
const uint32_t poly_32 = raid_poly_32;
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_read32(&v[l][i]);
q1 = p1 = v_read32(&v[l][i + 4]);
for (d = l - 1; d >= 0; --d) {
d0 = v_read32(&v[d][i]);
d1 = v_read32(&v[d][i + 4]);
p0 ^= d0;
p1 ^= d1;
q0 = x2_32(q0, poly_32);
q1 = x2_32(q1, poly_32);
q0 ^= d0;
q1 ^= d1;
}
v_write32(&p[i], p0);
v_write32(&p[i + 4], p1);
v_write32(&q[i], q0);
v_write32(&q[i + 4], q1);
}
}
/*
* GEN2 (double parity) 32bit C implementation using the AES G23 Q recurrence.
*/
static __always_inline void raid_gen2_int32_g23(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;
const uint32_t poly_32 = raid_poly_32;
uint32_t d0, q0, p0;
uint32_t d1, q1, p1;
uint32_t qold;
l = nd - 1;
p = v[nd];
q = v[nd + 1];
int g23_boundary = raid_g23_boundary(l - 1);
for (i = 0; i < size; i += 8) {
int boundary = g23_boundary;
q0 = p0 = v_read32(&v[l][i]);
q1 = p1 = v_read32(&v[l][i + 4]);
d = l - 1;
for (;;) {
/*
* All transitions above 'boundary' are x2.
*/
for (; d > boundary; --d) {
d0 = v_read32(&v[d][i]);
d1 = v_read32(&v[d][i + 4]);
p0 ^= d0;
p1 ^= d1;
q0 = x2_32(q0, poly_32);
q1 = x2_32(q1, poly_32);
q0 ^= d0;
q1 ^= d1;
}
/*
* boundary == -1 identifies the final x2-only segment.
* At this point all remaining disks have been consumed.
*/
if (boundary < 0)
break;
/*
* d == boundary.
*
* Perform the fixed G23 x3 transition and then add
* the current disk to P and Q.
*/
d0 = v_read32(&v[d][i]);
d1 = v_read32(&v[d][i + 4]);
p0 ^= d0;
p1 ^= d1;
qold = q0;
q0 = x2_32(q0, poly_32);
q0 ^= qold;
qold = q1;
q1 = x2_32(q1, poly_32);
q1 ^= qold;
q0 ^= d0;
q1 ^= d1;
--d;
/*
* G23 boundaries are exactly 51 transitions apart.
* After d = 50 there are no more x3 transitions.
*/
boundary -= 51;
if (boundary < 50)
boundary = -1;
}
v_write32(&p[i], p0);
v_write32(&p[i + 4], p1);
v_write32(&q[i], q0);
v_write32(&q[i + 4], q1);
}
}
void raid_gen2_int32_raid(int nd, size_t size, void **vv)
{
raid_gen2_int32_x2(nd, size, vv);
}
void raid_gen2_int32_aes(int nd, size_t size, void **vv)
{
if (raid_g23_x2_only(nd))
raid_gen2_int32_x2(nd, size, vv);
else
raid_gen2_int32_g23(nd, size, vv);
}
/*
* GEN2 (double parity) 64bit C implementation using only Q *= 2.
*/
static __always_inline void raid_gen2_int64_x2(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;
const uint64_t poly_64 = raid_poly_64;
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_read64(&v[l][i]);
q1 = p1 = v_read64(&v[l][i + 8]);
for (d = l - 1; d >= 0; --d) {
d0 = v_read64(&v[d][i]);
d1 = v_read64(&v[d][i + 8]);
p0 ^= d0;
p1 ^= d1;
q0 = x2_64(q0, poly_64);
q1 = x2_64(q1, poly_64);
q0 ^= d0;
q1 ^= d1;
}
v_write64(&p[i], p0);
v_write64(&p[i + 8], p1);
v_write64(&q[i], q0);
v_write64(&q[i + 8], q1);
}
}
/*
* GEN2 (double parity) 64bit C implementation using the AES G23 Q recurrence.
*/
static __always_inline void raid_gen2_int64_g23(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;
const uint64_t poly_64 = raid_poly_64;
uint64_t d0, q0, p0;
uint64_t d1, q1, p1;
uint64_t qold;
l = nd - 1;
p = v[nd];
q = v[nd + 1];
int g23_boundary = raid_g23_boundary(l - 1);
for (i = 0; i < size; i += 16) {
int boundary = g23_boundary;
q0 = p0 = v_read64(&v[l][i]);
q1 = p1 = v_read64(&v[l][i + 8]);
d = l - 1;
for (;;) {
/*
* All transitions above 'boundary' are x2.
*/
for (; d > boundary; --d) {
d0 = v_read64(&v[d][i]);
d1 = v_read64(&v[d][i + 8]);
p0 ^= d0;
p1 ^= d1;
q0 = x2_64(q0, poly_64);
q1 = x2_64(q1, poly_64);
q0 ^= d0;
q1 ^= d1;
}
/*
* boundary == -1 identifies the final x2-only segment.
* At this point all remaining disks have been consumed.
*/
if (boundary < 0)
break;
/*
* d == boundary.
*
* Perform the fixed G23 x3 transition and then add
* the current disk to P and Q.
*/
d0 = v_read64(&v[d][i]);
d1 = v_read64(&v[d][i + 8]);
p0 ^= d0;
p1 ^= d1;
qold = q0;
q0 = x2_64(q0, poly_64);
q0 ^= qold;
qold = q1;
q1 = x2_64(q1, poly_64);
q1 ^= qold;
q0 ^= d0;
q1 ^= d1;
--d;
/*
* G23 boundaries are exactly 51 transitions apart.
* After d = 50 there are no more x3 transitions.
*/
boundary -= 51;
if (boundary < 50)
boundary = -1;
}
v_write64(&p[i], p0);
v_write64(&p[i + 8], p1);
v_write64(&q[i], q0);
v_write64(&q[i + 8], q1);
}
}
void raid_gen2_int64_raid(int nd, size_t size, void **vv)
{
raid_gen2_int64_x2(nd, size, vv);
}
void raid_gen2_int64_aes(int nd, size_t size, void **vv)
{
if (raid_g23_x2_only(nd))
raid_gen2_int64_x2(nd, size, vv);
else
raid_gen2_int64_g23(nd, size, vv);
}
/*
* GENz (triple parity with powers of 2^-1) 32bit C implementation
*/
void raid_genz_int32_raid(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;
const uint32_t poly_32 = raid_poly_32;
const uint32_t inv2_32 = raid_inv2_32;
uint32_t d0, r0, q0, p0;
uint32_t d1, r1, q1, p1;
l = nd - 1;
p = v[nd];
q = v[nd + 1];
r = v[nd + 2];
for (i = 0; i < size; i += 8) {
r0 = q0 = p0 = v_read32(&v[l][i]);
r1 = q1 = p1 = v_read32(&v[l][i + 4]);
for (d = l - 1; d >= 0; --d) {
d0 = v_read32(&v[d][i]);
d1 = v_read32(&v[d][i + 4]);
p0 ^= d0;
p1 ^= d1;
q0 = x2_32(q0, poly_32);
q1 = x2_32(q1, poly_32);
q0 ^= d0;
q1 ^= d1;
r0 = d2_32(r0, inv2_32);
r1 = d2_32(r1, inv2_32);
r0 ^= d0;
r1 ^= d1;
}
v_write32(&p[i], p0);
v_write32(&p[i + 4], p1);
v_write32(&q[i], q0);
v_write32(&q[i + 4], q1);
v_write32(&r[i], r0);
v_write32(&r[i + 4], r1);
}
}
/*
* GENz (triple parity with powers of 2^-1) 64bit C implementation
*/
void raid_genz_int64_raid(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;
const uint64_t poly_64 = raid_poly_64;
const uint64_t inv2_64 = raid_inv2_64;
uint64_t d0, r0, q0, p0;
uint64_t d1, r1, q1, p1;
l = nd - 1;
p = v[nd];
q = v[nd + 1];
r = v[nd + 2];
for (i = 0; i < size; i += 16) {
r0 = q0 = p0 = v_read64(&v[l][i]);
r1 = q1 = p1 = v_read64(&v[l][i + 8]);
for (d = l - 1; d >= 0; --d) {
d0 = v_read64(&v[d][i]);
d1 = v_read64(&v[d][i + 8]);
p0 ^= d0;
p1 ^= d1;
q0 = x2_64(q0, poly_64);
q1 = x2_64(q1, poly_64);
q0 ^= d0;
q1 ^= d1;
r0 = d2_64(r0, inv2_64);
r1 = d2_64(r1, inv2_64);
r0 ^= d0;
r1 ^= d1;
}
v_write64(&p[i], p0);
v_write64(&p[i + 8], p1);
v_write64(&q[i], q0);
v_write64(&q[i + 8], q1);
v_write64(&r[i], r0);
v_write64(&r[i + 8], r1);
}
}
/*
* 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[d][i];
p0 ^= d0;
q0 ^= raid_gfmul[d0][raid_gfgen[1][d]];
r0 ^= raid_gfmul[d0][raid_gfgen[2][d]];
}
/* first disk with all coefficients at 1 */
d0 = v[0][i];
p0 ^= d0;
q0 ^= d0;
r0 ^= d0;
p[i] = p0;
q[i] = q0;
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[d][i];
p0 ^= d0;
q0 ^= raid_gfmul[d0][raid_gfgen[1][d]];
r0 ^= raid_gfmul[d0][raid_gfgen[2][d]];
s0 ^= raid_gfmul[d0][raid_gfgen[3][d]];
}
/* first disk with all coefficients at 1 */
d0 = v[0][i];
p0 ^= d0;
q0 ^= d0;
r0 ^= d0;
s0 ^= d0;
p[i] = p0;
q[i] = q0;
r[i] = r0;
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[d][i];
p0 ^= d0;
q0 ^= raid_gfmul[d0][raid_gfgen[1][d]];
r0 ^= raid_gfmul[d0][raid_gfgen[2][d]];
s0 ^= raid_gfmul[d0][raid_gfgen[3][d]];
t0 ^= raid_gfmul[d0][raid_gfgen[4][d]];
}
/* first disk with all coefficients at 1 */
d0 = v[0][i];
p0 ^= d0;
q0 ^= d0;
r0 ^= d0;
s0 ^= d0;
t0 ^= d0;
p[i] = p0;
q[i] = q0;
r[i] = r0;
s[i] = s0;
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[d][i];
p0 ^= d0;
q0 ^= raid_gfmul[d0][raid_gfgen[1][d]];
r0 ^= raid_gfmul[d0][raid_gfgen[2][d]];
s0 ^= raid_gfmul[d0][raid_gfgen[3][d]];
t0 ^= raid_gfmul[d0][raid_gfgen[4][d]];
u0 ^= raid_gfmul[d0][raid_gfgen[5][d]];
}
/* first disk with all coefficients at 1 */
d0 = v[0][i];
p0 ^= d0;
q0 ^= d0;
r0 ^= d0;
s0 ^= d0;
t0 ^= d0;
u0 ^= d0;
p[i] = p0;
q[i] = q0;
r[i] = r0;
s[i] = s0;
t[i] = t0;
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, use 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[2][2];
uint8_t G[2 * 2];
uint8_t V[2 * 2];
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 to 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;
}
}
}
void raid_register_int(void)
{
raid_gen_register(RAID_ALGO_CAUCHY_PAR3, "int8", raid_gen3_int8, RAID_POLY_ANY);
raid_gen_register(RAID_ALGO_CAUCHY_PAR4, "int8", raid_gen4_int8, RAID_POLY_ANY);
raid_gen_register(RAID_ALGO_CAUCHY_PAR5, "int8", raid_gen5_int8, RAID_POLY_ANY);
raid_gen_register(RAID_ALGO_CAUCHY_PAR6, "int8", raid_gen6_int8, RAID_POLY_ANY);
if (sizeof(void *) == 4) {
raid_gen_register(RAID_ALGO_CAUCHY_PAR1, "int32", raid_gen1_int32, RAID_POLY_ANY);
raid_gen_register(RAID_ALGO_CAUCHY_PAR2, "int32", raid_gen2_int32_raid, RAID_POLY_RAID);
raid_gen_register(RAID_ALGO_CAUCHY_PAR2, "int32", raid_gen2_int32_aes, RAID_POLY_AES);
raid_gen_register(RAID_ALGO_VANDERMONDE_PAR3, "int32", raid_genz_int32_raid, RAID_POLY_RAID);
} else {
raid_gen_register(RAID_ALGO_CAUCHY_PAR1, "int64", raid_gen1_int64, RAID_POLY_ANY);
raid_gen_register(RAID_ALGO_CAUCHY_PAR2, "int64", raid_gen2_int64_raid, RAID_POLY_RAID);
raid_gen_register(RAID_ALGO_CAUCHY_PAR2, "int64", raid_gen2_int64_aes, RAID_POLY_AES);
raid_gen_register(RAID_ALGO_VANDERMONDE_PAR3, "int64", raid_genz_int64_raid, RAID_POLY_RAID);
}
raid_rec_register(RAID_ALGO_CAUCHY_PAR1, "int8", raid_rec1_int8, RAID_POLY_ANY);
raid_rec_register(RAID_ALGO_CAUCHY_PAR2, "int8", raid_rec2_int8, RAID_POLY_ANY);
raid_rec_register(RAID_ALGO_CAUCHY_PAR3, "int8", raid_recX_int8, RAID_POLY_ANY);
raid_rec_register(RAID_ALGO_CAUCHY_PAR4, "int8", raid_recX_int8, RAID_POLY_ANY);
raid_rec_register(RAID_ALGO_CAUCHY_PAR5, "int8", raid_recX_int8, RAID_POLY_ANY);
raid_rec_register(RAID_ALGO_CAUCHY_PAR6, "int8", raid_recX_int8, RAID_POLY_ANY);
}
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