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snapraid/raid.c
Andrea Mazzoleni 5b60bd077d Minor comments and output changes.
2013-10-27 21:05:18 +01:00

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/*
* 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.
*
* You should have received a copy of the GNU General Public License
* along with this program. If not, see <http://www.gnu.org/licenses/>.
*/
/*
* The RAID5 and RAID6 support were originally derived from the libraid6
* library by H. Peter Anvin released with license "GPL2 or any later
* version", used in the Linux Kernel 2.6.38.
* This support was later completely rewritten (many times), but the
* H. Peter Anvin's Copyright may still apply.
*
* The RAIDTP (Triple Parity), RAIDQP (Quad parity), RAIDPP (Penta Parity)
* and RAIDHP (Hexa parity) support is original work implemented from
* scratch.
*
* For RAID5 and RAID6 it works like the Linux Kernel RAID and it's based
* on the Anvin's paper "The mathematics of RAID-6" [1].
*
* We compute the parity in the Galois Field GF(2^8) with the primitive
* polynomial x^8 + x^4 + x^3 + x^2 + 1 (285 decimal), starting from a set
* of N disk Di with 0<=i<N, using the equations:
*
* P = sum(Di)
* Q = sum(2^i * Di) with 0<=i<N
*
* To support RAIDTP (Triple Parity), it was first evaluated, and then
* dropped, the use of an extension of the same approach, with additional
* parity coefficients set as powers of 4, with equations:
*
* P = sum(Di)
* Q = sum(2^i * Di)
* R = sum(4^i * Di) with 0<=i<N
*
* This method is also the same used by ZFS to implement its RAIDZ3
* support, it works well, and it's very efficient.
*
* Unfortunately, the same approach doesn't work for RAIDQP (Quad Parity).
* Using additional parity coefficients set as power of 8 with equations:
*
* P = sum(Di)
* Q = sum(2^i * Di)
* R = sum(4^i * Di)
* S = sum(8^i * Di) with 0<=i<N
*
* we don't have a system of independent linear equations, and in some cases
* the equations are not solvable.
*
* This approach is expected to fail at some point, because the Vandermonde
* matrix used to compute the parity has no guarantee to have all
* submatrices not singular [2, Chap 11, Problem 7] and this is a requirement
* to have a MDS (Maximum Distance Separable) code [2, Chap 11, Theorem 8].
*
* If it surprises that even using a Vandermonde matrix we don't have a
* MDS code, consider that the matrix A we use to compute the parity, is
* not the MDS generator matrix G, but only a submatrix of it.
* The generator matrix G is the concatenation of I and A, as G = [I | A],
* where I is the identity matrix.
* Setting the matrix G as Vandermonde matrix would have guaranteed to have
* a MDS code, but setting only A as a Vandermonde matrix doesn't give
* this guarantee.
*
* Using the primitive polynomial 285, RAIDQP works for up to 21 data disks
* with parity coefficients "1,2,4,8". Changing polynomial to one of
* 391/451/463/487,
* it works for up to 27 disks with the same parity coefficients.
* Using different parity coefficients, like "5,13,27,35", it's possible to
* make it working for up to 33 disks. But no more.
*
* To support more disks it's possible to use GF(2^16) with primitive
* polynomial 100087 or 122563 that supports up to Hexa (6) Parity
* with parity coefficients 1,2,4,8,16,32 for up to 89 disks.
*
* To overcome these limitations we instead use an Extended Cauchy Matrix
* [3][4] to compute the parity.
* Such matrix has the mathematical property to have all the square
* submatrices not singular, resulting in always solvable equations, for
* any number of parities and for any number of disks.
*
* The problem of this approach is that the coefficients of the equations
* are not powers of the same value, not allowing to use the fast
* implementation described in the Anvin's paper [1].
*
* Hopefully there is a method to implement parallel multiplications
* using SSSE3 instructions [1][5]. Method already competitive with the
* computation of RAIDTP parity using power coefficients.
*
* Another important property of the Extended Cauchy matrix is that we can
* setup the first two rows with power coeffients equal at the RAID5 and
* RAID6 approach described in Anvin's paper [1], resulting in a compatible
* extension, and requiring SSSE3 instructions only if RAIDTP is used.
*
* We also "normalize" the matrix, multipling each row for a constant
* factor to make the first column with all 1.
*
* This results in the "normalized" Extended Cauchy matrix A[row,col]
* defined as:
*
* 01 01 01 01 01 01 01 01 01 01 01 01 01 01 01 01 01 01 01 01 01 01 01 01 01 01 01 ...
* 01 02 04 08 10 20 40 80 1d 3a 74 e8 cd 87 13 26 4c 98 2d 5a b4 75 ea c9 8f 03 06 ...
* 01 f5 d2 c4 9a 71 f1 7f fc 87 c1 c6 19 2f 40 55 3d ba 53 04 9c 61 34 8c 46 68 70 ...
* 01 bb a6 d7 c7 07 ce 82 4a 2f a5 9b b6 60 f1 ad e7 f4 06 d2 df 2e ca 65 5c 48 21 ...
* 01 97 7f 9c 7c 18 bd a2 58 1a da 74 70 a3 e5 47 29 07 f5 80 23 e9 fa 46 54 a0 99 ...
* 01 2b 3f cf 73 2c d6 ed cb 74 15 78 8a c1 17 c9 89 68 21 ab 76 3b 4b 5a 6e 0e b9 ...
* (see tables.h for the full matrix)
*
* This matrix supports 6 level of parity, one for each row, for up to 251
* data disks, one for each column, with all the 377,342,351,231 square
* submatrices not singular, verified also with brute-force.
*
* This matrix can be extended to support any number of parities, just adding
* additional rows, and removing one column for each row added.
* (see mktables.c for more details in how the matrix is generated)
*
* In details, parity is computed as:
*
* P = sum(Di)
* Q = sum(2^i * Di)
* R = sum(A[2,i] * Di)
* S = sum(A[3,i] * Di)
* T = sum(A[4,i] * Di)
* U = sum(A[5,i] * Di) with 0<=i<N
*
* To recover from a failure of six disks at indexes x,y,z,h,v,w,
* with 0<=x<y<z<h<v<w<N, we compute the parity of the available N-6 disks as:
*
* Pa = sum(Di)
* Qa = sum(2^i * Di)
* Ra = sum(A[2,i] * Di)
* Sa = sum(A[3,i] * Di)
* Ta = sum(A[4,i] * Di)
* Ua = sum(A[5,i] * Di) with 0<=i<N,i!=x,i!=y,i!=z,i!=h,i!=v,i!=w.
*
* And if we define:
*
* Pd = Pa + P
* Qd = Qa + Q
* Rd = Ra + R
* Sd = Sa + S
* Td = Ta + T
* Ud = Ua + U
*
* we can sum these two sets of equations, obtaining:
*
* Pd = Dx + Dy + Dz + Dh + Dv + Dw
* Qd = 2^x * Dx + 2^y * Dy + 2^z * Dz + 2^h * Dh + 2^v * Dv + 2^w * Dw
* Rd = A[2,x] * Dx + A[2,y] * Dy + A[2,z] * Dz + A[2,h] * Dh + A[2,v] * Dv + A[2,w] * Dw
* Sd = A[3,x] * Dx + A[3,y] * Dy + A[3,z] * Dz + A[3,h] * Dh + A[3,v] * Dv + A[3,w] * Dw
* Td = A[4,x] * Dx + A[4,y] * Dy + A[4,z] * Dz + A[4,h] * Dh + A[4,v] * Dv + A[4,w] * Dw
* Ud = A[5,x] * Dx + A[5,y] * Dy + A[5,z] * Dz + A[5,h] * Dh + A[5,v] * Dv + A[5,w] * Dw
*
* A linear system always solvable because the coefficients matrix is
* always not singular due the properties of the matrix A[].
*
* Resulting speed in x64, with 24 data disks, using a stripe of 256 KiB,
* for a Core i7-3740QM CPU @ 2.7GHz is:
*
* int8 int32 int64 sse2 sse2e ssse3 ssse3e
* raid5 9042 16698 26734
* raid6 3205 5478 13987 16287
* raidTP 828 6802 7186
* raidQP 637 5483 5843
* raidPP 513 4325 4629
* raidHP 428 3479 3866
*
* Values are in MiB/s of data processed, not counting generated parity.
*
* For comparison, a similar implementation using the power coeffients approach
* in the same condition, is only a little faster (16%) for RAIDTP with power
* coefficient "4", and equal for RAIDQP with power coefficient "8".
* RAIDQP became faster (10%) only using AVX instructions, thanks of the better
* registers allocation that AVX three operands PSHUFB makes possible.
*
* int32 int64 sse2 sse2e ssse3 ssse3e avxe
* raidTP 1406 2522 7240 7886 8071 8358
* raidQP 773 1375 4573 4678 5457 5778 6468
*
* References:
* [1] Anvin, "The mathematics of RAID-6", 2004
* [2] MacWilliams, Sloane, "The Theory of Error-Correcting Codes", 1977
* [3] Bl<42>mer, "An XOR-Based Erasure-Resilient Coding Scheme", 1995
* [4] Vinocha, Bhullar, Brar, "On Generator Cauchy Matrices of GDRS/GTRS Codes", 2012
* [5] Plank, "Screaming Fast Galois Field Arithmetic Using Intel SIMD Instructions", 2013
*/
#include "portable.h"
#include "raid.h"
#include "cpu.h"
#include "tables.h"
/**
* Dereference as uint8_t
*/
#define v_8(p) (*(uint8_t*)&(p))
/**
* Dereference as uint32_t
*/
#define v_32(p) (*(uint32_t*)&(p))
/**
* Dereference as uint64_t
*/
#define v_64(p) (*(uint64_t*)&(p))
/****************************************************************************/
/* specialized parity generation */
/*
* RAID5 32bit C implementation
*/
void raid5_int32(unsigned char** vbuf, unsigned data, unsigned size)
{
unsigned char* p;
int d, l;
unsigned i;
uint32_t p0;
uint32_t p1;
l = data - 1;
p = vbuf[data];
for(i=0;i<size;i+=8) {
p0 = v_32(vbuf[l][i]);
p1 = v_32(vbuf[l][i+4]);
for(d=l-1;d>=0;--d) {
p0 ^= v_32(vbuf[d][i]);
p1 ^= v_32(vbuf[d][i+4]);
}
v_32(p[i]) = p0;
v_32(p[i+4]) = p1;
}
}
/*
* RAID5 64bit C implementation
*/
void raid5_int64(unsigned char** vbuf, unsigned data, unsigned size)
{
unsigned char* p;
int d, l;
unsigned i;
uint64_t p0;
uint64_t p1;
l = data - 1;
p = vbuf[data];
for(i=0;i<size;i+=16) {
p0 = v_64(vbuf[l][i]);
p1 = v_64(vbuf[l][i+8]);
for(d=l-1;d>=0;--d) {
p0 ^= v_64(vbuf[d][i]);
p1 ^= v_64(vbuf[d][i+8]);
}
v_64(p[i]) = p0;
v_64(p[i+8]) = p1;
}
}
#if defined(__i386__) || defined(__x86_64__)
/*
* RAID5 SSE2 implementation
*
* Note that we don't have the corresponding x64 sse2ext function using more
* registers because processing a block of 64 bytes already fills
* the typical cache block, and processing 128 bytes doesn't increase
* performance.
*/
void raid5_sse2(unsigned char** vbuf, unsigned data, unsigned size)
{
unsigned char* p;
int d, l;
unsigned i;
l = data - 1;
p = vbuf[data];
for(i=0;i<size;i+=64) {
asm volatile("movdqa %0,%%xmm0" : : "m" (vbuf[l][i]));
asm volatile("movdqa %0,%%xmm1" : : "m" (vbuf[l][i+16]));
asm volatile("movdqa %0,%%xmm2" : : "m" (vbuf[l][i+32]));
asm volatile("movdqa %0,%%xmm3" : : "m" (vbuf[l][i+48]));
for(d=l-1;d>=0;--d) {
asm volatile("movdqa %0,%%xmm4" : : "m" (vbuf[d][i]));
asm volatile("movdqa %0,%%xmm5" : : "m" (vbuf[d][i+16]));
asm volatile("movdqa %0,%%xmm6" : : "m" (vbuf[d][i+32]));
asm volatile("movdqa %0,%%xmm7" : : "m" (vbuf[d][i+48]));
asm volatile("pxor %xmm4,%xmm0");
asm volatile("pxor %xmm5,%xmm1");
asm volatile("pxor %xmm6,%xmm2");
asm volatile("pxor %xmm7,%xmm3");
}
asm volatile("movntdq %%xmm0,%0" : "=m" (p[i]));
asm volatile("movntdq %%xmm1,%0" : "=m" (p[i+16]));
asm volatile("movntdq %%xmm2,%0" : "=m" (p[i+32]));
asm volatile("movntdq %%xmm3,%0" : "=m" (p[i+48]));
}
asm volatile("sfence" : : : "memory");
}
#endif
/**
* Multiply each byte of a uint32 by 2 in the GF(2^8).
*/
__attribute__((always_inline)) static inline uint32_t x2_32(uint32_t v)
{
uint32_t mask = v & 0x80808080U;
mask = (mask << 1) - (mask >> 7);
v = (v << 1) & 0xfefefefeU;
v ^= mask & 0x1d1d1d1dU;
return v;
}
/**
* Multiply each byte of a uint64 by 2 in the GF(2^8).
*/
__attribute__((always_inline)) static inline uint64_t x2_64(uint64_t v)
{
uint64_t mask = v & 0x8080808080808080ULL;
mask = (mask << 1) - (mask >> 7);
v = (v << 1) & 0xfefefefefefefefeULL;
v ^= mask & 0x1d1d1d1d1d1d1d1dULL;
return v;
}
/*
* RAID6 32bit C implementation
*/
void raid6_int32(unsigned char** vbuf, unsigned data, unsigned size)
{
unsigned char* p;
unsigned char* q;
int d, l;
unsigned i;
uint32_t d0, q0, p0;
uint32_t d1, q1, p1;
l = data - 1;
p = vbuf[data];
q = vbuf[data+1];
for(i=0;i<size;i+=8) {
q0 = p0 = v_32(vbuf[l][i]);
q1 = p1 = v_32(vbuf[l][i+4]);
for(d=l-1;d>=0;--d) {
d0 = v_32(vbuf[d][i]);
d1 = v_32(vbuf[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;
}
}
/*
* RAID6 64bit C implementation
*/
void raid6_int64(unsigned char** vbuf, unsigned data, unsigned size)
{
unsigned char* p;
unsigned char* q;
int d, l;
unsigned i;
uint64_t d0, q0, p0;
uint64_t d1, q1, p1;
l = data - 1;
p = vbuf[data];
q = vbuf[data+1];
for(i=0;i<size;i+=16) {
q0 = p0 = v_64(vbuf[l][i]);
q1 = p1 = v_64(vbuf[l][i+8]);
for(d=l-1;d>=0;--d) {
d0 = v_64(vbuf[d][i]);
d1 = v_64(vbuf[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;
}
}
#if defined(__i386__) || defined(__x86_64__)
static const struct gfconst16 {
unsigned char poly[16];
unsigned char mask[16];
} gfconst16 __attribute__((aligned(32))) = {
{ 0x1d, 0x1d, 0x1d, 0x1d, 0x1d, 0x1d, 0x1d, 0x1d, 0x1d, 0x1d, 0x1d, 0x1d, 0x1d, 0x1d, 0x1d, 0x1d },
{ 0x0f, 0x0f, 0x0f, 0x0f, 0x0f, 0x0f, 0x0f, 0x0f, 0x0f, 0x0f, 0x0f, 0x0f, 0x0f, 0x0f, 0x0f, 0x0f }
};
/*
* RAID6 SSE2 implementation
*/
void raid6_sse2(unsigned char** vbuf, unsigned data, unsigned size)
{
unsigned char* p;
unsigned char* q;
int d, l;
unsigned i;
l = data - 1;
p = vbuf[data];
q = vbuf[data+1];
asm volatile("movdqa %0,%%xmm7" : : "m" (gfconst16.poly[0]));
for(i=0;i<size;i+=32) {
asm volatile("movdqa %0,%%xmm0" : : "m" (vbuf[l][i]));
asm volatile("movdqa %0,%%xmm1" : : "m" (vbuf[l][i+16]));
asm volatile("movdqa %xmm0,%xmm2");
asm volatile("movdqa %xmm1,%xmm3");
for(d=l-1;d>=0;--d) {
asm volatile("pxor %xmm4,%xmm4");
asm volatile("pxor %xmm5,%xmm5");
asm volatile("pcmpgtb %xmm2,%xmm4");
asm volatile("pcmpgtb %xmm3,%xmm5");
asm volatile("paddb %xmm2,%xmm2");
asm volatile("paddb %xmm3,%xmm3");
asm volatile("pand %xmm7,%xmm4");
asm volatile("pand %xmm7,%xmm5");
asm volatile("pxor %xmm4,%xmm2");
asm volatile("pxor %xmm5,%xmm3");
asm volatile("movdqa %0,%%xmm4" : : "m" (vbuf[d][i]));
asm volatile("movdqa %0,%%xmm5" : : "m" (vbuf[d][i+16]));
asm volatile("pxor %xmm4,%xmm0");
asm volatile("pxor %xmm5,%xmm1");
asm volatile("pxor %xmm4,%xmm2");
asm volatile("pxor %xmm5,%xmm3");
}
asm volatile("movntdq %%xmm0,%0" : "=m" (p[i]));
asm volatile("movntdq %%xmm1,%0" : "=m" (p[i+16]));
asm volatile("movntdq %%xmm2,%0" : "=m" (q[i]));
asm volatile("movntdq %%xmm3,%0" : "=m" (q[i+16]));
}
asm volatile("sfence" : : : "memory");
}
#endif
#if defined(__x86_64__)
/*
* RAID6 SSE2 implementation
*
* Note that it uses 16 registers, meaning that x64 is required.
*/
void raid6_sse2ext(unsigned char** vbuf, unsigned data, unsigned size)
{
unsigned char* p;
unsigned char* q;
int d, l;
unsigned i;
l = data - 1;
p = vbuf[data];
q = vbuf[data+1];
asm volatile("movdqa %0,%%xmm15" : : "m" (gfconst16.poly[0]));
for(i=0;i<size;i+=64) {
asm volatile("movdqa %0,%%xmm0" : : "m" (vbuf[l][i]));
asm volatile("movdqa %0,%%xmm1" : : "m" (vbuf[l][i+16]));
asm volatile("movdqa %0,%%xmm2" : : "m" (vbuf[l][i+32]));
asm volatile("movdqa %0,%%xmm3" : : "m" (vbuf[l][i+48]));
asm volatile("movdqa %xmm0,%xmm4");
asm volatile("movdqa %xmm1,%xmm5");
asm volatile("movdqa %xmm2,%xmm6");
asm volatile("movdqa %xmm3,%xmm7");
for(d=l-1;d>=0;--d) {
asm volatile("pxor %xmm8,%xmm8");
asm volatile("pxor %xmm9,%xmm9");
asm volatile("pxor %xmm10,%xmm10");
asm volatile("pxor %xmm11,%xmm11");
asm volatile("pcmpgtb %xmm4,%xmm8");
asm volatile("pcmpgtb %xmm5,%xmm9");
asm volatile("pcmpgtb %xmm6,%xmm10");
asm volatile("pcmpgtb %xmm7,%xmm11");
asm volatile("paddb %xmm4,%xmm4");
asm volatile("paddb %xmm5,%xmm5");
asm volatile("paddb %xmm6,%xmm6");
asm volatile("paddb %xmm7,%xmm7");
asm volatile("pand %xmm15,%xmm8");
asm volatile("pand %xmm15,%xmm9");
asm volatile("pand %xmm15,%xmm10");
asm volatile("pand %xmm15,%xmm11");
asm volatile("pxor %xmm8,%xmm4");
asm volatile("pxor %xmm9,%xmm5");
asm volatile("pxor %xmm10,%xmm6");
asm volatile("pxor %xmm11,%xmm7");
asm volatile("movdqa %0,%%xmm8" : : "m" (vbuf[d][i]));
asm volatile("movdqa %0,%%xmm9" : : "m" (vbuf[d][i+16]));
asm volatile("movdqa %0,%%xmm10" : : "m" (vbuf[d][i+32]));
asm volatile("movdqa %0,%%xmm11" : : "m" (vbuf[d][i+48]));
asm volatile("pxor %xmm8,%xmm0");
asm volatile("pxor %xmm9,%xmm1");
asm volatile("pxor %xmm10,%xmm2");
asm volatile("pxor %xmm11,%xmm3");
asm volatile("pxor %xmm8,%xmm4");
asm volatile("pxor %xmm9,%xmm5");
asm volatile("pxor %xmm10,%xmm6");
asm volatile("pxor %xmm11,%xmm7");
}
asm volatile("movntdq %%xmm0,%0" : "=m" (p[i]));
asm volatile("movntdq %%xmm1,%0" : "=m" (p[i+16]));
asm volatile("movntdq %%xmm2,%0" : "=m" (p[i+32]));
asm volatile("movntdq %%xmm3,%0" : "=m" (p[i+48]));
asm volatile("movntdq %%xmm4,%0" : "=m" (q[i]));
asm volatile("movntdq %%xmm5,%0" : "=m" (q[i+16]));
asm volatile("movntdq %%xmm6,%0" : "=m" (q[i+32]));
asm volatile("movntdq %%xmm7,%0" : "=m" (q[i+48]));
}
asm volatile("sfence" : : : "memory");
}
#endif
/*
* RAIDTP 8bit C implementation
*
* Note that instead of a generic multiplicationt 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 on speed.
*/
void raidTP_int8(unsigned char** vbuf, unsigned data, unsigned size)
{
unsigned char* p;
unsigned char* q;
unsigned char* r;
int d, l;
unsigned i;
uint8_t d0, r0, q0, p0;
l = data - 1;
p = vbuf[data];
q = vbuf[data+1];
r = vbuf[data+2];
for(i=0;i<size;i+=1) {
r0 = q0 = p0 = 0;
for(d=l;d>=0;--d) {
d0 = v_8(vbuf[d][i]);
p0 ^= d0;
q0 ^= gfmul[d0][gfmatrix[1][d]];
r0 ^= gfmul[d0][gfmatrix[2][d]];
}
v_8(p[i]) = p0;
v_8(q[i]) = q0;
v_8(r[i]) = r0;
}
}
#if defined(__i386__) || defined(__x86_64__)
/*
* RAIDTP SSSE3 implementation
*/
void raidTP_ssse3(unsigned char** vbuf, unsigned data, unsigned size)
{
unsigned char* p;
unsigned char* q;
unsigned char* r;
int d, l;
unsigned i;
l = data - 1;
p = vbuf[data];
q = vbuf[data+1];
r = vbuf[data+2];
asm volatile("movdqa %0,%%xmm3" : : "m" (gfconst16.poly[0]));
asm volatile("movdqa %0,%%xmm7" : : "m" (gfconst16.mask[0]));
for(i=0;i<size;i+=16) {
asm volatile("pxor %xmm0,%xmm0");
asm volatile("pxor %xmm1,%xmm1");
asm volatile("pxor %xmm2,%xmm2");
for(d=l;d>=0;--d) {
asm volatile("movdqa %0,%%xmm4" : : "m" (vbuf[d][i]));
asm volatile("pxor %xmm5,%xmm5");
asm volatile("pcmpgtb %xmm1,%xmm5");
asm volatile("paddb %xmm1,%xmm1");
asm volatile("pand %xmm3,%xmm5");
asm volatile("pxor %xmm5,%xmm1");
asm volatile("pxor %xmm4,%xmm0");
asm volatile("pxor %xmm4,%xmm1");
asm volatile("movdqa %xmm4,%xmm5");
asm volatile("psraw $4,%xmm5");
asm volatile("pand %xmm7,%xmm4");
asm volatile("pand %xmm7,%xmm5");
asm volatile("movdqa %0,%%xmm6" : : "m" (gfpshufb[d][0][0][0]));
asm volatile("pshufb %xmm4,%xmm6");
asm volatile("pxor %xmm6,%xmm2");
asm volatile("movdqa %0,%%xmm6" : : "m" (gfpshufb[d][0][1][0]));
asm volatile("pshufb %xmm5,%xmm6");
asm volatile("pxor %xmm6,%xmm2");
}
asm volatile("movntdq %%xmm0,%0" : "=m" (p[i]));
asm volatile("movntdq %%xmm1,%0" : "=m" (q[i]));
asm volatile("movntdq %%xmm2,%0" : "=m" (r[i]));
}
asm volatile("sfence" : : : "memory");
}
#endif
#if defined(__x86_64__)
/*
* RAIDTP SSSE3 implementation
*
* Note that it uses 16 registers, meaning that x64 is required.
*/
void raidTP_ssse3ext(unsigned char** vbuf, unsigned data, unsigned size)
{
unsigned char* p;
unsigned char* q;
unsigned char* r;
int d, l;
unsigned i;
l = data - 1;
p = vbuf[data];
q = vbuf[data+1];
r = vbuf[data+2];
asm volatile("movdqa %0,%%xmm3" : : "m" (gfconst16.poly[0]));
asm volatile("movdqa %0,%%xmm11" : : "m" (gfconst16.mask[0]));
for(i=0;i<size;i+=32) {
asm volatile("pxor %xmm0,%xmm0");
asm volatile("pxor %xmm1,%xmm1");
asm volatile("pxor %xmm2,%xmm2");
asm volatile("pxor %xmm8,%xmm8");
asm volatile("pxor %xmm9,%xmm9");
asm volatile("pxor %xmm10,%xmm10");
for(d=l;d>=0;--d) {
asm volatile("movdqa %0,%%xmm4" : : "m" (vbuf[d][i]));
asm volatile("movdqa %0,%%xmm12" : : "m" (vbuf[d][i+16]));
asm volatile("pxor %xmm5,%xmm5");
asm volatile("pxor %xmm13,%xmm13");
asm volatile("pcmpgtb %xmm1,%xmm5");
asm volatile("pcmpgtb %xmm9,%xmm13");
asm volatile("paddb %xmm1,%xmm1");
asm volatile("paddb %xmm9,%xmm9");
asm volatile("pand %xmm3,%xmm5");
asm volatile("pand %xmm3,%xmm13");
asm volatile("pxor %xmm5,%xmm1");
asm volatile("pxor %xmm13,%xmm9");
asm volatile("pxor %xmm4,%xmm0");
asm volatile("pxor %xmm4,%xmm1");
asm volatile("pxor %xmm12,%xmm8");
asm volatile("pxor %xmm12,%xmm9");
asm volatile("movdqa %xmm4,%xmm5");
asm volatile("movdqa %xmm12,%xmm13");
asm volatile("psraw $4,%xmm5");
asm volatile("psraw $4,%xmm13");
asm volatile("pand %xmm11,%xmm4");
asm volatile("pand %xmm11,%xmm12");
asm volatile("pand %xmm11,%xmm5");
asm volatile("pand %xmm11,%xmm13");
asm volatile("movdqa %0,%%xmm6" : : "m" (gfpshufb[d][0][0][0]));
asm volatile("movdqa %0,%%xmm7" : : "m" (gfpshufb[d][0][1][0]));
asm volatile("movdqa %xmm6,%xmm14");
asm volatile("movdqa %xmm7,%xmm15");
asm volatile("pshufb %xmm4,%xmm6");
asm volatile("pshufb %xmm12,%xmm14");
asm volatile("pshufb %xmm5,%xmm7");
asm volatile("pshufb %xmm13,%xmm15");
asm volatile("pxor %xmm6,%xmm2");
asm volatile("pxor %xmm14,%xmm10");
asm volatile("pxor %xmm7,%xmm2");
asm volatile("pxor %xmm15,%xmm10");
}
asm volatile("movntdq %%xmm0,%0" : "=m" (p[i]));
asm volatile("movntdq %%xmm8,%0" : "=m" (p[i+16]));
asm volatile("movntdq %%xmm1,%0" : "=m" (q[i]));
asm volatile("movntdq %%xmm9,%0" : "=m" (q[i+16]));
asm volatile("movntdq %%xmm2,%0" : "=m" (r[i]));
asm volatile("movntdq %%xmm10,%0" : "=m" (r[i+16]));
}
asm volatile("sfence" : : : "memory");
}
#endif
/*
* RAIDQP 8bit C implementation
*
* Note that instead of a generic multiplicationt 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 on speed.
*/
void raidQP_int8(unsigned char** vbuf, unsigned data, unsigned size)
{
unsigned char* p;
unsigned char* q;
unsigned char* r;
unsigned char* s;
int d, l;
unsigned i;
uint8_t d0, s0, r0, q0, p0;
l = data - 1;
p = vbuf[data];
q = vbuf[data+1];
r = vbuf[data+2];
s = vbuf[data+3];
for(i=0;i<size;i+=1) {
s0 = r0 = q0 = p0 = 0;
for(d=l;d>=0;--d) {
d0 = v_8(vbuf[d][i]);
p0 ^= d0;
q0 ^= gfmul[d0][gfmatrix[1][d]];
r0 ^= gfmul[d0][gfmatrix[2][d]];
s0 ^= gfmul[d0][gfmatrix[3][d]];
}
v_8(p[i]) = p0;
v_8(q[i]) = q0;
v_8(r[i]) = r0;
v_8(s[i]) = s0;
}
}
#if defined(__i386__) || defined(__x86_64__)
/*
* RAIDQP SSSE3 implementation
*/
void raidQP_ssse3(unsigned char** vbuf, unsigned data, unsigned size)
{
unsigned char* p;
unsigned char* q;
unsigned char* r;
unsigned char* s;
int d, l;
unsigned i;
l = data - 1;
p = vbuf[data];
q = vbuf[data+1];
r = vbuf[data+2];
s = vbuf[data+3];
for(i=0;i<size;i+=16) {
asm volatile("pxor %xmm0,%xmm0");
asm volatile("pxor %xmm1,%xmm1");
asm volatile("pxor %xmm2,%xmm2");
asm volatile("pxor %xmm3,%xmm3");
for(d=l;d>=0;--d) {
asm volatile("movdqa %0,%%xmm7" : : "m" (gfconst16.poly[0]));
asm volatile("movdqa %0,%%xmm4" : : "m" (vbuf[d][i]));
asm volatile("pxor %xmm5,%xmm5");
asm volatile("pcmpgtb %xmm1,%xmm5");
asm volatile("paddb %xmm1,%xmm1");
asm volatile("pand %xmm7,%xmm5");
asm volatile("pxor %xmm5,%xmm1");
asm volatile("movdqa %0,%%xmm7" : : "m" (gfconst16.mask[0]));
asm volatile("pxor %xmm4,%xmm0");
asm volatile("pxor %xmm4,%xmm1");
asm volatile("movdqa %xmm4,%xmm5");
asm volatile("psraw $4,%xmm5");
asm volatile("pand %xmm7,%xmm4");
asm volatile("pand %xmm7,%xmm5");
asm volatile("movdqa %0,%%xmm6" : : "m" (gfpshufb[d][0][0][0]));
asm volatile("movdqa %0,%%xmm7" : : "m" (gfpshufb[d][0][1][0]));
asm volatile("pshufb %xmm4,%xmm6");
asm volatile("pshufb %xmm5,%xmm7");
asm volatile("pxor %xmm6,%xmm2");
asm volatile("pxor %xmm7,%xmm2");
asm volatile("movdqa %0,%%xmm6" : : "m" (gfpshufb[d][1][0][0]));
asm volatile("movdqa %0,%%xmm7" : : "m" (gfpshufb[d][1][1][0]));
asm volatile("pshufb %xmm4,%xmm6");
asm volatile("pshufb %xmm5,%xmm7");
asm volatile("pxor %xmm6,%xmm3");
asm volatile("pxor %xmm7,%xmm3");
}
asm volatile("movntdq %%xmm0,%0" : "=m" (p[i]));
asm volatile("movntdq %%xmm1,%0" : "=m" (q[i]));
asm volatile("movntdq %%xmm2,%0" : "=m" (r[i]));
asm volatile("movntdq %%xmm3,%0" : "=m" (s[i]));
}
asm volatile("sfence" : : : "memory");
}
#endif
#if defined(__x86_64__)
/*
* RAIDQP SSSE3 implementation
*
* Note that it uses 16 registers, meaning that x64 is required.
*/
void raidQP_ssse3ext(unsigned char** vbuf, unsigned data, unsigned size)
{
unsigned char* p;
unsigned char* q;
unsigned char* r;
unsigned char* s;
int d, l;
unsigned i;
l = data - 1;
p = vbuf[data];
q = vbuf[data+1];
r = vbuf[data+2];
s = vbuf[data+3];
for(i=0;i<size;i+=32) {
asm volatile("pxor %xmm0,%xmm0");
asm volatile("pxor %xmm1,%xmm1");
asm volatile("pxor %xmm2,%xmm2");
asm volatile("pxor %xmm3,%xmm3");
asm volatile("pxor %xmm8,%xmm8");
asm volatile("pxor %xmm9,%xmm9");
asm volatile("pxor %xmm10,%xmm10");
asm volatile("pxor %xmm11,%xmm11");
for(d=l;d>=0;--d) {
asm volatile("movdqa %0,%%xmm7" : : "m" (gfconst16.poly[0]));
asm volatile("movdqa %0,%%xmm15" : : "m" (gfconst16.mask[0]));
asm volatile("movdqa %0,%%xmm4" : : "m" (vbuf[d][i]));
asm volatile("movdqa %0,%%xmm12" : : "m" (vbuf[d][i+16]));
asm volatile("pxor %xmm5,%xmm5");
asm volatile("pxor %xmm13,%xmm13");
asm volatile("pcmpgtb %xmm1,%xmm5");
asm volatile("pcmpgtb %xmm9,%xmm13");
asm volatile("paddb %xmm1,%xmm1");
asm volatile("paddb %xmm9,%xmm9");
asm volatile("pand %xmm7,%xmm5");
asm volatile("pand %xmm7,%xmm13");
asm volatile("pxor %xmm5,%xmm1");
asm volatile("pxor %xmm13,%xmm9");
asm volatile("pxor %xmm4,%xmm0");
asm volatile("pxor %xmm4,%xmm1");
asm volatile("pxor %xmm12,%xmm8");
asm volatile("pxor %xmm12,%xmm9");
asm volatile("movdqa %xmm4,%xmm5");
asm volatile("movdqa %xmm12,%xmm13");
asm volatile("psraw $4,%xmm5");
asm volatile("psraw $4,%xmm13");
asm volatile("pand %xmm15,%xmm4");
asm volatile("pand %xmm15,%xmm12");
asm volatile("pand %xmm15,%xmm5");
asm volatile("pand %xmm15,%xmm13");
asm volatile("movdqa %0,%%xmm6" : : "m" (gfpshufb[d][0][0][0]));
asm volatile("movdqa %0,%%xmm7" : : "m" (gfpshufb[d][0][1][0]));
asm volatile("movdqa %xmm6,%xmm14");
asm volatile("movdqa %xmm7,%xmm15");
asm volatile("pshufb %xmm4,%xmm6");
asm volatile("pshufb %xmm12,%xmm14");
asm volatile("pshufb %xmm5,%xmm7");
asm volatile("pshufb %xmm13,%xmm15");
asm volatile("pxor %xmm6,%xmm2");
asm volatile("pxor %xmm14,%xmm10");
asm volatile("pxor %xmm7,%xmm2");
asm volatile("pxor %xmm15,%xmm10");
asm volatile("movdqa %0,%%xmm6" : : "m" (gfpshufb[d][1][0][0]));
asm volatile("movdqa %0,%%xmm7" : : "m" (gfpshufb[d][1][1][0]));
asm volatile("movdqa %xmm6,%xmm14");
asm volatile("movdqa %xmm7,%xmm15");
asm volatile("pshufb %xmm4,%xmm6");
asm volatile("pshufb %xmm12,%xmm14");
asm volatile("pshufb %xmm5,%xmm7");
asm volatile("pshufb %xmm13,%xmm15");
asm volatile("pxor %xmm6,%xmm3");
asm volatile("pxor %xmm14,%xmm11");
asm volatile("pxor %xmm7,%xmm3");
asm volatile("pxor %xmm15,%xmm11");
}
asm volatile("movntdq %%xmm0,%0" : "=m" (p[i]));
asm volatile("movntdq %%xmm8,%0" : "=m" (p[i+16]));
asm volatile("movntdq %%xmm1,%0" : "=m" (q[i]));
asm volatile("movntdq %%xmm9,%0" : "=m" (q[i+16]));
asm volatile("movntdq %%xmm2,%0" : "=m" (r[i]));
asm volatile("movntdq %%xmm10,%0" : "=m" (r[i+16]));
asm volatile("movntdq %%xmm3,%0" : "=m" (s[i]));
asm volatile("movntdq %%xmm11,%0" : "=m" (s[i+16]));
}
asm volatile("sfence" : : : "memory");
}
#endif
/*
* RAIDPP 8bit C implementation
*
* Note that instead of a generic multiplicationt 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 on speed.
*/
void raidPP_int8(unsigned char** vbuf, unsigned data, unsigned size)
{
unsigned char* p;
unsigned char* q;
unsigned char* r;
unsigned char* s;
unsigned char* t;
int d, l;
unsigned i;
uint8_t d0, t0, s0, r0, q0, p0;
l = data - 1;
p = vbuf[data];
q = vbuf[data+1];
r = vbuf[data+2];
s = vbuf[data+3];
t = vbuf[data+4];
for(i=0;i<size;i+=1) {
t0 = s0 = r0 = q0 = p0 = 0;
for(d=l;d>=0;--d) {
d0 = v_8(vbuf[d][i]);
p0 ^= d0;
q0 ^= gfmul[d0][gfmatrix[1][d]];
r0 ^= gfmul[d0][gfmatrix[2][d]];
s0 ^= gfmul[d0][gfmatrix[3][d]];
t0 ^= gfmul[d0][gfmatrix[4][d]];
}
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;
}
}
#if defined(__i386__) || defined(__x86_64__)
/*
* RAIDPP SSSE3 implementation
*/
#ifdef _WIN32
/* ensures that stack is aligned at 16 bytes because we allocate SSE registers in it */
__attribute__((force_align_arg_pointer))
#endif
void raidPP_ssse3(unsigned char** vbuf, unsigned data, unsigned size)
/* ensures that stack is aligned at 16 bytes because we allocate SSE registers in it */
{
unsigned char* p;
unsigned char* q;
unsigned char* r;
unsigned char* s;
unsigned char* t;
int d, l;
unsigned i;
unsigned char p0[16] __attribute__((aligned(16)));
l = data - 1;
p = vbuf[data];
q = vbuf[data+1];
r = vbuf[data+2];
s = vbuf[data+3];
t = vbuf[data+4];
for(i=0;i<size;i+=16) {
asm volatile("pxor %xmm0,%xmm0");
asm volatile("pxor %xmm1,%xmm1");
asm volatile("pxor %xmm2,%xmm2");
asm volatile("pxor %xmm3,%xmm3");
asm volatile("movdqa %%xmm0,%0" : "=m" (p0[0]));
for(d=l;d>=0;--d) {
asm volatile("movdqa %0,%%xmm4" : : "m" (vbuf[d][i]));
asm volatile("movdqa %0,%%xmm6" : : "m" (p0[0]));
asm volatile("movdqa %0,%%xmm7" : : "m" (gfconst16.poly[0]));
asm volatile("pxor %xmm5,%xmm5");
asm volatile("pcmpgtb %xmm0,%xmm5");
asm volatile("paddb %xmm0,%xmm0");
asm volatile("pand %xmm7,%xmm5");
asm volatile("pxor %xmm5,%xmm0");
asm volatile("pxor %xmm4,%xmm0");
asm volatile("pxor %xmm4,%xmm6");
asm volatile("movdqa %%xmm6,%0" : "=m" (p0));
asm volatile("movdqa %0,%%xmm7" : : "m" (gfconst16.mask[0]));
asm volatile("movdqa %xmm4,%xmm5");
asm volatile("psraw $4,%xmm5");
asm volatile("pand %xmm7,%xmm4");
asm volatile("pand %xmm7,%xmm5");
asm volatile("movdqa %0,%%xmm6" : : "m" (gfpshufb[d][0][0][0]));
asm volatile("movdqa %0,%%xmm7" : : "m" (gfpshufb[d][0][1][0]));
asm volatile("pshufb %xmm4,%xmm6");
asm volatile("pshufb %xmm5,%xmm7");
asm volatile("pxor %xmm6,%xmm1");
asm volatile("pxor %xmm7,%xmm1");
asm volatile("movdqa %0,%%xmm6" : : "m" (gfpshufb[d][1][0][0]));
asm volatile("movdqa %0,%%xmm7" : : "m" (gfpshufb[d][1][1][0]));
asm volatile("pshufb %xmm4,%xmm6");
asm volatile("pshufb %xmm5,%xmm7");
asm volatile("pxor %xmm6,%xmm2");
asm volatile("pxor %xmm7,%xmm2");
asm volatile("movdqa %0,%%xmm6" : : "m" (gfpshufb[d][2][0][0]));
asm volatile("movdqa %0,%%xmm7" : : "m" (gfpshufb[d][2][1][0]));
asm volatile("pshufb %xmm4,%xmm6");
asm volatile("pshufb %xmm5,%xmm7");
asm volatile("pxor %xmm6,%xmm3");
asm volatile("pxor %xmm7,%xmm3");
}
asm volatile("movdqa %0,%%xmm6" : : "m" (p0[0]));
asm volatile("movntdq %%xmm6,%0" : "=m" (p[i]));
asm volatile("movntdq %%xmm0,%0" : "=m" (q[i]));
asm volatile("movntdq %%xmm1,%0" : "=m" (r[i]));
asm volatile("movntdq %%xmm2,%0" : "=m" (s[i]));
asm volatile("movntdq %%xmm3,%0" : "=m" (t[i]));
}
asm volatile("sfence" : : : "memory");
}
#endif
#if defined(__x86_64__)
/*
* RAIDPP SSSE3 implementation
*
* Note that it uses 16 registers, meaning that x64 is required.
*/
void raidPP_ssse3ext(unsigned char** vbuf, unsigned data, unsigned size)
{
unsigned char* p;
unsigned char* q;
unsigned char* r;
unsigned char* s;
unsigned char* t;
int d, l;
unsigned i;
l = data - 1;
p = vbuf[data];
q = vbuf[data+1];
r = vbuf[data+2];
s = vbuf[data+3];
t = vbuf[data+4];
asm volatile("movdqa %0,%%xmm14" : : "m" (gfconst16.poly[0]));
asm volatile("movdqa %0,%%xmm15" : : "m" (gfconst16.mask[0]));
for(i=0;i<size;i+=16) {
asm volatile("pxor %xmm0,%xmm0");
asm volatile("pxor %xmm1,%xmm1");
asm volatile("pxor %xmm2,%xmm2");
asm volatile("pxor %xmm3,%xmm3");
asm volatile("pxor %xmm4,%xmm4");
for(d=l;d>=0;--d) {
asm volatile("movdqa %0,%%xmm10" : : "m" (vbuf[d][i]));
asm volatile("pxor %xmm11,%xmm11");
asm volatile("pcmpgtb %xmm1,%xmm11");
asm volatile("paddb %xmm1,%xmm1");
asm volatile("pand %xmm14,%xmm11");
asm volatile("pxor %xmm11,%xmm1");
asm volatile("pxor %xmm10,%xmm0");
asm volatile("pxor %xmm10,%xmm1");
asm volatile("movdqa %xmm10,%xmm11");
asm volatile("psraw $4,%xmm11");
asm volatile("pand %xmm15,%xmm10");
asm volatile("pand %xmm15,%xmm11");
asm volatile("movdqa %0,%%xmm12" : : "m" (gfpshufb[d][0][0][0]));
asm volatile("movdqa %0,%%xmm13" : : "m" (gfpshufb[d][0][1][0]));
asm volatile("pshufb %xmm10,%xmm12");
asm volatile("pshufb %xmm11,%xmm13");
asm volatile("pxor %xmm12,%xmm2");
asm volatile("pxor %xmm13,%xmm2");
asm volatile("movdqa %0,%%xmm12" : : "m" (gfpshufb[d][1][0][0]));
asm volatile("movdqa %0,%%xmm13" : : "m" (gfpshufb[d][1][1][0]));
asm volatile("pshufb %xmm10,%xmm12");
asm volatile("pshufb %xmm11,%xmm13");
asm volatile("pxor %xmm12,%xmm3");
asm volatile("pxor %xmm13,%xmm3");
asm volatile("movdqa %0,%%xmm12" : : "m" (gfpshufb[d][2][0][0]));
asm volatile("movdqa %0,%%xmm13" : : "m" (gfpshufb[d][2][1][0]));
asm volatile("pshufb %xmm10,%xmm12");
asm volatile("pshufb %xmm11,%xmm13");
asm volatile("pxor %xmm12,%xmm4");
asm volatile("pxor %xmm13,%xmm4");
}
asm volatile("movntdq %%xmm0,%0" : "=m" (p[i]));
asm volatile("movntdq %%xmm1,%0" : "=m" (q[i]));
asm volatile("movntdq %%xmm2,%0" : "=m" (r[i]));
asm volatile("movntdq %%xmm3,%0" : "=m" (s[i]));
asm volatile("movntdq %%xmm4,%0" : "=m" (t[i]));
}
asm volatile("sfence" : : : "memory");
}
#endif
/*
* RAIDHP 8bit C implementation
*
* Note that instead of a generic multiplicationt 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 on speed.
*/
void raidHP_int8(unsigned char** vbuf, unsigned data, unsigned size)
{
unsigned char* p;
unsigned char* q;
unsigned char* r;
unsigned char* s;
unsigned char* t;
unsigned char* u;
int d, l;
unsigned i;
uint8_t d0, u0, t0, s0, r0, q0, p0;
l = data - 1;
p = vbuf[data];
q = vbuf[data+1];
r = vbuf[data+2];
s = vbuf[data+3];
t = vbuf[data+4];
u = vbuf[data+5];
for(i=0;i<size;i+=1) {
u0 = t0 = s0 = r0 = q0 = p0 = 0;
for(d=l;d>=0;--d) {
d0 = v_8(vbuf[d][i]);
p0 ^= d0;
q0 ^= gfmul[d0][gfmatrix[1][d]];
r0 ^= gfmul[d0][gfmatrix[2][d]];
s0 ^= gfmul[d0][gfmatrix[3][d]];
t0 ^= gfmul[d0][gfmatrix[4][d]];
u0 ^= gfmul[d0][gfmatrix[5][d]];
}
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;
}
}
#if defined(__i386__) || defined(__x86_64__)
/*
* RAIDHP SSSE3 implementation
*/
#ifdef _WIN32
/* ensures that stack is aligned at 16 bytes because we allocate SSE registers in it */
__attribute__((force_align_arg_pointer))
#endif
void raidHP_ssse3(unsigned char** vbuf, unsigned data, unsigned size)
{
unsigned char* p;
unsigned char* q;
unsigned char* r;
unsigned char* s;
unsigned char* t;
unsigned char* u;
int d, l;
unsigned i;
unsigned char p0[16] __attribute__((aligned(16)));
unsigned char q0[16] __attribute__((aligned(16)));
l = data - 1;
p = vbuf[data];
q = vbuf[data+1];
r = vbuf[data+2];
s = vbuf[data+3];
t = vbuf[data+4];
u = vbuf[data+5];
for(i=0;i<size;i+=16) {
asm volatile("pxor %xmm0,%xmm0");
asm volatile("pxor %xmm1,%xmm1");
asm volatile("pxor %xmm2,%xmm2");
asm volatile("pxor %xmm3,%xmm3");
asm volatile("movdqa %%xmm0,%0" : "=m" (p0[0]));
asm volatile("movdqa %%xmm0,%0" : "=m" (q0[0]));
for(d=l;d>=0;--d) {
asm volatile("movdqa %0,%%xmm5" : : "m" (p0[0]));
asm volatile("movdqa %0,%%xmm6" : : "m" (q0[0]));
asm volatile("movdqa %0,%%xmm7" : : "m" (gfconst16.poly[0]));
asm volatile("pxor %xmm4,%xmm4");
asm volatile("pcmpgtb %xmm6,%xmm4");
asm volatile("paddb %xmm6,%xmm6");
asm volatile("pand %xmm7,%xmm4");
asm volatile("pxor %xmm4,%xmm6");
asm volatile("movdqa %0,%%xmm4" : : "m" (vbuf[d][i]));
asm volatile("pxor %xmm4,%xmm5");
asm volatile("pxor %xmm4,%xmm6");
asm volatile("movdqa %%xmm5,%0" : "=m" (p0));
asm volatile("movdqa %%xmm6,%0" : "=m" (q0));
asm volatile("movdqa %0,%%xmm7" : : "m" (gfconst16.mask[0]));
asm volatile("movdqa %xmm4,%xmm5");
asm volatile("psraw $4,%xmm5");
asm volatile("pand %xmm7,%xmm4");
asm volatile("pand %xmm7,%xmm5");
asm volatile("movdqa %0,%%xmm6" : : "m" (gfpshufb[d][0][0][0]));
asm volatile("movdqa %0,%%xmm7" : : "m" (gfpshufb[d][0][1][0]));
asm volatile("pshufb %xmm4,%xmm6");
asm volatile("pshufb %xmm5,%xmm7");
asm volatile("pxor %xmm6,%xmm0");
asm volatile("pxor %xmm7,%xmm0");
asm volatile("movdqa %0,%%xmm6" : : "m" (gfpshufb[d][1][0][0]));
asm volatile("movdqa %0,%%xmm7" : : "m" (gfpshufb[d][1][1][0]));
asm volatile("pshufb %xmm4,%xmm6");
asm volatile("pshufb %xmm5,%xmm7");
asm volatile("pxor %xmm6,%xmm1");
asm volatile("pxor %xmm7,%xmm1");
asm volatile("movdqa %0,%%xmm6" : : "m" (gfpshufb[d][2][0][0]));
asm volatile("movdqa %0,%%xmm7" : : "m" (gfpshufb[d][2][1][0]));
asm volatile("pshufb %xmm4,%xmm6");
asm volatile("pshufb %xmm5,%xmm7");
asm volatile("pxor %xmm6,%xmm2");
asm volatile("pxor %xmm7,%xmm2");
asm volatile("movdqa %0,%%xmm6" : : "m" (gfpshufb[d][3][0][0]));
asm volatile("movdqa %0,%%xmm7" : : "m" (gfpshufb[d][3][1][0]));
asm volatile("pshufb %xmm4,%xmm6");
asm volatile("pshufb %xmm5,%xmm7");
asm volatile("pxor %xmm6,%xmm3");
asm volatile("pxor %xmm7,%xmm3");
}
asm volatile("movdqa %0,%%xmm5" : : "m" (p0[0]));
asm volatile("movdqa %0,%%xmm6" : : "m" (q0[0]));
asm volatile("movntdq %%xmm5,%0" : "=m" (p[i]));
asm volatile("movntdq %%xmm6,%0" : "=m" (q[i]));
asm volatile("movntdq %%xmm0,%0" : "=m" (r[i]));
asm volatile("movntdq %%xmm1,%0" : "=m" (s[i]));
asm volatile("movntdq %%xmm2,%0" : "=m" (t[i]));
asm volatile("movntdq %%xmm3,%0" : "=m" (u[i]));
}
asm volatile("sfence" : : : "memory");
}
#endif
#if defined(__x86_64__)
/*
* RAIDHP SSSE3 implementation
*
* Note that it uses 16 registers, meaning that x64 is required.
*/
void raidHP_ssse3ext(unsigned char** vbuf, unsigned data, unsigned size)
{
unsigned char* p;
unsigned char* q;
unsigned char* r;
unsigned char* s;
unsigned char* t;
unsigned char* u;
int d, l;
unsigned i;
l = data - 1;
p = vbuf[data];
q = vbuf[data+1];
r = vbuf[data+2];
s = vbuf[data+3];
t = vbuf[data+4];
u = vbuf[data+5];
asm volatile("movdqa %0,%%xmm14" : : "m" (gfconst16.poly[0]));
asm volatile("movdqa %0,%%xmm15" : : "m" (gfconst16.mask[0]));
for(i=0;i<size;i+=16) {
asm volatile("pxor %xmm0,%xmm0");
asm volatile("pxor %xmm1,%xmm1");
asm volatile("pxor %xmm2,%xmm2");
asm volatile("pxor %xmm3,%xmm3");
asm volatile("pxor %xmm4,%xmm4");
asm volatile("pxor %xmm5,%xmm5");
for(d=l;d>=0;--d) {
asm volatile("movdqa %0,%%xmm10" : : "m" (vbuf[d][i]));
asm volatile("pxor %xmm11,%xmm11");
asm volatile("pcmpgtb %xmm1,%xmm11");
asm volatile("paddb %xmm1,%xmm1");
asm volatile("pand %xmm14,%xmm11");
asm volatile("pxor %xmm11,%xmm1");
asm volatile("pxor %xmm10,%xmm0");
asm volatile("pxor %xmm10,%xmm1");
asm volatile("movdqa %xmm10,%xmm11");
asm volatile("psraw $4,%xmm11");
asm volatile("pand %xmm15,%xmm10");
asm volatile("pand %xmm15,%xmm11");
asm volatile("movdqa %0,%%xmm12" : : "m" (gfpshufb[d][0][0][0]));
asm volatile("movdqa %0,%%xmm13" : : "m" (gfpshufb[d][0][1][0]));
asm volatile("pshufb %xmm10,%xmm12");
asm volatile("pshufb %xmm11,%xmm13");
asm volatile("pxor %xmm12,%xmm2");
asm volatile("pxor %xmm13,%xmm2");
asm volatile("movdqa %0,%%xmm12" : : "m" (gfpshufb[d][1][0][0]));
asm volatile("movdqa %0,%%xmm13" : : "m" (gfpshufb[d][1][1][0]));
asm volatile("pshufb %xmm10,%xmm12");
asm volatile("pshufb %xmm11,%xmm13");
asm volatile("pxor %xmm12,%xmm3");
asm volatile("pxor %xmm13,%xmm3");
asm volatile("movdqa %0,%%xmm12" : : "m" (gfpshufb[d][2][0][0]));
asm volatile("movdqa %0,%%xmm13" : : "m" (gfpshufb[d][2][1][0]));
asm volatile("pshufb %xmm10,%xmm12");
asm volatile("pshufb %xmm11,%xmm13");
asm volatile("pxor %xmm12,%xmm4");
asm volatile("pxor %xmm13,%xmm4");
asm volatile("movdqa %0,%%xmm12" : : "m" (gfpshufb[d][3][0][0]));
asm volatile("movdqa %0,%%xmm13" : : "m" (gfpshufb[d][3][1][0]));
asm volatile("pshufb %xmm10,%xmm12");
asm volatile("pshufb %xmm11,%xmm13");
asm volatile("pxor %xmm12,%xmm5");
asm volatile("pxor %xmm13,%xmm5");
}
asm volatile("movntdq %%xmm0,%0" : "=m" (p[i]));
asm volatile("movntdq %%xmm1,%0" : "=m" (q[i]));
asm volatile("movntdq %%xmm2,%0" : "=m" (r[i]));
asm volatile("movntdq %%xmm3,%0" : "=m" (s[i]));
asm volatile("movntdq %%xmm4,%0" : "=m" (t[i]));
asm volatile("movntdq %%xmm5,%0" : "=m" (u[i]));
}
asm volatile("sfence" : : : "memory");
}
#endif
/****************************************************************************/
/* parity generation */
/* internal forwarder */
static void (*raid5_gen)(unsigned char** vbuf, unsigned data, unsigned size);
static void (*raid6_gen)(unsigned char** vbuf, unsigned data, unsigned size);
static void (*raidTP_gen)(unsigned char** vbuf, unsigned data, unsigned size);
static void (*raidQP_gen)(unsigned char** vbuf, unsigned data, unsigned size);
static void (*raidPP_gen)(unsigned char** vbuf, unsigned data, unsigned size);
static void (*raidHP_gen)(unsigned char** vbuf, unsigned data, unsigned size);
void raid_gen(unsigned level, unsigned char** vbuf, unsigned data, unsigned size)
{
switch (level) {
case 1 : raid5_gen(vbuf, data, size); break;
case 2 : raid6_gen(vbuf, data, size); break;
case 3 : raidTP_gen(vbuf, data, size); break;
case 4 : raidQP_gen(vbuf, data, size); break;
case 5 : raidPP_gen(vbuf, data, size); break;
case 6 : raidHP_gen(vbuf, data, size); break;
default:
fprintf(stderr, "Invalid raid gen level\n");
exit(EXIT_FAILURE);
}
}
/****************************************************************************/
/* recovering */
/**
* GF a*b.
*/
static inline unsigned char mul(unsigned char a, unsigned char b)
{
return gfmul[a][b];
}
/**
* GF 1/a.
* Not defined for a == 0.
*/
static inline unsigned char inv(unsigned char v)
{
if (v == 0) {
fprintf(stderr, "GF division by zero\n");
exit(EXIT_FAILURE);
}
return gfinv[v];
}
/**
* GF 2^a.
*/
static inline unsigned char pow2(int v)
{
if (v < 0 || v > 254) {
fprintf(stderr, "GF invalid exponent\n");
exit(EXIT_FAILURE);
}
return gfexp2[v];
}
/**
* Gets the multiplication table for a specified value.
*/
static inline const unsigned char* table(unsigned char v)
{
return gfmul[v];
}
/**
* Computes the parity without the missing data blocks
* and store it in the buffers of such data blocks.
*/
static void raid_delta_1data(const int* d, const int* e, unsigned char** vbuf, unsigned data, unsigned char* zero, unsigned size)
{
unsigned char* p;
unsigned char* pa;
/* parity buffer */
p = vbuf[data+e[0]];
/* missing data blcks */
pa = vbuf[d[0]];
/* set at zero the missing data blocks */
vbuf[d[0]] = zero;
/* compute only for the level we really need */
vbuf[data+e[0]] = pa;
/* compute the parity */
raid_gen(e[0] + 1, vbuf, data, size);
/* restore as before */
vbuf[d[0]] = pa;
vbuf[data+e[0]] = p;
}
/**
* Computes the parity without the missing data blocks
* and store it in the buffers of such data blocks.
*/
static void raid_delta_2data(const int* d, const int* e, unsigned char** vbuf, unsigned data, unsigned char* zero, unsigned size)
{
unsigned char* p;
unsigned char* q;
unsigned char* pa;
unsigned char* qa;
/* parity buffer */
p = vbuf[data+e[0]];
q = vbuf[data+e[1]];
/* missing data blocks */
pa = vbuf[d[0]];
qa = vbuf[d[1]];
/* set at zero the missing data blocks */
vbuf[d[0]] = zero;
vbuf[d[1]] = zero;
/* compute the parity over the missing data blocks */
vbuf[data+e[0]] = pa;
vbuf[data+e[1]] = qa;
/* compute only for the level we really need */
raid_gen(e[1] + 1, vbuf, data, size);
/* restore as before */
vbuf[d[0]] = pa;
vbuf[d[1]] = qa;
vbuf[data+e[0]] = p;
vbuf[data+e[1]] = q;
}
/**
* Computes the parity without the missing data blocks
* and store it in the buffers of such data blocks.
*/
static void raid_delta_3data(const int* d, const int* e, unsigned char** vbuf, unsigned data, unsigned char* zero, unsigned size)
{
unsigned char* p;
unsigned char* q;
unsigned char* r;
unsigned char* pa;
unsigned char* qa;
unsigned char* ra;
/* parity buffer */
p = vbuf[data+e[0]];
q = vbuf[data+e[1]];
r = vbuf[data+e[2]];
/* missing data blocks */
pa = vbuf[d[0]];
qa = vbuf[d[1]];
ra = vbuf[d[2]];
/* set at zero the missing data blocks */
vbuf[d[0]] = zero;
vbuf[d[1]] = zero;
vbuf[d[2]] = zero;
/* compute the parity over the missing data blocks */
vbuf[data+e[0]] = pa;
vbuf[data+e[1]] = qa;
vbuf[data+e[2]] = ra;
/* compute only for the level we really need */
raid_gen(e[2] + 1, vbuf, data, size);
/* restore as before */
vbuf[d[0]] = pa;
vbuf[d[1]] = qa;
vbuf[d[2]] = ra;
vbuf[data+e[0]] = p;
vbuf[data+e[1]] = q;
vbuf[data+e[2]] = r;
}
/**
* Computes the parity without the missing data blocks
* and store it in the buffers of such data blocks.
*/
static void raid_delta_4data(const int* d, const int* e, unsigned char** vbuf, unsigned data, unsigned char* zero, unsigned size)
{
unsigned char* p;
unsigned char* q;
unsigned char* r;
unsigned char* s;
unsigned char* pa;
unsigned char* qa;
unsigned char* ra;
unsigned char* sa;
/* parity buffer */
p = vbuf[data+e[0]];
q = vbuf[data+e[1]];
r = vbuf[data+e[2]];
s = vbuf[data+e[3]];
/* missing data blocks */
pa = vbuf[d[0]];
qa = vbuf[d[1]];
ra = vbuf[d[2]];
sa = vbuf[d[3]];
/* set at zero the missing data blocks */
vbuf[d[0]] = zero;
vbuf[d[1]] = zero;
vbuf[d[2]] = zero;
vbuf[d[3]] = zero;
/* compute the parity over the missing data blocks */
vbuf[data+e[0]] = pa;
vbuf[data+e[1]] = qa;
vbuf[data+e[2]] = ra;
vbuf[data+e[3]] = sa;
/* compute only for the level we really need */
raid_gen(e[3] + 1, vbuf, data, size);
/* restore as before */
vbuf[d[0]] = pa;
vbuf[d[1]] = qa;
vbuf[d[2]] = ra;
vbuf[d[3]] = sa;
vbuf[data+e[0]] = p;
vbuf[data+e[1]] = q;
vbuf[data+e[2]] = r;
vbuf[data+e[3]] = s;
}
/**
* Computes the parity without the missing data blocks
* and store it in the buffers of such data blocks.
*/
static void raid_delta_5data(const int* d, const int* e, unsigned char** vbuf, unsigned data, unsigned char* zero, unsigned size)
{
unsigned char* p;
unsigned char* q;
unsigned char* r;
unsigned char* s;
unsigned char* t;
unsigned char* pa;
unsigned char* qa;
unsigned char* ra;
unsigned char* sa;
unsigned char* ta;
/* parity buffer */
p = vbuf[data+e[0]];
q = vbuf[data+e[1]];
r = vbuf[data+e[2]];
s = vbuf[data+e[3]];
t = vbuf[data+e[4]];
/* missing data blocks */
pa = vbuf[d[0]];
qa = vbuf[d[1]];
ra = vbuf[d[2]];
sa = vbuf[d[3]];
ta = vbuf[d[4]];
/* set at zero the missing data blocks */
vbuf[d[0]] = zero;
vbuf[d[1]] = zero;
vbuf[d[2]] = zero;
vbuf[d[3]] = zero;
vbuf[d[4]] = zero;
/* compute the parity over the missing data blocks */
vbuf[data+e[0]] = pa;
vbuf[data+e[1]] = qa;
vbuf[data+e[2]] = ra;
vbuf[data+e[3]] = sa;
vbuf[data+e[4]] = ta;
/* compute only for the level we really need */
raid_gen(e[4] + 1, vbuf, data, size);
/* restore as before */
vbuf[d[0]] = pa;
vbuf[d[1]] = qa;
vbuf[d[2]] = ra;
vbuf[d[3]] = sa;
vbuf[d[4]] = ta;
vbuf[data+e[0]] = p;
vbuf[data+e[1]] = q;
vbuf[data+e[2]] = r;
vbuf[data+e[3]] = s;
vbuf[data+e[4]] = t;
}
/**
* Computes the parity without the missing data blocks
* and store it in the buffers of such data blocks.
*/
static void raid_delta_6data(const int* d, const int* e, unsigned char** vbuf, unsigned data, unsigned char* zero, unsigned size)
{
unsigned char* p;
unsigned char* q;
unsigned char* r;
unsigned char* s;
unsigned char* t;
unsigned char* u;
unsigned char* pa;
unsigned char* qa;
unsigned char* ra;
unsigned char* sa;
unsigned char* ta;
unsigned char* ua;
/* parity buffer */
p = vbuf[data+e[0]];
q = vbuf[data+e[1]];
r = vbuf[data+e[2]];
s = vbuf[data+e[3]];
t = vbuf[data+e[4]];
u = vbuf[data+e[5]];
/* missing data blocks */
pa = vbuf[d[0]];
qa = vbuf[d[1]];
ra = vbuf[d[2]];
sa = vbuf[d[3]];
ta = vbuf[d[4]];
ua = vbuf[d[5]];
/* set at zero the missing data blocks */
vbuf[d[0]] = zero;
vbuf[d[1]] = zero;
vbuf[d[2]] = zero;
vbuf[d[3]] = zero;
vbuf[d[4]] = zero;
vbuf[d[5]] = zero;
/* compute the parity over the missing data blocks */
vbuf[data+e[0]] = pa;
vbuf[data+e[1]] = qa;
vbuf[data+e[2]] = ra;
vbuf[data+e[3]] = sa;
vbuf[data+e[4]] = ta;
vbuf[data+e[5]] = ua;
/* compute only for the level we really need */
raid_gen(e[5] + 1, vbuf, data, size);
/* restore as before */
vbuf[d[0]] = pa;
vbuf[d[1]] = qa;
vbuf[d[2]] = ra;
vbuf[d[3]] = sa;
vbuf[d[4]] = ta;
vbuf[d[5]] = ua;
vbuf[data+e[0]] = p;
vbuf[data+e[1]] = q;
vbuf[data+e[2]] = r;
vbuf[data+e[3]] = s;
vbuf[data+e[4]] = t;
vbuf[data+e[5]] = u;
}
/****************************************************************************/
/* specialized raid recovering */
/**
* Recover failure of one data block for RAID5.
*
* Starting from the equation:
*
* Pd = Dx
*
* and solving we get:
*
* Dx = Pd (this one is easy :D)
*/
static void raid5_recov_data(const int* d, unsigned char** vbuf, unsigned data, unsigned size)
{
unsigned char* p;
unsigned char* pa;
/* for RAID5 we can directly compute the mssing block */
/* and we don't need to use the zero buffer */
p = vbuf[data];
pa = vbuf[d[0]];
/* use the parity as missing data block */
vbuf[d[0]] = p;
/* compute the parity over the missing data block */
vbuf[data] = pa;
/* compute */
raid5_gen(vbuf, data, size);
/* restore as before */
vbuf[d[0]] = pa;
vbuf[data] = p;
}
/**
* Recover failure of two data blocks for RAID6.
*
* Starting from the equations:
*
* Pd = Dx + Dy
* Qd = 2^d[0] * Dx + 2^d[1] * Dy
*
* and solving we get:
*
* 1 2^(-d[0])
* Dy = ----------- * Pd + ----------- * Qd
* 2^(d[1]-d[0]) + 1 2^(d[1]-d[0]) + 1
*
* Dx = Dy + Pd
*
* with conditions:
*
* 2^d[0] != 0
* 2^(d[1]-d[0]) + 1 != 0
*
* That are always satisfied for any 0<=d[0]<d[1]<255.
*/
static void raid6_recov_2data(const int* d, const int* e, unsigned char** vbuf, unsigned data, unsigned char* zero, unsigned size)
{
unsigned i;
unsigned char* p;
unsigned char* pa;
unsigned char* q;
unsigned char* qa;
const unsigned char* T[2];
/* get multiplication tables */
T[0] = table( inv(pow2(d[1]-d[0]) ^ 1) );
T[1] = table( inv(pow2(d[0]) ^ pow2(d[1])) );
/* compute delta parity */
raid_delta_2data(d, e, vbuf, data, zero, size);
p = vbuf[data];
q = vbuf[data+1];
pa = vbuf[d[0]];
qa = vbuf[d[1]];
for(i=0;i<size;++i) {
/* delta */
unsigned char Pd = p[i] ^ pa[i];
unsigned char Qd = q[i] ^ qa[i];
/* reconstruct */
unsigned char Dy = T[0][Pd] ^ T[1][Qd];
unsigned char Dx = Pd ^ Dy;
/* set */
pa[i] = Dx;
qa[i] = Dy;
}
}
/****************************************************************************/
/* generic matrix recovering */
/**
* Gets the generator matrix coefficient for parity 'p' and disk 'd'.
*/
static unsigned char A(unsigned p, unsigned d)
{
return gfmatrix[p][d];
}
/**
* Inverts the square matrix M of size nxn into V.
* We use Gauss elimination to invert.
*/
static void invert(unsigned char* M, unsigned char* V, unsigned n)
{
unsigned i,j,k;
/* set the identity matrix in V */
for(i=0;i<n;++i) {
for(j=0;j<n;++j) {
V[i*n+j] = i == j;
}
}
/* for each element in the diagonal */
for(k=0;k<n;++k) {
unsigned char f;
/* if the diagonal element is 0 */
if (M[k*n+k] == 0) {
/* find the next row with element at the same position not 0 */
for(i=k+1;i<n;++i)
if (M[i*n+k] != 0)
break;
/* if not found, the matrix is singular */
if (i == n) {
fprintf(stderr, "GF inversion of a singular matrix\n");
exit(EXIT_FAILURE);
}
/* sum the row at the present one to make the diagonal element different than 0 */
/* here usually the two rows are swapped, but summing is also ok */
for(j=0;j<n;++j) {
M[k*n+j] ^= M[i*n+j];
V[k*n+j] ^= V[i*n+j];
}
}
/* make the diagonal element to be 1 */
f = inv(M[k*n+k]);
for(j=0;j<n;++j) {
M[k*n+j] = mul(f, M[k*n+j]);
V[k*n+j] = mul(f, V[k*n+j]);
}
/* make all the elements over and under the diagonal to be 0 */
for(i=0;i<n;++i) {
if (i == k)
continue;
f = M[i*n+k];
for(j=0;j<n;++j) {
M[i*n+j] ^= mul(f, M[k*n+j]);
V[i*n+j] ^= mul(f, V[k*n+j]);
}
}
}
}
/**
* Recover failure of one data block d[0] using parity e[0] for any RAID level.
*
* Starting from the equation:
*
* Pd = A[e[0],d[0]] * Dx
*
* and solving we get:
*
* Dx = A[e[0],d[0]]^-1 * Pd
*/
static void raid_recov_1data(const int* d, const int* e, unsigned char** vbuf, unsigned data, unsigned char* zero, unsigned size)
{
unsigned i;
unsigned char* p;
unsigned char* pa;
const unsigned char* T[1]; /* P factor to compute Dx */
/* if it's RAID5 uses the dedicated and fasteT[ ][2]unction */
if (e[0] == 0) {
raid5_recov_data(d, vbuf, data, size);
return;
}
/* get multiplication tables */
T[0] = table( inv(A(e[0],d[0])) );
/* compute delta parity */
raid_delta_1data(d, e, vbuf, data, zero, size);
p = vbuf[data+e[0]];
pa = vbuf[d[0]];
for(i=0;i<size;++i) {
/* delta */
unsigned char Pd = p[i] ^ pa[i];
/* reconstruct */
unsigned char Dx = T[0][Pd];
/* set */
pa[i] = Dx;
}
}
/**
* Recover failure of two data blocks d[0],d[1] using parity e[0],e[1] for any RAID level.
*
* Starting from the equations:
*
* Pd = A[e[0],d[0]] * Dx + A[e[0],d[1]] * Dy
* Qd = A[e[1],d[0]] * Dx + A[e[1],d[1]] * Dy
*
* we solve inverting the coefficients matrix.
*/
static void raid_recov_2data(const int* d, const int* e, unsigned char** vbuf, unsigned data, unsigned char* zero, unsigned size)
{
unsigned char* p;
unsigned char* pa;
unsigned char* q;
unsigned char* qa;
const unsigned N = 2;
const unsigned char* T[N][N];
unsigned char G[N*N];
unsigned char V[N*N];
unsigned i, j;
/* if it's RAID6 uses the dedicated and fasteT[ ][2]unction */
if (e[0] == 0 && e[1] == 1) {
raid6_recov_2data(d, e, vbuf, data, zero, size);
return;
}
/* setup the coefficients matrix */
for(i=0;i<N;++i) {
for(j=0;j<N;++j) {
G[i*N+j] = A(e[i],d[j]);
}
}
/* invert it to solve the system of linear equations */
invert(G, V, N);
/* get multiplication tables */
for(i=0;i<N;++i) {
for(j=0;j<N;++j) {
T[i][j] = table( V[i*N+j] );
}
}
/* compute delta parity */
raid_delta_2data(d, e, vbuf, data, zero, size);
p = vbuf[data+e[0]];
q = vbuf[data+e[1]];
pa = vbuf[d[0]];
qa = vbuf[d[1]];
for(i=0;i<size;++i) {
/* delta */
unsigned char Pd = p[i] ^ pa[i];
unsigned char Qd = q[i] ^ qa[i];
/* reconstruct */
unsigned char Dx = T[0][0][Pd] ^ T[0][1][Qd];
unsigned char Dy = T[1][0][Pd] ^ T[1][1][Qd];
/* set */
pa[i] = Dx;
qa[i] = Dy;
}
}
/**
* Recover failure of three data blocks d[0],d[1],d[2] using parity e[0],e[1],e[2] for any RAID level.
*
* Starting from the equations:
*
* Pd = A[e[0],d[0]] * Dx + A[e[0],d[1]] * Dy + A[e[0],d[2]] * Dz
* Qd = A[e[1],d[0]] * Dx + A[e[1],d[1]] * Dy + A[e[1],d[2]] * Dz
* Rd = A[e[2],d[0]] * Dx + A[e[2],d[1]] * Dy + A[e[2],d[2]] * Dz
*
* we solve inverting the coefficients matrix.
*/
static void raid_recov_3data(const int* d, const int* e, unsigned char** vbuf, unsigned data, unsigned char* zero, unsigned size)
{
unsigned char* p;
unsigned char* pa;
unsigned char* q;
unsigned char* qa;
unsigned char* r;
unsigned char* ra;
const unsigned N = 3;
const unsigned char* T[N][N];
unsigned char G[N*N];
unsigned char V[N*N];
unsigned i, j;
/* setup the coefficients matrix */
for(i=0;i<N;++i) {
for(j=0;j<N;++j) {
G[i*N+j] = A(e[i],d[j]);
}
}
/* invert it to solve the system of linear equations */
invert(G, V, N);
/* get multiplication tables */
for(i=0;i<N;++i) {
for(j=0;j<N;++j) {
T[i][j] = table( V[i*N+j] );
}
}
/* compute delta parity */
raid_delta_3data(d, e, vbuf, data, zero, size);
p = vbuf[data+e[0]];
q = vbuf[data+e[1]];
r = vbuf[data+e[2]];
pa = vbuf[d[0]];
qa = vbuf[d[1]];
ra = vbuf[d[2]];
for(i=0;i<size;++i) {
/* delta */
unsigned char Pd = p[i] ^ pa[i];
unsigned char Qd = q[i] ^ qa[i];
unsigned char Rd = r[i] ^ ra[i];
/* reconstruct */
unsigned char Dx = T[0][0][Pd] ^ T[0][1][Qd] ^ T[0][2][Rd];
unsigned char Dy = T[1][0][Pd] ^ T[1][1][Qd] ^ T[1][2][Rd];
unsigned char Dz = T[2][0][Pd] ^ T[2][1][Qd] ^ T[2][2][Rd];
/* set */
pa[i] = Dx;
qa[i] = Dy;
ra[i] = Dz;
}
}
/**
* Recover failure of four data blocks d[0],d[1],d[2],d[3] using parity e[0],e[1],e[2],e[3] for any RAID level.
*
* Starting from the equations:
*
* Pd = A[e[0],d[0]] * Dx + A[e[0],d[1]] * Dy + A[e[0],d[2]] * Dz + A[e[0],d[3]] * Dh
* Qd = A[e[1],d[0]] * Dx + A[e[1],d[1]] * Dy + A[e[1],d[2]] * Dz + A[e[1],d[3]] * Dh
* Rd = A[e[2],d[0]] * Dx + A[e[2],d[1]] * Dy + A[e[2],d[2]] * Dz + A[e[2],d[3]] * Dh
* Sd = A[e[3],d[0]] * Dx + A[e[3],d[1]] * Dy + A[e[3],d[2]] * Dz + A[e[3],d[3]] * Dh
*
* we solve inverting the coefficients matrix.
*/
static void raid_recov_4data(const int* d, const int* e, unsigned char** vbuf, unsigned data, unsigned char* zero, unsigned size)
{
unsigned char* p;
unsigned char* pa;
unsigned char* q;
unsigned char* qa;
unsigned char* r;
unsigned char* ra;
unsigned char* s;
unsigned char* sa;
const unsigned N = 4;
const unsigned char* T[N][N];
unsigned char G[N*N];
unsigned char V[N*N];
unsigned i, j;
/* setup the coefficients matrix */
for(i=0;i<N;++i) {
for(j=0;j<N;++j) {
G[i*N+j] = A(e[i],d[j]);
}
}
/* invert it to solve the system of linear equations */
invert(G, V, N);
/* get multiplication tables */
for(i=0;i<N;++i) {
for(j=0;j<N;++j) {
T[i][j] = table( V[i*N+j] );
}
}
/* compute delta parity */
raid_delta_4data(d, e, vbuf, data, zero, size);
p = vbuf[data+e[0]];
q = vbuf[data+e[1]];
r = vbuf[data+e[2]];
s = vbuf[data+e[3]];
pa = vbuf[d[0]];
qa = vbuf[d[1]];
ra = vbuf[d[2]];
sa = vbuf[d[3]];
for(i=0;i<size;++i) {
/* delta */
unsigned char Pd = p[i] ^ pa[i];
unsigned char Qd = q[i] ^ qa[i];
unsigned char Rd = r[i] ^ ra[i];
unsigned char Sd = s[i] ^ sa[i];
/* reconstruct */
unsigned char Dx = T[0][0][Pd] ^ T[0][1][Qd] ^ T[0][2][Rd] ^ T[0][3][Sd];
unsigned char Dy = T[1][0][Pd] ^ T[1][1][Qd] ^ T[1][2][Rd] ^ T[1][3][Sd];
unsigned char Dz = T[2][0][Pd] ^ T[2][1][Qd] ^ T[2][2][Rd] ^ T[2][3][Sd];
unsigned char Dh = T[3][0][Pd] ^ T[3][1][Qd] ^ T[3][2][Rd] ^ T[3][3][Sd];
/* set */
pa[i] = Dx;
qa[i] = Dy;
ra[i] = Dz;
sa[i] = Dh;
}
}
/**
* Recover failure of five data blocks d[0],d[1],d[2],d[3],d[4] using parity e[0],e[1],e[2],e[3],e[4] for any RAID level.
*
* Starting from the equations:
*
* Pd = A[e[0],d[0]] * Dx + A[e[0],d[1]] * Dy + A[e[0],d[2]] * Dz + A[e[0],d[3]] * Dh + A[e[0],d[4]] * Dv
* Qd = A[e[1],d[0]] * Dx + A[e[1],d[1]] * Dy + A[e[1],d[2]] * Dz + A[e[1],d[3]] * Dh + A[e[1],d[4]] * Dv
* Rd = A[e[2],d[0]] * Dx + A[e[2],d[1]] * Dy + A[e[2],d[2]] * Dz + A[e[2],d[3]] * Dh + A[e[2],d[4]] * Dv
* Sd = A[e[3],d[0]] * Dx + A[e[3],d[1]] * Dy + A[e[3],d[2]] * Dz + A[e[3],d[3]] * Dh + A[e[3],d[4]] * Dv
* Td = A[e[4],d[0]] * Dx + A[e[4],d[1]] * Dy + A[e[4],d[2]] * Dz + A[e[4],d[3]] * Dh + A[e[4],d[4]] * Dv
*
* we solve inverting the coefficients matrix.
*/
static void raid_recov_5data(const int* d, const int* e, unsigned char** vbuf, unsigned data, unsigned char* zero, unsigned size)
{
unsigned char* p;
unsigned char* pa;
unsigned char* q;
unsigned char* qa;
unsigned char* r;
unsigned char* ra;
unsigned char* s;
unsigned char* sa;
unsigned char* t;
unsigned char* ta;
const unsigned N = 5;
const unsigned char* T[N][N];
unsigned char G[N*N];
unsigned char V[N*N];
unsigned i, j;
/* setup the coefficients matrix */
for(i=0;i<N;++i) {
for(j=0;j<N;++j) {
G[i*N+j] = A(e[i],d[j]);
}
}
/* invert it to solve the system of linear equations */
invert(G, V, N);
/* get multiplication tables */
for(i=0;i<N;++i) {
for(j=0;j<N;++j) {
T[i][j] = table( V[i*N+j] );
}
}
/* compute delta parity */
raid_delta_5data(d, e, vbuf, data, zero, size);
p = vbuf[data+e[0]];
q = vbuf[data+e[1]];
r = vbuf[data+e[2]];
s = vbuf[data+e[3]];
t = vbuf[data+e[4]];
pa = vbuf[d[0]];
qa = vbuf[d[1]];
ra = vbuf[d[2]];
sa = vbuf[d[3]];
ta = vbuf[d[4]];
for(i=0;i<size;++i) {
/* delta */
unsigned char Pd = p[i] ^ pa[i];
unsigned char Qd = q[i] ^ qa[i];
unsigned char Rd = r[i] ^ ra[i];
unsigned char Sd = s[i] ^ sa[i];
unsigned char Td = t[i] ^ ta[i];
/* reconstruct */
unsigned char Dx = T[0][0][Pd] ^ T[0][1][Qd] ^ T[0][2][Rd] ^ T[0][3][Sd] ^ T[0][4][Td];
unsigned char Dy = T[1][0][Pd] ^ T[1][1][Qd] ^ T[1][2][Rd] ^ T[1][3][Sd] ^ T[1][4][Td];
unsigned char Dz = T[2][0][Pd] ^ T[2][1][Qd] ^ T[2][2][Rd] ^ T[2][3][Sd] ^ T[2][4][Td];
unsigned char Dh = T[3][0][Pd] ^ T[3][1][Qd] ^ T[3][2][Rd] ^ T[3][3][Sd] ^ T[3][4][Td];
unsigned char Dv = T[4][0][Pd] ^ T[4][1][Qd] ^ T[4][2][Rd] ^ T[4][3][Sd] ^ T[4][4][Td];
/* set */
pa[i] = Dx;
qa[i] = Dy;
ra[i] = Dz;
sa[i] = Dh;
ta[i] = Dv;
}
}
/**
* Recover failure of six data blocks d[0],d[1],d[2],d[3],d[4],d[5] using parity e[0],e[1],e[2],e[3],e[4],e[5] for any RAID level.
*
* Starting from the equations:
*
* Pd = A[e[0],d[0]] * Dx + A[e[0],d[1]] * Dy + A[e[0],d[2]] * Dz + A[e[0],d[3]] * Dh + A[e[0],d[4]] * Dv + A[e[0],d[5]] * Dw
* Qd = A[e[1],d[0]] * Dx + A[e[1],d[1]] * Dy + A[e[1],d[2]] * Dz + A[e[1],d[3]] * Dh + A[e[1],d[4]] * Dv + A[e[1],d[5]] * Dw
* Rd = A[e[2],d[0]] * Dx + A[e[2],d[1]] * Dy + A[e[2],d[2]] * Dz + A[e[2],d[3]] * Dh + A[e[2],d[4]] * Dv + A[e[2],d[5]] * Dw
* Sd = A[e[3],d[0]] * Dx + A[e[3],d[1]] * Dy + A[e[3],d[2]] * Dz + A[e[3],d[3]] * Dh + A[e[3],d[4]] * Dv + A[e[3],d[5]] * Dw
* Td = A[e[4],d[0]] * Dx + A[e[4],d[1]] * Dy + A[e[4],d[2]] * Dz + A[e[4],d[3]] * Dh + A[e[4],d[4]] * Dv + A[e[4],d[5]] * Dw
* Ud = A[e[5],d[0]] * Dx + A[e[5],d[1]] * Dy + A[e[5],d[2]] * Dz + A[e[5],d[3]] * Dh + A[e[5],d[4]] * Dv + A[e[5],d[5]] * Dw
*
* we solve inverting the coefficients matrix.
*/
static void raid_recov_6data(const int* d, const int* e, unsigned char** vbuf, unsigned data, unsigned char* zero, unsigned size)
{
unsigned char* p;
unsigned char* pa;
unsigned char* q;
unsigned char* qa;
unsigned char* r;
unsigned char* ra;
unsigned char* s;
unsigned char* sa;
unsigned char* t;
unsigned char* ta;
unsigned char* u;
unsigned char* ua;
const unsigned N = 6;
const unsigned char* T[N][N];
unsigned char G[N*N];
unsigned char V[N*N];
unsigned i, j;
/* setup the coefficients matrix */
for(i=0;i<N;++i) {
for(j=0;j<N;++j) {
G[i*N+j] = A(e[i],d[j]);
}
}
/* invert it to solve the system of linear equations */
invert(G, V, N);
/* get multiplication tables */
for(i=0;i<N;++i) {
for(j=0;j<N;++j) {
T[i][j] = table( V[i*N+j] );
}
}
/* compute delta parity */
raid_delta_6data(d, e, vbuf, data, zero, size);
p = vbuf[data+e[0]];
q = vbuf[data+e[1]];
r = vbuf[data+e[2]];
s = vbuf[data+e[3]];
t = vbuf[data+e[4]];
u = vbuf[data+e[5]];
pa = vbuf[d[0]];
qa = vbuf[d[1]];
ra = vbuf[d[2]];
sa = vbuf[d[3]];
ta = vbuf[d[4]];
ua = vbuf[d[5]];
for(i=0;i<size;++i) {
/* delta */
unsigned char Pd = p[i] ^ pa[i];
unsigned char Qd = q[i] ^ qa[i];
unsigned char Rd = r[i] ^ ra[i];
unsigned char Sd = s[i] ^ sa[i];
unsigned char Td = t[i] ^ ta[i];
unsigned char Ud = u[i] ^ ua[i];
/* reconstruct */
unsigned char Dx = T[0][0][Pd] ^ T[0][1][Qd] ^ T[0][2][Rd] ^ T[0][3][Sd] ^ T[0][4][Td] ^ T[0][5][Ud];
unsigned char Dy = T[1][0][Pd] ^ T[1][1][Qd] ^ T[1][2][Rd] ^ T[1][3][Sd] ^ T[1][4][Td] ^ T[1][5][Ud];
unsigned char Dz = T[2][0][Pd] ^ T[2][1][Qd] ^ T[2][2][Rd] ^ T[2][3][Sd] ^ T[2][4][Td] ^ T[2][5][Ud];
unsigned char Dh = T[3][0][Pd] ^ T[3][1][Qd] ^ T[3][2][Rd] ^ T[3][3][Sd] ^ T[3][4][Td] ^ T[3][5][Ud];
unsigned char Dv = T[4][0][Pd] ^ T[4][1][Qd] ^ T[4][2][Rd] ^ T[4][3][Sd] ^ T[4][4][Td] ^ T[4][5][Ud];
unsigned char Dw = T[5][0][Pd] ^ T[5][1][Qd] ^ T[5][2][Rd] ^ T[5][3][Sd] ^ T[5][4][Td] ^ T[5][5][Ud];
/* set */
pa[i] = Dx;
qa[i] = Dy;
ra[i] = Dz;
sa[i] = Dh;
ta[i] = Dv;
ua[i] = Dw;
}
}
void raid_recov(unsigned level, const int* d, const int* e, unsigned char** vbuf, unsigned data, unsigned char* zero, unsigned size)
{
switch (level) {
case 1 :
raid_recov_1data(d, e, vbuf, data, zero, size);
break;
case 2 :
raid_recov_2data(d, e, vbuf, data, zero, size);
break;
case 3 :
raid_recov_3data(d, e, vbuf, data, zero, size);
break;
case 4 :
raid_recov_4data(d, e, vbuf, data, zero, size);
break;
case 5 :
raid_recov_5data(d, e, vbuf, data, zero, size);
break;
case 6 :
raid_recov_6data(d, e, vbuf, data, zero, size);
break;
default:
fprintf(stderr, "Invalid raid recov level\n");
exit(EXIT_FAILURE);
}
}
/****************************************************************************/
/* init/done */
void raid_init(void)
{
raidTP_gen = raidTP_int8;
raidQP_gen = raidQP_int8;
raidPP_gen = raidPP_int8;
raidHP_gen = raidHP_int8;
if (sizeof(void*) == 4) {
raid5_gen = raid5_int32;
raid6_gen = raid6_int32;
} else {
raid5_gen = raid5_int64;
raid6_gen = raid6_int64;
}
#if defined(__i386__) || defined(__x86_64__)
if (cpu_has_sse2()) {
raid5_gen = raid5_sse2;
#if defined(__x86_64__)
if (cpu_has_slowextendedreg()) {
raid6_gen = raid6_sse2;
} else {
raid6_gen = raid6_sse2ext;
}
#else
raid6_gen = raid6_sse2;
#endif
}
if (cpu_has_ssse3() && !cpu_has_slowpshufb()) {
#if defined(__x86_64__)
raidTP_gen = raidTP_ssse3ext;
raidQP_gen = raidQP_ssse3ext;
raidPP_gen = raidPP_ssse3ext;
raidHP_gen = raidHP_ssse3ext;
#else
raidTP_gen = raidTP_ssse3;
raidQP_gen = raidQP_ssse3;
raidPP_gen = raidPP_ssse3;
raidHP_gen = raidHP_ssse3;
#endif
}
#endif
}
static struct raid_func {
const char* name;
void* p;
} RAID_FUNC[] = {
{ "int8", raidTP_int8 },
{ "int8", raidQP_int8 },
{ "int8", raidPP_int8 },
{ "int8", raidHP_int8 },
{ "int32", raid5_int32 },
{ "int64", raid5_int64 },
{ "int32", raid6_int32 },
{ "int64", raid6_int64 },
#if defined(__i386__) || defined(__x86_64__)
{ "sse2", raid5_sse2 },
{ "sse2", raid6_sse2 },
{ "ssse3", raidTP_ssse3 },
{ "ssse3", raidQP_ssse3 },
{ "ssse3", raidPP_ssse3 },
{ "ssse3", raidHP_ssse3 },
#endif
#if defined(__x86_64__)
{ "sse2e", raid6_sse2ext },
{ "ssse3e", raidTP_ssse3ext },
{ "ssse3e", raidQP_ssse3ext },
{ "ssse3e", raidPP_ssse3ext },
{ "ssse3e", raidHP_ssse3ext },
#endif
{ 0, 0 }
};
static const char* raid_tag(void* func)
{
struct raid_func* i = RAID_FUNC;
while (i->name != 0) {
if (i->p == func)
return i->name;
++i;
}
return "unknown";
}
const char* raid5_tag(void)
{
return raid_tag(raid5_gen);
}
const char* raid6_tag(void)
{
return raid_tag(raid6_gen);
}
const char* raidTP_tag(void)
{
return raid_tag(raidTP_gen);
}
const char* raidQP_tag(void)
{
return raid_tag(raidQP_gen);
}
const char* raidPP_tag(void)
{
return raid_tag(raidPP_gen);
}
const char* raidHP_tag(void)
{
return raid_tag(raidHP_gen);
}
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