snapraid/raid.c

/*
 * 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 02 04 08 10 20 40 80 1d 3a 74 e8 cd 87 13 26 4c 98 2d 5a b4 75...
 * 01 f5 d2 c4 9a 71 f1 7f fc 87 c1 c6 19 2f 40 55 3d ba 53 04 9c 61...
 * 01 bb a6 d7 c7 07 ce 82 4a 2f a5 9b b6 60 f1 ad e7 f4 06 d2 df 2e...
 * 01 97 7f 9c 7c 18 bd a2 58 1a da 74 70 a3 e5 47 29 07 f5 80 23 e9...
 * 01 2b 3f cf 73 2c d6 ed cb 74 15 78 8a c1 17 c9 89 68 21 ab 76 3b...
 * (see tables.h for the matrix with all the columns)
 *
 * 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 new row.
 * (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 8 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           11927   22075   36004
 *    raid6            3378    5874   18235   19164
 *   raidTP     844                                    8814    9419
 *   raidQP     665                                    6836    7415
 *   raidPP     537                                    5388    5686
 *   raidHP     449                                    4307    4789
 *
 * Values are in MiB/s of data processed, not counting generated parity.
 * You can replicate these results in your machine using the "snapraid -T"
 * command.
 *
 * For comparison, a similar implementation using the power coeffients
 * approach, is only a little faster (5%) for RAIDTP with power
 * coefficient "4", and with equal speed for RAIDQP with power coefficient
 * "8", even using AVX instructions to get a better registers allocation
 * with the three operands PSHUFB.
 *
 *                    int32   int64    sse2   sse2e   ssse3  ssse3e    avxe
 *    raidTP (power)   1511    2775    8625    9336    9645    9966
 *    raidQP (power)    842    1518    5195    5507    6278    6737    7410
 * 
 * References:
 * [1] Anvin, "The mathematics of RAID-6", 2004
 * [2] MacWilliams, Sloane, "The Theory of Error-Correcting Codes", 1977
 * [3] Bl<EFBFBD>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]);
		/* accessing disks in backward order doesn't affect speed */
		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]);
		/* accessing disks in backward order doesn't affect speed */
		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]));
		/* accessing disks in backward order doesn't affect speed */
		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 in 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) {
		p0 = q0 = r0 = 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]];
		}

		/* first disk with all coefficients at 1 */
		d0 = v_8(vbuf[0][i]);

		p0 ^= d0;
		q0 ^= d0;
		r0 ^= d0;

		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) {
		/* last disk without the by two multiplication */
		asm volatile("movdqa %0,%%xmm4" : : "m" (vbuf[l][i]));

		asm volatile("movdqa %xmm4,%xmm0");
		asm volatile("movdqa %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,%%xmm2" : : "m" (gfpshufb[l][0][0][0]));
		asm volatile("movdqa %0,%%xmm6" : : "m" (gfpshufb[l][0][1][0]));
		asm volatile("pshufb %xmm4,%xmm2");
		asm volatile("pshufb %xmm5,%xmm6");
		asm volatile("pxor   %xmm6,%xmm2");

		/* intermediate disks */
		for(d=l-1;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");
		}

		/* first disk with all coefficients at 1 */
		asm volatile("movdqa %0,%%xmm4" : : "m" (vbuf[0][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("pxor %xmm4,%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) {
		/* last disk without the by two multiplication */
		asm volatile("movdqa %0,%%xmm4" : : "m" (vbuf[l][i]));
		asm volatile("movdqa %0,%%xmm12" : : "m" (vbuf[l][i+16]));

		asm volatile("movdqa %xmm4,%xmm0");
		asm volatile("movdqa %xmm4,%xmm1");
		asm volatile("movdqa %xmm12,%xmm8");
		asm volatile("movdqa %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,%%xmm2" : : "m" (gfpshufb[l][0][0][0]));
		asm volatile("movdqa %0,%%xmm7" : : "m" (gfpshufb[l][0][1][0]));
		asm volatile("movdqa %xmm2,%xmm10");
		asm volatile("movdqa %xmm7,%xmm15");
		asm volatile("pshufb %xmm4,%xmm2");
		asm volatile("pshufb %xmm12,%xmm10");
		asm volatile("pshufb %xmm5,%xmm7");
		asm volatile("pshufb %xmm13,%xmm15");
		asm volatile("pxor   %xmm7,%xmm2");
		asm volatile("pxor   %xmm15,%xmm10");

		/* intermediate disks */
		for(d=l-1;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");
		}

		/* first disk with all coefficients at 1 */
		asm volatile("movdqa %0,%%xmm4" : : "m" (vbuf[0][i]));
		asm volatile("movdqa %0,%%xmm12" : : "m" (vbuf[0][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 %xmm4,%xmm2");
		asm volatile("pxor %xmm12,%xmm8");
		asm volatile("pxor %xmm12,%xmm9");
		asm volatile("pxor %xmm12,%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 in 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) {
		p0 = q0 = r0 = s0 = 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]];
		}

		/* first disk with all coefficients at 1 */
		d0 = v_8(vbuf[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;
	}
}

#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) {
		/* last disk without the by two multiplication */
		asm volatile("movdqa %0,%%xmm7" : : "m" (gfconst16.mask[0]));
		asm volatile("movdqa %0,%%xmm4" : : "m" (vbuf[l][i]));

		asm volatile("movdqa %xmm4,%xmm0");
		asm volatile("movdqa %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,%%xmm2" : : "m" (gfpshufb[l][0][0][0]));
		asm volatile("movdqa %0,%%xmm7" : : "m" (gfpshufb[l][0][1][0]));
		asm volatile("pshufb %xmm4,%xmm2");
		asm volatile("pshufb %xmm5,%xmm7");
		asm volatile("pxor   %xmm7,%xmm2");

		asm volatile("movdqa %0,%%xmm3" : : "m" (gfpshufb[l][1][0][0]));
		asm volatile("movdqa %0,%%xmm7" : : "m" (gfpshufb[l][1][1][0]));
		asm volatile("pshufb %xmm4,%xmm3");
		asm volatile("pshufb %xmm5,%xmm7");
		asm volatile("pxor   %xmm7,%xmm3");

		/* intermediate disks */
		for(d=l-1;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");
		}

		/* first disk with all coefficients at 1 */
		asm volatile("movdqa %0,%%xmm7" : : "m" (gfconst16.poly[0]));
		asm volatile("movdqa %0,%%xmm4" : : "m" (vbuf[0][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("pxor %xmm4,%xmm0");
		asm volatile("pxor %xmm4,%xmm1");
		asm volatile("pxor %xmm4,%xmm2");
		asm volatile("pxor %xmm4,%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) {
		/* last disk without the by two multiplication */
		asm volatile("movdqa %0,%%xmm15" : : "m" (gfconst16.mask[0]));
		asm volatile("movdqa %0,%%xmm4" : : "m" (vbuf[l][i]));
		asm volatile("movdqa %0,%%xmm12" : : "m" (vbuf[l][i+16]));

		asm volatile("movdqa %xmm4,%xmm0");
		asm volatile("movdqa %xmm4,%xmm1");
		asm volatile("movdqa %xmm12,%xmm8");
		asm volatile("movdqa %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,%%xmm2" : : "m" (gfpshufb[l][0][0][0]));
		asm volatile("movdqa %0,%%xmm7" : : "m" (gfpshufb[l][0][1][0]));
		asm volatile("movdqa %xmm2,%xmm10");
		asm volatile("movdqa %xmm7,%xmm15");
		asm volatile("pshufb %xmm4,%xmm2");
		asm volatile("pshufb %xmm12,%xmm10");
		asm volatile("pshufb %xmm5,%xmm7");
		asm volatile("pshufb %xmm13,%xmm15");
		asm volatile("pxor   %xmm7,%xmm2");
		asm volatile("pxor   %xmm15,%xmm10");

		asm volatile("movdqa %0,%%xmm3" : : "m" (gfpshufb[l][1][0][0]));
		asm volatile("movdqa %0,%%xmm7" : : "m" (gfpshufb[l][1][1][0]));
		asm volatile("movdqa %xmm3,%xmm11");
		asm volatile("movdqa %xmm7,%xmm15");
		asm volatile("pshufb %xmm4,%xmm3");
		asm volatile("pshufb %xmm12,%xmm11");
		asm volatile("pshufb %xmm5,%xmm7");
		asm volatile("pshufb %xmm13,%xmm15");
		asm volatile("pxor   %xmm7,%xmm3");
		asm volatile("pxor   %xmm15,%xmm11");

		/* intermediate disks */
		for(d=l-1;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");
		}

		/* first disk with all coefficients at 1 */
		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[0][i]));
		asm volatile("movdqa %0,%%xmm12" : : "m" (vbuf[0][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 %xmm4,%xmm2");
		asm volatile("pxor %xmm4,%xmm3");
		asm volatile("pxor %xmm12,%xmm8");
		asm volatile("pxor %xmm12,%xmm9");
		asm volatile("pxor %xmm12,%xmm10");
		asm volatile("pxor %xmm12,%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 in 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) {
		p0 = q0 = r0 = s0 = t0 = 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]];
		}
		
		/* first disk with all coefficients at 1 */
		d0 = v_8(vbuf[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;
	}
}

#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) {
		/* last disk without the by two multiplication */
		asm volatile("movdqa %0,%%xmm4" : : "m" (vbuf[l][i]));

		asm volatile("movdqa %xmm4,%xmm0");
		asm volatile("movdqa %%xmm4,%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,%%xmm1" : : "m" (gfpshufb[l][0][0][0]));
		asm volatile("movdqa %0,%%xmm7" : : "m" (gfpshufb[l][0][1][0]));
		asm volatile("pshufb %xmm4,%xmm1");
		asm volatile("pshufb %xmm5,%xmm7");
		asm volatile("pxor   %xmm7,%xmm1");

		asm volatile("movdqa %0,%%xmm2" : : "m" (gfpshufb[l][1][0][0]));
		asm volatile("movdqa %0,%%xmm7" : : "m" (gfpshufb[l][1][1][0]));
		asm volatile("pshufb %xmm4,%xmm2");
		asm volatile("pshufb %xmm5,%xmm7");
		asm volatile("pxor   %xmm7,%xmm2");

		asm volatile("movdqa %0,%%xmm3" : : "m" (gfpshufb[l][2][0][0]));
		asm volatile("movdqa %0,%%xmm7" : : "m" (gfpshufb[l][2][1][0]));
		asm volatile("pshufb %xmm4,%xmm3");
		asm volatile("pshufb %xmm5,%xmm7");
		asm volatile("pxor   %xmm7,%xmm3");

		/* intermediate disks */
		for(d=l-1;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");
		}

		/* first disk with all coefficients at 1 */
		asm volatile("movdqa %0,%%xmm4" : : "m" (vbuf[0][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,%xmm1");
		asm volatile("pxor %xmm4,%xmm2");
		asm volatile("pxor %xmm4,%xmm3");
		asm volatile("pxor %xmm4,%xmm6");

		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) {
		/* last disk without the by two multiplication */
		asm volatile("movdqa %0,%%xmm10" : : "m" (vbuf[l][i]));

		asm volatile("movdqa %xmm10,%xmm0");
		asm volatile("movdqa %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,%%xmm2" : : "m" (gfpshufb[l][0][0][0]));
		asm volatile("movdqa %0,%%xmm13" : : "m" (gfpshufb[l][0][1][0]));
		asm volatile("pshufb %xmm10,%xmm2");
		asm volatile("pshufb %xmm11,%xmm13");
		asm volatile("pxor   %xmm13,%xmm2");

		asm volatile("movdqa %0,%%xmm3" : : "m" (gfpshufb[l][1][0][0]));
		asm volatile("movdqa %0,%%xmm13" : : "m" (gfpshufb[l][1][1][0]));
		asm volatile("pshufb %xmm10,%xmm3");
		asm volatile("pshufb %xmm11,%xmm13");
		asm volatile("pxor   %xmm13,%xmm3");

		asm volatile("movdqa %0,%%xmm4" : : "m" (gfpshufb[l][2][0][0]));
		asm volatile("movdqa %0,%%xmm13" : : "m" (gfpshufb[l][2][1][0]));
		asm volatile("pshufb %xmm10,%xmm4");
		asm volatile("pshufb %xmm11,%xmm13");
		asm volatile("pxor   %xmm13,%xmm4");

		/* intermediate disks */
		for(d=l-1;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");
		}

		/* first disk with all coefficients at 1 */
		asm volatile("movdqa %0,%%xmm10" : : "m" (vbuf[0][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("pxor %xmm10,%xmm2");
		asm volatile("pxor %xmm10,%xmm3");
		asm volatile("pxor %xmm10,%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 in 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) {
		p0 = q0 = r0 = s0 = t0 = u0 = 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]];
		}
		
		/* first disk with all coefficients at 1 */
		d0 = v_8(vbuf[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;
	}
}

#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) {
		/* last disk without the by two multiplication */
		asm volatile("movdqa %0,%%xmm4" : : "m" (vbuf[l][i]));

		asm volatile("movdqa %%xmm4,%0" : "=m" (p0));
		asm volatile("movdqa %%xmm4,%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,%%xmm0" : : "m" (gfpshufb[l][0][0][0]));
		asm volatile("movdqa %0,%%xmm7" : : "m" (gfpshufb[l][0][1][0]));
		asm volatile("pshufb %xmm4,%xmm0");
		asm volatile("pshufb %xmm5,%xmm7");
		asm volatile("pxor   %xmm7,%xmm0");

		asm volatile("movdqa %0,%%xmm1" : : "m" (gfpshufb[l][1][0][0]));
		asm volatile("movdqa %0,%%xmm7" : : "m" (gfpshufb[l][1][1][0]));
		asm volatile("pshufb %xmm4,%xmm1");
		asm volatile("pshufb %xmm5,%xmm7");
		asm volatile("pxor   %xmm7,%xmm1");

		asm volatile("movdqa %0,%%xmm2" : : "m" (gfpshufb[l][2][0][0]));
		asm volatile("movdqa %0,%%xmm7" : : "m" (gfpshufb[l][2][1][0]));
		asm volatile("pshufb %xmm4,%xmm2");
		asm volatile("pshufb %xmm5,%xmm7");
		asm volatile("pxor   %xmm7,%xmm2");

		asm volatile("movdqa %0,%%xmm3" : : "m" (gfpshufb[l][3][0][0]));
		asm volatile("movdqa %0,%%xmm7" : : "m" (gfpshufb[l][3][1][0]));
		asm volatile("pshufb %xmm4,%xmm3");
		asm volatile("pshufb %xmm5,%xmm7");
		asm volatile("pxor   %xmm7,%xmm3");

		/* intermediate disks */
		for(d=l-1;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");
		}

		/* first disk with all coefficients at 1 */
		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[0][i]));
		asm volatile("pxor %xmm4,%xmm0");
		asm volatile("pxor %xmm4,%xmm1");
		asm volatile("pxor %xmm4,%xmm2");
		asm volatile("pxor %xmm4,%xmm3");
		asm volatile("pxor %xmm4,%xmm5");
		asm volatile("pxor %xmm4,%xmm6");

		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) {
		/* last disk without the by two multiplication */
		asm volatile("movdqa %0,%%xmm10" : : "m" (vbuf[l][i]));

		asm volatile("movdqa %xmm10,%xmm0");
		asm volatile("movdqa %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,%%xmm2" : : "m" (gfpshufb[l][0][0][0]));
		asm volatile("movdqa %0,%%xmm13" : : "m" (gfpshufb[l][0][1][0]));
		asm volatile("pshufb %xmm10,%xmm2");
		asm volatile("pshufb %xmm11,%xmm13");
		asm volatile("pxor   %xmm13,%xmm2");

		asm volatile("movdqa %0,%%xmm3" : : "m" (gfpshufb[l][1][0][0]));
		asm volatile("movdqa %0,%%xmm13" : : "m" (gfpshufb[l][1][1][0]));
		asm volatile("pshufb %xmm10,%xmm3");
		asm volatile("pshufb %xmm11,%xmm13");
		asm volatile("pxor   %xmm13,%xmm3");

		asm volatile("movdqa %0,%%xmm4" : : "m" (gfpshufb[l][2][0][0]));
		asm volatile("movdqa %0,%%xmm13" : : "m" (gfpshufb[l][2][1][0]));
		asm volatile("pshufb %xmm10,%xmm4");
		asm volatile("pshufb %xmm11,%xmm13");
		asm volatile("pxor   %xmm13,%xmm4");

		asm volatile("movdqa %0,%%xmm5" : : "m" (gfpshufb[l][3][0][0]));
		asm volatile("movdqa %0,%%xmm13" : : "m" (gfpshufb[l][3][1][0]));
		asm volatile("pshufb %xmm10,%xmm5");
		asm volatile("pshufb %xmm11,%xmm13");
		asm volatile("pxor   %xmm13,%xmm5");

		/* intermediate disks */
		for(d=l-1;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");
		}

		/* first disk with all coefficients at 1 */
		asm volatile("movdqa %0,%%xmm10" : : "m" (vbuf[0][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("pxor %xmm10,%xmm2");
		asm volatile("pxor %xmm10,%xmm3");
		asm volatile("pxor %xmm10,%xmm4");
		asm volatile("pxor %xmm10,%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)
{
	assert(data >= RAID_DATA_MIN && data <= RAID_DATA_MAX);

	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);
}