isa-l/erasure_code/ec_base.c

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#include <limits.h>
#include <string.h>		// for memset
#include "erasure_code.h"
#include "ec_base.h"		// for GF tables

void ec_init_tables(int k, int rows, unsigned char *a, unsigned char *g_tbls)
{
	int i, j;

	for (i = 0; i < rows; i++) {
		for (j = 0; j < k; j++) {
			gf_vect_mul_init(*a++, g_tbls);
			g_tbls += 32;
		}
	}
}

unsigned char gf_mul(unsigned char a, unsigned char b)
{
#ifndef GF_LARGE_TABLES
	int i;

	if ((a == 0) || (b == 0))
		return 0;

	return gff_base[(i = gflog_base[a] + gflog_base[b]) > 254 ? i - 255 : i];
#else
	return gf_mul_table_base[b * 256 + a];
#endif
}

unsigned char gf_inv(unsigned char a)
{
#ifndef GF_LARGE_TABLES
	if (a == 0)
		return 0;

	return gff_base[255 - gflog_base[a]];
#else
	return gf_inv_table_base[a];
#endif
}

void gf_gen_rs_matrix(unsigned char *a, int m, int k)
{
	int i, j;
	unsigned char p, gen = 1;

	memset(a, 0, k * m);
	for (i = 0; i < k; i++)
		a[k * i + i] = 1;

	for (i = k; i < m; i++) {
		p = 1;
		for (j = 0; j < k; j++) {
			a[k * i + j] = p;
			p = gf_mul(p, gen);
		}
		gen = gf_mul(gen, 2);
	}
}

void gf_gen_cauchy1_matrix(unsigned char *a, int m, int k)
{
	int i, j;
	unsigned char *p;

	// Identity matrix in high position
	memset(a, 0, k * m);
	for (i = 0; i < k; i++)
		a[k * i + i] = 1;

	// For the rest choose 1/(i + j) | i != j
	p = &a[k * k];
	for (i = k; i < m; i++)
		for (j = 0; j < k; j++)
			*p++ = gf_inv(i ^ j);

}

int gf_invert_matrix(unsigned char *in_mat, unsigned char *out_mat, const int n)
{
	int i, j, k;
	unsigned char temp;

	// Set out_mat[] to the identity matrix
	for (i = 0; i < n * n; i++)	// memset(out_mat, 0, n*n)
		out_mat[i] = 0;

	for (i = 0; i < n; i++)
		out_mat[i * n + i] = 1;

	// Inverse
	for (i = 0; i < n; i++) {
		// Check for 0 in pivot element
		if (in_mat[i * n + i] == 0) {
			// Find a row with non-zero in current column and swap
			for (j = i + 1; j < n; j++)
				if (in_mat[j * n + i])
					break;

			if (j == n)	// Couldn't find means it's singular
				return -1;

			for (k = 0; k < n; k++) {	// Swap rows i,j
				temp = in_mat[i * n + k];
				in_mat[i * n + k] = in_mat[j * n + k];
				in_mat[j * n + k] = temp;

				temp = out_mat[i * n + k];
				out_mat[i * n + k] = out_mat[j * n + k];
				out_mat[j * n + k] = temp;
			}
		}

		temp = gf_inv(in_mat[i * n + i]);	// 1/pivot
		for (j = 0; j < n; j++) {	// Scale row i by 1/pivot
			in_mat[i * n + j] = gf_mul(in_mat[i * n + j], temp);
			out_mat[i * n + j] = gf_mul(out_mat[i * n + j], temp);
		}

		for (j = 0; j < n; j++) {
			if (j == i)
				continue;

			temp = in_mat[j * n + i];
			for (k = 0; k < n; k++) {
				out_mat[j * n + k] ^= gf_mul(temp, out_mat[i * n + k]);
				in_mat[j * n + k] ^= gf_mul(temp, in_mat[i * n + k]);
			}
		}
	}
	return 0;
}

// Calculates const table gftbl in GF(2^8) from single input A
// gftbl(A) = {A{00}, A{01}, A{02}, ... , A{0f} }, {A{00}, A{10}, A{20}, ... , A{f0} }

void gf_vect_mul_init(unsigned char c, unsigned char *tbl)
{
	unsigned char c2 = (c << 1) ^ ((c & 0x80) ? 0x1d : 0);	//Mult by GF{2}
	unsigned char c4 = (c2 << 1) ^ ((c2 & 0x80) ? 0x1d : 0);	//Mult by GF{2}
	unsigned char c8 = (c4 << 1) ^ ((c4 & 0x80) ? 0x1d : 0);	//Mult by GF{2}

#if (__WORDSIZE == 64 || _WIN64 || __x86_64__) && (__BYTE_ORDER__ == __ORDER_LITTLE_ENDIAN__)
	unsigned long long v1, v2, v4, v8, *t;
	unsigned long long v10, v20, v40, v80;
	unsigned char c17, c18, c20, c24;

	t = (unsigned long long *)tbl;

	v1 = c * 0x0100010001000100ull;
	v2 = c2 * 0x0101000001010000ull;
	v4 = c4 * 0x0101010100000000ull;
	v8 = c8 * 0x0101010101010101ull;

	v4 = v1 ^ v2 ^ v4;
	t[0] = v4;
	t[1] = v8 ^ v4;

	c17 = (c8 << 1) ^ ((c8 & 0x80) ? 0x1d : 0);	//Mult by GF{2}
	c18 = (c17 << 1) ^ ((c17 & 0x80) ? 0x1d : 0);	//Mult by GF{2}
	c20 = (c18 << 1) ^ ((c18 & 0x80) ? 0x1d : 0);	//Mult by GF{2}
	c24 = (c20 << 1) ^ ((c20 & 0x80) ? 0x1d : 0);	//Mult by GF{2}

	v10 = c17 * 0x0100010001000100ull;
	v20 = c18 * 0x0101000001010000ull;
	v40 = c20 * 0x0101010100000000ull;
	v80 = c24 * 0x0101010101010101ull;

	v40 = v10 ^ v20 ^ v40;
	t[2] = v40;
	t[3] = v80 ^ v40;

#else // 32-bit or other
	unsigned char c3, c5, c6, c7, c9, c10, c11, c12, c13, c14, c15;
	unsigned char c17, c18, c19, c20, c21, c22, c23, c24, c25, c26, c27, c28, c29, c30,
	    c31;

	c3 = c2 ^ c;
	c5 = c4 ^ c;
	c6 = c4 ^ c2;
	c7 = c4 ^ c3;

	c9 = c8 ^ c;
	c10 = c8 ^ c2;
	c11 = c8 ^ c3;
	c12 = c8 ^ c4;
	c13 = c8 ^ c5;
	c14 = c8 ^ c6;
	c15 = c8 ^ c7;

	tbl[0] = 0;
	tbl[1] = c;
	tbl[2] = c2;
	tbl[3] = c3;
	tbl[4] = c4;
	tbl[5] = c5;
	tbl[6] = c6;
	tbl[7] = c7;
	tbl[8] = c8;
	tbl[9] = c9;
	tbl[10] = c10;
	tbl[11] = c11;
	tbl[12] = c12;
	tbl[13] = c13;
	tbl[14] = c14;
	tbl[15] = c15;

	c17 = (c8 << 1) ^ ((c8 & 0x80) ? 0x1d : 0);	//Mult by GF{2}
	c18 = (c17 << 1) ^ ((c17 & 0x80) ? 0x1d : 0);	//Mult by GF{2}
	c19 = c18 ^ c17;
	c20 = (c18 << 1) ^ ((c18 & 0x80) ? 0x1d : 0);	//Mult by GF{2}
	c21 = c20 ^ c17;
	c22 = c20 ^ c18;
	c23 = c20 ^ c19;
	c24 = (c20 << 1) ^ ((c20 & 0x80) ? 0x1d : 0);	//Mult by GF{2}
	c25 = c24 ^ c17;
	c26 = c24 ^ c18;
	c27 = c24 ^ c19;
	c28 = c24 ^ c20;
	c29 = c24 ^ c21;
	c30 = c24 ^ c22;
	c31 = c24 ^ c23;

	tbl[16] = 0;
	tbl[17] = c17;
	tbl[18] = c18;
	tbl[19] = c19;
	tbl[20] = c20;
	tbl[21] = c21;
	tbl[22] = c22;
	tbl[23] = c23;
	tbl[24] = c24;
	tbl[25] = c25;
	tbl[26] = c26;
	tbl[27] = c27;
	tbl[28] = c28;
	tbl[29] = c29;
	tbl[30] = c30;
	tbl[31] = c31;

#endif //__WORDSIZE == 64 || _WIN64 || __x86_64__
}

void gf_vect_dot_prod_base(int len, int vlen, unsigned char *v,
			   unsigned char **src, unsigned char *dest)
{
	int i, j;
	unsigned char s;
	for (i = 0; i < len; i++) {
		s = 0;
		for (j = 0; j < vlen; j++)
			s ^= gf_mul(src[j][i], v[j * 32 + 1]);

		dest[i] = s;
	}
}

void gf_vect_mad_base(int len, int vec, int vec_i,
		      unsigned char *v, unsigned char *src, unsigned char *dest)
{
	int i;
	unsigned char s;
	for (i = 0; i < len; i++) {
		s = dest[i];
		s ^= gf_mul(src[i], v[vec_i * 32 + 1]);
		dest[i] = s;
	}
}

void ec_encode_data_base(int len, int srcs, int dests, unsigned char *v,
			 unsigned char **src, unsigned char **dest)
{
	int i, j, l;
	unsigned char s;

	for (l = 0; l < dests; l++) {
		for (i = 0; i < len; i++) {
			s = 0;
			for (j = 0; j < srcs; j++)
				s ^= gf_mul(src[j][i], v[j * 32 + l * srcs * 32 + 1]);

			dest[l][i] = s;
		}
	}
}

void ec_encode_data_update_base(int len, int k, int rows, int vec_i, unsigned char *v,
				unsigned char *data, unsigned char **dest)
{
	int i, l;
	unsigned char s;

	for (l = 0; l < rows; l++) {
		for (i = 0; i < len; i++) {
			s = dest[l][i];
			s ^= gf_mul(data[i], v[vec_i * 32 + l * k * 32 + 1]);

			dest[l][i] = s;
		}
	}
}

void gf_vect_mul_base(int len, unsigned char *a, unsigned char *src, unsigned char *dest)
{
	//2nd element of table array is ref value used to fill it in
	unsigned char c = a[1];
	while (len-- > 0)
		*dest++ = gf_mul(c, *src++);
}