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THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS "AS IS" AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE ARE DISCLAIMED. IN NO EVENT SHALL THE COPYRIGHT OWNER OR CONTRIBUTORS BE LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE. **********************************************************************/ #include #include // 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++); } struct slver { unsigned short snum; unsigned char ver; unsigned char core; }; // Version info struct slver gf_vect_mul_init_slver_00020035; struct slver gf_vect_mul_init_slver = { 0x0035, 0x02, 0x00 }; struct slver ec_encode_data_base_slver_00010135; struct slver ec_encode_data_base_slver = { 0x0135, 0x01, 0x00 }; struct slver gf_vect_mul_base_slver_00010136; struct slver gf_vect_mul_base_slver = { 0x0136, 0x01, 0x00 }; struct slver gf_vect_dot_prod_base_slver_00010137; struct slver gf_vect_dot_prod_base_slver = { 0x0137, 0x01, 0x00 }; struct slver gf_mul_slver_00000214; struct slver gf_mul_slver = { 0x0214, 0x00, 0x00 }; struct slver gf_invert_matrix_slver_00000215; struct slver gf_invert_matrix_slver = { 0x0215, 0x00, 0x00 }; struct slver gf_gen_rs_matrix_slver_00000216; struct slver gf_gen_rs_matrix_slver = { 0x0216, 0x00, 0x00 }; struct slver gf_gen_cauchy1_matrix_slver_00000217; struct slver gf_gen_cauchy1_matrix_slver = { 0x0217, 0x00, 0x00 };