1 // SPDX-License-Identifier: GPL-2.0 2 /* 3 * Generic Reed Solomon encoder / decoder library 4 * 5 * Copyright 2002, Phil Karn, KA9Q 6 * May be used under the terms of the GNU General Public License (GPL) 7 * 8 * Adaption to the kernel by Thomas Gleixner (tglx@linutronix.de) 9 * 10 * Generic data width independent code which is included by the wrappers. 11 */ 12 { 13 struct rs_codec *rs = rsc->codec; 14 int deg_lambda, el, deg_omega; 15 int i, j, r, k, pad; 16 int nn = rs->nn; 17 int nroots = rs->nroots; 18 int fcr = rs->fcr; 19 int prim = rs->prim; 20 int iprim = rs->iprim; 21 uint16_t *alpha_to = rs->alpha_to; 22 uint16_t *index_of = rs->index_of; 23 uint16_t u, q, tmp, num1, num2, den, discr_r, syn_error; 24 /* Err+Eras Locator poly and syndrome poly The maximum value 25 * of nroots is 8. So the necessary stack size will be about 26 * 220 bytes max. 27 */ 28 uint16_t lambda[nroots + 1], syn[nroots]; 29 uint16_t b[nroots + 1], t[nroots + 1], omega[nroots + 1]; 30 uint16_t root[nroots], reg[nroots + 1], loc[nroots]; 31 int count = 0; 32 uint16_t msk = (uint16_t) rs->nn; 33 34 /* Check length parameter for validity */ 35 pad = nn - nroots - len; 36 BUG_ON(pad < 0 || pad >= nn); 37 38 /* Does the caller provide the syndrome ? */ 39 if (s != NULL) 40 goto decode; 41 42 /* form the syndromes; i.e., evaluate data(x) at roots of 43 * g(x) */ 44 for (i = 0; i < nroots; i++) 45 syn[i] = (((uint16_t) data[0]) ^ invmsk) & msk; 46 47 for (j = 1; j < len; j++) { 48 for (i = 0; i < nroots; i++) { 49 if (syn[i] == 0) { 50 syn[i] = (((uint16_t) data[j]) ^ 51 invmsk) & msk; 52 } else { 53 syn[i] = ((((uint16_t) data[j]) ^ 54 invmsk) & msk) ^ 55 alpha_to[rs_modnn(rs, index_of[syn[i]] + 56 (fcr + i) * prim)]; 57 } 58 } 59 } 60 61 for (j = 0; j < nroots; j++) { 62 for (i = 0; i < nroots; i++) { 63 if (syn[i] == 0) { 64 syn[i] = ((uint16_t) par[j]) & msk; 65 } else { 66 syn[i] = (((uint16_t) par[j]) & msk) ^ 67 alpha_to[rs_modnn(rs, index_of[syn[i]] + 68 (fcr+i)*prim)]; 69 } 70 } 71 } 72 s = syn; 73 74 /* Convert syndromes to index form, checking for nonzero condition */ 75 syn_error = 0; 76 for (i = 0; i < nroots; i++) { 77 syn_error |= s[i]; 78 s[i] = index_of[s[i]]; 79 } 80 81 if (!syn_error) { 82 /* if syndrome is zero, data[] is a codeword and there are no 83 * errors to correct. So return data[] unmodified 84 */ 85 count = 0; 86 goto finish; 87 } 88 89 decode: 90 memset(&lambda[1], 0, nroots * sizeof(lambda[0])); 91 lambda[0] = 1; 92 93 if (no_eras > 0) { 94 /* Init lambda to be the erasure locator polynomial */ 95 lambda[1] = alpha_to[rs_modnn(rs, 96 prim * (nn - 1 - eras_pos[0]))]; 97 for (i = 1; i < no_eras; i++) { 98 u = rs_modnn(rs, prim * (nn - 1 - eras_pos[i])); 99 for (j = i + 1; j > 0; j--) { 100 tmp = index_of[lambda[j - 1]]; 101 if (tmp != nn) { 102 lambda[j] ^= 103 alpha_to[rs_modnn(rs, u + tmp)]; 104 } 105 } 106 } 107 } 108 109 for (i = 0; i < nroots + 1; i++) 110 b[i] = index_of[lambda[i]]; 111 112 /* 113 * Begin Berlekamp-Massey algorithm to determine error+erasure 114 * locator polynomial 115 */ 116 r = no_eras; 117 el = no_eras; 118 while (++r <= nroots) { /* r is the step number */ 119 /* Compute discrepancy at the r-th step in poly-form */ 120 discr_r = 0; 121 for (i = 0; i < r; i++) { 122 if ((lambda[i] != 0) && (s[r - i - 1] != nn)) { 123 discr_r ^= 124 alpha_to[rs_modnn(rs, 125 index_of[lambda[i]] + 126 s[r - i - 1])]; 127 } 128 } 129 discr_r = index_of[discr_r]; /* Index form */ 130 if (discr_r == nn) { 131 /* 2 lines below: B(x) <-- x*B(x) */ 132 memmove (&b[1], b, nroots * sizeof (b[0])); 133 b[0] = nn; 134 } else { 135 /* 7 lines below: T(x) <-- lambda(x)-discr_r*x*b(x) */ 136 t[0] = lambda[0]; 137 for (i = 0; i < nroots; i++) { 138 if (b[i] != nn) { 139 t[i + 1] = lambda[i + 1] ^ 140 alpha_to[rs_modnn(rs, discr_r + 141 b[i])]; 142 } else 143 t[i + 1] = lambda[i + 1]; 144 } 145 if (2 * el <= r + no_eras - 1) { 146 el = r + no_eras - el; 147 /* 148 * 2 lines below: B(x) <-- inv(discr_r) * 149 * lambda(x) 150 */ 151 for (i = 0; i <= nroots; i++) { 152 b[i] = (lambda[i] == 0) ? nn : 153 rs_modnn(rs, index_of[lambda[i]] 154 - discr_r + nn); 155 } 156 } else { 157 /* 2 lines below: B(x) <-- x*B(x) */ 158 memmove(&b[1], b, nroots * sizeof(b[0])); 159 b[0] = nn; 160 } 161 memcpy(lambda, t, (nroots + 1) * sizeof(t[0])); 162 } 163 } 164 165 /* Convert lambda to index form and compute deg(lambda(x)) */ 166 deg_lambda = 0; 167 for (i = 0; i < nroots + 1; i++) { 168 lambda[i] = index_of[lambda[i]]; 169 if (lambda[i] != nn) 170 deg_lambda = i; 171 } 172 /* Find roots of error+erasure locator polynomial by Chien search */ 173 memcpy(®[1], &lambda[1], nroots * sizeof(reg[0])); 174 count = 0; /* Number of roots of lambda(x) */ 175 for (i = 1, k = iprim - 1; i <= nn; i++, k = rs_modnn(rs, k + iprim)) { 176 q = 1; /* lambda[0] is always 0 */ 177 for (j = deg_lambda; j > 0; j--) { 178 if (reg[j] != nn) { 179 reg[j] = rs_modnn(rs, reg[j] + j); 180 q ^= alpha_to[reg[j]]; 181 } 182 } 183 if (q != 0) 184 continue; /* Not a root */ 185 /* store root (index-form) and error location number */ 186 root[count] = i; 187 loc[count] = k; 188 /* If we've already found max possible roots, 189 * abort the search to save time 190 */ 191 if (++count == deg_lambda) 192 break; 193 } 194 if (deg_lambda != count) { 195 /* 196 * deg(lambda) unequal to number of roots => uncorrectable 197 * error detected 198 */ 199 count = -EBADMSG; 200 goto finish; 201 } 202 /* 203 * Compute err+eras evaluator poly omega(x) = s(x)*lambda(x) (modulo 204 * x**nroots). in index form. Also find deg(omega). 205 */ 206 deg_omega = deg_lambda - 1; 207 for (i = 0; i <= deg_omega; i++) { 208 tmp = 0; 209 for (j = i; j >= 0; j--) { 210 if ((s[i - j] != nn) && (lambda[j] != nn)) 211 tmp ^= 212 alpha_to[rs_modnn(rs, s[i - j] + lambda[j])]; 213 } 214 omega[i] = index_of[tmp]; 215 } 216 217 /* 218 * Compute error values in poly-form. num1 = omega(inv(X(l))), num2 = 219 * inv(X(l))**(fcr-1) and den = lambda_pr(inv(X(l))) all in poly-form 220 */ 221 for (j = count - 1; j >= 0; j--) { 222 num1 = 0; 223 for (i = deg_omega; i >= 0; i--) { 224 if (omega[i] != nn) 225 num1 ^= alpha_to[rs_modnn(rs, omega[i] + 226 i * root[j])]; 227 } 228 num2 = alpha_to[rs_modnn(rs, root[j] * (fcr - 1) + nn)]; 229 den = 0; 230 231 /* lambda[i+1] for i even is the formal derivative 232 * lambda_pr of lambda[i] */ 233 for (i = min(deg_lambda, nroots - 1) & ~1; i >= 0; i -= 2) { 234 if (lambda[i + 1] != nn) { 235 den ^= alpha_to[rs_modnn(rs, lambda[i + 1] + 236 i * root[j])]; 237 } 238 } 239 /* Apply error to data */ 240 if (num1 != 0 && loc[j] >= pad) { 241 uint16_t cor = alpha_to[rs_modnn(rs,index_of[num1] + 242 index_of[num2] + 243 nn - index_of[den])]; 244 /* Store the error correction pattern, if a 245 * correction buffer is available */ 246 if (corr) { 247 corr[j] = cor; 248 } else { 249 /* If a data buffer is given and the 250 * error is inside the message, 251 * correct it */ 252 if (data && (loc[j] < (nn - nroots))) 253 data[loc[j] - pad] ^= cor; 254 } 255 } 256 } 257 258 finish: 259 if (eras_pos != NULL) { 260 for (i = 0; i < count; i++) 261 eras_pos[i] = loc[i] - pad; 262 } 263 return count; 264 265 } 266