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 int count = 0; 25 int num_corrected; 26 uint16_t msk = (uint16_t) rs->nn; 27 28 /* 29 * The decoder buffers are in the rs control struct. They are 30 * arrays sized [nroots + 1] 31 */ 32 uint16_t *lambda = rsc->buffers + RS_DECODE_LAMBDA * (nroots + 1); 33 uint16_t *syn = rsc->buffers + RS_DECODE_SYN * (nroots + 1); 34 uint16_t *b = rsc->buffers + RS_DECODE_B * (nroots + 1); 35 uint16_t *t = rsc->buffers + RS_DECODE_T * (nroots + 1); 36 uint16_t *omega = rsc->buffers + RS_DECODE_OMEGA * (nroots + 1); 37 uint16_t *root = rsc->buffers + RS_DECODE_ROOT * (nroots + 1); 38 uint16_t *reg = rsc->buffers + RS_DECODE_REG * (nroots + 1); 39 uint16_t *loc = rsc->buffers + RS_DECODE_LOC * (nroots + 1); 40 41 /* Check length parameter for validity */ 42 pad = nn - nroots - len; 43 BUG_ON(pad < 0 || pad >= nn - nroots); 44 45 /* Does the caller provide the syndrome ? */ 46 if (s != NULL) { 47 for (i = 0; i < nroots; i++) { 48 /* The syndrome is in index form, 49 * so nn represents zero 50 */ 51 if (s[i] != nn) 52 goto decode; 53 } 54 55 /* syndrome is zero, no errors to correct */ 56 return 0; 57 } 58 59 /* form the syndromes; i.e., evaluate data(x) at roots of 60 * g(x) */ 61 for (i = 0; i < nroots; i++) 62 syn[i] = (((uint16_t) data[0]) ^ invmsk) & msk; 63 64 for (j = 1; j < len; j++) { 65 for (i = 0; i < nroots; i++) { 66 if (syn[i] == 0) { 67 syn[i] = (((uint16_t) data[j]) ^ 68 invmsk) & msk; 69 } else { 70 syn[i] = ((((uint16_t) data[j]) ^ 71 invmsk) & msk) ^ 72 alpha_to[rs_modnn(rs, index_of[syn[i]] + 73 (fcr + i) * prim)]; 74 } 75 } 76 } 77 78 for (j = 0; j < nroots; j++) { 79 for (i = 0; i < nroots; i++) { 80 if (syn[i] == 0) { 81 syn[i] = ((uint16_t) par[j]) & msk; 82 } else { 83 syn[i] = (((uint16_t) par[j]) & msk) ^ 84 alpha_to[rs_modnn(rs, index_of[syn[i]] + 85 (fcr+i)*prim)]; 86 } 87 } 88 } 89 s = syn; 90 91 /* Convert syndromes to index form, checking for nonzero condition */ 92 syn_error = 0; 93 for (i = 0; i < nroots; i++) { 94 syn_error |= s[i]; 95 s[i] = index_of[s[i]]; 96 } 97 98 if (!syn_error) { 99 /* if syndrome is zero, data[] is a codeword and there are no 100 * errors to correct. So return data[] unmodified 101 */ 102 return 0; 103 } 104 105 decode: 106 memset(&lambda[1], 0, nroots * sizeof(lambda[0])); 107 lambda[0] = 1; 108 109 if (no_eras > 0) { 110 /* Init lambda to be the erasure locator polynomial */ 111 lambda[1] = alpha_to[rs_modnn(rs, 112 prim * (nn - 1 - (eras_pos[0] + pad)))]; 113 for (i = 1; i < no_eras; i++) { 114 u = rs_modnn(rs, prim * (nn - 1 - (eras_pos[i] + pad))); 115 for (j = i + 1; j > 0; j--) { 116 tmp = index_of[lambda[j - 1]]; 117 if (tmp != nn) { 118 lambda[j] ^= 119 alpha_to[rs_modnn(rs, u + tmp)]; 120 } 121 } 122 } 123 } 124 125 for (i = 0; i < nroots + 1; i++) 126 b[i] = index_of[lambda[i]]; 127 128 /* 129 * Begin Berlekamp-Massey algorithm to determine error+erasure 130 * locator polynomial 131 */ 132 r = no_eras; 133 el = no_eras; 134 while (++r <= nroots) { /* r is the step number */ 135 /* Compute discrepancy at the r-th step in poly-form */ 136 discr_r = 0; 137 for (i = 0; i < r; i++) { 138 if ((lambda[i] != 0) && (s[r - i - 1] != nn)) { 139 discr_r ^= 140 alpha_to[rs_modnn(rs, 141 index_of[lambda[i]] + 142 s[r - i - 1])]; 143 } 144 } 145 discr_r = index_of[discr_r]; /* Index form */ 146 if (discr_r == nn) { 147 /* 2 lines below: B(x) <-- x*B(x) */ 148 memmove (&b[1], b, nroots * sizeof (b[0])); 149 b[0] = nn; 150 } else { 151 /* 7 lines below: T(x) <-- lambda(x)-discr_r*x*b(x) */ 152 t[0] = lambda[0]; 153 for (i = 0; i < nroots; i++) { 154 if (b[i] != nn) { 155 t[i + 1] = lambda[i + 1] ^ 156 alpha_to[rs_modnn(rs, discr_r + 157 b[i])]; 158 } else 159 t[i + 1] = lambda[i + 1]; 160 } 161 if (2 * el <= r + no_eras - 1) { 162 el = r + no_eras - el; 163 /* 164 * 2 lines below: B(x) <-- inv(discr_r) * 165 * lambda(x) 166 */ 167 for (i = 0; i <= nroots; i++) { 168 b[i] = (lambda[i] == 0) ? nn : 169 rs_modnn(rs, index_of[lambda[i]] 170 - discr_r + nn); 171 } 172 } else { 173 /* 2 lines below: B(x) <-- x*B(x) */ 174 memmove(&b[1], b, nroots * sizeof(b[0])); 175 b[0] = nn; 176 } 177 memcpy(lambda, t, (nroots + 1) * sizeof(t[0])); 178 } 179 } 180 181 /* Convert lambda to index form and compute deg(lambda(x)) */ 182 deg_lambda = 0; 183 for (i = 0; i < nroots + 1; i++) { 184 lambda[i] = index_of[lambda[i]]; 185 if (lambda[i] != nn) 186 deg_lambda = i; 187 } 188 189 if (deg_lambda == 0) { 190 /* 191 * deg(lambda) is zero even though the syndrome is non-zero 192 * => uncorrectable error detected 193 */ 194 return -EBADMSG; 195 } 196 197 /* Find roots of error+erasure locator polynomial by Chien search */ 198 memcpy(®[1], &lambda[1], nroots * sizeof(reg[0])); 199 count = 0; /* Number of roots of lambda(x) */ 200 for (i = 1, k = iprim - 1; i <= nn; i++, k = rs_modnn(rs, k + iprim)) { 201 q = 1; /* lambda[0] is always 0 */ 202 for (j = deg_lambda; j > 0; j--) { 203 if (reg[j] != nn) { 204 reg[j] = rs_modnn(rs, reg[j] + j); 205 q ^= alpha_to[reg[j]]; 206 } 207 } 208 if (q != 0) 209 continue; /* Not a root */ 210 211 if (k < pad) { 212 /* Impossible error location. Uncorrectable error. */ 213 return -EBADMSG; 214 } 215 216 /* store root (index-form) and error location number */ 217 root[count] = i; 218 loc[count] = k; 219 /* If we've already found max possible roots, 220 * abort the search to save time 221 */ 222 if (++count == deg_lambda) 223 break; 224 } 225 if (deg_lambda != count) { 226 /* 227 * deg(lambda) unequal to number of roots => uncorrectable 228 * error detected 229 */ 230 return -EBADMSG; 231 } 232 /* 233 * Compute err+eras evaluator poly omega(x) = s(x)*lambda(x) (modulo 234 * x**nroots). in index form. Also find deg(omega). 235 */ 236 deg_omega = deg_lambda - 1; 237 for (i = 0; i <= deg_omega; i++) { 238 tmp = 0; 239 for (j = i; j >= 0; j--) { 240 if ((s[i - j] != nn) && (lambda[j] != nn)) 241 tmp ^= 242 alpha_to[rs_modnn(rs, s[i - j] + lambda[j])]; 243 } 244 omega[i] = index_of[tmp]; 245 } 246 247 /* 248 * Compute error values in poly-form. num1 = omega(inv(X(l))), num2 = 249 * inv(X(l))**(fcr-1) and den = lambda_pr(inv(X(l))) all in poly-form 250 * Note: we reuse the buffer for b to store the correction pattern 251 */ 252 num_corrected = 0; 253 for (j = count - 1; j >= 0; j--) { 254 num1 = 0; 255 for (i = deg_omega; i >= 0; i--) { 256 if (omega[i] != nn) 257 num1 ^= alpha_to[rs_modnn(rs, omega[i] + 258 i * root[j])]; 259 } 260 261 if (num1 == 0) { 262 /* Nothing to correct at this position */ 263 b[j] = 0; 264 continue; 265 } 266 267 num2 = alpha_to[rs_modnn(rs, root[j] * (fcr - 1) + nn)]; 268 den = 0; 269 270 /* lambda[i+1] for i even is the formal derivative 271 * lambda_pr of lambda[i] */ 272 for (i = min(deg_lambda, nroots - 1) & ~1; i >= 0; i -= 2) { 273 if (lambda[i + 1] != nn) { 274 den ^= alpha_to[rs_modnn(rs, lambda[i + 1] + 275 i * root[j])]; 276 } 277 } 278 279 b[j] = alpha_to[rs_modnn(rs, index_of[num1] + 280 index_of[num2] + 281 nn - index_of[den])]; 282 num_corrected++; 283 } 284 285 /* 286 * We compute the syndrome of the 'error' and check that it matches 287 * the syndrome of the received word 288 */ 289 for (i = 0; i < nroots; i++) { 290 tmp = 0; 291 for (j = 0; j < count; j++) { 292 if (b[j] == 0) 293 continue; 294 295 k = (fcr + i) * prim * (nn-loc[j]-1); 296 tmp ^= alpha_to[rs_modnn(rs, index_of[b[j]] + k)]; 297 } 298 299 if (tmp != alpha_to[s[i]]) 300 return -EBADMSG; 301 } 302 303 /* 304 * Store the error correction pattern, if a 305 * correction buffer is available 306 */ 307 if (corr && eras_pos) { 308 j = 0; 309 for (i = 0; i < count; i++) { 310 if (b[i]) { 311 corr[j] = b[i]; 312 eras_pos[j++] = loc[i] - pad; 313 } 314 } 315 } else if (data && par) { 316 /* Apply error to data and parity */ 317 for (i = 0; i < count; i++) { 318 if (loc[i] < (nn - nroots)) 319 data[loc[i] - pad] ^= b[i]; 320 else 321 par[loc[i] - pad - len] ^= b[i]; 322 } 323 } 324 325 return num_corrected; 326 } 327