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 uint16_t msk = (uint16_t) rs->nn; 26 27 /* 28 * The decoder buffers are in the rs control struct. They are 29 * arrays sized [nroots + 1] 30 */ 31 uint16_t *lambda = rsc->buffers + RS_DECODE_LAMBDA * (nroots + 1); 32 uint16_t *syn = rsc->buffers + RS_DECODE_SYN * (nroots + 1); 33 uint16_t *b = rsc->buffers + RS_DECODE_B * (nroots + 1); 34 uint16_t *t = rsc->buffers + RS_DECODE_T * (nroots + 1); 35 uint16_t *omega = rsc->buffers + RS_DECODE_OMEGA * (nroots + 1); 36 uint16_t *root = rsc->buffers + RS_DECODE_ROOT * (nroots + 1); 37 uint16_t *reg = rsc->buffers + RS_DECODE_REG * (nroots + 1); 38 uint16_t *loc = rsc->buffers + RS_DECODE_LOC * (nroots + 1); 39 40 /* Check length parameter for validity */ 41 pad = nn - nroots - len; 42 BUG_ON(pad < 0 || pad >= nn - nroots); 43 44 /* Does the caller provide the syndrome ? */ 45 if (s != NULL) { 46 for (i = 0; i < nroots; i++) { 47 /* The syndrome is in index form, 48 * so nn represents zero 49 */ 50 if (s[i] != nn) 51 goto decode; 52 } 53 54 /* syndrome is zero, no errors to correct */ 55 return 0; 56 } 57 58 /* form the syndromes; i.e., evaluate data(x) at roots of 59 * g(x) */ 60 for (i = 0; i < nroots; i++) 61 syn[i] = (((uint16_t) data[0]) ^ invmsk) & msk; 62 63 for (j = 1; j < len; j++) { 64 for (i = 0; i < nroots; i++) { 65 if (syn[i] == 0) { 66 syn[i] = (((uint16_t) data[j]) ^ 67 invmsk) & msk; 68 } else { 69 syn[i] = ((((uint16_t) data[j]) ^ 70 invmsk) & msk) ^ 71 alpha_to[rs_modnn(rs, index_of[syn[i]] + 72 (fcr + i) * prim)]; 73 } 74 } 75 } 76 77 for (j = 0; j < nroots; j++) { 78 for (i = 0; i < nroots; i++) { 79 if (syn[i] == 0) { 80 syn[i] = ((uint16_t) par[j]) & msk; 81 } else { 82 syn[i] = (((uint16_t) par[j]) & msk) ^ 83 alpha_to[rs_modnn(rs, index_of[syn[i]] + 84 (fcr+i)*prim)]; 85 } 86 } 87 } 88 s = syn; 89 90 /* Convert syndromes to index form, checking for nonzero condition */ 91 syn_error = 0; 92 for (i = 0; i < nroots; i++) { 93 syn_error |= s[i]; 94 s[i] = index_of[s[i]]; 95 } 96 97 if (!syn_error) { 98 /* if syndrome is zero, data[] is a codeword and there are no 99 * errors to correct. So return data[] unmodified 100 */ 101 return 0; 102 } 103 104 decode: 105 memset(&lambda[1], 0, nroots * sizeof(lambda[0])); 106 lambda[0] = 1; 107 108 if (no_eras > 0) { 109 /* Init lambda to be the erasure locator polynomial */ 110 lambda[1] = alpha_to[rs_modnn(rs, 111 prim * (nn - 1 - (eras_pos[0] + pad)))]; 112 for (i = 1; i < no_eras; i++) { 113 u = rs_modnn(rs, prim * (nn - 1 - (eras_pos[i] + pad))); 114 for (j = i + 1; j > 0; j--) { 115 tmp = index_of[lambda[j - 1]]; 116 if (tmp != nn) { 117 lambda[j] ^= 118 alpha_to[rs_modnn(rs, u + tmp)]; 119 } 120 } 121 } 122 } 123 124 for (i = 0; i < nroots + 1; i++) 125 b[i] = index_of[lambda[i]]; 126 127 /* 128 * Begin Berlekamp-Massey algorithm to determine error+erasure 129 * locator polynomial 130 */ 131 r = no_eras; 132 el = no_eras; 133 while (++r <= nroots) { /* r is the step number */ 134 /* Compute discrepancy at the r-th step in poly-form */ 135 discr_r = 0; 136 for (i = 0; i < r; i++) { 137 if ((lambda[i] != 0) && (s[r - i - 1] != nn)) { 138 discr_r ^= 139 alpha_to[rs_modnn(rs, 140 index_of[lambda[i]] + 141 s[r - i - 1])]; 142 } 143 } 144 discr_r = index_of[discr_r]; /* Index form */ 145 if (discr_r == nn) { 146 /* 2 lines below: B(x) <-- x*B(x) */ 147 memmove (&b[1], b, nroots * sizeof (b[0])); 148 b[0] = nn; 149 } else { 150 /* 7 lines below: T(x) <-- lambda(x)-discr_r*x*b(x) */ 151 t[0] = lambda[0]; 152 for (i = 0; i < nroots; i++) { 153 if (b[i] != nn) { 154 t[i + 1] = lambda[i + 1] ^ 155 alpha_to[rs_modnn(rs, discr_r + 156 b[i])]; 157 } else 158 t[i + 1] = lambda[i + 1]; 159 } 160 if (2 * el <= r + no_eras - 1) { 161 el = r + no_eras - el; 162 /* 163 * 2 lines below: B(x) <-- inv(discr_r) * 164 * lambda(x) 165 */ 166 for (i = 0; i <= nroots; i++) { 167 b[i] = (lambda[i] == 0) ? nn : 168 rs_modnn(rs, index_of[lambda[i]] 169 - discr_r + nn); 170 } 171 } else { 172 /* 2 lines below: B(x) <-- x*B(x) */ 173 memmove(&b[1], b, nroots * sizeof(b[0])); 174 b[0] = nn; 175 } 176 memcpy(lambda, t, (nroots + 1) * sizeof(t[0])); 177 } 178 } 179 180 /* Convert lambda to index form and compute deg(lambda(x)) */ 181 deg_lambda = 0; 182 for (i = 0; i < nroots + 1; i++) { 183 lambda[i] = index_of[lambda[i]]; 184 if (lambda[i] != nn) 185 deg_lambda = i; 186 } 187 /* Find roots of error+erasure locator polynomial by Chien search */ 188 memcpy(®[1], &lambda[1], nroots * sizeof(reg[0])); 189 count = 0; /* Number of roots of lambda(x) */ 190 for (i = 1, k = iprim - 1; i <= nn; i++, k = rs_modnn(rs, k + iprim)) { 191 q = 1; /* lambda[0] is always 0 */ 192 for (j = deg_lambda; j > 0; j--) { 193 if (reg[j] != nn) { 194 reg[j] = rs_modnn(rs, reg[j] + j); 195 q ^= alpha_to[reg[j]]; 196 } 197 } 198 if (q != 0) 199 continue; /* Not a root */ 200 /* store root (index-form) and error location number */ 201 root[count] = i; 202 loc[count] = k; 203 /* If we've already found max possible roots, 204 * abort the search to save time 205 */ 206 if (++count == deg_lambda) 207 break; 208 } 209 if (deg_lambda != count) { 210 /* 211 * deg(lambda) unequal to number of roots => uncorrectable 212 * error detected 213 */ 214 return -EBADMSG; 215 } 216 /* 217 * Compute err+eras evaluator poly omega(x) = s(x)*lambda(x) (modulo 218 * x**nroots). in index form. Also find deg(omega). 219 */ 220 deg_omega = deg_lambda - 1; 221 for (i = 0; i <= deg_omega; i++) { 222 tmp = 0; 223 for (j = i; j >= 0; j--) { 224 if ((s[i - j] != nn) && (lambda[j] != nn)) 225 tmp ^= 226 alpha_to[rs_modnn(rs, s[i - j] + lambda[j])]; 227 } 228 omega[i] = index_of[tmp]; 229 } 230 231 /* 232 * Compute error values in poly-form. num1 = omega(inv(X(l))), num2 = 233 * inv(X(l))**(fcr-1) and den = lambda_pr(inv(X(l))) all in poly-form 234 */ 235 for (j = count - 1; j >= 0; j--) { 236 num1 = 0; 237 for (i = deg_omega; i >= 0; i--) { 238 if (omega[i] != nn) 239 num1 ^= alpha_to[rs_modnn(rs, omega[i] + 240 i * root[j])]; 241 } 242 num2 = alpha_to[rs_modnn(rs, root[j] * (fcr - 1) + nn)]; 243 den = 0; 244 245 /* lambda[i+1] for i even is the formal derivative 246 * lambda_pr of lambda[i] */ 247 for (i = min(deg_lambda, nroots - 1) & ~1; i >= 0; i -= 2) { 248 if (lambda[i + 1] != nn) { 249 den ^= alpha_to[rs_modnn(rs, lambda[i + 1] + 250 i * root[j])]; 251 } 252 } 253 /* Apply error to data */ 254 if (num1 != 0 && loc[j] >= pad) { 255 uint16_t cor = alpha_to[rs_modnn(rs,index_of[num1] + 256 index_of[num2] + 257 nn - index_of[den])]; 258 /* Store the error correction pattern, if a 259 * correction buffer is available */ 260 if (corr) { 261 corr[j] = cor; 262 } else { 263 /* If a data buffer is given and the 264 * error is inside the message, 265 * correct it */ 266 if (data && (loc[j] < (nn - nroots))) 267 data[loc[j] - pad] ^= cor; 268 } 269 } 270 } 271 272 if (eras_pos != NULL) { 273 for (i = 0; i < count; i++) 274 eras_pos[i] = loc[i] - pad; 275 } 276 return count; 277 278 } 279