Thomas Gleixner | 03ead84 | 2005-11-07 11:15:37 +0000 | [diff] [blame] | 1 | /* |
Linus Torvalds | 1da177e | 2005-04-16 15:20:36 -0700 | [diff] [blame] | 2 | * lib/reed_solomon/decode_rs.c |
| 3 | * |
| 4 | * Overview: |
| 5 | * Generic Reed Solomon encoder / decoder library |
Thomas Gleixner | 03ead84 | 2005-11-07 11:15:37 +0000 | [diff] [blame] | 6 | * |
Linus Torvalds | 1da177e | 2005-04-16 15:20:36 -0700 | [diff] [blame] | 7 | * Copyright 2002, Phil Karn, KA9Q |
| 8 | * May be used under the terms of the GNU General Public License (GPL) |
| 9 | * |
| 10 | * Adaption to the kernel by Thomas Gleixner (tglx@linutronix.de) |
| 11 | * |
Thomas Gleixner | 03ead84 | 2005-11-07 11:15:37 +0000 | [diff] [blame] | 12 | * $Id: decode_rs.c,v 1.7 2005/11/07 11:14:59 gleixner Exp $ |
Linus Torvalds | 1da177e | 2005-04-16 15:20:36 -0700 | [diff] [blame] | 13 | * |
| 14 | */ |
| 15 | |
Thomas Gleixner | 03ead84 | 2005-11-07 11:15:37 +0000 | [diff] [blame] | 16 | /* Generic data width independent code which is included by the |
Linus Torvalds | 1da177e | 2005-04-16 15:20:36 -0700 | [diff] [blame] | 17 | * wrappers. |
| 18 | */ |
Thomas Gleixner | 03ead84 | 2005-11-07 11:15:37 +0000 | [diff] [blame] | 19 | { |
Linus Torvalds | 1da177e | 2005-04-16 15:20:36 -0700 | [diff] [blame] | 20 | int deg_lambda, el, deg_omega; |
| 21 | int i, j, r, k, pad; |
| 22 | int nn = rs->nn; |
| 23 | int nroots = rs->nroots; |
| 24 | int fcr = rs->fcr; |
| 25 | int prim = rs->prim; |
| 26 | int iprim = rs->iprim; |
| 27 | uint16_t *alpha_to = rs->alpha_to; |
| 28 | uint16_t *index_of = rs->index_of; |
| 29 | uint16_t u, q, tmp, num1, num2, den, discr_r, syn_error; |
| 30 | /* Err+Eras Locator poly and syndrome poly The maximum value |
| 31 | * of nroots is 8. So the necessary stack size will be about |
| 32 | * 220 bytes max. |
| 33 | */ |
| 34 | uint16_t lambda[nroots + 1], syn[nroots]; |
| 35 | uint16_t b[nroots + 1], t[nroots + 1], omega[nroots + 1]; |
| 36 | uint16_t root[nroots], reg[nroots + 1], loc[nroots]; |
| 37 | int count = 0; |
| 38 | uint16_t msk = (uint16_t) rs->nn; |
| 39 | |
| 40 | /* Check length parameter for validity */ |
| 41 | pad = nn - nroots - len; |
Jörn Engel | 1dd7fdb | 2007-10-20 23:14:42 +0200 | [diff] [blame] | 42 | BUG_ON(pad < 0 || pad >= nn); |
Thomas Gleixner | 03ead84 | 2005-11-07 11:15:37 +0000 | [diff] [blame] | 43 | |
Linus Torvalds | 1da177e | 2005-04-16 15:20:36 -0700 | [diff] [blame] | 44 | /* Does the caller provide the syndrome ? */ |
Ferdinand Blomqvist | 2419d39 | 2019-06-20 17:10:37 +0300 | [diff] [blame] | 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 | } |
Linus Torvalds | 1da177e | 2005-04-16 15:20:36 -0700 | [diff] [blame] | 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) { |
Thomas Gleixner | 03ead84 | 2005-11-07 11:15:37 +0000 | [diff] [blame] | 66 | syn[i] = (((uint16_t) data[j]) ^ |
Linus Torvalds | 1da177e | 2005-04-16 15:20:36 -0700 | [diff] [blame] | 67 | invmsk) & msk; |
| 68 | } else { |
| 69 | syn[i] = ((((uint16_t) data[j]) ^ |
Thomas Gleixner | 03ead84 | 2005-11-07 11:15:37 +0000 | [diff] [blame] | 70 | invmsk) & msk) ^ |
Linus Torvalds | 1da177e | 2005-04-16 15:20:36 -0700 | [diff] [blame] | 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 { |
Thomas Gleixner | 03ead84 | 2005-11-07 11:15:37 +0000 | [diff] [blame] | 82 | syn[i] = (((uint16_t) par[j]) & msk) ^ |
Linus Torvalds | 1da177e | 2005-04-16 15:20:36 -0700 | [diff] [blame] | 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 | count = 0; |
| 102 | goto finish; |
| 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 */ |
Thomas Gleixner | 03ead84 | 2005-11-07 11:15:37 +0000 | [diff] [blame] | 111 | lambda[1] = alpha_to[rs_modnn(rs, |
Ferdinand Blomqvist | 5c345e2 | 2019-06-20 17:10:34 +0300 | [diff] [blame] | 112 | prim * (nn - 1 - (eras_pos[0] + pad)))]; |
Linus Torvalds | 1da177e | 2005-04-16 15:20:36 -0700 | [diff] [blame] | 113 | for (i = 1; i < no_eras; i++) { |
Ferdinand Blomqvist | 5c345e2 | 2019-06-20 17:10:34 +0300 | [diff] [blame] | 114 | u = rs_modnn(rs, prim * (nn - 1 - (eras_pos[i] + pad))); |
Linus Torvalds | 1da177e | 2005-04-16 15:20:36 -0700 | [diff] [blame] | 115 | for (j = i + 1; j > 0; j--) { |
| 116 | tmp = index_of[lambda[j - 1]]; |
| 117 | if (tmp != nn) { |
Thomas Gleixner | 03ead84 | 2005-11-07 11:15:37 +0000 | [diff] [blame] | 118 | lambda[j] ^= |
Linus Torvalds | 1da177e | 2005-04-16 15:20:36 -0700 | [diff] [blame] | 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)) { |
Thomas Gleixner | 03ead84 | 2005-11-07 11:15:37 +0000 | [diff] [blame] | 139 | discr_r ^= |
| 140 | alpha_to[rs_modnn(rs, |
Linus Torvalds | 1da177e | 2005-04-16 15:20:36 -0700 | [diff] [blame] | 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) { |
Thomas Gleixner | 03ead84 | 2005-11-07 11:15:37 +0000 | [diff] [blame] | 155 | t[i + 1] = lambda[i + 1] ^ |
Linus Torvalds | 1da177e | 2005-04-16 15:20:36 -0700 | [diff] [blame] | 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 | /* Find roots of error+erasure locator polynomial by Chien search */ |
| 189 | memcpy(®[1], &lambda[1], nroots * sizeof(reg[0])); |
| 190 | count = 0; /* Number of roots of lambda(x) */ |
| 191 | for (i = 1, k = iprim - 1; i <= nn; i++, k = rs_modnn(rs, k + iprim)) { |
| 192 | q = 1; /* lambda[0] is always 0 */ |
| 193 | for (j = deg_lambda; j > 0; j--) { |
| 194 | if (reg[j] != nn) { |
| 195 | reg[j] = rs_modnn(rs, reg[j] + j); |
| 196 | q ^= alpha_to[reg[j]]; |
| 197 | } |
| 198 | } |
| 199 | if (q != 0) |
| 200 | continue; /* Not a root */ |
| 201 | /* store root (index-form) and error location number */ |
| 202 | root[count] = i; |
| 203 | loc[count] = k; |
| 204 | /* If we've already found max possible roots, |
| 205 | * abort the search to save time |
| 206 | */ |
| 207 | if (++count == deg_lambda) |
| 208 | break; |
| 209 | } |
| 210 | if (deg_lambda != count) { |
| 211 | /* |
| 212 | * deg(lambda) unequal to number of roots => uncorrectable |
| 213 | * error detected |
| 214 | */ |
Jörn Engel | eb68450 | 2007-10-20 23:16:32 +0200 | [diff] [blame] | 215 | count = -EBADMSG; |
Linus Torvalds | 1da177e | 2005-04-16 15:20:36 -0700 | [diff] [blame] | 216 | goto finish; |
| 217 | } |
| 218 | /* |
| 219 | * Compute err+eras evaluator poly omega(x) = s(x)*lambda(x) (modulo |
| 220 | * x**nroots). in index form. Also find deg(omega). |
| 221 | */ |
| 222 | deg_omega = deg_lambda - 1; |
| 223 | for (i = 0; i <= deg_omega; i++) { |
| 224 | tmp = 0; |
| 225 | for (j = i; j >= 0; j--) { |
| 226 | if ((s[i - j] != nn) && (lambda[j] != nn)) |
| 227 | tmp ^= |
| 228 | alpha_to[rs_modnn(rs, s[i - j] + lambda[j])]; |
| 229 | } |
| 230 | omega[i] = index_of[tmp]; |
| 231 | } |
| 232 | |
| 233 | /* |
| 234 | * Compute error values in poly-form. num1 = omega(inv(X(l))), num2 = |
| 235 | * inv(X(l))**(fcr-1) and den = lambda_pr(inv(X(l))) all in poly-form |
| 236 | */ |
| 237 | for (j = count - 1; j >= 0; j--) { |
| 238 | num1 = 0; |
| 239 | for (i = deg_omega; i >= 0; i--) { |
| 240 | if (omega[i] != nn) |
Thomas Gleixner | 03ead84 | 2005-11-07 11:15:37 +0000 | [diff] [blame] | 241 | num1 ^= alpha_to[rs_modnn(rs, omega[i] + |
Linus Torvalds | 1da177e | 2005-04-16 15:20:36 -0700 | [diff] [blame] | 242 | i * root[j])]; |
| 243 | } |
| 244 | num2 = alpha_to[rs_modnn(rs, root[j] * (fcr - 1) + nn)]; |
| 245 | den = 0; |
| 246 | |
| 247 | /* lambda[i+1] for i even is the formal derivative |
| 248 | * lambda_pr of lambda[i] */ |
| 249 | for (i = min(deg_lambda, nroots - 1) & ~1; i >= 0; i -= 2) { |
| 250 | if (lambda[i + 1] != nn) { |
Thomas Gleixner | 03ead84 | 2005-11-07 11:15:37 +0000 | [diff] [blame] | 251 | den ^= alpha_to[rs_modnn(rs, lambda[i + 1] + |
Linus Torvalds | 1da177e | 2005-04-16 15:20:36 -0700 | [diff] [blame] | 252 | i * root[j])]; |
| 253 | } |
| 254 | } |
| 255 | /* Apply error to data */ |
| 256 | if (num1 != 0 && loc[j] >= pad) { |
Thomas Gleixner | 03ead84 | 2005-11-07 11:15:37 +0000 | [diff] [blame] | 257 | uint16_t cor = alpha_to[rs_modnn(rs,index_of[num1] + |
Linus Torvalds | 1da177e | 2005-04-16 15:20:36 -0700 | [diff] [blame] | 258 | index_of[num2] + |
| 259 | nn - index_of[den])]; |
| 260 | /* Store the error correction pattern, if a |
| 261 | * correction buffer is available */ |
| 262 | if (corr) { |
| 263 | corr[j] = cor; |
| 264 | } else { |
| 265 | /* If a data buffer is given and the |
| 266 | * error is inside the message, |
| 267 | * correct it */ |
| 268 | if (data && (loc[j] < (nn - nroots))) |
| 269 | data[loc[j] - pad] ^= cor; |
| 270 | } |
| 271 | } |
| 272 | } |
| 273 | |
| 274 | finish: |
| 275 | if (eras_pos != NULL) { |
| 276 | for (i = 0; i < count; i++) |
| 277 | eras_pos[i] = loc[i] - pad; |
| 278 | } |
| 279 | return count; |
| 280 | |
| 281 | } |