lib/reed_solomon/decode_rs.c

   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(&reg[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 }