lib/reed_solomon/decode_rs.c

   1 /*
   2  * lib/reed_solomon/decode_rs.c
   3  *
   4  * Overview:
   5  *   Generic Reed Solomon encoder / decoder library
   6  *
   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  *
  12  * $Id: decode_rs.c,v 1.7 2005/11/07 11:14:59 gleixner Exp $
  13  *
  14  */
  15
  16 /* Generic data width independent code which is included by the
  17  * wrappers.
  18  */
  19 {
  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;
  42         BUG_ON(pad < 0 || pad >= nn);
  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                 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 */
 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         /* Find roots of error+erasure locator polynomial by Chien search */
 189         memcpy(&reg[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                  */
 215                 count = -EBADMSG;
 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)
 241                                 num1 ^= alpha_to[rs_modnn(rs, omega[i] +
 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) {
 251                                 den ^= alpha_to[rs_modnn(rs, lambda[i + 1] +
 252                                                        i * root[j])];
 253                         }
 254                 }
 255                 /* Apply error to data */
 256                 if (num1 != 0 && loc[j] >= pad) {
 257                         uint16_t cor = alpha_to[rs_modnn(rs,index_of[num1] +
 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 }