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 1.6 2004/10/22 15:41:47 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         if (pad < 0 || pad >= nn)
  43                 return -ERANGE;
  44
  45         /* Does the caller provide the syndrome ? */
  46         if (s != NULL)
  47                 goto decode;
  48
  49         /* form the syndromes; i.e., evaluate data(x) at roots of
  50          * g(x) */
  51         for (i = 0; i < nroots; i++)
  52                 syn[i] = (((uint16_t) data[0]) ^ invmsk) & msk;
  53
  54         for (j = 1; j < len; j++) {
  55                 for (i = 0; i < nroots; i++) {
  56                         if (syn[i] == 0) {
  57                                 syn[i] = (((uint16_t) data[j]) ^
  58                                           invmsk) & msk;
  59                         } else {
  60                                 syn[i] = ((((uint16_t) data[j]) ^
  61                                            invmsk) & msk) ^
  62                                         alpha_to[rs_modnn(rs, index_of[syn[i]] +
  63                                                        (fcr + i) * prim)];
  64                         }
  65                 }
  66         }
  67
  68         for (j = 0; j < nroots; j++) {
  69                 for (i = 0; i < nroots; i++) {
  70                         if (syn[i] == 0) {
  71                                 syn[i] = ((uint16_t) par[j]) & msk;
  72                         } else {
  73                                 syn[i] = (((uint16_t) par[j]) & msk) ^
  74                                         alpha_to[rs_modnn(rs, index_of[syn[i]] +
  75                                                        (fcr+i)*prim)];
  76                         }
  77                 }
  78         }
  79         s = syn;
  80
  81         /* Convert syndromes to index form, checking for nonzero condition */
  82         syn_error = 0;
  83         for (i = 0; i < nroots; i++) {
  84                 syn_error |= s[i];
  85                 s[i] = index_of[s[i]];
  86         }
  87
  88         if (!syn_error) {
  89                 /* if syndrome is zero, data[] is a codeword and there are no
  90                  * errors to correct. So return data[] unmodified
  91                  */
  92                 count = 0;
  93                 goto finish;
  94         }
  95
  96  decode:
  97         memset(&lambda[1], 0, nroots * sizeof(lambda[0]));
  98         lambda[0] = 1;
  99
 100         if (no_eras > 0) {
 101                 /* Init lambda to be the erasure locator polynomial */
 102                 lambda[1] = alpha_to[rs_modnn(rs,
 103                                               prim * (nn - 1 - eras_pos[0]))];
 104                 for (i = 1; i < no_eras; i++) {
 105                         u = rs_modnn(rs, prim * (nn - 1 - eras_pos[i]));
 106                         for (j = i + 1; j > 0; j--) {
 107                                 tmp = index_of[lambda[j - 1]];
 108                                 if (tmp != nn) {
 109                                         lambda[j] ^=
 110                                                 alpha_to[rs_modnn(rs, u + tmp)];
 111                                 }
 112                         }
 113                 }
 114         }
 115
 116         for (i = 0; i < nroots + 1; i++)
 117                 b[i] = index_of[lambda[i]];
 118
 119         /*
 120          * Begin Berlekamp-Massey algorithm to determine error+erasure
 121          * locator polynomial
 122          */
 123         r = no_eras;
 124         el = no_eras;
 125         while (++r <= nroots) { /* r is the step number */
 126                 /* Compute discrepancy at the r-th step in poly-form */
 127                 discr_r = 0;
 128                 for (i = 0; i < r; i++) {
 129                         if ((lambda[i] != 0) && (s[r - i - 1] != nn)) {
 130                                 discr_r ^=
 131                                         alpha_to[rs_modnn(rs,
 132                                                           index_of[lambda[i]] +
 133                                                           s[r - i - 1])];
 134                         }
 135                 }
 136                 discr_r = index_of[discr_r];    /* Index form */
 137                 if (discr_r == nn) {
 138                         /* 2 lines below: B(x) <-- x*B(x) */
 139                         memmove (&b[1], b, nroots * sizeof (b[0]));
 140                         b[0] = nn;
 141                 } else {
 142                         /* 7 lines below: T(x) <-- lambda(x)-discr_r*x*b(x) */
 143                         t[0] = lambda[0];
 144                         for (i = 0; i < nroots; i++) {
 145                                 if (b[i] != nn) {
 146                                         t[i + 1] = lambda[i + 1] ^
 147                                                 alpha_to[rs_modnn(rs, discr_r +
 148                                                                   b[i])];
 149                                 } else
 150                                         t[i + 1] = lambda[i + 1];
 151                         }
 152                         if (2 * el <= r + no_eras - 1) {
 153                                 el = r + no_eras - el;
 154                                 /*
 155                                  * 2 lines below: B(x) <-- inv(discr_r) *
 156                                  * lambda(x)
 157                                  */
 158                                 for (i = 0; i <= nroots; i++) {
 159                                         b[i] = (lambda[i] == 0) ? nn :
 160                                                 rs_modnn(rs, index_of[lambda[i]]
 161                                                          - discr_r + nn);
 162                                 }
 163                         } else {
 164                                 /* 2 lines below: B(x) <-- x*B(x) */
 165                                 memmove(&b[1], b, nroots * sizeof(b[0]));
 166                                 b[0] = nn;
 167                         }
 168                         memcpy(lambda, t, (nroots + 1) * sizeof(t[0]));
 169                 }
 170         }
 171
 172         /* Convert lambda to index form and compute deg(lambda(x)) */
 173         deg_lambda = 0;
 174         for (i = 0; i < nroots + 1; i++) {
 175                 lambda[i] = index_of[lambda[i]];
 176                 if (lambda[i] != nn)
 177                         deg_lambda = i;
 178         }
 179         /* Find roots of error+erasure locator polynomial by Chien search */
 180         memcpy(&reg[1], &lambda[1], nroots * sizeof(reg[0]));
 181         count = 0;              /* Number of roots of lambda(x) */
 182         for (i = 1, k = iprim - 1; i <= nn; i++, k = rs_modnn(rs, k + iprim)) {
 183                 q = 1;          /* lambda[0] is always 0 */
 184                 for (j = deg_lambda; j > 0; j--) {
 185                         if (reg[j] != nn) {
 186                                 reg[j] = rs_modnn(rs, reg[j] + j);
 187                                 q ^= alpha_to[reg[j]];
 188                         }
 189                 }
 190                 if (q != 0)
 191                         continue;       /* Not a root */
 192                 /* store root (index-form) and error location number */
 193                 root[count] = i;
 194                 loc[count] = k;
 195                 /* If we've already found max possible roots,
 196                  * abort the search to save time
 197                  */
 198                 if (++count == deg_lambda)
 199                         break;
 200         }
 201         if (deg_lambda != count) {
 202                 /*
 203                  * deg(lambda) unequal to number of roots => uncorrectable
 204                  * error detected
 205                  */
 206                 count = -1;
 207                 goto finish;
 208         }
 209         /*
 210          * Compute err+eras evaluator poly omega(x) = s(x)*lambda(x) (modulo
 211          * x**nroots). in index form. Also find deg(omega).
 212          */
 213         deg_omega = deg_lambda - 1;
 214         for (i = 0; i <= deg_omega; i++) {
 215                 tmp = 0;
 216                 for (j = i; j >= 0; j--) {
 217                         if ((s[i - j] != nn) && (lambda[j] != nn))
 218                                 tmp ^=
 219                                     alpha_to[rs_modnn(rs, s[i - j] + lambda[j])];
 220                 }
 221                 omega[i] = index_of[tmp];
 222         }
 223
 224         /*
 225          * Compute error values in poly-form. num1 = omega(inv(X(l))), num2 =
 226          * inv(X(l))**(fcr-1) and den = lambda_pr(inv(X(l))) all in poly-form
 227          */
 228         for (j = count - 1; j >= 0; j--) {
 229                 num1 = 0;
 230                 for (i = deg_omega; i >= 0; i--) {
 231                         if (omega[i] != nn)
 232                                 num1 ^= alpha_to[rs_modnn(rs, omega[i] +
 233                                                         i * root[j])];
 234                 }
 235                 num2 = alpha_to[rs_modnn(rs, root[j] * (fcr - 1) + nn)];
 236                 den = 0;
 237
 238                 /* lambda[i+1] for i even is the formal derivative
 239                  * lambda_pr of lambda[i] */
 240                 for (i = min(deg_lambda, nroots - 1) & ~1; i >= 0; i -= 2) {
 241                         if (lambda[i + 1] != nn) {
 242                                 den ^= alpha_to[rs_modnn(rs, lambda[i + 1] +
 243                                                        i * root[j])];
 244                         }
 245                 }
 246                 /* Apply error to data */
 247                 if (num1 != 0 && loc[j] >= pad) {
 248                         uint16_t cor = alpha_to[rs_modnn(rs,index_of[num1] +
 249                                                        index_of[num2] +
 250                                                        nn - index_of[den])];
 251                         /* Store the error correction pattern, if a
 252                          * correction buffer is available */
 253                         if (corr) {
 254                                 corr[j] = cor;
 255                         } else {
 256                                 /* If a data buffer is given and the
 257                                  * error is inside the message,
 258                                  * correct it */
 259                                 if (data && (loc[j] < (nn - nroots)))
 260                                         data[loc[j] - pad] ^= cor;
 261                         }
 262                 }
 263         }
 264
 265 finish:
 266         if (eras_pos != NULL) {
 267                 for (i = 0; i < count; i++)
 268                         eras_pos[i] = loc[i] - pad;
 269         }
 270         return count;
 271
 272 }