LXR linux/lib/reed_solomon/decode

   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}
 327