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1// SPDX-License-Identifier: GPL-2.02/*3 * Generic Reed Solomon encoder / decoder library4 *5 * Copyright 2002, Phil Karn, KA9Q6 * 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 are30 * 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 zero50 */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 of60 * 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 no100 * errors to correct. So return data[] unmodified101 */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+erasure130 * locator polynomial131 */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 } else159 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-zero192 * => uncorrectable error detected193 */194 return -EBADMSG;195 }196 197 /* Find roots of error+erasure locator polynomial by Chien search */198 memcpy(®[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 time221 */222 if (++count == deg_lambda)223 break;224 }225 if (deg_lambda != count) {226 /*227 * deg(lambda) unequal to number of roots => uncorrectable228 * error detected229 */230 return -EBADMSG;231 }232 /*233 * Compute err+eras evaluator poly omega(x) = s(x)*lambda(x) (modulo234 * 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-form250 * Note: we reuse the buffer for b to store the correction pattern251 */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 derivative271 * 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 matches287 * the syndrome of the received word288 */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 a305 * correction buffer is available306 */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 else321 par[loc[i] - pad - len] ^= b[i];322 }323 }324 325 return num_corrected;326}327