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