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(®[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 } 273