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03ead842 | 1 | /* |
1da177e4 LT |
2 | * lib/reed_solomon/decode_rs.c |
3 | * | |
4 | * Overview: | |
5 | * Generic Reed Solomon encoder / decoder library | |
03ead842 | 6 | * |
1da177e4 LT |
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 | * | |
03ead842 | 12 | * $Id: decode_rs.c,v 1.7 2005/11/07 11:14:59 gleixner Exp $ |
1da177e4 LT |
13 | * |
14 | */ | |
15 | ||
03ead842 | 16 | /* Generic data width independent code which is included by the |
1da177e4 LT |
17 | * wrappers. |
18 | */ | |
03ead842 | 19 | { |
1da177e4 LT |
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; | |
03ead842 | 44 | |
1da177e4 | 45 | /* Does the caller provide the syndrome ? */ |
03ead842 | 46 | if (s != NULL) |
1da177e4 LT |
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) { | |
03ead842 | 57 | syn[i] = (((uint16_t) data[j]) ^ |
1da177e4 LT |
58 | invmsk) & msk; |
59 | } else { | |
60 | syn[i] = ((((uint16_t) data[j]) ^ | |
03ead842 | 61 | invmsk) & msk) ^ |
1da177e4 LT |
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 { | |
03ead842 | 73 | syn[i] = (((uint16_t) par[j]) & msk) ^ |
1da177e4 LT |
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 */ | |
03ead842 | 102 | lambda[1] = alpha_to[rs_modnn(rs, |
1da177e4 LT |
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) { | |
03ead842 | 109 | lambda[j] ^= |
1da177e4 LT |
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)) { | |
03ead842 TG |
130 | discr_r ^= |
131 | alpha_to[rs_modnn(rs, | |
1da177e4 LT |
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) { | |
03ead842 | 146 | t[i + 1] = lambda[i + 1] ^ |
1da177e4 LT |
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) | |
03ead842 | 232 | num1 ^= alpha_to[rs_modnn(rs, omega[i] + |
1da177e4 LT |
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) { | |
03ead842 | 242 | den ^= alpha_to[rs_modnn(rs, lambda[i + 1] + |
1da177e4 LT |
243 | i * root[j])]; |
244 | } | |
245 | } | |
246 | /* Apply error to data */ | |
247 | if (num1 != 0 && loc[j] >= pad) { | |
03ead842 | 248 | uint16_t cor = alpha_to[rs_modnn(rs,index_of[num1] + |
1da177e4 LT |
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 | } |