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dc8f923e | 1 | // SPDX-License-Identifier: GPL-2.0 |
03ead842 | 2 | /* |
3413e189 | 3 | * Generic Reed Solomon encoder / decoder library |
03ead842 | 4 | * |
1da177e4 LT |
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 | * | |
3413e189 | 10 | * Generic data width independent code which is included by the wrappers. |
1da177e4 | 11 | */ |
03ead842 | 12 | { |
21633981 | 13 | struct rs_codec *rs = rsc->codec; |
1da177e4 LT |
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; | |
1da177e4 | 24 | int count = 0; |
991305de | 25 | int num_corrected; |
1da177e4 LT |
26 | uint16_t msk = (uint16_t) rs->nn; |
27 | ||
45888b40 TG |
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 | ||
1da177e4 LT |
41 | /* Check length parameter for validity */ |
42 | pad = nn - nroots - len; | |
a343536f | 43 | BUG_ON(pad < 0 || pad >= nn - nroots); |
03ead842 | 44 | |
1da177e4 | 45 | /* Does the caller provide the syndrome ? */ |
ef4d6a85 FB |
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 | } | |
1da177e4 LT |
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) { | |
03ead842 | 67 | syn[i] = (((uint16_t) data[j]) ^ |
1da177e4 LT |
68 | invmsk) & msk; |
69 | } else { | |
70 | syn[i] = ((((uint16_t) data[j]) ^ | |
03ead842 | 71 | invmsk) & msk) ^ |
1da177e4 LT |
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 { | |
03ead842 | 83 | syn[i] = (((uint16_t) par[j]) & msk) ^ |
1da177e4 LT |
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 | */ | |
647cc9ec | 102 | return 0; |
1da177e4 LT |
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 */ | |
03ead842 | 111 | lambda[1] = alpha_to[rs_modnn(rs, |
2034a42d | 112 | prim * (nn - 1 - (eras_pos[0] + pad)))]; |
1da177e4 | 113 | for (i = 1; i < no_eras; i++) { |
2034a42d | 114 | u = rs_modnn(rs, prim * (nn - 1 - (eras_pos[i] + pad))); |
1da177e4 LT |
115 | for (j = i + 1; j > 0; j--) { |
116 | tmp = index_of[lambda[j - 1]]; | |
117 | if (tmp != nn) { | |
03ead842 | 118 | lambda[j] ^= |
1da177e4 LT |
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)) { | |
03ead842 TG |
139 | discr_r ^= |
140 | alpha_to[rs_modnn(rs, | |
1da177e4 LT |
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) { | |
03ead842 | 155 | t[i + 1] = lambda[i + 1] ^ |
1da177e4 LT |
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 | } | |
991305de FB |
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 | ||
1da177e4 LT |
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 */ | |
991305de FB |
210 | |
211 | if (k < pad) { | |
212 | /* Impossible error location. Uncorrectable error. */ | |
213 | return -EBADMSG; | |
214 | } | |
215 | ||
1da177e4 LT |
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 | */ | |
647cc9ec | 230 | return -EBADMSG; |
1da177e4 LT |
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 | |
991305de | 250 | * Note: we reuse the buffer for b to store the correction pattern |
1da177e4 | 251 | */ |
991305de | 252 | num_corrected = 0; |
1da177e4 LT |
253 | for (j = count - 1; j >= 0; j--) { |
254 | num1 = 0; | |
255 | for (i = deg_omega; i >= 0; i--) { | |
256 | if (omega[i] != nn) | |
03ead842 | 257 | num1 ^= alpha_to[rs_modnn(rs, omega[i] + |
1da177e4 LT |
258 | i * root[j])]; |
259 | } | |
991305de FB |
260 | |
261 | if (num1 == 0) { | |
262 | /* Nothing to correct at this position */ | |
263 | b[j] = 0; | |
264 | continue; | |
265 | } | |
266 | ||
1da177e4 LT |
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) { | |
03ead842 | 274 | den ^= alpha_to[rs_modnn(rs, lambda[i + 1] + |
1da177e4 LT |
275 | i * root[j])]; |
276 | } | |
277 | } | |
991305de FB |
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)]; | |
1da177e4 | 297 | } |
991305de FB |
298 | |
299 | if (tmp != alpha_to[s[i]]) | |
300 | return -EBADMSG; | |
1da177e4 LT |
301 | } |
302 | ||
991305de FB |
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 | } | |
1da177e4 | 323 | } |
1da177e4 | 324 | |
991305de | 325 | return num_corrected; |
1da177e4 | 326 | } |