1 | // SPDX-License-Identifier: GPL-2.0 |
2 | /* |
3 | * Generic Reed Solomon encoder / decoder library |
4 | * |
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 | * |
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 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 | |
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 zero |
50 | */ |
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 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) { |
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 no |
100 | * errors to correct. So return data[] unmodified |
101 | */ |
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+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)) { |
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 | } 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 | } |
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 | |
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 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 | */ |
230 | return -EBADMSG; |
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 |
250 | * Note: we reuse the buffer for b to store the correction pattern |
251 | */ |
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 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) { |
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 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)]; |
297 | } |
298 | |
299 | if (tmp != alpha_to[s[i]]) |
300 | return -EBADMSG; |
301 | } |
302 | |
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 | } |
323 | } |
324 | |
325 | return num_corrected; |
326 | } |
327 | |