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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}
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 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 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}