xref: /openbmc/linux/lib/reed_solomon/decode_rs.c (revision 991305de)
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(&reg[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