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