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 1.1.1.1 2007/08/03 18:53:48 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	if (pad < 0 || pad >= nn)
43		return -ERANGE;
44
45	/* Does the caller provide the syndrome ? */
46	if (s != NULL)
47		goto decode;
48
49	/* form the syndromes; i.e., evaluate data(x) at roots of
50	 * g(x) */
51	for (i = 0; i < nroots; i++)
52		syn[i] = (((uint16_t) data[0]) ^ invmsk) & msk;
53
54	for (j = 1; j < len; j++) {
55		for (i = 0; i < nroots; i++) {
56			if (syn[i] == 0) {
57				syn[i] = (((uint16_t) data[j]) ^
58					  invmsk) & msk;
59			} else {
60				syn[i] = ((((uint16_t) data[j]) ^
61					   invmsk) & msk) ^
62					alpha_to[rs_modnn(rs, index_of[syn[i]] +
63						       (fcr + i) * prim)];
64			}
65		}
66	}
67
68	for (j = 0; j < nroots; j++) {
69		for (i = 0; i < nroots; i++) {
70			if (syn[i] == 0) {
71				syn[i] = ((uint16_t) par[j]) & msk;
72			} else {
73				syn[i] = (((uint16_t) par[j]) & msk) ^
74					alpha_to[rs_modnn(rs, index_of[syn[i]] +
75						       (fcr+i)*prim)];
76			}
77		}
78	}
79	s = syn;
80
81	/* Convert syndromes to index form, checking for nonzero condition */
82	syn_error = 0;
83	for (i = 0; i < nroots; i++) {
84		syn_error |= s[i];
85		s[i] = index_of[s[i]];
86	}
87
88	if (!syn_error) {
89		/* if syndrome is zero, data[] is a codeword and there are no
90		 * errors to correct. So return data[] unmodified
91		 */
92		count = 0;
93		goto finish;
94	}
95
96 decode:
97	memset(&lambda[1], 0, nroots * sizeof(lambda[0]));
98	lambda[0] = 1;
99
100	if (no_eras > 0) {
101		/* Init lambda to be the erasure locator polynomial */
102		lambda[1] = alpha_to[rs_modnn(rs,
103					      prim * (nn - 1 - eras_pos[0]))];
104		for (i = 1; i < no_eras; i++) {
105			u = rs_modnn(rs, prim * (nn - 1 - eras_pos[i]));
106			for (j = i + 1; j > 0; j--) {
107				tmp = index_of[lambda[j - 1]];
108				if (tmp != nn) {
109					lambda[j] ^=
110						alpha_to[rs_modnn(rs, u + tmp)];
111				}
112			}
113		}
114	}
115
116	for (i = 0; i < nroots + 1; i++)
117		b[i] = index_of[lambda[i]];
118
119	/*
120	 * Begin Berlekamp-Massey algorithm to determine error+erasure
121	 * locator polynomial
122	 */
123	r = no_eras;
124	el = no_eras;
125	while (++r <= nroots) {	/* r is the step number */
126		/* Compute discrepancy at the r-th step in poly-form */
127		discr_r = 0;
128		for (i = 0; i < r; i++) {
129			if ((lambda[i] != 0) && (s[r - i - 1] != nn)) {
130				discr_r ^=
131					alpha_to[rs_modnn(rs,
132							  index_of[lambda[i]] +
133							  s[r - i - 1])];
134			}
135		}
136		discr_r = index_of[discr_r];	/* Index form */
137		if (discr_r == nn) {
138			/* 2 lines below: B(x) <-- x*B(x) */
139			memmove (&b[1], b, nroots * sizeof (b[0]));
140			b[0] = nn;
141		} else {
142			/* 7 lines below: T(x) <-- lambda(x)-discr_r*x*b(x) */
143			t[0] = lambda[0];
144			for (i = 0; i < nroots; i++) {
145				if (b[i] != nn) {
146					t[i + 1] = lambda[i + 1] ^
147						alpha_to[rs_modnn(rs, discr_r +
148								  b[i])];
149				} else
150					t[i + 1] = lambda[i + 1];
151			}
152			if (2 * el <= r + no_eras - 1) {
153				el = r + no_eras - el;
154				/*
155				 * 2 lines below: B(x) <-- inv(discr_r) *
156				 * lambda(x)
157				 */
158				for (i = 0; i <= nroots; i++) {
159					b[i] = (lambda[i] == 0) ? nn :
160						rs_modnn(rs, index_of[lambda[i]]
161							 - discr_r + nn);
162				}
163			} else {
164				/* 2 lines below: B(x) <-- x*B(x) */
165				memmove(&b[1], b, nroots * sizeof(b[0]));
166				b[0] = nn;
167			}
168			memcpy(lambda, t, (nroots + 1) * sizeof(t[0]));
169		}
170	}
171
172	/* Convert lambda to index form and compute deg(lambda(x)) */
173	deg_lambda = 0;
174	for (i = 0; i < nroots + 1; i++) {
175		lambda[i] = index_of[lambda[i]];
176		if (lambda[i] != nn)
177			deg_lambda = i;
178	}
179	/* Find roots of error+erasure locator polynomial by Chien search */
180	memcpy(&reg[1], &lambda[1], nroots * sizeof(reg[0]));
181	count = 0;		/* Number of roots of lambda(x) */
182	for (i = 1, k = iprim - 1; i <= nn; i++, k = rs_modnn(rs, k + iprim)) {
183		q = 1;		/* lambda[0] is always 0 */
184		for (j = deg_lambda; j > 0; j--) {
185			if (reg[j] != nn) {
186				reg[j] = rs_modnn(rs, reg[j] + j);
187				q ^= alpha_to[reg[j]];
188			}
189		}
190		if (q != 0)
191			continue;	/* Not a root */
192		/* store root (index-form) and error location number */
193		root[count] = i;
194		loc[count] = k;
195		/* If we've already found max possible roots,
196		 * abort the search to save time
197		 */
198		if (++count == deg_lambda)
199			break;
200	}
201	if (deg_lambda != count) {
202		/*
203		 * deg(lambda) unequal to number of roots => uncorrectable
204		 * error detected
205		 */
206		count = -1;
207		goto finish;
208	}
209	/*
210	 * Compute err+eras evaluator poly omega(x) = s(x)*lambda(x) (modulo
211	 * x**nroots). in index form. Also find deg(omega).
212	 */
213	deg_omega = deg_lambda - 1;
214	for (i = 0; i <= deg_omega; i++) {
215		tmp = 0;
216		for (j = i; j >= 0; j--) {
217			if ((s[i - j] != nn) && (lambda[j] != nn))
218				tmp ^=
219				    alpha_to[rs_modnn(rs, s[i - j] + lambda[j])];
220		}
221		omega[i] = index_of[tmp];
222	}
223
224	/*
225	 * Compute error values in poly-form. num1 = omega(inv(X(l))), num2 =
226	 * inv(X(l))**(fcr-1) and den = lambda_pr(inv(X(l))) all in poly-form
227	 */
228	for (j = count - 1; j >= 0; j--) {
229		num1 = 0;
230		for (i = deg_omega; i >= 0; i--) {
231			if (omega[i] != nn)
232				num1 ^= alpha_to[rs_modnn(rs, omega[i] +
233							i * root[j])];
234		}
235		num2 = alpha_to[rs_modnn(rs, root[j] * (fcr - 1) + nn)];
236		den = 0;
237
238		/* lambda[i+1] for i even is the formal derivative
239		 * lambda_pr of lambda[i] */
240		for (i = min(deg_lambda, nroots - 1) & ~1; i >= 0; i -= 2) {
241			if (lambda[i + 1] != nn) {
242				den ^= alpha_to[rs_modnn(rs, lambda[i + 1] +
243						       i * root[j])];
244			}
245		}
246		/* Apply error to data */
247		if (num1 != 0 && loc[j] >= pad) {
248			uint16_t cor = alpha_to[rs_modnn(rs,index_of[num1] +
249						       index_of[num2] +
250						       nn - index_of[den])];
251			/* Store the error correction pattern, if a
252			 * correction buffer is available */
253			if (corr) {
254				corr[j] = cor;
255			} else {
256				/* If a data buffer is given and the
257				 * error is inside the message,
258				 * correct it */
259				if (data && (loc[j] < (nn - nroots)))
260					data[loc[j] - pad] ^= cor;
261			}
262		}
263	}
264
265finish:
266	if (eras_pos != NULL) {
267		for (i = 0; i < count; i++)
268			eras_pos[i] = loc[i] - pad;
269	}
270	return count;
271
272}
273