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(&reg[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 
264 finish:
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 }
272