blob: 65bc718f0dc08a3490c20ee147f5a3f719d30dbe [file] [log] [blame]
Thomas Gleixner03ead842005-11-07 11:15:37 +00001/*
Linus Torvalds1da177e2005-04-16 15:20:36 -07002 * lib/reed_solomon/decode_rs.c
3 *
4 * Overview:
5 * Generic Reed Solomon encoder / decoder library
Thomas Gleixner03ead842005-11-07 11:15:37 +00006 *
Linus Torvalds1da177e2005-04-16 15:20:36 -07007 * 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 *
Thomas Gleixner03ead842005-11-07 11:15:37 +000012 * $Id: decode_rs.c,v 1.7 2005/11/07 11:14:59 gleixner Exp $
Linus Torvalds1da177e2005-04-16 15:20:36 -070013 *
14 */
15
Thomas Gleixner03ead842005-11-07 11:15:37 +000016/* Generic data width independent code which is included by the
Linus Torvalds1da177e2005-04-16 15:20:36 -070017 * wrappers.
18 */
Thomas Gleixner03ead842005-11-07 11:15:37 +000019{
Linus Torvalds1da177e2005-04-16 15:20:36 -070020 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;
Jörn Engel1dd7fdb2007-10-20 23:14:42 +020042 BUG_ON(pad < 0 || pad >= nn);
Thomas Gleixner03ead842005-11-07 11:15:37 +000043
Linus Torvalds1da177e2005-04-16 15:20:36 -070044 /* Does the caller provide the syndrome ? */
Thomas Gleixner03ead842005-11-07 11:15:37 +000045 if (s != NULL)
Linus Torvalds1da177e2005-04-16 15:20:36 -070046 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) {
Thomas Gleixner03ead842005-11-07 11:15:37 +000056 syn[i] = (((uint16_t) data[j]) ^
Linus Torvalds1da177e2005-04-16 15:20:36 -070057 invmsk) & msk;
58 } else {
59 syn[i] = ((((uint16_t) data[j]) ^
Thomas Gleixner03ead842005-11-07 11:15:37 +000060 invmsk) & msk) ^
Linus Torvalds1da177e2005-04-16 15:20:36 -070061 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 {
Thomas Gleixner03ead842005-11-07 11:15:37 +000072 syn[i] = (((uint16_t) par[j]) & msk) ^
Linus Torvalds1da177e2005-04-16 15:20:36 -070073 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 */
Thomas Gleixner03ead842005-11-07 11:15:37 +0000101 lambda[1] = alpha_to[rs_modnn(rs,
Linus Torvalds1da177e2005-04-16 15:20:36 -0700102 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) {
Thomas Gleixner03ead842005-11-07 11:15:37 +0000108 lambda[j] ^=
Linus Torvalds1da177e2005-04-16 15:20:36 -0700109 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)) {
Thomas Gleixner03ead842005-11-07 11:15:37 +0000129 discr_r ^=
130 alpha_to[rs_modnn(rs,
Linus Torvalds1da177e2005-04-16 15:20:36 -0700131 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) {
Thomas Gleixner03ead842005-11-07 11:15:37 +0000145 t[i + 1] = lambda[i + 1] ^
Linus Torvalds1da177e2005-04-16 15:20:36 -0700146 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 = -1;
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)
Thomas Gleixner03ead842005-11-07 11:15:37 +0000231 num1 ^= alpha_to[rs_modnn(rs, omega[i] +
Linus Torvalds1da177e2005-04-16 15:20:36 -0700232 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) {
Thomas Gleixner03ead842005-11-07 11:15:37 +0000241 den ^= alpha_to[rs_modnn(rs, lambda[i + 1] +
Linus Torvalds1da177e2005-04-16 15:20:36 -0700242 i * root[j])];
243 }
244 }
245 /* Apply error to data */
246 if (num1 != 0 && loc[j] >= pad) {
Thomas Gleixner03ead842005-11-07 11:15:37 +0000247 uint16_t cor = alpha_to[rs_modnn(rs,index_of[num1] +
Linus Torvalds1da177e2005-04-16 15:20:36 -0700248 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}