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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;
42 if (pad < 0 || pad >= nn)
43 return -ERANGE;
Thomas Gleixner03ead842005-11-07 11:15:37 +000044
Linus Torvalds1da177e2005-04-16 15:20:36 -070045 /* Does the caller provide the syndrome ? */
Thomas Gleixner03ead842005-11-07 11:15:37 +000046 if (s != NULL)
Linus Torvalds1da177e2005-04-16 15:20:36 -070047 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) {
Thomas Gleixner03ead842005-11-07 11:15:37 +000057 syn[i] = (((uint16_t) data[j]) ^
Linus Torvalds1da177e2005-04-16 15:20:36 -070058 invmsk) & msk;
59 } else {
60 syn[i] = ((((uint16_t) data[j]) ^
Thomas Gleixner03ead842005-11-07 11:15:37 +000061 invmsk) & msk) ^
Linus Torvalds1da177e2005-04-16 15:20:36 -070062 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 {
Thomas Gleixner03ead842005-11-07 11:15:37 +000073 syn[i] = (((uint16_t) par[j]) & msk) ^
Linus Torvalds1da177e2005-04-16 15:20:36 -070074 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 */
Thomas Gleixner03ead842005-11-07 11:15:37 +0000102 lambda[1] = alpha_to[rs_modnn(rs,
Linus Torvalds1da177e2005-04-16 15:20:36 -0700103 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) {
Thomas Gleixner03ead842005-11-07 11:15:37 +0000109 lambda[j] ^=
Linus Torvalds1da177e2005-04-16 15:20:36 -0700110 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)) {
Thomas Gleixner03ead842005-11-07 11:15:37 +0000130 discr_r ^=
131 alpha_to[rs_modnn(rs,
Linus Torvalds1da177e2005-04-16 15:20:36 -0700132 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) {
Thomas Gleixner03ead842005-11-07 11:15:37 +0000146 t[i + 1] = lambda[i + 1] ^
Linus Torvalds1da177e2005-04-16 15:20:36 -0700147 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)
Thomas Gleixner03ead842005-11-07 11:15:37 +0000232 num1 ^= alpha_to[rs_modnn(rs, omega[i] +
Linus Torvalds1da177e2005-04-16 15:20:36 -0700233 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) {
Thomas Gleixner03ead842005-11-07 11:15:37 +0000242 den ^= alpha_to[rs_modnn(rs, lambda[i + 1] +
Linus Torvalds1da177e2005-04-16 15:20:36 -0700243 i * root[j])];
244 }
245 }
246 /* Apply error to data */
247 if (num1 != 0 && loc[j] >= pad) {
Thomas Gleixner03ead842005-11-07 11:15:37 +0000248 uint16_t cor = alpha_to[rs_modnn(rs,index_of[num1] +
Linus Torvalds1da177e2005-04-16 15:20:36 -0700249 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}