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Linux/lib/reed_solomon/decode_rs.c

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  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         uint16_t msk = (uint16_t) rs->nn;
 26 
 27         /*
 28          * The decoder buffers are in the rs control struct. They are
 29          * arrays sized [nroots + 1]
 30          */
 31         uint16_t *lambda = rsc->buffers + RS_DECODE_LAMBDA * (nroots + 1);
 32         uint16_t *syn = rsc->buffers + RS_DECODE_SYN * (nroots + 1);
 33         uint16_t *b = rsc->buffers + RS_DECODE_B * (nroots + 1);
 34         uint16_t *t = rsc->buffers + RS_DECODE_T * (nroots + 1);
 35         uint16_t *omega = rsc->buffers + RS_DECODE_OMEGA * (nroots + 1);
 36         uint16_t *root = rsc->buffers + RS_DECODE_ROOT * (nroots + 1);
 37         uint16_t *reg = rsc->buffers + RS_DECODE_REG * (nroots + 1);
 38         uint16_t *loc = rsc->buffers + RS_DECODE_LOC * (nroots + 1);
 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 

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