summaryrefslogtreecommitdiffstats
path: root/lib/reed_solomon/decode_rs.c
blob: 1db74eb098d0eb6e8123d07ed4be795a09bf82ce (plain) (blame)
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
79
80
81
82
83
84
85
86
87
88
89
90
91
92
93
94
95
96
97
98
99
100
101
102
103
104
105
106
107
108
109
110
111
112
113
114
115
116
117
118
119
120
121
122
123
124
125
126
127
128
129
130
131
132
133
134
135
136
137
138
139
140
141
142
143
144
145
146
147
148
149
150
151
152
153
154
155
156
157
158
159
160
161
162
163
164
165
166
167
168
169
170
171
172
173
174
175
176
177
178
179
180
181
182
183
184
185
186
187
188
189
190
191
192
193
194
195
196
197
198
199
200
201
202
203
204
205
206
207
208
209
210
211
212
213
214
215
216
217
218
219
220
221
222
223
224
225
226
227
228
229
230
231
232
233
234
235
236
237
238
239
240
241
242
243
244
245
246
247
248
249
250
251
252
253
254
255
256
257
258
259
260
261
262
263
264
265
266
267
268
269
270
271
// SPDX-License-Identifier: GPL-2.0
/*
 * Generic Reed Solomon encoder / decoder library
 *
 * Copyright 2002, Phil Karn, KA9Q
 * May be used under the terms of the GNU General Public License (GPL)
 *
 * Adaption to the kernel by Thomas Gleixner (tglx@linutronix.de)
 *
 * Generic data width independent code which is included by the wrappers.
 */
{
	struct rs_codec *rs = rsc->codec;
	int deg_lambda, el, deg_omega;
	int i, j, r, k, pad;
	int nn = rs->nn;
	int nroots = rs->nroots;
	int fcr = rs->fcr;
	int prim = rs->prim;
	int iprim = rs->iprim;
	uint16_t *alpha_to = rs->alpha_to;
	uint16_t *index_of = rs->index_of;
	uint16_t u, q, tmp, num1, num2, den, discr_r, syn_error;
	int count = 0;
	uint16_t msk = (uint16_t) rs->nn;

	/*
	 * The decoder buffers are in the rs control struct. They are
	 * arrays sized [nroots + 1]
	 */
	uint16_t *lambda = rsc->buffers + RS_DECODE_LAMBDA * (nroots + 1);
	uint16_t *syn = rsc->buffers + RS_DECODE_SYN * (nroots + 1);
	uint16_t *b = rsc->buffers + RS_DECODE_B * (nroots + 1);
	uint16_t *t = rsc->buffers + RS_DECODE_T * (nroots + 1);
	uint16_t *omega = rsc->buffers + RS_DECODE_OMEGA * (nroots + 1);
	uint16_t *root = rsc->buffers + RS_DECODE_ROOT * (nroots + 1);
	uint16_t *reg = rsc->buffers + RS_DECODE_REG * (nroots + 1);
	uint16_t *loc = rsc->buffers + RS_DECODE_LOC * (nroots + 1);

	/* Check length parameter for validity */
	pad = nn - nroots - len;
	BUG_ON(pad < 0 || pad >= nn);

	/* Does the caller provide the syndrome ? */
	if (s != NULL)
		goto decode;

	/* form the syndromes; i.e., evaluate data(x) at roots of
	 * g(x) */
	for (i = 0; i < nroots; i++)
		syn[i] = (((uint16_t) data[0]) ^ invmsk) & msk;

	for (j = 1; j < len; j++) {
		for (i = 0; i < nroots; i++) {
			if (syn[i] == 0) {
				syn[i] = (((uint16_t) data[j]) ^
					  invmsk) & msk;
			} else {
				syn[i] = ((((uint16_t) data[j]) ^
					   invmsk) & msk) ^
					alpha_to[rs_modnn(rs, index_of[syn[i]] +
						       (fcr + i) * prim)];
			}
		}
	}

	for (j = 0; j < nroots; j++) {
		for (i = 0; i < nroots; i++) {
			if (syn[i] == 0) {
				syn[i] = ((uint16_t) par[j]) & msk;
			} else {
				syn[i] = (((uint16_t) par[j]) & msk) ^
					alpha_to[rs_modnn(rs, index_of[syn[i]] +
						       (fcr+i)*prim)];
			}
		}
	}
	s = syn;

	/* Convert syndromes to index form, checking for nonzero condition */
	syn_error = 0;
	for (i = 0; i < nroots; i++) {
		syn_error |= s[i];
		s[i] = index_of[s[i]];
	}

	if (!syn_error) {
		/* if syndrome is zero, data[] is a codeword and there are no
		 * errors to correct. So return data[] unmodified
		 */
		count = 0;
		goto finish;
	}

 decode:
	memset(&lambda[1], 0, nroots * sizeof(lambda[0]));
	lambda[0] = 1;

	if (no_eras > 0) {
		/* Init lambda to be the erasure locator polynomial */
		lambda[1] = alpha_to[rs_modnn(rs,
					      prim * (nn - 1 - eras_pos[0]))];
		for (i = 1; i < no_eras; i++) {
			u = rs_modnn(rs, prim * (nn - 1 - eras_pos[i]));
			for (j = i + 1; j > 0; j--) {
				tmp = index_of[lambda[j - 1]];
				if (tmp != nn) {
					lambda[j] ^=
						alpha_to[rs_modnn(rs, u + tmp)];
				}
			}
		}
	}

	for (i = 0; i < nroots + 1; i++)
		b[i] = index_of[lambda[i]];

	/*
	 * Begin Berlekamp-Massey algorithm to determine error+erasure
	 * locator polynomial
	 */
	r = no_eras;
	el = no_eras;
	while (++r <= nroots) {	/* r is the step number */
		/* Compute discrepancy at the r-th step in poly-form */
		discr_r = 0;
		for (i = 0; i < r; i++) {
			if ((lambda[i] != 0) && (s[r - i - 1] != nn)) {
				discr_r ^=
					alpha_to[rs_modnn(rs,
							  index_of[lambda[i]] +
							  s[r - i - 1])];
			}
		}
		discr_r = index_of[discr_r];	/* Index form */
		if (discr_r == nn) {
			/* 2 lines below: B(x) <-- x*B(x) */
			memmove (&b[1], b, nroots * sizeof (b[0]));
			b[0] = nn;
		} else {
			/* 7 lines below: T(x) <-- lambda(x)-discr_r*x*b(x) */
			t[0] = lambda[0];
			for (i = 0; i < nroots; i++) {
				if (b[i] != nn) {
					t[i + 1] = lambda[i + 1] ^
						alpha_to[rs_modnn(rs, discr_r +
								  b[i])];
				} else
					t[i + 1] = lambda[i + 1];
			}
			if (2 * el <= r + no_eras - 1) {
				el = r + no_eras - el;
				/*
				 * 2 lines below: B(x) <-- inv(discr_r) *
				 * lambda(x)
				 */
				for (i = 0; i <= nroots; i++) {
					b[i] = (lambda[i] == 0) ? nn :
						rs_modnn(rs, index_of[lambda[i]]
							 - discr_r + nn);
				}
			} else {
				/* 2 lines below: B(x) <-- x*B(x) */
				memmove(&b[1], b, nroots * sizeof(b[0]));
				b[0] = nn;
			}
			memcpy(lambda, t, (nroots + 1) * sizeof(t[0]));
		}
	}

	/* Convert lambda to index form and compute deg(lambda(x)) */
	deg_lambda = 0;
	for (i = 0; i < nroots + 1; i++) {
		lambda[i] = index_of[lambda[i]];
		if (lambda[i] != nn)
			deg_lambda = i;
	}
	/* Find roots of error+erasure locator polynomial by Chien search */
	memcpy(&reg[1], &lambda[1], nroots * sizeof(reg[0]));
	count = 0;		/* Number of roots of lambda(x) */
	for (i = 1, k = iprim - 1; i <= nn; i++, k = rs_modnn(rs, k + iprim)) {
		q = 1;		/* lambda[0] is always 0 */
		for (j = deg_lambda; j > 0; j--) {
			if (reg[j] != nn) {
				reg[j] = rs_modnn(rs, reg[j] + j);
				q ^= alpha_to[reg[j]];
			}
		}
		if (q != 0)
			continue;	/* Not a root */
		/* store root (index-form) and error location number */
		root[count] = i;
		loc[count] = k;
		/* If we've already found max possible roots,
		 * abort the search to save time
		 */
		if (++count == deg_lambda)
			break;
	}
	if (deg_lambda != count) {
		/*
		 * deg(lambda) unequal to number of roots => uncorrectable
		 * error detected
		 */
		count = -EBADMSG;
		goto finish;
	}
	/*
	 * Compute err+eras evaluator poly omega(x) = s(x)*lambda(x) (modulo
	 * x**nroots). in index form. Also find deg(omega).
	 */
	deg_omega = deg_lambda - 1;
	for (i = 0; i <= deg_omega; i++) {
		tmp = 0;
		for (j = i; j >= 0; j--) {
			if ((s[i - j] != nn) && (lambda[j] != nn))
				tmp ^=
				    alpha_to[rs_modnn(rs, s[i - j] + lambda[j])];
		}
		omega[i] = index_of[tmp];
	}

	/*
	 * Compute error values in poly-form. num1 = omega(inv(X(l))), num2 =
	 * inv(X(l))**(fcr-1) and den = lambda_pr(inv(X(l))) all in poly-form
	 */
	for (j = count - 1; j >= 0; j--) {
		num1 = 0;
		for (i = deg_omega; i >= 0; i--) {
			if (omega[i] != nn)
				num1 ^= alpha_to[rs_modnn(rs, omega[i] +
							i * root[j])];
		}
		num2 = alpha_to[rs_modnn(rs, root[j] * (fcr - 1) + nn)];
		den = 0;

		/* lambda[i+1] for i even is the formal derivative
		 * lambda_pr of lambda[i] */
		for (i = min(deg_lambda, nroots - 1) & ~1; i >= 0; i -= 2) {
			if (lambda[i + 1] != nn) {
				den ^= alpha_to[rs_modnn(rs, lambda[i + 1] +
						       i * root[j])];
			}
		}
		/* Apply error to data */
		if (num1 != 0 && loc[j] >= pad) {
			uint16_t cor = alpha_to[rs_modnn(rs,index_of[num1] +
						       index_of[num2] +
						       nn - index_of[den])];
			/* Store the error correction pattern, if a
			 * correction buffer is available */
			if (corr) {
				corr[j] = cor;
			} else {
				/* If a data buffer is given and the
				 * error is inside the message,
				 * correct it */
				if (data && (loc[j] < (nn - nroots)))
					data[loc[j] - pad] ^= cor;
			}
		}
	}

finish:
	if (eras_pos != NULL) {
		for (i = 0; i < count; i++)
			eras_pos[i] = loc[i] - pad;
	}
	return count;

}