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1 // SPDX-License-Identifier: GPL-2.0
2 /*
3  * Generic binary BCH encoding/decoding library
4  *
5  * Copyright © 2011 Parrot S.A.
6  *
7  * Author: Ivan Djelic <ivan.djelic@parrot.com>
8  *
9  * Description:
10  *
11  * This library provides runtime configurable encoding/decoding of binary
12  * Bose-Chaudhuri-Hocquenghem (BCH) codes.
13  *
14  * Call init_bch to get a pointer to a newly allocated bch_control structure for
15  * the given m (Galois field order), t (error correction capability) and
16  * (optional) primitive polynomial parameters.
17  *
18  * Call encode_bch to compute and store ecc parity bytes to a given buffer.
19  * Call decode_bch to detect and locate errors in received data.
20  *
21  * On systems supporting hw BCH features, intermediate results may be provided
22  * to decode_bch in order to skip certain steps. See decode_bch() documentation
23  * for details.
24  *
25  * Option CONFIG_BCH_CONST_PARAMS can be used to force fixed values of
26  * parameters m and t; thus allowing extra compiler optimizations and providing
27  * better (up to 2x) encoding performance. Using this option makes sense when
28  * (m,t) are fixed and known in advance, e.g. when using BCH error correction
29  * on a particular NAND flash device.
30  *
31  * Algorithmic details:
32  *
33  * Encoding is performed by processing 32 input bits in parallel, using 4
34  * remainder lookup tables.
35  *
36  * The final stage of decoding involves the following internal steps:
37  * a. Syndrome computation
38  * b. Error locator polynomial computation using Berlekamp-Massey algorithm
39  * c. Error locator root finding (by far the most expensive step)
40  *
41  * In this implementation, step c is not performed using the usual Chien search.
42  * Instead, an alternative approach described in [1] is used. It consists in
43  * factoring the error locator polynomial using the Berlekamp Trace algorithm
44  * (BTA) down to a certain degree (4), after which ad hoc low-degree polynomial
45  * solving techniques [2] are used. The resulting algorithm, called BTZ, yields
46  * much better performance than Chien search for usual (m,t) values (typically
47  * m >= 13, t < 32, see [1]).
48  *
49  * [1] B. Biswas, V. Herbert. Efficient root finding of polynomials over fields
50  * of characteristic 2, in: Western European Workshop on Research in Cryptology
51  * - WEWoRC 2009, Graz, Austria, LNCS, Springer, July 2009, to appear.
52  * [2] [Zin96] V.A. Zinoviev. On the solution of equations of degree 10 over
53  * finite fields GF(2^q). In Rapport de recherche INRIA no 2829, 1996.
54  */
55 
56 #ifndef USE_HOSTCC
57 #include <common.h>
58 #include <ubi_uboot.h>
59 
60 #include <linux/bitops.h>
61 #else
62 #include <errno.h>
63 #if defined(__FreeBSD__)
64 #include <sys/endian.h>
65 #else
66 #include <endian.h>
67 #endif
68 #include <stdint.h>
69 #include <stdlib.h>
70 #include <string.h>
71 
72 #undef cpu_to_be32
73 #define cpu_to_be32 htobe32
74 #define DIV_ROUND_UP(n,d) (((n) + (d) - 1) / (d))
75 #define kmalloc(size, flags)	malloc(size)
76 #define kzalloc(size, flags)	calloc(1, size)
77 #define kfree free
78 #define ARRAY_SIZE(arr) (sizeof(arr) / sizeof((arr)[0]))
79 #endif
80 
81 #include <asm/byteorder.h>
82 #include <linux/bch.h>
83 
84 #if defined(CONFIG_BCH_CONST_PARAMS)
85 #define GF_M(_p)               (CONFIG_BCH_CONST_M)
86 #define GF_T(_p)               (CONFIG_BCH_CONST_T)
87 #define GF_N(_p)               ((1 << (CONFIG_BCH_CONST_M))-1)
88 #else
89 #define GF_M(_p)               ((_p)->m)
90 #define GF_T(_p)               ((_p)->t)
91 #define GF_N(_p)               ((_p)->n)
92 #endif
93 
94 #define BCH_ECC_WORDS(_p)      DIV_ROUND_UP(GF_M(_p)*GF_T(_p), 32)
95 #define BCH_ECC_BYTES(_p)      DIV_ROUND_UP(GF_M(_p)*GF_T(_p), 8)
96 
97 #ifndef dbg
98 #define dbg(_fmt, args...)     do {} while (0)
99 #endif
100 
101 /*
102  * represent a polynomial over GF(2^m)
103  */
104 struct gf_poly {
105 	unsigned int deg;    /* polynomial degree */
106 	unsigned int c[0];   /* polynomial terms */
107 };
108 
109 /* given its degree, compute a polynomial size in bytes */
110 #define GF_POLY_SZ(_d) (sizeof(struct gf_poly)+((_d)+1)*sizeof(unsigned int))
111 
112 /* polynomial of degree 1 */
113 struct gf_poly_deg1 {
114 	struct gf_poly poly;
115 	unsigned int   c[2];
116 };
117 
118 #ifdef USE_HOSTCC
119 #if !defined(__DragonFly__) && !defined(__FreeBSD__)
fls(int x)120 static int fls(int x)
121 {
122 	int r = 32;
123 
124 	if (!x)
125 		return 0;
126 	if (!(x & 0xffff0000u)) {
127 		x <<= 16;
128 		r -= 16;
129 	}
130 	if (!(x & 0xff000000u)) {
131 		x <<= 8;
132 		r -= 8;
133 	}
134 	if (!(x & 0xf0000000u)) {
135 		x <<= 4;
136 		r -= 4;
137 	}
138 	if (!(x & 0xc0000000u)) {
139 		x <<= 2;
140 		r -= 2;
141 	}
142 	if (!(x & 0x80000000u)) {
143 		x <<= 1;
144 		r -= 1;
145 	}
146 	return r;
147 }
148 #endif
149 #endif
150 
151 /*
152  * same as encode_bch(), but process input data one byte at a time
153  */
encode_bch_unaligned(struct bch_control * bch,const unsigned char * data,unsigned int len,uint32_t * ecc)154 static void encode_bch_unaligned(struct bch_control *bch,
155 				 const unsigned char *data, unsigned int len,
156 				 uint32_t *ecc)
157 {
158 	int i;
159 	const uint32_t *p;
160 	const int l = BCH_ECC_WORDS(bch)-1;
161 
162 	while (len--) {
163 		p = bch->mod8_tab + (l+1)*(((ecc[0] >> 24)^(*data++)) & 0xff);
164 
165 		for (i = 0; i < l; i++)
166 			ecc[i] = ((ecc[i] << 8)|(ecc[i+1] >> 24))^(*p++);
167 
168 		ecc[l] = (ecc[l] << 8)^(*p);
169 	}
170 }
171 
172 /*
173  * convert ecc bytes to aligned, zero-padded 32-bit ecc words
174  */
load_ecc8(struct bch_control * bch,uint32_t * dst,const uint8_t * src)175 static void load_ecc8(struct bch_control *bch, uint32_t *dst,
176 		      const uint8_t *src)
177 {
178 	uint8_t pad[4] = {0, 0, 0, 0};
179 	unsigned int i, nwords = BCH_ECC_WORDS(bch)-1;
180 
181 	for (i = 0; i < nwords; i++, src += 4)
182 		dst[i] = (src[0] << 24)|(src[1] << 16)|(src[2] << 8)|src[3];
183 
184 	memcpy(pad, src, BCH_ECC_BYTES(bch)-4*nwords);
185 	dst[nwords] = (pad[0] << 24)|(pad[1] << 16)|(pad[2] << 8)|pad[3];
186 }
187 
188 /*
189  * convert 32-bit ecc words to ecc bytes
190  */
store_ecc8(struct bch_control * bch,uint8_t * dst,const uint32_t * src)191 static void store_ecc8(struct bch_control *bch, uint8_t *dst,
192 		       const uint32_t *src)
193 {
194 	uint8_t pad[4];
195 	unsigned int i, nwords = BCH_ECC_WORDS(bch)-1;
196 
197 	for (i = 0; i < nwords; i++) {
198 		*dst++ = (src[i] >> 24);
199 		*dst++ = (src[i] >> 16) & 0xff;
200 		*dst++ = (src[i] >>  8) & 0xff;
201 		*dst++ = (src[i] >>  0) & 0xff;
202 	}
203 	pad[0] = (src[nwords] >> 24);
204 	pad[1] = (src[nwords] >> 16) & 0xff;
205 	pad[2] = (src[nwords] >>  8) & 0xff;
206 	pad[3] = (src[nwords] >>  0) & 0xff;
207 	memcpy(dst, pad, BCH_ECC_BYTES(bch)-4*nwords);
208 }
209 
210 /**
211  * encode_bch - calculate BCH ecc parity of data
212  * @bch:   BCH control structure
213  * @data:  data to encode
214  * @len:   data length in bytes
215  * @ecc:   ecc parity data, must be initialized by caller
216  *
217  * The @ecc parity array is used both as input and output parameter, in order to
218  * allow incremental computations. It should be of the size indicated by member
219  * @ecc_bytes of @bch, and should be initialized to 0 before the first call.
220  *
221  * The exact number of computed ecc parity bits is given by member @ecc_bits of
222  * @bch; it may be less than m*t for large values of t.
223  */
encode_bch(struct bch_control * bch,const uint8_t * data,unsigned int len,uint8_t * ecc)224 void encode_bch(struct bch_control *bch, const uint8_t *data,
225 		unsigned int len, uint8_t *ecc)
226 {
227 	const unsigned int l = BCH_ECC_WORDS(bch)-1;
228 	unsigned int i, mlen;
229 	unsigned long m;
230 	uint32_t w, r[l+1];
231 	const uint32_t * const tab0 = bch->mod8_tab;
232 	const uint32_t * const tab1 = tab0 + 256*(l+1);
233 	const uint32_t * const tab2 = tab1 + 256*(l+1);
234 	const uint32_t * const tab3 = tab2 + 256*(l+1);
235 	const uint32_t *pdata, *p0, *p1, *p2, *p3;
236 
237 	if (ecc) {
238 		/* load ecc parity bytes into internal 32-bit buffer */
239 		load_ecc8(bch, bch->ecc_buf, ecc);
240 	} else {
241 		memset(bch->ecc_buf, 0, sizeof(r));
242 	}
243 
244 	/* process first unaligned data bytes */
245 	m = ((unsigned long)data) & 3;
246 	if (m) {
247 		mlen = (len < (4-m)) ? len : 4-m;
248 		encode_bch_unaligned(bch, data, mlen, bch->ecc_buf);
249 		data += mlen;
250 		len  -= mlen;
251 	}
252 
253 	/* process 32-bit aligned data words */
254 	pdata = (uint32_t *)data;
255 	mlen  = len/4;
256 	data += 4*mlen;
257 	len  -= 4*mlen;
258 	memcpy(r, bch->ecc_buf, sizeof(r));
259 
260 	/*
261 	 * split each 32-bit word into 4 polynomials of weight 8 as follows:
262 	 *
263 	 * 31 ...24  23 ...16  15 ... 8  7 ... 0
264 	 * xxxxxxxx  yyyyyyyy  zzzzzzzz  tttttttt
265 	 *                               tttttttt  mod g = r0 (precomputed)
266 	 *                     zzzzzzzz  00000000  mod g = r1 (precomputed)
267 	 *           yyyyyyyy  00000000  00000000  mod g = r2 (precomputed)
268 	 * xxxxxxxx  00000000  00000000  00000000  mod g = r3 (precomputed)
269 	 * xxxxxxxx  yyyyyyyy  zzzzzzzz  tttttttt  mod g = r0^r1^r2^r3
270 	 */
271 	while (mlen--) {
272 		/* input data is read in big-endian format */
273 		w = r[0]^cpu_to_be32(*pdata++);
274 		p0 = tab0 + (l+1)*((w >>  0) & 0xff);
275 		p1 = tab1 + (l+1)*((w >>  8) & 0xff);
276 		p2 = tab2 + (l+1)*((w >> 16) & 0xff);
277 		p3 = tab3 + (l+1)*((w >> 24) & 0xff);
278 
279 		for (i = 0; i < l; i++)
280 			r[i] = r[i+1]^p0[i]^p1[i]^p2[i]^p3[i];
281 
282 		r[l] = p0[l]^p1[l]^p2[l]^p3[l];
283 	}
284 	memcpy(bch->ecc_buf, r, sizeof(r));
285 
286 	/* process last unaligned bytes */
287 	if (len)
288 		encode_bch_unaligned(bch, data, len, bch->ecc_buf);
289 
290 	/* store ecc parity bytes into original parity buffer */
291 	if (ecc)
292 		store_ecc8(bch, ecc, bch->ecc_buf);
293 }
294 
modulo(struct bch_control * bch,unsigned int v)295 static inline int modulo(struct bch_control *bch, unsigned int v)
296 {
297 	const unsigned int n = GF_N(bch);
298 	while (v >= n) {
299 		v -= n;
300 		v = (v & n) + (v >> GF_M(bch));
301 	}
302 	return v;
303 }
304 
305 /*
306  * shorter and faster modulo function, only works when v < 2N.
307  */
mod_s(struct bch_control * bch,unsigned int v)308 static inline int mod_s(struct bch_control *bch, unsigned int v)
309 {
310 	const unsigned int n = GF_N(bch);
311 	return (v < n) ? v : v-n;
312 }
313 
deg(unsigned int poly)314 static inline int deg(unsigned int poly)
315 {
316 	/* polynomial degree is the most-significant bit index */
317 	return fls(poly)-1;
318 }
319 
parity(unsigned int x)320 static inline int parity(unsigned int x)
321 {
322 	/*
323 	 * public domain code snippet, lifted from
324 	 * http://www-graphics.stanford.edu/~seander/bithacks.html
325 	 */
326 	x ^= x >> 1;
327 	x ^= x >> 2;
328 	x = (x & 0x11111111U) * 0x11111111U;
329 	return (x >> 28) & 1;
330 }
331 
332 /* Galois field basic operations: multiply, divide, inverse, etc. */
333 
gf_mul(struct bch_control * bch,unsigned int a,unsigned int b)334 static inline unsigned int gf_mul(struct bch_control *bch, unsigned int a,
335 				  unsigned int b)
336 {
337 	return (a && b) ? bch->a_pow_tab[mod_s(bch, bch->a_log_tab[a]+
338 					       bch->a_log_tab[b])] : 0;
339 }
340 
gf_sqr(struct bch_control * bch,unsigned int a)341 static inline unsigned int gf_sqr(struct bch_control *bch, unsigned int a)
342 {
343 	return a ? bch->a_pow_tab[mod_s(bch, 2*bch->a_log_tab[a])] : 0;
344 }
345 
gf_div(struct bch_control * bch,unsigned int a,unsigned int b)346 static inline unsigned int gf_div(struct bch_control *bch, unsigned int a,
347 				  unsigned int b)
348 {
349 	return a ? bch->a_pow_tab[mod_s(bch, bch->a_log_tab[a]+
350 					GF_N(bch)-bch->a_log_tab[b])] : 0;
351 }
352 
gf_inv(struct bch_control * bch,unsigned int a)353 static inline unsigned int gf_inv(struct bch_control *bch, unsigned int a)
354 {
355 	return bch->a_pow_tab[GF_N(bch)-bch->a_log_tab[a]];
356 }
357 
a_pow(struct bch_control * bch,int i)358 static inline unsigned int a_pow(struct bch_control *bch, int i)
359 {
360 	return bch->a_pow_tab[modulo(bch, i)];
361 }
362 
a_log(struct bch_control * bch,unsigned int x)363 static inline int a_log(struct bch_control *bch, unsigned int x)
364 {
365 	return bch->a_log_tab[x];
366 }
367 
a_ilog(struct bch_control * bch,unsigned int x)368 static inline int a_ilog(struct bch_control *bch, unsigned int x)
369 {
370 	return mod_s(bch, GF_N(bch)-bch->a_log_tab[x]);
371 }
372 
373 /*
374  * compute 2t syndromes of ecc polynomial, i.e. ecc(a^j) for j=1..2t
375  */
compute_syndromes(struct bch_control * bch,uint32_t * ecc,unsigned int * syn)376 static void compute_syndromes(struct bch_control *bch, uint32_t *ecc,
377 			      unsigned int *syn)
378 {
379 	int i, j, s;
380 	unsigned int m;
381 	uint32_t poly;
382 	const int t = GF_T(bch);
383 
384 	s = bch->ecc_bits;
385 
386 	/* make sure extra bits in last ecc word are cleared */
387 	m = ((unsigned int)s) & 31;
388 	if (m)
389 		ecc[s/32] &= ~((1u << (32-m))-1);
390 	memset(syn, 0, 2*t*sizeof(*syn));
391 
392 	/* compute v(a^j) for j=1 .. 2t-1 */
393 	do {
394 		poly = *ecc++;
395 		s -= 32;
396 		while (poly) {
397 			i = deg(poly);
398 			for (j = 0; j < 2*t; j += 2)
399 				syn[j] ^= a_pow(bch, (j+1)*(i+s));
400 
401 			poly ^= (1 << i);
402 		}
403 	} while (s > 0);
404 
405 	/* v(a^(2j)) = v(a^j)^2 */
406 	for (j = 0; j < t; j++)
407 		syn[2*j+1] = gf_sqr(bch, syn[j]);
408 }
409 
gf_poly_copy(struct gf_poly * dst,struct gf_poly * src)410 static void gf_poly_copy(struct gf_poly *dst, struct gf_poly *src)
411 {
412 	memcpy(dst, src, GF_POLY_SZ(src->deg));
413 }
414 
compute_error_locator_polynomial(struct bch_control * bch,const unsigned int * syn)415 static int compute_error_locator_polynomial(struct bch_control *bch,
416 					    const unsigned int *syn)
417 {
418 	const unsigned int t = GF_T(bch);
419 	const unsigned int n = GF_N(bch);
420 	unsigned int i, j, tmp, l, pd = 1, d = syn[0];
421 	struct gf_poly *elp = bch->elp;
422 	struct gf_poly *pelp = bch->poly_2t[0];
423 	struct gf_poly *elp_copy = bch->poly_2t[1];
424 	int k, pp = -1;
425 
426 	memset(pelp, 0, GF_POLY_SZ(2*t));
427 	memset(elp, 0, GF_POLY_SZ(2*t));
428 
429 	pelp->deg = 0;
430 	pelp->c[0] = 1;
431 	elp->deg = 0;
432 	elp->c[0] = 1;
433 
434 	/* use simplified binary Berlekamp-Massey algorithm */
435 	for (i = 0; (i < t) && (elp->deg <= t); i++) {
436 		if (d) {
437 			k = 2*i-pp;
438 			gf_poly_copy(elp_copy, elp);
439 			/* e[i+1](X) = e[i](X)+di*dp^-1*X^2(i-p)*e[p](X) */
440 			tmp = a_log(bch, d)+n-a_log(bch, pd);
441 			for (j = 0; j <= pelp->deg; j++) {
442 				if (pelp->c[j]) {
443 					l = a_log(bch, pelp->c[j]);
444 					elp->c[j+k] ^= a_pow(bch, tmp+l);
445 				}
446 			}
447 			/* compute l[i+1] = max(l[i]->c[l[p]+2*(i-p]) */
448 			tmp = pelp->deg+k;
449 			if (tmp > elp->deg) {
450 				elp->deg = tmp;
451 				gf_poly_copy(pelp, elp_copy);
452 				pd = d;
453 				pp = 2*i;
454 			}
455 		}
456 		/* di+1 = S(2i+3)+elp[i+1].1*S(2i+2)+...+elp[i+1].lS(2i+3-l) */
457 		if (i < t-1) {
458 			d = syn[2*i+2];
459 			for (j = 1; j <= elp->deg; j++)
460 				d ^= gf_mul(bch, elp->c[j], syn[2*i+2-j]);
461 		}
462 	}
463 	dbg("elp=%s\n", gf_poly_str(elp));
464 	return (elp->deg > t) ? -1 : (int)elp->deg;
465 }
466 
467 /*
468  * solve a m x m linear system in GF(2) with an expected number of solutions,
469  * and return the number of found solutions
470  */
solve_linear_system(struct bch_control * bch,unsigned int * rows,unsigned int * sol,int nsol)471 static int solve_linear_system(struct bch_control *bch, unsigned int *rows,
472 			       unsigned int *sol, int nsol)
473 {
474 	const int m = GF_M(bch);
475 	unsigned int tmp, mask;
476 	int rem, c, r, p, k, param[m];
477 
478 	k = 0;
479 	mask = 1 << m;
480 
481 	/* Gaussian elimination */
482 	for (c = 0; c < m; c++) {
483 		rem = 0;
484 		p = c-k;
485 		/* find suitable row for elimination */
486 		for (r = p; r < m; r++) {
487 			if (rows[r] & mask) {
488 				if (r != p) {
489 					tmp = rows[r];
490 					rows[r] = rows[p];
491 					rows[p] = tmp;
492 				}
493 				rem = r+1;
494 				break;
495 			}
496 		}
497 		if (rem) {
498 			/* perform elimination on remaining rows */
499 			tmp = rows[p];
500 			for (r = rem; r < m; r++) {
501 				if (rows[r] & mask)
502 					rows[r] ^= tmp;
503 			}
504 		} else {
505 			/* elimination not needed, store defective row index */
506 			param[k++] = c;
507 		}
508 		mask >>= 1;
509 	}
510 	/* rewrite system, inserting fake parameter rows */
511 	if (k > 0) {
512 		p = k;
513 		for (r = m-1; r >= 0; r--) {
514 			if ((r > m-1-k) && rows[r])
515 				/* system has no solution */
516 				return 0;
517 
518 			rows[r] = (p && (r == param[p-1])) ?
519 				p--, 1u << (m-r) : rows[r-p];
520 		}
521 	}
522 
523 	if (nsol != (1 << k))
524 		/* unexpected number of solutions */
525 		return 0;
526 
527 	for (p = 0; p < nsol; p++) {
528 		/* set parameters for p-th solution */
529 		for (c = 0; c < k; c++)
530 			rows[param[c]] = (rows[param[c]] & ~1)|((p >> c) & 1);
531 
532 		/* compute unique solution */
533 		tmp = 0;
534 		for (r = m-1; r >= 0; r--) {
535 			mask = rows[r] & (tmp|1);
536 			tmp |= parity(mask) << (m-r);
537 		}
538 		sol[p] = tmp >> 1;
539 	}
540 	return nsol;
541 }
542 
543 /*
544  * this function builds and solves a linear system for finding roots of a degree
545  * 4 affine monic polynomial X^4+aX^2+bX+c over GF(2^m).
546  */
find_affine4_roots(struct bch_control * bch,unsigned int a,unsigned int b,unsigned int c,unsigned int * roots)547 static int find_affine4_roots(struct bch_control *bch, unsigned int a,
548 			      unsigned int b, unsigned int c,
549 			      unsigned int *roots)
550 {
551 	int i, j, k;
552 	const int m = GF_M(bch);
553 	unsigned int mask = 0xff, t, rows[16] = {0,};
554 
555 	j = a_log(bch, b);
556 	k = a_log(bch, a);
557 	rows[0] = c;
558 
559 	/* buid linear system to solve X^4+aX^2+bX+c = 0 */
560 	for (i = 0; i < m; i++) {
561 		rows[i+1] = bch->a_pow_tab[4*i]^
562 			(a ? bch->a_pow_tab[mod_s(bch, k)] : 0)^
563 			(b ? bch->a_pow_tab[mod_s(bch, j)] : 0);
564 		j++;
565 		k += 2;
566 	}
567 	/*
568 	 * transpose 16x16 matrix before passing it to linear solver
569 	 * warning: this code assumes m < 16
570 	 */
571 	for (j = 8; j != 0; j >>= 1, mask ^= (mask << j)) {
572 		for (k = 0; k < 16; k = (k+j+1) & ~j) {
573 			t = ((rows[k] >> j)^rows[k+j]) & mask;
574 			rows[k] ^= (t << j);
575 			rows[k+j] ^= t;
576 		}
577 	}
578 	return solve_linear_system(bch, rows, roots, 4);
579 }
580 
581 /*
582  * compute root r of a degree 1 polynomial over GF(2^m) (returned as log(1/r))
583  */
find_poly_deg1_roots(struct bch_control * bch,struct gf_poly * poly,unsigned int * roots)584 static int find_poly_deg1_roots(struct bch_control *bch, struct gf_poly *poly,
585 				unsigned int *roots)
586 {
587 	int n = 0;
588 
589 	if (poly->c[0])
590 		/* poly[X] = bX+c with c!=0, root=c/b */
591 		roots[n++] = mod_s(bch, GF_N(bch)-bch->a_log_tab[poly->c[0]]+
592 				   bch->a_log_tab[poly->c[1]]);
593 	return n;
594 }
595 
596 /*
597  * compute roots of a degree 2 polynomial over GF(2^m)
598  */
find_poly_deg2_roots(struct bch_control * bch,struct gf_poly * poly,unsigned int * roots)599 static int find_poly_deg2_roots(struct bch_control *bch, struct gf_poly *poly,
600 				unsigned int *roots)
601 {
602 	int n = 0, i, l0, l1, l2;
603 	unsigned int u, v, r;
604 
605 	if (poly->c[0] && poly->c[1]) {
606 
607 		l0 = bch->a_log_tab[poly->c[0]];
608 		l1 = bch->a_log_tab[poly->c[1]];
609 		l2 = bch->a_log_tab[poly->c[2]];
610 
611 		/* using z=a/bX, transform aX^2+bX+c into z^2+z+u (u=ac/b^2) */
612 		u = a_pow(bch, l0+l2+2*(GF_N(bch)-l1));
613 		/*
614 		 * let u = sum(li.a^i) i=0..m-1; then compute r = sum(li.xi):
615 		 * r^2+r = sum(li.(xi^2+xi)) = sum(li.(a^i+Tr(a^i).a^k)) =
616 		 * u + sum(li.Tr(a^i).a^k) = u+a^k.Tr(sum(li.a^i)) = u+a^k.Tr(u)
617 		 * i.e. r and r+1 are roots iff Tr(u)=0
618 		 */
619 		r = 0;
620 		v = u;
621 		while (v) {
622 			i = deg(v);
623 			r ^= bch->xi_tab[i];
624 			v ^= (1 << i);
625 		}
626 		/* verify root */
627 		if ((gf_sqr(bch, r)^r) == u) {
628 			/* reverse z=a/bX transformation and compute log(1/r) */
629 			roots[n++] = modulo(bch, 2*GF_N(bch)-l1-
630 					    bch->a_log_tab[r]+l2);
631 			roots[n++] = modulo(bch, 2*GF_N(bch)-l1-
632 					    bch->a_log_tab[r^1]+l2);
633 		}
634 	}
635 	return n;
636 }
637 
638 /*
639  * compute roots of a degree 3 polynomial over GF(2^m)
640  */
find_poly_deg3_roots(struct bch_control * bch,struct gf_poly * poly,unsigned int * roots)641 static int find_poly_deg3_roots(struct bch_control *bch, struct gf_poly *poly,
642 				unsigned int *roots)
643 {
644 	int i, n = 0;
645 	unsigned int a, b, c, a2, b2, c2, e3, tmp[4];
646 
647 	if (poly->c[0]) {
648 		/* transform polynomial into monic X^3 + a2X^2 + b2X + c2 */
649 		e3 = poly->c[3];
650 		c2 = gf_div(bch, poly->c[0], e3);
651 		b2 = gf_div(bch, poly->c[1], e3);
652 		a2 = gf_div(bch, poly->c[2], e3);
653 
654 		/* (X+a2)(X^3+a2X^2+b2X+c2) = X^4+aX^2+bX+c (affine) */
655 		c = gf_mul(bch, a2, c2);           /* c = a2c2      */
656 		b = gf_mul(bch, a2, b2)^c2;        /* b = a2b2 + c2 */
657 		a = gf_sqr(bch, a2)^b2;            /* a = a2^2 + b2 */
658 
659 		/* find the 4 roots of this affine polynomial */
660 		if (find_affine4_roots(bch, a, b, c, tmp) == 4) {
661 			/* remove a2 from final list of roots */
662 			for (i = 0; i < 4; i++) {
663 				if (tmp[i] != a2)
664 					roots[n++] = a_ilog(bch, tmp[i]);
665 			}
666 		}
667 	}
668 	return n;
669 }
670 
671 /*
672  * compute roots of a degree 4 polynomial over GF(2^m)
673  */
find_poly_deg4_roots(struct bch_control * bch,struct gf_poly * poly,unsigned int * roots)674 static int find_poly_deg4_roots(struct bch_control *bch, struct gf_poly *poly,
675 				unsigned int *roots)
676 {
677 	int i, l, n = 0;
678 	unsigned int a, b, c, d, e = 0, f, a2, b2, c2, e4;
679 
680 	if (poly->c[0] == 0)
681 		return 0;
682 
683 	/* transform polynomial into monic X^4 + aX^3 + bX^2 + cX + d */
684 	e4 = poly->c[4];
685 	d = gf_div(bch, poly->c[0], e4);
686 	c = gf_div(bch, poly->c[1], e4);
687 	b = gf_div(bch, poly->c[2], e4);
688 	a = gf_div(bch, poly->c[3], e4);
689 
690 	/* use Y=1/X transformation to get an affine polynomial */
691 	if (a) {
692 		/* first, eliminate cX by using z=X+e with ae^2+c=0 */
693 		if (c) {
694 			/* compute e such that e^2 = c/a */
695 			f = gf_div(bch, c, a);
696 			l = a_log(bch, f);
697 			l += (l & 1) ? GF_N(bch) : 0;
698 			e = a_pow(bch, l/2);
699 			/*
700 			 * use transformation z=X+e:
701 			 * z^4+e^4 + a(z^3+ez^2+e^2z+e^3) + b(z^2+e^2) +cz+ce+d
702 			 * z^4 + az^3 + (ae+b)z^2 + (ae^2+c)z+e^4+be^2+ae^3+ce+d
703 			 * z^4 + az^3 + (ae+b)z^2 + e^4+be^2+d
704 			 * z^4 + az^3 +     b'z^2 + d'
705 			 */
706 			d = a_pow(bch, 2*l)^gf_mul(bch, b, f)^d;
707 			b = gf_mul(bch, a, e)^b;
708 		}
709 		/* now, use Y=1/X to get Y^4 + b/dY^2 + a/dY + 1/d */
710 		if (d == 0)
711 			/* assume all roots have multiplicity 1 */
712 			return 0;
713 
714 		c2 = gf_inv(bch, d);
715 		b2 = gf_div(bch, a, d);
716 		a2 = gf_div(bch, b, d);
717 	} else {
718 		/* polynomial is already affine */
719 		c2 = d;
720 		b2 = c;
721 		a2 = b;
722 	}
723 	/* find the 4 roots of this affine polynomial */
724 	if (find_affine4_roots(bch, a2, b2, c2, roots) == 4) {
725 		for (i = 0; i < 4; i++) {
726 			/* post-process roots (reverse transformations) */
727 			f = a ? gf_inv(bch, roots[i]) : roots[i];
728 			roots[i] = a_ilog(bch, f^e);
729 		}
730 		n = 4;
731 	}
732 	return n;
733 }
734 
735 /*
736  * build monic, log-based representation of a polynomial
737  */
gf_poly_logrep(struct bch_control * bch,const struct gf_poly * a,int * rep)738 static void gf_poly_logrep(struct bch_control *bch,
739 			   const struct gf_poly *a, int *rep)
740 {
741 	int i, d = a->deg, l = GF_N(bch)-a_log(bch, a->c[a->deg]);
742 
743 	/* represent 0 values with -1; warning, rep[d] is not set to 1 */
744 	for (i = 0; i < d; i++)
745 		rep[i] = a->c[i] ? mod_s(bch, a_log(bch, a->c[i])+l) : -1;
746 }
747 
748 /*
749  * compute polynomial Euclidean division remainder in GF(2^m)[X]
750  */
gf_poly_mod(struct bch_control * bch,struct gf_poly * a,const struct gf_poly * b,int * rep)751 static void gf_poly_mod(struct bch_control *bch, struct gf_poly *a,
752 			const struct gf_poly *b, int *rep)
753 {
754 	int la, p, m;
755 	unsigned int i, j, *c = a->c;
756 	const unsigned int d = b->deg;
757 
758 	if (a->deg < d)
759 		return;
760 
761 	/* reuse or compute log representation of denominator */
762 	if (!rep) {
763 		rep = bch->cache;
764 		gf_poly_logrep(bch, b, rep);
765 	}
766 
767 	for (j = a->deg; j >= d; j--) {
768 		if (c[j]) {
769 			la = a_log(bch, c[j]);
770 			p = j-d;
771 			for (i = 0; i < d; i++, p++) {
772 				m = rep[i];
773 				if (m >= 0)
774 					c[p] ^= bch->a_pow_tab[mod_s(bch,
775 								     m+la)];
776 			}
777 		}
778 	}
779 	a->deg = d-1;
780 	while (!c[a->deg] && a->deg)
781 		a->deg--;
782 }
783 
784 /*
785  * compute polynomial Euclidean division quotient in GF(2^m)[X]
786  */
gf_poly_div(struct bch_control * bch,struct gf_poly * a,const struct gf_poly * b,struct gf_poly * q)787 static void gf_poly_div(struct bch_control *bch, struct gf_poly *a,
788 			const struct gf_poly *b, struct gf_poly *q)
789 {
790 	if (a->deg >= b->deg) {
791 		q->deg = a->deg-b->deg;
792 		/* compute a mod b (modifies a) */
793 		gf_poly_mod(bch, a, b, NULL);
794 		/* quotient is stored in upper part of polynomial a */
795 		memcpy(q->c, &a->c[b->deg], (1+q->deg)*sizeof(unsigned int));
796 	} else {
797 		q->deg = 0;
798 		q->c[0] = 0;
799 	}
800 }
801 
802 /*
803  * compute polynomial GCD (Greatest Common Divisor) in GF(2^m)[X]
804  */
gf_poly_gcd(struct bch_control * bch,struct gf_poly * a,struct gf_poly * b)805 static struct gf_poly *gf_poly_gcd(struct bch_control *bch, struct gf_poly *a,
806 				   struct gf_poly *b)
807 {
808 	struct gf_poly *tmp;
809 
810 	dbg("gcd(%s,%s)=", gf_poly_str(a), gf_poly_str(b));
811 
812 	if (a->deg < b->deg) {
813 		tmp = b;
814 		b = a;
815 		a = tmp;
816 	}
817 
818 	while (b->deg > 0) {
819 		gf_poly_mod(bch, a, b, NULL);
820 		tmp = b;
821 		b = a;
822 		a = tmp;
823 	}
824 
825 	dbg("%s\n", gf_poly_str(a));
826 
827 	return a;
828 }
829 
830 /*
831  * Given a polynomial f and an integer k, compute Tr(a^kX) mod f
832  * This is used in Berlekamp Trace algorithm for splitting polynomials
833  */
compute_trace_bk_mod(struct bch_control * bch,int k,const struct gf_poly * f,struct gf_poly * z,struct gf_poly * out)834 static void compute_trace_bk_mod(struct bch_control *bch, int k,
835 				 const struct gf_poly *f, struct gf_poly *z,
836 				 struct gf_poly *out)
837 {
838 	const int m = GF_M(bch);
839 	int i, j;
840 
841 	/* z contains z^2j mod f */
842 	z->deg = 1;
843 	z->c[0] = 0;
844 	z->c[1] = bch->a_pow_tab[k];
845 
846 	out->deg = 0;
847 	memset(out, 0, GF_POLY_SZ(f->deg));
848 
849 	/* compute f log representation only once */
850 	gf_poly_logrep(bch, f, bch->cache);
851 
852 	for (i = 0; i < m; i++) {
853 		/* add a^(k*2^i)(z^(2^i) mod f) and compute (z^(2^i) mod f)^2 */
854 		for (j = z->deg; j >= 0; j--) {
855 			out->c[j] ^= z->c[j];
856 			z->c[2*j] = gf_sqr(bch, z->c[j]);
857 			z->c[2*j+1] = 0;
858 		}
859 		if (z->deg > out->deg)
860 			out->deg = z->deg;
861 
862 		if (i < m-1) {
863 			z->deg *= 2;
864 			/* z^(2(i+1)) mod f = (z^(2^i) mod f)^2 mod f */
865 			gf_poly_mod(bch, z, f, bch->cache);
866 		}
867 	}
868 	while (!out->c[out->deg] && out->deg)
869 		out->deg--;
870 
871 	dbg("Tr(a^%d.X) mod f = %s\n", k, gf_poly_str(out));
872 }
873 
874 /*
875  * factor a polynomial using Berlekamp Trace algorithm (BTA)
876  */
factor_polynomial(struct bch_control * bch,int k,struct gf_poly * f,struct gf_poly ** g,struct gf_poly ** h)877 static void factor_polynomial(struct bch_control *bch, int k, struct gf_poly *f,
878 			      struct gf_poly **g, struct gf_poly **h)
879 {
880 	struct gf_poly *f2 = bch->poly_2t[0];
881 	struct gf_poly *q  = bch->poly_2t[1];
882 	struct gf_poly *tk = bch->poly_2t[2];
883 	struct gf_poly *z  = bch->poly_2t[3];
884 	struct gf_poly *gcd;
885 
886 	dbg("factoring %s...\n", gf_poly_str(f));
887 
888 	*g = f;
889 	*h = NULL;
890 
891 	/* tk = Tr(a^k.X) mod f */
892 	compute_trace_bk_mod(bch, k, f, z, tk);
893 
894 	if (tk->deg > 0) {
895 		/* compute g = gcd(f, tk) (destructive operation) */
896 		gf_poly_copy(f2, f);
897 		gcd = gf_poly_gcd(bch, f2, tk);
898 		if (gcd->deg < f->deg) {
899 			/* compute h=f/gcd(f,tk); this will modify f and q */
900 			gf_poly_div(bch, f, gcd, q);
901 			/* store g and h in-place (clobbering f) */
902 			*h = &((struct gf_poly_deg1 *)f)[gcd->deg].poly;
903 			gf_poly_copy(*g, gcd);
904 			gf_poly_copy(*h, q);
905 		}
906 	}
907 }
908 
909 /*
910  * find roots of a polynomial, using BTZ algorithm; see the beginning of this
911  * file for details
912  */
find_poly_roots(struct bch_control * bch,unsigned int k,struct gf_poly * poly,unsigned int * roots)913 static int find_poly_roots(struct bch_control *bch, unsigned int k,
914 			   struct gf_poly *poly, unsigned int *roots)
915 {
916 	int cnt;
917 	struct gf_poly *f1, *f2;
918 
919 	switch (poly->deg) {
920 		/* handle low degree polynomials with ad hoc techniques */
921 	case 1:
922 		cnt = find_poly_deg1_roots(bch, poly, roots);
923 		break;
924 	case 2:
925 		cnt = find_poly_deg2_roots(bch, poly, roots);
926 		break;
927 	case 3:
928 		cnt = find_poly_deg3_roots(bch, poly, roots);
929 		break;
930 	case 4:
931 		cnt = find_poly_deg4_roots(bch, poly, roots);
932 		break;
933 	default:
934 		/* factor polynomial using Berlekamp Trace Algorithm (BTA) */
935 		cnt = 0;
936 		if (poly->deg && (k <= GF_M(bch))) {
937 			factor_polynomial(bch, k, poly, &f1, &f2);
938 			if (f1)
939 				cnt += find_poly_roots(bch, k+1, f1, roots);
940 			if (f2)
941 				cnt += find_poly_roots(bch, k+1, f2, roots+cnt);
942 		}
943 		break;
944 	}
945 	return cnt;
946 }
947 
948 #if defined(USE_CHIEN_SEARCH)
949 /*
950  * exhaustive root search (Chien) implementation - not used, included only for
951  * reference/comparison tests
952  */
chien_search(struct bch_control * bch,unsigned int len,struct gf_poly * p,unsigned int * roots)953 static int chien_search(struct bch_control *bch, unsigned int len,
954 			struct gf_poly *p, unsigned int *roots)
955 {
956 	int m;
957 	unsigned int i, j, syn, syn0, count = 0;
958 	const unsigned int k = 8*len+bch->ecc_bits;
959 
960 	/* use a log-based representation of polynomial */
961 	gf_poly_logrep(bch, p, bch->cache);
962 	bch->cache[p->deg] = 0;
963 	syn0 = gf_div(bch, p->c[0], p->c[p->deg]);
964 
965 	for (i = GF_N(bch)-k+1; i <= GF_N(bch); i++) {
966 		/* compute elp(a^i) */
967 		for (j = 1, syn = syn0; j <= p->deg; j++) {
968 			m = bch->cache[j];
969 			if (m >= 0)
970 				syn ^= a_pow(bch, m+j*i);
971 		}
972 		if (syn == 0) {
973 			roots[count++] = GF_N(bch)-i;
974 			if (count == p->deg)
975 				break;
976 		}
977 	}
978 	return (count == p->deg) ? count : 0;
979 }
980 #define find_poly_roots(_p, _k, _elp, _loc) chien_search(_p, len, _elp, _loc)
981 #endif /* USE_CHIEN_SEARCH */
982 
983 /**
984  * decode_bch - decode received codeword and find bit error locations
985  * @bch:      BCH control structure
986  * @data:     received data, ignored if @calc_ecc is provided
987  * @len:      data length in bytes, must always be provided
988  * @recv_ecc: received ecc, if NULL then assume it was XORed in @calc_ecc
989  * @calc_ecc: calculated ecc, if NULL then calc_ecc is computed from @data
990  * @syn:      hw computed syndrome data (if NULL, syndrome is calculated)
991  * @errloc:   output array of error locations
992  *
993  * Returns:
994  *  The number of errors found, or -EBADMSG if decoding failed, or -EINVAL if
995  *  invalid parameters were provided
996  *
997  * Depending on the available hw BCH support and the need to compute @calc_ecc
998  * separately (using encode_bch()), this function should be called with one of
999  * the following parameter configurations -
1000  *
1001  * by providing @data and @recv_ecc only:
1002  *   decode_bch(@bch, @data, @len, @recv_ecc, NULL, NULL, @errloc)
1003  *
1004  * by providing @recv_ecc and @calc_ecc:
1005  *   decode_bch(@bch, NULL, @len, @recv_ecc, @calc_ecc, NULL, @errloc)
1006  *
1007  * by providing ecc = recv_ecc XOR calc_ecc:
1008  *   decode_bch(@bch, NULL, @len, NULL, ecc, NULL, @errloc)
1009  *
1010  * by providing syndrome results @syn:
1011  *   decode_bch(@bch, NULL, @len, NULL, NULL, @syn, @errloc)
1012  *
1013  * Once decode_bch() has successfully returned with a positive value, error
1014  * locations returned in array @errloc should be interpreted as follows -
1015  *
1016  * if (errloc[n] >= 8*len), then n-th error is located in ecc (no need for
1017  * data correction)
1018  *
1019  * if (errloc[n] < 8*len), then n-th error is located in data and can be
1020  * corrected with statement data[errloc[n]/8] ^= 1 << (errloc[n] % 8);
1021  *
1022  * Note that this function does not perform any data correction by itself, it
1023  * merely indicates error locations.
1024  */
decode_bch(struct bch_control * bch,const uint8_t * data,unsigned int len,const uint8_t * recv_ecc,const uint8_t * calc_ecc,const unsigned int * syn,unsigned int * errloc)1025 int decode_bch(struct bch_control *bch, const uint8_t *data, unsigned int len,
1026 	       const uint8_t *recv_ecc, const uint8_t *calc_ecc,
1027 	       const unsigned int *syn, unsigned int *errloc)
1028 {
1029 	const unsigned int ecc_words = BCH_ECC_WORDS(bch);
1030 	unsigned int nbits;
1031 	int i, err, nroots;
1032 	uint32_t sum;
1033 
1034 	/* sanity check: make sure data length can be handled */
1035 	if (8*len > (bch->n-bch->ecc_bits))
1036 		return -EINVAL;
1037 
1038 	/* if caller does not provide syndromes, compute them */
1039 	if (!syn) {
1040 		if (!calc_ecc) {
1041 			/* compute received data ecc into an internal buffer */
1042 			if (!data || !recv_ecc)
1043 				return -EINVAL;
1044 			encode_bch(bch, data, len, NULL);
1045 		} else {
1046 			/* load provided calculated ecc */
1047 			load_ecc8(bch, bch->ecc_buf, calc_ecc);
1048 		}
1049 		/* load received ecc or assume it was XORed in calc_ecc */
1050 		if (recv_ecc) {
1051 			load_ecc8(bch, bch->ecc_buf2, recv_ecc);
1052 			/* XOR received and calculated ecc */
1053 			for (i = 0, sum = 0; i < (int)ecc_words; i++) {
1054 				bch->ecc_buf[i] ^= bch->ecc_buf2[i];
1055 				sum |= bch->ecc_buf[i];
1056 			}
1057 			if (!sum)
1058 				/* no error found */
1059 				return 0;
1060 		}
1061 		compute_syndromes(bch, bch->ecc_buf, bch->syn);
1062 		syn = bch->syn;
1063 	}
1064 
1065 	err = compute_error_locator_polynomial(bch, syn);
1066 	if (err > 0) {
1067 		nroots = find_poly_roots(bch, 1, bch->elp, errloc);
1068 		if (err != nroots)
1069 			err = -1;
1070 	}
1071 	if (err > 0) {
1072 		/* post-process raw error locations for easier correction */
1073 		nbits = (len*8)+bch->ecc_bits;
1074 		for (i = 0; i < err; i++) {
1075 			if (errloc[i] >= nbits) {
1076 				err = -1;
1077 				break;
1078 			}
1079 			errloc[i] = nbits-1-errloc[i];
1080 			errloc[i] = (errloc[i] & ~7)|(7-(errloc[i] & 7));
1081 		}
1082 	}
1083 	return (err >= 0) ? err : -EBADMSG;
1084 }
1085 
1086 /*
1087  * generate Galois field lookup tables
1088  */
build_gf_tables(struct bch_control * bch,unsigned int poly)1089 static int build_gf_tables(struct bch_control *bch, unsigned int poly)
1090 {
1091 	unsigned int i, x = 1;
1092 	const unsigned int k = 1 << deg(poly);
1093 
1094 	/* primitive polynomial must be of degree m */
1095 	if (k != (1u << GF_M(bch)))
1096 		return -1;
1097 
1098 	for (i = 0; i < GF_N(bch); i++) {
1099 		bch->a_pow_tab[i] = x;
1100 		bch->a_log_tab[x] = i;
1101 		if (i && (x == 1))
1102 			/* polynomial is not primitive (a^i=1 with 0<i<2^m-1) */
1103 			return -1;
1104 		x <<= 1;
1105 		if (x & k)
1106 			x ^= poly;
1107 	}
1108 	bch->a_pow_tab[GF_N(bch)] = 1;
1109 	bch->a_log_tab[0] = 0;
1110 
1111 	return 0;
1112 }
1113 
1114 /*
1115  * compute generator polynomial remainder tables for fast encoding
1116  */
build_mod8_tables(struct bch_control * bch,const uint32_t * g)1117 static void build_mod8_tables(struct bch_control *bch, const uint32_t *g)
1118 {
1119 	int i, j, b, d;
1120 	uint32_t data, hi, lo, *tab;
1121 	const int l = BCH_ECC_WORDS(bch);
1122 	const int plen = DIV_ROUND_UP(bch->ecc_bits+1, 32);
1123 	const int ecclen = DIV_ROUND_UP(bch->ecc_bits, 32);
1124 
1125 	memset(bch->mod8_tab, 0, 4*256*l*sizeof(*bch->mod8_tab));
1126 
1127 	for (i = 0; i < 256; i++) {
1128 		/* p(X)=i is a small polynomial of weight <= 8 */
1129 		for (b = 0; b < 4; b++) {
1130 			/* we want to compute (p(X).X^(8*b+deg(g))) mod g(X) */
1131 			tab = bch->mod8_tab + (b*256+i)*l;
1132 			data = i << (8*b);
1133 			while (data) {
1134 				d = deg(data);
1135 				/* subtract X^d.g(X) from p(X).X^(8*b+deg(g)) */
1136 				data ^= g[0] >> (31-d);
1137 				for (j = 0; j < ecclen; j++) {
1138 					hi = (d < 31) ? g[j] << (d+1) : 0;
1139 					lo = (j+1 < plen) ?
1140 						g[j+1] >> (31-d) : 0;
1141 					tab[j] ^= hi|lo;
1142 				}
1143 			}
1144 		}
1145 	}
1146 }
1147 
1148 /*
1149  * build a base for factoring degree 2 polynomials
1150  */
build_deg2_base(struct bch_control * bch)1151 static int build_deg2_base(struct bch_control *bch)
1152 {
1153 	const int m = GF_M(bch);
1154 	int i, j, r;
1155 	unsigned int sum, x, y, remaining, ak = 0, xi[m];
1156 
1157 	/* find k s.t. Tr(a^k) = 1 and 0 <= k < m */
1158 	for (i = 0; i < m; i++) {
1159 		for (j = 0, sum = 0; j < m; j++)
1160 			sum ^= a_pow(bch, i*(1 << j));
1161 
1162 		if (sum) {
1163 			ak = bch->a_pow_tab[i];
1164 			break;
1165 		}
1166 	}
1167 	/* find xi, i=0..m-1 such that xi^2+xi = a^i+Tr(a^i).a^k */
1168 	remaining = m;
1169 	memset(xi, 0, sizeof(xi));
1170 
1171 	for (x = 0; (x <= GF_N(bch)) && remaining; x++) {
1172 		y = gf_sqr(bch, x)^x;
1173 		for (i = 0; i < 2; i++) {
1174 			r = a_log(bch, y);
1175 			if (y && (r < m) && !xi[r]) {
1176 				bch->xi_tab[r] = x;
1177 				xi[r] = 1;
1178 				remaining--;
1179 				dbg("x%d = %x\n", r, x);
1180 				break;
1181 			}
1182 			y ^= ak;
1183 		}
1184 	}
1185 	/* should not happen but check anyway */
1186 	return remaining ? -1 : 0;
1187 }
1188 
bch_alloc(size_t size,int * err)1189 static void *bch_alloc(size_t size, int *err)
1190 {
1191 	void *ptr;
1192 
1193 	ptr = kmalloc(size, GFP_KERNEL);
1194 	if (ptr == NULL)
1195 		*err = 1;
1196 	return ptr;
1197 }
1198 
1199 /*
1200  * compute generator polynomial for given (m,t) parameters.
1201  */
compute_generator_polynomial(struct bch_control * bch)1202 static uint32_t *compute_generator_polynomial(struct bch_control *bch)
1203 {
1204 	const unsigned int m = GF_M(bch);
1205 	const unsigned int t = GF_T(bch);
1206 	int n, err = 0;
1207 	unsigned int i, j, nbits, r, word, *roots;
1208 	struct gf_poly *g;
1209 	uint32_t *genpoly;
1210 
1211 	g = bch_alloc(GF_POLY_SZ(m*t), &err);
1212 	roots = bch_alloc((bch->n+1)*sizeof(*roots), &err);
1213 	genpoly = bch_alloc(DIV_ROUND_UP(m*t+1, 32)*sizeof(*genpoly), &err);
1214 
1215 	if (err) {
1216 		kfree(genpoly);
1217 		genpoly = NULL;
1218 		goto finish;
1219 	}
1220 
1221 	/* enumerate all roots of g(X) */
1222 	memset(roots , 0, (bch->n+1)*sizeof(*roots));
1223 	for (i = 0; i < t; i++) {
1224 		for (j = 0, r = 2*i+1; j < m; j++) {
1225 			roots[r] = 1;
1226 			r = mod_s(bch, 2*r);
1227 		}
1228 	}
1229 	/* build generator polynomial g(X) */
1230 	g->deg = 0;
1231 	g->c[0] = 1;
1232 	for (i = 0; i < GF_N(bch); i++) {
1233 		if (roots[i]) {
1234 			/* multiply g(X) by (X+root) */
1235 			r = bch->a_pow_tab[i];
1236 			g->c[g->deg+1] = 1;
1237 			for (j = g->deg; j > 0; j--)
1238 				g->c[j] = gf_mul(bch, g->c[j], r)^g->c[j-1];
1239 
1240 			g->c[0] = gf_mul(bch, g->c[0], r);
1241 			g->deg++;
1242 		}
1243 	}
1244 	/* store left-justified binary representation of g(X) */
1245 	n = g->deg+1;
1246 	i = 0;
1247 
1248 	while (n > 0) {
1249 		nbits = (n > 32) ? 32 : n;
1250 		for (j = 0, word = 0; j < nbits; j++) {
1251 			if (g->c[n-1-j])
1252 				word |= 1u << (31-j);
1253 		}
1254 		genpoly[i++] = word;
1255 		n -= nbits;
1256 	}
1257 	bch->ecc_bits = g->deg;
1258 
1259 finish:
1260 	kfree(g);
1261 	kfree(roots);
1262 
1263 	return genpoly;
1264 }
1265 
1266 /**
1267  * init_bch - initialize a BCH encoder/decoder
1268  * @m:          Galois field order, should be in the range 5-15
1269  * @t:          maximum error correction capability, in bits
1270  * @prim_poly:  user-provided primitive polynomial (or 0 to use default)
1271  *
1272  * Returns:
1273  *  a newly allocated BCH control structure if successful, NULL otherwise
1274  *
1275  * This initialization can take some time, as lookup tables are built for fast
1276  * encoding/decoding; make sure not to call this function from a time critical
1277  * path. Usually, init_bch() should be called on module/driver init and
1278  * free_bch() should be called to release memory on exit.
1279  *
1280  * You may provide your own primitive polynomial of degree @m in argument
1281  * @prim_poly, or let init_bch() use its default polynomial.
1282  *
1283  * Once init_bch() has successfully returned a pointer to a newly allocated
1284  * BCH control structure, ecc length in bytes is given by member @ecc_bytes of
1285  * the structure.
1286  */
init_bch(int m,int t,unsigned int prim_poly)1287 struct bch_control *init_bch(int m, int t, unsigned int prim_poly)
1288 {
1289 	int err = 0;
1290 	unsigned int i, words;
1291 	uint32_t *genpoly;
1292 	struct bch_control *bch = NULL;
1293 
1294 	const int min_m = 5;
1295 	const int max_m = 15;
1296 
1297 	/* default primitive polynomials */
1298 	static const unsigned int prim_poly_tab[] = {
1299 		0x25, 0x43, 0x83, 0x11d, 0x211, 0x409, 0x805, 0x1053, 0x201b,
1300 		0x402b, 0x8003,
1301 	};
1302 
1303 #if defined(CONFIG_BCH_CONST_PARAMS)
1304 	if ((m != (CONFIG_BCH_CONST_M)) || (t != (CONFIG_BCH_CONST_T))) {
1305 		printk(KERN_ERR "bch encoder/decoder was configured to support "
1306 		       "parameters m=%d, t=%d only!\n",
1307 		       CONFIG_BCH_CONST_M, CONFIG_BCH_CONST_T);
1308 		goto fail;
1309 	}
1310 #endif
1311 	if ((m < min_m) || (m > max_m))
1312 		/*
1313 		 * values of m greater than 15 are not currently supported;
1314 		 * supporting m > 15 would require changing table base type
1315 		 * (uint16_t) and a small patch in matrix transposition
1316 		 */
1317 		goto fail;
1318 
1319 	/* sanity checks */
1320 	if ((t < 1) || (m*t >= ((1 << m)-1)))
1321 		/* invalid t value */
1322 		goto fail;
1323 
1324 	/* select a primitive polynomial for generating GF(2^m) */
1325 	if (prim_poly == 0)
1326 		prim_poly = prim_poly_tab[m-min_m];
1327 
1328 	bch = kzalloc(sizeof(*bch), GFP_KERNEL);
1329 	if (bch == NULL)
1330 		goto fail;
1331 
1332 	bch->m = m;
1333 	bch->t = t;
1334 	bch->n = (1 << m)-1;
1335 	words  = DIV_ROUND_UP(m*t, 32);
1336 	bch->ecc_bytes = DIV_ROUND_UP(m*t, 8);
1337 	bch->a_pow_tab = bch_alloc((1+bch->n)*sizeof(*bch->a_pow_tab), &err);
1338 	bch->a_log_tab = bch_alloc((1+bch->n)*sizeof(*bch->a_log_tab), &err);
1339 	bch->mod8_tab  = bch_alloc(words*1024*sizeof(*bch->mod8_tab), &err);
1340 	bch->ecc_buf   = bch_alloc(words*sizeof(*bch->ecc_buf), &err);
1341 	bch->ecc_buf2  = bch_alloc(words*sizeof(*bch->ecc_buf2), &err);
1342 	bch->xi_tab    = bch_alloc(m*sizeof(*bch->xi_tab), &err);
1343 	bch->syn       = bch_alloc(2*t*sizeof(*bch->syn), &err);
1344 	bch->cache     = bch_alloc(2*t*sizeof(*bch->cache), &err);
1345 	bch->elp       = bch_alloc((t+1)*sizeof(struct gf_poly_deg1), &err);
1346 
1347 	for (i = 0; i < ARRAY_SIZE(bch->poly_2t); i++)
1348 		bch->poly_2t[i] = bch_alloc(GF_POLY_SZ(2*t), &err);
1349 
1350 	if (err)
1351 		goto fail;
1352 
1353 	err = build_gf_tables(bch, prim_poly);
1354 	if (err)
1355 		goto fail;
1356 
1357 	/* use generator polynomial for computing encoding tables */
1358 	genpoly = compute_generator_polynomial(bch);
1359 	if (genpoly == NULL)
1360 		goto fail;
1361 
1362 	build_mod8_tables(bch, genpoly);
1363 	kfree(genpoly);
1364 
1365 	err = build_deg2_base(bch);
1366 	if (err)
1367 		goto fail;
1368 
1369 	return bch;
1370 
1371 fail:
1372 	free_bch(bch);
1373 	return NULL;
1374 }
1375 
1376 /**
1377  *  free_bch - free the BCH control structure
1378  *  @bch:    BCH control structure to release
1379  */
free_bch(struct bch_control * bch)1380 void free_bch(struct bch_control *bch)
1381 {
1382 	unsigned int i;
1383 
1384 	if (bch) {
1385 		kfree(bch->a_pow_tab);
1386 		kfree(bch->a_log_tab);
1387 		kfree(bch->mod8_tab);
1388 		kfree(bch->ecc_buf);
1389 		kfree(bch->ecc_buf2);
1390 		kfree(bch->xi_tab);
1391 		kfree(bch->syn);
1392 		kfree(bch->cache);
1393 		kfree(bch->elp);
1394 
1395 		for (i = 0; i < ARRAY_SIZE(bch->poly_2t); i++)
1396 			kfree(bch->poly_2t[i]);
1397 
1398 		kfree(bch);
1399 	}
1400 }
1401