xref: /openbmc/u-boot/lib/bch.c (revision 8314bfe5)
1 /*
2  * Generic binary BCH encoding/decoding library
3  *
4  * SPDX-License-Identifier:	GPL-2.0
5  *
6  * Copyright © 2011 Parrot S.A.
7  *
8  * Author: Ivan Djelic <ivan.djelic@parrot.com>
9  *
10  * Description:
11  *
12  * This library provides runtime configurable encoding/decoding of binary
13  * Bose-Chaudhuri-Hocquenghem (BCH) codes.
14  *
15  * Call init_bch to get a pointer to a newly allocated bch_control structure for
16  * the given m (Galois field order), t (error correction capability) and
17  * (optional) primitive polynomial parameters.
18  *
19  * Call encode_bch to compute and store ecc parity bytes to a given buffer.
20  * Call decode_bch to detect and locate errors in received data.
21  *
22  * On systems supporting hw BCH features, intermediate results may be provided
23  * to decode_bch in order to skip certain steps. See decode_bch() documentation
24  * for details.
25  *
26  * Option CONFIG_BCH_CONST_PARAMS can be used to force fixed values of
27  * parameters m and t; thus allowing extra compiler optimizations and providing
28  * better (up to 2x) encoding performance. Using this option makes sense when
29  * (m,t) are fixed and known in advance, e.g. when using BCH error correction
30  * on a particular NAND flash device.
31  *
32  * Algorithmic details:
33  *
34  * Encoding is performed by processing 32 input bits in parallel, using 4
35  * remainder lookup tables.
36  *
37  * The final stage of decoding involves the following internal steps:
38  * a. Syndrome computation
39  * b. Error locator polynomial computation using Berlekamp-Massey algorithm
40  * c. Error locator root finding (by far the most expensive step)
41  *
42  * In this implementation, step c is not performed using the usual Chien search.
43  * Instead, an alternative approach described in [1] is used. It consists in
44  * factoring the error locator polynomial using the Berlekamp Trace algorithm
45  * (BTA) down to a certain degree (4), after which ad hoc low-degree polynomial
46  * solving techniques [2] are used. The resulting algorithm, called BTZ, yields
47  * much better performance than Chien search for usual (m,t) values (typically
48  * m >= 13, t < 32, see [1]).
49  *
50  * [1] B. Biswas, V. Herbert. Efficient root finding of polynomials over fields
51  * of characteristic 2, in: Western European Workshop on Research in Cryptology
52  * - WEWoRC 2009, Graz, Austria, LNCS, Springer, July 2009, to appear.
53  * [2] [Zin96] V.A. Zinoviev. On the solution of equations of degree 10 over
54  * finite fields GF(2^q). In Rapport de recherche INRIA no 2829, 1996.
55  */
56 
57 #ifndef USE_HOSTCC
58 #include <common.h>
59 #include <ubi_uboot.h>
60 
61 #include <linux/bitops.h>
62 #else
63 #include <errno.h>
64 #if defined(__FreeBSD__)
65 #include <sys/endian.h>
66 #else
67 #include <endian.h>
68 #endif
69 #include <stdint.h>
70 #include <stdlib.h>
71 #include <string.h>
72 
73 #undef cpu_to_be32
74 #define cpu_to_be32 htobe32
75 #define DIV_ROUND_UP(n,d) (((n) + (d) - 1) / (d))
76 #define kmalloc(size, flags)	malloc(size)
77 #define kzalloc(size, flags)	calloc(1, size)
78 #define kfree free
79 #define ARRAY_SIZE(arr) (sizeof(arr) / sizeof((arr)[0]))
80 #endif
81 
82 #include <asm/byteorder.h>
83 #include <linux/bch.h>
84 
85 #if defined(CONFIG_BCH_CONST_PARAMS)
86 #define GF_M(_p)               (CONFIG_BCH_CONST_M)
87 #define GF_T(_p)               (CONFIG_BCH_CONST_T)
88 #define GF_N(_p)               ((1 << (CONFIG_BCH_CONST_M))-1)
89 #else
90 #define GF_M(_p)               ((_p)->m)
91 #define GF_T(_p)               ((_p)->t)
92 #define GF_N(_p)               ((_p)->n)
93 #endif
94 
95 #define BCH_ECC_WORDS(_p)      DIV_ROUND_UP(GF_M(_p)*GF_T(_p), 32)
96 #define BCH_ECC_BYTES(_p)      DIV_ROUND_UP(GF_M(_p)*GF_T(_p), 8)
97 
98 #ifndef dbg
99 #define dbg(_fmt, args...)     do {} while (0)
100 #endif
101 
102 /*
103  * represent a polynomial over GF(2^m)
104  */
105 struct gf_poly {
106 	unsigned int deg;    /* polynomial degree */
107 	unsigned int c[0];   /* polynomial terms */
108 };
109 
110 /* given its degree, compute a polynomial size in bytes */
111 #define GF_POLY_SZ(_d) (sizeof(struct gf_poly)+((_d)+1)*sizeof(unsigned int))
112 
113 /* polynomial of degree 1 */
114 struct gf_poly_deg1 {
115 	struct gf_poly poly;
116 	unsigned int   c[2];
117 };
118 
119 #ifdef USE_HOSTCC
120 #if !defined(__DragonFly__) && !defined(__FreeBSD__)
121 static int fls(int x)
122 {
123 	int r = 32;
124 
125 	if (!x)
126 		return 0;
127 	if (!(x & 0xffff0000u)) {
128 		x <<= 16;
129 		r -= 16;
130 	}
131 	if (!(x & 0xff000000u)) {
132 		x <<= 8;
133 		r -= 8;
134 	}
135 	if (!(x & 0xf0000000u)) {
136 		x <<= 4;
137 		r -= 4;
138 	}
139 	if (!(x & 0xc0000000u)) {
140 		x <<= 2;
141 		r -= 2;
142 	}
143 	if (!(x & 0x80000000u)) {
144 		x <<= 1;
145 		r -= 1;
146 	}
147 	return r;
148 }
149 #endif
150 #endif
151 
152 /*
153  * same as encode_bch(), but process input data one byte at a time
154  */
155 static void encode_bch_unaligned(struct bch_control *bch,
156 				 const unsigned char *data, unsigned int len,
157 				 uint32_t *ecc)
158 {
159 	int i;
160 	const uint32_t *p;
161 	const int l = BCH_ECC_WORDS(bch)-1;
162 
163 	while (len--) {
164 		p = bch->mod8_tab + (l+1)*(((ecc[0] >> 24)^(*data++)) & 0xff);
165 
166 		for (i = 0; i < l; i++)
167 			ecc[i] = ((ecc[i] << 8)|(ecc[i+1] >> 24))^(*p++);
168 
169 		ecc[l] = (ecc[l] << 8)^(*p);
170 	}
171 }
172 
173 /*
174  * convert ecc bytes to aligned, zero-padded 32-bit ecc words
175  */
176 static void load_ecc8(struct bch_control *bch, uint32_t *dst,
177 		      const uint8_t *src)
178 {
179 	uint8_t pad[4] = {0, 0, 0, 0};
180 	unsigned int i, nwords = BCH_ECC_WORDS(bch)-1;
181 
182 	for (i = 0; i < nwords; i++, src += 4)
183 		dst[i] = (src[0] << 24)|(src[1] << 16)|(src[2] << 8)|src[3];
184 
185 	memcpy(pad, src, BCH_ECC_BYTES(bch)-4*nwords);
186 	dst[nwords] = (pad[0] << 24)|(pad[1] << 16)|(pad[2] << 8)|pad[3];
187 }
188 
189 /*
190  * convert 32-bit ecc words to ecc bytes
191  */
192 static void store_ecc8(struct bch_control *bch, uint8_t *dst,
193 		       const uint32_t *src)
194 {
195 	uint8_t pad[4];
196 	unsigned int i, nwords = BCH_ECC_WORDS(bch)-1;
197 
198 	for (i = 0; i < nwords; i++) {
199 		*dst++ = (src[i] >> 24);
200 		*dst++ = (src[i] >> 16) & 0xff;
201 		*dst++ = (src[i] >>  8) & 0xff;
202 		*dst++ = (src[i] >>  0) & 0xff;
203 	}
204 	pad[0] = (src[nwords] >> 24);
205 	pad[1] = (src[nwords] >> 16) & 0xff;
206 	pad[2] = (src[nwords] >>  8) & 0xff;
207 	pad[3] = (src[nwords] >>  0) & 0xff;
208 	memcpy(dst, pad, BCH_ECC_BYTES(bch)-4*nwords);
209 }
210 
211 /**
212  * encode_bch - calculate BCH ecc parity of data
213  * @bch:   BCH control structure
214  * @data:  data to encode
215  * @len:   data length in bytes
216  * @ecc:   ecc parity data, must be initialized by caller
217  *
218  * The @ecc parity array is used both as input and output parameter, in order to
219  * allow incremental computations. It should be of the size indicated by member
220  * @ecc_bytes of @bch, and should be initialized to 0 before the first call.
221  *
222  * The exact number of computed ecc parity bits is given by member @ecc_bits of
223  * @bch; it may be less than m*t for large values of t.
224  */
225 void encode_bch(struct bch_control *bch, const uint8_t *data,
226 		unsigned int len, uint8_t *ecc)
227 {
228 	const unsigned int l = BCH_ECC_WORDS(bch)-1;
229 	unsigned int i, mlen;
230 	unsigned long m;
231 	uint32_t w, r[l+1];
232 	const uint32_t * const tab0 = bch->mod8_tab;
233 	const uint32_t * const tab1 = tab0 + 256*(l+1);
234 	const uint32_t * const tab2 = tab1 + 256*(l+1);
235 	const uint32_t * const tab3 = tab2 + 256*(l+1);
236 	const uint32_t *pdata, *p0, *p1, *p2, *p3;
237 
238 	if (ecc) {
239 		/* load ecc parity bytes into internal 32-bit buffer */
240 		load_ecc8(bch, bch->ecc_buf, ecc);
241 	} else {
242 		memset(bch->ecc_buf, 0, sizeof(r));
243 	}
244 
245 	/* process first unaligned data bytes */
246 	m = ((unsigned long)data) & 3;
247 	if (m) {
248 		mlen = (len < (4-m)) ? len : 4-m;
249 		encode_bch_unaligned(bch, data, mlen, bch->ecc_buf);
250 		data += mlen;
251 		len  -= mlen;
252 	}
253 
254 	/* process 32-bit aligned data words */
255 	pdata = (uint32_t *)data;
256 	mlen  = len/4;
257 	data += 4*mlen;
258 	len  -= 4*mlen;
259 	memcpy(r, bch->ecc_buf, sizeof(r));
260 
261 	/*
262 	 * split each 32-bit word into 4 polynomials of weight 8 as follows:
263 	 *
264 	 * 31 ...24  23 ...16  15 ... 8  7 ... 0
265 	 * xxxxxxxx  yyyyyyyy  zzzzzzzz  tttttttt
266 	 *                               tttttttt  mod g = r0 (precomputed)
267 	 *                     zzzzzzzz  00000000  mod g = r1 (precomputed)
268 	 *           yyyyyyyy  00000000  00000000  mod g = r2 (precomputed)
269 	 * xxxxxxxx  00000000  00000000  00000000  mod g = r3 (precomputed)
270 	 * xxxxxxxx  yyyyyyyy  zzzzzzzz  tttttttt  mod g = r0^r1^r2^r3
271 	 */
272 	while (mlen--) {
273 		/* input data is read in big-endian format */
274 		w = r[0]^cpu_to_be32(*pdata++);
275 		p0 = tab0 + (l+1)*((w >>  0) & 0xff);
276 		p1 = tab1 + (l+1)*((w >>  8) & 0xff);
277 		p2 = tab2 + (l+1)*((w >> 16) & 0xff);
278 		p3 = tab3 + (l+1)*((w >> 24) & 0xff);
279 
280 		for (i = 0; i < l; i++)
281 			r[i] = r[i+1]^p0[i]^p1[i]^p2[i]^p3[i];
282 
283 		r[l] = p0[l]^p1[l]^p2[l]^p3[l];
284 	}
285 	memcpy(bch->ecc_buf, r, sizeof(r));
286 
287 	/* process last unaligned bytes */
288 	if (len)
289 		encode_bch_unaligned(bch, data, len, bch->ecc_buf);
290 
291 	/* store ecc parity bytes into original parity buffer */
292 	if (ecc)
293 		store_ecc8(bch, ecc, bch->ecc_buf);
294 }
295 
296 static inline int modulo(struct bch_control *bch, unsigned int v)
297 {
298 	const unsigned int n = GF_N(bch);
299 	while (v >= n) {
300 		v -= n;
301 		v = (v & n) + (v >> GF_M(bch));
302 	}
303 	return v;
304 }
305 
306 /*
307  * shorter and faster modulo function, only works when v < 2N.
308  */
309 static inline int mod_s(struct bch_control *bch, unsigned int v)
310 {
311 	const unsigned int n = GF_N(bch);
312 	return (v < n) ? v : v-n;
313 }
314 
315 static inline int deg(unsigned int poly)
316 {
317 	/* polynomial degree is the most-significant bit index */
318 	return fls(poly)-1;
319 }
320 
321 static inline int parity(unsigned int x)
322 {
323 	/*
324 	 * public domain code snippet, lifted from
325 	 * http://www-graphics.stanford.edu/~seander/bithacks.html
326 	 */
327 	x ^= x >> 1;
328 	x ^= x >> 2;
329 	x = (x & 0x11111111U) * 0x11111111U;
330 	return (x >> 28) & 1;
331 }
332 
333 /* Galois field basic operations: multiply, divide, inverse, etc. */
334 
335 static inline unsigned int gf_mul(struct bch_control *bch, unsigned int a,
336 				  unsigned int b)
337 {
338 	return (a && b) ? bch->a_pow_tab[mod_s(bch, bch->a_log_tab[a]+
339 					       bch->a_log_tab[b])] : 0;
340 }
341 
342 static inline unsigned int gf_sqr(struct bch_control *bch, unsigned int a)
343 {
344 	return a ? bch->a_pow_tab[mod_s(bch, 2*bch->a_log_tab[a])] : 0;
345 }
346 
347 static inline unsigned int gf_div(struct bch_control *bch, unsigned int a,
348 				  unsigned int b)
349 {
350 	return a ? bch->a_pow_tab[mod_s(bch, bch->a_log_tab[a]+
351 					GF_N(bch)-bch->a_log_tab[b])] : 0;
352 }
353 
354 static inline unsigned int gf_inv(struct bch_control *bch, unsigned int a)
355 {
356 	return bch->a_pow_tab[GF_N(bch)-bch->a_log_tab[a]];
357 }
358 
359 static inline unsigned int a_pow(struct bch_control *bch, int i)
360 {
361 	return bch->a_pow_tab[modulo(bch, i)];
362 }
363 
364 static inline int a_log(struct bch_control *bch, unsigned int x)
365 {
366 	return bch->a_log_tab[x];
367 }
368 
369 static inline int a_ilog(struct bch_control *bch, unsigned int x)
370 {
371 	return mod_s(bch, GF_N(bch)-bch->a_log_tab[x]);
372 }
373 
374 /*
375  * compute 2t syndromes of ecc polynomial, i.e. ecc(a^j) for j=1..2t
376  */
377 static void compute_syndromes(struct bch_control *bch, uint32_t *ecc,
378 			      unsigned int *syn)
379 {
380 	int i, j, s;
381 	unsigned int m;
382 	uint32_t poly;
383 	const int t = GF_T(bch);
384 
385 	s = bch->ecc_bits;
386 
387 	/* make sure extra bits in last ecc word are cleared */
388 	m = ((unsigned int)s) & 31;
389 	if (m)
390 		ecc[s/32] &= ~((1u << (32-m))-1);
391 	memset(syn, 0, 2*t*sizeof(*syn));
392 
393 	/* compute v(a^j) for j=1 .. 2t-1 */
394 	do {
395 		poly = *ecc++;
396 		s -= 32;
397 		while (poly) {
398 			i = deg(poly);
399 			for (j = 0; j < 2*t; j += 2)
400 				syn[j] ^= a_pow(bch, (j+1)*(i+s));
401 
402 			poly ^= (1 << i);
403 		}
404 	} while (s > 0);
405 
406 	/* v(a^(2j)) = v(a^j)^2 */
407 	for (j = 0; j < t; j++)
408 		syn[2*j+1] = gf_sqr(bch, syn[j]);
409 }
410 
411 static void gf_poly_copy(struct gf_poly *dst, struct gf_poly *src)
412 {
413 	memcpy(dst, src, GF_POLY_SZ(src->deg));
414 }
415 
416 static int compute_error_locator_polynomial(struct bch_control *bch,
417 					    const unsigned int *syn)
418 {
419 	const unsigned int t = GF_T(bch);
420 	const unsigned int n = GF_N(bch);
421 	unsigned int i, j, tmp, l, pd = 1, d = syn[0];
422 	struct gf_poly *elp = bch->elp;
423 	struct gf_poly *pelp = bch->poly_2t[0];
424 	struct gf_poly *elp_copy = bch->poly_2t[1];
425 	int k, pp = -1;
426 
427 	memset(pelp, 0, GF_POLY_SZ(2*t));
428 	memset(elp, 0, GF_POLY_SZ(2*t));
429 
430 	pelp->deg = 0;
431 	pelp->c[0] = 1;
432 	elp->deg = 0;
433 	elp->c[0] = 1;
434 
435 	/* use simplified binary Berlekamp-Massey algorithm */
436 	for (i = 0; (i < t) && (elp->deg <= t); i++) {
437 		if (d) {
438 			k = 2*i-pp;
439 			gf_poly_copy(elp_copy, elp);
440 			/* e[i+1](X) = e[i](X)+di*dp^-1*X^2(i-p)*e[p](X) */
441 			tmp = a_log(bch, d)+n-a_log(bch, pd);
442 			for (j = 0; j <= pelp->deg; j++) {
443 				if (pelp->c[j]) {
444 					l = a_log(bch, pelp->c[j]);
445 					elp->c[j+k] ^= a_pow(bch, tmp+l);
446 				}
447 			}
448 			/* compute l[i+1] = max(l[i]->c[l[p]+2*(i-p]) */
449 			tmp = pelp->deg+k;
450 			if (tmp > elp->deg) {
451 				elp->deg = tmp;
452 				gf_poly_copy(pelp, elp_copy);
453 				pd = d;
454 				pp = 2*i;
455 			}
456 		}
457 		/* di+1 = S(2i+3)+elp[i+1].1*S(2i+2)+...+elp[i+1].lS(2i+3-l) */
458 		if (i < t-1) {
459 			d = syn[2*i+2];
460 			for (j = 1; j <= elp->deg; j++)
461 				d ^= gf_mul(bch, elp->c[j], syn[2*i+2-j]);
462 		}
463 	}
464 	dbg("elp=%s\n", gf_poly_str(elp));
465 	return (elp->deg > t) ? -1 : (int)elp->deg;
466 }
467 
468 /*
469  * solve a m x m linear system in GF(2) with an expected number of solutions,
470  * and return the number of found solutions
471  */
472 static int solve_linear_system(struct bch_control *bch, unsigned int *rows,
473 			       unsigned int *sol, int nsol)
474 {
475 	const int m = GF_M(bch);
476 	unsigned int tmp, mask;
477 	int rem, c, r, p, k, param[m];
478 
479 	k = 0;
480 	mask = 1 << m;
481 
482 	/* Gaussian elimination */
483 	for (c = 0; c < m; c++) {
484 		rem = 0;
485 		p = c-k;
486 		/* find suitable row for elimination */
487 		for (r = p; r < m; r++) {
488 			if (rows[r] & mask) {
489 				if (r != p) {
490 					tmp = rows[r];
491 					rows[r] = rows[p];
492 					rows[p] = tmp;
493 				}
494 				rem = r+1;
495 				break;
496 			}
497 		}
498 		if (rem) {
499 			/* perform elimination on remaining rows */
500 			tmp = rows[p];
501 			for (r = rem; r < m; r++) {
502 				if (rows[r] & mask)
503 					rows[r] ^= tmp;
504 			}
505 		} else {
506 			/* elimination not needed, store defective row index */
507 			param[k++] = c;
508 		}
509 		mask >>= 1;
510 	}
511 	/* rewrite system, inserting fake parameter rows */
512 	if (k > 0) {
513 		p = k;
514 		for (r = m-1; r >= 0; r--) {
515 			if ((r > m-1-k) && rows[r])
516 				/* system has no solution */
517 				return 0;
518 
519 			rows[r] = (p && (r == param[p-1])) ?
520 				p--, 1u << (m-r) : rows[r-p];
521 		}
522 	}
523 
524 	if (nsol != (1 << k))
525 		/* unexpected number of solutions */
526 		return 0;
527 
528 	for (p = 0; p < nsol; p++) {
529 		/* set parameters for p-th solution */
530 		for (c = 0; c < k; c++)
531 			rows[param[c]] = (rows[param[c]] & ~1)|((p >> c) & 1);
532 
533 		/* compute unique solution */
534 		tmp = 0;
535 		for (r = m-1; r >= 0; r--) {
536 			mask = rows[r] & (tmp|1);
537 			tmp |= parity(mask) << (m-r);
538 		}
539 		sol[p] = tmp >> 1;
540 	}
541 	return nsol;
542 }
543 
544 /*
545  * this function builds and solves a linear system for finding roots of a degree
546  * 4 affine monic polynomial X^4+aX^2+bX+c over GF(2^m).
547  */
548 static int find_affine4_roots(struct bch_control *bch, unsigned int a,
549 			      unsigned int b, unsigned int c,
550 			      unsigned int *roots)
551 {
552 	int i, j, k;
553 	const int m = GF_M(bch);
554 	unsigned int mask = 0xff, t, rows[16] = {0,};
555 
556 	j = a_log(bch, b);
557 	k = a_log(bch, a);
558 	rows[0] = c;
559 
560 	/* buid linear system to solve X^4+aX^2+bX+c = 0 */
561 	for (i = 0; i < m; i++) {
562 		rows[i+1] = bch->a_pow_tab[4*i]^
563 			(a ? bch->a_pow_tab[mod_s(bch, k)] : 0)^
564 			(b ? bch->a_pow_tab[mod_s(bch, j)] : 0);
565 		j++;
566 		k += 2;
567 	}
568 	/*
569 	 * transpose 16x16 matrix before passing it to linear solver
570 	 * warning: this code assumes m < 16
571 	 */
572 	for (j = 8; j != 0; j >>= 1, mask ^= (mask << j)) {
573 		for (k = 0; k < 16; k = (k+j+1) & ~j) {
574 			t = ((rows[k] >> j)^rows[k+j]) & mask;
575 			rows[k] ^= (t << j);
576 			rows[k+j] ^= t;
577 		}
578 	}
579 	return solve_linear_system(bch, rows, roots, 4);
580 }
581 
582 /*
583  * compute root r of a degree 1 polynomial over GF(2^m) (returned as log(1/r))
584  */
585 static int find_poly_deg1_roots(struct bch_control *bch, struct gf_poly *poly,
586 				unsigned int *roots)
587 {
588 	int n = 0;
589 
590 	if (poly->c[0])
591 		/* poly[X] = bX+c with c!=0, root=c/b */
592 		roots[n++] = mod_s(bch, GF_N(bch)-bch->a_log_tab[poly->c[0]]+
593 				   bch->a_log_tab[poly->c[1]]);
594 	return n;
595 }
596 
597 /*
598  * compute roots of a degree 2 polynomial over GF(2^m)
599  */
600 static int find_poly_deg2_roots(struct bch_control *bch, struct gf_poly *poly,
601 				unsigned int *roots)
602 {
603 	int n = 0, i, l0, l1, l2;
604 	unsigned int u, v, r;
605 
606 	if (poly->c[0] && poly->c[1]) {
607 
608 		l0 = bch->a_log_tab[poly->c[0]];
609 		l1 = bch->a_log_tab[poly->c[1]];
610 		l2 = bch->a_log_tab[poly->c[2]];
611 
612 		/* using z=a/bX, transform aX^2+bX+c into z^2+z+u (u=ac/b^2) */
613 		u = a_pow(bch, l0+l2+2*(GF_N(bch)-l1));
614 		/*
615 		 * let u = sum(li.a^i) i=0..m-1; then compute r = sum(li.xi):
616 		 * r^2+r = sum(li.(xi^2+xi)) = sum(li.(a^i+Tr(a^i).a^k)) =
617 		 * u + sum(li.Tr(a^i).a^k) = u+a^k.Tr(sum(li.a^i)) = u+a^k.Tr(u)
618 		 * i.e. r and r+1 are roots iff Tr(u)=0
619 		 */
620 		r = 0;
621 		v = u;
622 		while (v) {
623 			i = deg(v);
624 			r ^= bch->xi_tab[i];
625 			v ^= (1 << i);
626 		}
627 		/* verify root */
628 		if ((gf_sqr(bch, r)^r) == u) {
629 			/* reverse z=a/bX transformation and compute log(1/r) */
630 			roots[n++] = modulo(bch, 2*GF_N(bch)-l1-
631 					    bch->a_log_tab[r]+l2);
632 			roots[n++] = modulo(bch, 2*GF_N(bch)-l1-
633 					    bch->a_log_tab[r^1]+l2);
634 		}
635 	}
636 	return n;
637 }
638 
639 /*
640  * compute roots of a degree 3 polynomial over GF(2^m)
641  */
642 static int find_poly_deg3_roots(struct bch_control *bch, struct gf_poly *poly,
643 				unsigned int *roots)
644 {
645 	int i, n = 0;
646 	unsigned int a, b, c, a2, b2, c2, e3, tmp[4];
647 
648 	if (poly->c[0]) {
649 		/* transform polynomial into monic X^3 + a2X^2 + b2X + c2 */
650 		e3 = poly->c[3];
651 		c2 = gf_div(bch, poly->c[0], e3);
652 		b2 = gf_div(bch, poly->c[1], e3);
653 		a2 = gf_div(bch, poly->c[2], e3);
654 
655 		/* (X+a2)(X^3+a2X^2+b2X+c2) = X^4+aX^2+bX+c (affine) */
656 		c = gf_mul(bch, a2, c2);           /* c = a2c2      */
657 		b = gf_mul(bch, a2, b2)^c2;        /* b = a2b2 + c2 */
658 		a = gf_sqr(bch, a2)^b2;            /* a = a2^2 + b2 */
659 
660 		/* find the 4 roots of this affine polynomial */
661 		if (find_affine4_roots(bch, a, b, c, tmp) == 4) {
662 			/* remove a2 from final list of roots */
663 			for (i = 0; i < 4; i++) {
664 				if (tmp[i] != a2)
665 					roots[n++] = a_ilog(bch, tmp[i]);
666 			}
667 		}
668 	}
669 	return n;
670 }
671 
672 /*
673  * compute roots of a degree 4 polynomial over GF(2^m)
674  */
675 static int find_poly_deg4_roots(struct bch_control *bch, struct gf_poly *poly,
676 				unsigned int *roots)
677 {
678 	int i, l, n = 0;
679 	unsigned int a, b, c, d, e = 0, f, a2, b2, c2, e4;
680 
681 	if (poly->c[0] == 0)
682 		return 0;
683 
684 	/* transform polynomial into monic X^4 + aX^3 + bX^2 + cX + d */
685 	e4 = poly->c[4];
686 	d = gf_div(bch, poly->c[0], e4);
687 	c = gf_div(bch, poly->c[1], e4);
688 	b = gf_div(bch, poly->c[2], e4);
689 	a = gf_div(bch, poly->c[3], e4);
690 
691 	/* use Y=1/X transformation to get an affine polynomial */
692 	if (a) {
693 		/* first, eliminate cX by using z=X+e with ae^2+c=0 */
694 		if (c) {
695 			/* compute e such that e^2 = c/a */
696 			f = gf_div(bch, c, a);
697 			l = a_log(bch, f);
698 			l += (l & 1) ? GF_N(bch) : 0;
699 			e = a_pow(bch, l/2);
700 			/*
701 			 * use transformation z=X+e:
702 			 * z^4+e^4 + a(z^3+ez^2+e^2z+e^3) + b(z^2+e^2) +cz+ce+d
703 			 * z^4 + az^3 + (ae+b)z^2 + (ae^2+c)z+e^4+be^2+ae^3+ce+d
704 			 * z^4 + az^3 + (ae+b)z^2 + e^4+be^2+d
705 			 * z^4 + az^3 +     b'z^2 + d'
706 			 */
707 			d = a_pow(bch, 2*l)^gf_mul(bch, b, f)^d;
708 			b = gf_mul(bch, a, e)^b;
709 		}
710 		/* now, use Y=1/X to get Y^4 + b/dY^2 + a/dY + 1/d */
711 		if (d == 0)
712 			/* assume all roots have multiplicity 1 */
713 			return 0;
714 
715 		c2 = gf_inv(bch, d);
716 		b2 = gf_div(bch, a, d);
717 		a2 = gf_div(bch, b, d);
718 	} else {
719 		/* polynomial is already affine */
720 		c2 = d;
721 		b2 = c;
722 		a2 = b;
723 	}
724 	/* find the 4 roots of this affine polynomial */
725 	if (find_affine4_roots(bch, a2, b2, c2, roots) == 4) {
726 		for (i = 0; i < 4; i++) {
727 			/* post-process roots (reverse transformations) */
728 			f = a ? gf_inv(bch, roots[i]) : roots[i];
729 			roots[i] = a_ilog(bch, f^e);
730 		}
731 		n = 4;
732 	}
733 	return n;
734 }
735 
736 /*
737  * build monic, log-based representation of a polynomial
738  */
739 static void gf_poly_logrep(struct bch_control *bch,
740 			   const struct gf_poly *a, int *rep)
741 {
742 	int i, d = a->deg, l = GF_N(bch)-a_log(bch, a->c[a->deg]);
743 
744 	/* represent 0 values with -1; warning, rep[d] is not set to 1 */
745 	for (i = 0; i < d; i++)
746 		rep[i] = a->c[i] ? mod_s(bch, a_log(bch, a->c[i])+l) : -1;
747 }
748 
749 /*
750  * compute polynomial Euclidean division remainder in GF(2^m)[X]
751  */
752 static void gf_poly_mod(struct bch_control *bch, struct gf_poly *a,
753 			const struct gf_poly *b, int *rep)
754 {
755 	int la, p, m;
756 	unsigned int i, j, *c = a->c;
757 	const unsigned int d = b->deg;
758 
759 	if (a->deg < d)
760 		return;
761 
762 	/* reuse or compute log representation of denominator */
763 	if (!rep) {
764 		rep = bch->cache;
765 		gf_poly_logrep(bch, b, rep);
766 	}
767 
768 	for (j = a->deg; j >= d; j--) {
769 		if (c[j]) {
770 			la = a_log(bch, c[j]);
771 			p = j-d;
772 			for (i = 0; i < d; i++, p++) {
773 				m = rep[i];
774 				if (m >= 0)
775 					c[p] ^= bch->a_pow_tab[mod_s(bch,
776 								     m+la)];
777 			}
778 		}
779 	}
780 	a->deg = d-1;
781 	while (!c[a->deg] && a->deg)
782 		a->deg--;
783 }
784 
785 /*
786  * compute polynomial Euclidean division quotient in GF(2^m)[X]
787  */
788 static void gf_poly_div(struct bch_control *bch, struct gf_poly *a,
789 			const struct gf_poly *b, struct gf_poly *q)
790 {
791 	if (a->deg >= b->deg) {
792 		q->deg = a->deg-b->deg;
793 		/* compute a mod b (modifies a) */
794 		gf_poly_mod(bch, a, b, NULL);
795 		/* quotient is stored in upper part of polynomial a */
796 		memcpy(q->c, &a->c[b->deg], (1+q->deg)*sizeof(unsigned int));
797 	} else {
798 		q->deg = 0;
799 		q->c[0] = 0;
800 	}
801 }
802 
803 /*
804  * compute polynomial GCD (Greatest Common Divisor) in GF(2^m)[X]
805  */
806 static struct gf_poly *gf_poly_gcd(struct bch_control *bch, struct gf_poly *a,
807 				   struct gf_poly *b)
808 {
809 	struct gf_poly *tmp;
810 
811 	dbg("gcd(%s,%s)=", gf_poly_str(a), gf_poly_str(b));
812 
813 	if (a->deg < b->deg) {
814 		tmp = b;
815 		b = a;
816 		a = tmp;
817 	}
818 
819 	while (b->deg > 0) {
820 		gf_poly_mod(bch, a, b, NULL);
821 		tmp = b;
822 		b = a;
823 		a = tmp;
824 	}
825 
826 	dbg("%s\n", gf_poly_str(a));
827 
828 	return a;
829 }
830 
831 /*
832  * Given a polynomial f and an integer k, compute Tr(a^kX) mod f
833  * This is used in Berlekamp Trace algorithm for splitting polynomials
834  */
835 static void compute_trace_bk_mod(struct bch_control *bch, int k,
836 				 const struct gf_poly *f, struct gf_poly *z,
837 				 struct gf_poly *out)
838 {
839 	const int m = GF_M(bch);
840 	int i, j;
841 
842 	/* z contains z^2j mod f */
843 	z->deg = 1;
844 	z->c[0] = 0;
845 	z->c[1] = bch->a_pow_tab[k];
846 
847 	out->deg = 0;
848 	memset(out, 0, GF_POLY_SZ(f->deg));
849 
850 	/* compute f log representation only once */
851 	gf_poly_logrep(bch, f, bch->cache);
852 
853 	for (i = 0; i < m; i++) {
854 		/* add a^(k*2^i)(z^(2^i) mod f) and compute (z^(2^i) mod f)^2 */
855 		for (j = z->deg; j >= 0; j--) {
856 			out->c[j] ^= z->c[j];
857 			z->c[2*j] = gf_sqr(bch, z->c[j]);
858 			z->c[2*j+1] = 0;
859 		}
860 		if (z->deg > out->deg)
861 			out->deg = z->deg;
862 
863 		if (i < m-1) {
864 			z->deg *= 2;
865 			/* z^(2(i+1)) mod f = (z^(2^i) mod f)^2 mod f */
866 			gf_poly_mod(bch, z, f, bch->cache);
867 		}
868 	}
869 	while (!out->c[out->deg] && out->deg)
870 		out->deg--;
871 
872 	dbg("Tr(a^%d.X) mod f = %s\n", k, gf_poly_str(out));
873 }
874 
875 /*
876  * factor a polynomial using Berlekamp Trace algorithm (BTA)
877  */
878 static void factor_polynomial(struct bch_control *bch, int k, struct gf_poly *f,
879 			      struct gf_poly **g, struct gf_poly **h)
880 {
881 	struct gf_poly *f2 = bch->poly_2t[0];
882 	struct gf_poly *q  = bch->poly_2t[1];
883 	struct gf_poly *tk = bch->poly_2t[2];
884 	struct gf_poly *z  = bch->poly_2t[3];
885 	struct gf_poly *gcd;
886 
887 	dbg("factoring %s...\n", gf_poly_str(f));
888 
889 	*g = f;
890 	*h = NULL;
891 
892 	/* tk = Tr(a^k.X) mod f */
893 	compute_trace_bk_mod(bch, k, f, z, tk);
894 
895 	if (tk->deg > 0) {
896 		/* compute g = gcd(f, tk) (destructive operation) */
897 		gf_poly_copy(f2, f);
898 		gcd = gf_poly_gcd(bch, f2, tk);
899 		if (gcd->deg < f->deg) {
900 			/* compute h=f/gcd(f,tk); this will modify f and q */
901 			gf_poly_div(bch, f, gcd, q);
902 			/* store g and h in-place (clobbering f) */
903 			*h = &((struct gf_poly_deg1 *)f)[gcd->deg].poly;
904 			gf_poly_copy(*g, gcd);
905 			gf_poly_copy(*h, q);
906 		}
907 	}
908 }
909 
910 /*
911  * find roots of a polynomial, using BTZ algorithm; see the beginning of this
912  * file for details
913  */
914 static int find_poly_roots(struct bch_control *bch, unsigned int k,
915 			   struct gf_poly *poly, unsigned int *roots)
916 {
917 	int cnt;
918 	struct gf_poly *f1, *f2;
919 
920 	switch (poly->deg) {
921 		/* handle low degree polynomials with ad hoc techniques */
922 	case 1:
923 		cnt = find_poly_deg1_roots(bch, poly, roots);
924 		break;
925 	case 2:
926 		cnt = find_poly_deg2_roots(bch, poly, roots);
927 		break;
928 	case 3:
929 		cnt = find_poly_deg3_roots(bch, poly, roots);
930 		break;
931 	case 4:
932 		cnt = find_poly_deg4_roots(bch, poly, roots);
933 		break;
934 	default:
935 		/* factor polynomial using Berlekamp Trace Algorithm (BTA) */
936 		cnt = 0;
937 		if (poly->deg && (k <= GF_M(bch))) {
938 			factor_polynomial(bch, k, poly, &f1, &f2);
939 			if (f1)
940 				cnt += find_poly_roots(bch, k+1, f1, roots);
941 			if (f2)
942 				cnt += find_poly_roots(bch, k+1, f2, roots+cnt);
943 		}
944 		break;
945 	}
946 	return cnt;
947 }
948 
949 #if defined(USE_CHIEN_SEARCH)
950 /*
951  * exhaustive root search (Chien) implementation - not used, included only for
952  * reference/comparison tests
953  */
954 static int chien_search(struct bch_control *bch, unsigned int len,
955 			struct gf_poly *p, unsigned int *roots)
956 {
957 	int m;
958 	unsigned int i, j, syn, syn0, count = 0;
959 	const unsigned int k = 8*len+bch->ecc_bits;
960 
961 	/* use a log-based representation of polynomial */
962 	gf_poly_logrep(bch, p, bch->cache);
963 	bch->cache[p->deg] = 0;
964 	syn0 = gf_div(bch, p->c[0], p->c[p->deg]);
965 
966 	for (i = GF_N(bch)-k+1; i <= GF_N(bch); i++) {
967 		/* compute elp(a^i) */
968 		for (j = 1, syn = syn0; j <= p->deg; j++) {
969 			m = bch->cache[j];
970 			if (m >= 0)
971 				syn ^= a_pow(bch, m+j*i);
972 		}
973 		if (syn == 0) {
974 			roots[count++] = GF_N(bch)-i;
975 			if (count == p->deg)
976 				break;
977 		}
978 	}
979 	return (count == p->deg) ? count : 0;
980 }
981 #define find_poly_roots(_p, _k, _elp, _loc) chien_search(_p, len, _elp, _loc)
982 #endif /* USE_CHIEN_SEARCH */
983 
984 /**
985  * decode_bch - decode received codeword and find bit error locations
986  * @bch:      BCH control structure
987  * @data:     received data, ignored if @calc_ecc is provided
988  * @len:      data length in bytes, must always be provided
989  * @recv_ecc: received ecc, if NULL then assume it was XORed in @calc_ecc
990  * @calc_ecc: calculated ecc, if NULL then calc_ecc is computed from @data
991  * @syn:      hw computed syndrome data (if NULL, syndrome is calculated)
992  * @errloc:   output array of error locations
993  *
994  * Returns:
995  *  The number of errors found, or -EBADMSG if decoding failed, or -EINVAL if
996  *  invalid parameters were provided
997  *
998  * Depending on the available hw BCH support and the need to compute @calc_ecc
999  * separately (using encode_bch()), this function should be called with one of
1000  * the following parameter configurations -
1001  *
1002  * by providing @data and @recv_ecc only:
1003  *   decode_bch(@bch, @data, @len, @recv_ecc, NULL, NULL, @errloc)
1004  *
1005  * by providing @recv_ecc and @calc_ecc:
1006  *   decode_bch(@bch, NULL, @len, @recv_ecc, @calc_ecc, NULL, @errloc)
1007  *
1008  * by providing ecc = recv_ecc XOR calc_ecc:
1009  *   decode_bch(@bch, NULL, @len, NULL, ecc, NULL, @errloc)
1010  *
1011  * by providing syndrome results @syn:
1012  *   decode_bch(@bch, NULL, @len, NULL, NULL, @syn, @errloc)
1013  *
1014  * Once decode_bch() has successfully returned with a positive value, error
1015  * locations returned in array @errloc should be interpreted as follows -
1016  *
1017  * if (errloc[n] >= 8*len), then n-th error is located in ecc (no need for
1018  * data correction)
1019  *
1020  * if (errloc[n] < 8*len), then n-th error is located in data and can be
1021  * corrected with statement data[errloc[n]/8] ^= 1 << (errloc[n] % 8);
1022  *
1023  * Note that this function does not perform any data correction by itself, it
1024  * merely indicates error locations.
1025  */
1026 int decode_bch(struct bch_control *bch, const uint8_t *data, unsigned int len,
1027 	       const uint8_t *recv_ecc, const uint8_t *calc_ecc,
1028 	       const unsigned int *syn, unsigned int *errloc)
1029 {
1030 	const unsigned int ecc_words = BCH_ECC_WORDS(bch);
1031 	unsigned int nbits;
1032 	int i, err, nroots;
1033 	uint32_t sum;
1034 
1035 	/* sanity check: make sure data length can be handled */
1036 	if (8*len > (bch->n-bch->ecc_bits))
1037 		return -EINVAL;
1038 
1039 	/* if caller does not provide syndromes, compute them */
1040 	if (!syn) {
1041 		if (!calc_ecc) {
1042 			/* compute received data ecc into an internal buffer */
1043 			if (!data || !recv_ecc)
1044 				return -EINVAL;
1045 			encode_bch(bch, data, len, NULL);
1046 		} else {
1047 			/* load provided calculated ecc */
1048 			load_ecc8(bch, bch->ecc_buf, calc_ecc);
1049 		}
1050 		/* load received ecc or assume it was XORed in calc_ecc */
1051 		if (recv_ecc) {
1052 			load_ecc8(bch, bch->ecc_buf2, recv_ecc);
1053 			/* XOR received and calculated ecc */
1054 			for (i = 0, sum = 0; i < (int)ecc_words; i++) {
1055 				bch->ecc_buf[i] ^= bch->ecc_buf2[i];
1056 				sum |= bch->ecc_buf[i];
1057 			}
1058 			if (!sum)
1059 				/* no error found */
1060 				return 0;
1061 		}
1062 		compute_syndromes(bch, bch->ecc_buf, bch->syn);
1063 		syn = bch->syn;
1064 	}
1065 
1066 	err = compute_error_locator_polynomial(bch, syn);
1067 	if (err > 0) {
1068 		nroots = find_poly_roots(bch, 1, bch->elp, errloc);
1069 		if (err != nroots)
1070 			err = -1;
1071 	}
1072 	if (err > 0) {
1073 		/* post-process raw error locations for easier correction */
1074 		nbits = (len*8)+bch->ecc_bits;
1075 		for (i = 0; i < err; i++) {
1076 			if (errloc[i] >= nbits) {
1077 				err = -1;
1078 				break;
1079 			}
1080 			errloc[i] = nbits-1-errloc[i];
1081 			errloc[i] = (errloc[i] & ~7)|(7-(errloc[i] & 7));
1082 		}
1083 	}
1084 	return (err >= 0) ? err : -EBADMSG;
1085 }
1086 
1087 /*
1088  * generate Galois field lookup tables
1089  */
1090 static int build_gf_tables(struct bch_control *bch, unsigned int poly)
1091 {
1092 	unsigned int i, x = 1;
1093 	const unsigned int k = 1 << deg(poly);
1094 
1095 	/* primitive polynomial must be of degree m */
1096 	if (k != (1u << GF_M(bch)))
1097 		return -1;
1098 
1099 	for (i = 0; i < GF_N(bch); i++) {
1100 		bch->a_pow_tab[i] = x;
1101 		bch->a_log_tab[x] = i;
1102 		if (i && (x == 1))
1103 			/* polynomial is not primitive (a^i=1 with 0<i<2^m-1) */
1104 			return -1;
1105 		x <<= 1;
1106 		if (x & k)
1107 			x ^= poly;
1108 	}
1109 	bch->a_pow_tab[GF_N(bch)] = 1;
1110 	bch->a_log_tab[0] = 0;
1111 
1112 	return 0;
1113 }
1114 
1115 /*
1116  * compute generator polynomial remainder tables for fast encoding
1117  */
1118 static void build_mod8_tables(struct bch_control *bch, const uint32_t *g)
1119 {
1120 	int i, j, b, d;
1121 	uint32_t data, hi, lo, *tab;
1122 	const int l = BCH_ECC_WORDS(bch);
1123 	const int plen = DIV_ROUND_UP(bch->ecc_bits+1, 32);
1124 	const int ecclen = DIV_ROUND_UP(bch->ecc_bits, 32);
1125 
1126 	memset(bch->mod8_tab, 0, 4*256*l*sizeof(*bch->mod8_tab));
1127 
1128 	for (i = 0; i < 256; i++) {
1129 		/* p(X)=i is a small polynomial of weight <= 8 */
1130 		for (b = 0; b < 4; b++) {
1131 			/* we want to compute (p(X).X^(8*b+deg(g))) mod g(X) */
1132 			tab = bch->mod8_tab + (b*256+i)*l;
1133 			data = i << (8*b);
1134 			while (data) {
1135 				d = deg(data);
1136 				/* subtract X^d.g(X) from p(X).X^(8*b+deg(g)) */
1137 				data ^= g[0] >> (31-d);
1138 				for (j = 0; j < ecclen; j++) {
1139 					hi = (d < 31) ? g[j] << (d+1) : 0;
1140 					lo = (j+1 < plen) ?
1141 						g[j+1] >> (31-d) : 0;
1142 					tab[j] ^= hi|lo;
1143 				}
1144 			}
1145 		}
1146 	}
1147 }
1148 
1149 /*
1150  * build a base for factoring degree 2 polynomials
1151  */
1152 static int build_deg2_base(struct bch_control *bch)
1153 {
1154 	const int m = GF_M(bch);
1155 	int i, j, r;
1156 	unsigned int sum, x, y, remaining, ak = 0, xi[m];
1157 
1158 	/* find k s.t. Tr(a^k) = 1 and 0 <= k < m */
1159 	for (i = 0; i < m; i++) {
1160 		for (j = 0, sum = 0; j < m; j++)
1161 			sum ^= a_pow(bch, i*(1 << j));
1162 
1163 		if (sum) {
1164 			ak = bch->a_pow_tab[i];
1165 			break;
1166 		}
1167 	}
1168 	/* find xi, i=0..m-1 such that xi^2+xi = a^i+Tr(a^i).a^k */
1169 	remaining = m;
1170 	memset(xi, 0, sizeof(xi));
1171 
1172 	for (x = 0; (x <= GF_N(bch)) && remaining; x++) {
1173 		y = gf_sqr(bch, x)^x;
1174 		for (i = 0; i < 2; i++) {
1175 			r = a_log(bch, y);
1176 			if (y && (r < m) && !xi[r]) {
1177 				bch->xi_tab[r] = x;
1178 				xi[r] = 1;
1179 				remaining--;
1180 				dbg("x%d = %x\n", r, x);
1181 				break;
1182 			}
1183 			y ^= ak;
1184 		}
1185 	}
1186 	/* should not happen but check anyway */
1187 	return remaining ? -1 : 0;
1188 }
1189 
1190 static void *bch_alloc(size_t size, int *err)
1191 {
1192 	void *ptr;
1193 
1194 	ptr = kmalloc(size, GFP_KERNEL);
1195 	if (ptr == NULL)
1196 		*err = 1;
1197 	return ptr;
1198 }
1199 
1200 /*
1201  * compute generator polynomial for given (m,t) parameters.
1202  */
1203 static uint32_t *compute_generator_polynomial(struct bch_control *bch)
1204 {
1205 	const unsigned int m = GF_M(bch);
1206 	const unsigned int t = GF_T(bch);
1207 	int n, err = 0;
1208 	unsigned int i, j, nbits, r, word, *roots;
1209 	struct gf_poly *g;
1210 	uint32_t *genpoly;
1211 
1212 	g = bch_alloc(GF_POLY_SZ(m*t), &err);
1213 	roots = bch_alloc((bch->n+1)*sizeof(*roots), &err);
1214 	genpoly = bch_alloc(DIV_ROUND_UP(m*t+1, 32)*sizeof(*genpoly), &err);
1215 
1216 	if (err) {
1217 		kfree(genpoly);
1218 		genpoly = NULL;
1219 		goto finish;
1220 	}
1221 
1222 	/* enumerate all roots of g(X) */
1223 	memset(roots , 0, (bch->n+1)*sizeof(*roots));
1224 	for (i = 0; i < t; i++) {
1225 		for (j = 0, r = 2*i+1; j < m; j++) {
1226 			roots[r] = 1;
1227 			r = mod_s(bch, 2*r);
1228 		}
1229 	}
1230 	/* build generator polynomial g(X) */
1231 	g->deg = 0;
1232 	g->c[0] = 1;
1233 	for (i = 0; i < GF_N(bch); i++) {
1234 		if (roots[i]) {
1235 			/* multiply g(X) by (X+root) */
1236 			r = bch->a_pow_tab[i];
1237 			g->c[g->deg+1] = 1;
1238 			for (j = g->deg; j > 0; j--)
1239 				g->c[j] = gf_mul(bch, g->c[j], r)^g->c[j-1];
1240 
1241 			g->c[0] = gf_mul(bch, g->c[0], r);
1242 			g->deg++;
1243 		}
1244 	}
1245 	/* store left-justified binary representation of g(X) */
1246 	n = g->deg+1;
1247 	i = 0;
1248 
1249 	while (n > 0) {
1250 		nbits = (n > 32) ? 32 : n;
1251 		for (j = 0, word = 0; j < nbits; j++) {
1252 			if (g->c[n-1-j])
1253 				word |= 1u << (31-j);
1254 		}
1255 		genpoly[i++] = word;
1256 		n -= nbits;
1257 	}
1258 	bch->ecc_bits = g->deg;
1259 
1260 finish:
1261 	kfree(g);
1262 	kfree(roots);
1263 
1264 	return genpoly;
1265 }
1266 
1267 /**
1268  * init_bch - initialize a BCH encoder/decoder
1269  * @m:          Galois field order, should be in the range 5-15
1270  * @t:          maximum error correction capability, in bits
1271  * @prim_poly:  user-provided primitive polynomial (or 0 to use default)
1272  *
1273  * Returns:
1274  *  a newly allocated BCH control structure if successful, NULL otherwise
1275  *
1276  * This initialization can take some time, as lookup tables are built for fast
1277  * encoding/decoding; make sure not to call this function from a time critical
1278  * path. Usually, init_bch() should be called on module/driver init and
1279  * free_bch() should be called to release memory on exit.
1280  *
1281  * You may provide your own primitive polynomial of degree @m in argument
1282  * @prim_poly, or let init_bch() use its default polynomial.
1283  *
1284  * Once init_bch() has successfully returned a pointer to a newly allocated
1285  * BCH control structure, ecc length in bytes is given by member @ecc_bytes of
1286  * the structure.
1287  */
1288 struct bch_control *init_bch(int m, int t, unsigned int prim_poly)
1289 {
1290 	int err = 0;
1291 	unsigned int i, words;
1292 	uint32_t *genpoly;
1293 	struct bch_control *bch = NULL;
1294 
1295 	const int min_m = 5;
1296 	const int max_m = 15;
1297 
1298 	/* default primitive polynomials */
1299 	static const unsigned int prim_poly_tab[] = {
1300 		0x25, 0x43, 0x83, 0x11d, 0x211, 0x409, 0x805, 0x1053, 0x201b,
1301 		0x402b, 0x8003,
1302 	};
1303 
1304 #if defined(CONFIG_BCH_CONST_PARAMS)
1305 	if ((m != (CONFIG_BCH_CONST_M)) || (t != (CONFIG_BCH_CONST_T))) {
1306 		printk(KERN_ERR "bch encoder/decoder was configured to support "
1307 		       "parameters m=%d, t=%d only!\n",
1308 		       CONFIG_BCH_CONST_M, CONFIG_BCH_CONST_T);
1309 		goto fail;
1310 	}
1311 #endif
1312 	if ((m < min_m) || (m > max_m))
1313 		/*
1314 		 * values of m greater than 15 are not currently supported;
1315 		 * supporting m > 15 would require changing table base type
1316 		 * (uint16_t) and a small patch in matrix transposition
1317 		 */
1318 		goto fail;
1319 
1320 	/* sanity checks */
1321 	if ((t < 1) || (m*t >= ((1 << m)-1)))
1322 		/* invalid t value */
1323 		goto fail;
1324 
1325 	/* select a primitive polynomial for generating GF(2^m) */
1326 	if (prim_poly == 0)
1327 		prim_poly = prim_poly_tab[m-min_m];
1328 
1329 	bch = kzalloc(sizeof(*bch), GFP_KERNEL);
1330 	if (bch == NULL)
1331 		goto fail;
1332 
1333 	bch->m = m;
1334 	bch->t = t;
1335 	bch->n = (1 << m)-1;
1336 	words  = DIV_ROUND_UP(m*t, 32);
1337 	bch->ecc_bytes = DIV_ROUND_UP(m*t, 8);
1338 	bch->a_pow_tab = bch_alloc((1+bch->n)*sizeof(*bch->a_pow_tab), &err);
1339 	bch->a_log_tab = bch_alloc((1+bch->n)*sizeof(*bch->a_log_tab), &err);
1340 	bch->mod8_tab  = bch_alloc(words*1024*sizeof(*bch->mod8_tab), &err);
1341 	bch->ecc_buf   = bch_alloc(words*sizeof(*bch->ecc_buf), &err);
1342 	bch->ecc_buf2  = bch_alloc(words*sizeof(*bch->ecc_buf2), &err);
1343 	bch->xi_tab    = bch_alloc(m*sizeof(*bch->xi_tab), &err);
1344 	bch->syn       = bch_alloc(2*t*sizeof(*bch->syn), &err);
1345 	bch->cache     = bch_alloc(2*t*sizeof(*bch->cache), &err);
1346 	bch->elp       = bch_alloc((t+1)*sizeof(struct gf_poly_deg1), &err);
1347 
1348 	for (i = 0; i < ARRAY_SIZE(bch->poly_2t); i++)
1349 		bch->poly_2t[i] = bch_alloc(GF_POLY_SZ(2*t), &err);
1350 
1351 	if (err)
1352 		goto fail;
1353 
1354 	err = build_gf_tables(bch, prim_poly);
1355 	if (err)
1356 		goto fail;
1357 
1358 	/* use generator polynomial for computing encoding tables */
1359 	genpoly = compute_generator_polynomial(bch);
1360 	if (genpoly == NULL)
1361 		goto fail;
1362 
1363 	build_mod8_tables(bch, genpoly);
1364 	kfree(genpoly);
1365 
1366 	err = build_deg2_base(bch);
1367 	if (err)
1368 		goto fail;
1369 
1370 	return bch;
1371 
1372 fail:
1373 	free_bch(bch);
1374 	return NULL;
1375 }
1376 
1377 /**
1378  *  free_bch - free the BCH control structure
1379  *  @bch:    BCH control structure to release
1380  */
1381 void free_bch(struct bch_control *bch)
1382 {
1383 	unsigned int i;
1384 
1385 	if (bch) {
1386 		kfree(bch->a_pow_tab);
1387 		kfree(bch->a_log_tab);
1388 		kfree(bch->mod8_tab);
1389 		kfree(bch->ecc_buf);
1390 		kfree(bch->ecc_buf2);
1391 		kfree(bch->xi_tab);
1392 		kfree(bch->syn);
1393 		kfree(bch->cache);
1394 		kfree(bch->elp);
1395 
1396 		for (i = 0; i < ARRAY_SIZE(bch->poly_2t); i++)
1397 			kfree(bch->poly_2t[i]);
1398 
1399 		kfree(bch);
1400 	}
1401 }
1402