xref: /linux/lib/bch.c (revision 4b132aacb0768ac1e652cf517097ea6f237214b9)
1 /*
2  * Generic binary BCH encoding/decoding library
3  *
4  * This program is free software; you can redistribute it and/or modify it
5  * under the terms of the GNU General Public License version 2 as published by
6  * the Free Software Foundation.
7  *
8  * This program is distributed in the hope that it will be useful, but WITHOUT
9  * ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or
10  * FITNESS FOR A PARTICULAR PURPOSE.  See the GNU General Public License for
11  * more details.
12  *
13  * You should have received a copy of the GNU General Public License along with
14  * this program; if not, write to the Free Software Foundation, Inc., 51
15  * Franklin St, Fifth Floor, Boston, MA 02110-1301 USA.
16  *
17  * Copyright © 2011 Parrot S.A.
18  *
19  * Author: Ivan Djelic <ivan.djelic@parrot.com>
20  *
21  * Description:
22  *
23  * This library provides runtime configurable encoding/decoding of binary
24  * Bose-Chaudhuri-Hocquenghem (BCH) codes.
25  *
26  * Call bch_init to get a pointer to a newly allocated bch_control structure for
27  * the given m (Galois field order), t (error correction capability) and
28  * (optional) primitive polynomial parameters.
29  *
30  * Call bch_encode to compute and store ecc parity bytes to a given buffer.
31  * Call bch_decode to detect and locate errors in received data.
32  *
33  * On systems supporting hw BCH features, intermediate results may be provided
34  * to bch_decode in order to skip certain steps. See bch_decode() documentation
35  * for details.
36  *
37  * Option CONFIG_BCH_CONST_PARAMS can be used to force fixed values of
38  * parameters m and t; thus allowing extra compiler optimizations and providing
39  * better (up to 2x) encoding performance. Using this option makes sense when
40  * (m,t) are fixed and known in advance, e.g. when using BCH error correction
41  * on a particular NAND flash device.
42  *
43  * Algorithmic details:
44  *
45  * Encoding is performed by processing 32 input bits in parallel, using 4
46  * remainder lookup tables.
47  *
48  * The final stage of decoding involves the following internal steps:
49  * a. Syndrome computation
50  * b. Error locator polynomial computation using Berlekamp-Massey algorithm
51  * c. Error locator root finding (by far the most expensive step)
52  *
53  * In this implementation, step c is not performed using the usual Chien search.
54  * Instead, an alternative approach described in [1] is used. It consists in
55  * factoring the error locator polynomial using the Berlekamp Trace algorithm
56  * (BTA) down to a certain degree (4), after which ad hoc low-degree polynomial
57  * solving techniques [2] are used. The resulting algorithm, called BTZ, yields
58  * much better performance than Chien search for usual (m,t) values (typically
59  * m >= 13, t < 32, see [1]).
60  *
61  * [1] B. Biswas, V. Herbert. Efficient root finding of polynomials over fields
62  * of characteristic 2, in: Western European Workshop on Research in Cryptology
63  * - WEWoRC 2009, Graz, Austria, LNCS, Springer, July 2009, to appear.
64  * [2] [Zin96] V.A. Zinoviev. On the solution of equations of degree 10 over
65  * finite fields GF(2^q). In Rapport de recherche INRIA no 2829, 1996.
66  */
67 
68 #include <linux/kernel.h>
69 #include <linux/errno.h>
70 #include <linux/init.h>
71 #include <linux/module.h>
72 #include <linux/slab.h>
73 #include <linux/bitops.h>
74 #include <linux/bitrev.h>
75 #include <asm/byteorder.h>
76 #include <linux/bch.h>
77 
78 #if defined(CONFIG_BCH_CONST_PARAMS)
79 #define GF_M(_p)               (CONFIG_BCH_CONST_M)
80 #define GF_T(_p)               (CONFIG_BCH_CONST_T)
81 #define GF_N(_p)               ((1 << (CONFIG_BCH_CONST_M))-1)
82 #define BCH_MAX_M              (CONFIG_BCH_CONST_M)
83 #define BCH_MAX_T	       (CONFIG_BCH_CONST_T)
84 #else
85 #define GF_M(_p)               ((_p)->m)
86 #define GF_T(_p)               ((_p)->t)
87 #define GF_N(_p)               ((_p)->n)
88 #define BCH_MAX_M              15 /* 2KB */
89 #define BCH_MAX_T              64 /* 64 bit correction */
90 #endif
91 
92 #define BCH_ECC_WORDS(_p)      DIV_ROUND_UP(GF_M(_p)*GF_T(_p), 32)
93 #define BCH_ECC_BYTES(_p)      DIV_ROUND_UP(GF_M(_p)*GF_T(_p), 8)
94 
95 #define BCH_ECC_MAX_WORDS      DIV_ROUND_UP(BCH_MAX_M * BCH_MAX_T, 32)
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[];   /* 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 static u8 swap_bits(struct bch_control *bch, u8 in)
119 {
120 	if (!bch->swap_bits)
121 		return in;
122 
123 	return bitrev8(in);
124 }
125 
126 /*
127  * same as bch_encode(), but process input data one byte at a time
128  */
129 static void bch_encode_unaligned(struct bch_control *bch,
130 				 const unsigned char *data, unsigned int len,
131 				 uint32_t *ecc)
132 {
133 	int i;
134 	const uint32_t *p;
135 	const int l = BCH_ECC_WORDS(bch)-1;
136 
137 	while (len--) {
138 		u8 tmp = swap_bits(bch, *data++);
139 
140 		p = bch->mod8_tab + (l+1)*(((ecc[0] >> 24)^(tmp)) & 0xff);
141 
142 		for (i = 0; i < l; i++)
143 			ecc[i] = ((ecc[i] << 8)|(ecc[i+1] >> 24))^(*p++);
144 
145 		ecc[l] = (ecc[l] << 8)^(*p);
146 	}
147 }
148 
149 /*
150  * convert ecc bytes to aligned, zero-padded 32-bit ecc words
151  */
152 static void load_ecc8(struct bch_control *bch, uint32_t *dst,
153 		      const uint8_t *src)
154 {
155 	uint8_t pad[4] = {0, 0, 0, 0};
156 	unsigned int i, nwords = BCH_ECC_WORDS(bch)-1;
157 
158 	for (i = 0; i < nwords; i++, src += 4)
159 		dst[i] = ((u32)swap_bits(bch, src[0]) << 24) |
160 			((u32)swap_bits(bch, src[1]) << 16) |
161 			((u32)swap_bits(bch, src[2]) << 8) |
162 			swap_bits(bch, src[3]);
163 
164 	memcpy(pad, src, BCH_ECC_BYTES(bch)-4*nwords);
165 	dst[nwords] = ((u32)swap_bits(bch, pad[0]) << 24) |
166 		((u32)swap_bits(bch, pad[1]) << 16) |
167 		((u32)swap_bits(bch, pad[2]) << 8) |
168 		swap_bits(bch, pad[3]);
169 }
170 
171 /*
172  * convert 32-bit ecc words to ecc bytes
173  */
174 static void store_ecc8(struct bch_control *bch, uint8_t *dst,
175 		       const uint32_t *src)
176 {
177 	uint8_t pad[4];
178 	unsigned int i, nwords = BCH_ECC_WORDS(bch)-1;
179 
180 	for (i = 0; i < nwords; i++) {
181 		*dst++ = swap_bits(bch, src[i] >> 24);
182 		*dst++ = swap_bits(bch, src[i] >> 16);
183 		*dst++ = swap_bits(bch, src[i] >> 8);
184 		*dst++ = swap_bits(bch, src[i]);
185 	}
186 	pad[0] = swap_bits(bch, src[nwords] >> 24);
187 	pad[1] = swap_bits(bch, src[nwords] >> 16);
188 	pad[2] = swap_bits(bch, src[nwords] >> 8);
189 	pad[3] = swap_bits(bch, src[nwords]);
190 	memcpy(dst, pad, BCH_ECC_BYTES(bch)-4*nwords);
191 }
192 
193 /**
194  * bch_encode - calculate BCH ecc parity of data
195  * @bch:   BCH control structure
196  * @data:  data to encode
197  * @len:   data length in bytes
198  * @ecc:   ecc parity data, must be initialized by caller
199  *
200  * The @ecc parity array is used both as input and output parameter, in order to
201  * allow incremental computations. It should be of the size indicated by member
202  * @ecc_bytes of @bch, and should be initialized to 0 before the first call.
203  *
204  * The exact number of computed ecc parity bits is given by member @ecc_bits of
205  * @bch; it may be less than m*t for large values of t.
206  */
207 void bch_encode(struct bch_control *bch, const uint8_t *data,
208 		unsigned int len, uint8_t *ecc)
209 {
210 	const unsigned int l = BCH_ECC_WORDS(bch)-1;
211 	unsigned int i, mlen;
212 	unsigned long m;
213 	uint32_t w, r[BCH_ECC_MAX_WORDS];
214 	const size_t r_bytes = BCH_ECC_WORDS(bch) * sizeof(*r);
215 	const uint32_t * const tab0 = bch->mod8_tab;
216 	const uint32_t * const tab1 = tab0 + 256*(l+1);
217 	const uint32_t * const tab2 = tab1 + 256*(l+1);
218 	const uint32_t * const tab3 = tab2 + 256*(l+1);
219 	const uint32_t *pdata, *p0, *p1, *p2, *p3;
220 
221 	if (WARN_ON(r_bytes > sizeof(r)))
222 		return;
223 
224 	if (ecc) {
225 		/* load ecc parity bytes into internal 32-bit buffer */
226 		load_ecc8(bch, bch->ecc_buf, ecc);
227 	} else {
228 		memset(bch->ecc_buf, 0, r_bytes);
229 	}
230 
231 	/* process first unaligned data bytes */
232 	m = ((unsigned long)data) & 3;
233 	if (m) {
234 		mlen = (len < (4-m)) ? len : 4-m;
235 		bch_encode_unaligned(bch, data, mlen, bch->ecc_buf);
236 		data += mlen;
237 		len  -= mlen;
238 	}
239 
240 	/* process 32-bit aligned data words */
241 	pdata = (uint32_t *)data;
242 	mlen  = len/4;
243 	data += 4*mlen;
244 	len  -= 4*mlen;
245 	memcpy(r, bch->ecc_buf, r_bytes);
246 
247 	/*
248 	 * split each 32-bit word into 4 polynomials of weight 8 as follows:
249 	 *
250 	 * 31 ...24  23 ...16  15 ... 8  7 ... 0
251 	 * xxxxxxxx  yyyyyyyy  zzzzzzzz  tttttttt
252 	 *                               tttttttt  mod g = r0 (precomputed)
253 	 *                     zzzzzzzz  00000000  mod g = r1 (precomputed)
254 	 *           yyyyyyyy  00000000  00000000  mod g = r2 (precomputed)
255 	 * xxxxxxxx  00000000  00000000  00000000  mod g = r3 (precomputed)
256 	 * xxxxxxxx  yyyyyyyy  zzzzzzzz  tttttttt  mod g = r0^r1^r2^r3
257 	 */
258 	while (mlen--) {
259 		/* input data is read in big-endian format */
260 		w = cpu_to_be32(*pdata++);
261 		if (bch->swap_bits)
262 			w = (u32)swap_bits(bch, w) |
263 			    ((u32)swap_bits(bch, w >> 8) << 8) |
264 			    ((u32)swap_bits(bch, w >> 16) << 16) |
265 			    ((u32)swap_bits(bch, w >> 24) << 24);
266 		w ^= r[0];
267 		p0 = tab0 + (l+1)*((w >>  0) & 0xff);
268 		p1 = tab1 + (l+1)*((w >>  8) & 0xff);
269 		p2 = tab2 + (l+1)*((w >> 16) & 0xff);
270 		p3 = tab3 + (l+1)*((w >> 24) & 0xff);
271 
272 		for (i = 0; i < l; i++)
273 			r[i] = r[i+1]^p0[i]^p1[i]^p2[i]^p3[i];
274 
275 		r[l] = p0[l]^p1[l]^p2[l]^p3[l];
276 	}
277 	memcpy(bch->ecc_buf, r, r_bytes);
278 
279 	/* process last unaligned bytes */
280 	if (len)
281 		bch_encode_unaligned(bch, data, len, bch->ecc_buf);
282 
283 	/* store ecc parity bytes into original parity buffer */
284 	if (ecc)
285 		store_ecc8(bch, ecc, bch->ecc_buf);
286 }
287 EXPORT_SYMBOL_GPL(bch_encode);
288 
289 static inline int modulo(struct bch_control *bch, unsigned int v)
290 {
291 	const unsigned int n = GF_N(bch);
292 	while (v >= n) {
293 		v -= n;
294 		v = (v & n) + (v >> GF_M(bch));
295 	}
296 	return v;
297 }
298 
299 /*
300  * shorter and faster modulo function, only works when v < 2N.
301  */
302 static inline int mod_s(struct bch_control *bch, unsigned int v)
303 {
304 	const unsigned int n = GF_N(bch);
305 	return (v < n) ? v : v-n;
306 }
307 
308 static inline int deg(unsigned int poly)
309 {
310 	/* polynomial degree is the most-significant bit index */
311 	return fls(poly)-1;
312 }
313 
314 static inline int parity(unsigned int x)
315 {
316 	/*
317 	 * public domain code snippet, lifted from
318 	 * http://www-graphics.stanford.edu/~seander/bithacks.html
319 	 */
320 	x ^= x >> 1;
321 	x ^= x >> 2;
322 	x = (x & 0x11111111U) * 0x11111111U;
323 	return (x >> 28) & 1;
324 }
325 
326 /* Galois field basic operations: multiply, divide, inverse, etc. */
327 
328 static inline unsigned int gf_mul(struct bch_control *bch, unsigned int a,
329 				  unsigned int b)
330 {
331 	return (a && b) ? bch->a_pow_tab[mod_s(bch, bch->a_log_tab[a]+
332 					       bch->a_log_tab[b])] : 0;
333 }
334 
335 static inline unsigned int gf_sqr(struct bch_control *bch, unsigned int a)
336 {
337 	return a ? bch->a_pow_tab[mod_s(bch, 2*bch->a_log_tab[a])] : 0;
338 }
339 
340 static inline unsigned int gf_div(struct bch_control *bch, unsigned int a,
341 				  unsigned int b)
342 {
343 	return a ? bch->a_pow_tab[mod_s(bch, bch->a_log_tab[a]+
344 					GF_N(bch)-bch->a_log_tab[b])] : 0;
345 }
346 
347 static inline unsigned int gf_inv(struct bch_control *bch, unsigned int a)
348 {
349 	return bch->a_pow_tab[GF_N(bch)-bch->a_log_tab[a]];
350 }
351 
352 static inline unsigned int a_pow(struct bch_control *bch, int i)
353 {
354 	return bch->a_pow_tab[modulo(bch, i)];
355 }
356 
357 static inline int a_log(struct bch_control *bch, unsigned int x)
358 {
359 	return bch->a_log_tab[x];
360 }
361 
362 static inline int a_ilog(struct bch_control *bch, unsigned int x)
363 {
364 	return mod_s(bch, GF_N(bch)-bch->a_log_tab[x]);
365 }
366 
367 /*
368  * compute 2t syndromes of ecc polynomial, i.e. ecc(a^j) for j=1..2t
369  */
370 static void compute_syndromes(struct bch_control *bch, uint32_t *ecc,
371 			      unsigned int *syn)
372 {
373 	int i, j, s;
374 	unsigned int m;
375 	uint32_t poly;
376 	const int t = GF_T(bch);
377 
378 	s = bch->ecc_bits;
379 
380 	/* make sure extra bits in last ecc word are cleared */
381 	m = ((unsigned int)s) & 31;
382 	if (m)
383 		ecc[s/32] &= ~((1u << (32-m))-1);
384 	memset(syn, 0, 2*t*sizeof(*syn));
385 
386 	/* compute v(a^j) for j=1 .. 2t-1 */
387 	do {
388 		poly = *ecc++;
389 		s -= 32;
390 		while (poly) {
391 			i = deg(poly);
392 			for (j = 0; j < 2*t; j += 2)
393 				syn[j] ^= a_pow(bch, (j+1)*(i+s));
394 
395 			poly ^= (1 << i);
396 		}
397 	} while (s > 0);
398 
399 	/* v(a^(2j)) = v(a^j)^2 */
400 	for (j = 0; j < t; j++)
401 		syn[2*j+1] = gf_sqr(bch, syn[j]);
402 }
403 
404 static void gf_poly_copy(struct gf_poly *dst, struct gf_poly *src)
405 {
406 	memcpy(dst, src, GF_POLY_SZ(src->deg));
407 }
408 
409 static int compute_error_locator_polynomial(struct bch_control *bch,
410 					    const unsigned int *syn)
411 {
412 	const unsigned int t = GF_T(bch);
413 	const unsigned int n = GF_N(bch);
414 	unsigned int i, j, tmp, l, pd = 1, d = syn[0];
415 	struct gf_poly *elp = bch->elp;
416 	struct gf_poly *pelp = bch->poly_2t[0];
417 	struct gf_poly *elp_copy = bch->poly_2t[1];
418 	int k, pp = -1;
419 
420 	memset(pelp, 0, GF_POLY_SZ(2*t));
421 	memset(elp, 0, GF_POLY_SZ(2*t));
422 
423 	pelp->deg = 0;
424 	pelp->c[0] = 1;
425 	elp->deg = 0;
426 	elp->c[0] = 1;
427 
428 	/* use simplified binary Berlekamp-Massey algorithm */
429 	for (i = 0; (i < t) && (elp->deg <= t); i++) {
430 		if (d) {
431 			k = 2*i-pp;
432 			gf_poly_copy(elp_copy, elp);
433 			/* e[i+1](X) = e[i](X)+di*dp^-1*X^2(i-p)*e[p](X) */
434 			tmp = a_log(bch, d)+n-a_log(bch, pd);
435 			for (j = 0; j <= pelp->deg; j++) {
436 				if (pelp->c[j]) {
437 					l = a_log(bch, pelp->c[j]);
438 					elp->c[j+k] ^= a_pow(bch, tmp+l);
439 				}
440 			}
441 			/* compute l[i+1] = max(l[i]->c[l[p]+2*(i-p]) */
442 			tmp = pelp->deg+k;
443 			if (tmp > elp->deg) {
444 				elp->deg = tmp;
445 				gf_poly_copy(pelp, elp_copy);
446 				pd = d;
447 				pp = 2*i;
448 			}
449 		}
450 		/* di+1 = S(2i+3)+elp[i+1].1*S(2i+2)+...+elp[i+1].lS(2i+3-l) */
451 		if (i < t-1) {
452 			d = syn[2*i+2];
453 			for (j = 1; j <= elp->deg; j++)
454 				d ^= gf_mul(bch, elp->c[j], syn[2*i+2-j]);
455 		}
456 	}
457 	dbg("elp=%s\n", gf_poly_str(elp));
458 	return (elp->deg > t) ? -1 : (int)elp->deg;
459 }
460 
461 /*
462  * solve a m x m linear system in GF(2) with an expected number of solutions,
463  * and return the number of found solutions
464  */
465 static int solve_linear_system(struct bch_control *bch, unsigned int *rows,
466 			       unsigned int *sol, int nsol)
467 {
468 	const int m = GF_M(bch);
469 	unsigned int tmp, mask;
470 	int rem, c, r, p, k, param[BCH_MAX_M];
471 
472 	k = 0;
473 	mask = 1 << m;
474 
475 	/* Gaussian elimination */
476 	for (c = 0; c < m; c++) {
477 		rem = 0;
478 		p = c-k;
479 		/* find suitable row for elimination */
480 		for (r = p; r < m; r++) {
481 			if (rows[r] & mask) {
482 				if (r != p)
483 					swap(rows[r], rows[p]);
484 				rem = r+1;
485 				break;
486 			}
487 		}
488 		if (rem) {
489 			/* perform elimination on remaining rows */
490 			tmp = rows[p];
491 			for (r = rem; r < m; r++) {
492 				if (rows[r] & mask)
493 					rows[r] ^= tmp;
494 			}
495 		} else {
496 			/* elimination not needed, store defective row index */
497 			param[k++] = c;
498 		}
499 		mask >>= 1;
500 	}
501 	/* rewrite system, inserting fake parameter rows */
502 	if (k > 0) {
503 		p = k;
504 		for (r = m-1; r >= 0; r--) {
505 			if ((r > m-1-k) && rows[r])
506 				/* system has no solution */
507 				return 0;
508 
509 			rows[r] = (p && (r == param[p-1])) ?
510 				p--, 1u << (m-r) : rows[r-p];
511 		}
512 	}
513 
514 	if (nsol != (1 << k))
515 		/* unexpected number of solutions */
516 		return 0;
517 
518 	for (p = 0; p < nsol; p++) {
519 		/* set parameters for p-th solution */
520 		for (c = 0; c < k; c++)
521 			rows[param[c]] = (rows[param[c]] & ~1)|((p >> c) & 1);
522 
523 		/* compute unique solution */
524 		tmp = 0;
525 		for (r = m-1; r >= 0; r--) {
526 			mask = rows[r] & (tmp|1);
527 			tmp |= parity(mask) << (m-r);
528 		}
529 		sol[p] = tmp >> 1;
530 	}
531 	return nsol;
532 }
533 
534 /*
535  * this function builds and solves a linear system for finding roots of a degree
536  * 4 affine monic polynomial X^4+aX^2+bX+c over GF(2^m).
537  */
538 static int find_affine4_roots(struct bch_control *bch, unsigned int a,
539 			      unsigned int b, unsigned int c,
540 			      unsigned int *roots)
541 {
542 	int i, j, k;
543 	const int m = GF_M(bch);
544 	unsigned int mask = 0xff, t, rows[16] = {0,};
545 
546 	j = a_log(bch, b);
547 	k = a_log(bch, a);
548 	rows[0] = c;
549 
550 	/* build linear system to solve X^4+aX^2+bX+c = 0 */
551 	for (i = 0; i < m; i++) {
552 		rows[i+1] = bch->a_pow_tab[4*i]^
553 			(a ? bch->a_pow_tab[mod_s(bch, k)] : 0)^
554 			(b ? bch->a_pow_tab[mod_s(bch, j)] : 0);
555 		j++;
556 		k += 2;
557 	}
558 	/*
559 	 * transpose 16x16 matrix before passing it to linear solver
560 	 * warning: this code assumes m < 16
561 	 */
562 	for (j = 8; j != 0; j >>= 1, mask ^= (mask << j)) {
563 		for (k = 0; k < 16; k = (k+j+1) & ~j) {
564 			t = ((rows[k] >> j)^rows[k+j]) & mask;
565 			rows[k] ^= (t << j);
566 			rows[k+j] ^= t;
567 		}
568 	}
569 	return solve_linear_system(bch, rows, roots, 4);
570 }
571 
572 /*
573  * compute root r of a degree 1 polynomial over GF(2^m) (returned as log(1/r))
574  */
575 static int find_poly_deg1_roots(struct bch_control *bch, struct gf_poly *poly,
576 				unsigned int *roots)
577 {
578 	int n = 0;
579 
580 	if (poly->c[0])
581 		/* poly[X] = bX+c with c!=0, root=c/b */
582 		roots[n++] = mod_s(bch, GF_N(bch)-bch->a_log_tab[poly->c[0]]+
583 				   bch->a_log_tab[poly->c[1]]);
584 	return n;
585 }
586 
587 /*
588  * compute roots of a degree 2 polynomial over GF(2^m)
589  */
590 static int find_poly_deg2_roots(struct bch_control *bch, struct gf_poly *poly,
591 				unsigned int *roots)
592 {
593 	int n = 0, i, l0, l1, l2;
594 	unsigned int u, v, r;
595 
596 	if (poly->c[0] && poly->c[1]) {
597 
598 		l0 = bch->a_log_tab[poly->c[0]];
599 		l1 = bch->a_log_tab[poly->c[1]];
600 		l2 = bch->a_log_tab[poly->c[2]];
601 
602 		/* using z=a/bX, transform aX^2+bX+c into z^2+z+u (u=ac/b^2) */
603 		u = a_pow(bch, l0+l2+2*(GF_N(bch)-l1));
604 		/*
605 		 * let u = sum(li.a^i) i=0..m-1; then compute r = sum(li.xi):
606 		 * r^2+r = sum(li.(xi^2+xi)) = sum(li.(a^i+Tr(a^i).a^k)) =
607 		 * u + sum(li.Tr(a^i).a^k) = u+a^k.Tr(sum(li.a^i)) = u+a^k.Tr(u)
608 		 * i.e. r and r+1 are roots iff Tr(u)=0
609 		 */
610 		r = 0;
611 		v = u;
612 		while (v) {
613 			i = deg(v);
614 			r ^= bch->xi_tab[i];
615 			v ^= (1 << i);
616 		}
617 		/* verify root */
618 		if ((gf_sqr(bch, r)^r) == u) {
619 			/* reverse z=a/bX transformation and compute log(1/r) */
620 			roots[n++] = modulo(bch, 2*GF_N(bch)-l1-
621 					    bch->a_log_tab[r]+l2);
622 			roots[n++] = modulo(bch, 2*GF_N(bch)-l1-
623 					    bch->a_log_tab[r^1]+l2);
624 		}
625 	}
626 	return n;
627 }
628 
629 /*
630  * compute roots of a degree 3 polynomial over GF(2^m)
631  */
632 static int find_poly_deg3_roots(struct bch_control *bch, struct gf_poly *poly,
633 				unsigned int *roots)
634 {
635 	int i, n = 0;
636 	unsigned int a, b, c, a2, b2, c2, e3, tmp[4];
637 
638 	if (poly->c[0]) {
639 		/* transform polynomial into monic X^3 + a2X^2 + b2X + c2 */
640 		e3 = poly->c[3];
641 		c2 = gf_div(bch, poly->c[0], e3);
642 		b2 = gf_div(bch, poly->c[1], e3);
643 		a2 = gf_div(bch, poly->c[2], e3);
644 
645 		/* (X+a2)(X^3+a2X^2+b2X+c2) = X^4+aX^2+bX+c (affine) */
646 		c = gf_mul(bch, a2, c2);           /* c = a2c2      */
647 		b = gf_mul(bch, a2, b2)^c2;        /* b = a2b2 + c2 */
648 		a = gf_sqr(bch, a2)^b2;            /* a = a2^2 + b2 */
649 
650 		/* find the 4 roots of this affine polynomial */
651 		if (find_affine4_roots(bch, a, b, c, tmp) == 4) {
652 			/* remove a2 from final list of roots */
653 			for (i = 0; i < 4; i++) {
654 				if (tmp[i] != a2)
655 					roots[n++] = a_ilog(bch, tmp[i]);
656 			}
657 		}
658 	}
659 	return n;
660 }
661 
662 /*
663  * compute roots of a degree 4 polynomial over GF(2^m)
664  */
665 static int find_poly_deg4_roots(struct bch_control *bch, struct gf_poly *poly,
666 				unsigned int *roots)
667 {
668 	int i, l, n = 0;
669 	unsigned int a, b, c, d, e = 0, f, a2, b2, c2, e4;
670 
671 	if (poly->c[0] == 0)
672 		return 0;
673 
674 	/* transform polynomial into monic X^4 + aX^3 + bX^2 + cX + d */
675 	e4 = poly->c[4];
676 	d = gf_div(bch, poly->c[0], e4);
677 	c = gf_div(bch, poly->c[1], e4);
678 	b = gf_div(bch, poly->c[2], e4);
679 	a = gf_div(bch, poly->c[3], e4);
680 
681 	/* use Y=1/X transformation to get an affine polynomial */
682 	if (a) {
683 		/* first, eliminate cX by using z=X+e with ae^2+c=0 */
684 		if (c) {
685 			/* compute e such that e^2 = c/a */
686 			f = gf_div(bch, c, a);
687 			l = a_log(bch, f);
688 			l += (l & 1) ? GF_N(bch) : 0;
689 			e = a_pow(bch, l/2);
690 			/*
691 			 * use transformation z=X+e:
692 			 * z^4+e^4 + a(z^3+ez^2+e^2z+e^3) + b(z^2+e^2) +cz+ce+d
693 			 * z^4 + az^3 + (ae+b)z^2 + (ae^2+c)z+e^4+be^2+ae^3+ce+d
694 			 * z^4 + az^3 + (ae+b)z^2 + e^4+be^2+d
695 			 * z^4 + az^3 +     b'z^2 + d'
696 			 */
697 			d = a_pow(bch, 2*l)^gf_mul(bch, b, f)^d;
698 			b = gf_mul(bch, a, e)^b;
699 		}
700 		/* now, use Y=1/X to get Y^4 + b/dY^2 + a/dY + 1/d */
701 		if (d == 0)
702 			/* assume all roots have multiplicity 1 */
703 			return 0;
704 
705 		c2 = gf_inv(bch, d);
706 		b2 = gf_div(bch, a, d);
707 		a2 = gf_div(bch, b, d);
708 	} else {
709 		/* polynomial is already affine */
710 		c2 = d;
711 		b2 = c;
712 		a2 = b;
713 	}
714 	/* find the 4 roots of this affine polynomial */
715 	if (find_affine4_roots(bch, a2, b2, c2, roots) == 4) {
716 		for (i = 0; i < 4; i++) {
717 			/* post-process roots (reverse transformations) */
718 			f = a ? gf_inv(bch, roots[i]) : roots[i];
719 			roots[i] = a_ilog(bch, f^e);
720 		}
721 		n = 4;
722 	}
723 	return n;
724 }
725 
726 /*
727  * build monic, log-based representation of a polynomial
728  */
729 static void gf_poly_logrep(struct bch_control *bch,
730 			   const struct gf_poly *a, int *rep)
731 {
732 	int i, d = a->deg, l = GF_N(bch)-a_log(bch, a->c[a->deg]);
733 
734 	/* represent 0 values with -1; warning, rep[d] is not set to 1 */
735 	for (i = 0; i < d; i++)
736 		rep[i] = a->c[i] ? mod_s(bch, a_log(bch, a->c[i])+l) : -1;
737 }
738 
739 /*
740  * compute polynomial Euclidean division remainder in GF(2^m)[X]
741  */
742 static void gf_poly_mod(struct bch_control *bch, struct gf_poly *a,
743 			const struct gf_poly *b, int *rep)
744 {
745 	int la, p, m;
746 	unsigned int i, j, *c = a->c;
747 	const unsigned int d = b->deg;
748 
749 	if (a->deg < d)
750 		return;
751 
752 	/* reuse or compute log representation of denominator */
753 	if (!rep) {
754 		rep = bch->cache;
755 		gf_poly_logrep(bch, b, rep);
756 	}
757 
758 	for (j = a->deg; j >= d; j--) {
759 		if (c[j]) {
760 			la = a_log(bch, c[j]);
761 			p = j-d;
762 			for (i = 0; i < d; i++, p++) {
763 				m = rep[i];
764 				if (m >= 0)
765 					c[p] ^= bch->a_pow_tab[mod_s(bch,
766 								     m+la)];
767 			}
768 		}
769 	}
770 	a->deg = d-1;
771 	while (!c[a->deg] && a->deg)
772 		a->deg--;
773 }
774 
775 /*
776  * compute polynomial Euclidean division quotient in GF(2^m)[X]
777  */
778 static void gf_poly_div(struct bch_control *bch, struct gf_poly *a,
779 			const struct gf_poly *b, struct gf_poly *q)
780 {
781 	if (a->deg >= b->deg) {
782 		q->deg = a->deg-b->deg;
783 		/* compute a mod b (modifies a) */
784 		gf_poly_mod(bch, a, b, NULL);
785 		/* quotient is stored in upper part of polynomial a */
786 		memcpy(q->c, &a->c[b->deg], (1+q->deg)*sizeof(unsigned int));
787 	} else {
788 		q->deg = 0;
789 		q->c[0] = 0;
790 	}
791 }
792 
793 /*
794  * compute polynomial GCD (Greatest Common Divisor) in GF(2^m)[X]
795  */
796 static struct gf_poly *gf_poly_gcd(struct bch_control *bch, struct gf_poly *a,
797 				   struct gf_poly *b)
798 {
799 	dbg("gcd(%s,%s)=", gf_poly_str(a), gf_poly_str(b));
800 
801 	if (a->deg < b->deg)
802 		swap(a, b);
803 
804 	while (b->deg > 0) {
805 		gf_poly_mod(bch, a, b, NULL);
806 		swap(a, b);
807 	}
808 
809 	dbg("%s\n", gf_poly_str(a));
810 
811 	return a;
812 }
813 
814 /*
815  * Given a polynomial f and an integer k, compute Tr(a^kX) mod f
816  * This is used in Berlekamp Trace algorithm for splitting polynomials
817  */
818 static void compute_trace_bk_mod(struct bch_control *bch, int k,
819 				 const struct gf_poly *f, struct gf_poly *z,
820 				 struct gf_poly *out)
821 {
822 	const int m = GF_M(bch);
823 	int i, j;
824 
825 	/* z contains z^2j mod f */
826 	z->deg = 1;
827 	z->c[0] = 0;
828 	z->c[1] = bch->a_pow_tab[k];
829 
830 	out->deg = 0;
831 	memset(out, 0, GF_POLY_SZ(f->deg));
832 
833 	/* compute f log representation only once */
834 	gf_poly_logrep(bch, f, bch->cache);
835 
836 	for (i = 0; i < m; i++) {
837 		/* add a^(k*2^i)(z^(2^i) mod f) and compute (z^(2^i) mod f)^2 */
838 		for (j = z->deg; j >= 0; j--) {
839 			out->c[j] ^= z->c[j];
840 			z->c[2*j] = gf_sqr(bch, z->c[j]);
841 			z->c[2*j+1] = 0;
842 		}
843 		if (z->deg > out->deg)
844 			out->deg = z->deg;
845 
846 		if (i < m-1) {
847 			z->deg *= 2;
848 			/* z^(2(i+1)) mod f = (z^(2^i) mod f)^2 mod f */
849 			gf_poly_mod(bch, z, f, bch->cache);
850 		}
851 	}
852 	while (!out->c[out->deg] && out->deg)
853 		out->deg--;
854 
855 	dbg("Tr(a^%d.X) mod f = %s\n", k, gf_poly_str(out));
856 }
857 
858 /*
859  * factor a polynomial using Berlekamp Trace algorithm (BTA)
860  */
861 static void factor_polynomial(struct bch_control *bch, int k, struct gf_poly *f,
862 			      struct gf_poly **g, struct gf_poly **h)
863 {
864 	struct gf_poly *f2 = bch->poly_2t[0];
865 	struct gf_poly *q  = bch->poly_2t[1];
866 	struct gf_poly *tk = bch->poly_2t[2];
867 	struct gf_poly *z  = bch->poly_2t[3];
868 	struct gf_poly *gcd;
869 
870 	dbg("factoring %s...\n", gf_poly_str(f));
871 
872 	*g = f;
873 	*h = NULL;
874 
875 	/* tk = Tr(a^k.X) mod f */
876 	compute_trace_bk_mod(bch, k, f, z, tk);
877 
878 	if (tk->deg > 0) {
879 		/* compute g = gcd(f, tk) (destructive operation) */
880 		gf_poly_copy(f2, f);
881 		gcd = gf_poly_gcd(bch, f2, tk);
882 		if (gcd->deg < f->deg) {
883 			/* compute h=f/gcd(f,tk); this will modify f and q */
884 			gf_poly_div(bch, f, gcd, q);
885 			/* store g and h in-place (clobbering f) */
886 			*h = &((struct gf_poly_deg1 *)f)[gcd->deg].poly;
887 			gf_poly_copy(*g, gcd);
888 			gf_poly_copy(*h, q);
889 		}
890 	}
891 }
892 
893 /*
894  * find roots of a polynomial, using BTZ algorithm; see the beginning of this
895  * file for details
896  */
897 static int find_poly_roots(struct bch_control *bch, unsigned int k,
898 			   struct gf_poly *poly, unsigned int *roots)
899 {
900 	int cnt;
901 	struct gf_poly *f1, *f2;
902 
903 	switch (poly->deg) {
904 		/* handle low degree polynomials with ad hoc techniques */
905 	case 1:
906 		cnt = find_poly_deg1_roots(bch, poly, roots);
907 		break;
908 	case 2:
909 		cnt = find_poly_deg2_roots(bch, poly, roots);
910 		break;
911 	case 3:
912 		cnt = find_poly_deg3_roots(bch, poly, roots);
913 		break;
914 	case 4:
915 		cnt = find_poly_deg4_roots(bch, poly, roots);
916 		break;
917 	default:
918 		/* factor polynomial using Berlekamp Trace Algorithm (BTA) */
919 		cnt = 0;
920 		if (poly->deg && (k <= GF_M(bch))) {
921 			factor_polynomial(bch, k, poly, &f1, &f2);
922 			if (f1)
923 				cnt += find_poly_roots(bch, k+1, f1, roots);
924 			if (f2)
925 				cnt += find_poly_roots(bch, k+1, f2, roots+cnt);
926 		}
927 		break;
928 	}
929 	return cnt;
930 }
931 
932 #if defined(USE_CHIEN_SEARCH)
933 /*
934  * exhaustive root search (Chien) implementation - not used, included only for
935  * reference/comparison tests
936  */
937 static int chien_search(struct bch_control *bch, unsigned int len,
938 			struct gf_poly *p, unsigned int *roots)
939 {
940 	int m;
941 	unsigned int i, j, syn, syn0, count = 0;
942 	const unsigned int k = 8*len+bch->ecc_bits;
943 
944 	/* use a log-based representation of polynomial */
945 	gf_poly_logrep(bch, p, bch->cache);
946 	bch->cache[p->deg] = 0;
947 	syn0 = gf_div(bch, p->c[0], p->c[p->deg]);
948 
949 	for (i = GF_N(bch)-k+1; i <= GF_N(bch); i++) {
950 		/* compute elp(a^i) */
951 		for (j = 1, syn = syn0; j <= p->deg; j++) {
952 			m = bch->cache[j];
953 			if (m >= 0)
954 				syn ^= a_pow(bch, m+j*i);
955 		}
956 		if (syn == 0) {
957 			roots[count++] = GF_N(bch)-i;
958 			if (count == p->deg)
959 				break;
960 		}
961 	}
962 	return (count == p->deg) ? count : 0;
963 }
964 #define find_poly_roots(_p, _k, _elp, _loc) chien_search(_p, len, _elp, _loc)
965 #endif /* USE_CHIEN_SEARCH */
966 
967 /**
968  * bch_decode - decode received codeword and find bit error locations
969  * @bch:      BCH control structure
970  * @data:     received data, ignored if @calc_ecc is provided
971  * @len:      data length in bytes, must always be provided
972  * @recv_ecc: received ecc, if NULL then assume it was XORed in @calc_ecc
973  * @calc_ecc: calculated ecc, if NULL then calc_ecc is computed from @data
974  * @syn:      hw computed syndrome data (if NULL, syndrome is calculated)
975  * @errloc:   output array of error locations
976  *
977  * Returns:
978  *  The number of errors found, or -EBADMSG if decoding failed, or -EINVAL if
979  *  invalid parameters were provided
980  *
981  * Depending on the available hw BCH support and the need to compute @calc_ecc
982  * separately (using bch_encode()), this function should be called with one of
983  * the following parameter configurations -
984  *
985  * by providing @data and @recv_ecc only:
986  *   bch_decode(@bch, @data, @len, @recv_ecc, NULL, NULL, @errloc)
987  *
988  * by providing @recv_ecc and @calc_ecc:
989  *   bch_decode(@bch, NULL, @len, @recv_ecc, @calc_ecc, NULL, @errloc)
990  *
991  * by providing ecc = recv_ecc XOR calc_ecc:
992  *   bch_decode(@bch, NULL, @len, NULL, ecc, NULL, @errloc)
993  *
994  * by providing syndrome results @syn:
995  *   bch_decode(@bch, NULL, @len, NULL, NULL, @syn, @errloc)
996  *
997  * Once bch_decode() has successfully returned with a positive value, error
998  * locations returned in array @errloc should be interpreted as follows -
999  *
1000  * if (errloc[n] >= 8*len), then n-th error is located in ecc (no need for
1001  * data correction)
1002  *
1003  * if (errloc[n] < 8*len), then n-th error is located in data and can be
1004  * corrected with statement data[errloc[n]/8] ^= 1 << (errloc[n] % 8);
1005  *
1006  * Note that this function does not perform any data correction by itself, it
1007  * merely indicates error locations.
1008  */
1009 int bch_decode(struct bch_control *bch, const uint8_t *data, unsigned int len,
1010 	       const uint8_t *recv_ecc, const uint8_t *calc_ecc,
1011 	       const unsigned int *syn, unsigned int *errloc)
1012 {
1013 	const unsigned int ecc_words = BCH_ECC_WORDS(bch);
1014 	unsigned int nbits;
1015 	int i, err, nroots;
1016 	uint32_t sum;
1017 
1018 	/* sanity check: make sure data length can be handled */
1019 	if (8*len > (bch->n-bch->ecc_bits))
1020 		return -EINVAL;
1021 
1022 	/* if caller does not provide syndromes, compute them */
1023 	if (!syn) {
1024 		if (!calc_ecc) {
1025 			/* compute received data ecc into an internal buffer */
1026 			if (!data || !recv_ecc)
1027 				return -EINVAL;
1028 			bch_encode(bch, data, len, NULL);
1029 		} else {
1030 			/* load provided calculated ecc */
1031 			load_ecc8(bch, bch->ecc_buf, calc_ecc);
1032 		}
1033 		/* load received ecc or assume it was XORed in calc_ecc */
1034 		if (recv_ecc) {
1035 			load_ecc8(bch, bch->ecc_buf2, recv_ecc);
1036 			/* XOR received and calculated ecc */
1037 			for (i = 0, sum = 0; i < (int)ecc_words; i++) {
1038 				bch->ecc_buf[i] ^= bch->ecc_buf2[i];
1039 				sum |= bch->ecc_buf[i];
1040 			}
1041 			if (!sum)
1042 				/* no error found */
1043 				return 0;
1044 		}
1045 		compute_syndromes(bch, bch->ecc_buf, bch->syn);
1046 		syn = bch->syn;
1047 	}
1048 
1049 	err = compute_error_locator_polynomial(bch, syn);
1050 	if (err > 0) {
1051 		nroots = find_poly_roots(bch, 1, bch->elp, errloc);
1052 		if (err != nroots)
1053 			err = -1;
1054 	}
1055 	if (err > 0) {
1056 		/* post-process raw error locations for easier correction */
1057 		nbits = (len*8)+bch->ecc_bits;
1058 		for (i = 0; i < err; i++) {
1059 			if (errloc[i] >= nbits) {
1060 				err = -1;
1061 				break;
1062 			}
1063 			errloc[i] = nbits-1-errloc[i];
1064 			if (!bch->swap_bits)
1065 				errloc[i] = (errloc[i] & ~7) |
1066 					    (7-(errloc[i] & 7));
1067 		}
1068 	}
1069 	return (err >= 0) ? err : -EBADMSG;
1070 }
1071 EXPORT_SYMBOL_GPL(bch_decode);
1072 
1073 /*
1074  * generate Galois field lookup tables
1075  */
1076 static int build_gf_tables(struct bch_control *bch, unsigned int poly)
1077 {
1078 	unsigned int i, x = 1;
1079 	const unsigned int k = 1 << deg(poly);
1080 
1081 	/* primitive polynomial must be of degree m */
1082 	if (k != (1u << GF_M(bch)))
1083 		return -1;
1084 
1085 	for (i = 0; i < GF_N(bch); i++) {
1086 		bch->a_pow_tab[i] = x;
1087 		bch->a_log_tab[x] = i;
1088 		if (i && (x == 1))
1089 			/* polynomial is not primitive (a^i=1 with 0<i<2^m-1) */
1090 			return -1;
1091 		x <<= 1;
1092 		if (x & k)
1093 			x ^= poly;
1094 	}
1095 	bch->a_pow_tab[GF_N(bch)] = 1;
1096 	bch->a_log_tab[0] = 0;
1097 
1098 	return 0;
1099 }
1100 
1101 /*
1102  * compute generator polynomial remainder tables for fast encoding
1103  */
1104 static void build_mod8_tables(struct bch_control *bch, const uint32_t *g)
1105 {
1106 	int i, j, b, d;
1107 	uint32_t data, hi, lo, *tab;
1108 	const int l = BCH_ECC_WORDS(bch);
1109 	const int plen = DIV_ROUND_UP(bch->ecc_bits+1, 32);
1110 	const int ecclen = DIV_ROUND_UP(bch->ecc_bits, 32);
1111 
1112 	memset(bch->mod8_tab, 0, 4*256*l*sizeof(*bch->mod8_tab));
1113 
1114 	for (i = 0; i < 256; i++) {
1115 		/* p(X)=i is a small polynomial of weight <= 8 */
1116 		for (b = 0; b < 4; b++) {
1117 			/* we want to compute (p(X).X^(8*b+deg(g))) mod g(X) */
1118 			tab = bch->mod8_tab + (b*256+i)*l;
1119 			data = i << (8*b);
1120 			while (data) {
1121 				d = deg(data);
1122 				/* subtract X^d.g(X) from p(X).X^(8*b+deg(g)) */
1123 				data ^= g[0] >> (31-d);
1124 				for (j = 0; j < ecclen; j++) {
1125 					hi = (d < 31) ? g[j] << (d+1) : 0;
1126 					lo = (j+1 < plen) ?
1127 						g[j+1] >> (31-d) : 0;
1128 					tab[j] ^= hi|lo;
1129 				}
1130 			}
1131 		}
1132 	}
1133 }
1134 
1135 /*
1136  * build a base for factoring degree 2 polynomials
1137  */
1138 static int build_deg2_base(struct bch_control *bch)
1139 {
1140 	const int m = GF_M(bch);
1141 	int i, j, r;
1142 	unsigned int sum, x, y, remaining, ak = 0, xi[BCH_MAX_M];
1143 
1144 	/* find k s.t. Tr(a^k) = 1 and 0 <= k < m */
1145 	for (i = 0; i < m; i++) {
1146 		for (j = 0, sum = 0; j < m; j++)
1147 			sum ^= a_pow(bch, i*(1 << j));
1148 
1149 		if (sum) {
1150 			ak = bch->a_pow_tab[i];
1151 			break;
1152 		}
1153 	}
1154 	/* find xi, i=0..m-1 such that xi^2+xi = a^i+Tr(a^i).a^k */
1155 	remaining = m;
1156 	memset(xi, 0, sizeof(xi));
1157 
1158 	for (x = 0; (x <= GF_N(bch)) && remaining; x++) {
1159 		y = gf_sqr(bch, x)^x;
1160 		for (i = 0; i < 2; i++) {
1161 			r = a_log(bch, y);
1162 			if (y && (r < m) && !xi[r]) {
1163 				bch->xi_tab[r] = x;
1164 				xi[r] = 1;
1165 				remaining--;
1166 				dbg("x%d = %x\n", r, x);
1167 				break;
1168 			}
1169 			y ^= ak;
1170 		}
1171 	}
1172 	/* should not happen but check anyway */
1173 	return remaining ? -1 : 0;
1174 }
1175 
1176 static void *bch_alloc(size_t size, int *err)
1177 {
1178 	void *ptr;
1179 
1180 	ptr = kmalloc(size, GFP_KERNEL);
1181 	if (ptr == NULL)
1182 		*err = 1;
1183 	return ptr;
1184 }
1185 
1186 /*
1187  * compute generator polynomial for given (m,t) parameters.
1188  */
1189 static uint32_t *compute_generator_polynomial(struct bch_control *bch)
1190 {
1191 	const unsigned int m = GF_M(bch);
1192 	const unsigned int t = GF_T(bch);
1193 	int n, err = 0;
1194 	unsigned int i, j, nbits, r, word, *roots;
1195 	struct gf_poly *g;
1196 	uint32_t *genpoly;
1197 
1198 	g = bch_alloc(GF_POLY_SZ(m*t), &err);
1199 	roots = bch_alloc((bch->n+1)*sizeof(*roots), &err);
1200 	genpoly = bch_alloc(DIV_ROUND_UP(m*t+1, 32)*sizeof(*genpoly), &err);
1201 
1202 	if (err) {
1203 		kfree(genpoly);
1204 		genpoly = NULL;
1205 		goto finish;
1206 	}
1207 
1208 	/* enumerate all roots of g(X) */
1209 	memset(roots , 0, (bch->n+1)*sizeof(*roots));
1210 	for (i = 0; i < t; i++) {
1211 		for (j = 0, r = 2*i+1; j < m; j++) {
1212 			roots[r] = 1;
1213 			r = mod_s(bch, 2*r);
1214 		}
1215 	}
1216 	/* build generator polynomial g(X) */
1217 	g->deg = 0;
1218 	g->c[0] = 1;
1219 	for (i = 0; i < GF_N(bch); i++) {
1220 		if (roots[i]) {
1221 			/* multiply g(X) by (X+root) */
1222 			r = bch->a_pow_tab[i];
1223 			g->c[g->deg+1] = 1;
1224 			for (j = g->deg; j > 0; j--)
1225 				g->c[j] = gf_mul(bch, g->c[j], r)^g->c[j-1];
1226 
1227 			g->c[0] = gf_mul(bch, g->c[0], r);
1228 			g->deg++;
1229 		}
1230 	}
1231 	/* store left-justified binary representation of g(X) */
1232 	n = g->deg+1;
1233 	i = 0;
1234 
1235 	while (n > 0) {
1236 		nbits = (n > 32) ? 32 : n;
1237 		for (j = 0, word = 0; j < nbits; j++) {
1238 			if (g->c[n-1-j])
1239 				word |= 1u << (31-j);
1240 		}
1241 		genpoly[i++] = word;
1242 		n -= nbits;
1243 	}
1244 	bch->ecc_bits = g->deg;
1245 
1246 finish:
1247 	kfree(g);
1248 	kfree(roots);
1249 
1250 	return genpoly;
1251 }
1252 
1253 /**
1254  * bch_init - initialize a BCH encoder/decoder
1255  * @m:          Galois field order, should be in the range 5-15
1256  * @t:          maximum error correction capability, in bits
1257  * @prim_poly:  user-provided primitive polynomial (or 0 to use default)
1258  * @swap_bits:  swap bits within data and syndrome bytes
1259  *
1260  * Returns:
1261  *  a newly allocated BCH control structure if successful, NULL otherwise
1262  *
1263  * This initialization can take some time, as lookup tables are built for fast
1264  * encoding/decoding; make sure not to call this function from a time critical
1265  * path. Usually, bch_init() should be called on module/driver init and
1266  * bch_free() should be called to release memory on exit.
1267  *
1268  * You may provide your own primitive polynomial of degree @m in argument
1269  * @prim_poly, or let bch_init() use its default polynomial.
1270  *
1271  * Once bch_init() has successfully returned a pointer to a newly allocated
1272  * BCH control structure, ecc length in bytes is given by member @ecc_bytes of
1273  * the structure.
1274  */
1275 struct bch_control *bch_init(int m, int t, unsigned int prim_poly,
1276 			     bool swap_bits)
1277 {
1278 	int err = 0;
1279 	unsigned int i, words;
1280 	uint32_t *genpoly;
1281 	struct bch_control *bch = NULL;
1282 
1283 	const int min_m = 5;
1284 
1285 	/* default primitive polynomials */
1286 	static const unsigned int prim_poly_tab[] = {
1287 		0x25, 0x43, 0x83, 0x11d, 0x211, 0x409, 0x805, 0x1053, 0x201b,
1288 		0x402b, 0x8003,
1289 	};
1290 
1291 #if defined(CONFIG_BCH_CONST_PARAMS)
1292 	if ((m != (CONFIG_BCH_CONST_M)) || (t != (CONFIG_BCH_CONST_T))) {
1293 		printk(KERN_ERR "bch encoder/decoder was configured to support "
1294 		       "parameters m=%d, t=%d only!\n",
1295 		       CONFIG_BCH_CONST_M, CONFIG_BCH_CONST_T);
1296 		goto fail;
1297 	}
1298 #endif
1299 	if ((m < min_m) || (m > BCH_MAX_M))
1300 		/*
1301 		 * values of m greater than 15 are not currently supported;
1302 		 * supporting m > 15 would require changing table base type
1303 		 * (uint16_t) and a small patch in matrix transposition
1304 		 */
1305 		goto fail;
1306 
1307 	if (t > BCH_MAX_T)
1308 		/*
1309 		 * we can support larger than 64 bits if necessary, at the
1310 		 * cost of higher stack usage.
1311 		 */
1312 		goto fail;
1313 
1314 	/* sanity checks */
1315 	if ((t < 1) || (m*t >= ((1 << m)-1)))
1316 		/* invalid t value */
1317 		goto fail;
1318 
1319 	/* select a primitive polynomial for generating GF(2^m) */
1320 	if (prim_poly == 0)
1321 		prim_poly = prim_poly_tab[m-min_m];
1322 
1323 	bch = kzalloc(sizeof(*bch), GFP_KERNEL);
1324 	if (bch == NULL)
1325 		goto fail;
1326 
1327 	bch->m = m;
1328 	bch->t = t;
1329 	bch->n = (1 << m)-1;
1330 	words  = DIV_ROUND_UP(m*t, 32);
1331 	bch->ecc_bytes = DIV_ROUND_UP(m*t, 8);
1332 	bch->a_pow_tab = bch_alloc((1+bch->n)*sizeof(*bch->a_pow_tab), &err);
1333 	bch->a_log_tab = bch_alloc((1+bch->n)*sizeof(*bch->a_log_tab), &err);
1334 	bch->mod8_tab  = bch_alloc(words*1024*sizeof(*bch->mod8_tab), &err);
1335 	bch->ecc_buf   = bch_alloc(words*sizeof(*bch->ecc_buf), &err);
1336 	bch->ecc_buf2  = bch_alloc(words*sizeof(*bch->ecc_buf2), &err);
1337 	bch->xi_tab    = bch_alloc(m*sizeof(*bch->xi_tab), &err);
1338 	bch->syn       = bch_alloc(2*t*sizeof(*bch->syn), &err);
1339 	bch->cache     = bch_alloc(2*t*sizeof(*bch->cache), &err);
1340 	bch->elp       = bch_alloc((t+1)*sizeof(struct gf_poly_deg1), &err);
1341 	bch->swap_bits = swap_bits;
1342 
1343 	for (i = 0; i < ARRAY_SIZE(bch->poly_2t); i++)
1344 		bch->poly_2t[i] = bch_alloc(GF_POLY_SZ(2*t), &err);
1345 
1346 	if (err)
1347 		goto fail;
1348 
1349 	err = build_gf_tables(bch, prim_poly);
1350 	if (err)
1351 		goto fail;
1352 
1353 	/* use generator polynomial for computing encoding tables */
1354 	genpoly = compute_generator_polynomial(bch);
1355 	if (genpoly == NULL)
1356 		goto fail;
1357 
1358 	build_mod8_tables(bch, genpoly);
1359 	kfree(genpoly);
1360 
1361 	err = build_deg2_base(bch);
1362 	if (err)
1363 		goto fail;
1364 
1365 	return bch;
1366 
1367 fail:
1368 	bch_free(bch);
1369 	return NULL;
1370 }
1371 EXPORT_SYMBOL_GPL(bch_init);
1372 
1373 /**
1374  *  bch_free - free the BCH control structure
1375  *  @bch:    BCH control structure to release
1376  */
1377 void bch_free(struct bch_control *bch)
1378 {
1379 	unsigned int i;
1380 
1381 	if (bch) {
1382 		kfree(bch->a_pow_tab);
1383 		kfree(bch->a_log_tab);
1384 		kfree(bch->mod8_tab);
1385 		kfree(bch->ecc_buf);
1386 		kfree(bch->ecc_buf2);
1387 		kfree(bch->xi_tab);
1388 		kfree(bch->syn);
1389 		kfree(bch->cache);
1390 		kfree(bch->elp);
1391 
1392 		for (i = 0; i < ARRAY_SIZE(bch->poly_2t); i++)
1393 			kfree(bch->poly_2t[i]);
1394 
1395 		kfree(bch);
1396 	}
1397 }
1398 EXPORT_SYMBOL_GPL(bch_free);
1399 
1400 MODULE_LICENSE("GPL");
1401 MODULE_AUTHOR("Ivan Djelic <ivan.djelic@parrot.com>");
1402 MODULE_DESCRIPTION("Binary BCH encoder/decoder");
1403