xref: /linux/lib/bch.c (revision a23e1966932464e1c5226cb9ac4ce1d5fc10ba22)
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 					tmp = rows[r];
484 					rows[r] = rows[p];
485 					rows[p] = tmp;
486 				}
487 				rem = r+1;
488 				break;
489 			}
490 		}
491 		if (rem) {
492 			/* perform elimination on remaining rows */
493 			tmp = rows[p];
494 			for (r = rem; r < m; r++) {
495 				if (rows[r] & mask)
496 					rows[r] ^= tmp;
497 			}
498 		} else {
499 			/* elimination not needed, store defective row index */
500 			param[k++] = c;
501 		}
502 		mask >>= 1;
503 	}
504 	/* rewrite system, inserting fake parameter rows */
505 	if (k > 0) {
506 		p = k;
507 		for (r = m-1; r >= 0; r--) {
508 			if ((r > m-1-k) && rows[r])
509 				/* system has no solution */
510 				return 0;
511 
512 			rows[r] = (p && (r == param[p-1])) ?
513 				p--, 1u << (m-r) : rows[r-p];
514 		}
515 	}
516 
517 	if (nsol != (1 << k))
518 		/* unexpected number of solutions */
519 		return 0;
520 
521 	for (p = 0; p < nsol; p++) {
522 		/* set parameters for p-th solution */
523 		for (c = 0; c < k; c++)
524 			rows[param[c]] = (rows[param[c]] & ~1)|((p >> c) & 1);
525 
526 		/* compute unique solution */
527 		tmp = 0;
528 		for (r = m-1; r >= 0; r--) {
529 			mask = rows[r] & (tmp|1);
530 			tmp |= parity(mask) << (m-r);
531 		}
532 		sol[p] = tmp >> 1;
533 	}
534 	return nsol;
535 }
536 
537 /*
538  * this function builds and solves a linear system for finding roots of a degree
539  * 4 affine monic polynomial X^4+aX^2+bX+c over GF(2^m).
540  */
541 static int find_affine4_roots(struct bch_control *bch, unsigned int a,
542 			      unsigned int b, unsigned int c,
543 			      unsigned int *roots)
544 {
545 	int i, j, k;
546 	const int m = GF_M(bch);
547 	unsigned int mask = 0xff, t, rows[16] = {0,};
548 
549 	j = a_log(bch, b);
550 	k = a_log(bch, a);
551 	rows[0] = c;
552 
553 	/* build linear system to solve X^4+aX^2+bX+c = 0 */
554 	for (i = 0; i < m; i++) {
555 		rows[i+1] = bch->a_pow_tab[4*i]^
556 			(a ? bch->a_pow_tab[mod_s(bch, k)] : 0)^
557 			(b ? bch->a_pow_tab[mod_s(bch, j)] : 0);
558 		j++;
559 		k += 2;
560 	}
561 	/*
562 	 * transpose 16x16 matrix before passing it to linear solver
563 	 * warning: this code assumes m < 16
564 	 */
565 	for (j = 8; j != 0; j >>= 1, mask ^= (mask << j)) {
566 		for (k = 0; k < 16; k = (k+j+1) & ~j) {
567 			t = ((rows[k] >> j)^rows[k+j]) & mask;
568 			rows[k] ^= (t << j);
569 			rows[k+j] ^= t;
570 		}
571 	}
572 	return solve_linear_system(bch, rows, roots, 4);
573 }
574 
575 /*
576  * compute root r of a degree 1 polynomial over GF(2^m) (returned as log(1/r))
577  */
578 static int find_poly_deg1_roots(struct bch_control *bch, struct gf_poly *poly,
579 				unsigned int *roots)
580 {
581 	int n = 0;
582 
583 	if (poly->c[0])
584 		/* poly[X] = bX+c with c!=0, root=c/b */
585 		roots[n++] = mod_s(bch, GF_N(bch)-bch->a_log_tab[poly->c[0]]+
586 				   bch->a_log_tab[poly->c[1]]);
587 	return n;
588 }
589 
590 /*
591  * compute roots of a degree 2 polynomial over GF(2^m)
592  */
593 static int find_poly_deg2_roots(struct bch_control *bch, struct gf_poly *poly,
594 				unsigned int *roots)
595 {
596 	int n = 0, i, l0, l1, l2;
597 	unsigned int u, v, r;
598 
599 	if (poly->c[0] && poly->c[1]) {
600 
601 		l0 = bch->a_log_tab[poly->c[0]];
602 		l1 = bch->a_log_tab[poly->c[1]];
603 		l2 = bch->a_log_tab[poly->c[2]];
604 
605 		/* using z=a/bX, transform aX^2+bX+c into z^2+z+u (u=ac/b^2) */
606 		u = a_pow(bch, l0+l2+2*(GF_N(bch)-l1));
607 		/*
608 		 * let u = sum(li.a^i) i=0..m-1; then compute r = sum(li.xi):
609 		 * r^2+r = sum(li.(xi^2+xi)) = sum(li.(a^i+Tr(a^i).a^k)) =
610 		 * u + sum(li.Tr(a^i).a^k) = u+a^k.Tr(sum(li.a^i)) = u+a^k.Tr(u)
611 		 * i.e. r and r+1 are roots iff Tr(u)=0
612 		 */
613 		r = 0;
614 		v = u;
615 		while (v) {
616 			i = deg(v);
617 			r ^= bch->xi_tab[i];
618 			v ^= (1 << i);
619 		}
620 		/* verify root */
621 		if ((gf_sqr(bch, r)^r) == u) {
622 			/* reverse z=a/bX transformation and compute log(1/r) */
623 			roots[n++] = modulo(bch, 2*GF_N(bch)-l1-
624 					    bch->a_log_tab[r]+l2);
625 			roots[n++] = modulo(bch, 2*GF_N(bch)-l1-
626 					    bch->a_log_tab[r^1]+l2);
627 		}
628 	}
629 	return n;
630 }
631 
632 /*
633  * compute roots of a degree 3 polynomial over GF(2^m)
634  */
635 static int find_poly_deg3_roots(struct bch_control *bch, struct gf_poly *poly,
636 				unsigned int *roots)
637 {
638 	int i, n = 0;
639 	unsigned int a, b, c, a2, b2, c2, e3, tmp[4];
640 
641 	if (poly->c[0]) {
642 		/* transform polynomial into monic X^3 + a2X^2 + b2X + c2 */
643 		e3 = poly->c[3];
644 		c2 = gf_div(bch, poly->c[0], e3);
645 		b2 = gf_div(bch, poly->c[1], e3);
646 		a2 = gf_div(bch, poly->c[2], e3);
647 
648 		/* (X+a2)(X^3+a2X^2+b2X+c2) = X^4+aX^2+bX+c (affine) */
649 		c = gf_mul(bch, a2, c2);           /* c = a2c2      */
650 		b = gf_mul(bch, a2, b2)^c2;        /* b = a2b2 + c2 */
651 		a = gf_sqr(bch, a2)^b2;            /* a = a2^2 + b2 */
652 
653 		/* find the 4 roots of this affine polynomial */
654 		if (find_affine4_roots(bch, a, b, c, tmp) == 4) {
655 			/* remove a2 from final list of roots */
656 			for (i = 0; i < 4; i++) {
657 				if (tmp[i] != a2)
658 					roots[n++] = a_ilog(bch, tmp[i]);
659 			}
660 		}
661 	}
662 	return n;
663 }
664 
665 /*
666  * compute roots of a degree 4 polynomial over GF(2^m)
667  */
668 static int find_poly_deg4_roots(struct bch_control *bch, struct gf_poly *poly,
669 				unsigned int *roots)
670 {
671 	int i, l, n = 0;
672 	unsigned int a, b, c, d, e = 0, f, a2, b2, c2, e4;
673 
674 	if (poly->c[0] == 0)
675 		return 0;
676 
677 	/* transform polynomial into monic X^4 + aX^3 + bX^2 + cX + d */
678 	e4 = poly->c[4];
679 	d = gf_div(bch, poly->c[0], e4);
680 	c = gf_div(bch, poly->c[1], e4);
681 	b = gf_div(bch, poly->c[2], e4);
682 	a = gf_div(bch, poly->c[3], e4);
683 
684 	/* use Y=1/X transformation to get an affine polynomial */
685 	if (a) {
686 		/* first, eliminate cX by using z=X+e with ae^2+c=0 */
687 		if (c) {
688 			/* compute e such that e^2 = c/a */
689 			f = gf_div(bch, c, a);
690 			l = a_log(bch, f);
691 			l += (l & 1) ? GF_N(bch) : 0;
692 			e = a_pow(bch, l/2);
693 			/*
694 			 * use transformation z=X+e:
695 			 * z^4+e^4 + a(z^3+ez^2+e^2z+e^3) + b(z^2+e^2) +cz+ce+d
696 			 * z^4 + az^3 + (ae+b)z^2 + (ae^2+c)z+e^4+be^2+ae^3+ce+d
697 			 * z^4 + az^3 + (ae+b)z^2 + e^4+be^2+d
698 			 * z^4 + az^3 +     b'z^2 + d'
699 			 */
700 			d = a_pow(bch, 2*l)^gf_mul(bch, b, f)^d;
701 			b = gf_mul(bch, a, e)^b;
702 		}
703 		/* now, use Y=1/X to get Y^4 + b/dY^2 + a/dY + 1/d */
704 		if (d == 0)
705 			/* assume all roots have multiplicity 1 */
706 			return 0;
707 
708 		c2 = gf_inv(bch, d);
709 		b2 = gf_div(bch, a, d);
710 		a2 = gf_div(bch, b, d);
711 	} else {
712 		/* polynomial is already affine */
713 		c2 = d;
714 		b2 = c;
715 		a2 = b;
716 	}
717 	/* find the 4 roots of this affine polynomial */
718 	if (find_affine4_roots(bch, a2, b2, c2, roots) == 4) {
719 		for (i = 0; i < 4; i++) {
720 			/* post-process roots (reverse transformations) */
721 			f = a ? gf_inv(bch, roots[i]) : roots[i];
722 			roots[i] = a_ilog(bch, f^e);
723 		}
724 		n = 4;
725 	}
726 	return n;
727 }
728 
729 /*
730  * build monic, log-based representation of a polynomial
731  */
732 static void gf_poly_logrep(struct bch_control *bch,
733 			   const struct gf_poly *a, int *rep)
734 {
735 	int i, d = a->deg, l = GF_N(bch)-a_log(bch, a->c[a->deg]);
736 
737 	/* represent 0 values with -1; warning, rep[d] is not set to 1 */
738 	for (i = 0; i < d; i++)
739 		rep[i] = a->c[i] ? mod_s(bch, a_log(bch, a->c[i])+l) : -1;
740 }
741 
742 /*
743  * compute polynomial Euclidean division remainder in GF(2^m)[X]
744  */
745 static void gf_poly_mod(struct bch_control *bch, struct gf_poly *a,
746 			const struct gf_poly *b, int *rep)
747 {
748 	int la, p, m;
749 	unsigned int i, j, *c = a->c;
750 	const unsigned int d = b->deg;
751 
752 	if (a->deg < d)
753 		return;
754 
755 	/* reuse or compute log representation of denominator */
756 	if (!rep) {
757 		rep = bch->cache;
758 		gf_poly_logrep(bch, b, rep);
759 	}
760 
761 	for (j = a->deg; j >= d; j--) {
762 		if (c[j]) {
763 			la = a_log(bch, c[j]);
764 			p = j-d;
765 			for (i = 0; i < d; i++, p++) {
766 				m = rep[i];
767 				if (m >= 0)
768 					c[p] ^= bch->a_pow_tab[mod_s(bch,
769 								     m+la)];
770 			}
771 		}
772 	}
773 	a->deg = d-1;
774 	while (!c[a->deg] && a->deg)
775 		a->deg--;
776 }
777 
778 /*
779  * compute polynomial Euclidean division quotient in GF(2^m)[X]
780  */
781 static void gf_poly_div(struct bch_control *bch, struct gf_poly *a,
782 			const struct gf_poly *b, struct gf_poly *q)
783 {
784 	if (a->deg >= b->deg) {
785 		q->deg = a->deg-b->deg;
786 		/* compute a mod b (modifies a) */
787 		gf_poly_mod(bch, a, b, NULL);
788 		/* quotient is stored in upper part of polynomial a */
789 		memcpy(q->c, &a->c[b->deg], (1+q->deg)*sizeof(unsigned int));
790 	} else {
791 		q->deg = 0;
792 		q->c[0] = 0;
793 	}
794 }
795 
796 /*
797  * compute polynomial GCD (Greatest Common Divisor) in GF(2^m)[X]
798  */
799 static struct gf_poly *gf_poly_gcd(struct bch_control *bch, struct gf_poly *a,
800 				   struct gf_poly *b)
801 {
802 	struct gf_poly *tmp;
803 
804 	dbg("gcd(%s,%s)=", gf_poly_str(a), gf_poly_str(b));
805 
806 	if (a->deg < b->deg) {
807 		tmp = b;
808 		b = a;
809 		a = tmp;
810 	}
811 
812 	while (b->deg > 0) {
813 		gf_poly_mod(bch, a, b, NULL);
814 		tmp = b;
815 		b = a;
816 		a = tmp;
817 	}
818 
819 	dbg("%s\n", gf_poly_str(a));
820 
821 	return a;
822 }
823 
824 /*
825  * Given a polynomial f and an integer k, compute Tr(a^kX) mod f
826  * This is used in Berlekamp Trace algorithm for splitting polynomials
827  */
828 static void compute_trace_bk_mod(struct bch_control *bch, int k,
829 				 const struct gf_poly *f, struct gf_poly *z,
830 				 struct gf_poly *out)
831 {
832 	const int m = GF_M(bch);
833 	int i, j;
834 
835 	/* z contains z^2j mod f */
836 	z->deg = 1;
837 	z->c[0] = 0;
838 	z->c[1] = bch->a_pow_tab[k];
839 
840 	out->deg = 0;
841 	memset(out, 0, GF_POLY_SZ(f->deg));
842 
843 	/* compute f log representation only once */
844 	gf_poly_logrep(bch, f, bch->cache);
845 
846 	for (i = 0; i < m; i++) {
847 		/* add a^(k*2^i)(z^(2^i) mod f) and compute (z^(2^i) mod f)^2 */
848 		for (j = z->deg; j >= 0; j--) {
849 			out->c[j] ^= z->c[j];
850 			z->c[2*j] = gf_sqr(bch, z->c[j]);
851 			z->c[2*j+1] = 0;
852 		}
853 		if (z->deg > out->deg)
854 			out->deg = z->deg;
855 
856 		if (i < m-1) {
857 			z->deg *= 2;
858 			/* z^(2(i+1)) mod f = (z^(2^i) mod f)^2 mod f */
859 			gf_poly_mod(bch, z, f, bch->cache);
860 		}
861 	}
862 	while (!out->c[out->deg] && out->deg)
863 		out->deg--;
864 
865 	dbg("Tr(a^%d.X) mod f = %s\n", k, gf_poly_str(out));
866 }
867 
868 /*
869  * factor a polynomial using Berlekamp Trace algorithm (BTA)
870  */
871 static void factor_polynomial(struct bch_control *bch, int k, struct gf_poly *f,
872 			      struct gf_poly **g, struct gf_poly **h)
873 {
874 	struct gf_poly *f2 = bch->poly_2t[0];
875 	struct gf_poly *q  = bch->poly_2t[1];
876 	struct gf_poly *tk = bch->poly_2t[2];
877 	struct gf_poly *z  = bch->poly_2t[3];
878 	struct gf_poly *gcd;
879 
880 	dbg("factoring %s...\n", gf_poly_str(f));
881 
882 	*g = f;
883 	*h = NULL;
884 
885 	/* tk = Tr(a^k.X) mod f */
886 	compute_trace_bk_mod(bch, k, f, z, tk);
887 
888 	if (tk->deg > 0) {
889 		/* compute g = gcd(f, tk) (destructive operation) */
890 		gf_poly_copy(f2, f);
891 		gcd = gf_poly_gcd(bch, f2, tk);
892 		if (gcd->deg < f->deg) {
893 			/* compute h=f/gcd(f,tk); this will modify f and q */
894 			gf_poly_div(bch, f, gcd, q);
895 			/* store g and h in-place (clobbering f) */
896 			*h = &((struct gf_poly_deg1 *)f)[gcd->deg].poly;
897 			gf_poly_copy(*g, gcd);
898 			gf_poly_copy(*h, q);
899 		}
900 	}
901 }
902 
903 /*
904  * find roots of a polynomial, using BTZ algorithm; see the beginning of this
905  * file for details
906  */
907 static int find_poly_roots(struct bch_control *bch, unsigned int k,
908 			   struct gf_poly *poly, unsigned int *roots)
909 {
910 	int cnt;
911 	struct gf_poly *f1, *f2;
912 
913 	switch (poly->deg) {
914 		/* handle low degree polynomials with ad hoc techniques */
915 	case 1:
916 		cnt = find_poly_deg1_roots(bch, poly, roots);
917 		break;
918 	case 2:
919 		cnt = find_poly_deg2_roots(bch, poly, roots);
920 		break;
921 	case 3:
922 		cnt = find_poly_deg3_roots(bch, poly, roots);
923 		break;
924 	case 4:
925 		cnt = find_poly_deg4_roots(bch, poly, roots);
926 		break;
927 	default:
928 		/* factor polynomial using Berlekamp Trace Algorithm (BTA) */
929 		cnt = 0;
930 		if (poly->deg && (k <= GF_M(bch))) {
931 			factor_polynomial(bch, k, poly, &f1, &f2);
932 			if (f1)
933 				cnt += find_poly_roots(bch, k+1, f1, roots);
934 			if (f2)
935 				cnt += find_poly_roots(bch, k+1, f2, roots+cnt);
936 		}
937 		break;
938 	}
939 	return cnt;
940 }
941 
942 #if defined(USE_CHIEN_SEARCH)
943 /*
944  * exhaustive root search (Chien) implementation - not used, included only for
945  * reference/comparison tests
946  */
947 static int chien_search(struct bch_control *bch, unsigned int len,
948 			struct gf_poly *p, unsigned int *roots)
949 {
950 	int m;
951 	unsigned int i, j, syn, syn0, count = 0;
952 	const unsigned int k = 8*len+bch->ecc_bits;
953 
954 	/* use a log-based representation of polynomial */
955 	gf_poly_logrep(bch, p, bch->cache);
956 	bch->cache[p->deg] = 0;
957 	syn0 = gf_div(bch, p->c[0], p->c[p->deg]);
958 
959 	for (i = GF_N(bch)-k+1; i <= GF_N(bch); i++) {
960 		/* compute elp(a^i) */
961 		for (j = 1, syn = syn0; j <= p->deg; j++) {
962 			m = bch->cache[j];
963 			if (m >= 0)
964 				syn ^= a_pow(bch, m+j*i);
965 		}
966 		if (syn == 0) {
967 			roots[count++] = GF_N(bch)-i;
968 			if (count == p->deg)
969 				break;
970 		}
971 	}
972 	return (count == p->deg) ? count : 0;
973 }
974 #define find_poly_roots(_p, _k, _elp, _loc) chien_search(_p, len, _elp, _loc)
975 #endif /* USE_CHIEN_SEARCH */
976 
977 /**
978  * bch_decode - decode received codeword and find bit error locations
979  * @bch:      BCH control structure
980  * @data:     received data, ignored if @calc_ecc is provided
981  * @len:      data length in bytes, must always be provided
982  * @recv_ecc: received ecc, if NULL then assume it was XORed in @calc_ecc
983  * @calc_ecc: calculated ecc, if NULL then calc_ecc is computed from @data
984  * @syn:      hw computed syndrome data (if NULL, syndrome is calculated)
985  * @errloc:   output array of error locations
986  *
987  * Returns:
988  *  The number of errors found, or -EBADMSG if decoding failed, or -EINVAL if
989  *  invalid parameters were provided
990  *
991  * Depending on the available hw BCH support and the need to compute @calc_ecc
992  * separately (using bch_encode()), this function should be called with one of
993  * the following parameter configurations -
994  *
995  * by providing @data and @recv_ecc only:
996  *   bch_decode(@bch, @data, @len, @recv_ecc, NULL, NULL, @errloc)
997  *
998  * by providing @recv_ecc and @calc_ecc:
999  *   bch_decode(@bch, NULL, @len, @recv_ecc, @calc_ecc, NULL, @errloc)
1000  *
1001  * by providing ecc = recv_ecc XOR calc_ecc:
1002  *   bch_decode(@bch, NULL, @len, NULL, ecc, NULL, @errloc)
1003  *
1004  * by providing syndrome results @syn:
1005  *   bch_decode(@bch, NULL, @len, NULL, NULL, @syn, @errloc)
1006  *
1007  * Once bch_decode() has successfully returned with a positive value, error
1008  * locations returned in array @errloc should be interpreted as follows -
1009  *
1010  * if (errloc[n] >= 8*len), then n-th error is located in ecc (no need for
1011  * data correction)
1012  *
1013  * if (errloc[n] < 8*len), then n-th error is located in data and can be
1014  * corrected with statement data[errloc[n]/8] ^= 1 << (errloc[n] % 8);
1015  *
1016  * Note that this function does not perform any data correction by itself, it
1017  * merely indicates error locations.
1018  */
1019 int bch_decode(struct bch_control *bch, const uint8_t *data, unsigned int len,
1020 	       const uint8_t *recv_ecc, const uint8_t *calc_ecc,
1021 	       const unsigned int *syn, unsigned int *errloc)
1022 {
1023 	const unsigned int ecc_words = BCH_ECC_WORDS(bch);
1024 	unsigned int nbits;
1025 	int i, err, nroots;
1026 	uint32_t sum;
1027 
1028 	/* sanity check: make sure data length can be handled */
1029 	if (8*len > (bch->n-bch->ecc_bits))
1030 		return -EINVAL;
1031 
1032 	/* if caller does not provide syndromes, compute them */
1033 	if (!syn) {
1034 		if (!calc_ecc) {
1035 			/* compute received data ecc into an internal buffer */
1036 			if (!data || !recv_ecc)
1037 				return -EINVAL;
1038 			bch_encode(bch, data, len, NULL);
1039 		} else {
1040 			/* load provided calculated ecc */
1041 			load_ecc8(bch, bch->ecc_buf, calc_ecc);
1042 		}
1043 		/* load received ecc or assume it was XORed in calc_ecc */
1044 		if (recv_ecc) {
1045 			load_ecc8(bch, bch->ecc_buf2, recv_ecc);
1046 			/* XOR received and calculated ecc */
1047 			for (i = 0, sum = 0; i < (int)ecc_words; i++) {
1048 				bch->ecc_buf[i] ^= bch->ecc_buf2[i];
1049 				sum |= bch->ecc_buf[i];
1050 			}
1051 			if (!sum)
1052 				/* no error found */
1053 				return 0;
1054 		}
1055 		compute_syndromes(bch, bch->ecc_buf, bch->syn);
1056 		syn = bch->syn;
1057 	}
1058 
1059 	err = compute_error_locator_polynomial(bch, syn);
1060 	if (err > 0) {
1061 		nroots = find_poly_roots(bch, 1, bch->elp, errloc);
1062 		if (err != nroots)
1063 			err = -1;
1064 	}
1065 	if (err > 0) {
1066 		/* post-process raw error locations for easier correction */
1067 		nbits = (len*8)+bch->ecc_bits;
1068 		for (i = 0; i < err; i++) {
1069 			if (errloc[i] >= nbits) {
1070 				err = -1;
1071 				break;
1072 			}
1073 			errloc[i] = nbits-1-errloc[i];
1074 			if (!bch->swap_bits)
1075 				errloc[i] = (errloc[i] & ~7) |
1076 					    (7-(errloc[i] & 7));
1077 		}
1078 	}
1079 	return (err >= 0) ? err : -EBADMSG;
1080 }
1081 EXPORT_SYMBOL_GPL(bch_decode);
1082 
1083 /*
1084  * generate Galois field lookup tables
1085  */
1086 static int build_gf_tables(struct bch_control *bch, unsigned int poly)
1087 {
1088 	unsigned int i, x = 1;
1089 	const unsigned int k = 1 << deg(poly);
1090 
1091 	/* primitive polynomial must be of degree m */
1092 	if (k != (1u << GF_M(bch)))
1093 		return -1;
1094 
1095 	for (i = 0; i < GF_N(bch); i++) {
1096 		bch->a_pow_tab[i] = x;
1097 		bch->a_log_tab[x] = i;
1098 		if (i && (x == 1))
1099 			/* polynomial is not primitive (a^i=1 with 0<i<2^m-1) */
1100 			return -1;
1101 		x <<= 1;
1102 		if (x & k)
1103 			x ^= poly;
1104 	}
1105 	bch->a_pow_tab[GF_N(bch)] = 1;
1106 	bch->a_log_tab[0] = 0;
1107 
1108 	return 0;
1109 }
1110 
1111 /*
1112  * compute generator polynomial remainder tables for fast encoding
1113  */
1114 static void build_mod8_tables(struct bch_control *bch, const uint32_t *g)
1115 {
1116 	int i, j, b, d;
1117 	uint32_t data, hi, lo, *tab;
1118 	const int l = BCH_ECC_WORDS(bch);
1119 	const int plen = DIV_ROUND_UP(bch->ecc_bits+1, 32);
1120 	const int ecclen = DIV_ROUND_UP(bch->ecc_bits, 32);
1121 
1122 	memset(bch->mod8_tab, 0, 4*256*l*sizeof(*bch->mod8_tab));
1123 
1124 	for (i = 0; i < 256; i++) {
1125 		/* p(X)=i is a small polynomial of weight <= 8 */
1126 		for (b = 0; b < 4; b++) {
1127 			/* we want to compute (p(X).X^(8*b+deg(g))) mod g(X) */
1128 			tab = bch->mod8_tab + (b*256+i)*l;
1129 			data = i << (8*b);
1130 			while (data) {
1131 				d = deg(data);
1132 				/* subtract X^d.g(X) from p(X).X^(8*b+deg(g)) */
1133 				data ^= g[0] >> (31-d);
1134 				for (j = 0; j < ecclen; j++) {
1135 					hi = (d < 31) ? g[j] << (d+1) : 0;
1136 					lo = (j+1 < plen) ?
1137 						g[j+1] >> (31-d) : 0;
1138 					tab[j] ^= hi|lo;
1139 				}
1140 			}
1141 		}
1142 	}
1143 }
1144 
1145 /*
1146  * build a base for factoring degree 2 polynomials
1147  */
1148 static int build_deg2_base(struct bch_control *bch)
1149 {
1150 	const int m = GF_M(bch);
1151 	int i, j, r;
1152 	unsigned int sum, x, y, remaining, ak = 0, xi[BCH_MAX_M];
1153 
1154 	/* find k s.t. Tr(a^k) = 1 and 0 <= k < m */
1155 	for (i = 0; i < m; i++) {
1156 		for (j = 0, sum = 0; j < m; j++)
1157 			sum ^= a_pow(bch, i*(1 << j));
1158 
1159 		if (sum) {
1160 			ak = bch->a_pow_tab[i];
1161 			break;
1162 		}
1163 	}
1164 	/* find xi, i=0..m-1 such that xi^2+xi = a^i+Tr(a^i).a^k */
1165 	remaining = m;
1166 	memset(xi, 0, sizeof(xi));
1167 
1168 	for (x = 0; (x <= GF_N(bch)) && remaining; x++) {
1169 		y = gf_sqr(bch, x)^x;
1170 		for (i = 0; i < 2; i++) {
1171 			r = a_log(bch, y);
1172 			if (y && (r < m) && !xi[r]) {
1173 				bch->xi_tab[r] = x;
1174 				xi[r] = 1;
1175 				remaining--;
1176 				dbg("x%d = %x\n", r, x);
1177 				break;
1178 			}
1179 			y ^= ak;
1180 		}
1181 	}
1182 	/* should not happen but check anyway */
1183 	return remaining ? -1 : 0;
1184 }
1185 
1186 static void *bch_alloc(size_t size, int *err)
1187 {
1188 	void *ptr;
1189 
1190 	ptr = kmalloc(size, GFP_KERNEL);
1191 	if (ptr == NULL)
1192 		*err = 1;
1193 	return ptr;
1194 }
1195 
1196 /*
1197  * compute generator polynomial for given (m,t) parameters.
1198  */
1199 static uint32_t *compute_generator_polynomial(struct bch_control *bch)
1200 {
1201 	const unsigned int m = GF_M(bch);
1202 	const unsigned int t = GF_T(bch);
1203 	int n, err = 0;
1204 	unsigned int i, j, nbits, r, word, *roots;
1205 	struct gf_poly *g;
1206 	uint32_t *genpoly;
1207 
1208 	g = bch_alloc(GF_POLY_SZ(m*t), &err);
1209 	roots = bch_alloc((bch->n+1)*sizeof(*roots), &err);
1210 	genpoly = bch_alloc(DIV_ROUND_UP(m*t+1, 32)*sizeof(*genpoly), &err);
1211 
1212 	if (err) {
1213 		kfree(genpoly);
1214 		genpoly = NULL;
1215 		goto finish;
1216 	}
1217 
1218 	/* enumerate all roots of g(X) */
1219 	memset(roots , 0, (bch->n+1)*sizeof(*roots));
1220 	for (i = 0; i < t; i++) {
1221 		for (j = 0, r = 2*i+1; j < m; j++) {
1222 			roots[r] = 1;
1223 			r = mod_s(bch, 2*r);
1224 		}
1225 	}
1226 	/* build generator polynomial g(X) */
1227 	g->deg = 0;
1228 	g->c[0] = 1;
1229 	for (i = 0; i < GF_N(bch); i++) {
1230 		if (roots[i]) {
1231 			/* multiply g(X) by (X+root) */
1232 			r = bch->a_pow_tab[i];
1233 			g->c[g->deg+1] = 1;
1234 			for (j = g->deg; j > 0; j--)
1235 				g->c[j] = gf_mul(bch, g->c[j], r)^g->c[j-1];
1236 
1237 			g->c[0] = gf_mul(bch, g->c[0], r);
1238 			g->deg++;
1239 		}
1240 	}
1241 	/* store left-justified binary representation of g(X) */
1242 	n = g->deg+1;
1243 	i = 0;
1244 
1245 	while (n > 0) {
1246 		nbits = (n > 32) ? 32 : n;
1247 		for (j = 0, word = 0; j < nbits; j++) {
1248 			if (g->c[n-1-j])
1249 				word |= 1u << (31-j);
1250 		}
1251 		genpoly[i++] = word;
1252 		n -= nbits;
1253 	}
1254 	bch->ecc_bits = g->deg;
1255 
1256 finish:
1257 	kfree(g);
1258 	kfree(roots);
1259 
1260 	return genpoly;
1261 }
1262 
1263 /**
1264  * bch_init - initialize a BCH encoder/decoder
1265  * @m:          Galois field order, should be in the range 5-15
1266  * @t:          maximum error correction capability, in bits
1267  * @prim_poly:  user-provided primitive polynomial (or 0 to use default)
1268  * @swap_bits:  swap bits within data and syndrome bytes
1269  *
1270  * Returns:
1271  *  a newly allocated BCH control structure if successful, NULL otherwise
1272  *
1273  * This initialization can take some time, as lookup tables are built for fast
1274  * encoding/decoding; make sure not to call this function from a time critical
1275  * path. Usually, bch_init() should be called on module/driver init and
1276  * bch_free() should be called to release memory on exit.
1277  *
1278  * You may provide your own primitive polynomial of degree @m in argument
1279  * @prim_poly, or let bch_init() use its default polynomial.
1280  *
1281  * Once bch_init() has successfully returned a pointer to a newly allocated
1282  * BCH control structure, ecc length in bytes is given by member @ecc_bytes of
1283  * the structure.
1284  */
1285 struct bch_control *bch_init(int m, int t, unsigned int prim_poly,
1286 			     bool swap_bits)
1287 {
1288 	int err = 0;
1289 	unsigned int i, words;
1290 	uint32_t *genpoly;
1291 	struct bch_control *bch = NULL;
1292 
1293 	const int min_m = 5;
1294 
1295 	/* default primitive polynomials */
1296 	static const unsigned int prim_poly_tab[] = {
1297 		0x25, 0x43, 0x83, 0x11d, 0x211, 0x409, 0x805, 0x1053, 0x201b,
1298 		0x402b, 0x8003,
1299 	};
1300 
1301 #if defined(CONFIG_BCH_CONST_PARAMS)
1302 	if ((m != (CONFIG_BCH_CONST_M)) || (t != (CONFIG_BCH_CONST_T))) {
1303 		printk(KERN_ERR "bch encoder/decoder was configured to support "
1304 		       "parameters m=%d, t=%d only!\n",
1305 		       CONFIG_BCH_CONST_M, CONFIG_BCH_CONST_T);
1306 		goto fail;
1307 	}
1308 #endif
1309 	if ((m < min_m) || (m > BCH_MAX_M))
1310 		/*
1311 		 * values of m greater than 15 are not currently supported;
1312 		 * supporting m > 15 would require changing table base type
1313 		 * (uint16_t) and a small patch in matrix transposition
1314 		 */
1315 		goto fail;
1316 
1317 	if (t > BCH_MAX_T)
1318 		/*
1319 		 * we can support larger than 64 bits if necessary, at the
1320 		 * cost of higher stack usage.
1321 		 */
1322 		goto fail;
1323 
1324 	/* sanity checks */
1325 	if ((t < 1) || (m*t >= ((1 << m)-1)))
1326 		/* invalid t value */
1327 		goto fail;
1328 
1329 	/* select a primitive polynomial for generating GF(2^m) */
1330 	if (prim_poly == 0)
1331 		prim_poly = prim_poly_tab[m-min_m];
1332 
1333 	bch = kzalloc(sizeof(*bch), GFP_KERNEL);
1334 	if (bch == NULL)
1335 		goto fail;
1336 
1337 	bch->m = m;
1338 	bch->t = t;
1339 	bch->n = (1 << m)-1;
1340 	words  = DIV_ROUND_UP(m*t, 32);
1341 	bch->ecc_bytes = DIV_ROUND_UP(m*t, 8);
1342 	bch->a_pow_tab = bch_alloc((1+bch->n)*sizeof(*bch->a_pow_tab), &err);
1343 	bch->a_log_tab = bch_alloc((1+bch->n)*sizeof(*bch->a_log_tab), &err);
1344 	bch->mod8_tab  = bch_alloc(words*1024*sizeof(*bch->mod8_tab), &err);
1345 	bch->ecc_buf   = bch_alloc(words*sizeof(*bch->ecc_buf), &err);
1346 	bch->ecc_buf2  = bch_alloc(words*sizeof(*bch->ecc_buf2), &err);
1347 	bch->xi_tab    = bch_alloc(m*sizeof(*bch->xi_tab), &err);
1348 	bch->syn       = bch_alloc(2*t*sizeof(*bch->syn), &err);
1349 	bch->cache     = bch_alloc(2*t*sizeof(*bch->cache), &err);
1350 	bch->elp       = bch_alloc((t+1)*sizeof(struct gf_poly_deg1), &err);
1351 	bch->swap_bits = swap_bits;
1352 
1353 	for (i = 0; i < ARRAY_SIZE(bch->poly_2t); i++)
1354 		bch->poly_2t[i] = bch_alloc(GF_POLY_SZ(2*t), &err);
1355 
1356 	if (err)
1357 		goto fail;
1358 
1359 	err = build_gf_tables(bch, prim_poly);
1360 	if (err)
1361 		goto fail;
1362 
1363 	/* use generator polynomial for computing encoding tables */
1364 	genpoly = compute_generator_polynomial(bch);
1365 	if (genpoly == NULL)
1366 		goto fail;
1367 
1368 	build_mod8_tables(bch, genpoly);
1369 	kfree(genpoly);
1370 
1371 	err = build_deg2_base(bch);
1372 	if (err)
1373 		goto fail;
1374 
1375 	return bch;
1376 
1377 fail:
1378 	bch_free(bch);
1379 	return NULL;
1380 }
1381 EXPORT_SYMBOL_GPL(bch_init);
1382 
1383 /**
1384  *  bch_free - free the BCH control structure
1385  *  @bch:    BCH control structure to release
1386  */
1387 void bch_free(struct bch_control *bch)
1388 {
1389 	unsigned int i;
1390 
1391 	if (bch) {
1392 		kfree(bch->a_pow_tab);
1393 		kfree(bch->a_log_tab);
1394 		kfree(bch->mod8_tab);
1395 		kfree(bch->ecc_buf);
1396 		kfree(bch->ecc_buf2);
1397 		kfree(bch->xi_tab);
1398 		kfree(bch->syn);
1399 		kfree(bch->cache);
1400 		kfree(bch->elp);
1401 
1402 		for (i = 0; i < ARRAY_SIZE(bch->poly_2t); i++)
1403 			kfree(bch->poly_2t[i]);
1404 
1405 		kfree(bch);
1406 	}
1407 }
1408 EXPORT_SYMBOL_GPL(bch_free);
1409 
1410 MODULE_LICENSE("GPL");
1411 MODULE_AUTHOR("Ivan Djelic <ivan.djelic@parrot.com>");
1412 MODULE_DESCRIPTION("Binary BCH encoder/decoder");
1413