xref: /linux/lib/bch.c (revision 9be85491619f1953b8a29590ca630be571941ffa)
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