xref: /openbmc/u-boot/lib/bch.c (revision 316f0d0f8f3cbeeefda043e69f3e4e6aa57f7f1d)
1  /*
2   * Generic binary BCH encoding/decoding library
3   *
4   * SPDX-License-Identifier:	GPL-2.0
5   *
6   * Copyright © 2011 Parrot S.A.
7   *
8   * Author: Ivan Djelic <ivan.djelic@parrot.com>
9   *
10   * Description:
11   *
12   * This library provides runtime configurable encoding/decoding of binary
13   * Bose-Chaudhuri-Hocquenghem (BCH) codes.
14   *
15   * Call init_bch to get a pointer to a newly allocated bch_control structure for
16   * the given m (Galois field order), t (error correction capability) and
17   * (optional) primitive polynomial parameters.
18   *
19   * Call encode_bch to compute and store ecc parity bytes to a given buffer.
20   * Call decode_bch to detect and locate errors in received data.
21   *
22   * On systems supporting hw BCH features, intermediate results may be provided
23   * to decode_bch in order to skip certain steps. See decode_bch() documentation
24   * for details.
25   *
26   * Option CONFIG_BCH_CONST_PARAMS can be used to force fixed values of
27   * parameters m and t; thus allowing extra compiler optimizations and providing
28   * better (up to 2x) encoding performance. Using this option makes sense when
29   * (m,t) are fixed and known in advance, e.g. when using BCH error correction
30   * on a particular NAND flash device.
31   *
32   * Algorithmic details:
33   *
34   * Encoding is performed by processing 32 input bits in parallel, using 4
35   * remainder lookup tables.
36   *
37   * The final stage of decoding involves the following internal steps:
38   * a. Syndrome computation
39   * b. Error locator polynomial computation using Berlekamp-Massey algorithm
40   * c. Error locator root finding (by far the most expensive step)
41   *
42   * In this implementation, step c is not performed using the usual Chien search.
43   * Instead, an alternative approach described in [1] is used. It consists in
44   * factoring the error locator polynomial using the Berlekamp Trace algorithm
45   * (BTA) down to a certain degree (4), after which ad hoc low-degree polynomial
46   * solving techniques [2] are used. The resulting algorithm, called BTZ, yields
47   * much better performance than Chien search for usual (m,t) values (typically
48   * m >= 13, t < 32, see [1]).
49   *
50   * [1] B. Biswas, V. Herbert. Efficient root finding of polynomials over fields
51   * of characteristic 2, in: Western European Workshop on Research in Cryptology
52   * - WEWoRC 2009, Graz, Austria, LNCS, Springer, July 2009, to appear.
53   * [2] [Zin96] V.A. Zinoviev. On the solution of equations of degree 10 over
54   * finite fields GF(2^q). In Rapport de recherche INRIA no 2829, 1996.
55   */
56  
57  #ifndef USE_HOSTCC
58  #include <common.h>
59  #include <ubi_uboot.h>
60  
61  #include <linux/bitops.h>
62  #else
63  #include <errno.h>
64  #if defined(__FreeBSD__)
65  #include <sys/endian.h>
66  #else
67  #include <endian.h>
68  #endif
69  #include <stdint.h>
70  #include <stdlib.h>
71  #include <string.h>
72  
73  #undef cpu_to_be32
74  #define cpu_to_be32 htobe32
75  #define DIV_ROUND_UP(n,d) (((n) + (d) - 1) / (d))
76  #define kmalloc(size, flags)	malloc(size)
77  #define kzalloc(size, flags)	calloc(1, size)
78  #define kfree free
79  #define ARRAY_SIZE(arr) (sizeof(arr) / sizeof((arr)[0]))
80  #endif
81  
82  #include <asm/byteorder.h>
83  #include <linux/bch.h>
84  
85  #if defined(CONFIG_BCH_CONST_PARAMS)
86  #define GF_M(_p)               (CONFIG_BCH_CONST_M)
87  #define GF_T(_p)               (CONFIG_BCH_CONST_T)
88  #define GF_N(_p)               ((1 << (CONFIG_BCH_CONST_M))-1)
89  #else
90  #define GF_M(_p)               ((_p)->m)
91  #define GF_T(_p)               ((_p)->t)
92  #define GF_N(_p)               ((_p)->n)
93  #endif
94  
95  #define BCH_ECC_WORDS(_p)      DIV_ROUND_UP(GF_M(_p)*GF_T(_p), 32)
96  #define BCH_ECC_BYTES(_p)      DIV_ROUND_UP(GF_M(_p)*GF_T(_p), 8)
97  
98  #ifndef dbg
99  #define dbg(_fmt, args...)     do {} while (0)
100  #endif
101  
102  /*
103   * represent a polynomial over GF(2^m)
104   */
105  struct gf_poly {
106  	unsigned int deg;    /* polynomial degree */
107  	unsigned int c[0];   /* polynomial terms */
108  };
109  
110  /* given its degree, compute a polynomial size in bytes */
111  #define GF_POLY_SZ(_d) (sizeof(struct gf_poly)+((_d)+1)*sizeof(unsigned int))
112  
113  /* polynomial of degree 1 */
114  struct gf_poly_deg1 {
115  	struct gf_poly poly;
116  	unsigned int   c[2];
117  };
118  
119  #ifdef USE_HOSTCC
120  #if !defined(__DragonFly__) && !defined(__FreeBSD__)
121  static int fls(int x)
122  {
123  	int r = 32;
124  
125  	if (!x)
126  		return 0;
127  	if (!(x & 0xffff0000u)) {
128  		x <<= 16;
129  		r -= 16;
130  	}
131  	if (!(x & 0xff000000u)) {
132  		x <<= 8;
133  		r -= 8;
134  	}
135  	if (!(x & 0xf0000000u)) {
136  		x <<= 4;
137  		r -= 4;
138  	}
139  	if (!(x & 0xc0000000u)) {
140  		x <<= 2;
141  		r -= 2;
142  	}
143  	if (!(x & 0x80000000u)) {
144  		x <<= 1;
145  		r -= 1;
146  	}
147  	return r;
148  }
149  #endif
150  #endif
151  
152  /*
153   * same as encode_bch(), but process input data one byte at a time
154   */
155  static void encode_bch_unaligned(struct bch_control *bch,
156  				 const unsigned char *data, unsigned int len,
157  				 uint32_t *ecc)
158  {
159  	int i;
160  	const uint32_t *p;
161  	const int l = BCH_ECC_WORDS(bch)-1;
162  
163  	while (len--) {
164  		p = bch->mod8_tab + (l+1)*(((ecc[0] >> 24)^(*data++)) & 0xff);
165  
166  		for (i = 0; i < l; i++)
167  			ecc[i] = ((ecc[i] << 8)|(ecc[i+1] >> 24))^(*p++);
168  
169  		ecc[l] = (ecc[l] << 8)^(*p);
170  	}
171  }
172  
173  /*
174   * convert ecc bytes to aligned, zero-padded 32-bit ecc words
175   */
176  static void load_ecc8(struct bch_control *bch, uint32_t *dst,
177  		      const uint8_t *src)
178  {
179  	uint8_t pad[4] = {0, 0, 0, 0};
180  	unsigned int i, nwords = BCH_ECC_WORDS(bch)-1;
181  
182  	for (i = 0; i < nwords; i++, src += 4)
183  		dst[i] = (src[0] << 24)|(src[1] << 16)|(src[2] << 8)|src[3];
184  
185  	memcpy(pad, src, BCH_ECC_BYTES(bch)-4*nwords);
186  	dst[nwords] = (pad[0] << 24)|(pad[1] << 16)|(pad[2] << 8)|pad[3];
187  }
188  
189  /*
190   * convert 32-bit ecc words to ecc bytes
191   */
192  static void store_ecc8(struct bch_control *bch, uint8_t *dst,
193  		       const uint32_t *src)
194  {
195  	uint8_t pad[4];
196  	unsigned int i, nwords = BCH_ECC_WORDS(bch)-1;
197  
198  	for (i = 0; i < nwords; i++) {
199  		*dst++ = (src[i] >> 24);
200  		*dst++ = (src[i] >> 16) & 0xff;
201  		*dst++ = (src[i] >>  8) & 0xff;
202  		*dst++ = (src[i] >>  0) & 0xff;
203  	}
204  	pad[0] = (src[nwords] >> 24);
205  	pad[1] = (src[nwords] >> 16) & 0xff;
206  	pad[2] = (src[nwords] >>  8) & 0xff;
207  	pad[3] = (src[nwords] >>  0) & 0xff;
208  	memcpy(dst, pad, BCH_ECC_BYTES(bch)-4*nwords);
209  }
210  
211  /**
212   * encode_bch - calculate BCH ecc parity of data
213   * @bch:   BCH control structure
214   * @data:  data to encode
215   * @len:   data length in bytes
216   * @ecc:   ecc parity data, must be initialized by caller
217   *
218   * The @ecc parity array is used both as input and output parameter, in order to
219   * allow incremental computations. It should be of the size indicated by member
220   * @ecc_bytes of @bch, and should be initialized to 0 before the first call.
221   *
222   * The exact number of computed ecc parity bits is given by member @ecc_bits of
223   * @bch; it may be less than m*t for large values of t.
224   */
225  void encode_bch(struct bch_control *bch, const uint8_t *data,
226  		unsigned int len, uint8_t *ecc)
227  {
228  	const unsigned int l = BCH_ECC_WORDS(bch)-1;
229  	unsigned int i, mlen;
230  	unsigned long m;
231  	uint32_t w, r[l+1];
232  	const uint32_t * const tab0 = bch->mod8_tab;
233  	const uint32_t * const tab1 = tab0 + 256*(l+1);
234  	const uint32_t * const tab2 = tab1 + 256*(l+1);
235  	const uint32_t * const tab3 = tab2 + 256*(l+1);
236  	const uint32_t *pdata, *p0, *p1, *p2, *p3;
237  
238  	if (ecc) {
239  		/* load ecc parity bytes into internal 32-bit buffer */
240  		load_ecc8(bch, bch->ecc_buf, ecc);
241  	} else {
242  		memset(bch->ecc_buf, 0, sizeof(r));
243  	}
244  
245  	/* process first unaligned data bytes */
246  	m = ((unsigned long)data) & 3;
247  	if (m) {
248  		mlen = (len < (4-m)) ? len : 4-m;
249  		encode_bch_unaligned(bch, data, mlen, bch->ecc_buf);
250  		data += mlen;
251  		len  -= mlen;
252  	}
253  
254  	/* process 32-bit aligned data words */
255  	pdata = (uint32_t *)data;
256  	mlen  = len/4;
257  	data += 4*mlen;
258  	len  -= 4*mlen;
259  	memcpy(r, bch->ecc_buf, sizeof(r));
260  
261  	/*
262  	 * split each 32-bit word into 4 polynomials of weight 8 as follows:
263  	 *
264  	 * 31 ...24  23 ...16  15 ... 8  7 ... 0
265  	 * xxxxxxxx  yyyyyyyy  zzzzzzzz  tttttttt
266  	 *                               tttttttt  mod g = r0 (precomputed)
267  	 *                     zzzzzzzz  00000000  mod g = r1 (precomputed)
268  	 *           yyyyyyyy  00000000  00000000  mod g = r2 (precomputed)
269  	 * xxxxxxxx  00000000  00000000  00000000  mod g = r3 (precomputed)
270  	 * xxxxxxxx  yyyyyyyy  zzzzzzzz  tttttttt  mod g = r0^r1^r2^r3
271  	 */
272  	while (mlen--) {
273  		/* input data is read in big-endian format */
274  		w = r[0]^cpu_to_be32(*pdata++);
275  		p0 = tab0 + (l+1)*((w >>  0) & 0xff);
276  		p1 = tab1 + (l+1)*((w >>  8) & 0xff);
277  		p2 = tab2 + (l+1)*((w >> 16) & 0xff);
278  		p3 = tab3 + (l+1)*((w >> 24) & 0xff);
279  
280  		for (i = 0; i < l; i++)
281  			r[i] = r[i+1]^p0[i]^p1[i]^p2[i]^p3[i];
282  
283  		r[l] = p0[l]^p1[l]^p2[l]^p3[l];
284  	}
285  	memcpy(bch->ecc_buf, r, sizeof(r));
286  
287  	/* process last unaligned bytes */
288  	if (len)
289  		encode_bch_unaligned(bch, data, len, bch->ecc_buf);
290  
291  	/* store ecc parity bytes into original parity buffer */
292  	if (ecc)
293  		store_ecc8(bch, ecc, bch->ecc_buf);
294  }
295  
296  static inline int modulo(struct bch_control *bch, unsigned int v)
297  {
298  	const unsigned int n = GF_N(bch);
299  	while (v >= n) {
300  		v -= n;
301  		v = (v & n) + (v >> GF_M(bch));
302  	}
303  	return v;
304  }
305  
306  /*
307   * shorter and faster modulo function, only works when v < 2N.
308   */
309  static inline int mod_s(struct bch_control *bch, unsigned int v)
310  {
311  	const unsigned int n = GF_N(bch);
312  	return (v < n) ? v : v-n;
313  }
314  
315  static inline int deg(unsigned int poly)
316  {
317  	/* polynomial degree is the most-significant bit index */
318  	return fls(poly)-1;
319  }
320  
321  static inline int parity(unsigned int x)
322  {
323  	/*
324  	 * public domain code snippet, lifted from
325  	 * http://www-graphics.stanford.edu/~seander/bithacks.html
326  	 */
327  	x ^= x >> 1;
328  	x ^= x >> 2;
329  	x = (x & 0x11111111U) * 0x11111111U;
330  	return (x >> 28) & 1;
331  }
332  
333  /* Galois field basic operations: multiply, divide, inverse, etc. */
334  
335  static inline unsigned int gf_mul(struct bch_control *bch, unsigned int a,
336  				  unsigned int b)
337  {
338  	return (a && b) ? bch->a_pow_tab[mod_s(bch, bch->a_log_tab[a]+
339  					       bch->a_log_tab[b])] : 0;
340  }
341  
342  static inline unsigned int gf_sqr(struct bch_control *bch, unsigned int a)
343  {
344  	return a ? bch->a_pow_tab[mod_s(bch, 2*bch->a_log_tab[a])] : 0;
345  }
346  
347  static inline unsigned int gf_div(struct bch_control *bch, unsigned int a,
348  				  unsigned int b)
349  {
350  	return a ? bch->a_pow_tab[mod_s(bch, bch->a_log_tab[a]+
351  					GF_N(bch)-bch->a_log_tab[b])] : 0;
352  }
353  
354  static inline unsigned int gf_inv(struct bch_control *bch, unsigned int a)
355  {
356  	return bch->a_pow_tab[GF_N(bch)-bch->a_log_tab[a]];
357  }
358  
359  static inline unsigned int a_pow(struct bch_control *bch, int i)
360  {
361  	return bch->a_pow_tab[modulo(bch, i)];
362  }
363  
364  static inline int a_log(struct bch_control *bch, unsigned int x)
365  {
366  	return bch->a_log_tab[x];
367  }
368  
369  static inline int a_ilog(struct bch_control *bch, unsigned int x)
370  {
371  	return mod_s(bch, GF_N(bch)-bch->a_log_tab[x]);
372  }
373  
374  /*
375   * compute 2t syndromes of ecc polynomial, i.e. ecc(a^j) for j=1..2t
376   */
377  static void compute_syndromes(struct bch_control *bch, uint32_t *ecc,
378  			      unsigned int *syn)
379  {
380  	int i, j, s;
381  	unsigned int m;
382  	uint32_t poly;
383  	const int t = GF_T(bch);
384  
385  	s = bch->ecc_bits;
386  
387  	/* make sure extra bits in last ecc word are cleared */
388  	m = ((unsigned int)s) & 31;
389  	if (m)
390  		ecc[s/32] &= ~((1u << (32-m))-1);
391  	memset(syn, 0, 2*t*sizeof(*syn));
392  
393  	/* compute v(a^j) for j=1 .. 2t-1 */
394  	do {
395  		poly = *ecc++;
396  		s -= 32;
397  		while (poly) {
398  			i = deg(poly);
399  			for (j = 0; j < 2*t; j += 2)
400  				syn[j] ^= a_pow(bch, (j+1)*(i+s));
401  
402  			poly ^= (1 << i);
403  		}
404  	} while (s > 0);
405  
406  	/* v(a^(2j)) = v(a^j)^2 */
407  	for (j = 0; j < t; j++)
408  		syn[2*j+1] = gf_sqr(bch, syn[j]);
409  }
410  
411  static void gf_poly_copy(struct gf_poly *dst, struct gf_poly *src)
412  {
413  	memcpy(dst, src, GF_POLY_SZ(src->deg));
414  }
415  
416  static int compute_error_locator_polynomial(struct bch_control *bch,
417  					    const unsigned int *syn)
418  {
419  	const unsigned int t = GF_T(bch);
420  	const unsigned int n = GF_N(bch);
421  	unsigned int i, j, tmp, l, pd = 1, d = syn[0];
422  	struct gf_poly *elp = bch->elp;
423  	struct gf_poly *pelp = bch->poly_2t[0];
424  	struct gf_poly *elp_copy = bch->poly_2t[1];
425  	int k, pp = -1;
426  
427  	memset(pelp, 0, GF_POLY_SZ(2*t));
428  	memset(elp, 0, GF_POLY_SZ(2*t));
429  
430  	pelp->deg = 0;
431  	pelp->c[0] = 1;
432  	elp->deg = 0;
433  	elp->c[0] = 1;
434  
435  	/* use simplified binary Berlekamp-Massey algorithm */
436  	for (i = 0; (i < t) && (elp->deg <= t); i++) {
437  		if (d) {
438  			k = 2*i-pp;
439  			gf_poly_copy(elp_copy, elp);
440  			/* e[i+1](X) = e[i](X)+di*dp^-1*X^2(i-p)*e[p](X) */
441  			tmp = a_log(bch, d)+n-a_log(bch, pd);
442  			for (j = 0; j <= pelp->deg; j++) {
443  				if (pelp->c[j]) {
444  					l = a_log(bch, pelp->c[j]);
445  					elp->c[j+k] ^= a_pow(bch, tmp+l);
446  				}
447  			}
448  			/* compute l[i+1] = max(l[i]->c[l[p]+2*(i-p]) */
449  			tmp = pelp->deg+k;
450  			if (tmp > elp->deg) {
451  				elp->deg = tmp;
452  				gf_poly_copy(pelp, elp_copy);
453  				pd = d;
454  				pp = 2*i;
455  			}
456  		}
457  		/* di+1 = S(2i+3)+elp[i+1].1*S(2i+2)+...+elp[i+1].lS(2i+3-l) */
458  		if (i < t-1) {
459  			d = syn[2*i+2];
460  			for (j = 1; j <= elp->deg; j++)
461  				d ^= gf_mul(bch, elp->c[j], syn[2*i+2-j]);
462  		}
463  	}
464  	dbg("elp=%s\n", gf_poly_str(elp));
465  	return (elp->deg > t) ? -1 : (int)elp->deg;
466  }
467  
468  /*
469   * solve a m x m linear system in GF(2) with an expected number of solutions,
470   * and return the number of found solutions
471   */
472  static int solve_linear_system(struct bch_control *bch, unsigned int *rows,
473  			       unsigned int *sol, int nsol)
474  {
475  	const int m = GF_M(bch);
476  	unsigned int tmp, mask;
477  	int rem, c, r, p, k, param[m];
478  
479  	k = 0;
480  	mask = 1 << m;
481  
482  	/* Gaussian elimination */
483  	for (c = 0; c < m; c++) {
484  		rem = 0;
485  		p = c-k;
486  		/* find suitable row for elimination */
487  		for (r = p; r < m; r++) {
488  			if (rows[r] & mask) {
489  				if (r != p) {
490  					tmp = rows[r];
491  					rows[r] = rows[p];
492  					rows[p] = tmp;
493  				}
494  				rem = r+1;
495  				break;
496  			}
497  		}
498  		if (rem) {
499  			/* perform elimination on remaining rows */
500  			tmp = rows[p];
501  			for (r = rem; r < m; r++) {
502  				if (rows[r] & mask)
503  					rows[r] ^= tmp;
504  			}
505  		} else {
506  			/* elimination not needed, store defective row index */
507  			param[k++] = c;
508  		}
509  		mask >>= 1;
510  	}
511  	/* rewrite system, inserting fake parameter rows */
512  	if (k > 0) {
513  		p = k;
514  		for (r = m-1; r >= 0; r--) {
515  			if ((r > m-1-k) && rows[r])
516  				/* system has no solution */
517  				return 0;
518  
519  			rows[r] = (p && (r == param[p-1])) ?
520  				p--, 1u << (m-r) : rows[r-p];
521  		}
522  	}
523  
524  	if (nsol != (1 << k))
525  		/* unexpected number of solutions */
526  		return 0;
527  
528  	for (p = 0; p < nsol; p++) {
529  		/* set parameters for p-th solution */
530  		for (c = 0; c < k; c++)
531  			rows[param[c]] = (rows[param[c]] & ~1)|((p >> c) & 1);
532  
533  		/* compute unique solution */
534  		tmp = 0;
535  		for (r = m-1; r >= 0; r--) {
536  			mask = rows[r] & (tmp|1);
537  			tmp |= parity(mask) << (m-r);
538  		}
539  		sol[p] = tmp >> 1;
540  	}
541  	return nsol;
542  }
543  
544  /*
545   * this function builds and solves a linear system for finding roots of a degree
546   * 4 affine monic polynomial X^4+aX^2+bX+c over GF(2^m).
547   */
548  static int find_affine4_roots(struct bch_control *bch, unsigned int a,
549  			      unsigned int b, unsigned int c,
550  			      unsigned int *roots)
551  {
552  	int i, j, k;
553  	const int m = GF_M(bch);
554  	unsigned int mask = 0xff, t, rows[16] = {0,};
555  
556  	j = a_log(bch, b);
557  	k = a_log(bch, a);
558  	rows[0] = c;
559  
560  	/* buid linear system to solve X^4+aX^2+bX+c = 0 */
561  	for (i = 0; i < m; i++) {
562  		rows[i+1] = bch->a_pow_tab[4*i]^
563  			(a ? bch->a_pow_tab[mod_s(bch, k)] : 0)^
564  			(b ? bch->a_pow_tab[mod_s(bch, j)] : 0);
565  		j++;
566  		k += 2;
567  	}
568  	/*
569  	 * transpose 16x16 matrix before passing it to linear solver
570  	 * warning: this code assumes m < 16
571  	 */
572  	for (j = 8; j != 0; j >>= 1, mask ^= (mask << j)) {
573  		for (k = 0; k < 16; k = (k+j+1) & ~j) {
574  			t = ((rows[k] >> j)^rows[k+j]) & mask;
575  			rows[k] ^= (t << j);
576  			rows[k+j] ^= t;
577  		}
578  	}
579  	return solve_linear_system(bch, rows, roots, 4);
580  }
581  
582  /*
583   * compute root r of a degree 1 polynomial over GF(2^m) (returned as log(1/r))
584   */
585  static int find_poly_deg1_roots(struct bch_control *bch, struct gf_poly *poly,
586  				unsigned int *roots)
587  {
588  	int n = 0;
589  
590  	if (poly->c[0])
591  		/* poly[X] = bX+c with c!=0, root=c/b */
592  		roots[n++] = mod_s(bch, GF_N(bch)-bch->a_log_tab[poly->c[0]]+
593  				   bch->a_log_tab[poly->c[1]]);
594  	return n;
595  }
596  
597  /*
598   * compute roots of a degree 2 polynomial over GF(2^m)
599   */
600  static int find_poly_deg2_roots(struct bch_control *bch, struct gf_poly *poly,
601  				unsigned int *roots)
602  {
603  	int n = 0, i, l0, l1, l2;
604  	unsigned int u, v, r;
605  
606  	if (poly->c[0] && poly->c[1]) {
607  
608  		l0 = bch->a_log_tab[poly->c[0]];
609  		l1 = bch->a_log_tab[poly->c[1]];
610  		l2 = bch->a_log_tab[poly->c[2]];
611  
612  		/* using z=a/bX, transform aX^2+bX+c into z^2+z+u (u=ac/b^2) */
613  		u = a_pow(bch, l0+l2+2*(GF_N(bch)-l1));
614  		/*
615  		 * let u = sum(li.a^i) i=0..m-1; then compute r = sum(li.xi):
616  		 * r^2+r = sum(li.(xi^2+xi)) = sum(li.(a^i+Tr(a^i).a^k)) =
617  		 * u + sum(li.Tr(a^i).a^k) = u+a^k.Tr(sum(li.a^i)) = u+a^k.Tr(u)
618  		 * i.e. r and r+1 are roots iff Tr(u)=0
619  		 */
620  		r = 0;
621  		v = u;
622  		while (v) {
623  			i = deg(v);
624  			r ^= bch->xi_tab[i];
625  			v ^= (1 << i);
626  		}
627  		/* verify root */
628  		if ((gf_sqr(bch, r)^r) == u) {
629  			/* reverse z=a/bX transformation and compute log(1/r) */
630  			roots[n++] = modulo(bch, 2*GF_N(bch)-l1-
631  					    bch->a_log_tab[r]+l2);
632  			roots[n++] = modulo(bch, 2*GF_N(bch)-l1-
633  					    bch->a_log_tab[r^1]+l2);
634  		}
635  	}
636  	return n;
637  }
638  
639  /*
640   * compute roots of a degree 3 polynomial over GF(2^m)
641   */
642  static int find_poly_deg3_roots(struct bch_control *bch, struct gf_poly *poly,
643  				unsigned int *roots)
644  {
645  	int i, n = 0;
646  	unsigned int a, b, c, a2, b2, c2, e3, tmp[4];
647  
648  	if (poly->c[0]) {
649  		/* transform polynomial into monic X^3 + a2X^2 + b2X + c2 */
650  		e3 = poly->c[3];
651  		c2 = gf_div(bch, poly->c[0], e3);
652  		b2 = gf_div(bch, poly->c[1], e3);
653  		a2 = gf_div(bch, poly->c[2], e3);
654  
655  		/* (X+a2)(X^3+a2X^2+b2X+c2) = X^4+aX^2+bX+c (affine) */
656  		c = gf_mul(bch, a2, c2);           /* c = a2c2      */
657  		b = gf_mul(bch, a2, b2)^c2;        /* b = a2b2 + c2 */
658  		a = gf_sqr(bch, a2)^b2;            /* a = a2^2 + b2 */
659  
660  		/* find the 4 roots of this affine polynomial */
661  		if (find_affine4_roots(bch, a, b, c, tmp) == 4) {
662  			/* remove a2 from final list of roots */
663  			for (i = 0; i < 4; i++) {
664  				if (tmp[i] != a2)
665  					roots[n++] = a_ilog(bch, tmp[i]);
666  			}
667  		}
668  	}
669  	return n;
670  }
671  
672  /*
673   * compute roots of a degree 4 polynomial over GF(2^m)
674   */
675  static int find_poly_deg4_roots(struct bch_control *bch, struct gf_poly *poly,
676  				unsigned int *roots)
677  {
678  	int i, l, n = 0;
679  	unsigned int a, b, c, d, e = 0, f, a2, b2, c2, e4;
680  
681  	if (poly->c[0] == 0)
682  		return 0;
683  
684  	/* transform polynomial into monic X^4 + aX^3 + bX^2 + cX + d */
685  	e4 = poly->c[4];
686  	d = gf_div(bch, poly->c[0], e4);
687  	c = gf_div(bch, poly->c[1], e4);
688  	b = gf_div(bch, poly->c[2], e4);
689  	a = gf_div(bch, poly->c[3], e4);
690  
691  	/* use Y=1/X transformation to get an affine polynomial */
692  	if (a) {
693  		/* first, eliminate cX by using z=X+e with ae^2+c=0 */
694  		if (c) {
695  			/* compute e such that e^2 = c/a */
696  			f = gf_div(bch, c, a);
697  			l = a_log(bch, f);
698  			l += (l & 1) ? GF_N(bch) : 0;
699  			e = a_pow(bch, l/2);
700  			/*
701  			 * use transformation z=X+e:
702  			 * z^4+e^4 + a(z^3+ez^2+e^2z+e^3) + b(z^2+e^2) +cz+ce+d
703  			 * z^4 + az^3 + (ae+b)z^2 + (ae^2+c)z+e^4+be^2+ae^3+ce+d
704  			 * z^4 + az^3 + (ae+b)z^2 + e^4+be^2+d
705  			 * z^4 + az^3 +     b'z^2 + d'
706  			 */
707  			d = a_pow(bch, 2*l)^gf_mul(bch, b, f)^d;
708  			b = gf_mul(bch, a, e)^b;
709  		}
710  		/* now, use Y=1/X to get Y^4 + b/dY^2 + a/dY + 1/d */
711  		if (d == 0)
712  			/* assume all roots have multiplicity 1 */
713  			return 0;
714  
715  		c2 = gf_inv(bch, d);
716  		b2 = gf_div(bch, a, d);
717  		a2 = gf_div(bch, b, d);
718  	} else {
719  		/* polynomial is already affine */
720  		c2 = d;
721  		b2 = c;
722  		a2 = b;
723  	}
724  	/* find the 4 roots of this affine polynomial */
725  	if (find_affine4_roots(bch, a2, b2, c2, roots) == 4) {
726  		for (i = 0; i < 4; i++) {
727  			/* post-process roots (reverse transformations) */
728  			f = a ? gf_inv(bch, roots[i]) : roots[i];
729  			roots[i] = a_ilog(bch, f^e);
730  		}
731  		n = 4;
732  	}
733  	return n;
734  }
735  
736  /*
737   * build monic, log-based representation of a polynomial
738   */
739  static void gf_poly_logrep(struct bch_control *bch,
740  			   const struct gf_poly *a, int *rep)
741  {
742  	int i, d = a->deg, l = GF_N(bch)-a_log(bch, a->c[a->deg]);
743  
744  	/* represent 0 values with -1; warning, rep[d] is not set to 1 */
745  	for (i = 0; i < d; i++)
746  		rep[i] = a->c[i] ? mod_s(bch, a_log(bch, a->c[i])+l) : -1;
747  }
748  
749  /*
750   * compute polynomial Euclidean division remainder in GF(2^m)[X]
751   */
752  static void gf_poly_mod(struct bch_control *bch, struct gf_poly *a,
753  			const struct gf_poly *b, int *rep)
754  {
755  	int la, p, m;
756  	unsigned int i, j, *c = a->c;
757  	const unsigned int d = b->deg;
758  
759  	if (a->deg < d)
760  		return;
761  
762  	/* reuse or compute log representation of denominator */
763  	if (!rep) {
764  		rep = bch->cache;
765  		gf_poly_logrep(bch, b, rep);
766  	}
767  
768  	for (j = a->deg; j >= d; j--) {
769  		if (c[j]) {
770  			la = a_log(bch, c[j]);
771  			p = j-d;
772  			for (i = 0; i < d; i++, p++) {
773  				m = rep[i];
774  				if (m >= 0)
775  					c[p] ^= bch->a_pow_tab[mod_s(bch,
776  								     m+la)];
777  			}
778  		}
779  	}
780  	a->deg = d-1;
781  	while (!c[a->deg] && a->deg)
782  		a->deg--;
783  }
784  
785  /*
786   * compute polynomial Euclidean division quotient in GF(2^m)[X]
787   */
788  static void gf_poly_div(struct bch_control *bch, struct gf_poly *a,
789  			const struct gf_poly *b, struct gf_poly *q)
790  {
791  	if (a->deg >= b->deg) {
792  		q->deg = a->deg-b->deg;
793  		/* compute a mod b (modifies a) */
794  		gf_poly_mod(bch, a, b, NULL);
795  		/* quotient is stored in upper part of polynomial a */
796  		memcpy(q->c, &a->c[b->deg], (1+q->deg)*sizeof(unsigned int));
797  	} else {
798  		q->deg = 0;
799  		q->c[0] = 0;
800  	}
801  }
802  
803  /*
804   * compute polynomial GCD (Greatest Common Divisor) in GF(2^m)[X]
805   */
806  static struct gf_poly *gf_poly_gcd(struct bch_control *bch, struct gf_poly *a,
807  				   struct gf_poly *b)
808  {
809  	struct gf_poly *tmp;
810  
811  	dbg("gcd(%s,%s)=", gf_poly_str(a), gf_poly_str(b));
812  
813  	if (a->deg < b->deg) {
814  		tmp = b;
815  		b = a;
816  		a = tmp;
817  	}
818  
819  	while (b->deg > 0) {
820  		gf_poly_mod(bch, a, b, NULL);
821  		tmp = b;
822  		b = a;
823  		a = tmp;
824  	}
825  
826  	dbg("%s\n", gf_poly_str(a));
827  
828  	return a;
829  }
830  
831  /*
832   * Given a polynomial f and an integer k, compute Tr(a^kX) mod f
833   * This is used in Berlekamp Trace algorithm for splitting polynomials
834   */
835  static void compute_trace_bk_mod(struct bch_control *bch, int k,
836  				 const struct gf_poly *f, struct gf_poly *z,
837  				 struct gf_poly *out)
838  {
839  	const int m = GF_M(bch);
840  	int i, j;
841  
842  	/* z contains z^2j mod f */
843  	z->deg = 1;
844  	z->c[0] = 0;
845  	z->c[1] = bch->a_pow_tab[k];
846  
847  	out->deg = 0;
848  	memset(out, 0, GF_POLY_SZ(f->deg));
849  
850  	/* compute f log representation only once */
851  	gf_poly_logrep(bch, f, bch->cache);
852  
853  	for (i = 0; i < m; i++) {
854  		/* add a^(k*2^i)(z^(2^i) mod f) and compute (z^(2^i) mod f)^2 */
855  		for (j = z->deg; j >= 0; j--) {
856  			out->c[j] ^= z->c[j];
857  			z->c[2*j] = gf_sqr(bch, z->c[j]);
858  			z->c[2*j+1] = 0;
859  		}
860  		if (z->deg > out->deg)
861  			out->deg = z->deg;
862  
863  		if (i < m-1) {
864  			z->deg *= 2;
865  			/* z^(2(i+1)) mod f = (z^(2^i) mod f)^2 mod f */
866  			gf_poly_mod(bch, z, f, bch->cache);
867  		}
868  	}
869  	while (!out->c[out->deg] && out->deg)
870  		out->deg--;
871  
872  	dbg("Tr(a^%d.X) mod f = %s\n", k, gf_poly_str(out));
873  }
874  
875  /*
876   * factor a polynomial using Berlekamp Trace algorithm (BTA)
877   */
878  static void factor_polynomial(struct bch_control *bch, int k, struct gf_poly *f,
879  			      struct gf_poly **g, struct gf_poly **h)
880  {
881  	struct gf_poly *f2 = bch->poly_2t[0];
882  	struct gf_poly *q  = bch->poly_2t[1];
883  	struct gf_poly *tk = bch->poly_2t[2];
884  	struct gf_poly *z  = bch->poly_2t[3];
885  	struct gf_poly *gcd;
886  
887  	dbg("factoring %s...\n", gf_poly_str(f));
888  
889  	*g = f;
890  	*h = NULL;
891  
892  	/* tk = Tr(a^k.X) mod f */
893  	compute_trace_bk_mod(bch, k, f, z, tk);
894  
895  	if (tk->deg > 0) {
896  		/* compute g = gcd(f, tk) (destructive operation) */
897  		gf_poly_copy(f2, f);
898  		gcd = gf_poly_gcd(bch, f2, tk);
899  		if (gcd->deg < f->deg) {
900  			/* compute h=f/gcd(f,tk); this will modify f and q */
901  			gf_poly_div(bch, f, gcd, q);
902  			/* store g and h in-place (clobbering f) */
903  			*h = &((struct gf_poly_deg1 *)f)[gcd->deg].poly;
904  			gf_poly_copy(*g, gcd);
905  			gf_poly_copy(*h, q);
906  		}
907  	}
908  }
909  
910  /*
911   * find roots of a polynomial, using BTZ algorithm; see the beginning of this
912   * file for details
913   */
914  static int find_poly_roots(struct bch_control *bch, unsigned int k,
915  			   struct gf_poly *poly, unsigned int *roots)
916  {
917  	int cnt;
918  	struct gf_poly *f1, *f2;
919  
920  	switch (poly->deg) {
921  		/* handle low degree polynomials with ad hoc techniques */
922  	case 1:
923  		cnt = find_poly_deg1_roots(bch, poly, roots);
924  		break;
925  	case 2:
926  		cnt = find_poly_deg2_roots(bch, poly, roots);
927  		break;
928  	case 3:
929  		cnt = find_poly_deg3_roots(bch, poly, roots);
930  		break;
931  	case 4:
932  		cnt = find_poly_deg4_roots(bch, poly, roots);
933  		break;
934  	default:
935  		/* factor polynomial using Berlekamp Trace Algorithm (BTA) */
936  		cnt = 0;
937  		if (poly->deg && (k <= GF_M(bch))) {
938  			factor_polynomial(bch, k, poly, &f1, &f2);
939  			if (f1)
940  				cnt += find_poly_roots(bch, k+1, f1, roots);
941  			if (f2)
942  				cnt += find_poly_roots(bch, k+1, f2, roots+cnt);
943  		}
944  		break;
945  	}
946  	return cnt;
947  }
948  
949  #if defined(USE_CHIEN_SEARCH)
950  /*
951   * exhaustive root search (Chien) implementation - not used, included only for
952   * reference/comparison tests
953   */
954  static int chien_search(struct bch_control *bch, unsigned int len,
955  			struct gf_poly *p, unsigned int *roots)
956  {
957  	int m;
958  	unsigned int i, j, syn, syn0, count = 0;
959  	const unsigned int k = 8*len+bch->ecc_bits;
960  
961  	/* use a log-based representation of polynomial */
962  	gf_poly_logrep(bch, p, bch->cache);
963  	bch->cache[p->deg] = 0;
964  	syn0 = gf_div(bch, p->c[0], p->c[p->deg]);
965  
966  	for (i = GF_N(bch)-k+1; i <= GF_N(bch); i++) {
967  		/* compute elp(a^i) */
968  		for (j = 1, syn = syn0; j <= p->deg; j++) {
969  			m = bch->cache[j];
970  			if (m >= 0)
971  				syn ^= a_pow(bch, m+j*i);
972  		}
973  		if (syn == 0) {
974  			roots[count++] = GF_N(bch)-i;
975  			if (count == p->deg)
976  				break;
977  		}
978  	}
979  	return (count == p->deg) ? count : 0;
980  }
981  #define find_poly_roots(_p, _k, _elp, _loc) chien_search(_p, len, _elp, _loc)
982  #endif /* USE_CHIEN_SEARCH */
983  
984  /**
985   * decode_bch - decode received codeword and find bit error locations
986   * @bch:      BCH control structure
987   * @data:     received data, ignored if @calc_ecc is provided
988   * @len:      data length in bytes, must always be provided
989   * @recv_ecc: received ecc, if NULL then assume it was XORed in @calc_ecc
990   * @calc_ecc: calculated ecc, if NULL then calc_ecc is computed from @data
991   * @syn:      hw computed syndrome data (if NULL, syndrome is calculated)
992   * @errloc:   output array of error locations
993   *
994   * Returns:
995   *  The number of errors found, or -EBADMSG if decoding failed, or -EINVAL if
996   *  invalid parameters were provided
997   *
998   * Depending on the available hw BCH support and the need to compute @calc_ecc
999   * separately (using encode_bch()), this function should be called with one of
1000   * the following parameter configurations -
1001   *
1002   * by providing @data and @recv_ecc only:
1003   *   decode_bch(@bch, @data, @len, @recv_ecc, NULL, NULL, @errloc)
1004   *
1005   * by providing @recv_ecc and @calc_ecc:
1006   *   decode_bch(@bch, NULL, @len, @recv_ecc, @calc_ecc, NULL, @errloc)
1007   *
1008   * by providing ecc = recv_ecc XOR calc_ecc:
1009   *   decode_bch(@bch, NULL, @len, NULL, ecc, NULL, @errloc)
1010   *
1011   * by providing syndrome results @syn:
1012   *   decode_bch(@bch, NULL, @len, NULL, NULL, @syn, @errloc)
1013   *
1014   * Once decode_bch() has successfully returned with a positive value, error
1015   * locations returned in array @errloc should be interpreted as follows -
1016   *
1017   * if (errloc[n] >= 8*len), then n-th error is located in ecc (no need for
1018   * data correction)
1019   *
1020   * if (errloc[n] < 8*len), then n-th error is located in data and can be
1021   * corrected with statement data[errloc[n]/8] ^= 1 << (errloc[n] % 8);
1022   *
1023   * Note that this function does not perform any data correction by itself, it
1024   * merely indicates error locations.
1025   */
1026  int decode_bch(struct bch_control *bch, const uint8_t *data, unsigned int len,
1027  	       const uint8_t *recv_ecc, const uint8_t *calc_ecc,
1028  	       const unsigned int *syn, unsigned int *errloc)
1029  {
1030  	const unsigned int ecc_words = BCH_ECC_WORDS(bch);
1031  	unsigned int nbits;
1032  	int i, err, nroots;
1033  	uint32_t sum;
1034  
1035  	/* sanity check: make sure data length can be handled */
1036  	if (8*len > (bch->n-bch->ecc_bits))
1037  		return -EINVAL;
1038  
1039  	/* if caller does not provide syndromes, compute them */
1040  	if (!syn) {
1041  		if (!calc_ecc) {
1042  			/* compute received data ecc into an internal buffer */
1043  			if (!data || !recv_ecc)
1044  				return -EINVAL;
1045  			encode_bch(bch, data, len, NULL);
1046  		} else {
1047  			/* load provided calculated ecc */
1048  			load_ecc8(bch, bch->ecc_buf, calc_ecc);
1049  		}
1050  		/* load received ecc or assume it was XORed in calc_ecc */
1051  		if (recv_ecc) {
1052  			load_ecc8(bch, bch->ecc_buf2, recv_ecc);
1053  			/* XOR received and calculated ecc */
1054  			for (i = 0, sum = 0; i < (int)ecc_words; i++) {
1055  				bch->ecc_buf[i] ^= bch->ecc_buf2[i];
1056  				sum |= bch->ecc_buf[i];
1057  			}
1058  			if (!sum)
1059  				/* no error found */
1060  				return 0;
1061  		}
1062  		compute_syndromes(bch, bch->ecc_buf, bch->syn);
1063  		syn = bch->syn;
1064  	}
1065  
1066  	err = compute_error_locator_polynomial(bch, syn);
1067  	if (err > 0) {
1068  		nroots = find_poly_roots(bch, 1, bch->elp, errloc);
1069  		if (err != nroots)
1070  			err = -1;
1071  	}
1072  	if (err > 0) {
1073  		/* post-process raw error locations for easier correction */
1074  		nbits = (len*8)+bch->ecc_bits;
1075  		for (i = 0; i < err; i++) {
1076  			if (errloc[i] >= nbits) {
1077  				err = -1;
1078  				break;
1079  			}
1080  			errloc[i] = nbits-1-errloc[i];
1081  			errloc[i] = (errloc[i] & ~7)|(7-(errloc[i] & 7));
1082  		}
1083  	}
1084  	return (err >= 0) ? err : -EBADMSG;
1085  }
1086  
1087  /*
1088   * generate Galois field lookup tables
1089   */
1090  static int build_gf_tables(struct bch_control *bch, unsigned int poly)
1091  {
1092  	unsigned int i, x = 1;
1093  	const unsigned int k = 1 << deg(poly);
1094  
1095  	/* primitive polynomial must be of degree m */
1096  	if (k != (1u << GF_M(bch)))
1097  		return -1;
1098  
1099  	for (i = 0; i < GF_N(bch); i++) {
1100  		bch->a_pow_tab[i] = x;
1101  		bch->a_log_tab[x] = i;
1102  		if (i && (x == 1))
1103  			/* polynomial is not primitive (a^i=1 with 0<i<2^m-1) */
1104  			return -1;
1105  		x <<= 1;
1106  		if (x & k)
1107  			x ^= poly;
1108  	}
1109  	bch->a_pow_tab[GF_N(bch)] = 1;
1110  	bch->a_log_tab[0] = 0;
1111  
1112  	return 0;
1113  }
1114  
1115  /*
1116   * compute generator polynomial remainder tables for fast encoding
1117   */
1118  static void build_mod8_tables(struct bch_control *bch, const uint32_t *g)
1119  {
1120  	int i, j, b, d;
1121  	uint32_t data, hi, lo, *tab;
1122  	const int l = BCH_ECC_WORDS(bch);
1123  	const int plen = DIV_ROUND_UP(bch->ecc_bits+1, 32);
1124  	const int ecclen = DIV_ROUND_UP(bch->ecc_bits, 32);
1125  
1126  	memset(bch->mod8_tab, 0, 4*256*l*sizeof(*bch->mod8_tab));
1127  
1128  	for (i = 0; i < 256; i++) {
1129  		/* p(X)=i is a small polynomial of weight <= 8 */
1130  		for (b = 0; b < 4; b++) {
1131  			/* we want to compute (p(X).X^(8*b+deg(g))) mod g(X) */
1132  			tab = bch->mod8_tab + (b*256+i)*l;
1133  			data = i << (8*b);
1134  			while (data) {
1135  				d = deg(data);
1136  				/* subtract X^d.g(X) from p(X).X^(8*b+deg(g)) */
1137  				data ^= g[0] >> (31-d);
1138  				for (j = 0; j < ecclen; j++) {
1139  					hi = (d < 31) ? g[j] << (d+1) : 0;
1140  					lo = (j+1 < plen) ?
1141  						g[j+1] >> (31-d) : 0;
1142  					tab[j] ^= hi|lo;
1143  				}
1144  			}
1145  		}
1146  	}
1147  }
1148  
1149  /*
1150   * build a base for factoring degree 2 polynomials
1151   */
1152  static int build_deg2_base(struct bch_control *bch)
1153  {
1154  	const int m = GF_M(bch);
1155  	int i, j, r;
1156  	unsigned int sum, x, y, remaining, ak = 0, xi[m];
1157  
1158  	/* find k s.t. Tr(a^k) = 1 and 0 <= k < m */
1159  	for (i = 0; i < m; i++) {
1160  		for (j = 0, sum = 0; j < m; j++)
1161  			sum ^= a_pow(bch, i*(1 << j));
1162  
1163  		if (sum) {
1164  			ak = bch->a_pow_tab[i];
1165  			break;
1166  		}
1167  	}
1168  	/* find xi, i=0..m-1 such that xi^2+xi = a^i+Tr(a^i).a^k */
1169  	remaining = m;
1170  	memset(xi, 0, sizeof(xi));
1171  
1172  	for (x = 0; (x <= GF_N(bch)) && remaining; x++) {
1173  		y = gf_sqr(bch, x)^x;
1174  		for (i = 0; i < 2; i++) {
1175  			r = a_log(bch, y);
1176  			if (y && (r < m) && !xi[r]) {
1177  				bch->xi_tab[r] = x;
1178  				xi[r] = 1;
1179  				remaining--;
1180  				dbg("x%d = %x\n", r, x);
1181  				break;
1182  			}
1183  			y ^= ak;
1184  		}
1185  	}
1186  	/* should not happen but check anyway */
1187  	return remaining ? -1 : 0;
1188  }
1189  
1190  static void *bch_alloc(size_t size, int *err)
1191  {
1192  	void *ptr;
1193  
1194  	ptr = kmalloc(size, GFP_KERNEL);
1195  	if (ptr == NULL)
1196  		*err = 1;
1197  	return ptr;
1198  }
1199  
1200  /*
1201   * compute generator polynomial for given (m,t) parameters.
1202   */
1203  static uint32_t *compute_generator_polynomial(struct bch_control *bch)
1204  {
1205  	const unsigned int m = GF_M(bch);
1206  	const unsigned int t = GF_T(bch);
1207  	int n, err = 0;
1208  	unsigned int i, j, nbits, r, word, *roots;
1209  	struct gf_poly *g;
1210  	uint32_t *genpoly;
1211  
1212  	g = bch_alloc(GF_POLY_SZ(m*t), &err);
1213  	roots = bch_alloc((bch->n+1)*sizeof(*roots), &err);
1214  	genpoly = bch_alloc(DIV_ROUND_UP(m*t+1, 32)*sizeof(*genpoly), &err);
1215  
1216  	if (err) {
1217  		kfree(genpoly);
1218  		genpoly = NULL;
1219  		goto finish;
1220  	}
1221  
1222  	/* enumerate all roots of g(X) */
1223  	memset(roots , 0, (bch->n+1)*sizeof(*roots));
1224  	for (i = 0; i < t; i++) {
1225  		for (j = 0, r = 2*i+1; j < m; j++) {
1226  			roots[r] = 1;
1227  			r = mod_s(bch, 2*r);
1228  		}
1229  	}
1230  	/* build generator polynomial g(X) */
1231  	g->deg = 0;
1232  	g->c[0] = 1;
1233  	for (i = 0; i < GF_N(bch); i++) {
1234  		if (roots[i]) {
1235  			/* multiply g(X) by (X+root) */
1236  			r = bch->a_pow_tab[i];
1237  			g->c[g->deg+1] = 1;
1238  			for (j = g->deg; j > 0; j--)
1239  				g->c[j] = gf_mul(bch, g->c[j], r)^g->c[j-1];
1240  
1241  			g->c[0] = gf_mul(bch, g->c[0], r);
1242  			g->deg++;
1243  		}
1244  	}
1245  	/* store left-justified binary representation of g(X) */
1246  	n = g->deg+1;
1247  	i = 0;
1248  
1249  	while (n > 0) {
1250  		nbits = (n > 32) ? 32 : n;
1251  		for (j = 0, word = 0; j < nbits; j++) {
1252  			if (g->c[n-1-j])
1253  				word |= 1u << (31-j);
1254  		}
1255  		genpoly[i++] = word;
1256  		n -= nbits;
1257  	}
1258  	bch->ecc_bits = g->deg;
1259  
1260  finish:
1261  	kfree(g);
1262  	kfree(roots);
1263  
1264  	return genpoly;
1265  }
1266  
1267  /**
1268   * init_bch - initialize a BCH encoder/decoder
1269   * @m:          Galois field order, should be in the range 5-15
1270   * @t:          maximum error correction capability, in bits
1271   * @prim_poly:  user-provided primitive polynomial (or 0 to use default)
1272   *
1273   * Returns:
1274   *  a newly allocated BCH control structure if successful, NULL otherwise
1275   *
1276   * This initialization can take some time, as lookup tables are built for fast
1277   * encoding/decoding; make sure not to call this function from a time critical
1278   * path. Usually, init_bch() should be called on module/driver init and
1279   * free_bch() should be called to release memory on exit.
1280   *
1281   * You may provide your own primitive polynomial of degree @m in argument
1282   * @prim_poly, or let init_bch() use its default polynomial.
1283   *
1284   * Once init_bch() has successfully returned a pointer to a newly allocated
1285   * BCH control structure, ecc length in bytes is given by member @ecc_bytes of
1286   * the structure.
1287   */
1288  struct bch_control *init_bch(int m, int t, unsigned int prim_poly)
1289  {
1290  	int err = 0;
1291  	unsigned int i, words;
1292  	uint32_t *genpoly;
1293  	struct bch_control *bch = NULL;
1294  
1295  	const int min_m = 5;
1296  	const int max_m = 15;
1297  
1298  	/* default primitive polynomials */
1299  	static const unsigned int prim_poly_tab[] = {
1300  		0x25, 0x43, 0x83, 0x11d, 0x211, 0x409, 0x805, 0x1053, 0x201b,
1301  		0x402b, 0x8003,
1302  	};
1303  
1304  #if defined(CONFIG_BCH_CONST_PARAMS)
1305  	if ((m != (CONFIG_BCH_CONST_M)) || (t != (CONFIG_BCH_CONST_T))) {
1306  		printk(KERN_ERR "bch encoder/decoder was configured to support "
1307  		       "parameters m=%d, t=%d only!\n",
1308  		       CONFIG_BCH_CONST_M, CONFIG_BCH_CONST_T);
1309  		goto fail;
1310  	}
1311  #endif
1312  	if ((m < min_m) || (m > max_m))
1313  		/*
1314  		 * values of m greater than 15 are not currently supported;
1315  		 * supporting m > 15 would require changing table base type
1316  		 * (uint16_t) and a small patch in matrix transposition
1317  		 */
1318  		goto fail;
1319  
1320  	/* sanity checks */
1321  	if ((t < 1) || (m*t >= ((1 << m)-1)))
1322  		/* invalid t value */
1323  		goto fail;
1324  
1325  	/* select a primitive polynomial for generating GF(2^m) */
1326  	if (prim_poly == 0)
1327  		prim_poly = prim_poly_tab[m-min_m];
1328  
1329  	bch = kzalloc(sizeof(*bch), GFP_KERNEL);
1330  	if (bch == NULL)
1331  		goto fail;
1332  
1333  	bch->m = m;
1334  	bch->t = t;
1335  	bch->n = (1 << m)-1;
1336  	words  = DIV_ROUND_UP(m*t, 32);
1337  	bch->ecc_bytes = DIV_ROUND_UP(m*t, 8);
1338  	bch->a_pow_tab = bch_alloc((1+bch->n)*sizeof(*bch->a_pow_tab), &err);
1339  	bch->a_log_tab = bch_alloc((1+bch->n)*sizeof(*bch->a_log_tab), &err);
1340  	bch->mod8_tab  = bch_alloc(words*1024*sizeof(*bch->mod8_tab), &err);
1341  	bch->ecc_buf   = bch_alloc(words*sizeof(*bch->ecc_buf), &err);
1342  	bch->ecc_buf2  = bch_alloc(words*sizeof(*bch->ecc_buf2), &err);
1343  	bch->xi_tab    = bch_alloc(m*sizeof(*bch->xi_tab), &err);
1344  	bch->syn       = bch_alloc(2*t*sizeof(*bch->syn), &err);
1345  	bch->cache     = bch_alloc(2*t*sizeof(*bch->cache), &err);
1346  	bch->elp       = bch_alloc((t+1)*sizeof(struct gf_poly_deg1), &err);
1347  
1348  	for (i = 0; i < ARRAY_SIZE(bch->poly_2t); i++)
1349  		bch->poly_2t[i] = bch_alloc(GF_POLY_SZ(2*t), &err);
1350  
1351  	if (err)
1352  		goto fail;
1353  
1354  	err = build_gf_tables(bch, prim_poly);
1355  	if (err)
1356  		goto fail;
1357  
1358  	/* use generator polynomial for computing encoding tables */
1359  	genpoly = compute_generator_polynomial(bch);
1360  	if (genpoly == NULL)
1361  		goto fail;
1362  
1363  	build_mod8_tables(bch, genpoly);
1364  	kfree(genpoly);
1365  
1366  	err = build_deg2_base(bch);
1367  	if (err)
1368  		goto fail;
1369  
1370  	return bch;
1371  
1372  fail:
1373  	free_bch(bch);
1374  	return NULL;
1375  }
1376  
1377  /**
1378   *  free_bch - free the BCH control structure
1379   *  @bch:    BCH control structure to release
1380   */
1381  void free_bch(struct bch_control *bch)
1382  {
1383  	unsigned int i;
1384  
1385  	if (bch) {
1386  		kfree(bch->a_pow_tab);
1387  		kfree(bch->a_log_tab);
1388  		kfree(bch->mod8_tab);
1389  		kfree(bch->ecc_buf);
1390  		kfree(bch->ecc_buf2);
1391  		kfree(bch->xi_tab);
1392  		kfree(bch->syn);
1393  		kfree(bch->cache);
1394  		kfree(bch->elp);
1395  
1396  		for (i = 0; i < ARRAY_SIZE(bch->poly_2t); i++)
1397  			kfree(bch->poly_2t[i]);
1398  
1399  		kfree(bch);
1400  	}
1401  }
1402