aboutsummaryrefslogtreecommitdiff
path: root/lib/bch.c
blob: ec53483774b5babe49437fa79537e4d80a91b13c (plain)
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
79
80
81
82
83
84
85
86
87
88
89
90
91
92
93
94
95
96
97
98
99
100
101
102
103
104
105
106
107
108
109
110
111
112
113
114
115
116
117
118
119
120
121
122
123
124
125
126
127
128
129
130
131
132
133
134
135
136
137
138
139
140
141
142
143
144
145
146
147
148
149
150
151
152
153
154
155
156
157
158
159
160
161
162
163
164
165
166
167
168
169
170
171
172
173
174
175
176
177
178
179
180
181
182
183
184
185
186
187
188
189
190
191
192
193
194
195
196
197
198
199
200
201
202
203
204
205
206
207
208
209
210
211
212
213
214
215
216
217
218
219
220
221
222
223
224
225
226
227
228
229
230
231
232
233
234
235
236
237
238
239
240
241
242
243
244
245
246
247
248
249
250
251
252
253
254
255
256
257
258
259
260
261
262
263
264
265
266
267
268
269
270
271
272
273
274
275
276
277
278
279
280
281
282
283
284
285
286
287
288
289
290
291
292
293
294
295
296
297
298
299
300
301
302
303
304
305
306
307
308
309
310
311
312
313
314
315
316
317
318
319
320
321
322
323
324
325
326
327
328
329
330
331
332
333
334
335
336
337
338
339
340
341
342
343
344
345
346
347
348
349
350
351
352
353
354
355
356
357
358
359
360
361
362
363
364
365
366
367
368
369
370
371
372
373
374
375
376
377
378
379
380
381
382
383
384
385
386
387
388
389
390
391
392
393
394
395
396
397
398
399
400
401
402
403
404
405
406
407
408
409
410
411
412
413
414
415
416
417
418
419
420
421
422
423
424
425
426
427
428
429
430
431
432
433
434
435
436
437
438
439
440
441
442
443
444
445
446
447
448
449
450
451
452
453
454
455
456
457
458
459
460
461
462
463
464
465
466
467
468
469
470
471
472
473
474
475
476
477
478
479
480
481
482
483
484
485
486
487
488
489
490
491
492
493
494
495
496
497
498
499
500
501
502
503
504
505
506
507
508
509
510
511
512
513
514
515
516
517
518
519
520
521
522
523
524
525
526
527
528
529
530
531
532
533
534
535
536
537
538
539
540
541
542
543
544
545
546
547
548
549
550
551
552
553
554
555
556
557
558
559
560
561
562
563
564
565
566
567
568
569
570
571
572
573
574
575
576
577
578
579
580
581
582
583
584
585
586
587
588
589
590
591
592
593
594
595
596
597
598
599
600
601
602
603
604
605
606
607
608
609
610
611
612
613
614
615
616
617
618
619
620
621
622
623
624
625
626
627
628
629
630
631
632
633
634
635
636
637
638
639
640
641
642
643
644
645
646
647
648
649
650
651
652
653
654
655
656
657
658
659
660
661
662
663
664
665
666
667
668
669
670
671
672
673
674
675
676
677
678
679
680
681
682
683
684
685
686
687
688
689
690
691
692
693
694
695
696
697
698
699
700
701
702
703
704
705
706
707
708
709
710
711
712
713
714
715
716
717
718
719
720
721
722
723
724
725
726
727
728
729
730
731
732
733
734
735
736
737
738
739
740
741
742
743
744
745
746
747
748
749
750
751
752
753
754
755
756
757
758
759
760
761
762
763
764
765
766
767
768
769
770
771
772
773
774
775
776
777
778
779
780
781
782
783
784
785
786
787
788
789
790
791
792
793
794
795
796
797
798
799
800
801
802
803
804
805
806
807
808
809
810
811
812
813
814
815
816
817
818
819
820
821
822
823
824
825
826
827
828
829
830
831
832
833
834
835
836
837
838
839
840
841
842
843
844
845
846
847
848
849
850
851
852
853
854
855
856
857
858
859
860
861
862
863
864
865
866
867
868
869
870
871
872
873
874
875
876
877
878
879
880
881
882
883
884
885
886
887
888
889
890
891
892
893
894
895
896
897
898
899
900
901
902
903
904
905
906
907
908
909
910
911
912
913
914
915
916
917
918
919
920
921
922
923
924
925
926
927
928
929
930
931
932
933
934
935
936
937
938
939
940
941
942
943
944
945
946
947
948
949
950
951
952
953
954
955
956
957
958
959
960
961
962
963
964
965
966
967
968
969
970
971
972
973
974
975
976
977
978
979
980
981
982
983
984
985
986
987
988
989
990
991
992
993
994
995
996
997
998
999
1000
1001
1002
1003
1004
1005
1006
1007
1008
1009
1010
1011
1012
1013
1014
1015
1016
1017
1018
1019
1020
1021
1022
1023
1024
1025
1026
1027
1028
1029
1030
1031
1032
1033
1034
1035
1036
1037
1038
1039
1040
1041
1042
1043
1044
1045
1046
1047
1048
1049
1050
1051
1052
1053
1054
1055
1056
1057
1058
1059
1060
1061
1062
1063
1064
1065
1066
1067
1068
1069
1070
1071
1072
1073
1074
1075
1076
1077
1078
1079
1080
1081
1082
1083
1084
1085
1086
1087
1088
1089
1090
1091
1092
1093
1094
1095
1096
1097
1098
1099
1100
1101
1102
1103
1104
1105
1106
1107
1108
1109
1110
1111
1112
1113
1114
1115
1116
1117
1118
1119
1120
1121
1122
1123
1124
1125
1126
1127
1128
1129
1130
1131
1132
1133
1134
1135
1136
1137
1138
1139
1140
1141
1142
1143
1144
1145
1146
1147
1148
1149
1150
1151
1152
1153
1154
1155
1156
1157
1158
1159
1160
1161
1162
1163
1164
1165
1166
1167
1168
1169
1170
1171
1172
1173
1174
1175
1176
1177
1178
1179
1180
1181
1182
1183
1184
1185
1186
1187
1188
1189
1190
1191
1192
1193
1194
1195
1196
1197
1198
1199
1200
1201
1202
1203
1204
1205
1206
1207
1208
1209
1210
1211
1212
1213
1214
1215
1216
1217
1218
1219
1220
1221
1222
1223
1224
1225
1226
1227
1228
1229
1230
1231
1232
1233
1234
1235
1236
1237
1238
1239
1240
1241
1242
1243
1244
1245
1246
1247
1248
1249
1250
1251
1252
1253
1254
1255
1256
1257
1258
1259
1260
1261
1262
1263
1264
1265
1266
1267
1268
1269
1270
1271
1272
1273
1274
1275
1276
1277
1278
1279
1280
1281
1282
1283
1284
1285
1286
1287
1288
1289
1290
1291
1292
1293
1294
1295
1296
1297
1298
1299
1300
1301
1302
1303
1304
1305
1306
1307
1308
1309
1310
1311
1312
1313
1314
1315
1316
1317
1318
1319
1320
1321
1322
1323
1324
1325
1326
1327
1328
1329
1330
1331
1332
1333
1334
1335
1336
1337
1338
1339
1340
1341
1342
1343
1344
1345
1346
1347
1348
1349
1350
1351
1352
1353
1354
1355
1356
1357
1358
1359
1360
1361
1362
1363
1364
1365
1366
1367
1368
1369
1370
1371
1372
1373
1374
1375
1376
1377
1378
1379
1380
1381
1382
1383
1384
1385
1386
1387
1388
1389
1390
1391
1392
1393
1394
1395
/*
 * Generic binary BCH encoding/decoding library
 *
 * SPDX-License-Identifier:	GPL-2.0
 *
 * Copyright © 2011 Parrot S.A.
 *
 * Author: Ivan Djelic <ivan.djelic@parrot.com>
 *
 * Description:
 *
 * This library provides runtime configurable encoding/decoding of binary
 * Bose-Chaudhuri-Hocquenghem (BCH) codes.
 *
 * Call init_bch to get a pointer to a newly allocated bch_control structure for
 * the given m (Galois field order), t (error correction capability) and
 * (optional) primitive polynomial parameters.
 *
 * Call encode_bch to compute and store ecc parity bytes to a given buffer.
 * Call decode_bch to detect and locate errors in received data.
 *
 * On systems supporting hw BCH features, intermediate results may be provided
 * to decode_bch in order to skip certain steps. See decode_bch() documentation
 * for details.
 *
 * Option CONFIG_BCH_CONST_PARAMS can be used to force fixed values of
 * parameters m and t; thus allowing extra compiler optimizations and providing
 * better (up to 2x) encoding performance. Using this option makes sense when
 * (m,t) are fixed and known in advance, e.g. when using BCH error correction
 * on a particular NAND flash device.
 *
 * Algorithmic details:
 *
 * Encoding is performed by processing 32 input bits in parallel, using 4
 * remainder lookup tables.
 *
 * The final stage of decoding involves the following internal steps:
 * a. Syndrome computation
 * b. Error locator polynomial computation using Berlekamp-Massey algorithm
 * c. Error locator root finding (by far the most expensive step)
 *
 * In this implementation, step c is not performed using the usual Chien search.
 * Instead, an alternative approach described in [1] is used. It consists in
 * factoring the error locator polynomial using the Berlekamp Trace algorithm
 * (BTA) down to a certain degree (4), after which ad hoc low-degree polynomial
 * solving techniques [2] are used. The resulting algorithm, called BTZ, yields
 * much better performance than Chien search for usual (m,t) values (typically
 * m >= 13, t < 32, see [1]).
 *
 * [1] B. Biswas, V. Herbert. Efficient root finding of polynomials over fields
 * of characteristic 2, in: Western European Workshop on Research in Cryptology
 * - WEWoRC 2009, Graz, Austria, LNCS, Springer, July 2009, to appear.
 * [2] [Zin96] V.A. Zinoviev. On the solution of equations of degree 10 over
 * finite fields GF(2^q). In Rapport de recherche INRIA no 2829, 1996.
 */

#ifndef USE_HOSTCC
#include <common.h>
#include <ubi_uboot.h>

#include <linux/bitops.h>
#else
#include <errno.h>
#include <endian.h>
#include <stdint.h>
#include <stdlib.h>
#include <string.h>

#undef cpu_to_be32
#define cpu_to_be32 htobe32
#define DIV_ROUND_UP(n,d) (((n) + (d) - 1) / (d))
#define kmalloc(size, flags)	malloc(size)
#define kzalloc(size, flags)	calloc(1, size)
#define kfree free
#define ARRAY_SIZE(arr) (sizeof(arr) / sizeof((arr)[0]))
#endif

#include <asm/byteorder.h>
#include <linux/bch.h>

#if defined(CONFIG_BCH_CONST_PARAMS)
#define GF_M(_p)               (CONFIG_BCH_CONST_M)
#define GF_T(_p)               (CONFIG_BCH_CONST_T)
#define GF_N(_p)               ((1 << (CONFIG_BCH_CONST_M))-1)
#else
#define GF_M(_p)               ((_p)->m)
#define GF_T(_p)               ((_p)->t)
#define GF_N(_p)               ((_p)->n)
#endif

#define BCH_ECC_WORDS(_p)      DIV_ROUND_UP(GF_M(_p)*GF_T(_p), 32)
#define BCH_ECC_BYTES(_p)      DIV_ROUND_UP(GF_M(_p)*GF_T(_p), 8)

#ifndef dbg
#define dbg(_fmt, args...)     do {} while (0)
#endif

/*
 * represent a polynomial over GF(2^m)
 */
struct gf_poly {
	unsigned int deg;    /* polynomial degree */
	unsigned int c[0];   /* polynomial terms */
};

/* given its degree, compute a polynomial size in bytes */
#define GF_POLY_SZ(_d) (sizeof(struct gf_poly)+((_d)+1)*sizeof(unsigned int))

/* polynomial of degree 1 */
struct gf_poly_deg1 {
	struct gf_poly poly;
	unsigned int   c[2];
};

#ifdef USE_HOSTCC
static int fls(int x)
{
	int r = 32;

	if (!x)
		return 0;
	if (!(x & 0xffff0000u)) {
		x <<= 16;
		r -= 16;
	}
	if (!(x & 0xff000000u)) {
		x <<= 8;
		r -= 8;
	}
	if (!(x & 0xf0000000u)) {
		x <<= 4;
		r -= 4;
	}
	if (!(x & 0xc0000000u)) {
		x <<= 2;
		r -= 2;
	}
	if (!(x & 0x80000000u)) {
		x <<= 1;
		r -= 1;
	}
	return r;
}
#endif

/*
 * same as encode_bch(), but process input data one byte at a time
 */
static void encode_bch_unaligned(struct bch_control *bch,
				 const unsigned char *data, unsigned int len,
				 uint32_t *ecc)
{
	int i;
	const uint32_t *p;
	const int l = BCH_ECC_WORDS(bch)-1;

	while (len--) {
		p = bch->mod8_tab + (l+1)*(((ecc[0] >> 24)^(*data++)) & 0xff);

		for (i = 0; i < l; i++)
			ecc[i] = ((ecc[i] << 8)|(ecc[i+1] >> 24))^(*p++);

		ecc[l] = (ecc[l] << 8)^(*p);
	}
}

/*
 * convert ecc bytes to aligned, zero-padded 32-bit ecc words
 */
static void load_ecc8(struct bch_control *bch, uint32_t *dst,
		      const uint8_t *src)
{
	uint8_t pad[4] = {0, 0, 0, 0};
	unsigned int i, nwords = BCH_ECC_WORDS(bch)-1;

	for (i = 0; i < nwords; i++, src += 4)
		dst[i] = (src[0] << 24)|(src[1] << 16)|(src[2] << 8)|src[3];

	memcpy(pad, src, BCH_ECC_BYTES(bch)-4*nwords);
	dst[nwords] = (pad[0] << 24)|(pad[1] << 16)|(pad[2] << 8)|pad[3];
}

/*
 * convert 32-bit ecc words to ecc bytes
 */
static void store_ecc8(struct bch_control *bch, uint8_t *dst,
		       const uint32_t *src)
{
	uint8_t pad[4];
	unsigned int i, nwords = BCH_ECC_WORDS(bch)-1;

	for (i = 0; i < nwords; i++) {
		*dst++ = (src[i] >> 24);
		*dst++ = (src[i] >> 16) & 0xff;
		*dst++ = (src[i] >>  8) & 0xff;
		*dst++ = (src[i] >>  0) & 0xff;
	}
	pad[0] = (src[nwords] >> 24);
	pad[1] = (src[nwords] >> 16) & 0xff;
	pad[2] = (src[nwords] >>  8) & 0xff;
	pad[3] = (src[nwords] >>  0) & 0xff;
	memcpy(dst, pad, BCH_ECC_BYTES(bch)-4*nwords);
}

/**
 * encode_bch - calculate BCH ecc parity of data
 * @bch:   BCH control structure
 * @data:  data to encode
 * @len:   data length in bytes
 * @ecc:   ecc parity data, must be initialized by caller
 *
 * The @ecc parity array is used both as input and output parameter, in order to
 * allow incremental computations. It should be of the size indicated by member
 * @ecc_bytes of @bch, and should be initialized to 0 before the first call.
 *
 * The exact number of computed ecc parity bits is given by member @ecc_bits of
 * @bch; it may be less than m*t for large values of t.
 */
void encode_bch(struct bch_control *bch, const uint8_t *data,
		unsigned int len, uint8_t *ecc)
{
	const unsigned int l = BCH_ECC_WORDS(bch)-1;
	unsigned int i, mlen;
	unsigned long m;
	uint32_t w, r[l+1];
	const uint32_t * const tab0 = bch->mod8_tab;
	const uint32_t * const tab1 = tab0 + 256*(l+1);
	const uint32_t * const tab2 = tab1 + 256*(l+1);
	const uint32_t * const tab3 = tab2 + 256*(l+1);
	const uint32_t *pdata, *p0, *p1, *p2, *p3;

	if (ecc) {
		/* load ecc parity bytes into internal 32-bit buffer */
		load_ecc8(bch, bch->ecc_buf, ecc);
	} else {
		memset(bch->ecc_buf, 0, sizeof(r));
	}

	/* process first unaligned data bytes */
	m = ((unsigned long)data) & 3;
	if (m) {
		mlen = (len < (4-m)) ? len : 4-m;
		encode_bch_unaligned(bch, data, mlen, bch->ecc_buf);
		data += mlen;
		len  -= mlen;
	}

	/* process 32-bit aligned data words */
	pdata = (uint32_t *)data;
	mlen  = len/4;
	data += 4*mlen;
	len  -= 4*mlen;
	memcpy(r, bch->ecc_buf, sizeof(r));

	/*
	 * split each 32-bit word into 4 polynomials of weight 8 as follows:
	 *
	 * 31 ...24  23 ...16  15 ... 8  7 ... 0
	 * xxxxxxxx  yyyyyyyy  zzzzzzzz  tttttttt
	 *                               tttttttt  mod g = r0 (precomputed)
	 *                     zzzzzzzz  00000000  mod g = r1 (precomputed)
	 *           yyyyyyyy  00000000  00000000  mod g = r2 (precomputed)
	 * xxxxxxxx  00000000  00000000  00000000  mod g = r3 (precomputed)
	 * xxxxxxxx  yyyyyyyy  zzzzzzzz  tttttttt  mod g = r0^r1^r2^r3
	 */
	while (mlen--) {
		/* input data is read in big-endian format */
		w = r[0]^cpu_to_be32(*pdata++);
		p0 = tab0 + (l+1)*((w >>  0) & 0xff);
		p1 = tab1 + (l+1)*((w >>  8) & 0xff);
		p2 = tab2 + (l+1)*((w >> 16) & 0xff);
		p3 = tab3 + (l+1)*((w >> 24) & 0xff);

		for (i = 0; i < l; i++)
			r[i] = r[i+1]^p0[i]^p1[i]^p2[i]^p3[i];

		r[l] = p0[l]^p1[l]^p2[l]^p3[l];
	}
	memcpy(bch->ecc_buf, r, sizeof(r));

	/* process last unaligned bytes */
	if (len)
		encode_bch_unaligned(bch, data, len, bch->ecc_buf);

	/* store ecc parity bytes into original parity buffer */
	if (ecc)
		store_ecc8(bch, ecc, bch->ecc_buf);
}

static inline int modulo(struct bch_control *bch, unsigned int v)
{
	const unsigned int n = GF_N(bch);
	while (v >= n) {
		v -= n;
		v = (v & n) + (v >> GF_M(bch));
	}
	return v;
}

/*
 * shorter and faster modulo function, only works when v < 2N.
 */
static inline int mod_s(struct bch_control *bch, unsigned int v)
{
	const unsigned int n = GF_N(bch);
	return (v < n) ? v : v-n;
}

static inline int deg(unsigned int poly)
{
	/* polynomial degree is the most-significant bit index */
	return fls(poly)-1;
}

static inline int parity(unsigned int x)
{
	/*
	 * public domain code snippet, lifted from
	 * http://www-graphics.stanford.edu/~seander/bithacks.html
	 */
	x ^= x >> 1;
	x ^= x >> 2;
	x = (x & 0x11111111U) * 0x11111111U;
	return (x >> 28) & 1;
}

/* Galois field basic operations: multiply, divide, inverse, etc. */

static inline unsigned int gf_mul(struct bch_control *bch, unsigned int a,
				  unsigned int b)
{
	return (a && b) ? bch->a_pow_tab[mod_s(bch, bch->a_log_tab[a]+
					       bch->a_log_tab[b])] : 0;
}

static inline unsigned int gf_sqr(struct bch_control *bch, unsigned int a)
{
	return a ? bch->a_pow_tab[mod_s(bch, 2*bch->a_log_tab[a])] : 0;
}

static inline unsigned int gf_div(struct bch_control *bch, unsigned int a,
				  unsigned int b)
{
	return a ? bch->a_pow_tab[mod_s(bch, bch->a_log_tab[a]+
					GF_N(bch)-bch->a_log_tab[b])] : 0;
}

static inline unsigned int gf_inv(struct bch_control *bch, unsigned int a)
{
	return bch->a_pow_tab[GF_N(bch)-bch->a_log_tab[a]];
}

static inline unsigned int a_pow(struct bch_control *bch, int i)
{
	return bch->a_pow_tab[modulo(bch, i)];
}

static inline int a_log(struct bch_control *bch, unsigned int x)
{
	return bch->a_log_tab[x];
}

static inline int a_ilog(struct bch_control *bch, unsigned int x)
{
	return mod_s(bch, GF_N(bch)-bch->a_log_tab[x]);
}

/*
 * compute 2t syndromes of ecc polynomial, i.e. ecc(a^j) for j=1..2t
 */
static void compute_syndromes(struct bch_control *bch, uint32_t *ecc,
			      unsigned int *syn)
{
	int i, j, s;
	unsigned int m;
	uint32_t poly;
	const int t = GF_T(bch);

	s = bch->ecc_bits;

	/* make sure extra bits in last ecc word are cleared */
	m = ((unsigned int)s) & 31;
	if (m)
		ecc[s/32] &= ~((1u << (32-m))-1);
	memset(syn, 0, 2*t*sizeof(*syn));

	/* compute v(a^j) for j=1 .. 2t-1 */
	do {
		poly = *ecc++;
		s -= 32;
		while (poly) {
			i = deg(poly);
			for (j = 0; j < 2*t; j += 2)
				syn[j] ^= a_pow(bch, (j+1)*(i+s));

			poly ^= (1 << i);
		}
	} while (s > 0);

	/* v(a^(2j)) = v(a^j)^2 */
	for (j = 0; j < t; j++)
		syn[2*j+1] = gf_sqr(bch, syn[j]);
}

static void gf_poly_copy(struct gf_poly *dst, struct gf_poly *src)
{
	memcpy(dst, src, GF_POLY_SZ(src->deg));
}

static int compute_error_locator_polynomial(struct bch_control *bch,
					    const unsigned int *syn)
{
	const unsigned int t = GF_T(bch);
	const unsigned int n = GF_N(bch);
	unsigned int i, j, tmp, l, pd = 1, d = syn[0];
	struct gf_poly *elp = bch->elp;
	struct gf_poly *pelp = bch->poly_2t[0];
	struct gf_poly *elp_copy = bch->poly_2t[1];
	int k, pp = -1;

	memset(pelp, 0, GF_POLY_SZ(2*t));
	memset(elp, 0, GF_POLY_SZ(2*t));

	pelp->deg = 0;
	pelp->c[0] = 1;
	elp->deg = 0;
	elp->c[0] = 1;

	/* use simplified binary Berlekamp-Massey algorithm */
	for (i = 0; (i < t) && (elp->deg <= t); i++) {
		if (d) {
			k = 2*i-pp;
			gf_poly_copy(elp_copy, elp);
			/* e[i+1](X) = e[i](X)+di*dp^-1*X^2(i-p)*e[p](X) */
			tmp = a_log(bch, d)+n-a_log(bch, pd);
			for (j = 0; j <= pelp->deg; j++) {
				if (pelp->c[j]) {
					l = a_log(bch, pelp->c[j]);
					elp->c[j+k] ^= a_pow(bch, tmp+l);
				}
			}
			/* compute l[i+1] = max(l[i]->c[l[p]+2*(i-p]) */
			tmp = pelp->deg+k;
			if (tmp > elp->deg) {
				elp->deg = tmp;
				gf_poly_copy(pelp, elp_copy);
				pd = d;
				pp = 2*i;
			}
		}
		/* di+1 = S(2i+3)+elp[i+1].1*S(2i+2)+...+elp[i+1].lS(2i+3-l) */
		if (i < t-1) {
			d = syn[2*i+2];
			for (j = 1; j <= elp->deg; j++)
				d ^= gf_mul(bch, elp->c[j], syn[2*i+2-j]);
		}
	}
	dbg("elp=%s\n", gf_poly_str(elp));
	return (elp->deg > t) ? -1 : (int)elp->deg;
}

/*
 * solve a m x m linear system in GF(2) with an expected number of solutions,
 * and return the number of found solutions
 */
static int solve_linear_system(struct bch_control *bch, unsigned int *rows,
			       unsigned int *sol, int nsol)
{
	const int m = GF_M(bch);
	unsigned int tmp, mask;
	int rem, c, r, p, k, param[m];

	k = 0;
	mask = 1 << m;

	/* Gaussian elimination */
	for (c = 0; c < m; c++) {
		rem = 0;
		p = c-k;
		/* find suitable row for elimination */
		for (r = p; r < m; r++) {
			if (rows[r] & mask) {
				if (r != p) {
					tmp = rows[r];
					rows[r] = rows[p];
					rows[p] = tmp;
				}
				rem = r+1;
				break;
			}
		}
		if (rem) {
			/* perform elimination on remaining rows */
			tmp = rows[p];
			for (r = rem; r < m; r++) {
				if (rows[r] & mask)
					rows[r] ^= tmp;
			}
		} else {
			/* elimination not needed, store defective row index */
			param[k++] = c;
		}
		mask >>= 1;
	}
	/* rewrite system, inserting fake parameter rows */
	if (k > 0) {
		p = k;
		for (r = m-1; r >= 0; r--) {
			if ((r > m-1-k) && rows[r])
				/* system has no solution */
				return 0;

			rows[r] = (p && (r == param[p-1])) ?
				p--, 1u << (m-r) : rows[r-p];
		}
	}

	if (nsol != (1 << k))
		/* unexpected number of solutions */
		return 0;

	for (p = 0; p < nsol; p++) {
		/* set parameters for p-th solution */
		for (c = 0; c < k; c++)
			rows[param[c]] = (rows[param[c]] & ~1)|((p >> c) & 1);

		/* compute unique solution */
		tmp = 0;
		for (r = m-1; r >= 0; r--) {
			mask = rows[r] & (tmp|1);
			tmp |= parity(mask) << (m-r);
		}
		sol[p] = tmp >> 1;
	}
	return nsol;
}

/*
 * this function builds and solves a linear system for finding roots of a degree
 * 4 affine monic polynomial X^4+aX^2+bX+c over GF(2^m).
 */
static int find_affine4_roots(struct bch_control *bch, unsigned int a,
			      unsigned int b, unsigned int c,
			      unsigned int *roots)
{
	int i, j, k;
	const int m = GF_M(bch);
	unsigned int mask = 0xff, t, rows[16] = {0,};

	j = a_log(bch, b);
	k = a_log(bch, a);
	rows[0] = c;

	/* buid linear system to solve X^4+aX^2+bX+c = 0 */
	for (i = 0; i < m; i++) {
		rows[i+1] = bch->a_pow_tab[4*i]^
			(a ? bch->a_pow_tab[mod_s(bch, k)] : 0)^
			(b ? bch->a_pow_tab[mod_s(bch, j)] : 0);
		j++;
		k += 2;
	}
	/*
	 * transpose 16x16 matrix before passing it to linear solver
	 * warning: this code assumes m < 16
	 */
	for (j = 8; j != 0; j >>= 1, mask ^= (mask << j)) {
		for (k = 0; k < 16; k = (k+j+1) & ~j) {
			t = ((rows[k] >> j)^rows[k+j]) & mask;
			rows[k] ^= (t << j);
			rows[k+j] ^= t;
		}
	}
	return solve_linear_system(bch, rows, roots, 4);
}

/*
 * compute root r of a degree 1 polynomial over GF(2^m) (returned as log(1/r))
 */
static int find_poly_deg1_roots(struct bch_control *bch, struct gf_poly *poly,
				unsigned int *roots)
{
	int n = 0;

	if (poly->c[0])
		/* poly[X] = bX+c with c!=0, root=c/b */
		roots[n++] = mod_s(bch, GF_N(bch)-bch->a_log_tab[poly->c[0]]+
				   bch->a_log_tab[poly->c[1]]);
	return n;
}

/*
 * compute roots of a degree 2 polynomial over GF(2^m)
 */
static int find_poly_deg2_roots(struct bch_control *bch, struct gf_poly *poly,
				unsigned int *roots)
{
	int n = 0, i, l0, l1, l2;
	unsigned int u, v, r;

	if (poly->c[0] && poly->c[1]) {

		l0 = bch->a_log_tab[poly->c[0]];
		l1 = bch->a_log_tab[poly->c[1]];
		l2 = bch->a_log_tab[poly->c[2]];

		/* using z=a/bX, transform aX^2+bX+c into z^2+z+u (u=ac/b^2) */
		u = a_pow(bch, l0+l2+2*(GF_N(bch)-l1));
		/*
		 * let u = sum(li.a^i) i=0..m-1; then compute r = sum(li.xi):
		 * r^2+r = sum(li.(xi^2+xi)) = sum(li.(a^i+Tr(a^i).a^k)) =
		 * u + sum(li.Tr(a^i).a^k) = u+a^k.Tr(sum(li.a^i)) = u+a^k.Tr(u)
		 * i.e. r and r+1 are roots iff Tr(u)=0
		 */
		r = 0;
		v = u;
		while (v) {
			i = deg(v);
			r ^= bch->xi_tab[i];
			v ^= (1 << i);
		}
		/* verify root */
		if ((gf_sqr(bch, r)^r) == u) {
			/* reverse z=a/bX transformation and compute log(1/r) */
			roots[n++] = modulo(bch, 2*GF_N(bch)-l1-
					    bch->a_log_tab[r]+l2);
			roots[n++] = modulo(bch, 2*GF_N(bch)-l1-
					    bch->a_log_tab[r^1]+l2);
		}
	}
	return n;
}

/*
 * compute roots of a degree 3 polynomial over GF(2^m)
 */
static int find_poly_deg3_roots(struct bch_control *bch, struct gf_poly *poly,
				unsigned int *roots)
{
	int i, n = 0;
	unsigned int a, b, c, a2, b2, c2, e3, tmp[4];

	if (poly->c[0]) {
		/* transform polynomial into monic X^3 + a2X^2 + b2X + c2 */
		e3 = poly->c[3];
		c2 = gf_div(bch, poly->c[0], e3);
		b2 = gf_div(bch, poly->c[1], e3);
		a2 = gf_div(bch, poly->c[2], e3);

		/* (X+a2)(X^3+a2X^2+b2X+c2) = X^4+aX^2+bX+c (affine) */
		c = gf_mul(bch, a2, c2);           /* c = a2c2      */
		b = gf_mul(bch, a2, b2)^c2;        /* b = a2b2 + c2 */
		a = gf_sqr(bch, a2)^b2;            /* a = a2^2 + b2 */

		/* find the 4 roots of this affine polynomial */
		if (find_affine4_roots(bch, a, b, c, tmp) == 4) {
			/* remove a2 from final list of roots */
			for (i = 0; i < 4; i++) {
				if (tmp[i] != a2)
					roots[n++] = a_ilog(bch, tmp[i]);
			}
		}
	}
	return n;
}

/*
 * compute roots of a degree 4 polynomial over GF(2^m)
 */
static int find_poly_deg4_roots(struct bch_control *bch, struct gf_poly *poly,
				unsigned int *roots)
{
	int i, l, n = 0;
	unsigned int a, b, c, d, e = 0, f, a2, b2, c2, e4;

	if (poly->c[0] == 0)
		return 0;

	/* transform polynomial into monic X^4 + aX^3 + bX^2 + cX + d */
	e4 = poly->c[4];
	d = gf_div(bch, poly->c[0], e4);
	c = gf_div(bch, poly->c[1], e4);
	b = gf_div(bch, poly->c[2], e4);
	a = gf_div(bch, poly->c[3], e4);

	/* use Y=1/X transformation to get an affine polynomial */
	if (a) {
		/* first, eliminate cX by using z=X+e with ae^2+c=0 */
		if (c) {
			/* compute e such that e^2 = c/a */
			f = gf_div(bch, c, a);
			l = a_log(bch, f);
			l += (l & 1) ? GF_N(bch) : 0;
			e = a_pow(bch, l/2);
			/*
			 * use transformation z=X+e:
			 * z^4+e^4 + a(z^3+ez^2+e^2z+e^3) + b(z^2+e^2) +cz+ce+d
			 * z^4 + az^3 + (ae+b)z^2 + (ae^2+c)z+e^4+be^2+ae^3+ce+d
			 * z^4 + az^3 + (ae+b)z^2 + e^4+be^2+d
			 * z^4 + az^3 +     b'z^2 + d'
			 */
			d = a_pow(bch, 2*l)^gf_mul(bch, b, f)^d;
			b = gf_mul(bch, a, e)^b;
		}
		/* now, use Y=1/X to get Y^4 + b/dY^2 + a/dY + 1/d */
		if (d == 0)
			/* assume all roots have multiplicity 1 */
			return 0;

		c2 = gf_inv(bch, d);
		b2 = gf_div(bch, a, d);
		a2 = gf_div(bch, b, d);
	} else {
		/* polynomial is already affine */
		c2 = d;
		b2 = c;
		a2 = b;
	}
	/* find the 4 roots of this affine polynomial */
	if (find_affine4_roots(bch, a2, b2, c2, roots) == 4) {
		for (i = 0; i < 4; i++) {
			/* post-process roots (reverse transformations) */
			f = a ? gf_inv(bch, roots[i]) : roots[i];
			roots[i] = a_ilog(bch, f^e);
		}
		n = 4;
	}
	return n;
}

/*
 * build monic, log-based representation of a polynomial
 */
static void gf_poly_logrep(struct bch_control *bch,
			   const struct gf_poly *a, int *rep)
{
	int i, d = a->deg, l = GF_N(bch)-a_log(bch, a->c[a->deg]);

	/* represent 0 values with -1; warning, rep[d] is not set to 1 */
	for (i = 0; i < d; i++)
		rep[i] = a->c[i] ? mod_s(bch, a_log(bch, a->c[i])+l) : -1;
}

/*
 * compute polynomial Euclidean division remainder in GF(2^m)[X]
 */
static void gf_poly_mod(struct bch_control *bch, struct gf_poly *a,
			const struct gf_poly *b, int *rep)
{
	int la, p, m;
	unsigned int i, j, *c = a->c;
	const unsigned int d = b->deg;

	if (a->deg < d)
		return;

	/* reuse or compute log representation of denominator */
	if (!rep) {
		rep = bch->cache;
		gf_poly_logrep(bch, b, rep);
	}

	for (j = a->deg; j >= d; j--) {
		if (c[j]) {
			la = a_log(bch, c[j]);
			p = j-d;
			for (i = 0; i < d; i++, p++) {
				m = rep[i];
				if (m >= 0)
					c[p] ^= bch->a_pow_tab[mod_s(bch,
								     m+la)];
			}
		}
	}
	a->deg = d-1;
	while (!c[a->deg] && a->deg)
		a->deg--;
}

/*
 * compute polynomial Euclidean division quotient in GF(2^m)[X]
 */
static void gf_poly_div(struct bch_control *bch, struct gf_poly *a,
			const struct gf_poly *b, struct gf_poly *q)
{
	if (a->deg >= b->deg) {
		q->deg = a->deg-b->deg;
		/* compute a mod b (modifies a) */
		gf_poly_mod(bch, a, b, NULL);
		/* quotient is stored in upper part of polynomial a */
		memcpy(q->c, &a->c[b->deg], (1+q->deg)*sizeof(unsigned int));
	} else {
		q->deg = 0;
		q->c[0] = 0;
	}
}

/*
 * compute polynomial GCD (Greatest Common Divisor) in GF(2^m)[X]
 */
static struct gf_poly *gf_poly_gcd(struct bch_control *bch, struct gf_poly *a,
				   struct gf_poly *b)
{
	struct gf_poly *tmp;

	dbg("gcd(%s,%s)=", gf_poly_str(a), gf_poly_str(b));

	if (a->deg < b->deg) {
		tmp = b;
		b = a;
		a = tmp;
	}

	while (b->deg > 0) {
		gf_poly_mod(bch, a, b, NULL);
		tmp = b;
		b = a;
		a = tmp;
	}

	dbg("%s\n", gf_poly_str(a));

	return a;
}

/*
 * Given a polynomial f and an integer k, compute Tr(a^kX) mod f
 * This is used in Berlekamp Trace algorithm for splitting polynomials
 */
static void compute_trace_bk_mod(struct bch_control *bch, int k,
				 const struct gf_poly *f, struct gf_poly *z,
				 struct gf_poly *out)
{
	const int m = GF_M(bch);
	int i, j;

	/* z contains z^2j mod f */
	z->deg = 1;
	z->c[0] = 0;
	z->c[1] = bch->a_pow_tab[k];

	out->deg = 0;
	memset(out, 0, GF_POLY_SZ(f->deg));

	/* compute f log representation only once */
	gf_poly_logrep(bch, f, bch->cache);

	for (i = 0; i < m; i++) {
		/* add a^(k*2^i)(z^(2^i) mod f) and compute (z^(2^i) mod f)^2 */
		for (j = z->deg; j >= 0; j--) {
			out->c[j] ^= z->c[j];
			z->c[2*j] = gf_sqr(bch, z->c[j]);
			z->c[2*j+1] = 0;
		}
		if (z->deg > out->deg)
			out->deg = z->deg;

		if (i < m-1) {
			z->deg *= 2;
			/* z^(2(i+1)) mod f = (z^(2^i) mod f)^2 mod f */
			gf_poly_mod(bch, z, f, bch->cache);
		}
	}
	while (!out->c[out->deg] && out->deg)
		out->deg--;

	dbg("Tr(a^%d.X) mod f = %s\n", k, gf_poly_str(out));
}

/*
 * factor a polynomial using Berlekamp Trace algorithm (BTA)
 */
static void factor_polynomial(struct bch_control *bch, int k, struct gf_poly *f,
			      struct gf_poly **g, struct gf_poly **h)
{
	struct gf_poly *f2 = bch->poly_2t[0];
	struct gf_poly *q  = bch->poly_2t[1];
	struct gf_poly *tk = bch->poly_2t[2];
	struct gf_poly *z  = bch->poly_2t[3];
	struct gf_poly *gcd;

	dbg("factoring %s...\n", gf_poly_str(f));

	*g = f;
	*h = NULL;

	/* tk = Tr(a^k.X) mod f */
	compute_trace_bk_mod(bch, k, f, z, tk);

	if (tk->deg > 0) {
		/* compute g = gcd(f, tk) (destructive operation) */
		gf_poly_copy(f2, f);
		gcd = gf_poly_gcd(bch, f2, tk);
		if (gcd->deg < f->deg) {
			/* compute h=f/gcd(f,tk); this will modify f and q */
			gf_poly_div(bch, f, gcd, q);
			/* store g and h in-place (clobbering f) */
			*h = &((struct gf_poly_deg1 *)f)[gcd->deg].poly;
			gf_poly_copy(*g, gcd);
			gf_poly_copy(*h, q);
		}
	}
}

/*
 * find roots of a polynomial, using BTZ algorithm; see the beginning of this
 * file for details
 */
static int find_poly_roots(struct bch_control *bch, unsigned int k,
			   struct gf_poly *poly, unsigned int *roots)
{
	int cnt;
	struct gf_poly *f1, *f2;

	switch (poly->deg) {
		/* handle low degree polynomials with ad hoc techniques */
	case 1:
		cnt = find_poly_deg1_roots(bch, poly, roots);
		break;
	case 2:
		cnt = find_poly_deg2_roots(bch, poly, roots);
		break;
	case 3:
		cnt = find_poly_deg3_roots(bch, poly, roots);
		break;
	case 4:
		cnt = find_poly_deg4_roots(bch, poly, roots);
		break;
	default:
		/* factor polynomial using Berlekamp Trace Algorithm (BTA) */
		cnt = 0;
		if (poly->deg && (k <= GF_M(bch))) {
			factor_polynomial(bch, k, poly, &f1, &f2);
			if (f1)
				cnt += find_poly_roots(bch, k+1, f1, roots);
			if (f2)
				cnt += find_poly_roots(bch, k+1, f2, roots+cnt);
		}
		break;
	}
	return cnt;
}

#if defined(USE_CHIEN_SEARCH)
/*
 * exhaustive root search (Chien) implementation - not used, included only for
 * reference/comparison tests
 */
static int chien_search(struct bch_control *bch, unsigned int len,
			struct gf_poly *p, unsigned int *roots)
{
	int m;
	unsigned int i, j, syn, syn0, count = 0;
	const unsigned int k = 8*len+bch->ecc_bits;

	/* use a log-based representation of polynomial */
	gf_poly_logrep(bch, p, bch->cache);
	bch->cache[p->deg] = 0;
	syn0 = gf_div(bch, p->c[0], p->c[p->deg]);

	for (i = GF_N(bch)-k+1; i <= GF_N(bch); i++) {
		/* compute elp(a^i) */
		for (j = 1, syn = syn0; j <= p->deg; j++) {
			m = bch->cache[j];
			if (m >= 0)
				syn ^= a_pow(bch, m+j*i);
		}
		if (syn == 0) {
			roots[count++] = GF_N(bch)-i;
			if (count == p->deg)
				break;
		}
	}
	return (count == p->deg) ? count : 0;
}
#define find_poly_roots(_p, _k, _elp, _loc) chien_search(_p, len, _elp, _loc)
#endif /* USE_CHIEN_SEARCH */

/**
 * decode_bch - decode received codeword and find bit error locations
 * @bch:      BCH control structure
 * @data:     received data, ignored if @calc_ecc is provided
 * @len:      data length in bytes, must always be provided
 * @recv_ecc: received ecc, if NULL then assume it was XORed in @calc_ecc
 * @calc_ecc: calculated ecc, if NULL then calc_ecc is computed from @data
 * @syn:      hw computed syndrome data (if NULL, syndrome is calculated)
 * @errloc:   output array of error locations
 *
 * Returns:
 *  The number of errors found, or -EBADMSG if decoding failed, or -EINVAL if
 *  invalid parameters were provided
 *
 * Depending on the available hw BCH support and the need to compute @calc_ecc
 * separately (using encode_bch()), this function should be called with one of
 * the following parameter configurations -
 *
 * by providing @data and @recv_ecc only:
 *   decode_bch(@bch, @data, @len, @recv_ecc, NULL, NULL, @errloc)
 *
 * by providing @recv_ecc and @calc_ecc:
 *   decode_bch(@bch, NULL, @len, @recv_ecc, @calc_ecc, NULL, @errloc)
 *
 * by providing ecc = recv_ecc XOR calc_ecc:
 *   decode_bch(@bch, NULL, @len, NULL, ecc, NULL, @errloc)
 *
 * by providing syndrome results @syn:
 *   decode_bch(@bch, NULL, @len, NULL, NULL, @syn, @errloc)
 *
 * Once decode_bch() has successfully returned with a positive value, error
 * locations returned in array @errloc should be interpreted as follows -
 *
 * if (errloc[n] >= 8*len), then n-th error is located in ecc (no need for
 * data correction)
 *
 * if (errloc[n] < 8*len), then n-th error is located in data and can be
 * corrected with statement data[errloc[n]/8] ^= 1 << (errloc[n] % 8);
 *
 * Note that this function does not perform any data correction by itself, it
 * merely indicates error locations.
 */
int decode_bch(struct bch_control *bch, const uint8_t *data, unsigned int len,
	       const uint8_t *recv_ecc, const uint8_t *calc_ecc,
	       const unsigned int *syn, unsigned int *errloc)
{
	const unsigned int ecc_words = BCH_ECC_WORDS(bch);
	unsigned int nbits;
	int i, err, nroots;
	uint32_t sum;

	/* sanity check: make sure data length can be handled */
	if (8*len > (bch->n-bch->ecc_bits))
		return -EINVAL;

	/* if caller does not provide syndromes, compute them */
	if (!syn) {
		if (!calc_ecc) {
			/* compute received data ecc into an internal buffer */
			if (!data || !recv_ecc)
				return -EINVAL;
			encode_bch(bch, data, len, NULL);
		} else {
			/* load provided calculated ecc */
			load_ecc8(bch, bch->ecc_buf, calc_ecc);
		}
		/* load received ecc or assume it was XORed in calc_ecc */
		if (recv_ecc) {
			load_ecc8(bch, bch->ecc_buf2, recv_ecc);
			/* XOR received and calculated ecc */
			for (i = 0, sum = 0; i < (int)ecc_words; i++) {
				bch->ecc_buf[i] ^= bch->ecc_buf2[i];
				sum |= bch->ecc_buf[i];
			}
			if (!sum)
				/* no error found */
				return 0;
		}
		compute_syndromes(bch, bch->ecc_buf, bch->syn);
		syn = bch->syn;
	}

	err = compute_error_locator_polynomial(bch, syn);
	if (err > 0) {
		nroots = find_poly_roots(bch, 1, bch->elp, errloc);
		if (err != nroots)
			err = -1;
	}
	if (err > 0) {
		/* post-process raw error locations for easier correction */
		nbits = (len*8)+bch->ecc_bits;
		for (i = 0; i < err; i++) {
			if (errloc[i] >= nbits) {
				err = -1;
				break;
			}
			errloc[i] = nbits-1-errloc[i];
			errloc[i] = (errloc[i] & ~7)|(7-(errloc[i] & 7));
		}
	}
	return (err >= 0) ? err : -EBADMSG;
}

/*
 * generate Galois field lookup tables
 */
static int build_gf_tables(struct bch_control *bch, unsigned int poly)
{
	unsigned int i, x = 1;
	const unsigned int k = 1 << deg(poly);

	/* primitive polynomial must be of degree m */
	if (k != (1u << GF_M(bch)))
		return -1;

	for (i = 0; i < GF_N(bch); i++) {
		bch->a_pow_tab[i] = x;
		bch->a_log_tab[x] = i;
		if (i && (x == 1))
			/* polynomial is not primitive (a^i=1 with 0<i<2^m-1) */
			return -1;
		x <<= 1;
		if (x & k)
			x ^= poly;
	}
	bch->a_pow_tab[GF_N(bch)] = 1;
	bch->a_log_tab[0] = 0;

	return 0;
}

/*
 * compute generator polynomial remainder tables for fast encoding
 */
static void build_mod8_tables(struct bch_control *bch, const uint32_t *g)
{
	int i, j, b, d;
	uint32_t data, hi, lo, *tab;
	const int l = BCH_ECC_WORDS(bch);
	const int plen = DIV_ROUND_UP(bch->ecc_bits+1, 32);
	const int ecclen = DIV_ROUND_UP(bch->ecc_bits, 32);

	memset(bch->mod8_tab, 0, 4*256*l*sizeof(*bch->mod8_tab));

	for (i = 0; i < 256; i++) {
		/* p(X)=i is a small polynomial of weight <= 8 */
		for (b = 0; b < 4; b++) {
			/* we want to compute (p(X).X^(8*b+deg(g))) mod g(X) */
			tab = bch->mod8_tab + (b*256+i)*l;
			data = i << (8*b);
			while (data) {
				d = deg(data);
				/* subtract X^d.g(X) from p(X).X^(8*b+deg(g)) */
				data ^= g[0] >> (31-d);
				for (j = 0; j < ecclen; j++) {
					hi = (d < 31) ? g[j] << (d+1) : 0;
					lo = (j+1 < plen) ?
						g[j+1] >> (31-d) : 0;
					tab[j] ^= hi|lo;
				}
			}
		}
	}
}

/*
 * build a base for factoring degree 2 polynomials
 */
static int build_deg2_base(struct bch_control *bch)
{
	const int m = GF_M(bch);
	int i, j, r;
	unsigned int sum, x, y, remaining, ak = 0, xi[m];

	/* find k s.t. Tr(a^k) = 1 and 0 <= k < m */
	for (i = 0; i < m; i++) {
		for (j = 0, sum = 0; j < m; j++)
			sum ^= a_pow(bch, i*(1 << j));

		if (sum) {
			ak = bch->a_pow_tab[i];
			break;
		}
	}
	/* find xi, i=0..m-1 such that xi^2+xi = a^i+Tr(a^i).a^k */
	remaining = m;
	memset(xi, 0, sizeof(xi));

	for (x = 0; (x <= GF_N(bch)) && remaining; x++) {
		y = gf_sqr(bch, x)^x;
		for (i = 0; i < 2; i++) {
			r = a_log(bch, y);
			if (y && (r < m) && !xi[r]) {
				bch->xi_tab[r] = x;
				xi[r] = 1;
				remaining--;
				dbg("x%d = %x\n", r, x);
				break;
			}
			y ^= ak;
		}
	}
	/* should not happen but check anyway */
	return remaining ? -1 : 0;
}

static void *bch_alloc(size_t size, int *err)
{
	void *ptr;

	ptr = kmalloc(size, GFP_KERNEL);
	if (ptr == NULL)
		*err = 1;
	return ptr;
}

/*
 * compute generator polynomial for given (m,t) parameters.
 */
static uint32_t *compute_generator_polynomial(struct bch_control *bch)
{
	const unsigned int m = GF_M(bch);
	const unsigned int t = GF_T(bch);
	int n, err = 0;
	unsigned int i, j, nbits, r, word, *roots;
	struct gf_poly *g;
	uint32_t *genpoly;

	g = bch_alloc(GF_POLY_SZ(m*t), &err);
	roots = bch_alloc((bch->n+1)*sizeof(*roots), &err);
	genpoly = bch_alloc(DIV_ROUND_UP(m*t+1, 32)*sizeof(*genpoly), &err);

	if (err) {
		kfree(genpoly);
		genpoly = NULL;
		goto finish;
	}

	/* enumerate all roots of g(X) */
	memset(roots , 0, (bch->n+1)*sizeof(*roots));
	for (i = 0; i < t; i++) {
		for (j = 0, r = 2*i+1; j < m; j++) {
			roots[r] = 1;
			r = mod_s(bch, 2*r);
		}
	}
	/* build generator polynomial g(X) */
	g->deg = 0;
	g->c[0] = 1;
	for (i = 0; i < GF_N(bch); i++) {
		if (roots[i]) {
			/* multiply g(X) by (X+root) */
			r = bch->a_pow_tab[i];
			g->c[g->deg+1] = 1;
			for (j = g->deg; j > 0; j--)
				g->c[j] = gf_mul(bch, g->c[j], r)^g->c[j-1];

			g->c[0] = gf_mul(bch, g->c[0], r);
			g->deg++;
		}
	}
	/* store left-justified binary representation of g(X) */
	n = g->deg+1;
	i = 0;

	while (n > 0) {
		nbits = (n > 32) ? 32 : n;
		for (j = 0, word = 0; j < nbits; j++) {
			if (g->c[n-1-j])
				word |= 1u << (31-j);
		}
		genpoly[i++] = word;
		n -= nbits;
	}
	bch->ecc_bits = g->deg;

finish:
	kfree(g);
	kfree(roots);

	return genpoly;
}

/**
 * init_bch - initialize a BCH encoder/decoder
 * @m:          Galois field order, should be in the range 5-15
 * @t:          maximum error correction capability, in bits
 * @prim_poly:  user-provided primitive polynomial (or 0 to use default)
 *
 * Returns:
 *  a newly allocated BCH control structure if successful, NULL otherwise
 *
 * This initialization can take some time, as lookup tables are built for fast
 * encoding/decoding; make sure not to call this function from a time critical
 * path. Usually, init_bch() should be called on module/driver init and
 * free_bch() should be called to release memory on exit.
 *
 * You may provide your own primitive polynomial of degree @m in argument
 * @prim_poly, or let init_bch() use its default polynomial.
 *
 * Once init_bch() has successfully returned a pointer to a newly allocated
 * BCH control structure, ecc length in bytes is given by member @ecc_bytes of
 * the structure.
 */
struct bch_control *init_bch(int m, int t, unsigned int prim_poly)
{
	int err = 0;
	unsigned int i, words;
	uint32_t *genpoly;
	struct bch_control *bch = NULL;

	const int min_m = 5;
	const int max_m = 15;

	/* default primitive polynomials */
	static const unsigned int prim_poly_tab[] = {
		0x25, 0x43, 0x83, 0x11d, 0x211, 0x409, 0x805, 0x1053, 0x201b,
		0x402b, 0x8003,
	};

#if defined(CONFIG_BCH_CONST_PARAMS)
	if ((m != (CONFIG_BCH_CONST_M)) || (t != (CONFIG_BCH_CONST_T))) {
		printk(KERN_ERR "bch encoder/decoder was configured to support "
		       "parameters m=%d, t=%d only!\n",
		       CONFIG_BCH_CONST_M, CONFIG_BCH_CONST_T);
		goto fail;
	}
#endif
	if ((m < min_m) || (m > max_m))
		/*
		 * values of m greater than 15 are not currently supported;
		 * supporting m > 15 would require changing table base type
		 * (uint16_t) and a small patch in matrix transposition
		 */
		goto fail;

	/* sanity checks */
	if ((t < 1) || (m*t >= ((1 << m)-1)))
		/* invalid t value */
		goto fail;

	/* select a primitive polynomial for generating GF(2^m) */
	if (prim_poly == 0)
		prim_poly = prim_poly_tab[m-min_m];

	bch = kzalloc(sizeof(*bch), GFP_KERNEL);
	if (bch == NULL)
		goto fail;

	bch->m = m;
	bch->t = t;
	bch->n = (1 << m)-1;
	words  = DIV_ROUND_UP(m*t, 32);
	bch->ecc_bytes = DIV_ROUND_UP(m*t, 8);
	bch->a_pow_tab = bch_alloc((1+bch->n)*sizeof(*bch->a_pow_tab), &err);
	bch->a_log_tab = bch_alloc((1+bch->n)*sizeof(*bch->a_log_tab), &err);
	bch->mod8_tab  = bch_alloc(words*1024*sizeof(*bch->mod8_tab), &err);
	bch->ecc_buf   = bch_alloc(words*sizeof(*bch->ecc_buf), &err);
	bch->ecc_buf2  = bch_alloc(words*sizeof(*bch->ecc_buf2), &err);
	bch->xi_tab    = bch_alloc(m*sizeof(*bch->xi_tab), &err);
	bch->syn       = bch_alloc(2*t*sizeof(*bch->syn), &err);
	bch->cache     = bch_alloc(2*t*sizeof(*bch->cache), &err);
	bch->elp       = bch_alloc((t+1)*sizeof(struct gf_poly_deg1), &err);

	for (i = 0; i < ARRAY_SIZE(bch->poly_2t); i++)
		bch->poly_2t[i] = bch_alloc(GF_POLY_SZ(2*t), &err);

	if (err)
		goto fail;

	err = build_gf_tables(bch, prim_poly);
	if (err)
		goto fail;

	/* use generator polynomial for computing encoding tables */
	genpoly = compute_generator_polynomial(bch);
	if (genpoly == NULL)
		goto fail;

	build_mod8_tables(bch, genpoly);
	kfree(genpoly);

	err = build_deg2_base(bch);
	if (err)
		goto fail;

	return bch;

fail:
	free_bch(bch);
	return NULL;
}

/**
 *  free_bch - free the BCH control structure
 *  @bch:    BCH control structure to release
 */
void free_bch(struct bch_control *bch)
{
	unsigned int i;

	if (bch) {
		kfree(bch->a_pow_tab);
		kfree(bch->a_log_tab);
		kfree(bch->mod8_tab);
		kfree(bch->ecc_buf);
		kfree(bch->ecc_buf2);
		kfree(bch->xi_tab);
		kfree(bch->syn);
		kfree(bch->cache);
		kfree(bch->elp);

		for (i = 0; i < ARRAY_SIZE(bch->poly_2t); i++)
			kfree(bch->poly_2t[i]);

		kfree(bch);
	}
}