Free Electrons

Embedded Linux Experts

   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
/*
 * Generic binary BCH encoding/decoding library
 *
 * This program is free software; you can redistribute it and/or modify it
 * under the terms of the GNU General Public License version 2 as published by
 * the Free Software Foundation.
 *
 * This program is distributed in the hope that it will be useful, but WITHOUT
 * ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or
 * FITNESS FOR A PARTICULAR PURPOSE.  See the GNU General Public License for
 * more details.
 *
 * You should have received a copy of the GNU General Public License along with
 * this program; if not, write to the Free Software Foundation, Inc., 51
 * Franklin St, Fifth Floor, Boston, MA 02110-1301 USA.
 *
 * 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.
 */

#include <linux/kernel.h>
#include <linux/errno.h>
#include <linux/init.h>
#include <linux/module.h>
#include <linux/slab.h>
#include <linux/bitops.h>
#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];
};

/*
 * 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);
}
EXPORT_SYMBOL_GPL(encode_bch);

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;
}
EXPORT_SYMBOL_GPL(decode_bch);

/*
 * 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;
}
EXPORT_SYMBOL_GPL(init_bch);

/**
 *  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);
	}
}
EXPORT_SYMBOL_GPL(free_bch);

MODULE_LICENSE("GPL");
MODULE_AUTHOR("Ivan Djelic <ivan.djelic@parrot.com>");
MODULE_DESCRIPTION("Binary BCH encoder/decoder");