2 * ECC algorithm for M-systems disk on chip. We use the excellent Reed
3 * Solmon code of Phil Karn (karn@ka9q.ampr.org) available under the
4 * GNU GPL License. The rest is simply to convert the disk on chip
5 * syndrom into a standard syndom.
7 * Author: Fabrice Bellard (fabrice.bellard@netgem.com)
8 * Copyright (C) 2000 Netgem S.A.
10 * This program is free software; you can redistribute it and/or modify
11 * it under the terms of the GNU General Public License as published by
12 * the Free Software Foundation; either version 2 of the License, or
13 * (at your option) any later version.
15 * This program is distributed in the hope that it will be useful,
16 * but WITHOUT ANY WARRANTY; without even the implied warranty of
17 * MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
18 * GNU General Public License for more details.
20 * You should have received a copy of the GNU General Public License
21 * along with this program; if not, write to the Free Software
22 * Foundation, Inc., 59 Temple Place, Suite 330, Boston, MA 02111-1307 USA
24 #include <linux/kernel.h>
25 #include <linux/module.h>
26 #include <asm/errno.h>
28 #include <asm/uaccess.h>
29 #include <linux/miscdevice.h>
30 #include <linux/delay.h>
31 #include <linux/slab.h>
32 #include <linux/init.h>
33 #include <linux/types.h>
35 #include <linux/mtd/compatmac.h> /* for min() in older kernels */
36 #include <linux/mtd/mtd.h>
37 #include <linux/mtd/doc2000.h>
40 /* need to undef it (from asm/termbits.h) */
43 #define MM 10 /* Symbol size in bits */
44 #define KK (1023-4) /* Number of data symbols per block */
45 #define B0 510 /* First root of generator polynomial, alpha form */
46 #define PRIM 1 /* power of alpha used to generate roots of generator poly */
47 #define NN ((1 << MM) - 1)
49 typedef unsigned short dtype
;
52 static const int Pp
[MM
+1] = { 1, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1 };
54 /* This defines the type used to store an element of the Galois Field
55 * used by the code. Make sure this is something larger than a char if
56 * if anything larger than GF(256) is used.
58 * Note: unsigned char will work up to GF(256) but int seems to run
59 * faster on the Pentium.
63 /* No legal value in index form represents zero, so
64 * we need a special value for this purpose
68 /* Compute x % NN, where NN is 2**MM - 1,
69 * without a slow divide
76 x
= (x
>> MM
) + (x
& NN
);
83 for(ci=(n)-1;ci >=0;ci--)\
87 #define COPY(a,b,n) {\
89 for(ci=(n)-1;ci >=0;ci--)\
93 #define COPYDOWN(a,b,n) {\
95 for(ci=(n)-1;ci >=0;ci--)\
101 /* generate GF(2**m) from the irreducible polynomial p(X) in Pp[0]..Pp[m]
102 lookup tables: index->polynomial form alpha_to[] contains j=alpha**i;
103 polynomial form -> index form index_of[j=alpha**i] = i
104 alpha=2 is the primitive element of GF(2**m)
105 HARI's COMMENT: (4/13/94) alpha_to[] can be used as follows:
106 Let @ represent the primitive element commonly called "alpha" that
107 is the root of the primitive polynomial p(x). Then in GF(2^m), for any
109 @^i = a(0) + a(1) @ + a(2) @^2 + ... + a(m-1) @^(m-1)
110 where the binary vector (a(0),a(1),a(2),...,a(m-1)) is the representation
111 of the integer "alpha_to[i]" with a(0) being the LSB and a(m-1) the MSB. Thus for
112 example the polynomial representation of @^5 would be given by the binary
113 representation of the integer "alpha_to[5]".
114 Similarily, index_of[] can be used as follows:
115 As above, let @ represent the primitive element of GF(2^m) that is
116 the root of the primitive polynomial p(x). In order to find the power
117 of @ (alpha) that has the polynomial representation
118 a(0) + a(1) @ + a(2) @^2 + ... + a(m-1) @^(m-1)
119 we consider the integer "i" whose binary representation with a(0) being LSB
120 and a(m-1) MSB is (a(0),a(1),...,a(m-1)) and locate the entry
121 "index_of[i]". Now, @^index_of[i] is that element whose polynomial
122 representation is (a(0),a(1),a(2),...,a(m-1)).
124 The element alpha_to[2^m-1] = 0 always signifying that the
125 representation of "@^infinity" = 0 is (0,0,0,...,0).
126 Similarily, the element index_of[0] = A0 always signifying
127 that the power of alpha which has the polynomial representation
128 (0,0,...,0) is "infinity".
133 generate_gf(dtype Alpha_to
[NN
+ 1], dtype Index_of
[NN
+ 1])
135 register int i
, mask
;
139 for (i
= 0; i
< MM
; i
++) {
141 Index_of
[Alpha_to
[i
]] = i
;
142 /* If Pp[i] == 1 then, term @^i occurs in poly-repr of @^MM */
144 Alpha_to
[MM
] ^= mask
; /* Bit-wise EXOR operation */
145 mask
<<= 1; /* single left-shift */
147 Index_of
[Alpha_to
[MM
]] = MM
;
149 * Have obtained poly-repr of @^MM. Poly-repr of @^(i+1) is given by
150 * poly-repr of @^i shifted left one-bit and accounting for any @^MM
151 * term that may occur when poly-repr of @^i is shifted.
154 for (i
= MM
+ 1; i
< NN
; i
++) {
155 if (Alpha_to
[i
- 1] >= mask
)
156 Alpha_to
[i
] = Alpha_to
[MM
] ^ ((Alpha_to
[i
- 1] ^ mask
) << 1);
158 Alpha_to
[i
] = Alpha_to
[i
- 1] << 1;
159 Index_of
[Alpha_to
[i
]] = i
;
166 * Performs ERRORS+ERASURES decoding of RS codes. bb[] is the content
167 * of the feedback shift register after having processed the data and
170 * Return number of symbols corrected, or -1 if codeword is illegal
171 * or uncorrectable. If eras_pos is non-null, the detected error locations
172 * are written back. NOTE! This array must be at least NN-KK elements long.
173 * The corrected data are written in eras_val[]. They must be xor with the data
174 * to retrieve the correct data : data[erase_pos[i]] ^= erase_val[i] .
176 * First "no_eras" erasures are declared by the calling program. Then, the
177 * maximum # of errors correctable is t_after_eras = floor((NN-KK-no_eras)/2).
178 * If the number of channel errors is not greater than "t_after_eras" the
179 * transmitted codeword will be recovered. Details of algorithm can be found
180 * in R. Blahut's "Theory ... of Error-Correcting Codes".
182 * Warning: the eras_pos[] array must not contain duplicate entries; decoder failure
183 * will result. The decoder *could* check for this condition, but it would involve
184 * extra time on every decoding operation.
187 eras_dec_rs(dtype Alpha_to
[NN
+ 1], dtype Index_of
[NN
+ 1],
188 gf bb
[NN
- KK
+ 1], gf eras_val
[NN
-KK
], int eras_pos
[NN
-KK
],
191 int deg_lambda
, el
, deg_omega
;
193 gf u
,q
,tmp
,num1
,num2
,den
,discr_r
;
194 gf lambda
[NN
-KK
+ 1], s
[NN
-KK
+ 1]; /* Err+Eras Locator poly
195 * and syndrome poly */
196 gf b
[NN
-KK
+ 1], t
[NN
-KK
+ 1], omega
[NN
-KK
+ 1];
197 gf root
[NN
-KK
], reg
[NN
-KK
+ 1], loc
[NN
-KK
];
198 int syn_error
, count
;
205 /* if remainder is zero, data[] is a codeword and there are no
206 * errors to correct. So return data[] unmodified
212 for(i
=1;i
<=NN
-KK
;i
++){
215 for(j
=1;j
<NN
-KK
;j
++){
218 tmp
= Index_of
[bb
[j
]];
220 for(i
=1;i
<=NN
-KK
;i
++)
221 s
[i
] ^= Alpha_to
[modnn(tmp
+ (B0
+i
-1)*PRIM
*j
)];
224 /* undo the feedback register implicit multiplication and convert
225 syndromes to index form */
227 for(i
=1;i
<=NN
-KK
;i
++) {
228 tmp
= Index_of
[s
[i
]];
230 tmp
= modnn(tmp
+ 2 * KK
* (B0
+i
-1)*PRIM
);
234 CLEAR(&lambda
[1],NN
-KK
);
238 /* Init lambda to be the erasure locator polynomial */
239 lambda
[1] = Alpha_to
[modnn(PRIM
* eras_pos
[0])];
240 for (i
= 1; i
< no_eras
; i
++) {
241 u
= modnn(PRIM
*eras_pos
[i
]);
242 for (j
= i
+1; j
> 0; j
--) {
243 tmp
= Index_of
[lambda
[j
- 1]];
245 lambda
[j
] ^= Alpha_to
[modnn(u
+ tmp
)];
249 /* Test code that verifies the erasure locator polynomial just constructed
250 Needed only for decoder debugging. */
252 /* find roots of the erasure location polynomial */
253 for(i
=1;i
<=no_eras
;i
++)
254 reg
[i
] = Index_of
[lambda
[i
]];
256 for (i
= 1,k
=NN
-Ldec
; i
<= NN
; i
++,k
= modnn(NN
+k
-Ldec
)) {
258 for (j
= 1; j
<= no_eras
; j
++)
260 reg
[j
] = modnn(reg
[j
] + j
);
261 q
^= Alpha_to
[reg
[j
]];
265 /* store root and error location number indices */
270 if (count
!= no_eras
) {
271 printf("\n lambda(x) is WRONG\n");
276 printf("\n Erasure positions as determined by roots of Eras Loc Poly:\n");
277 for (i
= 0; i
< count
; i
++)
278 printf("%d ", loc
[i
]);
283 for(i
=0;i
<NN
-KK
+1;i
++)
284 b
[i
] = Index_of
[lambda
[i
]];
287 * Begin Berlekamp-Massey algorithm to determine error+erasure
292 while (++r
<= NN
-KK
) { /* r is the step number */
293 /* Compute discrepancy at the r-th step in poly-form */
295 for (i
= 0; i
< r
; i
++){
296 if ((lambda
[i
] != 0) && (s
[r
- i
] != A0
)) {
297 discr_r
^= Alpha_to
[modnn(Index_of
[lambda
[i
]] + s
[r
- i
])];
300 discr_r
= Index_of
[discr_r
]; /* Index form */
302 /* 2 lines below: B(x) <-- x*B(x) */
303 COPYDOWN(&b
[1],b
,NN
-KK
);
306 /* 7 lines below: T(x) <-- lambda(x) - discr_r*x*b(x) */
308 for (i
= 0 ; i
< NN
-KK
; i
++) {
310 t
[i
+1] = lambda
[i
+1] ^ Alpha_to
[modnn(discr_r
+ b
[i
])];
312 t
[i
+1] = lambda
[i
+1];
314 if (2 * el
<= r
+ no_eras
- 1) {
315 el
= r
+ no_eras
- el
;
317 * 2 lines below: B(x) <-- inv(discr_r) *
320 for (i
= 0; i
<= NN
-KK
; i
++)
321 b
[i
] = (lambda
[i
] == 0) ? A0
: modnn(Index_of
[lambda
[i
]] - discr_r
+ NN
);
323 /* 2 lines below: B(x) <-- x*B(x) */
324 COPYDOWN(&b
[1],b
,NN
-KK
);
327 COPY(lambda
,t
,NN
-KK
+1);
331 /* Convert lambda to index form and compute deg(lambda(x)) */
333 for(i
=0;i
<NN
-KK
+1;i
++){
334 lambda
[i
] = Index_of
[lambda
[i
]];
339 * Find roots of the error+erasure locator polynomial by Chien
342 COPY(®
[1],&lambda
[1],NN
-KK
);
343 count
= 0; /* Number of roots of lambda(x) */
344 for (i
= 1,k
=NN
-Ldec
; i
<= NN
; i
++,k
= modnn(NN
+k
-Ldec
)) {
346 for (j
= deg_lambda
; j
> 0; j
--){
348 reg
[j
] = modnn(reg
[j
] + j
);
349 q
^= Alpha_to
[reg
[j
]];
354 /* store root (index-form) and error location number */
357 /* If we've already found max possible roots,
358 * abort the search to save time
360 if(++count
== deg_lambda
)
363 if (deg_lambda
!= count
) {
365 * deg(lambda) unequal to number of roots => uncorrectable
372 * Compute err+eras evaluator poly omega(x) = s(x)*lambda(x) (modulo
373 * x**(NN-KK)). in index form. Also find deg(omega).
376 for (i
= 0; i
< NN
-KK
;i
++){
378 j
= (deg_lambda
< i
) ? deg_lambda
: i
;
380 if ((s
[i
+ 1 - j
] != A0
) && (lambda
[j
] != A0
))
381 tmp
^= Alpha_to
[modnn(s
[i
+ 1 - j
] + lambda
[j
])];
385 omega
[i
] = Index_of
[tmp
];
390 * Compute error values in poly-form. num1 = omega(inv(X(l))), num2 =
391 * inv(X(l))**(B0-1) and den = lambda_pr(inv(X(l))) all in poly-form
393 for (j
= count
-1; j
>=0; j
--) {
395 for (i
= deg_omega
; i
>= 0; i
--) {
397 num1
^= Alpha_to
[modnn(omega
[i
] + i
* root
[j
])];
399 num2
= Alpha_to
[modnn(root
[j
] * (B0
- 1) + NN
)];
402 /* lambda[i+1] for i even is the formal derivative lambda_pr of lambda[i] */
403 for (i
= min(deg_lambda
,NN
-KK
-1) & ~1; i
>= 0; i
-=2) {
404 if(lambda
[i
+1] != A0
)
405 den
^= Alpha_to
[modnn(lambda
[i
+1] + i
* root
[j
])];
409 printf("\n ERROR: denominator = 0\n");
411 /* Convert to dual- basis */
415 /* Apply error to data */
417 eras_val
[j
] = Alpha_to
[modnn(Index_of
[num1
] + Index_of
[num2
] + NN
- Index_of
[den
])];
424 eras_pos
[i
] = loc
[i
];
428 /***************************************************************************/
429 /* The DOC specific code begins here */
431 #define SECTOR_SIZE 512
432 /* The sector bytes are packed into NB_DATA MM bits words */
433 #define NB_DATA (((SECTOR_SIZE + 1) * 8 + 6) / MM)
436 * Correct the errors in 'sector[]' by using 'ecc1[]' which is the
437 * content of the feedback shift register applyied to the sector and
438 * the ECC. Return the number of errors corrected (and correct them in
439 * sector), or -1 if error
441 int doc_decode_ecc(unsigned char sector
[SECTOR_SIZE
], unsigned char ecc1
[6])
443 int parity
, i
, nb_errors
;
446 int error_pos
[NN
-KK
], pos
, bitpos
, index
, val
;
447 dtype
*Alpha_to
, *Index_of
;
449 /* init log and exp tables here to save memory. However, it is slower */
450 Alpha_to
= kmalloc((NN
+ 1) * sizeof(dtype
), GFP_KERNEL
);
454 Index_of
= kmalloc((NN
+ 1) * sizeof(dtype
), GFP_KERNEL
);
460 generate_gf(Alpha_to
, Index_of
);
464 bb
[0] = (ecc1
[4] & 0xff) | ((ecc1
[5] & 0x03) << 8);
465 bb
[1] = ((ecc1
[5] & 0xfc) >> 2) | ((ecc1
[2] & 0x0f) << 6);
466 bb
[2] = ((ecc1
[2] & 0xf0) >> 4) | ((ecc1
[3] & 0x3f) << 4);
467 bb
[3] = ((ecc1
[3] & 0xc0) >> 6) | ((ecc1
[0] & 0xff) << 2);
469 nb_errors
= eras_dec_rs(Alpha_to
, Index_of
, bb
,
470 error_val
, error_pos
, 0);
474 /* correct the errors */
475 for(i
=0;i
<nb_errors
;i
++) {
477 if (pos
>= NB_DATA
&& pos
< KK
) {
482 /* extract bit position (MSB first) */
483 pos
= 10 * (NB_DATA
- 1 - pos
) - 6;
484 /* now correct the following 10 bits. At most two bytes
485 can be modified since pos is even */
486 index
= (pos
>> 3) ^ 1;
488 if ((index
>= 0 && index
< SECTOR_SIZE
) ||
489 index
== (SECTOR_SIZE
+ 1)) {
490 val
= error_val
[i
] >> (2 + bitpos
);
492 if (index
< SECTOR_SIZE
)
493 sector
[index
] ^= val
;
495 index
= ((pos
>> 3) + 1) ^ 1;
496 bitpos
= (bitpos
+ 10) & 7;
499 if ((index
>= 0 && index
< SECTOR_SIZE
) ||
500 index
== (SECTOR_SIZE
+ 1)) {
501 val
= error_val
[i
] << (8 - bitpos
);
503 if (index
< SECTOR_SIZE
)
504 sector
[index
] ^= val
;
509 /* use parity to test extra errors */
510 if ((parity
& 0xff) != 0)
519 EXPORT_SYMBOL_GPL(doc_decode_ecc
);
521 MODULE_LICENSE("GPL");
522 MODULE_AUTHOR("Fabrice Bellard <fabrice.bellard@netgem.com>");
523 MODULE_DESCRIPTION("ECC code for correcting errors detected by DiskOnChip 2000 and Millennium ECC hardware");