diff options
author | Linus Torvalds <torvalds@linux-foundation.org> | 2011-03-27 22:40:56 -0400 |
---|---|---|
committer | Linus Torvalds <torvalds@linux-foundation.org> | 2011-03-27 22:40:56 -0400 |
commit | a17d47300b4042a3893217c0c3f2d806fe1faa3b (patch) | |
tree | 91964353354d358cbafc350421e2bddb9455c73c /lib | |
parent | 04a6553f0766df3f56830c89b7da2f618b7ef0b0 (diff) | |
parent | 7bf7e370d5919112c223a269462cd0b546903829 (diff) |
Merge branch 'for-linus-1' of git://git.infradead.org/mtd-2.6
* 'for-linus-1' of git://git.infradead.org/mtd-2.6: (49 commits)
mtd: mtdswap: fix compilation warning
mtdswap: kill strict error handling option
mtd: nand: enable software BCH ECC in nand simulator
mtd: nand: add software BCH ECC support
mtd: fix printf format warnings, mostly lack of %zd for size_t, in mtdswap
mtd: sm_rtl: check kmalloc return value
mtd: cfi: add support for AMIC flashes (e.g. A29L160AT)
lib: add shared BCH ECC library
mtd: mxc_nand: fix OOB corruption when page size > 2KiB
mtd: DaVinci: Removed header file that is not required
mtd: pxa3xx_nand: clean the keep configure code
mtd: pxa3xx_nand: mtd scan id process could be defined by driver itself
mtd: pxa3xx_nand: unify prepare command
mtd: pxa3xx_nand: discard wait_for_event,write_cmd,__readid function
mtd: pxa3xx_nand: rework irq logic
mtd: pxa3xx_nand: make scan procedure more clear
mtd: speedtest: fix integer overflow
mtd: mxc_nand: fix read past buffer end
mtd: omap3: nand: report corrected ecc errors
jffs2: remove a trailing white space in commentaries
...
Diffstat (limited to 'lib')
-rw-r--r-- | lib/Kconfig | 39 | ||||
-rw-r--r-- | lib/Makefile | 1 | ||||
-rw-r--r-- | lib/bch.c | 1368 |
3 files changed, 1408 insertions, 0 deletions
diff --git a/lib/Kconfig b/lib/Kconfig index 23fa7a359db7..9c10e38fc609 100644 --- a/lib/Kconfig +++ b/lib/Kconfig | |||
@@ -158,6 +158,45 @@ config REED_SOLOMON_DEC16 | |||
158 | boolean | 158 | boolean |
159 | 159 | ||
160 | # | 160 | # |
161 | # BCH support is selected if needed | ||
162 | # | ||
163 | config BCH | ||
164 | tristate | ||
165 | |||
166 | config BCH_CONST_PARAMS | ||
167 | boolean | ||
168 | help | ||
169 | Drivers may select this option to force specific constant | ||
170 | values for parameters 'm' (Galois field order) and 't' | ||
171 | (error correction capability). Those specific values must | ||
172 | be set by declaring default values for symbols BCH_CONST_M | ||
173 | and BCH_CONST_T. | ||
174 | Doing so will enable extra compiler optimizations, | ||
175 | improving encoding and decoding performance up to 2x for | ||
176 | usual (m,t) values (typically such that m*t < 200). | ||
177 | When this option is selected, the BCH library supports | ||
178 | only a single (m,t) configuration. This is mainly useful | ||
179 | for NAND flash board drivers requiring known, fixed BCH | ||
180 | parameters. | ||
181 | |||
182 | config BCH_CONST_M | ||
183 | int | ||
184 | range 5 15 | ||
185 | help | ||
186 | Constant value for Galois field order 'm'. If 'k' is the | ||
187 | number of data bits to protect, 'm' should be chosen such | ||
188 | that (k + m*t) <= 2**m - 1. | ||
189 | Drivers should declare a default value for this symbol if | ||
190 | they select option BCH_CONST_PARAMS. | ||
191 | |||
192 | config BCH_CONST_T | ||
193 | int | ||
194 | help | ||
195 | Constant value for error correction capability in bits 't'. | ||
196 | Drivers should declare a default value for this symbol if | ||
197 | they select option BCH_CONST_PARAMS. | ||
198 | |||
199 | # | ||
161 | # Textsearch support is select'ed if needed | 200 | # Textsearch support is select'ed if needed |
162 | # | 201 | # |
163 | config TEXTSEARCH | 202 | config TEXTSEARCH |
diff --git a/lib/Makefile b/lib/Makefile index d7872b5c4c1c..ef0f28571156 100644 --- a/lib/Makefile +++ b/lib/Makefile | |||
@@ -69,6 +69,7 @@ obj-$(CONFIG_GENERIC_ALLOCATOR) += genalloc.o | |||
69 | obj-$(CONFIG_ZLIB_INFLATE) += zlib_inflate/ | 69 | obj-$(CONFIG_ZLIB_INFLATE) += zlib_inflate/ |
70 | obj-$(CONFIG_ZLIB_DEFLATE) += zlib_deflate/ | 70 | obj-$(CONFIG_ZLIB_DEFLATE) += zlib_deflate/ |
71 | obj-$(CONFIG_REED_SOLOMON) += reed_solomon/ | 71 | obj-$(CONFIG_REED_SOLOMON) += reed_solomon/ |
72 | obj-$(CONFIG_BCH) += bch.o | ||
72 | obj-$(CONFIG_LZO_COMPRESS) += lzo/ | 73 | obj-$(CONFIG_LZO_COMPRESS) += lzo/ |
73 | obj-$(CONFIG_LZO_DECOMPRESS) += lzo/ | 74 | obj-$(CONFIG_LZO_DECOMPRESS) += lzo/ |
74 | obj-$(CONFIG_XZ_DEC) += xz/ | 75 | obj-$(CONFIG_XZ_DEC) += xz/ |
diff --git a/lib/bch.c b/lib/bch.c new file mode 100644 index 000000000000..bc89dfe4d1b3 --- /dev/null +++ b/lib/bch.c | |||
@@ -0,0 +1,1368 @@ | |||
1 | /* | ||
2 | * Generic binary BCH encoding/decoding library | ||
3 | * | ||
4 | * This program is free software; you can redistribute it and/or modify it | ||
5 | * under the terms of the GNU General Public License version 2 as published by | ||
6 | * the Free Software Foundation. | ||
7 | * | ||
8 | * This program is distributed in the hope that it will be useful, but WITHOUT | ||
9 | * ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or | ||
10 | * FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for | ||
11 | * more details. | ||
12 | * | ||
13 | * You should have received a copy of the GNU General Public License along with | ||
14 | * this program; if not, write to the Free Software Foundation, Inc., 51 | ||
15 | * Franklin St, Fifth Floor, Boston, MA 02110-1301 USA. | ||
16 | * | ||
17 | * Copyright © 2011 Parrot S.A. | ||
18 | * | ||
19 | * Author: Ivan Djelic <ivan.djelic@parrot.com> | ||
20 | * | ||
21 | * Description: | ||
22 | * | ||
23 | * This library provides runtime configurable encoding/decoding of binary | ||
24 | * Bose-Chaudhuri-Hocquenghem (BCH) codes. | ||
25 | * | ||
26 | * Call init_bch to get a pointer to a newly allocated bch_control structure for | ||
27 | * the given m (Galois field order), t (error correction capability) and | ||
28 | * (optional) primitive polynomial parameters. | ||
29 | * | ||
30 | * Call encode_bch to compute and store ecc parity bytes to a given buffer. | ||
31 | * Call decode_bch to detect and locate errors in received data. | ||
32 | * | ||
33 | * On systems supporting hw BCH features, intermediate results may be provided | ||
34 | * to decode_bch in order to skip certain steps. See decode_bch() documentation | ||
35 | * for details. | ||
36 | * | ||
37 | * Option CONFIG_BCH_CONST_PARAMS can be used to force fixed values of | ||
38 | * parameters m and t; thus allowing extra compiler optimizations and providing | ||
39 | * better (up to 2x) encoding performance. Using this option makes sense when | ||
40 | * (m,t) are fixed and known in advance, e.g. when using BCH error correction | ||
41 | * on a particular NAND flash device. | ||
42 | * | ||
43 | * Algorithmic details: | ||
44 | * | ||
45 | * Encoding is performed by processing 32 input bits in parallel, using 4 | ||
46 | * remainder lookup tables. | ||
47 | * | ||
48 | * The final stage of decoding involves the following internal steps: | ||
49 | * a. Syndrome computation | ||
50 | * b. Error locator polynomial computation using Berlekamp-Massey algorithm | ||
51 | * c. Error locator root finding (by far the most expensive step) | ||
52 | * | ||
53 | * In this implementation, step c is not performed using the usual Chien search. | ||
54 | * Instead, an alternative approach described in [1] is used. It consists in | ||
55 | * factoring the error locator polynomial using the Berlekamp Trace algorithm | ||
56 | * (BTA) down to a certain degree (4), after which ad hoc low-degree polynomial | ||
57 | * solving techniques [2] are used. The resulting algorithm, called BTZ, yields | ||
58 | * much better performance than Chien search for usual (m,t) values (typically | ||
59 | * m >= 13, t < 32, see [1]). | ||
60 | * | ||
61 | * [1] B. Biswas, V. Herbert. Efficient root finding of polynomials over fields | ||
62 | * of characteristic 2, in: Western European Workshop on Research in Cryptology | ||
63 | * - WEWoRC 2009, Graz, Austria, LNCS, Springer, July 2009, to appear. | ||
64 | * [2] [Zin96] V.A. Zinoviev. On the solution of equations of degree 10 over | ||
65 | * finite fields GF(2^q). In Rapport de recherche INRIA no 2829, 1996. | ||
66 | */ | ||
67 | |||
68 | #include <linux/kernel.h> | ||
69 | #include <linux/errno.h> | ||
70 | #include <linux/init.h> | ||
71 | #include <linux/module.h> | ||
72 | #include <linux/slab.h> | ||
73 | #include <linux/bitops.h> | ||
74 | #include <asm/byteorder.h> | ||
75 | #include <linux/bch.h> | ||
76 | |||
77 | #if defined(CONFIG_BCH_CONST_PARAMS) | ||
78 | #define GF_M(_p) (CONFIG_BCH_CONST_M) | ||
79 | #define GF_T(_p) (CONFIG_BCH_CONST_T) | ||
80 | #define GF_N(_p) ((1 << (CONFIG_BCH_CONST_M))-1) | ||
81 | #else | ||
82 | #define GF_M(_p) ((_p)->m) | ||
83 | #define GF_T(_p) ((_p)->t) | ||
84 | #define GF_N(_p) ((_p)->n) | ||
85 | #endif | ||
86 | |||
87 | #define BCH_ECC_WORDS(_p) DIV_ROUND_UP(GF_M(_p)*GF_T(_p), 32) | ||
88 | #define BCH_ECC_BYTES(_p) DIV_ROUND_UP(GF_M(_p)*GF_T(_p), 8) | ||
89 | |||
90 | #ifndef dbg | ||
91 | #define dbg(_fmt, args...) do {} while (0) | ||
92 | #endif | ||
93 | |||
94 | /* | ||
95 | * represent a polynomial over GF(2^m) | ||
96 | */ | ||
97 | struct gf_poly { | ||
98 | unsigned int deg; /* polynomial degree */ | ||
99 | unsigned int c[0]; /* polynomial terms */ | ||
100 | }; | ||
101 | |||
102 | /* given its degree, compute a polynomial size in bytes */ | ||
103 | #define GF_POLY_SZ(_d) (sizeof(struct gf_poly)+((_d)+1)*sizeof(unsigned int)) | ||
104 | |||
105 | /* polynomial of degree 1 */ | ||
106 | struct gf_poly_deg1 { | ||
107 | struct gf_poly poly; | ||
108 | unsigned int c[2]; | ||
109 | }; | ||
110 | |||
111 | /* | ||
112 | * same as encode_bch(), but process input data one byte at a time | ||
113 | */ | ||
114 | static void encode_bch_unaligned(struct bch_control *bch, | ||
115 | const unsigned char *data, unsigned int len, | ||
116 | uint32_t *ecc) | ||
117 | { | ||
118 | int i; | ||
119 | const uint32_t *p; | ||
120 | const int l = BCH_ECC_WORDS(bch)-1; | ||
121 | |||
122 | while (len--) { | ||
123 | p = bch->mod8_tab + (l+1)*(((ecc[0] >> 24)^(*data++)) & 0xff); | ||
124 | |||
125 | for (i = 0; i < l; i++) | ||
126 | ecc[i] = ((ecc[i] << 8)|(ecc[i+1] >> 24))^(*p++); | ||
127 | |||
128 | ecc[l] = (ecc[l] << 8)^(*p); | ||
129 | } | ||
130 | } | ||
131 | |||
132 | /* | ||
133 | * convert ecc bytes to aligned, zero-padded 32-bit ecc words | ||
134 | */ | ||
135 | static void load_ecc8(struct bch_control *bch, uint32_t *dst, | ||
136 | const uint8_t *src) | ||
137 | { | ||
138 | uint8_t pad[4] = {0, 0, 0, 0}; | ||
139 | unsigned int i, nwords = BCH_ECC_WORDS(bch)-1; | ||
140 | |||
141 | for (i = 0; i < nwords; i++, src += 4) | ||
142 | dst[i] = (src[0] << 24)|(src[1] << 16)|(src[2] << 8)|src[3]; | ||
143 | |||
144 | memcpy(pad, src, BCH_ECC_BYTES(bch)-4*nwords); | ||
145 | dst[nwords] = (pad[0] << 24)|(pad[1] << 16)|(pad[2] << 8)|pad[3]; | ||
146 | } | ||
147 | |||
148 | /* | ||
149 | * convert 32-bit ecc words to ecc bytes | ||
150 | */ | ||
151 | static void store_ecc8(struct bch_control *bch, uint8_t *dst, | ||
152 | const uint32_t *src) | ||
153 | { | ||
154 | uint8_t pad[4]; | ||
155 | unsigned int i, nwords = BCH_ECC_WORDS(bch)-1; | ||
156 | |||
157 | for (i = 0; i < nwords; i++) { | ||
158 | *dst++ = (src[i] >> 24); | ||
159 | *dst++ = (src[i] >> 16) & 0xff; | ||
160 | *dst++ = (src[i] >> 8) & 0xff; | ||
161 | *dst++ = (src[i] >> 0) & 0xff; | ||
162 | } | ||
163 | pad[0] = (src[nwords] >> 24); | ||
164 | pad[1] = (src[nwords] >> 16) & 0xff; | ||
165 | pad[2] = (src[nwords] >> 8) & 0xff; | ||
166 | pad[3] = (src[nwords] >> 0) & 0xff; | ||
167 | memcpy(dst, pad, BCH_ECC_BYTES(bch)-4*nwords); | ||
168 | } | ||
169 | |||
170 | /** | ||
171 | * encode_bch - calculate BCH ecc parity of data | ||
172 | * @bch: BCH control structure | ||
173 | * @data: data to encode | ||
174 | * @len: data length in bytes | ||
175 | * @ecc: ecc parity data, must be initialized by caller | ||
176 | * | ||
177 | * The @ecc parity array is used both as input and output parameter, in order to | ||
178 | * allow incremental computations. It should be of the size indicated by member | ||
179 | * @ecc_bytes of @bch, and should be initialized to 0 before the first call. | ||
180 | * | ||
181 | * The exact number of computed ecc parity bits is given by member @ecc_bits of | ||
182 | * @bch; it may be less than m*t for large values of t. | ||
183 | */ | ||
184 | void encode_bch(struct bch_control *bch, const uint8_t *data, | ||
185 | unsigned int len, uint8_t *ecc) | ||
186 | { | ||
187 | const unsigned int l = BCH_ECC_WORDS(bch)-1; | ||
188 | unsigned int i, mlen; | ||
189 | unsigned long m; | ||
190 | uint32_t w, r[l+1]; | ||
191 | const uint32_t * const tab0 = bch->mod8_tab; | ||
192 | const uint32_t * const tab1 = tab0 + 256*(l+1); | ||
193 | const uint32_t * const tab2 = tab1 + 256*(l+1); | ||
194 | const uint32_t * const tab3 = tab2 + 256*(l+1); | ||
195 | const uint32_t *pdata, *p0, *p1, *p2, *p3; | ||
196 | |||
197 | if (ecc) { | ||
198 | /* load ecc parity bytes into internal 32-bit buffer */ | ||
199 | load_ecc8(bch, bch->ecc_buf, ecc); | ||
200 | } else { | ||
201 | memset(bch->ecc_buf, 0, sizeof(r)); | ||
202 | } | ||
203 | |||
204 | /* process first unaligned data bytes */ | ||
205 | m = ((unsigned long)data) & 3; | ||
206 | if (m) { | ||
207 | mlen = (len < (4-m)) ? len : 4-m; | ||
208 | encode_bch_unaligned(bch, data, mlen, bch->ecc_buf); | ||
209 | data += mlen; | ||
210 | len -= mlen; | ||
211 | } | ||
212 | |||
213 | /* process 32-bit aligned data words */ | ||
214 | pdata = (uint32_t *)data; | ||
215 | mlen = len/4; | ||
216 | data += 4*mlen; | ||
217 | len -= 4*mlen; | ||
218 | memcpy(r, bch->ecc_buf, sizeof(r)); | ||
219 | |||
220 | /* | ||
221 | * split each 32-bit word into 4 polynomials of weight 8 as follows: | ||
222 | * | ||
223 | * 31 ...24 23 ...16 15 ... 8 7 ... 0 | ||
224 | * xxxxxxxx yyyyyyyy zzzzzzzz tttttttt | ||
225 | * tttttttt mod g = r0 (precomputed) | ||
226 | * zzzzzzzz 00000000 mod g = r1 (precomputed) | ||
227 | * yyyyyyyy 00000000 00000000 mod g = r2 (precomputed) | ||
228 | * xxxxxxxx 00000000 00000000 00000000 mod g = r3 (precomputed) | ||
229 | * xxxxxxxx yyyyyyyy zzzzzzzz tttttttt mod g = r0^r1^r2^r3 | ||
230 | */ | ||
231 | while (mlen--) { | ||
232 | /* input data is read in big-endian format */ | ||
233 | w = r[0]^cpu_to_be32(*pdata++); | ||
234 | p0 = tab0 + (l+1)*((w >> 0) & 0xff); | ||
235 | p1 = tab1 + (l+1)*((w >> 8) & 0xff); | ||
236 | p2 = tab2 + (l+1)*((w >> 16) & 0xff); | ||
237 | p3 = tab3 + (l+1)*((w >> 24) & 0xff); | ||
238 | |||
239 | for (i = 0; i < l; i++) | ||
240 | r[i] = r[i+1]^p0[i]^p1[i]^p2[i]^p3[i]; | ||
241 | |||
242 | r[l] = p0[l]^p1[l]^p2[l]^p3[l]; | ||
243 | } | ||
244 | memcpy(bch->ecc_buf, r, sizeof(r)); | ||
245 | |||
246 | /* process last unaligned bytes */ | ||
247 | if (len) | ||
248 | encode_bch_unaligned(bch, data, len, bch->ecc_buf); | ||
249 | |||
250 | /* store ecc parity bytes into original parity buffer */ | ||
251 | if (ecc) | ||
252 | store_ecc8(bch, ecc, bch->ecc_buf); | ||
253 | } | ||
254 | EXPORT_SYMBOL_GPL(encode_bch); | ||
255 | |||
256 | static inline int modulo(struct bch_control *bch, unsigned int v) | ||
257 | { | ||
258 | const unsigned int n = GF_N(bch); | ||
259 | while (v >= n) { | ||
260 | v -= n; | ||
261 | v = (v & n) + (v >> GF_M(bch)); | ||
262 | } | ||
263 | return v; | ||
264 | } | ||
265 | |||
266 | /* | ||
267 | * shorter and faster modulo function, only works when v < 2N. | ||
268 | */ | ||
269 | static inline int mod_s(struct bch_control *bch, unsigned int v) | ||
270 | { | ||
271 | const unsigned int n = GF_N(bch); | ||
272 | return (v < n) ? v : v-n; | ||
273 | } | ||
274 | |||
275 | static inline int deg(unsigned int poly) | ||
276 | { | ||
277 | /* polynomial degree is the most-significant bit index */ | ||
278 | return fls(poly)-1; | ||
279 | } | ||
280 | |||
281 | static inline int parity(unsigned int x) | ||
282 | { | ||
283 | /* | ||
284 | * public domain code snippet, lifted from | ||
285 | * http://www-graphics.stanford.edu/~seander/bithacks.html | ||
286 | */ | ||
287 | x ^= x >> 1; | ||
288 | x ^= x >> 2; | ||
289 | x = (x & 0x11111111U) * 0x11111111U; | ||
290 | return (x >> 28) & 1; | ||
291 | } | ||
292 | |||
293 | /* Galois field basic operations: multiply, divide, inverse, etc. */ | ||
294 | |||
295 | static inline unsigned int gf_mul(struct bch_control *bch, unsigned int a, | ||
296 | unsigned int b) | ||
297 | { | ||
298 | return (a && b) ? bch->a_pow_tab[mod_s(bch, bch->a_log_tab[a]+ | ||
299 | bch->a_log_tab[b])] : 0; | ||
300 | } | ||
301 | |||
302 | static inline unsigned int gf_sqr(struct bch_control *bch, unsigned int a) | ||
303 | { | ||
304 | return a ? bch->a_pow_tab[mod_s(bch, 2*bch->a_log_tab[a])] : 0; | ||
305 | } | ||
306 | |||
307 | static inline unsigned int gf_div(struct bch_control *bch, unsigned int a, | ||
308 | unsigned int b) | ||
309 | { | ||
310 | return a ? bch->a_pow_tab[mod_s(bch, bch->a_log_tab[a]+ | ||
311 | GF_N(bch)-bch->a_log_tab[b])] : 0; | ||
312 | } | ||
313 | |||
314 | static inline unsigned int gf_inv(struct bch_control *bch, unsigned int a) | ||
315 | { | ||
316 | return bch->a_pow_tab[GF_N(bch)-bch->a_log_tab[a]]; | ||
317 | } | ||
318 | |||
319 | static inline unsigned int a_pow(struct bch_control *bch, int i) | ||
320 | { | ||
321 | return bch->a_pow_tab[modulo(bch, i)]; | ||
322 | } | ||
323 | |||
324 | static inline int a_log(struct bch_control *bch, unsigned int x) | ||
325 | { | ||
326 | return bch->a_log_tab[x]; | ||
327 | } | ||
328 | |||
329 | static inline int a_ilog(struct bch_control *bch, unsigned int x) | ||
330 | { | ||
331 | return mod_s(bch, GF_N(bch)-bch->a_log_tab[x]); | ||
332 | } | ||
333 | |||
334 | /* | ||
335 | * compute 2t syndromes of ecc polynomial, i.e. ecc(a^j) for j=1..2t | ||
336 | */ | ||
337 | static void compute_syndromes(struct bch_control *bch, uint32_t *ecc, | ||
338 | unsigned int *syn) | ||
339 | { | ||
340 | int i, j, s; | ||
341 | unsigned int m; | ||
342 | uint32_t poly; | ||
343 | const int t = GF_T(bch); | ||
344 | |||
345 | s = bch->ecc_bits; | ||
346 | |||
347 | /* make sure extra bits in last ecc word are cleared */ | ||
348 | m = ((unsigned int)s) & 31; | ||
349 | if (m) | ||
350 | ecc[s/32] &= ~((1u << (32-m))-1); | ||
351 | memset(syn, 0, 2*t*sizeof(*syn)); | ||
352 | |||
353 | /* compute v(a^j) for j=1 .. 2t-1 */ | ||
354 | do { | ||
355 | poly = *ecc++; | ||
356 | s -= 32; | ||
357 | while (poly) { | ||
358 | i = deg(poly); | ||
359 | for (j = 0; j < 2*t; j += 2) | ||
360 | syn[j] ^= a_pow(bch, (j+1)*(i+s)); | ||
361 | |||
362 | poly ^= (1 << i); | ||
363 | } | ||
364 | } while (s > 0); | ||
365 | |||
366 | /* v(a^(2j)) = v(a^j)^2 */ | ||
367 | for (j = 0; j < t; j++) | ||
368 | syn[2*j+1] = gf_sqr(bch, syn[j]); | ||
369 | } | ||
370 | |||
371 | static void gf_poly_copy(struct gf_poly *dst, struct gf_poly *src) | ||
372 | { | ||
373 | memcpy(dst, src, GF_POLY_SZ(src->deg)); | ||
374 | } | ||
375 | |||
376 | static int compute_error_locator_polynomial(struct bch_control *bch, | ||
377 | const unsigned int *syn) | ||
378 | { | ||
379 | const unsigned int t = GF_T(bch); | ||
380 | const unsigned int n = GF_N(bch); | ||
381 | unsigned int i, j, tmp, l, pd = 1, d = syn[0]; | ||
382 | struct gf_poly *elp = bch->elp; | ||
383 | struct gf_poly *pelp = bch->poly_2t[0]; | ||
384 | struct gf_poly *elp_copy = bch->poly_2t[1]; | ||
385 | int k, pp = -1; | ||
386 | |||
387 | memset(pelp, 0, GF_POLY_SZ(2*t)); | ||
388 | memset(elp, 0, GF_POLY_SZ(2*t)); | ||
389 | |||
390 | pelp->deg = 0; | ||
391 | pelp->c[0] = 1; | ||
392 | elp->deg = 0; | ||
393 | elp->c[0] = 1; | ||
394 | |||
395 | /* use simplified binary Berlekamp-Massey algorithm */ | ||
396 | for (i = 0; (i < t) && (elp->deg <= t); i++) { | ||
397 | if (d) { | ||
398 | k = 2*i-pp; | ||
399 | gf_poly_copy(elp_copy, elp); | ||
400 | /* e[i+1](X) = e[i](X)+di*dp^-1*X^2(i-p)*e[p](X) */ | ||
401 | tmp = a_log(bch, d)+n-a_log(bch, pd); | ||
402 | for (j = 0; j <= pelp->deg; j++) { | ||
403 | if (pelp->c[j]) { | ||
404 | l = a_log(bch, pelp->c[j]); | ||
405 | elp->c[j+k] ^= a_pow(bch, tmp+l); | ||
406 | } | ||
407 | } | ||
408 | /* compute l[i+1] = max(l[i]->c[l[p]+2*(i-p]) */ | ||
409 | tmp = pelp->deg+k; | ||
410 | if (tmp > elp->deg) { | ||
411 | elp->deg = tmp; | ||
412 | gf_poly_copy(pelp, elp_copy); | ||
413 | pd = d; | ||
414 | pp = 2*i; | ||
415 | } | ||
416 | } | ||
417 | /* di+1 = S(2i+3)+elp[i+1].1*S(2i+2)+...+elp[i+1].lS(2i+3-l) */ | ||
418 | if (i < t-1) { | ||
419 | d = syn[2*i+2]; | ||
420 | for (j = 1; j <= elp->deg; j++) | ||
421 | d ^= gf_mul(bch, elp->c[j], syn[2*i+2-j]); | ||
422 | } | ||
423 | } | ||
424 | dbg("elp=%s\n", gf_poly_str(elp)); | ||
425 | return (elp->deg > t) ? -1 : (int)elp->deg; | ||
426 | } | ||
427 | |||
428 | /* | ||
429 | * solve a m x m linear system in GF(2) with an expected number of solutions, | ||
430 | * and return the number of found solutions | ||
431 | */ | ||
432 | static int solve_linear_system(struct bch_control *bch, unsigned int *rows, | ||
433 | unsigned int *sol, int nsol) | ||
434 | { | ||
435 | const int m = GF_M(bch); | ||
436 | unsigned int tmp, mask; | ||
437 | int rem, c, r, p, k, param[m]; | ||
438 | |||
439 | k = 0; | ||
440 | mask = 1 << m; | ||
441 | |||
442 | /* Gaussian elimination */ | ||
443 | for (c = 0; c < m; c++) { | ||
444 | rem = 0; | ||
445 | p = c-k; | ||
446 | /* find suitable row for elimination */ | ||
447 | for (r = p; r < m; r++) { | ||
448 | if (rows[r] & mask) { | ||
449 | if (r != p) { | ||
450 | tmp = rows[r]; | ||
451 | rows[r] = rows[p]; | ||
452 | rows[p] = tmp; | ||
453 | } | ||
454 | rem = r+1; | ||
455 | break; | ||
456 | } | ||
457 | } | ||
458 | if (rem) { | ||
459 | /* perform elimination on remaining rows */ | ||
460 | tmp = rows[p]; | ||
461 | for (r = rem; r < m; r++) { | ||
462 | if (rows[r] & mask) | ||
463 | rows[r] ^= tmp; | ||
464 | } | ||
465 | } else { | ||
466 | /* elimination not needed, store defective row index */ | ||
467 | param[k++] = c; | ||
468 | } | ||
469 | mask >>= 1; | ||
470 | } | ||
471 | /* rewrite system, inserting fake parameter rows */ | ||
472 | if (k > 0) { | ||
473 | p = k; | ||
474 | for (r = m-1; r >= 0; r--) { | ||
475 | if ((r > m-1-k) && rows[r]) | ||
476 | /* system has no solution */ | ||
477 | return 0; | ||
478 | |||
479 | rows[r] = (p && (r == param[p-1])) ? | ||
480 | p--, 1u << (m-r) : rows[r-p]; | ||
481 | } | ||
482 | } | ||
483 | |||
484 | if (nsol != (1 << k)) | ||
485 | /* unexpected number of solutions */ | ||
486 | return 0; | ||
487 | |||
488 | for (p = 0; p < nsol; p++) { | ||
489 | /* set parameters for p-th solution */ | ||
490 | for (c = 0; c < k; c++) | ||
491 | rows[param[c]] = (rows[param[c]] & ~1)|((p >> c) & 1); | ||
492 | |||
493 | /* compute unique solution */ | ||
494 | tmp = 0; | ||
495 | for (r = m-1; r >= 0; r--) { | ||
496 | mask = rows[r] & (tmp|1); | ||
497 | tmp |= parity(mask) << (m-r); | ||
498 | } | ||
499 | sol[p] = tmp >> 1; | ||
500 | } | ||
501 | return nsol; | ||
502 | } | ||
503 | |||
504 | /* | ||
505 | * this function builds and solves a linear system for finding roots of a degree | ||
506 | * 4 affine monic polynomial X^4+aX^2+bX+c over GF(2^m). | ||
507 | */ | ||
508 | static int find_affine4_roots(struct bch_control *bch, unsigned int a, | ||
509 | unsigned int b, unsigned int c, | ||
510 | unsigned int *roots) | ||
511 | { | ||
512 | int i, j, k; | ||
513 | const int m = GF_M(bch); | ||
514 | unsigned int mask = 0xff, t, rows[16] = {0,}; | ||
515 | |||
516 | j = a_log(bch, b); | ||
517 | k = a_log(bch, a); | ||
518 | rows[0] = c; | ||
519 | |||
520 | /* buid linear system to solve X^4+aX^2+bX+c = 0 */ | ||
521 | for (i = 0; i < m; i++) { | ||
522 | rows[i+1] = bch->a_pow_tab[4*i]^ | ||
523 | (a ? bch->a_pow_tab[mod_s(bch, k)] : 0)^ | ||
524 | (b ? bch->a_pow_tab[mod_s(bch, j)] : 0); | ||
525 | j++; | ||
526 | k += 2; | ||
527 | } | ||
528 | /* | ||
529 | * transpose 16x16 matrix before passing it to linear solver | ||
530 | * warning: this code assumes m < 16 | ||
531 | */ | ||
532 | for (j = 8; j != 0; j >>= 1, mask ^= (mask << j)) { | ||
533 | for (k = 0; k < 16; k = (k+j+1) & ~j) { | ||
534 | t = ((rows[k] >> j)^rows[k+j]) & mask; | ||
535 | rows[k] ^= (t << j); | ||
536 | rows[k+j] ^= t; | ||
537 | } | ||
538 | } | ||
539 | return solve_linear_system(bch, rows, roots, 4); | ||
540 | } | ||
541 | |||
542 | /* | ||
543 | * compute root r of a degree 1 polynomial over GF(2^m) (returned as log(1/r)) | ||
544 | */ | ||
545 | static int find_poly_deg1_roots(struct bch_control *bch, struct gf_poly *poly, | ||
546 | unsigned int *roots) | ||
547 | { | ||
548 | int n = 0; | ||
549 | |||
550 | if (poly->c[0]) | ||
551 | /* poly[X] = bX+c with c!=0, root=c/b */ | ||
552 | roots[n++] = mod_s(bch, GF_N(bch)-bch->a_log_tab[poly->c[0]]+ | ||
553 | bch->a_log_tab[poly->c[1]]); | ||
554 | return n; | ||
555 | } | ||
556 | |||
557 | /* | ||
558 | * compute roots of a degree 2 polynomial over GF(2^m) | ||
559 | */ | ||
560 | static int find_poly_deg2_roots(struct bch_control *bch, struct gf_poly *poly, | ||
561 | unsigned int *roots) | ||
562 | { | ||
563 | int n = 0, i, l0, l1, l2; | ||
564 | unsigned int u, v, r; | ||
565 | |||
566 | if (poly->c[0] && poly->c[1]) { | ||
567 | |||
568 | l0 = bch->a_log_tab[poly->c[0]]; | ||
569 | l1 = bch->a_log_tab[poly->c[1]]; | ||
570 | l2 = bch->a_log_tab[poly->c[2]]; | ||
571 | |||
572 | /* using z=a/bX, transform aX^2+bX+c into z^2+z+u (u=ac/b^2) */ | ||
573 | u = a_pow(bch, l0+l2+2*(GF_N(bch)-l1)); | ||
574 | /* | ||
575 | * let u = sum(li.a^i) i=0..m-1; then compute r = sum(li.xi): | ||
576 | * r^2+r = sum(li.(xi^2+xi)) = sum(li.(a^i+Tr(a^i).a^k)) = | ||
577 | * u + sum(li.Tr(a^i).a^k) = u+a^k.Tr(sum(li.a^i)) = u+a^k.Tr(u) | ||
578 | * i.e. r and r+1 are roots iff Tr(u)=0 | ||
579 | */ | ||
580 | r = 0; | ||
581 | v = u; | ||
582 | while (v) { | ||
583 | i = deg(v); | ||
584 | r ^= bch->xi_tab[i]; | ||
585 | v ^= (1 << i); | ||
586 | } | ||
587 | /* verify root */ | ||
588 | if ((gf_sqr(bch, r)^r) == u) { | ||
589 | /* reverse z=a/bX transformation and compute log(1/r) */ | ||
590 | roots[n++] = modulo(bch, 2*GF_N(bch)-l1- | ||
591 | bch->a_log_tab[r]+l2); | ||
592 | roots[n++] = modulo(bch, 2*GF_N(bch)-l1- | ||
593 | bch->a_log_tab[r^1]+l2); | ||
594 | } | ||
595 | } | ||
596 | return n; | ||
597 | } | ||
598 | |||
599 | /* | ||
600 | * compute roots of a degree 3 polynomial over GF(2^m) | ||
601 | */ | ||
602 | static int find_poly_deg3_roots(struct bch_control *bch, struct gf_poly *poly, | ||
603 | unsigned int *roots) | ||
604 | { | ||
605 | int i, n = 0; | ||
606 | unsigned int a, b, c, a2, b2, c2, e3, tmp[4]; | ||
607 | |||
608 | if (poly->c[0]) { | ||
609 | /* transform polynomial into monic X^3 + a2X^2 + b2X + c2 */ | ||
610 | e3 = poly->c[3]; | ||
611 | c2 = gf_div(bch, poly->c[0], e3); | ||
612 | b2 = gf_div(bch, poly->c[1], e3); | ||
613 | a2 = gf_div(bch, poly->c[2], e3); | ||
614 | |||
615 | /* (X+a2)(X^3+a2X^2+b2X+c2) = X^4+aX^2+bX+c (affine) */ | ||
616 | c = gf_mul(bch, a2, c2); /* c = a2c2 */ | ||
617 | b = gf_mul(bch, a2, b2)^c2; /* b = a2b2 + c2 */ | ||
618 | a = gf_sqr(bch, a2)^b2; /* a = a2^2 + b2 */ | ||
619 | |||
620 | /* find the 4 roots of this affine polynomial */ | ||
621 | if (find_affine4_roots(bch, a, b, c, tmp) == 4) { | ||
622 | /* remove a2 from final list of roots */ | ||
623 | for (i = 0; i < 4; i++) { | ||
624 | if (tmp[i] != a2) | ||
625 | roots[n++] = a_ilog(bch, tmp[i]); | ||
626 | } | ||
627 | } | ||
628 | } | ||
629 | return n; | ||
630 | } | ||
631 | |||
632 | /* | ||
633 | * compute roots of a degree 4 polynomial over GF(2^m) | ||
634 | */ | ||
635 | static int find_poly_deg4_roots(struct bch_control *bch, struct gf_poly *poly, | ||
636 | unsigned int *roots) | ||
637 | { | ||
638 | int i, l, n = 0; | ||
639 | unsigned int a, b, c, d, e = 0, f, a2, b2, c2, e4; | ||
640 | |||
641 | if (poly->c[0] == 0) | ||
642 | return 0; | ||
643 | |||
644 | /* transform polynomial into monic X^4 + aX^3 + bX^2 + cX + d */ | ||
645 | e4 = poly->c[4]; | ||
646 | d = gf_div(bch, poly->c[0], e4); | ||
647 | c = gf_div(bch, poly->c[1], e4); | ||
648 | b = gf_div(bch, poly->c[2], e4); | ||
649 | a = gf_div(bch, poly->c[3], e4); | ||
650 | |||
651 | /* use Y=1/X transformation to get an affine polynomial */ | ||
652 | if (a) { | ||
653 | /* first, eliminate cX by using z=X+e with ae^2+c=0 */ | ||
654 | if (c) { | ||
655 | /* compute e such that e^2 = c/a */ | ||
656 | f = gf_div(bch, c, a); | ||
657 | l = a_log(bch, f); | ||
658 | l += (l & 1) ? GF_N(bch) : 0; | ||
659 | e = a_pow(bch, l/2); | ||
660 | /* | ||
661 | * use transformation z=X+e: | ||
662 | * z^4+e^4 + a(z^3+ez^2+e^2z+e^3) + b(z^2+e^2) +cz+ce+d | ||
663 | * z^4 + az^3 + (ae+b)z^2 + (ae^2+c)z+e^4+be^2+ae^3+ce+d | ||
664 | * z^4 + az^3 + (ae+b)z^2 + e^4+be^2+d | ||
665 | * z^4 + az^3 + b'z^2 + d' | ||
666 | */ | ||
667 | d = a_pow(bch, 2*l)^gf_mul(bch, b, f)^d; | ||
668 | b = gf_mul(bch, a, e)^b; | ||
669 | } | ||
670 | /* now, use Y=1/X to get Y^4 + b/dY^2 + a/dY + 1/d */ | ||
671 | if (d == 0) | ||
672 | /* assume all roots have multiplicity 1 */ | ||
673 | return 0; | ||
674 | |||
675 | c2 = gf_inv(bch, d); | ||
676 | b2 = gf_div(bch, a, d); | ||
677 | a2 = gf_div(bch, b, d); | ||
678 | } else { | ||
679 | /* polynomial is already affine */ | ||
680 | c2 = d; | ||
681 | b2 = c; | ||
682 | a2 = b; | ||
683 | } | ||
684 | /* find the 4 roots of this affine polynomial */ | ||
685 | if (find_affine4_roots(bch, a2, b2, c2, roots) == 4) { | ||
686 | for (i = 0; i < 4; i++) { | ||
687 | /* post-process roots (reverse transformations) */ | ||
688 | f = a ? gf_inv(bch, roots[i]) : roots[i]; | ||
689 | roots[i] = a_ilog(bch, f^e); | ||
690 | } | ||
691 | n = 4; | ||
692 | } | ||
693 | return n; | ||
694 | } | ||
695 | |||
696 | /* | ||
697 | * build monic, log-based representation of a polynomial | ||
698 | */ | ||
699 | static void gf_poly_logrep(struct bch_control *bch, | ||
700 | const struct gf_poly *a, int *rep) | ||
701 | { | ||
702 | int i, d = a->deg, l = GF_N(bch)-a_log(bch, a->c[a->deg]); | ||
703 | |||
704 | /* represent 0 values with -1; warning, rep[d] is not set to 1 */ | ||
705 | for (i = 0; i < d; i++) | ||
706 | rep[i] = a->c[i] ? mod_s(bch, a_log(bch, a->c[i])+l) : -1; | ||
707 | } | ||
708 | |||
709 | /* | ||
710 | * compute polynomial Euclidean division remainder in GF(2^m)[X] | ||
711 | */ | ||
712 | static void gf_poly_mod(struct bch_control *bch, struct gf_poly *a, | ||
713 | const struct gf_poly *b, int *rep) | ||
714 | { | ||
715 | int la, p, m; | ||
716 | unsigned int i, j, *c = a->c; | ||
717 | const unsigned int d = b->deg; | ||
718 | |||
719 | if (a->deg < d) | ||
720 | return; | ||
721 | |||
722 | /* reuse or compute log representation of denominator */ | ||
723 | if (!rep) { | ||
724 | rep = bch->cache; | ||
725 | gf_poly_logrep(bch, b, rep); | ||
726 | } | ||
727 | |||
728 | for (j = a->deg; j >= d; j--) { | ||
729 | if (c[j]) { | ||
730 | la = a_log(bch, c[j]); | ||
731 | p = j-d; | ||
732 | for (i = 0; i < d; i++, p++) { | ||
733 | m = rep[i]; | ||
734 | if (m >= 0) | ||
735 | c[p] ^= bch->a_pow_tab[mod_s(bch, | ||
736 | m+la)]; | ||
737 | } | ||
738 | } | ||
739 | } | ||
740 | a->deg = d-1; | ||
741 | while (!c[a->deg] && a->deg) | ||
742 | a->deg--; | ||
743 | } | ||
744 | |||
745 | /* | ||
746 | * compute polynomial Euclidean division quotient in GF(2^m)[X] | ||
747 | */ | ||
748 | static void gf_poly_div(struct bch_control *bch, struct gf_poly *a, | ||
749 | const struct gf_poly *b, struct gf_poly *q) | ||
750 | { | ||
751 | if (a->deg >= b->deg) { | ||
752 | q->deg = a->deg-b->deg; | ||
753 | /* compute a mod b (modifies a) */ | ||
754 | gf_poly_mod(bch, a, b, NULL); | ||
755 | /* quotient is stored in upper part of polynomial a */ | ||
756 | memcpy(q->c, &a->c[b->deg], (1+q->deg)*sizeof(unsigned int)); | ||
757 | } else { | ||
758 | q->deg = 0; | ||
759 | q->c[0] = 0; | ||
760 | } | ||
761 | } | ||
762 | |||
763 | /* | ||
764 | * compute polynomial GCD (Greatest Common Divisor) in GF(2^m)[X] | ||
765 | */ | ||
766 | static struct gf_poly *gf_poly_gcd(struct bch_control *bch, struct gf_poly *a, | ||
767 | struct gf_poly *b) | ||
768 | { | ||
769 | struct gf_poly *tmp; | ||
770 | |||
771 | dbg("gcd(%s,%s)=", gf_poly_str(a), gf_poly_str(b)); | ||
772 | |||
773 | if (a->deg < b->deg) { | ||
774 | tmp = b; | ||
775 | b = a; | ||
776 | a = tmp; | ||
777 | } | ||
778 | |||
779 | while (b->deg > 0) { | ||
780 | gf_poly_mod(bch, a, b, NULL); | ||
781 | tmp = b; | ||
782 | b = a; | ||
783 | a = tmp; | ||
784 | } | ||
785 | |||
786 | dbg("%s\n", gf_poly_str(a)); | ||
787 | |||
788 | return a; | ||
789 | } | ||
790 | |||
791 | /* | ||
792 | * Given a polynomial f and an integer k, compute Tr(a^kX) mod f | ||
793 | * This is used in Berlekamp Trace algorithm for splitting polynomials | ||
794 | */ | ||
795 | static void compute_trace_bk_mod(struct bch_control *bch, int k, | ||
796 | const struct gf_poly *f, struct gf_poly *z, | ||
797 | struct gf_poly *out) | ||
798 | { | ||
799 | const int m = GF_M(bch); | ||
800 | int i, j; | ||
801 | |||
802 | /* z contains z^2j mod f */ | ||
803 | z->deg = 1; | ||
804 | z->c[0] = 0; | ||
805 | z->c[1] = bch->a_pow_tab[k]; | ||
806 | |||
807 | out->deg = 0; | ||
808 | memset(out, 0, GF_POLY_SZ(f->deg)); | ||
809 | |||
810 | /* compute f log representation only once */ | ||
811 | gf_poly_logrep(bch, f, bch->cache); | ||
812 | |||
813 | for (i = 0; i < m; i++) { | ||
814 | /* add a^(k*2^i)(z^(2^i) mod f) and compute (z^(2^i) mod f)^2 */ | ||
815 | for (j = z->deg; j >= 0; j--) { | ||
816 | out->c[j] ^= z->c[j]; | ||
817 | z->c[2*j] = gf_sqr(bch, z->c[j]); | ||
818 | z->c[2*j+1] = 0; | ||
819 | } | ||
820 | if (z->deg > out->deg) | ||
821 | out->deg = z->deg; | ||
822 | |||
823 | if (i < m-1) { | ||
824 | z->deg *= 2; | ||
825 | /* z^(2(i+1)) mod f = (z^(2^i) mod f)^2 mod f */ | ||
826 | gf_poly_mod(bch, z, f, bch->cache); | ||
827 | } | ||
828 | } | ||
829 | while (!out->c[out->deg] && out->deg) | ||
830 | out->deg--; | ||
831 | |||
832 | dbg("Tr(a^%d.X) mod f = %s\n", k, gf_poly_str(out)); | ||
833 | } | ||
834 | |||
835 | /* | ||
836 | * factor a polynomial using Berlekamp Trace algorithm (BTA) | ||
837 | */ | ||
838 | static void factor_polynomial(struct bch_control *bch, int k, struct gf_poly *f, | ||
839 | struct gf_poly **g, struct gf_poly **h) | ||
840 | { | ||
841 | struct gf_poly *f2 = bch->poly_2t[0]; | ||
842 | struct gf_poly *q = bch->poly_2t[1]; | ||
843 | struct gf_poly *tk = bch->poly_2t[2]; | ||
844 | struct gf_poly *z = bch->poly_2t[3]; | ||
845 | struct gf_poly *gcd; | ||
846 | |||
847 | dbg("factoring %s...\n", gf_poly_str(f)); | ||
848 | |||
849 | *g = f; | ||
850 | *h = NULL; | ||
851 | |||
852 | /* tk = Tr(a^k.X) mod f */ | ||
853 | compute_trace_bk_mod(bch, k, f, z, tk); | ||
854 | |||
855 | if (tk->deg > 0) { | ||
856 | /* compute g = gcd(f, tk) (destructive operation) */ | ||
857 | gf_poly_copy(f2, f); | ||
858 | gcd = gf_poly_gcd(bch, f2, tk); | ||
859 | if (gcd->deg < f->deg) { | ||
860 | /* compute h=f/gcd(f,tk); this will modify f and q */ | ||
861 | gf_poly_div(bch, f, gcd, q); | ||
862 | /* store g and h in-place (clobbering f) */ | ||
863 | *h = &((struct gf_poly_deg1 *)f)[gcd->deg].poly; | ||
864 | gf_poly_copy(*g, gcd); | ||
865 | gf_poly_copy(*h, q); | ||
866 | } | ||
867 | } | ||
868 | } | ||
869 | |||
870 | /* | ||
871 | * find roots of a polynomial, using BTZ algorithm; see the beginning of this | ||
872 | * file for details | ||
873 | */ | ||
874 | static int find_poly_roots(struct bch_control *bch, unsigned int k, | ||
875 | struct gf_poly *poly, unsigned int *roots) | ||
876 | { | ||
877 | int cnt; | ||
878 | struct gf_poly *f1, *f2; | ||
879 | |||
880 | switch (poly->deg) { | ||
881 | /* handle low degree polynomials with ad hoc techniques */ | ||
882 | case 1: | ||
883 | cnt = find_poly_deg1_roots(bch, poly, roots); | ||
884 | break; | ||
885 | case 2: | ||
886 | cnt = find_poly_deg2_roots(bch, poly, roots); | ||
887 | break; | ||
888 | case 3: | ||
889 | cnt = find_poly_deg3_roots(bch, poly, roots); | ||
890 | break; | ||
891 | case 4: | ||
892 | cnt = find_poly_deg4_roots(bch, poly, roots); | ||
893 | break; | ||
894 | default: | ||
895 | /* factor polynomial using Berlekamp Trace Algorithm (BTA) */ | ||
896 | cnt = 0; | ||
897 | if (poly->deg && (k <= GF_M(bch))) { | ||
898 | factor_polynomial(bch, k, poly, &f1, &f2); | ||
899 | if (f1) | ||
900 | cnt += find_poly_roots(bch, k+1, f1, roots); | ||
901 | if (f2) | ||
902 | cnt += find_poly_roots(bch, k+1, f2, roots+cnt); | ||
903 | } | ||
904 | break; | ||
905 | } | ||
906 | return cnt; | ||
907 | } | ||
908 | |||
909 | #if defined(USE_CHIEN_SEARCH) | ||
910 | /* | ||
911 | * exhaustive root search (Chien) implementation - not used, included only for | ||
912 | * reference/comparison tests | ||
913 | */ | ||
914 | static int chien_search(struct bch_control *bch, unsigned int len, | ||
915 | struct gf_poly *p, unsigned int *roots) | ||
916 | { | ||
917 | int m; | ||
918 | unsigned int i, j, syn, syn0, count = 0; | ||
919 | const unsigned int k = 8*len+bch->ecc_bits; | ||
920 | |||
921 | /* use a log-based representation of polynomial */ | ||
922 | gf_poly_logrep(bch, p, bch->cache); | ||
923 | bch->cache[p->deg] = 0; | ||
924 | syn0 = gf_div(bch, p->c[0], p->c[p->deg]); | ||
925 | |||
926 | for (i = GF_N(bch)-k+1; i <= GF_N(bch); i++) { | ||
927 | /* compute elp(a^i) */ | ||
928 | for (j = 1, syn = syn0; j <= p->deg; j++) { | ||
929 | m = bch->cache[j]; | ||
930 | if (m >= 0) | ||
931 | syn ^= a_pow(bch, m+j*i); | ||
932 | } | ||
933 | if (syn == 0) { | ||
934 | roots[count++] = GF_N(bch)-i; | ||
935 | if (count == p->deg) | ||
936 | break; | ||
937 | } | ||
938 | } | ||
939 | return (count == p->deg) ? count : 0; | ||
940 | } | ||
941 | #define find_poly_roots(_p, _k, _elp, _loc) chien_search(_p, len, _elp, _loc) | ||
942 | #endif /* USE_CHIEN_SEARCH */ | ||
943 | |||
944 | /** | ||
945 | * decode_bch - decode received codeword and find bit error locations | ||
946 | * @bch: BCH control structure | ||
947 | * @data: received data, ignored if @calc_ecc is provided | ||
948 | * @len: data length in bytes, must always be provided | ||
949 | * @recv_ecc: received ecc, if NULL then assume it was XORed in @calc_ecc | ||
950 | * @calc_ecc: calculated ecc, if NULL then calc_ecc is computed from @data | ||
951 | * @syn: hw computed syndrome data (if NULL, syndrome is calculated) | ||
952 | * @errloc: output array of error locations | ||
953 | * | ||
954 | * Returns: | ||
955 | * The number of errors found, or -EBADMSG if decoding failed, or -EINVAL if | ||
956 | * invalid parameters were provided | ||
957 | * | ||
958 | * Depending on the available hw BCH support and the need to compute @calc_ecc | ||
959 | * separately (using encode_bch()), this function should be called with one of | ||
960 | * the following parameter configurations - | ||
961 | * | ||
962 | * by providing @data and @recv_ecc only: | ||
963 | * decode_bch(@bch, @data, @len, @recv_ecc, NULL, NULL, @errloc) | ||
964 | * | ||
965 | * by providing @recv_ecc and @calc_ecc: | ||
966 | * decode_bch(@bch, NULL, @len, @recv_ecc, @calc_ecc, NULL, @errloc) | ||
967 | * | ||
968 | * by providing ecc = recv_ecc XOR calc_ecc: | ||
969 | * decode_bch(@bch, NULL, @len, NULL, ecc, NULL, @errloc) | ||
970 | * | ||
971 | * by providing syndrome results @syn: | ||
972 | * decode_bch(@bch, NULL, @len, NULL, NULL, @syn, @errloc) | ||
973 | * | ||
974 | * Once decode_bch() has successfully returned with a positive value, error | ||
975 | * locations returned in array @errloc should be interpreted as follows - | ||
976 | * | ||
977 | * if (errloc[n] >= 8*len), then n-th error is located in ecc (no need for | ||
978 | * data correction) | ||
979 | * | ||
980 | * if (errloc[n] < 8*len), then n-th error is located in data and can be | ||
981 | * corrected with statement data[errloc[n]/8] ^= 1 << (errloc[n] % 8); | ||
982 | * | ||
983 | * Note that this function does not perform any data correction by itself, it | ||
984 | * merely indicates error locations. | ||
985 | */ | ||
986 | int decode_bch(struct bch_control *bch, const uint8_t *data, unsigned int len, | ||
987 | const uint8_t *recv_ecc, const uint8_t *calc_ecc, | ||
988 | const unsigned int *syn, unsigned int *errloc) | ||
989 | { | ||
990 | const unsigned int ecc_words = BCH_ECC_WORDS(bch); | ||
991 | unsigned int nbits; | ||
992 | int i, err, nroots; | ||
993 | uint32_t sum; | ||
994 | |||
995 | /* sanity check: make sure data length can be handled */ | ||
996 | if (8*len > (bch->n-bch->ecc_bits)) | ||
997 | return -EINVAL; | ||
998 | |||
999 | /* if caller does not provide syndromes, compute them */ | ||
1000 | if (!syn) { | ||
1001 | if (!calc_ecc) { | ||
1002 | /* compute received data ecc into an internal buffer */ | ||
1003 | if (!data || !recv_ecc) | ||
1004 | return -EINVAL; | ||
1005 | encode_bch(bch, data, len, NULL); | ||
1006 | } else { | ||
1007 | /* load provided calculated ecc */ | ||
1008 | load_ecc8(bch, bch->ecc_buf, calc_ecc); | ||
1009 | } | ||
1010 | /* load received ecc or assume it was XORed in calc_ecc */ | ||
1011 | if (recv_ecc) { | ||
1012 | load_ecc8(bch, bch->ecc_buf2, recv_ecc); | ||
1013 | /* XOR received and calculated ecc */ | ||
1014 | for (i = 0, sum = 0; i < (int)ecc_words; i++) { | ||
1015 | bch->ecc_buf[i] ^= bch->ecc_buf2[i]; | ||
1016 | sum |= bch->ecc_buf[i]; | ||
1017 | } | ||
1018 | if (!sum) | ||
1019 | /* no error found */ | ||
1020 | return 0; | ||
1021 | } | ||
1022 | compute_syndromes(bch, bch->ecc_buf, bch->syn); | ||
1023 | syn = bch->syn; | ||
1024 | } | ||
1025 | |||
1026 | err = compute_error_locator_polynomial(bch, syn); | ||
1027 | if (err > 0) { | ||
1028 | nroots = find_poly_roots(bch, 1, bch->elp, errloc); | ||
1029 | if (err != nroots) | ||
1030 | err = -1; | ||
1031 | } | ||
1032 | if (err > 0) { | ||
1033 | /* post-process raw error locations for easier correction */ | ||
1034 | nbits = (len*8)+bch->ecc_bits; | ||
1035 | for (i = 0; i < err; i++) { | ||
1036 | if (errloc[i] >= nbits) { | ||
1037 | err = -1; | ||
1038 | break; | ||
1039 | } | ||
1040 | errloc[i] = nbits-1-errloc[i]; | ||
1041 | errloc[i] = (errloc[i] & ~7)|(7-(errloc[i] & 7)); | ||
1042 | } | ||
1043 | } | ||
1044 | return (err >= 0) ? err : -EBADMSG; | ||
1045 | } | ||
1046 | EXPORT_SYMBOL_GPL(decode_bch); | ||
1047 | |||
1048 | /* | ||
1049 | * generate Galois field lookup tables | ||
1050 | */ | ||
1051 | static int build_gf_tables(struct bch_control *bch, unsigned int poly) | ||
1052 | { | ||
1053 | unsigned int i, x = 1; | ||
1054 | const unsigned int k = 1 << deg(poly); | ||
1055 | |||
1056 | /* primitive polynomial must be of degree m */ | ||
1057 | if (k != (1u << GF_M(bch))) | ||
1058 | return -1; | ||
1059 | |||
1060 | for (i = 0; i < GF_N(bch); i++) { | ||
1061 | bch->a_pow_tab[i] = x; | ||
1062 | bch->a_log_tab[x] = i; | ||
1063 | if (i && (x == 1)) | ||
1064 | /* polynomial is not primitive (a^i=1 with 0<i<2^m-1) */ | ||
1065 | return -1; | ||
1066 | x <<= 1; | ||
1067 | if (x & k) | ||
1068 | x ^= poly; | ||
1069 | } | ||
1070 | bch->a_pow_tab[GF_N(bch)] = 1; | ||
1071 | bch->a_log_tab[0] = 0; | ||
1072 | |||
1073 | return 0; | ||
1074 | } | ||
1075 | |||
1076 | /* | ||
1077 | * compute generator polynomial remainder tables for fast encoding | ||
1078 | */ | ||
1079 | static void build_mod8_tables(struct bch_control *bch, const uint32_t *g) | ||
1080 | { | ||
1081 | int i, j, b, d; | ||
1082 | uint32_t data, hi, lo, *tab; | ||
1083 | const int l = BCH_ECC_WORDS(bch); | ||
1084 | const int plen = DIV_ROUND_UP(bch->ecc_bits+1, 32); | ||
1085 | const int ecclen = DIV_ROUND_UP(bch->ecc_bits, 32); | ||
1086 | |||
1087 | memset(bch->mod8_tab, 0, 4*256*l*sizeof(*bch->mod8_tab)); | ||
1088 | |||
1089 | for (i = 0; i < 256; i++) { | ||
1090 | /* p(X)=i is a small polynomial of weight <= 8 */ | ||
1091 | for (b = 0; b < 4; b++) { | ||
1092 | /* we want to compute (p(X).X^(8*b+deg(g))) mod g(X) */ | ||
1093 | tab = bch->mod8_tab + (b*256+i)*l; | ||
1094 | data = i << (8*b); | ||
1095 | while (data) { | ||
1096 | d = deg(data); | ||
1097 | /* subtract X^d.g(X) from p(X).X^(8*b+deg(g)) */ | ||
1098 | data ^= g[0] >> (31-d); | ||
1099 | for (j = 0; j < ecclen; j++) { | ||
1100 | hi = (d < 31) ? g[j] << (d+1) : 0; | ||
1101 | lo = (j+1 < plen) ? | ||
1102 | g[j+1] >> (31-d) : 0; | ||
1103 | tab[j] ^= hi|lo; | ||
1104 | } | ||
1105 | } | ||
1106 | } | ||
1107 | } | ||
1108 | } | ||
1109 | |||
1110 | /* | ||
1111 | * build a base for factoring degree 2 polynomials | ||
1112 | */ | ||
1113 | static int build_deg2_base(struct bch_control *bch) | ||
1114 | { | ||
1115 | const int m = GF_M(bch); | ||
1116 | int i, j, r; | ||
1117 | unsigned int sum, x, y, remaining, ak = 0, xi[m]; | ||
1118 | |||
1119 | /* find k s.t. Tr(a^k) = 1 and 0 <= k < m */ | ||
1120 | for (i = 0; i < m; i++) { | ||
1121 | for (j = 0, sum = 0; j < m; j++) | ||
1122 | sum ^= a_pow(bch, i*(1 << j)); | ||
1123 | |||
1124 | if (sum) { | ||
1125 | ak = bch->a_pow_tab[i]; | ||
1126 | break; | ||
1127 | } | ||
1128 | } | ||
1129 | /* find xi, i=0..m-1 such that xi^2+xi = a^i+Tr(a^i).a^k */ | ||
1130 | remaining = m; | ||
1131 | memset(xi, 0, sizeof(xi)); | ||
1132 | |||
1133 | for (x = 0; (x <= GF_N(bch)) && remaining; x++) { | ||
1134 | y = gf_sqr(bch, x)^x; | ||
1135 | for (i = 0; i < 2; i++) { | ||
1136 | r = a_log(bch, y); | ||
1137 | if (y && (r < m) && !xi[r]) { | ||
1138 | bch->xi_tab[r] = x; | ||
1139 | xi[r] = 1; | ||
1140 | remaining--; | ||
1141 | dbg("x%d = %x\n", r, x); | ||
1142 | break; | ||
1143 | } | ||
1144 | y ^= ak; | ||
1145 | } | ||
1146 | } | ||
1147 | /* should not happen but check anyway */ | ||
1148 | return remaining ? -1 : 0; | ||
1149 | } | ||
1150 | |||
1151 | static void *bch_alloc(size_t size, int *err) | ||
1152 | { | ||
1153 | void *ptr; | ||
1154 | |||
1155 | ptr = kmalloc(size, GFP_KERNEL); | ||
1156 | if (ptr == NULL) | ||
1157 | *err = 1; | ||
1158 | return ptr; | ||
1159 | } | ||
1160 | |||
1161 | /* | ||
1162 | * compute generator polynomial for given (m,t) parameters. | ||
1163 | */ | ||
1164 | static uint32_t *compute_generator_polynomial(struct bch_control *bch) | ||
1165 | { | ||
1166 | const unsigned int m = GF_M(bch); | ||
1167 | const unsigned int t = GF_T(bch); | ||
1168 | int n, err = 0; | ||
1169 | unsigned int i, j, nbits, r, word, *roots; | ||
1170 | struct gf_poly *g; | ||
1171 | uint32_t *genpoly; | ||
1172 | |||
1173 | g = bch_alloc(GF_POLY_SZ(m*t), &err); | ||
1174 | roots = bch_alloc((bch->n+1)*sizeof(*roots), &err); | ||
1175 | genpoly = bch_alloc(DIV_ROUND_UP(m*t+1, 32)*sizeof(*genpoly), &err); | ||
1176 | |||
1177 | if (err) { | ||
1178 | kfree(genpoly); | ||
1179 | genpoly = NULL; | ||
1180 | goto finish; | ||
1181 | } | ||
1182 | |||
1183 | /* enumerate all roots of g(X) */ | ||
1184 | memset(roots , 0, (bch->n+1)*sizeof(*roots)); | ||
1185 | for (i = 0; i < t; i++) { | ||
1186 | for (j = 0, r = 2*i+1; j < m; j++) { | ||
1187 | roots[r] = 1; | ||
1188 | r = mod_s(bch, 2*r); | ||
1189 | } | ||
1190 | } | ||
1191 | /* build generator polynomial g(X) */ | ||
1192 | g->deg = 0; | ||
1193 | g->c[0] = 1; | ||
1194 | for (i = 0; i < GF_N(bch); i++) { | ||
1195 | if (roots[i]) { | ||
1196 | /* multiply g(X) by (X+root) */ | ||
1197 | r = bch->a_pow_tab[i]; | ||
1198 | g->c[g->deg+1] = 1; | ||
1199 | for (j = g->deg; j > 0; j--) | ||
1200 | g->c[j] = gf_mul(bch, g->c[j], r)^g->c[j-1]; | ||
1201 | |||
1202 | g->c[0] = gf_mul(bch, g->c[0], r); | ||
1203 | g->deg++; | ||
1204 | } | ||
1205 | } | ||
1206 | /* store left-justified binary representation of g(X) */ | ||
1207 | n = g->deg+1; | ||
1208 | i = 0; | ||
1209 | |||
1210 | while (n > 0) { | ||
1211 | nbits = (n > 32) ? 32 : n; | ||
1212 | for (j = 0, word = 0; j < nbits; j++) { | ||
1213 | if (g->c[n-1-j]) | ||
1214 | word |= 1u << (31-j); | ||
1215 | } | ||
1216 | genpoly[i++] = word; | ||
1217 | n -= nbits; | ||
1218 | } | ||
1219 | bch->ecc_bits = g->deg; | ||
1220 | |||
1221 | finish: | ||
1222 | kfree(g); | ||
1223 | kfree(roots); | ||
1224 | |||
1225 | return genpoly; | ||
1226 | } | ||
1227 | |||
1228 | /** | ||
1229 | * init_bch - initialize a BCH encoder/decoder | ||
1230 | * @m: Galois field order, should be in the range 5-15 | ||
1231 | * @t: maximum error correction capability, in bits | ||
1232 | * @prim_poly: user-provided primitive polynomial (or 0 to use default) | ||
1233 | * | ||
1234 | * Returns: | ||
1235 | * a newly allocated BCH control structure if successful, NULL otherwise | ||
1236 | * | ||
1237 | * This initialization can take some time, as lookup tables are built for fast | ||
1238 | * encoding/decoding; make sure not to call this function from a time critical | ||
1239 | * path. Usually, init_bch() should be called on module/driver init and | ||
1240 | * free_bch() should be called to release memory on exit. | ||
1241 | * | ||
1242 | * You may provide your own primitive polynomial of degree @m in argument | ||
1243 | * @prim_poly, or let init_bch() use its default polynomial. | ||
1244 | * | ||
1245 | * Once init_bch() has successfully returned a pointer to a newly allocated | ||
1246 | * BCH control structure, ecc length in bytes is given by member @ecc_bytes of | ||
1247 | * the structure. | ||
1248 | */ | ||
1249 | struct bch_control *init_bch(int m, int t, unsigned int prim_poly) | ||
1250 | { | ||
1251 | int err = 0; | ||
1252 | unsigned int i, words; | ||
1253 | uint32_t *genpoly; | ||
1254 | struct bch_control *bch = NULL; | ||
1255 | |||
1256 | const int min_m = 5; | ||
1257 | const int max_m = 15; | ||
1258 | |||
1259 | /* default primitive polynomials */ | ||
1260 | static const unsigned int prim_poly_tab[] = { | ||
1261 | 0x25, 0x43, 0x83, 0x11d, 0x211, 0x409, 0x805, 0x1053, 0x201b, | ||
1262 | 0x402b, 0x8003, | ||
1263 | }; | ||
1264 | |||
1265 | #if defined(CONFIG_BCH_CONST_PARAMS) | ||
1266 | if ((m != (CONFIG_BCH_CONST_M)) || (t != (CONFIG_BCH_CONST_T))) { | ||
1267 | printk(KERN_ERR "bch encoder/decoder was configured to support " | ||
1268 | "parameters m=%d, t=%d only!\n", | ||
1269 | CONFIG_BCH_CONST_M, CONFIG_BCH_CONST_T); | ||
1270 | goto fail; | ||
1271 | } | ||
1272 | #endif | ||
1273 | if ((m < min_m) || (m > max_m)) | ||
1274 | /* | ||
1275 | * values of m greater than 15 are not currently supported; | ||
1276 | * supporting m > 15 would require changing table base type | ||
1277 | * (uint16_t) and a small patch in matrix transposition | ||
1278 | */ | ||
1279 | goto fail; | ||
1280 | |||
1281 | /* sanity checks */ | ||
1282 | if ((t < 1) || (m*t >= ((1 << m)-1))) | ||
1283 | /* invalid t value */ | ||
1284 | goto fail; | ||
1285 | |||
1286 | /* select a primitive polynomial for generating GF(2^m) */ | ||
1287 | if (prim_poly == 0) | ||
1288 | prim_poly = prim_poly_tab[m-min_m]; | ||
1289 | |||
1290 | bch = kzalloc(sizeof(*bch), GFP_KERNEL); | ||
1291 | if (bch == NULL) | ||
1292 | goto fail; | ||
1293 | |||
1294 | bch->m = m; | ||
1295 | bch->t = t; | ||
1296 | bch->n = (1 << m)-1; | ||
1297 | words = DIV_ROUND_UP(m*t, 32); | ||
1298 | bch->ecc_bytes = DIV_ROUND_UP(m*t, 8); | ||
1299 | bch->a_pow_tab = bch_alloc((1+bch->n)*sizeof(*bch->a_pow_tab), &err); | ||
1300 | bch->a_log_tab = bch_alloc((1+bch->n)*sizeof(*bch->a_log_tab), &err); | ||
1301 | bch->mod8_tab = bch_alloc(words*1024*sizeof(*bch->mod8_tab), &err); | ||
1302 | bch->ecc_buf = bch_alloc(words*sizeof(*bch->ecc_buf), &err); | ||
1303 | bch->ecc_buf2 = bch_alloc(words*sizeof(*bch->ecc_buf2), &err); | ||
1304 | bch->xi_tab = bch_alloc(m*sizeof(*bch->xi_tab), &err); | ||
1305 | bch->syn = bch_alloc(2*t*sizeof(*bch->syn), &err); | ||
1306 | bch->cache = bch_alloc(2*t*sizeof(*bch->cache), &err); | ||
1307 | bch->elp = bch_alloc((t+1)*sizeof(struct gf_poly_deg1), &err); | ||
1308 | |||
1309 | for (i = 0; i < ARRAY_SIZE(bch->poly_2t); i++) | ||
1310 | bch->poly_2t[i] = bch_alloc(GF_POLY_SZ(2*t), &err); | ||
1311 | |||
1312 | if (err) | ||
1313 | goto fail; | ||
1314 | |||
1315 | err = build_gf_tables(bch, prim_poly); | ||
1316 | if (err) | ||
1317 | goto fail; | ||
1318 | |||
1319 | /* use generator polynomial for computing encoding tables */ | ||
1320 | genpoly = compute_generator_polynomial(bch); | ||
1321 | if (genpoly == NULL) | ||
1322 | goto fail; | ||
1323 | |||
1324 | build_mod8_tables(bch, genpoly); | ||
1325 | kfree(genpoly); | ||
1326 | |||
1327 | err = build_deg2_base(bch); | ||
1328 | if (err) | ||
1329 | goto fail; | ||
1330 | |||
1331 | return bch; | ||
1332 | |||
1333 | fail: | ||
1334 | free_bch(bch); | ||
1335 | return NULL; | ||
1336 | } | ||
1337 | EXPORT_SYMBOL_GPL(init_bch); | ||
1338 | |||
1339 | /** | ||
1340 | * free_bch - free the BCH control structure | ||
1341 | * @bch: BCH control structure to release | ||
1342 | */ | ||
1343 | void free_bch(struct bch_control *bch) | ||
1344 | { | ||
1345 | unsigned int i; | ||
1346 | |||
1347 | if (bch) { | ||
1348 | kfree(bch->a_pow_tab); | ||
1349 | kfree(bch->a_log_tab); | ||
1350 | kfree(bch->mod8_tab); | ||
1351 | kfree(bch->ecc_buf); | ||
1352 | kfree(bch->ecc_buf2); | ||
1353 | kfree(bch->xi_tab); | ||
1354 | kfree(bch->syn); | ||
1355 | kfree(bch->cache); | ||
1356 | kfree(bch->elp); | ||
1357 | |||
1358 | for (i = 0; i < ARRAY_SIZE(bch->poly_2t); i++) | ||
1359 | kfree(bch->poly_2t[i]); | ||
1360 | |||
1361 | kfree(bch); | ||
1362 | } | ||
1363 | } | ||
1364 | EXPORT_SYMBOL_GPL(free_bch); | ||
1365 | |||
1366 | MODULE_LICENSE("GPL"); | ||
1367 | MODULE_AUTHOR("Ivan Djelic <ivan.djelic@parrot.com>"); | ||
1368 | MODULE_DESCRIPTION("Binary BCH encoder/decoder"); | ||