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1400 lines
36 KiB
1400 lines
36 KiB
// SPDX-License-Identifier: GPL-2.0 |
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/* |
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* Generic binary BCH encoding/decoding library |
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* |
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* Copyright © 2011 Parrot S.A. |
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* |
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* Author: Ivan Djelic <[email protected]> |
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* |
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* Description: |
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* |
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* This library provides runtime configurable encoding/decoding of binary |
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* Bose-Chaudhuri-Hocquenghem (BCH) codes. |
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* |
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* Call init_bch to get a pointer to a newly allocated bch_control structure for |
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* the given m (Galois field order), t (error correction capability) and |
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* (optional) primitive polynomial parameters. |
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* |
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* Call encode_bch to compute and store ecc parity bytes to a given buffer. |
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* Call decode_bch to detect and locate errors in received data. |
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* |
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* On systems supporting hw BCH features, intermediate results may be provided |
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* to decode_bch in order to skip certain steps. See decode_bch() documentation |
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* for details. |
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* |
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* Option CONFIG_BCH_CONST_PARAMS can be used to force fixed values of |
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* parameters m and t; thus allowing extra compiler optimizations and providing |
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* better (up to 2x) encoding performance. Using this option makes sense when |
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* (m,t) are fixed and known in advance, e.g. when using BCH error correction |
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* on a particular NAND flash device. |
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* |
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* Algorithmic details: |
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* |
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* Encoding is performed by processing 32 input bits in parallel, using 4 |
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* remainder lookup tables. |
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* |
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* The final stage of decoding involves the following internal steps: |
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* a. Syndrome computation |
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* b. Error locator polynomial computation using Berlekamp-Massey algorithm |
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* c. Error locator root finding (by far the most expensive step) |
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* |
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* In this implementation, step c is not performed using the usual Chien search. |
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* Instead, an alternative approach described in [1] is used. It consists in |
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* factoring the error locator polynomial using the Berlekamp Trace algorithm |
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* (BTA) down to a certain degree (4), after which ad hoc low-degree polynomial |
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* solving techniques [2] are used. The resulting algorithm, called BTZ, yields |
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* much better performance than Chien search for usual (m,t) values (typically |
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* m >= 13, t < 32, see [1]). |
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* |
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* [1] B. Biswas, V. Herbert. Efficient root finding of polynomials over fields |
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* of characteristic 2, in: Western European Workshop on Research in Cryptology |
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* - WEWoRC 2009, Graz, Austria, LNCS, Springer, July 2009, to appear. |
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* [2] [Zin96] V.A. Zinoviev. On the solution of equations of degree 10 over |
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* finite fields GF(2^q). In Rapport de recherche INRIA no 2829, 1996. |
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*/ |
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#ifndef USE_HOSTCC |
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#include <common.h> |
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#include <ubi_uboot.h> |
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|
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#include <linux/bitops.h> |
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#else |
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#include <errno.h> |
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#if defined(__FreeBSD__) |
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#include <sys/endian.h> |
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#else |
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#include <endian.h> |
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#endif |
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#include <stdint.h> |
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#include <stdlib.h> |
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#include <string.h> |
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|
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#undef cpu_to_be32 |
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#define cpu_to_be32 htobe32 |
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#define DIV_ROUND_UP(n,d) (((n) + (d) - 1) / (d)) |
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#define kmalloc(size, flags) malloc(size) |
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#define kzalloc(size, flags) calloc(1, size) |
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#define kfree free |
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#define ARRAY_SIZE(arr) (sizeof(arr) / sizeof((arr)[0])) |
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#endif |
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#include <asm/byteorder.h> |
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#include <linux/bch.h> |
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|
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#if defined(CONFIG_BCH_CONST_PARAMS) |
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#define GF_M(_p) (CONFIG_BCH_CONST_M) |
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#define GF_T(_p) (CONFIG_BCH_CONST_T) |
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#define GF_N(_p) ((1 << (CONFIG_BCH_CONST_M))-1) |
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#else |
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#define GF_M(_p) ((_p)->m) |
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#define GF_T(_p) ((_p)->t) |
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#define GF_N(_p) ((_p)->n) |
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#endif |
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#define BCH_ECC_WORDS(_p) DIV_ROUND_UP(GF_M(_p)*GF_T(_p), 32) |
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#define BCH_ECC_BYTES(_p) DIV_ROUND_UP(GF_M(_p)*GF_T(_p), 8) |
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|
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#ifndef dbg |
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#define dbg(_fmt, args...) do {} while (0) |
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#endif |
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/* |
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* represent a polynomial over GF(2^m) |
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*/ |
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struct gf_poly { |
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unsigned int deg; /* polynomial degree */ |
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unsigned int c[0]; /* polynomial terms */ |
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}; |
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|
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/* given its degree, compute a polynomial size in bytes */ |
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#define GF_POLY_SZ(_d) (sizeof(struct gf_poly)+((_d)+1)*sizeof(unsigned int)) |
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|
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/* polynomial of degree 1 */ |
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struct gf_poly_deg1 { |
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struct gf_poly poly; |
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unsigned int c[2]; |
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}; |
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|
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#ifdef USE_HOSTCC |
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#if !defined(__DragonFly__) && !defined(__FreeBSD__) |
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static int fls(int x) |
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{ |
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int r = 32; |
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if (!x) |
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return 0; |
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if (!(x & 0xffff0000u)) { |
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x <<= 16; |
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r -= 16; |
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} |
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if (!(x & 0xff000000u)) { |
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x <<= 8; |
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r -= 8; |
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} |
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if (!(x & 0xf0000000u)) { |
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x <<= 4; |
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r -= 4; |
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} |
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if (!(x & 0xc0000000u)) { |
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x <<= 2; |
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r -= 2; |
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} |
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if (!(x & 0x80000000u)) { |
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x <<= 1; |
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r -= 1; |
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} |
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return r; |
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} |
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#endif |
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#endif |
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/* |
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* same as encode_bch(), but process input data one byte at a time |
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*/ |
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static void encode_bch_unaligned(struct bch_control *bch, |
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const unsigned char *data, unsigned int len, |
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uint32_t *ecc) |
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{ |
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int i; |
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const uint32_t *p; |
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const int l = BCH_ECC_WORDS(bch)-1; |
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|
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while (len--) { |
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p = bch->mod8_tab + (l+1)*(((ecc[0] >> 24)^(*data++)) & 0xff); |
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for (i = 0; i < l; i++) |
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ecc[i] = ((ecc[i] << 8)|(ecc[i+1] >> 24))^(*p++); |
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ecc[l] = (ecc[l] << 8)^(*p); |
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} |
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} |
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/* |
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* convert ecc bytes to aligned, zero-padded 32-bit ecc words |
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*/ |
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static void load_ecc8(struct bch_control *bch, uint32_t *dst, |
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const uint8_t *src) |
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{ |
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uint8_t pad[4] = {0, 0, 0, 0}; |
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unsigned int i, nwords = BCH_ECC_WORDS(bch)-1; |
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for (i = 0; i < nwords; i++, src += 4) |
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dst[i] = (src[0] << 24)|(src[1] << 16)|(src[2] << 8)|src[3]; |
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memcpy(pad, src, BCH_ECC_BYTES(bch)-4*nwords); |
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dst[nwords] = (pad[0] << 24)|(pad[1] << 16)|(pad[2] << 8)|pad[3]; |
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} |
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|
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/* |
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* convert 32-bit ecc words to ecc bytes |
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*/ |
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static void store_ecc8(struct bch_control *bch, uint8_t *dst, |
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const uint32_t *src) |
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{ |
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uint8_t pad[4]; |
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unsigned int i, nwords = BCH_ECC_WORDS(bch)-1; |
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for (i = 0; i < nwords; i++) { |
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*dst++ = (src[i] >> 24); |
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*dst++ = (src[i] >> 16) & 0xff; |
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*dst++ = (src[i] >> 8) & 0xff; |
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*dst++ = (src[i] >> 0) & 0xff; |
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} |
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pad[0] = (src[nwords] >> 24); |
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pad[1] = (src[nwords] >> 16) & 0xff; |
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pad[2] = (src[nwords] >> 8) & 0xff; |
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pad[3] = (src[nwords] >> 0) & 0xff; |
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memcpy(dst, pad, BCH_ECC_BYTES(bch)-4*nwords); |
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} |
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/** |
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* encode_bch - calculate BCH ecc parity of data |
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* @bch: BCH control structure |
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* @data: data to encode |
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* @len: data length in bytes |
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* @ecc: ecc parity data, must be initialized by caller |
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* |
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* The @ecc parity array is used both as input and output parameter, in order to |
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* allow incremental computations. It should be of the size indicated by member |
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* @ecc_bytes of @bch, and should be initialized to 0 before the first call. |
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* |
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* The exact number of computed ecc parity bits is given by member @ecc_bits of |
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* @bch; it may be less than m*t for large values of t. |
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*/ |
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void encode_bch(struct bch_control *bch, const uint8_t *data, |
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unsigned int len, uint8_t *ecc) |
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{ |
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const unsigned int l = BCH_ECC_WORDS(bch)-1; |
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unsigned int i, mlen; |
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unsigned long m; |
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uint32_t w, r[l+1]; |
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const uint32_t * const tab0 = bch->mod8_tab; |
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const uint32_t * const tab1 = tab0 + 256*(l+1); |
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const uint32_t * const tab2 = tab1 + 256*(l+1); |
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const uint32_t * const tab3 = tab2 + 256*(l+1); |
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const uint32_t *pdata, *p0, *p1, *p2, *p3; |
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if (ecc) { |
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/* load ecc parity bytes into internal 32-bit buffer */ |
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load_ecc8(bch, bch->ecc_buf, ecc); |
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} else { |
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memset(bch->ecc_buf, 0, sizeof(r)); |
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} |
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/* process first unaligned data bytes */ |
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m = ((unsigned long)data) & 3; |
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if (m) { |
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mlen = (len < (4-m)) ? len : 4-m; |
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encode_bch_unaligned(bch, data, mlen, bch->ecc_buf); |
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data += mlen; |
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len -= mlen; |
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} |
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/* process 32-bit aligned data words */ |
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pdata = (uint32_t *)data; |
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mlen = len/4; |
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data += 4*mlen; |
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len -= 4*mlen; |
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memcpy(r, bch->ecc_buf, sizeof(r)); |
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/* |
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* split each 32-bit word into 4 polynomials of weight 8 as follows: |
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* |
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* 31 ...24 23 ...16 15 ... 8 7 ... 0 |
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* xxxxxxxx yyyyyyyy zzzzzzzz tttttttt |
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* tttttttt mod g = r0 (precomputed) |
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* zzzzzzzz 00000000 mod g = r1 (precomputed) |
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* yyyyyyyy 00000000 00000000 mod g = r2 (precomputed) |
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* xxxxxxxx 00000000 00000000 00000000 mod g = r3 (precomputed) |
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* xxxxxxxx yyyyyyyy zzzzzzzz tttttttt mod g = r0^r1^r2^r3 |
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*/ |
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while (mlen--) { |
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/* input data is read in big-endian format */ |
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w = r[0]^cpu_to_be32(*pdata++); |
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p0 = tab0 + (l+1)*((w >> 0) & 0xff); |
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p1 = tab1 + (l+1)*((w >> 8) & 0xff); |
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p2 = tab2 + (l+1)*((w >> 16) & 0xff); |
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p3 = tab3 + (l+1)*((w >> 24) & 0xff); |
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for (i = 0; i < l; i++) |
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r[i] = r[i+1]^p0[i]^p1[i]^p2[i]^p3[i]; |
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r[l] = p0[l]^p1[l]^p2[l]^p3[l]; |
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} |
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memcpy(bch->ecc_buf, r, sizeof(r)); |
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/* process last unaligned bytes */ |
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if (len) |
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encode_bch_unaligned(bch, data, len, bch->ecc_buf); |
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/* store ecc parity bytes into original parity buffer */ |
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if (ecc) |
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store_ecc8(bch, ecc, bch->ecc_buf); |
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} |
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static inline int modulo(struct bch_control *bch, unsigned int v) |
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{ |
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const unsigned int n = GF_N(bch); |
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while (v >= n) { |
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v -= n; |
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v = (v & n) + (v >> GF_M(bch)); |
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} |
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return v; |
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} |
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/* |
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* shorter and faster modulo function, only works when v < 2N. |
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*/ |
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static inline int mod_s(struct bch_control *bch, unsigned int v) |
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{ |
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const unsigned int n = GF_N(bch); |
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return (v < n) ? v : v-n; |
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} |
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static inline int deg(unsigned int poly) |
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{ |
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/* polynomial degree is the most-significant bit index */ |
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return fls(poly)-1; |
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} |
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static inline int parity(unsigned int x) |
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{ |
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/* |
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* public domain code snippet, lifted from |
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* http://www-graphics.stanford.edu/~seander/bithacks.html |
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*/ |
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x ^= x >> 1; |
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x ^= x >> 2; |
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x = (x & 0x11111111U) * 0x11111111U; |
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return (x >> 28) & 1; |
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} |
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|
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/* Galois field basic operations: multiply, divide, inverse, etc. */ |
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static inline unsigned int gf_mul(struct bch_control *bch, unsigned int a, |
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unsigned int b) |
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{ |
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return (a && b) ? bch->a_pow_tab[mod_s(bch, bch->a_log_tab[a]+ |
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bch->a_log_tab[b])] : 0; |
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} |
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static inline unsigned int gf_sqr(struct bch_control *bch, unsigned int a) |
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{ |
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return a ? bch->a_pow_tab[mod_s(bch, 2*bch->a_log_tab[a])] : 0; |
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} |
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static inline unsigned int gf_div(struct bch_control *bch, unsigned int a, |
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unsigned int b) |
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{ |
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return a ? bch->a_pow_tab[mod_s(bch, bch->a_log_tab[a]+ |
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GF_N(bch)-bch->a_log_tab[b])] : 0; |
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} |
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static inline unsigned int gf_inv(struct bch_control *bch, unsigned int a) |
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{ |
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return bch->a_pow_tab[GF_N(bch)-bch->a_log_tab[a]]; |
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} |
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static inline unsigned int a_pow(struct bch_control *bch, int i) |
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{ |
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return bch->a_pow_tab[modulo(bch, i)]; |
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} |
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static inline int a_log(struct bch_control *bch, unsigned int x) |
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{ |
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return bch->a_log_tab[x]; |
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} |
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static inline int a_ilog(struct bch_control *bch, unsigned int x) |
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{ |
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return mod_s(bch, GF_N(bch)-bch->a_log_tab[x]); |
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} |
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/* |
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* compute 2t syndromes of ecc polynomial, i.e. ecc(a^j) for j=1..2t |
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*/ |
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static void compute_syndromes(struct bch_control *bch, uint32_t *ecc, |
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unsigned int *syn) |
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{ |
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int i, j, s; |
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unsigned int m; |
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uint32_t poly; |
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const int t = GF_T(bch); |
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s = bch->ecc_bits; |
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|
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/* make sure extra bits in last ecc word are cleared */ |
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m = ((unsigned int)s) & 31; |
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if (m) |
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ecc[s/32] &= ~((1u << (32-m))-1); |
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memset(syn, 0, 2*t*sizeof(*syn)); |
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|
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/* compute v(a^j) for j=1 .. 2t-1 */ |
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do { |
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poly = *ecc++; |
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s -= 32; |
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while (poly) { |
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i = deg(poly); |
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for (j = 0; j < 2*t; j += 2) |
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syn[j] ^= a_pow(bch, (j+1)*(i+s)); |
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poly ^= (1 << i); |
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} |
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} while (s > 0); |
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|
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/* v(a^(2j)) = v(a^j)^2 */ |
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for (j = 0; j < t; j++) |
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syn[2*j+1] = gf_sqr(bch, syn[j]); |
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} |
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static void gf_poly_copy(struct gf_poly *dst, struct gf_poly *src) |
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{ |
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memcpy(dst, src, GF_POLY_SZ(src->deg)); |
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} |
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static int compute_error_locator_polynomial(struct bch_control *bch, |
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const unsigned int *syn) |
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{ |
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const unsigned int t = GF_T(bch); |
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const unsigned int n = GF_N(bch); |
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unsigned int i, j, tmp, l, pd = 1, d = syn[0]; |
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struct gf_poly *elp = bch->elp; |
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struct gf_poly *pelp = bch->poly_2t[0]; |
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struct gf_poly *elp_copy = bch->poly_2t[1]; |
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int k, pp = -1; |
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memset(pelp, 0, GF_POLY_SZ(2*t)); |
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memset(elp, 0, GF_POLY_SZ(2*t)); |
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pelp->deg = 0; |
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pelp->c[0] = 1; |
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elp->deg = 0; |
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elp->c[0] = 1; |
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|
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/* use simplified binary Berlekamp-Massey algorithm */ |
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for (i = 0; (i < t) && (elp->deg <= t); i++) { |
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if (d) { |
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k = 2*i-pp; |
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gf_poly_copy(elp_copy, elp); |
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/* e[i+1](X) = e[i](X)+di*dp^-1*X^2(i-p)*e[p](X) */ |
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tmp = a_log(bch, d)+n-a_log(bch, pd); |
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for (j = 0; j <= pelp->deg; j++) { |
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if (pelp->c[j]) { |
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l = a_log(bch, pelp->c[j]); |
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elp->c[j+k] ^= a_pow(bch, tmp+l); |
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} |
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} |
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/* compute l[i+1] = max(l[i]->c[l[p]+2*(i-p]) */ |
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tmp = pelp->deg+k; |
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if (tmp > elp->deg) { |
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elp->deg = tmp; |
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gf_poly_copy(pelp, elp_copy); |
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pd = d; |
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pp = 2*i; |
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} |
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} |
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/* di+1 = S(2i+3)+elp[i+1].1*S(2i+2)+...+elp[i+1].lS(2i+3-l) */ |
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if (i < t-1) { |
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d = syn[2*i+2]; |
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for (j = 1; j <= elp->deg; j++) |
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d ^= gf_mul(bch, elp->c[j], syn[2*i+2-j]); |
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} |
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} |
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dbg("elp=%s\n", gf_poly_str(elp)); |
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return (elp->deg > t) ? -1 : (int)elp->deg; |
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} |
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|
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/* |
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* solve a m x m linear system in GF(2) with an expected number of solutions, |
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* and return the number of found solutions |
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*/ |
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static int solve_linear_system(struct bch_control *bch, unsigned int *rows, |
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unsigned int *sol, int nsol) |
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{ |
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const int m = GF_M(bch); |
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unsigned int tmp, mask; |
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int rem, c, r, p, k, param[m]; |
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|
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k = 0; |
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mask = 1 << m; |
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|
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/* Gaussian elimination */ |
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for (c = 0; c < m; c++) { |
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rem = 0; |
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p = c-k; |
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/* find suitable row for elimination */ |
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for (r = p; r < m; r++) { |
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if (rows[r] & mask) { |
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if (r != p) { |
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tmp = rows[r]; |
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rows[r] = rows[p]; |
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rows[p] = tmp; |
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} |
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rem = r+1; |
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break; |
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} |
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} |
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if (rem) { |
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/* perform elimination on remaining rows */ |
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tmp = rows[p]; |
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for (r = rem; r < m; r++) { |
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if (rows[r] & mask) |
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rows[r] ^= tmp; |
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} |
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} else { |
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/* elimination not needed, store defective row index */ |
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param[k++] = c; |
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} |
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mask >>= 1; |
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} |
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/* rewrite system, inserting fake parameter rows */ |
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if (k > 0) { |
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p = k; |
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for (r = m-1; r >= 0; r--) { |
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if ((r > m-1-k) && rows[r]) |
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/* system has no solution */ |
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return 0; |
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|
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rows[r] = (p && (r == param[p-1])) ? |
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p--, 1u << (m-r) : rows[r-p]; |
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} |
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} |
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|
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if (nsol != (1 << k)) |
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/* unexpected number of solutions */ |
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return 0; |
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|
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for (p = 0; p < nsol; p++) { |
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/* set parameters for p-th solution */ |
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for (c = 0; c < k; c++) |
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rows[param[c]] = (rows[param[c]] & ~1)|((p >> c) & 1); |
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|
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/* compute unique solution */ |
|
tmp = 0; |
|
for (r = m-1; r >= 0; r--) { |
|
mask = rows[r] & (tmp|1); |
|
tmp |= parity(mask) << (m-r); |
|
} |
|
sol[p] = tmp >> 1; |
|
} |
|
return nsol; |
|
} |
|
|
|
/* |
|
* this function builds and solves a linear system for finding roots of a degree |
|
* 4 affine monic polynomial X^4+aX^2+bX+c over GF(2^m). |
|
*/ |
|
static int find_affine4_roots(struct bch_control *bch, unsigned int a, |
|
unsigned int b, unsigned int c, |
|
unsigned int *roots) |
|
{ |
|
int i, j, k; |
|
const int m = GF_M(bch); |
|
unsigned int mask = 0xff, t, rows[16] = {0,}; |
|
|
|
j = a_log(bch, b); |
|
k = a_log(bch, a); |
|
rows[0] = c; |
|
|
|
/* buid linear system to solve X^4+aX^2+bX+c = 0 */ |
|
for (i = 0; i < m; i++) { |
|
rows[i+1] = bch->a_pow_tab[4*i]^ |
|
(a ? bch->a_pow_tab[mod_s(bch, k)] : 0)^ |
|
(b ? bch->a_pow_tab[mod_s(bch, j)] : 0); |
|
j++; |
|
k += 2; |
|
} |
|
/* |
|
* transpose 16x16 matrix before passing it to linear solver |
|
* warning: this code assumes m < 16 |
|
*/ |
|
for (j = 8; j != 0; j >>= 1, mask ^= (mask << j)) { |
|
for (k = 0; k < 16; k = (k+j+1) & ~j) { |
|
t = ((rows[k] >> j)^rows[k+j]) & mask; |
|
rows[k] ^= (t << j); |
|
rows[k+j] ^= t; |
|
} |
|
} |
|
return solve_linear_system(bch, rows, roots, 4); |
|
} |
|
|
|
/* |
|
* compute root r of a degree 1 polynomial over GF(2^m) (returned as log(1/r)) |
|
*/ |
|
static int find_poly_deg1_roots(struct bch_control *bch, struct gf_poly *poly, |
|
unsigned int *roots) |
|
{ |
|
int n = 0; |
|
|
|
if (poly->c[0]) |
|
/* poly[X] = bX+c with c!=0, root=c/b */ |
|
roots[n++] = mod_s(bch, GF_N(bch)-bch->a_log_tab[poly->c[0]]+ |
|
bch->a_log_tab[poly->c[1]]); |
|
return n; |
|
} |
|
|
|
/* |
|
* compute roots of a degree 2 polynomial over GF(2^m) |
|
*/ |
|
static int find_poly_deg2_roots(struct bch_control *bch, struct gf_poly *poly, |
|
unsigned int *roots) |
|
{ |
|
int n = 0, i, l0, l1, l2; |
|
unsigned int u, v, r; |
|
|
|
if (poly->c[0] && poly->c[1]) { |
|
|
|
l0 = bch->a_log_tab[poly->c[0]]; |
|
l1 = bch->a_log_tab[poly->c[1]]; |
|
l2 = bch->a_log_tab[poly->c[2]]; |
|
|
|
/* using z=a/bX, transform aX^2+bX+c into z^2+z+u (u=ac/b^2) */ |
|
u = a_pow(bch, l0+l2+2*(GF_N(bch)-l1)); |
|
/* |
|
* let u = sum(li.a^i) i=0..m-1; then compute r = sum(li.xi): |
|
* r^2+r = sum(li.(xi^2+xi)) = sum(li.(a^i+Tr(a^i).a^k)) = |
|
* u + sum(li.Tr(a^i).a^k) = u+a^k.Tr(sum(li.a^i)) = u+a^k.Tr(u) |
|
* i.e. r and r+1 are roots iff Tr(u)=0 |
|
*/ |
|
r = 0; |
|
v = u; |
|
while (v) { |
|
i = deg(v); |
|
r ^= bch->xi_tab[i]; |
|
v ^= (1 << i); |
|
} |
|
/* verify root */ |
|
if ((gf_sqr(bch, r)^r) == u) { |
|
/* reverse z=a/bX transformation and compute log(1/r) */ |
|
roots[n++] = modulo(bch, 2*GF_N(bch)-l1- |
|
bch->a_log_tab[r]+l2); |
|
roots[n++] = modulo(bch, 2*GF_N(bch)-l1- |
|
bch->a_log_tab[r^1]+l2); |
|
} |
|
} |
|
return n; |
|
} |
|
|
|
/* |
|
* compute roots of a degree 3 polynomial over GF(2^m) |
|
*/ |
|
static int find_poly_deg3_roots(struct bch_control *bch, struct gf_poly *poly, |
|
unsigned int *roots) |
|
{ |
|
int i, n = 0; |
|
unsigned int a, b, c, a2, b2, c2, e3, tmp[4]; |
|
|
|
if (poly->c[0]) { |
|
/* transform polynomial into monic X^3 + a2X^2 + b2X + c2 */ |
|
e3 = poly->c[3]; |
|
c2 = gf_div(bch, poly->c[0], e3); |
|
b2 = gf_div(bch, poly->c[1], e3); |
|
a2 = gf_div(bch, poly->c[2], e3); |
|
|
|
/* (X+a2)(X^3+a2X^2+b2X+c2) = X^4+aX^2+bX+c (affine) */ |
|
c = gf_mul(bch, a2, c2); /* c = a2c2 */ |
|
b = gf_mul(bch, a2, b2)^c2; /* b = a2b2 + c2 */ |
|
a = gf_sqr(bch, a2)^b2; /* a = a2^2 + b2 */ |
|
|
|
/* find the 4 roots of this affine polynomial */ |
|
if (find_affine4_roots(bch, a, b, c, tmp) == 4) { |
|
/* remove a2 from final list of roots */ |
|
for (i = 0; i < 4; i++) { |
|
if (tmp[i] != a2) |
|
roots[n++] = a_ilog(bch, tmp[i]); |
|
} |
|
} |
|
} |
|
return n; |
|
} |
|
|
|
/* |
|
* compute roots of a degree 4 polynomial over GF(2^m) |
|
*/ |
|
static int find_poly_deg4_roots(struct bch_control *bch, struct gf_poly *poly, |
|
unsigned int *roots) |
|
{ |
|
int i, l, n = 0; |
|
unsigned int a, b, c, d, e = 0, f, a2, b2, c2, e4; |
|
|
|
if (poly->c[0] == 0) |
|
return 0; |
|
|
|
/* transform polynomial into monic X^4 + aX^3 + bX^2 + cX + d */ |
|
e4 = poly->c[4]; |
|
d = gf_div(bch, poly->c[0], e4); |
|
c = gf_div(bch, poly->c[1], e4); |
|
b = gf_div(bch, poly->c[2], e4); |
|
a = gf_div(bch, poly->c[3], e4); |
|
|
|
/* use Y=1/X transformation to get an affine polynomial */ |
|
if (a) { |
|
/* first, eliminate cX by using z=X+e with ae^2+c=0 */ |
|
if (c) { |
|
/* compute e such that e^2 = c/a */ |
|
f = gf_div(bch, c, a); |
|
l = a_log(bch, f); |
|
l += (l & 1) ? GF_N(bch) : 0; |
|
e = a_pow(bch, l/2); |
|
/* |
|
* use transformation z=X+e: |
|
* z^4+e^4 + a(z^3+ez^2+e^2z+e^3) + b(z^2+e^2) +cz+ce+d |
|
* z^4 + az^3 + (ae+b)z^2 + (ae^2+c)z+e^4+be^2+ae^3+ce+d |
|
* z^4 + az^3 + (ae+b)z^2 + e^4+be^2+d |
|
* z^4 + az^3 + b'z^2 + d' |
|
*/ |
|
d = a_pow(bch, 2*l)^gf_mul(bch, b, f)^d; |
|
b = gf_mul(bch, a, e)^b; |
|
} |
|
/* now, use Y=1/X to get Y^4 + b/dY^2 + a/dY + 1/d */ |
|
if (d == 0) |
|
/* assume all roots have multiplicity 1 */ |
|
return 0; |
|
|
|
c2 = gf_inv(bch, d); |
|
b2 = gf_div(bch, a, d); |
|
a2 = gf_div(bch, b, d); |
|
} else { |
|
/* polynomial is already affine */ |
|
c2 = d; |
|
b2 = c; |
|
a2 = b; |
|
} |
|
/* find the 4 roots of this affine polynomial */ |
|
if (find_affine4_roots(bch, a2, b2, c2, roots) == 4) { |
|
for (i = 0; i < 4; i++) { |
|
/* post-process roots (reverse transformations) */ |
|
f = a ? gf_inv(bch, roots[i]) : roots[i]; |
|
roots[i] = a_ilog(bch, f^e); |
|
} |
|
n = 4; |
|
} |
|
return n; |
|
} |
|
|
|
/* |
|
* build monic, log-based representation of a polynomial |
|
*/ |
|
static void gf_poly_logrep(struct bch_control *bch, |
|
const struct gf_poly *a, int *rep) |
|
{ |
|
int i, d = a->deg, l = GF_N(bch)-a_log(bch, a->c[a->deg]); |
|
|
|
/* represent 0 values with -1; warning, rep[d] is not set to 1 */ |
|
for (i = 0; i < d; i++) |
|
rep[i] = a->c[i] ? mod_s(bch, a_log(bch, a->c[i])+l) : -1; |
|
} |
|
|
|
/* |
|
* compute polynomial Euclidean division remainder in GF(2^m)[X] |
|
*/ |
|
static void gf_poly_mod(struct bch_control *bch, struct gf_poly *a, |
|
const struct gf_poly *b, int *rep) |
|
{ |
|
int la, p, m; |
|
unsigned int i, j, *c = a->c; |
|
const unsigned int d = b->deg; |
|
|
|
if (a->deg < d) |
|
return; |
|
|
|
/* reuse or compute log representation of denominator */ |
|
if (!rep) { |
|
rep = bch->cache; |
|
gf_poly_logrep(bch, b, rep); |
|
} |
|
|
|
for (j = a->deg; j >= d; j--) { |
|
if (c[j]) { |
|
la = a_log(bch, c[j]); |
|
p = j-d; |
|
for (i = 0; i < d; i++, p++) { |
|
m = rep[i]; |
|
if (m >= 0) |
|
c[p] ^= bch->a_pow_tab[mod_s(bch, |
|
m+la)]; |
|
} |
|
} |
|
} |
|
a->deg = d-1; |
|
while (!c[a->deg] && a->deg) |
|
a->deg--; |
|
} |
|
|
|
/* |
|
* compute polynomial Euclidean division quotient in GF(2^m)[X] |
|
*/ |
|
static void gf_poly_div(struct bch_control *bch, struct gf_poly *a, |
|
const struct gf_poly *b, struct gf_poly *q) |
|
{ |
|
if (a->deg >= b->deg) { |
|
q->deg = a->deg-b->deg; |
|
/* compute a mod b (modifies a) */ |
|
gf_poly_mod(bch, a, b, NULL); |
|
/* quotient is stored in upper part of polynomial a */ |
|
memcpy(q->c, &a->c[b->deg], (1+q->deg)*sizeof(unsigned int)); |
|
} else { |
|
q->deg = 0; |
|
q->c[0] = 0; |
|
} |
|
} |
|
|
|
/* |
|
* compute polynomial GCD (Greatest Common Divisor) in GF(2^m)[X] |
|
*/ |
|
static struct gf_poly *gf_poly_gcd(struct bch_control *bch, struct gf_poly *a, |
|
struct gf_poly *b) |
|
{ |
|
struct gf_poly *tmp; |
|
|
|
dbg("gcd(%s,%s)=", gf_poly_str(a), gf_poly_str(b)); |
|
|
|
if (a->deg < b->deg) { |
|
tmp = b; |
|
b = a; |
|
a = tmp; |
|
} |
|
|
|
while (b->deg > 0) { |
|
gf_poly_mod(bch, a, b, NULL); |
|
tmp = b; |
|
b = a; |
|
a = tmp; |
|
} |
|
|
|
dbg("%s\n", gf_poly_str(a)); |
|
|
|
return a; |
|
} |
|
|
|
/* |
|
* Given a polynomial f and an integer k, compute Tr(a^kX) mod f |
|
* This is used in Berlekamp Trace algorithm for splitting polynomials |
|
*/ |
|
static void compute_trace_bk_mod(struct bch_control *bch, int k, |
|
const struct gf_poly *f, struct gf_poly *z, |
|
struct gf_poly *out) |
|
{ |
|
const int m = GF_M(bch); |
|
int i, j; |
|
|
|
/* z contains z^2j mod f */ |
|
z->deg = 1; |
|
z->c[0] = 0; |
|
z->c[1] = bch->a_pow_tab[k]; |
|
|
|
out->deg = 0; |
|
memset(out, 0, GF_POLY_SZ(f->deg)); |
|
|
|
/* compute f log representation only once */ |
|
gf_poly_logrep(bch, f, bch->cache); |
|
|
|
for (i = 0; i < m; i++) { |
|
/* add a^(k*2^i)(z^(2^i) mod f) and compute (z^(2^i) mod f)^2 */ |
|
for (j = z->deg; j >= 0; j--) { |
|
out->c[j] ^= z->c[j]; |
|
z->c[2*j] = gf_sqr(bch, z->c[j]); |
|
z->c[2*j+1] = 0; |
|
} |
|
if (z->deg > out->deg) |
|
out->deg = z->deg; |
|
|
|
if (i < m-1) { |
|
z->deg *= 2; |
|
/* z^(2(i+1)) mod f = (z^(2^i) mod f)^2 mod f */ |
|
gf_poly_mod(bch, z, f, bch->cache); |
|
} |
|
} |
|
while (!out->c[out->deg] && out->deg) |
|
out->deg--; |
|
|
|
dbg("Tr(a^%d.X) mod f = %s\n", k, gf_poly_str(out)); |
|
} |
|
|
|
/* |
|
* factor a polynomial using Berlekamp Trace algorithm (BTA) |
|
*/ |
|
static void factor_polynomial(struct bch_control *bch, int k, struct gf_poly *f, |
|
struct gf_poly **g, struct gf_poly **h) |
|
{ |
|
struct gf_poly *f2 = bch->poly_2t[0]; |
|
struct gf_poly *q = bch->poly_2t[1]; |
|
struct gf_poly *tk = bch->poly_2t[2]; |
|
struct gf_poly *z = bch->poly_2t[3]; |
|
struct gf_poly *gcd; |
|
|
|
dbg("factoring %s...\n", gf_poly_str(f)); |
|
|
|
*g = f; |
|
*h = NULL; |
|
|
|
/* tk = Tr(a^k.X) mod f */ |
|
compute_trace_bk_mod(bch, k, f, z, tk); |
|
|
|
if (tk->deg > 0) { |
|
/* compute g = gcd(f, tk) (destructive operation) */ |
|
gf_poly_copy(f2, f); |
|
gcd = gf_poly_gcd(bch, f2, tk); |
|
if (gcd->deg < f->deg) { |
|
/* compute h=f/gcd(f,tk); this will modify f and q */ |
|
gf_poly_div(bch, f, gcd, q); |
|
/* store g and h in-place (clobbering f) */ |
|
*h = &((struct gf_poly_deg1 *)f)[gcd->deg].poly; |
|
gf_poly_copy(*g, gcd); |
|
gf_poly_copy(*h, q); |
|
} |
|
} |
|
} |
|
|
|
/* |
|
* find roots of a polynomial, using BTZ algorithm; see the beginning of this |
|
* file for details |
|
*/ |
|
static int find_poly_roots(struct bch_control *bch, unsigned int k, |
|
struct gf_poly *poly, unsigned int *roots) |
|
{ |
|
int cnt; |
|
struct gf_poly *f1, *f2; |
|
|
|
switch (poly->deg) { |
|
/* handle low degree polynomials with ad hoc techniques */ |
|
case 1: |
|
cnt = find_poly_deg1_roots(bch, poly, roots); |
|
break; |
|
case 2: |
|
cnt = find_poly_deg2_roots(bch, poly, roots); |
|
break; |
|
case 3: |
|
cnt = find_poly_deg3_roots(bch, poly, roots); |
|
break; |
|
case 4: |
|
cnt = find_poly_deg4_roots(bch, poly, roots); |
|
break; |
|
default: |
|
/* factor polynomial using Berlekamp Trace Algorithm (BTA) */ |
|
cnt = 0; |
|
if (poly->deg && (k <= GF_M(bch))) { |
|
factor_polynomial(bch, k, poly, &f1, &f2); |
|
if (f1) |
|
cnt += find_poly_roots(bch, k+1, f1, roots); |
|
if (f2) |
|
cnt += find_poly_roots(bch, k+1, f2, roots+cnt); |
|
} |
|
break; |
|
} |
|
return cnt; |
|
} |
|
|
|
#if defined(USE_CHIEN_SEARCH) |
|
/* |
|
* exhaustive root search (Chien) implementation - not used, included only for |
|
* reference/comparison tests |
|
*/ |
|
static int chien_search(struct bch_control *bch, unsigned int len, |
|
struct gf_poly *p, unsigned int *roots) |
|
{ |
|
int m; |
|
unsigned int i, j, syn, syn0, count = 0; |
|
const unsigned int k = 8*len+bch->ecc_bits; |
|
|
|
/* use a log-based representation of polynomial */ |
|
gf_poly_logrep(bch, p, bch->cache); |
|
bch->cache[p->deg] = 0; |
|
syn0 = gf_div(bch, p->c[0], p->c[p->deg]); |
|
|
|
for (i = GF_N(bch)-k+1; i <= GF_N(bch); i++) { |
|
/* compute elp(a^i) */ |
|
for (j = 1, syn = syn0; j <= p->deg; j++) { |
|
m = bch->cache[j]; |
|
if (m >= 0) |
|
syn ^= a_pow(bch, m+j*i); |
|
} |
|
if (syn == 0) { |
|
roots[count++] = GF_N(bch)-i; |
|
if (count == p->deg) |
|
break; |
|
} |
|
} |
|
return (count == p->deg) ? count : 0; |
|
} |
|
#define find_poly_roots(_p, _k, _elp, _loc) chien_search(_p, len, _elp, _loc) |
|
#endif /* USE_CHIEN_SEARCH */ |
|
|
|
/** |
|
* decode_bch - decode received codeword and find bit error locations |
|
* @bch: BCH control structure |
|
* @data: received data, ignored if @calc_ecc is provided |
|
* @len: data length in bytes, must always be provided |
|
* @recv_ecc: received ecc, if NULL then assume it was XORed in @calc_ecc |
|
* @calc_ecc: calculated ecc, if NULL then calc_ecc is computed from @data |
|
* @syn: hw computed syndrome data (if NULL, syndrome is calculated) |
|
* @errloc: output array of error locations |
|
* |
|
* Returns: |
|
* The number of errors found, or -EBADMSG if decoding failed, or -EINVAL if |
|
* invalid parameters were provided |
|
* |
|
* Depending on the available hw BCH support and the need to compute @calc_ecc |
|
* separately (using encode_bch()), this function should be called with one of |
|
* the following parameter configurations - |
|
* |
|
* by providing @data and @recv_ecc only: |
|
* decode_bch(@bch, @data, @len, @recv_ecc, NULL, NULL, @errloc) |
|
* |
|
* by providing @recv_ecc and @calc_ecc: |
|
* decode_bch(@bch, NULL, @len, @recv_ecc, @calc_ecc, NULL, @errloc) |
|
* |
|
* by providing ecc = recv_ecc XOR calc_ecc: |
|
* decode_bch(@bch, NULL, @len, NULL, ecc, NULL, @errloc) |
|
* |
|
* by providing syndrome results @syn: |
|
* decode_bch(@bch, NULL, @len, NULL, NULL, @syn, @errloc) |
|
* |
|
* Once decode_bch() has successfully returned with a positive value, error |
|
* locations returned in array @errloc should be interpreted as follows - |
|
* |
|
* if (errloc[n] >= 8*len), then n-th error is located in ecc (no need for |
|
* data correction) |
|
* |
|
* if (errloc[n] < 8*len), then n-th error is located in data and can be |
|
* corrected with statement data[errloc[n]/8] ^= 1 << (errloc[n] % 8); |
|
* |
|
* Note that this function does not perform any data correction by itself, it |
|
* merely indicates error locations. |
|
*/ |
|
int decode_bch(struct bch_control *bch, const uint8_t *data, unsigned int len, |
|
const uint8_t *recv_ecc, const uint8_t *calc_ecc, |
|
const unsigned int *syn, unsigned int *errloc) |
|
{ |
|
const unsigned int ecc_words = BCH_ECC_WORDS(bch); |
|
unsigned int nbits; |
|
int i, err, nroots; |
|
uint32_t sum; |
|
|
|
/* sanity check: make sure data length can be handled */ |
|
if (8*len > (bch->n-bch->ecc_bits)) |
|
return -EINVAL; |
|
|
|
/* if caller does not provide syndromes, compute them */ |
|
if (!syn) { |
|
if (!calc_ecc) { |
|
/* compute received data ecc into an internal buffer */ |
|
if (!data || !recv_ecc) |
|
return -EINVAL; |
|
encode_bch(bch, data, len, NULL); |
|
} else { |
|
/* load provided calculated ecc */ |
|
load_ecc8(bch, bch->ecc_buf, calc_ecc); |
|
} |
|
/* load received ecc or assume it was XORed in calc_ecc */ |
|
if (recv_ecc) { |
|
load_ecc8(bch, bch->ecc_buf2, recv_ecc); |
|
/* XOR received and calculated ecc */ |
|
for (i = 0, sum = 0; i < (int)ecc_words; i++) { |
|
bch->ecc_buf[i] ^= bch->ecc_buf2[i]; |
|
sum |= bch->ecc_buf[i]; |
|
} |
|
if (!sum) |
|
/* no error found */ |
|
return 0; |
|
} |
|
compute_syndromes(bch, bch->ecc_buf, bch->syn); |
|
syn = bch->syn; |
|
} |
|
|
|
err = compute_error_locator_polynomial(bch, syn); |
|
if (err > 0) { |
|
nroots = find_poly_roots(bch, 1, bch->elp, errloc); |
|
if (err != nroots) |
|
err = -1; |
|
} |
|
if (err > 0) { |
|
/* post-process raw error locations for easier correction */ |
|
nbits = (len*8)+bch->ecc_bits; |
|
for (i = 0; i < err; i++) { |
|
if (errloc[i] >= nbits) { |
|
err = -1; |
|
break; |
|
} |
|
errloc[i] = nbits-1-errloc[i]; |
|
errloc[i] = (errloc[i] & ~7)|(7-(errloc[i] & 7)); |
|
} |
|
} |
|
return (err >= 0) ? err : -EBADMSG; |
|
} |
|
|
|
/* |
|
* generate Galois field lookup tables |
|
*/ |
|
static int build_gf_tables(struct bch_control *bch, unsigned int poly) |
|
{ |
|
unsigned int i, x = 1; |
|
const unsigned int k = 1 << deg(poly); |
|
|
|
/* primitive polynomial must be of degree m */ |
|
if (k != (1u << GF_M(bch))) |
|
return -1; |
|
|
|
for (i = 0; i < GF_N(bch); i++) { |
|
bch->a_pow_tab[i] = x; |
|
bch->a_log_tab[x] = i; |
|
if (i && (x == 1)) |
|
/* polynomial is not primitive (a^i=1 with 0<i<2^m-1) */ |
|
return -1; |
|
x <<= 1; |
|
if (x & k) |
|
x ^= poly; |
|
} |
|
bch->a_pow_tab[GF_N(bch)] = 1; |
|
bch->a_log_tab[0] = 0; |
|
|
|
return 0; |
|
} |
|
|
|
/* |
|
* compute generator polynomial remainder tables for fast encoding |
|
*/ |
|
static void build_mod8_tables(struct bch_control *bch, const uint32_t *g) |
|
{ |
|
int i, j, b, d; |
|
uint32_t data, hi, lo, *tab; |
|
const int l = BCH_ECC_WORDS(bch); |
|
const int plen = DIV_ROUND_UP(bch->ecc_bits+1, 32); |
|
const int ecclen = DIV_ROUND_UP(bch->ecc_bits, 32); |
|
|
|
memset(bch->mod8_tab, 0, 4*256*l*sizeof(*bch->mod8_tab)); |
|
|
|
for (i = 0; i < 256; i++) { |
|
/* p(X)=i is a small polynomial of weight <= 8 */ |
|
for (b = 0; b < 4; b++) { |
|
/* we want to compute (p(X).X^(8*b+deg(g))) mod g(X) */ |
|
tab = bch->mod8_tab + (b*256+i)*l; |
|
data = i << (8*b); |
|
while (data) { |
|
d = deg(data); |
|
/* subtract X^d.g(X) from p(X).X^(8*b+deg(g)) */ |
|
data ^= g[0] >> (31-d); |
|
for (j = 0; j < ecclen; j++) { |
|
hi = (d < 31) ? g[j] << (d+1) : 0; |
|
lo = (j+1 < plen) ? |
|
g[j+1] >> (31-d) : 0; |
|
tab[j] ^= hi|lo; |
|
} |
|
} |
|
} |
|
} |
|
} |
|
|
|
/* |
|
* build a base for factoring degree 2 polynomials |
|
*/ |
|
static int build_deg2_base(struct bch_control *bch) |
|
{ |
|
const int m = GF_M(bch); |
|
int i, j, r; |
|
unsigned int sum, x, y, remaining, ak = 0, xi[m]; |
|
|
|
/* find k s.t. Tr(a^k) = 1 and 0 <= k < m */ |
|
for (i = 0; i < m; i++) { |
|
for (j = 0, sum = 0; j < m; j++) |
|
sum ^= a_pow(bch, i*(1 << j)); |
|
|
|
if (sum) { |
|
ak = bch->a_pow_tab[i]; |
|
break; |
|
} |
|
} |
|
/* find xi, i=0..m-1 such that xi^2+xi = a^i+Tr(a^i).a^k */ |
|
remaining = m; |
|
memset(xi, 0, sizeof(xi)); |
|
|
|
for (x = 0; (x <= GF_N(bch)) && remaining; x++) { |
|
y = gf_sqr(bch, x)^x; |
|
for (i = 0; i < 2; i++) { |
|
r = a_log(bch, y); |
|
if (y && (r < m) && !xi[r]) { |
|
bch->xi_tab[r] = x; |
|
xi[r] = 1; |
|
remaining--; |
|
dbg("x%d = %x\n", r, x); |
|
break; |
|
} |
|
y ^= ak; |
|
} |
|
} |
|
/* should not happen but check anyway */ |
|
return remaining ? -1 : 0; |
|
} |
|
|
|
static void *bch_alloc(size_t size, int *err) |
|
{ |
|
void *ptr; |
|
|
|
ptr = kmalloc(size, GFP_KERNEL); |
|
if (ptr == NULL) |
|
*err = 1; |
|
return ptr; |
|
} |
|
|
|
/* |
|
* compute generator polynomial for given (m,t) parameters. |
|
*/ |
|
static uint32_t *compute_generator_polynomial(struct bch_control *bch) |
|
{ |
|
const unsigned int m = GF_M(bch); |
|
const unsigned int t = GF_T(bch); |
|
int n, err = 0; |
|
unsigned int i, j, nbits, r, word, *roots; |
|
struct gf_poly *g; |
|
uint32_t *genpoly; |
|
|
|
g = bch_alloc(GF_POLY_SZ(m*t), &err); |
|
roots = bch_alloc((bch->n+1)*sizeof(*roots), &err); |
|
genpoly = bch_alloc(DIV_ROUND_UP(m*t+1, 32)*sizeof(*genpoly), &err); |
|
|
|
if (err) { |
|
kfree(genpoly); |
|
genpoly = NULL; |
|
goto finish; |
|
} |
|
|
|
/* enumerate all roots of g(X) */ |
|
memset(roots , 0, (bch->n+1)*sizeof(*roots)); |
|
for (i = 0; i < t; i++) { |
|
for (j = 0, r = 2*i+1; j < m; j++) { |
|
roots[r] = 1; |
|
r = mod_s(bch, 2*r); |
|
} |
|
} |
|
/* build generator polynomial g(X) */ |
|
g->deg = 0; |
|
g->c[0] = 1; |
|
for (i = 0; i < GF_N(bch); i++) { |
|
if (roots[i]) { |
|
/* multiply g(X) by (X+root) */ |
|
r = bch->a_pow_tab[i]; |
|
g->c[g->deg+1] = 1; |
|
for (j = g->deg; j > 0; j--) |
|
g->c[j] = gf_mul(bch, g->c[j], r)^g->c[j-1]; |
|
|
|
g->c[0] = gf_mul(bch, g->c[0], r); |
|
g->deg++; |
|
} |
|
} |
|
/* store left-justified binary representation of g(X) */ |
|
n = g->deg+1; |
|
i = 0; |
|
|
|
while (n > 0) { |
|
nbits = (n > 32) ? 32 : n; |
|
for (j = 0, word = 0; j < nbits; j++) { |
|
if (g->c[n-1-j]) |
|
word |= 1u << (31-j); |
|
} |
|
genpoly[i++] = word; |
|
n -= nbits; |
|
} |
|
bch->ecc_bits = g->deg; |
|
|
|
finish: |
|
kfree(g); |
|
kfree(roots); |
|
|
|
return genpoly; |
|
} |
|
|
|
/** |
|
* init_bch - initialize a BCH encoder/decoder |
|
* @m: Galois field order, should be in the range 5-15 |
|
* @t: maximum error correction capability, in bits |
|
* @prim_poly: user-provided primitive polynomial (or 0 to use default) |
|
* |
|
* Returns: |
|
* a newly allocated BCH control structure if successful, NULL otherwise |
|
* |
|
* This initialization can take some time, as lookup tables are built for fast |
|
* encoding/decoding; make sure not to call this function from a time critical |
|
* path. Usually, init_bch() should be called on module/driver init and |
|
* free_bch() should be called to release memory on exit. |
|
* |
|
* You may provide your own primitive polynomial of degree @m in argument |
|
* @prim_poly, or let init_bch() use its default polynomial. |
|
* |
|
* Once init_bch() has successfully returned a pointer to a newly allocated |
|
* BCH control structure, ecc length in bytes is given by member @ecc_bytes of |
|
* the structure. |
|
*/ |
|
struct bch_control *init_bch(int m, int t, unsigned int prim_poly) |
|
{ |
|
int err = 0; |
|
unsigned int i, words; |
|
uint32_t *genpoly; |
|
struct bch_control *bch = NULL; |
|
|
|
const int min_m = 5; |
|
const int max_m = 15; |
|
|
|
/* default primitive polynomials */ |
|
static const unsigned int prim_poly_tab[] = { |
|
0x25, 0x43, 0x83, 0x11d, 0x211, 0x409, 0x805, 0x1053, 0x201b, |
|
0x402b, 0x8003, |
|
}; |
|
|
|
#if defined(CONFIG_BCH_CONST_PARAMS) |
|
if ((m != (CONFIG_BCH_CONST_M)) || (t != (CONFIG_BCH_CONST_T))) { |
|
printk(KERN_ERR "bch encoder/decoder was configured to support " |
|
"parameters m=%d, t=%d only!\n", |
|
CONFIG_BCH_CONST_M, CONFIG_BCH_CONST_T); |
|
goto fail; |
|
} |
|
#endif |
|
if ((m < min_m) || (m > max_m)) |
|
/* |
|
* values of m greater than 15 are not currently supported; |
|
* supporting m > 15 would require changing table base type |
|
* (uint16_t) and a small patch in matrix transposition |
|
*/ |
|
goto fail; |
|
|
|
/* sanity checks */ |
|
if ((t < 1) || (m*t >= ((1 << m)-1))) |
|
/* invalid t value */ |
|
goto fail; |
|
|
|
/* select a primitive polynomial for generating GF(2^m) */ |
|
if (prim_poly == 0) |
|
prim_poly = prim_poly_tab[m-min_m]; |
|
|
|
bch = kzalloc(sizeof(*bch), GFP_KERNEL); |
|
if (bch == NULL) |
|
goto fail; |
|
|
|
bch->m = m; |
|
bch->t = t; |
|
bch->n = (1 << m)-1; |
|
words = DIV_ROUND_UP(m*t, 32); |
|
bch->ecc_bytes = DIV_ROUND_UP(m*t, 8); |
|
bch->a_pow_tab = bch_alloc((1+bch->n)*sizeof(*bch->a_pow_tab), &err); |
|
bch->a_log_tab = bch_alloc((1+bch->n)*sizeof(*bch->a_log_tab), &err); |
|
bch->mod8_tab = bch_alloc(words*1024*sizeof(*bch->mod8_tab), &err); |
|
bch->ecc_buf = bch_alloc(words*sizeof(*bch->ecc_buf), &err); |
|
bch->ecc_buf2 = bch_alloc(words*sizeof(*bch->ecc_buf2), &err); |
|
bch->xi_tab = bch_alloc(m*sizeof(*bch->xi_tab), &err); |
|
bch->syn = bch_alloc(2*t*sizeof(*bch->syn), &err); |
|
bch->cache = bch_alloc(2*t*sizeof(*bch->cache), &err); |
|
bch->elp = bch_alloc((t+1)*sizeof(struct gf_poly_deg1), &err); |
|
|
|
for (i = 0; i < ARRAY_SIZE(bch->poly_2t); i++) |
|
bch->poly_2t[i] = bch_alloc(GF_POLY_SZ(2*t), &err); |
|
|
|
if (err) |
|
goto fail; |
|
|
|
err = build_gf_tables(bch, prim_poly); |
|
if (err) |
|
goto fail; |
|
|
|
/* use generator polynomial for computing encoding tables */ |
|
genpoly = compute_generator_polynomial(bch); |
|
if (genpoly == NULL) |
|
goto fail; |
|
|
|
build_mod8_tables(bch, genpoly); |
|
kfree(genpoly); |
|
|
|
err = build_deg2_base(bch); |
|
if (err) |
|
goto fail; |
|
|
|
return bch; |
|
|
|
fail: |
|
free_bch(bch); |
|
return NULL; |
|
} |
|
|
|
/** |
|
* free_bch - free the BCH control structure |
|
* @bch: BCH control structure to release |
|
*/ |
|
void free_bch(struct bch_control *bch) |
|
{ |
|
unsigned int i; |
|
|
|
if (bch) { |
|
kfree(bch->a_pow_tab); |
|
kfree(bch->a_log_tab); |
|
kfree(bch->mod8_tab); |
|
kfree(bch->ecc_buf); |
|
kfree(bch->ecc_buf2); |
|
kfree(bch->xi_tab); |
|
kfree(bch->syn); |
|
kfree(bch->cache); |
|
kfree(bch->elp); |
|
|
|
for (i = 0; i < ARRAY_SIZE(bch->poly_2t); i++) |
|
kfree(bch->poly_2t[i]); |
|
|
|
kfree(bch); |
|
} |
|
}
|
|
|