patch-2.1.66 linux/drivers/char/ftape/ecc.c
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- Lines: 894
- Date:
Wed Dec 31 16:00:00 1969
- Orig file:
v2.1.65/linux/drivers/char/ftape/ecc.c
- Orig date:
Thu Mar 14 01:51:41 1996
diff -u --recursive --new-file v2.1.65/linux/drivers/char/ftape/ecc.c linux/drivers/char/ftape/ecc.c
@@ -1,893 +0,0 @@
-/* Yo, Emacs! we're -*- Linux-C -*-
- *
- * Copyright (c) 1993 Ning and David Mosberger.
- *
- * This is based on code originally written by Bas Laarhoven (bas@vimec.nl)
- * and David L. Brown, Jr., and incorporates improvements suggested by
- * Kai Harrekilde-Petersen.
- *
- * This program is free software; you can redistribute it and/or
- * modify it under the terms of the GNU General Public License as
- * published by the Free Software Foundation; either version 2, or (at
- * your option) any later version.
- *
- * This program is distributed in the hope that it will be useful, but
- * WITHOUT ANY WARRANTY; without even the implied warranty of
- * MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU
- * General Public License for more details.
- *
- * You should have received a copy of the GNU General Public License
- * along with this program; see the file COPYING. If not, write to
- * the Free Software Foundation, 675 Mass Ave, Cambridge, MA 02139,
- * USA.
- *
- * $Source: /home/bas/distr/ftape-2.03b/RCS/ecc.c,v $
- * $Author: bas $
- *
- * $Revision: 1.32 $
- * $Date: 1995/04/22 07:30:15 $
- * $State: Beta $
- *
- * This file contains the Reed-Solomon error correction code
- * for the QIC-40/80 floppy-tape driver for Linux.
- */
-
-#include <linux/ftape.h>
-#include <stdio.h>
-#include <sys/errno.h>
-
-#include "tracing.h"
-#include "ecc.h"
-
-/*
- * Machines that are big-endian should define macro BIG_ENDIAN.
- * Unfortunately, there doesn't appear to be a standard include
- * file that works for all OSs.
- */
-
-#if defined(__sparc__) || defined(__hppa)
-#define BIG_ENDIAN
-#endif /* __sparc__ || __hppa */
-
-#if defined(__mips__)
-#error Find a smart way to determine the Endianness of the MIPS CPU
-#endif
-
-#ifdef TEST
-
-#undef TRACE()
-#undef TRACE_()
-#undef TRACE()
-#undef TRACEi()
-#undef TRACElx()
-#undef TRACE_FUN()
-#undef TRACE_EXIT
-#define printk printf
-#define TRACE_FUN( level, name) char __fun[] = name
-#define TRACE_EXIT
-#define TRACE_(l,m) { if (ftape_ecc_tracing >= (l) && (l) <= TOP_LEVEL) { \
- printk( "[%03d] " __FILE__ " (%s) - ", (int)ftape_trace_id++, __fun); \
- m; } }
-#define TRACE(l,m) TRACE_(l,printk(m".\n"))
-#define TRACEi(l,m,i) TRACE_(l,printk(m" %d.\n",i))
-#define TRACElx(l,m,i) TRACE_(l,printk(m" 0x%08lx.\n",i))
-
-int ftape_ecc_tracing = 1;
-unsigned char ftape_trace_id = 0;
-
-#endif /* TEST */
-
-/*
- * Notice: to minimize the potential for confusion, we use r to
- * denote the independent variable of the polynomials
- * in the Galois Field GF(2^8). We reserve x for polynomials
- * that that have coefficients in GF(2^8).
- *
- * The Galois Field in which coefficient arithmetic is performed are
- * the polynomials over Z_2 (i.e., 0 and 1) modulo the irreducible
- * polynomial f(r), where f(r)=r^8 + r^7 + r^2 + r + 1. A polynomial
- * is represented as a byte with the MSB as the coefficient of r^7 and
- * the LSB as the coefficient of r^0. For example, the binary
- * representation of f(x) is 0x187 (of course, this doesn't fit into 8
- * bits). In this field, the polynomial r is a primitive element.
- * That is, r^i with i in 0,...,255 enumerates all elements in the
- * field.
- *
- * The generator polynomial for the QIC-80 ECC is
- *
- * g(x) = x^3 + r^105*x^2 + r^105*x + 1
- *
- * which can be factored into:
- *
- * g(x) = (x-r^-1)(x-r^0)(x-r^1)
- *
- * the byte representation of the coefficients are:
- *
- * r^105 = 0xc0
- * r^-1 = 0xc3
- * r^0 = 0x01
- * r^1 = 0x02
- *
- * Notice that r^-1 = r^254 as exponent arithmetic is performed
- * modulo 2^8-1 = 255.
- *
- * For more information on Galois Fields and Reed-Solomon codes,
- * refer to any good book. I found _An Introduction to Error
- * Correcting Codes with Applications_ by S. A. Vanstone and
- * P. C. van Oorschot to be a good introduction into the former.
- * _CODING THEORY: The Essentials_ I found very useful for its
- * concise description of Reed-Solomon encoding/decoding.
- *
- */
-
-typedef unsigned char Matrix[3][3];
-
-/*
- * gfpow[] is defined such that gfpow[i] returns r^i if
- * i is in the range [0..255].
- */
-static const unsigned char gfpow[] =
-{
- 0x01, 0x02, 0x04, 0x08, 0x10, 0x20, 0x40, 0x80,
- 0x87, 0x89, 0x95, 0xad, 0xdd, 0x3d, 0x7a, 0xf4,
- 0x6f, 0xde, 0x3b, 0x76, 0xec, 0x5f, 0xbe, 0xfb,
- 0x71, 0xe2, 0x43, 0x86, 0x8b, 0x91, 0xa5, 0xcd,
- 0x1d, 0x3a, 0x74, 0xe8, 0x57, 0xae, 0xdb, 0x31,
- 0x62, 0xc4, 0x0f, 0x1e, 0x3c, 0x78, 0xf0, 0x67,
- 0xce, 0x1b, 0x36, 0x6c, 0xd8, 0x37, 0x6e, 0xdc,
- 0x3f, 0x7e, 0xfc, 0x7f, 0xfe, 0x7b, 0xf6, 0x6b,
- 0xd6, 0x2b, 0x56, 0xac, 0xdf, 0x39, 0x72, 0xe4,
- 0x4f, 0x9e, 0xbb, 0xf1, 0x65, 0xca, 0x13, 0x26,
- 0x4c, 0x98, 0xb7, 0xe9, 0x55, 0xaa, 0xd3, 0x21,
- 0x42, 0x84, 0x8f, 0x99, 0xb5, 0xed, 0x5d, 0xba,
- 0xf3, 0x61, 0xc2, 0x03, 0x06, 0x0c, 0x18, 0x30,
- 0x60, 0xc0, 0x07, 0x0e, 0x1c, 0x38, 0x70, 0xe0,
- 0x47, 0x8e, 0x9b, 0xb1, 0xe5, 0x4d, 0x9a, 0xb3,
- 0xe1, 0x45, 0x8a, 0x93, 0xa1, 0xc5, 0x0d, 0x1a,
- 0x34, 0x68, 0xd0, 0x27, 0x4e, 0x9c, 0xbf, 0xf9,
- 0x75, 0xea, 0x53, 0xa6, 0xcb, 0x11, 0x22, 0x44,
- 0x88, 0x97, 0xa9, 0xd5, 0x2d, 0x5a, 0xb4, 0xef,
- 0x59, 0xb2, 0xe3, 0x41, 0x82, 0x83, 0x81, 0x85,
- 0x8d, 0x9d, 0xbd, 0xfd, 0x7d, 0xfa, 0x73, 0xe6,
- 0x4b, 0x96, 0xab, 0xd1, 0x25, 0x4a, 0x94, 0xaf,
- 0xd9, 0x35, 0x6a, 0xd4, 0x2f, 0x5e, 0xbc, 0xff,
- 0x79, 0xf2, 0x63, 0xc6, 0x0b, 0x16, 0x2c, 0x58,
- 0xb0, 0xe7, 0x49, 0x92, 0xa3, 0xc1, 0x05, 0x0a,
- 0x14, 0x28, 0x50, 0xa0, 0xc7, 0x09, 0x12, 0x24,
- 0x48, 0x90, 0xa7, 0xc9, 0x15, 0x2a, 0x54, 0xa8,
- 0xd7, 0x29, 0x52, 0xa4, 0xcf, 0x19, 0x32, 0x64,
- 0xc8, 0x17, 0x2e, 0x5c, 0xb8, 0xf7, 0x69, 0xd2,
- 0x23, 0x46, 0x8c, 0x9f, 0xb9, 0xf5, 0x6d, 0xda,
- 0x33, 0x66, 0xcc, 0x1f, 0x3e, 0x7c, 0xf8, 0x77,
- 0xee, 0x5b, 0xb6, 0xeb, 0x51, 0xa2, 0xc3, 0x01
-};
-
-/*
- * This is a log table. That is, gflog[r^i] returns i (modulo f(r)).
- * gflog[0] is undefined and the first element is therefore not valid.
- */
-static const unsigned char gflog[256] =
-{
- 0xff, 0x00, 0x01, 0x63, 0x02, 0xc6, 0x64, 0x6a,
- 0x03, 0xcd, 0xc7, 0xbc, 0x65, 0x7e, 0x6b, 0x2a,
- 0x04, 0x8d, 0xce, 0x4e, 0xc8, 0xd4, 0xbd, 0xe1,
- 0x66, 0xdd, 0x7f, 0x31, 0x6c, 0x20, 0x2b, 0xf3,
- 0x05, 0x57, 0x8e, 0xe8, 0xcf, 0xac, 0x4f, 0x83,
- 0xc9, 0xd9, 0xd5, 0x41, 0xbe, 0x94, 0xe2, 0xb4,
- 0x67, 0x27, 0xde, 0xf0, 0x80, 0xb1, 0x32, 0x35,
- 0x6d, 0x45, 0x21, 0x12, 0x2c, 0x0d, 0xf4, 0x38,
- 0x06, 0x9b, 0x58, 0x1a, 0x8f, 0x79, 0xe9, 0x70,
- 0xd0, 0xc2, 0xad, 0xa8, 0x50, 0x75, 0x84, 0x48,
- 0xca, 0xfc, 0xda, 0x8a, 0xd6, 0x54, 0x42, 0x24,
- 0xbf, 0x98, 0x95, 0xf9, 0xe3, 0x5e, 0xb5, 0x15,
- 0x68, 0x61, 0x28, 0xba, 0xdf, 0x4c, 0xf1, 0x2f,
- 0x81, 0xe6, 0xb2, 0x3f, 0x33, 0xee, 0x36, 0x10,
- 0x6e, 0x18, 0x46, 0xa6, 0x22, 0x88, 0x13, 0xf7,
- 0x2d, 0xb8, 0x0e, 0x3d, 0xf5, 0xa4, 0x39, 0x3b,
- 0x07, 0x9e, 0x9c, 0x9d, 0x59, 0x9f, 0x1b, 0x08,
- 0x90, 0x09, 0x7a, 0x1c, 0xea, 0xa0, 0x71, 0x5a,
- 0xd1, 0x1d, 0xc3, 0x7b, 0xae, 0x0a, 0xa9, 0x91,
- 0x51, 0x5b, 0x76, 0x72, 0x85, 0xa1, 0x49, 0xeb,
- 0xcb, 0x7c, 0xfd, 0xc4, 0xdb, 0x1e, 0x8b, 0xd2,
- 0xd7, 0x92, 0x55, 0xaa, 0x43, 0x0b, 0x25, 0xaf,
- 0xc0, 0x73, 0x99, 0x77, 0x96, 0x5c, 0xfa, 0x52,
- 0xe4, 0xec, 0x5f, 0x4a, 0xb6, 0xa2, 0x16, 0x86,
- 0x69, 0xc5, 0x62, 0xfe, 0x29, 0x7d, 0xbb, 0xcc,
- 0xe0, 0xd3, 0x4d, 0x8c, 0xf2, 0x1f, 0x30, 0xdc,
- 0x82, 0xab, 0xe7, 0x56, 0xb3, 0x93, 0x40, 0xd8,
- 0x34, 0xb0, 0xef, 0x26, 0x37, 0x0c, 0x11, 0x44,
- 0x6f, 0x78, 0x19, 0x9a, 0x47, 0x74, 0xa7, 0xc1,
- 0x23, 0x53, 0x89, 0xfb, 0x14, 0x5d, 0xf8, 0x97,
- 0x2e, 0x4b, 0xb9, 0x60, 0x0f, 0xed, 0x3e, 0xe5,
- 0xf6, 0x87, 0xa5, 0x17, 0x3a, 0xa3, 0x3c, 0xb7
-};
-
-/*
- * This is a multiplication table for the factor
- * 0xc0 (i.e., r^105 (modulo f(r)).
- * gfmul_c0[f] returns r^105 * f(r) (modulo f(r)).
- */
-static const unsigned char gfmul_c0[256] =
-{
- 0x00, 0xc0, 0x07, 0xc7, 0x0e, 0xce, 0x09, 0xc9,
- 0x1c, 0xdc, 0x1b, 0xdb, 0x12, 0xd2, 0x15, 0xd5,
- 0x38, 0xf8, 0x3f, 0xff, 0x36, 0xf6, 0x31, 0xf1,
- 0x24, 0xe4, 0x23, 0xe3, 0x2a, 0xea, 0x2d, 0xed,
- 0x70, 0xb0, 0x77, 0xb7, 0x7e, 0xbe, 0x79, 0xb9,
- 0x6c, 0xac, 0x6b, 0xab, 0x62, 0xa2, 0x65, 0xa5,
- 0x48, 0x88, 0x4f, 0x8f, 0x46, 0x86, 0x41, 0x81,
- 0x54, 0x94, 0x53, 0x93, 0x5a, 0x9a, 0x5d, 0x9d,
- 0xe0, 0x20, 0xe7, 0x27, 0xee, 0x2e, 0xe9, 0x29,
- 0xfc, 0x3c, 0xfb, 0x3b, 0xf2, 0x32, 0xf5, 0x35,
- 0xd8, 0x18, 0xdf, 0x1f, 0xd6, 0x16, 0xd1, 0x11,
- 0xc4, 0x04, 0xc3, 0x03, 0xca, 0x0a, 0xcd, 0x0d,
- 0x90, 0x50, 0x97, 0x57, 0x9e, 0x5e, 0x99, 0x59,
- 0x8c, 0x4c, 0x8b, 0x4b, 0x82, 0x42, 0x85, 0x45,
- 0xa8, 0x68, 0xaf, 0x6f, 0xa6, 0x66, 0xa1, 0x61,
- 0xb4, 0x74, 0xb3, 0x73, 0xba, 0x7a, 0xbd, 0x7d,
- 0x47, 0x87, 0x40, 0x80, 0x49, 0x89, 0x4e, 0x8e,
- 0x5b, 0x9b, 0x5c, 0x9c, 0x55, 0x95, 0x52, 0x92,
- 0x7f, 0xbf, 0x78, 0xb8, 0x71, 0xb1, 0x76, 0xb6,
- 0x63, 0xa3, 0x64, 0xa4, 0x6d, 0xad, 0x6a, 0xaa,
- 0x37, 0xf7, 0x30, 0xf0, 0x39, 0xf9, 0x3e, 0xfe,
- 0x2b, 0xeb, 0x2c, 0xec, 0x25, 0xe5, 0x22, 0xe2,
- 0x0f, 0xcf, 0x08, 0xc8, 0x01, 0xc1, 0x06, 0xc6,
- 0x13, 0xd3, 0x14, 0xd4, 0x1d, 0xdd, 0x1a, 0xda,
- 0xa7, 0x67, 0xa0, 0x60, 0xa9, 0x69, 0xae, 0x6e,
- 0xbb, 0x7b, 0xbc, 0x7c, 0xb5, 0x75, 0xb2, 0x72,
- 0x9f, 0x5f, 0x98, 0x58, 0x91, 0x51, 0x96, 0x56,
- 0x83, 0x43, 0x84, 0x44, 0x8d, 0x4d, 0x8a, 0x4a,
- 0xd7, 0x17, 0xd0, 0x10, 0xd9, 0x19, 0xde, 0x1e,
- 0xcb, 0x0b, 0xcc, 0x0c, 0xc5, 0x05, 0xc2, 0x02,
- 0xef, 0x2f, 0xe8, 0x28, 0xe1, 0x21, 0xe6, 0x26,
- 0xf3, 0x33, 0xf4, 0x34, 0xfd, 0x3d, 0xfa, 0x3a
-};
-
-
-/*
- * Returns V modulo 255 provided V is in the range -255,-254,...,509.
- */
-static inline unsigned char mod255(int v)
-{
- if (v > 0) {
- if (v < 255) {
- return v;
- } else {
- return v - 255;
- }
- } else {
- return v + 255;
- }
-}
-
-
-/*
- * Add two numbers in the field. Addition in this field is
- * equivalent to a bit-wise exclusive OR operation---subtraction
- * is therefore identical to addition.
- */
-static inline unsigned char gfadd(unsigned char a, unsigned char b)
-{
- return a ^ b;
-}
-
-
-/*
- * Add two vectors of numbers in the field. Each byte in A and B get
- * added individually.
- */
-static inline unsigned long gfadd_long(unsigned long a, unsigned long b)
-{
- return a ^ b;
-}
-
-
-/*
- * Multiply two numbers in the field:
- */
-static inline unsigned char gfmul(unsigned char a, unsigned char b)
-{
- if (a && b) {
- return gfpow[mod255(gflog[a] + gflog[b])];
- } else {
- return 0;
- }
-}
-
-
-/*
- * Just like gfmul, except we have already looked up the log
- * of the second number.
- */
-static inline unsigned char gfmul_exp(unsigned char a, int b)
-{
- if (a) {
- return gfpow[mod255(gflog[a] + b)];
- } else {
- return 0;
- }
-}
-
-
-/*
- * Just like gfmul_exp, except that A is a vector of numbers. That is,
- * each byte in A gets multiplied by gfpow[mod255(B)].
- */
-static inline unsigned long gfmul_exp_long(unsigned long a, int b)
-{
- TRACE_FUN(8, "gfmul_exp_long");
- unsigned char t;
-
- if (sizeof(long) == 4) {
- TRACE_EXIT;
- return
- ((t = a >> 24 & 0xff) ? (((unsigned long) gfpow[mod255(gflog[t] + b)]) << 24) : 0) |
- ((t = a >> 16 & 0xff) ? (((unsigned long) gfpow[mod255(gflog[t] + b)]) << 16) : 0) |
- ((t = a >> 8 & 0xff) ? (((unsigned long) gfpow[mod255(gflog[t] + b)]) << 8) : 0) |
- ((t = a >> 0 & 0xff) ? (((unsigned long) gfpow[mod255(gflog[t] + b)]) << 0) : 0);
-#if !defined(linux)
- } else if (sizeof(long) == 8) {
- TRACE_EXIT;
- return
- ((t = a >> 56 & 0xff) ? (((unsigned long) gfpow[mod255(gflog[t] + b)]) << 56) : 0) |
- ((t = a >> 48 & 0xff) ? (((unsigned long) gfpow[mod255(gflog[t] + b)]) << 48) : 0) |
- ((t = a >> 40 & 0xff) ? (((unsigned long) gfpow[mod255(gflog[t] + b)]) << 40) : 0) |
- ((t = a >> 32 & 0xff) ? (((unsigned long) gfpow[mod255(gflog[t] + b)]) << 32) : 0) |
- ((t = a >> 24 & 0xff) ? (((unsigned long) gfpow[mod255(gflog[t] + b)]) << 24) : 0) |
- ((t = a >> 16 & 0xff) ? (((unsigned long) gfpow[mod255(gflog[t] + b)]) << 16) : 0) |
- ((t = a >> 8 & 0xff) ? (((unsigned long) gfpow[mod255(gflog[t] + b)]) << 8) : 0) |
- ((t = a >> 0 & 0xff) ? (((unsigned long) gfpow[mod255(gflog[t] + b)]) << 0) : 0);
-#endif
- } else {
- TRACEx1(1, "Error: size of long is %d bytes", (int) sizeof(long));
- }
- TRACE_EXIT;
- return -1;
-}
-
-
-/*
- * Divide two numbers in the field. Returns a/b (modulo f(x)).
- */
-static inline unsigned char gfdiv(unsigned char a, unsigned char b)
-{
- TRACE_FUN(8, "gfdiv");
- if (!b) {
- TRACE(-1, "Error: division by zero");
- return 0xff;
- } else if (a == 0) {
- return 0;
- } else {
- return gfpow[mod255(gflog[a] - gflog[b])];
- }
- TRACE_EXIT;
-}
-
-
-/*
- * The following functions return the inverse of the matrix of the
- * linear system that needs to be solved to determine the error
- * magnitudes. The first deals with matrices of rank 3, while the
- * second deals with matrices of rank 2. The error indices are passed
- * in arguments L0,..,L2 (0=first sector, 31=last sector). The
- * error indices must be sorted in ascending order, i.e., L0<L1<L2.
- *
- * The linear system that needs to be solved for the error
- * magnitudes is A * b = s, where s is the known vector of
- * syndromes, b is the vector of error magnitudes and A in
- * the ORDER=3 case:
- *
- * A_3 = {{1/r^L[0], 1/r^L[1], 1/r^L[2]},
- * { 1, 1, 1},
- * { r^L[0], r^L[1], r^L[2]}}
- */
-static inline int gfinv3(unsigned char l0, unsigned char l1, unsigned char l2, Matrix Ainv)
-{
- TRACE_FUN(8, "gfinv3");
- unsigned char det;
- unsigned char t20, t10, t21, t12, t01, t02;
- int log_det;
-
- /* compute some intermediate results: */
- t20 = gfpow[l2 - l0]; /* t20 = r^l2/r^l0 */
- t10 = gfpow[l1 - l0]; /* t10 = r^l1/r^l0 */
- t21 = gfpow[l2 - l1]; /* t21 = r^l2/r^l1 */
- t12 = gfpow[l1 - l2 + 255]; /* t12 = r^l1/r^l2 */
- t01 = gfpow[l0 - l1 + 255]; /* t01 = r^l0/r^l1 */
- t02 = gfpow[l0 - l2 + 255]; /* t02 = r^l0/r^l2 */
- /*
- * Calculate the determinant of matrix A_3^-1 (sometimes called
- * the Vandermonde determinant):
- */
- det = gfadd(t20, gfadd(t10, gfadd(t21, gfadd(t12, gfadd(t01, t02)))));
- if (!det) {
- TRACE(1, "Inversion failed (3 CRC errors, >0 CRC failures)");
- TRACE_EXIT;
- return 0;
- }
- log_det = 255 - gflog[det];
-
- /*
- * Now, calculate all of the coefficients:
- */
- Ainv[0][0] = gfmul_exp(gfadd(gfpow[l1], gfpow[l2]), log_det);
- Ainv[0][1] = gfmul_exp(gfadd(t21, t12), log_det);
- Ainv[0][2] = gfmul_exp(gfadd(gfpow[255 - l1], gfpow[255 - l2]), log_det);
-
- Ainv[1][0] = gfmul_exp(gfadd(gfpow[l0], gfpow[l2]), log_det);
- Ainv[1][1] = gfmul_exp(gfadd(t20, t02), log_det);
- Ainv[1][2] = gfmul_exp(gfadd(gfpow[255 - l0], gfpow[255 - l2]), log_det);
-
- Ainv[2][0] = gfmul_exp(gfadd(gfpow[l0], gfpow[l1]), log_det);
- Ainv[2][1] = gfmul_exp(gfadd(t10, t01), log_det);
- Ainv[2][2] = gfmul_exp(gfadd(gfpow[255 - l0], gfpow[255 - l1]), log_det);
-
- TRACE_EXIT;
- return 1;
-}
-
-
-static inline int gfinv2(unsigned char l0, unsigned char l1, Matrix Ainv)
-{
- TRACE_FUN(8, "gfinv2");
- unsigned char det;
- unsigned char t1, t2;
- int log_det;
-
- t1 = gfpow[255 - l0];
- t2 = gfpow[255 - l1];
- det = gfadd(t1, t2);
- if (!det) {
- TRACE(1, "Inversion failed (2 CRC errors, >0 CRC failures)");
- TRACE_EXIT;
- return 0;
- }
- log_det = 255 - gflog[det];
-
- /*
- * Now, calculate all of the coefficients:
- */
- Ainv[0][0] = Ainv[1][0] = gfpow[log_det];
-
- Ainv[0][1] = gfmul_exp(t2, log_det);
- Ainv[1][1] = gfmul_exp(t1, log_det);
-
- TRACE_EXIT;
- return 1;
-}
-
-
-/*
- * Multiply matrix A by vector S and return result in vector B.
- * M is assumed to be of order NxN, S and B of order Nx1.
- */
-static inline void gfmat_mul(int n, Matrix A, unsigned char *s, unsigned char *b)
-{
- int i, j;
- unsigned char dot_prod;
-
- for (i = 0; i < n; ++i) {
- dot_prod = 0;
- for (j = 0; j < n; ++j) {
- dot_prod = gfadd(dot_prod, gfmul(A[i][j], s[j]));
- }
- b[i] = dot_prod;
- }
-}
-
-
-
-/*
- * The Reed Solomon ECC codes are computed over the N-th byte of each
- * block, where N=SECTOR_SIZE. There are up to 29 blocks of data, and
- * 3 blocks of ECC. The blocks are stored contiguously in memory.
- * A segment, consequently, is assumed to have at least 4 blocks:
- * one or more data blocks plus three ECC blocks.
- *
- * Notice: In QIC-80 speak, a CRC error is a sector with an incorrect
- * CRC. A CRC failure is a sector with incorrect data, but
- * a valid CRC. In the error control literature, the former
- * is usually called "erasure", the latter "error."
- */
-/*
- * Compute the parity bytes for C columns of data, where C is the
- * number of bytes that fit into a long integer. We use a linear
- * feed-back register to do this. The parity bytes P[0], P[STRIDE],
- * P[2*STRIDE] are computed such that:
- *
- * x^k * p(x) + m(x) = 0 (modulo g(x))
- *
- * where k = NBLOCKS,
- * p(x) = P[0] + P[STRIDE]*x + P[2*STRIDE]*x^2, and
- * m(x) = sum_{i=0}^k m_i*x^i.
- * m_i = DATA[i*SECTOR_SIZE]
- */
-static inline void set_parity(unsigned long *data, int nblocks, unsigned long *p, int stride)
-{
- TRACE_FUN(8, "set_parity");
- unsigned long p0, p1, p2, t1, t2, *end;
-
- end = data + nblocks * (SECTOR_SIZE / sizeof(long));
- p0 = p1 = p2 = 0;
- while (data < end) {
- /*
- * The new parity bytes p0_i, p1_i, p2_i are computed from the old
- * values p0_{i-1}, p1_{i-1}, p2_{i-1} recursively as:
- *
- * p0_i = p1_{i-1} + r^105 * (m_{i-1} - p0_{i-1})
- * p1_i = p2_{i-1} + r^105 * (m_{i-1} - p0_{i-1})
- * p2_i = (m_{i-1} - p0_{i-1})
- *
- * With the initial condition: p0_0 = p1_0 = p2_0 = 0.
- */
- t1 = gfadd_long(*data, p0);
- /*
- * Multiply each byte in t1 by 0xc0:
- */
- if (sizeof(long) == 4) {
- t2 = ((unsigned long) gfmul_c0[t1 >> 24 & 0xff]) << 24 |
- ((unsigned long) gfmul_c0[t1 >> 16 & 0xff]) << 16 |
- ((unsigned long) gfmul_c0[t1 >> 8 & 0xff]) << 8 |
- ((unsigned long) gfmul_c0[t1 >> 0 & 0xff]) << 0;
-#if !defined(linux)
- } else if (sizeof(long) == 8) {
- t2 = ((unsigned long) gfmul_c0[t1 >> 56 & 0xff]) << 56 |
- ((unsigned long) gfmul_c0[t1 >> 48 & 0xff]) << 48 |
- ((unsigned long) gfmul_c0[t1 >> 40 & 0xff]) << 40 |
- ((unsigned long) gfmul_c0[t1 >> 32 & 0xff]) << 32 |
- ((unsigned long) gfmul_c0[t1 >> 24 & 0xff]) << 24 |
- ((unsigned long) gfmul_c0[t1 >> 16 & 0xff]) << 16 |
- ((unsigned long) gfmul_c0[t1 >> 8 & 0xff]) << 8 |
- ((unsigned long) gfmul_c0[t1 >> 0 & 0xff]) << 0;
-#endif
- } else {
- TRACEx1(1, "Error: long is of size %d", (int) sizeof(long));
- }
- p0 = gfadd_long(t2, p1);
- p1 = gfadd_long(t2, p2);
- p2 = t1;
- data += SECTOR_SIZE / sizeof(long);
- }
- *p = p0;
- p += stride;
- *p = p1;
- p += stride;
- *p = p2;
- TRACE_EXIT;
-}
-
-
-/*
- * Compute the 3 syndrome values. DATA should point to the first byte
- * of the column for which the syndromes are desired. The syndromes
- * are computed over the first NBLOCKS of rows. The three bytes will be
- * placed in S[0], S[1], and S[2].
- *
- * S[i] is the value of the "message" polynomial m(x) evaluated at the
- * i-th root of the generator polynomial g(x).
- *
- * As g(x)=(x-r^-1)(x-1)(x-r^1) we evaluate the message polynomial at
- * x=r^-1 to get S[0], at x=r^0=1 to get S[1], and at x=r to get S[2].
- * This could be done directly and efficiently via the Horner scheme.
- * However, it would require multiplication tables for the factors
- * r^-1 (0xc3) and r (0x02). The following scheme does not require
- * any multiplication tables beyond what's needed for set_parity()
- * anyway and is slightly faster if there are no errors and slightly
- * slower if there are errors. The latter is hopefully the infrequent
- * case.
- *
- * To understand the alternative algorithm, notice that
- * set_parity(m, k, p) computes parity bytes such that:
- *
- * x^k * p(x) = m(x) (modulo g(x)).
- *
- * That is, to evaluate m(r^m), where r^m is a root of g(x), we can
- * simply evaluate (r^m)^k*p(r^m). Also, notice that p is 0 if and
- * only if s is zero. That is, if all parity bytes are 0, we know
- * there is no error in the data and consequently there is no need to
- * compute s(x) at all! In all other cases, we compute s(x) from p(x)
- * by evaluating (r^m)^k*p(r^m) for m=-1, m=0, and m=1. The p(x)
- * polynomial is evaluated via the Horner scheme.
- */
-static int compute_syndromes(unsigned long *data, int nblocks, unsigned long *s)
-{
- unsigned long p[3];
-
- set_parity(data, nblocks, p, 1);
- if (p[0] | p[1] | p[2]) {
- /*
- * Some of the checked columns do not have a zero syndrome. For
- * simplicity, we compute the syndromes for all columns that we
- * have computed the remainders for.
- */
- s[0] = gfmul_exp_long(gfadd_long(p[0], gfmul_exp_long(gfadd_long(p[1],
- gfmul_exp_long(p[2], -1)), -1)), -nblocks);
- s[1] = gfadd_long(gfadd_long(p[2], p[1]), p[0]);
- s[2] = gfmul_exp_long(gfadd_long(p[0], gfmul_exp_long(gfadd_long(p[1],
- gfmul_exp_long(p[2], 1)), 1)), nblocks);
- return 0;
- } else {
- return 1;
- }
-}
-
-
-/*
- * Correct the block in the column pointed to by DATA. There are NBAD
- * CRC errors and their indices are in BAD_LOC[0], up to
- * BAD_LOC[NBAD-1]. If NBAD>1, Ainv holds the inverse of the matrix
- * of the linear system that needs to be solved to determine the error
- * magnitudes. S[0], S[1], and S[2] are the syndrome values. If row
- * j gets corrected, then bit j will be set in CORRECTION_MAP.
- */
-static inline int correct_block(unsigned char *data, int nblocks,
- int nbad, int *bad_loc, Matrix Ainv,
- unsigned char *s,
- BAD_SECTOR * correction_map)
-{
- TRACE_FUN(8, "correct_block");
- int ncorrected = 0;
- int i;
- unsigned char t1, t2;
- unsigned char c0, c1, c2; /* check bytes */
- unsigned char error_mag[3], log_error_mag;
- unsigned char *dp, l, e;
-
- switch (nbad) {
- case 0:
- /* might have a CRC failure: */
- if (s[0] == 0) {
- /* more than one error */
- TRACE(1, "ECC failed (0 CRC errors, >1 CRC failures)");
- TRACE_EXIT;
- return -1;
- } /* if */
- t1 = gfdiv(s[1], s[0]);
- if ((bad_loc[nbad++] = gflog[t1]) >= nblocks) {
- TRACE(1, "ECC failed (0 CRC errors, >1 CRC failures): ");
- TRACEi(1, "attempt to correct data at ", bad_loc[0]);
- TRACE_EXIT;
- return -1;
- }
- error_mag[0] = s[1];
- break;
- case 1:
- t1 = gfadd(gfmul_exp(s[1], bad_loc[0]), s[2]);
- t2 = gfadd(gfmul_exp(s[0], bad_loc[0]), s[1]);
- if (t1 == 0 && t2 == 0) {
- /* one erasure, no error: */
- Ainv[0][0] = gfpow[bad_loc[0]];
- } else if (t1 == 0 || t2 == 0) {
- /* one erasure and more than one error: */
- TRACE(1, "ECC failed (1 erasure, >1 error)");
- TRACE_EXIT;
- return -1;
- } else {
- /* one erasure, one error: */
- if ((bad_loc[nbad++] = gflog[gfdiv(t1, t2)]) >= nblocks) {
- TRACE(1, "ECC failed (1 CRC errors, >1 CRC failures): ");
- TRACEi(1, "attempt to correct data at ", bad_loc[1]);
- TRACE_EXIT;
- return -1;
- } /* if */
- if (!gfinv2(bad_loc[0], bad_loc[1], Ainv)) {
- /* inversion failed---must have more than one error */
- TRACE_EXIT;
- return -1;
- }
- }
- /*
- * FALL THROUGH TO ERROR MAGNITUDE COMPUTATION:
- */
- case 2:
- case 3:
- /* compute error magnitudes: */
- gfmat_mul(nbad, Ainv, s, error_mag);
- break;
-
- default:
- TRACE(1, "Internal Error: number of CRC errors > 3");
- TRACE_EXIT;
- return -1;
- }
-
- /*
- * Perform correction by adding ERROR_MAG[i] to the byte at offset
- * BAD_LOC[i]. Also add the value of the computed error polynomial
- * to the syndrome values. If the correction was successful, the
- * resulting check bytes should be zero (i.e., the corrected data
- * is a valid code word).
- */
- c0 = s[0];
- c1 = s[1];
- c2 = s[2];
- for (i = 0; i < nbad; ++i) {
- e = error_mag[i];
- if (e) {
- /* correct the byte at offset L by magnitude E: */
- l = bad_loc[i];
- dp = &data[l * SECTOR_SIZE];
- *dp = gfadd(*dp, e);
- *correction_map |= 1 << l;
- ++ncorrected;
-
- log_error_mag = gflog[e];
- c0 = gfadd(c0, gfpow[mod255(log_error_mag - l)]);
- c1 = gfadd(c1, e);
- c2 = gfadd(c2, gfpow[mod255(log_error_mag + l)]);
- }
- }
- if (c0 || c1 || c2) {
- TRACE(1, "ECC self-check failed, too many errors");
- TRACE_EXIT;
- return -1;
- }
- TRACE_EXIT;
- return ncorrected;
-}
-
-
-#if defined(ECC_SANITY_CHECK) || defined(ECC_PARANOID)
-
-/*
- * Perform a sanity check on the computed parity bytes:
- */
-static int sanity_check(unsigned long *data, int nblocks)
-{
- TRACE_FUN(8, "sanity_check");
- unsigned long s[3];
-
- if (!compute_syndromes(data, nblocks, s)) {
- TRACE(-1, "Internal Error: syndrome self-check failed");
- TRACE_EXIT;
- return 0;
- }
- TRACE_EXIT;
- return 1;
-}
-
-#endif /* defined(ECC_SANITY_CHECK) || defined(ECC_PARANOID) */
-
-
-
-/*
- * Compute the parity for an entire segment of data.
- */
-int ecc_set_segment_parity(struct memory_segment *mseg)
-{
- int i;
- unsigned char *parity_bytes;
-
- parity_bytes = &mseg->data[(mseg->blocks - 3) * SECTOR_SIZE];
- for (i = 0; i < SECTOR_SIZE; i += sizeof(long)) {
- set_parity((unsigned long *) &mseg->data[i], mseg->blocks - 3,
- (unsigned long *) &parity_bytes[i],
- SECTOR_SIZE / sizeof(long));
-#ifdef ECC_PARANOID
- if (!sanity_check((unsigned long *) &mseg->data[i], mseg->blocks)) {
- return -1;
- }
-#endif /* ECC_PARANOID */
- }
- return 0;
-}
-
-
-/*
- * Checks and corrects (if possible) the segment MSEG. Returns one of
- * ECC_OK, ECC_CORRECTED, and ECC_FAILED.
- */
-int ecc_correct_data(struct memory_segment *mseg)
-{
- TRACE_FUN(5, "ecc_correct_data");
- int col, i, result;
- int ncorrected = 0;
- int nerasures = 0; /* # of erasures (CRC errors) */
- int erasure_loc[3]; /* erasure locations */
- unsigned long ss[3];
- unsigned char s[3];
- Matrix Ainv;
-
- mseg->corrected = 0;
-
- /* find first column that has non-zero syndromes: */
- for (col = 0; col < SECTOR_SIZE; col += sizeof(long)) {
- if (!compute_syndromes((unsigned long *) &mseg->data[col],
- mseg->blocks, ss)) {
- /* something is wrong---have to fix things */
- break;
- }
- }
- if (col >= SECTOR_SIZE) {
- /* all syndromes are ok, therefore nothing to correct */
- TRACE_EXIT;
- return ECC_OK;
- }
- /* count the number of CRC errors if there were any: */
- if (mseg->read_bad) {
- for (i = 0; i < mseg->blocks; i++) {
- if (BAD_CHECK(mseg->read_bad, i)) {
- if (nerasures >= 3) {
- /* this is too much for ECC */
- TRACE(1, "ECC failed (>3 CRC errors)");
- TRACE_EXIT;
- return ECC_FAILED;
- } /* if */
- erasure_loc[nerasures++] = i;
- }
- }
- }
- /*
- * If there are at least 2 CRC errors, determine inverse of matrix
- * of linear system to be solved:
- */
- switch (nerasures) {
- case 2:
- if (!gfinv2(erasure_loc[0], erasure_loc[1], Ainv)) {
- TRACE_EXIT;
- return ECC_FAILED;
- }
- break;
- case 3:
- if (!gfinv3(erasure_loc[0], erasure_loc[1], erasure_loc[2], Ainv)) {
- TRACE_EXIT;
- return ECC_FAILED;
- }
- break;
- default:
- /* this is not an error condition... */
- break;
- }
-
- do {
- for (i = 0; i < sizeof(long); ++i) {
- s[0] = ss[0];
- s[1] = ss[1];
- s[2] = ss[2];
- if (s[0] | s[1] | s[2]) {
-#ifdef BIG_ENDIAN
- result = correct_block(&mseg->data[col + sizeof(long) - 1 - i],
- mseg->blocks,
- nerasures, erasure_loc, Ainv, s,
- &mseg->corrected);
-#else
- result = correct_block(&mseg->data[col + i], mseg->blocks,
- nerasures, erasure_loc, Ainv, s,
- &mseg->corrected);
-#endif
- if (result < 0) {
- TRACE_EXIT;
- return ECC_FAILED;
- }
- ncorrected += result;
- }
- ss[0] >>= 8;
- ss[1] >>= 8;
- ss[2] >>= 8;
- }
-
-#ifdef ECC_SANITY_CHECK
- if (!sanity_check((unsigned long *) &mseg->data[col], mseg->blocks)) {
- TRACE_EXIT;
- return ECC_FAILED;
- }
-#endif /* ECC_SANITY_CHECK */
-
- /* find next column with non-zero syndromes: */
- while ((col += sizeof(long)) < SECTOR_SIZE) {
- if (!compute_syndromes((unsigned long *) &mseg->data[col],
- mseg->blocks, ss)) {
- /* something is wrong---have to fix things */
- break;
- }
- }
- } while (col < SECTOR_SIZE);
- if (ncorrected && nerasures == 0) {
- TRACE(2, "block contained error not caught by CRC");
- }
- TRACEi((ncorrected > 0) ? 4 : 8, "number of corrections:", ncorrected);
- TRACE_EXIT;
- return ncorrected ? ECC_CORRECTED : ECC_OK;
-}
-
-/*** end of ecc.c ***/
FUNET's LINUX-ADM group, linux-adm@nic.funet.fi
TCL-scripts by Sam Shen, slshen@lbl.gov