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/*
*
* 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: /homes/cvs/ftape-stacked/ftape/lowlevel/ftape-ecc.c,v $
* $Revision: 1.3 $
* $Date: 1997/10/05 19:18:10 $
*
* This file contains the Reed-Solomon error correction code
* for the QIC-40/80 floppy-tape driver for Linux.
*/
#include <linux/ftape.h>
#include "../lowlevel/ftape-tracing.h"
#include "../lowlevel/ftape-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
/* 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 __u8 Matrix[3][3];
/*
* gfpow[] is defined such that gfpow[i] returns r^i if
* i is in the range [0..255].
*/
static const __u8 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 __u8 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 (mod f(r)).
* gfmul_c0[f] returns r^105 * f(r) (modulo f(r)).
*/
static const __u8 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 __u8 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 __u8 gfadd(__u8 a, __u8 b)
{
return a ^ b;
}
/* Add two vectors of numbers in the field. Each byte in A and B gets
* 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 __u8 gfmul(__u8 a, __u8 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 __u8 gfmul_exp(__u8 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)
{
__u8 t;
if (sizeof(long) == 4) {
return (
((t = (__u32)a >> 24 & 0xff) ?
(((__u32) gfpow[mod255(gflog[t] + b)]) << 24) : 0) |
((t = (__u32)a >> 16 & 0xff) ?
(((__u32) gfpow[mod255(gflog[t] + b)]) << 16) : 0) |
((t = (__u32)a >> 8 & 0xff) ?
(((__u32) gfpow[mod255(gflog[t] + b)]) << 8) : 0) |
((t = (__u32)a >> 0 & 0xff) ?
(((__u32) gfpow[mod255(gflog[t] + b)]) << 0) : 0));
} else if (sizeof(long) == 8) {
return (
((t = (__u64)a >> 56 & 0xff) ?
(((__u64) gfpow[mod255(gflog[t] + b)]) << 56) : 0) |
((t = (__u64)a >> 48 & 0xff) ?
(((__u64) gfpow[mod255(gflog[t] + b)]) << 48) : 0) |
((t = (__u64)a >> 40 & 0xff) ?
(((__u64) gfpow[mod255(gflog[t] + b)]) << 40) : 0) |
((t = (__u64)a >> 32 & 0xff) ?
(((__u64) gfpow[mod255(gflog[t] + b)]) << 32) : 0) |
((t = (__u64)a >> 24 & 0xff) ?
(((__u64) gfpow[mod255(gflog[t] + b)]) << 24) : 0) |
((t = (__u64)a >> 16 & 0xff) ?
(((__u64) gfpow[mod255(gflog[t] + b)]) << 16) : 0) |
((t = (__u64)a >> 8 & 0xff) ?
(((__u64) gfpow[mod255(gflog[t] + b)]) << 8) : 0) |
((t = (__u64)a >> 0 & 0xff) ?
(((__u64) gfpow[mod255(gflog[t] + b)]) << 0) : 0));
} else {
TRACE_FUN(ft_t_any);
TRACE_ABORT(-1, ft_t_err, "Error: size of long is %d bytes",
(int)sizeof(long));
}
}
/* Divide two numbers in the field. Returns a/b (modulo f(x)).
*/
static inline __u8 gfdiv(__u8 a, __u8 b)
{
if (!b) {
TRACE_FUN(ft_t_any);
TRACE_ABORT(0xff, ft_t_bug, "Error: division by zero");
} else if (a == 0) {
return 0;
} else {
return gfpow[mod255(gflog[a] - gflog[b])];
}
}
/* 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(__u8 l0,
__u8 l1,
__u8 l2,
Matrix Ainv)
{
__u8 det;
__u8 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_FUN(ft_t_any);
TRACE_ABORT(0, ft_t_err,
"Inversion failed (3 CRC errors, >0 CRC failures)");
}
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);
return 1;
}
static inline int gfinv2(__u8 l0, __u8 l1, Matrix Ainv)
{
__u8 det;
__u8 t1, t2;
int log_det;
t1 = gfpow[255 - l0];
t2 = gfpow[255 - l1];
det = gfadd(t1, t2);
if (!det) {
TRACE_FUN(ft_t_any);
TRACE_ABORT(0, ft_t_err,
"Inversion failed (2 CRC errors, >0 CRC failures)");
}
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);
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,
__u8 *s, __u8 *b)
{
int i, j;
__u8 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)
{
unsigned long p0, p1, p2, t1, t2, *end;
end = data + nblocks * (FT_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= (((__u32) gfmul_c0[(__u32)t1 >> 24 & 0xff]) << 24 |
((__u32) gfmul_c0[(__u32)t1 >> 16 & 0xff]) << 16 |
((__u32) gfmul_c0[(__u32)t1 >> 8 & 0xff]) << 8 |
((__u32) gfmul_c0[(__u32)t1 >> 0 & 0xff]) << 0);
} else if (sizeof(long) == 8) {
t2= (((__u64) gfmul_c0[(__u64)t1 >> 56 & 0xff]) << 56 |
((__u64) gfmul_c0[(__u64)t1 >> 48 & 0xff]) << 48 |
((__u64) gfmul_c0[(__u64)t1 >> 40 & 0xff]) << 40 |
((__u64) gfmul_c0[(__u64)t1 >> 32 & 0xff]) << 32 |
((__u64) gfmul_c0[(__u64)t1 >> 24 & 0xff]) << 24 |
((__u64) gfmul_c0[(__u64)t1 >> 16 & 0xff]) << 16 |
((__u64) gfmul_c0[(__u64)t1 >> 8 & 0xff]) << 8 |
((__u64) gfmul_c0[(__u64)t1 >> 0 & 0xff]) << 0);
} else {
TRACE_FUN(ft_t_any);
TRACE(ft_t_err, "Error: long is of size %d",
(int) sizeof(long));
TRACE_EXIT;
}
p0 = gfadd_long(t2, p1);
p1 = gfadd_long(t2, p2);
p2 = t1;
data += FT_SECTOR_SIZE / sizeof(long);
}
*p = p0;
p += stride;
*p = p1;
p += stride;
*p = p2;
return;
}
/* 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(__u8 *data, int nblocks,
int nbad, int *bad_loc, Matrix Ainv,
__u8 *s,
SectorMap * correction_map)
{
int ncorrected = 0;
int i;
__u8 t1, t2;
__u8 c0, c1, c2; /* check bytes */
__u8 error_mag[3], log_error_mag;
__u8 *dp, l, e;
TRACE_FUN(ft_t_any);
switch (nbad) {
case 0:
/* might have a CRC failure: */
if (s[0] == 0) {
/* more than one error */
TRACE_ABORT(-1, ft_t_err,
"ECC failed (0 CRC errors, >1 CRC failures)");
}
t1 = gfdiv(s[1], s[0]);
if ((bad_loc[nbad++] = gflog[t1]) >= nblocks) {
TRACE(ft_t_err,
"ECC failed (0 CRC errors, >1 CRC failures)");
TRACE_ABORT(-1, ft_t_err,
"attempt to correct data at %d", bad_loc[0]);
}
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_ABORT(-1, ft_t_err,
"ECC failed (1 erasure, >1 error)");
} else {
/* one erasure, one error: */
if ((bad_loc[nbad++] = gflog[gfdiv(t1, t2)])
>= nblocks) {
TRACE(ft_t_err, "ECC failed "
"(1 CRC errors, >1 CRC failures)");
TRACE_ABORT(-1, ft_t_err,
"attempt to correct data at %d",
bad_loc[1]);
}
if (!gfinv2(bad_loc[0], bad_loc[1], Ainv)) {
/* inversion failed---must have more
* than one error
*/
TRACE_EXIT -1;
}
}
/* FALL THROUGH TO ERROR MAGNITUDE COMPUTATION:
*/
case 2:
case 3:
/* compute error magnitudes: */
gfmat_mul(nbad, Ainv, s, error_mag);
break;
default:
TRACE_ABORT(-1, ft_t_err,
"Internal Error: number of CRC errors > 3");
}
/* 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 * FT_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_ABORT(-1, ft_t_err,
"ECC self-check failed, too many errors");
}
TRACE_EXIT 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(ft_t_any);
unsigned long s[3];
if (!compute_syndromes(data, nblocks, s)) {
TRACE_ABORT(0, ft_bug,
"Internal Error: syndrome self-check failed");
}
TRACE_EXIT 1;
}
#endif /* defined(ECC_SANITY_CHECK) || defined(ECC_PARANOID) */
/* Compute the parity for an entire segment of data.
*/
int ftape_ecc_set_segment_parity(struct memory_segment *mseg)
{
int i;
__u8 *parity_bytes;
parity_bytes = &mseg->data[(mseg->blocks - 3) * FT_SECTOR_SIZE];
for (i = 0; i < FT_SECTOR_SIZE; i += sizeof(long)) {
set_parity((unsigned long *) &mseg->data[i], mseg->blocks - 3,
(unsigned long *) &parity_bytes[i],
FT_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 ftape_ecc_correct_data(struct memory_segment *mseg)
{
int col, i, result;
int ncorrected = 0;
int nerasures = 0; /* # of erasures (CRC errors) */
int erasure_loc[3]; /* erasure locations */
unsigned long ss[3];
__u8 s[3];
Matrix Ainv;
TRACE_FUN(ft_t_flow);
mseg->corrected = 0;
/* find first column that has non-zero syndromes: */
for (col = 0; col < FT_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 >= FT_SECTOR_SIZE) {
/* all syndromes are ok, therefore nothing to correct */
TRACE_EXIT 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_ABORT(ECC_FAILED, ft_t_err,
"ECC failed (>3 CRC errors)");
} /* 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 ECC_FAILED;
}
break;
case 3:
if (!gfinv3(erasure_loc[0], erasure_loc[1],
erasure_loc[2], Ainv)) {
TRACE_EXIT 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 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 ECC_FAILED;
}
#endif /* ECC_SANITY_CHECK */
/* find next column with non-zero syndromes: */
while ((col += sizeof(long)) < FT_SECTOR_SIZE) {
if (!compute_syndromes((unsigned long *)
&mseg->data[col], mseg->blocks, ss)) {
/* something is wrong---have to fix things */
break;
}
}
} while (col < FT_SECTOR_SIZE);
if (ncorrected && nerasures == 0) {
TRACE(ft_t_warn, "block contained error not caught by CRC");
}
TRACE((ncorrected > 0) ? ft_t_noise : ft_t_any, "number of corrections: %d", ncorrected);
TRACE_EXIT ncorrected ? ECC_CORRECTED : ECC_OK;
}
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