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Diffstat (limited to 'drivers/char/ftape/lowlevel/ftape-ecc.c')
| -rw-r--r-- | drivers/char/ftape/lowlevel/ftape-ecc.c | 853 |
1 files changed, 853 insertions, 0 deletions
diff --git a/drivers/char/ftape/lowlevel/ftape-ecc.c b/drivers/char/ftape/lowlevel/ftape-ecc.c new file mode 100644 index 0000000..e5632f6 --- /dev/null +++ b/drivers/char/ftape/lowlevel/ftape-ecc.c @@ -0,0 +1,853 @@ +/* + * + * 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; +} |
