1da177e4c3
Initial git repository build. I'm not bothering with the full history, even though we have it. We can create a separate "historical" git archive of that later if we want to, and in the meantime it's about 3.2GB when imported into git - space that would just make the early git days unnecessarily complicated, when we don't have a lot of good infrastructure for it. Let it rip!
854 lines
26 KiB
C
854 lines
26 KiB
C
/*
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*
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* Copyright (c) 1993 Ning and David Mosberger.
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This is based on code originally written by Bas Laarhoven (bas@vimec.nl)
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and David L. Brown, Jr., and incorporates improvements suggested by
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Kai Harrekilde-Petersen.
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This program is free software; you can redistribute it and/or
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modify it under the terms of the GNU General Public License as
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published by the Free Software Foundation; either version 2, or (at
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your option) any later version.
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This program is distributed in the hope that it will be useful, but
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WITHOUT ANY WARRANTY; without even the implied warranty of
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MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU
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General Public License for more details.
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You should have received a copy of the GNU General Public License
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along with this program; see the file COPYING. If not, write to
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the Free Software Foundation, 675 Mass Ave, Cambridge, MA 02139,
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USA.
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*
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* $Source: /homes/cvs/ftape-stacked/ftape/lowlevel/ftape-ecc.c,v $
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* $Revision: 1.3 $
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* $Date: 1997/10/05 19:18:10 $
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*
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* This file contains the Reed-Solomon error correction code
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* for the QIC-40/80 floppy-tape driver for Linux.
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*/
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#include <linux/ftape.h>
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#include "../lowlevel/ftape-tracing.h"
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#include "../lowlevel/ftape-ecc.h"
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/* Machines that are big-endian should define macro BIG_ENDIAN.
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* Unfortunately, there doesn't appear to be a standard include file
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* that works for all OSs.
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*/
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#if defined(__sparc__) || defined(__hppa)
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#define BIG_ENDIAN
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#endif /* __sparc__ || __hppa */
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#if defined(__mips__)
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#error Find a smart way to determine the Endianness of the MIPS CPU
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#endif
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/* Notice: to minimize the potential for confusion, we use r to
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* denote the independent variable of the polynomials in the
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* Galois Field GF(2^8). We reserve x for polynomials that
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* that have coefficients in GF(2^8).
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*
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* The Galois Field in which coefficient arithmetic is performed are
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* the polynomials over Z_2 (i.e., 0 and 1) modulo the irreducible
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* polynomial f(r), where f(r)=r^8 + r^7 + r^2 + r + 1. A polynomial
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* is represented as a byte with the MSB as the coefficient of r^7 and
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* the LSB as the coefficient of r^0. For example, the binary
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* representation of f(x) is 0x187 (of course, this doesn't fit into 8
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* bits). In this field, the polynomial r is a primitive element.
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* That is, r^i with i in 0,...,255 enumerates all elements in the
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* field.
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*
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* The generator polynomial for the QIC-80 ECC is
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*
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* g(x) = x^3 + r^105*x^2 + r^105*x + 1
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*
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* which can be factored into:
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*
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* g(x) = (x-r^-1)(x-r^0)(x-r^1)
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*
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* the byte representation of the coefficients are:
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*
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* r^105 = 0xc0
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* r^-1 = 0xc3
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* r^0 = 0x01
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* r^1 = 0x02
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*
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* Notice that r^-1 = r^254 as exponent arithmetic is performed
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* modulo 2^8-1 = 255.
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*
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* For more information on Galois Fields and Reed-Solomon codes, refer
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* to any good book. I found _An Introduction to Error Correcting
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* Codes with Applications_ by S. A. Vanstone and P. C. van Oorschot
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* to be a good introduction into the former. _CODING THEORY: The
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* Essentials_ I found very useful for its concise description of
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* Reed-Solomon encoding/decoding.
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*
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*/
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typedef __u8 Matrix[3][3];
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/*
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* gfpow[] is defined such that gfpow[i] returns r^i if
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* i is in the range [0..255].
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*/
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static const __u8 gfpow[] =
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{
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0x01, 0x02, 0x04, 0x08, 0x10, 0x20, 0x40, 0x80,
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0x87, 0x89, 0x95, 0xad, 0xdd, 0x3d, 0x7a, 0xf4,
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0x6f, 0xde, 0x3b, 0x76, 0xec, 0x5f, 0xbe, 0xfb,
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0x71, 0xe2, 0x43, 0x86, 0x8b, 0x91, 0xa5, 0xcd,
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0x1d, 0x3a, 0x74, 0xe8, 0x57, 0xae, 0xdb, 0x31,
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0x62, 0xc4, 0x0f, 0x1e, 0x3c, 0x78, 0xf0, 0x67,
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0xce, 0x1b, 0x36, 0x6c, 0xd8, 0x37, 0x6e, 0xdc,
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0x3f, 0x7e, 0xfc, 0x7f, 0xfe, 0x7b, 0xf6, 0x6b,
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0xd6, 0x2b, 0x56, 0xac, 0xdf, 0x39, 0x72, 0xe4,
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0x4f, 0x9e, 0xbb, 0xf1, 0x65, 0xca, 0x13, 0x26,
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0x4c, 0x98, 0xb7, 0xe9, 0x55, 0xaa, 0xd3, 0x21,
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0x42, 0x84, 0x8f, 0x99, 0xb5, 0xed, 0x5d, 0xba,
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0xf3, 0x61, 0xc2, 0x03, 0x06, 0x0c, 0x18, 0x30,
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0x60, 0xc0, 0x07, 0x0e, 0x1c, 0x38, 0x70, 0xe0,
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0x47, 0x8e, 0x9b, 0xb1, 0xe5, 0x4d, 0x9a, 0xb3,
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0xe1, 0x45, 0x8a, 0x93, 0xa1, 0xc5, 0x0d, 0x1a,
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0x34, 0x68, 0xd0, 0x27, 0x4e, 0x9c, 0xbf, 0xf9,
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0x75, 0xea, 0x53, 0xa6, 0xcb, 0x11, 0x22, 0x44,
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0x88, 0x97, 0xa9, 0xd5, 0x2d, 0x5a, 0xb4, 0xef,
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0x59, 0xb2, 0xe3, 0x41, 0x82, 0x83, 0x81, 0x85,
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0x8d, 0x9d, 0xbd, 0xfd, 0x7d, 0xfa, 0x73, 0xe6,
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0x4b, 0x96, 0xab, 0xd1, 0x25, 0x4a, 0x94, 0xaf,
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0xd9, 0x35, 0x6a, 0xd4, 0x2f, 0x5e, 0xbc, 0xff,
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0x79, 0xf2, 0x63, 0xc6, 0x0b, 0x16, 0x2c, 0x58,
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0xb0, 0xe7, 0x49, 0x92, 0xa3, 0xc1, 0x05, 0x0a,
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0x14, 0x28, 0x50, 0xa0, 0xc7, 0x09, 0x12, 0x24,
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0x48, 0x90, 0xa7, 0xc9, 0x15, 0x2a, 0x54, 0xa8,
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0xd7, 0x29, 0x52, 0xa4, 0xcf, 0x19, 0x32, 0x64,
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0xc8, 0x17, 0x2e, 0x5c, 0xb8, 0xf7, 0x69, 0xd2,
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0x23, 0x46, 0x8c, 0x9f, 0xb9, 0xf5, 0x6d, 0xda,
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0x33, 0x66, 0xcc, 0x1f, 0x3e, 0x7c, 0xf8, 0x77,
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0xee, 0x5b, 0xb6, 0xeb, 0x51, 0xa2, 0xc3, 0x01
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};
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/*
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* This is a log table. That is, gflog[r^i] returns i (modulo f(r)).
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* gflog[0] is undefined and the first element is therefore not valid.
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*/
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static const __u8 gflog[256] =
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{
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0xff, 0x00, 0x01, 0x63, 0x02, 0xc6, 0x64, 0x6a,
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0x03, 0xcd, 0xc7, 0xbc, 0x65, 0x7e, 0x6b, 0x2a,
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0x04, 0x8d, 0xce, 0x4e, 0xc8, 0xd4, 0xbd, 0xe1,
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0x66, 0xdd, 0x7f, 0x31, 0x6c, 0x20, 0x2b, 0xf3,
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0x05, 0x57, 0x8e, 0xe8, 0xcf, 0xac, 0x4f, 0x83,
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0xc9, 0xd9, 0xd5, 0x41, 0xbe, 0x94, 0xe2, 0xb4,
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0x67, 0x27, 0xde, 0xf0, 0x80, 0xb1, 0x32, 0x35,
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0x6d, 0x45, 0x21, 0x12, 0x2c, 0x0d, 0xf4, 0x38,
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0x06, 0x9b, 0x58, 0x1a, 0x8f, 0x79, 0xe9, 0x70,
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0xd0, 0xc2, 0xad, 0xa8, 0x50, 0x75, 0x84, 0x48,
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0xca, 0xfc, 0xda, 0x8a, 0xd6, 0x54, 0x42, 0x24,
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0xbf, 0x98, 0x95, 0xf9, 0xe3, 0x5e, 0xb5, 0x15,
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0x68, 0x61, 0x28, 0xba, 0xdf, 0x4c, 0xf1, 0x2f,
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0x81, 0xe6, 0xb2, 0x3f, 0x33, 0xee, 0x36, 0x10,
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0x6e, 0x18, 0x46, 0xa6, 0x22, 0x88, 0x13, 0xf7,
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0x2d, 0xb8, 0x0e, 0x3d, 0xf5, 0xa4, 0x39, 0x3b,
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0x07, 0x9e, 0x9c, 0x9d, 0x59, 0x9f, 0x1b, 0x08,
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0x90, 0x09, 0x7a, 0x1c, 0xea, 0xa0, 0x71, 0x5a,
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0xd1, 0x1d, 0xc3, 0x7b, 0xae, 0x0a, 0xa9, 0x91,
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0x51, 0x5b, 0x76, 0x72, 0x85, 0xa1, 0x49, 0xeb,
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0xcb, 0x7c, 0xfd, 0xc4, 0xdb, 0x1e, 0x8b, 0xd2,
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0xd7, 0x92, 0x55, 0xaa, 0x43, 0x0b, 0x25, 0xaf,
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0xc0, 0x73, 0x99, 0x77, 0x96, 0x5c, 0xfa, 0x52,
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0xe4, 0xec, 0x5f, 0x4a, 0xb6, 0xa2, 0x16, 0x86,
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0x69, 0xc5, 0x62, 0xfe, 0x29, 0x7d, 0xbb, 0xcc,
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0xe0, 0xd3, 0x4d, 0x8c, 0xf2, 0x1f, 0x30, 0xdc,
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0x82, 0xab, 0xe7, 0x56, 0xb3, 0x93, 0x40, 0xd8,
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0x34, 0xb0, 0xef, 0x26, 0x37, 0x0c, 0x11, 0x44,
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0x6f, 0x78, 0x19, 0x9a, 0x47, 0x74, 0xa7, 0xc1,
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0x23, 0x53, 0x89, 0xfb, 0x14, 0x5d, 0xf8, 0x97,
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0x2e, 0x4b, 0xb9, 0x60, 0x0f, 0xed, 0x3e, 0xe5,
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0xf6, 0x87, 0xa5, 0x17, 0x3a, 0xa3, 0x3c, 0xb7
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};
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/* This is a multiplication table for the factor 0xc0 (i.e., r^105 (mod f(r)).
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* gfmul_c0[f] returns r^105 * f(r) (modulo f(r)).
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*/
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static const __u8 gfmul_c0[256] =
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{
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0x00, 0xc0, 0x07, 0xc7, 0x0e, 0xce, 0x09, 0xc9,
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0x1c, 0xdc, 0x1b, 0xdb, 0x12, 0xd2, 0x15, 0xd5,
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0x38, 0xf8, 0x3f, 0xff, 0x36, 0xf6, 0x31, 0xf1,
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0x24, 0xe4, 0x23, 0xe3, 0x2a, 0xea, 0x2d, 0xed,
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0x70, 0xb0, 0x77, 0xb7, 0x7e, 0xbe, 0x79, 0xb9,
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0x6c, 0xac, 0x6b, 0xab, 0x62, 0xa2, 0x65, 0xa5,
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0x48, 0x88, 0x4f, 0x8f, 0x46, 0x86, 0x41, 0x81,
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0x54, 0x94, 0x53, 0x93, 0x5a, 0x9a, 0x5d, 0x9d,
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0xe0, 0x20, 0xe7, 0x27, 0xee, 0x2e, 0xe9, 0x29,
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0xfc, 0x3c, 0xfb, 0x3b, 0xf2, 0x32, 0xf5, 0x35,
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0xd8, 0x18, 0xdf, 0x1f, 0xd6, 0x16, 0xd1, 0x11,
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0xc4, 0x04, 0xc3, 0x03, 0xca, 0x0a, 0xcd, 0x0d,
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0x90, 0x50, 0x97, 0x57, 0x9e, 0x5e, 0x99, 0x59,
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0x8c, 0x4c, 0x8b, 0x4b, 0x82, 0x42, 0x85, 0x45,
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0xa8, 0x68, 0xaf, 0x6f, 0xa6, 0x66, 0xa1, 0x61,
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0xb4, 0x74, 0xb3, 0x73, 0xba, 0x7a, 0xbd, 0x7d,
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0x47, 0x87, 0x40, 0x80, 0x49, 0x89, 0x4e, 0x8e,
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0x5b, 0x9b, 0x5c, 0x9c, 0x55, 0x95, 0x52, 0x92,
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0x7f, 0xbf, 0x78, 0xb8, 0x71, 0xb1, 0x76, 0xb6,
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0x63, 0xa3, 0x64, 0xa4, 0x6d, 0xad, 0x6a, 0xaa,
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0x37, 0xf7, 0x30, 0xf0, 0x39, 0xf9, 0x3e, 0xfe,
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0x2b, 0xeb, 0x2c, 0xec, 0x25, 0xe5, 0x22, 0xe2,
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0x0f, 0xcf, 0x08, 0xc8, 0x01, 0xc1, 0x06, 0xc6,
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0x13, 0xd3, 0x14, 0xd4, 0x1d, 0xdd, 0x1a, 0xda,
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0xa7, 0x67, 0xa0, 0x60, 0xa9, 0x69, 0xae, 0x6e,
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0xbb, 0x7b, 0xbc, 0x7c, 0xb5, 0x75, 0xb2, 0x72,
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0x9f, 0x5f, 0x98, 0x58, 0x91, 0x51, 0x96, 0x56,
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0x83, 0x43, 0x84, 0x44, 0x8d, 0x4d, 0x8a, 0x4a,
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0xd7, 0x17, 0xd0, 0x10, 0xd9, 0x19, 0xde, 0x1e,
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0xcb, 0x0b, 0xcc, 0x0c, 0xc5, 0x05, 0xc2, 0x02,
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0xef, 0x2f, 0xe8, 0x28, 0xe1, 0x21, 0xe6, 0x26,
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0xf3, 0x33, 0xf4, 0x34, 0xfd, 0x3d, 0xfa, 0x3a
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};
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/* Returns V modulo 255 provided V is in the range -255,-254,...,509.
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*/
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static inline __u8 mod255(int v)
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{
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if (v > 0) {
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if (v < 255) {
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return v;
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} else {
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return v - 255;
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}
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} else {
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return v + 255;
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}
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}
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/* Add two numbers in the field. Addition in this field is equivalent
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* to a bit-wise exclusive OR operation---subtraction is therefore
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* identical to addition.
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*/
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static inline __u8 gfadd(__u8 a, __u8 b)
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{
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return a ^ b;
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}
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/* Add two vectors of numbers in the field. Each byte in A and B gets
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* added individually.
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*/
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static inline unsigned long gfadd_long(unsigned long a, unsigned long b)
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{
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return a ^ b;
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}
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/* Multiply two numbers in the field:
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*/
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static inline __u8 gfmul(__u8 a, __u8 b)
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{
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if (a && b) {
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return gfpow[mod255(gflog[a] + gflog[b])];
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} else {
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return 0;
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}
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}
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/* Just like gfmul, except we have already looked up the log of the
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* second number.
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*/
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static inline __u8 gfmul_exp(__u8 a, int b)
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{
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if (a) {
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return gfpow[mod255(gflog[a] + b)];
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} else {
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return 0;
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}
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}
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/* Just like gfmul_exp, except that A is a vector of numbers. That
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* is, each byte in A gets multiplied by gfpow[mod255(B)].
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*/
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static inline unsigned long gfmul_exp_long(unsigned long a, int b)
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{
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__u8 t;
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if (sizeof(long) == 4) {
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return (
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((t = (__u32)a >> 24 & 0xff) ?
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(((__u32) gfpow[mod255(gflog[t] + b)]) << 24) : 0) |
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((t = (__u32)a >> 16 & 0xff) ?
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(((__u32) gfpow[mod255(gflog[t] + b)]) << 16) : 0) |
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((t = (__u32)a >> 8 & 0xff) ?
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(((__u32) gfpow[mod255(gflog[t] + b)]) << 8) : 0) |
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((t = (__u32)a >> 0 & 0xff) ?
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(((__u32) gfpow[mod255(gflog[t] + b)]) << 0) : 0));
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} else if (sizeof(long) == 8) {
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return (
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((t = (__u64)a >> 56 & 0xff) ?
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(((__u64) gfpow[mod255(gflog[t] + b)]) << 56) : 0) |
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((t = (__u64)a >> 48 & 0xff) ?
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(((__u64) gfpow[mod255(gflog[t] + b)]) << 48) : 0) |
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((t = (__u64)a >> 40 & 0xff) ?
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(((__u64) gfpow[mod255(gflog[t] + b)]) << 40) : 0) |
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((t = (__u64)a >> 32 & 0xff) ?
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(((__u64) gfpow[mod255(gflog[t] + b)]) << 32) : 0) |
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((t = (__u64)a >> 24 & 0xff) ?
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(((__u64) gfpow[mod255(gflog[t] + b)]) << 24) : 0) |
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((t = (__u64)a >> 16 & 0xff) ?
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(((__u64) gfpow[mod255(gflog[t] + b)]) << 16) : 0) |
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((t = (__u64)a >> 8 & 0xff) ?
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(((__u64) gfpow[mod255(gflog[t] + b)]) << 8) : 0) |
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((t = (__u64)a >> 0 & 0xff) ?
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(((__u64) gfpow[mod255(gflog[t] + b)]) << 0) : 0));
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} else {
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TRACE_FUN(ft_t_any);
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TRACE_ABORT(-1, ft_t_err, "Error: size of long is %d bytes",
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(int)sizeof(long));
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}
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}
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/* Divide two numbers in the field. Returns a/b (modulo f(x)).
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*/
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static inline __u8 gfdiv(__u8 a, __u8 b)
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{
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if (!b) {
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TRACE_FUN(ft_t_any);
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TRACE_ABORT(0xff, ft_t_bug, "Error: division by zero");
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} else if (a == 0) {
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return 0;
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} else {
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return gfpow[mod255(gflog[a] - gflog[b])];
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}
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}
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/* The following functions return the inverse of the matrix of the
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* linear system that needs to be solved to determine the error
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* magnitudes. The first deals with matrices of rank 3, while the
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* 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;
|
||
}
|