/* * ECC algorithm for M-systems disk on chip. We use the excellent Reed * Solmon code of Phil Karn (karn@ka9q.ampr.org) available under the * GNU GPL License. The rest is simply to convert the disk on chip * syndrom into a standard syndom. * * Author: Fabrice Bellard (fabrice.bellard@netgem.com)  * Copyright (C) 2000 Netgem S.A. * * $Id: docecc.c,v 1.5 2003/05/21 15:15:06 dwmw2 Exp $ * * 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 of the License, 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; if not, write to the Free Software * Foundation, Inc., 59 Temple Place, Suite 330, Boston, MA  02111-1307  USA */#include <linux/kernel.h>#include <linux/module.h>#include <asm/errno.h>#include <asm/io.h>#include <asm/uaccess.h>#include <linux/miscdevice.h>#include <linux/pci.h>#include <linux/delay.h>#include <linux/slab.h>#include <linux/sched.h>#include <linux/init.h>#include <linux/types.h>#include <linux/mtd/compatmac.h> /* for min() in older kernels */#include <linux/mtd/mtd.h>#include <linux/mtd/doc2000.h>/* need to undef it (from asm/termbits.h) */#undef B0#define MM 10 /* Symbol size in bits */#define KK (1023-4) /* Number of data symbols per block */#define B0 510 /* First root of generator polynomial, alpha form */#define PRIM 1 /* power of alpha used to generate roots of generator poly */#define	NN ((1 << MM) - 1)typedef unsigned short dtype;/* 1+x^3+x^10 */static const int Pp[MM+1] = { 1, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1 };/* This defines the type used to store an element of the Galois Field * used by the code. Make sure this is something larger than a char if * if anything larger than GF(256) is used. * * Note: unsigned char will work up to GF(256) but int seems to run * faster on the Pentium. */typedef int gf;/* No legal value in index form represents zero, so * we need a special value for this purpose */#define A0	(NN)/* Compute x % NN, where NN is 2**MM - 1, * without a slow divide */static inline gfmodnn(int x){  while (x >= NN) {    x -= NN;    x = (x >> MM) + (x & NN);  }  return x;}#define	CLEAR(a,n) {\int ci;\for(ci=(n)-1;ci >=0;ci--)\(a)[ci] = 0;\}#define	COPY(a,b,n) {\int ci;\for(ci=(n)-1;ci >=0;ci--)\(a)[ci] = (b)[ci];\}#define	COPYDOWN(a,b,n) {\int ci;\for(ci=(n)-1;ci >=0;ci--)\(a)[ci] = (b)[ci];\}#define Ldec 1/* generate GF(2**m) from the irreducible polynomial p(X) in Pp[0]..Pp[m]   lookup tables:  index->polynomial form   alpha_to[] contains j=alpha**i;                   polynomial form -> index form  index_of[j=alpha**i] = i   alpha=2 is the primitive element of GF(2**m)   HARI's COMMENT: (4/13/94) alpha_to[] can be used as follows:        Let @ represent the primitive element commonly called "alpha" that   is the root of the primitive polynomial p(x). Then in GF(2^m), for any   0 <= i <= 2^m-2,        @^i = a(0) + a(1) @ + a(2) @^2 + ... + a(m-1) @^(m-1)   where the binary vector (a(0),a(1),a(2),...,a(m-1)) is the representation   of the integer "alpha_to[i]" with a(0) being the LSB and a(m-1) the MSB. Thus for   example the polynomial representation of @^5 would be given by the binary   representation of the integer "alpha_to[5]".                   Similarily, index_of[] can be used as follows:        As above, let @ represent the primitive element of GF(2^m) that is   the root of the primitive polynomial p(x). In order to find the power   of @ (alpha) that has the polynomial representation        a(0) + a(1) @ + a(2) @^2 + ... + a(m-1) @^(m-1)   we consider the integer "i" whose binary representation with a(0) being LSB   and a(m-1) MSB is (a(0),a(1),...,a(m-1)) and locate the entry   "index_of[i]". Now, @^index_of[i] is that element whose polynomial     representation is (a(0),a(1),a(2),...,a(m-1)).   NOTE:        The element alpha_to[2^m-1] = 0 always signifying that the   representation of "@^infinity" = 0 is (0,0,0,...,0).        Similarily, the element index_of[0] = A0 always signifying   that the power of alpha which has the polynomial representation   (0,0,...,0) is "infinity". */static voidgenerate_gf(dtype Alpha_to[NN + 1], dtype Index_of[NN + 1]){  register int i, mask;  mask = 1;  Alpha_to[MM] = 0;  for (i = 0; i < MM; i++) {    Alpha_to[i] = mask;    Index_of[Alpha_to[i]] = i;    /* If Pp[i] == 1 then, term @^i occurs in poly-repr of @^MM */    if (Pp[i] != 0)      Alpha_to[MM] ^= mask;	/* Bit-wise EXOR operation */    mask <<= 1;	/* single left-shift */  }  Index_of[Alpha_to[MM]] = MM;  /*   * Have obtained poly-repr of @^MM. Poly-repr of @^(i+1) is given by   * poly-repr of @^i shifted left one-bit and accounting for any @^MM   * term that may occur when poly-repr of @^i is shifted.   */  mask >>= 1;  for (i = MM + 1; i < NN; i++) {    if (Alpha_to[i - 1] >= mask)      Alpha_to[i] = Alpha_to[MM] ^ ((Alpha_to[i - 1] ^ mask) << 1);    else      Alpha_to[i] = Alpha_to[i - 1] << 1;    Index_of[Alpha_to[i]] = i;  }  Index_of[0] = A0;  Alpha_to[NN] = 0;}/* * Performs ERRORS+ERASURES decoding of RS codes. bb[] is the content * of the feedback shift register after having processed the data and * the ECC. * * Return number of symbols corrected, or -1 if codeword is illegal * or uncorrectable. If eras_pos is non-null, the detected error locations * are written back. NOTE! This array must be at least NN-KK elements long. * The corrected data are written in eras_val[]. They must be xor with the data * to retrieve the correct data : data[erase_pos[i]] ^= erase_val[i] . *  * First "no_eras" erasures are declared by the calling program. Then, the * maximum # of errors correctable is t_after_eras = floor((NN-KK-no_eras)/2). * If the number of channel errors is not greater than "t_after_eras" the * transmitted codeword will be recovered. Details of algorithm can be found * in R. Blahut's "Theory ... of Error-Correcting Codes". * Warning: the eras_pos[] array must not contain duplicate entries; decoder failure * will result. The decoder *could* check for this condition, but it would involve * extra time on every decoding operation. * */static interas_dec_rs(dtype Alpha_to[NN + 1], dtype Index_of[NN + 1],            gf bb[NN - KK + 1], gf eras_val[NN-KK], int eras_pos[NN-KK],             int no_eras){  int deg_lambda, el, deg_omega;  int i, j, r,k;  gf u,q,tmp,num1,num2,den,discr_r;  gf lambda[NN-KK + 1], s[NN-KK + 1];	/* Err+Eras Locator poly					 * and syndrome poly */  gf b[NN-KK + 1], t[NN-KK + 1], omega[NN-KK + 1];  gf root[NN-KK], reg[NN-KK + 1], loc[NN-KK];  int syn_error, count;  syn_error = 0;  for(i=0;i<NN-KK;i++)      syn_error |= bb[i];  if (!syn_error) {    /* if remainder is zero, data[] is a codeword and there are no     * errors to correct. So return data[] unmodified     */    count = 0;    goto finish;  }    for(i=1;i<=NN-KK;i++){    s[i] = bb[0];  }  for(j=1;j<NN-KK;j++){    if(bb[j] == 0)      continue;    tmp = Index_of[bb[j]];        for(i=1;i<=NN-KK;i++)      s[i] ^= Alpha_to[modnn(tmp + (B0+i-1)*PRIM*j)];  }  /* undo the feedback register implicit multiplication and convert     syndromes to index form */  for(i=1;i<=NN-KK;i++) {      tmp = Index_of[s[i]];      if (tmp != A0)          tmp = modnn(tmp + 2 * KK * (B0+i-1)*PRIM);      s[i] = tmp;  }    CLEAR(&lambda[1],NN-KK);  lambda[0] = 1;  if (no_eras > 0) {    /* Init lambda to be the erasure locator polynomial */    lambda[1] = Alpha_to[modnn(PRIM * eras_pos[0])];    for (i = 1; i < no_eras; i++) {      u = modnn(PRIM*eras_pos[i]);      for (j = i+1; j > 0; j--) {	tmp = Index_of[lambda[j - 1]];	if(tmp != A0)	  lambda[j] ^= Alpha_to[modnn(u + tmp)];      }    }#if DEBUG >= 1    /* Test code that verifies the erasure locator polynomial just constructed       Needed only for decoder debugging. */        /* find roots of the erasure location polynomial */    for(i=1;i<=no_eras;i++)      reg[i] = Index_of[lambda[i]];    count = 0;    for (i = 1,k=NN-Ldec; i <= NN; i++,k = modnn(NN+k-Ldec)) {      q = 1;      for (j = 1; j <= no_eras; j++)	if (reg[j] != A0) {	  reg[j] = modnn(reg[j] + j);	  q ^= Alpha_to[reg[j]];