text: /*
   * 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 1.1 2000/11/03 12:43:43 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/malloc.h>
  #include <linux/sched.h>
  #include <linux/init.h>
  #include <linux/types.h>
  
  #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 gf
  modnn(int x)
  {
    while (x >= NN) {
      x -= NN;
      x = (x >> MM) + (x & NN);
    }
    return x;
  }
  
  #define	min(a,b)	((a) < (b) ? (a) : (b))
  
  #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 void
  generate_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 int
  eras_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]];
  	}
        if (q != 0)
  	continue;
        /* store root and error location number indices */
        root[count] = i;
        loc[count] = k;
        count++;
      }
      if (count != no_eras) {
        printf("\n lambda(x) is WRONG\n");
        count = -1;
        goto finish;
      }
  #if DEBUG >= 2
      printf("\n Erasure positions as determined by roots of Eras Loc Poly:\n");
      for (i = 0; i < count; i++)
        printf("%d ", loc[i]);
      printf("\n");
  #endif
  #endif
    }
    for(i=0;i<NN-KK+1;i++)
      b[i] = Index_of[lambda[i]];
    
    /*
     * Begin Berlekamp-Massey algorithm to determine error+erasure
     * locator polynomial
     */
    r = no_eras;
    el = no_eras;
    while (++r <= NN-KK) {	/* r is the step number */
      /* Compute discrepancy at the r-th step in poly-form */
      discr_r = 0;
      for (i = 0; i < r; i++){
        if ((lambda[i] != 0) && (s[r - i] != A0)) {
  	discr_r ^= Alpha_to[modnn(Index_of[lambda[i]] + s[r - i])];
        }
      }
      discr_r = Index_of[discr_r];	/* Index form */
      if (discr_r == A0) {
        /* 2 lines below: B(x) <-- x*B(x) */
        COPYDOWN(&b[1],b,NN-KK);
        b[0] = A0;
      } else {
        /* 7 lines below: T(x) <-- lambda(x) - discr_r*x*b(x) */
        t[0] = lambda[0];
        for (i = 0 ; i < NN-KK; i++) {
  	if(b[i] != A0)
  	  t[i+1] = lambda[i+1] ^ Alpha_to[modnn(discr_r + b[i])];
  	else
  	  t[i+1] = lambda[i+1];
        }
        if (2 * el <= r + no_eras - 1) {
  	el = r + no_eras - el;
  	/*
  	 * 2 lines below: B(x) <-- inv(discr_r) *
  	 * lambda(x)
  	 */
  	for (i = 0; i <= NN-KK; i++)
  	  b[i] = (lambda[i] == 0) ? A0 : modnn(Index_of[lambda[i]] - discr_r + NN);
        } else {
  	/* 2 lines below: B(x) <-- x*B(x) */
  	COPYDOWN(&b[1],b,NN-KK);
  	b[0] = A0;
        }
        COPY(lambda,t,NN-KK+1);
      }
    }
  
    /* Convert lambda to index form and compute deg(lambda(x)) */
    deg_lambda = 0;
    for(i=0;i<NN-KK+1;i++){
      lambda[i] = Index_of[lambda[i]];
      if(lambda[i] != A0)
        deg_lambda = i;
    }
    /*
     * Find roots of the error+erasure locator polynomial by Chien
     * Search
     */
    COPY(&reg[1],&lambda[1],NN-KK);
    count = 0;		/* Number of roots of lambda(x) */
    for (i = 1,k=NN-Ldec; i <= NN; i++,k = modnn(NN+k-Ldec)) {
      q = 1;
      for (j = deg_lambda; j > 0; j--){
        if (reg[j] != A0) {
  	reg[j] = modnn(reg[j] + j);
  	q ^= Alpha_to[reg[j]];
        }
      }
      if (q != 0)
        continue;
      /* store root (index-form) and error location number */
      root[count] = i;
      loc[count] = k;
      /* If we've already found max possible roots,
       * abort the search to save time
       */
      if(++count == deg_lambda)
        break;
    }
    if (deg_lambda != count) {
      /*
       * deg(lambda) unequal to number of roots => uncorrectable
       * error detected
       */
      count = -1;
      goto finish;
    }
    /*
     * Compute err+eras evaluator poly omega(x) = s(x)*lambda(x) (modulo
     * x**(NN-KK)). in index form. Also find deg(omega).
     */
    deg_omega = 0;
    for (i = 0; i < NN-KK;i++){
      tmp = 0;
      j = (deg_lambda < i) ? deg_lambda : i;
      for(;j >= 0; j--){
        if ((s[i + 1 - j] != A0) && (lambda[j] != A0))
  	tmp ^= Alpha_to[modnn(s[i + 1 - j] + lambda[j])];
      }
      if(tmp != 0)
        deg_omega = i;
      omega[i] = Index_of[tmp];
    }
    omega[NN-KK] = A0;
    
    /*
     * Compute error values in poly-form. num1 = omega(inv(X(l))), num2 =
     * inv(X(l))**(B0-1) and den = lambda_pr(inv(X(l))) all in poly-form
     */
    for (j = count-1; j >=0; j--) {
      num1 = 0;
      for (i = deg_omega; i >= 0; i--) {
        if (omega[i] != A0)
  	num1  ^= Alpha_to[modnn(omega[i] + i * root[j])];
      }
      num2 = Alpha_to[modnn(root[j] * (B0 - 1) + NN)];
      den = 0;
      
      /* lambda[i+1] for i even is the formal derivative lambda_pr of lambda[i] */
      for (i = min(deg_lambda,NN-KK-1) & ~1; i >= 0; i -=2) {
        if(lambda[i+1] != A0)
  	den ^= Alpha_to[modnn(lambda[i+1] + i * root[j])];
      }
      if (den == 0) {
  #if DEBUG >= 1
        printf("\n ERROR: denominator = 0\n");
  #endif
        /* Convert to dual- basis */
        count = -1;
        goto finish;
      }
      /* Apply error to data */
      if (num1 != 0) {
          eras_val[j] = Alpha_to[modnn(Index_of[num1] + Index_of[num2] + NN - Index_of[den])];
      } else {
          eras_val[j] = 0;
      }
    }
   finish:
    for(i=0;i<count;i++)
        eras_pos[i] = loc[i];
    return count;
  }
  
  /***************************************************************************/
  /* The DOC specific code begins here */
  
  #define SECTOR_SIZE 512
  /* The sector bytes are packed into NB_DATA MM bits words */
  #define NB_DATA (((SECTOR_SIZE + 1) * 8 + 6) / MM)
  
  /* 
   * Correct the errors in 'sector[]' by using 'ecc1[]' which is the
   * content of the feedback shift register applyied to the sector and
   * the ECC. Return the number of errors corrected (and correct them in
   * sector), or -1 if error 
   */
  int doc_decode_ecc(unsigned char sector[SECTOR_SIZE], unsigned char ecc1[6])
  {
      int parity, i, nb_errors;
      gf bb[NN - KK + 1];
      gf error_val[NN-KK];
      int error_pos[NN-KK], pos, bitpos, index, val;
      dtype *Alpha_to, *Index_of;
  
      /* init log and exp tables here to save memory. However, it is slower */
      Alpha_to = kmalloc((NN + 1) * sizeof(dtype), GFP_KERNEL);
      if (!Alpha_to)
          return -1;
      
      Index_of = kmalloc((NN + 1) * sizeof(dtype), GFP_KERNEL);
      if (!Index_of) {
          kfree(Alpha_to);
          return -1;
      }
  
      generate_gf(Alpha_to, Index_of);
  
      parity = ecc1[1];
  
      bb[0] =  (ecc1[4] & 0xff) | ((ecc1[5] & 0x03) << 8);
      bb[1] = ((ecc1[5] & 0xfc) >> 2) | ((ecc1[2] & 0x0f) << 6);
      bb[2] = ((ecc1[2] & 0xf0) >> 4) | ((ecc1[3] & 0x3f) << 4);
      bb[3] = ((ecc1[3] & 0xc0) >> 6) | ((ecc1[0] & 0xff) << 2);
  
      nb_errors = eras_dec_rs(Alpha_to, Index_of, bb, 
                              error_val, error_pos, 0);
      if (nb_errors <= 0)
          goto the_end;
  
      /* correct the errors */
      for(i=0;i<nb_errors;i++) {
          pos = error_pos[i];
          if (pos >= NB_DATA && pos < KK) {
              nb_errors = -1;
              goto the_end;
          }
          if (pos < NB_DATA) {
              /* extract bit position (MSB first) */
              pos = 10 * (NB_DATA - 1 - pos) - 6;
              /* now correct the following 10 bits. At most two bytes
                 can be modified since pos is even */
              index = (pos >> 3) ^ 1;
              bitpos = pos & 7;
              if ((index >= 0 && index < SECTOR_SIZE) || 
                  index == (SECTOR_SIZE + 1)) {
                  val = error_val[i] >> (2 + bitpos);
                  parity ^= val;
                  if (index < SECTOR_SIZE)
                      sector[index] ^= val;
              }
              index = ((pos >> 3) + 1) ^ 1;
              bitpos = (bitpos + 10) & 7;
              if (bitpos == 0)
                  bitpos = 8;
              if ((index >= 0 && index < SECTOR_SIZE) || 
                  index == (SECTOR_SIZE + 1)) {
                  val = error_val[i] << (8 - bitpos);
                  parity ^= val;
                  if (index < SECTOR_SIZE)
                      sector[index] ^= val;
              }
          }
      }
      
      /* use parity to test extra errors */
      if ((parity & 0xff) != 0)
          nb_errors = -1;
  
   the_end:
      kfree(Alpha_to);
      kfree(Index_of);
      return nb_errors;
  }
  
  