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/*

 * 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 1.1.1.1 2004-04-15 01:52:06 phoenix 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 gf

modnn(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

        @^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;

}

MODULE_LICENSE("GPL");

MODULE_AUTHOR("Fabrice Bellard <fabrice.bellard@netgem.com>");

MODULE_DESCRIPTION("ECC code for correcting errors detected by DiskOnChip 2000 and Millennium ECC hardware");