common/docecc.c

/*
 * 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 1.4 2001/10/02 15:05:13 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 <config.h>
#include <common.h>
#include <malloc.h>

#include <linux/mtd/doc2000.h>

#undef ECC_DEBUG
#undef PSYCHO_DEBUG

#if (CONFIG_COMMANDS & CFG_CMD_DOC)

/* 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
   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)];
      }
    }
#ifdef ECC_DEBUG
    /* 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;
    }
#ifdef PSYCHO_DEBUG
    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) {
#ifdef ECC_DEBUG
      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 = malloc((NN + 1) * sizeof(dtype));
    if (!Alpha_to)
        return -1;

    Index_of = malloc((NN + 1) * sizeof(dtype));
    if (!Index_of) {
        free(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:
    free(Alpha_to);
    free(Index_of);
    return nb_errors;
}

#endif /* (CONFIG_COMMANDS & CFG_CMD_DOC) */