common/docecc.c - github/trini/u-boot - Gitiles

 /*
  * 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)

 #define min(x,y) ((x)<(y)?(x):(y))

 /* 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) */
	/*
	* 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)

	#define min(x,y) ((x)<(y)?(x):(y))

	/* 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)PRIMj)];
	}

	/* 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) <-- xB(x) /
	COPYDOWN(&b[1],b,NN-KK);
	b[0] = A0;
	} else {
	/* 7 lines below: T(x) <-- lambda(x) - discr_rxb(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) <-- xB(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) */