Initial revision

1 files changed, 519 insertions, 0 deletions

diff --git a/common/docecc.c b/common/docecc.c
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--- /dev/null
+++ b/common/docecc.c
@@ -0,0 +1,519 @@
+/*
+ * 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) */