rslib: Fix remaining decoder flaws

The decoder is flawed in the following ways:

- The decoder sometimes fails silently, i.e. it announces success but
  returns a word that is not a codeword.

- The return value of the decoder is incoherent with respect to how
  fixed erasures are counted. If the word to be decoded is a codeword,
  then the decoder always returns zero even if some erasures are given.
  On the other hand, if the word to be decoded contains errors, then the
  number of erasures is always included in the count of corrected
  symbols. So the decoder handles erasures without symbol corruption
  inconsistently. This inconsistency probably doesn't affect anyone
  using the decoder, but it is inconsistent with the documentation.

- The error positions returned in eras_pos include all erasures, but the
  corrections are only set in the correction buffer if there actually is
  a symbol error. So if there are erasures without symbol corruption,
  then the correction buffer will contain errors (unless initialized to
  zero before calling the decoder) or some values will be unset (if the
  correction buffer is uninitialized).

- When correcting data in-place the decoder does not correct errors in
  the parity. On the other hand, when returning the errors in correction
  buffers, errors in the parity are included.

The respective fixed are:

- The syndrome of a codeword is always zero, and the syndrome is linear,
  .i.e, S(x+e) = S(x) + S(e). So compute the syndrome for the error and
  check whether it equals the syndrome of the received word. If it does,
  then we have decoded to a valid codeword, otherwise we know that we
  have an uncorrectable error. Fortunately, some unrecoverable error
  conditions can be detected earlier in the decoding, which saves some
  processing power.

- Simply count and return the number of symbols actually corrected.

- Make sure to only return positions where symbols were corrected.

- Also fix errors in parity when correcting in-place. Another option
  would be to completely disregard errors in the parity, but then the
  interface makes it impossible to write tests that test for silent
  failures.

Other changes:

- Only fill the correction buffer and error position buffer if both of
  them are provided. Otherwise correct in place. Previously the error
  position buffer was always populated with the positions of the
  corrected errors, irrespective of whether a correction buffer was
  supplied or not. The rationale for this change is that there seems to
  be two use cases for the decoder; correct in-place or use the
  correction buffers. The caller does not need the positions of the
  corrected errors when in-place correction is used. If in-place
  correction is not used, then both the correction buffer and error
  position buffer need to be populated.

Signed-off-by: Ferdinand Blomqvist <ferdinand.blomqvist@gmail.com>
Signed-off-by: Thomas Gleixner <tglx@linutronix.de>
Link: https://lkml.kernel.org/r/20190620141039.9874-8-ferdinand.blomqvist@gmail.com

lib/reed_solomon/decode_rs.c

@@ -22,6 +22,7 @@
 	uint16_t *index_of = rs->index_of;
 	uint16_t u, q, tmp, num1, num2, den, discr_r, syn_error;
 	int count = 0;
+	int num_corrected;
 	uint16_t msk = (uint16_t) rs->nn;
 
 	/*
@@ -184,6 +185,15 @@
 		if (lambda[i] != nn)
 			deg_lambda = i;
 	}
+
+	if (deg_lambda == 0) {
+		/*
+		 * deg(lambda) is zero even though the syndrome is non-zero
+		 * => uncorrectable error detected
+		 */
+		return -EBADMSG;
+	}
+
 	/* Find roots of error+erasure locator polynomial by Chien search */
 	memcpy(&reg[1], &lambda[1], nroots * sizeof(reg[0]));
 	count = 0;		/* Number of roots of lambda(x) */
@@ -197,6 +207,12 @@
 		}
 		if (q != 0)
 			continue;	/* Not a root */
+
+		if (k < pad) {
+			/* Impossible error location. Uncorrectable error. */
+			return -EBADMSG;
+		}
+
 		/* store root (index-form) and error location number */
 		root[count] = i;
 		loc[count] = k;
@@ -231,7 +247,9 @@
 	/*
 	 * Compute error values in poly-form. num1 = omega(inv(X(l))), num2 =
 	 * inv(X(l))**(fcr-1) and den = lambda_pr(inv(X(l))) all in poly-form
+	 * Note: we reuse the buffer for b to store the correction pattern
 	 */
+	num_corrected = 0;
 	for (j = count - 1; j >= 0; j--) {
 		num1 = 0;
 		for (i = deg_omega; i >= 0; i--) {
@@ -239,6 +257,13 @@
 				num1 ^= alpha_to[rs_modnn(rs, omega[i] +
 							i * root[j])];
 		}
+
+		if (num1 == 0) {
+			/* Nothing to correct at this position */
+			b[j] = 0;
+			continue;
+		}
+
 		num2 = alpha_to[rs_modnn(rs, root[j] * (fcr - 1) + nn)];
 		den = 0;
 
@@ -250,29 +275,52 @@
 						       i * root[j])];
 			}
 		}
-		/* Apply error to data */
+
-		if (num1 != 0 && loc[j] >= pad) {
+		b[j] = alpha_to[rs_modnn(rs, index_of[num1] +
-			uint16_t cor = alpha_to[rs_modnn(rs,index_of[num1] +
+					       index_of[num2] +
-						       index_of[num2] +
+					       nn - index_of[den])];
-						       nn - index_of[den])];
+		num_corrected++;
-			/* Store the error correction pattern, if a
+	}
-			 * correction buffer is available */
+
-			if (corr) {
+	/*
-				corr[j] = cor;
+	 * We compute the syndrome of the 'error' and check that it matches
-			} else {
+	 * the syndrome of the received word
-				/* If a data buffer is given and the
+	 */
-				 * error is inside the message,
+	for (i = 0; i < nroots; i++) {
-				 * correct it */
+		tmp = 0;
-				if (data && (loc[j] < (nn - nroots)))
+		for (j = 0; j < count; j++) {
-					data[loc[j] - pad] ^= cor;
+			if (b[j] == 0)
+				continue;
+
+			k = (fcr + i) * prim * (nn-loc[j]-1);
+			tmp ^= alpha_to[rs_modnn(rs, index_of[b[j]] + k)];
+		}
+
+		if (tmp != alpha_to[s[i]])
+			return -EBADMSG;
+	}
+
+	/*
+	 * Store the error correction pattern, if a
+	 * correction buffer is available
+	 */
+	if (corr && eras_pos) {
+		j = 0;
+		for (i = 0; i < count; i++) {
+			if (b[i]) {
+				corr[j] = b[i];
+				eras_pos[j++] = loc[i] - pad;
 			}
 		}
+	} else if (data && par) {
+		/* Apply error to data and parity */
+		for (i = 0; i < count; i++) {
+			if (loc[i] < (nn - nroots))
+				data[loc[i] - pad] ^= b[i];
+			else
+				par[loc[i] - pad - len] ^= b[i];
+		}
 	}
 
-	if (eras_pos != NULL) {
+	return  num_corrected;
-		for (i = 0; i < count; i++)
-			eras_pos[i] = loc[i] - pad;
-	}
-	return count;
-
 }