[PATCH v2 0/7] rslib: RS decoder is severely broken

[PATCH v2 0/7] rslib: RS decoder is severely broken

[Ferdinand Blomqvist]

This is the second revision of this series that fixes the bugs/flaws in
the RS decoder. This addresses all of Thomas' comments/suggestions.

Changes in v2:
- Replace code that requires the FPU (one small thing in test_rslib.c)
- More verbose changelog (patch 2/7)
- Clarifying comment (patch 7/7)
- Fixed some small whitespace issues (patches 1 and 5)

------

The Reed_Solomon library used in the kernel is based on Phil Karn's
fec library. When playing with this library I found a couple of bugs. It
turn out that all of these bugs, and some additional flaws, are present
in rslib.

The Reed-Solomon decoder has several bugs/flaws:

- Decoding of shortened codes is broken. The decoder only works as
  expected if there are no erasures.

- 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).

- Assumes that the syndromes provided by callers are in index form.
  This is simply undocumented.

- 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.

This series provides a module with tests for rslib and fixes all the
bugs/flaws. I am not sure that the provided self tests are written in
the 'right way'. I just looked at other self tests in lib and
implemented something similar.

The fixes are tested with the self tests. They should probably also be
tested with drivers etc. that use rslib, but it is unclear to me how to
do this.

I looked a bit on two of the drivers that use rslib:

drivers/mtd/nand/raw/cafe_nand.c
drivers/mtd/nand/raw/diskonchip.c

Both of them seem to do some additional error checking after calling
decode_rs16. Maybe this is needed because of the bugs in the decoder?

Ferdinand Blomqvist (7):
  rslib: Add tests for the encoder and decoder
  rslib: Fix decoding of shortened codes
  rslib: decode_rs: Fix length parameter check
  rslib: decode_rs: code cleanup
  rslib: Fix handling of of caller provided syndrome
  rslib: Update documentation
  rslib: Fix remaining decoder flaws

 lib/Kconfig.debug               |  12 +
 lib/reed_solomon/Makefile       |   2 +-
 lib/reed_solomon/decode_rs.c    | 115 +++++--
 lib/reed_solomon/reed_solomon.c |  12 +-
 lib/reed_solomon/test_rslib.c   | 516 ++++++++++++++++++++++++++++++++
 5 files changed, 622 insertions(+), 35 deletions(-)
 create mode 100644 lib/reed_solomon/test_rslib.c

-- 
2.17.2

[PATCH v2 1/7] rslib: Add tests for the encoder and decoder

[Ferdinand Blomqvist]

A Reed-Solomon code with minimum distance d can correct any error and
erasure pattern that satisfies 2 * #error + #erasures < d. If the
error correction capacity is exceeded, then correct decoding cannot be
guaranteed. The decoder must, however, return a valid codeword or report
failure.

There are two main tests:

- Check for correct behaviour up to the error correction capacity
- Check for correct behaviour beyond error corrupted capacity

Both tests are simple:

1. Generate random data
2. Encode data with the chosen code
3. Add errors and erasures to data
4. Decode the corrupted word
5. Check for correct behaviour

When testing up to capacity we test for:

- Correct decoding
- Correct return value (i.e. the number of corrected symbols)
- That the returned error positions are correct

There are two kinds of erasures; the erased symbol can be corrupted or
not. When counting the number of corrected symbols, erasures without
symbol corruption should not be counted. Similarly, the returned error
positions should only include positions where a correction is necessary.

We run the up to capacity tests for three different interfaces of
decode_rs:

- Use the correction buffers
- Use the correction buffers with syndromes provided by the caller
- Error correction in place (does not check the error positions)

When testing beyond capacity we test for silent failures. A silent
failure is when the decoder returns success but the returned word is not
a valid codeword.

There are a couple of options for the tests:

- Verbosity.

- Whether to test for correct behaviour beyond capacity. Default is to
  test beyond capacity.

- Whether to allow erasures without symbol corruption. Defaults to yes.

Note that the tests take a couple of minutes to complete.

Signed-off-by: Ferdinand Blomqvist <ferdinand.blomqvist@gmail.com>
---
 lib/Kconfig.debug             |  12 +
 lib/reed_solomon/Makefile     |   2 +-
 lib/reed_solomon/test_rslib.c | 516 ++++++++++++++++++++++++++++++++++
 3 files changed, 529 insertions(+), 1 deletion(-)
 create mode 100644 lib/reed_solomon/test_rslib.c

diff --git a/lib/Kconfig.debug b/lib/Kconfig.debug
index cbdfae379896..b0d71d9293dc 100644
--- a/lib/Kconfig.debug
+++ b/lib/Kconfig.debug
@@ -1754,6 +1754,18 @@ config RBTREE_TEST
 	  A benchmark measuring the performance of the rbtree library.
 	  Also includes rbtree invariant checks.
 
+config REED_SOLOMON_TEST
+	tristate "Reed-Solomon library test"
+	depends on DEBUG_KERNEL || m
+	select REED_SOLOMON
+	select REED_SOLOMON_ENC16
+	select REED_SOLOMON_DEC16
+	help
+	  This option enables the self-test function of rslib at boot,
+	  or at module load time.
+
+	  If unsure, say N.
+
 config INTERVAL_TREE_TEST
 	tristate "Interval tree test"
 	depends on DEBUG_KERNEL
diff --git a/lib/reed_solomon/Makefile b/lib/reed_solomon/Makefile
index ba9d7a3329eb..5d4fa68f26cb 100644
--- a/lib/reed_solomon/Makefile
+++ b/lib/reed_solomon/Makefile
@@ -4,4 +4,4 @@
 #
 
 obj-$(CONFIG_REED_SOLOMON) += reed_solomon.o
-
+obj-$(CONFIG_REED_SOLOMON_TEST) += test_rslib.o
diff --git a/lib/reed_solomon/test_rslib.c b/lib/reed_solomon/test_rslib.c
new file mode 100644
index 000000000000..aa40e7ba5824
--- /dev/null
+++ b/lib/reed_solomon/test_rslib.c
@@ -0,0 +1,516 @@
+// SPDX-License-Identifier: GPL-2.0
+/*
+ * Tests for Generic Reed Solomon encoder / decoder library
+ *
+ * Written by Ferdinand Blomqvist
+ * Based on previous work by Phil Karn, KA9Q
+ */
+#include <linux/rslib.h>
+#include <linux/kernel.h>
+#include <linux/module.h>
+#include <linux/moduleparam.h>
+#include <linux/random.h>
+#include <linux/slab.h>
+
+enum verbosity {
+	V_SILENT,
+	V_PROGRESS,
+	V_CSUMMARY
+};
+
+enum method {
+	CORR_BUFFER,
+	CALLER_SYNDROME,
+	IN_PLACE
+};
+
+#define __param(type, name, init, msg)		\
+	static type name = init;		\
+	module_param(name, type, 0444);		\
+	MODULE_PARM_DESC(name, msg)
+
+__param(int, v, V_PROGRESS, "Verbosity level");
+__param(int, ewsc, 1, "Erasures without symbol corruption");
+__param(int, bc, 1, "Test for correct behaviour beyond error correction capacity");
+
+struct etab {
+	int	symsize;
+	int	genpoly;
+	int	fcs;
+	int	prim;
+	int	nroots;
+	int	ntrials;
+};
+
+/* List of codes to test */
+static struct etab Tab[] = {
+	{2,	0x7,	1,	1,	1,	100000	},
+	{3,	0xb,	1,	1,	2,	100000	},
+	{3,	0xb,	1,	1,	3,	100000	},
+	{3,	0xb,	2,	1,	4,	100000	},
+	{4,	0x13,	1,	1,	4,	10000	},
+	{5,	0x25,	1,	1,	6,	1000	},
+	{6,	0x43,	3,	1,	8,	1000	},
+	{7,	0x89,	1,	1,	14,	500	},
+	{8,	0x11d,	1,	1,	30,	100	},
+	{8,	0x187,	112,	11,	32,	100	},
+	{9,	0x211,	1,	1,	33,	80	},
+	{0, 0, 0, 0, 0, 0},
+};
+
+
+struct estat {
+	int	dwrong;
+	int	irv;
+	int	wepos;
+	int	nwords;
+};
+
+struct bcstat {
+	int	rfail;
+	int	rsuccess;
+	int	noncw;
+	int	nwords;
+};
+
+struct wspace {
+	uint16_t	*c;		/* sent codeword */
+	uint16_t	*r;		/* received word */
+	uint16_t	*s;		/* syndrome */
+	uint16_t	*corr;		/* correction buffer */
+	int		*errlocs;
+	int		*derrlocs;
+};
+
+struct pad {
+	int	mult;
+	int	shift;
+};
+
+static struct pad pad_coef[] = {
+	{ 0, 0 },
+	{ 1, 2 },
+	{ 1, 1 },
+	{ 3, 2 },
+	{ 1, 0 },
+};
+
+static void free_ws(struct wspace *ws)
+{
+	if (!ws)
+		return;
+
+	kfree(ws->errlocs);
+	kfree(ws->c);
+	kfree(ws);
+}
+
+static struct wspace *alloc_ws(struct rs_codec *rs)
+{
+	int nroots = rs->nroots;
+	struct wspace *ws;
+	int nn = rs->nn;
+
+	ws = kzalloc(sizeof(*ws), GFP_KERNEL);
+	if (!ws)
+		return NULL;
+
+	ws->c = kmalloc_array(2 * (nn + nroots),
+				sizeof(uint16_t), GFP_KERNEL);
+	if (!ws->c)
+		goto err;
+
+	ws->r = ws->c + nn;
+	ws->s = ws->r + nn;
+	ws->corr = ws->s + nroots;
+
+	ws->errlocs = kmalloc_array(nn + nroots, sizeof(int), GFP_KERNEL);
+	if (!ws->errlocs)
+		goto err;
+
+	ws->derrlocs = ws->errlocs + nn;
+	return ws;
+
+err:
+	free_ws(ws);
+	return NULL;
+}
+
+
+/*
+ * Generates a random codeword and stores it in c. Generates random errors and
+ * erasures, and stores the random word with errors in r. Erasure positions are
+ * stored in derrlocs, while errlocs has one of three values in every position:
+ *
+ * 0 if there is no error in this position;
+ * 1 if there is a symbol error in this position;
+ * 2 if there is an erasure without symbol corruption.
+ *
+ * Returns the number of corrupted symbols.
+ */
+static int get_rcw_we(struct rs_control *rs, struct wspace *ws,
+			int len, int errs, int eras)
+{
+	int nroots = rs->codec->nroots;
+	int *derrlocs = ws->derrlocs;
+	int *errlocs = ws->errlocs;
+	int dlen = len - nroots;
+	int nn = rs->codec->nn;
+	uint16_t *c = ws->c;
+	uint16_t *r = ws->r;
+	int errval;
+	int errloc;
+	int i;
+
+	/* Load c with random data and encode */
+	for (i = 0; i < dlen; i++)
+		c[i] = prandom_u32() & nn;
+
+	memset(c + dlen, 0, nroots * sizeof(*c));
+	encode_rs16(rs, c, dlen, c + dlen, 0);
+
+	/* Make copyand add errors and erasures */
+	memcpy(r, c, len * sizeof(*r));
+	memset(errlocs, 0, len * sizeof(*errlocs));
+	memset(derrlocs, 0, nroots * sizeof(*derrlocs));
+
+	/* Generating random errors */
+	for (i = 0; i < errs; i++) {
+		do {
+			/* Error value must be nonzero */
+			errval = prandom_u32() & nn;
+		} while (errval == 0);
+
+		do {
+			/* Must not choose the same location twice */
+			errloc = prandom_u32() % len;
+		} while (errlocs[errloc] != 0);
+
+		errlocs[errloc] = 1;
+		r[errloc] ^= errval;
+	}
+
+	/* Generating random erasures */
+	for (i = 0; i < eras; i++) {
+		do {
+			/* Must not choose the same location twice */
+			errloc = prandom_u32() % len;
+		} while (errlocs[errloc] != 0);
+
+		derrlocs[i] = errloc;
+
+		if (ewsc && (prandom_u32() & 1)) {
+			/* Erasure with the symbol intact */
+			errlocs[errloc] = 2;
+		} else {
+			/* Erasure with corrupted symbol */
+			do {
+				/* Error value must be nonzero */
+				errval = prandom_u32() & nn;
+			} while (errval == 0);
+
+			errlocs[errloc] = 1;
+			r[errloc] ^= errval;
+			errs++;
+		}
+	}
+
+	return errs;
+}
+
+static void fix_err(uint16_t *data, int nerrs, uint16_t *corr, int *errlocs)
+{
+	int i;
+
+	for (i = 0; i < nerrs; i++)
+		data[errlocs[i]] ^= corr[i];
+}
+
+static void compute_syndrome(struct rs_control *rsc, uint16_t *data,
+				int len, uint16_t *syn)
+{
+	struct rs_codec *rs = rsc->codec;
+	uint16_t *alpha_to = rs->alpha_to;
+	uint16_t *index_of = rs->index_of;
+	int nroots = rs->nroots;
+	int prim = rs->prim;
+	int fcr = rs->fcr;
+	int i, j;
+
+	/* Calculating syndrome */
+	for (i = 0; i < nroots; i++) {
+		syn[i] = data[0];
+		for (j = 1; j < len; j++) {
+			if (syn[i] == 0) {
+				syn[i] = data[j];
+			} else {
+				syn[i] = data[j] ^
+					alpha_to[rs_modnn(rs, index_of[syn[i]]
+						+ (fcr + i) * prim)];
+			}
+		}
+	}
+
+	/* Convert to index form */
+	for (i = 0; i < nroots; i++)
+		syn[i] = rs->index_of[syn[i]];
+}
+
+/* Test up to error correction capacity */
+static void test_uc(struct rs_control *rs, int len, int errs,
+		int eras, int trials, struct estat *stat,
+		struct wspace *ws, int method)
+{
+	int dlen = len - rs->codec->nroots;
+	int *derrlocs = ws->derrlocs;
+	int *errlocs = ws->errlocs;
+	uint16_t *corr = ws->corr;
+	uint16_t *c = ws->c;
+	uint16_t *r = ws->r;
+	uint16_t *s = ws->s;
+	int derrs, nerrs;
+	int i, j;
+
+	for (j = 0; j < trials; j++) {
+		nerrs = get_rcw_we(rs, ws, len, errs, eras);
+
+		switch (method) {
+		case CORR_BUFFER:
+			derrs = decode_rs16(rs, r, r + dlen, dlen,
+					NULL, eras, derrlocs, 0, corr);
+			fix_err(r, derrs, corr, derrlocs);
+			break;
+		case CALLER_SYNDROME:
+			compute_syndrome(rs, r, len, s);
+			derrs = decode_rs16(rs, NULL, NULL, dlen,
+					s, eras, derrlocs, 0, corr);
+			fix_err(r, derrs, corr, derrlocs);
+			break;
+		case IN_PLACE:
+			derrs = decode_rs16(rs, r, r + dlen, dlen,
+					NULL, eras, derrlocs, 0, NULL);
+			break;
+		}
+
+		if (derrs != nerrs)
+			stat->irv++;
+
+		if (method != IN_PLACE) {
+			for (i = 0; i < derrs; i++) {
+				if (errlocs[derrlocs[i]] != 1)
+					stat->wepos++;
+			}
+		}
+
+		if (memcmp(r, c, len * sizeof(*r)))
+			stat->dwrong++;
+	}
+	stat->nwords += trials;
+}
+
+int ex_rs_helper(struct rs_control *rs, struct wspace *ws,
+		int len, int trials, int method)
+{
+	static const char * const desc[] = {
+		"Testing correction buffer interface...",
+		"Testing with caller provided syndrome...",
+		"Testing in-place interface..."
+	};
+
+	struct estat stat = {0, 0, 0, 0};
+	int nroots = rs->codec->nroots;
+	int errs, eras, retval;
+
+	if (v >= V_PROGRESS)
+		pr_info("  %s\n", desc[method]);
+
+	for (errs = 0; errs <= nroots / 2; errs++)
+		for (eras = 0; eras <= nroots - 2 * errs; eras++)
+			test_uc(rs, len, errs, eras, trials, &stat, ws, method);
+
+	if (v >= V_CSUMMARY) {
+		pr_info("    Decodes wrong:        %d / %d\n",
+				stat.dwrong, stat.nwords);
+		pr_info("    Wrong return value:   %d / %d\n",
+				stat.irv, stat.nwords);
+		if (method != IN_PLACE)
+			pr_info("    Wrong error position: %d\n", stat.wepos);
+	}
+
+	retval = stat.dwrong + stat.wepos + stat.irv;
+	if (retval && v >= V_PROGRESS)
+		pr_warn("    FAIL: %d decoding failures!\n", retval);
+
+	return retval;
+}
+
+int exercise_rs(struct rs_control *rs, struct wspace *ws,
+		int len, int trials)
+{
+
+	int retval = 0;
+	int i;
+
+	if (v >= V_PROGRESS)
+		pr_info("Testing up to error correction capacity...\n");
+
+	for (i = 0; i <= IN_PLACE; i++)
+		retval |= ex_rs_helper(rs, ws, len, trials, i);
+
+	return retval;
+}
+
+/* Tests for correct behaviour beyond error correction capacity */
+static void test_bc(struct rs_control *rs, int len, int errs,
+		int eras, int trials, struct bcstat *stat,
+		struct wspace *ws)
+{
+	int nroots = rs->codec->nroots;
+	int dlen = len - nroots;
+	int *derrlocs = ws->derrlocs;
+	uint16_t *corr = ws->corr;
+	uint16_t *r = ws->r;
+	int derrs, j;
+
+	for (j = 0; j < trials; j++) {
+		get_rcw_we(rs, ws, len, errs, eras);
+		derrs = decode_rs16(rs, r, r + dlen, dlen,
+				NULL, eras, derrlocs, 0, corr);
+		fix_err(r, derrs, corr, derrlocs);
+
+		if (derrs >= 0) {
+			stat->rsuccess++;
+
+			/*
+			 * We check that the returned word is actually a
+			 * codeword. The obious way to do this would be to
+			 * compute the syndrome, but we don't want to replicate
+			 * that code here. However, all the codes are in
+			 * systematic form, and therefore we can encode the
+			 * returned word, and see whether the parity changes or
+			 * not.
+			 */
+			memset(corr, 0, nroots * sizeof(*corr));
+			encode_rs16(rs, r, dlen, corr, 0);
+
+			if (memcmp(r + dlen, corr, nroots * sizeof(*corr)))
+				stat->noncw++;
+		} else {
+			stat->rfail++;
+		}
+	}
+	stat->nwords += trials;
+}
+
+int exercise_rs_bc(struct rs_control *rs, struct wspace *ws,
+		int len, int trials)
+{
+	struct bcstat stat = {0, 0, 0, 0};
+	int nroots = rs->codec->nroots;
+	int errs, eras, cutoff;
+
+	if (v >= V_PROGRESS)
+		pr_info("Testing beyond error correction capacity...\n");
+
+	for (errs = 1; errs <= nroots; errs++) {
+		eras = nroots - 2 * errs + 1;
+		if (eras < 0)
+			eras = 0;
+
+		cutoff = nroots <= len - errs ? nroots : len - errs;
+		for (; eras <= cutoff; eras++)
+			test_bc(rs, len, errs, eras, trials, &stat, ws);
+	}
+
+	if (v >= V_CSUMMARY) {
+		pr_info("  decoder gives up:        %d / %d\n",
+				stat.rfail, stat.nwords);
+		pr_info("  decoder returns success: %d / %d\n",
+				stat.rsuccess, stat.nwords);
+		pr_info("    not a codeword:        %d / %d\n",
+				stat.noncw, stat.rsuccess);
+	}
+
+	if (stat.noncw && v >= V_PROGRESS)
+		pr_warn("    FAIL: %d silent failures!\n", stat.noncw);
+
+	return stat.noncw;
+}
+
+static int run_exercise(struct etab *e)
+{
+	int nn = (1 << e->symsize) - 1;
+	int kk = nn - e->nroots;
+	struct rs_control *rsc;
+	int retval = -ENOMEM;
+	int max_pad = kk - 1;
+	int prev_pad = -1;
+	struct wspace *ws;
+	int i;
+
+	rsc = init_rs(e->symsize, e->genpoly, e->fcs, e->prim, e->nroots);
+	if (!rsc)
+		return retval;
+
+	ws = alloc_ws(rsc->codec);
+	if (!ws)
+		goto err;
+
+	retval = 0;
+	for (i = 0; i < ARRAY_SIZE(pad_coef); i++) {
+		int pad = (pad_coef[i].mult * max_pad) >> pad_coef[i].shift;
+		int len = nn - pad;
+
+		if (pad == prev_pad)
+			continue;
+
+		prev_pad = pad;
+		if (v >= V_PROGRESS) {
+			pr_info("Testing (%d,%d)_%d code...\n",
+					len, kk - pad, nn + 1);
+		}
+
+		retval |= exercise_rs(rsc, ws, len, e->ntrials);
+		if (bc)
+			retval |= exercise_rs_bc(rsc, ws, len, e->ntrials);
+	}
+
+	free_ws(ws);
+
+err:
+	free_rs(rsc);
+	return retval;
+}
+
+static int __init test_rslib_init(void)
+{
+	int fail, i;
+
+	for (i = 0; Tab[i].symsize != 0 ; i++) {
+		int retval;
+
+		retval = run_exercise(Tab + i);
+		if (retval < 0)
+			return -ENOMEM;
+
+		fail |= retval;
+	}
+
+	if (fail)
+		pr_warn("rslib: test failed\n");
+	else
+		pr_info("rslib: test ok\n");
+
+	return -EAGAIN; /* Fail will directly unload the module */
+}
+
+static void __exit test_rslib_exit(void)
+{
+}
+
+module_init(test_rslib_init)
+module_exit(test_rslib_exit)
+
+MODULE_LICENSE("GPL");
+MODULE_AUTHOR("Ferdinand Blomqvist");
+MODULE_DESCRIPTION("Reed-Solomon library test");
-- 
2.17.2

[PATCH v2 2/7] rslib: Fix decoding of shortened codes

[Ferdinand Blomqvist]

The decoding of shortenend codes is broken. It only works as expected if
there are no erasures.

When decoding with erasures, Lambda (the error and erasure locator
polynomial) is initialized from the given erasure positions. The pad
parameter is not accounted for by the initialisation code, and hence
Lambda is initialized from incorrect erasure positions. The fix is
to adjust the erasure positions by the supplied pad.

Signed-off-by: Ferdinand Blomqvist <ferdinand.blomqvist@gmail.com>
---
 lib/reed_solomon/decode_rs.c | 4 ++--
 1 file changed, 2 insertions(+), 2 deletions(-)

diff --git a/lib/reed_solomon/decode_rs.c b/lib/reed_solomon/decode_rs.c
index 1db74eb098d0..3313bf944ff1 100644
--- a/lib/reed_solomon/decode_rs.c
+++ b/lib/reed_solomon/decode_rs.c
@@ -99,9 +99,9 @@
 	if (no_eras > 0) {
 		/* Init lambda to be the erasure locator polynomial */
 		lambda[1] = alpha_to[rs_modnn(rs,
-					      prim * (nn - 1 - eras_pos[0]))];
+					prim * (nn - 1 - (eras_pos[0] + pad)))];
 		for (i = 1; i < no_eras; i++) {
-			u = rs_modnn(rs, prim * (nn - 1 - eras_pos[i]));
+			u = rs_modnn(rs, prim * (nn - 1 - (eras_pos[i] + pad)));
 			for (j = i + 1; j > 0; j--) {
 				tmp = index_of[lambda[j - 1]];
 				if (tmp != nn) {
-- 
2.17.2

[PATCH v2 3/7] rslib: decode_rs: Fix length parameter check

[Ferdinand Blomqvist]

The length of the data load must be at least one. Or in other words,
there must be room for at least 1 data and nroots parity symbols after
shortening the RS code.

Signed-off-by: Ferdinand Blomqvist <ferdinand.blomqvist@gmail.com>
---
 lib/reed_solomon/decode_rs.c | 2 +-
 1 file changed, 1 insertion(+), 1 deletion(-)

diff --git a/lib/reed_solomon/decode_rs.c b/lib/reed_solomon/decode_rs.c
index 3313bf944ff1..22006eaa41e6 100644
--- a/lib/reed_solomon/decode_rs.c
+++ b/lib/reed_solomon/decode_rs.c
@@ -39,7 +39,7 @@
 
 	/* Check length parameter for validity */
 	pad = nn - nroots - len;
-	BUG_ON(pad < 0 || pad >= nn);
+	BUG_ON(pad < 0 || pad >= nn - nroots);
 
 	/* Does the caller provide the syndrome ? */
 	if (s != NULL)
-- 
2.17.2

[PATCH v2 4/7] rslib: decode_rs: code cleanup

[Ferdinand Blomqvist]

Nothing useful was done after the finish label when count is negative so
return directly instead of jumping to finish.

Signed-off-by: Ferdinand Blomqvist <ferdinand.blomqvist@gmail.com>
---
 lib/reed_solomon/decode_rs.c | 7 ++-----
 1 file changed, 2 insertions(+), 5 deletions(-)

diff --git a/lib/reed_solomon/decode_rs.c b/lib/reed_solomon/decode_rs.c
index 22006eaa41e6..78629bbe6590 100644
--- a/lib/reed_solomon/decode_rs.c
+++ b/lib/reed_solomon/decode_rs.c
@@ -88,8 +88,7 @@
 		/* if syndrome is zero, data[] is a codeword and there are no
 		 * errors to correct. So return data[] unmodified
 		 */
-		count = 0;
-		goto finish;
+		return 0;
 	}
 
  decode:
@@ -202,8 +201,7 @@
 		 * deg(lambda) unequal to number of roots => uncorrectable
 		 * error detected
 		 */
-		count = -EBADMSG;
-		goto finish;
+		return -EBADMSG;
 	}
 	/*
 	 * Compute err+eras evaluator poly omega(x) = s(x)*lambda(x) (modulo
@@ -261,7 +259,6 @@
 		}
 	}
 
-finish:
 	if (eras_pos != NULL) {
 		for (i = 0; i < count; i++)
 			eras_pos[i] = loc[i] - pad;
-- 
2.17.2

[PATCH v2 5/7] rslib: Fix handling of of caller provided syndrome

[Ferdinand Blomqvist]

Check if the syndrome provided by the caller is zero, and act
accordingly.

Signed-off-by: Ferdinand Blomqvist <ferdinand.blomqvist@gmail.com>
---
 lib/reed_solomon/decode_rs.c | 14 ++++++++++++--
 1 file changed, 12 insertions(+), 2 deletions(-)

diff --git a/lib/reed_solomon/decode_rs.c b/lib/reed_solomon/decode_rs.c
index 78629bbe6590..b7264a712d46 100644
--- a/lib/reed_solomon/decode_rs.c
+++ b/lib/reed_solomon/decode_rs.c
@@ -42,8 +42,18 @@
 	BUG_ON(pad < 0 || pad >= nn - nroots);
 
 	/* Does the caller provide the syndrome ? */
-	if (s != NULL)
-		goto decode;
+	if (s != NULL) {
+		for (i = 0; i < nroots; i++) {
+			/* The syndrome is in index form,
+			 * so nn represents zero
+			 */
+			if (s[i] != nn)
+				goto decode;
+		}
+
+		/* syndrome is zero, no errors to correct  */
+		return 0;
+	}
 
 	/* form the syndromes; i.e., evaluate data(x) at roots of
 	 * g(x) */
-- 
2.17.2

[PATCH v2 6/7] rslib: Update documentation

[Ferdinand Blomqvist]

The decoder returns the number of corrected symbols, not bits.
The caller provided syndrome must be in index form.

Signed-off-by: Ferdinand Blomqvist <ferdinand.blomqvist@gmail.com>
---
 lib/reed_solomon/reed_solomon.c | 12 ++++++++----
 1 file changed, 8 insertions(+), 4 deletions(-)

diff --git a/lib/reed_solomon/reed_solomon.c b/lib/reed_solomon/reed_solomon.c
index e5fdc8b9e856..bbc01bad3053 100644
--- a/lib/reed_solomon/reed_solomon.c
+++ b/lib/reed_solomon/reed_solomon.c
@@ -340,7 +340,8 @@ EXPORT_SYMBOL_GPL(encode_rs8);
  *  @data:	data field of a given type
  *  @par:	received parity data field
  *  @len:	data length
- *  @s:		syndrome data field (if NULL, syndrome is calculated)
+ *  @s: 	syndrome data field, must be in index form
+ *		(if NULL, syndrome is calculated)
  *  @no_eras:	number of erasures
  *  @eras_pos:	position of erasures, can be NULL
  *  @invmsk:	invert data mask (will be xored on data, not on parity!)
@@ -354,7 +355,8 @@ EXPORT_SYMBOL_GPL(encode_rs8);
  *  decoding, so the caller has to ensure that decoder invocations are
  *  serialized.
  *
- *  Returns the number of corrected bits or -EBADMSG for uncorrectable errors.
+ *  Returns the number of corrected symbols or -EBADMSG for uncorrectable
+ *  errors. The count includes errors in the parity.
  */
 int decode_rs8(struct rs_control *rsc, uint8_t *data, uint16_t *par, int len,
 	       uint16_t *s, int no_eras, int *eras_pos, uint16_t invmsk,
@@ -391,7 +393,8 @@ EXPORT_SYMBOL_GPL(encode_rs16);
  *  @data:	data field of a given type
  *  @par:	received parity data field
  *  @len:	data length
- *  @s:		syndrome data field (if NULL, syndrome is calculated)
+ *  @s: 	syndrome data field, must be in index form
+ *		(if NULL, syndrome is calculated)
  *  @no_eras:	number of erasures
  *  @eras_pos:	position of erasures, can be NULL
  *  @invmsk:	invert data mask (will be xored on data, not on parity!)
@@ -403,7 +406,8 @@ EXPORT_SYMBOL_GPL(encode_rs16);
  *  decoding, so the caller has to ensure that decoder invocations are
  *  serialized.
  *
- *  Returns the number of corrected bits or -EBADMSG for uncorrectable errors.
+ *  Returns the number of corrected symbols or -EBADMSG for uncorrectable
+ *  errors. The count includes errors in the parity.
  */
 int decode_rs16(struct rs_control *rsc, uint16_t *data, uint16_t *par, int len,
 		uint16_t *s, int no_eras, int *eras_pos, uint16_t invmsk,
-- 
2.17.2

[PATCH v2 7/7] rslib: Fix remaining decoder flaws

[Ferdinand Blomqvist]

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>
---
 lib/reed_solomon/decode_rs.c | 88 ++++++++++++++++++++++++++++--------
 1 file changed, 68 insertions(+), 20 deletions(-)

diff --git a/lib/reed_solomon/decode_rs.c b/lib/reed_solomon/decode_rs.c
index b7264a712d46..805de84ae83d 100644
--- a/lib/reed_solomon/decode_rs.c
+++ b/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) {
-			uint16_t cor = alpha_to[rs_modnn(rs,index_of[num1] +
-						       index_of[num2] +
-						       nn - index_of[den])];
-			/* Store the error correction pattern, if a
-			 * correction buffer is available */
-			if (corr) {
-				corr[j] = cor;
-			} else {
-				/* If a data buffer is given and the
-				 * error is inside the message,
-				 * correct it */
-				if (data && (loc[j] < (nn - nroots)))
-					data[loc[j] - pad] ^= cor;
-			}
+
+		b[j] = alpha_to[rs_modnn(rs, index_of[num1] +
+					       index_of[num2] +
+					       nn - index_of[den])];
+		num_corrected++;
+	}
+
+	/*
+	 * We compute the syndrome of the 'error' and check that it matches
+	 * the syndrome of the received word
+	 */
+	for (i = 0; i < nroots; i++) {
+		tmp = 0;
+		for (j = 0; j < count; j++) {
+			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;
 	}
 
-	if (eras_pos != NULL) {
-		for (i = 0; i < count; i++)
-			eras_pos[i] = loc[i] - pad;
+	/*
+	 * 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];
+		}
 	}
-	return count;
 
+	return  num_corrected;
 }
-- 
2.17.2

Re: [PATCH v2 0/7] rslib: RS decoder is severely broken

[Thomas Gleixner]

Ferdinand,

On Thu, 20 Jun 2019, Ferdinand Blomqvist wrote:

> This is the second revision of this series that fixes the bugs/flaws in
> the RS decoder. This addresses all of Thomas' comments/suggestions.

I've picked up the lot and it's en route to 5.3.

Thanks a lot for your excellent work and your patience!

       tglx

[tip:core/rslib] rslib: Add tests for the encoder and decoder

[tip-bot for Ferdinand Blomqvist]

Commit-ID:  4b4f3accd80304781c648b26ce4d53df082a4087
Gitweb:     https://git.kernel.org/tip/4b4f3accd80304781c648b26ce4d53df082a4087
Author:     Ferdinand Blomqvist <ferdinand.blomqvist@gmail.com>
AuthorDate: Thu, 20 Jun 2019 17:10:33 +0300
Committer:  Thomas Gleixner <tglx@linutronix.de>
CommitDate: Wed, 26 Jun 2019 14:55:45 +0200

rslib: Add tests for the encoder and decoder

A Reed-Solomon code with minimum distance d can correct any error and
erasure pattern that satisfies 2 * #error + #erasures < d. If the
error correction capacity is exceeded, then correct decoding cannot be
guaranteed. The decoder must, however, return a valid codeword or report
failure.

There are two main tests:

- Check for correct behaviour up to the error correction capacity
- Check for correct behaviour beyond error corrupted capacity

Both tests are simple:

1. Generate random data
2. Encode data with the chosen code
3. Add errors and erasures to data
4. Decode the corrupted word
5. Check for correct behaviour

When testing up to capacity we test for:

- Correct decoding
- Correct return value (i.e. the number of corrected symbols)
- That the returned error positions are correct

There are two kinds of erasures; the erased symbol can be corrupted or
not. When counting the number of corrected symbols, erasures without
symbol corruption should not be counted. Similarly, the returned error
positions should only include positions where a correction is necessary.

We run the up to capacity tests for three different interfaces of
decode_rs:

- Use the correction buffers
- Use the correction buffers with syndromes provided by the caller
- Error correction in place (does not check the error positions)

When testing beyond capacity test for silent failures. A silent failure is
when the decoder returns success but the returned word is not a valid
codeword.

There are a couple of options for the tests:

- Verbosity.

- Whether to test for correct behaviour beyond capacity. Default is to
  test beyond capacity.

- Whether to allow erasures without symbol corruption. Defaults to yes.

Note that the tests take a couple of minutes to complete.

Signed-off-by: Ferdinand Blomqvist <ferdinand.blomqvist@gmail.com>
Signed-off-by: Thomas Gleixner <tglx@linutronix.de>
Link: https://lkml.kernel.org/r/20190620141039.9874-2-ferdinand.blomqvist@gmail.com

---
 lib/Kconfig.debug             |  12 +
 lib/reed_solomon/Makefile     |   2 +-
 lib/reed_solomon/test_rslib.c | 518 ++++++++++++++++++++++++++++++++++++++++++
 3 files changed, 531 insertions(+), 1 deletion(-)

diff --git a/lib/Kconfig.debug b/lib/Kconfig.debug
index cbdfae379896..b0d71d9293dc 100644
--- a/lib/Kconfig.debug
+++ b/lib/Kconfig.debug
@@ -1754,6 +1754,18 @@ config RBTREE_TEST
 	  A benchmark measuring the performance of the rbtree library.
 	  Also includes rbtree invariant checks.
 
+config REED_SOLOMON_TEST
+	tristate "Reed-Solomon library test"
+	depends on DEBUG_KERNEL || m
+	select REED_SOLOMON
+	select REED_SOLOMON_ENC16
+	select REED_SOLOMON_DEC16
+	help
+	  This option enables the self-test function of rslib at boot,
+	  or at module load time.
+
+	  If unsure, say N.
+
 config INTERVAL_TREE_TEST
 	tristate "Interval tree test"
 	depends on DEBUG_KERNEL
diff --git a/lib/reed_solomon/Makefile b/lib/reed_solomon/Makefile
index ba9d7a3329eb..5d4fa68f26cb 100644
--- a/lib/reed_solomon/Makefile
+++ b/lib/reed_solomon/Makefile
@@ -4,4 +4,4 @@
 #
 
 obj-$(CONFIG_REED_SOLOMON) += reed_solomon.o
-
+obj-$(CONFIG_REED_SOLOMON_TEST) += test_rslib.o
diff --git a/lib/reed_solomon/test_rslib.c b/lib/reed_solomon/test_rslib.c
new file mode 100644
index 000000000000..eb62e0393c80
--- /dev/null
+++ b/lib/reed_solomon/test_rslib.c
@@ -0,0 +1,518 @@
+// SPDX-License-Identifier: GPL-2.0
+/*
+ * Tests for Generic Reed Solomon encoder / decoder library
+ *
+ * Written by Ferdinand Blomqvist
+ * Based on previous work by Phil Karn, KA9Q
+ */
+#include <linux/rslib.h>
+#include <linux/kernel.h>
+#include <linux/module.h>
+#include <linux/moduleparam.h>
+#include <linux/random.h>
+#include <linux/slab.h>
+
+enum verbosity {
+	V_SILENT,
+	V_PROGRESS,
+	V_CSUMMARY
+};
+
+enum method {
+	CORR_BUFFER,
+	CALLER_SYNDROME,
+	IN_PLACE
+};
+
+#define __param(type, name, init, msg)		\
+	static type name = init;		\
+	module_param(name, type, 0444);		\
+	MODULE_PARM_DESC(name, msg)
+
+__param(int, v, V_PROGRESS, "Verbosity level");
+__param(int, ewsc, 1, "Erasures without symbol corruption");
+__param(int, bc, 1, "Test for correct behaviour beyond error correction capacity");
+
+struct etab {
+	int	symsize;
+	int	genpoly;
+	int	fcs;
+	int	prim;
+	int	nroots;
+	int	ntrials;
+};
+
+/* List of codes to test */
+static struct etab Tab[] = {
+	{2,	0x7,	1,	1,	1,	100000	},
+	{3,	0xb,	1,	1,	2,	100000	},
+	{3,	0xb,	1,	1,	3,	100000	},
+	{3,	0xb,	2,	1,	4,	100000	},
+	{4,	0x13,	1,	1,	4,	10000	},
+	{5,	0x25,	1,	1,	6,	1000	},
+	{6,	0x43,	3,	1,	8,	1000	},
+	{7,	0x89,	1,	1,	14,	500	},
+	{8,	0x11d,	1,	1,	30,	100	},
+	{8,	0x187,	112,	11,	32,	100	},
+	{9,	0x211,	1,	1,	33,	80	},
+	{0, 0, 0, 0, 0, 0},
+};
+
+
+struct estat {
+	int	dwrong;
+	int	irv;
+	int	wepos;
+	int	nwords;
+};
+
+struct bcstat {
+	int	rfail;
+	int	rsuccess;
+	int	noncw;
+	int	nwords;
+};
+
+struct wspace {
+	uint16_t	*c;		/* sent codeword */
+	uint16_t	*r;		/* received word */
+	uint16_t	*s;		/* syndrome */
+	uint16_t	*corr;		/* correction buffer */
+	int		*errlocs;
+	int		*derrlocs;
+};
+
+struct pad {
+	int	mult;
+	int	shift;
+};
+
+static struct pad pad_coef[] = {
+	{ 0, 0 },
+	{ 1, 2 },
+	{ 1, 1 },
+	{ 3, 2 },
+	{ 1, 0 },
+};
+
+static void free_ws(struct wspace *ws)
+{
+	if (!ws)
+		return;
+
+	kfree(ws->errlocs);
+	kfree(ws->c);
+	kfree(ws);
+}
+
+static struct wspace *alloc_ws(struct rs_codec *rs)
+{
+	int nroots = rs->nroots;
+	struct wspace *ws;
+	int nn = rs->nn;
+
+	ws = kzalloc(sizeof(*ws), GFP_KERNEL);
+	if (!ws)
+		return NULL;
+
+	ws->c = kmalloc_array(2 * (nn + nroots),
+				sizeof(uint16_t), GFP_KERNEL);
+	if (!ws->c)
+		goto err;
+
+	ws->r = ws->c + nn;
+	ws->s = ws->r + nn;
+	ws->corr = ws->s + nroots;
+
+	ws->errlocs = kmalloc_array(nn + nroots, sizeof(int), GFP_KERNEL);
+	if (!ws->errlocs)
+		goto err;
+
+	ws->derrlocs = ws->errlocs + nn;
+	return ws;
+
+err:
+	free_ws(ws);
+	return NULL;
+}
+
+
+/*
+ * Generates a random codeword and stores it in c. Generates random errors and
+ * erasures, and stores the random word with errors in r. Erasure positions are
+ * stored in derrlocs, while errlocs has one of three values in every position:
+ *
+ * 0 if there is no error in this position;
+ * 1 if there is a symbol error in this position;
+ * 2 if there is an erasure without symbol corruption.
+ *
+ * Returns the number of corrupted symbols.
+ */
+static int get_rcw_we(struct rs_control *rs, struct wspace *ws,
+			int len, int errs, int eras)
+{
+	int nroots = rs->codec->nroots;
+	int *derrlocs = ws->derrlocs;
+	int *errlocs = ws->errlocs;
+	int dlen = len - nroots;
+	int nn = rs->codec->nn;
+	uint16_t *c = ws->c;
+	uint16_t *r = ws->r;
+	int errval;
+	int errloc;
+	int i;
+
+	/* Load c with random data and encode */
+	for (i = 0; i < dlen; i++)
+		c[i] = prandom_u32() & nn;
+
+	memset(c + dlen, 0, nroots * sizeof(*c));
+	encode_rs16(rs, c, dlen, c + dlen, 0);
+
+	/* Make copyand add errors and erasures */
+	memcpy(r, c, len * sizeof(*r));
+	memset(errlocs, 0, len * sizeof(*errlocs));
+	memset(derrlocs, 0, nroots * sizeof(*derrlocs));
+
+	/* Generating random errors */
+	for (i = 0; i < errs; i++) {
+		do {
+			/* Error value must be nonzero */
+			errval = prandom_u32() & nn;
+		} while (errval == 0);
+
+		do {
+			/* Must not choose the same location twice */
+			errloc = prandom_u32() % len;
+		} while (errlocs[errloc] != 0);
+
+		errlocs[errloc] = 1;
+		r[errloc] ^= errval;
+	}
+
+	/* Generating random erasures */
+	for (i = 0; i < eras; i++) {
+		do {
+			/* Must not choose the same location twice */
+			errloc = prandom_u32() % len;
+		} while (errlocs[errloc] != 0);
+
+		derrlocs[i] = errloc;
+
+		if (ewsc && (prandom_u32() & 1)) {
+			/* Erasure with the symbol intact */
+			errlocs[errloc] = 2;
+		} else {
+			/* Erasure with corrupted symbol */
+			do {
+				/* Error value must be nonzero */
+				errval = prandom_u32() & nn;
+			} while (errval == 0);
+
+			errlocs[errloc] = 1;
+			r[errloc] ^= errval;
+			errs++;
+		}
+	}
+
+	return errs;
+}
+
+static void fix_err(uint16_t *data, int nerrs, uint16_t *corr, int *errlocs)
+{
+	int i;
+
+	for (i = 0; i < nerrs; i++)
+		data[errlocs[i]] ^= corr[i];
+}
+
+static void compute_syndrome(struct rs_control *rsc, uint16_t *data,
+				int len, uint16_t *syn)
+{
+	struct rs_codec *rs = rsc->codec;
+	uint16_t *alpha_to = rs->alpha_to;
+	uint16_t *index_of = rs->index_of;
+	int nroots = rs->nroots;
+	int prim = rs->prim;
+	int fcr = rs->fcr;
+	int i, j;
+
+	/* Calculating syndrome */
+	for (i = 0; i < nroots; i++) {
+		syn[i] = data[0];
+		for (j = 1; j < len; j++) {
+			if (syn[i] == 0) {
+				syn[i] = data[j];
+			} else {
+				syn[i] = data[j] ^
+					alpha_to[rs_modnn(rs, index_of[syn[i]]
+						+ (fcr + i) * prim)];
+			}
+		}
+	}
+
+	/* Convert to index form */
+	for (i = 0; i < nroots; i++)
+		syn[i] = rs->index_of[syn[i]];
+}
+
+/* Test up to error correction capacity */
+static void test_uc(struct rs_control *rs, int len, int errs,
+		int eras, int trials, struct estat *stat,
+		struct wspace *ws, int method)
+{
+	int dlen = len - rs->codec->nroots;
+	int *derrlocs = ws->derrlocs;
+	int *errlocs = ws->errlocs;
+	uint16_t *corr = ws->corr;
+	uint16_t *c = ws->c;
+	uint16_t *r = ws->r;
+	uint16_t *s = ws->s;
+	int derrs, nerrs;
+	int i, j;
+
+	for (j = 0; j < trials; j++) {
+		nerrs = get_rcw_we(rs, ws, len, errs, eras);
+
+		switch (method) {
+		case CORR_BUFFER:
+			derrs = decode_rs16(rs, r, r + dlen, dlen,
+					NULL, eras, derrlocs, 0, corr);
+			fix_err(r, derrs, corr, derrlocs);
+			break;
+		case CALLER_SYNDROME:
+			compute_syndrome(rs, r, len, s);
+			derrs = decode_rs16(rs, NULL, NULL, dlen,
+					s, eras, derrlocs, 0, corr);
+			fix_err(r, derrs, corr, derrlocs);
+			break;
+		case IN_PLACE:
+			derrs = decode_rs16(rs, r, r + dlen, dlen,
+					NULL, eras, derrlocs, 0, NULL);
+			break;
+		default:
+			continue;
+		}
+
+		if (derrs != nerrs)
+			stat->irv++;
+
+		if (method != IN_PLACE) {
+			for (i = 0; i < derrs; i++) {
+				if (errlocs[derrlocs[i]] != 1)
+					stat->wepos++;
+			}
+		}
+
+		if (memcmp(r, c, len * sizeof(*r)))
+			stat->dwrong++;
+	}
+	stat->nwords += trials;
+}
+
+int ex_rs_helper(struct rs_control *rs, struct wspace *ws,
+		int len, int trials, int method)
+{
+	static const char * const desc[] = {
+		"Testing correction buffer interface...",
+		"Testing with caller provided syndrome...",
+		"Testing in-place interface..."
+	};
+
+	struct estat stat = {0, 0, 0, 0};
+	int nroots = rs->codec->nroots;
+	int errs, eras, retval;
+
+	if (v >= V_PROGRESS)
+		pr_info("  %s\n", desc[method]);
+
+	for (errs = 0; errs <= nroots / 2; errs++)
+		for (eras = 0; eras <= nroots - 2 * errs; eras++)
+			test_uc(rs, len, errs, eras, trials, &stat, ws, method);
+
+	if (v >= V_CSUMMARY) {
+		pr_info("    Decodes wrong:        %d / %d\n",
+				stat.dwrong, stat.nwords);
+		pr_info("    Wrong return value:   %d / %d\n",
+				stat.irv, stat.nwords);
+		if (method != IN_PLACE)
+			pr_info("    Wrong error position: %d\n", stat.wepos);
+	}
+
+	retval = stat.dwrong + stat.wepos + stat.irv;
+	if (retval && v >= V_PROGRESS)
+		pr_warn("    FAIL: %d decoding failures!\n", retval);
+
+	return retval;
+}
+
+int exercise_rs(struct rs_control *rs, struct wspace *ws,
+		int len, int trials)
+{
+
+	int retval = 0;
+	int i;
+
+	if (v >= V_PROGRESS)
+		pr_info("Testing up to error correction capacity...\n");
+
+	for (i = 0; i <= IN_PLACE; i++)
+		retval |= ex_rs_helper(rs, ws, len, trials, i);
+
+	return retval;
+}
+
+/* Tests for correct behaviour beyond error correction capacity */
+static void test_bc(struct rs_control *rs, int len, int errs,
+		int eras, int trials, struct bcstat *stat,
+		struct wspace *ws)
+{
+	int nroots = rs->codec->nroots;
+	int dlen = len - nroots;
+	int *derrlocs = ws->derrlocs;
+	uint16_t *corr = ws->corr;
+	uint16_t *r = ws->r;
+	int derrs, j;
+
+	for (j = 0; j < trials; j++) {
+		get_rcw_we(rs, ws, len, errs, eras);
+		derrs = decode_rs16(rs, r, r + dlen, dlen,
+				NULL, eras, derrlocs, 0, corr);
+		fix_err(r, derrs, corr, derrlocs);
+
+		if (derrs >= 0) {
+			stat->rsuccess++;
+
+			/*
+			 * We check that the returned word is actually a
+			 * codeword. The obious way to do this would be to
+			 * compute the syndrome, but we don't want to replicate
+			 * that code here. However, all the codes are in
+			 * systematic form, and therefore we can encode the
+			 * returned word, and see whether the parity changes or
+			 * not.
+			 */
+			memset(corr, 0, nroots * sizeof(*corr));
+			encode_rs16(rs, r, dlen, corr, 0);
+
+			if (memcmp(r + dlen, corr, nroots * sizeof(*corr)))
+				stat->noncw++;
+		} else {
+			stat->rfail++;
+		}
+	}
+	stat->nwords += trials;
+}
+
+int exercise_rs_bc(struct rs_control *rs, struct wspace *ws,
+		int len, int trials)
+{
+	struct bcstat stat = {0, 0, 0, 0};
+	int nroots = rs->codec->nroots;
+	int errs, eras, cutoff;
+
+	if (v >= V_PROGRESS)
+		pr_info("Testing beyond error correction capacity...\n");
+
+	for (errs = 1; errs <= nroots; errs++) {
+		eras = nroots - 2 * errs + 1;
+		if (eras < 0)
+			eras = 0;
+
+		cutoff = nroots <= len - errs ? nroots : len - errs;
+		for (; eras <= cutoff; eras++)
+			test_bc(rs, len, errs, eras, trials, &stat, ws);
+	}
+
+	if (v >= V_CSUMMARY) {
+		pr_info("  decoder gives up:        %d / %d\n",
+				stat.rfail, stat.nwords);
+		pr_info("  decoder returns success: %d / %d\n",
+				stat.rsuccess, stat.nwords);
+		pr_info("    not a codeword:        %d / %d\n",
+				stat.noncw, stat.rsuccess);
+	}
+
+	if (stat.noncw && v >= V_PROGRESS)
+		pr_warn("    FAIL: %d silent failures!\n", stat.noncw);
+
+	return stat.noncw;
+}
+
+static int run_exercise(struct etab *e)
+{
+	int nn = (1 << e->symsize) - 1;
+	int kk = nn - e->nroots;
+	struct rs_control *rsc;
+	int retval = -ENOMEM;
+	int max_pad = kk - 1;
+	int prev_pad = -1;
+	struct wspace *ws;
+	int i;
+
+	rsc = init_rs(e->symsize, e->genpoly, e->fcs, e->prim, e->nroots);
+	if (!rsc)
+		return retval;
+
+	ws = alloc_ws(rsc->codec);
+	if (!ws)
+		goto err;
+
+	retval = 0;
+	for (i = 0; i < ARRAY_SIZE(pad_coef); i++) {
+		int pad = (pad_coef[i].mult * max_pad) >> pad_coef[i].shift;
+		int len = nn - pad;
+
+		if (pad == prev_pad)
+			continue;
+
+		prev_pad = pad;
+		if (v >= V_PROGRESS) {
+			pr_info("Testing (%d,%d)_%d code...\n",
+					len, kk - pad, nn + 1);
+		}
+
+		retval |= exercise_rs(rsc, ws, len, e->ntrials);
+		if (bc)
+			retval |= exercise_rs_bc(rsc, ws, len, e->ntrials);
+	}
+
+	free_ws(ws);
+
+err:
+	free_rs(rsc);
+	return retval;
+}
+
+static int __init test_rslib_init(void)
+{
+	int i, fail = 0;
+
+	for (i = 0; Tab[i].symsize != 0 ; i++) {
+		int retval;
+
+		retval = run_exercise(Tab + i);
+		if (retval < 0)
+			return -ENOMEM;
+
+		fail |= retval;
+	}
+
+	if (fail)
+		pr_warn("rslib: test failed\n");
+	else
+		pr_info("rslib: test ok\n");
+
+	return -EAGAIN; /* Fail will directly unload the module */
+}
+
+static void __exit test_rslib_exit(void)
+{
+}
+
+module_init(test_rslib_init)
+module_exit(test_rslib_exit)
+
+MODULE_LICENSE("GPL");
+MODULE_AUTHOR("Ferdinand Blomqvist");
+MODULE_DESCRIPTION("Reed-Solomon library test");

[tip:core/rslib] rslib: Fix decoding of shortened codes

[tip-bot for Ferdinand Blomqvist]

Commit-ID:  2034a42d1747fc1e1eeef2c6f1789c4d0762cb9c
Gitweb:     https://git.kernel.org/tip/2034a42d1747fc1e1eeef2c6f1789c4d0762cb9c
Author:     Ferdinand Blomqvist <ferdinand.blomqvist@gmail.com>
AuthorDate: Thu, 20 Jun 2019 17:10:34 +0300
Committer:  Thomas Gleixner <tglx@linutronix.de>
CommitDate: Wed, 26 Jun 2019 14:55:45 +0200

rslib: Fix decoding of shortened codes

The decoding of shortenend codes is broken. It only works as expected if
there are no erasures.

When decoding with erasures, Lambda (the error and erasure locator
polynomial) is initialized from the given erasure positions. The pad
parameter is not accounted for by the initialisation code, and hence
Lambda is initialized from incorrect erasure positions.

The fix is to adjust the erasure positions by the supplied pad.

Signed-off-by: Ferdinand Blomqvist <ferdinand.blomqvist@gmail.com>
Signed-off-by: Thomas Gleixner <tglx@linutronix.de>
Link: https://lkml.kernel.org/r/20190620141039.9874-3-ferdinand.blomqvist@gmail.com

---
 lib/reed_solomon/decode_rs.c | 4 ++--
 1 file changed, 2 insertions(+), 2 deletions(-)

diff --git a/lib/reed_solomon/decode_rs.c b/lib/reed_solomon/decode_rs.c
index 1db74eb098d0..3313bf944ff1 100644
--- a/lib/reed_solomon/decode_rs.c
+++ b/lib/reed_solomon/decode_rs.c
@@ -99,9 +99,9 @@
 	if (no_eras > 0) {
 		/* Init lambda to be the erasure locator polynomial */
 		lambda[1] = alpha_to[rs_modnn(rs,
-					      prim * (nn - 1 - eras_pos[0]))];
+					prim * (nn - 1 - (eras_pos[0] + pad)))];
 		for (i = 1; i < no_eras; i++) {
-			u = rs_modnn(rs, prim * (nn - 1 - eras_pos[i]));
+			u = rs_modnn(rs, prim * (nn - 1 - (eras_pos[i] + pad)));
 			for (j = i + 1; j > 0; j--) {
 				tmp = index_of[lambda[j - 1]];
 				if (tmp != nn) {

[tip:core/rslib] rslib: decode_rs: Fix length parameter check

[tip-bot for Ferdinand Blomqvist]

Commit-ID:  a343536f8f482be6932803a023f46d0fa723ae56
Gitweb:     https://git.kernel.org/tip/a343536f8f482be6932803a023f46d0fa723ae56
Author:     Ferdinand Blomqvist <ferdinand.blomqvist@gmail.com>
AuthorDate: Thu, 20 Jun 2019 17:10:35 +0300
Committer:  Thomas Gleixner <tglx@linutronix.de>
CommitDate: Wed, 26 Jun 2019 14:55:46 +0200

rslib: decode_rs: Fix length parameter check

The length of the data load must be at least one. Or in other words,
there must be room for at least 1 data and nroots parity symbols after
shortening the RS code.

Signed-off-by: Ferdinand Blomqvist <ferdinand.blomqvist@gmail.com>
Signed-off-by: Thomas Gleixner <tglx@linutronix.de>
Link: https://lkml.kernel.org/r/20190620141039.9874-4-ferdinand.blomqvist@gmail.com

---
 lib/reed_solomon/decode_rs.c | 2 +-
 1 file changed, 1 insertion(+), 1 deletion(-)

diff --git a/lib/reed_solomon/decode_rs.c b/lib/reed_solomon/decode_rs.c
index 3313bf944ff1..22006eaa41e6 100644
--- a/lib/reed_solomon/decode_rs.c
+++ b/lib/reed_solomon/decode_rs.c
@@ -39,7 +39,7 @@
 
 	/* Check length parameter for validity */
 	pad = nn - nroots - len;
-	BUG_ON(pad < 0 || pad >= nn);
+	BUG_ON(pad < 0 || pad >= nn - nroots);
 
 	/* Does the caller provide the syndrome ? */
 	if (s != NULL)

[tip:core/rslib] rslib: decode_rs: Code cleanup

[tip-bot for Ferdinand Blomqvist]

Commit-ID:  647cc9ece63fdba573a31bdafa54fb2d388c3c83
Gitweb:     https://git.kernel.org/tip/647cc9ece63fdba573a31bdafa54fb2d388c3c83
Author:     Ferdinand Blomqvist <ferdinand.blomqvist@gmail.com>
AuthorDate: Thu, 20 Jun 2019 17:10:36 +0300
Committer:  Thomas Gleixner <tglx@linutronix.de>
CommitDate: Wed, 26 Jun 2019 14:55:46 +0200

rslib: decode_rs: Code cleanup

Nothing useful was done after the finish label when count is negative so
return directly instead of jumping to finish.

Signed-off-by: Ferdinand Blomqvist <ferdinand.blomqvist@gmail.com>
Signed-off-by: Thomas Gleixner <tglx@linutronix.de>
Link: https://lkml.kernel.org/r/20190620141039.9874-5-ferdinand.blomqvist@gmail.com

---
 lib/reed_solomon/decode_rs.c | 7 ++-----
 1 file changed, 2 insertions(+), 5 deletions(-)

diff --git a/lib/reed_solomon/decode_rs.c b/lib/reed_solomon/decode_rs.c
index 22006eaa41e6..78629bbe6590 100644
--- a/lib/reed_solomon/decode_rs.c
+++ b/lib/reed_solomon/decode_rs.c
@@ -88,8 +88,7 @@
 		/* if syndrome is zero, data[] is a codeword and there are no
 		 * errors to correct. So return data[] unmodified
 		 */
-		count = 0;
-		goto finish;
+		return 0;
 	}
 
  decode:
@@ -202,8 +201,7 @@
 		 * deg(lambda) unequal to number of roots => uncorrectable
 		 * error detected
 		 */
-		count = -EBADMSG;
-		goto finish;
+		return -EBADMSG;
 	}
 	/*
 	 * Compute err+eras evaluator poly omega(x) = s(x)*lambda(x) (modulo
@@ -261,7 +259,6 @@
 		}
 	}
 
-finish:
 	if (eras_pos != NULL) {
 		for (i = 0; i < count; i++)
 			eras_pos[i] = loc[i] - pad;

[tip:core/rslib] rslib: Fix handling of of caller provided syndrome

[tip-bot for Ferdinand Blomqvist]

Commit-ID:  ef4d6a8556b637ad27c8c2a2cff1dda3da38e9a9
Gitweb:     https://git.kernel.org/tip/ef4d6a8556b637ad27c8c2a2cff1dda3da38e9a9
Author:     Ferdinand Blomqvist <ferdinand.blomqvist@gmail.com>
AuthorDate: Thu, 20 Jun 2019 17:10:37 +0300
Committer:  Thomas Gleixner <tglx@linutronix.de>
CommitDate: Wed, 26 Jun 2019 14:55:47 +0200

rslib: Fix handling of of caller provided syndrome

Check if the syndrome provided by the caller is zero, and act
accordingly.

Signed-off-by: Ferdinand Blomqvist <ferdinand.blomqvist@gmail.com>
Signed-off-by: Thomas Gleixner <tglx@linutronix.de>
Link: https://lkml.kernel.org/r/20190620141039.9874-6-ferdinand.blomqvist@gmail.com

---
 lib/reed_solomon/decode_rs.c | 14 ++++++++++++--
 1 file changed, 12 insertions(+), 2 deletions(-)

diff --git a/lib/reed_solomon/decode_rs.c b/lib/reed_solomon/decode_rs.c
index 78629bbe6590..b7264a712d46 100644
--- a/lib/reed_solomon/decode_rs.c
+++ b/lib/reed_solomon/decode_rs.c
@@ -42,8 +42,18 @@
 	BUG_ON(pad < 0 || pad >= nn - nroots);
 
 	/* Does the caller provide the syndrome ? */
-	if (s != NULL)
-		goto decode;
+	if (s != NULL) {
+		for (i = 0; i < nroots; i++) {
+			/* The syndrome is in index form,
+			 * so nn represents zero
+			 */
+			if (s[i] != nn)
+				goto decode;
+		}
+
+		/* syndrome is zero, no errors to correct  */
+		return 0;
+	}
 
 	/* form the syndromes; i.e., evaluate data(x) at roots of
 	 * g(x) */

[tip:core/rslib] rslib: Update documentation

[tip-bot for Ferdinand Blomqvist]

Commit-ID:  38cbae1434f8f7bbd8eaf24b29a385a4b88938fb
Gitweb:     https://git.kernel.org/tip/38cbae1434f8f7bbd8eaf24b29a385a4b88938fb
Author:     Ferdinand Blomqvist <ferdinand.blomqvist@gmail.com>
AuthorDate: Thu, 20 Jun 2019 17:10:38 +0300
Committer:  Thomas Gleixner <tglx@linutronix.de>
CommitDate: Wed, 26 Jun 2019 14:55:47 +0200

rslib: Update documentation

The decoder returns the number of corrected symbols, not bits.
The caller provided syndrome must be in index form.

Signed-off-by: Ferdinand Blomqvist <ferdinand.blomqvist@gmail.com>
Signed-off-by: Thomas Gleixner <tglx@linutronix.de>
Link: https://lkml.kernel.org/r/20190620141039.9874-7-ferdinand.blomqvist@gmail.com

---
 lib/reed_solomon/reed_solomon.c | 12 ++++++++----
 1 file changed, 8 insertions(+), 4 deletions(-)

diff --git a/lib/reed_solomon/reed_solomon.c b/lib/reed_solomon/reed_solomon.c
index e5fdc8b9e856..bbc01bad3053 100644
--- a/lib/reed_solomon/reed_solomon.c
+++ b/lib/reed_solomon/reed_solomon.c
@@ -340,7 +340,8 @@ EXPORT_SYMBOL_GPL(encode_rs8);
  *  @data:	data field of a given type
  *  @par:	received parity data field
  *  @len:	data length
- *  @s:		syndrome data field (if NULL, syndrome is calculated)
+ *  @s: 	syndrome data field, must be in index form
+ *		(if NULL, syndrome is calculated)
  *  @no_eras:	number of erasures
  *  @eras_pos:	position of erasures, can be NULL
  *  @invmsk:	invert data mask (will be xored on data, not on parity!)
@@ -354,7 +355,8 @@ EXPORT_SYMBOL_GPL(encode_rs8);
  *  decoding, so the caller has to ensure that decoder invocations are
  *  serialized.
  *
- *  Returns the number of corrected bits or -EBADMSG for uncorrectable errors.
+ *  Returns the number of corrected symbols or -EBADMSG for uncorrectable
+ *  errors. The count includes errors in the parity.
  */
 int decode_rs8(struct rs_control *rsc, uint8_t *data, uint16_t *par, int len,
 	       uint16_t *s, int no_eras, int *eras_pos, uint16_t invmsk,
@@ -391,7 +393,8 @@ EXPORT_SYMBOL_GPL(encode_rs16);
  *  @data:	data field of a given type
  *  @par:	received parity data field
  *  @len:	data length
- *  @s:		syndrome data field (if NULL, syndrome is calculated)
+ *  @s: 	syndrome data field, must be in index form
+ *		(if NULL, syndrome is calculated)
  *  @no_eras:	number of erasures
  *  @eras_pos:	position of erasures, can be NULL
  *  @invmsk:	invert data mask (will be xored on data, not on parity!)
@@ -403,7 +406,8 @@ EXPORT_SYMBOL_GPL(encode_rs16);
  *  decoding, so the caller has to ensure that decoder invocations are
  *  serialized.
  *
- *  Returns the number of corrected bits or -EBADMSG for uncorrectable errors.
+ *  Returns the number of corrected symbols or -EBADMSG for uncorrectable
+ *  errors. The count includes errors in the parity.
  */
 int decode_rs16(struct rs_control *rsc, uint16_t *data, uint16_t *par, int len,
 		uint16_t *s, int no_eras, int *eras_pos, uint16_t invmsk,

[tip:core/rslib] rslib: Fix remaining decoder flaws

[tip-bot for Ferdinand Blomqvist]

Commit-ID:  991305dee585dd9e3107b2e253778ed02ee3fbd1
Gitweb:     https://git.kernel.org/tip/991305dee585dd9e3107b2e253778ed02ee3fbd1
Author:     Ferdinand Blomqvist <ferdinand.blomqvist@gmail.com>
AuthorDate: Thu, 20 Jun 2019 17:10:39 +0300
Committer:  Thomas Gleixner <tglx@linutronix.de>
CommitDate: Wed, 26 Jun 2019 14:55:47 +0200

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 | 88 ++++++++++++++++++++++++++++++++++----------
 1 file changed, 68 insertions(+), 20 deletions(-)

diff --git a/lib/reed_solomon/decode_rs.c b/lib/reed_solomon/decode_rs.c
index b7264a712d46..805de84ae83d 100644
--- a/lib/reed_solomon/decode_rs.c
+++ b/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) {
-			uint16_t cor = alpha_to[rs_modnn(rs,index_of[num1] +
-						       index_of[num2] +
-						       nn - index_of[den])];
-			/* Store the error correction pattern, if a
-			 * correction buffer is available */
-			if (corr) {
-				corr[j] = cor;
-			} else {
-				/* If a data buffer is given and the
-				 * error is inside the message,
-				 * correct it */
-				if (data && (loc[j] < (nn - nroots)))
-					data[loc[j] - pad] ^= cor;
-			}
+
+		b[j] = alpha_to[rs_modnn(rs, index_of[num1] +
+					       index_of[num2] +
+					       nn - index_of[den])];
+		num_corrected++;
+	}
+
+	/*
+	 * We compute the syndrome of the 'error' and check that it matches
+	 * the syndrome of the received word
+	 */
+	for (i = 0; i < nroots; i++) {
+		tmp = 0;
+		for (j = 0; j < count; j++) {
+			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;
 	}
 
-	if (eras_pos != NULL) {
-		for (i = 0; i < count; i++)
-			eras_pos[i] = loc[i] - pad;
+	/*
+	 * 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];
+		}
 	}
-	return count;
 
+	return  num_corrected;
 }

Re: [PATCH v2 1/7] rslib: Add tests for the encoder and decoder

[Geert Uytterhoeven]

Hi Ferdinand,

On Thu, Jun 20, 2019 at 4:13 PM Ferdinand Blomqvist
<ferdinand.blomqvist@gmail.com> wrote:
> A Reed-Solomon code with minimum distance d can correct any error and
> erasure pattern that satisfies 2 * #error + #erasures < d. If the
> error correction capacity is exceeded, then correct decoding cannot be
> guaranteed. The decoder must, however, return a valid codeword or report
> failure.

> Note that the tests take a couple of minutes to complete.

On which hardware? ;-)

JFTR, the test succeeded on m68k, after 6 hours and 12 minutes of runtime
on an emulated Atari Falcon (ARAnyM hosted by an i7-4770).
So far I have no plans to run it on bare metal.

Gr{oetje,eeting}s,

                        Geert


--
Geert Uytterhoeven -- There's lots of Linux beyond ia32 -- geert@linux-m68k.org

In personal conversations with technical people, I call myself a hacker. But
when I'm talking to journalists I just say "programmer" or something like that.
                                -- Linus Torvalds

Re: [PATCH v2 1/7] rslib: Add tests for the encoder and decoder

[Thomas Gleixner]

On Tue, 9 Jul 2019, Geert Uytterhoeven wrote:

> Hi Ferdinand,
> 
> On Thu, Jun 20, 2019 at 4:13 PM Ferdinand Blomqvist
> <ferdinand.blomqvist@gmail.com> wrote:
> > A Reed-Solomon code with minimum distance d can correct any error and
> > erasure pattern that satisfies 2 * #error + #erasures < d. If the
> > error correction capacity is exceeded, then correct decoding cannot be
> > guaranteed. The decoder must, however, return a valid codeword or report
> > failure.
> 
> > Note that the tests take a couple of minutes to complete.
> 
> On which hardware? ;-)
> 
> JFTR, the test succeeded on m68k, after 6 hours and 12 minutes of runtime
> on an emulated Atari Falcon (ARAnyM hosted by an i7-4770).
> So far I have no plans to run it on bare metal.

It took about 4 minutes on a 10 year old lame desktop and was way faster on
one of the big irons.

Thanks,

	tglx