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

@@ -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

lib/reed_solomon/Makefile

@@ -4,4 +4,4 @@
 #
 
 obj-$(CONFIG_REED_SOLOMON) += reed_solomon.o
-
+obj-$(CONFIG_REED_SOLOMON_TEST) += test_rslib.o

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");