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-rw-r--r--lib/reed_solomon/decode_rs.c326
1 files changed, 326 insertions, 0 deletions
diff --git a/lib/reed_solomon/decode_rs.c b/lib/reed_solomon/decode_rs.c
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+++ b/lib/reed_solomon/decode_rs.c
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+// SPDX-License-Identifier: GPL-2.0
+/*
+ * Generic Reed Solomon encoder / decoder library
+ *
+ * Copyright 2002, Phil Karn, KA9Q
+ * May be used under the terms of the GNU General Public License (GPL)
+ *
+ * Adaption to the kernel by Thomas Gleixner (tglx@linutronix.de)
+ *
+ * Generic data width independent code which is included by the wrappers.
+ */
+{
+ struct rs_codec *rs = rsc->codec;
+ int deg_lambda, el, deg_omega;
+ int i, j, r, k, pad;
+ int nn = rs->nn;
+ int nroots = rs->nroots;
+ int fcr = rs->fcr;
+ int prim = rs->prim;
+ int iprim = rs->iprim;
+ uint16_t *alpha_to = rs->alpha_to;
+ 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;
+
+ /*
+ * The decoder buffers are in the rs control struct. They are
+ * arrays sized [nroots + 1]
+ */
+ uint16_t *lambda = rsc->buffers + RS_DECODE_LAMBDA * (nroots + 1);
+ uint16_t *syn = rsc->buffers + RS_DECODE_SYN * (nroots + 1);
+ uint16_t *b = rsc->buffers + RS_DECODE_B * (nroots + 1);
+ uint16_t *t = rsc->buffers + RS_DECODE_T * (nroots + 1);
+ uint16_t *omega = rsc->buffers + RS_DECODE_OMEGA * (nroots + 1);
+ uint16_t *root = rsc->buffers + RS_DECODE_ROOT * (nroots + 1);
+ uint16_t *reg = rsc->buffers + RS_DECODE_REG * (nroots + 1);
+ uint16_t *loc = rsc->buffers + RS_DECODE_LOC * (nroots + 1);
+
+ /* Check length parameter for validity */
+ pad = nn - nroots - len;
+ BUG_ON(pad < 0 || pad >= nn - nroots);
+
+ /* Does the caller provide the syndrome ? */
+ 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) */
+ for (i = 0; i < nroots; i++)
+ syn[i] = (((uint16_t) data[0]) ^ invmsk) & msk;
+
+ for (j = 1; j < len; j++) {
+ for (i = 0; i < nroots; i++) {
+ if (syn[i] == 0) {
+ syn[i] = (((uint16_t) data[j]) ^
+ invmsk) & msk;
+ } else {
+ syn[i] = ((((uint16_t) data[j]) ^
+ invmsk) & msk) ^
+ alpha_to[rs_modnn(rs, index_of[syn[i]] +
+ (fcr + i) * prim)];
+ }
+ }
+ }
+
+ for (j = 0; j < nroots; j++) {
+ for (i = 0; i < nroots; i++) {
+ if (syn[i] == 0) {
+ syn[i] = ((uint16_t) par[j]) & msk;
+ } else {
+ syn[i] = (((uint16_t) par[j]) & msk) ^
+ alpha_to[rs_modnn(rs, index_of[syn[i]] +
+ (fcr+i)*prim)];
+ }
+ }
+ }
+ s = syn;
+
+ /* Convert syndromes to index form, checking for nonzero condition */
+ syn_error = 0;
+ for (i = 0; i < nroots; i++) {
+ syn_error |= s[i];
+ s[i] = index_of[s[i]];
+ }
+
+ if (!syn_error) {
+ /* if syndrome is zero, data[] is a codeword and there are no
+ * errors to correct. So return data[] unmodified
+ */
+ return 0;
+ }
+
+ decode:
+ memset(&lambda[1], 0, nroots * sizeof(lambda[0]));
+ lambda[0] = 1;
+
+ 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] + pad)))];
+ for (i = 1; i < no_eras; 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) {
+ lambda[j] ^=
+ alpha_to[rs_modnn(rs, u + tmp)];
+ }
+ }
+ }
+ }
+
+ for (i = 0; i < nroots + 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 <= nroots) { /* 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 - 1] != nn)) {
+ discr_r ^=
+ alpha_to[rs_modnn(rs,
+ index_of[lambda[i]] +
+ s[r - i - 1])];
+ }
+ }
+ discr_r = index_of[discr_r]; /* Index form */
+ if (discr_r == nn) {
+ /* 2 lines below: B(x) <-- x*B(x) */
+ memmove (&b[1], b, nroots * sizeof (b[0]));
+ b[0] = nn;
+ } else {
+ /* 7 lines below: T(x) <-- lambda(x)-discr_r*x*b(x) */
+ t[0] = lambda[0];
+ for (i = 0; i < nroots; i++) {
+ if (b[i] != nn) {
+ t[i + 1] = lambda[i + 1] ^
+ alpha_to[rs_modnn(rs, 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 <= nroots; i++) {
+ b[i] = (lambda[i] == 0) ? nn :
+ rs_modnn(rs, index_of[lambda[i]]
+ - discr_r + nn);
+ }
+ } else {
+ /* 2 lines below: B(x) <-- x*B(x) */
+ memmove(&b[1], b, nroots * sizeof(b[0]));
+ b[0] = nn;
+ }
+ memcpy(lambda, t, (nroots + 1) * sizeof(t[0]));
+ }
+ }
+
+ /* Convert lambda to index form and compute deg(lambda(x)) */
+ deg_lambda = 0;
+ for (i = 0; i < nroots + 1; i++) {
+ lambda[i] = index_of[lambda[i]];
+ 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) */
+ for (i = 1, k = iprim - 1; i <= nn; i++, k = rs_modnn(rs, k + iprim)) {
+ q = 1; /* lambda[0] is always 0 */
+ for (j = deg_lambda; j > 0; j--) {
+ if (reg[j] != nn) {
+ reg[j] = rs_modnn(rs, reg[j] + j);
+ q ^= alpha_to[reg[j]];
+ }
+ }
+ 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;
+ /* 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
+ */
+ return -EBADMSG;
+ }
+ /*
+ * Compute err+eras evaluator poly omega(x) = s(x)*lambda(x) (modulo
+ * x**nroots). in index form. Also find deg(omega).
+ */
+ deg_omega = deg_lambda - 1;
+ for (i = 0; i <= deg_omega; i++) {
+ tmp = 0;
+ for (j = i; j >= 0; j--) {
+ if ((s[i - j] != nn) && (lambda[j] != nn))
+ tmp ^=
+ alpha_to[rs_modnn(rs, s[i - j] + lambda[j])];
+ }
+ omega[i] = index_of[tmp];
+ }
+
+ /*
+ * 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--) {
+ if (omega[i] != nn)
+ 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;
+
+ /* lambda[i+1] for i even is the formal derivative
+ * lambda_pr of lambda[i] */
+ for (i = min(deg_lambda, nroots - 1) & ~1; i >= 0; i -= 2) {
+ if (lambda[i + 1] != nn) {
+ den ^= alpha_to[rs_modnn(rs, lambda[i + 1] +
+ i * root[j])];
+ }
+ }
+
+ 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;
+ }
+
+ /*
+ * 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 num_corrected;
+}
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