272 lines
6.8 KiB
C
272 lines
6.8 KiB
C
/*
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* lib/reed_solomon/decode_rs.c
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*
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* Overview:
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* Generic Reed Solomon encoder / decoder library
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*
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* Copyright 2002, Phil Karn, KA9Q
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* May be used under the terms of the GNU General Public License (GPL)
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*
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* Adaption to the kernel by Thomas Gleixner (tglx@linutronix.de)
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*
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* $Id: decode_rs.c,v 1.7 2005/11/07 11:14:59 gleixner Exp $
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*
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*/
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/* Generic data width independent code which is included by the
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* wrappers.
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*/
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{
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int deg_lambda, el, deg_omega;
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int i, j, r, k, pad;
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int nn = rs->nn;
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int nroots = rs->nroots;
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int fcr = rs->fcr;
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int prim = rs->prim;
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int iprim = rs->iprim;
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uint16_t *alpha_to = rs->alpha_to;
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uint16_t *index_of = rs->index_of;
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uint16_t u, q, tmp, num1, num2, den, discr_r, syn_error;
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/* Err+Eras Locator poly and syndrome poly The maximum value
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* of nroots is 8. So the necessary stack size will be about
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* 220 bytes max.
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*/
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uint16_t lambda[nroots + 1], syn[nroots];
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uint16_t b[nroots + 1], t[nroots + 1], omega[nroots + 1];
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uint16_t root[nroots], reg[nroots + 1], loc[nroots];
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int count = 0;
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uint16_t msk = (uint16_t) rs->nn;
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/* Check length parameter for validity */
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pad = nn - nroots - len;
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if (pad < 0 || pad >= nn)
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return -ERANGE;
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/* Does the caller provide the syndrome ? */
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if (s != NULL)
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goto decode;
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/* form the syndromes; i.e., evaluate data(x) at roots of
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* g(x) */
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for (i = 0; i < nroots; i++)
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syn[i] = (((uint16_t) data[0]) ^ invmsk) & msk;
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for (j = 1; j < len; j++) {
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for (i = 0; i < nroots; i++) {
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if (syn[i] == 0) {
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syn[i] = (((uint16_t) data[j]) ^
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invmsk) & msk;
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} else {
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syn[i] = ((((uint16_t) data[j]) ^
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invmsk) & msk) ^
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alpha_to[rs_modnn(rs, index_of[syn[i]] +
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(fcr + i) * prim)];
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}
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}
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}
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for (j = 0; j < nroots; j++) {
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for (i = 0; i < nroots; i++) {
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if (syn[i] == 0) {
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syn[i] = ((uint16_t) par[j]) & msk;
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} else {
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syn[i] = (((uint16_t) par[j]) & msk) ^
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alpha_to[rs_modnn(rs, index_of[syn[i]] +
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(fcr+i)*prim)];
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}
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}
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}
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s = syn;
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/* Convert syndromes to index form, checking for nonzero condition */
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syn_error = 0;
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for (i = 0; i < nroots; i++) {
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syn_error |= s[i];
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s[i] = index_of[s[i]];
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}
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if (!syn_error) {
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/* if syndrome is zero, data[] is a codeword and there are no
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* errors to correct. So return data[] unmodified
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*/
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count = 0;
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goto finish;
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}
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decode:
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memset(&lambda[1], 0, nroots * sizeof(lambda[0]));
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lambda[0] = 1;
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if (no_eras > 0) {
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/* Init lambda to be the erasure locator polynomial */
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lambda[1] = alpha_to[rs_modnn(rs,
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prim * (nn - 1 - eras_pos[0]))];
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for (i = 1; i < no_eras; i++) {
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u = rs_modnn(rs, prim * (nn - 1 - eras_pos[i]));
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for (j = i + 1; j > 0; j--) {
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tmp = index_of[lambda[j - 1]];
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if (tmp != nn) {
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lambda[j] ^=
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alpha_to[rs_modnn(rs, u + tmp)];
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}
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}
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}
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}
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for (i = 0; i < nroots + 1; i++)
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b[i] = index_of[lambda[i]];
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/*
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* Begin Berlekamp-Massey algorithm to determine error+erasure
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* locator polynomial
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*/
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r = no_eras;
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el = no_eras;
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while (++r <= nroots) { /* r is the step number */
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/* Compute discrepancy at the r-th step in poly-form */
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discr_r = 0;
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for (i = 0; i < r; i++) {
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if ((lambda[i] != 0) && (s[r - i - 1] != nn)) {
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discr_r ^=
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alpha_to[rs_modnn(rs,
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index_of[lambda[i]] +
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s[r - i - 1])];
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}
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}
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discr_r = index_of[discr_r]; /* Index form */
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if (discr_r == nn) {
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/* 2 lines below: B(x) <-- x*B(x) */
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memmove (&b[1], b, nroots * sizeof (b[0]));
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b[0] = nn;
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} else {
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/* 7 lines below: T(x) <-- lambda(x)-discr_r*x*b(x) */
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t[0] = lambda[0];
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for (i = 0; i < nroots; i++) {
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if (b[i] != nn) {
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t[i + 1] = lambda[i + 1] ^
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alpha_to[rs_modnn(rs, discr_r +
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b[i])];
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} else
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t[i + 1] = lambda[i + 1];
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}
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if (2 * el <= r + no_eras - 1) {
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el = r + no_eras - el;
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/*
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* 2 lines below: B(x) <-- inv(discr_r) *
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* lambda(x)
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*/
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for (i = 0; i <= nroots; i++) {
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b[i] = (lambda[i] == 0) ? nn :
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rs_modnn(rs, index_of[lambda[i]]
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- discr_r + nn);
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}
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} else {
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/* 2 lines below: B(x) <-- x*B(x) */
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memmove(&b[1], b, nroots * sizeof(b[0]));
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b[0] = nn;
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}
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memcpy(lambda, t, (nroots + 1) * sizeof(t[0]));
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}
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}
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/* Convert lambda to index form and compute deg(lambda(x)) */
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deg_lambda = 0;
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for (i = 0; i < nroots + 1; i++) {
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lambda[i] = index_of[lambda[i]];
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if (lambda[i] != nn)
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deg_lambda = i;
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}
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/* Find roots of error+erasure locator polynomial by Chien search */
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memcpy(®[1], &lambda[1], nroots * sizeof(reg[0]));
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count = 0; /* Number of roots of lambda(x) */
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for (i = 1, k = iprim - 1; i <= nn; i++, k = rs_modnn(rs, k + iprim)) {
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q = 1; /* lambda[0] is always 0 */
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for (j = deg_lambda; j > 0; j--) {
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if (reg[j] != nn) {
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reg[j] = rs_modnn(rs, reg[j] + j);
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q ^= alpha_to[reg[j]];
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}
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}
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if (q != 0)
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continue; /* Not a root */
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/* store root (index-form) and error location number */
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root[count] = i;
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loc[count] = k;
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/* If we've already found max possible roots,
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* abort the search to save time
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*/
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if (++count == deg_lambda)
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break;
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}
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if (deg_lambda != count) {
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/*
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* deg(lambda) unequal to number of roots => uncorrectable
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* error detected
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*/
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count = -1;
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goto finish;
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}
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/*
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* Compute err+eras evaluator poly omega(x) = s(x)*lambda(x) (modulo
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* x**nroots). in index form. Also find deg(omega).
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*/
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deg_omega = deg_lambda - 1;
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for (i = 0; i <= deg_omega; i++) {
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tmp = 0;
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for (j = i; j >= 0; j--) {
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if ((s[i - j] != nn) && (lambda[j] != nn))
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tmp ^=
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alpha_to[rs_modnn(rs, s[i - j] + lambda[j])];
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}
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omega[i] = index_of[tmp];
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}
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/*
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* Compute error values in poly-form. num1 = omega(inv(X(l))), num2 =
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* inv(X(l))**(fcr-1) and den = lambda_pr(inv(X(l))) all in poly-form
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*/
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for (j = count - 1; j >= 0; j--) {
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num1 = 0;
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for (i = deg_omega; i >= 0; i--) {
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if (omega[i] != nn)
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num1 ^= alpha_to[rs_modnn(rs, omega[i] +
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i * root[j])];
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}
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num2 = alpha_to[rs_modnn(rs, root[j] * (fcr - 1) + nn)];
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den = 0;
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/* lambda[i+1] for i even is the formal derivative
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* lambda_pr of lambda[i] */
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for (i = min(deg_lambda, nroots - 1) & ~1; i >= 0; i -= 2) {
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if (lambda[i + 1] != nn) {
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den ^= alpha_to[rs_modnn(rs, lambda[i + 1] +
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i * root[j])];
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}
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}
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/* Apply error to data */
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if (num1 != 0 && loc[j] >= pad) {
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uint16_t cor = alpha_to[rs_modnn(rs,index_of[num1] +
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index_of[num2] +
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nn - index_of[den])];
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/* Store the error correction pattern, if a
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* correction buffer is available */
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if (corr) {
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corr[j] = cor;
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} else {
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/* If a data buffer is given and the
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* error is inside the message,
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* correct it */
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if (data && (loc[j] < (nn - nroots)))
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data[loc[j] - pad] ^= cor;
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}
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}
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}
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finish:
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if (eras_pos != NULL) {
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for (i = 0; i < count; i++)
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eras_pos[i] = loc[i] - pad;
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}
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return count;
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}
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