Linux-2.6.12-rc2
Initial git repository build. I'm not bothering with the full history, even though we have it. We can create a separate "historical" git archive of that later if we want to, and in the meantime it's about 3.2GB when imported into git - space that would just make the early git days unnecessarily complicated, when we don't have a lot of good infrastructure for it. Let it rip!
This commit is contained in:
Linus Torvalds
272
lib/reed_solomon/decode_rs.c
Normal file
272
lib/reed_solomon/decode_rs.c
Normal file
@@ -0,0 +1,272 @@
|
||||
/*
|
||||
* lib/reed_solomon/decode_rs.c
|
||||
*
|
||||
* Overview:
|
||||
* 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)
|
||||
*
|
||||
* $Id: decode_rs.c,v 1.6 2004/10/22 15:41:47 gleixner Exp $
|
||||
*
|
||||
*/
|
||||
|
||||
/* Generic data width independent code which is included by the
|
||||
* wrappers.
|
||||
*/
|
||||
{
|
||||
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;
|
||||
/* Err+Eras Locator poly and syndrome poly The maximum value
|
||||
* of nroots is 8. So the necessary stack size will be about
|
||||
* 220 bytes max.
|
||||
*/
|
||||
uint16_t lambda[nroots + 1], syn[nroots];
|
||||
uint16_t b[nroots + 1], t[nroots + 1], omega[nroots + 1];
|
||||
uint16_t root[nroots], reg[nroots + 1], loc[nroots];
|
||||
int count = 0;
|
||||
uint16_t msk = (uint16_t) rs->nn;
|
||||
|
||||
/* Check length parameter for validity */
|
||||
pad = nn - nroots - len;
|
||||
if (pad < 0 || pad >= nn)
|
||||
return -ERANGE;
|
||||
|
||||
/* Does the caller provide the syndrome ? */
|
||||
if (s != NULL)
|
||||
goto decode;
|
||||
|
||||
/* 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
|
||||
*/
|
||||
count = 0;
|
||||
goto finish;
|
||||
}
|
||||
|
||||
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]))];
|
||||
for (i = 1; i < no_eras; i++) {
|
||||
u = rs_modnn(rs, prim * (nn - 1 - eras_pos[i]));
|
||||
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;
|
||||
}
|
||||
/* Find roots of error+erasure locator polynomial by Chien search */
|
||||
memcpy(®[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 */
|
||||
/* 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
|
||||
*/
|
||||
count = -1;
|
||||
goto finish;
|
||||
}
|
||||
/*
|
||||
* 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
|
||||
*/
|
||||
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])];
|
||||
}
|
||||
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])];
|
||||
}
|
||||
}
|
||||
/* 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;
|
||||
}
|
||||
}
|
||||
}
|
||||
|
||||
finish:
|
||||
if (eras_pos != NULL) {
|
||||
for (i = 0; i < count; i++)
|
||||
eras_pos[i] = loc[i] - pad;
|
||||
}
|
||||
return count;
|
||||
|
||||
}
|
||||
Reference in New Issue
Block a user