diff options
Diffstat (limited to 'lib/reed_solomon/decode_rs.c')
-rw-r--r-- | lib/reed_solomon/decode_rs.c | 272 |
1 files changed, 272 insertions, 0 deletions
diff --git a/lib/reed_solomon/decode_rs.c b/lib/reed_solomon/decode_rs.c new file mode 100644 index 0000000..d401dec --- /dev/null +++ b/lib/reed_solomon/decode_rs.c @@ -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; + +} |