/* * 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 1.7 2005/11/07 11:14:59 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; BUG_ON(pad < 0 || pad >= nn); /* 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 = -EBADMSG; 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; }