/*

   * 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(&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 */
  		/* 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;
  
  }