lib/reed_solomon/decode_rs.c - fp2-dev/kernel/msm - Gitiles

 /*
  * 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;

 }
	/*
	* 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) <-- xB(x) /
	memmove (&b[1], b, nroots * sizeof (b[0]));
	b[0] = nn;
	} else {
	/* 7 lines below: T(x) <-- lambda(x)-discr_rxb(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) <-- xB(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;

	}