lib/reed_solomon/decode_rs.c - third_party/kernel - Git at Google

 // SPDX-License-Identifier: GPL-2.0
 /*
  * 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)
  *
  * Generic data width independent code which is included by the wrappers.
  */
 {
 	struct rs_codec *rs = rsc->codec;
 	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;
 	int count = 0;
 	int num_corrected;
 	uint16_t msk = (uint16_t) rs->nn;

 	/*
 	 * The decoder buffers are in the rs control struct. They are
 	 * arrays sized [nroots + 1]
 	 */
 	uint16_t *lambda = rsc->buffers + RS_DECODE_LAMBDA * (nroots + 1);
 	uint16_t *syn = rsc->buffers + RS_DECODE_SYN * (nroots + 1);
 	uint16_t *b = rsc->buffers + RS_DECODE_B * (nroots + 1);
 	uint16_t *t = rsc->buffers + RS_DECODE_T * (nroots + 1);
 	uint16_t *omega = rsc->buffers + RS_DECODE_OMEGA * (nroots + 1);
 	uint16_t *root = rsc->buffers + RS_DECODE_ROOT * (nroots + 1);
 	uint16_t *reg = rsc->buffers + RS_DECODE_REG * (nroots + 1);
 	uint16_t *loc = rsc->buffers + RS_DECODE_LOC * (nroots + 1);

 	/* Check length parameter for validity */
 	pad = nn - nroots - len;
 	BUG_ON(pad < 0 || pad >= nn - nroots);

 	/* Does the caller provide the syndrome ? */
 	if (s != NULL) {
 		for (i = 0; i < nroots; i++) {
 			/* The syndrome is in index form,
 			 * so nn represents zero
 			 */
 			if (s[i] != nn)
 				goto decode;
 		}

 		/* syndrome is zero, no errors to correct  */
 		return 0;
 	}

 	/* 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
 		 */
 		return 0;
 	}

  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] + pad)))];
 		for (i = 1; i < no_eras; i++) {
 			u = rs_modnn(rs, prim * (nn - 1 - (eras_pos[i] + pad)));
 			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;
 	}

 	if (deg_lambda == 0) {
 		/*
 		 * deg(lambda) is zero even though the syndrome is non-zero
 		 * => uncorrectable error detected
 		 */
 		return -EBADMSG;
 	}

 	/* 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 */

 		if (k < pad) {
 			/* Impossible error location. Uncorrectable error. */
 			return -EBADMSG;
 		}

 		/* 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
 		 */
 		return -EBADMSG;
 	}
 	/*
 	 * 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
 	 * Note: we reuse the buffer for b to store the correction pattern
 	 */
 	num_corrected = 0;
 	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])];
 		}

 		if (num1 == 0) {
 			/* Nothing to correct at this position */
 			b[j] = 0;
 			continue;
 		}

 		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])];
 			}
 		}

 		b[j] = alpha_to[rs_modnn(rs, index_of[num1] +
 					       index_of[num2] +
 					       nn - index_of[den])];
 		num_corrected++;
 	}

 	/*
 	 * We compute the syndrome of the 'error' and check that it matches
 	 * the syndrome of the received word
 	 */
 	for (i = 0; i < nroots; i++) {
 		tmp = 0;
 		for (j = 0; j < count; j++) {
 			if (b[j] == 0)
 				continue;

 			k = (fcr + i) * prim * (nn-loc[j]-1);
 			tmp ^= alpha_to[rs_modnn(rs, index_of[b[j]] + k)];
 		}

 		if (tmp != alpha_to[s[i]])
 			return -EBADMSG;
 	}

 	/*
 	 * Store the error correction pattern, if a
 	 * correction buffer is available
 	 */
 	if (corr && eras_pos) {
 		j = 0;
 		for (i = 0; i < count; i++) {
 			if (b[i]) {
 				corr[j] = b[i];
 				eras_pos[j++] = loc[i] - pad;
 			}
 		}
 	} else if (data && par) {
 		/* Apply error to data and parity */
 		for (i = 0; i < count; i++) {
 			if (loc[i] < (nn - nroots))
 				data[loc[i] - pad] ^= b[i];
 			else
 				par[loc[i] - pad - len] ^= b[i];
 		}
 	}

 	return  num_corrected;
 }
	// SPDX-License-Identifier: GPL-2.0
	/*
	* 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)
	*
	* Generic data width independent code which is included by the wrappers.
	*/
	{
	struct rs_codec *rs = rsc->codec;
	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;
	int count = 0;
	int num_corrected;
	uint16_t msk = (uint16_t) rs->nn;

	/*
	* The decoder buffers are in the rs control struct. They are
	* arrays sized [nroots + 1]
	*/
	uint16_t lambda = rsc->buffers + RS_DECODE_LAMBDA (nroots + 1);
	uint16_t syn = rsc->buffers + RS_DECODE_SYN (nroots + 1);
	uint16_t b = rsc->buffers + RS_DECODE_B (nroots + 1);
	uint16_t t = rsc->buffers + RS_DECODE_T (nroots + 1);
	uint16_t omega = rsc->buffers + RS_DECODE_OMEGA (nroots + 1);
	uint16_t root = rsc->buffers + RS_DECODE_ROOT (nroots + 1);
	uint16_t reg = rsc->buffers + RS_DECODE_REG (nroots + 1);
	uint16_t loc = rsc->buffers + RS_DECODE_LOC (nroots + 1);

	/* Check length parameter for validity */
	pad = nn - nroots - len;
	BUG_ON(pad < 0 \|\| pad >= nn - nroots);

	/* Does the caller provide the syndrome ? */
	if (s != NULL) {
	for (i = 0; i < nroots; i++) {
	/* The syndrome is in index form,
	* so nn represents zero
	*/
	if (s[i] != nn)
	goto decode;
	}

	/* syndrome is zero, no errors to correct */
	return 0;
	}

	/* 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
	*/
	return 0;
	}

	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] + pad)))];
	for (i = 1; i < no_eras; i++) {
	u = rs_modnn(rs, prim * (nn - 1 - (eras_pos[i] + pad)));
	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;
	}

	if (deg_lambda == 0) {
	/*
	* deg(lambda) is zero even though the syndrome is non-zero
	* => uncorrectable error detected
	*/
	return -EBADMSG;
	}

	/* 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 */

	if (k < pad) {
	/* Impossible error location. Uncorrectable error. */
	return -EBADMSG;
	}

	/* 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
	*/
	return -EBADMSG;
	}
	/*
	* 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
	* Note: we reuse the buffer for b to store the correction pattern
	*/
	num_corrected = 0;
	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])];
	}

	if (num1 == 0) {
	/* Nothing to correct at this position */
	b[j] = 0;
	continue;
	}

	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])];
	}
	}

	b[j] = alpha_to[rs_modnn(rs, index_of[num1] +
	index_of[num2] +
	nn - index_of[den])];
	num_corrected++;
	}

	/*
	* We compute the syndrome of the 'error' and check that it matches
	* the syndrome of the received word
	*/
	for (i = 0; i < nroots; i++) {
	tmp = 0;
	for (j = 0; j < count; j++) {
	if (b[j] == 0)
	continue;

	k = (fcr + i) * prim * (nn-loc[j]-1);
	tmp ^= alpha_to[rs_modnn(rs, index_of[b[j]] + k)];
	}

	if (tmp != alpha_to[s[i]])
	return -EBADMSG;
	}

	/*
	* Store the error correction pattern, if a
	* correction buffer is available
	*/
	if (corr && eras_pos) {
	j = 0;
	for (i = 0; i < count; i++) {
	if (b[i]) {
	corr[j] = b[i];
	eras_pos[j++] = loc[i] - pad;
	}
	}
	} else if (data && par) {
	/* Apply error to data and parity */
	for (i = 0; i < count; i++) {
	if (loc[i] < (nn - nroots))
	data[loc[i] - pad] ^= b[i];
	else
	par[loc[i] - pad - len] ^= b[i];
	}
	}

	return num_corrected;
	}