[linux-2.6-block.git] / lib / reed_solomon / decode_rs.c

// 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;
	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)
		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
		 */
		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;
	}
	/* 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
		 */
		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
	 */
	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;
			}
		}
	}

	if (eras_pos != NULL) {
		for (i = 0; i < count; i++)
			eras_pos[i] = loc[i] - pad;
	}
	return count;

}
Commit	Line	Data
dc8f923e	1	// SPDX-License-Identifier: GPL-2.0
03ead842	2	/*
3413e189	3	* Generic Reed Solomon encoder / decoder library
03ead842	4	*
1da177e4 LT	5	* Copyright 2002, Phil Karn, KA9Q
	6	* May be used under the terms of the GNU General Public License (GPL)
	7	*
	8	* Adaption to the kernel by Thomas Gleixner (tglx@linutronix.de)
	9	*
3413e189	10	* Generic data width independent code which is included by the wrappers.
1da177e4	11	*/
03ead842	12	{
21633981	13	struct rs_codec *rs = rsc->codec;
1da177e4 LT	14	int deg_lambda, el, deg_omega;
	15	int i, j, r, k, pad;
	16	int nn = rs->nn;
	17	int nroots = rs->nroots;
	18	int fcr = rs->fcr;
	19	int prim = rs->prim;
	20	int iprim = rs->iprim;
	21	uint16_t *alpha_to = rs->alpha_to;
	22	uint16_t *index_of = rs->index_of;
	23	uint16_t u, q, tmp, num1, num2, den, discr_r, syn_error;
1da177e4 LT	24	int count = 0;
	25	uint16_t msk = (uint16_t) rs->nn;
	26
45888b40 TG	27	/*
	28	* The decoder buffers are in the rs control struct. They are
	29	* arrays sized [nroots + 1]
	30	*/
	31	uint16_t lambda = rsc->buffers + RS_DECODE_LAMBDA (nroots + 1);
	32	uint16_t syn = rsc->buffers + RS_DECODE_SYN (nroots + 1);
	33	uint16_t b = rsc->buffers + RS_DECODE_B (nroots + 1);
	34	uint16_t t = rsc->buffers + RS_DECODE_T (nroots + 1);
	35	uint16_t omega = rsc->buffers + RS_DECODE_OMEGA (nroots + 1);
	36	uint16_t root = rsc->buffers + RS_DECODE_ROOT (nroots + 1);
	37	uint16_t reg = rsc->buffers + RS_DECODE_REG (nroots + 1);
	38	uint16_t loc = rsc->buffers + RS_DECODE_LOC (nroots + 1);
	39
1da177e4 LT	40	/* Check length parameter for validity */
1da177e4 LT	41	pad = nn - nroots - len;
a343536f	42	BUG_ON(pad < 0 \|\| pad >= nn - nroots);
03ead842	43
1da177e4	44	/* Does the caller provide the syndrome ? */
03ead842	45	if (s != NULL)
1da177e4 LT	46	goto decode;
	47
	48	/* form the syndromes; i.e., evaluate data(x) at roots of
	49	* g(x) */
	50	for (i = 0; i < nroots; i++)
	51	syn[i] = (((uint16_t) data[0]) ^ invmsk) & msk;
	52
	53	for (j = 1; j < len; j++) {
	54	for (i = 0; i < nroots; i++) {
	55	if (syn[i] == 0) {
03ead842	56	syn[i] = (((uint16_t) data[j]) ^
1da177e4 LT	57	invmsk) & msk;
	58	} else {
	59	syn[i] = ((((uint16_t) data[j]) ^
03ead842	60	invmsk) & msk) ^
1da177e4 LT	61	alpha_to[rs_modnn(rs, index_of[syn[i]] +
	62	(fcr + i) * prim)];
	63	}
	64	}
	65	}
	66
	67	for (j = 0; j < nroots; j++) {
	68	for (i = 0; i < nroots; i++) {
	69	if (syn[i] == 0) {
	70	syn[i] = ((uint16_t) par[j]) & msk;
	71	} else {
03ead842	72	syn[i] = (((uint16_t) par[j]) & msk) ^
1da177e4 LT	73	alpha_to[rs_modnn(rs, index_of[syn[i]] +
	74	(fcr+i)*prim)];
	75	}
	76	}
	77	}
	78	s = syn;
	79
	80	/* Convert syndromes to index form, checking for nonzero condition */
	81	syn_error = 0;
	82	for (i = 0; i < nroots; i++) {
	83	syn_error \|= s[i];
	84	s[i] = index_of[s[i]];
	85	}
	86
	87	if (!syn_error) {
	88	/* if syndrome is zero, data[] is a codeword and there are no
	89	* errors to correct. So return data[] unmodified
	90	*/
647cc9ec	91	return 0;
1da177e4 LT	92	}
	93
	94	decode:
	95	memset(&lambda[1], 0, nroots * sizeof(lambda[0]));
	96	lambda[0] = 1;
	97
	98	if (no_eras > 0) {
	99	/* Init lambda to be the erasure locator polynomial */
03ead842	100	lambda[1] = alpha_to[rs_modnn(rs,
2034a42d	101	prim * (nn - 1 - (eras_pos[0] + pad)))];
1da177e4	102	for (i = 1; i < no_eras; i++) {
2034a42d	103	u = rs_modnn(rs, prim * (nn - 1 - (eras_pos[i] + pad)));
1da177e4 LT	104	for (j = i + 1; j > 0; j--) {
	105	tmp = index_of[lambda[j - 1]];
	106	if (tmp != nn) {
03ead842	107	lambda[j] ^=
1da177e4 LT	108	alpha_to[rs_modnn(rs, u + tmp)];
	109	}
	110	}
	111	}
	112	}
	113
	114	for (i = 0; i < nroots + 1; i++)
	115	b[i] = index_of[lambda[i]];
	116
	117	/*
	118	* Begin Berlekamp-Massey algorithm to determine error+erasure
	119	* locator polynomial
	120	*/
	121	r = no_eras;
	122	el = no_eras;
	123	while (++r <= nroots) { /* r is the step number */
	124	/* Compute discrepancy at the r-th step in poly-form */
	125	discr_r = 0;
	126	for (i = 0; i < r; i++) {
	127	if ((lambda[i] != 0) && (s[r - i - 1] != nn)) {
03ead842 TG	128	discr_r ^=
03ead842 TG	129	alpha_to[rs_modnn(rs,
1da177e4 LT	130	index_of[lambda[i]] +
	131	s[r - i - 1])];
	132	}
	133	}
	134	discr_r = index_of[discr_r]; /* Index form */
	135	if (discr_r == nn) {
	136	/* 2 lines below: B(x) <-- xB(x) /
	137	memmove (&b[1], b, nroots * sizeof (b[0]));
	138	b[0] = nn;
	139	} else {
	140	/* 7 lines below: T(x) <-- lambda(x)-discr_rxb(x) */
	141	t[0] = lambda[0];
	142	for (i = 0; i < nroots; i++) {
	143	if (b[i] != nn) {
03ead842	144	t[i + 1] = lambda[i + 1] ^
1da177e4 LT	145	alpha_to[rs_modnn(rs, discr_r +
	146	b[i])];
	147	} else
	148	t[i + 1] = lambda[i + 1];
	149	}
	150	if (2 * el <= r + no_eras - 1) {
	151	el = r + no_eras - el;
	152	/*
	153	* 2 lines below: B(x) <-- inv(discr_r) *
	154	* lambda(x)
	155	*/
	156	for (i = 0; i <= nroots; i++) {
	157	b[i] = (lambda[i] == 0) ? nn :
	158	rs_modnn(rs, index_of[lambda[i]]
	159	- discr_r + nn);
	160	}
	161	} else {
	162	/* 2 lines below: B(x) <-- xB(x) /
	163	memmove(&b[1], b, nroots * sizeof(b[0]));
	164	b[0] = nn;
	165	}
	166	memcpy(lambda, t, (nroots + 1) * sizeof(t[0]));
	167	}
	168	}
	169
	170	/* Convert lambda to index form and compute deg(lambda(x)) */
	171	deg_lambda = 0;
	172	for (i = 0; i < nroots + 1; i++) {
	173	lambda[i] = index_of[lambda[i]];
	174	if (lambda[i] != nn)
	175	deg_lambda = i;
	176	}
	177	/* Find roots of error+erasure locator polynomial by Chien search */
	178	memcpy(&reg[1], &lambda[1], nroots * sizeof(reg[0]));
	179	count = 0; /* Number of roots of lambda(x) */
	180	for (i = 1, k = iprim - 1; i <= nn; i++, k = rs_modnn(rs, k + iprim)) {
	181	q = 1; /* lambda[0] is always 0 */
	182	for (j = deg_lambda; j > 0; j--) {
	183	if (reg[j] != nn) {
	184	reg[j] = rs_modnn(rs, reg[j] + j);
	185	q ^= alpha_to[reg[j]];
	186	}
	187	}
	188	if (q != 0)
	189	continue; /* Not a root */
	190	/* store root (index-form) and error location number */
	191	root[count] = i;
	192	loc[count] = k;
	193	/* If we've already found max possible roots,
	194	* abort the search to save time
	195	*/
	196	if (++count == deg_lambda)
	197	break;
	198	}
	199	if (deg_lambda != count) {
	200	/*
	201	* deg(lambda) unequal to number of roots => uncorrectable
	202	* error detected
	203	*/
647cc9ec	204	return -EBADMSG;
1da177e4 LT	205	}
	206	/*
	207	* Compute err+eras evaluator poly omega(x) = s(x)*lambda(x) (modulo
	208	* x**nroots). in index form. Also find deg(omega).
	209	*/
	210	deg_omega = deg_lambda - 1;
	211	for (i = 0; i <= deg_omega; i++) {
	212	tmp = 0;
	213	for (j = i; j >= 0; j--) {
	214	if ((s[i - j] != nn) && (lambda[j] != nn))
	215	tmp ^=
	216	alpha_to[rs_modnn(rs, s[i - j] + lambda[j])];
	217	}
	218	omega[i] = index_of[tmp];
	219	}
	220
	221	/*
	222	* Compute error values in poly-form. num1 = omega(inv(X(l))), num2 =
	223	* inv(X(l))**(fcr-1) and den = lambda_pr(inv(X(l))) all in poly-form
	224	*/
	225	for (j = count - 1; j >= 0; j--) {
	226	num1 = 0;
	227	for (i = deg_omega; i >= 0; i--) {
	228	if (omega[i] != nn)
03ead842	229	num1 ^= alpha_to[rs_modnn(rs, omega[i] +
1da177e4 LT	230	i * root[j])];
	231	}
	232	num2 = alpha_to[rs_modnn(rs, root[j] * (fcr - 1) + nn)];
	233	den = 0;
	234
	235	/* lambda[i+1] for i even is the formal derivative
	236	* lambda_pr of lambda[i] */
	237	for (i = min(deg_lambda, nroots - 1) & ~1; i >= 0; i -= 2) {
	238	if (lambda[i + 1] != nn) {
03ead842	239	den ^= alpha_to[rs_modnn(rs, lambda[i + 1] +
1da177e4 LT	240	i * root[j])];
	241	}
	242	}
	243	/* Apply error to data */
	244	if (num1 != 0 && loc[j] >= pad) {
03ead842	245	uint16_t cor = alpha_to[rs_modnn(rs,index_of[num1] +
1da177e4 LT	246	index_of[num2] +
	247	nn - index_of[den])];
	248	/* Store the error correction pattern, if a
	249	* correction buffer is available */
	250	if (corr) {
	251	corr[j] = cor;
	252	} else {
	253	/* If a data buffer is given and the
	254	* error is inside the message,
	255	* correct it */
	256	if (data && (loc[j] < (nn - nroots)))
	257	data[loc[j] - pad] ^= cor;
	258	}
	259	}
	260	}
	261
1da177e4 LT	262	if (eras_pos != NULL) {
	263	for (i = 0; i < count; i++)
	264	eras_pos[i] = loc[i] - pad;
	265	}
	266	return count;
	267
	268	}