[linux-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;
	/* 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;

}
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;
	24	/* Err+Eras Locator poly and syndrome poly The maximum value
	25	* of nroots is 8. So the necessary stack size will be about
	26	* 220 bytes max.
	27	*/
	28	uint16_t lambda[nroots + 1], syn[nroots];
	29	uint16_t b[nroots + 1], t[nroots + 1], omega[nroots + 1];
	30	uint16_t root[nroots], reg[nroots + 1], loc[nroots];
	31	int count = 0;
	32	uint16_t msk = (uint16_t) rs->nn;
	33
	34	/* Check length parameter for validity */
	35	pad = nn - nroots - len;
1dd7fdb1	36	BUG_ON(pad < 0 \|\| pad >= nn);
03ead842	37
1da177e4	38	/* Does the caller provide the syndrome ? */
03ead842	39	if (s != NULL)
1da177e4 LT	40	goto decode;
	41
	42	/* form the syndromes; i.e., evaluate data(x) at roots of
	43	* g(x) */
	44	for (i = 0; i < nroots; i++)
	45	syn[i] = (((uint16_t) data[0]) ^ invmsk) & msk;
	46
	47	for (j = 1; j < len; j++) {
	48	for (i = 0; i < nroots; i++) {
	49	if (syn[i] == 0) {
03ead842	50	syn[i] = (((uint16_t) data[j]) ^
1da177e4 LT	51	invmsk) & msk;
	52	} else {
	53	syn[i] = ((((uint16_t) data[j]) ^
03ead842	54	invmsk) & msk) ^
1da177e4 LT	55	alpha_to[rs_modnn(rs, index_of[syn[i]] +
	56	(fcr + i) * prim)];
	57	}
	58	}
	59	}
	60
	61	for (j = 0; j < nroots; j++) {
	62	for (i = 0; i < nroots; i++) {
	63	if (syn[i] == 0) {
	64	syn[i] = ((uint16_t) par[j]) & msk;
	65	} else {
03ead842	66	syn[i] = (((uint16_t) par[j]) & msk) ^
1da177e4 LT	67	alpha_to[rs_modnn(rs, index_of[syn[i]] +
	68	(fcr+i)*prim)];
	69	}
	70	}
	71	}
	72	s = syn;
	73
	74	/* Convert syndromes to index form, checking for nonzero condition */
	75	syn_error = 0;
	76	for (i = 0; i < nroots; i++) {
	77	syn_error \|= s[i];
	78	s[i] = index_of[s[i]];
	79	}
	80
	81	if (!syn_error) {
	82	/* if syndrome is zero, data[] is a codeword and there are no
	83	* errors to correct. So return data[] unmodified
	84	*/
	85	count = 0;
	86	goto finish;
	87	}
	88
	89	decode:
	90	memset(&lambda[1], 0, nroots * sizeof(lambda[0]));
	91	lambda[0] = 1;
	92
	93	if (no_eras > 0) {
	94	/* Init lambda to be the erasure locator polynomial */
03ead842	95	lambda[1] = alpha_to[rs_modnn(rs,
1da177e4 LT	96	prim * (nn - 1 - eras_pos[0]))];
	97	for (i = 1; i < no_eras; i++) {
	98	u = rs_modnn(rs, prim * (nn - 1 - eras_pos[i]));
	99	for (j = i + 1; j > 0; j--) {
	100	tmp = index_of[lambda[j - 1]];
	101	if (tmp != nn) {
03ead842	102	lambda[j] ^=
1da177e4 LT	103	alpha_to[rs_modnn(rs, u + tmp)];
	104	}
	105	}
	106	}
	107	}
	108
	109	for (i = 0; i < nroots + 1; i++)
	110	b[i] = index_of[lambda[i]];
	111
	112	/*
	113	* Begin Berlekamp-Massey algorithm to determine error+erasure
	114	* locator polynomial
	115	*/
	116	r = no_eras;
	117	el = no_eras;
	118	while (++r <= nroots) { /* r is the step number */
	119	/* Compute discrepancy at the r-th step in poly-form */
	120	discr_r = 0;
	121	for (i = 0; i < r; i++) {
	122	if ((lambda[i] != 0) && (s[r - i - 1] != nn)) {
03ead842 TG	123	discr_r ^=
03ead842 TG	124	alpha_to[rs_modnn(rs,
1da177e4 LT	125	index_of[lambda[i]] +
	126	s[r - i - 1])];
	127	}
	128	}
	129	discr_r = index_of[discr_r]; /* Index form */
	130	if (discr_r == nn) {
	131	/* 2 lines below: B(x) <-- xB(x) /
	132	memmove (&b[1], b, nroots * sizeof (b[0]));
	133	b[0] = nn;
	134	} else {
	135	/* 7 lines below: T(x) <-- lambda(x)-discr_rxb(x) */
	136	t[0] = lambda[0];
	137	for (i = 0; i < nroots; i++) {
	138	if (b[i] != nn) {
03ead842	139	t[i + 1] = lambda[i + 1] ^
1da177e4 LT	140	alpha_to[rs_modnn(rs, discr_r +
	141	b[i])];
	142	} else
	143	t[i + 1] = lambda[i + 1];
	144	}
	145	if (2 * el <= r + no_eras - 1) {
	146	el = r + no_eras - el;
	147	/*
	148	* 2 lines below: B(x) <-- inv(discr_r) *
	149	* lambda(x)
	150	*/
	151	for (i = 0; i <= nroots; i++) {
	152	b[i] = (lambda[i] == 0) ? nn :
	153	rs_modnn(rs, index_of[lambda[i]]
	154	- discr_r + nn);
	155	}
	156	} else {
	157	/* 2 lines below: B(x) <-- xB(x) /
	158	memmove(&b[1], b, nroots * sizeof(b[0]));
	159	b[0] = nn;
	160	}
	161	memcpy(lambda, t, (nroots + 1) * sizeof(t[0]));
	162	}
	163	}
	164
	165	/* Convert lambda to index form and compute deg(lambda(x)) */
	166	deg_lambda = 0;
	167	for (i = 0; i < nroots + 1; i++) {
	168	lambda[i] = index_of[lambda[i]];
	169	if (lambda[i] != nn)
	170	deg_lambda = i;
	171	}
	172	/* Find roots of error+erasure locator polynomial by Chien search */
	173	memcpy(&reg[1], &lambda[1], nroots * sizeof(reg[0]));
	174	count = 0; /* Number of roots of lambda(x) */
	175	for (i = 1, k = iprim - 1; i <= nn; i++, k = rs_modnn(rs, k + iprim)) {
	176	q = 1; /* lambda[0] is always 0 */
	177	for (j = deg_lambda; j > 0; j--) {
	178	if (reg[j] != nn) {
	179	reg[j] = rs_modnn(rs, reg[j] + j);
	180	q ^= alpha_to[reg[j]];
	181	}
	182	}
	183	if (q != 0)
	184	continue; /* Not a root */
	185	/* store root (index-form) and error location number */
	186	root[count] = i;
	187	loc[count] = k;
	188	/* If we've already found max possible roots,
	189	* abort the search to save time
	190	*/
	191	if (++count == deg_lambda)
	192	break;
	193	}
	194	if (deg_lambda != count) {
	195	/*
	196	* deg(lambda) unequal to number of roots => uncorrectable
	197	* error detected
	198	*/
eb684507	199	count = -EBADMSG;
1da177e4 LT	200	goto finish;
	201	}
	202	/*
	203	* Compute err+eras evaluator poly omega(x) = s(x)*lambda(x) (modulo
	204	* x**nroots). in index form. Also find deg(omega).
	205	*/
	206	deg_omega = deg_lambda - 1;
	207	for (i = 0; i <= deg_omega; i++) {
	208	tmp = 0;
	209	for (j = i; j >= 0; j--) {
	210	if ((s[i - j] != nn) && (lambda[j] != nn))
	211	tmp ^=
	212	alpha_to[rs_modnn(rs, s[i - j] + lambda[j])];
	213	}
	214	omega[i] = index_of[tmp];
	215	}
	216
	217	/*
	218	* Compute error values in poly-form. num1 = omega(inv(X(l))), num2 =
	219	* inv(X(l))**(fcr-1) and den = lambda_pr(inv(X(l))) all in poly-form
	220	*/
	221	for (j = count - 1; j >= 0; j--) {
	222	num1 = 0;
	223	for (i = deg_omega; i >= 0; i--) {
	224	if (omega[i] != nn)
03ead842	225	num1 ^= alpha_to[rs_modnn(rs, omega[i] +
1da177e4 LT	226	i * root[j])];
	227	}
	228	num2 = alpha_to[rs_modnn(rs, root[j] * (fcr - 1) + nn)];
	229	den = 0;
	230
	231	/* lambda[i+1] for i even is the formal derivative
	232	* lambda_pr of lambda[i] */
	233	for (i = min(deg_lambda, nroots - 1) & ~1; i >= 0; i -= 2) {
	234	if (lambda[i + 1] != nn) {
03ead842	235	den ^= alpha_to[rs_modnn(rs, lambda[i + 1] +
1da177e4 LT	236	i * root[j])];
	237	}
	238	}
	239	/* Apply error to data */
	240	if (num1 != 0 && loc[j] >= pad) {
03ead842	241	uint16_t cor = alpha_to[rs_modnn(rs,index_of[num1] +
1da177e4 LT	242	index_of[num2] +
	243	nn - index_of[den])];
	244	/* Store the error correction pattern, if a
	245	* correction buffer is available */
	246	if (corr) {
	247	corr[j] = cor;
	248	} else {
	249	/* If a data buffer is given and the
	250	* error is inside the message,
	251	* correct it */
	252	if (data && (loc[j] < (nn - nroots)))
	253	data[loc[j] - pad] ^= cor;
	254	}
	255	}
	256	}
	257
	258	finish:
	259	if (eras_pos != NULL) {
	260	for (i = 0; i < count; i++)
	261	eras_pos[i] = loc[i] - pad;
	262	}
	263	return count;
	264
	265	}