x-loader/lib/omap_bch_decoder.c - nest-learning-thermostat/5.1.5/x-loader - Git at Google

 /*
  * lib/omap_bch_decoder.c
  *
  * Whole BCH ECC Decoder (Post hardware generated syndrome decoding)
  *
  * Copyright (c) 2007 Texas Instruments
  *
  * Author: Sukumar Ghorai <s-ghorai@ti.com
  *		   Michael Fillinger <m-fillinger@ti.com>
  *
  * This program is free software; you can redistribute it and/or modify
  * it under the terms of the GNU General Public License version 2 as
  * published by the Free Software Foundation.
  *
  * This program is distributed "as is" WITHOUT ANY WARRANTY of any
  * kind, whether express or implied; without even the implied warranty
  * of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
  * GNU General Public License for more details.
  */

 #define printk //printf

 #define mm		13
 #define kk_shorten	4096
 #define nn		8191	/* Length of codeword, n = 2**mm - 1 */

 #define PPP	0x201B	/* Primary Polynomial : x^13 + x^4 + x^3 + x + 1 */
 #define P	0x001B	/* With omitted x^13 */
 #define POLY	12	/* degree of the primary Polynomial less one */

 /**
  * mpy_mod_gf - GALOIS field multiplier
  * Input  : A(x), B(x)
  * Output : A(x)*B(x) mod P(x)
  */
 static unsigned int mpy_mod_gf(unsigned int a, unsigned int b)
 {
 	unsigned int R = 0;
 	unsigned int R1 = 0;
 	unsigned int k = 0;

 	for (k = 0; k < mm; k++) {

 		R = (R << 1) & 0x1FFE;
 		if (R1 == 1)
 			R ^= P;

 		if (((a >> (POLY - k)) & 1) == 1)
 			R ^= b;

 		if (k < POLY)
 			R1 = (R >> POLY) & 1;
 	}
 	return R;
 }

 /**
  * chien - CHIEN search
  *
  * @location - Error location vector pointer
  *
  * Inputs  : ELP(z)
  *	     No. of found errors
  *	     Size of input codeword
  * Outputs : Up to 8 locations
  *	     No. of errors
  */
 static int chien(unsigned int select_4_8, int err_nums,
 				unsigned int err[], unsigned int *location)
 {
 	int i, count; /* Number of dectected errors */
 	/* Contains accumulation of evaluation at x^i (i:1->8) */
 	unsigned int gammas[8];
 	unsigned int alpha;
 	unsigned int bit, ecc_bits;
 	unsigned int elp_sum;

 	ecc_bits = (select_4_8 == 0) ? 52 : 104;

 	/* Start evaluation at Alpha**8192 and decreasing */
 	for (i = 0; i < 8; i++)
 		gammas[i] = err[i];

 	count = 0;
 	for (i = 1; (i <= nn) && (count < err_nums); i++) {

 		/* Result of evaluation at root */
 		elp_sum = 1 ^ gammas[0] ^ gammas[1] ^
 				gammas[2] ^ gammas[3] ^
 				gammas[4] ^ gammas[5] ^
 				gammas[6] ^ gammas[7];

 		alpha = PPP >> 1;
 		gammas[0] = mpy_mod_gf(gammas[0], alpha);
 		alpha = mpy_mod_gf(alpha, (PPP >> 1));	/* x alphha^-2 */
 		gammas[1] = mpy_mod_gf(gammas[1], alpha);
 		alpha = mpy_mod_gf(alpha, (PPP >> 1));	/* x alphha^-2 */
 		gammas[2] = mpy_mod_gf(gammas[2], alpha);
 		alpha = mpy_mod_gf(alpha, (PPP >> 1));	/* x alphha^-3 */
 		gammas[3] = mpy_mod_gf(gammas[3], alpha);
 		alpha = mpy_mod_gf(alpha, (PPP >> 1));	/* x alphha^-4 */
 		gammas[4] = mpy_mod_gf(gammas[4], alpha);
 		alpha = mpy_mod_gf(alpha, (PPP >> 1));	/* x alphha^-5 */
 		gammas[5] = mpy_mod_gf(gammas[5], alpha);
 		alpha = mpy_mod_gf(alpha, (PPP >> 1));	/* x alphha^-6 */
 		gammas[6] = mpy_mod_gf(gammas[6], alpha);
 		alpha = mpy_mod_gf(alpha, (PPP >> 1));	/* x alphha^-7 */
 		gammas[7] = mpy_mod_gf(gammas[7], alpha);

 		if (elp_sum == 0) {
 			/* calculate location */
 			bit = ((i-1) & ~7)|(7-((i-1) & 7));
 			location[count++] = kk_shorten - (bit - 2 * ecc_bits) - 1;
 		}
 	}

 	/* Failure: No. of detected errors != No. or corrected errors */
 	if (count != err_nums) {
 		count = -1;
 		/*	printk(KERN_INFO "BCH decoding failed\n");*/
 	}
 	/*
 	for (i = 0; i < count; i++)
 		printk(KERN_INFO "%d ", location[i]);
 	*/
 	return count;
 }

 /* synd : 16 Syndromes
  * return: gamaas - Coefficients to the error polynomial
  * return: : Number of detected errors
 */
 static unsigned int berlekamp(unsigned int select_4_8,
 			unsigned int synd[], unsigned int err[])
 {
 	int loop, iteration;
 	unsigned int LL = 0;		/* Detected errors */
 	unsigned int d = 0;	/* Distance between Syndromes and ELP[n](z) */
 	unsigned int invd = 0;		/* Inverse of d */
 	/* Intermediate ELP[n](z).
 	 * Final ELP[n](z) is Error Location Polynomial
 	 */
 	unsigned int gammas[16];
 	/* Intermediate normalized ELP[n](z) : D[n](z) */
 	unsigned int D[16];
 	/* Temporary value that holds an ELP[n](z) coefficient */
 	unsigned int next_gamma = 0;

 	int e = 0;
 	unsigned int sign = 0;
 	unsigned int u = 0;
 	unsigned int v = 0;
 	unsigned int C1 = 0, C2 = 0;
 	unsigned int ss = 0;
 	unsigned int tmp_v = 0, tmp_s = 0;
 	unsigned int tmp_poly;

 	/*-------------- Step 0 ------------------*/
 	for (loop = 0; loop < 16; loop++) {
 		gammas[loop] = 0;
 		D[loop] = 0;
 	}

 	gammas[0] = 1;
 	D[1] = 1;

 	iteration = 0;
 	LL = 0;
 	while ((iteration < ((select_4_8+1)*2*4)) &&
 			(LL <= ((select_4_8+1)*4))) {

 	  /*printk(KERN_INFO "\nIteration.............%d\n", iteration);*/
 		d = 0;
 		/* Step: 0 */
 		for (loop = 0; loop <= LL; loop++) {
 			tmp_poly = mpy_mod_gf(
 					gammas[loop], synd[iteration - loop]);
 			d ^= tmp_poly;
 			/*printk(KERN_INFO "%02d. s=0 LL=%x poly %x\n",
 			  loop, LL, tmp_poly);*/
 		}

 		/* Step 1: 1 cycle only to perform inversion */
 		v = d << 1;
 		e = -1;
 		sign = 1;
 		ss = 0x2000;
 		invd = 0;
 		u = PPP;
 		for (loop = 0; (d != 0) && (loop <= (2 * POLY)); loop++) {
 		  /*printk(KERN_INFO "%02d. s=1 LL=%x poly NULL\n",
 		    loop, LL);*/
 			C1 = (v >> 13) & 1;
 			C2 = C1 & sign;

 			sign ^= C2 ^ (e == 0);

 			tmp_v = v;
 			tmp_s = ss;

 			if (C1 == 1) {
 				v ^= u;
 				ss ^= invd;
 			}
 			v = (v << 1) & 0x3FFF;
 			if (C2 == 1) {
 				u = tmp_v;
 				invd = tmp_s;
 				e = -e;
 			}
 			invd >>= 1;
 			e--;
 		}

 		for (loop = 0; (d != 0) && (loop <= (iteration + 1)); loop++) {
 			/* Step 2
 			 * Interleaved with Step 3, if L<(n-k)
 			 * invd: Update of ELP[n](z) = ELP[n-1](z) - d.D[n-1](z)
 			 */

 			/* Holds value of ELP coefficient until precedent
 			 * value does not have to be used anymore
 			 */
 			tmp_poly = mpy_mod_gf(d, D[loop]);
 			/*printk(KERN_INFO "%02d. s=2 LL=%x poly %x\n",
 			  loop, LL, tmp_poly);*/

 			next_gamma = gammas[loop] ^ tmp_poly;
 			if ((2 * LL) < (iteration + 1)) {
 				/* Interleaving with Step 3
 				 * for parallelized update of ELP(z) and D(z)
 				 */
 			} else {
 				/* Update of ELP(z) only -> stay in Step 2 */
 				gammas[loop] = next_gamma;
 				if (loop == (iteration + 1)) {
 					/* to step 4 */
 					break;
 				}
 			}

 			/* Step 3
 			 * Always interleaved with Step 2 (case when L<(n-k))
 			 * Update of D[n-1](z) = ELP[n-1](z)/d
 			 */
 			D[loop] = mpy_mod_gf(gammas[loop], invd);
 			/*printk(KERN_INFO "%02d. s=3 LL=%x poly %x\n",
 			  loop, LL, D[loop]);*/

 			/* Can safely update ELP[n](z) */
 			gammas[loop] = next_gamma;

 			if (loop == (iteration + 1)) {
 				/* If update finished */
 				LL = iteration - LL + 1;
 				/* to step 4 */
 				break;
 			}
 			/* Else, interleaving to step 2*/
 		}

 		/* Step 4: Update D(z): i:0->L */
 		/* Final update of D[n](z) = D[n](z).z*/
 		for (loop = 0; loop < 15; loop++) /* Left Shift */
 			D[15 - loop] = D[14 - loop];

 		D[0] = 0;

 		iteration++;
 	} /* while */

 	/* Processing finished, copy ELP to final registers : 0->2t-1*/
 	for (loop = 0; loop < 8; loop++)
 		err[loop] = gammas[loop+1];

 	/*printk(KERN_INFO "\n Err poly:");
 	for (loop = 0; loop < 8; loop++)
 		printk(KERN_INFO "0x%x ", err[loop]);
 	*/
 	return LL;
 }

 /*
  * syndrome - Generate syndrome components from hw generate syndrome
  * r(x) = c(x) + e(x)
  * s(x) = c(x) mod g(x) + e(x) mod g(x) =  e(x) mod g(x)
  * so receiver checks if the syndrome s(x) = r(x) mod g(x) is equal to zero.
  * unsigned int s[16]; - Syndromes
  */
 static void syndrome(unsigned int select_4_8,
 					unsigned char *ecc, unsigned int syn[])
 {
 	unsigned int k, l, t;
 	unsigned int alpha_bit, R_bit;
 	int ecc_pos, ecc_min;

 	/* 2t-1 = 15 (for t=8) minimal polynomials of the first 15 powers of a
 	 * primitive elemmants of GF(m); Even powers minimal polynomials are
 	 * duplicate of odd powers' minimal polynomials.
 	 * Odd powers of alpha (1 to 15)
 	 */
 	unsigned int pow_alpha[8] = {0x0002, 0x0008, 0x0020, 0x0080,
 				 0x0200, 0x0800, 0x001B, 0x006C};

 	/*printk(KERN_INFO "\n ECC[0..n]: ");
 	for (k = 0; k < 13; k++)
 		printk(KERN_INFO "0x%x ", ecc[k]);
 	*/

 	if (select_4_8 == 0) {
 		t = 4;
 		ecc_pos = 55; /* bits(52-bits): 55->4 */
 		ecc_min = 4;
 	} else {
 		t = 8;
 		ecc_pos = 103; /* bits: 103->0 */
 		ecc_min = 0;
 	}

 	/* total numbber of syndrom to be used is 2t */
 	/* Step1: calculate the odd syndrome(s) */
 	R_bit = ((ecc[ecc_pos/8] >> (7 - ecc_pos%8)) & 1);
 	ecc_pos--;
 	for (k = 0; k < t; k++)
 		syn[2 * k] = R_bit;

 	while (ecc_pos >= ecc_min) {
 		R_bit = ((ecc[ecc_pos/8] >> (7 - ecc_pos%8)) & 1);
 		ecc_pos--;

 		for (k = 0; k < t; k++) {
 			/* Accumulate value of x^i at alpha^(2k+1) */
 			if (R_bit == 1)
 				syn[2*k] ^= pow_alpha[k];

 			/* Compute a**(2k+1), using LSFR */
 			for (l = 0; l < (2 * k + 1); l++) {
 				alpha_bit = (pow_alpha[k] >> POLY) & 1;
 				pow_alpha[k] = (pow_alpha[k] << 1) & 0x1FFF;
 				if (alpha_bit == 1)
 					pow_alpha[k] ^= P;
 			}
 		}
 	}

 	/* Step2: calculate the even syndrome(s)
 	 * Compute S(a), where a is an even power of alpha
 	 * Evenry even power of primitive element has the same minimal
 	 * polynomial as some odd power of elemets.
 	 * And based on S(a^2) = S^2(a)
 	 */
 	for (k = 0; k < t; k++)
 		syn[2*k+1] = mpy_mod_gf(syn[k], syn[k]);

 	/*printk(KERN_INFO "\n Syndromes: ");
 	for (k = 0; k < 16; k++)
 	printk(KERN_INFO "0x%x ", syn[k]);*/
 }

 /**
  * decode_bch - BCH decoder for 4- and 8-bit error correction
  *
  * @ecc - ECC syndrome generated by hw BCH engine
  * @err_loc - pointer to error location array
  *
  * This function does post sydrome generation (hw generated) decoding
  * for:-
  * Dimension of Galoise Field: m = 13
  * Length of codeword: n = 2**m - 1
  * Number of errors that can be corrected: 4- or 8-bits
  * Length of information bit: kk = nn - rr
  */
 int decode_bch(int select_4_8, unsigned char *ecc, unsigned int *err_loc)
 {
         int no_of_err, i;
 	unsigned int syn[16];	/* 16 Syndromes */
 	unsigned int err_poly[8];
 	/* Coefficients to the error polynomial
 	 * ELP(x) = 1 + err0.x + err1.x^2 + ... + err7.x^8
 	 */

 	/* perform manual initialization to avoid memset */
 	for (i=0; i<16; i++) {
 	  syn[i] = 0;
 	  if (i<8)
 	    err_poly[i] = 0;
 	}

 	/* Decoting involes three steps
 	 * 1. Compute the syndrom from teh received codeword,
 	 * 2. Find the error location polynomial from a set of equations
 	 *     derived from the syndrome,
 	 * 3. Use the error location polynomial to identify errants bits,
 	 *
 	 * And correcttion done by bit flips using error locaiton and expected
 	 * to be outseide of this implementation.
 	 */
 	syndrome(select_4_8, ecc, syn);
 	no_of_err = berlekamp(select_4_8, syn, err_poly);
 	if (no_of_err <= (4 << select_4_8))
 		no_of_err = chien(select_4_8, no_of_err, err_poly, err_loc);

 	return no_of_err;
 }
 EXPORT_SYMBOL(decode_bch);
	/*
	* lib/omap_bch_decoder.c
	*
	* Whole BCH ECC Decoder (Post hardware generated syndrome decoding)
	*
	* Copyright (c) 2007 Texas Instruments
	*
	* Author: Sukumar Ghorai <s-ghorai@ti.com
	* Michael Fillinger <m-fillinger@ti.com>
	*
	* This program is free software; you can redistribute it and/or modify
	* it under the terms of the GNU General Public License version 2 as
	* published by the Free Software Foundation.
	*
	* This program is distributed "as is" WITHOUT ANY WARRANTY of any
	* kind, whether express or implied; without even the implied warranty
	* of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
	* GNU General Public License for more details.
	*/

	#define printk //printf

	#define mm 13
	#define kk_shorten 4096
	#define nn 8191 /* Length of codeword, n = 2*mm - 1 /

	#define PPP 0x201B /* Primary Polynomial : x^13 + x^4 + x^3 + x + 1 */
	#define P 0x001B /* With omitted x^13 */
	#define POLY 12 /* degree of the primary Polynomial less one */

	/**
	* mpy_mod_gf - GALOIS field multiplier
	* Input : A(x), B(x)
	* Output : A(x)*B(x) mod P(x)
	*/
	static unsigned int mpy_mod_gf(unsigned int a, unsigned int b)
	{
	unsigned int R = 0;
	unsigned int R1 = 0;
	unsigned int k = 0;

	for (k = 0; k < mm; k++) {

	R = (R << 1) & 0x1FFE;
	if (R1 == 1)
	R ^= P;

	if (((a >> (POLY - k)) & 1) == 1)
	R ^= b;

	if (k < POLY)
	R1 = (R >> POLY) & 1;
	}
	return R;
	}

	/**
	* chien - CHIEN search
	*
	* @location - Error location vector pointer
	*
	* Inputs : ELP(z)
	* No. of found errors
	* Size of input codeword
	* Outputs : Up to 8 locations
	* No. of errors
	*/
	static int chien(unsigned int select_4_8, int err_nums,
	unsigned int err[], unsigned int *location)
	{
	int i, count; /* Number of dectected errors */
	/* Contains accumulation of evaluation at x^i (i:1->8) */
	unsigned int gammas[8];
	unsigned int alpha;
	unsigned int bit, ecc_bits;
	unsigned int elp_sum;

	ecc_bits = (select_4_8 == 0) ? 52 : 104;

	/* Start evaluation at Alpha*8192 and decreasing /
	for (i = 0; i < 8; i++)
	gammas[i] = err[i];

	count = 0;
	for (i = 1; (i <= nn) && (count < err_nums); i++) {

	/* Result of evaluation at root */
	elp_sum = 1 ^ gammas[0] ^ gammas[1] ^
	gammas[2] ^ gammas[3] ^
	gammas[4] ^ gammas[5] ^
	gammas[6] ^ gammas[7];

	alpha = PPP >> 1;
	gammas[0] = mpy_mod_gf(gammas[0], alpha);
	alpha = mpy_mod_gf(alpha, (PPP >> 1)); /* x alphha^-2 */
	gammas[1] = mpy_mod_gf(gammas[1], alpha);
	alpha = mpy_mod_gf(alpha, (PPP >> 1)); /* x alphha^-2 */
	gammas[2] = mpy_mod_gf(gammas[2], alpha);
	alpha = mpy_mod_gf(alpha, (PPP >> 1)); /* x alphha^-3 */
	gammas[3] = mpy_mod_gf(gammas[3], alpha);
	alpha = mpy_mod_gf(alpha, (PPP >> 1)); /* x alphha^-4 */
	gammas[4] = mpy_mod_gf(gammas[4], alpha);
	alpha = mpy_mod_gf(alpha, (PPP >> 1)); /* x alphha^-5 */
	gammas[5] = mpy_mod_gf(gammas[5], alpha);
	alpha = mpy_mod_gf(alpha, (PPP >> 1)); /* x alphha^-6 */
	gammas[6] = mpy_mod_gf(gammas[6], alpha);
	alpha = mpy_mod_gf(alpha, (PPP >> 1)); /* x alphha^-7 */
	gammas[7] = mpy_mod_gf(gammas[7], alpha);

	if (elp_sum == 0) {
	/* calculate location */
	bit = ((i-1) & ~7)\|(7-((i-1) & 7));
	location[count++] = kk_shorten - (bit - 2 * ecc_bits) - 1;
	}
	}

	/* Failure: No. of detected errors != No. or corrected errors */
	if (count != err_nums) {
	count = -1;
	/* printk(KERN_INFO "BCH decoding failed\n");*/
	}
	/*
	for (i = 0; i < count; i++)
	printk(KERN_INFO "%d ", location[i]);
	*/
	return count;
	}

	/* synd : 16 Syndromes
	* return: gamaas - Coefficients to the error polynomial
	* return: : Number of detected errors
	*/
	static unsigned int berlekamp(unsigned int select_4_8,
	unsigned int synd[], unsigned int err[])
	{
	int loop, iteration;
	unsigned int LL = 0; /* Detected errors */
	unsigned int d = 0; /* Distance between Syndromes and ELP[n](z) */
	unsigned int invd = 0; /* Inverse of d */
	/* Intermediate ELP[n](z).
	* Final ELP[n](z) is Error Location Polynomial
	*/
	unsigned int gammas[16];
	/* Intermediate normalized ELP[n](z) : D[n](z) */
	unsigned int D[16];
	/* Temporary value that holds an ELP[n](z) coefficient */
	unsigned int next_gamma = 0;

	int e = 0;
	unsigned int sign = 0;
	unsigned int u = 0;
	unsigned int v = 0;
	unsigned int C1 = 0, C2 = 0;
	unsigned int ss = 0;
	unsigned int tmp_v = 0, tmp_s = 0;
	unsigned int tmp_poly;

	/-------------- Step 0 ------------------/
	for (loop = 0; loop < 16; loop++) {
	gammas[loop] = 0;
	D[loop] = 0;
	}

	gammas[0] = 1;
	D[1] = 1;

	iteration = 0;
	LL = 0;
	while ((iteration < ((select_4_8+1)24)) &&
	(LL <= ((select_4_8+1)*4))) {

	/printk(KERN_INFO "\nIteration.............%d\n", iteration);/
	d = 0;
	/* Step: 0 */
	for (loop = 0; loop <= LL; loop++) {
	tmp_poly = mpy_mod_gf(
	gammas[loop], synd[iteration - loop]);
	d ^= tmp_poly;
	/*printk(KERN_INFO "%02d. s=0 LL=%x poly %x\n",
	loop, LL, tmp_poly);*/
	}

	/* Step 1: 1 cycle only to perform inversion */
	v = d << 1;
	e = -1;
	sign = 1;
	ss = 0x2000;
	invd = 0;
	u = PPP;
	for (loop = 0; (d != 0) && (loop <= (2 * POLY)); loop++) {
	/*printk(KERN_INFO "%02d. s=1 LL=%x poly NULL\n",
	loop, LL);*/
	C1 = (v >> 13) & 1;
	C2 = C1 & sign;

	sign ^= C2 ^ (e == 0);

	tmp_v = v;
	tmp_s = ss;

	if (C1 == 1) {
	v ^= u;
	ss ^= invd;
	}
	v = (v << 1) & 0x3FFF;
	if (C2 == 1) {
	u = tmp_v;
	invd = tmp_s;
	e = -e;
	}
	invd >>= 1;
	e--;
	}

	for (loop = 0; (d != 0) && (loop <= (iteration + 1)); loop++) {
	/* Step 2
	* Interleaved with Step 3, if L<(n-k)
	* invd: Update of ELP[n](z) = ELP[n-1](z) - d.D[n-1](z)
	*/

	/* Holds value of ELP coefficient until precedent
	* value does not have to be used anymore
	*/
	tmp_poly = mpy_mod_gf(d, D[loop]);
	/*printk(KERN_INFO "%02d. s=2 LL=%x poly %x\n",
	loop, LL, tmp_poly);*/

	next_gamma = gammas[loop] ^ tmp_poly;
	if ((2 * LL) < (iteration + 1)) {
	/* Interleaving with Step 3
	* for parallelized update of ELP(z) and D(z)
	*/
	} else {
	/* Update of ELP(z) only -> stay in Step 2 */
	gammas[loop] = next_gamma;
	if (loop == (iteration + 1)) {
	/* to step 4 */
	break;
	}
	}

	/* Step 3
	* Always interleaved with Step 2 (case when L<(n-k))
	* Update of D[n-1](z) = ELP[n-1](z)/d
	*/
	D[loop] = mpy_mod_gf(gammas[loop], invd);
	/*printk(KERN_INFO "%02d. s=3 LL=%x poly %x\n",
	loop, LL, D[loop]);*/

	/* Can safely update ELP[n](z) */
	gammas[loop] = next_gamma;

	if (loop == (iteration + 1)) {
	/* If update finished */
	LL = iteration - LL + 1;
	/* to step 4 */
	break;
	}
	/* Else, interleaving to step 2*/
	}

	/* Step 4: Update D(z): i:0->L */
	/* Final update of D[n](z) = D[n](z).z*/
	for (loop = 0; loop < 15; loop++) /* Left Shift */
	D[15 - loop] = D[14 - loop];

	D[0] = 0;

	iteration++;
	} /* while */

	/* Processing finished, copy ELP to final registers : 0->2t-1*/
	for (loop = 0; loop < 8; loop++)
	err[loop] = gammas[loop+1];

	/*printk(KERN_INFO "\n Err poly:");
	for (loop = 0; loop < 8; loop++)
	printk(KERN_INFO "0x%x ", err[loop]);
	*/
	return LL;
	}

	/*
	* syndrome - Generate syndrome components from hw generate syndrome
	* r(x) = c(x) + e(x)
	* s(x) = c(x) mod g(x) + e(x) mod g(x) = e(x) mod g(x)
	* so receiver checks if the syndrome s(x) = r(x) mod g(x) is equal to zero.
	* unsigned int s[16]; - Syndromes
	*/
	static void syndrome(unsigned int select_4_8,
	unsigned char *ecc, unsigned int syn[])
	{
	unsigned int k, l, t;
	unsigned int alpha_bit, R_bit;
	int ecc_pos, ecc_min;

	/* 2t-1 = 15 (for t=8) minimal polynomials of the first 15 powers of a
	* primitive elemmants of GF(m); Even powers minimal polynomials are
	* duplicate of odd powers' minimal polynomials.
	* Odd powers of alpha (1 to 15)
	*/
	unsigned int pow_alpha[8] = {0x0002, 0x0008, 0x0020, 0x0080,
	0x0200, 0x0800, 0x001B, 0x006C};

	/*printk(KERN_INFO "\n ECC[0..n]: ");
	for (k = 0; k < 13; k++)
	printk(KERN_INFO "0x%x ", ecc[k]);
	*/

	if (select_4_8 == 0) {
	t = 4;
	ecc_pos = 55; /* bits(52-bits): 55->4 */
	ecc_min = 4;
	} else {
	t = 8;
	ecc_pos = 103; /* bits: 103->0 */
	ecc_min = 0;
	}

	/* total numbber of syndrom to be used is 2t */
	/* Step1: calculate the odd syndrome(s) */
	R_bit = ((ecc[ecc_pos/8] >> (7 - ecc_pos%8)) & 1);
	ecc_pos--;
	for (k = 0; k < t; k++)
	syn[2 * k] = R_bit;

	while (ecc_pos >= ecc_min) {
	R_bit = ((ecc[ecc_pos/8] >> (7 - ecc_pos%8)) & 1);
	ecc_pos--;

	for (k = 0; k < t; k++) {
	/* Accumulate value of x^i at alpha^(2k+1) */
	if (R_bit == 1)
	syn[2*k] ^= pow_alpha[k];

	/* Compute a*(2k+1), using LSFR /
	for (l = 0; l < (2 * k + 1); l++) {
	alpha_bit = (pow_alpha[k] >> POLY) & 1;
	pow_alpha[k] = (pow_alpha[k] << 1) & 0x1FFF;
	if (alpha_bit == 1)
	pow_alpha[k] ^= P;
	}
	}
	}

	/* Step2: calculate the even syndrome(s)
	* Compute S(a), where a is an even power of alpha
	* Evenry even power of primitive element has the same minimal
	* polynomial as some odd power of elemets.
	* And based on S(a^2) = S^2(a)
	*/
	for (k = 0; k < t; k++)
	syn[2*k+1] = mpy_mod_gf(syn[k], syn[k]);

	/*printk(KERN_INFO "\n Syndromes: ");
	for (k = 0; k < 16; k++)
	printk(KERN_INFO "0x%x ", syn[k]);*/
	}

	/**
	* decode_bch - BCH decoder for 4- and 8-bit error correction
	*
	* @ecc - ECC syndrome generated by hw BCH engine
	* @err_loc - pointer to error location array
	*
	* This function does post sydrome generation (hw generated) decoding
	* for:-
	* Dimension of Galoise Field: m = 13
	* Length of codeword: n = 2**m - 1
	* Number of errors that can be corrected: 4- or 8-bits
	* Length of information bit: kk = nn - rr
	*/
	int decode_bch(int select_4_8, unsigned char ecc, unsigned int err_loc)
	{
	int no_of_err, i;
	unsigned int syn[16]; /* 16 Syndromes */
	unsigned int err_poly[8];
	/* Coefficients to the error polynomial
	* ELP(x) = 1 + err0.x + err1.x^2 + ... + err7.x^8
	*/

	/* perform manual initialization to avoid memset */
	for (i=0; i<16; i++) {
	syn[i] = 0;
	if (i<8)
	err_poly[i] = 0;
	}

	/* Decoting involes three steps
	* 1. Compute the syndrom from teh received codeword,
	* 2. Find the error location polynomial from a set of equations
	* derived from the syndrome,
	* 3. Use the error location polynomial to identify errants bits,
	*
	* And correcttion done by bit flips using error locaiton and expected
	* to be outseide of this implementation.
	*/
	syndrome(select_4_8, ecc, syn);
	no_of_err = berlekamp(select_4_8, syn, err_poly);
	if (no_of_err <= (4 << select_4_8))
	no_of_err = chien(select_4_8, no_of_err, err_poly, err_loc);

	return no_of_err;
	}
	EXPORT_SYMBOL(decode_bch);