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+/* The guts of the Reed-Solomon decoder, meant to be #included
+ * into a function body with the following typedefs, macros and variables supplied
+ * according to the code parameters:
+
+ * data_t - a typedef for the data symbol
+ * data_t data[] - array of NN data and parity symbols to be corrected in place
+ * retval - an integer lvalue into which the decoder's return code is written
+ * NROOTS - the number of roots in the RS code generator polynomial,
+ * which is the same as the number of parity symbols in a block.
+ Integer variable or literal.
+ * NN - the total number of symbols in a RS block. Integer variable or literal.
+ * PAD - the number of pad symbols in a block. Integer variable or literal.
+ * ALPHA_TO - The address of an array of NN elements to convert Galois field
+ * elements in index (log) form to polynomial form. Read only.
+ * INDEX_OF - The address of an array of NN elements to convert Galois field
+ * elements in polynomial form to index (log) form. Read only.
+ * MODNN - a function to reduce its argument modulo NN. May be inline or a macro.
+ * FCR - An integer literal or variable specifying the first consecutive root of the
+ * Reed-Solomon generator polynomial. Integer variable or literal.
+ * PRIM - The primitive root of the generator poly. Integer variable or literal.
+ * DEBUG - If set to 1 or more, do various internal consistency checking. Leave this
+ * undefined for production code
+
+ * The memset(), memmove(), and memcpy() functions are used. The appropriate header
+ * file declaring these functions (usually <string.h>) must be included by the calling
+ * program.
+ */
+
+
+#if !defined(NROOTS)
+#error "NROOTS not defined"
+#endif
+
+#if !defined(NN)
+#error "NN not defined"
+#endif
+
+#if !defined(PAD)
+#error "PAD not defined"
+#endif
+
+#if !defined(ALPHA_TO)
+#error "ALPHA_TO not defined"
+#endif
+
+#if !defined(INDEX_OF)
+#error "INDEX_OF not defined"
+#endif
+
+#if !defined(MODNN)
+#error "MODNN not defined"
+#endif
+
+#if !defined(FCR)
+#error "FCR not defined"
+#endif
+
+#if !defined(PRIM)
+#error "PRIM not defined"
+#endif
+
+#if !defined(NULL)
+#define NULL ((void *)0)
+#endif
+
+#undef MIN
+#define MIN(a,b) ((a) < (b) ? (a) : (b))
+#undef A0
+#define A0 (NN)
+
+{
+ int deg_lambda, el, deg_omega;
+ int i, j, r,k;
+ data_t u,q,tmp,num1,num2,den,discr_r;
+ data_t lambda[NROOTS+1], s[NROOTS]; /* Err+Eras Locator poly
+ * and syndrome poly */
+ data_t b[NROOTS+1], t[NROOTS+1], omega[NROOTS+1];
+ data_t root[NROOTS], reg[NROOTS+1], loc[NROOTS];
+ int syn_error, count;
+
+ /* form the syndromes; i.e., evaluate data(x) at roots of g(x) */
+ for(i=0;i<NROOTS;i++)
+ s[i] = data[0];
+
+ for(j=1;j<NN-PAD;j++){
+ for(i=0;i<NROOTS;i++){
+ if(s[i] == 0){
+ s[i] = data[j];
+ } else {
+ s[i] = data[j] ^ ALPHA_TO[MODNN(INDEX_OF[s[i]] + (FCR+i)*PRIM)];
+ }
+ }
+ }
+
+ /* 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;
+ }
+ 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[MODNN(PRIM*(NN-1-eras_pos[0]))];
+ for (i = 1; i < no_eras; i++) {
+ u = MODNN(PRIM*(NN-1-eras_pos[i]));
+ for (j = i+1; j > 0; j--) {
+ tmp = INDEX_OF[lambda[j - 1]];
+ if(tmp != A0)
+ lambda[j] ^= ALPHA_TO[MODNN(u + tmp)];
+ }
+ }
+
+#if DEBUG >= 1
+ /* Test code that verifies the erasure locator polynomial just constructed
+ Needed only for decoder debugging. */
+
+ /* find roots of the erasure location polynomial */
+ for(i=1;i<=no_eras;i++)
+ reg[i] = INDEX_OF[lambda[i]];
+
+ count = 0;
+ for (i = 1,k=IPRIM-1; i <= NN; i++,k = MODNN(k+IPRIM)) {
+ q = 1;
+ for (j = 1; j <= no_eras; j++)
+ if (reg[j] != A0) {
+ reg[j] = MODNN(reg[j] + j);
+ q ^= ALPHA_TO[reg[j]];
+ }
+ if (q != 0)
+ continue;
+ /* store root and error location number indices */
+ root[count] = i;
+ loc[count] = k;
+ count++;
+ }
+ if (count != no_eras) {
+ printf("count = %d no_eras = %d\n lambda(x) is WRONG\n",count,no_eras);
+ count = -1;
+ goto finish;
+ }
+#if DEBUG >= 2
+ printf("\n Erasure positions as determined by roots of Eras Loc Poly:\n");
+ for (i = 0; i < count; i++)
+ printf("%d ", loc[i]);
+ printf("\n");
+#endif
+#endif
+ }
+ 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] != A0)) {
+ discr_r ^= ALPHA_TO[MODNN(INDEX_OF[lambda[i]] + s[r-i-1])];
+ }
+ }
+ discr_r = INDEX_OF[discr_r]; /* Index form */
+ if (discr_r == A0) {
+ /* 2 lines below: B(x) <-- x*B(x) */
+ memmove(&b[1],b,NROOTS*sizeof(b[0]));
+ b[0] = A0;
+ } 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] != A0)
+ t[i+1] = lambda[i+1] ^ ALPHA_TO[MODNN(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) ? A0 : MODNN(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] = A0;
+ }
+ 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] != A0)
+ deg_lambda = i;
+ }
+ /* Find roots of the 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 = MODNN(k+IPRIM)) {
+ q = 1; /* lambda[0] is always 0 */
+ for (j = deg_lambda; j > 0; j--){
+ if (reg[j] != A0) {
+ reg[j] = MODNN(reg[j] + j);
+ q ^= ALPHA_TO[reg[j]];
+ }
+ }
+ if (q != 0)
+ continue; /* Not a root */
+ /* store root (index-form) and error location number */
+#if DEBUG>=2
+ printf("count %d root %d loc %d\n",count,i,k);
+#endif
+ 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 = -1;
+ 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] != A0) && (lambda[j] != A0))
+ tmp ^= ALPHA_TO[MODNN(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] != A0)
+ num1 ^= ALPHA_TO[MODNN(omega[i] + i * root[j])];
+ }
+ num2 = ALPHA_TO[MODNN(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] != A0)
+ den ^= ALPHA_TO[MODNN(lambda[i+1] + i * root[j])];
+ }
+#if DEBUG >= 1
+ if (den == 0) {
+ printf("\n ERROR: denominator = 0\n");
+ count = -1;
+ goto finish;
+ }
+#endif
+ /* Apply error to data */
+ if (num1 != 0 && loc[j] >= PAD) {
+ data[loc[j]-PAD] ^= ALPHA_TO[MODNN(INDEX_OF[num1] + INDEX_OF[num2] + NN - INDEX_OF[den])];
+ }
+ }
+ finish:
+ if(eras_pos != NULL){
+ for(i=0;i<count;i++)
+ eras_pos[i] = loc[i];
+ }
+ retval = count;
+}
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