/* 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;
}