/* Reed-Solomon decoder

 * Copyright 2002 Phil Karn, KA9Q

 * May be used under the terms of the GNU General Public License (GPL)

 */

#ifdef DEBUG

#include <stdio.h>

#endif

#include <string.h>

#include <strings.h>

#define NULL ((void *)0)

#define        min(a,b)        ((a) < (b) ? (a) : (b))

#ifdef FIXED

#include "fixed.h"

#elif defined(BIGSYM)

#include "int.h"

#else

#include "char.h"

#endif

int DECODE_RS(

#ifndef FIXED

void *p,

#endif

DTYPE *data, int *eras_pos, int no_eras){

#ifndef FIXED

  struct rs *rs = (struct rs *)p;

#endif

  int deg_lambda, el, deg_omega;

  int i, j, r,k;

  DTYPE u,q,tmp,num1,num2,den,discr_r;

  DTYPE lambda[NROOTS+1], s[NROOTS];        /* Err+Eras Locator poly

                                         * and syndrome poly */

  DTYPE b[NROOTS+1], t[NROOTS+1], omega[NROOTS+1];

  DTYPE 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;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 = 0;

  for (i = 0; i < NROOTS;i++){

    tmp = 0;

    j = (deg_lambda < i) ? deg_lambda : i;

    for(;j >= 0; j--){

      if ((s[i - j] != A0) && (lambda[j] != A0))

        tmp ^= ALPHA_TO[MODNN(s[i - j] + lambda[j])];

    }

    if(tmp != 0)

      deg_omega = i;

    omega[i] = INDEX_OF[tmp];

  }

  omega[NROOTS] = A0;

  /*

   * 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 (den == 0) {

#if DEBUG >= 1

      printf("\n ERROR: denominator = 0\n");

#endif

      count = -1;

      goto finish;

    }

    /* Apply error to data */

    if (num1 != 0) {

      data[loc[j]] ^= 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];

  }

  return count;

}