// SPDX-License-Identifier: LGPL-2.1-or-later

/*

 * Reed-Solomon decoder, based on libfec

 *

 * Copyright (C) 2002, Phil Karn, KA9Q

 * libcryptsetup modifications

 *   Copyright (C) 2017-2025 Red Hat, Inc. All rights reserved.

 */

#include <string.h>

#include <stdlib.h>

#include "rs.h"

#define MAX_NR_BUF 256

int decode_rs_char(struct rs* rs, data_t* data)

{

  int deg_lambda, el, deg_omega, syn_error, count;

  int i, j, r, k;

  data_t q, tmp, num1, num2, den, discr_r;

  data_t lambda[MAX_NR_BUF], s[MAX_NR_BUF]; /* Err+Eras Locator poly and syndrome poly */

  data_t b[MAX_NR_BUF], t[MAX_NR_BUF], omega[MAX_NR_BUF];

  data_t root[MAX_NR_BUF], reg[MAX_NR_BUF], loc[MAX_NR_BUF];

  if (rs->nroots >= MAX_NR_BUF)

    return -1;

  memset(s, 0, rs->nroots * sizeof(data_t));

  memset(b, 0, (rs->nroots + 1) * sizeof(data_t));

  /* form the syndromes; i.e., evaluate data(x) at roots of g(x) */

  for (i = 0; i < rs->nroots; i++)

    s[i] = data[0];

  for (j = 1; j < rs->nn - rs->pad; j++) {

    for (i = 0; i < rs->nroots; i++) {

      if (s[i] == 0) {

        s[i] = data[j];

      } else {

        s[i] = data[j] ^ rs->alpha_to[modnn(rs, rs->index_of[s[i]] + (rs->fcr + i) * rs->prim)];

      }

    }

  }

  /* Convert syndromes to index form, checking for nonzero condition */

  syn_error = 0;

  for (i = 0; i < rs->nroots; i++) {

    syn_error |= s[i];

    s[i] = rs->index_of[s[i]];

  }

  /*

   * if syndrome is zero, data[] is a codeword and there are no

   * errors to correct. So return data[] unmodified

   */

  if (!syn_error)

    return 0;

  memset(&lambda[1], 0, rs->nroots * sizeof(lambda[0]));

  lambda[0] = 1;

  for (i   = 0; i < rs->nroots + 1; i++)

    b[i] = rs->index_of[lambda[i]];

  /*

   * Begin Berlekamp-Massey algorithm to determine error+erasure

   * locator polynomial

   */

  r  = 0;

  el = 0;

  while (++r <= rs->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 ^= rs->alpha_to[modnn(rs, rs->index_of[lambda[i]] + s[r - i - 1])];

      }

    }

    discr_r = rs->index_of[discr_r]; /* Index form */

    if (discr_r == A0) {

      /* 2 lines below: B(x) <-- x*B(x) */

      memmove(&b[1], b, rs->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 < rs->nroots; i++) {

        if (b[i] != A0)

          t[i + 1] = lambda[i + 1] ^ rs->alpha_to[modnn(rs, discr_r + b[i])];

        else

          t[i + 1] = lambda[i + 1];

      }

      if (2 * el <= r - 1) {

        el = r - el;

        /*

         * 2 lines below: B(x) <-- inv(discr_r) *

         * lambda(x)

         */

        for (i   = 0; i <= rs->nroots; i++)

          b[i] = (lambda[i] == 0) ? A0 : modnn(rs, rs->index_of[lambda[i]] - discr_r + rs->nn);

      } else {

        /* 2 lines below: B(x) <-- x*B(x) */

        memmove(&b[1], b, rs->nroots * sizeof(b[0]));

        b[0] = A0;

      }

      memcpy(lambda, t, (rs->nroots + 1) * sizeof(t[0]));

    }

  }

  /* Convert lambda to index form and compute deg(lambda(x)) */

  deg_lambda = 0;

  for (i = 0; i < rs->nroots + 1; i++) {

    lambda[i] = rs->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], rs->nroots * sizeof(reg[0]));

  count = 0; /* Number of roots of lambda(x) */

  for (i = 1, k = rs->iprim - 1; i <= rs->nn; i++, k = modnn(rs, k + rs->iprim)) {

    q = 1; /* lambda[0] is always 0 */

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

      if (reg[j] != A0) {

        reg[j] = modnn(rs, reg[j] + j);

        q ^= rs->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;

  }

  /*

   * deg(lambda) unequal to number of roots => uncorrectable

   * error detected

   */

  if (deg_lambda != count)

    return -1;

  /*

   * Compute err+eras evaluator poly omega(x) = s(x)*lambda(x) (modulo

   * x**rs->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 ^= rs->alpha_to[modnn(rs, s[i - j] + lambda[j])];

    }

    omega[i] = rs->index_of[tmp];

  }

  /*

   * Compute error values in poly-form. num1 = omega(inv(X(l))), num2 =

   * inv(X(l))**(rs->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 ^= rs->alpha_to[modnn(rs, omega[i] + i * root[j])];

    }

    num2 = rs->alpha_to[modnn(rs, root[j] * (rs->fcr - 1) + rs->nn)];

    den  = 0;

    /* lambda[i+1] for i even is the formal derivative lambda_pr of lambda[i] */

    for (i = RS_MIN(deg_lambda, rs->nroots - 1) & ~1; i >= 0; i -= 2) {

      if (lambda[i + 1] != A0)

        den ^= rs->alpha_to[modnn(rs, lambda[i + 1] + i * root[j])];

    }

    /* Apply error to data */

    if (num1 != 0 && loc[j] >= rs->pad) {

      data[loc[j] - rs->pad] ^= rs->alpha_to[modnn(rs, rs->index_of[num1] +

              rs->index_of[num2] + rs->nn - rs->index_of[den])];

    }

  }

  return count;

}