user: Please show me the C implementation that matches the assembly code listed below:

```asm
<chk_3_err_only>:
  endbr64
  push   %rbp
  mov    %rsp,%rbp
  push   %r13
  push   %r12
  push   %rbx
  sub    $0x58,%rsp
  mov    %rdi,-0x68(%rbp)
  mov    %rsi,-0x70(%rbp)
  mov    %fs:0x28,%rax
  mov    %rax,-0x28(%rbp)
  xor    %eax,%eax
  movl   $0x0,-0x3c(%rbp)
  mov    -0x68(%rbp),%rax
  add    $0xa,%rax
  movzwl (%rax),%eax
  movzwl %ax,%r9d
  mov    -0x68(%rbp),%rax
  add    $0x8,%rax
  movzwl (%rax),%eax
  movzwl %ax,%r8d
  mov    -0x68(%rbp),%rax
  add    $0x6,%rax
  movzwl (%rax),%eax
  movzwl %ax,%ecx
  mov    -0x68(%rbp),%rax
  add    $0x4,%rax
  movzwl (%rax),%eax
  movzwl %ax,%edx
  mov    -0x68(%rbp),%rax
  add    $0x2,%rax
  movzwl (%rax),%eax
  movzwl %ax,%esi
  mov    -0x68(%rbp),%rax
  movzwl (%rax),%eax
  movzwl %ax,%eax
  sub    $0x8,%rsp
  lea    -0x38(%rbp),%rdi
  push   %rdi
  mov    %eax,%edi
  call   <find_3bit_err_coefs@plt>
  add    $0x10,%rsp
  movw   $0x1,-0x52(%rbp)
  jmp    L88
L138:
  movzwl -0x52(%rbp),%ebx
  movzwl -0x52(%rbp),%edx
  movzwl -0x52(%rbp),%eax
  mov    %edx,%esi
  mov    %eax,%edi
  call   <gf4096_mul@plt>
  movzwl %ax,%eax
  mov    %ebx,%esi
  mov    %eax,%edi
  call   <gf4096_mul@plt>
  movzwl %ax,%edx
  movzwl -0x34(%rbp),%eax
  movzwl %ax,%eax
  mov    %edx,%esi
  mov    %eax,%edi
  call   <gf4096_mul@plt>
  mov    %eax,%ebx
  movzwl -0x52(%rbp),%edx
  movzwl -0x52(%rbp),%eax
  mov    %edx,%esi
  mov    %eax,%edi
  call   <gf4096_mul@plt>
  movzwl %ax,%edx
  movzwl -0x36(%rbp),%eax
  movzwl %ax,%eax
  mov    %edx,%esi
  mov    %eax,%edi
  call   <gf4096_mul@plt>
  xor    %eax,%ebx
  movzwl -0x52(%rbp),%edx
  movzwl -0x38(%rbp),%eax
  movzwl %ax,%eax
  mov    %edx,%esi
  mov    %eax,%edi
  call   <gf4096_mul@plt>
  xor    %ebx,%eax
  xor    $0x1,%eax
  mov    %ax,-0x50(%rbp)
  cmpw   $0x0,-0x50(%rbp)
  jne    L93
  cmpl   $0x0,-0x3c(%rbp)
  jne    L52
  movzwl -0x52(%rbp),%eax
  mov    %ax,-0x58(%rbp)
  movl   $0x1,-0x3c(%rbp)
  jmp    L93
L52:
  cmpl   $0x1,-0x3c(%rbp)
  jne    L23
  movzwl -0x52(%rbp),%eax
  mov    %ax,-0x56(%rbp)
  movl   $0x2,-0x3c(%rbp)
  jmp    L93
L23:
  cmpl   $0x2,-0x3c(%rbp)
  jne    L93
  movzwl -0x52(%rbp),%eax
  mov    %ax,-0x54(%rbp)
  movl   $0x3,-0x3c(%rbp)
  jmp    L62
L93:
  movzwl -0x52(%rbp),%eax
  add    $0x1,%eax
  mov    %ax,-0x52(%rbp)
L88:
  cmpw   $0xffe,-0x52(%rbp)
  jbe    L138
L62:
  cmpl   $0x3,-0x3c(%rbp)
  je     L156
  mov    D26(%rip),%rax
  mov    (%rax),%eax
  neg    %eax
  jmp    L87
L156:
  movzwl -0x58(%rbp),%eax
  mov    %eax,%edi
  call   <gf4096_inv@plt>
  mov    %ax,-0x4e(%rbp)
  movzwl -0x56(%rbp),%eax
  mov    %eax,%edi
  call   <gf4096_inv@plt>
  mov    %ax,-0x4c(%rbp)
  movzwl -0x54(%rbp),%eax
  mov    %eax,%edi
  call   <gf4096_inv@plt>
  mov    %ax,-0x4a(%rbp)
  movzwl -0x4a(%rbp),%r9d
  movzwl -0x4c(%rbp),%r8d
  movzwl -0x4e(%rbp),%ecx
  mov    -0x68(%rbp),%rax
  add    $0x4,%rax
  movzwl (%rax),%eax
  movzwl %ax,%edx
  mov    -0x68(%rbp),%rax
  add    $0x2,%rax
  movzwl (%rax),%eax
  movzwl %ax,%esi
  mov    -0x68(%rbp),%rax
  movzwl (%rax),%eax
  movzwl %ax,%eax
  sub    $0x8,%rsp
  lea    -0x30(%rbp),%rdi
  push   %rdi
  mov    %eax,%edi
  call   <find_3bit_err_pats@plt>
  add    $0x10,%rsp
  movzwl -0x4e(%rbp),%edx
  movzwl -0x4e(%rbp),%eax
  mov    %edx,%esi
  mov    %eax,%edi
  call   <gf4096_mul@plt>
  mov    %ax,-0x48(%rbp)
  movzwl -0x48(%rbp),%edx
  movzwl -0x48(%rbp),%eax
  mov    %edx,%esi
  mov    %eax,%edi
  call   <gf4096_mul@plt>
  mov    %ax,-0x48(%rbp)
  movzwl -0x4e(%rbp),%edx
  movzwl -0x48(%rbp),%eax
  mov    %edx,%esi
  mov    %eax,%edi
  call   <gf4096_mul@plt>
  mov    %ax,-0x48(%rbp)
  movzwl -0x4e(%rbp),%edx
  movzwl -0x48(%rbp),%eax
  mov    %edx,%esi
  mov    %eax,%edi
  call   <gf4096_mul@plt>
  mov    %ax,-0x48(%rbp)
  movzwl -0x4e(%rbp),%edx
  movzwl -0x48(%rbp),%eax
  mov    %edx,%esi
  mov    %eax,%edi
  call   <gf4096_mul@plt>
  mov    %ax,-0x46(%rbp)
  movzwl -0x4c(%rbp),%edx
  movzwl -0x4c(%rbp),%eax
  mov    %edx,%esi
  mov    %eax,%edi
  call   <gf4096_mul@plt>
  mov    %ax,-0x44(%rbp)
  movzwl -0x44(%rbp),%edx
  movzwl -0x44(%rbp),%eax
  mov    %edx,%esi
  mov    %eax,%edi
  call   <gf4096_mul@plt>
  mov    %ax,-0x44(%rbp)
  movzwl -0x4c(%rbp),%edx
  movzwl -0x44(%rbp),%eax
  mov    %edx,%esi
  mov    %eax,%edi
  call   <gf4096_mul@plt>
  mov    %ax,-0x44(%rbp)
  movzwl -0x4c(%rbp),%edx
  movzwl -0x44(%rbp),%eax
  mov    %edx,%esi
  mov    %eax,%edi
  call   <gf4096_mul@plt>
  mov    %ax,-0x44(%rbp)
  movzwl -0x4c(%rbp),%edx
  movzwl -0x44(%rbp),%eax
  mov    %edx,%esi
  mov    %eax,%edi
  call   <gf4096_mul@plt>
  mov    %ax,-0x42(%rbp)
  movzwl -0x4a(%rbp),%edx
  movzwl -0x4a(%rbp),%eax
  mov    %edx,%esi
  mov    %eax,%edi
  call   <gf4096_mul@plt>
  mov    %ax,-0x40(%rbp)
  movzwl -0x40(%rbp),%edx
  movzwl -0x40(%rbp),%eax
  mov    %edx,%esi
  mov    %eax,%edi
  call   <gf4096_mul@plt>
  mov    %ax,-0x40(%rbp)
  movzwl -0x4a(%rbp),%edx
  movzwl -0x40(%rbp),%eax
  mov    %edx,%esi
  mov    %eax,%edi
  call   <gf4096_mul@plt>
  mov    %ax,-0x40(%rbp)
  movzwl -0x4a(%rbp),%edx
  movzwl -0x40(%rbp),%eax
  mov    %edx,%esi
  mov    %eax,%edi
  call   <gf4096_mul@plt>
  mov    %ax,-0x40(%rbp)
  movzwl -0x4a(%rbp),%edx
  movzwl -0x40(%rbp),%eax
  mov    %edx,%esi
  mov    %eax,%edi
  call   <gf4096_mul@plt>
  mov    %ax,-0x3e(%rbp)
  mov    -0x68(%rbp),%rax
  add    $0xc,%rax
  movzwl (%rax),%ebx
  movzwl -0x48(%rbp),%edx
  movzwl -0x30(%rbp),%eax
  movzwl %ax,%eax
  mov    %edx,%esi
  mov    %eax,%edi
  call   <gf4096_mul@plt>
  mov    %eax,%r12d
  movzwl -0x44(%rbp),%edx
  movzwl -0x2e(%rbp),%eax
  movzwl %ax,%eax
  mov    %edx,%esi
  mov    %eax,%edi
  call   <gf4096_mul@plt>
  xor    %eax,%r12d
  movzwl -0x40(%rbp),%edx
  movzwl -0x2c(%rbp),%eax
  movzwl %ax,%eax
  mov    %edx,%esi
  mov    %eax,%edi
  call   <gf4096_mul@plt>
  xor    %r12d,%eax
  cmp    %ax,%bx
  sete   %r13b
  mov    -0x68(%rbp),%rax
  add    $0xe,%rax
  movzwl (%rax),%ebx
  movzwl -0x46(%rbp),%edx
  movzwl -0x30(%rbp),%eax
  movzwl %ax,%eax
  mov    %edx,%esi
  mov    %eax,%edi
  call   <gf4096_mul@plt>
  mov    %eax,%r12d
  movzwl -0x42(%rbp),%edx
  movzwl -0x2e(%rbp),%eax
  movzwl %ax,%eax
  mov    %edx,%esi
  mov    %eax,%edi
  call   <gf4096_mul@plt>
  xor    %eax,%r12d
  movzwl -0x3e(%rbp),%edx
  movzwl -0x2c(%rbp),%eax
  movzwl %ax,%eax
  mov    %edx,%esi
  mov    %eax,%edi
  call   <gf4096_mul@plt>
  xor    %r12d,%eax
  cmp    %ax,%bx
  sete   %al
  and    %r13d,%eax
  test   %al,%al
  je     L115
  movzwl -0x4e(%rbp),%eax
  mov    %eax,%edi
  call   <err_pos@plt>
  cmp    $0xfff,%eax
  sete   %bl
  movzwl -0x4c(%rbp),%eax
  mov    %eax,%edi
  call   <err_pos@plt>
  cmp    $0xfff,%eax
  sete   %al
  or     %ebx,%eax
  movzbl %al,%ebx
  movzwl -0x4a(%rbp),%eax
  mov    %eax,%edi
  call   <err_pos@plt>
  cmp    $0xfff,%eax
  sete   %al
  movzbl %al,%eax
  or     %ebx,%eax
  test   %eax,%eax
  je     L63
  mov    D26(%rip),%rax
  mov    (%rax),%eax
  neg    %eax
  jmp    L87
L63:
  mov    -0x70(%rbp),%rax
  movw   $0x3,(%rax)
  movzwl -0x4e(%rbp),%eax
  mov    %eax,%edi
  call   <err_pos@plt>
  mov    %eax,%ecx
  mov    -0x70(%rbp),%rax
  add    $0x2,%rax
  mov    $0x55e,%edx
  sub    %ecx,%edx
  mov    %dx,(%rax)
  movzwl -0x4c(%rbp),%eax
  mov    %eax,%edi
  call   <err_pos@plt>
  mov    %eax,%ecx
  mov    -0x70(%rbp),%rax
  add    $0x4,%rax
  mov    $0x55e,%edx
  sub    %ecx,%edx
  mov    %dx,(%rax)
  movzwl -0x4a(%rbp),%eax
  mov    %eax,%edi
  call   <err_pos@plt>
  mov    %eax,%ecx
  mov    -0x70(%rbp),%rax
  add    $0x6,%rax
  mov    $0x55e,%edx
  sub    %ecx,%edx
  mov    %dx,(%rax)
  mov    -0x70(%rbp),%rax
  lea    0xa(%rax),%rdx
  movzwl -0x30(%rbp),%eax
  mov    %ax,(%rdx)
  mov    -0x70(%rbp),%rax
  lea    0xc(%rax),%rdx
  movzwl -0x2e(%rbp),%eax
  mov    %ax,(%rdx)
  mov    -0x70(%rbp),%rax
  lea    0xe(%rax),%rdx
  movzwl -0x2c(%rbp),%eax
  mov    %ax,(%rdx)
  mov    $0x0,%eax
  jmp    L87
L115:
  mov    D26(%rip),%rax
  mov    (%rax),%eax
  neg    %eax
L87:
  mov    -0x28(%rbp),%rdx
  sub    %fs:0x28,%rdx
  je     L150
  call   <__stack_chk_fail@plt>
L150:
  lea    -0x18(%rbp),%rsp
  pop    %rbx
  pop    %r12
  pop    %r13
  pop    %rbp
  ret
```

assistant: ```c
int chk_3_err_only(unsigned short *chk_syndrome_list, unsigned short *err_info) {
  unsigned short tmp0, tmp1, tmp2, tmp3, tmp4, tmp5;
  unsigned short coefs[4];
  unsigned short err_pats[4];
  int found_num_root = 0;
  unsigned short bit3_root0, bit3_root1, bit3_root2;
  unsigned short bit3_root0_inv, bit3_root1_inv, bit3_root2_inv;
  unsigned short err_loc_eqn, test_root;
  find_3bit_err_coefs(chk_syndrome_list[0], chk_syndrome_list[1], chk_syndrome_list[2], chk_syndrome_list[3], chk_syndrome_list[4], chk_syndrome_list[5], coefs);
  for (test_root = 0x1; test_root < 0xfff; test_root++) {
    err_loc_eqn = gf4096_mul(coefs[2], gf4096_mul(gf4096_mul(test_root, test_root), test_root)) ^ gf4096_mul(coefs[1], gf4096_mul(test_root, test_root)) ^ gf4096_mul(coefs[0], test_root) ^ 0x1;
    if (err_loc_eqn == 0x0) {
      if (found_num_root == 0) {
        bit3_root0 = test_root;
        found_num_root = 1;
      } else if (found_num_root == 1) {
        bit3_root1 = test_root;
        found_num_root = 2;
      } else if (found_num_root == 2) {
        bit3_root2 = test_root;
        found_num_root = 3;
        break;
      }
    }
  }
  if (found_num_root != 3)
    return -EINVAL;
  else {
    bit3_root0_inv = gf4096_inv(bit3_root0);
    bit3_root1_inv = gf4096_inv(bit3_root1);
    bit3_root2_inv = gf4096_inv(bit3_root2);
    find_3bit_err_pats(chk_syndrome_list[0], chk_syndrome_list[1], chk_syndrome_list[2], bit3_root0_inv, bit3_root1_inv, bit3_root2_inv, err_pats);
    tmp0 = gf4096_mul(bit3_root0_inv, bit3_root0_inv);
    tmp0 = gf4096_mul(tmp0, tmp0);
    tmp0 = gf4096_mul(tmp0, bit3_root0_inv);
    tmp0 = gf4096_mul(tmp0, bit3_root0_inv);
    tmp1 = gf4096_mul(tmp0, bit3_root0_inv);
    tmp2 = gf4096_mul(bit3_root1_inv, bit3_root1_inv);
    tmp2 = gf4096_mul(tmp2, tmp2);
    tmp2 = gf4096_mul(tmp2, bit3_root1_inv);
    tmp2 = gf4096_mul(tmp2, bit3_root1_inv);
    tmp3 = gf4096_mul(tmp2, bit3_root1_inv);
    tmp4 = gf4096_mul(bit3_root2_inv, bit3_root2_inv);
    tmp4 = gf4096_mul(tmp4, tmp4);
    tmp4 = gf4096_mul(tmp4, bit3_root2_inv);
    tmp4 = gf4096_mul(tmp4, bit3_root2_inv);
    tmp5 = gf4096_mul(tmp4, bit3_root2_inv);
    if ((chk_syndrome_list[6] == (gf4096_mul(err_pats[0], tmp0) ^ gf4096_mul(err_pats[1], tmp2) ^ gf4096_mul(err_pats[2], tmp4))) & (chk_syndrome_list[7] == (gf4096_mul(err_pats[0], tmp1) ^ gf4096_mul(err_pats[1], tmp3) ^ gf4096_mul(err_pats[2], tmp5)))) {
      if ((err_pos(bit3_root0_inv) == 0xfff) | (err_pos(bit3_root1_inv) == 0xfff) | (err_pos(bit3_root2_inv) == 0xfff)) {
        return -EINVAL;
      } else {
        err_info[0] = 0x3;
        err_info[1] = (0x55e - err_pos(bit3_root0_inv));
        err_info[2] = (0x55e - err_pos(bit3_root1_inv));
        err_info[3] = (0x55e - err_pos(bit3_root2_inv));
        err_info[5] = err_pats[0];
        err_info[6] = err_pats[1];
        err_info[7] = err_pats[2];
        return 0;
      }
    } else
      return -EINVAL;
  }
}
```