user: Demonstrate the C code that generates the assembly output below:

```asm
<Polynomial_Extrapolation_to_Zero>:
  endbr64
  push   %rbp
  mov    %rsp,%rbp
  mov    %rdi,-0x48(%rbp)
  mov    %rsi,-0x50(%rbp)
  mov    %rdx,-0x58(%rbp)
  movsd  %xmm0,-0x60(%rbp)
  mov    %ecx,-0x64(%rbp)
  cmpl   $0x0,-0x64(%rbp)
  jne    L118
  mov    -0x50(%rbp),%rax
  movsd  -0x60(%rbp),%xmm0
  movsd  %xmm0,(%rax)
  mov    $0x0,%eax
  jmp    L40
L118:
  mov    -0x64(%rbp),%eax
  cltq
  lea    0x0(,%rax,8),%rdx
  mov    -0x58(%rbp),%rax
  add    %rdx,%rax
  movsd  (%rax),%xmm0
  pxor   %xmm1,%xmm1
  ucomisd %xmm1,%xmm0
  jp     L135
  pxor   %xmm1,%xmm1
  ucomisd %xmm1,%xmm0
  jne    L135
  mov    -0x48(%rbp),%rax
  movsd  -0x60(%rbp),%xmm0
  movsd  %xmm0,(%rax)
  mov    $0xfffffffe,%eax
  jmp    L40
L135:
  pxor   %xmm0,%xmm0
  movsd  %xmm0,-0x30(%rbp)
  mov    -0x50(%rbp),%rax
  movsd  (%rax),%xmm0
  movsd  %xmm0,-0x28(%rbp)
  mov    -0x50(%rbp),%rax
  movsd  -0x60(%rbp),%xmm0
  movsd  %xmm0,(%rax)
  movl   $0x0,-0x34(%rbp)
  jmp    L122
L100:
  mov    -0x34(%rbp),%eax
  cltq
  lea    0x0(,%rax,8),%rdx
  mov    -0x50(%rbp),%rax
  add    %rdx,%rax
  movsd  (%rax),%xmm0
  pxor   %xmm1,%xmm1
  ucomisd %xmm1,%xmm0
  jp     L80
  pxor   %xmm1,%xmm1
  ucomisd %xmm1,%xmm0
  jne    L80
  pxor   %xmm0,%xmm0
  ucomisd -0x28(%rbp),%xmm0
  jp     L80
  pxor   %xmm0,%xmm0
  ucomisd -0x28(%rbp),%xmm0
  jne    L80
  mov    -0x64(%rbp),%eax
  cltq
  lea    0x0(,%rax,8),%rdx
  mov    -0x50(%rbp),%rax
  add    %rdx,%rax
  pxor   %xmm0,%xmm0
  movsd  %xmm0,(%rax)
  jmp    L46
L80:
  mov    -0x34(%rbp),%eax
  cltq
  lea    0x0(,%rax,8),%rdx
  mov    -0x50(%rbp),%rax
  add    %rdx,%rax
  movsd  (%rax),%xmm0
  subsd  -0x28(%rbp),%xmm0
  movsd  %xmm0,-0x20(%rbp)
  mov    -0x34(%rbp),%eax
  cltq
  lea    0x0(,%rax,8),%rdx
  mov    -0x50(%rbp),%rax
  add    %rdx,%rax
  movsd  (%rax),%xmm0
  subsd  -0x30(%rbp),%xmm0
  movsd  %xmm0,-0x18(%rbp)
  movsd  -0x18(%rbp),%xmm0
  subsd  -0x20(%rbp),%xmm0
  movsd  %xmm0,-0x10(%rbp)
  mov    -0x64(%rbp),%eax
  sub    -0x34(%rbp),%eax
  cltq
  shl    $0x3,%rax
  lea    -0x8(%rax),%rdx
  mov    -0x58(%rbp),%rax
  add    %rdx,%rax
  movsd  (%rax),%xmm0
  mov    -0x64(%rbp),%eax
  cltq
  lea    0x0(,%rax,8),%rdx
  mov    -0x58(%rbp),%rax
  add    %rdx,%rax
  movsd  (%rax),%xmm1
  divsd  %xmm1,%xmm0
  mulsd  -0x10(%rbp),%xmm0
  subsd  -0x18(%rbp),%xmm0
  movsd  %xmm0,-0x8(%rbp)
  pxor   %xmm0,%xmm0
  ucomisd -0x8(%rbp),%xmm0
  jp     L76
  pxor   %xmm0,%xmm0
  ucomisd -0x8(%rbp),%xmm0
  jne    L76
  mov    $0xffffffff,%eax
  jmp    L40
L76:
  movsd  -0x28(%rbp),%xmm0
  movsd  %xmm0,-0x30(%rbp)
  mov    -0x34(%rbp),%eax
  cltq
  add    $0x1,%rax
  lea    0x0(,%rax,8),%rdx
  mov    -0x50(%rbp),%rax
  add    %rdx,%rax
  movsd  (%rax),%xmm0
  movsd  %xmm0,-0x28(%rbp)
  mov    -0x34(%rbp),%eax
  cltq
  lea    0x0(,%rax,8),%rdx
  mov    -0x50(%rbp),%rax
  add    %rdx,%rax
  movsd  (%rax),%xmm1
  movsd  -0x20(%rbp),%xmm0
  mulsd  -0x18(%rbp),%xmm0
  divsd  -0x8(%rbp),%xmm0
  mov    -0x34(%rbp),%eax
  cltq
  add    $0x1,%rax
  lea    0x0(,%rax,8),%rdx
  mov    -0x50(%rbp),%rax
  add    %rdx,%rax
  addsd  %xmm1,%xmm0
  movsd  %xmm0,(%rax)
  addl   $0x1,-0x34(%rbp)
L122:
  mov    -0x34(%rbp),%eax
  cmp    -0x64(%rbp),%eax
  jl     L100
L46:
  mov    -0x64(%rbp),%eax
  cltq
  lea    0x0(,%rax,8),%rdx
  mov    -0x50(%rbp),%rax
  add    %rdx,%rax
  movsd  (%rax),%xmm0
  mov    -0x48(%rbp),%rax
  movsd  %xmm0,(%rax)
  mov    $0x0,%eax
L40:
  pop    %rbp
  ret
```

assistant: ```c
int Polynomial_Extrapolation_to_Zero(double *fzero, double tableau[], double x[], double f, int n) {
  double back_two_columns;
  double old_aux;
  double new_value;
  double vertical_diff;
  double backslant_diff;
  double forwardslant_diff;
  double denominator;
  int i;
  if (n == 0) {
    tableau[0] = f;
    return 0;
  }
  if (x[n] == 0.0) {
    *fzero = f;
    return -2;
  }
  back_two_columns = 0.0;
  old_aux = tableau[0];
  tableau[0] = f;
  for (i = 0; i < n; i++) {
    if (tableau[i] == 0 && old_aux == 0) {
      tableau[n] = 0.0;
      break;
    }
    vertical_diff = tableau[i] - old_aux;
    backslant_diff = tableau[i] - back_two_columns;
    forwardslant_diff = backslant_diff - vertical_diff;
    denominator = (x[n - i - 1] / x[n]) * forwardslant_diff - backslant_diff;
    if (denominator == 0.0)
      return -1;
    back_two_columns = old_aux;
    old_aux = tableau[i + 1];
    tableau[i + 1] = tableau[i] + vertical_diff * backslant_diff / denominator;
  }
  *fzero = tableau[n];
  return 0;
}
```