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

```asm
<matrixToHessenbergForm_Householder_double>:
  endbr64
  push   %rbx
  pxor   %xmm6,%xmm6
  mov    %rdi,%rbx
  sub    $0x20,%rsp
  movsd  0x18(%rdi),%xmm2
  movsd  0x30(%rdi),%xmm3
  movapd %xmm2,%xmm0
  movapd %xmm3,%xmm4
  mulsd  %xmm3,%xmm4
  mulsd  %xmm2,%xmm0
  addsd  %xmm4,%xmm0
  ucomisd %xmm0,%xmm6
  ja     L11
  sqrtsd %xmm0,%xmm0
  movsd  %xmm0,(%rsp)
L4:
  movapd %xmm2,%xmm0
  movsd  %xmm4,0x18(%rsp)
  movsd  %xmm3,0x10(%rsp)
  movsd  %xmm2,0x8(%rsp)
  call   <signbit@plt>
  movsd  (%rsp),%xmm1
  movsd  0x8(%rsp),%xmm2
  pxor   %xmm5,%xmm5
  movsd  0x18(%rsp),%xmm4
  movsd  0x10(%rsp),%xmm3
  mulsd  %xmm0,%xmm1
  addsd  %xmm2,%xmm1
  movapd %xmm1,%xmm2
  mulsd  %xmm1,%xmm2
  addsd  %xmm4,%xmm2
  ucomisd %xmm2,%xmm5
  ja     L5
  sqrtsd %xmm2,%xmm2
L32:
  divsd  %xmm2,%xmm1
  movsd  0x18(%rbx),%xmm4
  movsd  0x40(%rbx),%xmm5
  movsd  0x30(%rbx),%xmm11
  movsd  0x20(%rbx),%xmm10
  divsd  %xmm2,%xmm3
  movapd %xmm1,%xmm9
  movapd %xmm1,%xmm8
  movapd %xmm1,%xmm7
  mulsd  %xmm4,%xmm9
  mulsd  %xmm10,%xmm8
  movapd %xmm3,%xmm2
  movapd %xmm3,%xmm0
  mulsd  %xmm11,%xmm2
  movapd %xmm0,%xmm6
  mulsd  %xmm5,%xmm6
  addsd  %xmm2,%xmm9
  movsd  0x38(%rbx),%xmm2
  mulsd  %xmm2,%xmm3
  movapd %xmm9,%xmm12
  addsd  %xmm3,%xmm8
  movsd  0x28(%rbx),%xmm3
  mulsd  %xmm3,%xmm7
  addsd  %xmm6,%xmm7
  movapd %xmm1,%xmm6
  addsd  %xmm1,%xmm6
  mulsd  %xmm6,%xmm12
  subsd  %xmm12,%xmm4
  movapd %xmm0,%xmm12
  movsd  %xmm4,0x18(%rbx)
  movapd %xmm8,%xmm4
  mulsd  %xmm6,%xmm4
  subsd  %xmm4,%xmm10
  movapd %xmm7,%xmm4
  mulsd  %xmm6,%xmm4
  subsd  %xmm4,%xmm3
  movapd %xmm0,%xmm4
  addsd  %xmm0,%xmm4
  mulsd  %xmm3,%xmm12
  mulsd  %xmm4,%xmm9
  mulsd  %xmm4,%xmm8
  mulsd  %xmm4,%xmm7
  subsd  %xmm9,%xmm11
  movapd %xmm1,%xmm9
  subsd  %xmm8,%xmm2
  movsd  0x10(%rbx),%xmm8
  subsd  %xmm7,%xmm5
  movapd %xmm0,%xmm7
  movsd  %xmm11,0x30(%rbx)
  movsd  0x8(%rbx),%xmm11
  mulsd  %xmm8,%xmm7
  mulsd  %xmm11,%xmm9
  mulsd  %xmm5,%xmm0
  addsd  %xmm7,%xmm9
  movapd %xmm1,%xmm7
  mulsd  %xmm10,%xmm7
  mulsd  %xmm2,%xmm1
  addsd  %xmm12,%xmm7
  movapd %xmm6,%xmm12
  addsd  %xmm0,%xmm1
  mulsd  %xmm9,%xmm12
  movapd %xmm6,%xmm0
  mulsd  %xmm7,%xmm0
  subsd  %xmm12,%xmm11
  subsd  %xmm0,%xmm10
  movapd %xmm4,%xmm0
  mulsd  %xmm1,%xmm0
  movsd  %xmm11,0x8(%rbx)
  mulsd  %xmm6,%xmm1
  movsd  %xmm10,0x20(%rbx)
  subsd  %xmm0,%xmm5
  subsd  %xmm1,%xmm2
  movsd  %xmm5,0x40(%rbx)
  movapd %xmm9,%xmm5
  mulsd  %xmm4,%xmm5
  mulsd  %xmm7,%xmm4
  subsd  %xmm5,%xmm8
  movq   D3(%rip),%xmm5
  subsd  %xmm4,%xmm3
  xorpd  %xmm5,%xmm2
  movapd %xmm8,%xmm0
  movsd  %xmm2,0x38(%rbx)
  xorpd  %xmm5,%xmm0
  xorpd  %xmm5,%xmm3
  movsd  %xmm0,0x10(%rbx)
  movsd  %xmm3,0x28(%rbx)
  add    $0x20,%rsp
  pop    %rbx
  ret
L11:
  movsd  %xmm4,0x18(%rsp)
  movsd  %xmm3,0x10(%rsp)
  movsd  %xmm2,0x8(%rsp)
  call   <sqrt@plt>
  movsd  0x18(%rsp),%xmm4
  movsd  0x10(%rsp),%xmm3
  movsd  0x8(%rsp),%xmm2
  movsd  %xmm0,(%rsp)
  jmp    L4
L5:
  movapd %xmm2,%xmm0
  movsd  %xmm1,0x8(%rsp)
  movsd  %xmm3,(%rsp)
  call   <sqrt@plt>
  movsd  0x8(%rsp),%xmm1
  movsd  (%rsp),%xmm3
  movapd %xmm0,%xmm2
  jmp    L32
```

tool_calls: name: read_data
arguments: data_tag: D3
type: f32[2]

tool: {"D3": [0.0,-0.0]}

assistant: ```c
void matrixToHessenbergForm_Householder_double(double *A) {
  double vk[2] = {
      0.0,
      0.0,
  };
  double vk_norm = 0.0;
  double dot_array[3] = {0.0, 0.0, 0.0};
  vk[0] = A[3];
  vk[1] = A[6];
  vk_norm = sqrt(vk[0] * vk[0] + vk[1] * vk[1]);
  vk[0] += signbit(vk[0]) * vk_norm;
  vk_norm = sqrt(vk[0] * vk[0] + vk[1] * vk[1]);
  vk[0] /= vk_norm;
  vk[1] /= vk_norm;
  dot_array[0] = vk[0] * A[3] + vk[1] * A[6];
  dot_array[1] = vk[0] * A[4] + vk[1] * A[7];
  dot_array[2] = vk[0] * A[5] + vk[1] * A[8];
  A[3] -= 2 * vk[0] * dot_array[0];
  A[4] -= 2 * vk[0] * dot_array[1];
  A[5] -= 2 * vk[0] * dot_array[2];
  A[6] -= 2 * vk[1] * dot_array[0];
  A[7] -= 2 * vk[1] * dot_array[1];
  A[8] -= 2 * vk[1] * dot_array[2];
  dot_array[0] = vk[0] * A[1] + vk[1] * A[2];
  dot_array[1] = vk[0] * A[4] + vk[1] * A[5];
  dot_array[2] = vk[0] * A[7] + vk[1] * A[8];
  A[1] -= 2 * vk[0] * dot_array[0];
  A[2] -= 2 * vk[1] * dot_array[0];
  A[4] -= 2 * vk[0] * dot_array[1];
  A[5] -= 2 * vk[1] * dot_array[1];
  A[7] -= 2 * vk[0] * dot_array[2];
  A[8] -= 2 * vk[1] * dot_array[2];
  A[2] = -A[2];
  A[5] = -A[5];
  A[7] = -A[7];
}
```