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

```asm
<eigen_symm_2d>:
  endbr64
  push   %r13
  push   %r12
  push   %rbp
  push   %rbx
  sub    $0x18,%rsp
  mov    %rdi,%rbp
  mov    %rsi,%rbx
  mov    (%rdx),%rax
  mov    (%rax),%r13
  mov    0x8(%rax),%r12
  mov    0x8(%rdx),%rax
  movsd  0x8(%rax),%xmm2
  movq   %r12,%xmm0
  mulsd  %xmm0,%xmm0
  movq   %r13,%xmm3
  mulsd  %xmm2,%xmm3
  movapd %xmm3,%xmm1
  andpd  D49(%rip),%xmm1
  mulsd  D20(%rip),%xmm1
  comisd %xmm0,%xmm1
  jbe    L33
  movq   D49(%rip),%xmm0
  movq   %r13,%xmm1
  andpd  %xmm0,%xmm1
  andpd  %xmm2,%xmm0
  comisd %xmm1,%xmm0
  jbe    L34
  mov    %r13,(%rdi)
  movsd  %xmm2,0x8(%rdi)
  mov    0x8(%rsi),%rax
  movsd  D16(%rip),%xmm0
  movsd  %xmm0,0x8(%rax)
  mov    (%rsi),%rax
  movsd  %xmm0,(%rax)
  mov    0x8(%rsi),%rax
  movq   $0x0,(%rax)
  mov    (%rsi),%rax
  movq   $0x0,0x8(%rax)
  jmp    L66
L34:
  movsd  %xmm2,(%rdi)
  mov    %r13,0x8(%rdi)
  mov    0x8(%rsi),%rax
  movq   $0x0,0x8(%rax)
  mov    (%rsi),%rax
  movq   $0x0,(%rax)
  mov    0x8(%rsi),%rax
  movsd  D16(%rip),%xmm0
  movsd  %xmm0,(%rax)
  mov    (%rsi),%rax
  movsd  %xmm0,0x8(%rax)
  jmp    L66
L33:
  movapd %xmm2,%xmm4
  movq   %r13,%xmm6
  addsd  %xmm6,%xmm4
  movsd  %xmm4,0x8(%rsp)
  subsd  %xmm3,%xmm0
  mulsd  D3(%rip),%xmm0
  movapd %xmm4,%xmm1
  mulsd  %xmm4,%xmm1
  addsd  %xmm1,%xmm0
  pxor   %xmm1,%xmm1
  ucomisd %xmm0,%xmm1
  ja     L43
  sqrtsd %xmm0,%xmm0
L21:
  movsd  0x8(%rsp),%xmm5
  movapd %xmm5,%xmm2
  addsd  %xmm0,%xmm2
  movsd  D25(%rip),%xmm3
  mulsd  %xmm3,%xmm2
  subsd  %xmm0,%xmm5
  movapd %xmm5,%xmm0
  mulsd  %xmm3,%xmm0
  movq   D49(%rip),%xmm1
  movapd %xmm2,%xmm3
  andpd  %xmm1,%xmm3
  andpd  %xmm0,%xmm1
  comisd %xmm3,%xmm1
  jbe    L10
  movsd  %xmm2,0x0(%rbp)
  movsd  %xmm0,0x8(%rbp)
L18:
  movsd  0x0(%rbp),%xmm1
  movq   %r13,%xmm5
  subsd  %xmm5,%xmm1
  movq   %r12,%xmm0
  call   <hypot@plt>
  movsd  %xmm0,0x8(%rsp)
  movsd  0x8(%rbp),%xmm1
  movq   %r13,%xmm6
  subsd  %xmm6,%xmm1
  movq   %r12,%xmm0
  call   <hypot@plt>
  mov    (%rbx),%rax
  movq   %r12,%xmm1
  movsd  0x8(%rsp),%xmm7
  divsd  %xmm7,%xmm1
  movsd  %xmm1,(%rax)
  mov    (%rbx),%rax
  movsd  0x0(%rbp),%xmm1
  movq   %r13,%xmm5
  subsd  %xmm5,%xmm1
  divsd  %xmm7,%xmm1
  movsd  %xmm1,0x8(%rax)
  mov    0x8(%rbx),%rax
  movq   %r12,%xmm1
  divsd  %xmm0,%xmm1
  movsd  %xmm1,(%rax)
  mov    0x8(%rbx),%rax
  movsd  0x8(%rbp),%xmm1
  subsd  %xmm5,%xmm1
  divsd  %xmm0,%xmm1
  movsd  %xmm1,0x8(%rax)
L66:
  add    $0x18,%rsp
  pop    %rbx
  pop    %rbp
  pop    %r12
  pop    %r13
  ret
L43:
  call   <sqrt@plt>
  jmp    L21
L10:
  movsd  %xmm2,0x8(%rbp)
  movsd  %xmm0,0x0(%rbp)
  jmp    L18
```

tool_calls: name: parse_data
arguments: data_label: D49
type_infered: qword[2]
name: parse_data
arguments: data_label: D20
type_infered: byte[8]
name: parse_data
arguments: data_label: D16
type_infered: f64
name: parse_data
arguments: data_label: D3
type_infered: f64
name: parse_data
arguments: data_label: D25
type_infered: f32[2]

tool: {"D49": [0x7fffffffffffffff,0x0000000000000000]}

tool: {"D20": [0xbc,0x89,0xd8,0x97,0xb2,0xd2,0x9c,0x3c]}

tool: D16: 1

tool: D3: 4

tool: {"D25": [0.0,1.75]}

assistant: ```c
void eigen_symm_2d(double z[], double **V, double **X) {
  double a = X[0][0];
  double b = X[0][1];
  double c = X[1][1];
  const double epsilon = 1e-16;
  if (b * b < epsilon * fabs(a * c)) {
    if (fabs(a) < fabs(c)) {
      z[0] = a;
      z[1] = c;
      V[0][0] = V[1][1] = 1.0;
      V[0][1] = V[1][0] = 0.0;
    } else {
      z[0] = c;
      z[1] = a;
      V[0][0] = V[1][1] = 0.0;
      V[0][1] = V[1][0] = 1.0;
    }
    return;
  }
  double s = sqrt((a + c) * (a + c) + 4. * (b * b - a * c));
  double z1 = (a + c + s) / 2.;
  double z2 = (a + c - s) / 2.;
  if (fabs(z1) < fabs(z2)) {
    z[0] = z1;
    z[1] = z2;
  } else {
    z[1] = z1;
    z[0] = z2;
  }
  double d0 = hypot(b, z[0] - a);
  double d1 = hypot(b, z[1] - a);
  V[0][0] = b / d0;
  V[0][1] = (z[0] - a) / d0;
  V[1][0] = b / d1;
  V[1][1] = (z[1] - a) / d1;
}
```