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

```asm
<nfa>:
  endbr64
  push   %r13
  mov    %edi,%eax
  push   %r12
  push   %rbp
  mov    %edi,%ebp
  push   %rbx
  mov    %esi,%ebx
  sub    $0x48,%rsp
  or     %esi,%eax
  movsd  %xmm0,0x8(%rsp)
  movsd  %xmm1,(%rsp)
  js     L10
  cmp    %esi,%edi
  jl     L10
  movapd %xmm0,%xmm5
  pxor   %xmm0,%xmm0
  comisd %xmm5,%xmm0
  jae    L10
  comisd D143(%rip),%xmm5
  jb     L4
  nop
L10:
  lea    D85(%rip),%rdi
  call   <error@plt>
L4:
  test   %ebp,%ebp
  je     L8
  test   %ebx,%ebx
  je     L8
  pxor   %xmm5,%xmm5
  cvtsi2sd %ebp,%xmm5
  movsd  %xmm5,0x30(%rsp)
  cmp    %ebx,%ebp
  je     L80
  pxor   %xmm0,%xmm0
  movsd  D143(%rip),%xmm4
  cvtsi2sd %ebp,%xmm0
  movapd %xmm4,%xmm7
  subsd  0x8(%rsp),%xmm7
  addsd  %xmm4,%xmm0
  comisd D50(%rip),%xmm0
  movsd  %xmm7,0x18(%rsp)
  ja     L204
  call   <log_gamma_lanczos@plt>
  mov    D143(%rip),%rax
  movapd %xmm0,%xmm2
  movq   %rax,%xmm4
L162:
  pxor   %xmm7,%xmm7
  movsd  %xmm2,0x20(%rsp)
  cvtsi2sd %ebx,%xmm7
  movapd %xmm7,%xmm0
  movsd  %xmm7,0x10(%rsp)
  addsd  %xmm4,%xmm0
  comisd D50(%rip),%xmm0
  jbe    L63
  call   <log_gamma_windschitl@plt>
  mov    D143(%rip),%rax
  movsd  0x20(%rsp),%xmm2
  movq   %rax,%xmm4
L234:
  mov    %ebp,%eax
  pxor   %xmm5,%xmm5
  subsd  %xmm0,%xmm2
  sub    %ebx,%eax
  cvtsi2sd %eax,%xmm5
  movq   %xmm2,%r13
  movapd %xmm5,%xmm0
  movsd  %xmm5,0x20(%rsp)
  addsd  %xmm4,%xmm0
  comisd D50(%rip),%xmm0
  jbe    L110
  call   <log_gamma_windschitl@plt>
  movsd  %xmm0,0x28(%rsp)
L129:
  movsd  0x8(%rsp),%xmm0
  call   <log@plt>
  movq   %xmm0,%r12
  movsd  0x18(%rsp),%xmm0
  call   <log@plt>
  movq   %r12,%xmm5
  movsd  0x20(%rsp),%xmm3
  movq   %r13,%xmm2
  mulsd  0x10(%rsp),%xmm5
  subsd  0x28(%rsp),%xmm2
  mulsd  %xmm0,%xmm3
  addsd  %xmm5,%xmm2
  addsd  %xmm3,%xmm2
  movapd %xmm2,%xmm0
  movsd  %xmm2,0x28(%rsp)
  call   <exp@plt>
  pxor   %xmm1,%xmm1
  movsd  %xmm0,0x20(%rsp)
  call   <double_equal@plt>
  movsd  0x20(%rsp),%xmm3
  test   %rax,%rax
  mov    D143(%rip),%rax
  movq   %rax,%xmm4
  je     L219
  movsd  0x8(%rsp),%xmm0
  mulsd  0x30(%rsp),%xmm0
  movsd  0x10(%rsp),%xmm7
  comisd %xmm0,%xmm7
  ja     L92
L8:
  movsd  (%rsp),%xmm0
  xorpd  D111(%rip),%xmm0
L0:
  add    $0x48,%rsp
  pop    %rbx
  pop    %rbp
  pop    %r12
  pop    %r13
  ret
  nopw   0x0(%rax,%rax,1)
L204:
  call   <log_gamma_windschitl@plt>
  mov    D143(%rip),%rax
  movapd %xmm0,%xmm2
  movq   %rax,%xmm4
  jmp    L162
  nopw   0x0(%rax,%rax,1)
L219:
  add    $0x1,%ebx
  cmp    %ebx,%ebp
  jl     L192
  movq   D111(%rip),%xmm7
  movslq %ebx,%rbx
  movapd %xmm3,%xmm2
  lea    0x1(%rbp),%r12d
  movsd  0x8(%rsp),%xmm5
  lea    D107(%rip),%r13
  divsd  0x18(%rsp),%xmm5
  movaps %xmm7,0x30(%rsp)
  jmp    L93
L59:
  movsd  0x0(%r13,%rbx,8),%xmm0
  pxor   %xmm7,%xmm7
  ucomisd %xmm7,%xmm0
  jp     L248
  jne    L248
  pxor   %xmm6,%xmm6
  movapd %xmm4,%xmm0
  cvtsi2sd %ebx,%xmm6
  divsd  %xmm6,%xmm0
  movsd  %xmm0,0x0(%r13,%rbx,8)
L248:
  mulsd  %xmm1,%xmm0
  movapd %xmm5,%xmm6
  mulsd  %xmm0,%xmm6
  comisd %xmm0,%xmm4
  mulsd  %xmm6,%xmm3
  addsd  %xmm3,%xmm2
  ja     L117
L171:
  add    $0x1,%rbx
  cmp    %ebx,%ebp
  jl     L140
L93:
  mov    %r12d,%eax
  pxor   %xmm1,%xmm1
  sub    %ebx,%eax
  cvtsi2sd %eax,%xmm1
  cmp    $0x1869f,%ebx
  jle    L59
  pxor   %xmm6,%xmm6
  movapd %xmm4,%xmm0
  cvtsi2sd %ebx,%xmm6
  divsd  %xmm6,%xmm0
  jmp    L248
  nopw   0x0(%rax,%rax,1)
L117:
  movapd %xmm6,%xmm0
  movsd  %xmm3,0x28(%rsp)
  movsd  %xmm5,0x20(%rsp)
  movsd  %xmm6,0x18(%rsp)
  movsd  %xmm2,0x10(%rsp)
  call   <pow@plt>
  movsd  0x10(%rsp),%xmm2
  movsd  %xmm0,0x8(%rsp)
  movapd %xmm2,%xmm0
  call   <log10@plt>
  mov    D143(%rip),%rax
  movsd  0x18(%rsp),%xmm6
  xorpd  0x30(%rsp),%xmm0
  subsd  (%rsp),%xmm0
  movq   %rax,%xmm7
  movq   %rax,%xmm1
  movq   %rax,%xmm4
  movsd  0x10(%rsp),%xmm2
  subsd  0x8(%rsp),%xmm1
  subsd  %xmm6,%xmm7
  andpd  D49(%rip),%xmm0
  mulsd  D189(%rip),%xmm0
  movsd  0x28(%rsp),%xmm3
  movsd  0x20(%rsp),%xmm5
  divsd  %xmm7,%xmm1
  mulsd  %xmm2,%xmm0
  subsd  %xmm4,%xmm1
  mulsd  %xmm3,%xmm1
  comisd %xmm1,%xmm0
  jbe    L171
L140:
  movapd %xmm2,%xmm0
  call   <log10@plt>
  xorpd  0x30(%rsp),%xmm0
  subsd  (%rsp),%xmm0
  add    $0x48,%rsp
  pop    %rbx
  pop    %rbp
  pop    %r12
  pop    %r13
  ret
  nopw   0x0(%rax,%rax,1)
L110:
  call   <log_gamma_lanczos@plt>
  movsd  %xmm0,0x28(%rsp)
  jmp    L129
  nopl   0x0(%rax,%rax,1)
L63:
  call   <log_gamma_lanczos@plt>
  mov    D143(%rip),%rax
  movsd  0x20(%rsp),%xmm2
  movq   %rax,%xmm4
  jmp    L234
  nopl   0x0(%rax)
L92:
  movsd  0x28(%rsp),%xmm2
  xorpd  D111(%rip),%xmm2
  movapd %xmm2,%xmm0
  divsd  D165(%rip),%xmm0
  subsd  (%rsp),%xmm0
  add    $0x48,%rsp
  pop    %rbx
  pop    %rbp
  pop    %r12
  pop    %r13
  ret
  nopw   0x0(%rax,%rax,1)
L80:
  movsd  0x8(%rsp),%xmm0
  call   <log10@plt>
  movapd %xmm0,%xmm1
  movsd  (%rsp),%xmm0
  xorpd  D111(%rip),%xmm0
  mulsd  0x30(%rsp),%xmm1
  subsd  %xmm1,%xmm0
  jmp    L0
L192:
  movq   D111(%rip),%xmm4
  movapd %xmm3,%xmm2
  movaps %xmm4,0x30(%rsp)
  jmp    L140
```

tool_calls: name: parse_data
arguments: data_label: D143
datatype: f64[2]
name: parse_data
arguments: data_label: D85
datatype: string
name: parse_data
arguments: data_label: D50
datatype: f64[2]
name: parse_data
arguments: data_label: D111
datatype: f32[4]
name: parse_data
arguments: data_label: D49
datatype: qword[2]
name: parse_data
arguments: data_label: D189
datatype: f64
name: parse_data
arguments: data_label: D165
datatype: f64

tool: {"D143": [1.0,15.0]}

tool: D85: nfa: wrong n, k or p values.

tool: {"D50": [15.0,2.302585092994046]}

tool: {"D111": [0.0,-0.0,0.0,0.0]}

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

tool: D189: 0.1

tool: D165: 2.302585092994046

assistant: ```c
double nfa(int n, int k, double p, double logNT) {
  static double inv[100000];
  double tolerance = 0.1;
  double log1term, term, bin_term, mult_term, bin_tail, err, p_term;
  int i;
  if (n < 0 || k < 0 || k > n || p <= 0.0 || p >= 1.0)
    error("nfa: wrong n, k or p values.");
  if (n == 0 || k == 0)
    return -logNT;
  if (n == k)
    return -logNT - (double)n * log10(p);
  p_term = p / (1.0 - p);
  log1term = (((double)n + 1.0) > 15.0 ? log_gamma_windschitl((double)n + 1.0) : log_gamma_lanczos((double)n + 1.0)) - (((double)k + 1.0) > 15.0 ? log_gamma_windschitl((double)k + 1.0) : log_gamma_lanczos((double)k + 1.0)) - (((double)(n - k) + 1.0) > 15.0 ? log_gamma_windschitl((double)(n - k) + 1.0) : log_gamma_lanczos((double)(n - k) + 1.0)) + (double)k * log(p) + (double)(n - k) * log(1.0 - p);
  term = exp(log1term);
  if (double_equal(term, 0.0)) {
    if ((double)k > (double)n * p)
      return -log1term / 2.30258509299404568402 - logNT;
    else
      return -logNT;
  }
  bin_tail = term;
  for (i = k + 1; i <= n; i++) {
    bin_term = (double)(n - i + 1) * (i < 100000 ? (inv[i] != 0.0 ? inv[i] : (inv[i] = 1.0 / (double)i)) : 1.0 / (double)i);
    mult_term = bin_term * p_term;
    term *= mult_term;
    bin_tail += term;
    if (bin_term < 1.0) {
      err = term * ((1.0 - pow(mult_term, (double)(n - i + 1))) / (1.0 - mult_term) - 1.0);
      if (err < tolerance * fabs(-log10(bin_tail) - logNT) * bin_tail)
        break;
    }
  }
  return -log10(bin_tail) - logNT;
}
```