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

```asm
<mp_mul_rcmul_nt_in2>:
  endbr64
  push   %r15
  pxor   %xmm0,%xmm0
  push   %r14
  mov    %rsi,%r14
  push   %r13
  mov    %rdx,%r13
  push   %r12
  push   %rbp
  push   %rbx
  movslq %edi,%rbx
  cvtsi2sd %ebx,%xmm0
  sub    $0x38,%rsp
  movsd  D31(%rip),%xmm1
  lea    0x28(%rsp),%rbp
  lea    0x20(%rsp),%r12
  divsd  %xmm0,%xmm1
  mov    %r12,%rsi
  mov    %rbp,%rdi
  movapd %xmm1,%xmm0
  movsd  %xmm1,0x8(%rsp)
  call   <sincos@plt>
  movsd  0x28(%rsp),%xmm10
  movsd  0x20(%rsp),%xmm2
  mov    %ebx,%esi
  movsd  D36(%rip),%xmm1
  sar    %esi
  add    $0x1,%rbx
  movsd  D9(%rip),%xmm9
  mulsd  %xmm10,%xmm2
  movslq %esi,%rax
  mulsd  %xmm10,%xmm10
  movapd %xmm2,%xmm8
  movapd %xmm10,%xmm0
  addsd  %xmm2,%xmm8
  addsd  %xmm10,%xmm0
  movsd  %xmm8,0x18(%rsp)
  addsd  %xmm8,%xmm8
  subsd  %xmm0,%xmm1
  movsd  %xmm1,0x10(%rsp)
  movupd (%r14,%rax,8),%xmm1
  lea    0x0(%r13,%rax,8),%rax
  movupd (%rax),%xmm0
  movapd %xmm1,%xmm3
  unpcklpd %xmm1,%xmm3
  unpckhpd %xmm1,%xmm1
  mulpd  %xmm0,%xmm3
  shufpd $0x1,%xmm0,%xmm0
  mulpd  %xmm1,%xmm0
  movapd %xmm3,%xmm1
  subpd  %xmm0,%xmm1
  addpd  %xmm3,%xmm0
  movsd  %xmm1,%xmm0
  movups %xmm0,(%rax)
  pxor   %xmm0,%xmm0
  movapd %xmm0,%xmm1
  xchg   %ax,%ax
L13:
  mov    $0x2,%eax
  lea    -0x100(%rsi),%r15d
  cmp    %eax,%r15d
  cmovl  %eax,%r15d
  lea    -0x2(%rsi),%eax
  cmp    %eax,%r15d
  jg     L28
  cltq
  mov    %rbx,%rdx
  sub    %rax,%rdx
  shl    $0x3,%rdx
  lea    (%r14,%rdx,1),%rcx
  add    %r13,%rdx
  nopw   0x0(%rax,%rax,1)
L27:
  movapd %xmm10,%xmm3
  movapd %xmm8,%xmm10
  movapd %xmm2,%xmm6
  movsd  (%r14,%rax,8),%xmm5
  mulsd  %xmm2,%xmm10
  movapd %xmm9,%xmm2
  movsd  -0x8(%rcx),%xmm7
  movsd  0x8(%r14,%rax,8),%xmm12
  subsd  %xmm3,%xmm2
  movsd  (%rcx),%xmm13
  add    $0x10,%rdx
  add    $0x10,%rcx
  movapd %xmm5,%xmm14
  subsd  %xmm7,%xmm14
  mulsd  %xmm8,%xmm2
  addsd  %xmm1,%xmm10
  movapd %xmm12,%xmm1
  addsd  %xmm13,%xmm1
  movapd %xmm14,%xmm4
  mulsd  %xmm3,%xmm4
  mulsd  %xmm6,%xmm14
  addsd  %xmm0,%xmm2
  movapd %xmm1,%xmm0
  mulsd  %xmm6,%xmm0
  mulsd  %xmm3,%xmm1
  subsd  %xmm0,%xmm4
  addsd  %xmm14,%xmm1
  subsd  %xmm4,%xmm5
  addsd  %xmm4,%xmm7
  subsd  %xmm1,%xmm12
  subsd  %xmm1,%xmm13
  movsd  %xmm5,(%r14,%rax,8)
  movsd  %xmm12,0x8(%r14,%rax,8)
  movsd  %xmm7,-0x18(%rcx)
  movsd  %xmm13,-0x10(%rcx)
  movsd  0x0(%r13,%rax,8),%xmm11
  movsd  0x8(%r13,%rax,8),%xmm0
  movapd %xmm11,%xmm4
  movapd %xmm0,%xmm1
  mulsd  %xmm12,%xmm1
  mulsd  %xmm5,%xmm0
  mulsd  %xmm5,%xmm4
  mulsd  %xmm12,%xmm11
  subsd  %xmm1,%xmm4
  movsd  -0x10(%rdx),%xmm1
  addsd  %xmm0,%xmm11
  movsd  -0x18(%rdx),%xmm0
  movapd %xmm1,%xmm5
  mulsd  %xmm13,%xmm5
  movapd %xmm0,%xmm12
  mulsd  %xmm7,%xmm1
  mulsd  %xmm7,%xmm12
  movapd %xmm4,%xmm7
  mulsd  %xmm13,%xmm0
  subsd  %xmm5,%xmm12
  addsd  %xmm1,%xmm0
  movapd %xmm11,%xmm1
  subsd  %xmm12,%xmm7
  addsd  %xmm0,%xmm1
  movapd %xmm7,%xmm5
  mulsd  %xmm3,%xmm5
  movapd %xmm1,%xmm13
  mulsd  %xmm6,%xmm13
  mulsd  %xmm3,%xmm1
  mulsd  %xmm6,%xmm7
  addsd  %xmm13,%xmm5
  subsd  %xmm7,%xmm1
  subsd  %xmm5,%xmm4
  addsd  %xmm12,%xmm5
  subsd  %xmm1,%xmm11
  subsd  %xmm1,%xmm0
  movapd %xmm3,%xmm1
  movsd  %xmm4,0x0(%r13,%rax,8)
  movsd  %xmm11,0x8(%r13,%rax,8)
  sub    $0x2,%rax
  movsd  %xmm0,-0x10(%rdx)
  movapd %xmm6,%xmm0
  movsd  %xmm5,-0x18(%rdx)
  cmp    %eax,%r15d
  jle    L27
L28:
  movsd  %xmm8,(%rsp)
  cmp    $0x102,%esi
  jle    L5
  pxor   %xmm0,%xmm0
  mov    %r12,%rsi
  mov    %rbp,%rdi
  cvtsi2sd %r15d,%xmm0
  mulsd  0x8(%rsp),%xmm0
  call   <sincos@plt>
  mov    D9(%rip),%rax
  mov    %r15d,%esi
  movsd  0x28(%rsp),%xmm3
  movsd  0x20(%rsp),%xmm0
  movsd  0x10(%rsp),%xmm6
  movq   %rax,%xmm9
  movsd  0x18(%rsp),%xmm7
  movq   %rax,%xmm10
  movsd  (%rsp),%xmm8
  mulsd  %xmm9,%xmm3
  movapd %xmm6,%xmm1
  mulsd  %xmm9,%xmm0
  movapd %xmm7,%xmm2
  mulsd  %xmm3,%xmm1
  mulsd  %xmm0,%xmm2
  mulsd  %xmm0,%xmm6
  subsd  %xmm2,%xmm1
  movapd %xmm7,%xmm2
  mulsd  %xmm3,%xmm2
  subsd  %xmm1,%xmm10
  movq   %rax,%xmm1
  subsd  %xmm3,%xmm1
  addsd  %xmm6,%xmm2
  jmp    L13
  cs nopw 0x0(%rax,%rax,1)
L5:
  add    $0x38,%rsp
  pop    %rbx
  pop    %rbp
  pop    %r12
  pop    %r13
  pop    %r14
  pop    %r15
  ret
```

tool_calls: name: parse_data
arguments: data_tag: D31
type: byte[8]
name: parse_data
arguments: data_tag: D36
type: byte[8]
name: parse_data
arguments: data_tag: D9
type: f64

tool: {"D31": [0x18,0x2d,0x44,0x54,0xfb,0x21,0x09,0x40]}

tool: {"D36": [0x00,0x00,0x00,0x00,0x00,0x00,0xf0,0x3f]}

tool: D9: 0.5

assistant: ```c
void mp_mul_rcmul_nt_in2(int n, double *a, double *b) {
  int i, i0, j, k;
  double ec, w1r, w1i, wkr, wki, wdr, wdi, ss;
  double xr, xi, yr, yi, bjr, bji, bkr, bki;
  ec = 2 * ((double)1.570796326794896619231321691639751442098584) / n;
  wkr = 0;
  wki = 0;
  wdi = cos(ec);
  wdr = sin(ec);
  wdi *= wdr;
  wdr *= wdr;
  w1r = 1 - 2 * wdr;
  w1i = 2 * wdi;
  ss = 2 * w1i;
  i = n >> 1;
  xr = a[i];
  xi = a[i + 1];
  yr = b[i];
  yi = b[i + 1];
  b[i] = xr * yr - xi * yi;
  b[i + 1] = xr * yi + xi * yr;
  for (;;) {
    i0 = i - 4 * 64;
    if (i0 < 2) {
      i0 = 2;
    }
    for (j = i - 2; j >= i0; j -= 2) {
      k = n - j;
      xr = wkr + ss * wdi;
      xi = wki + ss * (((double)0.5) - wdr);
      wkr = wdr;
      wki = wdi;
      wdr = xr;
      wdi = xi;
      xr = a[j] - a[k];
      xi = a[j + 1] + a[k + 1];
      yr = wkr * xr - wki * xi;
      yi = wkr * xi + wki * xr;
      xr = a[j] - yr;
      xi = a[j + 1] - yi;
      yr = a[k] + yr;
      yi = a[k + 1] - yi;
      a[j] = xr;
      a[j + 1] = xi;
      a[k] = yr;
      a[k + 1] = yi;
      bjr = b[j] * xr - b[j + 1] * xi;
      bji = b[j] * xi + b[j + 1] * xr;
      bkr = b[k] * yr - b[k + 1] * yi;
      bki = b[k] * yi + b[k + 1] * yr;
      xr = bjr - bkr;
      xi = bji + bki;
      yr = wkr * xr + wki * xi;
      yi = wkr * xi - wki * xr;
      b[j] = bjr - yr;
      b[j + 1] = bji - yi;
      b[k] = bkr + yr;
      b[k + 1] = bki - yi;
    }
    if (i0 == 2) {
      break;
    }
    wkr = ((double)0.5) * sin(ec * i0);
    wki = ((double)0.5) * cos(ec * i0);
    wdr = ((double)0.5) - (wkr * w1r - wki * w1i);
    wdi = wkr * w1i + wki * w1r;
    wkr = ((double)0.5) - wkr;
    i = i0;
  }
}
```