user: Translate the below assembly code into C programming language:

```asm
<ktau>:
  endbr64
  push   %r15
  mov    %rdx,%r15
  push   %r14
  push   %r13
  mov    %r8,%r13
  push   %r12
  push   %rbp
  mov    %rdi,%rbp
  push   %rbx
  mov    %rsi,%rbx
  sub    $0x48,%rsp
  mov    0x88(%rsp),%rdi
  mov    0x90(%rsp),%rsi
  mov    %rdx,0x8(%rsp)
  mov    0x80(%rsp),%rax
  mov    %rcx,0x30(%rsp)
  mov    %rdi,0x28(%rsp)
  mov    (%rdx),%edi
  mov    %rsi,0x18(%rsp)
  mov    $0x8,%esi
  mov    %r9,0x20(%rsp)
  mov    %rax,0x10(%rsp)
  call   <calloc@plt>
  mov    (%r15),%edi
  mov    $0x8,%esi
  mov    %rax,%r12
  call   <calloc@plt>
  mov    0x20(%rsp),%rdx
  mov    0x28(%rsp),%rdi
  movq   $0x0,0x0(%r13)
  mov    0x18(%rsp),%rsi
  mov    %rax,%r14
  mov    0x10(%rsp),%rax
  movl   $0x1,(%rsp)
  movq   $0x0,(%rdx)
  movl   $0x0,(%rax)
  movl   $0x0,(%rdi)
  movl   $0x0,(%rsi)
  mov    (%r15),%r15d
  mov    %r13,0x38(%rsp)
  mov    %r15d,0x4(%rsp)
  nopl   0x0(%rax)
L61:
  xor    %edi,%edi
  nopw   0x0(%rax,%rax,1)
L180:
  mov    (%rsp),%eax
  mov    %edi,%edx
  lea    (%rax,%rdi,1),%r9d
  cmp    %r15d,%r9d
  cmovg  %r15d,%r9d
  lea    (%rax,%r9,1),%r13d
  mov    %r9d,%r8d
  cmp    %r15d,%r13d
  cmovg  %r15d,%r13d
  jmp    L240
  nopl   0x0(%rax,%rax,1)
L260:
  test   %al,%al
  jne    L369
  test   %sil,%sil
  je     L404
L369:
  mov    %r10d,%edx
L240:
  cmp    %r9d,%edx
  setl   %al
  cmp    %r13d,%r8d
  setl   %sil
  mov    %eax,%ecx
  mov    %eax,%r11d
  and    %sil,%cl
  je     L3
  movslq %edx,%r10
  movslq %r8d,%rcx
  mov    $0x0,%r11d
  movsd  (%rbx,%r10,8),%xmm2
  comisd (%rbx,%rcx,8),%xmm2
  movsd  0x0(%rbp,%r10,8),%xmm1
  movsd  0x0(%rbp,%rcx,8),%xmm0
  seta   %cl
  ucomisd %xmm0,%xmm1
  setnp  %r10b
  cmovne %r11d,%r10d
  and    %r10d,%ecx
  comisd %xmm0,%xmm1
  seta   %r10b
  or     %r10d,%ecx
  mov    %ecx,%r11d
  xor    $0x1,%r11d
L3:
  mov    %edx,%r10d
  test   %r11b,%r11b
  je     L360
  movslq %edx,%r11
  movslq %edi,%r10
  add    $0x1,%edi
  movsd  0x0(%rbp,%r11,8),%xmm0
  movsd  %xmm0,(%r14,%r10,8)
  movsd  (%rbx,%r11,8),%xmm0
  movsd  %xmm0,(%r12,%r10,8)
  lea    0x1(%rdx),%r10d
L360:
  cmp    %r9d,%edx
  setge  %dl
  and    %esi,%edx
  test   %cl,%cl
  jne    L336
  test   %dl,%dl
  je     L260
L336:
  movslq %r8d,%rcx
  movslq %edi,%rdx
  add    $0x1,%r8d
  add    $0x1,%edi
  movsd  0x0(%rbp,%rcx,8),%xmm0
  movsd  %xmm0,(%r14,%rdx,8)
  movsd  (%rbx,%rcx,8),%xmm0
  movsd  %xmm0,(%r12,%rdx,8)
  jmp    L260
  nopw   0x0(%rax,%rax,1)
L404:
  cmp    %r15d,%edi
  jl     L180
  shll   (%rsp)
  mov    (%rsp),%eax
  cmp    %r15d,%eax
  jge    L142
  mov    %rbx,%rax
  mov    %r12,%rbx
  mov    %rax,%r12
  mov    %rbp,%rax
  mov    %r14,%rbp
  mov    %rax,%r14
  jmp    L61
L142:
  mov    0x10(%rsp),%r9
  cmpl   $0x1,0x4(%rsp)
  mov    0x38(%rsp),%r13
  mov    (%r9),%esi
  jle    L36
  mov    0x8(%rsp),%r8
  mov    0x18(%rsp),%r10
  mov    $0x1,%eax
  mov    $0x1,%edi
  mov    $0x1,%edx
  jmp    L279
L47:
  movsd  (%r12,%rax,8),%xmm0
  add    $0x1,%edx
  ucomisd -0x8(%r12,%rax,8),%xmm0
  jp     L372
  jne    L372
  add    $0x1,%edi
L372:
  add    $0x1,%rax
  cmp    %eax,(%r8)
  jle    L182
L279:
  movsd  (%r14,%rax,8),%xmm0
  ucomisd -0x8(%r14,%rax,8),%xmm0
  jp     L301
  je     L47
L301:
  cmp    $0x1,%edx
  je     L372
  lea    -0x1(%rdx),%ecx
  imul   %ecx,%edx
  sar    %edx
  add    %edx,%esi
  mov    $0x1,%edx
  mov    %esi,(%r9)
  cmp    $0x1,%edi
  je     L372
  lea    -0x1(%rdi),%ecx
  add    $0x1,%rax
  imul   %edi,%ecx
  mov    $0x1,%edi
  sar    %ecx
  add    %ecx,(%r10)
  mov    (%r9),%esi
  cmp    %eax,(%r8)
  jg     L279
L182:
  lea    -0x1(%rdx),%eax
  imul   %edx,%eax
  sar    %eax
  add    %eax,%esi
  lea    -0x1(%rdi),%eax
  imul   %edi,%eax
  sar    %eax
L210:
  mov    0x10(%rsp),%rdi
  movl   $0x1,0x4(%rsp)
  mov    %esi,(%rdi)
  mov    0x18(%rsp),%rdi
  add    %eax,(%rdi)
  mov    0x8(%rsp),%rax
  mov    (%rax),%eax
  mov    %eax,(%rsp)
  nopl   0x0(%rax)
L156:
  xor    %esi,%esi
  nopw   0x0(%rax,%rax,1)
L48:
  mov    0x4(%rsp),%ecx
  mov    (%rsp),%eax
  lea    (%rcx,%rsi,1),%edi
  cmp    %eax,%edi
  cmovg  %eax,%edi
  lea    (%rcx,%rdi,1),%r15d
  mov    %edi,%r8d
  cmp    %eax,%r15d
  cmovg  %eax,%r15d
  mov    %esi,%eax
  jmp    L98
  nopl   0x0(%rax)
L337:
  test   %dl,%dl
  jne    L304
  test   %cl,%cl
  je     L90
L304:
  mov    %r9d,%eax
L98:
  cmp    %edi,%eax
  setl   %dl
  cmp    %r15d,%r8d
  setl   %cl
  mov    %edx,%r10d
  mov    %edx,%r11d
  and    %cl,%r10b
  je     L179
  movslq %eax,%r10
  movslq %r8d,%r9
  movsd  (%r12,%r10,8),%xmm0
  comisd (%r12,%r9,8),%xmm0
  seta   %r10b
  setbe  %r11b
L179:
  mov    %eax,%r9d
  test   %r11b,%r11b
  je     L190
  movslq %eax,%r11
  movslq %esi,%r9
  add    $0x1,%esi
  movsd  (%r14,%r11,8),%xmm0
  movsd  %xmm0,0x0(%rbp,%r9,8)
  movsd  (%r12,%r11,8),%xmm0
  movsd  %xmm0,(%rbx,%r9,8)
  lea    0x1(%rax),%r9d
L190:
  cmp    %edi,%eax
  setge  %al
  and    %ecx,%eax
  test   %r10b,%r10b
  jne    L252
  test   %al,%al
  je     L337
L252:
  movslq %r8d,%r10
  movslq %esi,%rax
  add    $0x1,%r8d
  add    $0x1,%esi
  movsd  (%r14,%r10,8),%xmm0
  movsd  %xmm0,0x0(%rbp,%rax,8)
  movsd  (%r12,%r10,8),%xmm0
  movsd  %xmm0,(%rbx,%rax,8)
  mov    %edi,%eax
  pxor   %xmm0,%xmm0
  sub    %r9d,%eax
  cvtsi2sd %eax,%xmm0
  addsd  0x0(%r13),%xmm0
  movsd  %xmm0,0x0(%r13)
  jmp    L337
  nop
L90:
  cmp    (%rsp),%esi
  jl     L48
  shll   0x4(%rsp)
  mov    %rbp,%rax
  mov    0x4(%rsp),%edi
  mov    %r14,%rbp
  cmp    (%rsp),%edi
  jge    L109
  mov    %r12,%rdx
  mov    %rax,%r14
  mov    %rbx,%r12
  mov    %rdx,%rbx
  jmp    L156
L109:
  mov    0x28(%rsp),%r8
  cmpl   $0x1,(%rsp)
  mov    (%r8),%ecx
  jle    L157
  mov    0x8(%rsp),%rdi
  mov    $0x1,%eax
  mov    $0x1,%edx
  jmp    L169
L185:
  add    $0x1,%edx
L322:
  add    $0x1,%rax
  cmp    %eax,(%rdi)
  jle    L352
L169:
  movsd  (%rbx,%rax,8),%xmm0
  ucomisd -0x8(%rbx,%rax,8),%xmm0
  jp     L139
  je     L185
L139:
  cmp    $0x1,%edx
  je     L322
  lea    -0x1(%rdx),%esi
  add    $0x1,%rax
  imul   %esi,%edx
  sar    %edx
  add    %edx,%ecx
  mov    $0x1,%edx
  mov    %ecx,(%r8)
  cmp    %eax,(%rdi)
  jg     L169
L352:
  lea    -0x1(%rdx),%eax
  imul   %edx,%eax
  sar    %eax
  add    %eax,%ecx
L157:
  mov    0x28(%rsp),%rax
  pxor   %xmm1,%xmm1
  pxor   %xmm0,%xmm0
  mov    0x10(%rsp),%rbx
  pxor   %xmm3,%xmm3
  pxor   %xmm2,%xmm2
  pxor   %xmm4,%xmm4
  mov    %ecx,(%rax)
  mov    0x8(%rsp),%rax
  cvtsi2sd %ecx,%xmm2
  mov    (%rax),%eax
  cvtsi2sdl (%rbx),%xmm3
  mov    0x18(%rsp),%rbx
  cvtsi2sd %eax,%xmm1
  mulsd  D0(%rip),%xmm1
  sub    $0x1,%eax
  cvtsi2sd %eax,%xmm0
  mov    0x20(%rsp),%rax
  cvtsi2sdl (%rbx),%xmm4
  mulsd  %xmm0,%xmm1
  movsd  %xmm1,(%rax)
  movsd  0x0(%r13),%xmm0
  addsd  %xmm0,%xmm0
  addsd  %xmm3,%xmm0
  addsd  %xmm2,%xmm0
  subsd  %xmm4,%xmm0
  subsd  %xmm0,%xmm1
  movsd  %xmm1,0x0(%r13)
  movsd  (%rax),%xmm1
  movapd %xmm1,%xmm0
  subsd  %xmm2,%xmm1
  subsd  %xmm3,%xmm0
  mulsd  %xmm1,%xmm0
  pxor   %xmm1,%xmm1
  ucomisd %xmm0,%xmm1
  ja     L219
  sqrtsd %xmm0,%xmm0
L287:
  mov    0x20(%rsp),%rax
  mov    %r12,%rdi
  movsd  %xmm0,(%rax)
  movsd  0x0(%r13),%xmm1
  mov    0x30(%rsp),%rax
  divsd  %xmm0,%xmm1
  movsd  %xmm1,(%rax)
  call   <free@plt>
  add    $0x48,%rsp
  mov    %r14,%rdi
  pop    %rbx
  pop    %rbp
  pop    %r12
  pop    %r13
  pop    %r14
  pop    %r15
  jmp    1070 <free@plt>
L36:
  xor    %eax,%eax
  jmp    L210
L219:
  call   <sqrt@plt>
  jmp    L287
```

tool_calls: name: retrieve_data
arguments: data_tag: D0
type_infered: f64

tool: D0: 0.5

assistant: ```c
void ktau(double *X, double *Y, int *N, double *tau, double *S, double *D, int *T, int *U, int *V) {
  int K, L, I, J, Iend, Jend;
  int i, j, m;
  double *Y2 = calloc(*N, sizeof(double));
  double *X2 = calloc(*N, sizeof(double));
  double *xptr, *yptr;
  bool Iflag, Jflag, Xflag;
  *S = 0.;
  *D = 0.;
  *T = 0;
  *U = 0;
  *V = 0;
  K = 1;
  do {
    L = 0;
    do {
      I = L;
      J = (I + K) < (*N) ? (I + K) : (*N);
      Iend = J;
      Jend = (J + K) < (*N) ? (J + K) : (*N);
      do {
        Iflag = (I < Iend);
        Jflag = (J < Jend);
        if (Iflag & Jflag) {
          Xflag = ((X[I] > X[J]) | ((X[I] == X[J]) & (Y[I] > Y[J])));
        } else {
          Xflag = false;
        }
        if ((Iflag & !Jflag) | (Iflag & Jflag & !Xflag)) {
          X2[L] = X[I];
          Y2[L] = Y[I];
          I++;
          L++;
        };
        if ((!Iflag && Jflag) | (Iflag && Jflag && Xflag)) {
          X2[L] = X[J];
          Y2[L] = Y[J];
          J++;
          L++;
        };
      } while (Iflag | Jflag);
    } while (L < *N);
    xptr = X;
    X = X2;
    X2 = xptr;
    yptr = Y;
    Y = Y2;
    Y2 = yptr;
    K *= 2;
  } while (K < *N);
  j = 1;
  m = 1;
  for (i = 1; i < *N; i++)
    if (X[i] == X[i - 1]) {
      j++;
      if (Y[i] == Y[i - 1])
        m++;
    } else if (j > 1) {
      *T += j * (j - 1) / 2;
      if (m > 1)
        *V += m * (m - 1) / 2;
      j = 1;
      m = 1;
    };
  *T += j * (j - 1) / 2;
  *V += m * (m - 1) / 2;
  K = 1;
  do {
    L = 0;
    do {
      I = L;
      J = (I + K) < (*N) ? (I + K) : (*N);
      Iend = J;
      Jend = (J + K) < (*N) ? (J + K) : (*N);
      do {
        Iflag = (I < Iend);
        Jflag = (J < Jend);
        if (Iflag & Jflag) {
          Xflag = (Y[I] > Y[J]);
        } else {
          Xflag = false;
        }
        if ((Iflag & !Jflag) | (Iflag & Jflag & !Xflag)) {
          X2[L] = X[I];
          Y2[L] = Y[I];
          I++;
          L++;
        };
        if ((!Iflag && Jflag) | (Iflag && Jflag && Xflag)) {
          X2[L] = X[J];
          Y2[L] = Y[J];
          *S += Iend - I;
          J++;
          L++;
        };
      } while ((Iflag | Jflag));
    } while (L < *N);
    xptr = X;
    X = X2;
    X2 = xptr;
    yptr = Y;
    Y = Y2;
    Y2 = yptr;
    K *= 2;
  } while (K < *N);
  j = 1;
  for (i = 1; i < *N; i++)
    if (Y[i] == Y[i - 1])
      j++;
    else if (j > 1) {
      *U += j * (j - 1) / 2;
      j = 1;
    };
  *U += j * (j - 1) / 2;
  *D = 0.5 * (*N) * (*N - 1);
  *S = *D - (2. * (*S) + *T + *U - *V);
  *D = sqrt((*D - *T) * (*D - *U));
  *tau = (*S) / (*D);
  free(Y2);
  free(X2);
}
```