user: 请从给定的汇编指令推导出C源代码:

```asm
<_backward>:
  endbr64
  push   %r15
  mov    %rsi,%r10
  mov    %rdx,%r11
  push   %r14
  push   %r13
  mov    %ecx,%r13d
  mov    %r8d,%ecx
  push   %r12
  push   %rbp
  push   %rbx
  test   %r13d,%r13d
  jle    L25
  lea    -0x1(%r8),%eax
  imul   %r13d,%eax
  cmp    $0x1,%r13d
  je     L144
  mov    %r13d,%esi
  movslq %eax,%r9
  pxor   %xmm0,%xmm0
  movapd D19(%rip),%xmm2
  shr    %esi
  lea    (%rdi,%r9,8),%rdx
  movsd  D19(%rip),%xmm1
  lea    -0x1(%rsi),%r8d
  shl    $0x4,%r8
  add    %rdx,%r8
L109:
  addsd  %xmm1,%xmm0
  mov    %rdx,%rsi
  movups %xmm2,(%rdx)
  add    $0x10,%rdx
  addsd  %xmm1,%xmm0
  cmp    %rsi,%r8
  jne    L109
  mov    %r13d,%edx
  and    $0xfffffffe,%edx
  test   $0x1,%r13b
  je     L24
L56:
  add    %eax,%edx
  addsd  %xmm1,%xmm0
  movslq %edx,%rdx
  movsd  %xmm1,(%rdi,%rdx,8)
  cmp    $0x1,%r13d
  je     L178
  movslq %eax,%r9
L24:
  mov    %r13d,%esi
  movapd %xmm0,%xmm2
  lea    (%rdi,%r9,8),%rdx
  shr    %esi
  unpcklpd %xmm2,%xmm2
  lea    -0x1(%rsi),%r8d
  shl    $0x4,%r8
  add    %rdx,%r8
L22:
  movupd (%rdx),%xmm1
  mov    %rdx,%rsi
  add    $0x10,%rdx
  divpd  %xmm2,%xmm1
  movups %xmm1,-0x10(%rdx)
  cmp    %r8,%rsi
  jne    L22
  mov    %r13d,%edx
  and    $0xfffffffe,%edx
  test   $0x1,%r13b
  je     L25
L148:
  add    %edx,%eax
  cltq
  lea    (%rdi,%rax,8),%rax
  movsd  (%rax),%xmm1
  divsd  %xmm0,%xmm1
  movsd  %xmm1,(%rax)
L25:
  sub    $0x2,%ecx
  mov    %ecx,-0x2c(%rsp)
  js     L118
  movslq %r13d,%rax
  imul   %r13d,%ecx
  pxor   %xmm4,%xmm4
  mov    %r13d,%r14d
  shl    $0x3,%rax
  and    $0xfffffffe,%r14d
  mov    %rax,-0x20(%rsp)
  mov    %r13d,%eax
  shr    %eax
  mov    %ecx,-0x30(%rsp)
  lea    -0x1(%rax),%ebp
  lea    -0x1(%r13),%eax
  mov    %rax,-0x18(%rsp)
  lea    0x8(%rdi),%rax
  add    $0x1,%rbp
  mov    %rax,-0x10(%rsp)
  shl    $0x4,%rbp
L77:
  test   %r13d,%r13d
  jle    L201
  movslq -0x30(%rsp),%rax
  mov    -0x10(%rsp),%rbx
  mov    %r10,%rsi
  xor    %ecx,%ecx
  movapd %xmm4,%xmm3
  lea    (%rdi,%rax,8),%r15
  lea    (%rax,%r13,1),%r9d
  add    -0x18(%rsp),%rax
  lea    (%rbx,%rax,8),%rax
  movslq %r9d,%r8
  mov    %r15,-0x28(%rsp)
  mov    %r15,%r12
  mov    %rax,-0x38(%rsp)
  shl    $0x3,%r8
  mov    -0x20(%rsp),%r15
  lea    (%r11,%r8,1),%rbx
  add    %rdi,%r8
  nopl   (%rax)
L153:
  cmp    $0x1,%r13d
  je     L18
  xor    %eax,%eax
  movapd %xmm4,%xmm1
L198:
  movupd (%rbx,%rax,1),%xmm0
  movupd (%rsi,%rax,1),%xmm5
  movupd (%r8,%rax,1),%xmm6
  add    $0x10,%rax
  mulpd  %xmm5,%xmm0
  mulpd  %xmm6,%xmm0
  addsd  %xmm0,%xmm1
  unpckhpd %xmm0,%xmm0
  addsd  %xmm0,%xmm1
  cmp    %rbp,%rax
  jne    L198
  mov    %r14d,%eax
  cmp    %r14d,%r13d
  je     L217
L33:
  lea    (%r9,%rax,1),%edx
  add    %ecx,%eax
  movslq %edx,%rdx
  cltq
  movsd  (%r10,%rax,8),%xmm0
  mulsd  (%r11,%rdx,8),%xmm0
  mulsd  (%rdi,%rdx,8),%xmm0
  addsd  %xmm0,%xmm1
L217:
  movsd  %xmm1,(%r12)
  addsd  %xmm1,%xmm3
  add    %r13d,%ecx
  add    %r15,%rsi
  add    $0x8,%r12
  cmp    %r12,-0x38(%rsp)
  jne    L153
  ucomisd %xmm4,%xmm3
  mov    -0x28(%rsp),%r15
  jp     L122
  jne    L122
L201:
  subl   $0x1,-0x2c(%rsp)
  mov    -0x2c(%rsp),%eax
  sub    %r13d,-0x30(%rsp)
  cmp    $0xffffffff,%eax
  jne    L77
L118:
  pop    %rbx
  pop    %rbp
  pop    %r12
  pop    %r13
  pop    %r14
  pop    %r15
  ret
  nop
L18:
  movapd %xmm4,%xmm1
  xor    %eax,%eax
  jmp    L33
L122:
  cmp    $0x1,%r13d
  je     L131
  movapd %xmm3,%xmm1
  lea    0x0(%rbp,%r15,1),%rax
  unpcklpd %xmm1,%xmm1
  nopl   0x0(%rax,%rax,1)
L96:
  movupd (%r15),%xmm0
  add    $0x10,%r15
  divpd  %xmm1,%xmm0
  movups %xmm0,-0x10(%r15)
  cmp    %r15,%rax
  jne    L96
  mov    %r14d,%eax
  cmp    %r14d,%r13d
  je     L201
L35:
  add    -0x30(%rsp),%eax
  cltq
  lea    (%rdi,%rax,8),%rax
  movsd  (%rax),%xmm0
  divsd  %xmm3,%xmm0
  movsd  %xmm0,(%rax)
  jmp    L201
L178:
  xor    %edx,%edx
  jmp    L148
L131:
  xor    %eax,%eax
  jmp    L35
L144:
  movsd  D19(%rip),%xmm1
  pxor   %xmm0,%xmm0
  xor    %edx,%edx
  jmp    L56
```

tool_calls: name: unpack_data
arguments: data_label: D19
type_guessed: f64[2]

tool: {"D19": [1.0,1.0]}

assistant: ```c
void _backward(double *beta, const double *A, const double *pobs, int N, int T) {
  int i, j, t;
  double sum, scaling;
  scaling = 0.0;
  for (i = 0; i < N; i++) {
    beta[(T - 1) * N + i] = 1.0;
    scaling += beta[(T - 1) * N + i];
  }
  for (i = 0; i < N; i++)
    beta[(T - 1) * N + i] /= scaling;
  for (t = T - 2; t >= 0; t--) {
    scaling = 0.0;
    for (i = 0; i < N; i++) {
      sum = 0.0;
      for (j = 0; j < N; j++) {
        sum += A[i * N + j] * pobs[(t + 1) * N + j] * beta[(t + 1) * N + j];
      }
      beta[t * N + i] = sum;
      scaling += sum;
    }
    if (scaling != 0)
      for (j = 0; j < N; j++)
        beta[t * N + j] /= scaling;
  }
}
```