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

```asm
<m_rot>:
  endbr64
  push   %rbp
  cvtss2sd %xmm0,%xmm0
  mov    %rsi,%rbp
  push   %rbx
  mov    %rdi,%rbx
  sub    $0x38,%rsp
  mov    %fs:0x28,%rax
  mov    %rax,0x28(%rsp)
  xor    %eax,%eax
  movsd  %xmm0,(%rsp)
  call   <sin@plt>
  pxor   %xmm9,%xmm9
  movsd  (%rsp),%xmm0
  cvtsi2ss %rax,%xmm9
  movss  %xmm9,0xc(%rsp)
  call   <cos@plt>
  pxor   %xmm8,%xmm8
  lea    0x1c(%rsp),%rdi
  mov    %rbp,%rsi
  cvtsi2ss %rax,%xmm8
  movss  %xmm8,(%rsp)
  call   <v_nrm@plt>
  movss  0x1c(%rsp),%xmm2
  pxor   %xmm0,%xmm0
  movss  D3(%rip),%xmm5
  movss  (%rsp),%xmm8
  movss  0xc(%rsp),%xmm9
  movl   $0x0,0xc(%rbx)
  movaps %xmm2,%xmm14
  movaps %xmm5,%xmm4
  movaps %xmm2,%xmm13
  movss  %xmm5,0x3c(%rbx)
  mulss  %xmm2,%xmm14
  movaps %xmm9,%xmm6
  movss  0x20(%rsp),%xmm1
  movss  0x24(%rsp),%xmm3
  mulss  %xmm0,%xmm6
  movaps %xmm2,%xmm12
  movl   $0x0,0x1c(%rbx)
  mulss  %xmm1,%xmm13
  movaps %xmm1,%xmm10
  movaps %xmm3,%xmm7
  movq   $0x0,0x2c(%rbx)
  mulss  %xmm3,%xmm7
  movaps %xmm1,%xmm11
  movq   $0x0,0x34(%rbx)
  mulss  %xmm3,%xmm12
  subss  %xmm14,%xmm4
  mulss  %xmm3,%xmm10
  mulss  %xmm9,%xmm3
  mulss  %xmm1,%xmm11
  xorps  D4(%rip),%xmm1
  mulss  %xmm8,%xmm4
  mulss  %xmm9,%xmm2
  mulss  %xmm9,%xmm1
  addss  %xmm14,%xmm4
  addss  %xmm6,%xmm4
  movss  %xmm4,(%rbx)
  movaps %xmm0,%xmm4
  subss  %xmm13,%xmm4
  mulss  %xmm8,%xmm4
  addss  %xmm13,%xmm4
  movaps %xmm3,%xmm13
  movaps %xmm4,%xmm3
  subss  %xmm13,%xmm4
  addss  %xmm13,%xmm3
  movss  %xmm4,0x10(%rbx)
  movaps %xmm5,%xmm4
  subss  %xmm11,%xmm4
  movss  %xmm3,0x4(%rbx)
  movaps %xmm0,%xmm3
  subss  %xmm10,%xmm0
  subss  %xmm12,%xmm3
  mulss  %xmm8,%xmm4
  mulss  %xmm8,%xmm0
  mulss  %xmm8,%xmm3
  addss  %xmm11,%xmm4
  addss  %xmm10,%xmm0
  addss  %xmm12,%xmm3
  addss  %xmm6,%xmm4
  movaps %xmm3,%xmm12
  subss  %xmm1,%xmm3
  movss  %xmm4,0x14(%rbx)
  movaps %xmm0,%xmm4
  subss  %xmm2,%xmm0
  addss  %xmm1,%xmm12
  addss  %xmm2,%xmm4
  movss  %xmm3,0x20(%rbx)
  movss  %xmm0,0x24(%rbx)
  movaps %xmm5,%xmm0
  subss  %xmm7,%xmm0
  movss  %xmm12,0x8(%rbx)
  movss  %xmm4,0x18(%rbx)
  mulss  %xmm8,%xmm0
  addss  %xmm7,%xmm0
  addss  %xmm6,%xmm0
  movss  %xmm0,0x28(%rbx)
  mov    0x28(%rsp),%rax
  sub    %fs:0x28,%rax
  jne    L0
  add    $0x38,%rsp
  pop    %rbx
  pop    %rbp
  ret
L0:
  call   <__stack_chk_fail@plt>
```

tool_calls: name: disassemble_data
arguments: data_label: D3
type: byte[4]
name: disassemble_data
arguments: data_label: D4
type: byte[16]

tool: {"D3": [0x00,0x00,0x80,0x3f]}

tool: {"D4": [0x00,0x00,0x00,0x80,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00]}

assistant: ```c
void m_rot(float *M, const float *v, float a) {
  float u[3];
  float U[16];
  float S[16];
  const float s = ((float)sin((double)a));
  const float c = ((float)cos((double)a));
  v_nrm(u, v);
  U[0] = u[0] * u[0];
  U[4] = u[0] * u[1];
  U[8] = u[0] * u[2];
  U[1] = u[1] * u[0];
  U[5] = u[1] * u[1];
  U[9] = u[1] * u[2];
  U[2] = u[2] * u[0];
  U[6] = u[2] * u[1];
  U[10] = u[2] * u[2];
  S[0] = 0.f;
  S[4] = -u[2];
  S[8] = u[1];
  S[1] = u[2];
  S[5] = 0.f;
  S[9] = -u[0];
  S[2] = -u[1];
  S[6] = u[0];
  S[10] = 0.f;
  M[0] = U[0] + c * (1.f - U[0]) + s * S[0];
  M[1] = U[1] + c * (0.f - U[1]) + s * S[1];
  M[2] = U[2] + c * (0.f - U[2]) + s * S[2];
  M[3] = 0.f;
  M[4] = U[4] + c * (0.f - U[4]) + s * S[4];
  M[5] = U[5] + c * (1.f - U[5]) + s * S[5];
  M[6] = U[6] + c * (0.f - U[6]) + s * S[6];
  M[7] = 0.f;
  M[8] = U[8] + c * (0.f - U[8]) + s * S[8];
  M[9] = U[9] + c * (0.f - U[9]) + s * S[9];
  M[10] = U[10] + c * (1.f - U[10]) + s * S[10];
  M[11] = 0.f;
  M[12] = 0.f;
  M[13] = 0.f;
  M[14] = 0.f;
  M[15] = 1.f;
}
```