user: Converte this assembly snippet into its equivalent C code:

```asm
<R_Pauli_Fixed_E>:
  endbr64
  push   %rbp
  mov    %rsp,%rbp
  push   %rbx
  sub    $0xc8,%rsp
  mov    %edi,-0x94(%rbp)
  mov    %esi,-0x98(%rbp)
  movsd  %xmm0,-0xa0(%rbp)
  mov    %rdx,-0xa8(%rbp)
  mov    %ecx,-0xac(%rbp)
  movsd  %xmm1,-0xb8(%rbp)
  mov    %r8,-0xc0(%rbp)
  mov    %r9,-0xc8(%rbp)
  mov    -0x98(%rbp),%eax
  add    $0x1,%eax
  imul   -0x98(%rbp),%eax
  pxor   %xmm0,%xmm0
  cvtsi2sd %eax,%xmm0
  movsd  %xmm0,-0x78(%rbp)
  movsd  D62(%rip),%xmm0
  movsd  %xmm0,-0x70(%rbp)
  movsd  -0x70(%rbp),%xmm0
  mulsd  %xmm0,%xmm0
  movsd  %xmm0,-0x70(%rbp)
  cmpl   $0x0,-0x98(%rbp)
  jne    L174
  movsd  -0x70(%rbp),%xmm0
  mulsd  -0xa0(%rbp),%xmm0
  movapd %xmm0,%xmm1
  mulsd  -0xa0(%rbp),%xmm1
  movsd  D103(%rip),%xmm0
  subsd  %xmm1,%xmm0
  movq   %xmm0,%rax
  movq   %rax,%xmm0
  call   <sqrt@plt>
  movq   %xmm0,%rax
  mov    %rax,-0x80(%rbp)
  jmp    L4
L174:
  pxor   %xmm0,%xmm0
  cvtsi2sdl -0x98(%rbp),%xmm0
  movsd  %xmm0,-0x68(%rbp)
  movsd  -0x68(%rbp),%xmm0
  mulsd  %xmm0,%xmm0
  movsd  -0x70(%rbp),%xmm1
  mulsd  -0xa0(%rbp),%xmm1
  mulsd  -0xa0(%rbp),%xmm1
  subsd  %xmm1,%xmm0
  movq   %xmm0,%rax
  movq   %rax,%xmm0
  call   <sqrt@plt>
  movq   %xmm0,%rax
  movq   %rax,%xmm7
  mulsd  -0x68(%rbp),%xmm7
  movsd  %xmm7,-0xd0(%rbp)
  movsd  -0x68(%rbp),%xmm1
  movsd  D103(%rip),%xmm0
  addsd  %xmm0,%xmm1
  movsd  -0x68(%rbp),%xmm2
  movsd  D103(%rip),%xmm0
  addsd  %xmm2,%xmm0
  mulsd  %xmm1,%xmm0
  movsd  -0x70(%rbp),%xmm1
  mulsd  -0xa0(%rbp),%xmm1
  mulsd  -0xa0(%rbp),%xmm1
  subsd  %xmm1,%xmm0
  movq   %xmm0,%rax
  movq   %rax,%xmm0
  call   <sqrt@plt>
  movsd  -0x68(%rbp),%xmm2
  movsd  D103(%rip),%xmm1
  addsd  %xmm2,%xmm1
  mulsd  %xmm1,%xmm0
  movsd  -0xd0(%rbp),%xmm1
  addsd  %xmm0,%xmm1
  movsd  -0x68(%rbp),%xmm0
  movapd %xmm0,%xmm2
  addsd  %xmm0,%xmm2
  movsd  D103(%rip),%xmm0
  addsd  %xmm0,%xmm2
  divsd  %xmm2,%xmm1
  movapd %xmm1,%xmm0
  movsd  %xmm0,-0x80(%rbp)
L4:
  mov    $0x0,%eax
  call   <N_LogGrid@plt>
  mov    %eax,-0x88(%rbp)
  mov    $0x0,%eax
  call   <log_amesh_LogGrid@plt>
  pxor   %xmm0,%xmm0
  cvtsi2sd %eax,%xmm0
  movsd  %xmm0,-0x60(%rbp)
  movsd  -0x60(%rbp),%xmm0
  mulsd  %xmm0,%xmm0
  movsd  %xmm0,-0x58(%rbp)
  mov    $0x0,%eax
  call   <r_LogGrid@plt>
  cltq
  mov    %rax,-0x50(%rbp)
  mov    $0x0,%eax
  call   <alloc_LogGrid@plt>
  cltq
  mov    %rax,-0x48(%rbp)
  mov    $0x0,%eax
  call   <alloc_LogGrid@plt>
  cltq
  mov    %rax,-0x40(%rbp)
  mov    $0x0,%eax
  call   <alloc_LogGrid@plt>
  cltq
  mov    %rax,-0x38(%rbp)
  mov    $0x0,%eax
  call   <alloc_LogGrid@plt>
  cltq
  mov    %rax,-0x30(%rbp)
  mov    $0x0,%eax
  call   <alloc_LogGrid@plt>
  cltq
  mov    %rax,-0x28(%rbp)
  movl   $0x0,-0x90(%rbp)
  jmp    L51
L104:
  mov    -0x90(%rbp),%eax
  cltq
  lea    0x0(,%rax,8),%rdx
  mov    -0xc0(%rbp),%rax
  add    %rdx,%rax
  pxor   %xmm0,%xmm0
  movsd  %xmm0,(%rax)
  mov    -0x90(%rbp),%eax
  cltq
  lea    0x0(,%rax,8),%rdx
  mov    -0xc8(%rbp),%rax
  add    %rdx,%rax
  pxor   %xmm0,%xmm0
  movsd  %xmm0,(%rax)
  mov    -0x90(%rbp),%eax
  cltq
  lea    0x0(,%rax,8),%rdx
  mov    -0x40(%rbp),%rax
  add    %rdx,%rax
  pxor   %xmm0,%xmm0
  movsd  %xmm0,(%rax)
  addl   $0x1,-0x90(%rbp)
L51:
  cmpl   $0x3,-0x90(%rbp)
  jle    L104
  movl   $0x0,-0x90(%rbp)
  jmp    L162
L61:
  mov    -0x90(%rbp),%eax
  cltq
  lea    0x0(,%rax,8),%rdx
  mov    -0x50(%rbp),%rax
  add    %rdx,%rax
  movsd  (%rax),%xmm0
  movsd  %xmm0,-0x18(%rbp)
  movsd  -0x18(%rbp),%xmm0
  mulsd  %xmm0,%xmm0
  movsd  %xmm0,-0x18(%rbp)
  mov    -0x90(%rbp),%eax
  cltq
  lea    0x0(,%rax,8),%rdx
  mov    -0xa8(%rbp),%rax
  add    %rdx,%rax
  movsd  (%rax),%xmm0
  subsd  -0xb8(%rbp),%xmm0
  addsd  %xmm0,%xmm0
  mulsd  -0x18(%rbp),%xmm0
  addsd  -0x78(%rbp),%xmm0
  mov    -0x90(%rbp),%eax
  cltq
  lea    0x0(,%rax,8),%rdx
  mov    -0x48(%rbp),%rax
  add    %rdx,%rax
  mulsd  -0x58(%rbp),%xmm0
  movsd  %xmm0,(%rax)
  addl   $0x1,-0x90(%rbp)
L162:
  mov    -0x90(%rbp),%eax
  cmp    -0x88(%rbp),%eax
  jl     L61
  mov    -0x28(%rbp),%rdx
  mov    -0xa8(%rbp),%rax
  mov    %rdx,%rsi
  mov    %rax,%rdi
  mov    $0x0,%eax
  call   <Derivative_LogGrid@plt>
  movl   $0x0,-0x90(%rbp)
  jmp    L140
L80:
  mov    -0x90(%rbp),%eax
  cltq
  lea    0x0(,%rax,8),%rdx
  mov    -0x50(%rbp),%rax
  add    %rdx,%rax
  movsd  (%rax),%xmm1
  mov    -0x90(%rbp),%eax
  cltq
  lea    0x0(,%rax,8),%rdx
  mov    -0x50(%rbp),%rax
  add    %rdx,%rax
  movsd  (%rax),%xmm0
  mulsd  %xmm1,%xmm0
  movsd  %xmm0,-0x18(%rbp)
  movsd  -0x58(%rbp),%xmm0
  movapd %xmm0,%xmm2
  mulsd  -0x18(%rbp),%xmm2
  movsd  -0x70(%rbp),%xmm0
  movq   D144(%rip),%xmm1
  xorpd  %xmm0,%xmm1
  mov    -0x90(%rbp),%eax
  cltq
  lea    0x0(,%rax,8),%rdx
  mov    -0xa8(%rbp),%rax
  add    %rdx,%rax
  movsd  (%rax),%xmm0
  subsd  -0xb8(%rbp),%xmm0
  mulsd  %xmm0,%xmm1
  mov    -0x90(%rbp),%eax
  cltq
  lea    0x0(,%rax,8),%rdx
  mov    -0xa8(%rbp),%rax
  add    %rdx,%rax
  movsd  (%rax),%xmm0
  subsd  -0xb8(%rbp),%xmm0
  movapd %xmm1,%xmm3
  mulsd  %xmm0,%xmm3
  movsd  -0x70(%rbp),%xmm1
  movsd  D2(%rip),%xmm0
  mulsd  %xmm0,%xmm1
  mov    -0x90(%rbp),%eax
  cltq
  lea    0x0(,%rax,8),%rdx
  mov    -0x28(%rbp),%rax
  add    %rdx,%rax
  movsd  (%rax),%xmm0
  mulsd  %xmm1,%xmm0
  mov    -0x90(%rbp),%eax
  cltq
  lea    0x0(,%rax,8),%rdx
  mov    -0x50(%rbp),%rax
  add    %rdx,%rax
  movsd  (%rax),%xmm4
  movsd  -0x70(%rbp),%xmm5
  movsd  D2(%rip),%xmm1
  mulsd  %xmm1,%xmm5
  mov    -0x90(%rbp),%eax
  cltq
  lea    0x0(,%rax,8),%rdx
  mov    -0xa8(%rbp),%rax
  add    %rdx,%rax
  movsd  (%rax),%xmm6
  movsd  -0xb8(%rbp),%xmm1
  subsd  %xmm6,%xmm1
  mulsd  %xmm1,%xmm5
  movsd  D103(%rip),%xmm1
  addsd  %xmm5,%xmm1
  mulsd  %xmm4,%xmm1
  divsd  %xmm1,%xmm0
  addsd  %xmm3,%xmm0
  mov    -0x90(%rbp),%eax
  cltq
  lea    0x0(,%rax,8),%rdx
  mov    -0x38(%rbp),%rax
  add    %rdx,%rax
  mulsd  %xmm2,%xmm0
  movsd  %xmm0,(%rax)
  movsd  -0x60(%rbp),%xmm0
  movq   D144(%rip),%xmm1
  xorpd  %xmm0,%xmm1
  mov    -0x90(%rbp),%eax
  cltq
  lea    0x0(,%rax,8),%rdx
  mov    -0x50(%rbp),%rax
  add    %rdx,%rax
  movsd  (%rax),%xmm0
  mulsd  %xmm0,%xmm1
  movsd  D2(%rip),%xmm0
  mulsd  %xmm1,%xmm0
  movapd %xmm0,%xmm1
  mulsd  -0x70(%rbp),%xmm1
  mov    -0x90(%rbp),%eax
  cltq
  lea    0x0(,%rax,8),%rdx
  mov    -0x28(%rbp),%rax
  add    %rdx,%rax
  movsd  (%rax),%xmm0
  mulsd  %xmm1,%xmm0
  movsd  -0x70(%rbp),%xmm2
  movsd  D2(%rip),%xmm1
  mulsd  %xmm1,%xmm2
  mov    -0x90(%rbp),%eax
  cltq
  lea    0x0(,%rax,8),%rdx
  mov    -0xa8(%rbp),%rax
  add    %rdx,%rax
  movsd  (%rax),%xmm3
  movsd  -0xb8(%rbp),%xmm1
  subsd  %xmm3,%xmm1
  mulsd  %xmm1,%xmm2
  movsd  D103(%rip),%xmm1
  addsd  %xmm2,%xmm1
  mov    -0x90(%rbp),%eax
  cltq
  lea    0x0(,%rax,8),%rdx
  mov    -0x30(%rbp),%rax
  add    %rdx,%rax
  divsd  %xmm1,%xmm0
  movsd  %xmm0,(%rax)
  addl   $0x1,-0x90(%rbp)
L140:
  mov    -0x90(%rbp),%eax
  cmp    -0x88(%rbp),%eax
  jl     L80
  movl   $0x0,-0x90(%rbp)
  jmp    L5
L32:
  mov    -0x90(%rbp),%eax
  cltq
  lea    0x0(,%rax,8),%rdx
  mov    -0x50(%rbp),%rax
  add    %rdx,%rax
  mov    (%rax),%rax
  mov    -0x90(%rbp),%edx
  movslq %edx,%rdx
  lea    0x0(,%rdx,8),%rcx
  mov    -0xc0(%rbp),%rdx
  lea    (%rcx,%rdx,1),%rbx
  movsd  -0x80(%rbp),%xmm0
  movapd %xmm0,%xmm1
  movq   %rax,%xmm0
  call   <pow@plt>
  movq   %xmm0,%rax
  mov    %rax,(%rbx)
  movsd  -0x60(%rbp),%xmm0
  movapd %xmm0,%xmm1
  mulsd  -0x80(%rbp),%xmm1
  mov    -0x90(%rbp),%eax
  cltq
  lea    0x0(,%rax,8),%rdx
  mov    -0xc0(%rbp),%rax
  add    %rdx,%rax
  movsd  (%rax),%xmm0
  mov    -0x90(%rbp),%eax
  cltq
  lea    0x0(,%rax,8),%rdx
  mov    -0xc8(%rbp),%rax
  add    %rdx,%rax
  mulsd  %xmm1,%xmm0
  movsd  %xmm0,(%rax)
  mov    -0x90(%rbp),%eax
  cltq
  lea    0x0(,%rax,8),%rdx
  mov    -0x30(%rbp),%rax
  add    %rdx,%rax
  movsd  (%rax),%xmm0
  movapd %xmm0,%xmm1
  addsd  -0x60(%rbp),%xmm1
  mov    -0x90(%rbp),%eax
  cltq
  lea    0x0(,%rax,8),%rdx
  mov    -0xc8(%rbp),%rax
  add    %rdx,%rax
  movsd  (%rax),%xmm0
  mulsd  %xmm0,%xmm1
  mov    -0x90(%rbp),%eax
  cltq
  lea    0x0(,%rax,8),%rdx
  mov    -0x48(%rbp),%rax
  add    %rdx,%rax
  movsd  (%rax),%xmm2
  mov    -0x90(%rbp),%eax
  cltq
  lea    0x0(,%rax,8),%rdx
  mov    -0x38(%rbp),%rax
  add    %rdx,%rax
  movsd  (%rax),%xmm0
  addsd  %xmm0,%xmm2
  mov    -0x90(%rbp),%eax
  cltq
  lea    0x0(,%rax,8),%rdx
  mov    -0xc0(%rbp),%rax
  add    %rdx,%rax
  movsd  (%rax),%xmm0
  mulsd  %xmm2,%xmm0
  mov    -0x90(%rbp),%eax
  cltq
  lea    0x0(,%rax,8),%rdx
  mov    -0x40(%rbp),%rax
  add    %rdx,%rax
  addsd  %xmm1,%xmm0
  movsd  %xmm0,(%rax)
  addl   $0x1,-0x90(%rbp)
L5:
  cmpl   $0x3,-0x90(%rbp)
  jle    L32
  movl   $0x0,-0x84(%rbp)
  movl   $0x3,-0x90(%rbp)
  jmp    L165
L167:
  mov    -0xc8(%rbp),%rdx
  mov    -0xc0(%rbp),%rcx
  mov    -0x90(%rbp),%eax
  mov    %rcx,%rsi
  mov    %eax,%edi
  mov    $0x0,%eax
  call   <Predictor_Out@plt>
  mov    %eax,%edx
  mov    -0x90(%rbp),%eax
  cltq
  add    $0x1,%rax
  lea    0x0(,%rax,8),%rcx
  mov    -0xc0(%rbp),%rax
  add    %rcx,%rax
  pxor   %xmm0,%xmm0
  cvtsi2sd %edx,%xmm0
  movsd  %xmm0,(%rax)
  mov    -0x40(%rbp),%rdx
  mov    -0xc8(%rbp),%rcx
  mov    -0x90(%rbp),%eax
  mov    %rcx,%rsi
  mov    %eax,%edi
  mov    $0x0,%eax
  call   <Predictor_Out@plt>
  mov    %eax,%edx
  mov    -0x90(%rbp),%eax
  cltq
  add    $0x1,%rax
  lea    0x0(,%rax,8),%rcx
  mov    -0xc8(%rbp),%rax
  add    %rcx,%rax
  pxor   %xmm0,%xmm0
  cvtsi2sd %edx,%xmm0
  movsd  %xmm0,(%rax)
  movl   $0x0,-0x8c(%rbp)
  jmp    L96
L39:
  mov    -0x90(%rbp),%eax
  cltq
  add    $0x1,%rax
  lea    0x0(,%rax,8),%rdx
  mov    -0x30(%rbp),%rax
  add    %rdx,%rax
  movsd  (%rax),%xmm0
  movapd %xmm0,%xmm1
  addsd  -0x60(%rbp),%xmm1
  mov    -0x90(%rbp),%eax
  cltq
  add    $0x1,%rax
  lea    0x0(,%rax,8),%rdx
  mov    -0xc8(%rbp),%rax
  add    %rdx,%rax
  movsd  (%rax),%xmm0
  mulsd  %xmm0,%xmm1
  mov    -0x90(%rbp),%eax
  cltq
  add    $0x1,%rax
  lea    0x0(,%rax,8),%rdx
  mov    -0x48(%rbp),%rax
  add    %rdx,%rax
  movsd  (%rax),%xmm2
  mov    -0x90(%rbp),%eax
  cltq
  add    $0x1,%rax
  lea    0x0(,%rax,8),%rdx
  mov    -0x38(%rbp),%rax
  add    %rdx,%rax
  movsd  (%rax),%xmm0
  addsd  %xmm0,%xmm2
  mov    -0x90(%rbp),%eax
  cltq
  add    $0x1,%rax
  lea    0x0(,%rax,8),%rdx
  mov    -0xc0(%rbp),%rax
  add    %rdx,%rax
  movsd  (%rax),%xmm0
  mulsd  %xmm2,%xmm0
  mov    -0x90(%rbp),%eax
  cltq
  add    $0x1,%rax
  lea    0x0(,%rax,8),%rdx
  mov    -0x40(%rbp),%rax
  add    %rdx,%rax
  addsd  %xmm1,%xmm0
  movsd  %xmm0,(%rax)
  mov    -0x40(%rbp),%rdx
  mov    -0xc8(%rbp),%rcx
  mov    -0x90(%rbp),%eax
  mov    %rcx,%rsi
  mov    %eax,%edi
  mov    $0x0,%eax
  call   <Corrector_Out@plt>
  mov    %eax,%edx
  mov    -0x90(%rbp),%eax
  cltq
  add    $0x1,%rax
  lea    0x0(,%rax,8),%rcx
  mov    -0xc8(%rbp),%rax
  add    %rcx,%rax
  pxor   %xmm0,%xmm0
  cvtsi2sd %edx,%xmm0
  movsd  %xmm0,(%rax)
  mov    -0xc8(%rbp),%rdx
  mov    -0xc0(%rbp),%rcx
  mov    -0x90(%rbp),%eax
  mov    %rcx,%rsi
  mov    %eax,%edi
  mov    $0x0,%eax
  call   <Corrector_Out@plt>
  mov    %eax,%edx
  mov    -0x90(%rbp),%eax
  cltq
  add    $0x1,%rax
  lea    0x0(,%rax,8),%rcx
  mov    -0xc0(%rbp),%rax
  add    %rcx,%rax
  pxor   %xmm0,%xmm0
  cvtsi2sd %edx,%xmm0
  movsd  %xmm0,(%rax)
  addl   $0x1,-0x8c(%rbp)
L96:
  cmpl   $0x5,-0x8c(%rbp)
  jle    L39
  addl   $0x1,-0x90(%rbp)
L165:
  mov    -0x90(%rbp),%eax
  cmp    -0xac(%rbp),%eax
  jl     L167
  mov    -0xc0(%rbp),%rcx
  mov    -0x80(%rbp),%rdx
  mov    -0xac(%rbp),%eax
  mov    %rcx,%rsi
  movq   %rdx,%xmm0
  mov    %eax,%edi
  mov    $0x1,%eax
  call   <Norm_LogGrid@plt>
  pxor   %xmm0,%xmm0
  cvtsi2sd %eax,%xmm0
  movsd  %xmm0,-0x20(%rbp)
  mov    -0x20(%rbp),%rax
  movq   %rax,%xmm0
  call   <sqrt@plt>
  movapd %xmm0,%xmm1
  movsd  D103(%rip),%xmm0
  divsd  %xmm1,%xmm0
  movsd  %xmm0,-0x20(%rbp)
  movl   $0x0,-0x90(%rbp)
  jmp    L11
L0:
  mov    -0x90(%rbp),%eax
  cltq
  lea    0x0(,%rax,8),%rdx
  mov    -0xc0(%rbp),%rax
  add    %rdx,%rax
  movsd  (%rax),%xmm0
  mov    -0x90(%rbp),%eax
  cltq
  lea    0x0(,%rax,8),%rdx
  mov    -0xc0(%rbp),%rax
  add    %rdx,%rax
  mulsd  -0x20(%rbp),%xmm0
  movsd  %xmm0,(%rax)
  mov    -0x90(%rbp),%eax
  cltq
  lea    0x0(,%rax,8),%rdx
  mov    -0xc8(%rbp),%rax
  add    %rdx,%rax
  movsd  (%rax),%xmm0
  mov    -0x90(%rbp),%eax
  cltq
  lea    0x0(,%rax,8),%rdx
  mov    -0xc8(%rbp),%rax
  add    %rdx,%rax
  mulsd  -0x20(%rbp),%xmm0
  movsd  %xmm0,(%rax)
  addl   $0x1,-0x90(%rbp)
L11:
  mov    -0x90(%rbp),%eax
  cmp    -0xac(%rbp),%eax
  jle    L0
  mov    -0xac(%rbp),%eax
  add    $0x1,%eax
  mov    %eax,-0x90(%rbp)
  jmp    L173
L135:
  mov    -0x90(%rbp),%eax
  cltq
  lea    0x0(,%rax,8),%rdx
  mov    -0xc0(%rbp),%rax
  add    %rdx,%rax
  pxor   %xmm0,%xmm0
  movsd  %xmm0,(%rax)
  mov    -0x90(%rbp),%eax
  cltq
  lea    0x0(,%rax,8),%rdx
  mov    -0xc8(%rbp),%rax
  add    %rdx,%rax
  pxor   %xmm0,%xmm0
  movsd  %xmm0,(%rax)
  addl   $0x1,-0x90(%rbp)
L173:
  mov    -0x90(%rbp),%eax
  cmp    -0x88(%rbp),%eax
  jl     L135
  mov    -0x48(%rbp),%rax
  mov    %rax,%rdi
  mov    $0x0,%eax
  call   <dealloc_LogGrid@plt>
  mov    -0x40(%rbp),%rax
  mov    %rax,%rdi
  mov    $0x0,%eax
  call   <dealloc_LogGrid@plt>
  mov    -0x38(%rbp),%rax
  mov    %rax,%rdi
  mov    $0x0,%eax
  call   <dealloc_LogGrid@plt>
  mov    -0x30(%rbp),%rax
  mov    %rax,%rdi
  mov    $0x0,%eax
  call   <dealloc_LogGrid@plt>
  mov    -0x28(%rbp),%rax
  mov    %rax,%rdi
  mov    $0x0,%eax
  call   <dealloc_LogGrid@plt>
  nop
  mov    -0x8(%rbp),%rbx
  leave
  ret
```

tool_calls: name: extract_symbolic_data
arguments: label: D62
type: byte[8]
name: extract_symbolic_data
arguments: label: D103
type: f64
name: extract_symbolic_data
arguments: label: D144
type: f32[2]
name: extract_symbolic_data
arguments: label: D2
type: f64

tool: {"D62": [0x26,0x45,0x94,0xdd,0xd3,0xe3,0x7d,0x3f]}

tool: D103: 1

tool: {"D144": [0.0,-0.0]}

tool: D2: 0.5

assistant: ```c
void R_Pauli_Fixed_E(n, l, Z, v, match, E, u, uprime) int n, l;
double Z;
double v[];
int match;
double E;
double u[], uprime[];
{
  int i, j, node, Ngrid;
  double log_amesh, log_amesh2, fss, gamma, L2, L0, r2, sum, *r, *f_upp, *dv, *frp, *fr, *upp;
  L2 = ((double)(l * (l + 1)));
  fss = 1.0 / 137.03602;
  fss = fss * fss;
  if (l == 0)
    gamma = sqrt(1.0 - fss * Z * Z);
  else {
    L0 = (double)l;
    gamma = (sqrt(L0 * L0 - fss * Z * Z) * L0 + sqrt((L0 + 1.0) * (L0 + 1) - fss * Z * Z) * (L0 + 1.0)) / (2.0 * L0 + 1.0);
  }
  Ngrid = N_LogGrid();
  log_amesh = log_amesh_LogGrid();
  log_amesh2 = log_amesh * log_amesh;
  r = r_LogGrid();
  f_upp = alloc_LogGrid();
  upp = alloc_LogGrid();
  fr = alloc_LogGrid();
  frp = alloc_LogGrid();
  dv = alloc_LogGrid();
  for (i = 0; i < 4; ++i) {
    u[i] = 0.0;
    uprime[i] = 0.0;
    upp[i] = 0.0;
  }
  for (i = 0; i < Ngrid; ++i) {
    r2 = r[i];
    r2 = r2 * r2;
    f_upp[i] = log_amesh2 * (L2 + 2.0 * (v[i] - E) * r2);
  }
  Derivative_LogGrid(v, dv);
  for (i = 0; i < Ngrid; ++i) {
    r2 = r[i] * r[i];
    fr[i] = log_amesh2 * r2 * (-fss * (v[i] - E) * (v[i] - E) + 0.5 * fss * dv[i] / (r[i] * (1.0 + 0.5 * fss * (E - v[i]))));
    frp[i] = -log_amesh * r[i] * 0.5 * fss * dv[i] / (1.0 + 0.5 * fss * (E - v[i]));
  }
  for (i = 0; i < 4; ++i) {
    u[i] = pow(r[i], gamma);
    uprime[i] = log_amesh * gamma * u[i];
    upp[i] = (log_amesh + frp[i]) * uprime[i] + (f_upp[i] + fr[i]) * u[i];
  }
  node = 0;
  for (i = 3; i < match; ++i) {
    u[i + 1] = Predictor_Out(i, u, uprime);
    uprime[i + 1] = Predictor_Out(i, uprime, upp);
    for (j = 0; j < 6; ++j) {
      upp[i + 1] = (log_amesh + frp[i + 1]) * uprime[i + 1] + (f_upp[i + 1] + fr[i + 1]) * u[i + 1];
      uprime[i + 1] = Corrector_Out(i, uprime, upp);
      u[i + 1] = Corrector_Out(i, u, uprime);
    }
  }
  sum = Norm_LogGrid(match, gamma, u);
  sum = 1.0 / sqrt(sum);
  for (i = 0; i <= match; ++i) {
    u[i] = sum * u[i];
    uprime[i] = sum * uprime[i];
  }
  for (i = match + 1; i < Ngrid; ++i) {
    u[i] = 0.0;
    uprime[i] = 0.0;
  }
  dealloc_LogGrid(f_upp);
  dealloc_LogGrid(upp);
  dealloc_LogGrid(fr);
  dealloc_LogGrid(frp);
  dealloc_LogGrid(dv);
  return;
}
```