void fft4(_Complex double *Y, _Complex double *X) {
  _Complex double a51, a52, t29, t30, a53, a54, t31, a55;
  a51 = *(X);
  a52 = *((X + 2));
  t29 = (a51 + a52);
  t30 = (a51 - a52);
  a53 = *((X + 1));
  a54 = *((X + 3));
  t31 = (a53 + a54);
  *(Y) = (t29 + t31);
  *((Y + 2)) = (t29 - t31);
  a55 = (1.0if * (a53 - a54));
  *((Y + 1)) = (t30 + a55);
  *((Y + 3)) = (t30 - a55);
}


x86 assembly (clang, -O0):
<fft4>:
push   %rbp
mov    %rsp,%rbp
sub    $0xc0,%rsp
mov    %rdi,-0x8(%rbp)
mov    %rsi,-0x10(%rbp)
mov    -0x10(%rbp),%rax
movsd  (%rax),%xmm1
movsd  0x8(%rax),%xmm0
movsd  %xmm1,-0x20(%rbp)
movsd  %xmm0,-0x18(%rbp)
mov    -0x10(%rbp),%rax
movsd  0x20(%rax),%xmm1
movsd  0x28(%rax),%xmm0
movsd  %xmm1,-0x30(%rbp)
movsd  %xmm0,-0x28(%rbp)
movsd  -0x20(%rbp),%xmm1
movsd  -0x18(%rbp),%xmm0
movsd  -0x30(%rbp),%xmm3
movsd  -0x28(%rbp),%xmm2
addsd  %xmm3,%xmm1
addsd  %xmm2,%xmm0
movsd  %xmm1,-0x40(%rbp)
movsd  %xmm0,-0x38(%rbp)
movsd  -0x20(%rbp),%xmm1
movsd  -0x18(%rbp),%xmm0
movsd  -0x30(%rbp),%xmm3
movsd  -0x28(%rbp),%xmm2
subsd  %xmm3,%xmm1
subsd  %xmm2,%xmm0
movsd  %xmm1,-0x50(%rbp)
movsd  %xmm0,-0x48(%rbp)
mov    -0x10(%rbp),%rax
movsd  0x10(%rax),%xmm1
movsd  0x18(%rax),%xmm0
movsd  %xmm1,-0x60(%rbp)
movsd  %xmm0,-0x58(%rbp)
mov    -0x10(%rbp),%rax
movsd  0x30(%rax),%xmm1
movsd  0x38(%rax),%xmm0
movsd  %xmm1,-0x70(%rbp)
movsd  %xmm0,-0x68(%rbp)
movsd  -0x60(%rbp),%xmm1
movsd  -0x58(%rbp),%xmm0
movsd  -0x70(%rbp),%xmm3
movsd  -0x68(%rbp),%xmm2
addsd  %xmm3,%xmm1
addsd  %xmm2,%xmm0
movsd  %xmm1,-0x80(%rbp)
movsd  %xmm0,-0x78(%rbp)
movsd  -0x40(%rbp),%xmm1
movsd  -0x38(%rbp),%xmm0
movsd  -0x80(%rbp),%xmm3
movsd  -0x78(%rbp),%xmm2
addsd  %xmm3,%xmm1
addsd  %xmm2,%xmm0
mov    -0x8(%rbp),%rax
movsd  %xmm1,(%rax)
movsd  %xmm0,0x8(%rax)
movsd  -0x40(%rbp),%xmm1
movsd  -0x38(%rbp),%xmm0
movsd  -0x80(%rbp),%xmm3
movsd  -0x78(%rbp),%xmm2
subsd  %xmm3,%xmm1
subsd  %xmm2,%xmm0
mov    -0x8(%rbp),%rax
movsd  %xmm1,0x20(%rax)
movsd  %xmm0,0x28(%rax)
movsd  -0x60(%rbp),%xmm4
movsd  -0x58(%rbp),%xmm2
movsd  -0x70(%rbp),%xmm1
movsd  -0x68(%rbp),%xmm0
subsd  %xmm1,%xmm4
movsd  %xmm4,-0xc0(%rbp)
ff
subsd  %xmm0,%xmm2
movsd  %xmm2,-0xb8(%rbp)
ff
xorps  %xmm0,%xmm0
mulsd  %xmm4,%xmm0
movsd  0xd8e(%rip),%xmm3
mulsd  %xmm2,%xmm3
xorps  %xmm1,%xmm1
mulsd  %xmm2,%xmm1
movsd  0xd7b(%rip),%xmm2
mulsd  %xmm4,%xmm2
subsd  %xmm3,%xmm0
movsd  %xmm0,-0xb0(%rbp)
ff
addsd  %xmm2,%xmm1
movsd  %xmm1,-0xa8(%rbp)
ff
ucomisd %xmm0,%xmm0
movsd  %xmm0,-0xa0(%rbp)
ff
movsd  %xmm1,-0x98(%rbp)
ff
jnp    1315 <fft4+0x215>
movsd  -0xa8(%rbp),%xmm1
ff
movsd  -0xb0(%rbp),%xmm0
ff
ucomisd %xmm1,%xmm1
movsd  %xmm0,-0xa0(%rbp)
ff
movsd  %xmm1,-0x98(%rbp)
ff
jnp    1315 <fft4+0x215>
movsd  -0xb8(%rbp),%xmm3
ff
movsd  -0xc0(%rbp),%xmm2
ff
xorps  %xmm0,%xmm0
movsd  0xd00(%rip),%xmm1
call   13a0 <__muldc3>
movsd  %xmm0,-0xa0(%rbp)
ff
movsd  %xmm1,-0x98(%rbp)
ff
movsd  -0xa0(%rbp),%xmm1
ff
movsd  -0x98(%rbp),%xmm0
ff
movsd  %xmm1,-0x90(%rbp)
ff
movsd  %xmm0,-0x88(%rbp)
ff
movsd  -0x50(%rbp),%xmm1
movsd  -0x48(%rbp),%xmm0
movsd  -0x90(%rbp),%xmm3
ff
movsd  -0x88(%rbp),%xmm2
ff
addsd  %xmm3,%xmm1
addsd  %xmm2,%xmm0
mov    -0x8(%rbp),%rax
movsd  %xmm1,0x10(%rax)
movsd  %xmm0,0x18(%rax)
movsd  -0x50(%rbp),%xmm1
movsd  -0x48(%rbp),%xmm0
movsd  -0x90(%rbp),%xmm3
ff
movsd  -0x88(%rbp),%xmm2
ff
subsd  %xmm3,%xmm1
subsd  %xmm2,%xmm0
mov    -0x8(%rbp),%rax
movsd  %xmm1,0x30(%rax)
movsd  %xmm0,0x38(%rax)
add    $0xc0,%rsp
pop    %rbp
ret
xchg   %ax,%ax

x86 assembly (clang, -O2):
<fft4>:
push   %rbx
sub    $0x10,%rsp
mov    %rdi,%rbx
movupd (%rsi),%xmm5
movupd 0x10(%rsi),%xmm2
movupd 0x20(%rsi),%xmm0
movupd 0x30(%rsi),%xmm1
movapd %xmm5,%xmm3
addpd  %xmm0,%xmm3
subpd  %xmm0,%xmm5
movapd %xmm2,%xmm0
addpd  %xmm1,%xmm0
movapd %xmm3,%xmm4
addpd  %xmm0,%xmm4
movupd %xmm4,(%rdi)
subpd  %xmm0,%xmm3
movupd %xmm3,0x20(%rdi)
subpd  %xmm1,%xmm2
xorpd  %xmm0,%xmm0
mulpd  %xmm2,%xmm0
movapd %xmm2,%xmm1
shufpd $0x1,%xmm2,%xmm1
movapd %xmm0,%xmm3
subpd  %xmm1,%xmm3
addpd  %xmm0,%xmm1
movapd %xmm1,%xmm0
movsd  %xmm3,%xmm0
ucomisd %xmm3,%xmm3
jp     118f <fft4+0x8f>
movapd %xmm5,%xmm1
addpd  %xmm0,%xmm1
movupd %xmm1,0x10(%rbx)
subpd  %xmm0,%xmm5
movupd %xmm5,0x30(%rbx)
add    $0x10,%rsp
pop    %rbx
ret
unpckhpd %xmm1,%xmm1
ucomisd %xmm1,%xmm1
jnp    1173 <fft4+0x73>
movapd %xmm2,%xmm3
unpckhpd %xmm2,%xmm3
movsd  0xe57(%rip),%xmm1
xorpd  %xmm0,%xmm0
movapd %xmm5,(%rsp)
call   11d0 <__muldc3>
movapd (%rsp),%xmm5
unpcklpd %xmm1,%xmm0
jmp    1173 <fft4+0x73>
cs nopw 0x0(%rax,%rax,1)
nopl   0x0(%rax)

LLVM IR (-O0):
define void @fft4({ double, double }* %0, { double, double }* %1) {
%3 = alloca { double, double }*
%4 = alloca { double, double }*
%5 = alloca { double, double }
%6 = alloca { double, double }
%7 = alloca { double, double }
%8 = alloca { double, double }
%9 = alloca { double, double }
%10 = alloca { double, double }
%11 = alloca { double, double }
%12 = alloca { double, double }
store { double, double }* %0, { double, double }** %3
store { double, double }* %1, { double, double }** %4
%13 = load { double, double }*, { double, double }** %4
%14 = getelementptr inbounds { double, double }, { double, double }* %13, i32 0, i32 0
%15 = load double, double* %14
%16 = getelementptr inbounds { double, double }, { double, double }* %13, i32 0, i32 1
%17 = load double, double* %16
%18 = getelementptr inbounds { double, double }, { double, double }* %5, i32 0, i32 0
%19 = getelementptr inbounds { double, double }, { double, double }* %5, i32 0, i32 1
store double %15, double* %18
store double %17, double* %19
%20 = load { double, double }*, { double, double }** %4
%21 = getelementptr inbounds { double, double }, { double, double }* %20, i64 2
%22 = getelementptr inbounds { double, double }, { double, double }* %21, i32 0, i32 0
%23 = load double, double* %22
%24 = getelementptr inbounds { double, double }, { double, double }* %21, i32 0, i32 1
%25 = load double, double* %24
%26 = getelementptr inbounds { double, double }, { double, double }* %6, i32 0, i32 0
%27 = getelementptr inbounds { double, double }, { double, double }* %6, i32 0, i32 1
store double %23, double* %26
store double %25, double* %27
%28 = getelementptr inbounds { double, double }, { double, double }* %5, i32 0, i32 0
%29 = load double, double* %28
%30 = getelementptr inbounds { double, double }, { double, double }* %5, i32 0, i32 1
%31 = load double, double* %30
%32 = getelementptr inbounds { double, double }, { double, double }* %6, i32 0, i32 0
%33 = load double, double* %32
%34 = getelementptr inbounds { double, double }, { double, double }* %6, i32 0, i32 1
%35 = load double, double* %34
%36 = fadd double %29, %33
%37 = fadd double %31, %35
%38 = getelementptr inbounds { double, double }, { double, double }* %7, i32 0, i32 0
%39 = getelementptr inbounds { double, double }, { double, double }* %7, i32 0, i32 1
store double %36, double* %38
store double %37, double* %39
%40 = getelementptr inbounds { double, double }, { double, double }* %5, i32 0, i32 0
%41 = load double, double* %40
%42 = getelementptr inbounds { double, double }, { double, double }* %5, i32 0, i32 1
%43 = load double, double* %42
%44 = getelementptr inbounds { double, double }, { double, double }* %6, i32 0, i32 0
%45 = load double, double* %44
%46 = getelementptr inbounds { double, double }, { double, double }* %6, i32 0, i32 1
%47 = load double, double* %46
%48 = fsub double %41, %45
%49 = fsub double %43, %47
%50 = getelementptr inbounds { double, double }, { double, double }* %8, i32 0, i32 0
%51 = getelementptr inbounds { double, double }, { double, double }* %8, i32 0, i32 1
store double %48, double* %50
store double %49, double* %51
%52 = load { double, double }*, { double, double }** %4
%53 = getelementptr inbounds { double, double }, { double, double }* %52, i64 1
%54 = getelementptr inbounds { double, double }, { double, double }* %53, i32 0, i32 0
%55 = load double, double* %54
%56 = getelementptr inbounds { double, double }, { double, double }* %53, i32 0, i32 1
%57 = load double, double* %56
%58 = getelementptr inbounds { double, double }, { double, double }* %9, i32 0, i32 0
%59 = getelementptr inbounds { double, double }, { double, double }* %9, i32 0, i32 1
store double %55, double* %58
store double %57, double* %59
%60 = load { double, double }*, { double, double }** %4
%61 = getelementptr inbounds { double, double }, { double, double }* %60, i64 3
%62 = getelementptr inbounds { double, double }, { double, double }* %61, i32 0, i32 0
%63 = load double, double* %62
%64 = getelementptr inbounds { double, double }, { double, double }* %61, i32 0, i32 1
%65 = load double, double* %64
%66 = getelementptr inbounds { double, double }, { double, double }* %10, i32 0, i32 0
%67 = getelementptr inbounds { double, double }, { double, double }* %10, i32 0, i32 1
store double %63, double* %66
store double %65, double* %67
%68 = getelementptr inbounds { double, double }, { double, double }* %9, i32 0, i32 0
%69 = load double, double* %68
%70 = getelementptr inbounds { double, double }, { double, double }* %9, i32 0, i32 1
%71 = load double, double* %70
%72 = getelementptr inbounds { double, double }, { double, double }* %10, i32 0, i32 0
%73 = load double, double* %72
%74 = getelementptr inbounds { double, double }, { double, double }* %10, i32 0, i32 1
%75 = load double, double* %74
%76 = fadd double %69, %73
%77 = fadd double %71, %75
%78 = getelementptr inbounds { double, double }, { double, double }* %11, i32 0, i32 0
%79 = getelementptr inbounds { double, double }, { double, double }* %11, i32 0, i32 1
store double %76, double* %78
store double %77, double* %79
%80 = getelementptr inbounds { double, double }, { double, double }* %7, i32 0, i32 0
%81 = load double, double* %80
%82 = getelementptr inbounds { double, double }, { double, double }* %7, i32 0, i32 1
%83 = load double, double* %82
%84 = getelementptr inbounds { double, double }, { double, double }* %11, i32 0, i32 0
%85 = load double, double* %84
%86 = getelementptr inbounds { double, double }, { double, double }* %11, i32 0, i32 1
%87 = load double, double* %86
%88 = fadd double %81, %85
%89 = fadd double %83, %87
%90 = load { double, double }*, { double, double }** %3
%91 = getelementptr inbounds { double, double }, { double, double }* %90, i32 0, i32 0
%92 = getelementptr inbounds { double, double }, { double, double }* %90, i32 0, i32 1
store double %88, double* %91
store double %89, double* %92
%93 = getelementptr inbounds { double, double }, { double, double }* %7, i32 0, i32 0
%94 = load double, double* %93
%95 = getelementptr inbounds { double, double }, { double, double }* %7, i32 0, i32 1
%96 = load double, double* %95
%97 = getelementptr inbounds { double, double }, { double, double }* %11, i32 0, i32 0
%98 = load double, double* %97
%99 = getelementptr inbounds { double, double }, { double, double }* %11, i32 0, i32 1
%100 = load double, double* %99
%101 = fsub double %94, %98
%102 = fsub double %96, %100
%103 = load { double, double }*, { double, double }** %3
%104 = getelementptr inbounds { double, double }, { double, double }* %103, i64 2
%105 = getelementptr inbounds { double, double }, { double, double }* %104, i32 0, i32 0
%106 = getelementptr inbounds { double, double }, { double, double }* %104, i32 0, i32 1
store double %101, double* %105
store double %102, double* %106
%107 = getelementptr inbounds { double, double }, { double, double }* %9, i32 0, i32 0
%108 = load double, double* %107
%109 = getelementptr inbounds { double, double }, { double, double }* %9, i32 0, i32 1
%110 = load double, double* %109
%111 = getelementptr inbounds { double, double }, { double, double }* %10, i32 0, i32 0
%112 = load double, double* %111
%113 = getelementptr inbounds { double, double }, { double, double }* %10, i32 0, i32 1
%114 = load double, double* %113
%115 = fsub double %108, %112
%116 = fsub double %110, %114
%117 = fmul double 0.000000e+00, %115
%118 = fmul double 1.000000e+00, %116
%119 = fmul double 0.000000e+00, %116
%120 = fmul double 1.000000e+00, %115
%121 = fsub double %117, %118
%122 = fadd double %119, %120
%123 = fcmp uno double %121, %121
br i1 %123, label %124, label %130
124: ; preds = %2
%125 = fcmp uno double %122, %122
br i1 %125, label %126, label %130
126: ; preds = %124
%127 = call { double, double } @__muldc3(double 0.000000e+00, double 1.000000e+00, double %115, double %116)
%128 = extractvalue { double, double } %127, 0
%129 = extractvalue { double, double } %127, 1
br label %130
130: ; preds = %126, %124, %2
%131 = phi double [ %121, %2 ], [ %121, %124 ], [ %128, %126 ]
%132 = phi double [ %122, %2 ], [ %122, %124 ], [ %129, %126 ]
%133 = getelementptr inbounds { double, double }, { double, double }* %12, i32 0, i32 0
%134 = getelementptr inbounds { double, double }, { double, double }* %12, i32 0, i32 1
store double %131, double* %133
store double %132, double* %134
%135 = getelementptr inbounds { double, double }, { double, double }* %8, i32 0, i32 0
%136 = load double, double* %135
%137 = getelementptr inbounds { double, double }, { double, double }* %8, i32 0, i32 1
%138 = load double, double* %137
%139 = getelementptr inbounds { double, double }, { double, double }* %12, i32 0, i32 0
%140 = load double, double* %139
%141 = getelementptr inbounds { double, double }, { double, double }* %12, i32 0, i32 1
%142 = load double, double* %141
%143 = fadd double %136, %140
%144 = fadd double %138, %142
%145 = load { double, double }*, { double, double }** %3
%146 = getelementptr inbounds { double, double }, { double, double }* %145, i64 1
%147 = getelementptr inbounds { double, double }, { double, double }* %146, i32 0, i32 0
%148 = getelementptr inbounds { double, double }, { double, double }* %146, i32 0, i32 1
store double %143, double* %147
store double %144, double* %148
%149 = getelementptr inbounds { double, double }, { double, double }* %8, i32 0, i32 0
%150 = load double, double* %149
%151 = getelementptr inbounds { double, double }, { double, double }* %8, i32 0, i32 1
%152 = load double, double* %151
%153 = getelementptr inbounds { double, double }, { double, double }* %12, i32 0, i32 0
%154 = load double, double* %153
%155 = getelementptr inbounds { double, double }, { double, double }* %12, i32 0, i32 1
%156 = load double, double* %155
%157 = fsub double %150, %154
%158 = fsub double %152, %156
%159 = load { double, double }*, { double, double }** %3
%160 = getelementptr inbounds { double, double }, { double, double }* %159, i64 3
%161 = getelementptr inbounds { double, double }, { double, double }* %160, i32 0, i32 0
%162 = getelementptr inbounds { double, double }, { double, double }* %160, i32 0, i32 1
store double %157, double* %161
store double %158, double* %162
ret void
}

LLVM IR (-O2):
define void @fft4({ double, double }* nocapture writeonly %0, { double, double }* nocapture %1) {
%3 = bitcast { double, double }* %1 to <2 x double>*
%4 = load <2 x double>, <2 x double>* %3
%5 = getelementptr inbounds { double, double }, { double, double }* %1, i64 2, i32 0
%6 = bitcast double* %5 to <2 x double>*
%7 = load <2 x double>, <2 x double>* %6
%8 = fadd <2 x double> %4, %7
%9 = fsub <2 x double> %4, %7
%10 = getelementptr inbounds { double, double }, { double, double }* %1, i64 1, i32 0
%11 = bitcast double* %10 to <2 x double>*
%12 = load <2 x double>, <2 x double>* %11
%13 = getelementptr inbounds { double, double }, { double, double }* %1, i64 3, i32 0
%14 = bitcast double* %13 to <2 x double>*
%15 = load <2 x double>, <2 x double>* %14
%16 = fadd <2 x double> %12, %15
%17 = fadd <2 x double> %8, %16
%18 = bitcast { double, double }* %0 to <2 x double>*
store <2 x double> %17, <2 x double>* %18
%19 = fsub <2 x double> %8, %16
%20 = getelementptr inbounds { double, double }, { double, double }* %0, i64 2, i32 0
%21 = bitcast double* %20 to <2 x double>*
store <2 x double> %19, <2 x double>* %21
%22 = fsub <2 x double> %12, %15
%23 = fmul <2 x double> %22, zeroinitializer
%24 = extractelement <2 x double> %22, i64 1
%25 = extractelement <2 x double> %22, i64 0
%26 = shufflevector <2 x double> %22, <2 x double> undef, <2 x i32> <i32 1, i32 0>
%27 = fsub <2 x double> %23, %26
%28 = fadd <2 x double> %23, %26
%29 = shufflevector <2 x double> %27, <2 x double> %28, <2 x i32> <i32 0, i32 3>
%30 = extractelement <2 x double> %27, i64 0
%31 = fcmp uno double %30, 0.000000e+00
br i1 %31, label %32, label %41
32: ; preds = %2
%33 = extractelement <2 x double> %28, i64 1
%34 = fcmp uno double %33, 0.000000e+00
br i1 %34, label %35, label %41
35: ; preds = %32
%36 = tail call { double, double } @__muldc3(double 0.000000e+00, double 1.000000e+00, double %25, double %24)
%37 = extractvalue { double, double } %36, 0
%38 = extractvalue { double, double } %36, 1
%39 = insertelement <2 x double> poison, double %37, i64 0
%40 = insertelement <2 x double> %39, double %38, i64 1
br label %41
41: ; preds = %35, %32, %2
%42 = phi <2 x double> [ %29, %2 ], [ %29, %32 ], [ %40, %35 ]
%43 = fadd <2 x double> %9, %42
%44 = getelementptr inbounds { double, double }, { double, double }* %0, i64 1, i32 0
%45 = bitcast double* %44 to <2 x double>*
store <2 x double> %43, <2 x double>* %45
%46 = fsub <2 x double> %9, %42
%47 = getelementptr inbounds { double, double }, { double, double }* %0, i64 3, i32 0
%48 = bitcast double* %47 to <2 x double>*
store <2 x double> %46, <2 x double>* %48
ret void
}