void rifft4pt(float *ioptr, float scale) {
  float f0r, f0i, f1r, f1i, f2r, f2i, f3r, f3i;
  float t0r, t0i, t1r, t1i;
  float w0r = 1.0 / 1.414213562373095048801688724209698078569;
  const float Two = 2.0;
  t0r = ioptr[0];
  t0i = ioptr[1];
  f2r = ioptr[2];
  f2i = ioptr[3];
  f1r = Two * ioptr[4];
  f1i = Two * ioptr[5];
  f3r = ioptr[6];
  f3i = ioptr[7];
  f0r = t0r + t0i;
  f0i = t0r - t0i;
  t1r = f2r + f3r;
  t1i = f2i - f3i;
  t0r = f2r - f3r;
  t0i = f2i + f3i;
  f2r = t1r - w0r * t0r - w0r * t0i;
  f2i = t1i + w0r * t0r - w0r * t0i;
  f3r = Two * t1r - f2r;
  f3i = f2i - Two * t1i;
  t0r = f0r + f1r;
  t0i = f0i - f1i;
  f1r = f0r - f1r;
  f1i = f0i + f1i;
  t1r = f2r - f3r;
  t1i = f2i - f3i;
  f2r = f2r + f3r;
  f2i = f2i + f3i;
  f0r = t0r + f2r;
  f0i = t0i + f2i;
  f2r = t0r - f2r;
  f2i = t0i - f2i;
  f3r = f1r + t1i;
  f3i = f1i - t1r;
  f1r = f1r - t1i;
  f1i = f1i + t1r;
  ioptr[0] = scale * f0r;
  ioptr[1] = scale * f0i;
  ioptr[2] = scale * f1r;
  ioptr[3] = scale * f1i;
  ioptr[4] = scale * f2r;
  ioptr[5] = scale * f2i;
  ioptr[6] = scale * f3r;
  ioptr[7] = scale * f3i;
}


x86 assembly (clang, -O0):
<rifft4pt>:
push   %rbp
mov    %rsp,%rbp
mov    %rdi,-0x8(%rbp)
movss  %xmm0,-0xc(%rbp)
movss  0xeef(%rip),%xmm0
movss  %xmm0,-0x40(%rbp)
movss  0xede(%rip),%xmm0
movss  %xmm0,-0x44(%rbp)
mov    -0x8(%rbp),%rax
movss  (%rax),%xmm0
movss  %xmm0,-0x30(%rbp)
mov    -0x8(%rbp),%rax
movss  0x4(%rax),%xmm0
movss  %xmm0,-0x34(%rbp)
mov    -0x8(%rbp),%rax
movss  0x8(%rax),%xmm0
movss  %xmm0,-0x20(%rbp)
mov    -0x8(%rbp),%rax
movss  0xc(%rax),%xmm0
movss  %xmm0,-0x24(%rbp)
mov    -0x8(%rbp),%rax
movss  0xe96(%rip),%xmm0
mulss  0x10(%rax),%xmm0
movss  %xmm0,-0x18(%rbp)
mov    -0x8(%rbp),%rax
movss  0xe80(%rip),%xmm0
mulss  0x14(%rax),%xmm0
movss  %xmm0,-0x1c(%rbp)
mov    -0x8(%rbp),%rax
movss  0x18(%rax),%xmm0
movss  %xmm0,-0x28(%rbp)
mov    -0x8(%rbp),%rax
movss  0x1c(%rax),%xmm0
movss  %xmm0,-0x2c(%rbp)
movss  -0x30(%rbp),%xmm0
addss  -0x34(%rbp),%xmm0
movss  %xmm0,-0x10(%rbp)
movss  -0x30(%rbp),%xmm0
subss  -0x34(%rbp),%xmm0
movss  %xmm0,-0x14(%rbp)
movss  -0x20(%rbp),%xmm0
addss  -0x28(%rbp),%xmm0
movss  %xmm0,-0x38(%rbp)
movss  -0x24(%rbp),%xmm0
subss  -0x2c(%rbp),%xmm0
movss  %xmm0,-0x3c(%rbp)
movss  -0x20(%rbp),%xmm0
subss  -0x28(%rbp),%xmm0
movss  %xmm0,-0x30(%rbp)
movss  -0x24(%rbp),%xmm0
addss  -0x2c(%rbp),%xmm0
movss  %xmm0,-0x34(%rbp)
movss  -0x38(%rbp),%xmm0
movss  -0x40(%rbp),%xmm1
movss  -0x30(%rbp),%xmm2
movd   %xmm1,%eax
xor    $0x80000000,%eax
movd   %eax,%xmm1
mulss  %xmm2,%xmm1
addss  %xmm0,%xmm1
movss  -0x40(%rbp),%xmm0
movss  -0x34(%rbp),%xmm2
movd   %xmm0,%eax
xor    $0x80000000,%eax
movd   %eax,%xmm0
mulss  %xmm2,%xmm0
addss  %xmm1,%xmm0
movss  %xmm0,-0x20(%rbp)
movss  -0x3c(%rbp),%xmm0
movss  -0x40(%rbp),%xmm1
movss  -0x30(%rbp),%xmm2
mulss  %xmm2,%xmm1
addss  %xmm0,%xmm1
movss  -0x40(%rbp),%xmm0
movss  -0x34(%rbp),%xmm2
movd   %xmm0,%eax
xor    $0x80000000,%eax
movd   %eax,%xmm0
mulss  %xmm2,%xmm0
addss  %xmm1,%xmm0
movss  %xmm0,-0x24(%rbp)
movss  -0x38(%rbp),%xmm0
movss  -0x20(%rbp),%xmm1
movd   %xmm1,%eax
xor    $0x80000000,%eax
movd   %eax,%xmm1
addss  %xmm0,%xmm0
addss  %xmm1,%xmm0
movss  %xmm0,-0x28(%rbp)
movss  -0x24(%rbp),%xmm0
movss  -0x3c(%rbp),%xmm1
addss  %xmm1,%xmm1
subss  %xmm1,%xmm0
movss  %xmm0,-0x2c(%rbp)
movss  -0x10(%rbp),%xmm0
addss  -0x18(%rbp),%xmm0
movss  %xmm0,-0x30(%rbp)
movss  -0x14(%rbp),%xmm0
subss  -0x1c(%rbp),%xmm0
movss  %xmm0,-0x34(%rbp)
movss  -0x10(%rbp),%xmm0
subss  -0x18(%rbp),%xmm0
movss  %xmm0,-0x18(%rbp)
movss  -0x14(%rbp),%xmm0
addss  -0x1c(%rbp),%xmm0
movss  %xmm0,-0x1c(%rbp)
movss  -0x20(%rbp),%xmm0
subss  -0x28(%rbp),%xmm0
movss  %xmm0,-0x38(%rbp)
movss  -0x24(%rbp),%xmm0
subss  -0x2c(%rbp),%xmm0
movss  %xmm0,-0x3c(%rbp)
movss  -0x20(%rbp),%xmm0
addss  -0x28(%rbp),%xmm0
movss  %xmm0,-0x20(%rbp)
movss  -0x24(%rbp),%xmm0
addss  -0x2c(%rbp),%xmm0
movss  %xmm0,-0x24(%rbp)
movss  -0x30(%rbp),%xmm0
addss  -0x20(%rbp),%xmm0
movss  %xmm0,-0x10(%rbp)
movss  -0x34(%rbp),%xmm0
addss  -0x24(%rbp),%xmm0
movss  %xmm0,-0x14(%rbp)
movss  -0x30(%rbp),%xmm0
subss  -0x20(%rbp),%xmm0
movss  %xmm0,-0x20(%rbp)
movss  -0x34(%rbp),%xmm0
subss  -0x24(%rbp),%xmm0
movss  %xmm0,-0x24(%rbp)
movss  -0x18(%rbp),%xmm0
addss  -0x3c(%rbp),%xmm0
movss  %xmm0,-0x28(%rbp)
movss  -0x1c(%rbp),%xmm0
subss  -0x38(%rbp),%xmm0
movss  %xmm0,-0x2c(%rbp)
movss  -0x18(%rbp),%xmm0
subss  -0x3c(%rbp),%xmm0
movss  %xmm0,-0x18(%rbp)
movss  -0x1c(%rbp),%xmm0
addss  -0x38(%rbp),%xmm0
movss  %xmm0,-0x1c(%rbp)
movss  -0xc(%rbp),%xmm0
mulss  -0x10(%rbp),%xmm0
mov    -0x8(%rbp),%rax
movss  %xmm0,(%rax)
movss  -0xc(%rbp),%xmm0
mulss  -0x14(%rbp),%xmm0
mov    -0x8(%rbp),%rax
movss  %xmm0,0x4(%rax)
movss  -0xc(%rbp),%xmm0
mulss  -0x18(%rbp),%xmm0
mov    -0x8(%rbp),%rax
movss  %xmm0,0x8(%rax)
movss  -0xc(%rbp),%xmm0
mulss  -0x1c(%rbp),%xmm0
mov    -0x8(%rbp),%rax
movss  %xmm0,0xc(%rax)
movss  -0xc(%rbp),%xmm0
mulss  -0x20(%rbp),%xmm0
mov    -0x8(%rbp),%rax
movss  %xmm0,0x10(%rax)
movss  -0xc(%rbp),%xmm0
mulss  -0x24(%rbp),%xmm0
mov    -0x8(%rbp),%rax
movss  %xmm0,0x14(%rax)
movss  -0xc(%rbp),%xmm0
mulss  -0x28(%rbp),%xmm0
mov    -0x8(%rbp),%rax
movss  %xmm0,0x18(%rax)
movss  -0xc(%rbp),%xmm0
mulss  -0x2c(%rbp),%xmm0
mov    -0x8(%rbp),%rax
movss  %xmm0,0x1c(%rax)
pop    %rbp
ret

x86 assembly (clang, -O2):
<rifft4pt>:
movss  (%rdi),%xmm3
movss  0x4(%rdi),%xmm4
movsd  0x8(%rdi),%xmm6
movsd  0x10(%rdi),%xmm2
addps  %xmm2,%xmm2
movlhps %xmm2,%xmm2
movsd  0x18(%rdi),%xmm5
movaps %xmm3,%xmm1
addss  %xmm4,%xmm1
subss  %xmm4,%xmm3
movaps %xmm3,%xmm4
shufps $0x0,%xmm1,%xmm4
shufps $0x0,%xmm3,%xmm1
movaps %xmm6,%xmm3
addps  %xmm5,%xmm3
subps  %xmm5,%xmm6
movaps %xmm6,%xmm5
shufps $0x1,%xmm3,%xmm5
shufps $0xe2,%xmm3,%xmm5
shufps $0x0,%xmm6,%xmm6
mulps  0xead(%rip),%xmm6
addps  %xmm5,%xmm6
shufps $0x55,%xmm3,%xmm3
mulps  0xeaf(%rip),%xmm3
addps  %xmm6,%xmm3
movaps 0xeb5(%rip),%xmm6
xorps  %xmm3,%xmm6
movaps %xmm3,%xmm7
mulps  0xeb8(%rip),%xmm5
movss  %xmm6,%xmm7
addps  %xmm7,%xmm5
addps  %xmm2,%xmm1
subps  %xmm2,%xmm4
shufps $0x9c,%xmm4,%xmm1
shufps $0x78,%xmm1,%xmm1
movaps %xmm3,%xmm2
addps  %xmm5,%xmm2
subps  %xmm5,%xmm3
shufps $0x14,%xmm3,%xmm2
movaps %xmm1,%xmm3
subps  %xmm2,%xmm3
addps  %xmm1,%xmm2
movaps %xmm2,%xmm1
shufps $0x32,%xmm3,%xmm1
movaps %xmm3,%xmm4
shufps $0x84,%xmm1,%xmm4
shufps $0x32,%xmm2,%xmm3
shufps $0x84,%xmm3,%xmm2
shufps $0x0,%xmm0,%xmm0
mulps  %xmm0,%xmm2
movups %xmm2,(%rdi)
mulps  %xmm4,%xmm0
movups %xmm0,0x10(%rdi)
ret

LLVM IR (-O0):
define void @rifft4pt(float* %0, float %1) {
%3 = alloca float*
%4 = alloca float
%5 = alloca float
%6 = alloca float
%7 = alloca float
%8 = alloca float
%9 = alloca float
%10 = alloca float
%11 = alloca float
%12 = alloca float
%13 = alloca float
%14 = alloca float
%15 = alloca float
%16 = alloca float
%17 = alloca float
%18 = alloca float
store float* %0, float** %3
store float %1, float* %4
store float 0x3FE6A09E60000000, float* %17
store float 2.000000e+00, float* %18
%19 = load float*, float** %3
%20 = getelementptr inbounds float, float* %19, i64 0
%21 = load float, float* %20
store float %21, float* %13
%22 = load float*, float** %3
%23 = getelementptr inbounds float, float* %22, i64 1
%24 = load float, float* %23
store float %24, float* %14
%25 = load float*, float** %3
%26 = getelementptr inbounds float, float* %25, i64 2
%27 = load float, float* %26
store float %27, float* %9
%28 = load float*, float** %3
%29 = getelementptr inbounds float, float* %28, i64 3
%30 = load float, float* %29
store float %30, float* %10
%31 = load float*, float** %3
%32 = getelementptr inbounds float, float* %31, i64 4
%33 = load float, float* %32
%34 = fmul float 2.000000e+00, %33
store float %34, float* %7
%35 = load float*, float** %3
%36 = getelementptr inbounds float, float* %35, i64 5
%37 = load float, float* %36
%38 = fmul float 2.000000e+00, %37
store float %38, float* %8
%39 = load float*, float** %3
%40 = getelementptr inbounds float, float* %39, i64 6
%41 = load float, float* %40
store float %41, float* %11
%42 = load float*, float** %3
%43 = getelementptr inbounds float, float* %42, i64 7
%44 = load float, float* %43
store float %44, float* %12
%45 = load float, float* %13
%46 = load float, float* %14
%47 = fadd float %45, %46
store float %47, float* %5
%48 = load float, float* %13
%49 = load float, float* %14
%50 = fsub float %48, %49
store float %50, float* %6
%51 = load float, float* %9
%52 = load float, float* %11
%53 = fadd float %51, %52
store float %53, float* %15
%54 = load float, float* %10
%55 = load float, float* %12
%56 = fsub float %54, %55
store float %56, float* %16
%57 = load float, float* %9
%58 = load float, float* %11
%59 = fsub float %57, %58
store float %59, float* %13
%60 = load float, float* %10
%61 = load float, float* %12
%62 = fadd float %60, %61
store float %62, float* %14
%63 = load float, float* %15
%64 = load float, float* %17
%65 = load float, float* %13
%66 = fneg float %64
%67 = call float @llvm.fmuladd.f32(float %66, float %65, float %63)
%68 = load float, float* %17
%69 = load float, float* %14
%70 = fneg float %68
%71 = call float @llvm.fmuladd.f32(float %70, float %69, float %67)
store float %71, float* %9
%72 = load float, float* %16
%73 = load float, float* %17
%74 = load float, float* %13
%75 = call float @llvm.fmuladd.f32(float %73, float %74, float %72)
%76 = load float, float* %17
%77 = load float, float* %14
%78 = fneg float %76
%79 = call float @llvm.fmuladd.f32(float %78, float %77, float %75)
store float %79, float* %10
%80 = load float, float* %15
%81 = load float, float* %9
%82 = fneg float %81
%83 = call float @llvm.fmuladd.f32(float 2.000000e+00, float %80, float %82)
store float %83, float* %11
%84 = load float, float* %10
%85 = load float, float* %16
%86 = call float @llvm.fmuladd.f32(float -2.000000e+00, float %85, float %84)
store float %86, float* %12
%87 = load float, float* %5
%88 = load float, float* %7
%89 = fadd float %87, %88
store float %89, float* %13
%90 = load float, float* %6
%91 = load float, float* %8
%92 = fsub float %90, %91
store float %92, float* %14
%93 = load float, float* %5
%94 = load float, float* %7
%95 = fsub float %93, %94
store float %95, float* %7
%96 = load float, float* %6
%97 = load float, float* %8
%98 = fadd float %96, %97
store float %98, float* %8
%99 = load float, float* %9
%100 = load float, float* %11
%101 = fsub float %99, %100
store float %101, float* %15
%102 = load float, float* %10
%103 = load float, float* %12
%104 = fsub float %102, %103
store float %104, float* %16
%105 = load float, float* %9
%106 = load float, float* %11
%107 = fadd float %105, %106
store float %107, float* %9
%108 = load float, float* %10
%109 = load float, float* %12
%110 = fadd float %108, %109
store float %110, float* %10
%111 = load float, float* %13
%112 = load float, float* %9
%113 = fadd float %111, %112
store float %113, float* %5
%114 = load float, float* %14
%115 = load float, float* %10
%116 = fadd float %114, %115
store float %116, float* %6
%117 = load float, float* %13
%118 = load float, float* %9
%119 = fsub float %117, %118
store float %119, float* %9
%120 = load float, float* %14
%121 = load float, float* %10
%122 = fsub float %120, %121
store float %122, float* %10
%123 = load float, float* %7
%124 = load float, float* %16
%125 = fadd float %123, %124
store float %125, float* %11
%126 = load float, float* %8
%127 = load float, float* %15
%128 = fsub float %126, %127
store float %128, float* %12
%129 = load float, float* %7
%130 = load float, float* %16
%131 = fsub float %129, %130
store float %131, float* %7
%132 = load float, float* %8
%133 = load float, float* %15
%134 = fadd float %132, %133
store float %134, float* %8
%135 = load float, float* %4
%136 = load float, float* %5
%137 = fmul float %135, %136
%138 = load float*, float** %3
%139 = getelementptr inbounds float, float* %138, i64 0
store float %137, float* %139
%140 = load float, float* %4
%141 = load float, float* %6
%142 = fmul float %140, %141
%143 = load float*, float** %3
%144 = getelementptr inbounds float, float* %143, i64 1
store float %142, float* %144
%145 = load float, float* %4
%146 = load float, float* %7
%147 = fmul float %145, %146
%148 = load float*, float** %3
%149 = getelementptr inbounds float, float* %148, i64 2
store float %147, float* %149
%150 = load float, float* %4
%151 = load float, float* %8
%152 = fmul float %150, %151
%153 = load float*, float** %3
%154 = getelementptr inbounds float, float* %153, i64 3
store float %152, float* %154
%155 = load float, float* %4
%156 = load float, float* %9
%157 = fmul float %155, %156
%158 = load float*, float** %3
%159 = getelementptr inbounds float, float* %158, i64 4
store float %157, float* %159
%160 = load float, float* %4
%161 = load float, float* %10
%162 = fmul float %160, %161
%163 = load float*, float** %3
%164 = getelementptr inbounds float, float* %163, i64 5
store float %162, float* %164
%165 = load float, float* %4
%166 = load float, float* %11
%167 = fmul float %165, %166
%168 = load float*, float** %3
%169 = getelementptr inbounds float, float* %168, i64 6
store float %167, float* %169
%170 = load float, float* %4
%171 = load float, float* %12
%172 = fmul float %170, %171
%173 = load float*, float** %3
%174 = getelementptr inbounds float, float* %173, i64 7
store float %172, float* %174
ret void
}

LLVM IR (-O2):
define void @rifft4pt(float* nocapture %0, float %1) {
%3 = load float, float* %0
%4 = getelementptr inbounds float, float* %0, i64 1
%5 = load float, float* %4
%6 = getelementptr inbounds float, float* %0, i64 2
%7 = bitcast float* %6 to <2 x float>*
%8 = load <2 x float>, <2 x float>* %7
%9 = getelementptr inbounds float, float* %0, i64 4
%10 = bitcast float* %9 to <2 x float>*
%11 = load <2 x float>, <2 x float>* %10
%12 = fmul <2 x float> %11, <float 2.000000e+00, float 2.000000e+00>
%13 = shufflevector <2 x float> %12, <2 x float> poison, <4 x i32> <i32 0, i32 1, i32 0, i32 1>
%14 = getelementptr inbounds float, float* %0, i64 6
%15 = bitcast float* %14 to <2 x float>*
%16 = load <2 x float>, <2 x float>* %15
%17 = insertelement <2 x float> poison, float %3, i64 0
%18 = shufflevector <2 x float> %17, <2 x float> poison, <2 x i32> zeroinitializer
%19 = insertelement <2 x float> poison, float %5, i64 0
%20 = shufflevector <2 x float> %19, <2 x float> poison, <2 x i32> zeroinitializer
%21 = fadd <2 x float> %18, %20
%22 = fsub <2 x float> %18, %20
%23 = shufflevector <2 x float> %21, <2 x float> %22, <4 x i32> <i32 0, i32 3, i32 0, i32 3>
%24 = fadd <2 x float> %8, %16
%25 = fsub <2 x float> %8, %16
%26 = shufflevector <2 x float> %24, <2 x float> %25, <2 x i32> <i32 0, i32 3>
%27 = fsub <2 x float> %8, %16
%28 = fadd <2 x float> %8, %16
%29 = shufflevector <2 x float> %27, <2 x float> undef, <2 x i32> zeroinitializer
%30 = call <2 x float> @llvm.fmuladd.v2f32(<2 x float> %29, <2 x float> <float 0xBFE6A09E60000000, float 0x3FE6A09E60000000>, <2 x float> %26)
%31 = shufflevector <2 x float> %28, <2 x float> undef, <2 x i32> <i32 1, i32 1>
%32 = call <2 x float> @llvm.fmuladd.v2f32(<2 x float> %31, <2 x float> <float 0xBFE6A09E60000000, float 0xBFE6A09E60000000>, <2 x float> %30)
%33 = shufflevector <2 x float> %32, <2 x float> poison, <4 x i32> <i32 0, i32 1, i32 1, i32 0>
%34 = extractelement <2 x float> %32, i64 0
%35 = fneg float %34
%36 = insertelement <2 x float> %32, float %35, i64 0
%37 = call <2 x float> @llvm.fmuladd.v2f32(<2 x float> %26, <2 x float> <float 2.000000e+00, float -2.000000e+00>, <2 x float> %36)
%38 = shufflevector <2 x float> %37, <2 x float> poison, <4 x i32> <i32 0, i32 1, i32 1, i32 0>
%39 = fadd <4 x float> %23, %13
%40 = fsub <4 x float> %23, %13
%41 = shufflevector <4 x float> %39, <4 x float> %40, <4 x i32> <i32 0, i32 5, i32 6, i32 3>
%42 = fadd <4 x float> %33, %38
%43 = fsub <4 x float> %33, %38
%44 = shufflevector <4 x float> %42, <4 x float> %43, <4 x i32> <i32 0, i32 1, i32 6, i32 7>
%45 = fsub <4 x float> %41, %44
%46 = fadd <4 x float> %41, %44
%47 = shufflevector <4 x float> %45, <4 x float> %46, <4 x i32> <i32 0, i32 1, i32 6, i32 3>
%48 = shufflevector <4 x float> %46, <4 x float> %45, <4 x i32> <i32 0, i32 1, i32 6, i32 3>
%49 = insertelement <4 x float> poison, float %1, i64 0
%50 = shufflevector <4 x float> %49, <4 x float> poison, <4 x i32> zeroinitializer
%51 = fmul <4 x float> %48, %50
%52 = bitcast float* %0 to <4 x float>*
store <4 x float> %51, <4 x float>* %52
%53 = fmul <4 x float> %47, %50
%54 = bitcast float* %9 to <4 x float>*
store <4 x float> %53, <4 x float>* %54
ret void
}