; LLVM IR from 0r-gh0/NUMERICAL_ANALYSIS :: CODES (POWER_METHOD_FINAL)

; Unoptimized IR (clang -disable-llvm-passes):
target datalayout = "e-m:e-p270:32:32-p271:32:32-p272:64:64-i64:64-i128:128-f80:128-n8:16:32:64-S128"
target triple = "x86_64-unknown-linux-gnu"

; Function Attrs: nocallback nofree nosync nounwind willreturn memory(argmem: readwrite)
declare void @llvm.lifetime.start.p0(i64 immarg, ptr nocapture) #0

; Function Attrs: nocallback nofree nosync nounwind speculatable willreturn memory(none)
declare double @llvm.fmuladd.f64(double, double, double) #1

; Function Attrs: nocallback nofree nosync nounwind willreturn memory(argmem: readwrite)
declare void @llvm.lifetime.end.p0(i64 immarg, ptr nocapture) #0

; Function Attrs: nounwind
declare double @sqrt(double noundef) #2

; Function Attrs: nounwind uwtable
define dso_local double @FrobNorm(ptr noundef %0, ptr noundef %1, i32 noundef %2) #3 {
  %4 = alloca ptr, align 8
  %5 = alloca ptr, align 8
  %6 = alloca i32, align 4
  %7 = alloca double, align 8
  %8 = alloca i32, align 4
  store ptr %0, ptr %4, align 8, !tbaa !5
  store ptr %1, ptr %5, align 8, !tbaa !5
  store i32 %2, ptr %6, align 4, !tbaa !9
  call void @llvm.lifetime.start.p0(i64 8, ptr %7) #4
  store double 0.000000e+00, ptr %7, align 8, !tbaa !11
  call void @llvm.lifetime.start.p0(i64 4, ptr %8) #4
  store i32 1, ptr %8, align 4, !tbaa !9
  br label %9

9:                                                ; preds = %39, %3
  %10 = load i32, ptr %8, align 4, !tbaa !9
  %11 = load i32, ptr %6, align 4, !tbaa !9
  %12 = icmp sle i32 %10, %11
  br i1 %12, label %14, label %13

13:                                               ; preds = %9
  call void @llvm.lifetime.end.p0(i64 4, ptr %8) #4
  br label %42

14:                                               ; preds = %9
  %15 = load ptr, ptr %4, align 8, !tbaa !5
  %16 = load i32, ptr %8, align 4, !tbaa !9
  %17 = sext i32 %16 to i64
  %18 = getelementptr inbounds double, ptr %15, i64 %17
  %19 = load double, ptr %18, align 8, !tbaa !11
  %20 = load ptr, ptr %5, align 8, !tbaa !5
  %21 = load i32, ptr %8, align 4, !tbaa !9
  %22 = sext i32 %21 to i64
  %23 = getelementptr inbounds double, ptr %20, i64 %22
  %24 = load double, ptr %23, align 8, !tbaa !11
  %25 = fsub double %19, %24
  %26 = load ptr, ptr %4, align 8, !tbaa !5
  %27 = load i32, ptr %8, align 4, !tbaa !9
  %28 = sext i32 %27 to i64
  %29 = getelementptr inbounds double, ptr %26, i64 %28
  %30 = load double, ptr %29, align 8, !tbaa !11
  %31 = load ptr, ptr %5, align 8, !tbaa !5
  %32 = load i32, ptr %8, align 4, !tbaa !9
  %33 = sext i32 %32 to i64
  %34 = getelementptr inbounds double, ptr %31, i64 %33
  %35 = load double, ptr %34, align 8, !tbaa !11
  %36 = fsub double %30, %35
  %37 = load double, ptr %7, align 8, !tbaa !11
  %38 = call double @llvm.fmuladd.f64(double %25, double %36, double %37)
  store double %38, ptr %7, align 8, !tbaa !11
  br label %39

39:                                               ; preds = %14
  %40 = load i32, ptr %8, align 4, !tbaa !9
  %41 = add nsw i32 %40, 1
  store i32 %41, ptr %8, align 4, !tbaa !9
  br label %9, !llvm.loop !13

42:                                               ; preds = %13
  %43 = load double, ptr %7, align 8, !tbaa !11
  %44 = call double @sqrt(double noundef %43) #4
  call void @llvm.lifetime.end.p0(i64 8, ptr %7) #4
  ret double %44
}

attributes #0 = { nocallback nofree nosync nounwind willreturn memory(argmem: readwrite) }
attributes #1 = { nocallback nofree nosync nounwind speculatable willreturn memory(none) }
attributes #2 = { nounwind "no-trapping-math"="true" "stack-protector-buffer-size"="8" "target-cpu"="x86-64" "target-features"="+cmov,+cx8,+fxsr,+mmx,+sse,+sse2,+x87" "tune-cpu"="generic" }
attributes #3 = { nounwind uwtable "min-legal-vector-width"="0" "no-trapping-math"="true" "stack-protector-buffer-size"="8" "target-cpu"="x86-64" "target-features"="+cmov,+cx8,+fxsr,+mmx,+sse,+sse2,+x87" "tune-cpu"="generic" }
attributes #4 = { nounwind }

!llvm.module.flags = !{!0, !1, !2, !3}
!llvm.ident = !{!4}

!0 = !{i32 1, !"wchar_size", i32 4}
!1 = !{i32 8, !"PIC Level", i32 2}
!2 = !{i32 7, !"PIE Level", i32 2}
!3 = !{i32 7, !"uwtable", i32 2}
!4 = !{!"clang version 19.1.0 (git@github.com:llvm/llvm-project.git a4bf6cd7cfb1a1421ba92bca9d017b49936c55e4)"}
!5 = !{!6, !6, i64 0}
!6 = !{!"any pointer", !7, i64 0}
!7 = !{!"omnipotent char", !8, i64 0}
!8 = !{!"Simple C/C++ TBAA"}
!9 = !{!10, !10, i64 0}
!10 = !{!"int", !7, i64 0}
!11 = !{!12, !12, i64 0}
!12 = !{!"double", !7, i64 0}
!13 = distinct !{!13, !14}
!14 = !{!"llvm.loop.mustprogress"}


; Optimized IR (opt -passes='default<O3>'):
target datalayout = "e-m:e-p270:32:32-p271:32:32-p272:64:64-i64:64-i128:128-f80:128-n8:16:32:64-S128"
target triple = "x86_64-unknown-linux-gnu"

; Function Attrs: mustprogress nocallback nofree nosync nounwind speculatable willreturn memory(none)
declare double @llvm.fmuladd.f64(double, double, double) #0

; Function Attrs: mustprogress nofree nounwind willreturn memory(write)
declare double @sqrt(double noundef) local_unnamed_addr #1

; Function Attrs: nofree nounwind memory(write, argmem: readwrite) uwtable
define dso_local double @FrobNorm(ptr nocapture noundef readonly %0, ptr nocapture noundef readonly %1, i32 noundef %2) local_unnamed_addr #2 {
  %.not13 = icmp slt i32 %2, 1
  br i1 %.not13, label %._crit_edge, label %.lr.ph.preheader

.lr.ph.preheader:                                 ; preds = %3
  %4 = zext nneg i32 %2 to i64
  %xtraiter = and i64 %4, 3
  %5 = icmp ult i32 %2, 4
  br i1 %5, label %._crit_edge.loopexit.unr-lcssa, label %.lr.ph.preheader.new

.lr.ph.preheader.new:                             ; preds = %.lr.ph.preheader
  %unroll_iter = and i64 %4, 2147483644
  br label %.lr.ph

._crit_edge.loopexit.unr-lcssa:                   ; preds = %.lr.ph, %.lr.ph.preheader
  %.lcssa.ph = phi double [ poison, %.lr.ph.preheader ], [ %36, %.lr.ph ]
  %indvars.iv.unr = phi i64 [ 1, %.lr.ph.preheader ], [ %indvars.iv.next.3, %.lr.ph ]
  %.01214.unr = phi double [ 0.000000e+00, %.lr.ph.preheader ], [ %36, %.lr.ph ]
  %lcmp.mod.not = icmp eq i64 %xtraiter, 0
  br i1 %lcmp.mod.not, label %._crit_edge, label %.lr.ph.epil

.lr.ph.epil:                                      ; preds = %._crit_edge.loopexit.unr-lcssa, %.lr.ph.epil
  %indvars.iv.epil = phi i64 [ %indvars.iv.next.epil, %.lr.ph.epil ], [ %indvars.iv.unr, %._crit_edge.loopexit.unr-lcssa ]
  %.01214.epil = phi double [ %11, %.lr.ph.epil ], [ %.01214.unr, %._crit_edge.loopexit.unr-lcssa ]
  %epil.iter = phi i64 [ %epil.iter.next, %.lr.ph.epil ], [ 0, %._crit_edge.loopexit.unr-lcssa ]
  %6 = getelementptr inbounds double, ptr %0, i64 %indvars.iv.epil
  %7 = load double, ptr %6, align 8, !tbaa !5
  %8 = getelementptr inbounds double, ptr %1, i64 %indvars.iv.epil
  %9 = load double, ptr %8, align 8, !tbaa !5
  %10 = fsub double %7, %9
  %11 = tail call double @llvm.fmuladd.f64(double %10, double %10, double %.01214.epil)
  %indvars.iv.next.epil = add nuw nsw i64 %indvars.iv.epil, 1
  %epil.iter.next = add i64 %epil.iter, 1
  %epil.iter.cmp.not = icmp eq i64 %epil.iter.next, %xtraiter
  br i1 %epil.iter.cmp.not, label %._crit_edge, label %.lr.ph.epil, !llvm.loop !9

._crit_edge:                                      ; preds = %._crit_edge.loopexit.unr-lcssa, %.lr.ph.epil, %3
  %.012.lcssa = phi double [ 0.000000e+00, %3 ], [ %.lcssa.ph, %._crit_edge.loopexit.unr-lcssa ], [ %11, %.lr.ph.epil ]
  %12 = tail call double @sqrt(double noundef %.012.lcssa) #3
  ret double %12

.lr.ph:                                           ; preds = %.lr.ph, %.lr.ph.preheader.new
  %indvars.iv = phi i64 [ 1, %.lr.ph.preheader.new ], [ %indvars.iv.next.3, %.lr.ph ]
  %.01214 = phi double [ 0.000000e+00, %.lr.ph.preheader.new ], [ %36, %.lr.ph ]
  %niter = phi i64 [ 0, %.lr.ph.preheader.new ], [ %niter.next.3, %.lr.ph ]
  %13 = getelementptr inbounds double, ptr %0, i64 %indvars.iv
  %14 = load double, ptr %13, align 8, !tbaa !5
  %15 = getelementptr inbounds double, ptr %1, i64 %indvars.iv
  %16 = load double, ptr %15, align 8, !tbaa !5
  %17 = fsub double %14, %16
  %18 = tail call double @llvm.fmuladd.f64(double %17, double %17, double %.01214)
  %indvars.iv.next = add nuw nsw i64 %indvars.iv, 1
  %19 = getelementptr inbounds double, ptr %0, i64 %indvars.iv.next
  %20 = load double, ptr %19, align 8, !tbaa !5
  %21 = getelementptr inbounds double, ptr %1, i64 %indvars.iv.next
  %22 = load double, ptr %21, align 8, !tbaa !5
  %23 = fsub double %20, %22
  %24 = tail call double @llvm.fmuladd.f64(double %23, double %23, double %18)
  %indvars.iv.next.1 = add nuw nsw i64 %indvars.iv, 2
  %25 = getelementptr inbounds double, ptr %0, i64 %indvars.iv.next.1
  %26 = load double, ptr %25, align 8, !tbaa !5
  %27 = getelementptr inbounds double, ptr %1, i64 %indvars.iv.next.1
  %28 = load double, ptr %27, align 8, !tbaa !5
  %29 = fsub double %26, %28
  %30 = tail call double @llvm.fmuladd.f64(double %29, double %29, double %24)
  %indvars.iv.next.2 = add nuw nsw i64 %indvars.iv, 3
  %31 = getelementptr inbounds double, ptr %0, i64 %indvars.iv.next.2
  %32 = load double, ptr %31, align 8, !tbaa !5
  %33 = getelementptr inbounds double, ptr %1, i64 %indvars.iv.next.2
  %34 = load double, ptr %33, align 8, !tbaa !5
  %35 = fsub double %32, %34
  %36 = tail call double @llvm.fmuladd.f64(double %35, double %35, double %30)
  %indvars.iv.next.3 = add nuw nsw i64 %indvars.iv, 4
  %niter.next.3 = add i64 %niter, 4
  %niter.ncmp.3 = icmp eq i64 %niter.next.3, %unroll_iter
  br i1 %niter.ncmp.3, label %._crit_edge.loopexit.unr-lcssa, label %.lr.ph, !llvm.loop !11
}

attributes #0 = { mustprogress nocallback nofree nosync nounwind speculatable willreturn memory(none) }
attributes #1 = { mustprogress nofree nounwind willreturn memory(write) "no-trapping-math"="true" "stack-protector-buffer-size"="8" "target-cpu"="x86-64" "target-features"="+cmov,+cx8,+fxsr,+mmx,+sse,+sse2,+x87" "tune-cpu"="generic" }
attributes #2 = { nofree nounwind memory(write, argmem: readwrite) uwtable "min-legal-vector-width"="0" "no-trapping-math"="true" "stack-protector-buffer-size"="8" "target-cpu"="x86-64" "target-features"="+cmov,+cx8,+fxsr,+mmx,+sse,+sse2,+x87" "tune-cpu"="generic" }
attributes #3 = { nounwind }

!llvm.module.flags = !{!0, !1, !2, !3}
!llvm.ident = !{!4}

!0 = !{i32 1, !"wchar_size", i32 4}
!1 = !{i32 8, !"PIC Level", i32 2}
!2 = !{i32 7, !"PIE Level", i32 2}
!3 = !{i32 7, !"uwtable", i32 2}
!4 = !{!"clang version 19.1.0 (git@github.com:llvm/llvm-project.git a4bf6cd7cfb1a1421ba92bca9d017b49936c55e4)"}
!5 = !{!6, !6, i64 0}
!6 = !{!"double", !7, i64 0}
!7 = !{!"omnipotent char", !8, i64 0}
!8 = !{!"Simple C/C++ TBAA"}
!9 = distinct !{!9, !10}
!10 = !{!"llvm.loop.unroll.disable"}
!11 = distinct !{!11, !12}
!12 = !{!"llvm.loop.mustprogress"}


; Effective O3 passes: EarlyCSEPass,GVNPass,GlobalOptPass,IndVarSimplifyPass,InferFunctionAttrsPass,InstCombinePass,InstSimplifyPass,JumpThreadingPass,LCSSAPass,LoopRotatePass,LoopSimplifyPass,LoopUnrollPass,PostOrderFunctionAttrsPass,SROAPass,SimplifyCFGPass,TailCallElimPass