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

7:                                                ; preds = %25, %2
  %8 = load i32, ptr %6, align 4, !tbaa !9
  %9 = load i32, ptr %4, align 4, !tbaa !9
  %10 = icmp sle i32 %8, %9
  br i1 %10, label %12, label %11

11:                                               ; preds = %7
  call void @llvm.lifetime.end.p0(i64 4, ptr %6) #4
  br label %28

12:                                               ; preds = %7
  %13 = load ptr, ptr %3, align 8, !tbaa !5
  %14 = load i32, ptr %6, align 4, !tbaa !9
  %15 = sext i32 %14 to i64
  %16 = getelementptr inbounds double, ptr %13, i64 %15
  %17 = load double, ptr %16, align 8, !tbaa !11
  %18 = load ptr, ptr %3, align 8, !tbaa !5
  %19 = load i32, ptr %6, align 4, !tbaa !9
  %20 = sext i32 %19 to i64
  %21 = getelementptr inbounds double, ptr %18, i64 %20
  %22 = load double, ptr %21, align 8, !tbaa !11
  %23 = load double, ptr %5, align 8, !tbaa !11
  %24 = call double @llvm.fmuladd.f64(double %17, double %22, double %23)
  store double %24, ptr %5, align 8, !tbaa !11
  br label %25

25:                                               ; preds = %12
  %26 = load i32, ptr %6, align 4, !tbaa !9
  %27 = add nsw i32 %26, 1
  store i32 %27, ptr %6, align 4, !tbaa !9
  br label %7, !llvm.loop !13

28:                                               ; preds = %11
  %29 = load double, ptr %5, align 8, !tbaa !11
  %30 = call double @sqrt(double noundef %29) #4
  call void @llvm.lifetime.end.p0(i64 8, ptr %5) #4
  ret double %30
}

; Function Attrs: nocallback nofree nosync nounwind willreturn memory(argmem: readwrite)
declare void @llvm.lifetime.start.p0(i64 immarg, ptr nocapture) #1

; Function Attrs: nocallback nofree nosync nounwind speculatable willreturn memory(none)
declare double @llvm.fmuladd.f64(double, double, double) #2

; Function Attrs: nocallback nofree nosync nounwind willreturn memory(argmem: readwrite)
declare void @llvm.lifetime.end.p0(i64 immarg, ptr nocapture) #1

; Function Attrs: nounwind
declare double @sqrt(double noundef) #3

attributes #0 = { 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 #1 = { nocallback nofree nosync nounwind willreturn memory(argmem: readwrite) }
attributes #2 = { nocallback nofree nosync nounwind speculatable willreturn memory(none) }
attributes #3 = { 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 #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: nofree nounwind memory(write, argmem: readwrite) uwtable
define dso_local double @Normalize(ptr nocapture noundef readonly %0, i32 noundef %1) local_unnamed_addr #0 {
  %.not9 = icmp slt i32 %1, 1
  br i1 %.not9, label %._crit_edge, label %.lr.ph.preheader

.lr.ph.preheader:                                 ; preds = %2
  %3 = zext nneg i32 %1 to i64
  %xtraiter = and i64 %3, 3
  %4 = icmp ult i32 %1, 4
  br i1 %4, label %._crit_edge.loopexit.unr-lcssa, label %.lr.ph.preheader.new

.lr.ph.preheader.new:                             ; preds = %.lr.ph.preheader
  %unroll_iter = and i64 %3, 2147483644
  %invariant.gep = getelementptr inbounds i8, ptr %0, i64 8
  %invariant.gep16 = getelementptr inbounds i8, ptr %0, i64 16
  %invariant.gep18 = getelementptr inbounds i8, ptr %0, i64 24
  br label %.lr.ph

._crit_edge.loopexit.unr-lcssa:                   ; preds = %.lr.ph, %.lr.ph.preheader
  %.lcssa.ph = phi double [ poison, %.lr.ph.preheader ], [ %17, %.lr.ph ]
  %indvars.iv.unr = phi i64 [ 1, %.lr.ph.preheader ], [ %indvars.iv.next.3, %.lr.ph ]
  %.0810.unr = phi double [ 0.000000e+00, %.lr.ph.preheader ], [ %17, %.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 ]
  %.0810.epil = phi double [ %7, %.lr.ph.epil ], [ %.0810.unr, %._crit_edge.loopexit.unr-lcssa ]
  %epil.iter = phi i64 [ %epil.iter.next, %.lr.ph.epil ], [ 0, %._crit_edge.loopexit.unr-lcssa ]
  %5 = getelementptr inbounds double, ptr %0, i64 %indvars.iv.epil
  %6 = load double, ptr %5, align 8, !tbaa !5
  %7 = tail call double @llvm.fmuladd.f64(double %6, double %6, double %.0810.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, %2
  %.08.lcssa = phi double [ 0.000000e+00, %2 ], [ %.lcssa.ph, %._crit_edge.loopexit.unr-lcssa ], [ %7, %.lr.ph.epil ]
  %8 = tail call double @sqrt(double noundef %.08.lcssa) #3
  ret double %8

.lr.ph:                                           ; preds = %.lr.ph, %.lr.ph.preheader.new
  %indvars.iv = phi i64 [ 1, %.lr.ph.preheader.new ], [ %indvars.iv.next.3, %.lr.ph ]
  %.0810 = phi double [ 0.000000e+00, %.lr.ph.preheader.new ], [ %17, %.lr.ph ]
  %niter = phi i64 [ 0, %.lr.ph.preheader.new ], [ %niter.next.3, %.lr.ph ]
  %9 = getelementptr inbounds double, ptr %0, i64 %indvars.iv
  %10 = load double, ptr %9, align 8, !tbaa !5
  %11 = tail call double @llvm.fmuladd.f64(double %10, double %10, double %.0810)
  %gep = getelementptr inbounds double, ptr %invariant.gep, i64 %indvars.iv
  %12 = load double, ptr %gep, align 8, !tbaa !5
  %13 = tail call double @llvm.fmuladd.f64(double %12, double %12, double %11)
  %gep17 = getelementptr inbounds double, ptr %invariant.gep16, i64 %indvars.iv
  %14 = load double, ptr %gep17, align 8, !tbaa !5
  %15 = tail call double @llvm.fmuladd.f64(double %14, double %14, double %13)
  %gep19 = getelementptr inbounds double, ptr %invariant.gep18, i64 %indvars.iv
  %16 = load double, ptr %gep19, align 8, !tbaa !5
  %17 = tail call double @llvm.fmuladd.f64(double %16, double %16, double %15)
  %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
}

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

; Function Attrs: mustprogress nofree nounwind willreturn memory(write)
declare double @sqrt(double noundef) local_unnamed_addr #2

attributes #0 = { 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 #1 = { mustprogress nocallback nofree nosync nounwind speculatable willreturn memory(none) }
attributes #2 = { 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 #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,LICMPass,LoopRotatePass,LoopSimplifyPass,LoopUnrollPass,PostOrderFunctionAttrsPass,SROAPass,SimplifyCFGPass,TailCallElimPass