; LLVM IR from SanketSarmalkar/Numerical_Methods :: Divided_Differences/DirectDifference.ll (Z7protermidPd)

; 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: mustprogress nounwind uwtable
define dso_local noundef double @_Z7protermidPd(i32 noundef %0, double noundef %1, ptr noundef %2) #0 {
  %4 = alloca i32, align 4
  %5 = alloca double, align 8
  %6 = alloca ptr, align 8
  %7 = alloca float, align 4
  %8 = alloca i32, align 4
  store i32 %0, ptr %4, align 4, !tbaa !5
  store double %1, ptr %5, align 8, !tbaa !9
  store ptr %2, ptr %6, align 8, !tbaa !11
  call void @llvm.lifetime.start.p0(i64 4, ptr %7) #2
  store float 1.000000e+00, ptr %7, align 4, !tbaa !13
  call void @llvm.lifetime.start.p0(i64 4, ptr %8) #2
  store i32 0, ptr %8, align 4, !tbaa !5
  br label %9

9:                                                ; preds = %26, %3
  %10 = load i32, ptr %8, align 4, !tbaa !5
  %11 = load i32, ptr %4, align 4, !tbaa !5
  %12 = icmp slt i32 %10, %11
  br i1 %12, label %14, label %13

13:                                               ; preds = %9
  call void @llvm.lifetime.end.p0(i64 4, ptr %8) #2
  br label %29

14:                                               ; preds = %9
  %15 = load float, ptr %7, align 4, !tbaa !13
  %16 = fpext float %15 to double
  %17 = load double, ptr %5, align 8, !tbaa !9
  %18 = load ptr, ptr %6, align 8, !tbaa !11
  %19 = load i32, ptr %8, align 4, !tbaa !5
  %20 = sext i32 %19 to i64
  %21 = getelementptr inbounds double, ptr %18, i64 %20
  %22 = load double, ptr %21, align 8, !tbaa !9
  %23 = fsub double %17, %22
  %24 = fmul double %16, %23
  %25 = fptrunc double %24 to float
  store float %25, ptr %7, align 4, !tbaa !13
  br label %26

26:                                               ; preds = %14
  %27 = load i32, ptr %8, align 4, !tbaa !5
  %28 = add nsw i32 %27, 1
  store i32 %28, ptr %8, align 4, !tbaa !5
  br label %9, !llvm.loop !15

29:                                               ; preds = %13
  %30 = load float, ptr %7, align 4, !tbaa !13
  %31 = fpext float %30 to double
  call void @llvm.lifetime.end.p0(i64 4, ptr %7) #2
  ret double %31
}

; 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 willreturn memory(argmem: readwrite)
declare void @llvm.lifetime.end.p0(i64 immarg, ptr nocapture) #1

attributes #0 = { mustprogress 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 = { 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 = !{!"int", !7, i64 0}
!7 = !{!"omnipotent char", !8, i64 0}
!8 = !{!"Simple C++ TBAA"}
!9 = !{!10, !10, i64 0}
!10 = !{!"double", !7, i64 0}
!11 = !{!12, !12, i64 0}
!12 = !{!"any pointer", !7, i64 0}
!13 = !{!14, !14, i64 0}
!14 = !{!"float", !7, i64 0}
!15 = distinct !{!15, !16}
!16 = !{!"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 nofree norecurse nosync nounwind willreturn memory(argmem: read) uwtable
define dso_local noundef double @_Z7protermidPd(i32 noundef %0, double noundef %1, ptr nocapture noundef readonly %2) local_unnamed_addr #0 {
  %4 = icmp sgt i32 %0, 0
  br i1 %4, label %.lr.ph.preheader, label %._crit_edge

.lr.ph.preheader:                                 ; preds = %3
  %wide.trip.count = zext nneg i32 %0 to i64
  %xtraiter = and i64 %wide.trip.count, 3
  %5 = icmp ult i32 %0, 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 %wide.trip.count, 2147483644
  br label %.lr.ph

._crit_edge.loopexit.unr-lcssa:                   ; preds = %.lr.ph, %.lr.ph.preheader
  %.lcssa.ph = phi float [ poison, %.lr.ph.preheader ], [ %36, %.lr.ph ]
  %indvars.iv.unr = phi i64 [ 0, %.lr.ph.preheader ], [ %indvars.iv.next.3, %.lr.ph ]
  %.078.unr = phi float [ 1.000000e+00, %.lr.ph.preheader ], [ %36, %.lr.ph ]
  %lcmp.mod.not = icmp eq i64 %xtraiter, 0
  br i1 %lcmp.mod.not, label %._crit_edge.loopexit, 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 ]
  %.078.epil = phi float [ %11, %.lr.ph.epil ], [ %.078.unr, %._crit_edge.loopexit.unr-lcssa ]
  %epil.iter = phi i64 [ %epil.iter.next, %.lr.ph.epil ], [ 0, %._crit_edge.loopexit.unr-lcssa ]
  %6 = fpext float %.078.epil to double
  %7 = getelementptr inbounds double, ptr %2, i64 %indvars.iv.epil
  %8 = load double, ptr %7, align 8, !tbaa !5
  %9 = fsub double %1, %8
  %10 = fmul double %9, %6
  %11 = fptrunc double %10 to float
  %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.loopexit, label %.lr.ph.epil, !llvm.loop !9

._crit_edge.loopexit:                             ; preds = %.lr.ph.epil, %._crit_edge.loopexit.unr-lcssa
  %.lcssa = phi float [ %.lcssa.ph, %._crit_edge.loopexit.unr-lcssa ], [ %11, %.lr.ph.epil ]
  %12 = fpext float %.lcssa to double
  br label %._crit_edge

._crit_edge:                                      ; preds = %._crit_edge.loopexit, %3
  %.07.lcssa = phi double [ 1.000000e+00, %3 ], [ %12, %._crit_edge.loopexit ]
  ret double %.07.lcssa

.lr.ph:                                           ; preds = %.lr.ph, %.lr.ph.preheader.new
  %indvars.iv = phi i64 [ 0, %.lr.ph.preheader.new ], [ %indvars.iv.next.3, %.lr.ph ]
  %.078 = phi float [ 1.000000e+00, %.lr.ph.preheader.new ], [ %36, %.lr.ph ]
  %niter = phi i64 [ 0, %.lr.ph.preheader.new ], [ %niter.next.3, %.lr.ph ]
  %13 = fpext float %.078 to double
  %14 = getelementptr inbounds double, ptr %2, i64 %indvars.iv
  %15 = load double, ptr %14, align 8, !tbaa !5
  %16 = fsub double %1, %15
  %17 = fmul double %16, %13
  %18 = fptrunc double %17 to float
  %indvars.iv.next = or disjoint i64 %indvars.iv, 1
  %19 = fpext float %18 to double
  %20 = getelementptr inbounds double, ptr %2, i64 %indvars.iv.next
  %21 = load double, ptr %20, align 8, !tbaa !5
  %22 = fsub double %1, %21
  %23 = fmul double %22, %19
  %24 = fptrunc double %23 to float
  %indvars.iv.next.1 = or disjoint i64 %indvars.iv, 2
  %25 = fpext float %24 to double
  %26 = getelementptr inbounds double, ptr %2, i64 %indvars.iv.next.1
  %27 = load double, ptr %26, align 8, !tbaa !5
  %28 = fsub double %1, %27
  %29 = fmul double %28, %25
  %30 = fptrunc double %29 to float
  %indvars.iv.next.2 = or disjoint i64 %indvars.iv, 3
  %31 = fpext float %30 to double
  %32 = getelementptr inbounds double, ptr %2, i64 %indvars.iv.next.2
  %33 = load double, ptr %32, align 8, !tbaa !5
  %34 = fsub double %1, %33
  %35 = fmul double %34, %31
  %36 = fptrunc double %35 to float
  %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 nofree norecurse nosync nounwind willreturn memory(argmem: read) 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" }

!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++ TBAA"}
!9 = distinct !{!9, !10}
!10 = !{!"llvm.loop.unroll.disable"}
!11 = distinct !{!11, !12}
!12 = !{!"llvm.loop.mustprogress"}


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