; LLVM IR from ShahjalalShohag/code-library :: Math (Linear Recurrence With Polynomial Coefficients)

; 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"

%"class.std::vector" = type { %"struct.std::_Vector_base" }
%"struct.std::_Vector_base" = type { %"struct.std::_Vector_base<int, std::allocator<int>>::_Vector_impl" }
%"struct.std::_Vector_base<int, std::allocator<int>>::_Vector_impl" = type { %"struct.std::_Vector_base<int, std::allocator<int>>::_Vector_impl_data" }
%"struct.std::_Vector_base<int, std::allocator<int>>::_Vector_impl_data" = type { ptr, ptr, ptr }
%"class.std::vector.1" = type { %"struct.std::_Vector_base.2" }
%"struct.std::_Vector_base.2" = type { %"struct.std::_Vector_base<std::vector<int>, std::allocator<std::vector<int>>>::_Vector_impl" }
%"struct.std::_Vector_base<std::vector<int>, std::allocator<std::vector<int>>>::_Vector_impl" = type { %"struct.std::_Vector_base<std::vector<int>, std::allocator<std::vector<int>>>::_Vector_impl_data" }
%"struct.std::_Vector_base<std::vector<int>, std::allocator<std::vector<int>>>::_Vector_impl_data" = type { ptr, ptr, ptr }

@.str.7 = external hidden unnamed_addr constant [7 x i8], align 1
@.str.8 = external hidden unnamed_addr constant [1 x i8], align 1

; 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 willreturn memory(argmem: readwrite)
declare void @llvm.lifetime.end.p0(i64 immarg, ptr nocapture) #0

; Function Attrs: mustprogress uwtable
declare dso_local void @_Z8extendediRKSt6vectorIS_IiSaIiEESaIS1_EERKS1_i(ptr dead_on_unwind noalias writable sret(%"class.std::vector") align 8, i32 noundef, ptr noundef nonnull align 8 dereferenceable(24), ptr noundef nonnull align 8 dereferenceable(24), i32 noundef) #1

; Function Attrs: mustprogress nounwind uwtable
declare dso_local noundef i64 @_ZNKSt6vectorIiSaIiEE4sizeEv(ptr noundef nonnull align 8 dereferenceable(24)) #2 align 2

declare i32 @__gxx_personality_v0(...)

; Function Attrs: mustprogress nounwind uwtable
declare dso_local noundef nonnull align 4 dereferenceable(4) ptr @_ZNSt6vectorIiSaIiEEixEm(ptr noundef nonnull align 8 dereferenceable(24), i64 noundef) #2 align 2

; Function Attrs: mustprogress nounwind uwtable
declare dso_local void @_ZNSt6vectorIiSaIiEED2Ev(ptr noundef nonnull align 8 dereferenceable(24)) unnamed_addr #2 align 2

; Function Attrs: mustprogress uwtable
declare dso_local void @_Z24find_recurrence_relationRKSt6vectorIiSaIiEEiib(ptr dead_on_unwind noalias writable sret(%"class.std::vector.1") align 8, ptr noundef nonnull align 8 dereferenceable(24), i32 noundef, i32 noundef, i1 noundef zeroext) #1

; Function Attrs: mustprogress nounwind uwtable
declare dso_local void @_ZNSt6vectorIS_IiSaIiEESaIS1_EED2Ev(ptr noundef nonnull align 8 dereferenceable(24)) unnamed_addr #2 align 2

; Function Attrs: mustprogress uwtable
define dso_local void @_Z22show_extended_sequenceiRKSt6vectorIiSaIiEEii(i32 noundef %0, ptr noundef nonnull align 8 dereferenceable(24) %1, i32 noundef %2, i32 noundef %3) #1 personality ptr @__gxx_personality_v0 {
  %5 = alloca i32, align 4
  %6 = alloca ptr, align 8
  %7 = alloca i32, align 4
  %8 = alloca i32, align 4
  %9 = alloca %"class.std::vector.1", align 8
  %10 = alloca %"class.std::vector", align 8
  %11 = alloca ptr, align 8
  %12 = alloca i32, align 4
  %13 = alloca i32, align 4
  store i32 %0, ptr %5, align 4, !tbaa !5
  store ptr %1, ptr %6, align 8, !tbaa !9
  store i32 %2, ptr %7, align 4, !tbaa !5
  store i32 %3, ptr %8, align 4, !tbaa !5
  call void @llvm.lifetime.start.p0(i64 24, ptr %9) #4
  %14 = load ptr, ptr %6, align 8, !tbaa !9
  %15 = load i32, ptr %7, align 4, !tbaa !5
  %16 = load i32, ptr %8, align 4, !tbaa !5
  call void @_Z24find_recurrence_relationRKSt6vectorIiSaIiEEiib(ptr dead_on_unwind writable sret(%"class.std::vector.1") align 8 %9, ptr noundef nonnull align 8 dereferenceable(24) %14, i32 noundef %15, i32 noundef %16, i1 noundef zeroext true)
  call void @llvm.lifetime.start.p0(i64 24, ptr %10) #4
  %17 = load i32, ptr %5, align 4, !tbaa !5
  %18 = load ptr, ptr %6, align 8, !tbaa !9
  %19 = load i32, ptr %8, align 4, !tbaa !5
  invoke void @_Z8extendediRKSt6vectorIS_IiSaIiEESaIS1_EERKS1_i(ptr dead_on_unwind writable sret(%"class.std::vector") align 8 %10, i32 noundef %17, ptr noundef nonnull align 8 dereferenceable(24) %9, ptr noundef nonnull align 8 dereferenceable(24) %18, i32 noundef %19)
          to label %20 unwind label %27

20:                                               ; preds = %4
  call void @llvm.lifetime.start.p0(i64 4, ptr %13) #4
  store i32 0, ptr %13, align 4, !tbaa !5
  br label %21

21:                                               ; preds = %39, %20
  %22 = load i32, ptr %13, align 4, !tbaa !5
  %23 = call noundef i64 @_ZNKSt6vectorIiSaIiEE4sizeEv(ptr noundef nonnull align 8 dereferenceable(24) %10) #4
  %24 = trunc i64 %23 to i32
  %25 = icmp slt i32 %22, %24
  br i1 %25, label %31, label %26

26:                                               ; preds = %21
  call void @llvm.lifetime.end.p0(i64 4, ptr %13) #4
  br label %46

27:                                               ; preds = %4
  %28 = landingpad { ptr, i32 }
          cleanup
  %29 = extractvalue { ptr, i32 } %28, 0
  store ptr %29, ptr %11, align 8
  %30 = extractvalue { ptr, i32 } %28, 1
  store i32 %30, ptr %12, align 4
  br label %54

31:                                               ; preds = %21
  %32 = load i32, ptr %13, align 4, !tbaa !5
  %33 = load i32, ptr %13, align 4, !tbaa !5
  %34 = sext i32 %33 to i64
  %35 = call noundef nonnull align 4 dereferenceable(4) ptr @_ZNSt6vectorIiSaIiEEixEm(ptr noundef nonnull align 8 dereferenceable(24) %10, i64 noundef %34) #4
  %36 = load i32, ptr %35, align 4, !tbaa !5
  %37 = invoke i32 (ptr, ...) @printf(ptr noundef @.str.7, i32 noundef %32, i32 noundef %36)
          to label %38 unwind label %42

38:                                               ; preds = %31
  br label %39

39:                                               ; preds = %38
  %40 = load i32, ptr %13, align 4, !tbaa !5
  %41 = add nsw i32 %40, 1
  store i32 %41, ptr %13, align 4, !tbaa !5
  br label %21, !llvm.loop !11

42:                                               ; preds = %31
  %43 = landingpad { ptr, i32 }
          cleanup
  %44 = extractvalue { ptr, i32 } %43, 0
  store ptr %44, ptr %11, align 8
  %45 = extractvalue { ptr, i32 } %43, 1
  store i32 %45, ptr %12, align 4
  call void @llvm.lifetime.end.p0(i64 4, ptr %13) #4
  br label %53

46:                                               ; preds = %26
  %47 = invoke i32 @puts(ptr noundef @.str.8)
          to label %48 unwind label %49

48:                                               ; preds = %46
  call void @_ZNSt6vectorIiSaIiEED2Ev(ptr noundef nonnull align 8 dereferenceable(24) %10) #4
  call void @llvm.lifetime.end.p0(i64 24, ptr %10) #4
  call void @_ZNSt6vectorIS_IiSaIiEESaIS1_EED2Ev(ptr noundef nonnull align 8 dereferenceable(24) %9) #4
  call void @llvm.lifetime.end.p0(i64 24, ptr %9) #4
  ret void

49:                                               ; preds = %46
  %50 = landingpad { ptr, i32 }
          cleanup
  %51 = extractvalue { ptr, i32 } %50, 0
  store ptr %51, ptr %11, align 8
  %52 = extractvalue { ptr, i32 } %50, 1
  store i32 %52, ptr %12, align 4
  br label %53

53:                                               ; preds = %49, %42
  call void @_ZNSt6vectorIiSaIiEED2Ev(ptr noundef nonnull align 8 dereferenceable(24) %10) #4
  br label %54

54:                                               ; preds = %53, %27
  call void @llvm.lifetime.end.p0(i64 24, ptr %10) #4
  call void @_ZNSt6vectorIS_IiSaIiEESaIS1_EED2Ev(ptr noundef nonnull align 8 dereferenceable(24) %9) #4
  call void @llvm.lifetime.end.p0(i64 24, ptr %9) #4
  br label %55

55:                                               ; preds = %54
  %56 = load ptr, ptr %11, align 8
  %57 = load i32, ptr %12, align 4
  %58 = insertvalue { ptr, i32 } poison, ptr %56, 0
  %59 = insertvalue { ptr, i32 } %58, i32 %57, 1
  resume { ptr, i32 } %59
}

declare i32 @printf(ptr noundef, ...) #3

declare i32 @puts(ptr noundef) #3

attributes #0 = { nocallback nofree nosync nounwind willreturn memory(argmem: readwrite) }
attributes #1 = { mustprogress 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 #2 = { 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 #3 = { "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 = !{!"int", !7, i64 0}
!7 = !{!"omnipotent char", !8, i64 0}
!8 = !{!"Simple C++ TBAA"}
!9 = !{!10, !10, i64 0}
!10 = !{!"any pointer", !7, i64 0}
!11 = distinct !{!11, !12}
!12 = !{!"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"

%"class.std::vector" = type { %"struct.std::_Vector_base" }
%"struct.std::_Vector_base" = type { %"struct.std::_Vector_base<int, std::allocator<int>>::_Vector_impl" }
%"struct.std::_Vector_base<int, std::allocator<int>>::_Vector_impl" = type { %"struct.std::_Vector_base<int, std::allocator<int>>::_Vector_impl_data" }
%"struct.std::_Vector_base<int, std::allocator<int>>::_Vector_impl_data" = type { ptr, ptr, ptr }
%"class.std::vector.1" = type { %"struct.std::_Vector_base.2" }
%"struct.std::_Vector_base.2" = type { %"struct.std::_Vector_base<std::vector<int>, std::allocator<std::vector<int>>>::_Vector_impl" }
%"struct.std::_Vector_base<std::vector<int>, std::allocator<std::vector<int>>>::_Vector_impl" = type { %"struct.std::_Vector_base<std::vector<int>, std::allocator<std::vector<int>>>::_Vector_impl_data" }
%"struct.std::_Vector_base<std::vector<int>, std::allocator<std::vector<int>>>::_Vector_impl_data" = type { ptr, ptr, ptr }

@.str.7 = external hidden unnamed_addr constant [7 x i8], align 1
@.str.8 = external hidden unnamed_addr constant [1 x i8], align 1

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

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

; Function Attrs: mustprogress uwtable
declare dso_local void @_Z8extendediRKSt6vectorIS_IiSaIiEESaIS1_EERKS1_i(ptr dead_on_unwind noalias writable sret(%"class.std::vector") align 8, i32 noundef, ptr noundef nonnull align 8 dereferenceable(24), ptr noundef nonnull align 8 dereferenceable(24), i32 noundef) local_unnamed_addr #1

; Function Attrs: mustprogress nounwind uwtable
declare dso_local noundef i64 @_ZNKSt6vectorIiSaIiEE4sizeEv(ptr noundef nonnull align 8 dereferenceable(24)) local_unnamed_addr #2 align 2

declare i32 @__gxx_personality_v0(...)

; Function Attrs: mustprogress nounwind uwtable
declare dso_local noundef nonnull align 4 dereferenceable(4) ptr @_ZNSt6vectorIiSaIiEEixEm(ptr noundef nonnull align 8 dereferenceable(24), i64 noundef) local_unnamed_addr #2 align 2

; Function Attrs: mustprogress nounwind uwtable
declare dso_local void @_ZNSt6vectorIiSaIiEED2Ev(ptr noundef nonnull align 8 dereferenceable(24)) unnamed_addr #2 align 2

; Function Attrs: mustprogress uwtable
declare dso_local void @_Z24find_recurrence_relationRKSt6vectorIiSaIiEEiib(ptr dead_on_unwind noalias writable sret(%"class.std::vector.1") align 8, ptr noundef nonnull align 8 dereferenceable(24), i32 noundef, i32 noundef, i1 noundef zeroext) local_unnamed_addr #1

; Function Attrs: mustprogress nounwind uwtable
declare dso_local void @_ZNSt6vectorIS_IiSaIiEESaIS1_EED2Ev(ptr noundef nonnull align 8 dereferenceable(24)) unnamed_addr #2 align 2

; Function Attrs: mustprogress uwtable
define dso_local void @_Z22show_extended_sequenceiRKSt6vectorIiSaIiEEii(i32 noundef %0, ptr noundef nonnull align 8 dereferenceable(24) %1, i32 noundef %2, i32 noundef %3) local_unnamed_addr #1 personality ptr @__gxx_personality_v0 {
  %5 = alloca %"class.std::vector.1", align 8
  %6 = alloca %"class.std::vector", align 8
  call void @llvm.lifetime.start.p0(i64 24, ptr nonnull %5) #4
  call void @_Z24find_recurrence_relationRKSt6vectorIiSaIiEEiib(ptr dead_on_unwind nonnull writable sret(%"class.std::vector.1") align 8 %5, ptr noundef nonnull align 8 dereferenceable(24) %1, i32 noundef %2, i32 noundef %3, i1 noundef zeroext true)
  call void @llvm.lifetime.start.p0(i64 24, ptr nonnull %6) #4
  invoke void @_Z8extendediRKSt6vectorIS_IiSaIiEESaIS1_EERKS1_i(ptr dead_on_unwind nonnull writable sret(%"class.std::vector") align 8 %6, i32 noundef %0, ptr noundef nonnull align 8 dereferenceable(24) %5, ptr noundef nonnull align 8 dereferenceable(24) %1, i32 noundef %3)
          to label %.preheader unwind label %11

.preheader:                                       ; preds = %4
  %7 = call noundef i64 @_ZNKSt6vectorIiSaIiEE4sizeEv(ptr noundef nonnull align 8 dereferenceable(24) %6) #4
  %8 = trunc i64 %7 to i32
  %9 = icmp sgt i32 %8, 0
  br i1 %9, label %.lr.ph, label %._crit_edge

._crit_edge:                                      ; preds = %.lr.ph, %.preheader
  %10 = call i32 @puts(ptr noundef nonnull dereferenceable(1) @.str.8)
  call void @_ZNSt6vectorIiSaIiEED2Ev(ptr noundef nonnull align 8 dereferenceable(24) %6) #4
  call void @llvm.lifetime.end.p0(i64 24, ptr nonnull %6) #4
  call void @_ZNSt6vectorIS_IiSaIiEESaIS1_EED2Ev(ptr noundef nonnull align 8 dereferenceable(24) %5) #4
  call void @llvm.lifetime.end.p0(i64 24, ptr nonnull %5) #4
  ret void

11:                                               ; preds = %4
  %12 = landingpad { ptr, i32 }
          cleanup
  call void @llvm.lifetime.end.p0(i64 24, ptr nonnull %6) #4
  call void @_ZNSt6vectorIS_IiSaIiEESaIS1_EED2Ev(ptr noundef nonnull align 8 dereferenceable(24) %5) #4
  call void @llvm.lifetime.end.p0(i64 24, ptr nonnull %5) #4
  resume { ptr, i32 } %12

.lr.ph:                                           ; preds = %.preheader, %.lr.ph
  %indvars.iv = phi i64 [ %indvars.iv.next, %.lr.ph ], [ 0, %.preheader ]
  %13 = call noundef nonnull align 4 dereferenceable(4) ptr @_ZNSt6vectorIiSaIiEEixEm(ptr noundef nonnull align 8 dereferenceable(24) %6, i64 noundef %indvars.iv) #4
  %14 = load i32, ptr %13, align 4, !tbaa !5
  %15 = trunc nuw nsw i64 %indvars.iv to i32
  %16 = call i32 (ptr, ...) @printf(ptr noundef nonnull dereferenceable(1) @.str.7, i32 noundef %15, i32 noundef %14)
  %indvars.iv.next = add nuw nsw i64 %indvars.iv, 1
  %17 = call noundef i64 @_ZNKSt6vectorIiSaIiEE4sizeEv(ptr noundef nonnull align 8 dereferenceable(24) %6) #4
  %sext = shl i64 %17, 32
  %18 = ashr exact i64 %sext, 32
  %19 = icmp slt i64 %indvars.iv.next, %18
  br i1 %19, label %.lr.ph, label %._crit_edge, !llvm.loop !9
}

; Function Attrs: nofree nounwind
declare noundef i32 @printf(ptr nocapture noundef readonly, ...) local_unnamed_addr #3

; Function Attrs: nofree nounwind
declare noundef i32 @puts(ptr nocapture noundef readonly) local_unnamed_addr #3

attributes #0 = { mustprogress nocallback nofree nosync nounwind willreturn memory(argmem: readwrite) }
attributes #1 = { mustprogress 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 #2 = { 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 #3 = { nofree 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 = !{!"int", !7, i64 0}
!7 = !{!"omnipotent char", !8, i64 0}
!8 = !{!"Simple C++ TBAA"}
!9 = distinct !{!9, !10}
!10 = !{!"llvm.loop.mustprogress"}


; Effective O3 passes: EarlyCSEPass,GlobalOptPass,IndVarSimplifyPass,InferFunctionAttrsPass,InstCombinePass,JumpThreadingPass,LoopRotatePass,LoopSimplifyPass,LoopUnrollPass,SROAPass,SimplifyCFGPass