; LLVM IR from TheAlgorithms/C-Plus-Plus :: numerical_methods (gram_schmidt)

; 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::basic_ostream" = type { ptr, %"class.std::basic_ios" }
%"class.std::basic_ios" = type { %"class.std::ios_base", ptr, i8, i8, ptr, ptr, ptr, ptr }
%"class.std::ios_base" = type { ptr, i64, i64, i32, i32, i32, ptr, %"struct.std::ios_base::_Words", [8 x %"struct.std::ios_base::_Words"], i32, ptr, %"class.std::locale" }
%"struct.std::ios_base::_Words" = type { ptr, i64 }
%"class.std::locale" = type { ptr }

@_ZSt4cout = external global %"class.std::basic_ostream", align 8
@.str = external hidden unnamed_addr constant [8 x i8], align 1
@.str.1 = external hidden unnamed_addr constant [3 x i8], align 1
@.str.2 = external hidden unnamed_addr constant [2 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: mustprogress nounwind uwtable
declare dso_local noundef nonnull align 8 dereferenceable(8) ptr @_ZNKSt5arrayIdLm10EEixEm(ptr noundef nonnull align 8 dereferenceable(80), i64 noundef) #1 align 2

; 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
define dso_local void @_ZN17numerical_methods12gram_schmidt7displayERKiS2_RKSt5arrayIS3_IdLm10EELm20EE(ptr noundef nonnull align 4 dereferenceable(4) %0, ptr noundef nonnull align 4 dereferenceable(4) %1, ptr noundef nonnull align 8 dereferenceable(1600) %2) #2 {
  %4 = alloca ptr, align 8
  %5 = alloca ptr, align 8
  %6 = alloca ptr, align 8
  %7 = alloca i32, align 4
  %8 = alloca i32, align 4
  %9 = alloca i32, align 4
  store ptr %0, ptr %4, align 8, !tbaa !5
  store ptr %1, ptr %5, align 8, !tbaa !5
  store ptr %2, ptr %6, align 8, !tbaa !5
  call void @llvm.lifetime.start.p0(i64 4, ptr %7) #5
  store i32 0, ptr %7, align 4, !tbaa !9
  br label %10

10:                                               ; preds = %44, %3
  %11 = load i32, ptr %7, align 4, !tbaa !9
  %12 = load ptr, ptr %4, align 8, !tbaa !5
  %13 = load i32, ptr %12, align 4, !tbaa !9
  %14 = icmp slt i32 %11, %13
  br i1 %14, label %16, label %15

15:                                               ; preds = %10
  store i32 2, ptr %8, align 4
  call void @llvm.lifetime.end.p0(i64 4, ptr %7) #5
  br label %47

16:                                               ; preds = %10
  %17 = call noundef nonnull align 8 dereferenceable(8) ptr @_ZStlsISt11char_traitsIcEERSt13basic_ostreamIcT_ES5_PKc(ptr noundef nonnull align 8 dereferenceable(8) @_ZSt4cout, ptr noundef @.str)
  %18 = load i32, ptr %7, align 4, !tbaa !9
  %19 = add nsw i32 %18, 1
  %20 = call noundef nonnull align 8 dereferenceable(8) ptr @_ZNSolsEi(ptr noundef nonnull align 8 dereferenceable(8) %17, i32 noundef %19)
  %21 = call noundef nonnull align 8 dereferenceable(8) ptr @_ZStlsISt11char_traitsIcEERSt13basic_ostreamIcT_ES5_PKc(ptr noundef nonnull align 8 dereferenceable(8) %20, ptr noundef @.str.1)
  call void @llvm.lifetime.start.p0(i64 4, ptr %9) #5
  store i32 0, ptr %9, align 4, !tbaa !9
  br label %22

22:                                               ; preds = %39, %16
  %23 = load i32, ptr %9, align 4, !tbaa !9
  %24 = load ptr, ptr %5, align 8, !tbaa !5
  %25 = load i32, ptr %24, align 4, !tbaa !9
  %26 = icmp slt i32 %23, %25
  br i1 %26, label %28, label %27

27:                                               ; preds = %22
  store i32 5, ptr %8, align 4
  call void @llvm.lifetime.end.p0(i64 4, ptr %9) #5
  br label %42

28:                                               ; preds = %22
  %29 = load ptr, ptr %6, align 8, !tbaa !5
  %30 = load i32, ptr %7, align 4, !tbaa !9
  %31 = sext i32 %30 to i64
  %32 = call noundef nonnull align 8 dereferenceable(80) ptr @_ZNKSt5arrayIS_IdLm10EELm20EEixEm(ptr noundef nonnull align 8 dereferenceable(1600) %29, i64 noundef %31) #5
  %33 = load i32, ptr %9, align 4, !tbaa !9
  %34 = sext i32 %33 to i64
  %35 = call noundef nonnull align 8 dereferenceable(8) ptr @_ZNKSt5arrayIdLm10EEixEm(ptr noundef nonnull align 8 dereferenceable(80) %32, i64 noundef %34) #5
  %36 = load double, ptr %35, align 8, !tbaa !11
  %37 = call noundef nonnull align 8 dereferenceable(8) ptr @_ZNSolsEd(ptr noundef nonnull align 8 dereferenceable(8) @_ZSt4cout, double noundef %36)
  %38 = call noundef nonnull align 8 dereferenceable(8) ptr @_ZStlsISt11char_traitsIcEERSt13basic_ostreamIcT_ES5_PKc(ptr noundef nonnull align 8 dereferenceable(8) %37, ptr noundef @.str.2)
  br label %39

39:                                               ; preds = %28
  %40 = load i32, ptr %9, align 4, !tbaa !9
  %41 = add nsw i32 %40, 1
  store i32 %41, ptr %9, align 4, !tbaa !9
  br label %22, !llvm.loop !13

42:                                               ; preds = %27
  %43 = call noundef nonnull align 8 dereferenceable(8) ptr @_ZStlsISt11char_traitsIcEERSt13basic_ostreamIcT_ES5_c(ptr noundef nonnull align 8 dereferenceable(8) @_ZSt4cout, i8 noundef signext 10)
  br label %44

44:                                               ; preds = %42
  %45 = load i32, ptr %7, align 4, !tbaa !9
  %46 = add nsw i32 %45, 1
  store i32 %46, ptr %7, align 4, !tbaa !9
  br label %10, !llvm.loop !15

47:                                               ; preds = %15
  ret void
}

; Function Attrs: inlinehint mustprogress uwtable
declare noundef nonnull align 8 dereferenceable(8) ptr @_ZStlsISt11char_traitsIcEERSt13basic_ostreamIcT_ES5_PKc(ptr noundef nonnull align 8 dereferenceable(8), ptr noundef) #3

declare noundef nonnull align 8 dereferenceable(8) ptr @_ZNSolsEi(ptr noundef nonnull align 8 dereferenceable(8), i32 noundef) #4

; Function Attrs: mustprogress uwtable
declare noundef nonnull align 8 dereferenceable(8) ptr @_ZNSolsEd(ptr noundef nonnull align 8 dereferenceable(8), double noundef) #2 align 2

; Function Attrs: mustprogress nounwind uwtable
declare dso_local noundef nonnull align 8 dereferenceable(80) ptr @_ZNKSt5arrayIS_IdLm10EELm20EEixEm(ptr noundef nonnull align 8 dereferenceable(1600), i64 noundef) #1 align 2

; Function Attrs: inlinehint mustprogress uwtable
declare noundef nonnull align 8 dereferenceable(8) ptr @_ZStlsISt11char_traitsIcEERSt13basic_ostreamIcT_ES5_c(ptr noundef nonnull align 8 dereferenceable(8), i8 noundef signext) #3

attributes #0 = { nocallback nofree nosync nounwind willreturn memory(argmem: readwrite) }
attributes #1 = { 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 #2 = { 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 #3 = { inlinehint 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 #4 = { "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 #5 = { 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++ 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"}
!15 = distinct !{!15, !14}


; 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::basic_ostream" = type { ptr, %"class.std::basic_ios" }
%"class.std::basic_ios" = type { %"class.std::ios_base", ptr, i8, i8, ptr, ptr, ptr, ptr }
%"class.std::ios_base" = type { ptr, i64, i64, i32, i32, i32, ptr, %"struct.std::ios_base::_Words", [8 x %"struct.std::ios_base::_Words"], i32, ptr, %"class.std::locale" }
%"struct.std::ios_base::_Words" = type { ptr, i64 }
%"class.std::locale" = type { ptr }

@_ZSt4cout = external global %"class.std::basic_ostream", align 8
@.str = external hidden unnamed_addr constant [8 x i8], align 1
@.str.1 = external hidden unnamed_addr constant [3 x i8], align 1
@.str.2 = external hidden unnamed_addr constant [2 x i8], align 1

; Function Attrs: mustprogress nounwind uwtable
declare dso_local noundef nonnull align 8 dereferenceable(8) ptr @_ZNKSt5arrayIdLm10EEixEm(ptr noundef nonnull align 8 dereferenceable(80), i64 noundef) local_unnamed_addr #0 align 2

; Function Attrs: mustprogress uwtable
define dso_local void @_ZN17numerical_methods12gram_schmidt7displayERKiS2_RKSt5arrayIS3_IdLm10EELm20EE(ptr nocapture noundef nonnull readonly align 4 dereferenceable(4) %0, ptr nocapture noundef nonnull readonly align 4 dereferenceable(4) %1, ptr noundef nonnull align 8 dereferenceable(1600) %2) local_unnamed_addr #1 {
  %4 = load i32, ptr %0, align 4, !tbaa !5
  %5 = icmp sgt i32 %4, 0
  br i1 %5, label %.lr.ph13, label %._crit_edge14

._crit_edge14:                                    ; preds = %._crit_edge, %3
  ret void

.lr.ph13:                                         ; preds = %3, %._crit_edge
  %indvars.iv16 = phi i64 [ %indvars.iv.next17, %._crit_edge ], [ 0, %3 ]
  %6 = tail call noundef nonnull align 8 dereferenceable(8) ptr @_ZStlsISt11char_traitsIcEERSt13basic_ostreamIcT_ES5_PKc(ptr noundef nonnull align 8 dereferenceable(8) @_ZSt4cout, ptr noundef nonnull @.str)
  %indvars.iv.next17 = add nuw nsw i64 %indvars.iv16, 1
  %7 = trunc nuw nsw i64 %indvars.iv.next17 to i32
  %8 = tail call noundef nonnull align 8 dereferenceable(8) ptr @_ZNSolsEi(ptr noundef nonnull align 8 dereferenceable(8) %6, i32 noundef %7)
  %9 = tail call noundef nonnull align 8 dereferenceable(8) ptr @_ZStlsISt11char_traitsIcEERSt13basic_ostreamIcT_ES5_PKc(ptr noundef nonnull align 8 dereferenceable(8) %8, ptr noundef nonnull @.str.1)
  %10 = load i32, ptr %1, align 4, !tbaa !5
  %11 = icmp sgt i32 %10, 0
  br i1 %11, label %.lr.ph, label %._crit_edge

._crit_edge:                                      ; preds = %.lr.ph, %.lr.ph13
  %12 = tail call noundef nonnull align 8 dereferenceable(8) ptr @_ZStlsISt11char_traitsIcEERSt13basic_ostreamIcT_ES5_c(ptr noundef nonnull align 8 dereferenceable(8) @_ZSt4cout, i8 noundef signext 10)
  %13 = load i32, ptr %0, align 4, !tbaa !5
  %14 = sext i32 %13 to i64
  %15 = icmp slt i64 %indvars.iv.next17, %14
  br i1 %15, label %.lr.ph13, label %._crit_edge14, !llvm.loop !9

.lr.ph:                                           ; preds = %.lr.ph13, %.lr.ph
  %indvars.iv = phi i64 [ %indvars.iv.next, %.lr.ph ], [ 0, %.lr.ph13 ]
  %16 = tail call noundef nonnull align 8 dereferenceable(80) ptr @_ZNKSt5arrayIS_IdLm10EELm20EEixEm(ptr noundef nonnull align 8 dereferenceable(1600) %2, i64 noundef %indvars.iv16) #4
  %17 = tail call noundef nonnull align 8 dereferenceable(8) ptr @_ZNKSt5arrayIdLm10EEixEm(ptr noundef nonnull align 8 dereferenceable(80) %16, i64 noundef %indvars.iv) #4
  %18 = load double, ptr %17, align 8, !tbaa !11
  %19 = tail call noundef nonnull align 8 dereferenceable(8) ptr @_ZNSolsEd(ptr noundef nonnull align 8 dereferenceable(8) @_ZSt4cout, double noundef %18)
  %20 = tail call noundef nonnull align 8 dereferenceable(8) ptr @_ZStlsISt11char_traitsIcEERSt13basic_ostreamIcT_ES5_PKc(ptr noundef nonnull align 8 dereferenceable(8) %19, ptr noundef nonnull @.str.2)
  %indvars.iv.next = add nuw nsw i64 %indvars.iv, 1
  %21 = load i32, ptr %1, align 4, !tbaa !5
  %22 = sext i32 %21 to i64
  %23 = icmp slt i64 %indvars.iv.next, %22
  br i1 %23, label %.lr.ph, label %._crit_edge, !llvm.loop !13
}

; Function Attrs: inlinehint mustprogress uwtable
declare noundef nonnull align 8 dereferenceable(8) ptr @_ZStlsISt11char_traitsIcEERSt13basic_ostreamIcT_ES5_PKc(ptr noundef nonnull align 8 dereferenceable(8), ptr noundef) local_unnamed_addr #2

declare noundef nonnull align 8 dereferenceable(8) ptr @_ZNSolsEi(ptr noundef nonnull align 8 dereferenceable(8), i32 noundef) local_unnamed_addr #3

; Function Attrs: mustprogress uwtable
declare noundef nonnull align 8 dereferenceable(8) ptr @_ZNSolsEd(ptr noundef nonnull align 8 dereferenceable(8), double noundef) local_unnamed_addr #1 align 2

; Function Attrs: mustprogress nounwind uwtable
declare dso_local noundef nonnull align 8 dereferenceable(80) ptr @_ZNKSt5arrayIS_IdLm10EELm20EEixEm(ptr noundef nonnull align 8 dereferenceable(1600), i64 noundef) local_unnamed_addr #0 align 2

; Function Attrs: inlinehint mustprogress uwtable
declare noundef nonnull align 8 dereferenceable(8) ptr @_ZStlsISt11char_traitsIcEERSt13basic_ostreamIcT_ES5_c(ptr noundef nonnull align 8 dereferenceable(8), i8 noundef signext) local_unnamed_addr #2

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 = { 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 = { inlinehint 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 #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 = distinct !{!9, !10}
!10 = !{!"llvm.loop.mustprogress"}
!11 = !{!12, !12, i64 0}
!12 = !{!"double", !7, i64 0}
!13 = distinct !{!13, !10}


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