; 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"

; Function Attrs: mustprogress nounwind uwtable
define dso_local noundef double @_ZN17numerical_methods12gram_schmidt11dot_productERKSt5arrayIdLm10EES4_RKi(ptr noundef nonnull align 8 dereferenceable(80) %0, ptr noundef nonnull align 8 dereferenceable(80) %1, ptr noundef nonnull align 4 dereferenceable(4) %2) #0 {
  %4 = alloca ptr, align 8
  %5 = alloca ptr, align 8
  %6 = alloca ptr, align 8
  %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 ptr %2, ptr %6, align 8, !tbaa !5
  call void @llvm.lifetime.start.p0(i64 8, ptr %7) #3
  store double 0.000000e+00, ptr %7, align 8, !tbaa !9
  call void @llvm.lifetime.start.p0(i64 4, ptr %8) #3
  store i32 0, ptr %8, align 4, !tbaa !11
  br label %9

9:                                                ; preds = %28, %3
  %10 = load i32, ptr %8, align 4, !tbaa !11
  %11 = load ptr, ptr %6, align 8, !tbaa !5
  %12 = load i32, ptr %11, align 4, !tbaa !11
  %13 = icmp slt i32 %10, %12
  br i1 %13, label %15, label %14

14:                                               ; preds = %9
  call void @llvm.lifetime.end.p0(i64 4, ptr %8) #3
  br label %31

15:                                               ; preds = %9
  %16 = load ptr, ptr %4, align 8, !tbaa !5
  %17 = load i32, ptr %8, align 4, !tbaa !11
  %18 = sext i32 %17 to i64
  %19 = call noundef nonnull align 8 dereferenceable(8) ptr @_ZNKSt5arrayIdLm10EEixEm(ptr noundef nonnull align 8 dereferenceable(80) %16, i64 noundef %18) #3
  %20 = load double, ptr %19, align 8, !tbaa !9
  %21 = load ptr, ptr %5, align 8, !tbaa !5
  %22 = load i32, ptr %8, align 4, !tbaa !11
  %23 = sext i32 %22 to i64
  %24 = call noundef nonnull align 8 dereferenceable(8) ptr @_ZNKSt5arrayIdLm10EEixEm(ptr noundef nonnull align 8 dereferenceable(80) %21, i64 noundef %23) #3
  %25 = load double, ptr %24, align 8, !tbaa !9
  %26 = load double, ptr %7, align 8, !tbaa !9
  %27 = call double @llvm.fmuladd.f64(double %20, double %25, double %26)
  store double %27, ptr %7, align 8, !tbaa !9
  br label %28

28:                                               ; preds = %15
  %29 = load i32, ptr %8, align 4, !tbaa !11
  %30 = add nsw i32 %29, 1
  store i32 %30, ptr %8, align 4, !tbaa !11
  br label %9, !llvm.loop !13

31:                                               ; preds = %14
  %32 = load double, ptr %7, align 8, !tbaa !9
  call void @llvm.lifetime.end.p0(i64 8, ptr %7) #3
  ret double %32
}

; Function Attrs: nocallback nofree nosync nounwind willreturn memory(argmem: readwrite)
declare void @llvm.lifetime.start.p0(i64 immarg, ptr nocapture) #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) #0 align 2

; 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

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 = { nocallback nofree nosync nounwind speculatable willreturn memory(none) }
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 = !{!"any pointer", !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 = !{!"int", !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 nounwind uwtable
define dso_local noundef double @_ZN17numerical_methods12gram_schmidt11dot_productERKSt5arrayIdLm10EES4_RKi(ptr noundef nonnull align 8 dereferenceable(80) %0, ptr noundef nonnull align 8 dereferenceable(80) %1, ptr nocapture noundef nonnull readonly align 4 dereferenceable(4) %2) local_unnamed_addr #0 {
  %4 = load i32, ptr %2, align 4, !tbaa !5
  %5 = icmp sgt i32 %4, 0
  br i1 %5, label %.lr.ph, label %._crit_edge

._crit_edge:                                      ; preds = %.lr.ph, %3
  %.08.lcssa = phi double [ 0.000000e+00, %3 ], [ %10, %.lr.ph ]
  ret double %.08.lcssa

.lr.ph:                                           ; preds = %3, %.lr.ph
  %indvars.iv = phi i64 [ %indvars.iv.next, %.lr.ph ], [ 0, %3 ]
  %.089 = phi double [ %10, %.lr.ph ], [ 0.000000e+00, %3 ]
  %6 = tail call noundef nonnull align 8 dereferenceable(8) ptr @_ZNKSt5arrayIdLm10EEixEm(ptr noundef nonnull align 8 dereferenceable(80) %0, i64 noundef %indvars.iv) #2
  %7 = load double, ptr %6, align 8, !tbaa !9
  %8 = tail call noundef nonnull align 8 dereferenceable(8) ptr @_ZNKSt5arrayIdLm10EEixEm(ptr noundef nonnull align 8 dereferenceable(80) %1, i64 noundef %indvars.iv) #2
  %9 = load double, ptr %8, align 8, !tbaa !9
  %10 = tail call double @llvm.fmuladd.f64(double %7, double %9, double %.089)
  %indvars.iv.next = add nuw nsw i64 %indvars.iv, 1
  %11 = load i32, ptr %2, align 4, !tbaa !5
  %12 = sext i32 %11 to i64
  %13 = icmp slt i64 %indvars.iv.next, %12
  br i1 %13, label %.lr.ph, label %._crit_edge, !llvm.loop !11
}

; 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 nocallback nofree nosync nounwind speculatable willreturn memory(none)
declare double @llvm.fmuladd.f64(double, double, double) #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 = { mustprogress nocallback nofree nosync nounwind speculatable willreturn memory(none) }
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 = 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