; LLVM IR from Dutta-SD/Numerical_Methods :: Calculus (Integral_numerical)

; 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"

@.str = external hidden unnamed_addr constant [23 x i8], align 1

; Function Attrs: nounwind uwtable
declare dso_local double @f(double noundef) #0

; Function Attrs: nounwind uwtable
define dso_local void @Trapezoidal_Integral(double noundef %0, double noundef %1, i32 noundef %2) #0 {
  %4 = alloca double, align 8
  %5 = alloca double, align 8
  %6 = alloca i32, align 4
  %7 = alloca double, align 8
  %8 = alloca double, align 8
  %9 = alloca i32, align 4
  %10 = alloca double, align 8
  store double %0, ptr %4, align 8, !tbaa !5
  store double %1, ptr %5, align 8, !tbaa !5
  store i32 %2, ptr %6, align 4, !tbaa !9
  call void @llvm.lifetime.start.p0(i64 8, ptr %7) #3
  call void @llvm.lifetime.start.p0(i64 8, ptr %8) #3
  call void @llvm.lifetime.start.p0(i64 4, ptr %9) #3
  call void @llvm.lifetime.start.p0(i64 8, ptr %10) #3
  %11 = load double, ptr %5, align 8, !tbaa !5
  %12 = load double, ptr %4, align 8, !tbaa !5
  %13 = fsub double %11, %12
  %14 = load i32, ptr %6, align 4, !tbaa !9
  %15 = sitofp i32 %14 to double
  %16 = fdiv double %13, %15
  store double %16, ptr %10, align 8, !tbaa !5
  %17 = load double, ptr %5, align 8, !tbaa !5
  %18 = call double @f(double noundef %17)
  %19 = load double, ptr %4, align 8, !tbaa !5
  %20 = call double @f(double noundef %19)
  %21 = fadd double %18, %20
  %22 = fdiv double %21, 2.000000e+00
  store double %22, ptr %8, align 8, !tbaa !5
  store i32 1, ptr %9, align 4, !tbaa !9
  br label %23

23:                                               ; preds = %35, %3
  %24 = load i32, ptr %9, align 4, !tbaa !9
  %25 = load i32, ptr %6, align 4, !tbaa !9
  %26 = icmp slt i32 %24, %25
  br i1 %26, label %27, label %38

27:                                               ; preds = %23
  %28 = load double, ptr %4, align 8, !tbaa !5
  %29 = load double, ptr %10, align 8, !tbaa !5
  %30 = fadd double %28, %29
  store double %30, ptr %4, align 8, !tbaa !5
  %31 = load double, ptr %8, align 8, !tbaa !5
  %32 = load double, ptr %4, align 8, !tbaa !5
  %33 = call double @f(double noundef %32)
  %34 = fadd double %31, %33
  store double %34, ptr %8, align 8, !tbaa !5
  br label %35

35:                                               ; preds = %27
  %36 = load i32, ptr %9, align 4, !tbaa !9
  %37 = add nsw i32 %36, 1
  store i32 %37, ptr %9, align 4, !tbaa !9
  br label %23, !llvm.loop !11

38:                                               ; preds = %23
  %39 = load double, ptr %10, align 8, !tbaa !5
  %40 = load double, ptr %8, align 8, !tbaa !5
  %41 = fmul double %39, %40
  store double %41, ptr %7, align 8, !tbaa !5
  %42 = load double, ptr %7, align 8, !tbaa !5
  %43 = call i32 (ptr, ...) @printf(ptr noundef @.str, double noundef %42)
  call void @llvm.lifetime.end.p0(i64 8, ptr %10) #3
  call void @llvm.lifetime.end.p0(i64 4, ptr %9) #3
  call void @llvm.lifetime.end.p0(i64 8, ptr %8) #3
  call void @llvm.lifetime.end.p0(i64 8, ptr %7) #3
  ret void
}

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

declare i32 @printf(ptr noundef, ...) #2

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

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 = { "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 = !{!10, !10, i64 0}
!10 = !{!"int", !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"

@.str = external hidden unnamed_addr constant [23 x i8], align 1

; Function Attrs: nounwind uwtable
declare dso_local double @f(double noundef) local_unnamed_addr #0

; Function Attrs: nounwind uwtable
define dso_local void @Trapezoidal_Integral(double noundef %0, double noundef %1, i32 noundef %2) local_unnamed_addr #0 {
  %4 = fsub double %1, %0
  %5 = sitofp i32 %2 to double
  %6 = fdiv double %4, %5
  %7 = tail call double @f(double noundef %1)
  %8 = tail call double @f(double noundef %0)
  %9 = fadd double %7, %8
  %10 = fmul double %9, 5.000000e-01
  %11 = icmp sgt i32 %2, 1
  br i1 %11, label %.lr.ph, label %._crit_edge

.lr.ph:                                           ; preds = %3, %.lr.ph
  %.018 = phi double [ %12, %.lr.ph ], [ %0, %3 ]
  %.01417 = phi i32 [ %15, %.lr.ph ], [ 1, %3 ]
  %.01516 = phi double [ %14, %.lr.ph ], [ %10, %3 ]
  %12 = fadd double %6, %.018
  %13 = tail call double @f(double noundef %12)
  %14 = fadd double %.01516, %13
  %15 = add nuw nsw i32 %.01417, 1
  %exitcond.not = icmp eq i32 %15, %2
  br i1 %exitcond.not, label %._crit_edge, label %.lr.ph, !llvm.loop !5

._crit_edge:                                      ; preds = %.lr.ph, %3
  %.015.lcssa = phi double [ %10, %3 ], [ %14, %.lr.ph ]
  %16 = fmul double %6, %.015.lcssa
  %17 = tail call i32 (ptr, ...) @printf(ptr noundef nonnull dereferenceable(1) @.str, double noundef %16)
  ret void
}

; Function Attrs: nofree nounwind
declare noundef i32 @printf(ptr nocapture noundef readonly, ...) local_unnamed_addr #1

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 = { 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" }

!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 = distinct !{!5, !6}
!6 = !{!"llvm.loop.mustprogress"}


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