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

; 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 [53 x i8], align 1
@.str.1 = external hidden unnamed_addr constant [17 x i8], align 1

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

; Function Attrs: nocallback nofree nosync nounwind speculatable willreturn memory(none)
declare double @llvm.fmuladd.f64(double, double, double) #1

; Function Attrs: nounwind uwtable
define dso_local void @Euler_Method() #0 {
  %1 = alloca double, align 8
  %2 = alloca double, align 8
  %3 = alloca double, align 8
  %4 = alloca i32, align 4
  call void @llvm.lifetime.start.p0(i64 8, ptr %1) #4
  store double 0.000000e+00, ptr %1, align 8, !tbaa !5
  call void @llvm.lifetime.start.p0(i64 8, ptr %2) #4
  store double 1.000000e+00, ptr %2, align 8, !tbaa !5
  call void @llvm.lifetime.start.p0(i64 8, ptr %3) #4
  store double 5.000000e-02, ptr %3, align 8, !tbaa !5
  call void @llvm.lifetime.start.p0(i64 4, ptr %4) #4
  %5 = call i32 (ptr, ...) @printf(ptr noundef @.str)
  store i32 0, ptr %4, align 4, !tbaa !9
  br label %6

6:                                                ; preds = %22, %0
  %7 = load i32, ptr %4, align 4, !tbaa !9
  %8 = icmp slt i32 %7, 5
  br i1 %8, label %9, label %25

9:                                                ; preds = %6
  %10 = load double, ptr %1, align 8, !tbaa !5
  %11 = load double, ptr %2, align 8, !tbaa !5
  %12 = call i32 (ptr, ...) @printf(ptr noundef @.str.1, double noundef %10, double noundef %11)
  %13 = load double, ptr %2, align 8, !tbaa !5
  %14 = load double, ptr %3, align 8, !tbaa !5
  %15 = load double, ptr %1, align 8, !tbaa !5
  %16 = load double, ptr %2, align 8, !tbaa !5
  %17 = call double @f(double noundef %15, double noundef %16)
  %18 = call double @llvm.fmuladd.f64(double %14, double %17, double %13)
  store double %18, ptr %2, align 8, !tbaa !5
  %19 = load double, ptr %1, align 8, !tbaa !5
  %20 = load double, ptr %3, align 8, !tbaa !5
  %21 = fadd double %19, %20
  store double %21, ptr %1, align 8, !tbaa !5
  br label %22

22:                                               ; preds = %9
  %23 = load i32, ptr %4, align 4, !tbaa !9
  %24 = add nsw i32 %23, 1
  store i32 %24, ptr %4, align 4, !tbaa !9
  br label %6, !llvm.loop !11

25:                                               ; preds = %6
  call void @llvm.lifetime.end.p0(i64 4, ptr %4) #4
  call void @llvm.lifetime.end.p0(i64 8, ptr %3) #4
  call void @llvm.lifetime.end.p0(i64 8, ptr %2) #4
  call void @llvm.lifetime.end.p0(i64 8, ptr %1) #4
  ret void
}

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

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

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

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 speculatable willreturn memory(none) }
attributes #2 = { nocallback nofree nosync nounwind willreturn memory(argmem: readwrite) }
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 = !{!"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 [53 x i8], align 1
@.str.1 = external hidden unnamed_addr constant [17 x i8], align 1

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

; Function Attrs: mustprogress nocallback nofree nosync nounwind speculatable willreturn memory(none)
declare double @llvm.fmuladd.f64(double, double, double) #1

; Function Attrs: nounwind uwtable
define dso_local void @Euler_Method() local_unnamed_addr #0 {
  %1 = tail call i32 (ptr, ...) @printf(ptr noundef nonnull dereferenceable(1) @.str)
  %2 = tail call i32 (ptr, ...) @printf(ptr noundef nonnull dereferenceable(1) @.str.1, double noundef 0.000000e+00, double noundef 1.000000e+00)
  %3 = tail call double @f(double noundef 0.000000e+00, double noundef 1.000000e+00)
  %4 = tail call double @llvm.fmuladd.f64(double %3, double 5.000000e-02, double 1.000000e+00)
  %5 = tail call i32 (ptr, ...) @printf(ptr noundef nonnull dereferenceable(1) @.str.1, double noundef 5.000000e-02, double noundef %4)
  %6 = tail call double @f(double noundef 5.000000e-02, double noundef %4)
  %7 = tail call double @llvm.fmuladd.f64(double %6, double 5.000000e-02, double %4)
  %8 = tail call i32 (ptr, ...) @printf(ptr noundef nonnull dereferenceable(1) @.str.1, double noundef 1.000000e-01, double noundef %7)
  %9 = tail call double @f(double noundef 1.000000e-01, double noundef %7)
  %10 = tail call double @llvm.fmuladd.f64(double %9, double 5.000000e-02, double %7)
  %11 = tail call i32 (ptr, ...) @printf(ptr noundef nonnull dereferenceable(1) @.str.1, double noundef 0x3FC3333333333334, double noundef %10)
  %12 = tail call double @f(double noundef 0x3FC3333333333334, double noundef %10)
  %13 = tail call double @llvm.fmuladd.f64(double %12, double 5.000000e-02, double %10)
  %14 = tail call i32 (ptr, ...) @printf(ptr noundef nonnull dereferenceable(1) @.str.1, double noundef 2.000000e-01, double noundef %13)
  %15 = tail call double @f(double noundef 2.000000e-01, double noundef %13)
  ret void
}

; Function Attrs: nofree nounwind
declare noundef i32 @printf(ptr nocapture noundef readonly, ...) local_unnamed_addr #2

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 = { mustprogress nocallback nofree nosync nounwind speculatable willreturn memory(none) }
attributes #2 = { 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)"}


; Effective O3 passes: GVNPass,GlobalOptPass,IndVarSimplifyPass,InferFunctionAttrsPass,InstCombinePass,LoopRotatePass,SROAPass,SimplifyCFGPass,TailCallElimPass