; LLVM IR from ShahjalalShohag/code-library :: Number Theory/Lucas Theorem.ll (Z5lucasxx)

; 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"

%struct.combi = type { i32, %"class.std::vector", %"class.std::vector", %"class.std::vector" }
%"class.std::vector" = type { %"struct.std::_Vector_base" }
%"struct.std::_Vector_base" = type { %"struct.std::_Vector_base<modint<1000003>, std::allocator<modint<1000003>>>::_Vector_impl" }
%"struct.std::_Vector_base<modint<1000003>, std::allocator<modint<1000003>>>::_Vector_impl" = type { %"struct.std::_Vector_base<modint<1000003>, std::allocator<modint<1000003>>>::_Vector_impl_data" }
%"struct.std::_Vector_base<modint<1000003>, std::allocator<modint<1000003>>>::_Vector_impl_data" = type { ptr, ptr, ptr }
%struct.modint = type { i32 }

@C = external dso_local global %struct.combi, align 8

; Function Attrs: mustprogress uwtable
define dso_local i32 @_Z5lucasxx(i64 noundef %0, i64 noundef %1) #0 {
  %3 = alloca %struct.modint, align 4
  %4 = alloca i64, align 8
  %5 = alloca i64, align 8
  %6 = alloca %struct.modint, align 4
  %7 = alloca %struct.modint, align 4
  store i64 %0, ptr %4, align 8, !tbaa !5
  store i64 %1, ptr %5, align 8, !tbaa !5
  %8 = load i64, ptr %5, align 8, !tbaa !5
  %9 = load i64, ptr %4, align 8, !tbaa !5
  %10 = icmp sgt i64 %8, %9
  br i1 %10, label %11, label %12

11:                                               ; preds = %2
  call void @_ZN6modintILi1000003EEC2Ei(ptr noundef nonnull align 4 dereferenceable(4) %3, i32 noundef 0)
  br label %39

12:                                               ; preds = %2
  %13 = load i64, ptr %4, align 8, !tbaa !5
  %14 = icmp slt i64 %13, 1000003
  br i1 %14, label %15, label %22

15:                                               ; preds = %12
  %16 = load i64, ptr %4, align 8, !tbaa !5
  %17 = trunc i64 %16 to i32
  %18 = load i64, ptr %5, align 8, !tbaa !5
  %19 = trunc i64 %18 to i32
  %20 = call i32 @_ZN5combi3ncrEii(ptr noundef nonnull align 8 dereferenceable(80) @C, i32 noundef %17, i32 noundef %19)
  %21 = getelementptr inbounds %struct.modint, ptr %3, i32 0, i32 0
  store i32 %20, ptr %21, align 4
  br label %39

22:                                               ; preds = %12
  call void @llvm.lifetime.start.p0(i64 4, ptr %6) #4
  %23 = load i64, ptr %4, align 8, !tbaa !5
  %24 = sdiv i64 %23, 1000003
  %25 = load i64, ptr %5, align 8, !tbaa !5
  %26 = sdiv i64 %25, 1000003
  %27 = call i32 @_Z5lucasxx(i64 noundef %24, i64 noundef %26)
  %28 = getelementptr inbounds %struct.modint, ptr %6, i32 0, i32 0
  store i32 %27, ptr %28, align 4
  %29 = load i64, ptr %4, align 8, !tbaa !5
  %30 = srem i64 %29, 1000003
  %31 = load i64, ptr %5, align 8, !tbaa !5
  %32 = srem i64 %31, 1000003
  %33 = call i32 @_Z5lucasxx(i64 noundef %30, i64 noundef %32)
  %34 = getelementptr inbounds %struct.modint, ptr %7, i32 0, i32 0
  store i32 %33, ptr %34, align 4
  %35 = getelementptr inbounds %struct.modint, ptr %7, i32 0, i32 0
  %36 = load i32, ptr %35, align 4
  %37 = call i32 @_ZNK6modintILi1000003EEmlES0_(ptr noundef nonnull align 4 dereferenceable(4) %6, i32 %36)
  %38 = getelementptr inbounds %struct.modint, ptr %3, i32 0, i32 0
  store i32 %37, ptr %38, align 4
  call void @llvm.lifetime.end.p0(i64 4, ptr %6) #4
  br label %39

39:                                               ; preds = %22, %15, %11
  %40 = getelementptr inbounds %struct.modint, ptr %3, i32 0, i32 0
  %41 = load i32, ptr %40, align 4
  ret i32 %41
}

; Function Attrs: mustprogress nounwind uwtable
declare dso_local void @_ZN6modintILi1000003EEC2Ei(ptr noundef nonnull align 4 dereferenceable(4), i32 noundef) unnamed_addr #1 align 2

; Function Attrs: inlinehint mustprogress uwtable
declare dso_local i32 @_ZN5combi3ncrEii(ptr noundef nonnull align 8 dereferenceable(80), i32 noundef, i32 noundef) #2 align 2

; Function Attrs: nocallback nofree nosync nounwind willreturn memory(argmem: readwrite)
declare void @llvm.lifetime.start.p0(i64 immarg, ptr nocapture) #3

; Function Attrs: inlinehint mustprogress uwtable
declare dso_local i32 @_ZNK6modintILi1000003EEmlES0_(ptr noundef nonnull align 4 dereferenceable(4), i32) #2 align 2

; Function Attrs: nocallback nofree nosync nounwind willreturn memory(argmem: readwrite)
declare void @llvm.lifetime.end.p0(i64 immarg, ptr nocapture) #3

attributes #0 = { 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 #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 = { 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 = { nocallback nofree nosync nounwind willreturn memory(argmem: readwrite) }
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 = !{!"long long", !7, i64 0}
!7 = !{!"omnipotent char", !8, i64 0}
!8 = !{!"Simple C++ TBAA"}


; 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"

%struct.combi = type { i32, %"class.std::vector", %"class.std::vector", %"class.std::vector" }
%"class.std::vector" = type { %"struct.std::_Vector_base" }
%"struct.std::_Vector_base" = type { %"struct.std::_Vector_base<modint<1000003>, std::allocator<modint<1000003>>>::_Vector_impl" }
%"struct.std::_Vector_base<modint<1000003>, std::allocator<modint<1000003>>>::_Vector_impl" = type { %"struct.std::_Vector_base<modint<1000003>, std::allocator<modint<1000003>>>::_Vector_impl_data" }
%"struct.std::_Vector_base<modint<1000003>, std::allocator<modint<1000003>>>::_Vector_impl_data" = type { ptr, ptr, ptr }
%struct.modint = type { i32 }

@C = external dso_local global %struct.combi, align 8

; Function Attrs: mustprogress uwtable
define dso_local i32 @_Z5lucasxx(i64 noundef %0, i64 noundef %1) local_unnamed_addr #0 {
  %3 = alloca %struct.modint, align 4
  %4 = alloca %struct.modint, align 4
  %5 = icmp sgt i64 %1, %0
  br i1 %5, label %6, label %7

6:                                                ; preds = %2
  call void @_ZN6modintILi1000003EEC2Ei(ptr noundef nonnull align 4 dereferenceable(4) %3, i32 noundef 0)
  %.pre = load i32, ptr %3, align 4
  br label %common.ret

7:                                                ; preds = %2
  %8 = icmp slt i64 %0, 1000003
  br i1 %8, label %9, label %13

9:                                                ; preds = %7
  %10 = trunc i64 %0 to i32
  %11 = trunc i64 %1 to i32
  %12 = tail call i32 @_ZN5combi3ncrEii(ptr noundef nonnull align 8 dereferenceable(80) @C, i32 noundef %10, i32 noundef %11)
  br label %common.ret

common.ret:                                       ; preds = %6, %9, %13
  %common.ret.op = phi i32 [ %20, %13 ], [ %12, %9 ], [ %.pre, %6 ]
  ret i32 %common.ret.op

13:                                               ; preds = %7
  call void @llvm.lifetime.start.p0(i64 4, ptr nonnull %4) #4
  %14 = udiv i64 %0, 1000003
  %15 = sdiv i64 %1, 1000003
  %16 = tail call i32 @_Z5lucasxx(i64 noundef %14, i64 noundef %15)
  store i32 %16, ptr %4, align 4
  %17 = urem i64 %0, 1000003
  %18 = srem i64 %1, 1000003
  %19 = tail call i32 @_Z5lucasxx(i64 noundef %17, i64 noundef %18)
  %20 = call i32 @_ZNK6modintILi1000003EEmlES0_(ptr noundef nonnull align 4 dereferenceable(4) %4, i32 %19)
  call void @llvm.lifetime.end.p0(i64 4, ptr nonnull %4) #4
  br label %common.ret
}

; Function Attrs: mustprogress nounwind uwtable
declare dso_local void @_ZN6modintILi1000003EEC2Ei(ptr noundef nonnull align 4 dereferenceable(4), i32 noundef) unnamed_addr #1 align 2

; Function Attrs: inlinehint mustprogress uwtable
declare dso_local i32 @_ZN5combi3ncrEii(ptr noundef nonnull align 8 dereferenceable(80), i32 noundef, i32 noundef) local_unnamed_addr #2 align 2

; Function Attrs: mustprogress nocallback nofree nosync nounwind willreturn memory(argmem: readwrite)
declare void @llvm.lifetime.start.p0(i64 immarg, ptr nocapture) #3

; Function Attrs: inlinehint mustprogress uwtable
declare dso_local i32 @_ZNK6modintILi1000003EEmlES0_(ptr noundef nonnull align 4 dereferenceable(4), i32) local_unnamed_addr #2 align 2

; Function Attrs: mustprogress nocallback nofree nosync nounwind willreturn memory(argmem: readwrite)
declare void @llvm.lifetime.end.p0(i64 immarg, ptr nocapture) #3

attributes #0 = { 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 #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 = { 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 = { mustprogress nocallback nofree nosync nounwind willreturn memory(argmem: readwrite) }
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)"}


; Effective O3 passes: DSEPass,EarlyCSEPass,GVNPass,GlobalOptPass,IPSCCPPass,InferFunctionAttrsPass,InstCombinePass,SROAPass,SimplifyCFGPass,TailCallElimPass