; LLVM IR from ShahjalalShohag/code-library :: Number Theory (Rational Approximation)

; 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_istream" = type { ptr, i64, %"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 }
%"class.std::basic_ostream" = type { ptr, %"class.std::basic_ios" }
%"struct.std::pair" = type { i64, i64 }

@_ZSt3cin = external global %"class.std::basic_istream", align 8
@_ZSt4cout = external global %"class.std::basic_ostream", align 8

; Function Attrs: mustprogress uwtable
declare dso_local { i64, i64 } @_Z11approximateex(x86_fp80 noundef, i64 noundef) #0

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

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

; Function Attrs: mustprogress norecurse uwtable
define dso_local noundef i32 @main() #2 {
  %1 = alloca i32, align 4
  %2 = alloca i32, align 4
  %3 = alloca x86_fp80, align 16
  %4 = alloca i64, align 8
  %5 = alloca %"struct.std::pair", align 8
  store i32 0, ptr %1, align 4
  %6 = call noundef zeroext i1 @_ZNSt8ios_base15sync_with_stdioEb(i1 noundef zeroext false)
  %7 = load ptr, ptr @_ZSt3cin, align 8, !tbaa !5
  %8 = getelementptr i8, ptr %7, i64 -24
  %9 = load i64, ptr %8, align 8
  %10 = getelementptr inbounds i8, ptr @_ZSt3cin, i64 %9
  %11 = call noundef ptr @_ZNSt9basic_iosIcSt11char_traitsIcEE3tieEPSo(ptr noundef nonnull align 8 dereferenceable(264) %10, ptr noundef null)
  call void @llvm.lifetime.start.p0(i64 4, ptr %2) #6
  %12 = call noundef nonnull align 8 dereferenceable(16) ptr @_ZNSirsERi(ptr noundef nonnull align 8 dereferenceable(16) @_ZSt3cin, ptr noundef nonnull align 4 dereferenceable(4) %2)
  br label %13

13:                                               ; preds = %17, %0
  %14 = load i32, ptr %2, align 4, !tbaa !8
  %15 = add nsw i32 %14, -1
  store i32 %15, ptr %2, align 4, !tbaa !8
  %16 = icmp ne i32 %14, 0
  br i1 %16, label %17, label %34

17:                                               ; preds = %13
  call void @llvm.lifetime.start.p0(i64 16, ptr %3) #6
  %18 = call noundef nonnull align 8 dereferenceable(16) ptr @_ZNSirsERe(ptr noundef nonnull align 8 dereferenceable(16) @_ZSt3cin, ptr noundef nonnull align 16 dereferenceable(16) %3)
  call void @llvm.lifetime.start.p0(i64 8, ptr %4) #6
  store i64 1000000000, ptr %4, align 8, !tbaa !11
  call void @llvm.lifetime.start.p0(i64 16, ptr %5) #6
  %19 = load x86_fp80, ptr %3, align 16, !tbaa !13
  %20 = load i64, ptr %4, align 8, !tbaa !11
  %21 = call { i64, i64 } @_Z11approximateex(x86_fp80 noundef %19, i64 noundef %20)
  %22 = getelementptr inbounds { i64, i64 }, ptr %5, i32 0, i32 0
  %23 = extractvalue { i64, i64 } %21, 0
  store i64 %23, ptr %22, align 8
  %24 = getelementptr inbounds { i64, i64 }, ptr %5, i32 0, i32 1
  %25 = extractvalue { i64, i64 } %21, 1
  store i64 %25, ptr %24, align 8
  %26 = getelementptr inbounds %"struct.std::pair", ptr %5, i32 0, i32 0
  %27 = load i64, ptr %26, align 8, !tbaa !15
  %28 = call noundef nonnull align 8 dereferenceable(8) ptr @_ZNSolsEx(ptr noundef nonnull align 8 dereferenceable(8) @_ZSt4cout, i64 noundef %27)
  %29 = call noundef nonnull align 8 dereferenceable(8) ptr @_ZStlsISt11char_traitsIcEERSt13basic_ostreamIcT_ES5_c(ptr noundef nonnull align 8 dereferenceable(8) %28, i8 noundef signext 32)
  %30 = getelementptr inbounds %"struct.std::pair", ptr %5, i32 0, i32 1
  %31 = load i64, ptr %30, align 8, !tbaa !17
  %32 = call noundef nonnull align 8 dereferenceable(8) ptr @_ZNSolsEx(ptr noundef nonnull align 8 dereferenceable(8) %29, i64 noundef %31)
  %33 = call noundef nonnull align 8 dereferenceable(8) ptr @_ZStlsISt11char_traitsIcEERSt13basic_ostreamIcT_ES5_c(ptr noundef nonnull align 8 dereferenceable(8) %32, i8 noundef signext 10)
  call void @llvm.lifetime.end.p0(i64 16, ptr %5) #6
  call void @llvm.lifetime.end.p0(i64 8, ptr %4) #6
  call void @llvm.lifetime.end.p0(i64 16, ptr %3) #6
  br label %13, !llvm.loop !18

34:                                               ; preds = %13
  call void @llvm.lifetime.end.p0(i64 4, ptr %2) #6
  ret i32 0
}

declare noundef zeroext i1 @_ZNSt8ios_base15sync_with_stdioEb(i1 noundef zeroext) #3

; Function Attrs: mustprogress nounwind uwtable
declare noundef ptr @_ZNSt9basic_iosIcSt11char_traitsIcEE3tieEPSo(ptr noundef nonnull align 8 dereferenceable(264), ptr noundef) #4 align 2

declare noundef nonnull align 8 dereferenceable(16) ptr @_ZNSirsERi(ptr noundef nonnull align 8 dereferenceable(16), ptr noundef nonnull align 4 dereferenceable(4)) #3

; Function Attrs: mustprogress uwtable
declare noundef nonnull align 8 dereferenceable(16) ptr @_ZNSirsERe(ptr noundef nonnull align 8 dereferenceable(16), ptr noundef nonnull align 16 dereferenceable(16)) #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) #5

; Function Attrs: mustprogress uwtable
declare noundef nonnull align 8 dereferenceable(8) ptr @_ZNSolsEx(ptr noundef nonnull align 8 dereferenceable(8), i64 noundef) #0 align 2

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 = { nocallback nofree nosync nounwind willreturn memory(argmem: readwrite) }
attributes #2 = { mustprogress norecurse 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 = { 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 #5 = { 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 #6 = { 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 = !{!"vtable pointer", !7, i64 0}
!7 = !{!"Simple C++ TBAA"}
!8 = !{!9, !9, i64 0}
!9 = !{!"int", !10, i64 0}
!10 = !{!"omnipotent char", !7, i64 0}
!11 = !{!12, !12, i64 0}
!12 = !{!"long long", !10, i64 0}
!13 = !{!14, !14, i64 0}
!14 = !{!"long double", !10, i64 0}
!15 = !{!16, !12, i64 0}
!16 = !{!"_ZTSSt4pairIxxE", !12, i64 0, !12, i64 8}
!17 = !{!16, !12, i64 8}
!18 = distinct !{!18, !19}
!19 = !{!"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"

%"class.std::basic_istream" = type { ptr, i64, %"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 }
%"class.std::basic_ostream" = type { ptr, %"class.std::basic_ios" }

@_ZSt3cin = external global %"class.std::basic_istream", align 8
@_ZSt4cout = external global %"class.std::basic_ostream", align 8

; Function Attrs: mustprogress uwtable
declare dso_local { i64, i64 } @_Z11approximateex(x86_fp80 noundef, i64 noundef) local_unnamed_addr #0

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

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

; Function Attrs: mustprogress norecurse uwtable
define dso_local noundef i32 @main() local_unnamed_addr #2 {
  %1 = alloca i32, align 4
  %2 = alloca x86_fp80, align 16
  %3 = tail call noundef zeroext i1 @_ZNSt8ios_base15sync_with_stdioEb(i1 noundef zeroext false)
  %4 = load ptr, ptr @_ZSt3cin, align 8, !tbaa !5
  %5 = getelementptr i8, ptr %4, i64 -24
  %6 = load i64, ptr %5, align 8
  %7 = getelementptr inbounds i8, ptr @_ZSt3cin, i64 %6
  %8 = tail call noundef ptr @_ZNSt9basic_iosIcSt11char_traitsIcEE3tieEPSo(ptr noundef nonnull align 8 dereferenceable(264) %7, ptr noundef null)
  call void @llvm.lifetime.start.p0(i64 4, ptr nonnull %1) #6
  %9 = call noundef nonnull align 8 dereferenceable(16) ptr @_ZNSirsERi(ptr noundef nonnull align 8 dereferenceable(16) @_ZSt3cin, ptr noundef nonnull align 4 dereferenceable(4) %1)
  %10 = load i32, ptr %1, align 4, !tbaa !8
  %11 = add nsw i32 %10, -1
  store i32 %11, ptr %1, align 4, !tbaa !8
  %.not1 = icmp eq i32 %10, 0
  br i1 %.not1, label %._crit_edge, label %.lr.ph

.lr.ph:                                           ; preds = %0, %.lr.ph
  call void @llvm.lifetime.start.p0(i64 16, ptr nonnull %2) #6
  %12 = call noundef nonnull align 8 dereferenceable(16) ptr @_ZNSirsERe(ptr noundef nonnull align 8 dereferenceable(16) @_ZSt3cin, ptr noundef nonnull align 16 dereferenceable(16) %2)
  %13 = load x86_fp80, ptr %2, align 16, !tbaa !11
  %14 = call { i64, i64 } @_Z11approximateex(x86_fp80 noundef %13, i64 noundef 1000000000)
  %15 = extractvalue { i64, i64 } %14, 0
  %16 = extractvalue { i64, i64 } %14, 1
  %17 = call noundef nonnull align 8 dereferenceable(8) ptr @_ZNSolsEx(ptr noundef nonnull align 8 dereferenceable(8) @_ZSt4cout, i64 noundef %15)
  %18 = call noundef nonnull align 8 dereferenceable(8) ptr @_ZStlsISt11char_traitsIcEERSt13basic_ostreamIcT_ES5_c(ptr noundef nonnull align 8 dereferenceable(8) %17, i8 noundef signext 32)
  %19 = call noundef nonnull align 8 dereferenceable(8) ptr @_ZNSolsEx(ptr noundef nonnull align 8 dereferenceable(8) %18, i64 noundef %16)
  %20 = call noundef nonnull align 8 dereferenceable(8) ptr @_ZStlsISt11char_traitsIcEERSt13basic_ostreamIcT_ES5_c(ptr noundef nonnull align 8 dereferenceable(8) %19, i8 noundef signext 10)
  call void @llvm.lifetime.end.p0(i64 16, ptr nonnull %2) #6
  %21 = load i32, ptr %1, align 4, !tbaa !8
  %22 = add nsw i32 %21, -1
  store i32 %22, ptr %1, align 4, !tbaa !8
  %.not = icmp eq i32 %21, 0
  br i1 %.not, label %._crit_edge, label %.lr.ph, !llvm.loop !13

._crit_edge:                                      ; preds = %.lr.ph, %0
  call void @llvm.lifetime.end.p0(i64 4, ptr nonnull %1) #6
  ret i32 0
}

declare noundef zeroext i1 @_ZNSt8ios_base15sync_with_stdioEb(i1 noundef zeroext) local_unnamed_addr #3

; Function Attrs: mustprogress nounwind uwtable
declare noundef ptr @_ZNSt9basic_iosIcSt11char_traitsIcEE3tieEPSo(ptr noundef nonnull align 8 dereferenceable(264), ptr noundef) local_unnamed_addr #4 align 2

declare noundef nonnull align 8 dereferenceable(16) ptr @_ZNSirsERi(ptr noundef nonnull align 8 dereferenceable(16), ptr noundef nonnull align 4 dereferenceable(4)) local_unnamed_addr #3

; Function Attrs: mustprogress uwtable
declare noundef nonnull align 8 dereferenceable(16) ptr @_ZNSirsERe(ptr noundef nonnull align 8 dereferenceable(16), ptr noundef nonnull align 16 dereferenceable(16)) 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 #5

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

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 nocallback nofree nosync nounwind willreturn memory(argmem: readwrite) }
attributes #2 = { mustprogress norecurse 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 = { 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 #5 = { 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 #6 = { 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 = !{!"vtable pointer", !7, i64 0}
!7 = !{!"Simple C++ TBAA"}
!8 = !{!9, !9, i64 0}
!9 = !{!"int", !10, i64 0}
!10 = !{!"omnipotent char", !7, i64 0}
!11 = !{!12, !12, i64 0}
!12 = !{!"long double", !10, i64 0}
!13 = distinct !{!13, !14}
!14 = !{!"llvm.loop.mustprogress"}


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