; LLVM IR from sgtlaugh/algovault :: code_library (faulhaber's_formula)

; 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: nounwind uwtable
define dso_local i32 @expo(i64 noundef %0, i32 noundef %1) #0 {
  %3 = alloca i64, align 8
  %4 = alloca i32, align 4
  %5 = alloca i64, align 8
  store i64 %0, ptr %3, align 8, !tbaa !5
  store i32 %1, ptr %4, align 4, !tbaa !9
  %6 = load i64, ptr %3, align 8, !tbaa !5
  %7 = srem i64 %6, 1000000007
  store i64 %7, ptr %3, align 8, !tbaa !5
  call void @llvm.lifetime.start.p0(i64 8, ptr %5) #2
  store i64 1, ptr %5, align 8, !tbaa !5
  br label %8

8:                                                ; preds = %20, %2
  %9 = load i32, ptr %4, align 4, !tbaa !9
  %10 = icmp ne i32 %9, 0
  br i1 %10, label %11, label %27

11:                                               ; preds = %8
  %12 = load i32, ptr %4, align 4, !tbaa !9
  %13 = and i32 %12, 1
  %14 = icmp ne i32 %13, 0
  br i1 %14, label %15, label %20

15:                                               ; preds = %11
  %16 = load i64, ptr %5, align 8, !tbaa !5
  %17 = load i64, ptr %3, align 8, !tbaa !5
  %18 = mul nsw i64 %16, %17
  %19 = srem i64 %18, 1000000007
  store i64 %19, ptr %5, align 8, !tbaa !5
  br label %20

20:                                               ; preds = %15, %11
  %21 = load i64, ptr %3, align 8, !tbaa !5
  %22 = load i64, ptr %3, align 8, !tbaa !5
  %23 = mul nsw i64 %21, %22
  %24 = srem i64 %23, 1000000007
  store i64 %24, ptr %3, align 8, !tbaa !5
  %25 = load i32, ptr %4, align 4, !tbaa !9
  %26 = ashr i32 %25, 1
  store i32 %26, ptr %4, align 4, !tbaa !9
  br label %8, !llvm.loop !11

27:                                               ; preds = %8
  %28 = load i64, ptr %5, align 8, !tbaa !5
  %29 = srem i64 %28, 1000000007
  %30 = trunc i64 %29 to i32
  call void @llvm.lifetime.end.p0(i64 8, ptr %5) #2
  ret i32 %30
}

; 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

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 = { 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/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"

; Function Attrs: nofree norecurse nosync nounwind memory(none) uwtable
define dso_local range(i32 -1000000006, 1000000007) i32 @expo(i64 noundef %0, i32 noundef %1) local_unnamed_addr #0 {
  %.not13 = icmp eq i32 %1, 0
  br i1 %.not13, label %._crit_edge, label %.lr.ph

.lr.ph:                                           ; preds = %2, %7
  %.01016.in = phi i64 [ %8, %7 ], [ %0, %2 ]
  %.015 = phi i64 [ %.1, %7 ], [ 1, %2 ]
  %.0914 = phi i32 [ %9, %7 ], [ %1, %2 ]
  %.01016 = srem i64 %.01016.in, 1000000007
  %3 = and i32 %.0914, 1
  %.not11 = icmp eq i32 %3, 0
  br i1 %.not11, label %7, label %4

4:                                                ; preds = %.lr.ph
  %5 = mul nsw i64 %.015, %.01016
  %6 = srem i64 %5, 1000000007
  br label %7

7:                                                ; preds = %4, %.lr.ph
  %.1 = phi i64 [ %6, %4 ], [ %.015, %.lr.ph ]
  %8 = mul nsw i64 %.01016, %.01016
  %9 = ashr i32 %.0914, 1
  %.not = icmp ult i32 %.0914, 2
  br i1 %.not, label %._crit_edge.loopexit, label %.lr.ph, !llvm.loop !5

._crit_edge.loopexit:                             ; preds = %7
  %10 = srem i64 %.1, 1000000007
  %11 = trunc nsw i64 %10 to i32
  br label %._crit_edge

._crit_edge:                                      ; preds = %._crit_edge.loopexit, %2
  %.0.lcssa = phi i32 [ 1, %2 ], [ %11, %._crit_edge.loopexit ]
  ret i32 %.0.lcssa
}

attributes #0 = { nofree norecurse nosync nounwind memory(none) 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" }

!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,IPSCCPPass,InferFunctionAttrsPass,InstCombinePass,InstSimplifyPass,LCSSAPass,LoopRotatePass,LoopSimplifyPass,LoopUnrollPass,PostOrderFunctionAttrsPass,SROAPass,SimplifyCFGPass