Matrix exponential fails

[gdalle]

julia> using Enzyme

julia> x = rand(2, 2)
2×2 Matrix{Float64}:
 0.133862  0.197559
 0.265893  0.474916

julia> dx = Enzyme.make_zero(x)
2×2 Matrix{Float64}:
 0.0  0.0
 0.0  0.0

julia> exp(x)
2×2 Matrix{Float64}:
 1.17714  0.271507
 0.36542  1.64585

julia> autodiff(Forward, exp, Duplicated, Duplicated(x, dx))
┌ Warning: Using fallback BLAS replacements for (["dgemm_64_", "dsyrk_64_", "dnrm2_64_"]), performance may be degraded
└ @ Enzyme.Compiler ~/.julia/packages/GPUCompiler/U36Ed/src/utils.jl:59
ERROR: Enzyme execution failed.
Enzyme compilation failed.
Current scope: 
; Function Attrs: mustprogress willreturn
define internal fastcc void @preprocess_julia_gebal__19748({ i64, i64, {} addrspace(10)* }* noalias nocapture nofree noundef nonnull writeonly sret({ i64, i64, {} addrspace(10)* }) align 8 dereferenceable(24) %0, [1 x {} addrspace(10)*]* noalias nocapture nofree noundef nonnull writeonly align 8 dereferenceable(8) "enzyme_inactive" "enzymejl_returnRoots" %1, {} addrspace(10)* noundef nonnull align 16 dereferenceable(40) "enzymejl_parmtype"="127156449281104" "enzymejl_parmtype_ref"="2" %2) unnamed_addr #109 !dbg !12652 {
top:
  %3 = alloca i64, align 16
  %4 = bitcast i64* %3 to i8*
  %5 = alloca i64, align 16
  %6 = bitcast i64* %5 to i8*
  %7 = alloca i64, align 16
  %8 = bitcast i64* %7 to i8*
  %9 = alloca i8, align 1
  %10 = alloca i64, align 16
  %11 = bitcast i64* %10 to i8*
  %12 = alloca i64, align 16
  %13 = bitcast i64* %12 to i8*
  %newstruct74 = alloca [2 x i64], align 8
  %14 = call {}*** @julia.get_pgcstack() #110
  %ptls_field80 = getelementptr inbounds {}**, {}*** %14, i64 2
  %15 = bitcast {}*** %ptls_field80 to i64***
  %ptls_load8182 = load i64**, i64*** %15, align 8, !tbaa !113
  %16 = getelementptr inbounds i64*, i64** %ptls_load8182, i64 2
  %safepoint = load i64*, i64** %16, align 8, !tbaa !117, !invariant.load !112
  fence syncscope("singlethread") seq_cst
  call void @julia.safepoint(i64* %safepoint) #110, !dbg !12653
  fence syncscope("singlethread") seq_cst
  %17 = addrspacecast {} addrspace(10)* %2 to {} addrspace(10)* addrspace(11)*, !dbg !12654
  %arraysize_ptr = getelementptr inbounds {} addrspace(10)*, {} addrspace(10)* addrspace(11)* %17, i64 3, !dbg !12654
  %18 = bitcast {} addrspace(10)* addrspace(11)* %arraysize_ptr to i64 addrspace(11)*, !dbg !12654
  %arraysize = load i64, i64 addrspace(11)* %18, align 8, !dbg !12654, !tbaa !117, !range !126, !invariant.load !112, !alias.scope !127, !noalias !130
  %arraysize_ptr2 = getelementptr inbounds {} addrspace(10)*, {} addrspace(10)* addrspace(11)* %17, i64 4, !dbg !12654
  %19 = bitcast {} addrspace(10)* addrspace(11)* %arraysize_ptr2 to i64 addrspace(11)*, !dbg !12654
  %arraysize3 = load i64, i64 addrspace(11)* %19, align 16, !dbg !12654, !tbaa !117, !range !126, !invariant.load !112, !alias.scope !127, !noalias !130
  %.not = icmp eq i64 %arraysize, %arraysize3, !dbg !12657
  br i1 %.not, label %L13, label %L6, !dbg !12658

L6:                                               ; preds = %top
  %20 = getelementptr inbounds [2 x i64], [2 x i64]* %newstruct74, i64 0, i64 0, !dbg !12659
  store i64 %arraysize, i64* %20, align 8, !dbg !12659, !tbaa !319, !alias.scope !321, !noalias !12660
  %21 = getelementptr inbounds [2 x i64], [2 x i64]* %newstruct74, i64 0, i64 1, !dbg !12659
  store i64 %arraysize3, i64* %21, align 8, !dbg !12659, !tbaa !319, !alias.scope !321, !noalias !12660
  %22 = addrspacecast [2 x i64]* %newstruct74 to [2 x i64] addrspace(11)*, !dbg !12658
  %23 = call fastcc nonnull {} addrspace(10)* @julia_string_19657({} addrspace(10)* nofree noundef nonnull align 16 addrspacecast ({}* inttoptr (i64 127156352624368 to {}*) to {} addrspace(10)*), [2 x i64] addrspace(11)* nocapture nofree noundef nonnull readonly align 8 dereferenceable(16) %22) #110, !dbg !12658
  %current_task75102 = getelementptr inbounds {}**, {}*** %14, i64 -14, !dbg !12658
  %current_task75 = bitcast {}*** %current_task75102 to {}**, !dbg !12658
  %box76 = call noalias nonnull dereferenceable(8) "enzyme_inactive" {} addrspace(10)* @julia.gc_alloc_obj({}** nonnull %current_task75, i64 noundef 8, {} addrspace(10)* noundef addrspacecast ({}* inttoptr (i64 127156287023792 to {}*) to {} addrspace(10)*)) #111, !dbg !12658
  %24 = bitcast {} addrspace(10)* %box76 to [1 x {} addrspace(10)*] addrspace(10)*, !dbg !12658
  %25 = getelementptr [1 x {} addrspace(10)*], [1 x {} addrspace(10)*] addrspace(10)* %24, i64 0, i64 0, !dbg !12658
  store {} addrspace(10)* %23, {} addrspace(10)* addrspace(10)* %25, align 8, !dbg !12658, !tbaa !181, !alias.scope !185, !noalias !12663
  %26 = addrspacecast {} addrspace(10)* %box76 to {} addrspace(12)*, !dbg !12658
  call void @ijl_throw({} addrspace(12)* %26) #112, !dbg !12658
  unreachable, !dbg !12658

L13:                                              ; preds = %top
  %27 = addrspacecast {} addrspace(10)* %2 to { i8 addrspace(13)*, i64, i16, i16, i32 } addrspace(11)*, !dbg !12664
  %arraylen_ptr = getelementptr inbounds { i8 addrspace(13)*, i64, i16, i16, i32 }, { i8 addrspace(13)*, i64, i16, i16, i32 } addrspace(11)* %27, i64 0, i32 1, !dbg !12664
  %arraylen = load i64, i64 addrspace(11)* %arraylen_ptr, align 8, !dbg !12664, !tbaa !117, !range !126, !invariant.load !112, !alias.scope !127, !noalias !130
  %.not83 = icmp eq i64 %arraylen, 0, !dbg !12669
  br i1 %.not83, label %L60, label %L29, !dbg !12665

L29:                                              ; preds = %L13
  %28 = addrspacecast {} addrspace(10)* %2 to double addrspace(13)* addrspace(11)*, !dbg !12671
  %arrayptr84 = load double addrspace(13)*, double addrspace(13)* addrspace(11)* %28, align 16, !dbg !12671, !tbaa !117, !invariant.load !112, !alias.scope !12672, !noalias !130, !nonnull !112
  %value_phi6114 = load double, double addrspace(13)* %arrayptr84, align 8, !dbg !12673, !tbaa !274, !alias.scope !185, !noalias !186
  %29 = fsub double %value_phi6114, %value_phi6114, !dbg !12674
  %30 = fcmp ord double %29, 0.000000e+00, !dbg !12677
  br i1 %30, label %L41.lr.ph, label %L38, !dbg !12676

L41.lr.ph:                                        ; preds = %L29
  %31 = add nuw nsw i64 %arraylen, 1, !dbg !12676
  br label %L41, !dbg !12676

L38.loopexit:                                     ; preds = %L53
  br label %L38, !dbg !12679

L38:                                              ; preds = %L38.loopexit, %L29
  %32 = call fastcc [1 x {} addrspace(10)*] @julia_ArgumentError_19561({} addrspace(10)* nofree noundef nonnull align 32 addrspacecast ({}* inttoptr (i64 127156347529312 to {}*) to {} addrspace(10)*)) #110, !dbg !12679
  %current_task885 = getelementptr inbounds {}**, {}*** %14, i64 -14, !dbg !12679
  %current_task8 = bitcast {}*** %current_task885 to {}**, !dbg !12679
  %box = call noalias nonnull dereferenceable(8) "enzyme_inactive" {} addrspace(10)* @julia.gc_alloc_obj({}** nonnull %current_task8, i64 noundef 8, {} addrspace(10)* noundef addrspacecast ({}* inttoptr (i64 127156310686912 to {}*) to {} addrspace(10)*)) #111, !dbg !12679
  %33 = bitcast {} addrspace(10)* %box to [1 x {} addrspace(10)*] addrspace(10)*, !dbg !12679
  %34 = extractvalue [1 x {} addrspace(10)*] %32, 0, !dbg !12679
  %35 = getelementptr [1 x {} addrspace(10)*], [1 x {} addrspace(10)*] addrspace(10)* %33, i64 0, i64 0, !dbg !12679
  store {} addrspace(10)* %34, {} addrspace(10)* addrspace(10)* %35, align 8, !dbg !12679, !tbaa !181, !alias.scope !185, !noalias !12663
  %36 = addrspacecast {} addrspace(10)* %box to {} addrspace(12)*, !dbg !12679
  call void @ijl_throw({} addrspace(12)* %36) #112, !dbg !12679
  unreachable, !dbg !12679

L41:                                              ; preds = %L53, %L41.lr.ph
  %iv = phi i64 [ %iv.next, %L53 ], [ 0, %L41.lr.ph ]
  %37 = add nuw i64 %iv, 2, !dbg !12680
  %iv.next = add nuw nsw i64 %iv, 1, !dbg !12680
  %exitcond.not = icmp eq i64 %37, %31, !dbg !12680
  br i1 %exitcond.not, label %L60.loopexit, label %L53, !dbg !12682

L53:                                              ; preds = %L41
  %38 = add nsw i64 %37, -1, !dbg !12684
  %39 = getelementptr inbounds double, double addrspace(13)* %arrayptr84, i64 %38, !dbg !12686
  %40 = add nuw i64 %37, 1, !dbg !12687
  %value_phi6 = load double, double addrspace(13)* %39, align 8, !dbg !12673, !tbaa !274, !alias.scope !185, !noalias !186
  %41 = fsub double %value_phi6, %value_phi6, !dbg !12674
  %42 = fcmp ord double %41, 0.000000e+00, !dbg !12677
  br i1 %42, label %L41, label %L38.loopexit, !dbg !12676

L60.loopexit:                                     ; preds = %L41
  br label %L60, !dbg !12688

L60:                                              ; preds = %L60.loopexit, %L13
  %current_task1788 = getelementptr inbounds {}**, {}*** %14, i64 -14, !dbg !12688
  %current_task17 = bitcast {}*** %current_task1788 to {}**, !dbg !12688
  %43 = call noalias nonnull {} addrspace(10)* @ijl_alloc_array_1d({} addrspace(10)* noundef addrspacecast ({}* inttoptr (i64 127156239837216 to {}*) to {} addrspace(10)*), i64 %arraysize) #113, !dbg !12691
  store i8 66, i8* %9, align 1, !dbg !12696, !tbaa !739, !alias.scope !185, !noalias !12663
  store i64 %arraysize, i64* %10, align 16, !dbg !12696, !tbaa !739, !alias.scope !185, !noalias !12663
  %.not93 = icmp eq i64 %arraysize, 0, !dbg !12700
  %44 = select i1 %.not93, i64 1, i64 %arraysize, !dbg !12702
  store i64 %44, i64* %12, align 16, !dbg !12696, !tbaa !739, !alias.scope !185, !noalias !12663
  %45 = addrspacecast {} addrspace(10)* %2 to {} addrspace(11)*, !dbg !12703
  %46 = call nonnull {}* @julia.pointer_from_objref({} addrspace(11)* noundef %45) #114, !dbg !12703
  %47 = bitcast {}* %46 to i8**, !dbg !12703
  %arrayptr39 = load i8*, i8** %47, align 8, !dbg !12703, !tbaa !117, !invariant.load !112, !alias.scope !127, !noalias !130, !nonnull !112
  %48 = ptrtoint i8* %arrayptr39 to i64, !dbg !12703
  %bitcast_coercion47 = ptrtoint i64* %5 to i64, !dbg !12704
  %bitcast_coercion51 = ptrtoint i64* %3 to i64, !dbg !12704
  %49 = addrspacecast {} addrspace(10)* %43 to {} addrspace(11)*, !dbg !12703
  %50 = call nonnull {}* @julia.pointer_from_objref({} addrspace(11)* %49) #114, !dbg !12703
  %51 = bitcast {}* %50 to i8**, !dbg !12703
  %arrayptr53 = load i8*, i8** %51, align 8, !dbg !12703, !tbaa !750, !alias.scope !753, !noalias !754, !nonnull !112
  %52 = ptrtoint i8* %arrayptr53 to i64, !dbg !12703
  %bitcast_coercion57 = ptrtoint i64* %7 to i64, !dbg !12704
  call void @dgebal_64_(i8* noundef nonnull %9, i8* noundef nonnull %11, i64 %48, i8* noundef nonnull %13, i64 noundef %bitcast_coercion47, i64 noundef %bitcast_coercion51, i64 %52, i64 noundef %bitcast_coercion57, i64 noundef 1) #110 [ "jl_roots"({} addrspace(10)* null, {} addrspace(10)* %43, {} addrspace(10)* null, {} addrspace(10)* null, {} addrspace(10)* null, {} addrspace(10)* %2, {} addrspace(10)* null, {} addrspace(10)* null) ], !dbg !12699
  %53 = load i64, i64* %7, align 16, !dbg !12706, !tbaa !739, !alias.scope !185, !noalias !186
  %.not95 = icmp eq i64 %53, 0, !dbg !12709
  br i1 %.not95, label %L176, label %L166, !dbg !12710

L166:                                             ; preds = %L60
  %54 = icmp sgt i64 %53, -1, !dbg !12711
  br i1 %54, label %L173, label %L168, !dbg !12712

L168:                                             ; preds = %L166
  %55 = sub i64 0, %53, !dbg !12713
  call void @llvm.lifetime.end.p0i8(i64 noundef 8, i8* noundef nonnull %4) #110
  call void @llvm.lifetime.end.p0i8(i64 noundef 8, i8* noundef nonnull %6) #110
  call void @llvm.lifetime.end.p0i8(i64 noundef 8, i8* noundef nonnull %8) #110
  call void @llvm.lifetime.end.p0i8(i64 noundef 1, i8* noundef nonnull %9) #110
  call void @llvm.lifetime.end.p0i8(i64 noundef 8, i8* noundef nonnull %11) #110
  call void @llvm.lifetime.end.p0i8(i64 noundef 8, i8* noundef nonnull %13) #110
  %56 = call noalias nonnull "enzyme_inactive" {} addrspace(10)* @ijl_box_int64(i64 signext %55) #113, !dbg !12714
  %57 = call nonnull {} addrspace(10)* ({} addrspace(10)* ({} addrspace(10)*, {} addrspace(10)**, i32, {} addrspace(10)*)*, {} addrspace(10)*, {} addrspace(10)*, ...) @julia.call2({} addrspace(10)* ({} addrspace(10)*, {} addrspace(10)**, i32, {} addrspace(10)*)* noundef nonnull @ijl_invoke, {} addrspace(10)* noundef addrspacecast ({}* inttoptr (i64 127156268451584 to {}*) to {} addrspace(10)*), {} addrspace(10)* noundef addrspacecast ({}* inttoptr (i64 127156246650304 to {}*) to {} addrspace(10)*), {} addrspace(10)* addrspacecast ({}* inttoptr (i64 127156347531504 to {}*) to {} addrspace(10)*), {} addrspace(10)* nonnull %56, {} addrspace(10)* addrspacecast ({}* inttoptr (i64 127156347531472 to {}*) to {} addrspace(10)*)) #115, !dbg !12714
  %box61 = call noalias nonnull dereferenceable(8) "enzyme_inactive" {} addrspace(10)* @julia.gc_alloc_obj({}** nonnull %current_task17, i64 noundef 8, {} addrspace(10)* noundef addrspacecast ({}* inttoptr (i64 127156310686912 to {}*) to {} addrspace(10)*)) #111, !dbg !12714
  %58 = bitcast {} addrspace(10)* %box61 to [1 x {} addrspace(10)*] addrspace(10)*, !dbg !12714
  %59 = getelementptr [1 x {} addrspace(10)*], [1 x {} addrspace(10)*] addrspace(10)* %58, i64 0, i64 0, !dbg !12714
  store {} addrspace(10)* %57, {} addrspace(10)* addrspace(10)* %59, align 8, !dbg !12714, !tbaa !181, !alias.scope !185, !noalias !12663
  %60 = addrspacecast {} addrspace(10)* %box61 to {} addrspace(12)*, !dbg !12714
  call void @ijl_throw({} addrspace(12)* %60) #112, !dbg !12714
  unreachable, !dbg !12714

L173:                                             ; preds = %L166
  call void @llvm.lifetime.end.p0i8(i64 noundef 8, i8* noundef nonnull %4) #110
  call void @llvm.lifetime.end.p0i8(i64 noundef 8, i8* noundef nonnull %6) #110
  call void @llvm.lifetime.end.p0i8(i64 noundef 8, i8* noundef nonnull %8) #110
  call void @llvm.lifetime.end.p0i8(i64 noundef 1, i8* noundef nonnull %9) #110
  call void @llvm.lifetime.end.p0i8(i64 noundef 8, i8* noundef nonnull %11) #110
  call void @llvm.lifetime.end.p0i8(i64 noundef 8, i8* noundef nonnull %13) #110
  %box66 = call noalias nonnull dereferenceable(8) "enzyme_inactive" {} addrspace(10)* @julia.gc_alloc_obj({}** nonnull %current_task17, i64 noundef 8, {} addrspace(10)* noundef addrspacecast ({}* inttoptr (i64 127156276572992 to {}*) to {} addrspace(10)*)) #111, !dbg !12715
  %memcpy_refined_dst = bitcast {} addrspace(10)* %box66 to i64 addrspace(10)*, !dbg !12715
  store i64 %53, i64 addrspace(10)* %memcpy_refined_dst, align 8, !dbg !12715, !tbaa !181, !alias.scope !185, !noalias !12663
  %61 = addrspacecast {} addrspace(10)* %box66 to {} addrspace(12)*, !dbg !12715
  call void @ijl_throw({} addrspace(12)* %61) #112, !dbg !12715
  unreachable, !dbg !12715

L176:                                             ; preds = %L60
  %62 = load i64, i64* %5, align 16, !dbg !12716, !tbaa !739, !alias.scope !185, !noalias !186
  %63 = load i64, i64* %3, align 16, !dbg !12716, !tbaa !739, !alias.scope !185, !noalias !186
  %64 = getelementptr inbounds [1 x {} addrspace(10)*], [1 x {} addrspace(10)*]* %1, i64 0, i64 0, !dbg !12718
  store {} addrspace(10)* %43, {} addrspace(10)** %64, align 8, !dbg !12718, !noalias !12719
  %.repack = getelementptr inbounds { i64, i64, {} addrspace(10)* }, { i64, i64, {} addrspace(10)* }* %0, i64 0, i32 0, !dbg !12718
  store i64 %62, i64* %.repack, align 8, !dbg !12718, !noalias !12719
  %.repack96 = getelementptr inbounds { i64, i64, {} addrspace(10)* }, { i64, i64, {} addrspace(10)* }* %0, i64 0, i32 1, !dbg !12718
  store i64 %63, i64* %.repack96, align 8, !dbg !12718, !noalias !12719
  %.repack98 = getelementptr inbounds { i64, i64, {} addrspace(10)* }, { i64, i64, {} addrspace(10)* }* %0, i64 0, i32 2, !dbg !12718
  store {} addrspace(10)* %43, {} addrspace(10)** %.repack98, align 8, !dbg !12718, !noalias !12719
  ret void, !dbg !12718
}

No forward mode derivative found for dgebal_64_
 at context:   call void @dgebal_64_(i8* noundef nonnull %9, i8* noundef nonnull %11, i64 %48, i8* noundef nonnull %13, i64 noundef %bitcast_coercion47, i64 noundef %bitcast_coercion51, i64 %52, i64 noundef %bitcast_coercion57, i64 noundef 1) #110 [ "jl_roots"({} addrspace(10)* null, {} addrspace(10)* %43, {} addrspace(10)* null, {} addrspace(10)* null, {} addrspace(10)* null, {} addrspace(10)* %2, {} addrspace(10)* null, {} addrspace(10)* null) ], !dbg !216

Stacktrace:
 [1] gebal!
   @ ~/.julia/juliaup/julia-1.10.2+0.x64.linux.gnu/share/julia/stdlib/v1.10/LinearAlgebra/src/lapack.jl:221


Stacktrace:
  [1] throwerr(cstr::Cstring)
    @ Enzyme.Compiler ~/.julia/packages/Enzyme/l4FS0/src/compiler.jl:1289
  [2] gebal!
    @ ~/.julia/juliaup/julia-1.10.2+0.x64.linux.gnu/share/julia/stdlib/v1.10/LinearAlgebra/src/lapack.jl:221
  [3] exp!
    @ ~/.julia/juliaup/julia-1.10.2+0.x64.linux.gnu/share/julia/stdlib/v1.10/LinearAlgebra/src/dense.jl:654
  [4] exp
    @ ~/.julia/juliaup/julia-1.10.2+0.x64.linux.gnu/share/julia/stdlib/v1.10/LinearAlgebra/src/dense.jl:594 [inlined]
  [5] fwddiffejulia_exp_19479wrap
    @ ~/.julia/juliaup/julia-1.10.2+0.x64.linux.gnu/share/julia/stdlib/v1.10/LinearAlgebra/src/dense.jl:0
  [6] macro expansion
    @ ~/.julia/packages/Enzyme/l4FS0/src/compiler.jl:5378 [inlined]
  [7] enzyme_call
    @ ~/.julia/packages/Enzyme/l4FS0/src/compiler.jl:5056 [inlined]
  [8] ForwardModeThunk
    @ ~/.julia/packages/Enzyme/l4FS0/src/compiler.jl:5001 [inlined]
  [9] autodiff(::ForwardMode{FFIABI}, f::Const{typeof(exp)}, ::Type{Duplicated}, args::Duplicated{Matrix{Float64}})
    @ Enzyme ~/.julia/packages/Enzyme/l4FS0/src/Enzyme.jl:324
 [10] autodiff(::ForwardMode{FFIABI}, ::typeof(exp), ::Type, ::Duplicated{Matrix{Float64}})
    @ Enzyme ~/.julia/packages/Enzyme/l4FS0/src/Enzyme.jl:224
 [11] top-level scope
    @ REPL[70]:1

[wsmoses]

Duplicate of #1222.

@vchuravy this is the need for lapack functions, either proper or fallback.

Rules for this are welcome!