Fix CI on Julia 1.13 and nightly

[devmotion]

CI has been failing on every PR since early 2026: GitHub's julia: 1 now resolves to Julia 1.13, and nightly to 1.14-DEV. Root causes, each traced to an upstream change:

1. All @gpu tests error on Julia ≥ 1.13.0-DEV.300 (224 errors)

_gpu_macro spliced the function value _gpu_test into the @test call. Since JuliaLang/julia#57839 (d934b032ea5b, 1.13.0-DEV.300), @test f(args...) lowers to Test.eval_test_function(f, args, kwargs, quoted_func::Union{Expr,Symbol}, …), so every @gpu test threw a MethodError (the CI log shows "Test threw exception" with no message). The fix splices the name instead.

2. GPU tests need JLArrays 0.4 (supersedes #846)

Once the @gpu tests actually run, muladd (3×3), Diagonal * Matrix, and tr hit "Scalar indexing is disallowed" on 1.13. JLArrays 0.1 caps GPUArrays at 10.3.1, which predates Julia ≥ 1.12's LinearAlgebra changes: tr(::StridedMatrix) scalar loop, the 2×2/3×3 matmul3x3! path, and Diagonal mul!. GPUArrays 12.1 (JLArrays 0.4.2) overrides these. Compat is now JLArrays = "0.1, 0.4" (Julia 1.6 still resolves 0.1).

The vararg * broadcast @gpu_broken test now passes on 1.13. Checked locally: it is still broken on 1.6, 1.10, 1.11, and 1.12, and passes on 1.13 with both GPUArrays 10.3.1 and 12.1.0. It's now gated on VERSION >= v"1.13".

JLArrays 0.4 also implements reverse without scalar indexing, so the reverse @gpu_broken tests now pass with it. They're gated on parentmodule(reverse, Tuple{JLArray{Float32,1}}) !== Base.

3. Matrix functions of Hermitian{<:Real} (194 failures)

Since JuliaLang/julia#55951 (4d2184159b15, 1.12.0-DEV.1322), real-valued f(::Hermitian{<:Real}) returns Hermitian, not Symmetric. _matfun now matches the primal type under that exact version bound. All 15 matrix-function rules and sincos go through _matfun, so this is the single place to change. The equivalent test gate lives in one helper. This supersedes #840/#833.

Since JuliaLang/LinearAlgebra.jl#1359 (44b6bc177f, 1.13.0-DEV.887), exp and positive semi-definite sqrt are computed as (U * √D) * (U * √D)', not as U * D * U'. The primal then differed from f(A) by roundoff (36 Y_ad == Y failures). _matfun now reproduces Base's computation exactly. Checked locally: the primal is bitwise identical to f(A) for all 15 functions on 1.6, 1.12, 1.13 and 1.14-DEV.

4. Zygote integration (Threads.@spawn)

On 1.13, Threads.@spawn calls Threads._spawn_set_thrpool(::Task, ::Symbol), which wraps a foreigncall that Zygote can't differentiate. It's now marked @non_differentiable (guarded with isdefined, following the existing pattern in nondiff.jl). Verified by the IntegrationTest/Zygote job: the structures.jl foreigncall errors are gone. A guarded test in base.jl checks that the rule is defined.

5. JuliaInterpreter: nightly precompile crash, plus world age

JuliaInterpreter 0.9.46 (capped by the test-only compat 0.8,0.9) fails to precompile on 1.14-DEV. Compat is now "0.9, 0.12": only the minors CI actually resolves (1.6 → 0.9.x, 1.13/nightly → 0.12).

JuliaInterpreter 0.12 respects world age, which exposed two things:

• Tests that did @eval using … / @eval struct … inside an interpreted @testset couldn't see the new bindings. They now use local bindings or a top-level struct.
• The sortslices rrule was never inferrable; 0.9 hid this. Its pullback captured an index tuple whose type depends on the value of dims, and it now rebuilds that tuple inside the pullback (via a _sortslices_inds helper shared with the frule).

6. Upcoming LinearAlgebra changes (nightly)

• LinearAlgebra.__normalize! was removed in fix normalize and normalize! JuliaLang/LinearAlgebra.jl#1634. The normalize rrules now use a local copy of the current upstream normalize! logic, reusing the precomputed norm. It is bitwise identical to normalize on nightly. On older Julia it differs only by a few ulp for complex inputs with subnormal norm. New tests cover the subnormal-norm branch.
• Adjoint(::Adjoint) / Transpose(::Transpose) now throw (Disallow double wrap with Adjoint or Transpose JuliaLang/LinearAlgebra.jl#1739). Those test cases are skipped where the double wrap is not allowed.

7. Workflows never ran on main

CI, IntegrationTest, and JuliaNightly triggered on push: branches: [master], but the default branch is main.

8. Testsets run compiled on Julia 1.14 (nightly)

JuliaInterpreter 0.12.0 (latest release) doesn't support 1.14-DEV. It fails on a new foreigncall form ("ccall function name tuple can have at most 2 elements"; 1420 errors per job). It also looked up methods with Type{T} signatures, so it missed rules that ChainRulesCore's macros defined with Core.TypeEgal{T} self-types: rrule(Float64, 1.2) returned nothing when interpreted. ChainRulesCore 1.26.2 (JuliaDiff/ChainRulesCore.jl#714) uses Type{T} again, but the foreigncall failure remains. On VERSION >= v"1.14.0-DEV" the testsets now run compiled.

9. lu rules for singular matrices

Since JuliaLang/LinearAlgebra.jl#1529 (Julia 1.14), BLAS triangular solves throw on a zero diagonal. On ≤ 1.13 they returned Inf/NaN. So the lu! frule threw a SingularException for singular A with check=false, because it divided by all of U.

For square and wide A, the factors are differentiable as long as only the last pivot is zero. The rules computed L \ (P * ΔA) / U, which uses U[q, q] even though the derivative doesn't depend on it.

• Square and wide A: the frule and the lu pullback now share one branch that only inverts the leading (q-1)×(q-1) block of U. This gives the correct derivative when the last pivot is zero.
• No derivative: the rules return NaN, matching the previous behaviour with check=false. That's an earlier zero pivot, which makes L discontinuous, or a zero last pivot of tall A.
• Detecting the cases: F.info gives the index of the first zero pivot. It is negated for unpivoted LU since LU factorization: add allowsingular keyword argument JuliaLang/julia#52957, so the rules negate it back under the version bound 1.11.0-DEV.1535.

Compared with master, the new rules have the same allocations and are within ±7% of its speed (n = 10 to 500). They're slightly more accurate against a BigFloat reference.

New tests run test_frule/test_rrule at matrices whose last pivot is exactly zero: square and wide shapes, RowMaximum and NoPivot. The test matrices use dyadic L with |L[i, j]| < 1 and power-of-two pivots, so LAPACK factors them exactly. Further tests check for NaN on tall A with a zero last pivot and on zeros(n, n). The existing check=false rrule test never ran the pullback, because its tangent had no factors.

Known remaining failures (not fixable here)

• IntegrationTest/Zygote: Zygote's gradcheck_p2.jl hard-codes @test … broken = VERSION >= v"1.12" && MT <: Hermitian{Float64} for matrix functions and sincos. With fix 3 these now pass, so they report 17 "Unexpected Pass". Zygote needs to drop those broken flags.

JuliaNightly is green: the 1.14 ambiguities failure (@non_differentiable Array(::AbstractArray{Bool}) vs rrule(::Type{Array}, ::HermOrSym), JuliaDiff/ChainRulesCore.jl#713) is fixed in ChainRulesCore 1.26.2.

Version bumped to 1.73.1.

🤖 Generated with Claude Code

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Closes #840. Closes #833. Closes #842. Closes #845. Closes #846. Closes #828. Closes #817.