[ChrisRackauckas-Claude]

Ignore this PR until it has been reviewed by @ChrisRackauckas.

What / why

NLsolveJL documented autodiff as ":central, :forward, or ADTypes". NLsolve 5.0.0 (NLSolversBase 8) switched its own autodiff keyword from Symbol to ADTypes.AbstractADType, so OnceDifferentiable(f!, u0, resid; autodiff = :central) now throws a TypeError and the Wrappers group fails on master (https://github.com/SciML/NonlinearSolve.jl/actions/runs/33251921454).

Rather than translate the Symbols at the call site, this makes ADTypes the interface, matching the rest of NonlinearSolve:

• The default is now AutoFiniteDiff(; fdtype = Val(:central)) — exactly what :central meant, and also NLSolversBase 8's own default, so numerics are unchanged.
• :central / :forward are normalized to AutoFiniteDiff(; fdtype = Val(:central)) / AutoForwardDiff() in the constructor, with a Base.depwarn. They keep working; alg.autodiff is now always an AbstractADType.
• The extension drops both isa Symbol branches and passes the backend straight to NLsolve, which drives DifferentiationInterface generically.

Non-breaking, so 4.28.1 → 4.29.0. Actually removing the Symbols is a 5.0 change.

Why not just unify onto construct_extension_jac

The obvious cleanup — delete the "let NLsolve do the AD" branch and always use NonlinearSolveBase.construct_extension_jac, like CMINPACK and friends — does not work. I tried it; it fails the existing forward_ad_tests__item1.jl two ways:

Scalar AD: Error During Test at test/Wrappers/forward_ad_tests__item1.jl:22
  MethodError: no method matching setindex(::Float64, ::Float64, ::Int64)
    [1] setindex(::Float64, ::Float64, ::Int64)
      @ FiniteDiff ~/.julia/packages/FiniteDiff/Z4dvL/src/FiniteDiff.jl:45

Jacobian: Error During Test at test/Wrappers/forward_ad_tests__item1.jl:41
  DimensionMismatch: arrays could not be broadcast to a common size: a has axes Base.OneTo(4) and b has axes Base.OneTo(2)

construct_extension_jac is broken for scalar u0 (hands a bare Real to DI.jacobian) and for non-vector u0 (feeds the flattened u to prob.f, which still expects the original shape). Both are pre-existing and affect every wrapper — they are simply unreachable today because each wrapper short-circuits that path on its default autodiff. Filed separately with a standalone MWE: #1215. This PR routes around it; construct_extension_jac is still used when the problem supplies jac or jac_prototype.

Verification

GROUP=Wrappers julia --project -e 'using Pkg; Pkg.test()', Julia 1.12.4 linux, resolving NLsolve v5.0.1 / NLSolversBase v8.0.1.

Before (unmodified master c498eaf):

Scalar AD: Error During Test at test/Wrappers/forward_ad_tests__item1.jl:22
  TypeError: in keyword argument autodiff, expected ADTypes.AbstractADType, got a value of type Symbol
Jacobian: Error During Test at test/Wrappers/forward_ad_tests__item1.jl:41
  TypeError: in keyword argument autodiff, expected ADTypes.AbstractADType, got a value of type Symbol
Test Summary: | Pass Error Total Time
ForwardDiff.jl Integration | 130672 2 130674 7m18.1s
ERROR: LoadError: Some tests did not pass: 130672 passed, 0 failed, 2 errored, 0 broken.
exit=1

Pin evidence (master with [compat] NLsolve = "4.5" restored in Project.toml and test/Wrappers/Project.toml, nothing else changed) — confirms NLsolve 5 is the trigger:

⌅ [2774e3e8] + NLsolve v4.5.1
⌅ [d41bc354] + NLSolversBase v7.10.0
ForwardDiff.jl Integration | 135631 135631 7m44.6s
Nonlinear Root Finding Problems | 58 58 18.9s
     Testing NonlinearSolve tests passed
exit=0

After (this branch, NLsolve v5.0.1 / NLSolversBase v8.0.1):

ForwardDiff.jl Integration | 135631  135631  7m38.8s
Simple Scalar Problem | 13 13  38.1s
Simple Vector Problem | 12 1 13  11.7s
Power Method  | 19 6 25  27.8s
Anderson does not allocate dense Jacobian (#862) | 2 2  1.3s
LeastSquaresOptim.jl | 40 40  36.7s
FastLevenbergMarquardt.jl + CMINPACK: Jacobian Provided | 9 9  15.9s
FastLevenbergMarquardt.jl + CMINPACK: Jacobian Not Provided | 27 27  18.0s
FastLevenbergMarquardt.jl + StaticArrays | 1 1  2.1s
Steady State Problems | 16 16  10.6s
Nonlinear Root Finding Problems | 63 63  20.1s
     Testing NonlinearSolve tests passed
exit=0

Nonlinear Root Finding Problems goes 58 → 63: test/Wrappers/rootfind_tests__item2.jl now runs the solve over AutoFiniteDiff(; fdtype = Val(:central)), AutoForwardDiff(), :central and :forward, and asserts the Symbols normalize to the right backends. The discriminating tests are the pre-existing ones in forward_ad_tests__item1.jl and rootfind_tests__item2.jl; the latter never ran on CI because the group aborts after the first errored @safetestset.

The deprecation path fires as intended:

┌ Warning: `NLsolveJL(autodiff = :central)` is deprecated, pass `AutoFiniteDiff(; fdtype = Val(:central))` instead.

Runic --check and typos pass on all changed files.

Not verified

• macOS, Julia lts and pre channels — CI covers these.
• Other test groups (Core, Downstream, QA) were not run locally. The change touches src/extension_algs.jl and ext/NonlinearSolveNLsolveExt.jl; nothing outside NLsolveJL construction reads alg.autodiff.
• Docs build was not run. The NLsolveJL docstring changed, so docs/make.jl is worth a look on CI.

For a reviewer to push back on

• Default choice. I kept central finite differencing to preserve today's numerics. The consistent choice with the rest of NonlinearSolve would be autodiff = nothing (auto-select → ForwardDiff), which is faster but silently changes results for existing NLsolveJL() users. That belongs in a 5.0, not here.
• ADTypes now go to NLsolve, not construct_extension_jac. Previously an explicit ADType took the construct_extension_jac path when prob.f.jac === nothing. It now goes to NLsolve unless jac or jac_prototype is set. That is what dodges construct_extension_jac is broken for scalar and non-vector u0 with an explicit ADTypes backend #1215, and both are DI-backed, but it does mean a jac_prototype-less sparsity setup no longer gets NonlinearSolve's coloring — there was no such path exercised in the tests.
• Version bump. Called this minor (4.29.0) on the grounds that Symbols still work. If the changed default representation counts as breaking for anyone pattern-matching on alg.autodiff, say so.

🤖 Generated with Claude Code (model: claude-opus-5[1m])
https://claude.ai/code/session_01QTnjBBwmH4EMvxpEVNCqua