[Beforerr]

This PR makes ForwardDiff usable under juliac --trim=safe and removes a library load at startup for programs that never use special functions.

Problem

1. using ForwardDiff always loads SpecialFunctions and OpenSpecFun_jll. A trimmed executable keeps OpenSpecFun_jll.__init__, so every launch opens libopenspecfun, even when no special function is ever called. In a minimal trimmed program, that roughly doubles startup time.
2. gradient(f, x), jacobian(f, x), jacobian(f!, y, x) and hessian(f, x) infer as Any for x::Vector{Float64}, so --trim=safe rejects them, including when another package makes the call. Only calls with an explicit Chunk{N} config compile.

Root cause

For (2): Chunk(x) returns a Union of 13 Chunk{N} types. That is too wide to union-split, so building the default config is a dynamic dispatch.

Fix

1. SpecialFunctions becomes a weak dependency. ForwardDiffSpecialFunctionsExt defines the Dual methods for SpecialFunctions, plus logabsgamma and gamma_inc, and rules of other modules whose derivative calls SpecialFunctions (today only NaNMath.lgamma). User-visible change: NaNMath.lgamma on a Dual now needs SpecialFunctions loaded.
2. Opt-in static dispatch on the default chunk size. With the new static_default_chunk preference, methods without a config branch on the chunk size before building it, one branch per size pickchunksize can return, so they infer concretely. It is off by default because the first call then compiles every chunk size (first hessian(f, rand(9)): 0.5 s → 3.5 s); with it off, behavior is unchanged. Documented in advanced.md.

Verification

• New CI job builds and runs a --trim=safe executable from test/trim with the preference set, comparing results for n = 3 and 20 with the JIT. Passes locally on Julia 1.14.0-alpha1; without the preference the build fails with unresolved calls to hessian/HessianConfig.
• With the preference off, first-call latency matches master.

[codecov]

Codecov Report

❌ Patch coverage is 93.10345% with 4 lines in your changes missing coverage. Please review.
✅ Project coverage is 91.22%. Comparing base (a3c0f4f) to head (56031c7).

Files with missing lines	Patch %	Lines
src/prelude.jl	20.00%	4 Missing ⚠️

Additional details and impacted files

@@            Coverage Diff             @@
##           master     #864      +/-   ##
==========================================
- Coverage   91.23%   91.22%   -0.01%     
==========================================
  Files          11       12       +1     
  Lines        1072     1117      +45     
==========================================
+ Hits          978     1019      +41     
- Misses         94       98       +4     

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[devmotion]

There's no point in having a SpecialFunctions extension - it's a hard dependency of DiffRules and hence the extension is always loaded. One would first need something like JuliaDiff/DiffRules.jl#120 that removes such hard dependencies in DiffRules.

[Beforerr]

Hi @devmotion . I checked that DiffRules declares SpecialFunctions in [deps] but never imports it, so the extension stays unloaded unless the user loads SpecialFunctions.

With this PR

using ForwardDiff
haskey(Base.loaded_modules, SpecialFunctions) = false
get_extension(ForwardDiff, :ForwardDiffSpecialFunctionsExt) = nothing

In a minimal trimmed program, removing SpecialFunctions hard dep halved the startup time.