Replace recursive-Node ScalarExpressionFunction with isbits flat form

[lxmota]

Summary

Supersedes #309. Three-commit PR:

1. Rewrites ScalarExpressionFunction's storage from the recursive Node{T, DEFAULT_MAX_DEGREE} form introduced by Symbolic differentiation for juliac-safe dynamic Dirichlet BCs #309 to a fixed-size NTuple of FlatNode records, making the function itself isbits.
2. Routes ScalarExpressionFunction through symbolic time derivatives in DirichletBCFunction so the untyped DirichletBCs(mesh, dof, bcs) constructor — the one create_parameters calls — produces fully isbits {F, F, F} BC funcs automatically, without callers needing to thread an F type parameter.
3. Adds a typed Base.size(::AbstractContinuousField, ::Int)::Int overload so the trim verifier can resolve the call site Carina uses to report node counts in the setup log.

The isbits property dissolves the GPU↔juliac conflict that #309's recursive-Node storage would have created downstream in Carina:

• BC evaluation in FEC.update_bc_values! runs in-place on the GPU with no host↔device sync per time step (the function passes through KernelAbstractions kernels as a value argument).
• The function also survives juliac --trim — the storage is pure data, no closures, no @eval, no RuntimeGeneratedFunctions.

The symbolic differentiation logic from #309 carries over. It still operates on the recursive Node{T, D} form (cleanest for constant folding through tree rewriting); the boundary with the persistent flat storage is _unflatten / _flatten, called once per differentiate invocation at TOML-parse time.

What this change deletes (from main, ex-#309)

• struct ScalarExpressionFunction{T} <: AbstractExpressionFunction{T, Node{T, DEFAULT_MAX_DEGREE}, ntuple_type} — the recursive-Node-backed struct.
• Its four call methods (the new struct preserves the same signatures).
• differentiate(f, var_name::String) — the string-keyed public API (replaced by the integer form; a string convenience overload remains, but requires an explicit var_names list since the function no longer stores it).

What this change adds

Commit 1 — Replace recursive-Node ScalarExpressionFunction with isbits flat form (7c79988)

• src/Expressions.jl

  • FlatNode{T} struct (1-based indices, isbits) and FEC_EXPR_MAX_NODES = 256 cap. Carina's biggest second-derivative tree (Gaussian-pulse BC) is ~100 nodes; 256 gives 2-3× headroom at ~6 KB per function.
  • _flatten(::Node{T,D}) (preorder DFS) and _unflatten inverse.
  • _apply_unary_op / _apply_binary_op open-coded op-code dispatch and _eval_node recursive walker over the flat tuple.
  • Replacement ScalarExpressionFunction storing the flat NTuple; all existing call signatures preserved ((var::T), (vars::AbstractVector{T}), (X::SVector{ND, T}), (X::SVector{ND, T}, t::T)) so downstream consumers in FEC and Carina need no changes.

• src/bcs/DirichletBCs.jl — juliac-safe DirichletBCs{F} constructor switches from Expressions.differentiate(bc.func, "t") to Expressions.differentiate(bc.func, Int(bc.func.num_vars)), following the convention that the last variable in the user's expression is time.

• test/TestExpressions.jl — rewrites Symbolic differentiation for juliac-safe dynamic Dirichlet BCs #309's differentiate tests onto the integer-index API; adds isbits property check; keeps the parser precedence test from Symbolic differentiation for juliac-safe dynamic Dirichlet BCs #309.

• test/TestBCs.jl — replaces Symbolic differentiation for juliac-safe dynamic Dirichlet BCs #309's juliac-safe DirichletBCs tests with flat-form equivalents.

Diff: +320 / -138 lines across 4 files (large minus block = the recursive-Node infrastructure being removed).

Commit 2 — Auto-route ScalarExpressionFunction through symbolic time derivatives (727fc7c)

• src/bcs/DirichletBCs.jl — new DirichletBCFunction(func::ScalarExpressionFunction) specialization that takes time derivatives via Expressions.differentiate (not ForwardDiff), producing an all-isbits DirichletBCFunction{F, F, F} from a single positional arg. Three motivations:
  1. The legacy DirichletBCFunction(func::F) where F <: Function constructor builds closures around ForwardDiff.derivative, which the SEF call signature ((X::SVector{ND, T}, t::T) where T <: Number) cannot consume — ForwardDiff.Dual{Tag, Float64, 1} is not Float64. Without this overload, any caller passing a ScalarExpressionFunction through create_parameters would have crashed at first BC evaluation.
  2. With this overload, the untyped DirichletBCs(mesh, dof, bcs) container constructor — which is what create_parameters already routes through — gives callers the juliac-safe symbolic path automatically. Callers no longer need to opt in via DirichletBCs{F}(mesh, dof, bcs).
  3. The resulting DirichletBCFunction{F, F, F} is isbits and identically typed to what the typed constructor produces, so GPU dispatch is unchanged.

Diff: +16 / -0 lines, all in DirichletBCs.jl.

Commit 3 — Add typed size(::AbstractContinuousField, ::Int)::Int overload (4042615)

• src/Fields.jl — direct two-arg method with concrete Int(NF) arithmetic in the body and ::Int return type. Surfaced by a juliac --trim dry-run of Carina: the generic Base.size(A, d)::Int fallback runs size(A)[d] and infers the result as ::Any whenever the field's NF type parameter isn't fully bound at the call site. Carina's setup log emits size(field, 2) to report node counts, so the abstract-::Any flowed through several downstream lines as unresolved calls. The two-arg overload keeps inference exact regardless of how the field's type is bound upstream.

Diff: +12 / -1 lines, all in Fields.jl.

Test plan

• FEC suite: 18187 / 18187 (commit 1 matches Symbolic differentiation for juliac-safe dynamic Dirichlet BCs #309's count — same test items, integer-index API; commits 2 and 3 added no new tests but their behaviour is exercised by the existing juliac-safe DirichletBCs{F} test and any user of size(::AbstractContinuousField, ::Int)).
• Carina suite against this branch via local path dep: 188 / 188.
• isbitstype(ScalarExpressionFunction{Float64}) confirmed at REPL.
• isbitstype(DirichletBCFunction(::ScalarExpressionFunction)) confirmed — wholly isbits, no captured closures.
• Gaussian-pulse 1st and 2nd time derivatives match analytical to machine precision at multiple sample points.

Migration note

The only breaking API change vs #309 is differentiate(f, var_name::String) → differentiate(f, var_idx::Integer). A string-name convenience overload differentiate(f, var_names, var_name) remains for the common parse-time case where the caller has the var-name list in scope. Internal users (FEC's DirichletBCs juliac path) are already updated.

The var_names list is no longer stored on the ScalarExpressionFunction (it's a Vector{String} — not isbits — and would have broken the GPU kernel argument story). Callers that need to look up names later should keep their own copy.

The SEF overload added in commit 2 and the size overload added in commit 3 are purely additive — DirichletBCFunction(::Function) continues to work unchanged for any non-SEF callable, and size(::AbstractContinuousField) (one-arg) is untouched.

🤖 Generated with Claude Code

[codecov]

Codecov Report

❌ Patch coverage is 91.45299% with 10 lines in your changes missing coverage. Please review.
✅ Project coverage is 68.73%. Comparing base (0ddce93) to head (4042615).

Files with missing lines	Patch %	Lines
src/bcs/DirichletBCs.jl	37.50%	5 Missing ⚠️
src/Expressions.jl	96.15%	4 Missing ⚠️
src/Fields.jl	80.00%	1 Missing ⚠️

Additional details and impacted files

@@            Coverage Diff             @@
##             main     #310      +/-   ##
==========================================
- Coverage   71.59%   68.73%   -2.87%     
==========================================
  Files          56       56              
  Lines        5112     5204      +92     
==========================================
- Hits         3660     3577      -83     
- Misses       1452     1627     +175     

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[cmhamel]

Removed a stale dependency but otherwise looks great to me!