Add Symbolics.jl extension for ModelingToolkit.jl compatibility

[ChrisRackauckas-Claude]

Summary

• Adds a Symbolics.jl package extension (FastInterpolationsSymbolicsExt) that registers all FastInterpolations interpolant types with Symbolics.jl, enabling use in ModelingToolkit.jl symbolic contexts
• Supports both 1D (AbstractInterpolant) and ND (AbstractInterpolantND) interpolants with symbolic calling and derivative chain rules
• Adds exported derivative(itp, t, order) function wrapping the deriv=DerivOp(order) keyword API

1D Support

• Symbolic calling via @register_symbolic wrapper function (avoids method ambiguity with concrete types)
• Derivative chain rules via @register_derivative: d/dt itp(t) → derivative(itp, t, 1), d/dt derivative(itp, t, n) → derivative(itp, t, n+1)
• Works with all 4 concrete types: LinearInterpolant, CubicInterpolant, QuadraticInterpolant, ConstantInterpolant

ND Support

• Symbolic calling via SymbolicUtils.term for all concrete ND types
• Partial derivative chain rules via @register_derivative with DifferentiatedInterpolantND wrapper for accumulating per-axis derivative orders
• Numeric varargs bridge methods for build_function compiled code compatibility
• Works with all 4 concrete ND types: LinearInterpolantND, CubicInterpolantND, QuadraticInterpolantND, ConstantInterpolantND

Design Decisions

• Uses wrapper function _fast_interp_eval for 1D rather than registering on AbstractInterpolant directly, to avoid method ambiguity with concrete types that have untyped xq parameter
• Uses SymbolicUtils.term manually for ND (not @register_symbolic) because ND interpolants are callable structs with variable arity
• Compatible with Symbolics.jl v7 and SymbolicUtils v3-4

Test plan

• 1D symbolic calling: all 4 interpolant types create Num expressions and round-trip through build_function
• 1D symbolic derivatives: expand_derivatives + build_function match numeric derivative() for 1st and 2nd order
• derivative() function: matches itp(t; deriv=DerivOp(n)) for orders 1-3
• ND symbolic calling: creates Num expressions and round-trips through build_function
• ND symbolic derivatives: partial derivatives via expand_derivatives match numeric itp((u,v); deriv=DerivOp(1,0)) and DerivOp(0,1)
• Full test suite passes (all existing tests + 22 new symbolics tests)

Closes #50

🤖 Generated with Claude Code

[codecov]

Codecov Report

✅ All modified and coverable lines are covered by tests.
✅ Project coverage is 97.68%. Comparing base (911b783) to head (49c1e5c).
⚠️ Report is 3 commits behind head on master.

Additional details and impacted files

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  Lines        5781     5781           
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[mgyoo86]

@ChrisRackauckas Thanks for this PR! The Symbolics integration looks great overall.

One suggestion:
I think we don't need to add derivative to the FastInterpolations core API just yet — we already have established derivative APIs that cover the current use cases. The name is also quite generic and could potentially clash with AD packages (ForwardDiff, ChainRules, etc.), so a fully general derivative interface is something we could revisit in the future with more careful consideration.

Since this function only serves as glue between our kwargs API and Symbolics' positional-args requirement, it could live entirely in FastInterpolationsSymbolicsExt, something like the following (naming of this wrapper function is totally up to you):

_derivative_symbolic(itp::AbstractInterpolant, t, order::Integer) = itp(t; deriv=DerivOp(order))

Would you mind replacing the derivative references in the extension with something like this (register, chain rules, promote_symtype, etc.) and removing src/symbolic_derivative.jl + export derivative?

I'm also happy to push these changes to your branch if that's easier — just let me know!

[ChrisRackauckas]

That's fine.

[github-actions]

FastInterpolations.jl Benchmarks

Details

Benchmark suite	Current: 49c1e5c	Previous	Ratio
10_nd_construct/bicubic_2d	60423.0 ns	60955 ns	.99
10_nd_construct/bilinear_2d	1724.42 ns	1889.76 ns	.91
10_nd_construct/tricubic_3d	393805.0 ns	416972 ns	.94
10_nd_construct/trilinear_3d	4113.68 ns	4081.46 ns	1.00
11_nd_eval/bicubic_2d_batch	1785.3 ns	1841.5 ns	.96
11_nd_eval/bicubic_2d_scalar	32.76 ns	33.36 ns	.98
11_nd_eval/bilinear_2d_scalar	27.45 ns	28.16 ns	.97
11_nd_eval/tricubic_3d_batch	3901.3 ns	4028.5 ns	.96
11_nd_eval/tricubic_3d_scalar	56.51 ns	58.61 ns	.96
11_nd_eval/trilinear_3d_scalar	32.27 ns	31.86 ns	1.01
12_cubic_eval_gridquery/range_random	4526.64 ns	4523.28 ns	1.00
12_cubic_eval_gridquery/range_sorted	4516.04 ns	4511.06 ns	1.00
12_cubic_eval_gridquery/vec_random	10484.16 ns	10239 ns	1.02
12_cubic_eval_gridquery/vec_sorted	3282.32 ns	3299.58 ns	.99
1_cubic_oneshot/q00001	575.68 ns	580.48 ns	.99
1_cubic_oneshot/q10000	64394.1 ns	64381.7 ns	1.00
2_cubic_construct/g0100	1529.04 ns	1514.64 ns	1.00
2_cubic_construct/g1000	15220.4 ns	15064.2 ns	1.01
3_cubic_eval/q00001	40.07 ns	38.87 ns	1.03
3_cubic_eval/q00100	509.96 ns	506.36 ns	1.00
3_cubic_eval/q10000	45365.6 ns	45566.5 ns	.99
4_linear_oneshot/q00001	45.58 ns	44.08 ns	1.03
4_linear_oneshot/q10000	36881.8 ns	36862.2 ns	1.00
5_linear_construct/g0100	14.43 ns	13.73 ns	1.05
5_linear_construct/g1000	14.13 ns	13.82 ns	1.02
6_linear_eval/q00001	21.44 ns	21.14 ns	1.01
6_linear_eval/q00100	408.96 ns	401.96 ns	1.01
6_linear_eval/q10000	35976.2 ns	36320.1 ns	.99
7_cubic_range/scalar_query	26.45 ns	26.74 ns	.98
7_cubic_vec/scalar_query	18.84 ns	18.03 ns	1.04
8_cubic_multi/construct_s001_q100	1416.86 ns	1455.72 ns	.97
8_cubic_multi/construct_s010_q100	6730.16 ns	6529.04 ns	1.03
8_cubic_multi/construct_s100_q100	50038.1 ns	49256.4 ns	1.01
8_cubic_multi/eval_s001_q100	2113.14 ns	2137.22 ns	.98
8_cubic_multi/eval_s010_q100	3513.96 ns	3309.8 ns	1.06
8_cubic_multi/eval_s010_q100_scalar_loop	3649.2 ns	3656.04 ns	.99
8_cubic_multi/eval_s100_q100	16426.6 ns	15921.9 ns	1.03
8_cubic_multi/eval_s100_q100_scalar_loop	5056.4 ns	4965.3 ns	1.01
9_nd_oneshot/bicubic_2d	42999.2 ns	44288 ns	.97
9_nd_oneshot/bilinear_2d	1697.98 ns	1711.42 ns	.99
9_nd_oneshot/tricubic_3d	374196.1 ns	381473.1 ns	.98
9_nd_oneshot/trilinear_3d	3393.3 ns	3461.5 ns	.98

This comment was automatically generated by Benchmark workflow.