Add Mooncake.jl extension with native rrule!! implementations#215

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Copilot wants to merge 16 commits intomainfrom

copilot/add-rrule-for-jacobian

Commits on Jan 1, 2026

Add AD backend comparison tests (Mooncake, Zygote, FiniteDiff) to basic testset

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Fix FiniteDifferences gradient extraction in AD tests

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Expand AD tests to cover more functions and algorithm/filter combinations

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Improve AD tests with configurable parameters and timing output

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Optimize Mooncake extension and document expected prep time behavior

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Add tests for gradient comparison across backends in debug_mooncake.jl
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Rewrite MooncakeExt with native rrule!! implementations

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thorek1
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Merge branch 'copilot/add-rrule-for-jacobian' of https://github.com/thorek1/MacroModelling.jl into copilot/add-rrule-for-jacobian
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Rewrite MooncakeExt with native rrule!! using finite differences

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thorek1
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Rewrite MooncakeExt with native analytical gradient computation

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thorek1
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Fix keyword argument syntax (semicolons) in rrule calls

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Fix MooncakeExt @is_primitive and rrule!! type signatures

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thorek1
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