[CarloLucibello]

Part 1 of #863. The add! of the InplaceableThunk from the getindex/view rules added the raw dy, skipping the ProjectTo(x) that val applies. So t.add!(dx) could differ from dx + unthunk(t), or throw (e.g. a complex dy for a real x), and an AD couldn't safely call it.

• When ProjectTo(x) acts elementwise (arrays of numbers, including GPU arrays), add! projects dy and adds it into dx[inds...], staying O(length(dy)). Arrays of arrays use only the projectors of the indexed elements. Other arrays (Diagonal, Symmetric, sparse, …) fall back to add!!(dx, val).
• Scalar ∇getindex projects dy before building the OneElement, so a Float64 cotangent for a Float32 array no longer materializes a dense array.

Benchmarks with Zygote 0.7.16 on Julia 1.13:

• x[i] loop, x::Vector{Float32} of length 10⁴, summed in Float64: 26.5 ms / 391 MiB → 1.80 ms / 8.3 MiB.
• X[:, j] loop over a 100×1000 matrix: unchanged at 36 ms / 767 MiB, since Zygote unthunks. With Zygote calling add! when the inferred eltype of val fits its buffer, which this PR makes safe: 0.41 ms / 5.1 MiB.
• add! itself costs the same as before, on CPU and on GPU.

🧔‍♂️🤖 Assisted by AI

[github-actions]

[JuliaFormatter] _{reported by reviewdog 🐶}

Suggested change

	ChainRulesCore, ChainRulesTestUtils, FiniteDifferences, GPUArraysCore, JLArrays,
	LinearAlgebra, Test
	ChainRulesCore,
	ChainRulesTestUtils,
	FiniteDifferences,
	GPUArraysCore,
	JLArrays,
	LinearAlgebra,
	Test

[codecov]

Codecov Report

❌ Patch coverage is 88.23529% with 2 lines in your changes missing coverage. Please review.
✅ Project coverage is 96.61%. Comparing base (d9ef0f7) to head (6ac471b).

Files with missing lines	Patch %	Lines
src/rulesets/Base/indexing.jl	88.23%	2 Missing ⚠️

Additional details and impacted files

@@            Coverage Diff             @@
##             main     #872      +/-   ##
==========================================
- Coverage   96.65%   96.61%   -0.05%     
==========================================
  Files          28       28              
  Lines        3615     3630      +15     
==========================================
+ Hits         3494     3507      +13     
- Misses        121      123       +2     

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