Add challenge 78: 2D FFT (Medium)

[claude]

Summary

• Adds challenge 78: 2D Fast Fourier Transform (Medium difficulty)
• Teaches GPU programmers to implement a 2D DFT using row-column decomposition
• Key concepts: batched 1D FFTs, coalesced vs strided memory access for row/column passes, and shared-memory Cooley-Tukey butterfly kernels

Challenge Details

• Input: 2D complex signal of shape M × N stored as interleaved real/imaginary float pairs (row-major, M*N*2 total floats)
• Output: 2D DFT spectrum, same layout
• Performance test: M = 2,048, N = 2,048

Why this is interesting

The 2D FFT is a great GPU challenge because:

1. Row-wise FFTs have perfect memory coalescing, but column-wise FFTs access strided memory — forcing solvers to think about a transpose or shared-memory approach
2. Requires implementing a correct Cooley-Tukey butterfly in shared memory (handling power-of-2 vs non-power-of-2 sizes)
3. Classic primitive used in image processing, PDE solvers, and convolution-via-FFT

Checklist

• challenge.html starts with <p>, has <h2> sections, first example matches generate_example_test(), uses LaTeX matrices for 2D data
• challenge.py inherits ChallengeBase, all 6 methods present, assertions on shape/dtype/device, 10 functional test cases
• All 6 starter files present and follow format conventions
• Linting passes (pre-commit run --all-files)
• Validated with run_challenge.py --action run

🤖 Generated with Claude Code

[claude]

Challenge Validation: 2D FFT (Challenge #78)

Reviewed all files against the CLAUDE.md checklist and validated with a working CUDA solution.

Checklist Verification

challenge.html ✅

• Starts with <p>
• <h2> sections: Implementation Requirements, Example, Constraints
• First example (M=2, N=2, impulse signal) matches generate_example_test()
• Uses LaTeX \begin{bmatrix} consistently for 2D matrix display
• Performance bullet: M = 2,048, N = 2,048

challenge.py ✅

• Inherits ChallengeBase correctly
• All 6 required methods present
• reference_impl has shape and dtype assertions
• 10 functional test cases covering edge cases (1×1, 2×2), power-of-2 (16×16, 32×64), non-power-of-2 (3×5, 30×30), and realistic sizes (256×256, 512×512)
• Performance test (2048×2048 × 2 × float32 ≈ 32MB per tensor) fits 5× in 16GB VRAM

Starter files ✅ (all 6 present)

• CUDA/Mojo: use are device pointers (medium challenge, no parenthetical)
• PyTorch/Triton/CuTe: use are tensors on the GPU
• JAX: uses # signal is a tensor on GPU (grammatically correct for single input) with # return output tensor directly
• All starters compile/run but produce no correct output

Solution Validation

Wrote a pure CUDA row-column DFT implementation and submitted via run_challenge.py --action run:

Status: success ✓ Test passed

All 10 functional test cases passed and the performance test (2048×2048) completed successfully. Challenge is ready to merge.