Add challenge 107: Hadamard Transform (Medium)

[claude]

Summary

• Adds challenge 107: Hadamard Transform at medium difficulty.
• Solvers compute the orthonormal Walsh-Hadamard transform of every row of a (B, N) matrix, where N is a power of two, using the fast butterfly schedule (O(N log N)).
• Real-world inference relevance: Hadamard rotations are the core kernel in QuaRot / QuIP# style low-bit LLM quantization, where activations are rotated by a Hadamard matrix before INT4 / INT8 matmul to spread out outliers.
• Teaches per-row work distribution, shared-memory layout, and __syncthreads() between the log2(N) butterfly stages — meaningfully harder than an elementwise op, simpler than a full FFT.

Files

• challenges/medium/107_hadamard_transform/challenge.py — reference impl (pure PyTorch view/add/sub, works on CUDA and XLA), 10 functional tests covering N = 1, 2, 4, 16, 8, 32, 128, 1024, 64, 2048 with zeros, constants, mixed signs, and large rows.
• challenges/medium/107_hadamard_transform/challenge.html — problem statement with recursive H_N definition and stage-by-stage worked example.
• All 6 starters (.cu, .pytorch.py, .triton.py, .jax.py, .cute.py, .mojo).

Validation

• pre-commit run --all-files — passes.
• Verified reference impl locally: H @ H = I, constant rows produce a single non-zero coefficient at index 0, example [1, 2, 3, 4] → [5, -1, -2, 0].
• Submitted a CUDA solution via scripts/run_challenge.py --action submit on a T4 — all tests pass.

Test plan

• pre-commit run --all-files clean
• Reference impl matches by-hand Hadamard transform on the example
• CUDA reference solution passes full functional + performance suite on T4
• Reviewer spot-checks HTML rendering and example layout