bench: spectral-analysis perf spike (window asm ladder + pipeline profile)

[tfcollins]

Summary

Exploratory, self-contained performance spike under bench/ (no src/ changes) investigating how fast genalyzer's spectral-analysis math can go, down to hand-tuned AVX-256 assembly. Two pieces:

1. Blackman-Harris window optimization ladder (bench/bh_window_bench.cpp, bench/bh_window_asm.S): T0 baseline (std::cos ×3/sample) → T1 no-transcendentals (phasor recurrence) → T2 AVX-256 intrinsics → T3 hand-tuned asm → T4 multithreaded. Each tier verified vs T0 (max-abs-err < 1e-9).
2. Real-pipeline profile (bench/profile/): stage breakdown of the actual fft() path.

Findings

• Window: the ~8–10× single-core speedup comes entirely from killing the transcendentals (T0→T1). SIMD (T2) and hand-tuned assembly (T3) add essentially nothing — once the data-independent window is precomputed, the apply loop is memory-bandwidth-bound. Multicore (T4) only wins at large nfft+navg.
• Pipeline profile (the bigger result): with averaging (navg>1), reduce_and_scale — the per-bin std::arg(atan2) + std::polar(sincos) stage — is 47–68% of the entire transform, 1.5–4.6× the FFT itself. Since analysis consumes mean-square magnitude and only reads phase at a handful of tone bins, most of those navg×nfft atan2 calls appear to be wasted work. This is the next optimization target.

Build/run: bench/build.sh && bench/bh_window_bench. Details in bench/README.md, bench/profile/PROFILE.md, and the spec/plan/session-state docs under docs/superpowers/.

Test Plan

• All tier correctness gates pass (anchor + per-tier vs T0, incl. renorm-coverage)
• No src/ modifications (profiling instrumentation was temporary, reverted)
• Reviewer sanity-check of the AVX-256 asm kernel and profiling methodology

Note: throwaway research spike for measurement/learning, not intended as production code.