Add performance analysis: implementation gaps vs structural limits relative to FFTW

[pankgeorg]

A written analysis of why FFTA is slower than FFTW on each size class, separating what is an implementation gap (fixable within the current design) from what is structural (pure-Julia, size-generic recursion, no SIMD codelet library), with a per-class ceiling estimate and a prioritised work list.

It is based on the sweep in #128 (benchmark/REPORT.md, which this document links to — the link resolves once #128 lands) plus targeted experiments: a precomputed-twiddle variant of the O(n²) leaf, a breakdown of the Bluestein and rfft paths, FFTW's actual plan choices on the same sizes, and a small @generated straight-line codelet generator to measure Julia's compile-latency cost for codelets (< 1 s up to 64 points, 1.0–1.6× FFTW).

Short version: no size class is structurally stuck at ≥ 4×; the large gaps (composites with factors 5/7, primes, small ND, 2D rfft) come from twiddles being recomputed per execution, O(n²) leaves without codelets, per-call Bluestein allocation, and the mapslices/full-complex real paths. The structural residue is the last ~1.3–2× on cache-resident sizes (SIMD across butterflies) and the cache-blocked large-n path that FFTW's MEASURE planner finds.

I'll open an issue with the proposed PR sequence so the plan can be discussed before code lands.

Update: a companion run of the suite on an x86-64 (AVX2) machine is now part of #128, and its per-class comparison against the aarch64 run showed that the x86-64 penalty is concentrated on the non-radix-4 kernels (5/7-rich composites up to 3.8× worse relative to FFTW, powers of two only 1.21×), not spread uniformly as a vector-width effect. §5.3a records the data, §5.3 and the ceiling table (§6) are adjusted per class, and radix-5/7 butterflies move up the work list on x86-64.

[codecov]

Codecov Report

✅ All modified and coverable lines are covered by tests.
✅ Project coverage is 98.80%. Comparing base (7aeb327) to head (a5e9900).
⚠️ Report is 4 commits behind head on main.

Additional details and impacted files

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  Coverage   98.80%   98.80%           
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  Files           5        5           
  Lines         585      585           
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  Hits          578      578           
  Misses          7        7           

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