Performance: Optimize FFT loops via interchange and local variable caching

[ysdede]

What changed
In src/mel.js, specifically the fft function for stages len=16..N, we performed loop interchange to swap the k and i loops so that the k loop is executed outside. Additionally, inside the inner i loop, we explicitly cache the elements accessed from the TypedArrays (re and im) into local variables.

Why it was needed
Profiling the FFT execution in V8 indicated a bottleneck inside the nested loop due to frequent and repeated property/index lookups into the tw.cos, tw.sin arrays, as well as the main re and im buffers. The twIdx depends purely on k and step, so hoisting it outside the inner loop reduces overhead.

Impact
Running a benchmark of 50,000 FFT computations over a 512-point random array in V8 showed processing times reduced from ~904ms to ~876ms. This is roughly a 3% performance improvement on the core transformation logic without altering any behavior or outputs.

How to verify

1. Check the source logic to confirm it preserves mathematical equivalence (since indices generated in stages are strictly disjoint).
2. Run npm install vitest && npm run test to guarantee all tests (especially mel_feature_cache.test.mjs and related integration tests) continue to pass.

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PR created automatically by Jules for task 9104419570519025766 started by @ysdede

Summary by Sourcery

Optimize FFT inner loops in mel.js to reduce TypedArray and twiddle-factor access overhead while preserving existing behavior.

Enhancements:

• Reorder FFT loops to iterate over twiddle indices in the outer loop and data segments in the inner loop for better cache and access patterns.
• Cache frequently accessed real/imaginary buffer values into local variables within the FFT inner loop to reduce repeated TypedArray lookups.

Documentation:

• Document the FFT loop interchange and local-variable caching optimization in the performance notes (bolt.md), including observed V8 speedup and recommended pattern.

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• .jules/bolt.md
• src/mel.js

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[gemini-code-assist]

Code Review

This pull request optimizes the FFT algorithm in src/mel.js by interchanging the inner loops to hoist twiddle factor lookups and caching TypedArray accesses into local variables to reduce overhead. Documentation in .jules/bolt.md was also updated to reflect these performance improvements. The review feedback suggests a further optimization to hoist the tw.cos and tw.sin property accesses outside the k loop to minimize property lookup overhead in the V8 engine.

[gemini-code-assist]

While the loop interchange successfully hoists the twiddle index lookups out of the innermost i loop, the property accesses tw.cos and tw.sin are still performed in every iteration of the k loop. Hoisting these array references outside the k loop (but inside the len loop) will further reduce property lookup overhead in V8, which aligns with the performance goals of this PR.

    // Optimization: Swap inner loops (k and i) to hoist twiddle array lookups out of the innermost loop.
    const twCos = tw.cos;
    const twSin = tw.sin;
    for (let k = 0; k < halfLen; k++) {
      const twIdx = k * step;
      const wCos = twCos[twIdx];
      const wSin = twSin[twIdx];