Skill v1.0.0
currentAutomated scan100/100version: "1.0.0" name: audio-numerics-review description: > Reviews audio DSP code for numerical correctness. Use when the user asks to review, audit, or check DSP code for correctness issues — filters, feedback loops, fixed-point arithmetic, accumulation loops, or any numeric computation in audio code. Trigger on "check this filter for NaN", "why does my reverb blow up?", "is this numerically stable?", "why do I hear DC in my output?". Pairs with audio-dsp-review (realtime safety); this skill covers numeric correctness. Flag issues proactively.
Audio Numerics Review
Floating-point is not real math. IEEE 754 edge cases — denormals, NaN propagation, catastrophic cancellation, precision loss — silently produce wrong audio output without crashing. You won't find them with a debugger; you find them by knowing where to look.
Step 1 — Find numeric-critical paths
Locate every function doing floating-point or integer DSP: filter state loops, feedback delay lines, envelope followers, RMS/energy accumulators, pitch detectors, fixed-point paths (CMSIS-DSP, SIMD int16/int32), any division whose denominator may be zero.
Step 2 — Scan for violations
| Violation | Where to look | Symptom | |
|---|---|---|---|
| Denormal floats | IIR state vars, reverb tanks, delay feedback | Sudden 100× CPU spike when signal decays | |
| NaN / Inf | Divisions, sqrt, acos/asin, peak normalizers | Silence or noise that can't be traced | |
| Catastrophic cancellation | DC-blocking filters, near-Nyquist biquads, first-order diff | Noise floor jumps, loss of precision | |
| Fixed-point overflow | Q15/Q31 multiply, CMSIS paths, SIMD int16 | Audible distortion / wrapping | |
| Precision loss | RMS/energy sums, mixing buses, long loops | Accumulated DC offset, incorrect levels | |
| FTZ/DAZ absent | prepareToPlay/stream-open — no mode setup | Denormals hit on some hosts but not others |
For code examples and platform-specific notes see references/numerics-pitfalls.md.
Step 3 — Write the review
## Audio Numerics Review: `[file / function]`### Verdict[Safe | Has critical violations | Warnings only] — one sentence summary### Critical Violations**[Category]: [description]**`file:line` — `offending code`Why: one sentence on the numeric riskFix: concrete suggestion### Warnings[same format]### What's Done Well[guarded divisions, double accumulators, FTZ setup, etc.]### Recommended Fixes (priority order)1. ...
Quick fix table
| Violation | Safe alternative | |
|---|---|---|
| Denormal in feedback | ScopedNoDenormals; FTZ+DAZ in prepareToPlay; DC-offset clamp | |
| Division by zero | (denom > 1e-6f) ? num/denom : fallback | |
sqrt/acos/asin unclamped | std::sqrt(std::max(0.f, x)), std::clamp inputs | |
| NaN propagating silently | assert(!std::isnan(y)) in debug; validate at entry points | |
| Cancellation in coefficients | Compute coefficients in double; use numerically stable forms | |
| Fixed-point overflow | Promote to wider type before multiply; __SSAT, CMSIS saturating ops | |
| Precision loss in long sum | double accumulator or Kahan compensated summation | |
| FTZ/DAZ absent | Set explicitly in prepareToPlay; use ScopedNoDenormals per-block |