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validation and profiles

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Miha Kralj
2026-02-26 22:02:52 -08:00
parent 9ab37c1200
commit 8a1ba95173
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lib/numerics/normdist/Normdist.md
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@@ -86,6 +86,33 @@ NORMDIST(source, period, mu, sigma):
return 0.5 * (1 + erf)
```
## Performance Profile
### Operation Count (Streaming Mode)
Normal distribution CDF uses an erfc() rational approximation (Abramowitz & Stegun) — O(1) closed form.
| Operation | Count | Cost (cycles) | Subtotal |
| :--- | :---: | :---: | :---: |
| z = (x - mu) / sigma | 1 | 4 cy | ~4 cy |
| erfc(z / sqrt(2)) rational approx | 1 | 15 cy | ~15 cy |
| Scale by 0.5 | 1 | 1 cy | ~1 cy |
| NaN guard + state update | 1 | 2 cy | ~2 cy |
| **Total** | **O(1)** | — | **~22 cy** |
O(1) per evaluation. The rational polynomial erfc approximation has 7-term expansion, accurate to 1e-7. Division by sigma precomputed as multiplication by 1/sigma.
### Batch Mode (SIMD Analysis)
| Operation | Vectorizable? | Notes |
| :--- | :---: | :--- |
| z = (x - mu) / sigma | Yes | Vector<double> FMA |
| erfc() rational polynomial | Partial | Polynomial evaluable via Horner + Vector |
| Final scale | Yes | Vector multiply |
The Horner polynomial evaluation in erfc() is SIMD-vectorizable. Expected 3× batch speedup over scalar using Vector<double> for the polynomial terms.
## Resources
- Gauss, C.F. "Theoria Motus Corporum Coelestium." 1809.