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validation and profiles

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Miha Kralj
2026-02-26 22:02:52 -08:00
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lib/numerics/expdist/Expdist.md
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@@ -63,6 +63,34 @@ EXPDIST(source, period, lambda):
return 1.0 - exp(-lambda * x)
```
## Performance Profile
### Operation Count (Streaming Mode)
Exponential distribution CDF = 1 - exp(-lambda * x) — a trivially cheap closed-form evaluation.
| Operation | Count | Cost (cycles) | Subtotal |
| :--- | :---: | :---: | :---: |
| Input validation (lambda > 0; x >= 0) | 2 | 2 cy | ~4 cy |
| lambda * x multiply | 1 | 3 cy | ~3 cy |
| exp(-lambda*x) | 1 | 20 cy | ~20 cy |
| 1 - exp result | 1 | 1 cy | ~1 cy |
| NaN guard + state update | 1 | 2 cy | ~2 cy |
| **Total** | **O(1)** | — | **~30 cy** |
Cheapest distribution implementation — single exp() call dominates. No series expansion, no iterative solver.
### Batch Mode (SIMD Analysis)
| Operation | Vectorizable? | Notes |
| :--- | :---: | :--- |
| lambda * x | Yes | Vector<double> multiply |
| exp() | Partial | _mm256_exp_pd with SVML; or scalar loop |
| 1 - result | Yes | Vector subtract |
With SVML exp: 4 outputs per AVX2 cycle. Without SVML: scalar loop but still O(1) per output. Batch is trivially parallelizable.
## Resources
- Erlang, A.K. "The Theory of Probabilities and Telephone Conversations." Nyt Tidsskrift for Matematik B, 1909.