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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/fdist/Fdist.md
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@@ -64,6 +64,33 @@ FDIST(source, period, d1, d2):
return betaReg(t, d1/2, d2/2)
```
## Performance Profile
### Operation Count (Streaming Mode)
F-distribution CDF uses regularized incomplete beta function — same cost structure as BetaDist.
| Operation | Count | Cost (cycles) | Subtotal |
| :--- | :---: | :---: | :---: |
| Input validation (d1, d2 > 0; x >= 0) | 3 | 2 cy | ~6 cy |
| Transform x to beta variable | 1 | 3 cy | ~3 cy |
| Regularized incomplete beta (Lentz CF, ~20 iter) | ~20 | 15 cy | ~300 cy |
| NaN guard + state update | 1 | 2 cy | ~2 cy |
| **Total** | **O(1)** | — | **~311 cy** |
O(1) per evaluation. Dominated by the continued fraction solver, same as Beta/T distributions. Degrees-of-freedom parameters affect convergence speed slightly.
### Batch Mode (SIMD Analysis)
| Operation | Vectorizable? | Notes |
| :--- | :---: | :--- |
| x transformation | Yes | Vector arithmetic |
| Continued fraction | No | Sequential convergence |
| Output assignment | Yes | Trivial |
No SIMD benefit for the core evaluation. Outer loop across observations parallelizable with PLINQ for bulk p-value computation.
## Resources
- Fisher, R.A. "On a Distribution Yielding the Error Functions of Several Well Known Statistics." Proc. International Mathematical Congress, Toronto, 1924.