[cdhainaut]

Summary

Replace the clipped exponential form of the analysis-confidence sigmoid with the mathematically equivalent overflow-free form

0.5 * (1 + tanh(x / 2))

and add a public-API regression test that evaluates a vectorized case far outside the training distribution and checks that both the forward values and CasADi MX reverse derivatives remain finite.

Context

In NeuralFoil 0.2.2, sufficiently negative confidence logits can overflow exp(-x). The forward aerodynamic outputs remain finite, but the overflowing node can contaminate an MX reverse sweep with 0 * inf, producing NaN derivatives.

Current master already prevents the reproducer from failing by clipping the sigmoid input. The tanh form removes the overflowing exponential path and the float64-derived clipping constants altogether while preserving the sigmoid values to floating-point precision over the active range.

Validation

python -m pytest tests -q: 32 passed.

The regression case produces non-finite MX reverse entries at indices 5, 6, and 7 with the installed NeuralFoil 0.2.2, and finite forward and reverse values with this change. The two sigmoid forms differ by at most 2.22e-16 over 20,001 points on [-40, 40].

Fixes #10.