Module normal 

Normal (Gaussian) distribution — pdf / cdf / quantile, the canonical engine-wide implementation. The CDF is ½·erfc(−z/√2) over the shared super::special::erfc (full precision), and the quantile is Acklam’s rational inverse refined by one Halley step (≈ machine precision). Domain libraries (financial_modeling’s Black–Scholes, etc.) should call these instead of re-deriving a local normal_cdf.

Functions

cdf

Normal cdf with mean mu, std-dev sigma (> 0).

pdf

Normal pdf with mean mu, std-dev sigma (> 0).

quantile

Inverse normal cdf with mean mu, std-dev sigma.

standard_cdf

Standard-normal cdf Φ(z) = ½·erfc(−z/√2).

standard_pdf

Standard-normal pdf φ(z).

standard_quantile

Inverse standard-normal cdf Φ⁻¹(p), 0 < p < 1 (Acklam + one Halley refinement). ±∞ at the endpoints.

two_sided_p

Two-sided p-value for a standard-normal (z) statistic: 2·(1 − Φ(|z|)).