pub fn normal_cdf(x: f64) -> f64Expand description
Standard normal cumulative distribution function $\Phi(x)$, evaluated with Hart’s rational approximation.
Every option price, delta, theta and rho in this module passes through here, so this
function’s accuracy is their ceiling. Hart’s form holds close to double precision across the
body and both tails — tests/golden_reference_option_diff.rs pins it against independently
generated reference values. The earlier Abramowitz & Stegun 7.1.26 approximation used here was accurate
to about $1.5 \times 10^{-7}$ absolute, which showed up as errors of that order times the
price level in every quantity derived from it.
Beyond $|x| = 37$ the result is 0 or 1 in double precision, and is returned as such.