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normal_cdf

Function normal_cdf 

Source
pub fn normal_cdf(x: f64) -> f64
Expand 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.