picomath

module Phi (phi) where

phi x = let
    -- constants
    a1 =  0.254829592
    a2 = -0.284496736
    a3 =  1.421413741
    a4 = -1.453152027
    a5 =  1.061405429
    p  =  0.3275911

    -- Save the sign of x
    sign = if x >= 0 then 1 else -1
    a = abs(x)/sqrt(2.0)

    -- A&S formula 7.1.26
    t = 1.0/(1.0 + p*a)
    y = 1.0 - (((((a5*t + a4)*t) + a3)*t + a2)*t + a1)*t*exp(-a*a)
    in 0.5*(1.0 + sign*y)