package main

import "math"

// NormCDF computes the Cumulative Density Function of a Standard Normal
// Distribution.
// Code adapted from https://www.johndcook.com/blog/cpp_phi/
func NormCDF(z float64) float64 {
	// constants
	var a1, a2, a3, a4, a5, p, t, y, sign float64

	a1 = 0.254829592
	a2 = -0.284496736
	a3 = 1.421413741
	a4 = -1.453152027
	a5 = 1.061405429
	p = 0.3275911

	sign = 1
	if z < 0 {
		sign = -1
	}
	x := math.Abs(z) / math.Sqrt2

	t = 1.0 / (1.0 + p*x)
	y = 1.0 - (((((a5*t+a4)*t)+a3)*t+a2)*t+a1)*t*math.Exp(-x*x)

	return 0.5 * (1.0 + sign*y)
}

// NormPDF computes the Probability Density Function of a Standard Normal
// Distribution.
func NormPDF(z float64) float64 {
	return 1 / math.Sqrt(2*math.Pi) * math.Exp(-math.Pow(z, 2)/2)
}