(50g) Normal Distribution

[Albert Chan]

Hi, John Keith

You are right. On a calculator, 3 Exp method maybe faster.

I did the test on the computer. Cost of PDF function is dominated by Exp.
2 Exp method take 2X as long, 3 Exp method take 2.83X (using C language)

"Splitting" factor 1/√(2 pi) inside Exp reduce error somewhat:

PHP Code:

def pdf(x, k=0.08106146679532726, exp=math.exp, floor=math.floor):
    b = 0.5 * floor(x * x) # k = 1 - ln(√(2 pi))
    xi = floor(x)          # same k for binary or decimal float
    xf = x - xi
    return exp(-b - 1.) * exp(b - 0.5*xi*xi - xi*xf - 0.5*xf*xf + k)