Gamma Function

[buttshark]

I'm sure someone's done it already, but screw it; here you go.

Code: Select all

gamma(n)
{
	static pi := 3.14159265358979323846
	static g := 5.2421875
	static coeffs := [.99999999999999709182, 57.156235665862923517, -59.597960355475491248, 14.136097974741747174, -0.49191381609762019978, .000033994649984811888699, .000046523628927048575665, -.000098374475304879564677, .00015808870322491248884, -.00021026444172410488319, .00021743961811521264320, -.00016431810653676389022, .000084418223983852743293, -.000026190838401581408670, .0000036899182659531622704]
	if(Mod(n, 1))
	{
		if(n < 0)
		{
			denom := n
			loop % -floor(n) - 1
				denom *= n + A_Index
			return gamma(Mod(n + 1, 1)) / denom
		}
		else
		{
			n1 := coeffs[1]
			loop % coeffs.length() - 1
				n1 += coeffs[A_Index + 1] / (n + A_Index)
			return n1 * sqrt(2 * pi) / n * n3 := (n + g) ** (n + 0.5) * exp(-n - g)
		}
	}
	else
	{
		if(n > 0)
		{
			ret := 1
			loop % n - 2
				ret *= A_Index + 1
			return ret
		}
	}
}