A GO implementation of the hyper geometric value calculation algorithm found at http://www.sciencedirect.com/science/article/pii/S1570866706000499

hyperquick.go

package hypergeometric

func invJm(n, x, N, m float64) float64 {
    return (1-x/(m+1))/(1-(n-1-x)/(N-1-m));
}

func HyperQuick(n,x,N,M int64) float64 {
/*
	Given N balls, M of which are black and the rest are white, 
	what is the probability C(n,x,N,M) that out of n balls selected 
	uniformly at random without replacement, at most x are black? 

	HyperQuick algorithm
	http://www.sciencedirect.com/science/article/pii/S1570866706000499
*/

 	n_float := float64(n)
 	x_float := float64(x)
 	N_float := float64(N)

	//accuracy e
 	var e float64
 	e = 0.000001

	//loop1: fixed number of steps
	var s, ak, bk float64
	var k int64
	s =1.0

	for k=x; k < M-1; k++ {
		s = s * invJm(float64(n_float), float64(x), float64(N), float64(k)) + 1.0
	}

	//loop2: variable number of steps according to accuracy e
	ak = s;
	bk = s;
	k = M-2

	epsk:=2*e;

	for ((k<N-(n-x)-1) && (epsk>e)) {
		ck := ak/bk;
		k = k+1;
		jjm := invJm(n_float,x_float,N_float,float64(k));
		bk = bk*jjm+1.0;
		ak = ak*jjm;
		epsk = (N_float-(n_float-x_float)-1-float64(k))*(ck-ak/bk);
	}

	result := 1 - (ak/bk-epsk/2);
	return result
}