util.cpp

const double MAXLOG = 7.09782712893383996732224E2;	// log(MAXNUM)
const double biginv =  2.22044604925031308085e-16;
const double big = 4.503599627370496e15;
const double MACHEP = 1.11022302462515654042E-16;

double igam(double a, double x);
double igamc(double a, double x);
double normal_CDF(double x);

double igamc(double a, double x){
	double ans, ax, c, yc, r, t, y, z;
	double pk, pkm1, pkm2, qk, qkm1, qkm2;

	if ( (x <= 0) || ( a <= 0) )
		return( 1.0 );

	if ( (x < 1.0) || (x < a) )
		return( 1.e0 - igam(a,x) );

	ax = a * log(x) - x - lgamma(a);

	if ( ax < -MAXLOG ) {
		printf("igamc: UNDERFLOW\n");
		return 0.0;
	}
	ax = exp(ax);

	/* continued fraction */
	y = 1.0 - a;
	z = x + y + 1.0;
	c = 0.0;
	pkm2 = 1.0;
	qkm2 = x;
	pkm1 = x + 1.0;
	qkm1 = z * x;
	ans = pkm1/qkm1;

	do {
		c += 1.0;
		y += 1.0;
		z += 2.0;
		yc = y * c;
		pk = pkm1 * z  -  pkm2 * yc;
		qk = qkm1 * z  -  qkm2 * yc;
		if ( qk != 0 ) {
			r = pk/qk;
			t = fabs( (ans - r)/r );
			ans = r;
		}
		else
			t = 1.0;
		pkm2 = pkm1;
		pkm1 = pk;
		qkm2 = qkm1;
		qkm1 = qk;
		if ( fabs(pk) > big ) {
			pkm2 *= biginv;
			pkm1 *= biginv;
			qkm2 *= biginv;
			qkm1 *= biginv;
		}
	} while ( t > MACHEP );

	return ans*ax;
}

double igam(double a, double x){
	double ans, ax, c, r;

	if ( (x <= 0) || ( a <= 0) )
		return 0.0;

	if ( (x > 1.0) && (x > a ) )
		return 1.e0 - igamc(a,x);

	/* Compute  x**a * exp(-x) / gamma(a)  */
	ax = a * log(x) - x - lgamma(a);
	if ( ax < -MAXLOG ) {
		printf("igam: UNDERFLOW\n");
		return 0.0;
	}
	ax = exp(ax);

	/* power series */
	r = a;
	c = 1.0;
	ans = 1.0;

	do {
		r += 1.0;
		c *= x/r;
		ans += c;
	} while ( c/ans > MACHEP );

	return ans * ax/a;
}

double normal_CDF(double x){
    return (1+erf(x/sqrt(2)))/2;
}