Method erf

ij/src/main/java/ij/util/IJMath.java:18–28

(double x)

	 * Except for low and high x, it is based on the type erf(x) = sgn(x) * sqrt(1-exp(-x^2*f(x)),
	 * with the function f(x) having a smooth transition from 4/pi = 1.273... at x=0 to 1 at high x */
	public static double erf(double x) {
		double x2 = sqr(x);
		if (x2 < 1e-8)
			return (2/Math.sqrt(Math.PI))*x*(1+x2*(-1./3.+x2*(1./10.)));  // Taylor series for low x
		double erf = x2 > 36 ? 1 :  //the polynomials go crazy for some large x2; erf(6) is 1 - 2e-17, less than ulp from 1
				Math.sqrt(1 - Math.exp(-sqr(x*((2/Math.sqrt(Math.PI) - A) + A *
				(1 + x2*x2*(B + x2*(C + x2*(H + x2*I)))) /
				(1 + x2*(D + x2*(E + x2*(F + x2*G))))
				))));
		return x>0 ? erf : -erf; //could be Math.copySign in Java 1.6 & up
	}

	static double sqr(double x) {
		return x*x;