Question

is there a JavaScript implementation of the Inverse Error Function?
This would implement the Gauss inverse error function. Approximations are ok.

Answer 1

Why yes. There is.

The following code uses built-in JavaScript functions and implments Abramowitz and Stegun’s algorithm as described here:

    function erfinv(x){
        var z;
        var a  = 0.147;                                                   
        var the_sign_of_x;
        if(0==x) {
            the_sign_of_x = 0;
        } else if(x>0){
            the_sign_of_x = 1;
        } else {
            the_sign_of_x = -1;
        }

        if(0 != x) {
            var ln_1minus_x_sqrd = Math.log(1-x*x);
            var ln_1minusxx_by_a = ln_1minus_x_sqrd / a;
            var ln_1minusxx_by_2 = ln_1minus_x_sqrd / 2;
            var ln_etc_by2_plus2 = ln_1minusxx_by_2 + (2/(Math.PI * a));
            var first_sqrt = Math.sqrt((ln_etc_by2_plus2*ln_etc_by2_plus2)-ln_1minusxx_by_a);
            var second_sqrt = Math.sqrt(first_sqrt - ln_etc_by2_plus2);
            z = second_sqrt * the_sign_of_x;
        } else { // x is zero
            z = 0;
        }
  return z;
}