function retval = atanNUMA(x, n)

a = 2.0^(-n/2);
b = x / (1.0 + sqrt(1.0+x^2));
c = 1.0;
d = 1.0;
vec = [];
while 1.0-a > 2^(-n)
    c = 2*c / (1.0 + a);
    d = 2*a*b / (1.0 + b^2);
    d = d / (1.0 + sqrt(1.0 - d^2));
    d = (b + d) / (1.0 - b*d);
    b = d / (1.0 + sqrt(1.0 + d^2));
    a = 2*sqrt(a) / (1.0+a);
    vec = [vec c*log((1+b)/(1-b))];
end
retval = vec;
end