When using these formulae, one must ensure that does not exceed 1 due to a floating point error ( is only real for ). only approaches 1 for "antipodal" points (on opposite sides of the sphere)—in this region, relatively large numerical errors tend to arise in the formula when finite precision is used. Because is then large (approaching , half the circumference) a small error is often not a major concern in this unusual case (although there are other great-circle distance formulas that avoid this problem). (The formula above is sometimes written in terms of the arctangent function, but this suffers from similar numerical problems near .)