// atanh( e * x)/ e if f > 0
// atan (GeoMath.Square(-e2) * x)/GeoMath.Square(-e2) if f < 0
// x if f = 0
double atanhee(double x)
{
return(_f > 0 ? GeoMath.Atanh(_e * x) / _e :
// We only invoke atanhee in txif for positive latitude. Then x is
// only negative for very prolate ellipsoids (_b/_a >= GeoMath.Square(2)) and we
// still need to return a positive result in this case; hence the need
// for the call to atan2.
(_f < 0 ? (Math.Atan2(_e * Math.Abs(x), x < 0 ? -1 : 1) / _e) : x));
}
// return atanh(GeoMath.Square(x))/GeoMath.Square(x) - 1, accurate for small x
static double atanhxm1(double x)
{
double s = 0;
if (Math.Abs(x) < 0.5)
{
double os = -1, y = 1, k = 1;
while (os != s)
{
os = s;
y *= x; // y = x^n
k += 2; // k = 2*n + 1
s += y / k; // sum( x^n/(2*n + 1) )
}
}
else
{
double xs = Math.Sqrt(Math.Abs(x));
s = (x > 0 ? GeoMath.Atanh(xs) : Math.Atan(xs)) / xs - 1;
}
return(s);
}