private static DecimalX lnNewton(DecimalX x, int scale)
{
DecimalX term;
var sp1 = scale + 1;
var n = x;
// Convergence tolerance = 5*(10^-(scale+1))
var tolerance = DecimalX.Create(5);
tolerance = tolerance.MovePointLeft(sp1);
// Loop until the approximations converge
// (two successive approximations are within the tolerance).
do
{
// e^x
var eToX = x.Exp(sp1);
// (e^x - n)/e^x
term = eToX.Subtract(n).CDivide(eToX, sp1, RoundingMode.Down);
// x - (e^x - n)/e^x
x = x.Subtract(term);
} while (term.CompareTo(tolerance) > 0);
x = DecimalX.Rescale(x, -scale, RoundingMode.HalfEven);
return(x);
}