public static double Log1P(double x)
{
//Author: John D Cook, licence: public domain
// http://www.johndcook.com/blog/csharp_log_one_plus_x/
if (x <= -1.0)
{
string msg = String.Format("Invalid input argument: {0}", x);
throw new ArgumentOutOfRangeException(msg);
}
if (Math.Abs(x) > 1e-4)
{
// x is large enough that the obvious evaluation is OK
return Math.Log(1.0 + x);
}
// Use Taylor approx. log(1 + x) = x - x^2/2 with error roughly x^3/3
// Since |x| < 10^-4, |x|^3 < 10^-12, relative error less than 10^-8
return (-0.5*x + 1.0)*x;
}