Stand-alone C# code for log(1+x)

See the C++ version of this page for documentation.

 

    using System;
    
    // compute log(1+x) without losing precision for small values of x
    static double LogOnePlusX(double 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;
    }
    

This code is in the public domain. Do whatever you want to with it, no strings attached.

Other versions: C++, Python

Stand-alone numerical code

 

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