Functional Fibonacci

Fib1.cs

public static ulong fib1(int n)
{
    ulong a = 0;
    ulong b = 1;
    for (int i = 0; i < n; i++)
    {
        ulong temp = a;
        a = b;
        b = temp + b;
    }
    return a;
}

Fib2.cs

public static int fib2(int n)
{
    return n > 1 ? fib2(n - 1) + fib2(n - 2) : n;
}

Fib3.cs

public static Func<int,int> fib3()
{
    Func<int, int> fib = null;
    fib = n => n <= 1 ? n : fib(n - 1) + fib(n - 2);
    return fib;
}

Fib4.cs

public static Func<int,int> fib4()
{
    var t = new Dictionary<int,int>();
    Func<int, int> fib = null;
    fib = x => 
    {
        if (t.ContainsKey(x)) return t[x];

        if (x <=2) return 1;

        var result = fib(x-1) + fib(x-2);
        t.Add(x,result);

        return result;
    };
    return fib;
}

Fib5.cs

public static Func<int,int> fib5()
{
    Func<int, int> fib = null;
    fib = n => n <= 1 ? n : fib(n - 1) + fib(n - 2);                       
    fib = fib.Memoize();
    return fib;
}

public static class Ext 
{
    public static Func<T, TResult> Memoize<T, TResult>(this Func<T, TResult> func)
    {
        var t = new Dictionary<T, TResult>();
        return n =>
        {
            TResult r;
            if (!t.TryGetValue(n, out r))
            {
                r = func(n);
                t.Add(n, r);
            }
            return r;
        };
    }
}

Fib6-7.cs

static readonly double sqrt5 = Math.Sqrt(5);
static readonly double p1 = (1 + sqrt5) / 2;
static readonly double p2 = -1 * (p1 - 1);

public static ulong fib6(int n) 
{
    double n1 = Math.Pow(p1, n);
    double n2 = Math.Pow(p2, n);
    return (ulong)((n1-n2)/sqrt5);
}

public static ulong fib7(int n)
{
    double n1 = 1.0;
    double n2 = 1.0;
    for (int i=0; i<n; i++)     // ist trotzdem Pure da identisch zu Math.Pow ?
    {
        n1*=p1;
        n2*=p2;
    }
    return (ulong)((n1-n2)/sqrt5);
}