Test if a number is fibonacci

Question

I know how to make the list of the Fibonacci numbers, but i don\'t know how can i test if a given number belongs to the fibonacci list - one way that comes in mind is genera

Answer 1

Based on earlier answers by me and psmears, I've written this C# code.

It goes through the steps slowly, and it can clearly be reduced and optimized:

// Input: T: number to test.
// Output: idx: index of the number in the Fibonacci sequence.
//    eg: idx for 8 is 6. (0, 1, 1, 2, 3, 5, 8)
// Return value: True if Fibonacci, False otherwise.
static bool IsFib(long T, out int idx)
{
    double root5 = Math.Sqrt(5);
    double PSI = (1 + root5) / 2;

    // For reference, IsFib(72723460248141) should show it is the 68th Fibonacci number

    double a;

    a = T*root5;
    a = Math.Log(a) / Math.Log(PSI);
    a += 0.5;
    a = Math.Floor(a);
    idx = (Int32)a;

    long u = (long)Math.Floor(Math.Pow(PSI, a)/root5 + 0.5);

    if (u == T)
    {
        return true;
    }
    else
    {
        idx = 0;
        return false;
    }
}

Testing reveals this works for the first 69 Fibonacci numbers, but breaks down for the 70th.

F(69) = 117,669,030,460,994 - Works
F(70) = 190,392,490,709,135 - Fails

In all, unless you're using a BigInt library of some kind, it is probably better to have a simple lookup table of the Fibonacci Numbers and check that, rather than run an algorithm.

A list of the first 300 Numbers is readily available online.

But this code does outline a workable algorithm, provided you have enough precision, and don't overflow your number representation system.