how to calculate 2^n modulo 1000000007 , n = 10^9

Question

what is the fastest method to calculate this, i saw some people using matrices and when i searched on the internet, they talked about eigen values and eigen vectors (no idea

Answer 1

C code for calculating 2^n

    const int mod = 1e9+7;

    //Here base is assumed to be 2
    int cal_pow(int x){
        int res;
        if (x == 0) res=1;
        else if (x == 1)    res=2;
        else {
            res = cal_pow(x/2);
            if (x % 2 == 0) 
                res = (res * res) % mod;
            else
                res = (((res*res) % mod) * 2) % mod;
        }
        return res;
    }