Calculate the Fibonacci sequence in logarithmic time

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// calculates nth term of fibonacci, 1 indexed
Procedure Fib_Naive(int n):
    if(n < 3):
        return 1;
        end_if
    return Fib_Naive(n-1) + Fib_Naive(n-2)
end_Fib_Naive

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// calculates nth term of fibonacci, 1 indexed
Procedure Fib(int n):
        if(n < 3): return 1;
        int prev = 1;
        int cur = 1;
        for i = 3...n:
            int temp = cur;
            cur += prev;
            prev = temp;
        end_for
return cur;
end_Fib

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public int fib(int N) {
        if(N == 0) return 0;
        int[] sol = fibHelp(N);
        
        return sol[1];
    }
    
    public int[] fibHelp(int n) {
        if(n == 1) {
            return new int[] {0,1};
        }
        int m = n/2;
        
        int[] temp = fibHelp(m);
        
        int fPrev = temp[0];
        int fCur = temp[1];
        
        int prev = (fPrev * fPrev) + (fCur * fCur);
        int cur = fCur * (2 * fPrev + fCur);
        int next = prev + cur;
        
        if(n % 2 == 0) { 
            return new int[] {prev, cur};
        }
        else {
            return new int[] {cur, next};
        }
    }

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