GFact | Finding nth Fibonacci Number using Golden Ratio

We have discussed different methods to find nth Fibonacci Number. Following is another mathematically correct way to find the same. nth Fibonacci Number : Here φ is golden ratio with value as The above formula seems to be good for finding nth Fibonacci Number in O(Logn) time as integer power of a number can be calculated in O(Logn) time. But this solution doesn't work practically because φ is stored as a floating point number and when we calculate powers of φ, important bits may be lost in the process and we may get incorrect answer. References: https://www.youtube.com/watch?v=-EQTVuAhSFY https://en.wikipedia.org/wiki/Fibonacci_number