Ah yes, another entry in the "I'll compute Fibonacci fast!... oh no" genre.

My favorite of the genre so far is https://www.youtube.com/watch?v=KzT9I1d-LlQ , which tries to compute a big Fibonacci number in under a second. It doesn't do the modulus, so it has to do big integer arithmetic, and so is really about doing big multiplications with FFTs. But then it funnily spins off into a series of videos as the author keeps dryly realizing their code is extremely wasteful (ending in finally just using GMP).