Yeah, I almost said “suppose you were writing a Fibonacci program because who did you annoy to make this your life now...”
Like, obviously you’re not going to be writing `fib(n)` for real. I still claim that other languages — not just Python, either — make it easier to express cleverer algorithms than C does. You can’t write anything in Rust you can’t write in C, but it’ll probably be easier to say it more efficiently, and more correctly, in Rust. And much of the time, using a better design is going to blow compiler improvements out of the water.
(The professor was right if you limit the scope of the statement to “programs written in C or assembler”, of course. Unless you’re a freaking genius, a compiler’s going to write better object code.)
If for some reason you really wanted to compute Fib(n) for ridiculously large numbers of n, you would probably use that [Fib(n), Fib(n-1)] = A [Fib(n-1), Fib(n-2)] for the transition matrix A = [[1, 1], [1, 0]] and thus [Fib(n+1), Fib(n)] = A^n [Fib(1), Fib(0)] and then use exponentiation by squaring to compute A^n directly and thus Fib(n) in log_2(n) steps.
You'd unroll it to a loop on both C and Python. Fibonacci doesn't need a cache. It needs K previous values, where K=1.