Efficient implementations of Fibonacci function with interesting results

[stevengj]

@chakravala

the performance is bad because you are using naive implementations. It would probably be much quicker using arb with Nemo package and using the Chakravala algorithm to approximate the square root.

The sqrt function for BigFloat is calling mpfr_sqrt from the MPFR library; if MPFR is using a “naive” algorithm, you should file an issue with MPFR, but I’m skeptical of that assertion without evidence.