[WJW]

The Fibonacci series grows so fast that for "large" values of N you'll need a arbitrary size integer implementation anyway, so at that point you might as well go for a (non-IEEE) arbitrary size float type and get all the significant digits you need.

[nimithryn]

You’ll still need to compute the digits of Phi though, and then exponentiate that. My intuition is that using ints is still faster.