That it's the fastest is pretty surprising to me. Both Binet and matrix multiplication require exponentiation to n, which can be done in O(log n) multiplications (not n-1) using a clever recursion (and indeed numpy uses it). 2x2 matrices aren't exactly the hardest to multiply either, but I figured that the floating point operations with the Binet formula would enough baggage that would make it slower than the matrix method. Edit: I just saw Someone's comment - I guess that explains it.