In C++, you will write code to empirically compare the performance of a naive and a fast 2 2 matrix exponentiation method. The naive matrix exponentiation method consists of successive computation of matrix products: mn = Qn i=1 m = m m m m | {z } n times . The fast matrix exponentiation algorithm involves successive squaring.

Sample Run:

Enter the top-left, top-right, bottom-left and bottom-right entries of the first matrix: 52 45 87 95 'Enter the top-left, top-right, bottom-left and bottom-right entries of the second matrix: 452 789 654 123

m1 = [[52, 45], [87, 95]]

m2 = [[452, 789], [654, 123]]

(m1 - m2)(m1 + m2) = ........

|(m1 - m2)(m1 + m2)| = ........

Which Fibonacci number do you wish to compute? 250 Fib(250) = ........

Empirical Analysis of Naive vs Fast Matrix Exponentiation in Generating 19 Terms of the Fibonacci Sequence