Amdahl's Law We are asked to assess the relative merits of adding a specialized matrix multiplication unit to a computer. This unit will be able to provide a speedup of 20 during execution on the matrix multiplication unit compared to operation without the matrix multiplication unit. 1. Draw a graph plotting overall speedup as a percentage of the computation performed on the matrix multiplication unit. [y-axis overall speedup, x-axis percent matrix mul- tiplication unit utilization.] Make sure that you also tabulate the speedup for the case of matrix multiplication unit utilization at 25%, 50%, 75% and 100%. 2. What percent of matrix multiplication unit utilization results in an overall speedup of two? 3. What percent of matrix multiplication unit utilization results in half the maximum overall speedup? 4. Assume that the matrix multiplication unit can be utilized by 70% of application programs. It is suggested by the hardware team that the matrix multiplication unit speedup of 20 can be doubled, albeit at significant engineering cost. An alternative would be to adopt compiler optimizations. In such a case, how much additional time would the compiler optimization have to dedicate to using the matrix multiplication unit with a speedup of 20 in order to match the overall performance under the new matrix multiplication unit? Provide your answers to two decimal points of precision (or leave as a fraction). Analyzing Parallelization with Amdahl's Law Consider an application that executes at different points in time using 1, 2 and 32 cores. The fraction of time for which the application executes on one core is 5%. What fraction of time does the application execute using 2 and 32 cores if the final overall speedup is 4? Specialized hardware for matrix multiplication represents a central theme in hardware for accelerating deep learning algorithms, e.g. Google's Tensor Processing Unit.