In this exercise, we examine the effect of the interconnection network topology on the clock cycles per instruction (CPI) of programs running on a 64-processor distributed-memory multiprocessor. The processor clock rate is 3.3 GHz and the base CPI of an application with all references hitting in the cache is 0.5. Assume that 0.2% of the instructions involve a remote communication reference. The cost of a remote communication reference is (100 + 10h) ns, where h is the number of communication network hops that a remote reference has to make to the remote processor memory and back. Assume that all communication links are bidirectional. a. Calculate the worst-case remote communication cost when the 64 processors are arranged as a ring, as an 8x8 processor grid, or as a hypercube. (Hint: The longest communication path on a 2n hypercube has n links.)
b. Compare the base CPI of the application with no remote communication to the CPI achieved with each of the three topologies in part (a).
c. How much faster is the application with no remote communication compared to its performance with remote communication on each of the three topologies in part (a).