The Anton communication network is a 3D, 8 8 8 torus, where each node in

The Anton communication network is a 3D, 8 х 8 х 8 torus, where each node in the system has six links to neighboring nodes. Latency for a packet to transit single link is about 50 ns. Ignore on-chip switching time between links for this exercise.

a. What is the diameter (maximumnumber of hops between a pair of nodes) of the communication network? Given that diameter, what is the shortest latency required to broadcast a single value from one node of the machine to all 512 nodes of the machine?

b. Assuming that adding up two values takes zero time, what is the shortest latency to add up a sum over 512 values to a single node, where each value starts on a different node of the machine?

c. Once again assume that you want to perform the sum over 512 values, but you want each of the 512 nodes of the system to end up with a copy of the sum. Of course you could perform a global reduction followed by a broadcast. Can you do the combined operation in less time? This pattern is called an all-reduce. Compare the times of your all-reduce pattern to the time of a broadcast from a single node or a global sum to a single node. Compare the bandwidth used by the all-reduce pattern with the other patterns.