In Problem 5.12, we were able to reduce the CPE for the prefix-sum computation to 3.00, limited by the latency of floating-point addition on this machine. Simple loop unrolling does not improve things. Using a combination of loop unrolling and reassociation, write code for a prefix sum that achieves a CPE less than the latency of floating-point addition on your machine. Doing this requires actually increasing the number of additions performed. For example, our version with two-way unrolling requires three additions per iteration, while our version with four-way unrolling requires five. Our best implementation achieves a CPE of 1.67 on our reference machine.
Determine how the throughput and latency limits of your machine limit the minimum CPE you can achieve for the prefix-sum operation.