Consider the following computation: F = (Axy + Byz - Czx) (A + B ...

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Consider the following computation: F = (Axy + Byz - Czx) × (A + B − C) Suppose we wish to implement this computation using a multifunction pipeline consisting of two MUL- TIPLY stages, one ADD stage and one SUBTRACT. The scheduling diagram for one iteration of this computation is shown next. A X X X + B X X y C F X X X + Figure 1: Pipeline 1 Scheduling Diagram B Time Steps 0 1 2 3 4 5 a) Construct a reservation table for this pipeline (pipelinel) assuming availability of 2 MULTIPLYers, one ADDer and one SUBTRACTor. Find an optimal latency cycle for iterating 200 computations on pipelinel. b) To improve performance, we are going to use a 2-stage MULTIPLYer unit. We still assume 2 MUL- TIPLYers, one ADDer and one SUBTRACTor. Under the new arrangements, construct a new scheduling diagram and a new reservation table for this pipeline (pipeline2). Find an optimal latency cycle for 400 iterations on pipeline2. How do the speedups of pipelinel and pipeline2 compare? c) Let's assume each ADDer and SUBTRACTor has about 200ns delay and the original single-stage MULTIPLYer has 500ns delay. After partitioning, each MULTIPLY stage has about 250ns delay. Under these assumptions, which pipeline is potentially faster, after all? Consider the following computation: F = (Axy + Byz - Czx) × (A + B − C) Suppose we wish to implement this computation using a multifunction pipeline consisting of two MUL- TIPLY stages, one ADD stage and one SUBTRACT. The scheduling diagram for one iteration of this computation is shown next. A X X X + B X X y C F X X X + Figure 1: Pipeline 1 Scheduling Diagram B Time Steps 0 1 2 3 4 5 a) Construct a reservation table for this pipeline (pipelinel) assuming availability of 2 MULTIPLYers, one ADDer and one SUBTRACTor. Find an optimal latency cycle for iterating 200 computations on pipelinel. b) To improve performance, we are going to use a 2-stage MULTIPLYer unit. We still assume 2 MUL- TIPLYers, one ADDer and one SUBTRACTor. Under the new arrangements, construct a new scheduling diagram and a new reservation table for this pipeline (pipeline2). Find an optimal latency cycle for 400 iterations on pipeline2. How do the speedups of pipelinel and pipeline2 compare? c) Let's assume each ADDer and SUBTRACTor has about 200ns delay and the original single-stage MULTIPLYer has 500ns delay. After partitioning, each MULTIPLY stage has about 250ns delay. Under these assumptions, which pipeline is potentially faster, after all?

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