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Algorithms and Parallel Computing by Fayez Gebali

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18.6 DESIGN 1: DESIGN SPACE EXPLORATION WHEN s1 = [1 −1]

Figure 18.2 shows the DAG for the polynomial division algorithm based on our timing function choice s1. The equitemporal planes are the diagonal lines shown as gray lines on the right of the diagram. The associated time index values are shown at the right of the diagram. We note from the figure that the signals corresponding to the coefficients of B and the estimated q output are all pipelined, as indicated by the arrows connecting the nodes. However, the estimated partial results for Q and R are broadcast, as indicated by the diagonal lines without arrows. There are three simple projection vectors such that all of them satisfy Eq. 18.21 for the scheduling function in Eq. 18.17. The three projection vectors will produce three designs:

(18.22) c18e022

(18.23) c18e023

(18.24) c18e024

Figure 18.2 Directed acyclic graph (DAG) for polynomial division algorithm when s1 = [1 −1], n = 9, and m = 5.

c18f002

The corresponding projection matrices are

(18.25)

(18.26)

(18.27)

Our design space now allows for three configurations for each projection ...

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