Algorithms and Parallel Computing

11.10 EFFECT OF PROJECTION OPERATION ON DATA

Now that we know both the projection and scheduling functions, we are able to study how the input and output variables map to the projected domain .

11.10.1 Output Data M₁

The pipeline direction for the output data is mapped to the vector given by

(11.108)

Therefore, the output data will map to pipelining arrows along the k-axis (vertical lines) in the resulting multiprocessor architecture shown in Fig. 11.6.

The initialization and extraction points for the output data are found in Eq. 11.51. The initialization point for input M₁(c₁, c₂) map in to the point .

(11.109)

Similarly, the extraction point for input M₁(c₁, c₂) map in to the point .

(11.110)

11.10.2 Input Data M₂

The broadcast direction for input data is mapped to the vector ...