Polyhedral Process Networks - Signal Processing Systems - page 1332

Fig. 7 A process network corresponding to the sequential program in Fig. 1 exploiting reuse

the same statement. Any value that was already read by the given process will then
be obtained from the last of those reads from the same process instead of from the
process that actually wrote the value.

Example 15. In Example 1 , we have shown a process network (Fig. 2 ) derived from
the code in Fig. 1 without exploiting reuse inside the Sobel process. Figure 7 shows
a process network derived from the same code, but in this case with reuse. The
first network was created by only considering the write to array a in Line 13 of
Fig. 1 as a possible source for the reads in Line 6, while the second was created
by also considering all the reads in Line 6 as possible sources. It is clear from the
figures that in the first network the Sobel process does not communicate with itself,
while in the second network it does. What may not be apparent, however, is that in
both networks there are nine channels from the ReadImage process to the Sobel
process. The second figure only shows three channels because the software used
to generate these process networks automatically combines some communication
channels if this combination does not affect the type of the channels, as explained
at the end of Sect. 6.1 . The number of channels from the first process to the second
has not changed because each read in Line 6 reads at least one value that is not
read by any of the other reads. However, even though the number of channels may
not have changed, the number of values transmitted over these channels has been
drastically reduced. In particular, the image read by the ReadImage process is
now transmitted only once, instead of nearly nine times.
Performing

last (W+R) before R under S;
with W , R and S as in Example 14 produces the same results as before because R
only includes a single access relation and there is no reuse within a single access. If
we change it to include all reads from the given statement, then this operation would
exploit the reuse in the combined accesses.