April 2011
Intermediate to advanced
364 pages
10h 8m
English
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17.6 DAG NODE PROJECTION
The projection operation is a many-to-one function that maps several nodes of
the DAG onto a single node, which constitutes the resulting 
. Thus, several
operations in the DAG are mapped to a single thread. The projection operation allows thread or hardware economy by multiplexing several operations in the
DAG on a single node in 
. Chapters 10 and 11 explained how to perform the projection operation using a projection matrix P. To obtain the projection matrix, we need to define a desired projection direction d. The vector d belongs to the null- space of P. Since we are dealing with a 2-D DAG, matrix P is a row vector and d is a column vector. A valid projection direction d must satisfy the inequality
There are many projection vectors that satisfy Eq. 17.27 for the scheduling function s1. For simplicity, we choose three of them:
(17.28)
(17.29)
(17.30)
The corresponding projection matrices are given by
(17.31)
(17.32)
(17.33) ...
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