By Guang R. Gao

This monograph advanced from my Ph. D dissertation accomplished on the Laboratory of computing device technology, MIT, throughout the summer time of 1986. In my dissertation I proposed a pipelined code mapping scheme for array operations on static dataflow architectures. the most addition to this paintings is located in bankruptcy 12, reflecting new study effects built over the last 3 years given that I joined McGill University-results established upon the rules in my dissertation. The terminology dataflow delicate­ ware pipelining has been continually used due to the fact that book of our 1988 paper at the argument-fetching dataflow structure version at McGill college [43]. within the first a part of this e-book we describe the static facts circulation graph version as an operational version for concurrent computation. we glance at timing issues for software graph execution on a fantastic static dataflow computing device, study the proposal of pipe lining, and symbolize its functionality. We speak about balancing ideas used to remodel convinced graphs into absolutely pipelined information circulate graphs. particularly, we convey how optimum balancing of an acyclic info circulation graph could be formulated as a linear programming challenge for which an optimum answer exists. As an enormous outcome, we express the optimum balancing challenge of acyclic information circulate graphs is reduceable to a category of linear programming challenge, the web­ paintings circulation challenge, for which famous effective algorithms exist. This consequence disproves the conjecture that such difficulties are computationally hard.

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Chapter 4 also introduces the major code blocks: array creation expressions built using the foraH and for-construct language constructs. Lastly, the mapping of array operations organized in these code blocks are also the focus of this chapter. Chapter 5 provides an overview of the basic code mapping scheme. It addresses the topic of array representations used in pipelined code mapping, and it also introduces a static data flow graph language (SDFGL) as an object language for the code mapping scheme.

We can uniquely label the actors by an integer function L : V ---t Z, such that L( v) = j, where j is the path length from s to v. Now V can be partitioned into mutually exclusive and collectively exhaustive sets of nodes, or stages of nodes Yo, VI, . , Vm , such that Vj = {v, where L(v) = Note L(s) = 0, L(t) = m, where m is the length of each path from s to t. Obviously, we have: n. 1. Vo = is}, 2. if node u and 3. Vm ~ Vj and there is an edge e = (u,v) in E, then v ~ Vj+1. = it}. We can also partition E into mutually exclusive and collectively exhaustive sets of edges (also called stages of edges) EI ...

2(b) two sets of tokens are pipelined through the graph, and the actors in stages 1 and 3 are enabled and can be executed concurrently. Thus, the two forms of parallelism are fully exploited. The power of fine-grain parallelism in a dataflow computer derives from machine-level programs having large pipelines in which thousands of actors in hundreds of stages are executed concurrently. Each actor in the pipe is activated in a totally data-driven manner, and no explicit sequential control is needed.

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