By Guang R. Gao

This monograph advanced from my Ph. D dissertation accomplished on the Laboratory of machine technological know-how, MIT, in the course of the summer season 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 examine effects constructed over the last 3 years on the grounds that I joined McGill University-results dependent upon the foundations in my dissertation. The terminology dataflow delicate­ ware pipelining has been constantly used because e-book of our 1988 paper at the argument-fetching dataflow structure version at McGill collage [43]. within the first a part of this booklet we describe the static info movement graph version as an operational version for concurrent computation. we glance at timing concerns for software graph execution on an incredible static dataflow desktop, study the inspiration of pipe lining, and represent its functionality. We speak about balancing ideas used to remodel convinced graphs into totally pipelined facts stream graphs. specifically, we convey how optimum balancing of an acyclic info movement graph might be formulated as a linear programming challenge for which an optimum answer exists. As a huge end result, we express the optimum balancing challenge of acyclic facts move graphs is reduceable to a category of linear programming challenge, the web­ paintings circulate challenge, for which recognized effective algorithms exist. This end result disproves the conjecture that such difficulties are computationally hard.

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13: Stage Partitioning of a Balanced Pipeline observe that at time ti (0::; i ::; m), one token is presented at each arc in Ei, and all other arcs are empty. Hence, during cycle time Ti all actors in stage i are enabled and fired, and no actors in other stages are enabled. The above observation can also be phrased: A run can be advanced at its maximum speed (one stage of nodes per cycle time), under the condition that it is not blocked. The initial emptiness of the pipe is certainly a sufficient condition.

In this case, the total size of buffering introduced for balancing is five. There may be more than one balanced version of a data flow graph. 1(b). 1( c) is an optimal solution. In general, we have the following definition: 1 There are different ways to implement FIFO buffers; however, we defer discussion of these implementations until Chapter 11 [46). 1: An Example of Balancing Algorithmic Aspects of Pipeline Balancing 43 Definition. Let G' be a balanced graph for G. If G' uses the least amount of buffering among all balanced graphs of G, then G' is called an optimal balanced graph of G.

We use a clock with cycle time T as the timing reference for computations by data flow programs. We also assume, without loss of generality, that the firing of any enabled actor may only happen at the beginning of a clock cycle. This assumption gives the execution of data flow programs a somewhat "synchronous" behavior, which facilitates the study of their pipelined execution. In a data flow program, many actors may become enabled at the same time. An important performance criteria of the machine is how long the firing of an enabled actor may be delayed.

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