A Code Mapping Scheme for Dataflow Software Pipelining by Guang R. Gao

By Guang R. Gao

This monograph advanced from my Ph. D dissertation accomplished on the Laboratory of laptop technological know-how, MIT, through 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 built over the last 3 years for the reason that I joined McGill University-results established upon the rules in my dissertation. The terminology dataflow delicate­ ware pipelining has been continually used in view that e-book of our 1988 paper at the argument-fetching dataflow structure version at McGill college [43]. within the first a part of this ebook we describe the static info stream graph version as an operational version for concurrent computation. we glance at timing issues for application graph execution on a terrific static dataflow computing device, study the idea of pipe lining, and represent its functionality. We talk about balancing recommendations used to remodel definite graphs into absolutely pipelined facts move graphs. particularly, we express how optimum balancing of an acyclic information circulate graph may be formulated as a linear programming challenge for which an optimum resolution exists. As an immense consequence, we express the optimum balancing challenge of acyclic info circulation graphs is reduceable to a category of linear programming challenge, the web­ paintings stream challenge, for which recognized effective algorithms exist. This consequence disproves the conjecture that such difficulties are computationally hard.

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For each set ofinput values, an iteration subgraph will generate exactly one set of result values, unless the computation diverges. , those that have exactly one set of result tokens generated at the output arc for each set of tokens presented at the input arcs [47]. In fact, the data flow graphs derived from expressions found in most user programs, including the conditional subgraphs and iteration subgraphs, are well-behaved [47]. 2 The Determinancy and Functionality of Static Data Flow Graphs Recall that the state of computation of a data flow program is defined in terms of its configurations and that firing rules determine execution sequences corresponding to the change of states in the computation process.

The state of a computation is described by configurations and firing rules governing the transition between configurations. Data values are denoted by placing tokens on the arcs. A configuration is an assignment of tokens in the graph. One configuration is advanced to another by the firing of actors. , the T-gate, F-gate, switch, and merge actors to be studied later), the firing rules for static dataflow model are quite simple: Regular Firing Rules: 1. An actor becomes enabled iff all of its input arcs have one token and all of its output arcs are empty.

Input: A one-in-one-out weighted data flow graph G with input node s and output node t. = (V,E) Output: A balanced graph G'. Step 1: Compute the max-cost function L for G. Step 2: For each arc e=( u,v) in E construct a buffer of size L(v) - L(u) and insert the buffer on e. Step 3: Return the result graph.

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