By Guang R. Gao
This monograph advanced from my Ph. D dissertation accomplished on the Laboratory of laptop 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 examine effects built over the last 3 years when you consider that I joined McGill University-results established upon the foundations in my dissertation. The terminology dataflow smooth ware pipelining has been continually used due to the fact that ebook of our 1988 paper at the argument-fetching dataflow structure version at McGill college . within the first a part of this ebook we describe the static info circulation graph version as an operational version for concurrent computation. we glance at timing issues for software graph execution on an awesome static dataflow laptop, research the idea of pipe lining, and symbolize its functionality. We speak about balancing suggestions used to remodel yes graphs into totally pipelined info circulation graphs. specifically, we exhibit how optimum balancing of an acyclic info movement graph may be formulated as a linear programming challenge for which an optimum resolution exists. As a big outcome, we convey the optimum balancing challenge of acyclic facts stream graphs is reduceable to a category of linear programming challenge, the web paintings circulation challenge, for which recognized effective algorithms exist. This end result disproves the conjecture that such difficulties are computationally hard.
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Additional info for A Code Mapping Scheme for Dataflow Software Pipelining
Chapters 4 through 9 are devoted to the development of our pipelined code mapping scheme. Chapter 4 specifies the representation of the source language. In particular, it introduces PIP VAL-a subset of Val used as the source language for the application programs that are to be mapped. 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 2 The Static Data Flow Model In this chapter we describe the static data flow graph model as an operational model for concurrent computation. This model has evolved from a number of graph operational models for studying concurrent computation. Earlier models concentrated more on basic theoretical aspects, such as decidability properties of concurrent computations: deadlock, non determinacy, equivalence of program graphs, and expressive power for parallelism [7,76,109]. Later works were oriented toward operational models of practical programming languages designed for dataflow computers [14,29,42,38,123].
12 A Code Mapping Scheme for Dataflow Software Pipelining Since we are concerned with how to utilize the regularity of array operations, we concentrate on two particular array creation constructsforall and for-construct. The forall construct allows a programmer to specify the construction of an array where similar independent computations are performed to determine each element. The following expression defines a onedimensional array X from an input array A: X := array[real] := forall i in [0, m+1] % range spec construct if i = 0 then A[i] elseifi = m+1 then A[i] else (A[i-1]+A[i]+A[i+1])/3 endif endall The for-construct expression, proposed as a special case of Val's for-iter, is used to specify construction of an array where certain forms of data dependencies exist between elements.