By Guang R. Gao
This monograph advanced from my Ph. D dissertation accomplished on the Laboratory of desktop 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 past 3 years considering I joined McGill University-results dependent upon the foundations in my dissertation. The terminology dataflow gentle ware pipelining has been continually used considering the fact that book of our 1988 paper at the argument-fetching dataflow structure version at McGill collage . within the first a part of this publication we describe the static info circulate graph version as an operational version for concurrent computation. we glance at timing issues for software graph execution on an excellent static dataflow laptop, learn the inspiration of pipe lining, and signify its functionality. We speak about balancing thoughts used to rework convinced graphs into totally pipelined info circulation graphs. particularly, we convey how optimum balancing of an acyclic facts circulate graph could be formulated as a linear programming challenge for which an optimum answer exists. As a tremendous end result, we exhibit the optimum balancing challenge of acyclic information stream graphs is reduceable to a category of linear programming challenge, the internet paintings circulate challenge, for which famous effective algorithms exist. This consequence disproves the conjecture that such difficulties are computationally hard.
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This monograph advanced from my Ph. D dissertation accomplished on the Laboratory of machine technology, MIT, throughout 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 given that I joined McGill University-results established upon the rules in my dissertation.
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Extra info for A Code Mapping Scheme for Dataflow Software Pipelining
1 The procedure to perform such transformations is called balancing the data flow graph. 1. 1(a) shows an unbalanced graph with eight nodes. 1( a). 1(b). Each buffer is denoted by a box with a number denoting the size of the buffer. 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).
C D[n] .... 3: Pipelining of Array Operations D. The core portion of each of several benchmarks of scientific computa- tion that we have studied consists of multiple code blocks, for example, in the order of 10-100 code blocks. 4. In this example there are three input arrays, A B, and C, and an output array Y. There are also internal arrays, 11 J 12, 13, and 14, defined by the code blocks. We are particularly interested in the case where each code block is defined by forall or for-construct.
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. 2. An enabled actor may fire, and once fired, all tokens on its input arcs are removed, and a token is placed on each of its output arcs. 1 we show a static data flow graph and a succession of several possible configurations for the expression: (a+b) X (c-d) Here we adopt an earlier notation convention that a token on an arc is represented by the presence of a large dot.