David J. Kuck. The Structure of Computers and Computations. John Wiley and Sons, New York, 1978. Volume 1.  Home/Search   Document Not in Database   Summary   Related Articles   Check

....m eme variable. Cela est utile autant pour la parall elisation, que pour le slicing (cf section 2.2.4) ou la di erentiation. La forme classique pour repr esenter ces relations est le graphe de d ependances. Il en existe plusieurs variantes, dont le data ow graph, le 8 data dependence graph [71] [5] le program dependence graph [45] ou le dependence ow graph [84] L utilisation de ces graphes dans le cas particulier de la parall elisation est d ecrit dans [95] 43] 5] ou [33] et pour la comparaison de sous programmes dans [86] ou [6] Consid erant l exemple centaur, on peut ....

Kuck D.J. "The structure of computers and computations", volume 1. Wiley, 1978.

....In section 7 we outhne several unresolved issues to be investigated in future work. 2 Data Dependence A data dependence exists between two statements S1 and S2 if there is a path from S1 to S2 and both statements access the same location in memory. There are four types of data dependence [8, 9]: True (flow) dependence S1 writes a memory location that S2 later reads. Anti dependence S1 reads a memory location that S2 later writes. Output dependence S1 writes a memory location that S2 later writes. Input dependence S1 reads a memory location that S2 later reads. Compile time ....

D. Kuck. The Structure of Computers and Computa- tions, Volume 1. Wiley, New York, NY, 1978.

....no statement depends directly upon itself. In order to uncover the recurrence, it is necessary to first uncover the individual statement to statement dependences. ACM Transactions on Programming Languages and Systems, Vol. 9, No. 4, October 1987. Kuck and others at the University of Illinois [18, 32] have defined three types of dependence that can hold between statements. Definition. If control flow within a program can reach statement S2 after passing through S, then S2 depends on S, written S x S2, if (1) S2 uses the output of S. This type of dependence is known as true dependence ....

....execute each statement that does not depend upon itself in D in parallel; all others are part of a recurrence. There is a small wrinkle, however. The parallel statements must be executed in an order that is consistent with the dependence relation D . To view it in the manner suggested by Kuck [18], consider D as a graph in which individual statements are nodes and in which pairs in the relation are represented by directed edges. Figure 6 contains an example of such a graph. Cycles in this graph ACM Transactions on Programming Languages and Systems, Vol. 9, No. 4, October 1987. Fig. 7. The ....

KUCK, D.J. The Structure of Computers and Computations, Vol. 1, Wiley, New York, 1978.

....demonstrated. We believe that a broad class of recurrences can be efficiently accelerated, and we demonstrate the acceleration of one important class of recurrences within this paper. The height reduction of arithmetic recurrences has been extensively studied in the literature; see, for example, [1 5]. The techniques used in these papers introduce computational redundancy in order to reduce the solution time of a recurrence on a parallel computer but do not carefully optimize the solution of recurrences for processors with limited instruction level parallelism. A frequently discussed solution ....

D. J. Kuck. The structure of Computers and Computations. (Wiley, New York, 1978). 24

....caused by either data or control dependences. Most of the prior work on height reduction relates to data height reduction, i.e. height reduction of critical paths caused by data dependences. Early work in this area introduced techniques such as tree height reduction of arithmetic expressions [6]. More recent work demonstrated techniques, called symmetric and blocked back substitution, for cyclic height reduction of arithmetic expressions in software pipelined loops [7] There has been some prior work in alleviating the effects of control dependences. The use of speculative execution is ....

D.J. Kuck. The structure of Computers and Computations. (Wiley, New York, 1978).

....c d e f g (a) c) d) b) c d e g b f a a c c e f g b c d a e a c g f h h h h d b d Figure 2. Equivalent factored forms. 2 Tree height reduction: an example Tree height reduction [7] was originally proposed in the scope of optimizing compilers for the generation of code in multiprocessor systems. The same techniques are applicable to the optimization of combinational circuits. Figure 2 illustrates an example. The tree in Figure 2(a) represents a factored form obtained from ....

D. Kuck. The Structure of Computers and Computation. John Wiley & Sons, 1978.

....Although parallel execution time, concurrency, scalability, and speed up have been proposed in the literature as performance metrics, the use of speed up dominate the literature. The notion of speed up was initially used to estimate the performance benefit of a multiprocessor over a uniprocessor [3]. Later, speed up has been proposed as a metric to estimate the performance of parallel and distributed algorithms [4] and parallel processor architectures [5] The most common definition of speed up is the ratio of the execution time of the best known serial algorithm to the execution time of ....

David J. Kuck. The Structure of Computers and Computations, Vol. 1. John Wiley and Sons, New York, 1978.

....other hand, suppose we remove the assignment to X. Then redundant execution is safe, because the values assigned to S and R are the same for all processors executing the two remaining assignments, for all possible interleavings. We refer to standard definitions of data dependence for a variable X [9]: Flow: A flow dependence exists if X is modified and subsequently accessed. Storage Related: A storage related dependence exists if X is accessed and subsequently modified (an antidependence) or if X is modified and subsequently modified (an output dependence) The safety of redundant ....

David J. Kuck. The Structure of Computers and Computations. John Wiley and Sons, 1978.

....networks. Algorithms suitable for systolization arise in diverse areas such as signal, image, and language processing, graphics, and linear systems. The parallelization of programs is certainly not a new idea. There has been a great deal of research in the area of parallelizing compilation [46]. It has differed from our approach in two respects. Although parallelizing compilers also produce parallel programs, it is only recently that they have become available for asynchronous distributed memory multiprocessors, i.e. processor networks. Before, they targeted vector processors ....

D. J. Kuck. The Structure of Computers and Computations. John Wiley & Sons, 1978.

....of the execution branches. Parallel code generation for shared memory multiprocessors is outlined. Keywords: Conditional statements, critical path, dependence graph, DO loops, parallelizing compilers. 1. Introduction Restructuring compilers rely on data dependence analysis. Dependence relations [1] essentially specify the semantically relevant constraints on execution ordering of operations within loops. In this paper, the information provided by dependences is used to estimate the number of processors needed to execute the loop in minimum time. Machine dependent overheads involved in ....

Kuck D.J., "The Structure of Computers and Computation", vol.1, John Wiley & Sons, 1978.

....compiler are given in Figure 1.5. The difference between this diagram and the one in Figure 1.4 is the inclusion of dependence analysis before the planning phase. Dependence analysis is a key component in a parallelizing compiler, used to understand the pattern of memory accesses in a program [Kuc78] Parallelization preserves the meaning of a program as long as the order of accesses to an individual memory location is retained. In dependence analysis, pairwise comparisons of memory accesses are performed to determine if they can reference the same location. In a compiler performing ....

....representing the leading dimension size in A s declaration. If the compiler were to automatically perform the translation and substitute for k, the resulting reference to A(1,i) in daxpy would be A(1 (j 1) ij (i 1) ii,1) This subscript expression is complex enough to defy the dependence analysis [Kuc78] on which scalar replacement and unroll and jam rely. The value of ii depends on the parameter job so we trace backwards through the program to locate the value of job. In dgemm, the value of job passed into dgemv 69 main tme prnt dgemm0 dgemm1 : dgemm7 dgemv1 dgemv3 daxpy P P P P ....

D. J. Kuck. The Structure of Computers and Computations, volume 1. John Wiley and Sons, New York, 1978.

....Most real tools also need to study the relations between dioeerent uses of a given variable. This is true for parallelization, slicing, or A.D. These relations classically form a graph, known as the dependence graph. There exist may variants, such as the data AEow graph, the data dependence graph [71] [5] the program dependence graph [45] or the dependence AEow graph [84] Use of these graphs for parallelization is described in [95] 43] 5] or [33] and for comparison of program fragments in [86] or [6] Let us now focus on the state of the art for our two short term goals, automatic ....

Kuck D.J. "The structure of computers and computations", volume 1. Wiley, 1978.

....optimization of machine code[HG83] GM86] Fis81] This paper explores the application of loop restructuring transformations developed for vectorization to a general purpose pipelined architecture. Wolfe [PW86] catalogues a number of such transformations. The techniques of data dependence analysis[Kuc78], Ken80] Wol82] All83] provide information on the safety and the pro tability of restructuring transformations. Two metrics are de ned in the next sections: machine balance and loop balance. Together, these metrics provide an estimate of how eciently a given loop can be executed on a ....

....later, statement w may access the same location. When at least one of these statements modi es that location, these edges represent execution order requirements: the source of an edge must be executed before the sink. Dependences are classi ed by whether each statement modi es the memory accessed[Kuc78]. If neither statement modi es M , the dependence is called an input dependence. If the rst statement modi es M but the second statement does not, then the dependence is called a true dependence. If the second statement modi es M but not the rst, the dependence is an anti dependence. If both ....

D. J. Kuck. The Structure of Computers and Computation. Volume 1, John Wiley & Sons, New York, 1978.

....speed [Henn96] 2.2. Register File Design Research into the trade offs between register files and caches has resulted in a wide variety of engineering solutions since the earliest days of computer architecture. Hardware registers (also called scratchpads) have been used since the early 1960s [Kuck78]. Table 2.2 gives a selected overview of this history. We will comment on a few of the machines listed in the table where they are relevant. The CDC 6600 series machines had a total of 24 registers. Loads to 7 of the 8 address registers had interesting side effects. A load into register ....

David J. Kuck. The Structure of Computers and Computations. John Wiley & Sons, Pittsburgh, Pennsylvania, 1978.

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David J. Kuck. The Structure of Computers and Computations. John Wiley and Sons, New York, 1978. Volume 1.

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Kuck, D.J., The Structure of Computers and Computations, Vol. 1, John Wiley and Sons, New York, NY (1978).

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D. J. Kuck, The Structure of Computers and Computations, John Wiley, New York, NY, 1978.

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D. J. Kuck, The Structure of Computers and Computations, John Wiley, New York, NY, 1978. 92

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KUCK, D. The Structure of Computers and Computations, vol. 1. John Wiley and Sons, New York, 1987.

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Kuck D.J., "The Structure of Computers and Computation", vol.1, John Wiley & Sons, 1978.

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D. J. Kuck, The Structure of Computers and Computations, Vol.1, John Wiley & Sons, 1978.

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D. J. Kuck. The Structure of Computers and Computations,,volume I. John Wiley & Sons, Inc., NY, 1978. 143

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D. Kuck. The Structure of Computers and Computations. John Wiley & Sons, Inc., 1978.

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D. J. Kuck, The Structure of Computers and Computations. NewYork: Wiley, 1978, vol. I.

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D. J. Kuck. The Structure of Computers and Computations,, volume I. John Wiley & Sons, Inc., NY, 1978. 143

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