R. Hartley and A. Casavant, "Tree-height minimization in pipelined architectures, " IEEE International Conference on Computer-Aided Design (ICCAD), pp. 112-115, 1989.  Home/Search   Document Not in Database   Summary   Related Articles   Check

.... distributivity and commutativity are the three most often used algebraic transformations [Wae50] Most often they are treated under the paradigm of tree height reduction, although several authors discuss in detail the critical path minimization of general DAG s (directed acyclic graph) [Tri87, Har89, Lob91, Dun92]. Recently, algebraic transformations have been generalized to cover other algebraic axioms such as inverse elements (e.g. and were applied with the goal of minimizing design area under throughput and latency constraints [Pot91] Other algebraic transformations are related to other axioms in ....

R. Hartley, A. Casavant: "Tree-height Minimization in Pipelined Architectures", IEEE ICCAD, pp.112-115, 1989.

....the initiation interval and memory traffic) using application benchmarks. In addition, we will evaluate the tradeoffs between the performance improvement of the optimizations and the performance degradation due to higher register requirements. Loop transformations such as tree height reduction [HC89] try to transform the loop in order to improve the intrinsic parallelism of the dependence graph. We plan to do research on similar transformations to reduce the intrinsic register requirements of the loop i.e. to reduce the schedule independent lower bound of the register requirements. As an ....

R. Hartley and A. Casavant. Tree-height minimization in pipelined architectures. In Proc. Int. Symp. Circuits and Systems, 1989.

....of high level language compilers, the main area of research and application of algebraic optimization methods has been extended to high level synthesis during the recent years. Algebraic optimization techniques have been employed for improving resource utilization [11] tree height minimization [4, 5], maximization of data throughput [7] 6] and minimization of power consumption [2] see [11] for a comprehensive overview) Although all published approaches are very powerful in their own domain, most of them have certain restrictions concerning the set of supported transformation rules ....

R. Hartley and A. E. Casavant. Tree-Height Minimization in Pipelined Architectures. Proceedings of the International Conference on Computer-Aided Design, pages 112-- 115, 1989.

.... subexpression replication and associativity, where the first one acts as an enabling transformation for the second one [Mil88] Associativity, distributivity and commutativity are the three most often used algebraic transformations, commonly treated under the paradigm of tree height reduction [Tri87, Har89, Lob91, Dun92]. When retiming is the only transformation of interest and the goal is the minimization of the critical path, several algorithms designed by Leiserson and Saxe provide an optimal solution in polynomial time [Lei91] When the goal is minimal area or power, the problem has been proven to be ....

R. Hartley, et al. Tree-height minimization in pipelined architectures. ICCAD, pp.112-115, 1989.

....used flow graph transformations to improve the parallelism of the design. Tree height reduction uses the commutativity and distributivity properties of language operators to decrease the height of a long expression chain, and exposes the potential parallelism within a complicated data flow graph [31, 67]. Pipelining is another frequently applied transformation in HLS [71] Other commonly used transformations include loop folding [23, 88] software pipelining [26, 77] and retiming [76] Hardware specific transformations at the logic, RT and system levels can be applied to the intermediate ....

R. Hartley and A. Casavant, "Tree-Height Minimization in Pipelined Architectures," Digest of Technical Papers, International Conference on Computer-Aided Design (ICCAD), pp. 112-115, November 1989.

....try to reduce the critical path by exploiting parallelism beyond source level data dependences. Techniques that extract parallelism beyond data dependences have received attention in the high level synthesis and digital signal processing communities. A few techniques based on tree height reduction [8, 17, 13] have been proposed to shorten, at the expense of using extra operations, the critical paths consisting of a sequence of associative operations. But these techniques do not extract parallelism in recurrent loops involving additions intermixed with other operations such as multiplications beyond ....

R. Hartley and A. Casavant, "Tree height minimization in pipelined architectures", Proceedings of 1989 IEEE International Conference on CAD, Santa Clara, California, November 1989.

....2 :s 2) This IIR filter contains two recurrences (s = f(s 1) and s = f(s 2) which correspond to two cycles in the associated signal flow graph (see also fig. 4) The second example is the well known N tap FIR filter. A compact description in the applicative (flow graph oriented) language Silage [10] is: 1 In the DSP literature, the term recursion is often used as a synonym of recurrence. In this paper, recursion will be reserved to denote self referential functions in the sense of programming languages. x[0] in; y[0] 0; i = 1 . N) x[i] x[i 1] 1; y[i] y[i 1] h[i] x[i] ....

....it is probably not even necessary to implement the methodology in a CAD tool. 4: Evaluation on realistic test vehicles Our first illustration is extracted from typical recursive image processing algorithms working on local neighbourhoods and which update the image content. A Silage description [10] for the algorithm is provided next: i : 0 . I 1 ) j : 0 . J 1 ) begin img[i] j] f(img[i] j k] oldimg[i] j] end; We will assume that a data path has been constructed to execute the function f ( Given a specific mismatch M between the achieved throughput and the required ....

R.I.Hartley, A.Casavant, "Tree-height minimization in pipelined architectures", Proc. IEEE Int. Conf. Comp. Aided Design, Santa Clara CA, pp.112-115, Nov. 1989.

....scalable parallel computation implementing IIR filters as the number of computing units increases. Techniques that extract parallelism beyond LCD s have received attention in the high level synthesis and digital signal processing communities. A few techniques based on tree height reduction [6, 14, 13] have been proposed to reduce, using extra operations, the length of critical paths of computations consisting of a sequence of additions. However, these techniques are unable to generate scalable schedules for computations with differing types of operations intermixed, e.g. linear recurrences. ....

....of N . We chose to neglect the memory efficiency in the following schedule in favor of readability. for i = 0; N= 0 1 do each step in parallel with p FU s 1. x[ k 2] a[ k 2] k 1] 3 x[ k 1] t[1] a[ k 3] k 2] 3 a[ k 4] k 3] t[2] c[ k 3] 3 a[ k 4] k 3] t[6] = c[ k 5] 3 a[ k 6] k 5] t[13] c[ k 8] 3 a[ k 9] k 8] t[23] c[ k 3] 3 a[ k 4] k 3] 2. x[ k 2] x[ k 2] c[ k 2] t[3] t[2] c[ k 4] t[7] t[6] c[ k 6] t[14] t[13] c[ k 9] t[24] t[23] c[ k 13] t[4] a[ k 5] k 4] a[ k 6] k ....

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R. Hartley and A. Casavant, "Tree height minimization in pipelined architectures", Proceedings of 1989 IEEE International Conference on CAD, Santa Clara, California, November 1989.

....structures and function hierarchy. In order to arrive at efficient synthesis results, it has been recognized that transformations on algorithm specifications are crucial. Up to now this issue has been investigated mainly for data flow transformations on scalar processing, as in digital filters [6, 15, 19]. We claim however that these transformations are even more crucial in the presence of M D signals. Indeed, studies on memory organization for M D signals [8, 26] have shown that, for instance, loop transformations can have effects that influence implementation costs in the order of several ....

R. Hartley, A. Casavant. "Tree Height Minimization in Pipelined Architectures", IEEE Int. Conference on Computer-Aided Design, pp. 112-115, 1989.

....common subexpression elimination, constant folding, constant propagation and rather simple optimizations based on strength reduction. In the area of high level synthesis algebraic transformations have been particularly used for improving resource utilization [18] 17] tree height minimization [6] [7] the maximization of data throughput [8] 10] and minimization of power consumption [3] The use of algebraic transformations in combination with complex components (e.g. MACs) was first proposed in [14] However, to the author s knowledge there is no optimization technique that exploits ....

R. Hartley and A. E. Casavant. Tree-Height Minimization in Pipelined Architectures. Proceedings of the International Conference on Computer-Aided Design, pages 112--115, 1989.

....to reduce the critical path by exploiting parallelism beyond data dependences. Techniques that extract parallelism beyond data dependences have just started to receive attention in the high level synthesis and digital signal processing communities. A few techniques based on tree height reduction [7, 11, 9] have been proposed to shorten, using extra operations, the critical paths consisting of a sequence of associative operations, e.g. a sequence of additions or a sequence of multiplications. But these techniques do not extract parallelism in recurrent loops involving additions and multiplications ....

R. Hartley and A. Casavant, "Tree height minimization in pipelined architectures", Proceedings of 1989 IEEE International Conference on CAD, Santa Clara, California, November 1989.

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R. Hartley and A. Casavant, "Tree-height minimization in pipelined architectures, " IEEE International Conference on Computer-Aided Design (ICCAD), pp. 112-115, 1989.

No context found.

R. Hartley and A. Casavant, "Tree-Height Minimization in pipelined architectures", IEEE Trans. on Computer Aided Design, vol. 8, pp. 112-115, 1989.

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R. Hartley and A. E. Casavant, "Tree-Height Minimization in Pipelined Architectures", Proc. of ICCAD, 1989.

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