M. Potkonjak and J. Rabaey, "Optimizing the resource utilization using transformations, " IEEE/ACM International Conference on Computer-Aided Design (ICCAD), pp. 88-91, 1991.  Home/Search   Document Not in Database   Summary   Related Articles   Check

....Design and Peformance Keywords: Carry save adder, layout, high performance 1. INTRODUCTION The optimization of arithmetic expression has been the subject of intensive investigation in the several phases of design process. A lot of techniques for synthesizing arithmetic circuits are proposed [1] [12] A carry save adder (CSA) module [20] is one of the most frequently used implementations in the operation level since it has an advantage of fast timing possibility with, if any, little area penalty. Permission to make digital or hard copies of all or part of this work for personal or ....

M. Potkonjak and J. Rabaey, "Optimizing Resource Utilization Using Transformations", Proc. of ICCAD, 1991.

.... Merged arithmetic refers to the direct implementation of multioperator arithmetic expressions without breaking down into individual operators [17, 10, 18] This approach often employs arithmetic relations to achieve a cross operator implementation with a single addition reduction tree [14]. Merged arithmetic can achieve higher speed by reducing the number of carry propagation chain, and often has a smaller circuit size and lower power consumption. However, due to the lack of intermediate signals representing the individual operator decomposition, merged arithmetic circuits are an ....

M. Potkonjak and J. Rabaey. Optimizing resource utilization using transformations. IEEE Trans. on CAD, 13(3):277--292, 1994.

....rate of the loop can be approximated to the rate at which the steady state is invoked. Several techniques have been developed to obtain the optimal steady state pattern [3, 4, 5, 6, 7] Among these, Retiming techniques [8, 9, 10] are promising and have also been used in highlevel synthesis [11, 12, 13], DSP domains [14, 15] and hardware software codesign [16] Sanchez [10] and Chao et al. 13] use retiming techniques for pipelining under resource constraints. Results show that the UNRET technique proposed in [10] performs better than the well known pipelining schemes like percolation based ....

M. Potkonjak, J. Rabaey. "Optimizing resource utilization using transformations". In IEEE transactions on ComputerAided Design of Integrated Circuits and Systems, volume 13, March 1994.

....constraint accommodation. Related work regarding this has focused primarily on interface synthesis separated from scheduling. Influential interface synthesis work is attributed to Borriello[12] Some scheduling techniques expose more problem parallelism through graph transformations [1] 81] 99][111]. Algebraic and retiming transformations restructure the DFG or CDFG. Hence, a new number of problem graph vertices or edges may result. Although ABSS may implicitly perform some algebraic and retiming transformations through use of nondeterministic alternatives, this is not the focus of this ....

M. Potkonjak and J. Rabaey, "Optimizing Resource Utilization Using Transformations ", IEEE Trans. CAD/ICAS, vol.13, no.3, pp. 277-292, March 1994.

....carry signal) per bit The optimization of additions using CSA was explored in [1] but the transformations were done at the word level. While arithmetic optimizations have been studied extensively and arithmetic properties such as commutativity and associativity have been applied in various forms [2, 3], to our knowledge, there has been no previous work that exploits the representation flexibility in optimizing the carry save additions at the bit level. Thus, this work also provides a useful link between word level carry save optimization (e.g. 1] and bit level optimization. In this paper, ....

M. Potkonjak and J. Rabaey, "Optimizing resource utilization using transformations," in Proc. IEEE Int. Conf. Computer-Aided Design, pp. 88--91, Nov. 1991.

....carry signal) per bit The optimization of additions using CSA was explored in [1] but the transformations were done at the word level. While arithmetic optimizations have been studied extensively and arithmetic properties such as commutativity and associativity have been applied in various forms [2], 3] to our knowledge, there has been no previous work that exploits the representation flexibility in optimizing the carrysave additions at the bit level. Thus, this work also provides a useful link between word level carry save optimization (e.g. 1] and bit level optimization. In this ....

M. Potkonjak and J. Rabaey, "Optimizing resource utilization using transformations," in Proc.

....interval. In the extreme, if sufficient resources are available, the design can be executed in one control step through full chaining. It is clear that the design cannot run faster than this without modification of the CDFG using techniques such as pipelining or behavioral transformation [21] [22]. V. PERFORMANCE DRIVEN HIGH LEVEL SYNTHESIS Performance driven HLS requires the solution of the PDS problem and also control synthesis. We solve the PDS problem assuming variable operation delay and variable control step interval and targeting minimal latency exploiting the BLC. This section ....

M. Potkonjak and J. Rabaey, "Optimizing resource utilization using transformations," IEEE Trans. Computer-Aided Design, vol. 13, pp. 277--292, Mar. 1994.

....limited to a generic global optimisation technique on a subset of the possible transformations. Also using transformations for direct area optimisation has not yet attracted much attention. Local resource utilisation optimisation has been done using transformations steered by stochastic techniques [7]. Sometimes area optimisation is a secondary goal in throughput optimisation [8] Because most transformations are well known [9, 10, 11] selecting a set of transformations is relatively simple. It is however extremely important to reduce the set to a minimal size to limit the search space. This ....

....This dependency makes finding an efficient and effective ordering both desirable and very difficult in almost all cases. Therefore, most research relies on manually selected orderings [11, 12, 13, 14] One way to tackle the ordering problem is by executing random moves using simulated annealing [7]. However, a stochastic method such as simulated annealing is based on the assumption that many small and independent moves can be performed very fast. But transformations are dependent, and their applicability always has to be checked prior to execution, which makes them relatively slow. The ....

M. Potkonjak, J. Rabaey, "Optimizing Resource Utilization using Transformations," in Proceedings of ICCAD-91, pp. 88-91, Nov. 1991.

....with lower cost are obtained. Techniques presented in [14 and 19] can be used for changing the implementation suggestion. 3. 2 Related work Several design systems for VLSI design based on the concept of transformational design exist or are under construction as part of larger projects (e.g. HYPER [20, 12, 21, 22], CAMAD [23, 24] SynGuide [25, 18] GATE [14] Yorktown [26] ESPRIT FORMAT[27] however most of them are restricted to optimizations at a single abstraction level (algebraic, loop, common subexpression elimination, retiming and scheduling transformations) some, such as GATE and HYPER, include ....

....optimized designs described in [32, 33] When compared to the synthesis results obtained with View Synthesis the improvement is 75 , from 2613 down to 685 gates. In addition our implementation is about twice as fast and would require less than half the power as compared to the optimized designs [22, 23]. For the prototype implementation the improvement in the number of instructions over the previous manually designed implementation was about 10 . This relatively small gain was caused by the difficulty of efficiently implementing the more complex control structure which becomes a dominant factor ....

M. Potkonjak, J. Rabaey, Optimizing Resource Utilization Using Transformations, IEEE Transactions on Computer-Aided Design of Integrated Circuits and Systems, vol. 13, no. 3, March 1994.

....are very important because they allow for the efficient mapping to hardware and reduction of the number of operation kinds which is essential for the application of common subexpression elimination and sharing transformations. These classes of transformations are missing in the Hyper system [Bro92, Cha92 and Pot94] and the CAMAD system [Pen89, Pen94] and only partially used in [Jan94] 1994 P.F.A. Middelhoek University of Twente 18 Transformation New Primitive Uses Comment algebraic 7 associativity n y 1 distributivity n y 1 commutativity n y 1 identity n y 2 (inverse) self inverse n y 2 strength ....

M. Potkonjak, J. Rabaey, Optimizing Resource Utilization Using Transformations, IEEE Transactions on Computer-Aided design of Integrated Circuits and Systems, vol. 13, no. 3, March 1994

....Work Similar application of compiler optimizations to tasks in high level synthesis has been done before [BhLe90] Camp90] Walk82] but differ from this work in the design models and approach. Interactive use of similar transformations for sequential circuit behavior, retiming, has been done by [PoRa91] and [MSBS91] However, retiming differs fundamentally from rescheduling in the underlying data being transformed. Retiming tools manipulate register transfer (RT) level descriptions of circuits. Typically for retiming, the connectivity of registers to operational units is manipulated so that the ....

Potkonjak, M. and Rabaey, J., "Optimizing Resource Utilization using Transformations", Proceedings of the IEEE Conference on Computer-Aided Design, pp. 88--91, 1991. 1991.

....be used and in what order. In this design approach decisions and their alternatives become clear which increases the insight of the designer [Middelhoek95] stimulating his creativity. The feasibility of transformational design, especially for DSP design applications, becomes more and more clear[Middelhoek95, Potkonjak94, Chandrakasan95]. Transformational design until now is used for area, time as well as power optimisation objectives. Figure 1 shows informally how the critical path in a specification can be reduced just by using a transformation based on the associativity of addition. TRANSFORMATIONAL DESIGN OF DIGITAL ....

.... In the transformational design system CAMAD an extended Petrinet representation is used [Peng94] Several kinds of mixed or separate data flow and control flow representations are defined [Gayski, Camposanoa b] In respect with DSP design several kinds of signal flow graph representations are used [Samson93, Potkonjak94] . What all these representations have in common is that they define a kind of graph, not necessarily a mathematical graph, in which nodes represent operations and the composition of these operations is described by TRANSFORMATIONAL DESIGN OF DIGITAL SYSTEMS RELATED TO GRAPH REWRITING 3 edges. A ....

M. Potkonjak, J. Rabaey, Optimizing resource utilization using transformations, in IEEE transactions on CAD of integrated circuits ans systems Vol. 13. No.3 March 1994, pp 277-292.

....design systems have been developed in recent years both for software and hardware design. In this paper we give a short list of references to work in the hardware domain. A more complete discussion can be found in [MiR96] The HYPER system developed at the University of Berkeley [Bro92, Cha92, IPS93, Pot94, CPM95] provides a set of automatic algorithmic level design optimization. Within the context of HYPER automatic optimization scripts have been developed for different purposes, including optimizing resource utilization, critical path and power reduction, and to improving testability. Transformations in ....

M. Potkonjak, J. Rabaey, Optimizing Resource Utilization Using Transformations, IEEE Transactions on ComputerAided Design of Integrated Circuits and Systems, Vol. 13, No. 3, March 1994.

....what order. In this design approach decisions and their alternatives become clear which increases the insight of the designer [1] stimulating his creativity. The feasibility of transformational design, especially for DSP (Digital Signal Processing) design applications, becomes more and more clear [1, 2, 3]. Until now transformational design is used for area, time as well as power optimisation objectives. Figure 1 shows informally how the critical path in a specification can be reduced just by using a transformation based on the associativity of addition. The transformation rule is specified ....

.... b) Transformation rule based on associativity of c) Result of applying the transformation rule on nodes 5 and 8 of the graph in a) Although transformational design is assumed to be formally well founded more attention often seems to be given to show its feasibility than to its formal aspects [2, 3, 4]. Correctness is related to the semantics of a design representation, the specified behaviour. To proof the behaviour preserving characteristic of transformations the representation(s) on which the transformations are defined need to have a formal semantics. Only a few of the commonly used ....

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M. Potkonjak, J. Rabaey, Optimizing resource utilization using transformations, IEEE Trans. on CAD, Vol. 13. No.3 March 1994, pp 277-292.

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M. Potkonjak and J. Rabaey, "Optimizing the resource utilization using transformations, " IEEE/ACM International Conference on Computer-Aided Design (ICCAD), pp. 88-91, 1991.

....Due to its importance, a variety of approaches have also been proposed for Register Assignment [11] Finally, transformations are considered by many as the behavioral synthesis task with the highest potential to optimize a design. In the last two decades, a number of approaches have been proposed [8,9]. A more comprehensive analysis of high level synthesis, Scheduling, Register Assignment, and Transformations can be found in [3] 3. TECHNICAL PRELIMINARIES 3.1 Global Flow: High Level Synthesis Traditionally, the global flow of high level synthesis has consisted of two major steps: i) ....

M. Potkonjak., J. Rabaey. "Optimizing resource utilization using transformation." IEEE Trans. on CAD, Vol.13, (no.3), pp. 277--292, 1994.

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M. Potkonjak, J. Rabaey: "Optimizing the Resource Utiliza tion Using Transformations", Proc. IEEE ICCAD-91, Santa Clara, pp. 88-91, November 1991.

....manual derivation of scripts which en[brces static ordering of transformations according to the experience achieved by extensive experimentation on small benchmark sets. The fourth approach has been recently gaining popularity. It is based on use of probabilistic algo rithms as a search mechanism [Cha92, Pot91 a] The new approach aims at closing the gap between the run time and the quality of results, by combining the power of computationally intensive optimization for derivation of proper subsequences of transformations, and the user ability to conduct global search process. 2. KNOWLEDGE BASED ....

M. Potkonjak, J. Rabaey: "Optimizing Resource Utilization Using Transformations", IEEE International Conference on Computer-Aided Design, pp. 88-91, 1991.

....and its date appear, and notice is given that copying is by permission of the Association for Computing Machinery. To copy otherwise, or to republish, requires a fee and or specific permission. 1995 ACM 0 89791 756 1 95 0006 3. 50 software pipelining to generate complex time shapes [Goo89, Pot94, Lam88]. However only recently has some limited work been done on relaxing the assumption that all phases are zero and explicitly manipulating the phases. Perhaps the first direct effort at directly manipulating the phases as part of an algorithm transformation was described by [Sri94] who applied it to ....

....delay by a chain of k nodes with unit cycle delays. 5. Optimizing Area and Power Using Rephasing It has recently been demonstrated that retiming at behavioral level can be effectively used to improve resource utilization of the targeted design, and therefore reduce the implementation area [Pot94]. However, the effectiveness of retiming for area optimization is often limited by granularity and input output bottlenecks. Figure 4a shows a typical example of this situation. It is assumed that the available time is 4 control steps. Retiming can not be applied on the initial CDFG because any ....

M. Potkonjak, J. Rabaey: "Optimizing Resource Utilization Using Transformations" IEEE Transactions on CAD, Vol. 13, No. 3, pp. 277-292, March 1994.

....alterations in the computational structure such that the behavior (the relationship between output and input data) is maintained. Transformations are used extensively in several computer science, computer engineering, and CAD areas, most often in compilers [22] and behavioral level synthesis [23] [24]. This section shows how transformations, using specifically tailored optimization techniques, can significantly reduce the area overhead for designs with BISR requirements. A. Key Ideas and Motivational Examples The basic idea behind using transformations in behaviorallevel synthesis for HBISR ....

....routines add resources using the stress functions of Section IV B, in determining which hardware to add and the order in which to try the fault scenarios. For the core optimization, two approaches are employed: a probabilistic sampling algorithm and a pipelining based algorithm [24]. This probabilistic sampling algorithm applies two types of basic moves: retiming and generalized associativity, where the later is a transformation that combines associativity, inverse element law, and commutativity moves. The algorithm has two phases. The first phase is a global search using ....

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M. Potkonjak and J. Rabaey, "Optimizing resource utilization using transformations," in Proc. IEEE Int. Conf. Computer-Aided Design, 1991, pp. 88--91.

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M. Potkonjak and J. Rabaey, "Optimizing the Resource Utilization Using Transformations", Proc. IEEE ICCAD Conference, Santa Clara, pp. 88-91, November 1991. ###### ###### ### ######## ##

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M. Potkonjak and J. Rabaey, "Optimizing Resource Utilization using Transformations", IEEE Trans. on Computer Aided Design, Vol. 13, No 3, pp 277-292, March 1994.

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M.Potkonjak, J.Rabaey, "Optimizing resource utilization using transformations", Proc. IEEE Int. Conf. Comp. Aided Design, Santa Clara CA, pp.88-91, Nov. 1991.

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M.Potkonjak, J.Rabaey, "Optimizing resource utilization using transformations", Proc. IEEE Int. Conf. Comp. Aided Design, Santa Clara CA, pp.88-91, Nov. 1991.

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M. Potkonjak and J. Rabaey, "Optimizing resource utilization using transformations," in Proc. IEEE Int. Conf. Computer-Aided Design, 1991, pp. 88--91.

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