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Serkan Askar Ma iej Ciesielski Department of Ele tri al & Computer Engineering University of Massa husetts, Amherst, MA 01003 fsaskar, iesielg e s.umass.edu Abstra t|This paper addresses the problem of layout design automation of datapath ells. We present a novel approa h to transistor pla ement problem for ustom datapath designs and demonstrate that it an be applied to pra ti al designs. Our approa h is based on an analyti al model whi h employs a mixed integer linear programming (MILP) te hnique. The novelty and originality of the method is the eÆ ient management of the omplexity of the underlying mathemati al model. Our prototype tool automati ally handles transistor merging, folding, and intraell omponent sharing. I. Introdu tion Layout generation for high-performan e datapaths has been typi ally done manually due to stringent requirements imposed on area and performan e of su h ir uits. So far, datapath layout did not enjoy the bene ts of design automation due to high orrelation between quality of layout and ir uit performan e. However, as the omplexity of datapath stru tures grows the requirement on turnaround time be omes riti al, whi h makes datapath layout automation inevitable. Datapaths are hara terized by highly regular layout stru tures. Typi al datapath oorplan onsists of an array of bit sli es and words of identi al bit ells. Sin e ea h bit sli e is repli ated a number of times (determined by the datapath width) with very little or no modi ation, layout generation of su h regular stru tures redu es to a areful design, often by means of handrafting, of individual ells. This paper addresses the problem of automating layout design of datapath ells. Spe i ally, it on entrates on the transistor pla ement problem. Although pla ement and routing are tightly interrelated, they are often performed as separate design phases in order to manage enormous design omplexity. Furthermore, modern multi-layer routing te hnology makes it possible to route layout stru tures with di usion-limited pla ement, provided that suÆ ient spa ing for onta ts is provided to fa ilitate the subsequent routing. Due to high repetition of datapath ells the task of datapath layout optimization redu es to minimizing the area of individual ells, subje t to routability and performan e onstraints. Several te hniques and algorithms have been proposed in the past to automate transistor pla ement. These algorithms an be broadly lassi ed as deterministi and sto hasti . Among the deterministi algorithms, for e dire ted, eigenvalue, and geometrybased onstru tive methods have been used extensively [1℄, [2℄, [3℄, [4℄. Sto hasti methods are represented by simulated annealing and geneti algorithms, whi h are known for their ability to handle multi-dimensional ost fun tion [5℄. Pla e & route tools, su h as KOAN/ANAGRAM [6℄ and PUPPY [7℄, designed spe ifi ally for analog devi es, are best examples of layout te hniques based on simulated annealing. Our approa h to ustom datapath layout is based on a deterministi analyti al model using mathemati al programming te hniques. We present a novel approa h to transistor pla ement problem and demonstrate that it an be applied to pra ti al datapath designs. Our method is based on an analyti al approa h whi h This work was supported by a grant from Compaq's Alpha Development Group employs a mixed integer linear programming (MILP) te hnique. MILP has been previously proposed for oorplanning and ell pla ement [8℄ and is known to su er from omputational omplexity problem. The novelty and originality of our method is the eÆ ient management of the omplexity of the underlying mathemati al model. II. Datapath Design Problem A number of onstraints is imposed on the design of datapaths, whether it is done manually or automati ally. These onstraints must properly apture the requirements imposed by the global datapath oorplan, omponent geometries, and te hnology requirements. This se tion provides a brief overview of the onstraints and obje tives in the automated design of ustom datapath. A. Bit-sli e Constraints Figure 1 shows an outline of a typi al datapath ell in a verti al orientation. The width (pit h) of the bit-sli e is xed, typi ally delimited by VDD/VSS power supply rails. Signal nets are onne ted to the ell omponents by means of bristles. Verti al bristles are data lines, providing wiring between di erent fun tional ells within the same bit sli e. Horizontal bristles provide ontrol lines between fun tionally identi al ells of di erent bit-sli es. Data lines run in parallel to the power rails. Control lines span the width of the datapath in the dire tion perpendi ular to the power rails. The physi al lo ation of the bristles is typi ally known prior to pla ement of omponents in the ell. VSS VDD to be Height minimized