We present an efficient optimization scheme for gate sizing in the presence of process variations. Using a posynomial delay model, the delay constraints are modified to incorporate uncertainty in the transistor widths and effective channel lengths due to the process variations. An uncertainty ellipsoid method is used to model the random parameter variations. Spatial correlations of intra-die width and channel length variations are incorporated in the optimization procedure. The resulting optimization problem is relaxed to be a Geometric Program and is efficiently solved using convex optimization tools. The effectiveness of our robust gate sizing scheme is demonstrated by applying the optimization on the ISCAS '85 benchmark circuits and testing the optimized circuits by performing Monte Carlo simulations to model the process variations. By varying the size of the uncertainty ellipsoids, a trade-off between area and robustness is explored. Experimental results show that the timing yield of the robustly optimized circuits improves manifold over the traditional deterministically sized circuits. As compared to the worst-case design, the robust gate sizing solution having the same area, has fewer timing violations.
As across-chip interconnect delays can exceed a clock cycle, wire pipelining becomes essential in high performance designs. Although it allows higher clock frequencies, it may change the microarchitecture altogether because of the arbitrary increase in the latencies of the paths and cycles of the circuit. This paper proposes a method to regain the functionality of a wire-pipelined circuit. In this approach, increased cycle latencies are compensated by slowing down the issue rate of the inputs. Our method finds the optimal value of the slowdown required for a circuit as it directly affects the throughput of the circuit. We also incorporate area minimization in our formulation to minimize the number of extra flip-flops added to the circuit. The formulation is tested on circuits derived from ISCAS benchmarks and the results suggest that wire pipelining increases the overall throughput in most of the cases.
We present an efficient optimization scheme for gate sizing in the presence of process variations. Using a posynomial delay model, the delay constraints are modified to incorporate uncertainty in the transistor widths and effective channel lengths due to the process variations. An uncertainty ellipsoid method is used to model the random parameter variations. Spatial correlations of intra-die width and channel length variations are incorporated in the optimization procedure. The resulting optimization problem is relaxed to be a Geometric Program and is efficiently solved using convex optimization tools. The effectiveness of our robust gate sizing scheme is demonstrated by applying the optimization on the ISCAS '85 benchmark circuits and testing the optimized circuits by performing Monte Carlo simulations to model the process variations. By varying the size of the uncertainty ellipsoids, a trade-off between area and robustness is explored. Experimental results show that the timing yield of the robustly optimized circuits improves manifold over the traditional deterministically sized circuits. As compared to the worst-case design, the robust gate sizing solution having the same area, has fewer timing violations.
Since across-chip interconnect delays can exceed a clock cycle in nanometer technologies, it has become essential in high performance designs to add flip-flops on wires with multi-cycle delays. Although such a wire pipelining strategy allows higher operating frequencies, it can reduce the delivered performance of a microarchitecture, since the extra flip-flops inserted may increase the operation latencies and stall cycles. Moreover, the addition of latencies on some wires can have a large impact on the overall performance while other wires are relatively insensitive to additional latencies. This varying sensitivity suggests the need for a throughput-aware strategy for pipelining the interconnects that interacts closely with the physical design step, which determines the lengths of these multicycle wires. We use a statistical design of experiments strategy based on a multifactorial design, which intelligently uses a limited number of simulations to rank the importance of the wires. When applied at the floorplanning level, our results show improvements both in the overall system performance and in the total wire length when compared with an existing technique.
As across-chip wire delays exceed a clock cycle, interconnect pipelining becomes essential. However, the arbitrary insertion of flip-flops can change the differentials of latencies along paths in the circuit, and this can cause the implemented circuit to have a different functionality than was intended by the designer. Although it is possible to use design techniques that maintain the functionality of the circuit, an additional concern is a reduction in the throughput. This may be overcome by careful choices at various stages of design that impact the across-chip wire latencies. This paper surveys the published work on wire-pipelining, describes its impact on circuit as well as system level throughput, and outlines some of the problems to be resolved in formulating a wirepipelining centric strategy for physical design.
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