Computing the entire area/power consumption versus delay tradeoff curve for gate sizing with a piecewise linear simulator

The gate sizing problem is the problem of finding load drive capabilities for all gates in a given Boolean network such, that a given delay limit is kept, and the necessary cost in terms of active area usage and/or power consumption is minimal. This paper describes a way to obtain the entire cost versus delay tradeoff curve of a combinational logic circuit in an efficient way. Every point on the resulting curve is the global optimum of the corresponding gate sizing problem. The problem is solved by mapping it onto piecewise linear models in such a way, that a piecewise linear (circuit) simulator can do the job. It is shown that this setup is very efficient, and can produce tradeoff curves for large circuits (thousands of gates) in a few minutes. Benchmark results for the entire set of MCNC '91 two-level examples are give

Variability-Aware VLSI Design Automation For Nanoscale Technologies

As technology scaling enters the nanometer regime, design of large scale ICs gets more challenging due to shrinking feature sizes and increasing design complexity. Aggressive scaling causes significant degradation in reliability, increased susceptibility to fabrication and environmental randomness and increased dynamic and leakage power dissipation. In this work, we investigate these scaling issues in large scale integrated systems. This dissertation proposes to develop variability-aware design methodologies by proposing design analysis, design-time optimization, post-silicon tunability and runtime-adaptivity based optimization techniques for handling variability. We discuss our research in the area of variability-aware analysis, specifically focusing on the problem of statistical timing analysis. The first technique presents the concept of error budgeting that achieves significant runtime speedups during statistical timing analysis. The second work presents a general framework for non-linear non-Gaussian statistical timing analysis considering correlations. Further, we present our work on design-time optimization schemes that are applicable during physical synthesis. Firstly, we present a buffer insertion technique that considers wire-length uncertainty and proposes algorithms to perform probabilistic buffer insertion. Secondly, we present a stochastic optimization framework based on Monte-Carlo technique considering fabrication variability. This optimization framework can be applied to problems that can be modeled as linear programs without without imposing any assumptions on the nature of the variability. Subsequently, we present our work on post-silicon tunability based design optimization. This work presents a design management framework that can be used to balance the effort spent on pre-silicon (through gate sizing) and post-silicon optimization (through tunable clock-tree buffers) while maximizing the yield gains. Lastly, we present our work on variability-aware runtime optimization techniques. We look at the problem of runtime supply voltage scaling for dynamic power optimization, and propose a framework to consider the impact of variability on the reliability of such designs. We propose a probabilistic design synthesis technique where reliability of the design is a primary optimization metric

A design flow for performance planning : new paradigms for iteration free synthesis

In conventional design, higher levels of synthesis produce a netlist, from which layout synthesis builds a mask specification for manufacturing. Timing anal ysis is built into a feedback loop to detect timing violations which are then used to update specifications to synthesis. Such iteration is undesirable, and for very high performance designs, infeasible. The problem is likely to become much worse with future generations of technology. To achieve a non-iterative design flow, early synthesis stages should use wire planning to distribute delays over the functional elements and interconnect, and layout synthesis should use its degrees of freedom to realize those delays

Timing Closure in Chip Design

Achieving timing closure is a major challenge to the physical design of a computer chip. Its task is to find a physical realization fulfilling the speed specifications. In this thesis, we propose new algorithms for the key tasks of performance optimization, namely repeater tree construction; circuit sizing; clock skew scheduling; threshold voltage optimization and plane assignment. Furthermore, a new program flow for timing closure is developed that integrates these algorithms with placement and clocktree construction. For repeater tree construction a new algorithm for computing topologies, which are later filled with repeaters, is presented. To this end, we propose a new delay model for topologies that not only accounts for the path lengths, as existing approaches do, but also for the number of bifurcations on a path, which introduce extra capacitance and thereby delay. In the extreme cases of pure power optimization and pure delay optimization the optimum topologies regarding our delay model are minimum Steiner trees and alphabetic code trees with the shortest possible path lengths. We presented a new, extremely fast algorithm that scales seamlessly between the two opposite objectives. For special cases, we prove the optimality of our algorithm. The efficiency and effectiveness in practice is demonstrated by comprehensive experimental results. The task of circuit sizing is to assign millions of small elementary logic circuits to elements from a discrete set of logically equivalent, predefined physical layouts such that power consumption is minimized and all signal paths are sufficiently fast. In this thesis we develop a fast heuristic approach for global circuit sizing, followed by a local search into a local optimum. Our algorithms use, in contrast to existing approaches, the available discrete layout choices and accurate delay models with slew propagation. The global approach iteratively assigns slew targets to all source pins of the chip and chooses a discrete layout of minimum size preserving the slew targets. In comprehensive experiments on real instances, we demonstrate that the worst path delay is within 7% of its lower bound on average after a few iterations. The subsequent local search reduces this gap to 2% on average. Combining global and local sizing we are able to size more than 5.7 million circuits within 3 hours. For the clock skew scheduling problem we develop the first algorithm with a strongly polynomial running time for the cycle time minimization in the presence of different cycle times and multi-cycle paths. In practice, an iterative local search method is much more efficient. We prove that this iterative method maximizes the worst slack, even when restricting the feasible schedule to certain time intervals. Furthermore, we enhance the iterative local approach to determine a lexicographically optimum slack distribution. The clock skew scheduling problem is then generalized to allow for simultaneous data path optimization. In fact, this is a time-cost tradeoff problem. We developed the first combinatorial algorithm for computing time-cost tradeoff curves in graphs that may contain cycles. Starting from the lowest-cost solution, the algorithm iteratively computes a descent direction by a minimum cost flow computation. The maximum feasible step length is then determined by a minimum ratio cycle computation. This approach can be used in chip design for several optimization tasks, e.g. threshold voltage optimization or plane assignment. Finally, the optimization routines are combined into a timing closure flow. Here, the global placement is alternated with global performance optimization. Netweights are used to penalize the length of critical nets during placement. After the global phase, the performance is improved further by applying more comprehensive optimization routines on the most critical paths. In the end, the clock schedule is optimized and clocktrees are inserted. Computational results of the design flow are obtained on real-world computer chips

Optimization Schemes for Variability-Driven VLSI Design Automation

Today's IC design is facing several challenges due to increasing circuit complexity and decreasing feature size, as it pushes to extend Moore's law into nano-scale dimensions. Apart from the challenges that arise directly as a result of feature scaling (e.g., increasing leakage power, reliability issues), imperfections in the manufacturing process have recently turned into a major design hurdle, due to the variations they cause in the device and interconnect parameters from their target values. From an IC design automation perspective, a shift in paradigm, from deterministic to probabilistic, is needed to handle the unpredictable nature of these fabrication variations. In such a probabilistic paradigm, the varying circuit parameters such as leakage power or delay should be accurately modeled, and their correlations due to common sources of variations or physical location on the chip should be well captured. Moreover, variability-driven (probabilistic) design automation needs to efficiently generate a high quality solution. A particular challenge in variability-driven design automation is to define optimality measures among candidate solutions, which allow for inferior solutions to be removed from the solution space thus reducing the run-time complexity. In this dissertation, the superiority probability is introduced as such an optimality measure, and two methods are proposed to compute this probability: an accurate Conditional Monte Carlo simulation method, and an efficient moment-matching approximation method. The effectiveness of using the superiority probability is shown in the context of two important design automation applications: 1) the buffer insertion problem, 2) the dual-Vth leakage optimization problem. Another important task in variability-driven design automation is to develop optimization techniques that can provably generate the optimal solution in an efficient way. In this dissertation, the application of the gate sizing problem is explored to optimally reduce the loss due to fabrication variations in the presence of a timing constraint. The presented formulation, in contrast with the existing variability-driven approaches which are all based on heuristics, is provably optimal. Moreover, unlike existing approaches, it is independent of any assumption on the source and nature of variations

Discrete Gate Sizing Methodologies for Delay, Area and Power Optimization

The modeling of an individual gate and the optimization of circuit performance has long been a critical issue in the VLSI industry. In this work, we first study of the gate sizing problem for today\u27s industrial designs, and explore the contributions and limitations of all the existing approaches, which mainly suffer from producing only continuous solutions, using outdated timing models or experiencing performance inefficiency. In this dissertation, we present our new discrete gate sizing technique which optimizes different aspects of circuit performance, including delay, area and power consumption. And our method is fast and efficient as it applies the local search instead of global exhaustive search during gate size selection process, which greatly reduces the search space and improves the computation complexity. In addition to that, it is also flexible with different timing models, and it is able to deal with the constraints of input/output slew and output load capacitance, under which very few previous research works were reported. We then propose a new timing model, which is derived from the classic Elmore delay model, but takes the features of modern timing models from standard cell library. With our new timing model, we are able to formulate the combinatorial discrete sizing problem as a simplified mathematical expression and apply it to existing Lagrangian relaxation method, which is shown to converge to optimal solution. We demonstrate that the classic Elmore delay model based gate sizing approaches can still be valid. Therefore, our work might provide a new look into the numerous Elmore delay model based research works in various areas (such as placement, routing, layout, buffer insertion, timing analysis, etc.)

CMOS circuit speed and power optimization using simplified RC delay model

A simplified RC delay model which is expressed explicitly in terms of transistor widths is presented to easily perform circuit analysis and quickly optimize the transistor widths for delay and power without having to do tedious layout or schematic simulation. A novel heuristic gradient descent method is used to effectively solve the optimization problem. Popular parallel prefix adders such as Brent-Kung, Skylansky and Kogge-Stone adders are modeled using the proposed simplified RC delay model and a power-delay performance comparison is done after optimization to show the ability of the model. The optimization results suggest that the Brent-Kung adder is more efficient in terms of both delay and power by having the lowest power-delay product followed by the Skylansky adder and then the Kogge-Stone adder