Performance and power optimization in VLSI physical design

As VLSI technology enters the nanoscale regime, a great amount of efforts have been made to reduce interconnect delay. Among them, buffer insertion stands out as an effective technique for timing optimization. A dramatic rise in on-chip buffer density has been witnessed. For example, in two recent IBM ASIC designs, 25% gates are buffers. In this thesis, three buffer insertion algorithms are presented for the procedure of performance and power optimization. The second chapter focuses on improving circuit performance under inductance effect. The new algorithm works under the dynamic programming framework and runs in provably linear time for multiple buffer types due to two novel techniques: restrictive cost bucketing and efficient delay update. The experimental results demonstrate that our linear time algorithm consistently outperforms all known RLC buffering algorithms in terms of both solution quality and runtime. That is, the new algorithm uses fewer buffers, runs in shorter time and the buffered tree has better timing. The third chapter presents a method to guarantee a high fidelity signal transmission in global bus. It proposes a new redundant via insertion technique to reduce via variation and signal distortion in twisted differential line. In addition, a new buffer insertion technique is proposed to synchronize the transmitted signals, thus further improving the effectiveness of the twisted differential line. Experimental results demonstrate a 6GHz signal can be transmitted with high fidelity using the new approaches. In contrast, only a 100MHz signal can be reliably transmitted using a single-end bus with power/ground shielding. Compared to conventional twisted differential line structure, our new techniques can reduce the magnitude of noise by 45% as witnessed in our simulation. The fourth chapter proposes a buffer insertion and gate sizing algorithm for million plus gates. The algorithm takes a combinational circuit as input instead of individual nets and greatly reduces the buffer and gate cost of the entire circuit. The algorithm has two main features: 1) A circuit partition technique based on the criticality of the primary inputs, which provides the scalability for the algorithm, and 2) A linear programming formulation of non-linear delay versus cost tradeoff, which formulates the simultaneous buffer insertion and gate sizing into linear programming problem. Experimental results on ISCAS85 circuits show that even without the circuit partition technique, the new algorithm achieves 17X speedup compared with path based algorithm. In the meantime, the new algorithm saves 16.0% buffer cost, 4.9% gate cost, 5.8% total cost and results in less circuit delay

Effective network grid synthesis and optimization for high performance very large scale integration system design

制度:新 ; 文部省報告番号:甲2642号 ; 学位の種類:博士(工学) ; 授与年月日:2008/3/15 ; 早大学位記番号:新480

Some Applications of the Weighted Combinatorial Laplacian

The weighted combinatorial Laplacian of a graph is a symmetric matrix which is the discrete analogue of the Laplacian operator. In this thesis, we will study a new application of this matrix to matching theory yielding a new characterization of factor-criticality in graphs and matroids. Other applications are from the area of the physical design of very large scale integrated circuits. The placement of the gates includes the minimization of a quadratic form given by a weighted Laplacian. A method based on the dual constrained subgradient method is proposed to solve the simultaneous placement and gate-sizing problem. A crucial step of this method is the projection to the flow space of an associated graph, which can be performed by minimizing a quadratic form given by the unweighted combinatorial Laplacian.Andwendungen der gewichteten kombinatorischen Laplace-Matrix Die gewichtete kombinatorische Laplace-Matrix ist das diskrete Analogon des Laplace-Operators. In dieser Arbeit stellen wir eine neuartige Charakterisierung von Faktor-Kritikalität von Graphen und Matroiden mit Hilfe dieser Matrix vor. Wir untersuchen andere Anwendungen im Bereich des Entwurfs von höchstintegrierten Schaltkreisen. Die Platzierung basiert auf der Minimierung einer quadratischen Form, die durch eine gewichtete kombinatorische Laplace-Matrix gegeben ist. Wir präsentieren einen Algorithmus für das allgemeine simultane Platzierungs- und Gattergrößen-Optimierungsproblem, der auf der dualen Subgradientenmethode basiert. Ein wichtiger Bestandteil dieses Verfahrens ist eine Projektion auf den Flussraum eines assoziierten Graphen, die als die Minimierung einer durch die Laplace-Matrix gegebenen quadratischen Form aufgefasst werden kann

34th Midwest Symposium on Circuits and Systems-Final Program

Organized by the Naval Postgraduate School Monterey California. Cosponsored by the IEEE Circuits and Systems Society. Symposium Organizing Committee: General Chairman-Sherif Michael, Technical Program-Roberto Cristi, Publications-Michael Soderstrand, Special Sessions- Charles W. Therrien, Publicity: Jeffrey Burl, Finance: Ralph Hippenstiel, and Local Arrangements: Barbara Cristi

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

HIGH PERFORMANCE CLOCK DISTRIBUTION FOR HIGH-SPEED VLSI SYSTEMS

Tohoku University堀口 進課

DREAMPlaceFPGA-MP: An Open-Source GPU-Accelerated Macro Placer for Modern FPGAs with Cascade Shapes and Region Constraints

FPGA macro placement plays a pivotal role in routability and timing closer to the modern FPGA physical design flow. In modern FPGAs, macros could be subject to complex cascade shape constraints requiring instances to be placed in consecutive sites. In addition, in real-world FPGA macro placement scenarios, designs could have various region constraints that specify boundaries within which certain design instances and macros should be placed. In this work, we present DREAMPlaceFPGA-MP, an open-source GPU-accelerated FPGA macro-placer that efficiently generates legal placements for macros while honoring cascade shape requirements and region constraints. Treating multiple macros in a cascade shape as a large single instance and restricting instances to their respective regions, DREAMPlaceFPGA-MP obtains roughly legal placements. The macros are legalized in multiple steps to efficiently handle cascade shapes and region constraints. Our experimental results demonstrate that DREAMPlaceFPGA-MP is among the top contestants of the MLCAD 2023 FPGA Macro-Placement Contest