Lagrangian relaxation-based multi-threaded discrete gate sizer

In integrated circuit design gate sizing is one of the key optimization techniques which is repeatedly invoked to trade-off delays for area and/or power of the gates during logic design and physical design stages. With increasing design sizes of a million gates and larger, discrete gate sizes and non-convex delay models the gate sizing algorithms that were designed for continuous sizes and convex delay models are slow and timing inaccurate. Of the several published discrete gate sizing algorithms, recent works have shown that Lagrangian relaxation based gate sizers have produced designs with the lowest power on average with high timing accuracy. But they are also very slow due to a large number of expensive timing updates spread across hundreds of iterations of solving the Lagrangian sub-problem. In this thesis we present a Lagrangian relaxation based multi-threaded discrete gate sizer for fast timing and power reduction by swapping the gate sizes and the threshold voltages. We developed two parallelization enabling techniques to reduce the runtime of Lagrangian sub-problem solver, namely, mutual exclusion edge (MEE) assignment and directed acyclic graph (DAG) based netlist traversal. MEEs are dummy edges assigned to reduce computational dependencies among gates sharing one or more common fan-ins. DAG based netlist traversal facilitates simultaneous resizing of gates belonging to different topological levels. We designed a Lagrange multiplier update framework that enables rapid convergence of the timing recovery and power recovery algorithms. To reduce the runtime of timing updates, we proposed a simple and fast-to-compute effective capacitance model and several mechanisms to calibrate the timing models to improve their accuracy. Compared to the state-of-the-art gate sizer, our proposed gate sizer is on average 15x faster and the optimized designs have only 1.7\% higher power. In digital synchronous designs simultaneous gate sizing and clock skew scheduling provides significantly more power saving. We extend the gate sizer to simultaneously schedule the clock skew. It can achieve an average of 18.8\% more reduction in power with only 20\% increase in the runtime

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

MOCAST 2021

The 10th International Conference on Modern Circuit and System Technologies on Electronics and Communications (MOCAST 2021) will take place in Thessaloniki, Greece, from July 5th to July 7th, 2021. The MOCAST technical program includes all aspects of circuit and system technologies, from modeling to design, verification, implementation, and application. This Special Issue presents extended versions of top-ranking papers in the conference. The topics of MOCAST include:Analog/RF and mixed signal circuits;Digital circuits and systems design;Nonlinear circuits and systems;Device and circuit modeling;High-performance embedded systems;Systems and applications;Sensors and systems;Machine learning and AI applications;Communication; Network systems;Power management;Imagers, MEMS, medical, and displays;Radiation front ends (nuclear and space application);Education in circuits, systems, and communications

High-performance Global Routing for Trillion-gate Systems-on-Chips.

Due to aggressive transistor scaling, modern-day CMOS circuits have continually increased in both complexity and productivity. Modern semiconductor designs have narrower and more resistive wires, thereby shifting the performance bottleneck to interconnect delay. These trends considerably impact timing closure and call for improvements in high-performance physical design tools to keep pace with the current state of IC innovation. As leading-edge designs may incorporate tens of millions of gates, algorithm and software scalability are crucial to achieving reasonable turnaround time. Moreover, with decreasing device sizes, optimizing traditional objectives is no longer sufficient. Our research focuses on (i) expanding the capabilities of standalone global routing, (ii) extending global routing for use in different design applications, and (iii) integrating routing within broader physical design optimizations and flows, e.g., congestion-driven placement. Our first global router relies on integer-linear programming (ILP), and can solve fairly large problem instances to optimality. Our second iterative global router relies on Lagrangian relaxation, where we relax the routing violation constraints to allowing routing overflow at a penalty. In both approaches, our desire is to give the router the maximum degree of freedom within a specified context. Empirically, both routers produce competitive results within a reasonable amount of runtime. To improve routability, we explore the incorporation of routing with placement, where the router estimates congestion and feeds this information to the placer. In turn, the emphasis on runtime is heightened, as the router will be invoked multiple times. Empirically, our placement-and-route framework significantly improves the final solution’s routability than performing the steps sequentially. To further enhance routability-driven placement, we (i) leverage incrementality to generate fast and accurate congestion maps, and (ii) develop several techniques to relieve cell-based and layout-based congestion. To broaden the scope of routing, we integrate a global router in a chip-design flow that addresses the buffer explosion problem.PHDComputer Science and EngineeringUniversity of Michigan, Horace H. Rackham School of Graduate Studieshttp://deepblue.lib.umich.edu/bitstream/2027.42/98025/1/jinhu_1.pd

Timing optimization during the physical synthesis of cell-based VLSI circuits

Tese (doutorado) - Universidade Federal de Santa Catarina, Centro Tecnológico, Programa de Pós-Graduação em Engenharia de Automação e Sistemas, Florianópolis, 2016.Abstract : The evolution of CMOS technology made possible integrated circuits with billions of transistors assembled into a single silicon chip, giving rise to the jargon Very-Large-Scale Integration (VLSI). The required clock frequency affects the performance of a VLSI circuit and induces timing constraints that must be properly handled by synthesis tools. During the physical synthesis of VLSI circuits, several optimization techniques are used to iteratively reduce the number of timing violations until the target clock frequency is met. The dramatic increase of interconnect delay under technology scaling represents one of the major challenges for the timing closure of modern VLSI circuits. In this scenario, effective interconnect synthesis techniques play a major role. That is why this thesis targets two timing optimization problems for effective interconnect synthesis: Incremental Timing-Driven Placement (ITDP) and Incremental Timing-Driven Layer Assignment (ITLA). For solving the ITDP problem, this thesis proposes a new Lagrangian Relaxation formulation that minimizes timing violations for both setup and hold timing constraints. This work also proposes a netbased technique that uses Lagrange multipliers as net-weights, which are dynamically updated using an accurate timing analyzer. The netbased technique makes use of a novel discrete search to relocate cells by employing the Euclidean distance to define a proper neighborhood. For solving the ITLA problem, this thesis proposes a network flow approach that handles simultaneously critical and non-critical segments, and exploits a few flow conservation conditions to extract timing information for each net segment individually, thereby enabling the use of an external timing engine. The experimental validation using benchmark suites derived from industrial circuits demonstrates the effectiveness of the proposed techniques when compared with state-of-the-art works.A evolução da tecnologia CMOS viabilizou a fabricação de circuitos integrados contendo bilhões de transistores em uma única pastilha de silício, dando origem ao jargão Very-Large-Scale Integration (VLSI). A frequência-alvo de operação de um circuito VLSI afeta o seu desempenho e induz restrições de timing que devem ser manipuladas pelas ferramentas de síntese. Durante a síntese física de circuitos VLSI, diversas técnicas de otimização são usadas para iterativamente reduzir o número de violações de timing até que a frequência-alvo de operação seja atingida. O aumento dramático do atraso das interconexões devido à evolução tecnológica representa um dos maiores desafios para o fluxo de timing closure de circuitos VLSI contemporâneos. Nesse cenário, técnicas de síntese de interconexão eficientes têm um papel fundamental. Por este motivo, esta tese aborda dois problemas de otimização de timing para uma síntese eficiente das interconexões de um circuito VLSI: Incremental Timing-Driven Placement (ITDP) e Incremental Timing-Driven Layer Assignment (ITLA). Para resolver o problema de ITDP, esta tese propõe uma nova formulação utilizando Relaxação Lagrangeana que tem por objetivo a minimização simultânea das violações de timing para restrições do tipo setup e hold. Este trabalho também propõe uma técnica que utiliza multiplicadores de Lagrange como pesos para as interconexões, os quais são atualizados dinamicamente através dos resultados de uma ferramenta de análise de timing. Tal técnica realoca as células do circuito por meio de uma nova busca discreta que adota a distância Euclidiana como vizinhança.Para resolver o problema de ITLA, esta tese propõe uma abordagem em fluxo em redes que otimiza simultaneamente segmentos críticos e não-críticos, e explora algumas condições de fluxo para extrair as informações de timing para cada segmento individualmente, permitindo assim o uso de uma ferramenta de timing externa. A validação experimental, utilizando benchmarks derivados de circuitos industriais, demonstra a eficiência das técnicas propostas quando comparadas com trabalhos estado da arte

Energy Management Systems and Potential Applications of Quantum Computing in the Energy Sector

The combined use of technologies plays a key role in the energy transition towards a green and sustainable economy, driven by the European Green Deal initiatives and the Paris Agreement to achieve climate neutrality in the European Union (EU) by 2050. Indeed, all viable solutions with no barriers to innovation should be considered if a fair, cost-effective, competitive, and green transition is to be ensured.Energy hubs enable the synergy of different forms of energy by exploiting their specific vir-tues. However, their management in an integrated context must be entrusted to automated manage-ment systems capable of making real-time decisions.This PhD thesis aims to assess the main potential applications of quantum computing to the energy sector in the current development scenario of quantum technologies, as well as provide the elements for modelling an energy hub and managing uncertainties.The thesis is organized as follows. Chapter 1 provides an introduction to energy manage-ment systems. The concept of an energy hub and its mathematical modelling are introduced in chap-ter 2. Chapter 3 introduces the fundamentals of energy supply. Chapter 4 examines potential use cases for quantum computing in the energy sector. Chapter 5 addresses the modelling of uncertain parameters. Chapter 6 concludes the thesis with a case study of two urban districts modelled as mul-ticarrier energy hubs connected by a multicarrier energy infrastructure providing electricity, gas and hydrogen. The conclusions are drawn in chapter 7. The appendices with additional insights enrich the thesis, which is full of comments and bibliographical references

Design and Analysis of Power Distribution Networks in VLSI Circuits.

Rapidly switching currents of the on-chip devices can cause fluctuations in the supply voltage which can be classified as IR and Ldi/dt drops. The voltage fluctuations in a supply network can inject noise in a circuit which may lead to functional failures of the design. Power supply integrity verification is, therefore, a critical concern in high-performance designs. Also, with decreasing supply voltages, gate-delay is becoming increasingly sensitive to supply voltage variation. With ever-diminishing clock periods, accurate analysis of the impact of supply voltage on circuit performance has also become critical. Increasing power consumption and clock frequency have exacerbated the Ldi/dt drop in every new technology generation. The Ldi/dt drop has become the dominant portion of the overall supply-drop in high performance designs. On-die passive decap, which has traditionally been used for suppressing Ldi/dt, has become expensive due to its area and leakage power overhead. This has created an urgent need for novel circuit techniques to suppress the Ldi/dt drop in power distribution networks. We provide accurate algorithmic solutions for determining the worst-case supply-drop and the impact of supply noise on circuit performance. We propose a path-based and a block-based approach for computing the maximum circuit delay under power supply fluctuations. We also propose an early-mode supply-drop estimation approach and a statistical approach for power grid analysis. All the proposed approaches are vectorless and account for both IR and Ldi/dt drops. We also propose a performance-aware decoupling capacitance allocation technique which uses timing slacks to drive the optimization. Finally, we present analog as well as all-digital circuit techniques for inductive supply noise suppression. The proposed all-digital circuit techniques were implemented in a test-chip, fabricated in a 0.13µm CMOS process. Measurements on the test-chip demonstrate a reduction in the supply fluctuations by 57% for a ramp loads and by 75% during resonance. We also present a low-power, all-digital on-chip oscilloscope for accurate measurement of supply noise. Supply noise measurements obtained from the on-chip oscilloscope were validated to conform well to those obtained from a traditional supply-drop monitor and direct on-chip probing.Ph.D.Electrical EngineeringUniversity of Michigan, Horace H. Rackham School of Graduate Studieshttp://deepblue.lib.umich.edu/bitstream/2027.42/58508/1/spant_1.pd

Lotsizing and scheduling in the glass container industry

Manufacturing organizations are keen to improve their competitive position in the global marketplace by increasing operational performance. Production planning is crucial to this end and represents one of the most challenging tasks managers are facing today. Among a large number of alternatives, production planning processes help decision-making by tradingoff conflicting objectives in the presence of technological, marketing and financial constraints.Two important classes of such problems are lotsizing and scheduling. Proofs from complexity theory supported by computational experiments clearly show the hardness of solving lotsizing and scheduling problems.Motivated by a real-world case, the glass container industry production planning and scheduling problem is studied in depth. Due to its inherent complexity and to the frequent interdependencies between decisions that are made at and affect different organizational echelons, the system is decomposed into a two-level hierarchically organized planning structure: long-term and short-term levels.This dissertation explores extensions of lotsizing and scheduling problems that appear in both levels. We address these variants in two research directions. On one hand, we develop and implement different approaches to obtain good quality solutions, as metaheuristics (namely variable neighborhood search) and Lagrangian-based heuristics, as well as other special-purpose heuristics. On the other hand, we try to combine new stronger models and valid inequalities based on the polyhedral structure of these problems to tighten linear relaxations and speed up the solution process.Manufacturing organizations are keen to improve their competitive position in the global marketplace by increasing operational performance. Production planning is crucial to this end and represents one of the most challenging tasks managers are facing today. Among a large number of alternatives, production planning processes help decision-making by tradingoff conflicting objectives in the presence of technological, marketing and financial constraints.Two important classes of such problems are lotsizing and scheduling. Proofs from complexity theory supported by computational experiments clearly show the hardness of solving lotsizing and scheduling problems.Motivated by a real-world case, the glass container industry production planning and scheduling problem is studied in depth. Due to its inherent complexity and to the frequent interdependencies between decisions that are made at and affect different organizational echelons, the system is decomposed into a two-level hierarchically organized planning structure: long-term and short-term levels.This dissertation explores extensions of lotsizing and scheduling problems that appear in both levels. We address these variants in two research directions. On one hand, we develop and implement different approaches to obtain good quality solutions, as metaheuristics (namely variable neighborhood search) and Lagrangian-based heuristics, as well as other special-purpose heuristics. On the other hand, we try to combine new stronger models and valid inequalities based on the polyhedral structure of these problems to tighten linear relaxations and speed up the solution process

Buffer insertion in large circuits using look-ahead and back-off techniques

Buffer insertion is an essential technique for reducing interconnect delay in submicron circuits. Though it is a well researched area, there is a need for robust and effective algorithms to perform buffer insertion at the circuit level. This thesis proposes a new buffer insertion algorithm for large circuits. The algorithm finds a buffering solution for the entire circuit such that buffer cost is minimized and the timing requirements of the circuit are satisfied. The algorithm iteratively inserts buffers in the circuit improving the circuit delay step by step. At the core of this algorithm are very simple but extremely effective techniques that constructively guide the search for a good buffering solution. A flexibility to adapt to the user's requirements and the ability to reduce the number of buffers are the strengths of this algorithm. Experimental results on ISCAS85 benchmark circuits show that the proposed algorithm, on average, yields 36% reduction in the number of buffers, and runs three times faster than one of the best known previously researched algorithms

On the deployment of on-chip noise sensors

The relentless technology scaling has led to significantly reduced noise margin and complicated functionalities. As such, design time techniques per se are less likely to ensure power integrity, resulting in runtime voltage emergencies. To alleviate the issue, recently several works have shed light on the possibilities of dynamic noise management systems. Most of these works rely on on-chip noise sensors to accurately capture voltage emergencies. However, they all assume that the placement of the sensors is given. It remains an open problem in the literature how to optimally place a given number of noise sensors for best voltage emergency detection. The problem of noise sensor placement is defined at first along with a novel sensing quality metric (SQM) to be maximized. The threshold voltage for noise sensors to report emergencies serves as a critical tuning knob between the system failure rate and false alarms. The problem of minimizing the system alarm rate subject to a given system failure rate constraint is formulated. It is further shown that with the help of IDDQ measurements during testing which reveal process variation information, it is possible and efficient to compute a per-chip optimal threshold voltage threshold. In the third chapter, a novel framework to predict the resonance frequency using existing on-chip noise sensors, based on the theory of 1-bit compressed sensing is proposed. The proposed framework can help to achieve the resonance frequency of individual chips so as to effectively avoid resonance noise at runtime --Abstract, page iii