High-performance and Low-power Clock Network Synthesis in the Presence of Variation.

Semiconductor technology scaling requires continuous evolution of all aspects of physical design of integrated circuits. Among the major design steps, clock-network synthesis has been greatly affected by technology scaling, rendering existing methodologies inadequate. Clock routing was previously sufficient for smaller ICs, but design difficulty and structural complexity have greatly increased as interconnect delay and clock frequency increased in the 1990s. Since a clock network directly influences IC performance and often consumes a substantial portion of total power, both academia and industry developed synthesis methodologies to achieve low skew, low power and robustness from PVT variations. Nevertheless, clock network synthesis under tight constraints is currently the least automated step in physical design and requires significant manual intervention, undermining turn-around-time. The need for multi-objective optimization over a large parameter space and the increasing impact of process variation make clock network synthesis particularly challenging. Our work identifies new objectives, constraints and concerns in the clock-network synthesis for systems-on-chips and microprocessors. To address them, we generate novel clock-network structures and propose changes in traditional physical-design flows. We develop new modeling techniques and algorithms for clock power optimization subject to tight skew constraints in the presence of process variations. In particular, we offer SPICE-accurate optimizations of clock networks, coordinated to reduce nominal skew below 5 ps, satisfy slew constraints and trade-off skew, insertion delay and power, while tolerating variations. To broaden the scope of clock-network-synthesis optimizations, we propose new techniques and a methodology to reduce dynamic power consumption by 6.8%-11.6% for large IC designs with macro blocks by integrating clock network synthesis within global placement. We also present a novel non-tree topology that is 2.3x more power-efficient than mesh structures. We fuse several clock trees to create large-scale redundancy in a clock network to bridge the gap between tree-like and mesh-like topologies. Integrated optimization techniques for high-quality clock networks described in this dissertation strong empirical results in experiments with recent industry-released benchmarks in the presence of process variation. Our software implementations were recognized with the first-place awards at the ISPD 2009 and ISPD 2010 Clock-Network Synthesis Contests organized by IBM Research and Intel Research.Ph.D.Electrical EngineeringUniversity of Michigan, Horace H. Rackham School of Graduate Studieshttp://deepblue.lib.umich.edu/bitstream/2027.42/89711/1/ejdjsy_1.pd

Analysis and optimization of VLSI Clock Distribution Networks for skew variability reduction

As VLSI technology moves into the Ultra-Deep Sub-Micron (UDSM) era, manufacturing variations, power supply noise and temperature variations greatly affect the performance and yield of VLSI circuits. Clock Distribution Network (CDN), which is one of the biggest and most important nets in any synchronous VLSI chip, is especially sensitive to these variations. To address this problem variability-aware analysis and optimization techniques for VLSI circuits are needed. In the first part of this thesis an analytical bound for the unwanted skew due to interconnect variation is established. Experimental results show that this bound is safer, tighter and computationally faster than existing approaches. This bound could be used in variation-aware clock tree synthesis.The second part of the thesis deals with optimizing a given clock tree to minimize the unwanted skew variations. Non-tree CDNs have been recognized as a promising approach to overcome the variation problem. We propose a novel non-tree CDN obtained by adding cross links in an existing clock tree. We analyze the effect of the link insertion on clock skew variability and propose link insertion schemes. The non-tree CDNs so obtained are shown to be highly tolerant to skew variability with very little increase in total wire-length. This can be used in applications such as ASIC design where a significant increase in the total wire-length is unacceptable

Fast interconnect optimization

As the continuous trend of Very Large Scale Integration (VLSI) circuits technology scaling and frequency increases, delay optimization techniques for interconnect are increasingly important for achieving timing closure of high performance designs. For the gigahertz microprocessor and multi-million gate ASIC designs it is crucial to have fast algorithms in the design automation tools for many classical problems in the field to shorten time to market of the VLSI chip. This research presents algorithmic techniques and constructive models for two such problems: (1) Fast buffer insertion for delay optimization, (2) Wire sizing for delay optimization and variation minimization on non-tree networks. For the buffer insertion problem, this dissertation proposes several innovative speedup techniques for different problem formulations and the realistic requirement. For the basic buffer insertion problem, an O(n log2 n) optimal algorithm that runs much faster than the previous classical van GinnekenÂs O(n2) algorithm is proposed, where n is the number of buffer positions. For modern design libraries that contain hundreds of buffers, this research also proposes an optimal algorithm in O(bn2) time for b buffer types, a significant improvement over the previous O(b2n2) algorithm by Lillis, Cheng and Lin. For nets with small numbers of sinks and large numbers of buffer positions, a simple O(mn) optimal algorithm is proposed, where m is the number of sinks. For the buffer insertion with minimum cost problem, the problem is first proved to be NP-complete. Then several optimal and approximation techniques are proposed to further speed up the buffer insertion algorithm with resource control for big industrial designs. For the wire sizing problem, we propose a systematic method to size the wires of general non-tree RC networks. The new method can be used for delay optimization and variation reduction

Improved algorithms for link-based non-tree clock networks for skew variability reduction

In the nanometer VLSI technology, the variation effects like manufacturing variation, power supply noise, temperature etc. become very significant. As one of the most vital nets in any synchronous VLSI chip, the Clock Distribution Network (CDN) is especially sensitive to these variations. Recently proposed link-based non-tree [1] addresses this problem by constructing a non-tree that is significantly more tolerant to variations when compared to a clock tree. Although the two algorithms proposed in [1] are effective in reducing the skew variability, they have a few drawbacks including high com-plexity, lengthy links and uneven link distribution across the clock network. In this paper, we propose two new algorithms that can overcome these disadvantages. The effectiveness of the proposed algorithms has been validated using HSPICE based Monte Carlo simulations. Experimental results show that the new algorithms are able to achieve the same or better skew reduction with an average of 5 % wire length increase when compared to the 15 % wire length increase of the existing algorithms in [1]. Moreover, the new algorithms scale extremely well to big clock networks, i.e., the bigger the clock network, the less overall link cost (less than 2 % for the biggest benchmark we have)

Clock routing for high performance microprocessor designs.

Tian, Haitong.Chinese abstract is on unnumbered page.Thesis (M.Phil.)--Chinese University of Hong Kong, 2011.Includes bibliographical references (p. 65-74).Abstracts in English and Chinese.Abstract --- p.iAcknowledgement --- p.iiiChapter 1 --- Introduction --- p.1Chapter 1.1 --- Motivations --- p.1Chapter 1.2 --- Our Contributions --- p.2Chapter 1.3 --- Organization of the Thesis --- p.3Chapter 2 --- Background Study --- p.4Chapter 2.1 --- Traditional Clock Routing Problem --- p.4Chapter 2.2 --- Tree-Based Clock Routing Algorithms --- p.5Chapter 2.2.1 --- Clock Routing Using H-tree --- p.5Chapter 2.2.2 --- Method of Means and Medians(MMM) --- p.6Chapter 2.2.3 --- Geometric Matching Algorithm (GMA) --- p.8Chapter 2.2.4 --- Exact Zero-Skew Algorithm --- p.9Chapter 2.2.5 --- Deferred Merge Embedding (DME) --- p.10Chapter 2.2.6 --- Boundary Merging and Embedding (BME) Algorithm --- p.14Chapter 2.2.7 --- Planar Clock Routing Algorithm --- p.17Chapter 2.2.8 --- Useful-skew Tree Algorithm --- p.18Chapter 2.3 --- Non-Tree Clock Distribution Networks --- p.19Chapter 2.3.1 --- Grid (Mesh) Structure --- p.20Chapter 2.3.2 --- Spine Structure --- p.20Chapter 2.3.3 --- Hybrid Structure --- p.21Chapter 2.4 --- Post-grid Clock Routing Problem --- p.22Chapter 2.5 --- Limitations of the Previous Work --- p.24Chapter 3 --- Post-Grid Clock Routing Problem --- p.26Chapter 3.1 --- Introduction --- p.26Chapter 3.2 --- Problem Definition --- p.27Chapter 3.3 --- Our Approach --- p.30Chapter 3.3.1 --- Delay-driven Path Expansion Algorithm --- p.31Chapter 3.3.2 --- Pre-processing to Connect Critical ports --- p.34Chapter 3.3.3 --- Post-processing to Reduce Capacitance --- p.36Chapter 3.4 --- Experimental Results --- p.39Chapter 3.4.1 --- Experiment Setup --- p.39Chapter 3.4.2 --- Validations of the Delay and Slew Estimation --- p.39Chapter 3.4.3 --- Comparisons with the Tree Grow (TG) Approach --- p.41Chapter 3.4.4 --- Lowest Achievable Delays --- p.42Chapter 3.4.5 --- Simulation Results --- p.42Chapter 4 --- Non-tree Based Post-Grid Clock Routing Problem --- p.44Chapter 4.1 --- Introduction --- p.44Chapter 4.2 --- Handling Ports with Large Load Capacitances --- p.46Chapter 4.2.1 --- Problem Ports Identification --- p.47Chapter 4.2.2 --- Non-Tree Construction --- p.47Chapter 4.2.3 --- Wire Link Selection --- p.48Chapter 4.3 --- Path Expansion in Non-tree Algorithm --- p.51Chapter 4.4 --- Limitations of the Non-tree Algorithm --- p.51Chapter 4.5 --- Experimental Results --- p.51Chapter 4.5.1 --- Experiment Setup --- p.51Chapter 4.5.2 --- Validations of the Delay and Slew Estimation --- p.52Chapter 4.5.3 --- Lowest Achievable Delays --- p.53Chapter 4.5.4 --- Results on New Benchmarks --- p.53Chapter 4.5.5 --- Simulation Results --- p.55Chapter 5 --- Efficient Partitioning-based Extension --- p.57Chapter 5.1 --- Introduction --- p.57Chapter 5.2 --- Partition-based Extension --- p.58Chapter 5.3 --- Experimental Results --- p.61Chapter 5.3.1 --- Experiment Setup --- p.61Chapter 5.3.2 --- Running Time Improvement with Partitioning Technique --- p.61Chapter 6 --- Conclusion --- p.63Bibliography --- p.6

Algorithms for the scaling toward nanometer VLSI physical synthesis

Along the history of Very Large Scale Integration (VLSI), we have successfully scaled down the size of transistors, scaled up the speed of integrated circuits (IC) and the number of transistors in a chip - these are just a few examples of our achievement in VLSI scaling. It is projected to enter the nanometer (timing estimation and buffer planning for global routing and other early stages such as floorplanning. A novel path based buffer insertion scheme is also included, which can overcome the weakness of the net based approaches. Part-2 Circuit clustering techniques with the application in Field-Programmable Gate Array (FPGA) technology mapping The problem of timing driven n-way circuit partitioning with application to FPGA technology mapping is studied and a hierarchical clustering approach is presented for the latest multi-level FPGA architectures. Moreover, a more general delay model is included in order to accurately characterize the delay behavior of the clusters and circuit elements

Post Routing Performance Optimization via Multi-Link Insertion and Non-Uniform Wiresizing

Most existing performance-driven and clock routing algorithms construct optimal routing topology for each net individually without considering its routability on the chip, so they can not guarantee performance after all nets are routed. This paper proposes a new approach for post routing performance optimization via multi-link insertion and non-uniform wiresizing, which improves the performance of a net topology obtained from a global routing solution. Unlike previous approaches, it can achieve reduction in both maximum delay and skew to satisfy user specified constraints and minimizes the routing resource consumed. During optimization, the topology of the net is kept routable. Experiments show that link insertion and wiresizing can improve net performance significantly, and among all approaches, multi-link insertion and wiresizing achieves the best performance and area efficiency. 1 Introduction The advent of sub-micron and deep sub-micron technologies has made interconnect routing..

Lexicographic path searches for FPGA routing

This dissertation reports on studies of the application of lexicographic graph searches to solve problems in FPGA detailed routing. Our contributions include the derivation of iteration limits for scalar implementations of negotiation congestion for standard floating point types and the identification of pathological cases for path choice. In the study of the routability-driven detailed FPGA routing problem, we show universal detailed routability is NP-complete based on a related proof by Lee and Wong. We describe the design of a lexicographic composition operator of totally-ordered monoids as path cost metrics and show its optimality under an adapted A* search. Our new router, CornNC, based on lexicographic composition of congestion and wirelength, established a new minimum track count for the FPGA Place and Route Challenge. For the problem of long-path timing-driven FPGA detailed routing, we show that long-path budgeted detailed routability is NP-complete by reduction to universal detailed routability. We generalise the lexicographic composition to any finite length and verify its optimality under A* search. The application of the timing budget solution of Ghiasi et al. is used to solve the long-path timing budget problem for FPGA connections. Our delay-clamped spiral lexicographic composition design, SpiralRoute, ensures connection based budgets are always met, thus achieves timing closure when it successfully routes. For 113 test routing instances derived from standard benchmarks, SpiralRoute found 13 routable instances with timing closure that were unroutable by a scalar negotiated congestion router and achieved timing closure in another 27 cases when the scalar router did not, at the expense of increased runtime. We also study techniques to improve SpiralRoute runtimes, including a data structure of a trie augmented by data stacks for minimum element retrieval, and the technique of step tomonoid elimination in reducing the retrieval depth in a trie of stacks structure

Sincronização em sistemas integrados a alta velocidade

Doutoramento em Engenharia ElectrotécnicaA distribui ção de um sinal relógio, com elevada precisão espacial (baixo skew) e temporal (baixo jitter ), em sistemas sí ncronos de alta velocidade tem-se revelado uma tarefa cada vez mais demorada e complexa devido ao escalonamento da tecnologia. Com a diminuição das dimensões dos dispositivos e a integração crescente de mais funcionalidades nos Circuitos Integrados (CIs), a precisão associada as transições do sinal de relógio tem sido cada vez mais afectada por varia ções de processo, tensão e temperatura. Esta tese aborda o problema da incerteza de rel ogio em CIs de alta velocidade, com o objetivo de determinar os limites do paradigma de desenho sí ncrono. Na prossecu ção deste objectivo principal, esta tese propõe quatro novos modelos de incerteza com âmbitos de aplicação diferentes. O primeiro modelo permite estimar a incerteza introduzida por um inversor est atico CMOS, com base em parâmetros simples e su cientemente gen éricos para que possa ser usado na previsão das limitações temporais de circuitos mais complexos, mesmo na fase inicial do projeto. O segundo modelo, permite estimar a incerteza em repetidores com liga ções RC e assim otimizar o dimensionamento da rede de distribui ção de relógio, com baixo esfor ço computacional. O terceiro modelo permite estimar a acumula ção de incerteza em cascatas de repetidores. Uma vez que este modelo tem em considera ção a correla ção entre fontes de ruí do, e especialmente util para promover t ecnicas de distribui ção de rel ogio e de alimentação que possam minimizar a acumulação de incerteza. O quarto modelo permite estimar a incerteza temporal em sistemas com m ultiplos dom ínios de sincronismo. Este modelo pode ser facilmente incorporado numa ferramenta autom atica para determinar a melhor topologia para uma determinada aplicação ou para avaliar a tolerância do sistema ao ru ído de alimentação. Finalmente, usando os modelos propostos, são discutidas as tendências da precisão de rel ogio. Conclui-se que os limites da precisão do rel ogio são, em ultima an alise, impostos por fontes de varia ção dinâmica que se preveem crescentes na actual l ogica de escalonamento dos dispositivos. Assim sendo, esta tese defende a procura de solu ções em outros ní veis de abstração, que não apenas o ní vel f sico, que possam contribuir para o aumento de desempenho dos CIs e que tenham um menor impacto nos pressupostos do paradigma de desenho sí ncrono.Distributing a the clock simultaneously everywhere (low skew) and periodically everywhere (low jitter) in high-performance Integrated Circuits (ICs) has become an increasingly di cult and time-consuming task, due to technology scaling. As transistor dimensions shrink and more functionality is packed into an IC, clock precision becomes increasingly a ected by Process, Voltage and Temperature (PVT) variations. This thesis addresses the problem of clock uncertainty in high-performance ICs, in order to determine the limits of the synchronous design paradigm. In pursuit of this main goal, this thesis proposes four new uncertainty models, with di erent underlying principles and scopes. The rst model targets uncertainty in static CMOS inverters. The main advantage of this model is that it depends only on parameters that can easily be obtained. Thus, it can provide information on upcoming constraints very early in the design stage. The second model addresses uncertainty in repeaters with RC interconnects, allowing the designer to optimise the repeater's size and spacing, for a given uncertainty budget, with low computational e ort. The third model, can be used to predict jitter accumulation in cascaded repeaters, like clock trees or delay lines. Because it takes into consideration correlations among variability sources, it can also be useful to promote oorplan-based power and clock distribution design in order to minimise jitter accumulation. A fourth model is proposed to analyse uncertainty in systems with multiple synchronous domains. It can be easily incorporated in an automatic tool to determine the best topology for a given application or to evaluate the system's tolerance to power-supply noise. Finally, using the proposed models, this thesis discusses clock precision trends. Results show that limits in clock precision are ultimately imposed by dynamic uncertainty, which is expected to continue increasing with technology scaling. Therefore, it advocates the search for solutions at other abstraction levels, and not only at the physical level, that may increase system performance with a smaller impact on the assumptions behind the synchronous design paradigm