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An automatic layout generator for integrated circuit design Lin, Lan 2001

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An Automatic Layout Generator for Integrated Circuit Design by Lan Lin B.Eng., Nanjing University of Aeronautics and Astronautics, 1996 M.Eng., Nanjing University of Aeronautics and Astronautics, 1999 A THESIS SUBMITTED IN PARTIAL FULFILLMENT OF THE REQUIREMENTS FOR THE DEGREE OF Master of Science in THE FACULTY OF GRADUATE STUDIES (Department of Computer Science) we accept this thesis as conforming to the required standard THE UNIVERSITY OF BRITISH COLUMBIA August 2001 © Lan Lin, 2001 In present ing this thes i s /essay in partial fulf i l lment of the requirements for an advanced degree at the University of British Columbia, I agree that the Library shall make it freely avai lable for reference and study. I further agree that permission for extensive copying for this thesis for scholarly purposes may be granted by the Head of my department or by his or her representatives. It is understood that copying or publication of this thesis for financial gain shall not be al lowed without my written permission. Auyus-t , zoo] Date Department of Computer Sc ience The University of British Columbia 2366 Main mall Vancouver, B C Canada V6T 1Z4 A B S T R A C T ! In integrated circuit design, one of the most tedious and time-consuming steps is the generation of the layout. During the last decade, considerable effort has been invested in the development of CAD tools dedicated to the automation of this step. This effort has been largely motivated by a need for alternatives to manual layout to greatly reduce the development time and cost. This thesis describes my contribution through the implementation of a flexible and automatic integrated circuit layout generator. With this tool, the designer only needs to depict the circuit at a high level, while the tool works out the details of the design and produces the final layout. In comparison with most of the current layout synthesis tools, my tool aims to realize the generality while still preserving most of the efficiency of the hand design, and facilitate greater reuse. The solution is based on constraint solving. The tool is written in Java. Two architectural styles are followed in the whole design, call-and-return and object-oriented. Experimental results demonstrate the effectiveness of the tool in generating layouts comparable to manual designs, with very quick turn-around time and no manual intervention. i i •CONTENTS! A B S T R A C T ii CONTENTS «» L I S T OF T A B L E S v L I S T OF FIGURES vi ACKNOWLEDGEMENTS vii DEDICATION viii C H A P T E R 1 INTRODUCTION 1 1.1 Motivation and Problem Statement 1 1.2 Related Work 2 1.3 Overview of the Current Solution 4 1.4 Thesis Outline 6 1.5 Contributions 6 C H A P T E R 2 U S E R A P I 9 2.1 An Example 9 2.2 The User's View 12 2.3 The Layout Generator's View 15 2.4 The Complete View 17 2.5 Example Code for the Adder 19 C H A P T E R 3 PRIMITIVE O B J E C T GENERATORS 2 2 3.1 Interfaces 23 3.2 Cost Function 27 3.3 Device Merging 27 3.4 Routing 29 C H A P T E R 4 LINEAR P R O G R A M INTERFACE 3 1 4.1 Constraint Generation 31 4.2 Constraint Solving 34 iii 4.2.1 LPABO Solver .,..36 4.2.2 A Depth-first-traversal Algorithm 37 CHAPTER 5 M A G I C INTERFACE 39 5.1 Interfaces 39 CHAPTER 6 EXPERIMENTS 41 6.1 Methodology 41 6.2 Results 41 CHAPTER 7 CONCLUSIONS AND FUTURE WORK 46 BIBLIOGRAPHY 48 APPENDIX A LAYOUT GENERATION T O O L SOURCE 52 APPENDIX B LAYOUT GENERATION E X A M P L E SOURCE 101 APPENDIX C LPABO INPUT AND OUTPUT DATA FORMAT 106 APPENDIX D M A G I C FILE FORMAT 115 iv r Table 2.1 Interface Signal 17 Table 2.2 Class Circuit 18 Table 2.3 Class Row 18 Table 3.1 Class GeomRowProto 25 Table 4.1 Class ConstraintSet 33 Table 4.2 Interfaces LPfactory and OPfactory, Classes Lpabo and Opt 35 Table 5.1 Class MagicOutput 39 Table 5.2 Class Magic Writer 40 Table 6.1 Example Cell Density 45 Table A. 1 Index of Layout Generation Tool Source 52 Table B. 1 Index of Layout Generation Example Source 101 Table C. 1 Index of LPABO Input and Output Data Format 106 Figure 1.1 The Architecture of the Tool 8 Figure 2.1 A One-bit Full Adder (FA) : 9 Figure 2.2 Implementation of A One-bit Full Adder 10 Figure 2.3 User Specification of A One-bit FA 11 Figure 2.4 An n-bit Ripple-carry Adder 12 Figure 2.5 Code Fragment of An n-bit Ripple-carry Adder 12 Figure 2.6 Implementations of the Signal Interface 13 Figure 2.7 Subclasses of Circuit 14 Figure 2.8 Class Hierarchy of Row 15 Figure 2.9 Code Fragment of Class SumBlock 20 Figure 2.10 Code Fragment of Class OneBitFA 21 Figure 3.1 Object and Constraint Generation 23 Figure 3.2 Member Variables of Class GeomRow 24 Figure 3.3 Device Merging Cases and Transistor Building Bricks 28 Figure 6.1 Example Layout for One Single Inverter Placement 42 Figure 6.2 Example Layout for Inverter Row Placement 43 Figure 6.3 Example Layout for Inverter Array Placement : 43 Figure 6.4 Comparison of Generated Layout with Manual Design for FifoStage 44 vi A C K N O W L E D G E M E N T S ; I would like to gratefully acknowledge my supervisor, Dr. Mark Greenstreet, for opening the new field for me, as well as for staying with me with extensive patience and encouragement with every bit of my progress during the past year. This work would not have been possible without his enthusiastic supervision, invaluable guidance, and generous financial support. I also wish to thank Dr. Mike Feeley and Dr. Kris De Voider for taking the time being my second readers, and for providing me with many insightful comments. I owe my gratitude to Albert Lai, who taught me many valuable lessons in this project, and was always generous in his help. Special thanks go to Dr. Alan Ffu, Brian Winters, Alvin Albrecht, Marius Laza, and my project partner, Yang Lu, for discussing every problem with me with their great ideas and creating such a harmonious atmosphere in the ISD lab. I am grateful to all my friends at UBC, for being my surrogate family during the years I have stayed here and for their continued moral support. Their friendship makes me feel warm and makes my life in this alien land much easier. Finally I am forever indebted to my parents, Tao Lin and Xiuying Zhou, my twin brother, Song Lin, and my husband, Fengguang Song. My present status in life, this M.Sc. included, is a result of their extrordinary will, efforts and sacrifices. I am only that much more grateful for all that they have done for me. Mere words cannot express my deep appreciation enough. L A N LIN The University of British Columbia August 2001 vii To my parents, my twin brother, and my husband, for their endless love, understanding and support. viii Modern technology changes toward deep sub-micron process technologies, and the accompanying increase in the complexity of VLSI designs, have driven an ongoing conversion from hand design to the extensive use of computer aided layout tools to support the layout process. Manual layout using polygon layout editors is both time-consuming and error-prone; therefore, the development of automatic layout tools is an area of ongoing interest to free the designers from design rule considerations and allow them to focus on the topology of the design, thus increasing design productivity [Dunlop 80] [Lotvin 84] [Marple 88] [Dao 93]. 1.1 Motivation and Problem Statement In integrated circuit design, one of the most tedious and time-consuming steps is the generation of the layout. Invariably, it requires that the designer be quite familiar with the physical design process, and the impact of layout geometry on circuit functionality and performance. Such a designer must know in advance every detail of the design process. During the last decade, considerable effort has been invested in the development of C A D tools dedicated to the automation of this step. This effort has been largely motivated by a need for alternatives to manual layout to greatly reduce the development time and cost. Although the regularity of some inner structures in these circuits has made such automation more feasible, it is not a trivial problem to automatically generate layouts competitive with handcrafted ones. The main problems are the increasing number of gates to be placed and interconnected, the optimization of the global size of the chip [Mathias 98], and the availability of more compact layouts while still ensuring performance close to that of a manual design. Indeed, the goal of any technique, whether it is behavior-, logic-, or layout-related, is to produce optimum circuits that meet the designer's specifications. By 1 optimum circuit, I mean an implementation where the designer and the tool achieve the best tradeoff of design metrics for the entire circuit. Important metrics for CMOS circuits today include delay (e.g., input to output propagation, clock period), silicon area, and power [Lefebvre 97]. As Steve Duval 1 pointed out in his talk at UBC Commerce in 1999 [Duvall 99], "optimization has, or promises to have, a significant impact on design productivity". Physical design involves the placement of circuit blocks and transistors on the integrated circuit "floorplan" and the routing of wires providing the electrical connections among these elements. Automatic place and route tools, which have been in use by the semiconductor industry for years, are faced with new challenges as the need for performance-based physical design has increased and as new layout strategies have been developed. Furthermore, circuit design involves the translation of logic functions into gate- or transistor-level equivalents. Until recently, most circuit design was performed manually by design engineers using schematic editors and circuit simulators. With the increasing magnitude of the circuit design problem, the industry has been moving toward automation of most of the circuit design process. This leads to the development of automatic circuit optimization capabilities spanning a broad class of problems, from transistor and wire sizing to direct synthesis of circuit topologies from logic statements. Last but not least, architectural design involves specifying the high level structure of an integrated circuit, which remains a largely manual process. Because architectural design decisions have an overwhelming impact on downstream design activities, models, tools, and techniques for architectural-level optimization are gaining more and more attention. 1.2 Related W o r k The most common approaches to layout automation have been layout generators, re-compaction of existing libraries, and automatic layout synthesis [Lefebvre 97]. Many papers have been published in this area and several systems developed in industry have covered a variety of layout styles and circuit structures and addressed many practical problems [Hill 85] [Wimer 87] [Chen 89] [Domic 89] [Ong 89] [Poirier 89] [Tani 91] [Sadakane 95] [Gupta 96] [Guruswamy 97]. 2 Procedural layout generators are a means of capturing the layout design in a somewhat design-rule independent fashion. However, each cell has to be supported by its own specific generator, which must be created by an experienced cell designer. On the other hand, generators also tend to be unfriendly to drastic changes in cell architecture and interconnect technology [Lefebvre 97]. Compaction of existing layout data provides a somewhat more elegant solution. A significant drawback mitigates the benefit by requiring the availability of existing layouts substantially the same as the intended library as a starting point. Again, like procedural generators, compactors do not lend themselves well to architectural changes [Lefebvre 97]. Layout synthesis, in contrast to the above methods, is concerned with creating layouts starting with only a transistor level netlist. Without requiring any pre-existing specific layout information, it provides an overall flexibility in the context of future advances in the state of the art in circuit synthesis. Nevertheless, in some cases, these solutions are not fully automatic, are inadequate for standard cell synthesis, or are obsolete due to rapidly changing process and design technology. Finally, no system has been reported in the literature that provides robust solutions to the practical problems essential to synthesizing high performance layout in a fully automatic manner with handcrafted density in current process technologies [Guruswamy 97]. The realization of any custom circuit requires three primary implementation phases: • Creation of a transistor circuit topology that provides a specific digital function. By topology I mean the allocation of N and P type transistors (or other devices) and their interconnections. • Sizing and ordering the transistors in the circuit topology. • Placing, routing and compacting the above transistors into a layout. A l l of the phases involve tradeoffs of design metrics that must be optimized not only within each phase but also across all phases [Lefebvre 97] (e.g., performance-driven transistor placement, performance-driven detailed routing). 3 C A D layout tools often represent transistors and contacts as the intersection of polygons on separate layers (e.g., Magic 1 does this with its "active" and "contact" layers). More recently, the trend has been toward object-based layout [Matheson 85] [Draney 89] [Duh 95] [Lakos 97]. Interesting advances have also been achieved in the field of constraint generation [Mogaki 91] [Choudhury 93]. In treating devices as objects and grouping semantically related geometry on multiple layers to form a single cohesive unit, we manipulate devices at a level of abstraction higher than that of intersecting polygons. The netlist is also explicit in the internal representation. Each device type can be parameterized to form a generator. In this sense, a single generator element can adapt to any valid size based on the current value of its arguments, which further increases the flexibility [Lakos 97]. 1.3 Overview of the Current Solution This thesis describes my contribution through the implementation of a flexible and automatic integrated circuit layout generator, the purpose of which is to exempt the designer from the tedious and time-consuming routine of manual layout. With this tool, the designer only needs to depict the circuit at a high level, while the tool works out the details of the design and produces the final layout. The solution is based on constraint solving. The tool is written in Java. From a software engineering perspective, I apply object-oriented methodology to VLSI chip design. Classes and interfaces are both carefully constructed to share the properties of abstraction, encapsulation, openness, and equilibrium, and follow the two principle aspects of OO design [Lea 94]: • The external, problem-space view: Descriptions of properties, responsibilities, capabilities and supported services as seen by software clients or the outside world. • The internal, solution-space view: Static and dynamic descriptions, constraints, and contracts among other components, delegates, collaborators and helpers, each of Magic is an interactive layout editor supporting on-line design rule checking and circuit extraction. It was developed by the group of John Ousterhout at the University of California at Berkeley [Ousterhout 84]. 4 which is known only with respect to a possibly incomplete external view (e.g., a class, but where the actual member may conform to a stronger subclass). The architecture of my tool is illustrated in Figure 1.1 along with the design flow. Applying the user API, the designer writes a Java program to describe the design. In his eyes, the circuit consists of a list of electrical connections and a list of relative placements. Under the user interface, four packages are defined to turn this high-level abstract description into its concrete geometry generation: • The Circuit package: Provides the user-level API to describe the circuit. • The Constraints package: Focused on constraint generation and solving. • The Router package: Does the routing. • The Magic package: Outputs the circuit in Magic format. As stated in Section 1.2, most of the previous layout synthesis tools have two common problems. First, they are normally designed for a schematic layout style, and thus are inefficient in producing general layouts. For example, some regular inner structures, such as the memory cell and the data-path, have their corresponding synthesis tools. However, the designer needs to define and figure out details of the remaining irregular part of the whole layout. Second, they are usually too specific in a domain. These synthesis tools, such as those for the Arithmetic Logic Unit (ALU), the register file, and the arithmetic units in digital signal processing, all have a few parameters in their templates. In this way, these tools write into the code the topological solution, which makes them work in their own very narrow application domains. There are 10 to 20 such tools to produce efficient layouts for different parts of the whole circuit design. Nevertheless, for the other parts, designers still need to do them by hand, which is quite inefficient. In comparison, our tool aims to realize the generality while still preserving most efficiency of the hand design. It can relieve the designer from much low-level design tedium and generate more reusable components and promote reuse for any kind of manual design. The first step in using our tool may take the designer some time to 5 describe the geometry of some building blocks, but later steps are simplified by assembling such blocks, which facilitate greater reuse. 1.4 Thesis Outline This chapter gives an introduction of the problem to solve, the basic idea behind my work, the overview of my tool, and its main contributions. In Chapter 2, I explain the user-level API. It is what the designer uses to write an abstract high-level description of the circuit that she desires to build. Chapter 3 presents the interfaces to the primitive object generator and the Router package. Chapter 4 describes the interface to the Linear Program (LP) package. Chapter 5 illustrates the Magic Interface. Chapter 6 describes some experiments with this tool and presents some test results. Finally, I present my conclusions in Chapter 7 along with some suggestions for possible future research. Appendices A and B contain listings of all the source code for the prototype of the tool. 1.5 Contributions Today's highest performance designs require extensive manual layout and layout optimization for performance reasons. Tomorrow's designs will require a similar level of physical design quality simply to ensure that the circuit works at all, due to the challenging electrical problems of D S M (Distributed Shared Memory) design. However, the design time for full-custom layout is prohibitive, and full-custom design flows tend to be incompatible with the verification required for complex designs. My supervisor, Mark Greenstreet, has the conjecture that a novel approach could be developed to raise physical design to a higher level, automating many tasks such as routing, compaction, and transistor and wire sizing. My work is to test the hypothesis and prove that we can do layouts productively. Preliminary results on small circuits are approaching the density of full-custom, expert-crafted layouts with far less effort. The key insight in this research is that behavioral descriptions are not an abstraction of physical designs. In practice, designers employ abstraction hierarchies for behavioral, geometrical, and timing aspects of their designs. While traditional C A D tools focus on the behavioral to sub-optimal 6 designs and/or manual layout, my tool aims to provide a general high-level solution. I come up with a novel exploratory implementation of a practical piece of nontrivial software. The primary contributions of my work lie in: • The specification, design and implementation of an architecture and prototype for the tool (Chapter 2, 3, 4, 5). • Demonstration of the automation of a layout optimization typical of handcrafted layout. In particular, allowing diffusion and contact sharing in transistor placement and geometry generation (Chapter 3). • Demonstration of parameterized layout objects and the encapsulation of design rules into a separate module. In particular, flexibility in drawing optimal layouts with user-defined signal width and transistor width, and in supporting a wide variety of process technologies (Chapter 2). 7 Figure 1.1 The Architecture of the Tool 8 CHAPTER 2 U S E R A P ? This chapter illustrates the user-level API. As for many other layout automation systems, the inputs to my tool consist of a netlist of sized transistors and signals with their interconnections, as well as a list of relative placements, which define the layout topology. The drawing methodology is based on placing small elementary parts side by side or below each other, while allowing diffusion and contact sharing along either side of generated transistors. Since the key components such as transistor placement, detailed routing, and layout compaction must be flexible enough to support a wide variety of processes, this tool aims to generate layouts for real designs including support of design using new deep sub-micron process technologies and enable design rule changes to existing designs or processes. A description of the technology being used, which specifies the width/spacing rules for all mask layers, is included as a parameter for the layout generator. Two architectural styles are followed in the whole design, call-and-return and object-oriented. 2.1 An Example I will begin with a simple example, a one-bit full adder (FA). As shown in Figure 2.1, it has three inputs and two outputs. A B * t FA in Sum = AXORBXOR Q, C 0 U t = AB + BC i n + C i nA 'in Sum Figure 2.1 A One-bit Full Adder (FA) 9 A simple circuit implementation of a one-bit full adder is shown below (Figure 2.2) using two complex gates and two inverters: C o u t = AB + Cin(A + B) Sum = C„„,(A + B + Cin) + ABCi„ Accordingly, the designer needs to define a sum block and a carry block, for the generation of the sum and the carry respectively. Inside each block the geometrical object can be viewed as a stack of slices. A slice can be a wire (e.g., power, ground), a row of transistors, or a region for channel routing (between .P and N transistor regions). What he needs to provide at this stage is no more than a description of the design in terms of different row slices, the relative positions of adjacent transistors, as well as all the electrical connections between any two terminals or between any terminal and any signal wire. Thus the user only needs to describe the electrical connections and the relative positions of all the cells and sub-cells in the circuit partitioning; the routing and physical placement are handled by my tool. In this case, he assembles the one-bit adder by simply mirroring the carry block and putting it below the sum block. The two blocks share the ground rail and fit nicely into a one-bit F A cell (Figure 2.3). The layout generator for the merged ground wire ensures that the width of the wire is sufficient for the sum of the currents on the two component wires. It is then easy to build an n-bit ripple-carry adder from n one-bit full adders (Figure 2.4). This can be written as a for-loop with the creation of n instances of the pre-Figure 2.2 Implementation of A One-bit Full Adder 10 defined OneBitFA cell (Figure 2.5). My tool performs the routing between cells, using the channels of the individual cells. The designer is thus freed from concerns of specifying additional routing regions. The tool determines the details of the layout geometry to implement the routing as well as the physical placement of transistors as a part of the automatic layout generation process. r — — — — — — — — — — — — — — — — — — —— — — — —— — ___________ —N. Vdd P-transistor Region i>, i»21>, i»4 F 7 p,r p 5 p„ Routing Region N-transistor Region N , N 2 N 3 N 4 N 7 N 6 N 5 N 8 Gnd SumBlock Vdd P-transistor Region I'o I'm I'M I'M I*i2 1*14 Routing Region N-transistor Region N , N 1 0 N „ N B - N , 2 " N M " Gnd > Vdd P-transistor Region P, P2 P, P 4 P 7 P* P s P s Routing Region N-transistor Region Ni N 2 N 3 N 4 N 7 N 6 N 5 N 8 Gnd N-transistor Region N , N I O N „ N « N , 2 N.4 Routing Region P-transistor Region P9 Pio Pll PlJ Pl2 1*14 Vdd CarryBlock.mirrorY( ).below(SumBlock) CarryBlock Figure 2.3 User Specification of A One-bit FA 11 A„-i B„.i An.2 Bn.2 A„.3 Bn.3 A i B , A 0 B 0 * * Cout F A * * F A Sum„.i F A Sumn_2 F A Sumn.i Sumi 1 i i r <- F A r v i n Sum0 Figure 2.4 An n-bit Ripple-carry Adder OneBitFA fa = new OneBitFA(...); Circuit c =fa.circuit(); Signal A[0J = c.a(); Signal BfO] = c.b(); Signal Cin = c.cin(); Signal Sum[0] = c.sum(); forfint i=l; i<n; { fa - new OneBitFA(...); fa. circuit(). cin(). connect( c. cout() ); c = fa.circuit().left(c); Signal A[i] = fa.circuit().a(); Signal Bfi] = fa.circuit().b(); Signal Sum[i] - fa. circuitf). sum(); if(i == (n-1)) Signal Cout = fa. circuitf). cout(); I Figure 2.5 Code Fragment of An n-bit Ripple-carry Adder 2.2 The User's View From the example mentioned above, we are able to understand the objects and operations needed in the API from the user's point of view. We need a class to specify a circuit. A circuit can be placed to the left, right, bottom or top of any other circuit. A circuit can also be mirrored vertically or horizontally. Implementation of the circuit requires the description of different electrical terminals, which can be connected to each other. I will describe the Signal interface first, as seen by the user, because it is simple and I will need it later to define a circuit cell. A Signal is something that can be 12 connected to other Signals,. Therefore it has a connect method, which takes a Signal as a parameter and returns a Signal to make chaining of the connect operations easier. For example, to connect Signals u, v, and w together, one writes: u.connect(v).connect(w). There are four implementations of the Signal interface (see Figure 2.6): DefaultSignal, Power, Ground, and Terminal. Class DefaultSignal is the basic one that we can use to define any kind of signal in the circuit (e.g., the global signal, the clock signal, the input/output signal). Class Power and Class Ground are both subclasses of Class Row (see Section 2.3); they need to implement Signal because they can be electrically connected to other signals or to transistor terminals. The fact that Java does not support multiple-inheritance also explains why I chose to make Signal an interface. Class Terminal represents any kind of terminal (source/gate/drain) of a transistor. Similarly, a Terminal can be connected to Signals as well as other Terminals. Now, let us take a look at the high-level description of a circuit. In the designer's eyes, a circuit consists of smaller and more elementary parts; we call them cells. A circuit in this view is nothing but a combination of these cells. There are four mechanisms for arranging cells: • Put one cell to the left of the other cell. • Put one cell below the other cell. • The left-and-right mirroring of a cell. • The up-and-down mirroring of a cell. Class DefaultSignal Figure 2.6 Implementations of the Signal Interface 13 Correspondingly there are four inner subclasses of the abstract class Circuit. Circuit is made an abstract class instead of an interface to support the definition of these subclasses. One more subclass of Circuit, CircuitRow, represents a circuit composed of only one row. Based on the above-mentioned combination methods, single-row cells are placed together to build the final circuit (Figure 2.7). Inside the cell, each slice is defined as a subclass of abstract Class Row. Both Power and Ground have parameters in their constructors for passing a user-defined signal width, which can be larger than the minimum width of metal 1 in order to support both IR drop and electromigration requirements. Power takes one more parameter of a Signal in its constructor to distinguish between different electrical conventions. RoutingRow represents the channel routing region between P and N transistor regions. Global wires such as clocks are included in the routing region. This allows, for example, the same gate design without any manual changes in designs with different clocking methodologies. The merging of two cells next to each other with different global signals is also made much easier by expanding the routing regions of both. subclass Circuit.Left subclass Circuit.Below subclass CircuitRow subclass Circuit.MirrorX ill subclass Circuit. MirrorY Figure 2.7 Subclasses of Circuit Classes RowNTran and RowPTran are used to represent N-type and P-type transistor rows. Like CircuitRow, either contains only one transistor in a row. 14 Accordingly I defined Class Transistor, and its subclasses NTransistor and PTransistor. A Transistor is composed of three Terminals representing its source, gate, and drain. It also supports the mirrorX operation. A user-defined transistor width is passed as a parameter to the constructor to support optimal transistor sizing. A row of an arbitrary number of transistors, therefore, is obtained by putting these rows next to each other with the Left method. The hierarchy of Class Row and its subclasses is shown in Figure 2.8. Class Row is a lot like Class Circuit. It also has two inner subclasses Row.Left and Row.MirrorX to support the merging of two rows next to each other and the left-right mirroring of a row. Like Circuit, Row is made an abstract class instead of an interface to support the definition of the two subclasses. In retrospect, I could have made Row a subclass of Circuit, thus omitting the need for the definition of CircuitRow. subclass PRow subclass RowNTran Figure 2.8 Class Hierarchy of Row 2.3 The Layout Generator's View The operations of my tool's API that the user invokes construct data structures that describe the desired design for the layout generation methods. Thus the rest of the tool 15 also needs to obtain data from the API. First, it needs to find the set of electrical nodes and the terminals connected to each node. Class Node is designed for this purpose, to describe a list of electrically connected Signals. The Signal interface defines two methods, node and setNode, which are invoked primarily by router classes. Method node returns the Signal's Node, and Method setNode sets its Node to a specific value. The node method provides a way to record all the connections in the netlist. The netlist is used by the router methods to determine which connections to make. The details of the netlist and the router, however, are hidden from the typical user. For each circuit, the tool needs to get the rows of the circuit. And similarly, for each row, it needs to get the objects of the row. In either case, the target can be a circuit or a row that can be further expanded, or the target is a primitive circuit or row object. The getRows method returns an enumeration of the rows in the circuit cell in a bottom-first or top-first order, according to a parameter passed by the caller. Circuit is made an abstract class since every inner subclass implements this method in its own specific manner. The getTerminals method returns an enumeration of the terminals in a row, if there are any, in a left-first or right-first order (also passed as a parameter). Accordingly, Row is also an abstract class. There is one more abstract method, toGeom, in the definition of the class Row. It transforms the high-level description of a row to a geometrical representation, in terms of polygons and rectangles. I will address this transformation in Chapter 3. In the implementation of the tool, I tried to make it technology independent. Three classes are designed for this purpose, Technology, Scmos and Layer. Technology has four member variables, which describe its associated layers, the minimum width of each layer, and the minimum spacing (or overhang) between every two. Method addLayer adds layers to the technology description. Methods addMinWidth, addMinOverhang, and addMinSep add different design rules to the particular technology file to ensure geometric design rule correctness in generated layouts. Technology also has a setTech method to specify the technology to be used in this tool. In this way designers can select the design rules for other processes by simply writing a technology class, and specifying the new technology through the calling of setTech. The current implementation provides one technology class, Scmos, which corresponds to the 16 MOSIS scalable CMOS (SCMOS) design rules2. For the detailed implementation on this, please refer to Appendix A. 2.4 The Complete View The user describes the circuit at a high level in terms of relative placements and electrical connections. Using the methods in the API, she then creates a Circuit object that can be passed to the MagicOutput.outputToMagic method to produce a layout file. This layout generation deals with many inplementation details such as decomposing the user description into rows and flattened structures. To support sophisticated users, I include methods that are primarily for layout generation in the API. Table 2.1, Table 2.2, and Table 2.3 show the complete set of methods and structures of the key classes and interfaces in the API. They are given to make some comparison and for a better understanding of the architectural design. This is also how a sophisticated user might view the API and what she needs to know about before building any advanced application on it. In the tables below and throughout the following chapters, I use Sans Serif font to illustrate methods that typical users need to know, and Roman Italic font to illustrate those used primarily by the layout generator. Public interface Signal Method Summji} Signal connect(Signal x) Makes a connection with the specified signal. Node node() Returns the signal's electrical node. void setNode(Node rid) Sets the signal's electrical node to the specified value. Table 2.1 Interface Signal 2 http://www.mosis.org/Technical/Desigm-ules/scrnos/scirios-main.html 17 public abstract class Circuit Inner Class Summ Protected class Circuit. Left Protected class Protected class Protected class Circuit. Below Circuit.MirrorX Ci rcuit. M irror Y Method Summary Circuit f l l t l i f i ^ left(Circuit that) Puts this circuit to the left of a specified circuit and returns the new circuit. Circuit below(Circuit that) Puts this circuit below a specified circuit and returns the new circuit. Circuit mirrorX() Returns the mirroring of the circuit in the X direction. Circuit mirrorY() Returns the mirroring of the circuit in the Y direction. abstract Enumeration getRows(boolean bottomFirst) Returns an enumeration of the rows in the circuit in the specified order. Table 2.2 Class Circuit public abstract class Row Inner Class Summt Protected class iry '' 1 , ' Row. Left Protected class Row. MirrorX (Table 2.3, continued on next page) 18 (continuation of Table 2.3) Method Summary Row left(Row that) Puts this row to the left of a specified row and returns the new row. Row mirrorX() Returns the mirroring of the row in the X direction. abstract Enumeration getTerminals(boolean leftFirst) Returns an enumeration of the terminals in the row in the specified order. abstract GeomRow toGeom(Technology t, boolean leftFirst) Returns a geometrical representation of the row with the specified technology and order. abstract Row toTranrowf boolean leftFirst) Returns the symbolic representation of the row if it is a transistor row, otherwise returns null3. Table 2.3 Class Row For the complete code of the API, please refer to Appendix A. Furthermore, Class FifoStage in Appendix B shows how the API can be used to describe a simple target circuit. 2.5 Example Code for the Adder I conclude this chapter by showing code fragments written with this API for the adder example. Figure 2.9 shows a code fragment of Class SumBlock. Class CarryBlock is similar. Based on them we write the code for Class OneBitFA as shown in Figure 2.10. The code for Class Adder is based on the code fragment in Figure 2.5. 3 Another implementation might be providing a default that does nothing and is overridden by transistor row subclasses. 19 public class SumBlock ( private Signal A, B, Cin, Sum, Cout; private Circuit c; public Signal a() j return A; } public Circuit circuit() { return c; } public SumBlock(Signal _Vdd) f A = new DefaultSignal( ); Power Vdd = new Power(_Vdd, 6); Ground Gnd = new Ground(6); RoutingRow rr = new RoutingRowf); Transistorf][] t = { { new PTransistor(8), //create 8 instances of PTransistor ). { new NTransistor( 4), //create 8 instances of NTransistor } }; t[ 0]f O].source(). connect( tfO][ I ].drain()). connect( t[0][2 ]. source()). connect(Vdd) t[0][0]. drain(). connect( t[0][l]. source()). connect( t[0][2]. drain() ); //more remaining connections Row prow = (new RowPTran((PTransistor)(t[0][0]))) .left(new RowPTran((PTransistor)(t[0][]]))) .left(new RowPTran((PTransistor)(t[0][7] ))); Row nrow= {new RowNTran( (NTransistor)( t[J][0]))) .left(new RowNTran((NTransistor)(t[ J ][]]))) . .left(new RowNTran((NTransistor)(t[J][7]))); c = (new CircuitRow(Gnd)) .belowfnew CircuitRow((NRow)(nrow.toTranrow()))) .below(new CircuitRow(rr)) .below(new CircuitRowf(PRow)(prow.toTranrow()))) .below(new CircuitRow(Vdd)); / Figure 2.9 Code Fragment of Class SumBlock 20 public class OneBitFA { private Signal A, B, Cin, Sum, Cout; private Circuit c; public OneBitFA(Signal _Vdd) { SumBlock sb = new SumBlock(_Vdd); CarryBlock cb - new CarryBlock(_Vdd); A = sb.a().connect(cb.a()); B = sb.b(). connect( cb. b()); Cin = sb.cin().connect(cb.cin()); Cout = sb.cout().connect(cb.cout()); Sum = sb.sum(); c = cb.circuit().mirrorY().below(sb.circuit()); J I Figure 2.10 Code Fragment of Class OneBitFA 21 ( J i i \ i » i i . u 3 PRIMITIVE OBJECT GENERATJORSJ This chapter describes the interfaces to the primitive object generators and the Router package. They are used to convert the description of relative placements and electrical connections into the geometrical representation, in terms of polygons and rectangles. This description is primarily for software developers, who are extending or enhancing this tool. Normally the details of placement, primitive object generation and routing should be hidden from the typical user. However, an advanced user might use these features to build a sophisticated application above it, or to improve the current method. This chapter describes optimizations applied in the generation of geometry, including the incorporation of cost functions in the constraint solver and a device merging technique that constructs optimal transistor chains with the minimum number of diffusion gaps. Figure 3.1 shows the architecture of the code for object and constraint generation in the expansion from the user description into rows and flattened structures. It takes a Circuit object as input and produces a collection of constraints and rectangles as output. The constraint set is sent to the solver (see Chapter 4) together with an objective function to produce the optimal layout (optimal with respect to the objective function that currently permits minimization). Based on the estimated initial placement of components, the Router package computes the channel density it will need, introduces new constraints when necessary, and does the routing. Then the linear program is solved again with a new objective function to minimize the total wire length. Once a solution is found and sent to the Magic package (see Chapter 5), the designer gets the final generated layout. The interfaces described in this chapter transform circuit description from the abstract rows, stacks of rows, and electrical connections used by the designer to collections of rectangles, constraints, and signals used by later phases of layout generation. This includes: • Expansion into rows and flattened structures: Decomposing the user description of a circuit into rows, and in each row obtaining a collection of symbolic rectangles 22 with appropriate constraints (see Section 3.1). In general, power or ground rows consist of rectangles on metal 1, routing rows consist of geometry generated by routing models, and transistor rows have rectangles on seven different layers. • "Peep hole" optimization: Merging of two primitive rows of the same type placed together, and merging inside a primitive row object. In particular, power or ground wires are made long enough to span both objects and wide enough to support the total current required. Routing regions are extended to include the global signals of both. Transistor rows are constructed with special care to ensure proper source/drain sharing (see Section 3.3). Circuit 1 ~ GeomCircuti(...) GeomCircuit 1 GeomCircuit.toGeom(...) Rectangle hashmap Layer 1 Rectangle list. Constraint set equality constraints inequality constraints Circuit.getRows(...) ii 1 Row Row Row 11 1 Row.toGeom(...) C ) Figure 3.1 Object and Constraint Generation 3.1 Interfaces 23 The geometrical circuit can be seen as a stack of different geometrical rows subject to certain additional constraints. Class GeomCircuit, GeomRow, and GeomRowProto provide the interfaces to this transformation and the Router package. Figure 3.2 shows the member variables of Class GeomRow, corresponding to what should be produced by Row.toGeomQ. GeomRow signals ^ a list of signals appearing in this row rectangles constraints j | a constraint set for the coordinates of rectangles a collection of rectangles on different layers top, bottom, left, right 1 boundary box limits for each layer I Figure 3.2 Member Variables of Class GeomRow A GeomRow is a collection of rectangles, constraints, and signals. Each GeomRow object is used in two phases. First, the toGeom method of the Row object that the designer has created creates one empty GeomRow object and then adds rectangles, constraints, and signals to this object. The GeomRow object enters its second phase when it is included into a GeomCircuit object, from which it enumerates its rectangles, constraints and signals for later phases of layout generation. I enforce this two-phase model by introducing another class GeomRowProto. The toGeom method creates GeomRowProto objects and uses their addRectangle, addConstraint, and addSignal methods to build its collections. These methods are summarized in Table 3.1. When finished, the toGeom method creates a GeomRow object from the GeomRowProto. This allows routers, constraint solvers, and other aspects of layout generation to assume that GeomRow objects are immutable, which fits naturally with the declaration style of constraint programming. 24 public class GeomRowProto Constructor Sumrn;n \ GeomRowProto(Technology t) Constructs a new GeomRowProto object with the specified technology. GeomRowProto(GeomRow g], GeomRow g2, Technology t, boolean leftFirst) Constructs a new GeomRowProto object merging the two GeomRow objects in the specified order and using the design rules of the specified technology. Method Summary, R i '_!_> i -,_l_Lii__li i .V : void addSignal(Signal s) Adds the specified signal to the geometrical representation of this row. void addSignal(List s) Adds the list of signals to the geometrical representation of this row. void addRectangle(Rectangle r, Layer layer) Adds the specified rectangle to the specified layer. void addRectangle(Variable xO, Variable yO, Variable xl, Variable yl, Layer layer) Adds a rectangle with the specified bottom-left and top-right coordinates to the specified layer. void addRectangle(Map m) Adds all the rectangles in the specified map. void addConstraint(ConstraintSet c) Adds the specified constraint set. void addConstraint(Variable vO, Variable vl, double d) Adds constraint: vl -\>0 s=d. void addTop(Variable t, Layer layer) Specifies t as the top variable in Layer layer. (Table 3.1, continued on next page) 25 (continuation of Table 3.1) void addBottom(Variable b, Layer layer) Specifies b as the bottom variable in Layer layer. void addLeft(Variable I, Layer layer) Specifies I as the left variable in Layer layer. void addRightfVariable r, Layer layer) Specifies r as the right variable in Layer layer. void nullifyO Nullifies the GeomRowProto object and gets it garbage collected. Table 3.1 Class GeomRowProto GeomRowProto has another constructor that accepts two GeomRow objects. This is used when two rows are put next to each other. Both of their geometrical representations are derived first. Method addConstraint and the overridden version of methods addSignal and addRectangle merge the constraints, signals and rectangles into the combined geometrical row object. The left and right boundary limits are determined by their relative positions to each other indicated by the leftFirst parameter, and the bottom and top boundary limits are ensured to satisfy those of the two component objects. Horizontal spacing constraints are added as required, to keep the right boundary limit of one layer of the left component separated from the left boundary limit of the other layer of the right component by at least the minimum separation of the two layers in the design rule definition. The leftFirst parameter is again used here to tell which is the left component and which is the right. Class GeomCircuit takes a Circuit object as a parameter in its constructor. By invoking the toGeomCircuit method, it turns each row into its geometrical representation, accumulates the rectangles and constraints involved, adds more vertical constraints between adjacent rows when necessary to keep them sufficiently separated, and adjusts power and ground rails to match the length of adjacent transistor rows. Vertically adjacent cells share the same global signal (e.g., power or ground rails) or 26 routing region when merged into a bigger circuit. Otherwise, some spacing constraints must be added to keep one cell sufficiently above the other to ensure that all design rules are satisfied. At this point we get the geometrical representation of the whole circuit. As in the combination of two rows, the bottom and top boundary limits are used here to add some vertical spacing constraints to keep one row sufficiently above the other in the stacking of the rows into the final circuit. 3.2 Cost Function In order to achieve a layout as dense as manual layout after the component placement, I applied a cost metric that reduces the cell perimeter (width plus length) and minimizes diffusion in transistor placement. This is guaranteed not only in the primitive object generator (e.g., power, ground, transistor rows), but also in the merging of two rows next to each other and in the stacking of a number of row slices into the whole circuit. 3.3 Device Merging Merging of transistor terminals can achieve significant savings in layout area. Inside a transistor row, there are three ways to connect a terminal to other terminals or signal wires in the circuit netlist: • If one source/drain is not connected to its neighboring drain/source, then there is no sharing in between. Two contacts with sufficient horizontal separation should be drawn (Figure 3.3(a)). • If one source/drain is connected to its neighboring drain/source and nothing else, then these two terminals share the diffusion region between them. No contact needs to be drawn (Figure 3.3(b)). • If one source/drain is connected not only to its neighboring drain/source, but also to at least one other terminal or signal wire, then they share the contact between them. Only one contact needs to be drawn (Figure 3.3(c)). 27 (a) no sharing (b) diffusion sharing (c) contact sharing mm '' (d) building bricks Figure 3.3 Device Merging Cases and Transistor Building Bricks To automate terminal sharing, I divided the drawing of a transistor's layout into the drawing of small fixed elementary parts, which I call bricks, assembled to constitute any desired transistor structure. Many of the possible MOS structures may be obtained using only two different bricks presented in Figure 3.3(d); I call them " G " and "C" (representing gate structure and contact) respectively. By this means the three cases in device merging can be simply represented by a string of symbols (e.g., " C G C C G C " for (a), "CGGC" for (b), "CGCGC" for (c)). The geometrical generation of a transistor row is implemented in two steps. First, a symbolic representation is derived from the high-level description, based on the interconnections defined by the user. Method Row.toTranrow makes this transformation and creates an equivalent NRow or PRow object. NRow and PRow are transistor rows retrieved from a symbolic representation; they are defined to implement the source and drain sharing between transistor terminals. Second, the transistor row layout with device merging is drawn from this symbolic representation. This is done by the toGeom method of Class NRow and Class PRow. Special attention needs to be paid when the two merging terminals are different in width, in which case the method aligns them carefully and determines the width of the sharing contact or diffusion. 28 3.4 Routing The next step after the placement of all the transistors and other structures in the layout is to connect the layout using wires on available layers according to the netlist. Routing has a profound impact on the quality of the final layout. Poor routing of nets includes unnecessary crossover of wires, circuitous routes, and redundant vias and contacts, all of which impair electrical performance and adversely affect yield and area [Guruswamy 97]. I considered a simple approach where three layers are available for routing: polysilicon, metall, and metal2. Owing to the high resistance of diffusion, it is primarily used to interconnect adjacent transistors that share common signal nets. Similarly, due to the high resistance of polysilicon, polysilicon wires are limited to connect transistor gates. Channel routing algorithms are often used in layout automation systems. Another graduate student in our department, Yang Lu, is implementing routers using the API provided by my prototype. In the pre-routing step, power/ground supply routing is performed by placing vertical taps to source/drain connections. Currently she has successfully finished the detailed routing in the single routing row between two transistor rows, and the generalization to the global routing which supports routing with more than two rows of transistors, and is still working on the compaction of the routing results to produce smaller designs. Like the other layout generators described earlier, the router generates geometry in terms of constraints. Consider a design with a single routing row. The channel consists of several parallel routing tracks. The channel density provides a lower bound on the number of the tracks as follows. Sweep the channel from left to right. Every time we see the leftmost terminal of a net, we increment the density. Every time we see the rightmost terminal of a net, we decrement the density. The channel density is the highest density encountered in the sweep. Then we are able to do acceptable routing based on the initial transistor placement. We create a Vector of routing tracks. Each element of this Vector is either empty (i.e., null) or occupied by a particular net. Again we sweep from left to right. Each time we see the left end of a net, we allocate it to an empty track. If there is no empty track (routing can require more tracks than the channel density), we introduce 29 a new track, which also explains our use of a Vector (that can expand) instead of an array (that can't grow). Each time we see the right end of a net, we mark the corresponding track as empty. For any terminal of the net, we add a vertical wire (in polysilicon or metal2) from the terminal in the row of transistors to the track. To produce an efficient router, this simple algorithm can be augmented to support dog-legging (wires with jogs) and other optimizations. The router is implemented using my tool's interface to obtain the netlist, ordered lists of terminals, and the initial (unrouted) placement. The router uses the addRectangle and addConstraint methods to specify the geometry of its solution. 30 C n \ PIER 4 This chapter deals with the linear program interface. First, I describe constraint generation. Then, I present constraint solving. A linear program consists of a set of linear constraints and an optimization vector, which is called "the cost function": Find x that minimizes c'*x where c is the optimization vector; A_eq and A_ineq are matrices; and b_eq and b_ineq are vectors. 4.1 Constraint Generation As stated in Chapter 3, the layout generator produces a circuit in terms of constraints and rectangles. A rectangle has variables defining its left, right, bottom and top limits. At the beginning it is symbolic (just in terms of variables, and values have not yet been bound to the variables). After constraint solving it is concrete (in terms of real values of the variables). A key idea in the constraint solver is the distinction between a variable and a valuation. For example, given the inequalities: Y > X + 2 and X > Z + 3 (X, Y , Z are variables), these two constraints are satisfied by the valuation X = 3, Y = 5, Z = 0. They are also satisfied by the valuation X = 10, Y = 100, Z = 2. Typically, the sets of constraints that arise in our tool have an infinite set of satisfying valuations. We use an objective function to select an optimal valuation. subject to A_eq*x = b_eq and A_ineq*x > b_ineq, (1) 31 By separating variables from their values, additional constraints can be added as layout generation proceeds. For instance, this allows the router to add constraints to ensure that there is enough space to complete the routing successfully. In particular, we first solve the constraints prior to any routing. This provides initial placement hints for the router. The router adds constraints, and the final placement after routing may be much different with the initial placement prior to routing. In this framework, each rectangle is defined by a layer and four symbolic variables: left, right, bottom and top. The layout generation methods introduce constraints for each of these variables. The constraint solver then finds a valuation that satisfies these constraints and optimizes the objective function. This valuation is used to output the rectangle with concrete coordinate values. The Variable class implements Java. lang.Comparable as Variable objects are used as keys for a map. Other than that, Variable objects only need to have a unique identity. This is because values come from the constraint solver later. The matrices A_eq and A_ineq in (1) tend to be very sparse for this application and this might create linear programming problems with hundreds or thousands of variables, but only two variables in each constraint (i.e., each row in the matrix) (e.g., in the form of " V i - V 0 > 4", " V 3 - V 2 = 2"). We do not want to create a matrix that explicitly represents all of the zeros, because it may take much longer to initialize the matrix than to solve the linear programming problem. Therefore, either in the case of an inequality constraint representing A ' * X > b, or in the case of an equality constraint representing A ' * X = b, we can represent A ' as a collection of pairs: one element of the pair is the variable, and the other is the coefficient for that variable. For example, if we have the inequality: V173- V g 4 > 3, we represent A ' as {(V173, 1), ( V 8 4 , -1)} and b as 3. This has the added advantage that we can build the constraints without knowing the complete set of variables. Accordingly, Class Coefficient is constructed to represent such 2-tuples of the form (variable, coefficient), and Class RowVector takes an array of Coefficient objects as a parameter to represent the left-hand expression of a constraint. Class Constraint then takes a RowVector object and a double value in its constructor representing its left-hand expression and right-hand value respectively. 32 To represent the set of linear constraints in the linear program, Class ConstraintSet needs to be defined. Although the linear program solver wants the constraints in the form of matrices, we do not want to use matrices as we build up the constraints, to avoid excessive copying. Instead, we represent the syntactic structure of constraints in the same way as we do for building rows in the circuit in Chapter 2. A ConstraintSet object can be a primitive constraint (i.e., an equality constraint or an inequality constraint), or the conjunction of two constraint sets. The design of ConstraintSet is shown in Table 4.1. Like Class Row, it is made an abstract class instead of an interface to support the definition of three inner subclasses ConstraintSet.Eq, ConstraintSet.InEq, and ConstraintSet.And. This allows its inner classes to implement the getEqualities and getlnEqualities methods specifically. public abstract class ConstraintSet Inner Class Summary - • * . " , ' protected static class i ConstraintSet.Eq protected static class ConstraintSet. InEq protected class ConstraintSet.And . Method Summary static ConstraintSet equality (RowVector a, double b) Returns an equality constraint of the form "aX = b" . static ConstraintSet simpleEq(Variable vl, Variable v2, double d) Returns an equality constraint of the form "v2 - vl = d" . static ConstraintSet inequality(RowVector a, double b) Returns an inequality constraint of the form "aX > b" . Static ConstraintSet simpleIneq(Variable vl, Variable v2, double d) Returns an inequality constraint of the form "v2 - vl > d" . (Table 4.1, continued on next page) 33 Ccontinuation of Table 4.1) ConstraintSet and(ConstraintSet that) Returns a conjunction of this constraint set with the other specified constraint set. abstract Enumeration getEqualitiesf) Returns an enumeration of equality constraints in this constraint set. abstract Enumeration getlnEqualitiesf) Returns an enumeration of inequality constraints in this constraint set. Table 4.1 Class ConstraintSet 4.2 Constraint Solving To get values for these variables from the constraint solver, we need to define a valuation first. A valuation maps variables to values. This mapping allows us to solve the same set of constraints with different optimization vectors, or add more constraints and solve the augmented linear program, and get different values for the variables in both cases. Since RowVector and Valuation objects both associate Variable objects with values, a RowVector object containing all the variables in one problem instance is passed as a parameter in the constructor of Class Valuation. The methods setValue and eval are used to set a value to a variable or get the value of a variable in one valuation. Based on this, LinearProgram is designed as an interface that has a solve method returning a Valuation object. It is made an interface to incorporate two different methods in the solving process. 34 Interface LPfactory and Class Lpabo provide interfaces to LP A B O 4 . Interface OPfactory and Class Opt provide interfaces to a depth-first-traversal algorithm. By linking this tool to the former or the latter, we are able to get either an optimal solution or a fast, feasible and good solution for the problem. A comparison between them is made in Table 4.2. public interface LPfactory public interface OPfactory Method Summary [ create(ConstraintSet cs, | RowVector c1, RowVector | c2, RowVector c3, List create(ConstraintSet cs, LinearProgram | list"!, List Iist2) LinearProgram RowVector r) public class Lpabo implements LinearProgram public class Opt implements LinearProgram Inner Class Summary static class \ Lpabo. Factory static class ; Opt. Factory I Implements LPfactory \ implements OPfactory Held Sunmui} public final static LPfactory | factory = public final static OPfactory factory = | new new | FactoryQ Factory() Method Summary Valuation ; solveQ Valuation \ solveQ Table 4.2 Interfaces LPfactory and OPfactory, Classes Lpabo and Opt LPfactory and OPfactory are two interfaces that both define a create method returning a LinearProgram object. They only differ with each other in the parameters 4 LPABO is the interior-point method based linear programming solver developed by Prof. Park, Soondal and the members of Operations Research Laboratory in Dept. of Industrial Engineering at Seoul National University. 35 required for the create method. Lpabo and Opt are both classes that implement the LinearProgram interface, thus they both have a solve method that returns a Valuation object. Since the two methods need different parameters sent to the solver, these two classes accept different parameters in their constructors. By defining a static field/actory that creates an instance of a static inner class Factory, which, again implements the LPfactory or OPfactory interface, we are able to pass different parameters from our tool to the two different solving processes. A valuation is obtained by simply invoking Lpabo.factory.create(.. .).solve() or Opt.factory.create(.. .).solve(). 4.2.1 LPABO Solver In my tool I used L P A B O 5.72. It supports the MPS input format5. The first step of the solve method is to write the linear program to be solved into a file in the MPS format (e.g., "circuit.dat" in Appendix C). Then, by calling Runtime.getRuntime().exec(...) (in java.lang), we get the runtime object associated with the current lava application and execute the specified command and arguments in a separate process. After that we use the Process.waitFor() (in java.lang) invocation to block until the linear program solver is done. The output from the solver is saved in a file named "lpabo.out". An example output file is also given in Appendix C. The last step of the solve method is to read the solution from this output file and return a Valuation object to the tool for further processing. The output from the LP solver is a possible optimal solution. However, I met with one problem in the use of L P A B O . Solutions for L P A B O typically had variables with very large values, even when I had specified the upper and lower bounds for each variable. I had to carefully construct the cost function and include in it more variables than necessary to make sure I get a bounded solution from the solver. This resulted in an abnormally complex cost function in the problem definition, and led to ongoing difficulties. I suspect that the many degrees of freedom in the problem (including invariants under arbitrary shifts) led to the problem. To obtain meaningful solutions, I had to turn to an alternative solving method. 5 MPS input format was introduced by IBM. It is a way of creating inputs for linear and integer programs. 36 4.2.2 A Depth-first-traversal Algorithm An alternative approach to find a fast, feasible and good solution for the problem is the use of a depth-first-traversal algorithm, based on the fact that all the constraints take the form of " V i - V 0 > 4" and " V 3 - V 2 = 2". The idea lies in viewing the constraint system as a directed constraint graph, with vertices representing variables and edges representing constraints between the connecting nodes. For example, constraint " V | - Vn > 4" establishes an edge pointing from node(Vi) to node(Vn) labelled with the value 4. Thus for each inequality constraint in the system, a left constraint is added to the variable with coefficient "1" (meaning the value of this variable should be more than that of the pointed variable by at least the edge weight), and at the same time a right constraint is added to the variable with coefficient " - 1 " (meaning the value of this variable should be less than that of the pointing variable by at least the edge weight). In this way it is easy to solve the constraint system by walking backward from unconstrained variables (i.e., variables with no outgoing edges), first for the left constraint and then for the right constraint. The left constraints produce lower bounds for the values of each variable, and the right constraints produce upper bounds. Averaging the two bounds produces reasonable values. Although this solving process doesn't take into consideration the cost function in this linear program, it does provide a feasible and good solution in very small amount of time. Methods addLeftConstraint, addRightConstraint, lo, and hi in Class Variable are defined accordingly to add left or right constraints to this variable and in the end to compute the lower and upper bound values. Another problem may arise in this methodology, that is, the dealing with equality constraints in the system. In this case the equality constraint can be replaced with an inequality constraint associated with the appropriate substitution. For example, if we have constraints " V 3 - V 2 = 2" and " V 2 - Vo> 4", we can replace the equality constraint with the inequality constraint "V3 - V 0 > 6", and reconsider the modified system. Methods reduce Equalities, reduce, and reducelnequalities in Class Opt, based on the "union find" algorithm, ensure that all variables connected by equality relations map to the same variable with appropriate constants, and reconstruct the inequality constraint set 37 accordingly. When the value of V3 is known, we can get the value of V2 by subtracting the value of V 3 by 2 (V 3 - V 2 = 2). Classes ConstraintEdge, Expr, Equality and Inequality are some helper classes in this solving process. I used the depth-first-traversal algorithm successfully in my prototype and obtained very satisfying results from the solver. For. details on the implementation of the LP interface, please refer to Appendix A andB. 38 ; : : y C H ^ T O R 5 ^ ^ , M A G I C INWRFACB This chapter talks about the Magic interface. It accepts the geometrical representation of a circuit and a valuation from the constraint solver, maps values to coordinates of rectangles on different layers, and writes to an output file in Magic format. 5.1 Interfaces There are two classes in the Magic package, MagicOutput and MagicWriter. After showing their structures in Table 5.1 and 5.2, I will explain how they interact with each other to produce the final layout. public class MagicOutput Method Summary. static void outputToMagic(Circuit circuit, String fileName, Technology tech, String LPsolver) Turns the circuit into its geometrical representation using the specified technology, solves the system using the specified LP solver, and writes the result to a specified file. static void writeToFile(String fdeName, GeomCircuit g, Technology t, Valuation v) Maps values from a valuation to a geometrical representation of a circuit in a specified technology, and writes the result to a specified file. static void writeLayer(MagicWriter writer, String layername, Enumeration rectangles, Valuation, v) Maps values from a valuation to coordinates of rectangles on a specific layer, and writes this layer to the output file. Table 5.1 Class MagicOutput 39 public class MagicWriter Constructor Summary MagicWriter(String filename, String technology) Creates a buffered character-output stream with the specified file name, and writes the technology information and timestamp information to the output file. Method Summary void beginLayer{String layerName) Writes the beginning of a new layer into the Magic file. void addRectangle(int xl, intyl, int x2, inty2) Writes the four coordinates of a rectangle into the Magic file. void beginLabels() Starts writing labels into the Magic file. void close() Writes the end of the Magic file and closes the output stream. Table 5.2 Class MagicWriter An example Magic file ("FifoStage.mag") is included in Appendix D. By invoking the static method MagicOutput.outputToMagic(...), we pass a String for the file name, a Circuit object, a Technology definition and a String for the name of the LP solver to the Magic interface, and get the geometrical representation of the circuit together with a Valuation from the solver. The static method MagicOutput.writeToFile is further invoked. A MagicWriter object is constructed with the creation of a buffered character-output stream with the specified file name and the appending of the file head, technology information, and timestamp information. Then for each layer defined in this technology, it writes the layer name, maps values from the valuation to coordinates of the rectangles on this layer, and writes every rectangle description into the file. After this is done, it writes the end of the file and closes the output stream. 40 CHAPTER 6 EXPERIMENTS 6.1 Methodology I tested my tool using four examples. My goal was to produce layouts comparable to skilled manual design. In my experiments I let my tool generate the component placement for the target circuit, the result of which represented the initial placements and could be sent to the Router package to do the routing. At the routing stage, more constraints might be added when necessary to produce the final layout. So the goal I aim to achieve in the component placement stage is to generate an optimal circuit with the minimum area. By doing so more space and flexibility are reserved for the routing stage to help produce the most efficient final layout. The first example is a single inverter with 6X power and ground width and 8X, P-transistor and N-transistor width. The second is a row of seven such inverters placed together. The third is an inverter array composed of three such inverter rows stacked together, with sharing power/ground rails between adjacent rows. The fourth is in comparison with a manual layout "FifoStage.mag", in which there are two power rails and one ground rail (6A, wide each), eight P-transistors and ten N-transistors of width 4A, 6X, 8X-, 10X, and 12A,. Appropriate source/drain sharing is achieved based on the interconnections between these terminals. The experiments were run on a Sun SPARC SUNW, Ultra-5_10 workstation using technology SCMOS SCN3M.35. The lava code was compiled using JDK-1.3. The time necessary for the layout to be generated depends on the dimensions and the complexity of the target circuit, but never exceeds a few seconds for our experiments. 6.2 Results 41 Figure 6 .1 , 6.2, and 6.3 show the layouts generated by my tool for the three inverter-related examples. From them we can see that these layouts realize the maximum area reduction and are as dense as manual design with respect to component placement. They are design rule correct (DRC) and satisfy the minimum separation between layers. What's more, they are elegant in supporting user-defined signal width and transistor width, and dealing with the stacking of smaller cells into a bigger circuit with proper global wire sharing and width adjustment. Figure 6.4 shows the manual layout of "FifoStage.mag" and the layout generated by my tool for the same circuit (both before routing and after routing). Besides the above-mentioned good points, in this example we are able to see appropriate device merging between transistor terminals, which is exactly what the designer employs in her manual layout. Similarly this layout is as dense as possible in the component placement, which leaves much possibility for the routing stage to produce competent automatic layout. The layout after routing is not efficient enough, but it works now, and we are working on the compaction and more efficient routing algorithms. To further illustrate the density of these layouts, Table 6.1 shows the height, width, and area of these cells. Al l the layouts are as dense as possible after the component placement. Figure 6.1 Example Layout for One Single Inverter Placement 42 Figure 6.2 Example Layout for Inverter Row Placement Figure 6.3 Example Layout for Inverter Array Placement 43 (a) manual layout Figure 6.4 Comparison of Generated Layout with Manual Design for FifoStage 44 Example Height (X) Width (k) Cell Area (X2) One Inverter 44 12 528 Inverter Row 44 108 4752 Inverter Array 132 108 14256 FifoStage (before routing) 88 52 4576 FifoStage (after routing) 176 70 12320 Manual FifoStage 94 66 6204 Table 6.1 Example Cell Density The current tool is only a preliminary prototype. A full comparison with other layout methods will require a completed router and more experience with real designs. I expect that designers should be able to produce acceptable layouts with substantially less effort than manual design with some increase in area. I hope that an area penalty of 20-30% should be achievable while dramatically reducing the design time. At the other end of the spectrum are tools that synthesize layouts from electrical netlists or behavioral descriptions. Typically, such tools make poor use of regular structures that often appear in designs, such as in data-paths, register files, or memory. In my tool, regular structures can be expressed using the structuring and control features of the host language, Java. Thus, it should be easy for the designer to describe good implementations of these structures. I do not forsee my tool offering any advantages for highly unstructured designs such as a random logic to implement an arbitrary finite state machine. Here, synthesis tools excel (because there is no good manual layout). Finding good ways to integrate synthesis techniques into my tool is a promising area for future research. 45 CHAPTER 7 CONCLU^'O As covered in this thesis, automatic circuit layout generation involves the deployment and integration of many design automation techniques to produce high quality layouts from an initial transistor level or low level description. This thesis identifies opportunities for circuit optimization across design phases, and describes a fully automatic layout generation tool implemented in Java. The system is flexible enough to handle many process technologies and a wide variety of layout styles. The tool is fully automatic and provides several options to the user to customize the layout. The tool considers performance and generates dense, design rule correct layouts. Experimental results indicate that the area of generated layouts is competitive with manually designed cells for the circuits tried. Run times plus the times needed to write the description of the circuit are dramatically shorter than a human would require to manually create similar layouts, allowing a designer to try more topological variations to obtain an optimal design. Moreover, this tool allows us to target new technologies as they emerge, since only changes in the input technology file are needed. As most other systems developed in the area of automatic layout generation, this tool also focuses on specific, fundamental problems related to transistor placement, routing, and compaction, and is described mainly to demonstrate its specific innovations. The more general direction for future work, and the promise of greater impact, is to look back on many ignored but practical problems essential to fully automatic layout generation, such as transistor folding6 to meet cell height requirements and minimum width, well and substrate tie insertion to meet tie coverage requirements in an area efficient way, input/output port placement on a routing grid for compatibility with place and route tools, circuit performance issues, automatic jog insertion to minimize area and 6 Transistor folding is the process of splitting a transistor into multiple transistors of smaller widths connected in parallel. Intelligent transistor folding is crucial to automatic layout generation because it automatically generates area-optimized layouts. 46 wire length to achieve hand-packed density, and more flexible architectures, such as transistor stacking. Considerable further research needs to be done. The current tool is definitely a prototype, and in many ways, it is an experiment to demostrate that we are able to generate layouts using very simple techniques. In particular, I provide the API that makes it easy for the designer to describe the design topology. The designer uses the structuring mechanisms of Object-Oriented programming to construct complicated designs using the simple API. Tedious details of physical placement and routing are handled by my tool. Future research along this line should address how more issues of design and optimization can be incorporated into the simple framework. First, many optimization problems for layout synthesis can be expressed or approximated by linear or convex programming problems. These include, for example, retiming, transistor sizing and performance-driven routing. As many of these problems are NP-complete, formulations based on linear or convex programming are necessarily approximations. Our hope is that these convex formulations will lead to predictable results allowing the designer to find good layouts. On the other hand, unlike most of the efforts made in the layout synthesis that are dedicated to specific improvements, our tool aims to provide a general high-level solution and free the designer from the need to get familiar with quite a few different optimization tools. We hope that in this way our tool will incorporate all the different optimization tools into a general framework, and by Object-Oriented design have an object view of the circuit and apply the structuring mechanisms. More efforts still need to be made to incorporate different optimization features into our prototype. 47 [Chen 89] C. C. Chen and S.-L. Chow. 'The Layout Synthesizer: An Automatic Netlist-to-layout System". In the 26,h ACM/IEEE Design Automation Conference, pages 232-238, 1989. [Choudhury 93] U . Choudhury and A. Sangiovanni-Vincentelli. "Automatic Generation of Parasitic Constraints for Performance-constrained Physical Design of Analog Circuits". IEEE Transactions on Coputer-Aided Design, Vol. 12, pages 208-224, February 1993. [Dao 93] Joseph Dao, Nobu Matsumoto, Tsuneo Hamai, Chusei Ogawa, and Shojiro Mori. " A Compaction Method for Full Chip VLSI Layouts". In the 30th ACM/IEEE Design Automation Conference, 1993. [Domic 89] A. Domic, S. Levitin, N . Phillips, C. Thai, T. Shiple, D. Bhavsar, and C. Bissel. "CLEO: A CMOS Layout Generator". Proceedings ofICCAD-89, pages 340-343, 1989. [Draney 89] M . Draney, R. "Method and Apparatus for Recording and Rearranging Representations of Objects in A Coordinate System". U.S. patent #4829446, 1989. [Duh 95] J. Duh, T. G. Matheson, and E. Hepler. "Efficiently Embedding Expertise in High-density Process-portable, Standard Cell Generators". Proceedings of IEEE Custom Integrated Circuit Conference, pages 497-500, 1995. [Dunlop 80] A. E. Dunlop. "SLIM: The Translation of Symbolic Layout into Mask Data". Proceedings of the 17th ACM/IEEE Design Automation Conference, pages 595-602, 1980. [Duvall 99] Steve Duvall. "Optimization Problems in Integrated Circuit Design". In a seminar held at UBC Commerce in 1999. 48 [Gamma 95] [Gupta 96] [Gupta 97] [Guruswamy 97] [Hill 85] [Lakos 97] [Lea 94] [Lefebvre 97] [Lotvin 84] [Krambeck 82] Erich Gamma, Richard Helm, Ralph Johnson, and John Vlissides. Design Patterns: Elements of Reusable Object-Oriented Software. Addison-Wesley, 1995. A. Gupta, S. The and J. P. Hayes. "XPRESS: A Cell Layout Generator with Integrated Transistor Folding". Proceedings of European Design and Test Conference, March 1996, pages 393-400. Avaneendra Gupta and John P. Hayes. "CLIP: An Optimizing Layout Generator for Two-Dimensional CMOS Cells". In the 34th ACM/IEEE Design Automation Conference, 1997. Mohan Guruswamy, Robert L . Maziasz, Daniel Dulitz, Srilata Raman, Venkat Chiluvuri, Andrea Fernandez, and Larry G. Jones. "CELLERITY: A Fully Automatic Layout Synthesis System for Standard Cell Libraries". In the 34th ACM/IEEE Design Automation Conference, 1997. Dwight D. Hill . "Sc2: A Hybrid Automatic Layout System". Proceedings ofICCAD-85, pages 172-174, 1985. John Lakos. 'Technology Retargeting for IC Layout". In the 34th ACM/IEEE Design Automation Conference, 1997. Doug Lea. "Christopher Alexander: An Introduction for Object-Oriented Designers". In Software Engineering Notes, 1994. Martin Lefebvre, David Marple, and Carl Sechen. 'The Future of Custom Cell Generation in Physical Synthesis". In the 34th ACM/IEEE Design Automation Conference, 1997. M . Lotvin, B. Juran, and R. Goldi. " A M O E B A : A Symbolic VLSI Layout System". Proceedings of the 21s' ACM/IEEE Design Automation Conference, pages 294-300, 1984. R. H . Krambeck, C. M . Lee, and H . S. Law. "High-speed Compact Circuits with CMOS". IEEE Journal of Solid-State Circuits, Vol. 17, pages 614-619, June 1982. 49 [Marple 88] [Matheson 85] [Mathias 98] [Mogaki 91] [Ong 89] [Ousterhout 84] [Park 00] [Poirier 89] [Rekhi 95] [Sadakane 95] D. Marple, M . Smulders, and H . Hegen. "An Efficient Compactor for 45° Layout". Proceedings of the 25th ACM/IEEE Design Automation Conference, pages 396-402, 1988. T. G. Matheson, C. Christensen, and M . R. Buric. " A Software Environment for Buliding Core Microprocessor Compilers". Proceedings oflCCD, pages 221-224, 1985. Herve Mathias, Josette Berger-Toussan, Gilles Jacquemod, Frederic Gaffiot, and Michel Le Helley. " F L A G : A Flexible Layout Generator for Analog MOS Transistors". IEEE Journal of Solid-State Circuits, Vol. 33, No. 6, June 1998. M . Mogaki, N . Kato, N . Shimada, and Y . Yamada. " A Layout Improvement Method Based on Constraint Propagation for Analog LSI's". In the 28th ACM/IEEE Design Automation Conference, pages 510-513, 1991. C.-L. Ong, J.-T. L i , and C.-Y. Lo. "GENAC: An Automatic Cell Synthesis Tool". In the 26th ACM/IEEE Design Automation Conference, pages 239-244, 1989. J. Ousterhout, G. Hamachi, R. Mayo, W. Scott, and G. Taylor. "Magic: A VLSI Layout System". Proceedings of the 27" Design Automation Conference, pages 152-159, 1984. Soondal Park. "LPABO ver 5.72 User Manual (2000.5.2)". http://orlab.snu. ac. kr/pub/software/lpabo/lpabo572. wp C. J. Poirier. "Excellerator: Custom CMOS Leaf Cell Layout Generator". IEEE Transactions on CAD, Vol. 8, No. 7, July 1989, pages 744-755. Sanjay Rekhi, J. Donald Trotter, and Daniel H. Linder. "Automatic Layout Synthesis of Leaf Cells". In the 32nd ACM/IEEE Design Automation Conference, 1995. T. Sadakane, H. Nakao, and M . Terai. " A New Hierarchical Algorithm for Transistor Placement in CMOS Macro Cell Design". Proceedings ofCICC-95, pages 461-464, 1995. 50 [Serdar 99] Tatjana Serdar and Carl Sechen. " A K O R D : Transistor Level and Mixed Transistor/Gate Level Placement Tool for Digital Data Paths". In International Conference on CAD, November 1999. [Tani 91] K. Tani, K. Izumi, M . Kashimura, T. Matsuda and T. Fujii. 'Two-dimensional Layout Synthesis for Large-scale CMOS Circuits". Proceedings oflCCAD-91, pages 490-493, 1991. [Weste 93] Neil H . E. Weste and Kamran Eshragian. Principles of CMOS VLSI Design. 2 n d Edition. Addison-Wesley, 1993. [Wimer 87] S.Wimer, R. Pinter, and J. Feldman. "Optimal Chaining of CMOS Transistors in A Functional Cell". IEEE Transactions on CAD, Vol. 6, No. 5, September 1987, pages 795-801. 51 A P P E N D I X A L A Y O U T G E N E R A T I O N T O O L S O U R C E This appendix contains full source code for my layout generation tool. The Circuit package is presented first, followed by the Constraints package and the Magic package. Table A . l lists the index of all the source files. package Circuit abstract class Circuit 55 class CircuitlnvalidException 56 class CircuitRow 57 class DefaultSignal 57 class GeomCircuit 58 class GeomRow 60 class GeomRowProto 61 class Ground 64 class Layer 65 class NRow 65 class NTransistor 67 class Node 67 class PRow 68 class PTransistor 69 class Power 70 class Rectangle 71 class RoutingRow 71 (Table A. 1, continued on next page) 52 (continuation of Table AJ) abstract class Row 72 class RowNTran 75 class RowPTran 76 abstract class RowTran 77 class Scmos 77 interface Signal 78 abstract class Trow 79 class Technology 79 class Terminal 80 class Transistor 81 package Constraints - • ' class Coefficient 82 class Constraint 82 class ConstraintEdge 83 class ConstraintGraph 83 abstract class ConstraintSet 86 class Equality 88 class Etpr 89 class Inequality 89 interface LPfactory 90 interface LinearProgram 90 class Lpabo 91 interface OPfactory 93 class Opr 94 class RowVector 96 (Table A. I, continued on next page) 53 (continuation of Table A.l) class Valuation 96 class Variable package Magic 97 class MagicOutput 99 class MagicWriter 100 Table A . l Index of Layout Generation Tool Source 54 U -H I o (3 o ai xt QJ -QJ • E cu tn cu r-l U rH - W G U . 4-1 dJ 4J - X E X a; <d — .fl ~ 4-> 4-1 U •H u O I  rQ — 4-1 E o ent; C rH • Cd rH QJ fl CN 0) rH SH rH O 3 CO CO 4J E QJ H QJ £ C 4J X! -H 4-) a QJ Xl 3 M O - H 4J o a o u X QJ — O — s _ tn rrj I  4-1 PS I J3 I  4-» Ed 3 tn 3 rG -u - -H TJ - *J E » OJ 0 0 rH M CO OJ 3 a) —. QJ O rH o r>- 4-1 u Pi X! Pi rH fl 4-> •H -H U u — 0> 4J a QJ QJ o 3 Ti X U .fl 3 0. 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X a -HQJ (fl (fl -H 01 Vi 0) VJ 3 QJ 01 0) CJ > v. 3 CJ a > QJ 0 cn Q Oi •ri 0 Vl > u QJ Vi AJ 0) JJ Oi CO • Vl 0) 01 01 3 <j QJ QJ X 3 Vi > 3 QJ a x: > •ri 3 > cn 01 QJ 0 0 • AJ rH AJ cd JJ Vi JJ rfl > E (J -ri Di 0 fl VI VI u X VJ > VJ 01 3 UH to o 3 O tu 3 OJ 01 QJ VJ OJ •ri o Vi O UH > u AJ > QJ •ri xi tn > TJ UH •ri VJ cn AJ CO 4J QJ c •ri AJ Jfl X Oi 3 01 o o o JJ rO CJ rd 01 > 3 rH 0 CJ in X) cn -ri > QJ U 4J CJ o Vi 0) (fl AJ CO OJ rfl QJ Vi Vi cn UH > -H cn CJ u Jfl QJ 01 3 rH Vl -H 3 -ri tn CO •ri > U •ri OJ O (fl Jfl 3 rH rd C Jfl > * to > E- ub X Cd 3 — a 98 U O XI IJ TJ J J in OJ U OJ ffl 3 3 u u o o •H O Pi TJ ffl Ui rH fj O jfl 9 ' a •n E — XI W 3 01 O fO O JH G Jfl JH O JH U - Jfl S fl •H — J-> 10 U rH 4H fd ffl II -H -rH 3 )H (J w U 3 O — OJ OJ CJ Tj <—. O O " CJ CJ U OJ XJ 3 3 OJ OJ fl fl * J jq OJ fO fl -H 3" a 0) O rH I O *-1 1—1 I CJ CJ U C » 1 — a ~ ertex > fl QJ fl > 0 -H •H Ol XJ JH XJ 3 fd 3 fd > JH 0) 0 tn Oi XJ rd UH tn JJ fl QJ > 0 C Ol Ol rH —. 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C xJ Ol > 3 C • JH o jj TJ 0 — ffl • 3 fl QJ 3 tn CU •H rH tn H -H 3 rd O ffl XJ — OJ QJ 0 XJ QJ > tn ffl JH m D (TJ Jfl fl VH • u tn c > VH QJ rH (fl XJ > a rH QJ in -H -H -H QJ Ol ui > ffl H ffl Tj cfl 0 UH QJ Ui 0 Ol > UH T J J J J J Ol rd Oi JH tn UH o VH X a UH QJ X QJ > Oi fl -H 3 QJ QJ QJ X 3 JJ QJ Oi QJ J J ffl Jfl G (Q XJ 0) > XJ Jfl 0) 01 3 Ul G • Ol ffl Ol a QJ O Cn VH rH JH m XJ J J Ol o T J Oi T J Tj Jfl -H fl OJ rH OJ 0) JH 3 J J 3 tn — J ffl VH XJ XJ -H > fd > Oi JH QJ -H QJ 01 ffl ffl o rd u w T J 0 > JH Ol 0) u xJ C 3 xJ II 0) x" in QJ UH J J T J JH rd rj tn fl -H rH Ui VH QJ OJ tn Ui > rH W 3 > tn > fl -rH rd tn 0 J J 0) tn QJ w JJ 0 QJ QJ ffl o (0 in > 3 ffl s JH T J tn J J Ot 3 II OJ fl CO Q CJ VH XJ — OJ CJ tn QJ w J J fl T J QJ JH 0 J J C J J fl JJ fl Cn 3 -H fd > XJ 3 -H W 3 tn O — ffl o QJ O • - OJ W •H 3 XJ jfl —' 3 Oi •H rd XJ 0) 2 ffl Ot -H Oi -H — Ol Di C fd •H ll VH o 3 (0 JH 3 1  Ol tn Cn • JJ fl 0 VH JH OJ tn II a -H JH XJ O T J rd T J QJ 3 II ffl — 3 OJ * •H u J J J J UH > OJ JH JJ in U J Ui Jfl Ui Oi rH A Oi t H^ + Oi c JH in tO 3 rH u X 3 XJ tn 3 3 JJ — T J O TJ — 0 T J ^ JJ c O Xi rH -H QJ T J to fl o XJ fl in ffl tn ffl * tn . OJ ' Ui rH o JJ fd xJ — o o u T J o QJ o o u JH JH JH TJ XJ u JH Ol T J T J Tj Tj Tj T J T J T J T J Tj TJ Tj o Cn QJ 3 01 QJ fl QJ Ol QJ c T J ffl G G G G C fl fl C G fl fl OJ fl H  O > > OJ UH OJ Jfl c UH 0 Ui Ol ffl ffl ffl ffl ffl ffl ffl 01 ffl ffl QJ ffl UH Jfl -H UH -H a 3 Jfl XJ -H UH -H T J a a a a a a a a a a a a 3 rH XJ JH 3 xJ x a Xi XJ JH 3 Jj 3 OJ a a a a a a a a a a a a XI J J CQ fd fd QJ fd Jfl JJ PQ rd O rd rd Ti rd rd rd rd rd rd rj fd fd tn to Ol JH J J • 3 tn H to Ol JH  • C rH 3 ffl OJ JH UH JH 3 fl QJ QJ CJl UH UH UH UH UH UH UH UH UH UH UH VH CN U -H E QJ 3 3 XJ CJ -H rH T J 3 3 3 3 3 3 3 3 3 3 3 3 3 •H H 3 •H > Xi 3 •H JH •H W JH XI XJ XI XJ XI XJ XJ XJ XI XI XI JJ rH J J 3 Jfl QJ Pi J J fl Jfl OJ Xi m ui 3 JH Xi to Ui 3 JH 3 fl VH a — a Z.8 3 G w & H J J O J J 4-> Ol QJ jfl [fl -rH CJ Ol C H § -H -H — J J — J J rj to — jfl bi a ty cn G i a • — — — Xi JJ JJ • c LJI a H ffl L« rjj QJ — Qj •—• S II — JJ -• C ~ G 01 IH un JH Ot tH 3 -H 3 OJ JJ JJ Jj — QJ OJ OJ U — SH to JH QJ UH iH r J J J J : O in -0) rO rfl — & 3 ty w & W 3 W 3 H 3 H JJ H OJ JJ UH Ol —- ffl O • cr oi ffl ~ hi • U — UH — (3 UH O JJ JJ OJ • OJ rji OJ to QJ — OJ OJ to •H JH QJ JJ O •H -H E JJ to -H rO rO rH fl jfl rfl — & 3 0* W rH & hi 3 to QJ CO W 3 H OJ QJ 3 H JJ -H J J -rH H QJ JJ X i» JJ JJ U J Di -H OJ tJJ -rH QJ 0 • rH ty Dl QJ — . rfl J J to w o — 3 0) rH 3 3 JJ & Ol rH & UH rfl Jfl W 3 W 0 J J J J Di 3 3 II X 3 a OJ jfl CO "rt H O OJ H u Dl 3 JH JJ -H Jj z JJ 3 -H -H — OJ JJ XOJ rrj JH Ol rfl 0 OJ Dl J J J J 0- JH 3 Oi to Jfl W JJ OJ 0) J J 3 ty Cn C xi JJ Jj •H ui -H H Oi u u ai JH •H 3 OJ QJ UH JJ SH hi •r~i •r-i -H J3 UH Xi J H u CD II -rH || II 3 3 O O -H JH QJ iH JH 0) oi QJ CN 3 Pi QJ QJ to OJ to QJ UH rH rH OJ -H OJ QJ JH — jJ rH J J 3 O XJ ffl 0 ffl fl3 Ui -H > -H J J Ol QJ ept ROW Var Jj QJ ain Ol in u w JH rfl Jj X XI >i 0* Jj J J P J 3 hi J J ffl Ol 3 to to OJ J J -H G -H 3 rfl QJ i 3 rfl M Jj rfl o > to •rt s J J ffl rfl ffl 3 ~ - JH u rfl QJ JJ rH 3 g J J 3 rH QJ O — JJ •H • -rt hi ffl QJ C & •H • O CO JJ rH ffl OJ rH -H OJ g U rH • U 3 J J •<H rfl 3 VH W rfl 3 •H •H 1 rH O QJ & JH o rH Jfl SH -H CO UH SH C J Jj c/l rfl J J a  U J J UH - -0 ffl J J & m Jj 3 CO JJ QJ rH Ol JJ CO J J to 3 3 ll fl X tfl ffl 3 01 ffl o > > u TJ jfl JJ •H W (H J3 OJ ffl o to O to — to C J — ~ QJ — C Di Grfl JJ JJ ffl VH 3 2 rH O Jj —- Jj Jj > TJ ffl -H •H SH QJ QJ — VH S O rfl 3 JJ. G 3 G G3 JJ SH rfl J J Dl Di 3 O S JJ QJ 3 UH 3 -H -H QJ ffl ffl 0 - X JH to O E ffl to U VH ffl ffl fl - rfl C H -H JH ffl -3 C 3 -H W rfl QJ O 3 M 3 SH fl JH u u J J CO 0 0 O J J rfl o Xi -n a J J -— I  -H -H 3 >, Tj UH G U •H -H fl J3 0 XJ to 3 ffl to O1 0] — UH UH QJ J J S3 O JJ JJ VH 25 3 O rfl O VH 3 3 hi G U UH UH G -H tj rfl rfl OJ 3 VH J3 SH 0 JH 0 fl 0 — OJ ffl rH SH rH SH g rfl u 3 U — Jfl E 3 CJ H CJ XJ r-, O O I  rfl CO JJ TJ O QJ rH QJ 3 OJ •H jJ -H — JJ (0 J J " CJ CJ H rj to ffl G O i 3 3 rH ffl rH UH rfl ffl U 3 O ffl Jj fl 01 < CN 3 3 W O JH VH J H -H Jfl JH -H 01 -H rH fl 3 3 ffl rH JJ C 3 O 3 3 JJ 3 JJ Xj ffl OJ ffl JH G CJ C TJ CTl hi c W 3 3 XI a a ro — fl H •H C G 0 -H -H 0)O SH SH QJ  JJ 0 u TJ fl jJ U 3 u 3 3 to G Ul TJ -H I I  CJ C OJ VH o\o •H JJ -H J J SH UH ffl JH Jj J J ffl rH rH QJ QJ 0 3 O > 3 o « -Q SH JJ. SH •H J J •H OJ O H 3 4J QJ G o in 3 — a — 3a rH QJ XI rlfl ubl o —  U U 0 ffl 01 VH J J O 0 u JH JH a Xi a — a arn ty 3 rfl W & s s s K I OJ J J UH Ol —oi o CP Oi ffl —-hi • u — U H — S UH O JJ JJ ffl ffl U H CO rH U ffl G — J J -~» J J hi tO 0* UH fl G hi ffl H -rt "— rH —' 88 & ^ U W -H -H co rfl ffl G CO > > -rH Xi rfl -H OJ — cn — u Cf) -H •H -H U rH •H rfl W X -4J UJ -OJ ffl QJ rfl •nH rjiH O 4-J II G QJ OJ QJ QJ dt iH CO H CO U CO CO X} X) rfl ffl XI Xi a a > I u II A > r-l > riable _vl, Variable ackage Constraints ; ublic class Inequalit private Variable vl; private Variable v2; private int c; public Variable vl{) return vl; } public Variable v2() return v2; } public int c() { return c; } public Inequality(Va vl = _vl; v2 = _v2; c = _c; 9-06 3 3 •jj tt a 4J - j W U -w > u C 3 a o o H u a j 16 4-1 AJ „ D» Dl 3 OJ 3 0) OJ 3 Oi 3 al •~! al > AJ > 3 4-1 3 A-l ft 3 ft 34-1 -H -H 3 3 O 0 > 1 > ~ cH 1 tH + + + + AJ + + A-l O OJ U O OJ (N Di Dl (N Di Di tu 3 tH U 3 fN Cn -H •H AJ -H AJ fO a + Vl tn + Vl tn Cu 3 •H th AJ tn •H rH J3 4J St •H rHrd 0) D) XI Di XI tn > rH + 3 3 3 3 AJ to XI — OJ tn V-l - 0) tn Vi 3 *n fd tu fl) — tn OJ -H CO • Di D) 4-1 Di Dl AJ OJ 6 O Vl 3 rH 3 01 3 CN 3 0) 3 -H ffl XI <d s u II •H AJ ft U II •H AJ a AJ rH fd > U r-j 3 i-> U ID 3 AJ -H Cd ft J V AJ fd CQ H 3 4-1 rd CQ H 3 rH 01 j •n O - n 3 t o — 0 n 3 ft O — 0 rfl VI ft tn = — — . •- 4J c 3 II 11 II rH Vt CO O O O ft ft in * — — Dl AJ AJ AJ -H Tj AJ • H 3 • ft 01 Vl + • o !5 = . i O f l i oi AJ I AJ Di : oi 3 i Di 01 I • rH * ' 3 • 8 £ 1 i O 3 I  ll -n 01 AJ 0) -H ft AJ -3 — O 3 > -H Vl Vi — AJ Di tn 3 •3H tn AJ • co A J f d - H O D l A J A J - ft ftAJ-H 0 J j 3 r O A J A J C 3 3 > A J AJ 3 Vi rH 0 O O ll ii H rj (U "w I CO o O -H rH 3 tn • o + > — in AJ O Di QJ 01 C U • rH • -H 0) — 3 • <d w AJ rd = — in Vi O p 11 II • ll o + + in AJ • to Dl O ft Xt tn 3 V i U 3 - H f t f t V i 3 A-> I CJ —• QJ M CN > O AJ 3 AJ tn 0 U -H 01 QJ 'tH I OJ Vl CN 01 > O AJ -H 3 AJ 01 rH O CJ "H | Di OJ rH £ 1 -- 3 H tn o AJ AJ u oi tn tn I - J rH o 3 vi in u AJ -H O "rH I rd U CJ I -Di 3 - 3 Ul cj oi rJ -<d •H 01 o AJ AJ cu »J CJ oi cn 3 QJ O 1 01 AJ 1 01 CJ j E rd > 4J AJ CN ffl QJU 3 •- CN 01 U Vi Ul • n oi tn CN AJ CO 1 & 0 CJE u u 01 AJ AJ & 1 O •H 3 Vl cn •H 6 A rH AJ rH 0 -H rj o 13 ft QJ tH rd AJ rH >i Vl xt ft S co CJ Vi u 1 Vl Oi ftj •H AJ iH AJ 0) 0 o a tn 3 Vl in > AJ Vi AJ O H o tn C 3 cn H CN u cu rH 3 XI rd AJ •H o o -H 4J 4J fd u 3 o •H rj Vi CJ rH CJ oi t-4 Ul in Cu rj OJ o rd -H ft AJ 0) -H -H QJ B CN Vi o AJ AJ iJ cn > 0 tn 3 •H 3 3 3 tn XI 1 tn •H VTJ cn 3 tn o O (3 tn rH CN m rd J c rH 3 ro <o U tn cj Oi j ft CJu CJ CJ II II Vi O > > Vi rd •j 1 1 CJ U 3 CJ fd <d -H rH QJ 0) QJ rH CN • -H AJ rH CJ CJ AJ AJ AJ CJ II II ll 4J 0 rH 01 01 rd rd -H Ul cn •H Xt Vi en Di AJ CJ > > > tn tH CN m •H •H AJ 3 CN fd Vi Vi Vl -H -H -H -H X! 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OJ JJ ' C O J • Xi Ui • i — Jj - —-~ CJ — > — OJ > — tn JH — JJ JJ — JJ xi £ _ un D) . - rjj fjj oj -H ' — E fH rH JH QJ QJ Dl • £ rH fi JJ JJ (fl H fd U O 3 QJ j j 01 0) JH JH O JH JH QJ tn JJ JJ >i QJ CJ CJ fl rH QJ QJ J Di SH Pj Di XJ, QJ 3 JH -H -rt tf SH JH 3 3 ! -H E* I t ^ S fl • I O O rH U CJ O O < tf tf • JJ JJ Jj Jj JJ Jj >i QJ QJ QJ QJ OJ 01 VH OI OI OI DI OI OI O jJ JJ JJ JJ JJ JJ JJ CJ -rt -H -rt -H -H -H ffl 3 3 3 3 3 3 UH CJ (J U U O CJ . VH JH JH JH JH JH Di 3 3 O > fl O _ J QJ QJ i 0) Oi I JH tn ll — CJ QJ < - Oi I X O O O O -H VH 001 rH B CJ 01 jJ eni ws X _ 01 0) -H M 0 — Dt J J Vt iH U <= jJ + 3 ffl 3 3 Jfl A 3 O a. Ol fl 0) rH U J J A -H rH •H J J n) •H -rl b a. > VJ — o 0) rH + QJ ffl 4-1 — 01 rH JJ >1 CJ 3 •o cn -Di i i o fl 01 >i 2 OJ J J X w O • r i Vi - *9 • 3 Jfl co Vj g 3 o J J 0) u 01 (3 -H M a J J J-l e " VJ — QJ + >i 2 + 01 •H fl + OJ Jj rfl VJ V) A u -Vl ^ o 2 — J J rH 01 rH 3 A x — s 01 Jfl 01 -H rH + >1 X X 0 w * u Vl Vi rH 4J i u rH Oi rfl Vi cn O A •H 01 Oi -H -ri 3 3 fl • fl H + Jfl rH H A Di 4-1 4-» MH 3 2 TJ fl 3 Jj 0) cn Tj ffl -H -H W 01 0) Jfl J J M + -H •9 E M H Oi TJ rH VJ 0 II u CO 3 3 3 3 3 3 -H 01 -H -. 0) 9! CO - 0) 4J 0 0) U Tj -H 01 MH MH Oi Jj E U m Vl tH •H 01 VJ • S ~» >1 • 01 -H VJ V Di 01 V Jfl V O Di Vi J J 0) ll 3 E — Oi — 3 J J 01 v 3 Vi 01 V J J V o ffl 0) CO E CQ 01 O 01 •H 01 >i « 01 ffl 01 J5 01 01 CN o 2 MH OJ 3 rH J J J 3 ffl -~ 3 4J c 3 3 U -H MH VJ 2 i * 0) -rl 0 H 3 01 •rl J 0) •H CJ QJ j 01 -ri — 01 • r i 01 •H W fl 01 01 ffl Oi J J J 3 VJ 01 Jj J 3 J J J OJ jJ •fl 3 01 J J J cn (N Dl ID cn m J J rH 2 3 •ri 3 jfl 3 3 •H 3 •H -H 3 oi -H 3 -H •ri 3 cn -H 3 o ffl > ffl •H -H 0) VJ 0) u • VJ 0) Ol VJ 0) TJ Vi OJ D> U OJ O Vi 0) rH £ ffl rH 01 Vl UH rH I  3 3 0) * J jJ 3 c Oi 3 3 TJ 3 3 OJ 3 c -H 3 3 U rH u J J 3 - -H - J J 3 3 rQ • ffl J3 CJ • Ol ffl u -~ <JH J J J J J J — O O J J 4J J J J J J J cn Di CJ > -H MH fl fl fl <JH 3 3 TJ 3 3 TJ fl 3 TJ 3 3 TJ fl 3 3 ffl Vl •H -H Ol "H o o O -H ^ O o -H O O •H O O •H O o • H 0 O O 0 rH Vl rfl o 0 0 o 3 CJ & xt a 2 > > > > ffl rfl E 3 a •H a [ 3 2 L ^ ? P E J W I X _ B : ^ L A Y O U T G E N E R / I T T O N E ^ M P L E S O U R C E ) This appendix includes the four example source tested in Chapter 6. In a similar way, the designer can write a description of a target circuit using the API provided in Appendix A. Table B . l lists the index of all the example files. class FifoStage 102 class Inv 103 class Invs 104 class newlnv 105 Table B.l Index of Layout Generation Example Source 101 H VH VH VH M OOOOO -rt -H -rt - H (3 fB rrj rrj rrj rrj § I? VH VH JH JH JH 3 3 3 3 3 CD QJ 0) OJ OJ G G a G G JJ ~ U PH ro U G — J — C EH — I CN O rH CN ( u u J J J J u u J J OJ QJ - H i_> u —-OJ O J — U — VH U U fl — — QJ — — OJ g c u QJ J J 3 QJ JH c J J J J G O J U G G u G UO fi 3 O U u G J J U G O OQJ G Q J O J GOOQ) QJ O « QJ O U UG O fl O W - G G U Dl G U • a u a •- u * •— G G • • a — — O - * — - O C N — ' - — . — 0 " 0 — O _ — U ffl u - ^ - n - U - U ~ ^  U — ~ — — C fJJ ~ PH — J J ~ ro <D ~ — U ~ CD ~ QJ OJd QJ QJ •rt U — J - J Q J 3 — • — ' U C C N V H — U — rj ci ~ . — U -rt U U rrj V H — 3 U O — J-l VH -rt *—• 3 '—' IH '—' VH — — — Vjrd U U VH 3 QJ O JH — QJ — 3 <d JJ O QJ 3 QJ G J J Q J Q J 3 V H 3 3 Tj 0 4 - J — fl JJ JJ JJ O JH — Ul U O u O - U U O T) OO rairjjJOUirjunTju - rdwrcl M JJ rd (fl in . ui Ul .-. • Ol U W QJ Ol QJ • • U — Dl • tn • U Ol Ol • <-, . . H • OJ • fi • G <~• *—• QJ • • r-, QJ • • r-, —, r-. •-' H r - . g r - . C - — rt N fi ^ - r t CN C —. IT) *-• rH CO r— •—'OGCNOCNO1—' ' G •—. O m G ro CN ' r-i ' •—' O ^ ^ o 1 — ' U * — ' U - — . r - , o c N ' — • m o ro r-. r-. •—' O '—i U n • f-^ • rH rH (J •—' •—' CN •—. CN U '—> •—• CN 1—' rO fO J-l •—' H -O — <H— . j_) ro " CN •—• • CN ro '—' J-l — JJ - — >—• — •—• — JJ JJ ._. j j ._. . . . J_J — . _ . J J — JJ JJ j j '—• JJ .—- JJ •—' JJ —' '—' '— .—- JJ JJ —• JJ —- — J j j j — JJ —- — U JJ — — — OJ — O J J J J J — U — JJ — j J — — — j j U J J J J OJ U J J G - U U J J U U U G O J J J U J J — U G J J J J U Q J U U G o j u - r t U r t O V H O j a j - r t G U Q j u o j Q j - r t u u a j f l Q J O J G G f f l ' O f f l f l f f l f l G G f l G Q J G O J j J G f O O j a J f l G fi fl o a G H G O G o a a r J O G a c c d a r t G c a o a a U O G T j a M G m O O T j U f l O f l D l O ' O f l C O U 0 0 UO • O • O - U U • - O U O • U • O O U • U U —- • U " U " U r i • • r-. U • O —- - r - , U U • • — ... . ^ - c N • •—. •—. CN •— • —. • ro —• rrt • QJ — _ _• ~ ._. _ ~ QJ —. — — U r r t fl — •—• ' ' r—i r—. R £ ,_, £ £ _ £ (H [ J t N fl fl VH Tj - H QJ ro QJ rH QJ CN -rt -rt CN -rt QJ -rt QJ ro -rt ro QJ OJ -rt V-i Tj -rt -rt fl Tj frJjJ'—'jJ — jJ*—'rrj rrj •—• rrj JJ rd u • rd J J J J rd flTj rfl rd 0>MrdJJrdJjrdJJVHVHJJVHmVHmJJVjJJrrjrdVHO>MVH W — TJ Dl —^Di^— Di — Tj Tj — Tj D I T J D>-TJ — DiDiTJ tn — T J TJ • U r • U ' U r U r O ( U O O OJ rH Q  CN QJ O rH Q J l T l O O r H QJ rH 0) CN -tf  QJ O CN w ^ m l , j^ _ ^ t l ^ p l 9 ^ ^ r t , t ^ ^ ^ r_^ i ^ r ^ ^ m O O O O O O O O O H H O CN CN fN tN O CN O CN CN CN CO O r O r O - — r j ^ - O L - u ^ u ^ . . , U — — — — U —' u — — -—U— ^ J J • J J J J - J J • J J - J J J J - j J j J j J j J - j J • j j j j j j j j - J J J J O O O r JJ JJ JJ ; r o r O H r H r H C N C N C N C N C N C N J J J J J J J J J J J J J J J J J J J J J J V l V t V l V l J l k r l r l r l V l r l r l V l r l r l r l V l O O O O O O O O O O O O O O O O O uiuiuiuiuiuiuiuiuiinuiuiuiuiuiuiui V l V j r l r l r l V l r l V l r l r l V l V l V l r l r l r l r l E H 6 H H E H H S r H t H g r ? H f ? 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Dl TJ 01 3 • • • 0 EH EH 8H 01 3 3 3 0 3 3 3 3 3 U 01 CJ CJ CJ U CJ . VJ VJ VJ VJ VJ II EH -H -H -H -H -H . ft CJ CJ U CJ CJ U ' O I T j T J T J T J T J T J T J T J T j T j ! 3 T J T J T J T J T J T J T J T J T J T J I > > > > > > > > > > i „ _ . : tntnuitntntntnintnu] T J > > > > > > > > > > \Tltitititititititititi C J 3 3 3 C 3 3 G G C C G J J -H II 1  II II II U f l o i W u i i / i i / i w i o M t n i f l • H 14 > > > > > > > > > > - J 3 3 3 G 3 B 3 3 3 : Q H H H H M I fl u VJ JJ •H UH U QJ — Vl — -H JJ U -H • fl QJ CJ — Vi JJ '—' • CJ -H JJ -~ Vj fl -H H U 3 JJ U Vj CJ -H • -H Vi fl 01 u •H CJ — U Vi JJ O) I • -H 4H — i D> CJ QJ JJ I —' • rH UH JJ XI -01 — Vl — -H JJ U •H • fl TJ CJ — Vj JJ —. . u — J J H J J •H J J CJ -H fl -H • fl CJ fl Tj CJ VJ CJ — Vj -H VJ J J -H I U "H UH CJ I • CJ 01 • I UH • rH UH . — rd • — SOI 4-1 J-l O U 3 C/l > 3~ 3 "rl CJ n() fl VI -rl CJ rH J-l H 4J 0 O fl rH  rH -rl o -rl -rl OJ rd fl rH -H rfl JJ O 3 3 U rfl rfl 3 •ri rl 3 •H CT Vl C A EL 3 CJfl 4-1 CJ W -rf -rH D) Di 0 VJ u CN 0 CO •H ro rd in to CJ •H •H •H H fl Dl > > rd CJ] c CJ  3 CJ 3 IT) -H o rd CO rd rH OJ 01 Vi Vi Vj rH U CJ £ CJ 4J J-l U fl u 3 U 3 rfl rd JJ •rl jJ -rl JJ CN JJ jJ 4-1 JJ CJ > > rH 01 01 01 rH IH u U rl U •rl -H -H Xt Vi ub M ub VJ o 0 0 O O rH Vj Vl fl ub ub Dl a 9> a & & x> a a a a a 3 & & & E 6 A < -rl -H •rl •H •H a — o 3 vJ 0 cn 01 -rl - Di tn •H 3 3 — — frj S j - J J VJ I 3 $ i 0) rfl -JJ VJ — -(fl TJ TJ ' - 3 3 - ~ — O O — 3 TJ Oi — £ TJ O TJ Cu VJ g ifl rH > — V^ — O fl> 3 3 3 3 3 • OOOOO — - Oi 04 04 Oi Oi ro . J J J J J J J J U (J (fl UJ J J CH flTJ33flflfl3 04 •lHU>CJOUtJCJO in a— 3 a - •• 01 — jJ fl JJ u CJ 0) - — VJ Vj Vj Vi Vt rH ' JJ -rl -H -H -rl -rl OJ CJ CJ U CJ CJ CJ XJ -H fl rfl Ol fl OJ C VJ 3 a 3 3 fl O O fl 3 3 3 3 — oi oi ** 3 fl u Vi VJ VJ VJ U * -, TJ 3 O O 3 a • — -II II II II 3 TJ 3 O J J J J Oi Tj O 04 in cn 01 -QJ B J 3 cn VJ VI J J rfl fl a -Vj VJ J J J J J J J J 4J § S! ' 04 M 3 EH O CM 04 Cu Di TJ Oi 3 3 3 in U CJ U U U . VJ Vi Vj Vj Vi II a CJ CJ u u u CJ in 3 Di & O Ifl M CJ -H UH 3 VJ rH 01 OJ -H " 3 CJ a. >>>>>>>>> G C G G C G G G G 333333333 G G G G G C G G G > > > > > > > > > G G G G G C G G G 4J J J J J Jj jJ Jj Vj •ri •rl -ri -r| •H -rl •rl •ri CJ fl fl fl fl 3 fl 3 m o U U u U u CJ J J J J Vj VJ Vj VJ Vi u Vj •rl Ol J J •H •ri •rl •rl -ri •ri •rl QJ fl 2 fi-CJ u CJ u u u CJ rH CJ E O CN CN •rl in (0 xt — U TJ 01 Di CJ 3 --rl 3 — 3 3 — 3 3 3 3 3 fl J J H — O Jj O J J 0 J J O J J o J J o J J 0 J J u • X3 •rl rH -H •rl rH •ri •rl rH •H •ri VH 01 U OJ 3 Ql -J 0) 3 QJ fl 01 fl 0) fl 0) fl •ri rH - 01 XI U .Q U XI U XJ CJ XJ CJ Xi CJ XI CJ u J J J J Vj • Vj Vi V  V  V  Vj •rl • -rl — -ri •rl -rt •ri •ri •rl 4J J J r> 3 cn U — CJ U CJ CJ CJ CJ UH •ri J J cj g Jj 4J • J J J J Jj Jj Jj 01 fl •rl M E •rlro -H ro -H ro •rl ro •rlro •rlro -rl ro u fl •rl 0 3 (fl 3 X) fl U fl TJ fl 013 UHfl Ol Vi CJ U Ul U 0 — CJ u CJ U u t-t •ri Vj VJ 3 VJ 3 Vl 3 VI 3 Vl 3 VJ 3 VJ 3 4J u •rl u 0 -ri o -rl O •ri o •rl 0 -rl 0 -rl O •rl U •H U U rH CJ rH CJ rH U rH U rH U 3 Jj Di TJ TJ 01 • 01 01 OJ QJ OJ 01 U UH J J (0 TJ TJ rH XJ rH X) H JD. rH Xt rH XI i-H XI Xt VJ 0) UH S > > (fl xt • CJ TJ 0) Di •rl 01 0 U rH £•«in cn II II II 1  ll J J > > I  3 3 fl rH CN "31 in r- a H M J J J J J J J J jJ J J J J 4J J J •H •rl -ri •ri •ri •rl -ri •ri A 3 3 3 3 fl fl fl 3 3 3 0 01OJ CJ CJ CJ u CJ U CJ CJ3 3 Vi VI Vj u VI VI Vj V  J J -rl •rl •ri •rl -l-i •ri •rl A II ll CJ U CJ u u u CJ CJ a m ro jj J J J J Jj Jj J J JJ J J A UH Di •H •ri •ri •rl •H •rl -H o 3 fl fl fl 3 3 3 3 CJ in cn CJ u 0 CJ CJ CJ 0 U •H > > V  Vj VI Vj V  VJ Vi Vi Oi 3 3 -IH •ri •H •rl •ri -rl -rl •rl rfl HHM o CJ CJ CJ O CJ CJ U 2 A P P E N D I X G L P A B O I N P U T A N D O U T P U T D A T A F O R M A T This appendix contains a sample input data file in the MPS format to the L P A B O solver and a sample output file from the L P A B O solver. Table C . l lists the entries for each section of the input or output file. circuit.dat (input data file for LPABO) * 107 declaration of rows of equality constraints 107 declaration of rows of inequality constraints 107 declaration of the objective function 108 declaration of the equality/inequality coefficients 108 declaration of the equality/inequality right-hand side lp;iho.(iut (ou.put file from I.PABOi 110 11: variable values 112 dual variable values 112 value of the objective function 114 Table C. l Index of LPABO Input and Output Data Format 106 L0\ OHfNn-ji/nor-cDmo oouoouoouooou ra OiHO)rO^Ul^ r>C£)CnOrHM S 801 rH rH rH rH rH rH I ( rH rH rH rH rH tH rH i trHiHHOOOOOOOOOOOOOOOOOOOOOOOOOOOOO rHiHrHtHTHrHiHiHrHrHcHrHcHtHrHiHHHHHrHHHrHHHrHrHrH O O O O O O O O O O O O O O O O ^00rH(NOJOlrO^Ln^LnLnCAiHfNMM > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > brjrjhjrjrjrjhjrjrjroh, f J l l l l l I l I I I I I l l l l n i l l l l l l l l l l l l H o o o o o o o o o o o o rHrNrv>^ i^ r^^ a}O^OrHOjrO^Ln rHrHrHrHrHrHrHrHiHrNC^ rSr^CNCN(NM rHrHrHrHrHrHrHrHrHrHiHrHrHrHrHrHrHrHrHrHrHtHrHrHtHrHrt • J 601 O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O H H H H H r i H H H H H H H H H r l H H H r i H H H H H H H H H H H H H r H H H H H H H H H H r i H H H H H H H H H H H H OrHOJrO^Ln^r>COCTiOi-lfN > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > rHr^rO^UiVDr^COCAO r - O J W H H r l H H H H H H H M > > > > > > > > > > > > > > m r- oo ai o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o Ln^vor>p-o3coai<TtoorttH HHHrtrHrHHrtrHrNir^rN (NM M <i i n io ^ O H • J l n a ) O l r ^ l n ^ c ^ o H l f l ^ o c o ^ m o o H H o ^ l n ^ ^ m O ' 3 | c rHtNrNMCNf^Ogrorornr^ > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > on o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o O O O O O O O ^ O r ' O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O Ul«3[^00CJ^OrHrNr0^invDr~C0C^OH rHrHrHtHiH<N0J01<NNr^ o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o H H H H H H r t H H H H H H H H H H H r i d r i H H H H r i H H r i H H H H H H H H H r i H H C O C N O O C N O O C O O O C N O O O O r o ^ i n v o r ^ c o c n o H o a r o ^ i ^ v n r H r H H H r H r H r H r N n q n q r N r ^ r ^ r ^ r ^ o H N n 1 H H H H H r H t H H H T H H H r H H r H H H H H H H H H H H W H i H H r H H r H r H H r H r H r H H H i - I H H N f O I U H O M n m H H H H H p S t f t f t f p r , P - t f p Z p Z & K K p i K p i Q i p i p Z o i Q i p i H r ^ ) ^ ^ l n ^ ^ o 3 C T ^ O H r ^ l ^ ^ ^ l n k o ^ M c ^ o H ( ^ l ( » l ' J l n ^ o ^ o D c ^ O H > > > > > > > > > > > > > > > > > > > > > > > > >>>>>>>>>>>>>>>>> Ill o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o O O O O O O O O O O O O O O O O O O O O O O O O O O O H H H H H H H H H H H H H H H H H H H H H H r l H H H r i r - ( ^ l O l O H c N n ' 3 l m ^ o ^ a ) c ^ O H N ^ O T J m \ o ^ a ) m o H ( N M r H r H r H r H r H r H r H r H r H r H r H r H r H r H i H r H r H r ^ O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O r H t H r H r H r H r H H r H r H H r H r H r H H r H i H H O r H C N r o ^ L n v o r ^ c o a i O i H r s r o ^ i n k D r ^ < x i c r i o rHr^r0^lilVi3r>0DCftOiHrSrn^Ln r > r > r > r > r > r > r > r > r ^ c o c Q a o c o c o < » _ . , , . M *J 1/1 ifl . , M (N M (N IN (N OJ H rH rH <-( H H • C J j r / j U i w r j j W O j r v i t o z\\ + + + + Q l Q j a j Q J O i a i O i O I O l Q J O i Q J O i O i Q J O i Q I O l O i Q J O l C N c ^ o i v o o o o o o o o v o v o v o i n v o v o i n o o o O O O C D O O O O O O O C O C O C O O C O C O O O O O a D O T T O C O O O O O O O O O T C O C O i H C O C O i H O O O r j T f r t r O O O O O O O O r H r H r O r H r O r H i n O O O o o o D o o c o o o o o o o o c o c o c o r a r ^ c c i c o o o o QJ OJ o o o o o o o o o o o o OJ 01 o o o o o o o o o o o o 01 0) o o o o o o o o o o o o QJ 01 o o o o o o o o o o o o 01 OJ 0) OJ OJ O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O i n L n i n V O O O O O O O O V O V O V O V O V O V O V O O O O O O O O O O O O O O O O O > > > > > > > > > > > > > > > > > > + + + + + + + + 0 1 0 1 0 1 0 0 1 0 1 0 ) 0 1 0 1 0 1 0 1 0 1 0 ) 0 ) 0 1 0 1 0 1 m o o o H o r > - > * o « d | o o o o o o o o i H O O l C O O r H O O O O O O O O O O O v o o m c n o c n r o o r o o o o o o o o o r O O r f r H O C n V O O V O O O O O O O O O r o o r o n ' o c n v o o v o o o o o o o o o m O r 0 V 0 O C n r l i O n " O O O O O O O O 00 • r M N l N N M H O O H H O H H r H r ^ r o ^ i J i v o r ^ c o c n O r H r ^ r o - ^ i n v o r -B i p J p l B J l l S p l D i B i B l H H H H H H H H oJoioioioio-oia: vo co oo cn r~ m cn CO OJ 00 fN O O O O OJ ro oo I 1 I rH O ro 01 0) 01 O rH rj VQ ro ro rji • LO OJ ro vo H H H O O r/ (Ji O rH CO rH • o i n vo o • • • ro Ol ro cn O 01 0) QJ 01 i n cn cn r- vo r - vo co o i ro i n cn cn • o o i n cn cn o i o • o i n i n m cn O • O rH CO rH o • • • • r f Ol rH VO vo CN rji m cn m cn rO rH O O O O oo oo r- i I l I co oo O QJ QJ 01 QJ ro ro Ol r- VO f- Ol . -HI ro rO Ol rH rH rH O rH Ol CO [-• r f r ~ vo o O u i *o I ro r f i n vo c— 01 0) cn cn vo vo CO CO CO CO rH fO r- r-1 O O l + + 01 0) O O o o o o o o o o o o OJ 01 cn o vo o CO o CO o ro O r- o QJ ai O O o o o o o o o o o o o o o o o o o o o o o o rf rf tn in o o QJ 01 OJ QJ rf rf rf rf i n tN o i o i o o o o rH 00 CO CO 01 QJ 01 rf rf Ti" 0 1 0 4 0 1 o o o 00 00 00 QJ 01 QJ o i m vo O O CO O O O + + + QJ 0) QJ >COOOO0COCOCOGOCO00CO< O O O + + + OJ 01 QJ • r j -a1 r r 1 I N CN O J l o o o 1 CO 00 CO I CO 00 CO I V O r H H r H r H r H V D V O V O L n u O i n u n i n u l L n V O V D V O V D U l L n L O U ^ ~ H . 0 2 2 2 Z 2 2 M ' 3 , O ^ ^ ( ^ l U ) O ^ ( N ^ r ) O 0 l a ) ( N O ' ^ l C D ( ^ l O C 0 ' q l H ( ^ l ^ n H l l ^ >>>>>>>>>>>>> >>>>>>>>>> >>> i >j i n IO r> a j o i i en r- r> o vo c OJ OJ T VO in o VO LD OJ OJ "3" "31 OJ OJ OJ O CO - J H O 00 O CN O 00 O "3" O 00 VD lA O CN iH VD O O Cfl o I I I OJ OJ OJ CO CN rH CO O o a s vo co CN O VO VD CN m o r-+ + 1 + + I I + + + + + + o j a j o j a j d j Q j o j Q j o j Q j Q j o j d j Q j o j c b o o o ^ o r > ^ o o o o o o o o ^ o ^ o o ^ C T i o o o o o o ' t f c ^ o o ^ o i o o ^ c j i o O ' t f c n o o o o O O O V 0 O r 0 0 Q O O O O O O O O ' d , O O O " a l o O O O O O O ^ l , O O O ^ J i O O O ' 3 ' O O O ' * O O O O O O O O C O O ^ r ^ O O O O O O O O H r n O O i H r O O O O O O O r t r o O O r H r n O O r H r o O O r t r O O O O O 0 0 0 0 3 0 V O O T O O O O O O O O O O O c O O C N V D O O O O O O O O V D r H O O V O r H O O O O O O V D r H O O V O r H O O V O i H O O V D i H O O O O O O O l / l O i H C N O O O O O O O O C N C N O O C N C N O O O O O O C N C N O O C N C N O O C N C N O O C N C N O O O O ( O r H f ^ ^ C O ^ J i r H O O O O D O ^ P C N O O O O O O O O V O ' riOlO' r H O O O O O V O - C r H O V O ' rH O VO ' r H O U D - C r H O O O ^ ^ V O r > C O C 3 ^ 0 r H C N r 0 ^ i n v O f > C « ( 7 l O r- i— r ^ ^ r > r ~ c o w a c o c o a ) r o « r x c o f f i o \ c n c ^ + + + + + + + + + c u Q j t j j Q j Q j o j o j a j Q j a j a j Q J O J O J U O O O O O c n O O O C D O ' t f O O O O O O O O t H C N O O T H C N O O O O O O r H C N O O r H C N O O r H r N O O r H C N O O O O O O r H C N O O O O O O O T H O O O C N O O O O O O O O O o o o o o v o o o o L n o r o o o o o o o o o c ^ o o o o o r o o o o ^ o v o o o o o o o O O O O O r ^ O O O r ^ O V O O O O O o o o o o L n o o o r o o ^ o o o o o o o o v o i n o < rH O i r N c ^ r o L n r o o o c N C N O o o o o o o o u ^ L n o o QOCJ^OrHCNrO^U^VOr-OOCnO r H H C N C N C N C N C N C N C N C N C N C N C O r n c v l r n r O C O r ^ + I I I I I I O O ^ O ^ O O H i n ^ M T j i n r i i n r O O l r O I J l H I N l f i r - H H o O ' J O O O l l ) ( N u l ^ f l ^ • m r s r - ^ c D N ^ l c o ^ r J C O l X l ^ f l O O H m o o i N O i M J i ' j M O r - O H o n m o n O r l N o o ^ n o o l n ^ ^ O l * l / l l n M M ( J \ { ^ ^ H • * ^ • l O l / l ^ o o o i D H O O c D f J i O M O i B i / i n n w i o i n i r j t N r o f f l ^ O O N f N O O M h N l O ^ r O l O i r i W ^ h O l O i n t N l O r l f O O O VO T TJ. TJ- 5* *j r- • 4-» 3 Id u 0 a 0) -H rH Cqo fd J J zat 3 rH fd 0 O QJ TJ -H o Xi A 0 OJ o rH CN m i n VO r - CO o CN Lf) VO r- CO o H CN m JJ >i J J 0) J J 3 m m ro m ro rO •<J m i n i n i n U 3 3 u lA rH rH rH rH rH rH rH rH (H rH rH rH rH rH rH rH rH rH cd a •H fd 0 CN tf tf tf tf tf tf tf tf tf tf tf tf tf tf tf tf tf tf tf tf tf tf tf tf 0 | SS vw in QJ £ TJ i n QJ OJ Di U Di •H C rH ng DO Oi 3 3 •H rH Oi 3 in W QJ CO •H VH •H 0 -H J J rH O CN >< >< >- >< >< > r* >* >H r* > g •H ad ep al de •§ lv 3 •H ta AB tn QJ tH QJ JH u U o o a 3 Xi V tf tf tn o tn tf E-< 6-" u o u u o u u QJ QJ QJ QJ fJJ QJ QJ oi oi to in ci in ui o o o o o o o APPENDIX D MAGIC FILE FORMAT This appendix includes a sample file in the Magic format, the generated "FifoStage.mag". 115 hi r< rt K i h h( h( ht r t r t r t a n n r t r t U H P K ffl h" fD CD fD fD n> (D fD A ra o n o o n n o rt rt r r r r r t 3 fD fD fD fD o o o o n n n r t hththththththt r t n rt rt rt fD ID ni o o o rt rt fD ro o o rt rt tl n fD TO o o rt rt tl M fl) fD n n r t h t h t M ^ ^ ^ ^ ^ n h H M n A r t r t rt rr rr r r r t rt i (D fD fD (D fD fD o o o o o o fD fD fD fD fD fD CD o n o n n o o o r t r t r t r t r t r t r t r t T j I -J H H H P M I O Ul CO VO NJ I lO P H H P I U U W U H W *D it1 H J UJ W U W W W H H I I -J H P HHO H H-> J W pi U I H> !->• VO VO r-» r ' - J - J U* I 1 • J - J H H W W UJ W OJ i t - J CO H W W W W yi OJ H W h1 OJ -J -O M I h-> I • Ul P U H | | | | U W s i J W OJ OJ OJ W sj r 1 NJ I I I I ' NJ OJ to OJ VOVOU1LTIOJ-OOJ-J 1 I I I I 1 I I fD fD (D fD (D i o o o n n i • rt rt rr rr t i h H h( A fD fD (D A O O O rt rt rt 3 ht ht I fD fD I O O I rt rt i h( h( hf ht rt A f D f D f D A (D <D fD fD O O O o o o o rt rt " • rt "O rt rt rt ) ht rt I fD fD I O O 1 rt rt t fD fD O O rt rt H A h t h f h t r t h t h l H ^ r t h H H r t K r t r n A r t r t r t h t r t fDfOfDfDfDfDfDfDfDfDfDfDfDrDfDfDA(DfDrD o o o o o n o o o o o o o o o o o o o rtrtrtrtrtrtrtrtrtrtrtrtrtrtrtrt'O rt rt n fD fD o o rt rt H> h-> -O I Ul O I CD V M »> V I -O tO CO OJ OJ OJ > -0, -J U"l t/l U~T I ^ P M - J tO CA CO Ul O Ul CA r - J il> 1 NJ tO tO NJ •J-J-J-JMWOJOJWuiLni ~ J - J Ui (Ji H> h-1 I 1 P - J cn I f . p to u i 1 CO I I P P O W I I CO vo I vo vo I I . - J 00 116 AHrlrlrlrlr-frlriArlr-ll A' (O1 fll ft' 'ffl 'fl> fti (0 CD A (T> rrj i n n n n o n o o n o i fD r t r t r t r r r r r T f t r t T J rr r t i a r t fj, p i i (-» " J w i i PI vo i H Ul K Ul H PJ - J V UJ i i OJ - j 3 vo I VMM t OJ OJ VO -J >J M W Ul Ul I I V r - 1 1 - J Ul OJ OJ V t—1 I I—1 I VO Ul Ul Ul LTi OJ OJ I t—* M P - J I I I I Vl P UJ IJ P U U P P -Ol OJ ro Ul OJ I I to to 117 

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