Showing papers in "IEEE Transactions on Computer-Aided Design of Integrated Circuits and Systems in 1994"

FlowMap: an optimal technology mapping algorithm for delay optimization in lookup-table based FPGA designs

Abstract: The field programmable gate-array (FPGA) has become an important technology in VLSI ASIC designs. In the past few years, a number of heuristic algorithms have been proposed for technology mapping in lookup-table (LUT) based FPGA designs, but none of them guarantees optimal solutions for general Boolean networks and little is known about how far their solutions are away from the optimal ones. This paper presents a theoretical breakthrough which shows that the LUT-based FPGA technology mapping problem for depth minimization can be solved optimally in polynomial time. A key step in our algorithm is to compute a minimum height K-feasible cut in a network, which is solved optimally in polynomial time based on network flow computation. Our algorithm also effectively minimizes the number of LUT's by maximizing the volume of each cut and by several post-processing operations. Based on these results, we have implemented an LUT-based FPGA mapping package called FlowMap. We have tested FlowMap on a large set of benchmark examples and compared it with other LUT-based FPGA mapping algorithms for delay optimization, including Chortle-d, MIS-pga-delay, and DAG-Map. FlowMap reduces the LUT network depth by up to 7% and reduces the number of LUT's by up to 50% compared to the three previous methods. >

Symbolic model checking for sequential circuit verification

Abstract: The temporal logic model checking algorithm of Clarke, Emerson, and Sistla (1986) is modified to represent state graphs using binary decision diagrams (BDD's) and partitioned transition relations. Because this representation captures some of the regularity in the state space of circuits with data path logic, we are able to verify circuits with an extremely large number of states. We demonstrate this new technique on a synchronous pipelined design with approximately 5/spl times/10/sup 120/ states. Our model checking algorithm handles full CTL with fairness constraints. Consequently, we are able to express a number of important liveness and fairness properties, which would otherwise not be expressible in CTL. We give empirical results on the performance of the algorithm applied to both synchronous and asynchronous circuits with data path logic. >

Spectral K-way ratio-cut partitioning and clustering

Abstract: Recent research on partitioning has focused on the ratio-cut cost metric, which maintains a balance between the cost of the edges cut and the sizes of the partitions without fixing the size of the partitions a priori. Iterative approaches and spectral approaches to two-way ratio-cut partitioning have yielded higher quality partitioning results. In this paper, we develop a spectral approach to multi-way ratio-cut partitioning that provides a generalization of the ratio-cut cost metric to L-way partitioning and a lower bound on this cost metric. Our approach involves finding the k smallest eigenvalue/eigenvector pairs of the Laplacian of the graph. The eigenvectors provide an embedding of the graph's n vertices into a k-dimensional subspace. We devise a time and space efficient clustering heuristic to coerce the points in the embedding into k partitions. Advancement over the current work is evidenced by the results of experiments on the standard benchmarks. >

Modeling the "Effective capacitance" for the RC interconnect of CMOS gates

Abstract: With finer line widths and faster switching speeds, the resistance of on-chip metal interconnect is having a dominant impact on the timing behavior of logic gates. Specifically, the gates are switching faster and the interconnect delays are getting longer due to scaling. This results in a trend in which the RC interconnect delay is beginning to comprise a larger portion of the overall logic stage delay. This shift in relative delay dominance from the gate to the RC interconnect is increased by resistance shielding. That is, as the gate "resistance" gets smaller and the metal resistance gets larger, the gate no longer "sees" the total net capacitance and the gate delay may be significantly less than expected. This trend complicates the timing analysis of digital circuits, which relies upon simple, empirical gate delay equations for efficiency. In this paper, we develop an analytical expression for the "effective load capacitance" of a pc interconnect. In addition, when there is significant shielding, the response waveforms at the gate output may have a large exponential tail. We show that this waveform tail can strongly influence the delay of the RC interconnect. Therefore, we propose an extension of the effective capacitance equation that captures the complete waveform response accurately, with a two-piece gate-output-waveform approximation. >

Broad-side delay test

Abstract: A broad-side delay test is a form of a scan-based delay test, where the first vector of the pair is scanned into the chain and the second vector of the pair is the combinational circuit's response to this first vector. This delay test form is called "broad-side" since the second vector of the delay test pair is provided in a broad-side fashion, namely through the logic. This paper concentrates on several issues concerning broad-side delay test. It analyzes the effectiveness of broad-side delay test; shows how to compute broad-side delay test vectors; shows how to generate broad-side delay test vectors using existing tools that were aimed at stuck-at faults; shows how to compute the detection probability of a transition fault using broad-side pseudo-random patterns; shows the results of experiments conducted on the ISCAS sequential benchmarks; and discusses some concerns of the broad-side delay test strategy. It is shown that the broad-side method is inferior to the skewed-load method, which is another form of scan-based transition test. There is, however, a merit in combining the skewed-load method with the broad-side method. This combined method will achieve a higher transition fault coverage than each individual method alone. >

RICE: rapid interconnect circuit evaluation using AWE

Abstract: This paper describes the Rapid Interconnect Circuit Evaluator (RICE) software developed specifically to analyze RC and RLC interconnect circuit models of virtually any size and complexity RICE focuses specifically on the passive interconnect problem by applying the moment-matching technique of Asymptotic Waveform Evaluation (AWE) and application-specific circuit analysis techniques to yield large gains in run-time efficiency over circuit simulation without sacrificing accuracy Moreover, this focus of AWE on passive interconnect problems permits the use of moment-matching techniques that produce stable, pre-characterized, reduced-order models for RC and RLC interconnects RICE is demonstrated to be as accurate as a transient circuit simulation with hundreds or thousands of times the efficiency The use of RICE is demonstrated on several VLSI interconnect and off-chip microstrip models >

Recursive learning: a new implication technique for efficient solutions to CAD problems-test, verification, and optimization

Abstract: Motivated by the problem of test pattern generation in digital circuits, this paper presents a novel technique called recursive learning that is able to perform a logic analysis on digital circuits. By recursively calling certain learning functions, it is possible to extract all logic dependencies between signals in a circuit and to perform precise implications for a given set of value assignments. This is of fundamental importance because it represents a new solution to the Boolean satisfiability problem. Thus, what we present is a new and uniform conceptual framework for a wide range of CAD problems including, but not limited to, test pattern generation, design verification, as well as logic optimization problems. Previous test generators for combinational and sequential circuits use a decision tree to systematically explore the search space when trying to generate a test vector. Recursive learning represents an attractive alternative. Using recursive learning with sufficient depth of recursion during the test generation process guarantees that implications are performed precisely; i.e., all necessary assignments for fault detection are identified at every stage of the algorithm so that no backtracks can occur. Consequently, no decision tree is needed to guarantee the completeness of the test generation algorithm. Recursive learning is not restricted to a particular logic alphabet and can be combined with most test generators for combinational and sequential circuits. Experimental results that demonstrate the efficiency of recursive learning are compared with the conventional branch-and-bound technique for test generation in combinational circuits. In particular, redundancy identification by recursive learning is demonstrated to be much more efficient than by previously reported techniques. In an important recent development, recursive learning has been shown to provide significant progress in design verification problems. Also importantly, recursive learning-based techniques have already been shown to be useful for logic optimization. Specifically, techniques based on recursive learning have already yielded better optimized circuits than the well known MIS-II. >

Circuit analysis and optimization driven by worst-case distances

Abstract: In this paper, a new methodology for integrated circuit design considering the inevitable manufacturing and operating tolerances is presented. It is based on a new concept for specification analysis that provides exact worst-case transistor model parameters and exact worst-case operating conditions. Corresponding worst-case distances provide a key measure for the performance, the yield, and the robustness of a circuit. A new deterministic method for parametric circuit design that is based on worst-case distances is presented. It comprises nominal design, worst-case analysis, yield optimization, and design centering. In contrast to current approaches, it uses standard circuit simulators and at the same time considers deterministic design parameters of integrated circuits at reasonable computational costs. The most serious disadvantage of geometric approaches to design centering is eliminated, as the method's complexity increases only linearly with the number of design variables. >

Minimizing production test time to detect faults in analog circuits

Abstract: Analog testing is a difficult task without a clearcut methodology. Analog circuits are tested for satisfying their specifications, not for faults. Given the high cost of testing analog specifications, it is proposed that tests for analog circuits should be designed to detect faults. Therefore analog fault modeling is discussed. Based on an analysis of the types of tests needed for different types of faults, algorithms for fault-driven test set selection are presented. A major reduction in testing time should come from reducing the number of specification tests that need to be performed. Hence algorithms are presented for minimizing specification testing time. After specification testing time is minimized, the resulting test sets are supplemented with some simple, possibly non-specification, tests to achieve 100% fault coverage. Examples indicate that fault-driven test set development can lead to drastic reductions in production testing time. >

An edge-based heuristic for Steiner routing

Abstract: A new approximation heuristic for finding a rectilinear Steiner tree of a set of nodes is presented. It starts with a rectilinear minimum spanning tree of the nodes and repeatedly connects a node to the nearest point on the rectangular layout of an edge, removing the longest edge of the loop thus formed. A simple implementation of the heuristic using conventional data structures is compared with previously existing algorithms. The performance (i.e., quality of the route produced) of our algorithm is as good as the best reported algorithm, while the running time is an order of magnitude better than that of this best algorithm. It is also shown that the asymptotic time complexity for the algorithm can be improved to O(n log n), where n is the number of points in the set. >

EVBDD-based algorithms for integer linear programming, spectral transformation, and function decomposition

Abstract: Edge-Valued Binary-Decision Diagrams (EVBDD's) are directed acyclic graphs that can represent and manipulate integer functions as effectively as Ordered Binary-Decision Diagrams OBDD's) do for Boolean functions. They have been used in logic verification for showing the equivalence between Boolean functions and arithmetic functions. In this paper, we present EVBDD-based algorithms for solving integer linear programs, computing spectral coefficients of Boolean functions, and performing function decomposition. These algorithms have been implemented in C under the SIS environment and experimental results are provided. >

Iterative placement improvement by network flow methods

Abstract: We describe an efficient iterative improvement procedure for row-based cell placement with special emphasis on the objective function used to model net lengths. Two new net models are introduced and we prove theoretically that the net models are accurate approximations of the widely used half perimeter of a rectangle enclosing all pins of a net. In addition, unlike the half perimeter model, our net models allow us to compute costs for assigning cells to locations independently for all cells to be placed simultaneously. This offers our algorithm an important advantage compared to other iterative improvement techniques: many cells can be placed simultaneously by formulating placement as a network flow problem. This makes our algorithm more independent from a processing sequence than standard iterative improvement techniques. Finally, we compare our method to some existing algorithms including TimberWolfSC 5.4. We ran all of the algorithms on the SIGDA Benchmark Suite. We found that our method produced solutions with up to 23% less layout area while using an order of magnitude less running time compared to TimberWolfSC 5.4. >

Inverter models of CMOS gates for supply current and delay evaluation

Abstract: The subject of this paper is the reduction of transistor-level models of CMOS logic gates to equivalent inverters, for the purpose of computing the supply current in digital circuits. No restrictions are applied to either the number of switching inputs or the transition times and relative delays of the input voltages. The relative positions of the switching inputs are also accounted for in the case of series-connected MOSFET's. When combined with our previously reported CMOS inverter model, the peak current is obtained in a time approximately three orders faster than HSPICE with the level-3 MOSFET model. The corresponding accuracy is around 12%. If the current waveform is required, the speed improvement is about an order less. Since the inverter model also yields the delay at no extra cost, the timing of the current waveforms can be done automatically, without recourse to a timing simulator. Although the emphasis here is on CMOS static gates, the method is applicable to dynamic logic gates as well. >

Complexity of the lookup-table minimization problem for FPGA technology mapping

Abstract: One of the main objectives in the process of mapping a digital circuit onto a LUT-based FPGA structure is minimizing the total number of lookup tables needed to implement the circuit. This will increase the size of the circuit that can be implemented using the available FPGA structure. In this paper, we show that even restricted cases of the lookup-table minimization for FPGA technology mapping are NP-complete (even when K is a small constant), and that it can be solved optimally for all values of K on a tree input in O(min{nK, nlogn}) time where n is the number of nodes in the network and K is the input capacity of the LUT's. Based on our algorithm for trees, we present a polynomial time heuristic algorithm for general Boolean networks. Experimental results confirm substantial decrease on the number of LUT's on a number of MCNC logic synthesis benchmarks compared to the algorithms that allow no or just local exploitation of Boolean properties of the circuit. We obtain 10% to 80% improvement on the number of LUT's compared to the previous algorithms (even though we allow very limited operations, e.g., we do not exploit Boolean properties of the circuits or decompose nodes). >

Automated transformation of algorithms into register-transfer level implementations

Abstract: This paper describes a high-level synthesis system, called CAMAD, for transforming algorithms into hardware implementation structures at register-transfer level. The algorithms are used to specify the behaviors of the hardware to be designed. They are first translated into a formal representation model which is based on timed Petri nets and consists of separate but related descriptions of control and data path. The formal model is used as an intermediate design representation and supports an iterative transformation approach to high-level synthesis. The basic idea is that once the behavioral specification is translated into the initial design representation, it can be viewed as a primitive implementation. Correctness-preserving transformations are then used to successively transform the initial design into an efficient implementation. Selection of transformations is guided by an optimization strategy which makes design decisions concerning operation scheduling, data path allocation, and control allocation simultaneously. The integration of these several synthesis subtasks has resulted in a better chance to reach the globally optimal solution. Experimental results show that our approach produces improved register-transfer designs, especially in the cases when the designed hardware consists of data paths and control logics that are tightly coupled. >

Closing the gap: near-optimal Steiner trees in polynomial time

Abstract: The minimum rectilinear Steiner tree (MRST) problem arises in global routing and wiring estimation, as well as in many other areas. The MRST problem is known to be NP-hard, and the best performing MRST heuristic to date is the Iterated 1-Steiner (I1S) method recently proposed by Kahng and Robins (see ibid., vol. 11, p. 893-902, 1992). In this paper, we develop a straightforward, efficient implementation of I1S, achieving a speedup factor of three orders of magnitude over previous implementations. We also give a parallel implementation that achieves near-linear speedup on multiple processors. Several performance-improving enhancements enable us to obtain Steiner trees with average cost within 0.25% of optimal, and our methods produce optimal solutions in up to 90% of the cases for typical nets. We generalize I1S and its variants to three dimensions, as well as to the case where all the pins lie on k parallel planes, which arises in, e.g., multilayer routing. Motivated by the goal of reducing the running times of our algorithms, we prove that any pointset in the Manhattan plane has a minimum spanning tree (MST) with maximum degree 4, and that in three-dimensional Manhattan space every pointset has an MST with maximum degree of 14 (the best previous upper bounds on the maximum MST degree in two and three dimensions are 6 and 26, respectively); these results are of independent theoretical interest and also settle an open problem in complexity theory. >

Time-domain macromodels for VLSI interconnect analysis

Abstract: This paper presents a method of obtaining time-domain macromodels of VLSI interconnection networks for circuit simulation. The goal of this work is to include interconnect parasitics in a circuit simulation as efficiently as possible, without significantly compromising accuracy. Stability issues and enhancements to incorporate transmission line interconnects are also discussed. A unified circuit simulation framework, incorporating different classes of interconnects and based on the proposed macromodels, is described. The simplicity and generality of the macromodels is demonstrated through examples employing RC- and RLC-interconnects. >

Electrical model of the floating gate defect in CMOS ICs: implications on I/sub DDQ/ testing

Abstract: The behavior of an MOS transistor with an open in the polygate path (floating transistor gate defect) is investigated and its effect on the quiescent power supply current I/sub DDQ/ is studied. The possible detection of this defect by current testing is explored in fully complementary CMOS circuits. The behavior of a transistor with its floating gate is modeled using the coupling capacitances in the floating gate and the charge in the transistor gate. The poly-bulk and metal-poly capacitances are found to be two significant parameters in determining the degree of conduction on the affected transistor. The induced voltage in the floating gate and the quiescent current are estimated by analytical expressions. The model is compared with SPICE 2 simulations. Good agreement is observed between the simple analytical expressions, simulations and experimental measures performed on defective circuits. In addition, it is shown that the floating gate transistor can be modeled as a weakly conductive stuck-on transistor or as a stuck-open transistor depending on the values of the parameters characterizing the defect. >

An approach to the analysis and detection of crosstalk faults in digital VLSI circuits

Abstract: The continuous reduction of the device size in integrated circuits and the increase in the switching rate cause parasitic capacitances between conducting layers to become dominant and cause logic errors in the circuits. Therefore, capacitive couplings can be considered as potential logic faults. Classical fault models do not cover this class of faults. This paper presents a logic level characterization and fault model for crosstalk faults. The authors also show how a fault list of such faults can be generated from the layout data, and give an automatic test pattern generation procedure for them. >

Exact and heuristic algorithms for the minimization of incompletely specified state machines

Abstract: In this paper we present two exact algorithms for state minimization of FSM's. Our results prove that exact state minimization is feasible for a large class of practical examples, certainly including most hand-designed FSM's. We also present heuristic algorithms, that can handle large, machine-generated, FSM's. The possibly many different reduced machines with the same number of states have different implementation costs. We discuss two steps of the minimization procedure, called state mapping and solution shrinking, that have received little prior attention to the literature, though they play a significant role in delivering an optimally implemented reduced machine. We also introduce an algorithm whose main virtue is the ability to cope with very general cost functions, while providing high performance. >

Circuit-level electrothermal simulation of electrical overstress failures in advanced MOS I/O protection devices

Abstract: Previous work on electrothermal simulation using network analysis techniques has been of limited use due to the lack of avalanche breakdown modeling capability and the models to efficiently describe the temperature dynamics. Particularly, simulation of electrical overstress (EOS) and electrostatic discharge (ESD), which are important threats to IC reliability, require an accurate description of temperature-dependent device electrical behaviour including breakdown phenomenon. This paper presents electrothermal device models and their implementation in a new circuit-level electrothermal simulator iETSIM. Simulation results for an I/O protection device in an advanced MOS process are presented to demonstrate iETSIM's ability to accurately model device behaviour up to the onset of second breakdown. >

Steady-state and transient analysis of submicron devices using energy balance and simplified hydrodynamic models

Abstract: The differences between two widely used intermediate-level charge transport models are investigated. The origins of the models are reviewed, and mathematical relationships between the models are established. The practical consequences of the differences are investigated by comparing results obtained for several submicron structures. The predictions of the two models are shown to differ qualitatively, as well as quantitatively, for certain situations. An appendix summarizes the numerical techniques used to implement the models in a device simulator. >

Adaptively controlled explicit simulation

Abstract: Adaptively Controlled Explicit Simulation (ACES) is a timing simulation methodology for the verification of the transient behavior of integrated circuits. A new adaptively controlled explicit integration approximation is used that overcomes stability problems encountered in earlier explicit techniques. Circuit partitioning is employed, which allows event driven simulation and exploitation of circuit latency. Piecewise linear models are used for nonlinear devices, allowing efficient simulation of MOS, bipolar, and BiMOS circuits. Simulation accuracy in ACES can be varied by controlling the accuracy of either the integration approximation or the piecewise linear device models. With the combination of generality, exploitation of circuit latency, and ability to vary accuracy effectively, ACES provides an efficient environment for transient simulation of integrated circuits and systems. >

Lower-bound performance estimation for the high-level synthesis scheduling problem

Abstract: A given behavioral specification can be implemented on a large number of register-transfer level designs. Instead of producing several designs and selecting the best one, synthesis systems may use estimation to reduce the design space. In this paper, we present a new technique for computing a lower-bound completion time for non-pipelined resource-constrained scheduling problem. Given a data flow graph, a set of resources, resource delays and a clock cycle, we derive a lower-bound on the completion time of a schedule. Our technique can handle chaining, multi-cycle operations and pipelined modules. The technique is very fast and experimental results show that it is also very tight. >

RESIST: a recursive test pattern generation algorithm for path delay faults considering various test classes

Abstract: This paper presents RESIST, a recursive test pattern generation (TPG) algorithm for path delay fault testing of scanbased circuits. Five test classes are introduced and their properties are discussed. We present an algorithm for deriving a logic system for TPG that results in an earlier recognition of conflicting value assignments. RESIST uses the logic system derived for each test class for an optimal search strategy. In contrast to other approaches, it exploits the fact that many paths in a circuit have common subpaths. RESIST sensitizes those subpaths only once, reducing the number of value assignments during path sensitization significantly. In addition, our procedure identifies large sets of untestable path delay faults without enumerating them. RESIST is capable of performing TPG for all path delay faults in all ISCAS-85 and ISCAS-89 circuits. For the first time, results for all path delay faults in circuit c6288 are presented. A comparison with other TPG systems revealed that RESIST is significantly faster than all previously published methods. >

Simultaneous functional-unit binding and floorplanning

Abstract: As device feature size decreases, interconnection delay becomes the dominating factor of system performance. Thus it is important that accurate physical information is used during high level synthesis. In this paper, we consider the problem of simultaneously performing functional-unit binding and floorplanning. Experimental results indicate that our approach to combine binding and floorplanning is superior to the traditional approach of separating the two tasks.

Optimal algorithms for bubble sort based non-Manhattan channel routing

Abstract: It has been pointed out that, in many cases, results generated by non-Manhattan channel routers will be better than those generated by Manhattan routers. Non-optimal bubble sort based algorithms for non-Manhattan channel routing have been proposed in the literature by also allowing connections in the +45/spl deg/ and /spl minus/45/spl deg/ directions. In this paper, optimal algorithms are proposed for the two-layer and three-layer non-Manhattan channel routing problems based on an identical problem formulation. The time complexities of our algorithms and the existing algorithm (which produces the best results so far) are O(K/sup 2/ * N) and O(K * N/sup 2/), respectively, where N is the number of terminals (i.e., the length) of the channel and N is the number of routing tracks (i.e., the height) in the channel. K is always less than N, and in most cases is much smaller than N. Clearly, a significant improvement in time complexity over the existing algorithm (which produces the best results so far) is achieved, while ensuring optimality. >

Architectural level test generation for microprocessors

Abstract: Hierarchically designed microprocessor-like VLSI circuits have complex data paths and embedded control machines to execute instructions. When a test pattern has to be applied to the input of an embedded module, determination of a sequence of instructions, which will apply this pattern and propagate the fault effects, is extremely difficult. After the instruction sequence is derived, to assign values at all interior lines without conflicts is also very difficult. In this paper, we propose a separation of test generation process into two phases: path analysis and value analysis. In the phase of path analysis, a new methodology for automatic assembly of a sequence of instructions is proposed to satisfy the internal test goals. In the phase of value analysis, an equation-solving algorithm is used to compute an exact value solution for all interior lines. This new ATPG methodology containing techniques for both path and value analysis forms a complete solution for a variety of microprocessor-like circuits. This new approach has been implemented and experimented on six high-level circuits. The results show that our approach is very effective in achieving complete automation for high-level test generation. >

Routability-driven technology mapping for lookup table-based FPGA's

Abstract: A new algorithm for technology mapping of lookup table-based Field-Programmable Gate Arrays (FPGA's) is presented. It has the capability of producing compact designs (minimizing the number of cells (CLB's)), as well as the flexibility of trading routability with compactness of a design. Research in this area has focussed on minimizing the number of cells. However, minimizing the number of cells without regard to routability is ineffective. Since placement and routing is really the most time-consuming part of the FPGA design process, producing a routable design with a slightly larger number of cells is preferable than producing a design using fewer cells which is difficult to route, or in the worst case unroutable. We have implemented our algorithm in the Rmap program, and studied routability of two other mappers with respect to Rmap. Rmap produces mappings with better routability characteristics, and more significantly Rmap produces routable mappings when other mappers do not. >

On the intrinsic Rent parameter and spectra-based partitioning methodologies

Abstract: The complexity of circuit designs has necessitated a top-down approach to layout synthesis. A large body of work shows that a good layout hierarchy, or partitioning tree, as measured by the associated Rent parameter, will correspond to an area-efficient layout. We define the intrinsic Rent parameter of a netlist to be the minimum possible Rent parameter of any partitioning tree for the netlist. Experimental results show that spectra-based ratio cut partitioning algorithms yield partitioning trees with the lowest observed Rent parameter over all benchmarks and over all algorithms tested. For examples where the intrinsic Rent parameter is known, spectral ratio cut partitioning yields a partitioning tree with Rent parameter essentially identical to this theoretical optimum. These results have deep implications with respect to both the choice of partitioning algorithms for top-down layout, as well as new approaches to layout area estimation. The paper concludes with directions for future research, including several promising techniques for fast estimation of the (intrinsic) Rent parameter. >