Padmini Gopalakrishnan

Exploring regular fabrics to optimize the performance-cost trade-off

While advances in semiconductor technologies have pushed achievable scale and performance to phenomenal limits for ICs, nanoscale physical realities dictate IC production based on what we can afford. We believe that IC design and manufacturing can be made more affordable, and reliable, by removing some design and implementation flexibility and enforcing new forms of design regularity. This paper discusses some of the trade-offs to consider for determination of how much regularity a particular IC or application can afford. A Via Patterned Gate Array is proposed as one such example that trades performance for cost by way of new forms of design regularity.

Exploring logic block granularity for regular fabrics

Driven by the economics of design and manufacturing nanoscale integrated circuits, an emphasis is being placed on developing new, regular logic fabrics that leverage the regularity and programmability of FPGAs, yet deliver a level of performance and density close to ASICs. One example of such a fabric is a Via-Patterned Gate Array (VPGA) according to Pillegi et al. (2002), which employs ASIC style global routing on top of an array of patternable logic blocks (PLBs). Previous works (Koorapaty et al., 2003; Koorapaty, 2003; Pileggi et al., 2003) showed that by employing even limited heterogeneity for the VPGA logic blocks, namely combining a 3-LUT with two 3-input Nand gates, one can achieve performance comparable to that provided by standard cells. Since the area cost for such heterogeneity id far less for FPGAs, we can explore new configurations of via-configurable logic blocks that offer greater heterogeneity and granularity to achieve even higher performance. In this paper, we present a new, more granular, via-patterned heterogeneous logic block architecture and compare it to a less granular LUT-based heterogeneous PLB. Our results show higher performance and more effective packing of the logic functions due to increased granularity.

Asymptotic probability extraction for non-normal distributions of circuit performance

While process variations are becoming more significant with each new IC technology generation, they are often modeled via linear regression models so that the resulting performance variations can be captured via normal distributions. Nonlinear (e.g. quadratic) response surface models can be utilized to capture larger scale process variations; however, such models result in non-normal distributions for circuit performance which are difficult to capture since the distribution model is unknown. In this paper we propose an asymptotic probability extraction method, APEX, for estimating the unknown random distribution when using nonlinear response surface modeling. APEX first uses a binomial moment evaluation to efficiently compute the high order moments of the unknown distribution, and then applies moment matching to approximate the characteristic function of the random circuit performance by an efficient rational function. A simple statistical timing example and an analog circuit example demonstrate that APEX can provide better accuracy than Monte Carlo simulation with 10 samples and achieve orders of magnitude more efficiency. We also show the error incurred by the popular normal modeling assumption using standard IC technologies.

Asymptotic Probability Extraction for Nonnormal Performance Distributions

While process variations are becoming more significant with each new IC technology generation, they are often modeled via linear regression models so that the resulting performance variations can be captured via normal distributions. Nonlinear response surface models (e.g., quadratic polynomials) can be utilized to capture larger scale process variations; however, such models result in nonnormal distributions for circuit performance. These performance distributions are difficult to capture efficiently since the distribution model is unknown. In this paper, an asymptotic-probability-extraction (APEX) method for estimating the unknown random distribution when using a nonlinear response surface modeling is proposed. The APEX begins by efficiently computing the high-order moments of the unknown distribution and then applies moment matching to approximate the characteristic function of the random distribution by an efficient rational function. It is proven that such a moment-matching approach is asymptotically convergent when applied to quadratic response surface models. In addition, a number of novel algorithms and methods, including binomial moment evaluation, PDF/CDF shifting, nonlinear companding and reverse evaluation, are proposed to improve the computation efficiency and/or approximation accuracy. Several circuit examples from both digital and analog applications demonstrate that APEX can provide better accuracy than a Monte Carlo simulation with 104 samples and achieve up to 10times more efficiency. The error, incurred by the popular normal modeling assumption for several circuit examples designed in standard IC technologies, is also shown

Robust Analog/RF Circuit Design With Projection-Based Performance Modeling

In this paper, a robust analog design (ROAD) tool for post-tuning (i.e., locally optimizing) analog/RF circuits is proposed. Starting from an initial design derived from hand analysis or analog circuit optimization based on simplified models, ROAD extracts accurate performance models via transistor-level simulation and iteratively improves the circuit performance by a sequence of geometric programming steps. Importantly, ROAD sets up all design constraints to include large-scale process and environmental variations, thereby facilitating the tradeoff between yield and performance. A crucial component of ROAD is a novel projection-based scheme for quadratic (both polynomial and posynomial) performance modeling, which allows our approach to scale well to large problem sizes. A key feature of this projection-based scheme is a new implicit power iteration algorithm to find the optimal projection space and extract the unknown model coefficients with robust convergence. The efficacy of ROAD is demonstrated on several circuit examples

Robust analog/RF circuit design with projection-based posynomial modeling

We propose a robust analog design tool (ROAD) for post-tuning analog/RF circuits. Starting from an initial design derived from hand analysis or analog circuit synthesis based on simplified models, ROAD extracts accurate posynomial performance models via transistor-level simulation and optimizes the circuit by geometric programming. Importantly, ROAD sets up all design constraints to include large-scale process variations to facilitate the tradeoff between yield and performance. A novel convex formulation of the robust design problem is utilized to improve the optimization efficiency and to produce a solution that is superior to other local tuning methods. In addition, a novel projection-based approach for posynomial fitting is used to facilitate scaling to large problem sizes. A new implicit power iteration algorithm is proposed to find the optimal projection space and extract the posynomial coefficients with robust convergence. The efficacy of ROAD is demonstrated on several circuit examples.

Architecture-aware FPGA placement using metric embedding

Since performance on FPGAs is dominated by the routing architecture rather than wire length, we propose a new architecture-aware approach to initial FPGA placement that models the relationship between performance and the routing grid, using concepts from graph embedding and metric geometry. Our approach, CAPRI, can be viewed as an embedding of a graph representing the net list into a metric space that is representative of the FPGA. First, we develop an analytic metric of distance that models delays along the FPGA routing grid. We then embed a net list into the defined metric space using matrix projections and online bipartite matching. Experimental comparisons with the popular FPGA tool, VPR, show that with CAPRIs initial solution, the resulting placements show median improvements of 10% in critical path delays for the larger MCNC benchmarks. Total placement runtime is also improved by 2times on average

Benchmarking diagnosis algorithms with a diverse set of IC deformations

Diagnosis algorithms for integrated circuits (ICs) are typically developed and evaluated using a limited number of logic-level models of defect behaviors. However, it is well-known that real IC defects exhibit behavior well outside these models. Consequently, the utility of IC diagnosis methodologies may be uncertain. A simulation-based benchmarking strategy is developed that uses circuit-level models to describe the complex nature of real defects. Specifically, we have proposed a simple yet powerful strategy using a small circuit and a set of bounded deformations (i.e., defects) for measuring the effectiveness of diagnosis techniques. Evaluation of several simple and commercial diagnosis algorithms indicates that this form of diagnosis benchmarking is viable.

An analysis of the wire-load model uncertainty problem

Traditional integrated-circuit (IC) design methodologies have used wire-load models during logic synthesis to estimate the expected impact of the metal wiring on the gate delays. These models are based on wire-length statistics from legacy designs to facilitate a top-down IC design flow process. Recently, there has been increased concern regarding the efficacy of wire-load models as deep-submicrometer (DSM) interconnect parasitics begin to dominate the delay of digital IC logic gates. Some technology projections (Sylvester and Keutzer, 1998) have suggested that wire-load models will remain effective to block sizes on the order of 50 000 gates. This suggests that existing top-down synthesis methodologies will not have to be changed substantially since this is approximately the maximum size for which logic synthesis is effective. However, our analyses on production designs show that the problem is not quite so straightforward and the efficacy of synthesis using wire-load models depends upon technology data as well as specific characteristics of the design and the granularity of available physical information. We analyze these effects and dependencies in detail in this paper and draw some conclusions regarding the future challenges associated with top-down IC design and block synthesis, in particular, in the DSM design era.

Overcoming wireload model uncertainty during physical design

The advent of deep sub-micron technologies has created a number of problems for existing design methodologies. Most prominent among them is the problem of timing closure, whereby design time is dramatically increased due to iterations between gate-level synthesis and physical design. It is well known that the heart of this problem lies in the use of wireload models based on wirelength statistics from legacy designs. Some technology projections in have suggested that wireload models will remain effective to block sizes on the order of 50k gates. This suggests that synthesis will not have to be changed much since this is approximately the maximum size for which logic synthesis is effective. However, our analyses on production designs show that the problem is not quite so straightforward, and the efficacy of synthesis using wireload models depends upon technology data as well as specific characteristics of the design. We analyze these effects and dependencies in detail in this paper, and draw some conclusions about the amount of physical information that is required for synthesis to be effective. Finally, we discuss the implications on hierarchical design flows, and propose a solution via physical prototyping.